In a hypothesis test for a mean in one population, where you have H subscript 0 colon space mu space equals space 40 comma space H subscript A colon space mu space not equal to space 40 and the population standard deviation is sigma space equals space 12, what are the critical value(s) of the sample mean x with bar on top if your sample size is 36 and the significance level alpha = 0. 05?


Group of answer choices

Answers

Answer 1

Using the t-distribution table with a sample size of 36 and a significance level of 0.05, we find the critical t-value to be ±2.03 (with 34 degrees of freedom, which is n-1).

What are the critical values of the sample mean for a hypothesis test with a sample size of 36, population standard deviation of 12, significance level of 0.05, and null hypothesis of μ = 40?

To explain, we use the t-distribution to find the critical values because the population standard deviation is known. Since the alternative hypothesis is two-tailed (H_A: μ ≠ 40), we need to find two critical values.

With a sample size of 36, the degrees of freedom are 34 (n-1), so we use a t-distribution table with 34 degrees of freedom and a significance level of 0.05. From the table, we find the critical t-value to be ±2.03.

Therefore, if the calculated t-value falls outside of this range, we can reject the null hypothesis H0: μ = 40 in favor of the alternative hypothesis H_A: μ ≠ 40.

Learn more about Hypothesis

brainly.com/question/31804924

#SPJ11


Related Questions

Identify the differentiation rule needed in order to find the derivative of
each of the following functions with respect to x.
a) y = sinxcosx
b) y = sin(cosx)
c) y = sin-x
d) y = sinx + cosx

Answers

product rule, chain rule, and sum rule are utilized to assess a subordinate of y = sin(x)cos(x), a subsidiary of y = sin(cos(x)), a subordinate of y = sin(-x), a subsidiary of y = sin(x) + cos(x).

a) subordinate of y = sin(x)cos(x) can be assessed by utilizing the product rule.

[tex]y' = (cos(x))(cos(x)) + (sin(x))(-sin(x)) = cos^2(x) - sin^2(x)[/tex]

b) chain rule is used  to find the derivative of y = sin(cos(x)):

y' = (cos(x))(cos(cos(x)))

c) chain rule is used  to find the derivative of y = sin(-x):

y' = -cos(-x) = -cos(x)

d) derivative of y = sin(x) + cos(x)  can be evaluated by using sum rule

y' = cos(x) - sin(x)

learn more about product rule

brainly.com/question/30117847

#SPJ4

If christen sells five out of eight of her clothes to maria and one out of four of them to alexandra what fraction of her clothes is left

Answers

The fraction of her clothes that is left is 1/8.

To solve this problem, we first need to determine the fractions of clothes Christen sells to Maria and Alexandra. Christen sells 5/8 of her clothes to Maria and 1/4 to Alexandra. To find the total fraction of clothes sold, we can add these two fractions:

(5/8) + (1/4)

To add fractions, we need a common denominator. In this case, the least common denominator is 8. We can convert 1/4 to 2/8:

(5/8) + (2/8) = 7/8

Christen sold 7/8 of her clothes to Maria and Alexandra. To find the fraction of clothes left, we subtract this value from the total, which is 1:

1 - (7/8) = 1/8

So, Christen has 1/8 of her clothes left after selling to Maria and Alexandra.

Learn more about fraction here: https://brainly.com/question/30154928

#SPJ11

The joint density function for a pair of random variables X and Y is given. (Round your answers to four decimal places.) f(x, y) = Cx(1 + y) if 0 <= x <= 2, 0 <= y <= 4 otherwise f(x,y) = 0
(a) Find the value of the constant C. I already have 1/24.
(b) Find P(X <= 1, Y <= 1)
(c) Find P(X + Y <= 1).

Answers

(a) The value of the constant is 1/24, (b) P(X<=1,Y<=1)  is 5/48 and (c)  P(X + Y <= 1) is also 5/48

(a) The constant C can be found by using the fact that the total probability of the joint density function over the entire space is equal to 1. Therefore, we integrate the joint density function over the region where it is defined and set it equal to 1:

∫∫f(x,y) dA = 1

∫[0,2]∫[0,4] Cx(1+y) dy dx = 1

C∫[0,2]x[(y+(y²)/2)] [0,4] dx = 1

C(24/5) = 1

C = 5/24

(b) To find P(X <= 1, Y <= 1), we integrate the joint density function over the region where X <= 1 and Y <= 1:

P(X<=1,Y<=1) = ∫[0,1]∫[0,1] (5/24) x(1+y) dy dx

= (5/24) ∫[0,1] x(1+(1/2)) dx

= (5/24) [(1/2) + (1/6)]

= 5/48

(c) To find P(X + Y <= 1), we integrate the joint density function over the region where X + Y <= 1:

P(X+Y<=1) = ∫[0,1]∫[0,1-x] (5/24) x(1+y) dy dx

= (5/24) ∫[0,1] x(1+(1-x)/2) dx

= (5/24) [(1/2) - (1/12)]

= 5/48

Therefore, P(X + Y <= 1) = 5/48.

