Determine the volume of sphere with a radius of six inches. What is the volume of the sphere in terms of π?

The difference in volume between the two compartments is given as follows:

346.4 cm³.

The volume of a prism is obtained as the multiplication of the area of the base of the prism by the height of the prism, as follows:

The height of the base of the prism in this problem is given as follows:

h² + 5² = 10²

\(h = \sqrt{10^2 - 5^2}\)

h = 8.66.

Hence the base is composed as follows:

Hence the base area is given as follows:

Ab = 5 x 8.66 + 2 x 1/2 x 5 x 8.66

Ab = 86.6 cm².

The height is given as follows:

7 cm.

Hence the volume is:

7 x 86.6 = 606.2 cm³.

The height of the taller prism is given as follows:

11 cm.

Hence the volume is:

11 x 86.6 = 952.6 cm³.

Hence the difference of volumes is of:

952.6 - 606.2 = 346.4 cm³.

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Answer:

\(4+x=22\)

Step-by-step explanation:

Hope this helps

Answer:

52

Step-by-step explanation:

RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.

Answer:

52 degrees

Step-by-step explanation:

right angle = 90

90-38=52

So RTQ = 52 degrees

Answer:

326

Step-by-step explanation:

The value of the given expression is 326.

Given:

The given expression 2 hundreds + 12 tens + 6 ones.

To find:

The value of the given expression.

Explanation:

The numeric form of given expression is:

2 hundreds + 12 tens + 6 ones

2 hundreds + 12 tens + 6 ones

2 hundreds + 12 tens + 6 ones

Therefore, the value of the given expression is 326.

Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(3 + 7)

20 = 2(10)

20 = 20 (True).

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Answer:

It's B, C, and E on Edge2020. I took the Unit Test Review and I was right.

The total amount that Isaiah spent at the store is $27.44.

Given that, Isaiah spent $19.60 on a gift for his mother.

Let the total amount be x.

A statement that the values of two mathematical expressions are equal (indicated by the sign =).

The amount that was spent on gifts was 5/7 of the total amount.

Now, 5/7×x=19.60

⇒x=$27.44

Therefore, the total amount that Isaiah spent at the store is $27.44.

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Answer:

\(x^4-12x^3+54x^2-108x+81\)

Step-by-step explanation:

We have been given the following binomial expansion for (a + b)⁴:

\(\boxed{(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4}\)

To use this to expand and simplify (x - 3)⁴, first identity the values of a and b:

Substitute the values of a and b into the expansion, and simplify:

\(\begin{aligned}(x-3)^4&=x^4+4x^3(-3)+6x^2(-3)^2+4x(-3)^3+(-3)^4\\\\&=x^4+4x^3(-3)+6x^2(9)+4x(-27)+81\\\\&=x^4-12x^3+54x^2-108x+81\end{aligned}\)

Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let the total sum of money be x.

Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:

2/9 * x = 20000

Multiplying both sides by 9/2, we get:

x = 90000

Now, we can find the shares of B and C as follows:

B's share = 3/9 * 90000 = 30000

C's share = 4/9 * 90000 = 40000

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Answer:A number is divisible by 2 if it ends in 2, 4, 6, 8 or 0. A number is divisible by 5 if it ends in 5 or 0. A number is divisible by 10 if it ends in a 0.Apr 8, 2018

Answer:

3434

Step-by-step explanation:

The conclusion that should be made on the question using a significance level of α=0.05 is; Option A; Fail to reject H₀

We are given the hypotheses;

Null Hypothesis; H₀; p = 0.25

Alternative hypothesis; Hₐ; p > 0.25

p^ = 0.3

p-value = 0.068

Now, we are told that the significance level is α = 0.05

      Now, the law in hypotheses testing is that when the p-value is less tan or equal to the significance level, we will reject the null hypothesis but when the p-value is greater than the significance value, we fail to reject the null hypothesis(H₀)

Now, in our question the p-value of 0.068 is greater than the significance level of 0.05 and thus we will fail to reject the null hypothesis.

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Answer:

y = 2*x - 4

Step-by-step explanation:

The general equation for a line is:

y = a*x + b

Where a is the slope and b is the y-intercept.

In this case, we know that the line passes through (4, 4) and the y-intercept is -4.

Then:

b = -4

So our line is something like:

y = a*x - 4

Now, we know that the line passes through (4, 4), which means that when x = 4, y = 4.

If we replace these values in the equation, we get:

4 = a*4 - 4

Now we can solve this for a.

4 = a*4 - 4

4 + 4 = a*4

8 = a*4

8/4 = a = 2

Then the equation for the line is:

y = 2*x - 4

Answer:

17.8

Step-by-step explanation:

You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

The number of sea stars is 64.

What is a ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.

In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."

This ratio is expressed in fraction form as a/b. We utilize the same method for further simplifying a ratio as we use for further simplifying a fraction.

According to the question,

Ratio of sea stars to wolf eels = 4:5

Number of rock fish= 5/8 (Number of sea stars)

Number of wolf eels - Number of rock fish = 40

Using the given information, we get,

Number of sea stars = 8/5 (Number of rock fish)

On simplification,

Number of wolf eels = 80

So, number of sea stars = (4/5)*80

                                          = 64

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The rear windshield wiper of a car rotated 120 degrees, as shown in the figure. The area cleared by the wiper blade is approximately 205.875 square inches.

