What is the volume of this rectangular prism

Answer:

π^3x^4.

Step-by-step explanation:

Required product is [tex] {(\pi)}^{3}\times {x}^{4} [/tex]

What is exponents ?

Meaning of an exponent is the number of times a number is multiplied by itself.

An exponent is defined as a method of expressing large numbers in terms of powers. That is, the exponent refers to how many times a number is multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 x 6 x 6 x 6. This can be written as 64. Here, 4 is the exponent and 6 is the base. It can be read by raising 6 to 4 degrees.

By some examples we can understand this concept.

Example -1,

[tex]2 \times 2 \times 2 = {2}^{3} [/tex]

Example -2,

[tex]5 \times 5 \times 5 \times 5 = {5}^{4} [/tex]

Example-3,

[tex]8 \times 8 \times 8 \times 6 \times 6 = {8}^{3} \times {6}^{2} [/tex]

We want to find what is the product of π⋅π⋅π⋅x⋅x⋅x⋅x using exponents.

Given, [tex]\pi.\pi.\pi.x.x.x.x[/tex]

Here,

[tex]\pi.\pi.\pi.x.x.x.x \\ = {\pi}^{3} \times {x}^{4} [/tex]

Therefore,required product is [tex] {(\pi)}^{3}\times {x}^{4} [/tex]

Exponent related one more question:

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Answer:

Step-by-step explanation:

Markup means the amount added to the cost price, so it means like adding to the cost. Ex: $18:00 + 15%

A markup is the amount added to the cost price to cover overhead and profit

M<1=25

M<2=55

M<3=65

M<4=25

M<5=35

M<6=65

M<7=55

M<8=35

Answer:

9,12,15 because Pythagorean theorem

1. 10z - 5

2. -16k + 32

3. -20a + 75

4. 6n + 7.2

5. 5n - 41

6. n = 3

7. x = -8

8. r = -2

9. y = 2

10. a = 1

11. n = -2.23333333 ( this is the only problem im unsure of answer )

Answer:

4.5

Step-by-step explanation:

20= 85+5÷x

85+5=90

20=90÷x

Divide 90 by 20 and you end up with 4.5.

Count the number of cubes in the first layer.

There is 16 cubes in the first layer.

Now divide the total number of cubes by the cubes per layer:

48 cubes / 16 cubes per layer = 3 layers.

Option A. A rectangular prism and a cylinder is the correct option.

Explanation:

First option is true as the vertical cross sections of both rectangular prism and cylinder are rectangles.

Second option is false (The vertical cross section through the base of a rectangular prism is a rectangle)

Third option is false (The vertical cross section through the base of a cone is a triangle)

Fourth option is false (The vertical cross section through the base of a pyramid is a triangle)

A, prism and cylinder is correct.

Answer:

I also got 27.44 mg.

Step-by-step explanation:

Use the function given to you:

A(t)=le^rt

l: Initial Amount (50)

r: Rate (-.1) (Negative because the medicine is exiting the bloodstream at 10% per hour

t: 6 (the specific time value you are evaluating the function at.

A(6)=50e^-.1(6)=27.44

Answer:

Angelo : 4

Luis : 2.9

Xavier : 3.8

Angel : 3.4

Step-by-step explanation:

As mentioned in the question, tip is 20% of the bill. Therefore, to calculate the tip each person should leave can be calculated by sum of all items and taking 20% of of the amount

1) Angelo = 2 + 8 + 10 = 20

total tip = 20% of 20 = 20/100 * 20 = 4

2) Luis = 1.50 + 8 + 5 = 14.5

total tip = 20% of 14.5 = 20/100 * 14.5 = 2.9

1) Xavier = 2 + 10 + 7 = 19

total tip = 20% of 19 = 20/100 * 19 = 3.8

1) Angel = 2 + 5 + 10 = 17

total tip = 20% of 17 = 20/100 * 17 = 3.4

Answer:

Angelo : 4

Luis : 2.9

Xavier : 3.8

Angel : 3.4

Sorry if this is wrong mate, but I got it as -203! Hope I helped!

Answer:

w > 9

Step-by-step explanation:

Solve the inequality by using inverse operations.

-4w - 2 < -38

-4w < -36

w > 9

Like solving equations, inequalities should be solved using inverse operations. However, unlike equations, when you divide or multiply by a negative the sign changes.

Answer:

The answer is 18.

Step-by-step explanation:

Perimeter is P, length is L, and width is W. So, P is L plus L plus W plus W. If L is 30, then L plus L is 60. Do the P minus 60, which is 36. So, to find width, use that.

W plus W is the last part of P, and P minus 60 is 36. So, for one width, it is 36 divided by 2, which is our answer: 18.

Final answer:

To determine the width of the playground when the length of the fence is given as 30 feet and the perimeter is 96 feet, apply the formula for the perimeter of a rectangle and solve for the width, resulting in a width of 18 feet.

Explanation:

Given information:

Perimeter of the playground is 96 feet.

Length of one side of the fence is 30 feet.

To find: Width of the playground.

Step-by-step solution:

Let the length of the playground be L feet and the width be W feet.

Given, 2L + 2W = 96 (perimeter formula) and L = 30 (given)

Substitute L = 30 into the perimeter formula to find W: 2(30) + 2W = 96 => 60 + 2W = 96 => 2W = 36 => W = 18 feet.

Therefore, the width of the playground is 18 feet.

Answer:the answer is B

Step-by-step explanation:

The graph shows how the inequality was resolved: Option B is -X-3 >

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Answer:

I believe it is 0.5

Step-by-step explanation:

If you flip a normal coin (called a “fair” coin in probability parlance), you normally have no way to predict whether it will come up heads or tails. Both outcomes are equally likely. There is one bit of uncertainty; the probability of a head, written p(h), is 0.5 and the probability of a tail (p(t)) is 0.5. The sum of the probabilities of all the possible outcomes adds up to 1.0, the number of bits of uncertainty we had about the outcome before the flip. Since exactly one of the four outcomes has to happen, the sum of the probabilities for the four possibilities has to be 1.0. To relate this to information theory, this is like saying there is one bit of uncertainty about which of the four outcomes will happen before each pair of coin flips. And since each combination is equally likely, the probability of each outcome is 1/4 = 0.25. Assuming the coin is fair (has the same probability of heads and tails), the chance of guessing correctly is 50%, so you'd expect half the guesses to be correct and half to be wrong. So, if we ask the subject to guess heads or tails for each of 100 coin flips, we'd expect about 50 of the guesses to be correct. Suppose a new subject walks into the lab and manages to guess heads or tails correctly for 60 out of 100 tosses. Evidence of precognition, or perhaps the subject's possessing a telekinetic power which causes the coin to land with the guessed face up? Well,…no. In all likelihood, we've observed nothing more than good luck. The probability of 60 correct guesses out of 100 is about 2.8%, which means that if we do a large number of experiments flipping 100 coins, about every 35 experiments we can expect a score of 60 or better, purely due to chance.

Answer:

The correct answer option is 0.5.

Step-by-step explanation:

If we have a fair coin then it means that it has a 50 % chance of landing heads up and a 50% chance of landing tails up.

A fair coin is one which has two sides: head and tail.

Since their are two sides to each fair coin, so the probability of landing for each of the side should add up to 1 (which is the total probability).

Therefore, likelihood that a fair coin will land heads or tails is 0.5.

Answer:

The average rate of change ​is m = 3.4 models of paper shredders per year

Step-by-step explanation:

The rate of change m of a function is:

[tex]m = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

In this problem the function receives a variable x = year and returns a variable f(x) = models of paper shredders

We know that for [tex]x = 1998[/tex], [tex]f(x) = 2[/tex]

We also know that for [tex]x = 2008[/tex], [tex]f(x) = 36[/tex].

Then we can calculate the average rate of change using these values.

[tex]m = \frac{f(2008)-f(1998)}{2008-1998}[/tex]

[tex]m = \frac{36-2}{2008-1998}[/tex]

[tex]m = 3.4[/tex]

The average rate of change in the number of paper shredder models produced by the company from 1998 to 2008 is 3.4 models per year.

To calculate the average rate of change, we can use the formula (Change in Y) / (Change in X). In this case, 'Y' is the number of paper shredder models and 'X' is the time, in years. In 2008 the company manufactured 36 models which is an increase from the 2 models they made in 1998.

The change in 'Y' (ΔY) would therefore be (36 - 2) = 34. The change in 'X' (ΔX) would be (2008 - 1998) = 10 years. Therefore, the average rate of change would be ΔY / ΔX = 34 / 10 = 3.4.

This suggests that, on average, the company has been producing an additional 3.4 models of paper shredders each year over this 10 year period in response to rising concerns about identity theft.

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Answer:

[tex](x^{9}y^\frac{1}{3})[/tex]

or

[tex](x^{9}\sqrt[3]{y})[/tex]

Step-by-step explanation:

Given in the question an expression

[tex](x^{27}y )^\frac{1}{3}[/tex]

We will apply the power rule

The "power rule" tells us that to raise a power to a power, just multiply the exponents.

[tex](x^{27*\frac{1}{3} }y^\frac{1}{3})[/tex]

[tex](x^{9}y^\frac{1}{3})[/tex]

As we know that

[tex]x^{1/n} = \sqrt[n]{x}[/tex]

so we can write the above expression as

[tex](x^{9}\sqrt[3]{y})[/tex]

Answer:

3∛(xy)

Step-by-step explanation:

(x27y)^1/3

Simplified form will be 3/x³y³

Because;

27^(1/3) = 3

x^(1/3) = ∛x

y^(1/3) = ∛y

Which gives us 3∛(xy)

The solution to the given equation that results in positive integer values for x and y is x=3, y=1. Therefore, multiplying x and y together, xy = 3.

The given mathematical equation is (x·2)+x(2^2)+(y·2^3)+(y·2^4)=42. We can simplify this to 2x + 4x + 8y + 16y = 42, which simplifies further to 6x + 24y = 42. Dividing the whole equation by 6 to make the calculation simpler, we get x + 4y = 7. The solution to this equation that has positive integers for both x and y is x = 3, y = 1. Therefore, to find the value of xy, you simply multiply x and y together, and get xy = 3.

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The positive integer solutions for[tex]\(x\)[/tex] and [tex]\(y\)[/tex] in [tex]\(x + 4y = 7\)[/tex] are [tex]\(x = 3\)[/tex] and[tex]\(y = 1\)[/tex]. The value of [tex]\(xy\)[/tex]  is 3.

Let's simplify the given expression and solve for x and y.

[tex]\( (x \cdot 2) + x \cdot (2^2) + (y \cdot 2^3) + (y \cdot 2^4) = 42 \)[/tex]

Simplify each term:

[tex]\( 2x + 4x + 8y + 16y = 42 \)[/tex]

Combine like terms:

[tex]\( 6x + 24y = 42 \)[/tex]

Divide both sides by the greatest common factor, which is 6:

[tex]\( x + 4y = 7 \)[/tex]

Now, we need to find positive integer solutions for x and y that satisfy this equation.

One possible solution is x = 3 and y = 1, as:

[tex]\( 3 + 4 \cdot 1 = 7 \)[/tex]

Now, find the product [tex]\(xy\)[/tex] :

[tex]\( xy = 3 \cdot 1 = 3 \)[/tex]

So, the value of [tex]\(xy\)[/tex]  is 3.

Answer:

A=78.23in²

Step-by-step explanation:

First we need to solve for the radius. The volume of a cylinder can be found using the formula:

[tex]V=\pi r^{2} h[/tex]

Now we have the variables:

V = 1177.5 in³

h = 15

r = ?

[tex]1177.5=\pi r^{2}15[/tex]

[tex]\dfrac{1177.5}{15}=\dfrac{\pi r^{2} }{15}[/tex]

[tex]78.5=\pi r^{2}[/tex]

[tex]\dfrac{78.5}{\pi }=\dfrac{\pi r^{2} }{\pi }[/tex]

[tex]r^{2}[/tex]≅24.99

[tex]\sqrt{r^{2} }[/tex]≅[tex]\sqrt{24.99}[/tex]

r≅4.99in

Now since we're looking for the area of the base, we can use the formula for the area of a circle which is:

[tex]A=\pi r^{2}[/tex]

[tex]A=\pi (4.99)^{2}[/tex]

A=78.23in²

Answer:

The slopes are 3 and 0. The points (-2,-7) and (1,2) has a greater slope.

Step-by-step explanation:

To find the slope, substitute the points into the slope formula.

[tex]m = \frac{y_2-y_1}{x_2-x_1} =\frac{2--7}{1--2} =\frac{9}{3} =3[/tex]

[tex]m = \frac{y_2-y_1}{x_2-x_1} =\frac{-2--2}{8-5} =\frac{0}{3} =0[/tex]

The points (-2,-7) and (1,2) has a greater slope.

Answer:

The volcanoes are formed adjacent to a convergent plate boundary, in which the denser plate subducts under a less denser plate. These subducting plates undergoes partial melting at greater depths and the magma is forced to rise up towards the over-riding plate, resulting in the formation of the volcano and chains of volcanoes.

These volcanoes when undergoes eruptions, releases various types of gases. They are such as the Carbon dioxide (CO₂), Water vapor (H₂O), Sulfur dioxide (SO₂), Hydrogen sulfide (H₂S) and Carbon monoxide (CO).

These gases are harmful to the atmosphere as it creases the green house effect thereby increasing the earth's global temperature.

Answer:

3/8

Step-by-step explanation:

it is greater than 2/8

Answer:   [tex]\bold{d)\quad f^{-1}(x)=\dfrac{e^x}{5}}[/tex]

Step-by-step explanation:

To find the inverse, swap the x's and y's and solve for y. Note: f(x) is y

[tex]y = ln(5x)\\\\\text{Swap the x's and y's:}\\x=ln(5y)\\\\\text{Apply e to both sides:}\\e^x=e^{ln(5y)}\\\\e^{ln}\ \text{cancels out:}\\e^x=5y\\\\\text{Divide both sides by 5:}\\\dfrac{e^x}{5}=y\\\\\large \boxed{f^{-1}(x)=\dfrac{e^x}{5}}[/tex]

is -8 a choice because im pretty sure it’s -8

Answer:

The y-intercept would be -2

Answer:

24 days

Step-by-step explanation:

April = 30 days

100% = 1.0

80% = 0.8

If 1 x 30 = 30

then 0.8 x 30 = 24

Answer:

24

Step-by-step explanation:

0.8 x 30 = 24

80% = 0.8

April = 30 days

HOPE THIS HELPED!!!!! XD

Can I have brain? please

Answer:

The height is 7 m.

Step-by-step explanation:

Volume = 1/3 * area of the base * height, so

28 = 1/3 * 3 * 4 * h

4h = 28

h = 7.

Answer:

The correct statement is:

Step-by-step explanation:

Hence, the equation of the function f(x) is calculated by a two-point formula as:

[tex]y-2=\dfrac{-1-2}{1-0}\times (x-0)\\\\y-2=\dfrac{-3}{1}\times x\\\\y-2=-3x\\\\y=-3x+2[/tex]

( On comparing the equation of f(x) with slope intercept form.

i.e. y=mx+c

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

We get slope of f(x)= -3

and y-intercept= 2

[tex]g(x)=-3x-6[/tex]

Hence, slope of g(x) = -3

and y-intercept= -6

Hence, we get that the slope of f(x) and g(x) is same.

( i.e. -3)

Answer:

see explanation

Step-by-step explanation:

The terms form a geometric sequence with n th term

[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = ......

r = [tex]\frac{-6}{3}[/tex] = [tex]\frac{12}{-6}[/tex] = - 2 and a = 3, hence

[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex] ← explicit formula

Answer: 49 feet to the third power

Step-by-step explanation:

1. 3.5 x 2= 7

2. 7 x 7= 49

Answer: [tex]49\ ft^3[/tex]

Step-by-step explanation:

The volume of rectangular prism is given by :-

[tex]\text{Volume}=l*w*h[/tex], hwre l is the length , w is width and h is height of prism.

The given dimensions of rectangular prism :

Length : 2 ft

Width : 7 ft.

Height : 3.5 ft.

Now, the volume of rectangular prism is given by :-

[tex]\text{Volume}=7\times2\times3.5\\\\\Rightarrow\text{Volume}=49\ ft^3[/tex]

Hence, the volume of this right rectangular prism =  [tex]49\ ft^3[/tex]