Find the volume of the cone in terms of pi.
15 cm
12 cm
9 cm

Therefore, the probability that a randomly selected family owns a cat is 0.257. Therefore, the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat is 0.778.

Probability is a branch of mathematics that deals with the study of random events or situations. It involves the quantification of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 representing impossibility and 1 representing certainty. The theory of probability provides a framework for making predictions, analyzing data, and making decisions in situations involving uncertainty or randomness.

Here,

Let's use the following events:

D: family owns a dog

C: family owns a cat

From the problem statement, we know:

P(D) = 0.3

P(C|D) = 0.2

P(C) = 0.34

1. To find the probability that a randomly selected family owns a cat, we can use the law of total probability:

P(C) = P(C|D) * P(D) + P(C|not D) * P(not D)

We don't know P(C|not D), but we can find it using the fact that P(not D) = 1 - P(D):

P(C|not D) = (P(C) - P(C|D) * P(D)) / P(not D)

P(C|not D) = (0.34 - 0.2 * 0.3) / (1 - 0.3)

P(C|not D) = 0.2857

Substituting the values:

P(C) = 0.2 * 0.3 + 0.2857 * 0.7

P(C) = 0.257

2. To find the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat, we can use Bayes' theorem:

P(not D|C) = P(C|not D) * P(not D) / P(C)

Substituting the values:

P(not D|C) = 0.2857 * 0.7 / 0.257

P(not D|C) = 0.778

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Complete question:

In a certain community, 30% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 34% of all the families own a cat. What is the probability that a randomly selected family owns a cat? What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

\(\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}\)

Step-by-step explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

First, we can calculate the area of the circular base:

\(A_{\text{circle}} = \pi r^2\)

\(A_{\text{base}} = \pi (0.75 \text{ in})^2\)

\(A_{\text{base}} = 0.5625\pi \text{ in}^2\)

Next, we can calculate the area of the rectangular side:

\(A_\text{rect} = l \cdot w\)

\(A_\text{side} = (4\text{ in}) \cdot C_\text{base}\)

Since the width of the side is the circumference of the base, we need to calculate that first.

\(C_\text{circle} = 2 \pi r\)

\(C_\text{base} = 2 \pi (0.75 \text{ in})\)

\(C_\text{base} = 1.5 \pi \text{ in}\)

Now, we can plug that back into the equation for the area of the side:

\(A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})\)

\(A_\text{side} = 6\pi \text{ in}^2\)

Finally, we can solve for the surface area of the can by adding the area of each of its parts.

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

\(SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2\)

\(\boxed{SA = 7.125\pi \text{ in}^2}\)

\(\boxed{SA \approx 22.4 \text{ in}^2}\)

Answer:

10 inches

Step-by-step explanation:

15 days/3 days =5

5 x 2 =10

Answer:

B. 144√3 in².

Step-by-step explanation:

Given the following data;

Sides of length = 24 inches

Mathematically, the area of an equilateral triangle is given by the formula;

A = √3 * s²/4

Where, s represents the sides of length.

Substituting into the formula, we have;

A = √3 * 24²/4

A = √3 * 576/4

A = √3 * 144

A = 144√3 in²

Answer:

Mode 4

Step-by-step explanation:

Mean x¯¯¯ 4.3333333333333

Median x˜ 4

Mode 4

Range 7

Minimum 2

Maximum 9

Count n 6

Sum 26

Quartiles Quartiles:

Q1 --> 3

Q2 --> 4

Q3 --> 4

The tangent ratio is an illustration of the trigonometry identity

The value of x that is not a solution of tan(x) = 1 is 3\(\pi\)/4

The trigonometry identity is given as:

tan(x) = 1

Next, we test the x values using a calculator.

When \(x = -7\pi/4\), we have:

tan(-7\(\pi\)/4) = 1

When x = 3\(\pi\)/4, we have:

tan(3\(\pi\)/4) = -1

When x = 5\(\pi\)/4, we have:

tan(5\(\pi\)/4) = 1

When x = \(\pi\)/4, we have:

tan(\(\pi\)/4) = 1

Hence, the value of x that is not a solution of tan(x) = 1 is 3\(\pi\)/4

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Answer:

x=-1/2

Step-by-step explanation:

-3(x-4)= -9(x-1)

-3x+12= -9x+9

-3x+9x= 9-12

6x= -3

x=-3/6

x= -1/2

In response to the query, we have that Hence, the following are the answers to this equation: 5x - 2 = 0 or x - 1 = 0 Thus, x = 2/5 or x = 1.

