Find the volume of the sphere.
Either enter an exact answer in terms of pi or use 3.14 for pi and round your final answer to the nearest hundredth

radius=8

The probability of event A happening given that both B and C occur can be calculated using conditional probability.

Since events B and C are independent, the probability of both events occurring is simply the product of their individual probabilities: P(B ∩ C) = P(B) × P(C) = 0.78 × 0.55 = 0.429.

To find the probability of A happening given B and C, we use the formula for conditional probability: P(A | B ∩ C) = P(A ∩ B ∩ C) / P(B ∩ C).

Since A, B, and C are independent events, P(A ∩ B ∩ C) = P(A) × P(B) × P(C). Therefore, P(A | B ∩ C) = (P(A) × P(B) × P(C)) / P(B ∩ C) = (0.57 × 0.78 × 0.55) / 0.429 ≈ 0.631.

Thus, the probability of event A happening given that both B and C occur is approximately 0.631 or 63.1%.

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Answer:

B

Step-by-step explanation:

Given g(x) then g(x + a) is a horizontal translation of g(x)

• If a > 0 then a shift to the left of a units

• If a < 0 then a shift to the right of a units

h(x) = g(x - 3) = (x - 3)² with a < 0

The graph of h(x) is the graph of g(x) horizontally shifted right 3 units

The largest number among the given options is (101001)2, which is option D.

To determine the largest number among the given options, we need to convert each number into its decimal form and compare them.

A. (101001)2 A. (101001)2:

This number is in binary format. To convert it to decimal, we use the place value system. Starting from the rightmost digit, we assign powers of 2 to each bit. The decimal value is calculated by adding up the values of the bits multiplied by their respective powers of 2.

(101001)2 = 12^5 + 02^4 + 12^3 + 02^2 + 02^1 + 12^0

= 32 + 0 + 8 + 0 + 0 + 1

= 41

B. (2B)16 = 216^1 + 1116^0 = 32 + 11 = 43

C. (52)s: The base "s" is not specified, so we cannot determine its decimal value.

D. 50

Comparing the values we obtained:

41 < 43 < 50

Therefore, the largest number among the given options is 50, which corresponds to option D.

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Answer:

\(\huge\boxed{\sf x = 85}\)

Step-by-step explanation:

0.2x - 6 = 11

0.2x = 11 + 6

0.2x = 17

x = 17/0.2

\(\rule[225]{225}{2}\)

Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \purple {━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)

hope it helps!

The number of new cases of a disorder in a population that emerge in a particular time interval is called the incidence.

Incidence refers to the rate at which a new event occurs in a population. Incidence takes into account the variable time period during which a disease-free individual becomes at risk of spreading the disease.

In incident calculations, the quantifier is the number of events that have occurred in a given time. Then the quantifier of the denominator is the population that is at risk of experiencing the event during this period.

Simply put, incidence refers to new cases and is used to determine the etiology of the disease. While prevalence is more widely used to refer to health status in certain populations.

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Answer:

x^3 = 1000

Step-by-step explanation:

Answer:

The correct answer is - 3 hours.

Step-by-step explanation:

Given:

Price of parts: $200

Price of labor: $75/hour

Total cost: $425

Solution:

Let x = x of hours work done on the car

The inequality can be represented as:

425 = 75x + 200

Solving this inequality, we find that

225 =75x

or

x = 3

Thus, It means that the mechanic will take at least 3 hrs to work on his car.

Answer:

1. (3, -1) 2. (-1, 3) 3. (2, 0) 4. (1, 0)

Step-by-step explanation:

Sorry the graphs' numbers keep changing, but hope this helps!

Answer:

52

38

Step-by-step explanation:

Answer:

32.0 or 32/1 or 64/2

Answer:

1, 3, and 4 are correct

Step-by-step explanation:

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

Answer:

estimate 215 answer 10

Step-by-step explanation:

The blue curve represents the original function f(x), and the red curve represents its inverse f^(-1)(x). We can see that the two curves are reflections of each other across the line y=x, which confirms that we have found the correct inverse function.

To find the inverse of the function f(x) = x^2 - 2x, we can follow these steps:

Step 1: Replace f(x) with y, so that we have y = x^2 - 2x.

Step 2: Solve for x in terms of y. To do this, we can use the quadratic formula:

x = [2 ± sqrt(4 - 4y)] / 2 = 1 ± sqrt(1 - y)

Note that we have used the fact that x ≤ 1, which means that the solution with the minus sign in front of the square root is not valid. Therefore, the inverse function is:

f^(-1)(y) = 1 + sqrt(1 - y)

To check our answer algebraically, we can verify that f(f^(-1)(y)) = y and f^(-1)(f(x)) = x for all values of x and y.

f(f^(-1)(y)) = f(1 + sqrt(1 - y)) = (1 + sqrt(1 - y))^2 - 2(1 + sqrt(1 - y)) = y

f^(-1)(f(x)) = 1 + sqrt(1 - (x^2 - 2x)) = 1 + sqrt(3 - (x - 1)^2)

Both of these checks confirm that we have found the correct inverse function.

To check our answer graphically, we can plot the original function and its inverse on the same set of axes:

graph of f(x) = x^2 - 2x and its inverse function

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Answer:

3 1/3 ÷ 4/5 = 25/6 =4 1/6

Result in decimals: 4.1666666666667

Answer:

The answer is 5/4

For the first expression, 3 multiplies 3 plus 1 divided by the denominator 3

= 3×3 +1÷3

=10/3

then with the second expression, the division sign changes to a multiplication sign . Immediately it changes,4/5 turns to become 5/4

so now it will be

10/3×5/4

=15/12

=5/4

The cost of one apple is $0.70.

Let's assume that the cost of one apple is "a" dollars and the cost of one banana is "b" dollars. We can create two equations based on the information given:

4a + 9b = 12.70 ...(1)

8a + 11b = 17.70 ...(2)

To solve for "a", we can use elimination method by multiplying equation (1) by 8 and equation (2) by -4, so that the coefficients of "a" in both equations will be equal and opposite:

32a + 72b = 101.60

-32a - 44b = -70.80

Adding these two equations, we get:

28b = 30.80

Simplifying and solving for "b", we get:

b = 1.10

Now, we can substitute the value of "b" in equation (1) and solve for "a":

4a + 9(1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = 0.70

Therefore, the cost of one apple is $0.70.

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The system of equations with no solutions is the second one:

3x - 7y = 22

4.5x - 10.5y = 44

When we have a system of linear equations, the only case where the system has no solutions is when both of the lines are parallel lines (thus, the lines never intercept).

So we need to identify the system of linear equations where the lines are parallel.

If you look at the second system of equations, we have:

3x - 7y = 22

4.5x - 10.5y = 44

We can multiply the first equation by 1.5 to get:

1.5*(3x - 7y) = 1.5*22

4.5x - 10.5y = 33

Then the system is:

4.5x - 10.5y = 33

4.5x - 10.5y = 44

We can see that these lines are parallel,and thus, this system has no solutions.

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The margin of error is 2.326 for the supplied values of  c, σ, and n, which are 0.98, 0.78, and 150 respectively.

Margin is the term used to describe the equity that a trader has in their account. Using funds borrowed from a broker to buy stocks is referred to as "marging" or "buying on margin." Instead of a typical brokerage account, you must have a margin account to execute this. Beginning with your gross profit, which is the distinction between revenue and COGS, you may compute profit margin. Find the percentage of revenue that represents gross profit next. Calculate it by dividing your gross profit by your revenue. You can calculate your margin % by multiplying the sum by 100.

Given that,

Population standard deviation =  

 = 0.78

Sample size = n =150

α = 1 - 98% = 1 - 0.98 = 0.02

α= 2 = 0.02/ 2 = 0.01

Z*α = 2 = 0.01 = 2.326     (  Using z table    )  

Margin of error = E =  Z

The margin of error is 2.326 for the supplied values of  c, σ, and n, which are 0.98, 0.78, and 150 respectively.

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Yes, you did it right.... You put the lowest fahrentheit in the first blank, then the highest fahrentheit in the second blank. That is saying that the range of temperatures in the US is between -79.8 and 134 degrees Fahrenheit.

Answer:

C. r = 28.50 ÷ 3

Step-by-step explanation:

You have to divide to see the rate

Given:

\(\to \text{time}= 3 \ hours\\\\\to \text{total eran}= \$28.50 \\\\\)

To find:

earn per hour=?

Solution:

\(\to \text{time}= 3 \ hours\\\\\to \text{total eran}= \$28.50 \\\\\)

calculate earn per hour:

\(= \frac{\text{total earn }}{ \text{time}}\\\\= \frac{28.50}{3}\\\\= \$ 9.5\\\\\)

Therefore, the answer is "$9.5".

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Using statistics helps us make decisions based on empirical evidence, which is obtained through data analysis and inference.

Statistics provides us with a set of tools and methods to collect, analyze, and interpret data. By applying statistical techniques, we can make decisions based on evidence derived from empirical observations and measurements.

Statistics allows us to summarize and describe data, identify patterns and relationships, and draw conclusions from samples or populations. It helps us quantify uncertainty and assess the strength of evidence supporting different claims or hypotheses.

Decision-making based on statistics involves making inferences about a larger population based on the information available from a sample. By using probability theory and statistical models, we can estimate population parameters, test hypotheses, and make predictions about future events or outcomes.

Statistics provides a systematic and rigorous framework for evaluating evidence and reducing bias in decision-making. It allows us to objectively assess the reliability and validity of information, making decisions that are informed by data-driven analysis rather than intuition or anecdotal evidence.

In summary, statistics helps us make decisions based on evidence obtained through data analysis, enabling us to draw reliable conclusions, quantify uncertainty, and make informed choices in various fields such as business, medicine, social sciences, and more.

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The area of sector ABC is 14.24 units.

The area of sector of a circle is the amount of space enclosed within the boundary of the sector. A sector always originates from the center of the circle. The sector of a circle is defined as the portion of a circle that is enclosed between its two radii and the arc adjoining them. The semi-circle is the most common sector of a circle, which represents half a circle. The space enclosed by the sector of a circle is called the area of the sector. There are two types of sectors: minor and major sectors. A minor sector is a sector that is less than a semi-circle, whereas, a major sector is a sector greater than a semi-circle.

m∠ABC =  θ = 102°

Radius of circle = AB = r = 4 units

Area of sector of a circle

Area = (θ/360°) × πr²

Substitute the above values in the formula:

Area = (102/360) × π ×4²

= 14.24188 square units

Rounding off to the nearest hundredth decimal,

Area  = 14.24 square units

Thus, the area of sector ABC is 14.24 units.

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Answer:

46

Step-by-step explanation:

6 x 5 + \((-4)^{2}\)

= 30 + (16)

= 30 + 16

= 46

So, the answer is 46

Answer:

A and C

Step-by-step explanation:

For any relation to be considered a function, each domain value (x-value) must have exactly one range value (y-value). If a relation contains an x-value that has two or more y-value related/mapped to it, the relation is not a function.

Let's examine each option given.

Option A: each x-value has exactly one y-value related or assigned to it. Therefore, the relation is A FUNCTION.

Option B: the x-value, 4, has two y-values, 12 and 15 assigned to it. Therefore, the relation is NOT A FUNCTION.

Option C: each x-value has exactly one y-value related or assigned to it. Therefore, the relation is A FUNCTION.

