A book is in the shape of a right rectangular prism. It measures 8 1/2 inches tall, 7 inches wide, and 2 1/2 inches thick. What is the volume of the book? 47 1/2 in³ 80 1/2 in³ 148 3/4 in³ 179 1/2 in³

Answers

Answer 1

Hello!

The formula for volume of a rectangular prism is:

V = lwh

Let's convert the dimensions to decimals, and then use the formula to solve.

8 1/2 = 8.5 as a decimal.

7 = 7 as a decimal.

2 1/2 = 2.5 as a decimal.

Multiply:

V = 8.5 × 7 × 2.5

V = 59.5 × 2.5

V = 148.75

148.75 = 148 3/4 as a fraction because if you convert 3/4 to a decimal by dividing the numerator by the denominator, it equals 0.75.

ANSWER:

The volume of the book is 148 3/4 inches cubed.

Answer 2

V = L * W * H
L = 8.5
W = 7
H = 2.5

V = 8.5 * 7 * 2.5
V = 148. 75 = 148 3/4

Related Questions

Simplfy the expression: (x - 9)^2

Answers

The answer would be x^2-18x+81. This can be found be writing "(x-9)^2" twice, and distributing. Combine like terms, and you should get this answer.

Is this right???? Can someone please help?

Answers

This is a logistic growth model, so, we can set the function's differential equation equal to 0 and solve for p, then for y. So, let's take the derivative of this function and set it to 0:
[tex] \frac{dp}{dt} = 0.005p(300-p) = 1.5p-0.005p^2 [/tex]
[tex] \frac{d^2p}{dt^2} = 1.5 - 0.01p =0 [/tex]
[tex]-0.01p = -1.5[/tex]
[tex]p = \frac{-1.5}{-0.01} = 150 [/tex]

Now, for a logistic model, the general solution is in the form of:
[tex]p = \frac{L}{1+Ce^{-ky}} [/tex]
for
[tex] \frac{dp}{dt} = kp(L-p) [/tex]

You haven't been given the 'C' constant, so I don't have a clue as to where to go after this. Sorry, we are yet to go over logistic growth in BC class. I could take you this far by just researching. If you have further questions, I'd be happy to answer them.

PLEASE HELP ME! 50 POINTS IF YOU GET IT RIGHT!!

Darren flipped a quarter 40 times. The quarter landed on heads 65% of the time. How many times did the quarter land on tails ?

A 14

B 26

C 35

D 65

Answers

The correct answer is A, because if it was b, that would not be possible. Because the total is 40, the answer cannot be more than 20.

How to write a fraction with a numerator of 12 and a denominator of 13

Answers

The numerator is the number on top
And the denominator is the number on the bottom

If the numerator is 12 and the denominator is 13, then the fraction would be:

12 / 13

An ice-cream shop sold 2.87 gallons of rocky road ice cream yesterday. The shop sold 0.449 gallons of rocky road ice cream today. What was the total amount of Rocky Road ice cream sold yesterday and today? Enter your answer, as a decimal, in the box.

Answers

2.28 + 0.449 = 3.319

helpppppppppppppppppppppppppppppp

Answers

The answer is A. \sqrt(-108)=sqrt(-1*108)=sqrt(-1)*sqrt(108)=i*\sqrt(36*3)=i*\sqrt(36)*\sqrt(3)=6i*\sqrt(3). \sqrt(-3)=\sqrt(-1*3)=\sqrt(-1)*\sqrt(3)=i*\sqrt(3). \sqrt(-108)-\sqrt(-3)=6i*\sqrt(3)-i*\sqrt(3)=5i*\sqrt(3).

root (-108) -raiz (-3)
First we rewrite the expressions:
root (-36 * 3) -raiz (-3)
6 * root (-3) -raiz (-3)
5 * root (-3)
5 * root (3) * root (-1)
By definition:
i = root (-1)
Substituting:
5 * root (3) * i
Answer:
5 * root (3) * i
option 1

A jar contains 3 red, 4 blue, and 2 white marbles. What is the probability that a marble drawn at random is not red?

Answers

2/3 is the probability that a marble drawn at random is not red.

Answer:

Probability that a marble drawn at random is not red = [tex]\frac{2}{3}[/tex].

Step-by-step explanation:

Given : A jar contains 3 red, 4 blue, and 2 white marbles.

To find : What is the probability that a marble drawn at random is not red.

Solution : We have given that

Red marbles = 3.

White marbles = 2.

Blue marbles = 4

Total marbles = 9

Marbles that are not red = white + blue =2+4 = 6.

Probability that a marble drawn at random is not red = [tex]\frac{Number\ of\ marbles\ not\ red}{Total\ that\ number\ of\ marbles}[/tex].

Probability that a marble drawn at random is not red = [tex]\frac{6}{9}[/tex].

Probability that a marble drawn at random is not red = [tex]\frac{2}{3}[/tex].

Therefore, Probability that a marble drawn at random is not red = [tex]\frac{2}{3}[/tex].

SHIFT 2: 18 25 56 42 29 38 54 47 35 30. SHIFT 2: 23 19 50 49 67 34 30 59 40 33. SHIFT 3: 19 22 24 40 45 29 33 29 39 59. SHIFT 4: 21 23 25 40 35 19 70 40 22 23. The summary statistics for all of the workers at a steel factory are shown. Four sample groups were taken from each of the four shifts. For which sample group is the mean closest to the population mean?

Answers

To answer this question you will need to calculate the mean for each of the Shifts and then compare those means to the mean of all the data given. I have attached a picture of the means for each shift and the population mean (all the data).

Shift 1 is the closest to the population mean. It is 37.4, and the population mean is 35.9.

an architect created plans for a house using a scale factor of 1:16 . In the plans, the floor of the house has an area of 7 square feet. What is area of the floor in the actual house?

Answers

To figure this out you would need to create a rectangle with dimensions that give you an area of 7 ft.². The easiest example would be a rectangle that is one by seven. If the scale is 1:16, that means for every foot it is actually representing 16 feet. The actual length and width would be found by multiplying 1×16 and 7×16. The true dimensions then would be 16 x 112. Multiply this together to get a total area of 1792 ft.².

Answer:

The answer above me is correct

Step-by-step explanation:

Cause he big brain

Which of the six trigonometric functions do not depend on the value of r?

Answers

If we construct a triangle in a circle of radius [tex]r[/tex], the radius of the circle will be the hypotenuse of our triangle, and the legs will be [tex]x[/tex] and [tex]y[/tex] as you can see in the picture.
Now we can construct our trigonometric ratios for our triangle as usual:
[tex]sin \alpha = \frac{y}{r} [/tex]
[tex]cos \beta = \frac{x}{r} [/tex]
[tex]tan \beta = \frac{y}{x} [/tex]
[tex]csc \beta = \frac{r}{y} [/tex]
[tex]sec \beta = \frac{r}{x} [/tex]
[tex]cot \beta = \frac{x}{y} [/tex]

As you can see the only two trigonometric functions that don't depend on the value of [tex]r[/tex] are tangent and cotangent.

There are 60 sixth graders, 50 seventh graders, and 70 eighth graders at your school. Every student gets entered in a raffle. What is the probability that an eighth-grade student will win the raffle?

Answers

There is a 10% chance that an eighth grader will in

7/18
Hope this helps:)

x + y = 21 3y + x = 19 Which value of x is part of a solution to this system of equations?

Answers

we have that
x + y = 21
3y + x = 19

using a graph tool
see the attached figure

the solution is the point (22,-1)

the answer is
the value of x is 22

Final answer:

The value of x that is part of a solution to this system of equations is 22.

Explanation:

To find the value of x in the system of equations:

x + y = 213y + x = 19

We can use the method of elimination or substitution. Let's use substitution for this example:

Solve the first equation for y: y = 21 - x.Substitute the expression for y into the second equation: 3(21 - x) + x = 19.Simplify and solve for x: 63 - 3x + x = 19.Combine like terms: 63 - 2x = 19.Subtract 63 from both sides: -2x = -44.Divide by -2: x = 22.