To know more about joint density function, refer here:
https://brainly.com/question/29848433#
#SPJ11

Which expression is equivalent to: (5²)⁴ ?
(Exponent Form Only, please)

Answers

.....................

3.
Two overlapping triangles have the angle
measures shown.
15°
X=
10
Jo
40°
What are the values of x, y, and z?
____________, Z=_
_y=
43°
52⁰

Answers

Answer:

x = 73, y = 88, z = 45

Step-by-step explanation:

40+52+y = 180 (Angle Sum Property)

=> y = 180-40-52

=> y = 88

x + (15 + 40) + 52 = 180 (Angle Sum Property)

=>x = 180 - 52 - 55

=> x = 73

40 + 43 + (52+z)  = 180

=> z = 180 -53 - 40 -43

=> z = 45

Two days later, Kelly surveyed the same 13 classmates and found that none of them had been given math homework since she last surveyed them.



By how much does the mean of Kelly’s second data set change in comparison with the mean of the data set in her original survey? Explain how to determine the change in the means without calculating the mean of either data set

Answers

The mean of Kelly's second data set doesn't change compared to the mean of her original survey because none of the classmates were given math homework.

To determine the change in the means without calculating the mean of either data set, you can compare the number of data points, the range, and any outliers. If the number of data points and the range are the same and there are no outliers, then the means will be the same.

In this case, since none of the classmates had math homework in both surveys, there are no changes in the data set, and the means remain the same. Therefore, there is no change in the mean of Kelly's second data set compared to her original survey.

To know more about data points click on below link:

https://brainly.com/question/17148634#

#SPJ11

Select the correct answer from each drop-down menu. José and Manuel are soccer players who both play center forward for their respective teams. The table shows the total number of goals they each scored in each of the past 10 seasons. Season José Manuel 1 7 17 2 12 23 3 17 21 4 4 31 5 18 30 6 25 5 7 38 26 8 32 37 9 37 19 10 11 9 The measure of center that best represents the data is mean , and its values for José and Manuel are and , respectively. Comparing this measure of center for José’s and Manuel's data sets shows that generally scores more goals in a game

Answers

The measure of center that best represents the data is mean and its values for José and Manuel are 20.1 and 21.8, respectively. Comparing the mean values, José generally scores less goals in a game than Manuel.

What is the measure of center for the number of goals scored?

To find the measure of center that best represents the data, we will use the mean.

The measure is calculated by adding up all the values and dividing by the total number of values.

The mean number of goals for José is:

= (7+12+17+4+18+25+38+32+37+11)/10

= 20.1

The mean number of goals for Manuel is:

= (17+23+21+31+30+5+26+37+19+9)/10

= 21.8.

Read more about measure of center

brainly.com/question/15214370

#SPJ4

Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.

Answers

The value of x in the given circle is 18.1 units.

Given is a circle, where two radii are given one chord is given,

We need to find the value of the x which is also the radius,

We know all the radii in a circle are equal,

So, here the radius = 7.9+10.2 = 18.1 units.

Hence the value of x in the given circle is 18.1 units.

Learn more about radius click;

https://brainly.com/question/13449316

#SPJ1

Miss Marge has a large fish tank in her
office. Does her fish tank hold 100 liters
or 100 mL of water?

Answers

100 liters because liters is greater than ml

Task: Attend to Precision


Instructions


A circular pizza box logo has a sector with a central angle of 80% and a diameter of 16 inches.


Complete each of the 2 activitas for this Task.


Activity 1 of 2


Find the area of the sector.


Note: Please round to the nearest tenth


Activity 2 of 2


The unit of measurement for my answer is choose

Answers

Area of sector = 161.1 square inches

Activity 1:

The radius of the pizza is half of its diameter, which is 16/2 = 8 inches.

The central angle of the sector is 80%, which is 0.8 times 360 degrees = 288 degrees.

To find the area of the sector, we use the formula:

Area of sector = (central angle / 360) x πr^2

Area of sector = (288 / 360) x π x 8^2

Area of sector = (0.8) x π x 64

Area of sector = 161.1 square inches (rounded to the nearest tenth)

Activity 2:

The unit of measurement for the area of the sector is square inches (in²).

To know more about Area of sector refer here:

https://brainly.com/question/7512468

#SPJ11

Help with the question in photo please

Answers

Answer:

AB = 15

Step-by-step explanation:

6(6 + x + 6) = 7(7 + 11)

72 + 6x = 126

6x = 126 - 72 = 54

x = 54/6

   = 9.

So AB = 9 + 6 = 15.

Write an equation to represent the following statement.
282828 is 121212 less than kkk.

Answers

An equation representing the statement that 282828 is 121212 less than kkk is kkk = 282828 + 121212.

What is an equation?

An equation is a mathematical statement showing that two or more mathematical or algebraic expressions share equality or equivalence.

Equations are represented using the equal symbol (=).

Unlike equations, mathematical expressions do not use the equal symbol.

282828 = kkk - 121212

kkk = 282828 + 121212

Thus, one way of representing the statement that that 282828 is 121212 less than kkk is by forming an equation like kkk = 282828 + 121212.

