Answer:
Step-by-step explanation:
C (Wait for another defendant, check with him and write this answer)
using calculations show that the height of the barrel of oil is 96.82cm
Answer:
Step-by-step explanation:
V = πr²h
h = V/(πr²)
V = 42 gal
42 gal x 3.7854 l/gal = 158.987 l
158.987 l = 158,987 ml = 158,987 cm³
r = 18/2 = 9 in
9 in x 2.54 cm/in = 22.86 cm
h = (158987 cm³) / π(22.86 cm)² ≈ 96.82 cm
depending on how you round, the more precise answer is 96.8285 ≈ 96.83
In 2011 Staci invested $14,500 in a savings account for her newborn son. The account pays 3.5% interest each year. Determine the accrued value of the account in the year 2029, when her son will go to college. Round your answer the nearest cent.
The accrued value of Staci's investment in the account in the year 2029 is $26933.59
Calculating the accrued value of the accountThe statements in the question can be sumarrized as
Invested amount = $14,500Rate of interest = 3.5% compounded annually.The formula to calculate amount on investment is
Amount = P * (1 + r)ⁿ
Where
P = Principal = 14,500r = Rate = 3.5%n = time = 2029 - 2011 = 18When the values are substituted in the amount equation, we have
Amount = 14500 * (1 + 3.5%)¹⁸
Evaluate
Amount = 26933.59
Hence, the amount after the investment is $26933.59
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a 10 x 10 x 10 cub is painter red on all faces and then cut into ten 10 x 10 x 1 slices each slice is then cut into twenty five 2 x 2 x 1 blocks how many of the 250 blocks have exactly on face painted red
There are exactly 250 blocks with exactly one face painted red.
What is cube ?
A cube is a three-dimensional solid shape with six square faces of equal size that meet at 90-degree angles. It is a special case of a rectangular prism, where all of the edges have the same length.
When the 10 x 10 x 10 cube is painted red on all faces, it means that all of the 1000 unit cubes inside the large cube are red.
When the cube is cut into ten 10 x 10 x 1 slices, each slice will contain 100 unit cubes. When each slice is cut into twenty-five 2 x 2 x 1 blocks, each block will contain 4 unit cubes.
Therefore, each 2 x 2 x 1 block will come from 4 unit cubes, and each unit cube will contribute to 4 different blocks.
To count the number of blocks with exactly one face painted red, we can focus on the blocks that have a red face on the bottom (or top) and three unpainted faces on the other sides. Each such block will correspond to one of the 100 unit cubes in a slice, and there are 10 slices, so there are 1000 such blocks in total.
However, each of these blocks has four unit cubes, so we need to divide by 4 to get the number of blocks. Therefore, the answer is:
1000 ÷ 4 = 250
Therefore, there are exactly 250 blocks with exactly one face painted red.
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0.6/(-0.9- -0.5 x -0.3)
The value of the expression is -0.8
What is PEDMAS?PEDMAS can be described as a mathematical acronym that is used for the representation of arithmetic operations on the basis of how they are to be carried out sequentially in an equation.
The alphabet represents different operations. They are;
P represents parenthesesE represents exponentsD represents divisionM represents multiplicationA represents additionS represents subtractionFrom the information given, we have that;
0.6/(-0.9- -0.5 x -0.3)
Multiply the values
0.6/(-0.9 +0. 15)
add the values
0.6/0. 75
Now, divide the values
-0.8
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Solve the following system of equations.
The solutions for the system of equations " 3x²-2y²+5=0 and 2x²-y²+2=0" are :
First Solution : x = 1, y = 2
Second Solution : x = 1, y = -2
Third Solution : x = -1, y = 2
Fourth Solution : x = -1 , y = 2.
In order to solve the system of equations 3x²-2y²+5=0 and 2x²-y²+2=0, we use substitution method;
From the second equation, we solve for y² in terms of x²:
The second equation is : 2x² - y² + 2 = 0;
We get, y² = 2x² + 2
Substitute this expression for y² into the first equation:
We get,
3x² - 2(2x² + 2) + 5 = 0
3x² - 4x² - 4 + 5 = 0
-x² + 1 = 0
x² = 1
We get, x = ±1
Substitute these values of x into the equation for y²:
y² = 2x² + 2
For x = 1, y² = 4,
Which means the solution set is (1,2) and (1,-2),
For x = -1, y² = 4
the solution set is (-1,2) and (-1,-2).
Therefore, the solutions to the system of equations are (1, 2), (1,-2), (-1,2) and (-1, 2).
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Find the missing side lengths. Leave your answers as radicals in simplest form.
The value of m and n are 2√3 and 4√3/3 respectively.
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
There are special angles in trigonometry, examples are; 60° , 30° and 90°. This angles have exact values and can be calculated without using calculator.
Tan 60 = n/2
√3 = n/2
n = 2√3
cos 60 = 2/m
√3/2 = 2/m
m√3 = 4
m = 4/√3
= 4√3/3
Therefore the value of m and n are 2√3 and 4√3/3 respectively.
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what is the range of data?
40
42
54
96
what is the median of the data?
64.5
72.5
74.5
75
what is the mode of the data?
5
70
75
88
The range, median and mode of the data-set are given as follows:
Range: 42.Median: 74.5.Mode: 75.How to obtain the features?Considering the stem-and-leaf plot, the data-set is given as follows:
54, 55, 60, 66, 69, 72, 73, 74, 75, 75, 81, 82, 88, 89, 95, 96.
The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus:
96 - 54 = 52.
The data-set has an even cardinality of 16, hence the median is calculated as the mean of the two middle elements as follows:
Median = (74 + 75)/2
Median = 74.5.
The mode of a data-set is the observation that appears the most times in the data-set, hence it is of 75, which is the only observation that appears twice in the data-set.
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A company may acquire property, plant, equipment, and intangible assets for cash, in exchange for a deferred payment contract, by exchanging other assets, or by a combination of these methods. Identify six types of costs that should be capitalized as the cost of a parcel of land. For your answer, assume that the land has an existing building that is to be removed in the immediate future so that a new building can be constructed on the site. At what amount should a company record an asset acquired in exchange for a deferred payment contract? In general, at what amount should assets received in exchange for other nonmonetary assets be valued? Specifically, at what amount should a company value a new machine acquired by exchanging an older, similar machine and paying cash?
Six types of costs are:
Closing costsPurchase costBrokerage commissionsSurveying feesDemolition costsSite preparation costsHow the asset is to be recordedFor assets attained in exchange for a deferred payment contract, the asset should be documented at its fair worth, which is the prevailing market rate. If establishing the fair value of the asset proves to be impracticable, the asset should be recorded based on the current value of upcoming payments due under the deferred payment agreement, stated using an apposite interest rate.
Generally, assets acquired in exchange of other non-monetary commodities should be appraised at their fair worth. If the truthful appraisal of the exchanged assets is uncertain, the assets should be noted down according to the seized amount of the items provided, including any received or paid cash during the transaction.
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Find the critical points of the function f (x) = x − 1 /x^2 + 3
there is no real number that can be raised to the third power to give a negative number, there are no real solutions to this equation. Therefore, there are no critical points of the function f(x) = x - 1/x² + 3.
what is critical points ?
In calculus, critical points are points on a function where its derivative is either zero or undefined. These points are important because they can indicate the location of maximum or minimum values of the function or points of inflection where the concavity of the function changes.
In the given question,
To find the critical points of the function f(x) = x - 1/x² + 3, we need to find the values of x where the derivative of the function is equal to zero or undefined.
First, we need to find the derivative of the function:
f'(x) = 1 + 2/x³
Next, we set the derivative equal to zero and solve for x:
1 + 2/x³ = 0
2/x³ = -1
x³ = -2
Since there is no real number that can be raised to the third power to give a negative number, there are no real solutions to this equation. Therefore, there are no critical points of the function f(x) = x - 1/x² + 3.
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This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
Responses
The surface area of the cube is 384 mm².
What is a cube:A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Since there are six square that makes up a cube, to find the surface area of the cube, we find the area of one of the square and multiply by six
A = 6L²...................... Equation 1Where:
A = Surface area of the cubeL = Length of the side of the cubeFrom the question,
Given:
L = 8 mmSubstitute this value into equation 1
A = 6×8²A = 6×64A = 384 mm²Hence the right option is D. 384 mm².
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 how many kilograms are in 14500 grams
Answer: 14.5 kg
Step-by-step explanation:
Find the measure of the angle between the two vectors. u = -7i and v = -4i + 4j
4. What is the equation of the given graph?
1
A) y=-2x-3
B) y = -1/2x +3
C) y=1/2x-3
D)y=1/2x-3
Answer: D
Step-by-step explanation:
The equation for a linear function is y = mx + b
We first need to find the slope of the object, we can see here than it perfectly lands on the point, (0, -3) and (6,0). We can use this formula to determine the slope:
(y2 - y1)/(x2 - x1)
Now let's plug in the numbers.
(0 + 3) / (6 - 0)
3/6
1/2
Now we know the slope is 1/2 and the y-intercept is -3, so let's make it into a slope-intercept form.
y = 1/2x - 3
What integer values of x make the statement -3/x lesser than -x/3 true?
x=0
x=2
x=3
Any interger greater than -3
Any integer less than -3
x=1
You need to choose more than 1 answer
The integer values that make the statement true are x = -3, -2, -1, 1, 2, 3
We have,
We can start by multiplying both sides of the inequality by -3x to get rid of the denominators:
-3/x < -x/3
Multiplying by -3x on both sides.
-9 < -x²
Rearranging.
x² < 9
Taking the square root of both sides.
|x| < 3
This means that x can take any integer value between -3 and 3, excluding 0.
Thus,
The integer values are x = -3, -2, -1, 1, 2, 3
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In AJKL, m/J = (8x - 7), m/K = (x + 7)°, and m/L= (2x + 15)°. What
is the value of x?
Therefore, the equation for that value x = 6, and m(A) = 90.
What is a formula or equation?A mathematical equation expresses two things as being equal to one another, or as having the same value and worth. A specific equation that expresses a significant link between variables and numbers is called a formula.
The fact that the sum of a triangle's angles is 180 degrees must be used to determine the value of x. Angles J, A, and K in the triangle AJK allow us to write:
m(J) + m(A) + m(K) = 180
We can substitute the given angle measures into this equation:
(8x - 7) + m(A) + (x + 7) = 180
Simplifying this equation, we get:
9x + m(A) = 180 - 7 - 7
9x + m(A) = 166
We can use the same reasoning for triangle AJL:
m(J) + m(A) + m(L) = 180
Substituting the given angle measures, we get:
(8x - 7) + m(A) + (2x + 15) = 180
Simplifying this equation, we get:
10x + m(A) = 172
The two unknowns in our current set of equations are x and m(A). By removing the first equation from the second, we can find m(A):
10x + m(A) = 172
(9x + m(A) = 166)
x = 6
Now that we know x, we can substitute it into either equation to find m(A):
8x - 7 + m(A) + x + 7 = 180
15x + m(A) = 180
m(A) = 180 - 15x
Substituting x = 6, we get:
m(A) = 180 - 15(6) = 90
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On average, a front desk operator receives 2 calls per 30 seconds.
(1)Find the probability that at most 1 call is received in 10 seconds
The probability that at most 1 call is received in 10 seconds is given as follows:
0.8557 = 85.57%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are listed and explained as follows:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.On average, a front desk operator receives 2 calls per 30 seconds, hence the mean for 10 seconds, which is one third of the time, is given as follows:
[tex]\mu = \frac{2}{3}[/tex]
The probability of at most one call is given as follows:
P(X <= 1) = P(X = 0) + P(X = 1)
Hence:
[tex]P(X = 0) = \frac{e^{-\frac{2}{3}}\frac{2}{3}^{0}}{(0)!} = 0.5134[/tex][tex]P(X = 1) = \frac{e^{-\frac{2}{3}}\frac{2}{3}^{1}}{(1)!} = 0.3423[/tex]Hence:
P(X <= 1) = P(X = 0) + P(X = 1) = 0.5134 + 0.3423 = 0.8557 = 85.57%.
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Suppose a person were to breath an average of 13 times per minute. How many days would it take for them to breathe one billion times? Round your answer to the nearest single days.
Answer:
12 / min
720 / hr
17,280 / day
6,307,200 / yr
Now divide 1,000,000,000 by 6,307,200 (darn close to your 158!)
Please help with these two equations, and please show work as well, thank you!
The simplified polynomial for the area and perimeter of the rectangles are:
13). Area = 5x² + 40, Perimeter = 12x + 16
14). Area = x² + 10x + 12, Perimeter = 4x + 20
How to evaluate for the area and perimeter of the rectanglesArea of rectangle = Length × Width
Perimeter of rectangle = 2(Length + Width)
13). Area of the rectangle = 5x × (x + 8)
Area of the rectangle = 5x² + 40
Perimeter of the rectangle = 2[5x + (x + 8)]
Perimeter of the rectangle = 2(6x + 8)
Perimeter of the rectangle = 12x + 16
12). Area of the rectangle = (x + 3)(x + 7)
Area of the rectangle = x² + 7x + 3x + 21
Area of the rectangle = x² + 10x + 21
Perimeter of the rectangle = 2[(x + 3) + (x + 7)]
Perimeter of the rectangle = 2(2x + 10)
Perimeter of the rectangle = 4x + 20.
Therefore, the simplified polynomial for the area and perimeter of the rectangles are:
13). Area = 5x² + 40, Perimeter = 12x + 16
14). Area = x² + 10x + 12, Perimeter = 4x + 20
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An angle measures 125°. Through what fraction of a circle does the angle turn?
If an angle measure 125° then the angle measures a fraction of 25/72 of a full circle.
What is a circle?A circle is a two-dimensional geometric shape that is defined as the set of all points that are equidistant from a single point, called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle, passing through the center, is called the diameter. The circumference of a circle is the distance around the edge or perimeter of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π (pi) is a mathematical constant that represents the ratio of the circumference to the diameter of a circle, approximately equal to 3.14159.
According to the given informationA circle has 360 degrees. To find what fraction of a circle an angle measures, we can divide the angle by 360. In this case, the angle measures 125 degrees, so the fraction of a circle it turns can be calculated as:
125/360 = 0.347222222...
To simplify this fraction, we can multiply both the numerator and denominator by 2:
125/360 = (1252)/(3602) = 250/720
We can further simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 10:
250/720 = (2510)/(7210) = 25/72
Therefore, the angle measures a fraction of 25/72 of a full circle.
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if (-8,3) lies on the circle and its Center is (-4,3) find the radius
If (-8,3) lies on the circle and its Center is (-4,3) then, the radius of the circle is 4.
We know that the center of the circle is (-4, 3). Let's call the radius of the circle "r".
The distance between the center of the circle and the point (-8, 3) on the circle is equal to the radius "r".
Using the distance formula, we can find the distance between these two points;
d =√[(x2 - x1)² + (y2 - y1)²]
d = √[(-8 - (-4))² + (3 - 3)²]
d = √[(-8 + 4)² + 0²]
d = √[4²]
d = 4
Since the distance between the center of the circle and the point on the circle is equal to the radius, we have;
r = d = 4
Therefore, the radius of the circle is 4.
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The sum of two numbers is 49. One number is 23 more than the other. Find the numbers.
The larger number is:
The smaller number is:
Answer:
Larger number: 36
Smaller number: 13
HELP MEEEEE PLEASEEE SOMEONEEEE :(
The function is not defined for x > 5, as a result ƒ(7) does not exist.
How did we arrive at this assertion?The given piece-wise function is:
f(x) = {x - 2}²- 1
1
-x+1
x < 2
x = 2
2 < x ≤ 5
Step 2
f(x) = (x-2)² - 1
1
-x+1
x < 2
x = 2
2 < x ≤ 5
Note that the function is not defined for x > 5.
Step 3
Since the function is not defined for > 5, therefore ƒ(7) does not exist.
The function is not defined for x > 5, therefore ƒ(7) does not exist.
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-3k - 7 ≤ 17 help!!!!!!!!!!!!!!!
You are making scarves for presents. Each scarf needs 5/6 yd of fabric. How many yards of fabric do you need for 6 scarves?
Hypothesis testing question.
From a sample of 30 patients, Divoc Health Group found that the mean days for a patient to discharge is 25 days. The hospitalization duration was assumed to follow a normal distribution. Last year, the mean days for a patient to discharge was 20 days with a standard deviation of 5 days. Divoc Health Group suspects that the mean days for a patient to discharge has increased because of Covid-19 cases and other health-related issues. Divoc Health Group decides to carry out a hypothesis test.
a) State the null and alternative hypotheses.
b) At a 5% significance level, is there sufficient evidence to conclude that the mean days for a patient to discharge has increased? Show all steps clearly. [Express your answers up to 3 decimal places]
Based on the information, Divoc Health Group now samples an additional 10 clients. The mean days for a patient to discharge were 22 days.
c) Using the new information, construct a 95% confidence interval for the mean days for a patient to discharge. [Express your answers up to 3 decimal places]
d) What is the minimum sample size required if Divoc Health Group wants to estimate the mean days for a patient to discharge to within 2 days of error with a 99% confidence?
a) Null: Mean = 20 days; Alt: Mean > 20 days. b) supported by t-value 6.708 > critical value at α=0.05. c) 95% confidence interval for mean patient discharge time is between 20.528 and 23.472 days, d) 99% confidence, a minimum sample size of 67 patients is required.
a) The null hypothesis is that the mean days for a patient to discharge is still 20 days, while the alternative hypothesis is that the mean days for a patient to discharge has increased and is now greater than 20 days.
Null hypothesis: 0: = 20
Alternative hypothesis: 1: > 20
b) We can use a one-sample t-test to test the hypothesis. We will use a significance level of 0.05.
The test statistic is given by:
t = (x - ) / (s / √n)
where x is the sample mean, is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Here, x = 25, = 20, s = 5, and n = 30. Plugging these values into the formula, we get:
t = (25 - 20) / (5 / √30) = 6.708
The degrees of freedom (df) for the t-distribution is n - 1 = 29. Using a t-table or calculator, the p-value for a one-tailed test with df = 29 and t = 6.708 is < 0.0001.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. There is sufficient evidence to conclude that the mean days for a patient to discharge has increased.
c) To construct a 95% confidence interval for the mean days for a patient to discharge, we use the formula:
CI = x ± tα/2 * (s/√n)
where x is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the critical value for a t-distribution with df = n-1 and α = 0.05/2 = 0.025.
Here, x = 22, s = 5, and n = 40 (30 from the first sample + 10 from the second sample). The critical value for tα/2 with df = 39 is 2.022.
Plugging these values into the formula, we get:
CI = 22 ± 2.022 * (5/√40) = (20.528, 23.472)
Therefore, we can be 95% confident that the true mean days for a patient to discharge is between 20.528 and 23.472 days.
d) To find the minimum sample size required to estimate the mean days for a patient to discharge to within 2 days of error with a 99% confidence, we use the formula:
n = (zα/2 * s / E)²
where zα/2 is the critical value for a z-distribution with α = 0.01/2 = 0.005, s is the sample standard deviation (which we assume is the same as before, i.e., s = 5), and E is the desired margin of error (which is 2 days).
Plugging in the values, we get:
n = (2.576 * 5 / 2)² = 66.18
Therefore, the minimum sample size required is 67 patients.
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sum of 213341 & 444233 base 5
Answer:
1213124
To add 213341 and 444233 in base 5, we need to line up the digits of the two numbers according to their place values, and then add them digit by digit, carrying over to the next place value if the sum of the digits is 5 or greater.
Here's how to do it:
2 1 3 3 4 1
+ 4 4 4 2 3 3
-----------------------
1 2 1 3 1 2 4
Therefore, the sum of 213341 and 444233 in base 5 is 1213124.
Man I don’t even know how to solve this, can y’all help me???
Answer:
3
Step-by-step explanation:
The inverse function returns the original value for which a function gave the output.
This means if there is a function f(x) and at x = a, f(a) = k then f⁻¹(k) = a
This may be difficult to grasp with variables but essentially returning to the specific question
if f(3) = 17
then
f⁻¹(17) = 3
And that is the answer
Pyramid A and Pyramid B are similar. Pyramid A has a volume of 648m° and Pyramid B has a volume of 1029m?. What is the ratio of the surface areas of Pyramid A to Pyramid B?
The ratio of the surface area of Pyramid A to Pyramid B is: 36/49
We have the information from the question is:
Pyramid A and Pyramid B are similar.
The volume of Pyramid A is 648 [tex]m^3[/tex]
The volume of Pyramid B is 1029 [tex]m^3[/tex]
To find the ratio of the surface areas of Pyramid A to Pyramid B.
Now, As we know that:
If two solids are similar, then the ratio of their volumes is equal to the cube
of the ratio of their corresponding linear measures.
[tex]\frac{Vol of A}{Vol of B} =(\frac{a}{b} )^3 =\frac{684}{1029}=\frac{216}{343}\\ \\ \frac{a}{b}=\frac{6}{7}[/tex]
If two solids are similar, then the n ratio of their surface areas is equal to the square of the ratio of their corresponding linear measures.
Surface area of A/ Surface area of B [tex]=(\frac{a}{b} )^2=\frac{36}{49}[/tex]
So, the ratio of the surface area of Pyramid A to Pyramid B is: 36/49
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I would love some help please 11-13
(11) The value of expression 3/y + 2y/4 when y = 4 is [tex]2\frac{3}{4}[/tex].
Hence the correct option is (b).
(12) The value of expression 12/y + 3y/4 when y = 8 is [tex]7\frac{1}{2}[/tex].
Hence the correct option is (c).
(13) 2x/3 + 4 = 10 equation does x = 9.
Hence the correct option is (b).
(11) The given expression is,
3/y + 2y/4 = 3/y + y/2
Substituting the value of y = 4 we get,
3/4 + 4/2 = 3/4 + 2 = [tex]2\frac{3}{4}[/tex].
Hence the correct option is (b).
(12) The given expression is,
12/y + 3y/4
Substituting y = 8 in the given equation we get,
12/8 + (3*8)/4 = 3/2 + 6 = 1 + 1/2 + 6 = [tex]7\frac{1}{2}[/tex].
Hence the correct option is (c).
(13) Given the solution is x =9.
For first option: (2/3)*9 - 6 = 6 - 6 = 0
2x/3 - 6 = 12 does not satisfied by x = 9.
For second option: (2/3)*9 + 4 = 6 + 4 = 10
So, x = 9 satisfies 2x/3 + 4 = 10.
For third option: 3*9 - 12 = 27 - 12 = 15
So x = 9 does not satisfy 3x - 12 = 21.
For fourth option: 3*9 + 12 = 27 + 12 = 39
So x = 9 does not satisfy 3x + 12 = 19.
Hence the correct option is (b).
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What is the value of sine at 330