A quadratic equation in a single variable is x ax2+bx+c=0, a form of quadratic equation. a 0. The fact that this polynomial is of second sample guarantees that it comprises at least one solution according to the Basic Theorem of Algebra. Solutions might be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least single word in it has to be rounded. The formula "ax2 + bx + c = 0" constitutes one of the widely used solutions for complex numbers. where the undefined variable "X" is represented by the numerical values or constants a, b, and c.

2x² - 9x - 18 = 0

Secondly, we must identify two integers whose total is -9 and whose product is 2(-18)=-36. These are the numbers -12 and +3. Hence, we may say:

2x² - 9x - 18 = (2x + 3)(x - 6) = 0

Hence, the following are the answers to this equation:

2x + 3 = 0 or x - 6 = 0

Thus, x = -3/2 or 6.

8x² + 2x - 3 = 0

8x² + 2x - 3 = (4x - 3) (4x - 3)

(2x + 1) = 0

Hence, the following are the answers to this equation:

4x - 3 = 0 or 2x + 1 = 0

Thus, either x = 3/4 or x = -1/2.

5x² - 11x + 2 = 0

5x² - 11x + 2 = (5x - 2)(x - 1) = 0

Hence, the following are the answers to this equation:

5x - 2 = 0 or x - 1 = 0

Thus, x = 2/5 or x = 1.

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Answer:

the second one would be the correct anwser i think.

Step-by-step explanation:

Answer: 0.1112

Step-by-step explanation:

Let X be a random variable .

Given: A normal population has a mean m=33 and standard deviation s = 9.

The probability that a randomly chosen value will be greater than 44 will be :-

\(P(X>44)=P(\dfrac{X-m}{s}>\dfrac{44-33}{9})\\\\=P(Z>\dfrac{11}{9})\\\\=P(Z>1.22)\\\\ =1-P(Z<1.22)\\\\=1-0.8888\\\\=0.1112\)

Hence, the probability that a randomly chosen value will be greater than 44 = 0.1112

A normal population has a mean m=33 and standard deviation s = 9. the probability that a randomly chosen value will be greater than 44 is - 28.774%

Given:

mean m=33

standard deviation s = 9

probability = ?

Solution:

(34-39)/9 = -0.5556

which mean

P(Z<-0.5556) ≈ 0.28774

or 28.774%

Thus, A normal population has a mean m=33 and standard deviation s = 9. the probability that a randomly chosen value will be greater than 44 is - 28.774%

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Answer:

f(3) = -2

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

f(3) is simply asking for the y-value when x = 3. According to the graph, when x = 3, y = -2.

Therefore, f(3) = -2

Answer:

Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)

Step-by-step explanation:

3x+4=7x-4

add 7x to each side of equation 4x+3x+-7x=-4x+7x+-7x

combine like terms 7x+-7x=0

4+ -4x =-4 +0

4+-4x= -4

add -4 to each side of equation 4+ -4 +-4x=-4+-4

combine like terms -4 +4=0

0+ -4x = -4+ -4

combine like terms -4+-4=-8

-4x =-8

divide each side by-4

x=2

simplifying

x = 2

Answer:

x = 10.47

Step-by-step explanation:

circumference = 2 * 10 * π = 20π

centre angle of a circle (in radiant) = 2π

x : 20π = π/3 : 2π

x = (20π * π/3)/ 2π

x = 10 * π/3

x = 10π/3

x = 10.466667

x = 10.47

Answer:

\(180\)

Step-by-step explanation:

\(6 \times 2 \times 3 \times 5\)

\(12 \times 15\)

\(=180\)

Steps to solve:

6 * 2 + 3 - 5

~Multiply

12 + 3 - 5

~Add

15 - 5

~Subtract

10

Best of Luck!

Answer:

7 books

Step-by-step explanation:

$62.50 - $10 = $52.50

$52.50 ÷ $7.50 = 7

You bought 7 books.

The lengths equal to 3 yards 16 inches are 3 yards, 108 inches, 3.44 yards (approximately), and 108.44 inches (approximately).

To determine the lengths that are equal to 3 yards 16 inches, we need to convert the measurements into a consistent unit. Since both yards and inches are units of length, we can convert the inches into yards or the yards into inches to find the equivalent lengths.

1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches).

Therefore, 3 yards is equal to 3 * 36 = 108 inches.

Now, we can compare 108 inches to 3 yards 16 inches.

108 inches is equal to 3 yards, so it matches the given length.

To convert 16 inches into yards, we divide it by 36 since 1 yard = 36 inches. 16 inches / 36 = 0.44 yards.

Therefore, 3 yards 16 inches is equivalent to:

3 yards

108 inches

3 yards 0.44 yards (or approximately 3.44 yards)

108 inches 0.44 yards (or approximately 108.44 inches)

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Answer:

4736 because count add them together or do it your way

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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a) The combined number of $3 carwashes for cars, c, and $5 carwashes for trucks or SUVs, t, needed can be represented by the equation y = c + t.

b) If only 5 cars are washed, the number of trucks or SUVs needed to be washed to raise the full $915 is 180.

An equation is a mathematical statement that shows that two mathematical expressions are equal or equivalent.

Equations use the equation symbol (=) to show the equality of expressions.

The total amount needed for the new equipment = $915

The charge for a car wash per car = $3

The charge for cash wash per truck or SUV = $5

Let the number of cars = c

Let the number of trucks or SUVs = t

c + t = y... Equation 1

3c + 5t = 915... Equation 2

If the number of cars, c = 5

From equation 2:

3c + 5t = 915

3(5) + 5t = 915

15 + 5t = 915

5t = 900

t = 180

Thus, from equation 2, we can determine that if cars are 5, the trucks or SUVs must be 180 to meet the target.

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Answer: We can use the formula:

time = distance / speed

to calculate the time it will take Jeanine to complete the trip, assuming she drives at or below the speed limit.

She has already driven 45 miles, so she has 240 - 45 = 195 miles left to travel.

If she drives at 65 miles per hour or less, the maximum speed limit, her travel time will be:

time = distance / speed

time = 195 miles / 65 miles per hour

time = 3 hours

So Jeanine can expect to spend an additional 3 hours completing the trip, assuming she drives at or below the speed limit.

Step-by-step explanation:

Answer:

5/8 of the pizza was eaten

Step-by-step explanation:

1/4=2/8

2/8+3/8=5/8

Answer:

5/8

Step-by-step explanation:

3/8 + 1/4

1/4 x 2 = 2/8

3/8 + 2/8 = 5/8

Answer:

x = 35

Step-by-step explanation:

The sum of the angles of a triangle is 180°.

\(x+55+90=180\\x+145=180\\x=35\)

Answer:

\({ \boxed{ \mathfrak{ \: answer : \: { \rm{35\degree}}}}}\)

Step-by-step explanation:

\({ \rm{55 \degree + 90\degree + x = 180\degree}} \\ { \tt{ \{angle \: sum \: of \: a \: triangle \}}} \\ { \rm{145\degree + x = 180\degree}} \\ { \rm{x = 35\degree}}\)

The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

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A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

Answer:

13.2 miles

Step-by-step explanation:

We can use the following conversion factors:

1 mile = 5,280 feet

Using this conversion, we can divide the height of the volcano in feet by 5,280 to get the height in miles:

69,657.652 ft ÷ 5,280 ft/mi ≈ 13.2 mi

Therefore, the height of the volcano on the recently discovered planet is approximately 13.2 miles.

Hopes this helps

Answer:

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the valve pressure is significantly different from 5.5 psi.

P-value = 0.04

Test statistic z=2.05

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the valve pressure is significantly different from 5.5 psi.

Then, the null and alternative hypothesis are:

\(H_0: \mu=5.5\\\\H_a:\mu\neq 5.5\)

The significance level is 0.02.

The sample has a size n=270.

The sample mean is M=5.6.

The standard deviation of the population is known and has a value of σ=0.8.

We can calculate the standard error as:

\(\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.8}{\sqrt{270}}=0.049\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{M-\mu}{\sigma_M}=\dfrac{5.6-5.5}{0.049}=\dfrac{0.1}{0.049}=2.054\)

This test is a two-tailed test, so the P-value for this test is calculated as:

\(\text{P-value}=2\cdot P(z>2.054)=0.04\)

As the P-value (0.04) is bigger than the significance level (0.02), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the valve pressure is significantly different from 5.5 psi.

Answer:

Absolute Value = to 0.5 :  0.5

Absolute Value = 5:   5

Absolute Value = 6:   6

Absolute Value = 60:  60

Step-by-step explanation:

Answer:

I'm guessing this is what you need

Step-by-step explanation: