An alarming number of U.S. adults are either overweight or obese. The distinction between overweight and obese is made on the basis of body mass index (BMI), expressed as weight/height2. An adult is considered overweight if the BMI is 25 or more but less than 30. An obese adult will have a BMI of 30 or greater. According to a January 2012 article in the Journal of the American Medical Association, 33.1% of the adult population in the United States is overweight and 35.7% is obese. Use this information to answer the following questions.
a. What is the probability that a randomly selected adult is either overweight or obese? (Round your answer to 3 decimal places.)
b. What is the probability that a randomly selected adult is neither overweight nor obese? (Round your answer to 3 decimal places.)
c. Are the events "overweight" and "obese" exhaustive?
A. Yes because you cannot be both overweight and obese.
B. Yes because you can be both overweight and obese.
C. No because you may either be overweight or obese.
D. No because you may be neither overweight nor obese.

Answers

Answer 1

Answer:

a. The probability that a randomly selected adult is either overweight or obese is:

= 68.8%.

b. The probability that a randomly selected adult is neither overweight nor obese is:

= 31.2%

c.

D. No because you may be neither overweight nor obese.  The events "overweight" and "obese" are not exhaustive.

Step-by-step explanation:

Overweight adult = BMI ≥ 25 but < 30

Obese adult = BMI ≥ 30

Journal of the American Medical Association:

Overweight adult population in the United States = 33.1%

Obese adult population in the United States = 35.7%

The probability that a randomly selected adult is either overweight or obese = Percentage of overweight adult population + Percentage of obese adult population

= 33.1% + 35.7%

= 68.8%

The probability that a randomly selected adult is neither overweight nor obese = 1 - 68.8%

= 31.2%

The events "overweight" and "obese" can only be exhaustive if their combined probabilities of occurrence equals 1 or 100%.


Related Questions

1. Find the slope of a line that passes through (3,-5) and (6,-6)
m=____
2. y=7 x+2
m=___
5. Find the slope of a line that passes through ( 4.5, 3.5) and (9.5, 5.5)
m=_____
6. y=-3 x-4
m=_____

Answers

The slope the lines in the given functions are -1/3, 7, 0.4 and -3

Slope of a Line

The is the ratio of the rise to run of the graph or the ratio of change in y- coordinate to the change in the x-coordinate.

The formula of slope is given as;

m = y₂ - y₁ / x₂ - x₁

1)

The points are

A = (3, -5)B = (6, -6)

Applying the formula of slope of a line

m = -6 - (-5) / 6 - 3)

m = -6 + 5 / 3

m = -1/3

slope is - 1/3

2) The equation 7x + 2 is a linear equation which is modeled as y = mx + c

where m is the slope and c is the y - intercept

The slope of the linear equation y = 7x + 2 is 7

slope is 7

5) Using the formula of slope of a line

m = y₂ - y₁ / x₂ - x₁

m = 5.5 - 3.5 / 9.5 - 4.5

m = 0.4

Slope is 0.4

6) The linear function y = -3x - 4

Comparing the function with y = mx + c

The slope is -3

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Question 3 Write a method that solves for x in the quadratic equation. The parameters are a, b, c, and boolean flag that indicates whether it will solve the equation with addition or subtraction in the numerator. 2-4ac ㄨㄧ- 2a Source: Wikipedia The method will return the value of x

Answers

On solving the providewd question we can say that, public static double solve(double a, double b, double c, boolean flag )

What is quadratic equation?

A quadratic equation is a quadratic polynomial in one variable that looks like this: x = ax2 + bx + c. a 0. This polynomial has at least one solution since it is a second-order polynomial, according to the Fundamental Theorem of Algebra. The answer can actually work or be difficult.

public static double solve(double a, double b, double c, boolean flag)

{     double d = Math.sqrt(b*b - 4*a*c);     if(flag)

{         return (-b + d) / (2*a);     }

else {         return (-b - d) / (2*a);     } }

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A rectangle is split into four triangle as shown. What is the area of shade triangle?

Answers

Answer:

First of all u need to find the rectangle area then subtract the area of three triangles.

step1 : 3×4=12

step2: 1×4/2 + 2×3/2 + 3×1/2 = 6.5

Answer = 12 - 6.5 = 5.5

Can somebody please tell me how do i solves these. Thank you.

Answers

1. The statement is false, as the differential equation is of the second order but it is nonlinear.

2. The statement is false, as the differential equation is linear.

3. The third statement is correct, as the differential equation is of the fourth order and nonlinear.

How to classify the differential equations?

Regarding to linearity, the differential equations are classified as follows:

Linear: the derivatives of y are multiplied only by terms that do not contain the variable y.Non-linear: the derivatives of y are multiplied by terms that contain the variable y.

Regarding the order, it is given by the order of the highest derivative in the differential equation.

For question 1, the differential equation y''y + (y')² = sin(x) is in fact of the second order, as the highest derivative is y'' (second derivative), but it is nonlinear, due to the multiplication of y by y''.

Hence the differential equation for question 2 is linear, as the multipliers to the derivatives are of x and -1, neither of which contains the variable y.

For question 3, we have that:

The differential equation is of the fourth order, as y''' x y' = y''''.The differential equation is nonlinear, due to the multiplication of y by xy'''.

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Give slope for these points blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah

Answers

The slope equation is:  [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

The slope of the points (0, 2) and (1, -3) is: -5

The slope of the points (-5, -8) and (10, 12): 4/3

First graph: m = 1

Second graph: m = -2/3.

What is the Slope of a Line?

The slope of a line is calculated using the formula below:

Slope (m) = rise/run = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Therefore, the equation of the slope is expressed as:  [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Find the slope of the points (0, 2) and (1, -3):

m = change in y / change in x = (-3 - 2) / (1 - 0)

m = -5/1

Slope (m) = -5

Find the slope of the points (-5, -8) and (10, 12):

Slope (m) = (12 -(-8)) / (10 - (-5))

m = 20/15

m = 4/3

Find the slope of the first graph:

Slope (m) = rise/run = 1/1

m = 1

The slope of the second graph = rise/run = -2/3.

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Question 1 of 10
What is the slope formula?
OA. ₂-₁,
Y/₂-1/₁
OB. -
X₂-X₁
O c. 2-₁
X₂-1/₁
D. +₁
Y/₂+1/₁
SUBMIT

Answers

Answer:

(y2-y1)/(x2/x1)

Step-by-step explanation:

Well uh I hope you get it

I'm not sure about this question DO NOT MIND THE TEXT IN THE BOX JUST ANSWER PLEASEEE!!

DONT ASNWER IF YOU DONT KNOW!

Answers

Answer:

You had it right, now all you have to do it add 18 and 30 and 4 and 3 and you should get your answer, than you take the answer and write 48r+7w=55rw

Step-by-step explanation:

I added 18, 30, 4, and 3. I got 48 for the 18 and 30 and 7 for the 4 and 3

Using - your favorite statistics software package, you generate scatter plot which displays a linear form You find regression equation and the standard deviation for both variablesThe standard deviation for X is 1.34, and the standard deviation for y is 3.6. The regression equation is reported 4 1.891 What fraction of the variation in y can be explained by the variation in the values of x? (

Answers

The regression line is yˆ = 4 + 1.891x , the coefficient of determination of two variables or the fraction of the variation in y that can be explained by the variation in the values of x is 0.51..

Here the fitted regression equation of y on x is

yˆ = 4 + 1.891x ---(*)

where, x --> Independent variable

yˆ --> predicted value of the dependent variable

Now, b₁ = slope cofficient = 1.891 ~ 1.91

(estimated from least squares method)

We have given that,

Standard deviations for X = 1.34 = sₓ say

Standard deviations for Y = 3.6 = sᵧ say

we know, b₁ = r₀( sₓ/sᵧ ) where ro is corr(X,Y)

=> 1.91 = r₀ (3.6/1.34)

=> 1.91×1.34/ 3.6 = r₀

=> r₀ = 0.71944

Defining, R² = cofficient of determination of two variables = Proportion of variation in Y , explained by the variation in the value of X, through the regression model.

= (r₀)² = (0.71944)² = 0.505442

R² = 0.505442 ~ 0.51 (in two decimals)

Hence, the cofficient of determination is 0.51..

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Complete question:

Using your favorite statistics software package, you generate a scatter plot which displays a linear form. You find a regression equation and the standard deviation for both variables. The standard deviation for x is 1.34 , and the standard deviation for y is 3.6 . The regression equation is reported as y = 4 + 1.891x . What fraction of the variation in y can be explained by the variation in the values of x? (Enter your answer as a decimal between 1 and 2.)

Evaluate the expression when y=6 and x=9.

5y-x

Answers

Answer:

21

Step-by-step explanation:

y=6 and x=9.

5y x

= 5(6) – 9

= 30 – 9

= 21

i hope this helped

The correct answer is 29. You multiply 5 times 6 and subtract by 9. Follow the PEMDAS rules.

Charlie starts to sove a system of linear equations graphically. he puts both equations into slope-intercept form and notices that the lines have the same slope. based on this information only, which of the following statements is true?A. The system could have no solution, one solution, or infinitely mani solutionsB. The system has no solution because two equations with the same slope never intersectC. The system has either no solution or infinitely many solutions, depending on the y-interceptsD. The system has infinitely many solutions because two equations with the same slope represent the same lineHx - 4y = -10Kx + 3y = -15

Answers

C. The system has either no solution or infinitely many solutions, depending on the y-intercepts

what is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

If the slopes of both lines are same then the lines are parallel. Now, both the equations can represent same line or two different lines. If the equations represent the same line, then they are coincident and have infinite number of solutions, else if the equations represent two different lines with same slope then they are parallel and hence will never intersect, and therefore won't have any solution

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The system has either no solution or infinitely many solutions, depending on the y-intercepts

If the slopes of both lines are same then the lines are parallel. Now, both the equations can represent same line or two different lines. If the equations represent the same line, then they are coincident and have infinite number of solutions, else if the equations represent two different lines with same slope then they are parallel and hence will never intersect, and therefore won't have any solution

Rocky spends 1 3/4 hours working out
on Monday, 2½ hours on Wednesday and 5/6 of
an hour on Friday. How much time did he spend
working out this week.

Answers

Answer:

5 1/12 hours

Step-by-step explanation:

You need a common denominator and that would be 12

1 [tex]\frac{9}{12}[/tex]       ([tex]\frac{3}{4}[/tex] x [tex]\frac{3}{3}[/tex]) another name for [tex]\frac{3}{3}[/tex] is 1.  You are making an equivalent fraction

2 [tex]\frac{6}{12}[/tex]      ([tex]\frac{1}{2}[/tex] x [tex]\frac{6}{6}[/tex])

[tex]\frac{10}{12}[/tex]          ([tex]\frac{5}{6}[/tex] x [tex]\frac{2}{2}[/tex])

1 [tex]\frac{9}{12}[/tex] + 2 [tex]\frac{6}{12}[/tex] + [tex]\frac{10}{12}[/tex] = 3 [tex]\frac{25}{12}[/tex]

I can break [tex]\frac{25}{12}[/tex] into [tex]\frac{12}{12}[/tex] + [tex]\frac{12}{12}[/tex] + [tex]\frac{1}{12}[/tex]  Another name for [tex]\frac{12}{12}[/tex] is 1

3 + 1 + 1 + [tex]\frac{1}{12}[/tex]

5 [tex]\frac{1}{12}[/tex]

Solve the following equation:
3x^2= -12
a.
X = 2
b. x=-2
C.
No real solutions
d.
X = ‡2

Answers

3x^2= -12

Divide each side by factors that do NOT contain the variable

This means X = +/- 2 (with imaginary number)

statistics that specify how likely findings are to be true for other populations or in other locales is called statistics.

Answers

The study of data collection, analysis, presentation, and interpretation is known as statistics.

Given,

What is statistics?

Data collection, analysis, presentation, and interpretation are all part of the science of statistics. Much of the early motivation for the subject of statistics came from governmental needs for information on a variety of economic activity and census data.

Types of statistics;

Based on the characteristics, the various statistical kinds are divided: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as using pie charts, bar graphs, or tables.

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Choose the function whose graph is given by:
A. y=-3.5cos x
B. y=3.5sin x
C. y=sin(3x)
D. y=2.5sin x

Answers

Answer:

A a option is right because cause 3 is near to zero that's value one and y 3.5 x 1near equal to 3 something

Are there any circles for which the relationship between the diameter and the circumference cannot be represented by π? explain

Answers

Well, the diameter and circumference scale perfectly. Therefore, the ratio will remain the same regardless of how big or tiny the circle is. For all circles, circumference is equal to x diameter. There are no exceptions because this is the definition of.

Give an example of diameter.

If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to a circle's diameter, which is a line segment that extends from one end of the circle to the other end while passing through the center.

What is a circle's circumference?

A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).

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1. What is the vertical distance between (5, –12) to (5, 17)?

2. What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards?

3. The point (–7, 6) was reflected over an axis to become the point (7, 6). Which axis was it reflected over? Explain.

Answers

The required solutions for each of the questions are obtained as 29 units, 235.2 cubic yards and y axis respectively.

What is the distance formula?

The distance formula in coordinate geometry is used to find the distance between two points  whose coordinates are given as (x₁, y₁) and (x₂, y₂) as √((x₁ - x₂)^2 + (y₁ - y₂)^2).

By knowing the sides, the area of different polygons can be found.

(1) The vertical distance between points (5, –12) and (5, 17) is given by distance formula as below,

√((5 - 5)² + (-12 - 17)²) = 17

(2) The volume of the rectangular prism is given as,

Volume = Area of base × Height of the prism

             = 14(¹/₅) × 7 × 8

              = 21/5 × 56 = 235.2

(3) The given points are (–7, 6) and (7, 6).

It is clear that after reflection y coordinate does not change.

Which implies that the axis of symmetry is y axis.

Thus, the axis of reflection is y axis.

Hence, the vertical distance between points, the volume of the prism and  the axis of reflection are 29 units, 235.2 cubic yards and y axis respectively.

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What is the volume of this figure?

Answers

The Volume of the given figure is 264 cubic units

What is Volume?

Volume is a measurement of three-dimensional space that is occupied. It is frequently mathematically quantified using SI-derived units or different imperial or US customary units. The concept of length is linked to the definition of volume.

Solution:

Volume of Cuboid = Length * Breadth * Height

Volume of Cuboid 1 = 8*5*5 = 200 cubic units

Volume of Cuboid 2 = 8*8*1 = 64 cubic units

Total Volume = 200 + 64 = 264 cubic units

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Select the correct answer. Consider the following equation. − 16 ⁢ p + 37 = 49 − 21 ⁢ p Select the equation that has the same solution as the given equation. A. − 55 + 12 ⁢ p = 5 ⁢ p + 16 B. − 14 + 6 ⁢ p = − 9 − 6 ⁢ p C. 2 + 1.25 ⁢ p = − 3.75 ⁢ p + 10 D. 3 2 ⁢ p − 5 + 9 4 ⁢ p = 7 − 5 4 ⁢ p

Answers

The equation that has the same solution as − 16 ⁢p + 37 = 49 − 21 ⁢p is (3/2)p - 5 + (9/4)p = 7 - (5/4)p thus option (C) is correct.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation.

As per the given equation,

− 16 ⁢p + 37 = 49 − 21 ⁢p

-16p + 21p = 49 - 37

5p = 12

p = 12/5 = 2.4

In the equation,(3/2)p - 5 + (9/4)p = 7 - (5/4)p

(3/2)p + (9/4)p + (5/4)p = 7 + 5

5p = 12

p = 2.4

Hence "The equation (3/2)p - 5 + (9/4)p = 7 - (5/4)p has the same solution as  − 16 ⁢p + 37 = 49 − 21 ⁢p ".

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Kimberly’s whole family has colds so she makes a 6-quart pot of chicken noodle soup and serves everyone a bowl. Her family has a total of 4 people. If each of Kimberly’s bowls hold about 2 cups how many bowls of soup are left in the pot

Answers

The quantity of bowls of soup are left in the pot aftee serving her family is 16 cups

How many cups are left?

Quantity of chicken noodle soup made = 6-quartNumber of people in Kimberly's family = 4Volume of bowl = 2 cups

Convert quarts to cups:

1 quarts = 4 cups6 quarts = 24 cups

Total quantity of soup served = Number of people in Kimberly's family × Volume of bowl

= 4 × 2

= 8 cups

Quantity of bowls of soup are left in the pot = Quantity of chicken noodle soup made - Total quantity of soup served

= 24 cups - 8 cups

= 16 cups

In conclusion, 16 cups of soup are left in the pot after serving.

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The greatest common factor of 250 and 300 is?

Answers

Answer:

250 / 50 = 5

300 / 50 = 6

Therefore, the greatest common factor of 250 and 300 is 50.its also known as a number to be divided so you can get the lowest fraction

Step-by-step explanation:

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The greatest common factor of 250 and 300 is 50

What is the greatest common factor of two numbers?

The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number.

Given here: The numbers as 250 and 350

Steps to find GCF

Find the prime factorization of 250

250 = 2 × 5 × 5 × 5

Find the prime factorization of 300

300 = 2 × 2 × 3 × 5 × 5

To find the GCF, multiply all the prime factors common to both numbers

Hence, GCF = 2 × 5 × 5  GCF = 50

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Realiza las siguientes potencias

Answers

The powers is 5 - 1/2³.

What is Exponents and Powers?

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

The number of times a number has been multiplied by itself is referred to as an exponent.

Given:

(5 - [tex]2^{-3}[/tex])

As, we know that

[tex]a^{-m[/tex] = 1/ [tex]a^m[/tex]

Then, (5 - [tex]2^{-3}[/tex])

= 5 - 1/2³

= 5-1/8

= 40-1/8

= 39/8

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The Translation of attached question is

Make the following powers

The sum of heart rate readings taken five times for of Kundaval and Kulazhi are 400 and 360 respectively. And their projected deviations are 3,16 and 2.0 respectively. If you were. a doctor, who would you treat immediately?.​

Answers

If i were a doctor, the person I would treat immediately is; Kundaval because he has higher heart rate and larger projected deviation.

How to interpret Mean and Standard deviation?

We are given that;

Sum of heart rates taken 5 times for Kundaval = 400

Sum of heart rates taken 5 times for Kulazhi = 360

Projected deviation for Kundaval = 3.16

Projected deviation for Kulazhi = 2.0

Now, mean simply means the average of a set of given data while standard deviation is defined as a measure of how dispersed the data is in relation to the mean.

Thus, as a doctor, I would prioritize the treatment of the patient that has higher heart rate and larger projected deviation. Thus, we would conclude that Kundaval, whose sum of heart rate readings is 400 and whose projected deviation is 3.16 would be the one that should be treated first.

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determine the equation of the parabola that opens up, has vertex (7,7) and a focal diameter of 16.

Answers

The equation of a parabola that opens up and has a vertex at (7,7) can be written in the form

y = a(x - 7)^2 + 7.

The focal diameter of the parabola is 16, which means that the distance from the vertex to the focus is 8 (since the focal diameter is the sum of the distances from the vertex to the focus and from the vertex to the directrix).

To find the equation of the parabola, we need to determine the value of a that will give us the correct focal diameter. The distance from the vertex to the focus is given by the equation sqrt(4a(y - 7)), so we can set this equal to 8 and solve for a:

sqrt(4a(y - 7)) = 8

4a(y - 7) = 64

a(y - 7) = 16

a = 16 / (y - 7)

Substituting this value of a back into the equation for the parabola gives us:

y = (16 / (y - 7))(x - 7)^2 + 7

This is the equation of the parabola that opens up, has a vertex at (7,7), and a focal diameter of 16.

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A rectangular walkway is 38 feet long and has a perimeter of 80 feet the department of public works wants to spread gravel on the walkways how many square feet of gravel are needed to cover the entire walkway ?

Answers

Answer:

76 [tex]ft^{2}[/tex]

Step-by-step explanation:

We are looking for the area of the walkway.

Area = length times width.

We know the length, we need to find the width.

Perimeter is the distance around the rectangle.  It is two length and two widths.

p = 2l + 2w

80 = 2(38) + 2W

80 = 76 + 2W  Subtract 76 from both sides.

80 - 76 = 76 - 76 + 2w

4 = 2w Divide both sides by 2

[tex]\frac{4}{2}[/tex] = [tex]\frac{2w}{2}[/tex]

2 = w

Now that we know the width we can find the area

a = 38 x 2

a = 76 [tex]ft^{2}[/tex]

Answer:

Length=38 ft

breadth=?

Perimeter=80 ft

we know,

Perimeter= 2(length+breadth)

or,80ft=2(38 ft + breadth)

or,40 ft=38ft + breadth

or,breadth=40 ft-38 ft

:. breadth=2 ft

Now,

Area of walkway= length ×breadth

=38 ft×2 ft=76 ft²

Hence,72 square feet of gravel is required to cover the entire walkway.

{20 PTS}
4/6 = ??? x 1/6
what number makes this equation true? fill in the blank

Answers

It’s 4. To find you just divide the answer (4/6) by 1/6 and to divide using a fraction you first invert it and then just multiply. So they way it works is you take 4/6 • 6/1 the 6’s cancel out and you end up with 4/1 which equals just 4.
Hope this helps :)

Olivia and liam paint their houses. Olivia can paint her house in 9 hours while liam paints his in 7 hours. If olivia and liam painted together, write an equation that would find the time in hours t it. would take them to paint a house.

Answers

Answer:

t = 7/9 * 9 + 7/9 * 7 = 14 hours

Step-by-step explanation:

Mr Jenkins runs a large arable farm.
He grows three times as much wheat than barley,
and three times as much barley than corn. Farmer
Jenkins grows twice as much corn as pumpkins.
Mr Jenkins's farm has an area of 270 acres.

Answers

Set

that

x acres.

wood to

then

2x

are

used

to grow

and 6x acres. are

used

to grow barley.

and

16x

acres

Ore

used

to

grow

where.

§ set up

riddles

according

to quation

x +

2x

+6

x

+ 16x

=

270

{total oven is

270

acres?

252

=270

x = 10.8

solve

equersion

for 23

So

10.8

acnes

are

used

to

grow

pumpkins.

Find the z-score such that the area under the standard normal curve to its left is 0.2

Answers

The z-score such that the area under standard normal curve to its left is 0.2 is found as -0.84.

Explain the term Z-score?

A mathematical table known as the Z table, also known as the Z-score table or the standard normal table, is used to determine the likelihood that the z-score number is below, above, or in between the values just on standard normal distribution.

Z-scores are the most used name for standard scores. Its similar concepts, like as z-values, standardized factors, and normal scores, are utilized in this article.A positive Z score score implies that the raw score is higher than the distribution's mean.For instance, a z-score of 2 indicates that the result is two standard deviations above the mean.If the Z score is negative, the distribution's mean is below the raw score value.

For the stated question,

You simply need to discover the location of 0.2 on the z-score table and then its z-score. (The area to the left of a z-score is shown in the table)

Our z-score is -(0.8 + 0.04) =  - 0.84 as a result.

Thus, the z-score such that the area under the standard normal curve to its left is 0.2 is found as -0.84.

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A large rectangular prism is 12 inches long, 9 inches wide, and 6 inches tall. A small rectangular prism is also 12 inches long, but it's only 3 inches wide and 3 inches tall.
How many small prisms would it take to fill the large prism?

Answers

The required number of small prism that would be fill in the large prism is given as 6

As mentioned in the question, a large rectangular prism is 12 inches long, 9 inches wide, and 6 inches tall. A small rectangular prism is also 12 inches long, but it's only 3 inches wide and 3 inches tall.

Here,
The volume of the large prism = 12 × 9 × 6
                                              = 648 inches cube
The volume of the small prism = 12 × 3 × 3
                                              = 108 inches cube,


The ratio of the volume of the large prism to a small prism will give the number of small prisms needed to fill the large prism. So,
n = 648 / 108  = 6 / 1

Thus, the required number of small prism that would be filled in the large prism is given as 6.

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Let ƒ(x) = 8(1/4)^X+³ — 4.
The graph of f(x) is translated 4 units down to form the graph of g(x).

Answers

The function f(x) is translated by 4 units down to form a function g(x) will be written below.

[tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8\\[/tex]

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

[tex]f(x) = 8 \times \left (\dfrac{1}{4} \right )^{x^3} - 4[/tex]

Simplify the equation, then we have

[tex]f(x) = 8 \times \left (\dfrac{1}{4} \right )^{x^3} - 4\\\\\\f(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 4[/tex]

The function f(x) is translated by 4 units down to form a function g(x) will be given as,

[tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 4-4\\\\\\g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8[/tex]

The function f(x) is translated by 4 units down to form a function g(x) will be [tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8\\[/tex]. The graph is drawn below.

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