Thus, the value of x that is part of a solution to this system of equations is 22.

Cylinder a has a radius of 6 cm. Cylinder b has the same height and a radius half as long as cylinder a. What fraction of the volume of cylinder a is the volume of cylinder b what fraction of the volume of cylinder is the volume of cylinder? Explain.

Answers

The formula for the volume of a cylinder is π × radius^2 × height. The π and height will remain the same, so the only difference will be in the radius. 6^2 = 36, and 3^2 = 9, so 9 is 1/4 of 36 (36 ÷ 4 = 9) which means that the answer is 1/4. I hope this helps!

Answer:

the answer is 1/4

Step-by-step explanation:

What is the simplest form of this binomial expression?

a4 − b4

Answers

Answer:

[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]

Step-by-step explanation:

The given expression is

[tex]a^{4}-b^{4}[/tex]

This expression is the difference of two perfect squares, and their square roots are

[tex]\sqrt{a^{4}} =a^{2}\\ \sqrt{b^{4}} =b^{2}[/tex]

Now, the difference of two perfect squares can be factored as

[tex]x^{2} -y^{2}=(x+y)(x-y)[/tex]

So, if we apply this rule, the result would be

[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]

Therefore, the simplest form of the binomial expression is

[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]

Answer and work in images

At school athletic events you can buy 3 drinks and 2 hot dogs for $4.80 or you can buy 1 drink and 1 hot dog for $2.00. How much does 1 hot dog cost?

Answers

Let the cost of each drink is $x and the cost of each hot dog is $y.
According to the given data, 3 drinks and 2 hot dogs cost $4.80. In equation form, we can write it as:

[tex]3x+2y=4.80[/tex]

1 drink and 1 hot dog costs $2.00. In equation form, we can write it as:

[tex]x+y=2[/tex]
[tex]x=2-y[/tex]

Using this value of x in first equation, we get:

[tex]3(2-y)+2y=4.80 \\ 6-3y+2y=4.80 \\ 6-y=4.80 \\ y=6-4.80 \\ y= 1.20[/tex]

Thus the cost of one hot dog is $1.20

this is a question in which simultaneous equations are used to find out the answer.
There are 2 unknown values which we name as x and y
x - price of a drink
y - price of a hotdog

although we don't know the values of the above 2 terms x and y, we know the relationships of these 2 terms as the the sums of these 2 have been given
therefore we can build 2 equations using the information we have been given

3 drinks = 3*x and 2 hotdogs = 2*y
we build the first equation using this information

1 - 3x + 2y = $ 4.80

1 drink and 1 hotdog costs $2.00
we can build the second equation using this information

2 - x + y = $ 2.00

first we have to find out the value of one unknown term, for this we need to eliminate the second unknown so that we are left with one unknown term in the equation
if we want to eliminate y, 2nd equation should be multiplied by 2
2. 2(x + y = 2)
the answer after multiplying all the terms by 2, lets call that the 3rd equation

3. 2x + 2y = 4
when we subtract 1st from the 2nd equation,
3x + 2y = 4.8 ( - ) 2x + 2y = 4
lets subtract like terms from like terms
3x - 2x = x
2y - 2y = 0
4.8 - 4 = 0.8
after subtracting the final equation looks like this;
x = 0.8
since we know x now, substitute x in the equation 2
x + y = 2
0.8 + y = 2
to find out y
y = 2 - 0.8
y = 1.2
Therefore price of a drink is $0.80
and price of hotdog is $1.20

There are 18 girls and 12 boys in class. What is the probability that a new kid in senior class will be a boy?

Answers

there are 18 + 12 total students.

18 are girls and 12 are boys, since the total is 30 students, that's the amount of probable outcomes, and since there are 12 boys, that's the amount of favorable outcomes, thus

12/30 or 0.4, 0.4 * 100 is 40%.

12 is 0.3% of what number?

Answers

Hello,

Here is your answer:

The proper answer to this question is "4,000".

Your answer is 4,000!

If you need anymore help feel free to ask me!

Hope this helps!

Answer:

4,000

Step-by-step explanation:

Solve these simultaneous equations:

5x+2y=24 and 4x+3y=10

Answers

From the second equation: y=(10-4x)/3
Substitute y to the first equation:
5x+2[(10-4x)/3] = 24

5x+[(20/3)-(8x/3)]=24

5x-(8x/3)=24-(20/3)

(15x-8x)/3=17.333

7x=17.333(3)

x=7.428

Using the second equation to find value of y:

y=(10-4x)/3; Substitute the value of x=7.428

y=[10-4(7.428)]/3

y= -6.571 (negative 6.571)

To solve the simultaneous equations 5x+2y=24 and 4x+3y=10, we use the elimination method, leading to a solution of x = 7.43 and y = -6.575.

To solve the simultaneous equations 5x+2y=24 and 4x+3y=10, we can use the method of elimination or substitution. Here, we will solve it using the elimination method.

Multiply the first equation by 3 and the second equation by 2 to make the coefficients of y equal in magnitude. This gives us 15x + 6y = 72 and 8x + 6y = 20.

Subtract the second new equation from the first to eliminate y. This gives 7x = 52.

Divide by 7 to solve for x, which gives x = 52 / 7 or x = 7.43 (approximately).

Substitute x = 7.43 back into one of the original equations to solve for y. Using the first equation, 5(7.43) + 2y = 24, we get 2y = 24 - 37.15, which simplifies to 2y = -13.15, and finally y = -6.575.

Therefore, the solution to the simultaneous equations is x = 7.43 and y = -6.575.

The sequence an= 27(1/3)^n-1 is graphed below. find the average rate of change between n=2 and n=4

A. - 1/4
B. 1/4
C. -4
D. 4

Answers

the average rate of change, is pretty much just the "slope" of the graph, therefore since we know that when n = 2, y = 9, notice the point (2,9), and when n = 4, y = 1, notice the point (4,1), thus

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 2 &,& 9~) % (c,d) &&(~ 4 &,& 1~) \end{array} \\\\\\ % slope = m \stackrel{\textit{average rate of change}}{slope} = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-9}{4-2}\implies \cfrac{-8}{2}\implies -4[/tex]

What is the factored form of 6x2 + 13x + 6? (x + 4)(x + 9) (2x + 3)(3x + 2) (2x + 6)(3x + 1) (6x + 1)(6x + 1)?

Answers

6x2 + 13x + 6 = (2x + 3)(3x + 2)

Answer: B

Step-by-step explanation:

just did on edge

During a construction project, heavy rain filled construction cones with water. The diameter of a cone is 12 in. and the height is 27 in.

What is the volume of the water that filled one cone?

Enter your answer as a decimal in the box. Use 3.14 for pi.

Answers

volume of cone=[tex]\frac{1}{3}h \pi r^2[/tex]

diameter/2=r
12/2=6=r
h=27

volume=[tex]\frac{1}{3}(27)(3.14)(6^2)[/tex]
volume=[tex]1017.36 in^3[/tex]

How will buying auto insurance help you?

Answers

if you get in a wreck they help pay for the damage

When buying a (auto insurance), this can help you so as if you were about to get in a wreck, this insurance can help you pay to what ever happened, but it also depends on the case, either the other person will pay it though his own insurance, so yes, this would really help you.

The area of a rectangular television screen is 3456 in^2. The width of that screen is 24 inches longer than the length. What is a quadratic equation the represents the area of the screen? What are the dimensions of the screen?

Answers

1. The problem says that the television has a rectangular shape. So, the formula for caculate the area of a rectangle is:

A=LxW

"A" is the area of the rectangle (A=3456 inches²).
"L" is the the length of the rectangle.
"W" is the width of the rectangle.

2. The width of the screen is 24 inches longer than the length. This can be expressed as below:

W=24+L

3. Then, you must substitute W=24+L into the formula A=LxW:

A=LxW
3456=L(24+L)
3456=24L+L²

4. The quadratic equation is:

L²+24L-3456=0

5. When you solve the quadratic equation, you obtain:

L=48 inches

6. Finally, you must substitute the value of the length, into W=24+L:

W=24+L
W=24+48
W=72 inches

7. Therefore, the dimensions of the screen are:

L=48 inches
W=72 inches

Final Answer:

Quadratic equation: [tex]$ x^2 + 24x - 3456 = 0 $[/tex]

Dimensions: Length = 48 inches, Width = 72 inches

Explanation:

To find the quadratic equation representing the area of the screen, we first need to express the area as a product of its length (L) and width (W). Given that the width is 24 inches longer than the length, we can represent the width as [tex]$ L + 24 $[/tex]. Thus, the equation becomes [tex]$ L \times (L + 24) = 3456 $[/tex], which simplifies to the quadratic equation [tex]$ x^2 + 24x - 3456 = 0 $[/tex], where x represents the length of the screen. Solving this equation yields the length x as 48 inches. Substituting this value back into [tex]$ L + 24 $[/tex] gives the width as 72 inches. Therefore, the dimensions of the screen are 48 inches by 72 inches.

In the problem · N = 1, N must be _____. the additive inverse of the multiplicative inverse of the additive identity the multiplicative identity NEXT

Answers

The value N as shown in the question must be the multiplicative identity.

Multiplicative identity

The term multiplicative identity refers to that with which a number is multiplied and the result remains that number. Multiplying a number by its multiplicative identity returns the same value.

Therefore, the the problem, we can see that the value N as shown in the question must be the multiplicative identity.

Learn more about multiplicative identity: https://brainly.com/question/514731

Answer: the multiplicative inverse of 3/4

Step-by-step explanation: its right :)

A gift bag is shaped like a rectangular prism and has a volume of 1152 cubic inches. The width of the bag is w, the length is 2w+4, and the height of the bag is 18-w (which is greater than the width). What are the dimensions of the bag?

Answers

1. You must use the formula for calculate the volume of a rectangular prism, which is:

V=(h)(l)(w)

V: It is the volumen of the rectangular prism (V=1152 inches³).
h: It is the height of the rectangular prism (h=18-w).
l:It is the lenght of the rectangular prism (l=2w+4).

2. When you substitute these calues into the formula, you obtain:

V=(h)(l)(w)
1152=(18-w)(2w+4)(w)
(18-w)(2w+4)(w)-1152=0

3. Then, you should mutiply them:

36w²-2w³+72w-4w²-1152=0
32w²-2w³+72w-1152=0

4. When you factor, you obtain:

2(w-16)(w-6)(w+6)

w1=16
w2=6
w3=-6

5. The problem says that the height is greater than the width, therefore, the widht is:

w=6 inches

6. The length is:

l=2w+4
l=2(6)+4
l=16 inches

7. And the height is:

h=18-w
h=18-6
h=12 inches

What are the dimensions of the bag?

The dimensions of the bag are:

l=16 inches
h=12 inches
w=6 inches

Final answer:

In this high school math question, you will solve for the dimensions of a gift bag shaped like a rectangular prism using the given volume and expressions for width, length, and height.

Explanation:

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, the volume of the gift bag is 1152 cubic inches, so we have 1152 = w(2w+4)(18-w).

Solving this equation leads to w = 8, which means the width is 8 inches, length is 20 inches, and height is 10 inches.

Therefore, the dimensions of the gift bag are 8 inches width, 20 inches length, and 10 inches height.

Find the area of the figure.

Answers

Area of the big rectangle =
40yd x 36yd = 1440yd2

Area of the small rectangle =
20yd x 10yd = 200yd2

area of the figure = big rectangle - small rectangle

1440-200
=1240yd2

Suppose the probability that a randomly selected man, aged 55-59, will die of cancer during the course of the year is startfraction 300 over 100 comma 000 endfraction 300 100,000. how would you find the probability that at least 1 man out of 1,000 of this age will die of cancer during the course of the year?

Answers

Final answer:

To assess the likelihood of at least one cancer death among 1,000 men, calculate the probability none die and subtract from one. The actuarially fair premiums for men with and without family cancer history are different, but when combined for the whole group, there's a risk of adverse selection affecting the company.

Explanation:

To find the probability that at least one man out of 1,000 aged 55-59 will die of cancer in a year, given that the probability for any one man is 300/100,000, we first find the probability that no man dies of cancer and then subtract this from 1 (the certainty). The probability that a randomly chosen man will not die from cancer in the year is 1 - 300/100,000 = 99,700/100,000.

The probability that all 1,000 men do not die of cancer is (99,700/100,000)^1,000. Subtracting this from 1 gives us the probability that at least one man out of 1,000 will die of cancer in the year:

1 - (99,700/100,000)^1,000

For the life insurance question, to calculate the actuarially fair premium for each group, we use the probability of death and expected payout. For the group with family history (20% of 1,000 men), the probability is 1/50, and for the group without (80% of 1,000 men), it's 1/200. Thus, the premiums would be:

Group with history: (1/50) * $100,000 = $2,000Group without history: (1/200) * $100,000 = $500

An actuarially fair premium for the group as a whole requires weighted averaging:

Premium whole group = (20% * $2,000) + (80% * $500) = $400 + $400 = $800

If the company charges this combined premium, it faces adverse selection; higher-risk individuals are more likely to purchase insurance, driving costs up.

A farmer can buy two types of plant food, mix a and mix
b. each cubic yard of mix a contains 20 pounds of phosphoric acid, 30 pounds of nitrogen, and 5 pounds of potash. each cubic yard of mix b contains 10 pounds of phosphoric acid, 30 pounds of nitrogen, and 10 pounds of potash. the minimum monthly requirements are 440 pounds of phosphoric acid, 990 pounds of nitrogen, and 200 pounds of potash. if mix a costs $20 per cubic yard and mix b costs $30 per cubic yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimum cost? what is this cost?

Answers

Final answer:

To find the minimum cost of blending the plant food mixes, set up a system of equations to calculate the quantities of each mix needed. Solve the equations to find the values of x and y, then calculate the cost using the mix prices.

Explanation:

To find the minimum cost of blending the plant food mixes, we need to set up a system of equations and solve for the quantities of each mix needed. Let's let x be the number of cubic yards of mix a and y be the number of cubic yards of mix b that the farmer needs.

The total pounds of phosphoric acid required from mix a and mix b should equal the minimum monthly requirement of 440 pounds. This gives us the equation: 20x + 10y = 440.

The total pounds of nitrogen required from mix a and mix b should equal the minimum monthly requirement of 990 pounds. This gives us the equation: 30x + 30y = 990.

The total pounds of potash required from mix a and mix b should equal the minimum monthly requirement of 200 pounds. This gives us the equation: 5x + 10y = 200.

Solving this system of equations will give us the values of x and y. Once we have these values, we can calculate the cost by multiplying the quantity of each mix by their respective prices and adding them together.

If you see these clouds in the sky, which type of weather might you expect?

(Points : 3)
fog
no precipitation
heavy rain or snow
thunderstorms

Answers

The answer to your question is thunderstorms.
The picture is filled with a lot of dark clouds, in which there will be a probability for thunderstorms to occur. We all know that when there is lightning, thunder will occur after it. With the photo given, there will be the probability of thunderstorm with heavy rain.

I WANT DIAGRAM
A vertical tower subtends a right angle on the top of 10m high flagstaff.if distance between them is 20m,find the height of the tower

Answers

Let us consider a triangle where AB to be the flagstaff of 10 m and BC to be of 20 m as the distance between the tower and the flag.
Considering ABC and ADE as triangle
AB = 10 = CE
BC = 20 = AE
Calculating the values of ABC
tan x = AB/BC
tan x = 10/20
10/tan x = 20..............(1)
Calculating the values of ADE
tan(90-x) = DE/AE
cot x = DE/20
DE/cot x = 20 .............(2)
Solving equations 1 & 2
10/tan x = DE/cot x
DE = 40
Hence the total height of the tower is DE+CE = 40+10= 50 m.

Other Questions

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