Learn more about equations at https://brainly.com/question/2972832.

#SPJ1

Help



level a


polly works in a zoo and needs to build pens where animals can live and be safe. the walls of the pens are made out of cubes that are connected together. polly has 40 cubes and wants to make the largest pen possible, so the animals can move around freely but not get loose. build the largest area using all 40 cubes. your walls must:


• be fully enclosed, no doors or windows so polly’s animals can’t get out.


• have a height of one cube.


• each cube must be joined cube face to cube face.


help polly by making several shaped pens and determine what pen provides the largest area for the animals. you might want to build the pen on the grid paper first, so that it will be easier to determine the area.


use the grid paper to show the shape of the pen. explain to polly why you believe your pen is the largest one that can be made.

Answers

The rectangular pen with dimensions 5 x 6 x 2 is the largest pen that can be made using all 40 cubes.

To maximize the area of the pen, we need to create a rectangular shape. We can use all 40 cubes to create a rectangular pen with dimensions 5 x 6 x 2.

To build the pen, we can use 10 cubes for the base layer, then add 15 cubes for the second layer, and finally add 15 cubes for the third layer, creating a total of 40 cubes.

The base layer will be a rectangle with dimensions 5 x 6, and we will use 10 cubes to create it. Then we can stack two more layers of cubes on top of the base layer, each layer will have dimensions 5 x 6 and will use 15 cubes.

To prove that this pen has the largest area that can be made with 40 cubes, we can compare it with other possible shapes. For example, if we try to create a cube-shaped pen, we would only be able to create a cube with side length 3, which would have a volume of 27 and therefore could not use all 40 cubes.

Therefore, the rectangular pen with dimensions 5 x 6 x 2 is the largest pen that can be made using all 40 cubes.

To know more about rectangle refer here:

https://brainly.com/question/29123947

#SPJ11

In Exercises 1-4 find the measure of the red arc or chord in C

Answers

The red arc or chord in the key of C, or the solution to the provided question based on the circle, is 11.

What is Chord?

A chord is a piece of a straight line that connects two points on a circle's circumference. When it crosses the circle at two different locations, it is also occasionally referred to as a secant.

The following formula can be used to determine a chord's length:

chord length = 2*radius*sin(angle/2)

where angle is the central angle that the chord is subtended by, and radius is the radius of the circle. In geometry and trigonometry, chords are frequently used to compute circle properties including area, circumference, and arc length.

Since the circle P ≅ circle C

In circle P the radius of PN =7 and

chord LM = 11 with an angle 104°

And  In circle C  the radius =7 and Circle and chord QR are both making the same angle. P = 104°

So the circle P ≅ circle C

The red arc or chord in C is consequently 11.

To know more about circumference, visit:

https://brainly.com/question/27447563

#SPJ1

If the range of f (x) = startroot m x endroot and the range of g (x) = m startroot x endroot are the same, which statement is true about the value of m?

Answers

The only possible value of m that would make the ranges of f(x) and g(x) the same is any positive real number.

The range of a function is the set of all possible output values. In this case, we are given that the ranges of two functions, f(x) and g(x), are the same.

The function f(x) = √(mx) has a domain of x ≥ 0, since the square root of a negative number is not a real number. The function g(x) = m√x has a domain of x ≥ 0 for the same reason.

To find the range of these functions, we need to consider the possible values of the input x. For f(x), as x increases, the output √(mx) also increases, and as x approaches infinity, so does the output. For g(x), as x increases, the output m√x also increases, and as x approaches infinity, so does the output.

Therefore, if the ranges of f(x) and g(x) are the same, this means that they both have the same maximum and minimum values, and these values are achieved at the same inputs.

In particular, if we consider the minimum value of the range, this is achieved when x = 0, since both functions are defined only for non-negative inputs. At x = 0, we have f(0) = g(0) = 0, so the minimum value of the range is 0.

To find the maximum value of the range, we need to consider the behavior of the functions as x approaches infinity. As noted above, both functions increase without bound as x increases, so the maximum value of the range is infinity.

Therefore, the only possible value of m that would make the ranges of f(x) and g(x) the same is any positive real number.

To know more about startroot and endroot , refer here :

https://brainly.com/question/25996972#

#SPJ11

Jules took the first piece of a pizza, and Margo noticed that, by doing so, Jules made an angle. Jules estimated he made a 20 degree angle and Margo estimated he made a 45 degree angle. Who is right? How did you determine your answer?

Answers

Margo is right; Jules made a 45 degree angle.

How can we determine who is right about the angle measurement?

To determine who is right about the angle made by Jules while taking the first piece of pizza, we need to compare their estimates of 20 degrees and 45 degrees.

Since angles are measured using a protractor or other measuring tools, we rely on accurate measurement techniques to determine their values. If both Jules and Margo used appropriate measuring tools and techniques, we would expect their measurements to be close.

However, a 20-degree angle is significantly smaller than a 45-degree angle. Therefore, based on the provided information, Margo's estimate of a 45-degree angle seems more reasonable and likely to be correct.

Learn more about pizza
brainly.com/question/23055668
#SPJ11

A manufacturer of plumbing fixtures has developed a new type of washerless faucet. let rho-p(a randomly selected faucet of this type will develop a leak within 2 years under normal use). the manufacturer has decided to proceed with production unless it can be determined that p is too large; the borderline acceptable value of p is specified as 0.10. the manufacturer decides to subject n of these faucets to accelerated testing (approximating 2 years of normal use). with x = the number among the n faucets that leak before the test concludes, production will commence unless the observed x is too large. it is decided that if p = 0.10, the probability of not proceeding should be at most 0.10, whereas if rho = 0.30 the probability of proceeding should be at most 0.10. (assume the rejection region takes the form reject h if x2 c for some c. round your answers to three decimal places.)
1. what are the error probabilities for n10? p-value- can n- 10 be used?
a. it is not possible to use n = 10 because there is no value of x which results in a p-value
b. it is not possible to use n10 because it results in b(0.3)> 0.1
c. it is not possible to use n 10 because it results in b(0.3)<0.1 0.1.
d. it is possible to use n = 10 because both the p-value and β(0.3) are less than 0.1
e. it is possible to use 10 because both the p-value and b(0.3) are greater than 0.1
what are the error probabilities for n-20? p-value = β(0-3) = can n 20 be used?
a. it is not possible to use n = 20 because there is no value of x which results in a p-value
b. it is not possible to use n 20 because it results in b(0.3)0.1
c. it is not possible to use n 20 because it results in b(0.3) < 0.1
d. it is possible to use n 20 because both the p-value and b(0.3) are less than 0.1
e. it is possible to use n 20 because both the p-value and b(0.3) are greater than 0.1
2. what are the error probabilities for n-25? p-value . p(0.3) can n 25 be used?
a. it is not possible to use n-25 because there is no value of x which results in a p-value
b. it is not possible to use n 25 because it results in b(o.3) > 0.1
c. it is not possible to use n 25 because it results in b(0.3) < 0.1
d. it is possible to use n 25 because both the p-value and b(0.3) are less than 0.1
e. it is possible to use n 25 because both the p-value and b(0.3) are greater than 0.1 0.1.

Answers

It is not possible to use n = 10.

It is not possible to use n = 20.

It is possible to use n = 25.

1. The error probabilities for n = 10 are as follows:

- P-value: It is not possible to use n = 10 because there is no value of x which results in a p-value.
- Beta (0.3): B(0.3) > 0.1, which means the probability of failing to reject the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is too high.

Therefore, it is not possible to use n = 10.

2. The error probabilities for n = 20 are as follows:

- P-value: It is not possible to use n = 20 because it results in a beta error probability (B(0.3)) < 0.1, which means the probability of incorrectly rejecting the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is too low.
- Beta (0.3): B(0.3) > 0.1, which means the probability of failing to reject the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is too high.

Therefore, it is not possible to use n = 20.

3. The error probabilities for n = 25 are as follows:

- P-value: P(0.3) < 0.1, which means the probability of incorrectly rejecting the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is low enough to proceed with production.
- Beta (0.3): B(0.3) < 0.1, which means the probability of failing to reject the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is low enough to proceed with production.

Therefore, it is possible to use n = 25.

To learn more about hypothesis, refer below:

https://brainly.com/question/29519577

#SPJ11

The water in Earth’s oceans has a volume of about 3.2x10^8 cubic miles. There are about 1.1 x10^12 gallons in 1 cubic mile. How many gallon jugs would it take to hold all the ocean water on Earth? Show your work. Write your answer using scientific notation

Answers

If he water in Earth’s oceans has a volume of about 3.2x10⁸ cubic miles, it would take 3.52x10²⁰ gallon jugs to hold all the water in Earth's oceans.

To calculate how many gallon jugs it would take to hold all the ocean water on Earth, we need to multiply the volume of the water by the conversion factor from cubic miles to gallons.

Given that the water in Earth's oceans has a volume of about 3.2x10⁸ cubic miles and there are about 1.1x10¹² gallons in 1 cubic mile, we can calculate the total number of gallons using the following equation:

Total gallons = (Volume in cubic miles) x (Gallons per cubic mile)

Substituting the given values, we get:

Total gallons = (3.2x10⁸) x (1.1x10¹²) = 3.52x10²⁰

This number is very large and is written in scientific notation to make it more manageable. Scientific notation is a compact way of writing very large or very small numbers using a power of ten. In this case, the number is expressed as a coefficient (3.52) multiplied by 10 raised to the power of 20 (10²⁰).

To learn more about quantity click on,

https://brainly.com/question/29200960

#SPJ1

Mike wants to fence three sides of a rectangular patio that is adjacent to the back of his house, The area of the patio is 192 ft2 and the length is 4 feet longer than the width. Find how much fencing Mike will need

Answers

Mike will need 28 feet of fencing.

To solve the problem, we can use the formula for the area of a rectangle:

A = L × W

where A is the area, L is the length, and W is the width.

We know that the area of the patio is 192 ft^2, so we can write:

192 = L × W

We also know that the length is 4 feet longer than the width, so we can write:

L = W + 4

Substituting L = W + 4 into the equation for the area, we get:

192 = (W + 4) × W

Expanding the right side of the equation, we get:

192 = W^2 + 4W

Rearranging, we get a quadratic equation in standard form:

W^2 + 4W - 192 = 0

We can solve for W by factoring or using the quadratic formula, but in this case, we can recognize that 12 and -16 are two numbers that multiply to -192 and add up to 4. Therefore, we can write:

W^2 + 4W - 192 = (W + 16) × (W - 12) = 0

This gives us two possible values for W: W = -16 or W = 12. Since the width cannot be negative, we reject the solution W = -16 and choose W = 12.

Using the equation L = W + 4, we find that the length is L = 16.

Finally, we can calculate the amount of fencing Mike will need by adding up the lengths of the three sides that need to be fenced. The two lengths are L = 16 feet each, and the width is W = 12 feet. Therefore, Mike will need a total of 16 + 16 + 12 = 44 feet of fencing. However, since one side of the patio is adjacent to the back of his house, he only needs to fence three sides.

Therefore, he will need 44 - 16 = 28 feet of fencing.

To learn more about quadratic equation  here

https://brainly.com/question/30098550

#SPJ4

an economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in california. suppose that the mean income is found to be $24 for a random sample of 1417 people. assume the population standard deviation is known to be $5.1 . construct the 99% confidence interval for the mean per capita income in thousands of dollars. round your answers to one decimal place.

Answers

The mean per capita income in thousands of dollars with 99% confidence interval and sample size of 1417 is equal to CI = (23.7, 24.3).

Construct the 99% confidence interval for the mean per capita income, use the formula,

CI = x ± Z× (σ / √n)

where

x is the sample mean,

σ is the population standard deviation,

n is the sample size,

Z is the z-score corresponding to the desired level of confidence.

Using attached z-score table,

For a 99% confidence interval, the corresponding z-score is 2.58

Substituting the given values, we get,

⇒CI = 24 ± 2.58 × (5.1 / √1417)

Simplifying the expression inside the parentheses, we get,

⇒CI = 24 ± 0.349

⇒CI = (23.7, 24.3)

Rounding to one decimal place, the confidence interval is (23.7, 24.3) thousands of dollars.

Therefore, the 99% confidence interval for the mean per capita income is CI = (23.7, 24.3).

learn more about confidence interval here

brainly.com/question/29320814

#SPJ4

Which values for an and b make the polynomial 9x^10 + ax^b + 100 a perfect square trinomial?

Answers

Answer:

To make the polynomial 9x^10 + ax^b + 100 a perfect square trinomial, we need to add a constant term to it such that it becomes a square of a binomial.

Let's first write the square of a binomial in general form:

(a + b)^2 = a^2 + 2ab + b^2

If we compare this general form with our polynomial, we can see that the first term, 9x^10, is equal to (3x^5)^2, which means that we can write our polynomial as:

(3x^5)^2 + ax^b + 100 = (3x^5 + c)^2

Expanding the right-hand side of this equation, we get:

(3x^5 + c)^2 = 9x^10 + 6cx^15 + c^2

Comparing the coefficient of x^15 on both sides, we get:

6c = 0

Since c cannot be zero (otherwise we would end up with the original polynomial), this means that we must have:

c = 0

Therefore, we can write our polynomial as:

(3x^5)^2 + ax^b + 100 = (3x^5)^2

Expanding the right-hand side, we get:

(3x^5)^2 = 9x^10

Therefore, we must have:

a = 0

b = 10

So the values of a and b that make the polynomial 9x^10 + ax^b + 100 a perfect square trinomial are a = 0 and b = 10.

HELP
The average human body temperature is 98.6° F, but it can vary by as much as 1.8° F. Write an inequality to represent the normal temperature range of the human body, where t represents body temperature.

|t − 1.8| ≥ 98.6
|t − 1.8| ≤ 98.6
|t − 98.6| ≥ 1.8
|t − 98.6| ≤ 1.8

Answers

The inequality which is used to represent normal "temperature-range" for  "human-body", is (d) |t − 98.6| ≤ 1.8.

The "average-temperature" of body is = 98.6° F, and it can vary by 1.8°F.

The inequality |t − 98.6| ≤ 1.8 indicates that the absolute difference between the body temperature and the average temperature is less than or equal to 1.8° F.

This means that the body temperature t can vary within a range of 1.8° F from the average temperature of 98.6° F.

Which means, the temperature cam range from :

⇒ 98.6-1.8 ≤ t ≤ 98.6+1.8,

⇒ 96.8 ≤ t ≤ 100.4;

Therefore, the correct inequality is (d) |t − 98.6| ≤ 1.8.

Learn more about Inequality here

https://brainly.com/question/29053875

#SPJ1

The given question is incomplete, the complete question is

The average human body temperature is 98.6° F, but it can vary by as much as 1.8° F. Write an inequality to represent the normal temperature range of the human body, where t represents body temperature.

(a) |t − 1.8| ≥ 98.6

(b) |t − 1.8| ≤ 98.6

(c) |t − 98.6| ≥ 1.8

(d) |t − 98.6| ≤ 1.8

Answer: |t − 98.6| ≤ 1.8

Step-by-step explanation: If takes then takes then takes then takes then takes.

In order for a triangle to be acute, what relationship must c2 have with a2 + b2?
group of answer choices

c2>a2+b2




c2



c2=a2+b2

Answers

In order for a triangle to be acute, the relationship that c² must have with a² + b² is c² < a² + b².

An acute triangle is a triangle in which all three angles are acute angles, which means they are less than 90 degrees. In other words, an acute triangle is a triangle with three acute angles.

To understand why the relationship between c^2 (the square of the longest side) and a^2 + b^2 (the sum of the squares of the other two sides) is important in determining whether a triangle is acute, we need to delve into the concept of the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as c^2 = a^2 + b^2, where c represents the hypotenuse, and a and b represent the other two sides.

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side.

This can be visualized as follows: If we were to draw a right triangle with the shorter sides represented by segments a and b, and the longest side represented by segment c, the acute triangle would be formed by making the length of segment c shorter than the length determined by the Pythagorean theorem. This ensures that the angle opposite to the longest side remains acute.

On the other hand, if c^2 were equal to a^2 + b^2, we would have a right triangle, not an acute triangle. If c^2 were greater than a^2 + b^2, we would have an obtuse triangle since the angle opposite to the longest side would be greater than 90 degrees.

To know more about triangle refer here:

https://brainly.com/question/2773823#

#SPJ11

10 m


20 m


30


1. ¿Qué fracción de camino representan los 10 m?



2. Si la casa se encuentra a del camino, ¿cuántos metros son?_25


3. ¿A los cuántos metros está representado del camino?


4. ¿Qué fracción representa los 20 m del camino?


j


Resuelve los problemas.

Answers

Step-by-step explanation:

Los 10 m representan 1/3 del camino, ya que si sumamos 10 + 20 + 30, obtenemos la distancia total del camino, que es 60 m.

Si la casa se encuentra a 25 m del camino, entonces está a una distancia de 5 m del final del camino, ya que 25 + 5 = 30. Por lo tanto, la casa está a 2/3 del camino, es decir, a una fracción de 2/3 de la distancia total del camino.

La casa está representada a 2/3 del camino, lo que corresponde a una distancia de 40 m (2/3 de 60 m). Por lo tanto, la casa está representada a 40 m del comienzo del camino.

Los 20 m representan 1/3 del camino, ya que si sumamos 10 + 20 + 30, obtenemos la distancia total del camino, que es 60 m. Por lo tanto, los 20 m representan la misma fracción que los 10 m, que es 1/3 del camino.

To know more about obtenemos refer here

https://brainly.com/question/20242798#

#SPJ11

Keegan deposited $675 in a savings account that pays 4.8% annual interest compounded quarterly.
Write the compound interest formula to represent Keegan's investment after 5 years.
How much money will Keegan have in the account after 5 years?

Answers

Keegan will have approximately $878.85 in the account after 5 years.

What is Compound interest ?

Compound interest is the interest that is earned not only on the initial amount of money invested (known as the principal), but also on any interest earned on that principal over time. In other words, compound interest is interest on interest.

The compound interest formula is given by:

A = P[tex](1 + r/n)^{nt}[/tex]

where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, Keegan deposited $675, the annual interest rate is 4.8%, the interest is compounded quarterly, and the investment is for 5 years. Therefore, we can plug in these values into the formula to get:

A = 675[tex](1 + 0.048/4)^{20}[/tex]

A = 675[tex](1.012)^{20}[/tex]

A ≈ $878.85

Therefore, Keegan will have approximately $878.85 in the account after 5 years.

To learn more about Compound interest from given link.

https://brainly.com/question/14740098

#SPJ1

when rounding to the nearest hundred what is the greatest whole number that rounds to 500

Answers

The greatest whole number that rounds to 500 when rounding to the nearest hundred is 550.

When rounding a number to the nearest hundred, you need to look at the digit in the tens place. If that digit is 5 or greater, you round up the hundreds digit; if it is less than 5, you round down the hundreds digit.

For example, let's say we have the number 2,548. The digit in the tens place is 4, which is less than 5, so we round down the hundreds digit (2) to get 2,500.

Now, if we are looking for the greatest whole number that rounds to 500 when rounded to the nearest hundred, we need to find the largest number that has 5 in the tens place and 0 in the ones place. That number is 550. When we round 550 to the nearest hundred, we get 500.

Therefore, the greatest whole number that rounds to 500 when rounded to the nearest hundred is 550.

Learn more about rounded number at https://brainly.com/question/30568820

#SPJ11

It takes an apprentice four times as long as the experienced plumber to replace the pipes under an old house. If it takes them 15 hours when they work together, how long would it take the apprentice alone?

Answers



Let's assume that the experienced plumber can complete the job in x hours.

According to the problem, the apprentice takes four times as long as the experienced plumber to complete the job. Therefore, the apprentice can complete the same job in 4x hours.

If they work together, they can complete the job in 15 hours. Therefore, we can write the following equation based on their combined work rate:

1/x + 1/4x = 1/15

Multiplying both sides by the common denominator of 60x gives:

60 + 15 = 4x

75 = 4x

x = 75/4

x = 18.75

Therefore, the experienced plumber can complete the job in 18.75 hours.

Using the relationship that the apprentice takes four times as long as the experienced plumber to complete the job, we can find the time it takes for the apprentice to complete the job alone:

4x = 4(18.75) = 75

Therefore, the apprentice would take 75 hours to complete the job alone.

Mika has a rectangular fish tank that is 65 cm wide and 85 cm long. When completely full, the tank holds 221 L of water. She plans to fill the tank? full, and she wants to find the height of the water. 4 1 L - 1000 cm3 volume = xwxh Mika is calculating what the height of the water will be. Choose ALL correct steps that would be included in her calculation Find the height of the tank: 4 A) x 40 = 30 cm 4 Find 3 the height of the tank: 4 4 X 30 - 40 cm Find the height of the tank 3 x 85 - 30 cm 4 DS Divide the length and width by the volume to find height: 65 x 70 - 40 cm 168 x 1000 Divide the volume by the length and width to find height: 221 x 1000 - 40 cm 65 XSS​

Answers

The height of tank which is 65 cm wide and 85 cm long is 40 cm and when it is 3/4 filled the water height is 30cm.

Mika can follow these steps to find the height of the water:

1. Convert the volume from liters to cubic centimeters: 221 L * 1000 cm³/L = 221,000 cm³
2. Calculate the total volume of the tank: V = lwh (where V is the volume, l is the length, w is the width, and h is the height)
3. Solve for the height of the tank: 221,000 cm³ = 65 cm * 85 cm * h
4. Calculate the height of the tank: h = 221,000 cm³ / (65 cm * 85 cm) ≈ 40 cm
5. Since Mika plans to fill the tank 3/4 full, calculate the height of the water: (3/4) * 40 cm = 30 cm

So, the correct steps are:

- Divide the volume by the length and width to find the height
- Calculate the total volume of the tank
- Find the height of the tank
- Calculate the height of the tank
- Calculate the height of the water when the tank is 3/4 full

The height of the water will be 30 cm.

Learn more about dimension of cube and cuboid : https://brainly.com/question/19754639

#SPJ11

Brian has two cubes.

. The first cube has a volume of 125 cm3.

. The second cube has a volume of 343 cm3.


What is the difference in the area of one face of the second cube and the area of one face of the first cube?


A. 2 cm2

B. 24 cm2

C. 49 cm2

D. 218 cm2
Help asap

Answers

If the first cube has a volume of 125 cm³ and the second cube has a volume of 343 cm³, the difference in the area of one face of the second cube and the area of one face of the first cube is 24cm². The answer is B. 24 cm².

To find the difference in the area of one face of each cube, we first need to find the side length of each cube. Since the volume of a cube is equal to the side length cubed (V = s³), we can find the side length by taking the cube root of the volume.

For the first cube:
Volume = 125 cm³
Side length = cube root of 125 = 5 cm

For the second cube:
Volume = 343 cm³
Side length = cube root of 343 = 7 cm

Next, we find the area of one face of each cube. The area of one face of a cube is equal to the side length squared (A = s²).

Area of one face of the first cube:
A1 = 5² = 25 cm²

Area of one face of the second cube:
A2 = 7² = 49 cm²

Finally, find the difference in the area of one face of each cube:
Difference = A2 - A1 = 49 cm² - 25 cm² = 24 cm²

The answer is B. 24 cm².

More on cube area: https://brainly.com/question/14994710

#SPJ11

1_.the quadratic should have an exponent of which: 1,2 , or 3?

2_.the parabola ending its life going down should have a leading coefficient sign of positive or negative?


3._which would be the correct equation: y=x^2 or y=-x^2?

Answers

A quadratic function should have an exponent of 2, a parabola ending its life by going down should have a leading coefficient sign of negative, and either y = x^2 or y = -x^2 can be a valid equation for a quadratic function, with the choice depending on the direction of the desired parabola.

1. The quadratic should have an exponent of 2, as a quadratic is a polynomial of degree 2.
2. A parabola ending its life by going down should have a leading coefficient sign of negative, as this indicates that the quadratic term has a negative coefficient and the parabola opens downwards.
3. Both equations, y = x^2 and y = -x^2, are valid equations for a quadratic function. The main difference between them is the direction in which the parabola opens. The equation y = x^2 represents a parabola that opens upwards, while y = -x^2 represents a parabola that opens downwards. The choice of which equation to use depends on the specific context and the direction of the desired parabola.

Learn more about exponent: https://brainly.com/question/11975096

#SPJ11

Other Questions
What was the Social goal of the redeemers? and what is the evidence to support it? Help me I will give you A reaction that occurs when 23 grams of iron (II) chloridereacts with sodium phosphate forming iron (II) phosphate and sodium chloride. What is the limiting reagent? How much sodium chloride can be formed?3FeCl2 + 2Na3PO4-Fe3 (PO4)2 +6NaCl Calculate the standard free-energy changes for the following reactions at 25c: (a) h2(g) + br2(l) 2hbr(g) Name and briefly describe the three basic parts of Earth. If both the electric and magnetic fields of an electromagnetic wave double in magnitude, how does the intensity of the wave change Circle the correct answer. Which sentence from the passage best supports the idea that Michael Jordan is a talented basketball player? "In the third quarter, I felt like I couldn't catch my wind, Jordan said. I was just trying to get myself through it. "" B "In the fourth quarter, Jordan scored 18 more points. " C "Then, with only 25 seconds left in the game, he scored a 3-point shot, and the Bulls beat the Jazz by only two points. " D "I almost played myself into passing out just to win a basketball game,' Jordan admitted later. " A rental car company charges $22 per day to rent a car at 0.08 for every mile driven Samuel wants to rent a car knowing that he plans to drive 450 miles he has at most to spend $80 right and solve an inequality which could determine X the number of days Samuel can afford rent Austin within his budget Tight Knit is an online store that sells two different tiers of monthly subscription boxes with knitting supplies. Recently, the number of basic subscriptions has been decreasing by 5 each month, while the number of deluxe subscriptions has been increasing by 8 each month. This month, the company had 288 basic subscriptions and 93 deluxe subscriptions.How many months will it take for the number of basic subscriptions to match the number of deluxe subscriptions? How do you use the definition of a derivative to find f' given f(x)=4x+3 at x>-3/4? Help asap will give 100 points and brainiestwhat is the mean absolute deviation for doctor as data set on corrective lenses? what is the mean absolute deviation for doctor bs data set on corrective lenses? write a sentence comparing the variation of the two data sets using their mean absolute deviations. If a piece of metal at 150 *C is placed in a beaker with 50 ml water at 60*C. a. What is likely to happen to the temperature of the water in the beaker?. b. What is likely to happen to change with the metal?. Did you know that children believe they should be involved in the selection and ejection of their teachers and administrators? Children particularly say this in their fifth and middle school years. When they receive a poor grade for classwork, they place the responsibility on the instructor and demand that they be fired because they are not performing their duties properly.The position I opted for was that Schrum Memorial Middle School students ought to be involved in the selection and dismissal of their teachers and administrators. I vehemently dispute this assertion. These are my motivations: One, students lack the necessary experience for both. Two, having the student fill either of these roles may have an impact. Third, if the student discovers that they have fired administrators and good students and have hired teachers who don't care about the education of the other students, it may be difficult for them to get employment. Some Background Information: A kid back at Elementary School wished theyre teacher was fired because they got a bad grade on their test and the teacher was apparently not helping them. They weren't paying attention in class, the teacher claimed, despite her best efforts to assist them.Kids believe it's cool that they should be involved in the hiring and firing of their teachers, but they are unaware of the potential consequences for their own careers. It will be difficult for them to find employment because they fired all the teachers who were supposed to be instructing the students. Just explain how to do it with the answer please. Refer to FIGURE 1.1 below showing landforms associated with answer the following questions. 1.1.1Identify landforms K and L. respectively. 1.1.2Did landforms K and L develop from horizontal or inclined rock strata? (1 x 1) (1) (a) Which landform, K or L, is in the furthest stage of development? (1x1) (1) (1 x 2) (2) (b) Give ONE reason for your answer in Question 1.1.3 (a). Where in South Africa will this landscape typically be found? (2 x 1) (2) 1.1.5 Differentiate between slope decline and slope retreat. (1 x 1) (1) (2 x 2) (4) 1.1.6 Initially (at first) landforms K and L will be reduced from the sides and will not be lowered. Explain why. (2 x 2) (4) A scale drawing of a rectangular park had a scale of 1 cm = 90 m.What is the actual area of the park in meters squared? Which gas, Cl2 (g) or COCl2(g) , will deviate most from the ideal gas law at low temperature?Justify your choice 1. How was the success of the railroads influenced by propaganda? A. Railway proponents convinced the public to donate money to railroad construction. B. Companies began advertising national trade and shipping, which bolstered railway traffic C. Business owners sent representatives across the country by rail to advertise and sell their products. D. Railway promoters spread word that the opportunities for personal and financial advancement were only achievable through migration Is it false that, ""Many or most vernacular or traditional languages on the continent of Afrika use the letter K. This was changed with the arrival of Europeans who substituted the K for a C. Today, the use of the letter K signifies Afrikan unity and the constituting of a shared political language."? The still developing prefrontal cortex and the full development of the limbic system are at least partially responsible for: What is one of the major reasons why these European countries decided to join together to form the European Union?a) They wanted to be better prepared to help other nations in Africa and Southeast Asia after the occurrence of natural disasters.b) They wanted to form one central government and make foreign policy decisions together.c) They wanted to preserve the natural resources and wildlife that exists throughout Europe.d) They wanted to prevent future war and conflict between each other by working together economically.