The problem states that a car’s rear windshield wiper rotates 120 degrees, as shown in the figure. Our aim is to find the area cleared by the wiper.

The wiper's arm is represented by a line segment and has a length of 14 inches.

The wiper's blade is perpendicular to the arm and has a length of 25 inches.

Angular degree measure indicates how far around a central point an object has traveled, relative to a complete circle. A full circle is 360 degrees, and 120 degrees is a third of that.

As a result, the area cleared by the wiper blade is the sector of a circle with radius 25 inches and central angle 120 degrees.

The formula for calculating the area of a sector of a circle is: A = (θ/360)πr², where A is the area of the sector, θ is the central angle of the sector, π is the mathematical constant pi (3.14), and r is the radius of the circle.

In this situation, the sector's central angle θ is 120 degrees, the radius r is 25 inches, and π is a constant of 3.14.A = (120/360) x 3.14 x 25²= 0.33 x 3.14 x 625= 205.875 square inches, rounded to the nearest thousandth.

Therefore, the area cleared by the wiper blade is approximately 205.875 square inches.

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Part a: Kelsey should make 36 pendants

Part b: Kelsey needs to make 26 more pendants

Rent of the booth at the craft fair = $200

The material cost of each pendant = is $7.80

The selling cost of each pendant = is $13.50

Let Kelsey make x number of pendants

Formulating the inequality equation we get:

Selling cost of each pendant*Number of pendants >= Rent of the booth + Material cost of each pendant*Number of pendants

= 13.50x >= 200 + 7.80x

Solving the inequality we get:

13.50x >=200+7.80x

5.70x >= 200

x >= 35.08

So, she should make a total of 36 pendants

Considering that she has already made 10 pendants. She needs 26 more pendants.

Although a part of your question is missing, you might refer to this full question: Kelsey makes pendants that she would like to sell at an upcoming craft fair. She must pay $200 to rent a booth at the craft fair. The materials for each pendant cost $7.80, and she plans to sell each pendant for $13.50. To make a profit, she must make more money than she spends. Kelsey has already made 10 pendants. Part A: Write and solve an inequality to show how many pendants Kelsey should make. Show the steps of your solutions. Part B: Given that Kelsey has already made 10 pendants, how many additional pendants must she make and sell to make a profit?

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The given function is expressed as

f(x) = 3x^3 - x^2 + 4x - 2

This is a cubic function which also means that it is an odd function.

The graph of the function is shown below

Based on the interest rate and the period of compounding, the annual percentage yield on the CD would be 1. 77%

The annualized return can be found by using the Effective Annual Rate (EAR) formula which is:
= ( 1 + annual rate / Compounding periods in a year) ^ number of compounding periods in a year - 1

Solving for the annual percentage yield is therefore:

= ( 1 + 1.75% / 365) ³⁶⁵ - 1

= 1.017654 - 1

= 0. 01765

= 1.77%

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Given the area of the house and the basement, the basement accounts for 21.67 percent of the total square footage.​

Percentage is simply number or ratio expressed as a fraction of 100.

It is expressed as;

Percentage = ( Part / Whole ) × 100%

Given that;

Percentage = ( Part / Whole ) × 100%

Percentage = ( 455ft² / 2100ft² ) × 100%

Percentage = 0.21666 × 100%

Percentage = 21.67%

Given the area of the house and the basement, the basement accounts for 21.67 percent of the total square footage.​

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We know that the faster she climbs, the less time the climb will take.

As you can observe, the given relationship is between her speed and the height of the climb. We can deduct that this situation can be modeled by the speed in function of the time.

However, let's analyze each answer choice.

Choice A can't be right because the height of the mountain is not variable, that is, the mountain won't change its height.

Choice B is relating time and speed which, as we said before, the situation involves a relationship between time and speed.

To know which region is the solution to the pair of inequalities, we are going to graph the two lines first:

Since y<2, then the shaded region that represents the solutions is:

In the answer choices, the option E.

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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Answer:

Step-by-step explanation:

16x⁸ - 81y⁸ is the difference of squares.

16x⁸ - 81y⁸ = (4x⁴)² - (9y⁴)² = (4x⁴ + 9y⁴)(4x⁴ - 9y⁴)

Note that 4x⁴ - 9y⁴ is also the difference of squares.

4x⁴ - 9y⁴ = (2x²) - (3y²)² = (2x² + 3y²)(2x² - 3y²)

16x⁸ - 81y⁸ = (4x⁴ + 9y⁴)(2x² + 3y²)(2x² - 3y²)

Answer:

\(c > -1\)

Step-by-step explanation:

\(2c-10 < 3c-9\\-10 < c-9\\-1 < c\\c > -1\)

The number of days took to get the video of Felipe 1024 views is 4.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The relationship between the elapsed time in days, d, since the video was uploaded and the total number of views, v, that the video received is modeled by the equation,

v = 4^(1.25d)

We have to find d when v = 1024

1024 = 4^(1.25d)

We have the rule for exponents aᵇⁿ = (aᵇ)ⁿ

1024 = \((4^{1.25} )^d\)

1024 = (5.6569)^d

Taking logarithms on both sides,

㏒ (1024) = ㏒ [(5.6569)^d]

We have the exponent rule for logarithm, ㏒ (aᵇ) = b ㏒ (a)

㏒ (1024) = d ㏒ (5.6569)

d = ㏒ (1024) / ㏒ (5.6569)

d = 4

Hence it took 4 days to for Felipe's video to get 1024 views.

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