A sphere has a radius of 5 inches. What is its volume?
Sphere V =
np3
1. Substitute the radius into the formula:
2. Evaluate the power:
V = 4(53)
V = T(125)
V = 125
3.
Simplify:
in.

Answer:

I know

Step-by-step explanation:

The length of each equal side of the isosceles triangle Pythagorean theorem is equal to the square root of half the square of the length of the base.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

To find the length of an isosceles triangle, we need to consider the two equal sides as the legs of a right-angled triangle, and the remaining side as the hypotenuse.

Let's denote the length of the equal sides as "a" and the length of the remaining side (the base) as "b".

According to the Pythagorean theorem, we have:

[tex]a^2 + a^2 = b^2[/tex]

Simplifying this equation, we get:

[tex]2a^2 = b^2[/tex]

To find the length of the equal sides, we can solve for "a" by taking the square root of both sides:

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

Therefore, the length of each equal side of the isosceles triangle Pythagorean theorem is equal to the square root of half the square of the length of the base.

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Answer:

right answer is 8cm

Step-by-step explanation:

if QM=x

so. Om=32+x

ON=64+16=80

(32+x)/x=80/16

32+x=5x

4x=32

x=8

Answer:

3 steps per second.

Step-by-step explanation:

Find the Unit Rates of each going up and down:

--> 30/6 unit rate is 5 steps per second.

--> 30/15 unit rate is 2 steps per second.

Now subtract them to get the amount if the elevator wasn't moving:

--> 5-2= 3.

Final answer:

To find Tommy's rate (in steps per second) if the escalator stopped moving, calculate his speed going up and going down, then subtract the speed going down from the speed going up.

Explanation:

To find Tommy's rate (in steps per second) if the escalator stopped moving, we need to calculate his speed when going up and when going down.

When going up, Tommy covers 30 steps in 6 seconds. So his speed going up is 30 steps / 6 seconds = 5 steps per second.

When going down, Tommy covers 30 steps in 15 seconds. So his speed going down is 30 steps / 15 seconds = 2 steps per second.

If the escalator stopped moving, Tommy's rate would be the difference between his speed going up and his speed going down. So his rate would be 5 steps per second - 2 steps per second = 3 steps per second.

Answer:

A) 60π cm³

Step-by-step explanation:

Given:

The radius of the base of a metallic rod is 2 centimetres, and its height is 15 centimetres.

Question asked:

What is the volume of this cylinder?

Solution:

As we know''

[tex]Volume\ of\ cylinder=\pi r^{2} h[/tex]

                                [tex]=\pi \times2\times2\times15\\ \\ =60\pi[/tex]

Therefore, the volume of this cylinder will be [tex]60\pi\ cm^{3}[/tex]

Answer:

The correct option is option (A)

The volume of the metallic rod is 60π cm³.

Step-by-step explanation:

Cylinder:

The radius of the base of metallic rod is 2 cm and its height is 15 cm.

Here r= 2 cm, h= 15 cm, [tex]\pi =\frac{22}7[/tex]

The volume of metallic rod is

=πr²h

=π(2 cm)² (15 cm)

=π(4)(15) cm³

=60π cm³

Answer:

325

Step-by-step explanation:

Answer:

y= -2

Step-by-step explanation:

Answer:

y = -2

Step-by-step explanation:

Answer:

[tex]176\pi in.^3[/tex]

Step-by-step explanation:

The figure of the problem is missing: find it in attachment.

In this problem, the container has a shape of a cylinder.

The volume of a cylinder is given by the formula:

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

where

V is the volume

r is the radius of the base of the cylinder

h is its height

For the container in this problem, we have:

r = 4 in. is the radius of the base

h = 11 in. is the height of the container

Substituting into the formula, we can find the volume of the container, and so the volume of grain that it can contain:

[tex]V=\pi (4)^2 (11)=176\pi in.^3[/tex]

The given cylinder container can hold 44π cubic inches of grain. This is calculated using the formula for the volume of a cylinder which is πr²h.

To compute the amount of grain a cylindrical container can hold, you would have to calculate the cylinder's volume. The formula for the volume of a cylinder is πr²h, where r represents the radius, and h represents the height.

In this case, the diameter is 4 inches, so the radius (r) would be 2 inches. The height (h) of the cylinder is 11 inches. So, substituting these values into the formula gives us:

Volume = π(2²) x 11 = 44π cubic inches

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Answer:

[tex]69^{\circ}[/tex]

Step-by-step explanation:

We are given that

Length of minor arc AB=12 feet

Radius of circle=r=10 feet

Let x  be the measure of central angle subtended by minor arc AB.

We know that

Length of an arc=[tex]\frac{Central\;angle}{360}\times 2\pi r[/tex]

Where [tex]\pi=3.14[/tex]

Using the formula

[tex]12=\frac{x}{360}\times 2\times 3.14\times 10[/tex]

[tex]x=\frac{12\times 360}{2\times 3.14\times 10}[/tex]

[tex]x=69^{\circ}[/tex]

Answer:

false

Step-by-step explanation:

this has one answer and that would be 270 degrees.

Answer:

B

Step-by-step explanation:

It's the right answer

The expected value of the given scenario is -$4.80

The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.

The expected value refers to the value for a person who decides to purchase one ticket.

And that value is the sum of the values of the different possible scenarios.

There are two scenarios, wining and losing.

Note that we need to subtract the cost of the ticket (i.e. $5) from the return.

Winning :-

Probability 1 out of 500 chances

Return expected: ($100 - $5) *1/500 = $95 * 1/500 = $0.19

Losing :-

Probability 499 out of 500 chances

Return expected: (0 - $5)*499/500 = -$4.99

The expected value is the sum of the two returns: $0.19 - $4.99 = -$4.80 (it is negative).

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Answer:

3 meters must be drained off so that the water levels falls to 5 meters.

Step-by-step explanation:

Look at all the measurements given and try to find one that matches the amount of room needed to be drained out.

Answer:

-25

Step-by-step explanation:

(-4 + 5n) × 3= 7n - 212

-12 + 15n = 7n - 212

8n = -200

n = -25

Answer:

The number is -25

Step-by-step explanation:

(-4 +5n)*3 = 7n-212

Distribute

-12 +15n = 7n -212

Subtract 7n from each side

-12 +15n-7n = 7n-7n -212

-12 +8n = -212

Add 12 to each side

-12+12 +8n = -212+12

8n = -200

Divide each side by 8

8n/8 = -200 /8

n =-25

Answer:

ft

Step-by-step explanation:

just the most common

area

i would say feet, so it could be like ''the room is 45 feet long'' or something

Answer:

700 cubic feet

Step-by-step explanation:

Volume of scale model = 35 cubic feet

ratio of the dimensions of the model to the dimensions of the store was 1:20

Therefore

dimensions of the model/ dimensions of the store = 1/20

we know that in scaling

dimensions of the model/ dimensions of the store = Volume of scale model / volume of the actual department store

Now substituting the value of scale model in the above ratio equation we have

1/20 = 35/volume of the actual department store

=> volume of the actual department store = 35*20 = 700

Therefore volume of the actual department store is 700 cubic feet

Answer:

30

Step-by-step explanation:

40- 10 equals 30

the range is the maximum divided by the minimum.

The odds would be 7/8 that at least one would be a heads.

To find your answer, see each coin flip as unrelated to the last one.

For the first coin flip, you can either get heads or tails. So, there's only 2 possible outcomes.

Flip 1 (Outcome 1): H or T

Flip 1 (Outcome 2): H or T

But when it comes to the second flip, now each outcome has two possible "sub-outcomes" of their own. So there's now four total outcomes.

Flip 2 (Outcome 1) : H, H

Flip 2 (Outcome 2) : H, T

Flip 2 (Outcome 3) : T, H

Flip 2 (Outcome 4) : T, T

On the third flip, there would now be 8 outcomes. As each "sub-outcome" has own of their own.

Flip 3 (Outcome 1) : H, H, H

Flip 3 (Outcome 2) : H, H, T

Flip 3 (Outcome 3) : H, T, H

Flip 3 (Outcome 4 : H, T, T

Flip 3 (Outcome 5) : T, H, H

Flip 3 (Outcome 6) : T, H, T

Flip 3 (Outcome 7) : T, T, H

Flip 3 (Outcome 8): T, T, T

So all but one of the eight outcomes have at least one heads drawn. Due to this, the odds of an heads happening would be 7/8 within all of the possible outcomes.

Answer: adjacent and hypotenuse

Step-by-step explanation: Cos theta is adjacent/Hypotenuse

Final answer:

Inverse cosine is used to find an angle measure when we know the length of the adjacent side and the hypotenuse in a right triangle.

Explanation:

The inverse cosine function, also known as arccosine, is used to find a given angle measure when we know the length of the side adjacent to the angle and the length of the hypotenuse of a right triangle. The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. By using the inverse cosine function, we can find the angle whose cosine is the given ratio. This is particularly useful in trigonometry for solving right triangles or when dealing with any scenario where angle and side lengths are related through the cosine ratio.

In mathematical terms, if we have a right triangle with an angle labeled as θ (theta), and we know the lengths of the side adjacent to θ (adjacent) and the hypotenuse (hypotenuse), the cosine of θ is given by-

cos(θ) = adjacent / hypotenuse

To find the angle measure θ based on the ratio of these two sides, we would compute-

θ = arc cos(adjacent / hypotenuse).

Answer:

the new price is... i think 180

Step-by-step explanation:

Answer:

The answer to this would be 662.

Step-by-step explanation:

Sigma notation calls for the sum of the terms in the sequence.

Answer:

15

∑ 5(-2)^n-1

n =4

Step-by-step explanation:

15 and n = 4 should be on top (15) and below (n = 4) of the ∑

hope this helps :]

Answer:

D

Step-by-step explanation:

2 multiplying by any number even or odd=even number

Final answer:

The correct answer is D) 2(ab + 1), because multiplying an odd number (ab + 1) by 2 results in an even number.

Explanation:

The question asks which expression must be even if integers a and b are even. We know that the product of two even numbers is always even. Therefore, ab is even.

When we add 1 to an even number, the result is odd, so ab + 1 is odd. Multiplying by 3, as in option C, won't change the oddness, so 3(ab + 1) is also odd. The expression in option E, a2 + b2 + 1, will be odd for the same reason - the sum of even squares is even, and adding 1 makes it odd.

However, option D multiplies the odd number ab + 1 by 2, guaranteeing that the result is even regardless of the values of a and b since any number multiplied by 2 is even. Thus, the correct answer is D) 2(ab + 1).

[tex]\boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}[/tex]

A quartic function is a function given by the the following equation in standard form:

[tex]f(x)=a_{4}x^4+a_{3}x^3+a_{2}x^2+a_{1}x+a_{0} \\ \\ \\ Where: \\ \\ a_{4},a_{3},a_{2},a_{1},a_{0} \ \text{are constant} \\ \\ \text{and} \ a_{4} \ \text{is the leading coefficient}[/tex]

From the statement we must assume the leading coefficient of f(x) is 11, so:

[tex]a_{4}=11[/tex]

The zeros are:

[tex]x=-6 \\ \\ x=-5 \\ \\ x=-2 \\ \\ x=11[/tex]

So, we can write:

[tex]f(x)=11(x-(-6))(x-(-5))(x-(-2))(x-11) \\ \\ \\ So: \\ \\ \mathrm{Rule}:-\left(-a\right)=a \\ \\ \\ Then: \\ \\ f(x)=11\left(x+6\right)\left(x+5\right)\left(x+2\right)\left(x-11\right)[/tex]

[tex]Expand:\left(x+6\right)\left(x+5\right):\ x^2+11x+30: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^2+11x+30\right)\left(x+2\right)\left(x-11\right) \\ \\ \\ Expand:\left(x^2+11x+30\right)\left(x+2\right):\ x^3+13x^2+52x+60: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^3+13x^2+52x+60\right)\left(x-11\right)[/tex]

[tex]Expand: \left(x^3+13x^2+52x+60\right)\left(x-11\right):\ x^4+2x^3-91x^2-512x-660 \\ (Distributive \ property)[/tex]

Finally:

[tex]f(x) = 11(x^4 + 2x^3 - 91x^2 - 512x - 660) \\ \\ \boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}[/tex]

Answer:

8 crickets

Step-by-step explanation:

since 20% is in percent form, if you convert it to a whole number, it is 2. That means that Brad's lizard ate 2 crickets and there are 8 left.

look at the attached picture⤴

Hope it will help u...

Final answer:

To express the square root of 24 in simplest radical form, we break down 24 into 4 and 6, and since 4 is a perfect square, the simplified expression is 2√6.

Explanation:

To find the expression equal to the square root of 24, we can simplify the square root by looking for perfect square factors within 24. The number 24 can be factored into 4 and 6, where 4 is a perfect square. Therefore, we have:

As a result, the simplified expression equal to the square root of 24 is 2√6.

Answer:

Answer 2 is correct, 740

Step-by-step explanation:

The rounded equation would be 10 (50+20) + 40. So if you do the equation then it would be 740

Answer is B! Correct on exam!

Step-by-step explanation:

1. Identify the values for a, h, and k: a= 1/2 h= -1 k= 4. (Remember that the sign of h changes!)

2. Determine vertex: (-1,4)

3. Determine x and y for focus: X= -1 (same as vertex) y= K + 1/4(a)

Substitute what we know into that formula: y= 4 + 1/4(1/2)

y= 4 + 1/2 so y= 4 1/2.

4. Determine directrix: y= k - 1/4(a) ]

Substitute in what we know: y= 4 - 1/4(1/2)

y= 4-1/2 so y= 3 1/2

The focus and directrix of the parabola are (-1, 9/2) and y=7/2 respectively.

The given function is y = 1/2(x+1)² + 4.

We need to find the focus and directrix of the parabola.

A parabola is a set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola and the line is called the directrix. The focus lies on the axis of symmetry of the parabola.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Directrix: Use the vertex form to find the directrix

y=7/2

Focus: Use the vertex form to find the focus.

(-1, 9/2)

Axis of symmetry: x=-1

The coordinates to plot the graph are as follows:

(-3, 6), (-2, 9/2), (-1, 4), (0, 9/2) and (1, 6).

Therefore, the focus and directrix of the parabola are (-1, 9/2) and y=7/2 respectively.

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Answer:

The answer is the last choice, x=70 and the labeled angles are 110 and 70

Answer:

c

Step-by-step explanation:

because all your doing is picking the smallest and the biggest number and i just got it right .

Answer:C

Step-by-step explanation: 0.8 lb and 1.2 lb

Answer:

3/14

Step-by-step explanation:

5+3+2+4=14....

3 yellow

Answer:

c. 720 cm

Step-by-step explanation: