A rhombus has a perimeter of 88 and


two acute angles that measure 40° each.


Find the length of the shorter diagonal.


PLEASE HELP ME ASAP

Answers

Answer 1

The length of the shorter diagonal is approximately 7.07 units.

A rhombus is a four-sided polygon in which all sides are equal in length. It is also called a diamond shape because it is often used for diamond-shaped figures. In this case, we are given that the perimeter of the rhombus is 88. Since all sides of the rhombus are equal, we can divide the perimeter by 4 to find the length of one side.

88 ÷ 4 = 22

Therefore, each side of the rhombus measures 22 units.

We are also given that two of the angles in the rhombus are acute angles measuring 40° each. Since all angles in a rhombus are equal, we can find the measure of the other two angles by subtracting the sum of the acute angles from 360.

360 - 2(40) = 280

Each of the other two angles measures 140°.

To find the length of the shorter diagonal, we can use the formula:

Shorter diagonal = (2 × Area) / Length of longer diagonal

The area of a rhombus can be found by multiplying the length of the longer diagonal by the length of the shorter diagonal and then dividing by 2.

Area = (diagonal1 × diagonal2) / 2

We know that the longer diagonal is twice the length of the shorter diagonal.

Longer diagonal = 2 × Shorter diagonal

Substituting these values into the formula, we get:

Shorter diagonal = (2 × (22 × Shorter diagonal × sin 40°)) / (2 × Longer diagonal)

Simplifying, we get:

Shorter diagonal = (22 × Shorter diagonal × sin 40°) / Longer diagonal

Plugging in the values we know, we get:

Shorter diagonal = (22 × Shorter diagonal × sin 40°) / (2 × Shorter diagonal)

Shorter diagonal = 11 × sin 40°

Using a calculator, we can find that:

Shorter diagonal ≈ 7.07

Therefore, the length of the shorter diagonal is approximately 7.07 units.

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Related Questions

if a researcher finds a small difference in average test scores between a large sample (over 700) of experimental participants and a large sample (same size) of control participants, it is very likely that the difference is

Answers

The null and alternative hypotheses are H₀: μ₁ - μ₂ = 0 and H₁: μ₁- μ₂ ≠ 0 and the test statistic value is equal to 0.45.

The null hypothesis (H₀) states,

That there is no significant difference between the population means of the experimental group and the control group.

The alternative hypothesis (H₁) states that there is a significant difference between the two means.

State the hypotheses as,

H₀: μ₁ - μ₂ = 0 (there is no difference in means)

H₁: μ₁- μ₂ ≠ 0 (there is a difference in means)

where μ₁ is the population mean of the experimental group

And μ₂ is the population mean of the control group.

The test statistic,

Use the t-test formula,

t = (x - μ) / (s / sqrt(n))

where x is the sample mean = 102

μ is the hypothesized population mean = 100

s is the sample standard deviation =88

n is the sample size= 10

Plugging in the values, we get,

t = (102 - 100) / (88 / sqrt(10))

 = 0.45

Therefore, the null and the alternative hypotheses states that H₀: μ₁ - μ₂ = 0 there is no difference in means and H₁: μ₁- μ₂ ≠ 0 there is a difference in means and the test statistic for a sample mean of 102 is 0.45.

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The given question is incomplete, I answer the question in general according to my knowledge:

If a researcher finds a small difference in average test scores between a large sample of 700 experimental participants with a standard deviation of  88, a mean of 100, and with a sample size of 10.  

a. State the null and the alternative hypotheses.

b. Compute the test statistic for sample mean 102.

Help translations and reflections

Answers

Thus, Coordinates of image of points A', B' and C' are- A'(-6, 10), B'(-2, -8), C'(4 , -7)

Explain about the reflection along the y-axis:

A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting any symbol in a line or a point.

The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).

Given coordinates of points A, B and C

A(6, 10), B(2, -8), C(-4 , -7)

After reflection  (x, y) ---> (-x, y).

Thus,  Coordinates of image of points A', B' and C' are-

A'(-6, 10), B'(-2, -8), C'(4 , -7)

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A florist sells flower bouquets. the table shows the prices for various amounts and kinds of bouquets.
total price
bouquets
2
flower
daisies
tulips
roses
$23.90
$60.80
2
1
2
a
the expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is
$18.45 more than a bouquet of tulips.
b
the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is
$18.45 more than a bouquet of daisies.
с
the expression 23.90 - 60.80 represents that a bouquet of tulips is $36.90 more than a
bouquet of daisies.
d
the expression 60.80 - 23.90 represents that a bouquet of daises is $36.90 more than a
bouquet of tulips.

Answers

The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.

The given table shows the prices for various amounts and kinds of bouquets sold by a florist. The prices depend on the number and type of flowers in the bouquet. The table shows prices for bouquets of 2 flowers with daisies, tulips, and roses.

The expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is $18.45 more expensive than a bouquet of tulips. This is because the cost of a 2-flower bouquet of daisies is $23.90 and the cost of a 2-flower bouquet of tulips is $60.80, so the difference between them is $36.90.

However, we subtract 2 from each price to get the price of the actual flowers in the bouquet, which are the same for both daisies and tulips. Therefore, we get the difference of $18.45.

Similarly, the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is $18.45 more expensive than a bouquet of daisies. Here, we subtract the price of a 2-flower bouquet of daisies plus the cost of 2 flowers from the price of a 2-flower bouquet of tulips.

Again, the actual cost of flowers in both bouquets is the same, so we get the difference of $18.45.

The expressions 23.90 - 60.80 and 60.80 - 23.90 represent the price difference between bouquets of daisies and tulips, respectively. The former expression gives a negative result of $36.90, which means that a bouquet of tulips is $36.90 more expensive than a bouquet of daisies.

The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.

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52.03×9.81

I’ve been having troubles with decimals and I need some help with this. Thanks.

Answers

To multiply 52.03 by 9.81, you can first ignore the decimal points and multiply 5203 by 981:

5203 x 981 = 5100843

Next, count the total number of decimal places in the original numbers being multiplied (2 in 52.03 and 2 in 9.81) and add them together to get 4.

Finally, place the decimal point in the product so that there are 4 digits to the right of the decimal point. Counting from the right, this means placing the decimal point after the third digit:

5203 x 981 = 5100843
52.03 x 9.81 = 510.0843

Therefore, 52.03 multiplied by 9.81 is equal to 510.0843.

Robert uses f(x)=1000(1. 0375)^x to calculate the interest he earns each year for his savings account. What is the annual rate as a percent?

Answers

The annual rate as a percent is approximately 4.86% per year.

To find the annual rate as a percent, we first need to understand the function that Robert is using. The function [tex]f(x) = 1000(1.0375)^x[/tex] represents the amount of money Robert earns each year based on his initial investment of $1000 and the interest rate of 3.75% (as represented by the value 1.0375, which is 1 + 0.0375).

To calculate the annual rate as a percent, we need to isolate the interest rate from the function. We can do this by using logarithms. Taking the logarithm of both sides of the equation, we get:

log(f(x)) = log(1000) + x*log(1.0375)

Now, we can solve for the interest rate (represented by the value of 1.0375) by dividing both sides of the equation by x and then taking the antilog of the result:

1.0375 = antilog[(log(f(x)) - log(1000))/x]

Using this formula, we can plug in any value for x (representing the number of years Robert has held his investment) and find the corresponding interest rate. For example, if Robert has held his investment for 5 years, we can calculate the interest rate as:

1.0375 = antilog[(log(f(5)) - log(1000))/5]

This gives us an interest rate of approximately 4.86% per year. So, to answer the original question, the annual rate as a percent is approximately 4.86%.

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Find the function, f, that satisfies the following conditions f"(x)=-sin x/2, f'(π) = 0, f(π/3)=-3

Answers

The function f(x) = -4*sin(x/2) - 1 is the solution that meets the specified conditions.

To find the function, f, that satisfies the given conditions f"(x) = -sin(x/2), f'(π) = 0, and f(π/3) = -3, we need to integrate the given second derivative twice and apply the boundary conditions. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x).
1. Integrate f"(x) = -sin(x/2) with respect to x to find f'(x):
  f'(x) = ∫(-sin(x/2)) dx = -2*cos(x/2) + C1, where C1 is the integration constant
2. Apply the boundary condition f'(π) = 0:
  0 = -2*cos(π/2) + C1
  C1 = 0, since cos(π/2) = 0.
3. Now, f'(x) = -2*cos(x/2).
4. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x):
  f(x) = ∫(-2*cos(x/2)) dx = -4*sin(x/2) + C2, where C2 is the integration constant.
5. Apply the boundary condition f(π/3) = -3:
  -3 = -4*sin(π/6) + C2
  -3 = -4*(1/2) + C2
  C2 = -1.
So, the function f(x) that satisfies the given conditions is f(x) = -4*sin(x/2) - 1.

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Please help with this​

Answers

a) The table is completed as follows:

x = -5, y = -3.x = 0, y = 2.x = 3, y = 5.

b) The graph is given by the image presented at the end of the answer.

How to calculate the numeric value of a function or of an expression?

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

y=  x + 2.

Hence the numeric values of the function are given as follows:

x = -5, y = -5 + 2 = -3.x = 0, y = 0 + 2 = 2.x = 3, y = 3 + 2 = 5.

Then the graph is constructed connecting two of these points and tracing a line through them.

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the function g(x) = x2 is transformed to obtain function h: h(x) = g(x) + 1. Which statement describes how the graph of h is different from the graph of g? A. The graph of h is the graph of g horizontally shifted right 1 unit. B. The graph of h is the graph of g vertically shifted up 1 unit. C. The graph of h is the graph of g vertically shifted down 1 unit. D. The graph of h is the graph of g horizontally shifted left 1 unit.

Answers

The statement that  describes how the graph of h is different from the graph of g is: B. The graph of h is the graph of g vertically shifted up 1 unit.

Which statement describes how the graph of h is different from the graph of g?

The function h(x) = g(x) + 1 is obtained by adding a constant (1) to the output of the function g(x) = x^2. This means that the graph of h(x) will be the same as the graph of g(x), except that every point on the graph of h(x) will be shifted vertically upward by 1 unit.

Therefore, the correct statement is: B. The graph of h is the graph of g vertically shifted up 1 unit.

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The equation, with a restriction on x, is the terminal side of an angle theta in standard position. 5x + y = 0, x ≥ 0 Give the exact values of the six trigonometric functions of theta. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sin theta = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed. Rationalize all denominators.) B. The function is undefined.

Answers

Sin theta = -5/sqrt(26) Is the correct option , To find the six trigonometric functions of theta, we need to first find the values of x and y on the terminal side of theta. From the given equation, 5x + y = 0 and x ≥ 0, we can solve for y in terms of x:

y = -5x

Since x ≥ 0, we know that (x, y) lies in the fourth quadrant. We can now use the Pythagorean theorem to find the length of the hypotenuse:

r =[tex]sqrt(x^2 + y^2) = sqrt(x^2 + (-5x)^2) = sqrt(26x^2)[/tex]

Now we can find the six trigonometric functions:

sin(theta) = y/r = [tex]-5x/sqrt(26x^2) = -5/sqrt(26)[/tex]

cos(theta) = x/r =[tex]x/sqrt(26x^2) = 1/sqrt(26)[/tex]

tan(theta) = y/x = -5x/x = -5

csc(theta) = r/y = [tex]sqrt(26x^2)/(-5x) = -sqrt(26)/5[/tex]

sec(theta) = r/x = sqrt(26x^2)/x = sqrt(26)/1 = sqrt(26)

cot(theta) = 1/tan(theta) = -1/5

Therefore, the exact values of the six trigonometric functions of theta are:

sin(theta) = -5/sqrt(26)

cos(theta) = 1/sqrt(26)

tan(theta) = -5

csc(theta) = -sqrt(26)/5

sec(theta) = sqrt(26)

cot(theta) = -1/5

Answer: A. sin theta = -5/sqrt(26)

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Please help

Factor out the GCF.
6x²-3x - 18

Factor completely and show/explain each step.

Answers

Answer:

3(x - 2)(2x + 3)

Step-by-step explanation:

6x² - 3x - 18 ← factor out GCF of 3 from each term

= 3(2x² - x - 6) ← factor the quadratic

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 6 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

2x² - 4x + 3x - 6 ( factor the first/second and third/fourth terms )

= 2x(x - 2) + 3(x - 2) ← factor out (x - 2) from each term

= (x - 2)(2x + 3) ← in factored form

then

6x² - 3x - 18 = 3(x - 2)(2x + 3)

Hallie and Mattie donated blue jeans to the clothing drive. Hallie donated 4 pairs of blue jeans. Mattie donated 6 pairs of blue jeans. Write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans.

6:14
2 to 3
2 over 4
1 to 10

Answers

the correct ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans is 2:3. Thus, option B is correct.

What is the ratio?

To write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans, we need to find the common factor between the number of pairs of blue jeans each person donated.

Hallie donated 4 pairs of blue jeans, and Mattie donated 6 pairs of blue jeans.

The common factor between 4 and 6 is 2. We can divide both 4 and 6 by 2 to get:

Hallie donated 2 pairs of blue jeans.

Mattie donated 3 pairs of blue jeans.

Now we can write the ratio of Hallie's donation to Mattie's donation as:

2:3

Therefore, the correct ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans is 2:3.

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An agricultural scientist collected data to study the relationship between the amount of nitrogen added to a comfield and the number of


bushels of com produced. This is the regression line of the data, where y is measured in bushes and is measured in pounds of nitrogen


0. 43


What is the meaning of the intercept of the regression line?


O A When no nitrogen is added to the field, 28. 7 bushels of corn are produced


When 28. 7 pounds of nitrogen is added to the held, no bushels of corn are produced


When 0. 43 pounds of nitrogen is added to the field. 28. 7 bushels of corn are produced


B. When 38. 7 pounds of nitrogen is added to the field, 0. 43 bushels of com are produced

Answers

The meaning of the intercept of the regression line is option B- When 38. 7 pounds of nitrogen is added to the field, 0. 43 bushels of com are produced

We are given the equation of the experiment that tells a relationship.

y = 0.43x + 28.5

The linear regression line is an algebraic model to show the relationship between the two models by putting the value of one variable to get the value of the other.

A linear regression line can be represented as,

y = Ax + B

Here y is the dependent variable and x is the explanatory variable. A is the slope of the line and

B is the intercept here. In the given equation there are two variables given.

Variable x representsthe amount of nitrogen added, and the variable y represents the number of bushels of corn produced.

As putting the value of x, y increases with the value of number 0.43. Therefore, as we are increasing the value of the nitrogen by one unit, the number of bushels of corn produced is increasing by 0.43 units. Hence, for every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.

Therefore option B is the correct option.

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The complete question is "An agricultural scientist collected data to study the relationship between the amount of nitrogen added to a cornfield and the number of

bushels of corn produced. This is the regression line of the data, where y is measured in bushels of corn and x is measured in pounds of

nitrogen.

y = 0.43x + 28.5

What is the meaning of the slope of the regression line?

O A. For every 0.43 pounds of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.

OB. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.

OC. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.

OD. For every 28.5 pounds of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels."

Help me— My brain goes brrr in this question word problem thing ; - ;

A table tennis ball has a radius of 0. 04m. Estimate how many table tennis balls you could fit into the coin building! [search up what it is—]

( Width: 20m | height: 110m )


- How did you calculate your estimate?

- Explain how accurate you think your prediction is?

( Show Work. )

Answers

Number of balls ≈ [tex]1.03 * 10^9[/tex]

To calculate how many table tennis balls can fit into the coin building, we need to first figure out the volume of the building and the volume of the table tennis ball.

Then, we can divide the volume of the building by the volume of the ball to get an estimate of the number of balls that can fit inside.

The volume of a table tennis ball can be calculated using the formula for the volume of a sphere, which is:

V = (4/3)πr³

where V is the volume, π is pi (approximately 3.14), and r is the radius of the ball. In this case, the radius is given as 0.04m, so we can plug that in and get:

V = (4/3) x 3.14 x 0.04³

[tex]V =2.14 * 10^{-5} m^3[/tex]

Next, we need to find the volume of the coin building. The building has a width of 20m and a height of 110m, but we don't know its depth.

Let's assume that the building is a rectangular prism with a depth of 10m. Then, we can calculate its volume using the formula:

V = l x w x h

where l is the length, w is the width, and h is the height. Plugging in the given values, we get:

V = 20 x 10 x 110

V = 22000 m³

Now, we can divide the volume of the building by the volume of the ball to get an estimate of how many balls can fit inside:

Number of balls ≈ [tex]V_building / V_ball[/tex]

Number of balls ≈ 22000 / 2.14 x [tex]10^-5[/tex]

Number of balls ≈ [tex]1.03 * 10^9[/tex]

So we can estimate that approximately 1.03 billion table tennis balls can fit into the coin building.

As for the accuracy of this prediction, it's important to keep in mind that we made some assumptions and estimations in our calculations.

For example, we assumed that the building is a rectangular prism with a depth of 10m, which may not be completely accurate.

Additionally, we rounded some of our values and used approximations for pi.

Therefore, our estimate should be considered as a rough approximation rather than an exact calculation. Nonetheless, it gives us an idea of the scale of the building and how many objects it can hold.

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What is the volume of this shape? help me please i really need help

Answers

The volume of the given shape is 125 unit³ if the length is 5 unit, breadth is 5 unit, and height is 5 unit.

A cube is a three-dimensional geometric shape that has six identical square faces, where each face meets at a right angle with the adjacent faces. It is a regular polyhedron, meaning that all of its faces are congruent (identical) and its edges are of equal length.

Volume of cube = length × breadth × height

length = 5 unit

breadth = 5 unit

height = 5 unit

Volume = 5 × 5 × 5

= 125 unit³

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Connor invests $1,400 in a savings account that compounds annually at a 9% interest rate. Determine how much money Connor will have after 4 years. Round to the nearest cent

Answers

Connor will have $ 1975.4 if he invests $1,400 with a 9% interest rate that compounds annually for 4 years.

Compound interest is given by the formula:

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

where A is the amount

P is the principal

r is the rate of interest

n is the frequency with the interest is compounded in a year

t is the time

P = $ 1,400

r = 9% or 0.09

t = 4 years

Since the interest is compounded annually the frequency of the compounding is 1.

n = 1

A = 1400 [tex](1 +\frac{0.09}{1})^{1*4[/tex]

= 1400 [tex](1.09)^4[/tex]

= 1400 * 1.411

= $ 1975.4

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Find the value of c step by step

PLEASE HELP

Answers

Answer:

c = 12

Step-by-step explanation:

[tex] {5}^{2} + {c}^{2} = {13}^{2} [/tex]

[tex]25 + {c}^{2} = 169[/tex]

[tex] {c}^{2} = 144[/tex]

[tex]c = 12[/tex]





1. The following circles are not drawn to scale. Find the area of each circle. (Use as an approximation for TT. )

21 cm

Lesson 17 Problem Set

81 ft

45

2

cm

Answers

The area of the circles are 1384.74 cm², 20601.54 cm² and 1589.625 cm²

Finding the area of each circle

From the question, we have the following parameters that can be used in our computation:

Radii = 21 cm, 81 ft, 45/2 cm

The area of a circle is calculated as

Area = πr²

substitute the known values in the above equation, so, we have the following representation

Area = 3.14 * 21² = 1384.74

Area = 3.14 * 81² = 20601.54

Area = 3.14 * (45/2)² = 1589.625

Hence, the area of the circles are 1384.74 cm², 20601.54 cm² and 1589.625 cm²

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The ages of a and b are in the ratio 8:3.6 years later their ages are ok the ratio 9:4.Find their present ages

Answers

Answer:

The present ages of A and B will be 48 and 18 years.

Step-by-step explanation:

Let the coefficient be x.

A's age = 8x

B's age = 3x

Six years hence,

Ages will be 8x+6 and 3x+6.

Now, As per the question,

(8x+6) /(3x+6) = 9/4

32x+24 = 27x+54

5x = 30

x = 6.

Which is a function of a protein macromolecule? a. keeping organisms warm b. providing quick energy for cells c. moving material in and out of cells d. passing traits to offspring

Answers

One if the functions of a protein macromolecule is: c. moving material in and out of cells

What is the Function of a Protein Macromolecule?

Proteins can be described as a complex macromolecules that are responsible for several key functions such as the regulation of cells, tissue, and organs of living organisms including their structure.

Proteins also help in performing the following:

Regulation of gene expression

Structural support, and

Many other cellular processes.

Therefore, a function of a protein macromolecule is: c. moving material in and out of cells.

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1. Order: Kefzol 1. 125 g IV q6h


A Kefzol labeled 225 mg per 4mL


How many L?

Answers

To determine the number of liters needed for an order of Kefzol 1.125 g IV q6h, we first need to convert the grams to milligrams.
1.125 g = 1,125 mg

Next, we need to calculate the total volume of Kefzol needed for each dose.

225 mg is equal to 4 mL, so:

1,125 mg ÷ 225 mg/mL = 5 mL

Therefore, each dose of Kefzol requires 5 mL.

To determine the number of liters needed for the entire order, we need to know how many doses will be given per day.

Assuming a standard dosing schedule of q6h, this means the patient will receive 4 doses per day.

So, the total volume of Kefzol needed per day is:

4 doses/day x 5 mL/dose = 20 mL/day

To convert this to liters, we divide by 1000:

20 mL/day ÷ 1000 = 0.02 L/day

Therefore, for an order of Kefzol 1.125 g IV q6h, we will need approximately 0.02 liters per day.

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Chad buys pineapples, watermelons, and a bag of grapes for a fruit salad. He spends a total of $29.68 on the fruit salad. Pineapples
cost $2.15 each, and watermelons cost $3.75 each. The bag of grapes costs $4.48.
Create an equation to model this situation, where p represents the number of pineapples Chad can purchase and w represents the
number of watermelons he can purchase.

Answers

An equation that models the situation, where p represents the number of pineapples Chad can purchase and w represents the number of watermelons he can purchase will be; 2.15p + 3.75w = 25.20.

Let's use the given information to create an equation to model this situation. We know that Chad spends a total of $29.68 on the fruit salad, so we can start with;

2.15p + 3.75w + 4.48 = 29.68

This equation represents the total cost of the fruit salad, which includes the cost of the pineapples (2.15p), the cost of the watermelons (3.75w), and the cost of the bag of grapes (4.48).

To make this equation more specific to the problem of finding the number of pineapples and watermelons Chad can purchase, we need to use the variables p and w to represent those quantities. We can set up a second equation based on the information given about the total number of fruits;

p + w + 1 = T

Here, T represents the total number of fruits in the salad, and we add 1 to account for the bag of grapes.

Now we can use substitution to eliminate the variable T. Solving for T in terms of p and w;

T = p + w + 1

Substitute this expression for T into first equation;

2.15p + 3.75w + 4.48 = 29.68

Simplify;

2.15p + 3.75w = 25.20

Therefore, the model of this situation is; 2.15p + 3.75w = 25.20

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You work at Dave's Donut Shop. Dave has asked you to determine how much each box of a dozen donuts should cost. There are 12 donuts in one dozen. You determine that it costs $0. 32 to make each donut. Each box costs $0. 18 per square foot of cardboard. There are 144 square inches in 1 square foot.

The total cost for one dozen donuts include the cost to make the donuts and the cost of the box. Create an expression to model the cost for one dozen donuts where t represents the total surface area of the box

create an expression to model the total cost for one dozen donuts where t represents the total surface area of the box in square feet.

help please :(​

Answers

The cost for one donut is $0.32, so the cost for one dozen donuts is:

12 donuts x $0.32/donut = $3.84

The cost for the cardboard box is $0.18 per square foot of cardboard, and there are 144 square inches in 1 square foot, so the cost per square inch of cardboard is:

$0.18 / 144 sq in = $0.00125/sq in

If t represents the total surface area of the box in square inches, then the cost of the box is:

t x $0.00125/sq in

To convert square inches to square feet, we divide by 144:

t/144 square feet x $0.18/square foot = t x $0.00125/sq in

Thus, the expression to model the total cost for one dozen donuts where t represents the total surface area of the box in square feet is:

$3.84 + (t/144) x $0.18

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There is a 40% chance that weather causes one or more days of school to be canceled each year. Use the table of simulated values to find the experimental probability that weather will cause school to be canceled in at least three of the next four school years. Use the digits 1 through 4 as years with a cancellation

Answers

The experimental probability of weather causing school to be canceled in at least three of the next four school years is (3+1)/24, which simplifies to 1/6 or approximately 0.1667.

What is the experimental probability of weather?

To find the experimental probability of weather causing school to be canceled in at least three of the next four school years, we need to count the number of times there were three or more cancellations in each set of four years and divide that by the total number of sets of four years.

According to the table of simulated values, there are 24 sets of four years. Out of these, there were three or more cancellations in three sets of four years, and there were four cancellations in one set of four years.  Therefore, the experimental probability of weather causing school to be canceled in at least three of the next four school years is 20%.

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HELP ASAP ! Given the rectangle in this example, and a scale factor of 3.5, what are the side lengths of the new rectangle?

Answers

Answer:

Length: 22 inches × 3.5 = 77 inches

Width: 10 inches × 3.5 = 35 inches

Consider the function f(x) = 1 – 5x², -3 ≤ x ≤ 2. The absolute maximum value is and this occurs at x equals The absolute minimum value is and this occurs at x equals

Answers

The absolute maximum value of f(x) on the interval [-3, 2] is 1, which occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -49, which occurs at x = 2.

To find the absolute maximum and minimum values of the function f(x) = 1 - 5x² on the interval [-3, 2], we first find the critical points of f(x) and then evaluate f(x) at the critical points and endpoints of the interval.

The derivative of f(x) is:

f'(x) = -10x

Setting f'(x) = 0, we get:

-10x = 0

which has only one critical point at x = 0.

Now, we evaluate f(x) at the critical point and endpoints of the interval:

f(-3) = 1 - 5(-3)² = -44

f(0) = 1 - 5(0)² = 1

f(2) = 1 - 5(2)² = -49

Therefore, the absolute maximum value of f(x) on the interval [-3, 2] is 1, which occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -49, which occurs at x = 2.

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HELP
I need all the help to figure this annoying thing out

Answers

Answer:

x = 30 , y = 54

Step-by-step explanation:

the figure is a trapezium

each lower base angle is supplementary to the upper base angle on the same side, then

4x + y + 6 = 180 ( subtract 6 from both sides )

4x + y = 174 ( subtract 4x from both sides )

y = 174 - 4x → (1)

and

2x + 12 + 2y = 180 → (2)

substitute y = 174 - 4x into (2)

2x + 12 + 2(174 - 4x) = 180

2x + 12 + 348 - 8x = 180

- 6x + 360 = 180 ( subtract 360 from both sides )

- 6x = - 180 ( divide both sides by - 6 )

x = 30

substitute x = 30 into (1)

y = 174 - 4(30) = 174 - 120 = 54

thus x = 30 and y = 54

from a circular sheet of a radius 5cm, a circle of radius 3cm is removed. find the area of the remaining sheet

Answers

Area of remaining sheet = 50. 28cm²

Check the picture below.

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=5\\ r=3 \end{cases}\implies A=\pi (5^2-3^2)\implies A\approx 50.27~cm^2[/tex]

The salaries of professional baseball players are heavily skewed right with a mean of $3. 2 million and a standard


deviation of $2 million. A baseball analyst randomly selects 40 athletes and records the mean salary. Which of the


following best describes the sampling distribution of all possible samples of size 40?


skewed right with a mean of 3. 2 million and a standard deviation of 2 million


skewed right with a mean of 3. 2 million and a standard deviation of 0. 32 million


approximately Normal with a mean of 3. 2 million and a standard deviation of 2 million


approximately Normal with a mean of 3. 2 million and a standard deviation of 0. 32 million

Answers

The best answer is approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million.

The sampling distribution of the mean of a sample is approximately normal if the sample size is sufficiently large, regardless of the distribution of the population from which the sample is drawn.

According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean, which is $3.2$ million. The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size, which is [tex]$2/\sqrt{40} \approx 0.3162$[/tex] million.

Therefore, the best answer is approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million.

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Which coordinates below form a rectangle that is a translation of the rectangle
shown above?
A(0, 3), (0, 9), (5, 3), (5,9)
B(0, 0), (0, 3), (5, 0), (5, 3)
C(0, 0), (4,0), (0, 4)
D(7, 0), (7, 3), (12, 0), (12, 3)

Answers

A. all the other are dilated and the only reasonable answer would have to be A

i need help quickk please

Answers

The true statements about the rectangular prism are Prism B has a greater volume than Prism C, Prism B has the greatest volume, and Prism A has the least volume.

What is the volume of each of the prisms?

To understand, the differences between the prisms and therefore to verify the statements about them, let's calculate the volume of each by using the formula length x width x height.

Prism A: 2 x 2 x  3= 12 cubic units

Prism B: 2 x 3 x 4 = 24 cubic units

Prism C: 3 x 2 x 3 = 18cubic units

Based on this, the statements A, D, and E are correct.

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