Option D: the x-value, 1, has two y-values, -1 and 1 assigned to it. Also, x-value, 3, has two y-values, 2 and -2 assigned to it. Therefore, the relation is NOT A FUNCTION.

Answer:

Step-by-step explanation

Frist, the area = ab = 30 m^2 and the perimeter = 2(a + b) = 34 m or a + b = 17 m (2). Solving (1) and (2), a = 15 m and b = 2 m. Since it is a rectangle, the dimensions are (all in m) so the answer is: 15, 2, 15, 2.

Answer:

THe kitchen is 8 by 10

Step-by-step explanation:

x = width

y = length

Area = xy = 80 m²

Perimeter = 2x + 2y = 36 m

2x = 36 - 2y

x = 18 - y   substitute into equation 1

(18 - y)(y) = 80

-y² + 18y - 80 = 0    find roots of y by factoring

y² - 18y + 80 = 0

(y - 8)(y - 10) = 0

y = 8, 10

Since xy = 80, then:

x = 80/10 = 8, or, x = 80/8 = 10

Now you have your dimensions: 8 and 10

To check the answers:

8 x 10 = 80 m²

2(8) + 2 (10) = 36 m

Answers are correct!

Answer: 178.3

Step-by-step explanation:

Use cos to find the value of x: cos(27)=350/x

You will find x = 392.81

Using this value, find sin(27):  Sin(27)=y/392.81

You will find y=178.33

Rounding to the nearest tenth, you get 178.3

The probability (to the nearest percent) of a randomly thrown dart landing somewhere in the red shaded regions is approximately 2%.

To find the probability of a randomly thrown dart landing somewhere in the red shaded regions, we need to determine the ratio of the area of the red shaded regions to the total area.

Let's break down the problem step by step:

We are given that the area of the inner circle is 256π. Let's denote this area as A_inner.

The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius. From the given information, we can determine the radius of the inner circle.

A_inner = πr^2

256π = πr^2

r^2 = 256

r = 16

So, the radius of the inner circle is 16 units.

Now, let's consider the area of the red shaded regions. These regions consist of the area between the inner circle and the outer circle, as well as the five triangular regions formed by the sides of the pentagon.

The area between the two circles can be calculated as the difference between the areas of the two circles:

A_red = A_outer - A_inner

To find the area of the outer circle, we need to determine its radius. Since the outer circle is inscribed in the pentagon, the distance from the center of the circle to any vertex of the pentagon is the radius.

Let's denote the radius of the outer circle as R. The distance from the center of the circle to a vertex of the pentagon is also the apothem (a) of the pentagon.

Using trigonometry, we can calculate the apothem of a regular pentagon:

a = Rcos(36°)

Since the pentagon is regular, each interior angle is 108°, and the central angle of the isosceles triangle formed by the radius, apothem, and one side of the pentagon is 36°.

From the given information, we know that the apothem (a) is equal to the radius of the inner circle, which is 16 units.

16 = Rcos(36°)

Solving for R:

R = 16 / cos(36°)

R ≈ 19.82

The radius of the outer circle is approximately 19.82 units.

Now, we can calculate the area of the red shaded regions:

A_red = πR^2 - A_inner

= π(19.82)^2 - 256π

= 1238.22π - 256π

= 982.22π

Finally, we can calculate the probability of a randomly thrown dart landing somewhere in the red shaded regions by dividing the area of the red shaded regions by the total area, which is the area of the outer circle:

Probability = (A_red / A_outer) * 100

Plugging in the values:

Probability = (982.22π / πR^2) * 100

= (982.22 / 19.82^2) * 100

≈ 2.51%

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Answer:

Step-by-step explanation:

811.98*7.5%= 60.898

811.98+60.898= 872.787 round to $872.79

Answer:

$872.88

Step-by-step explanation:

811.98 x 7.5%= 811.98 x 0.075

811.98 x 0.075= 60.90

811.98+60.90= 872.88

The value of AB in triangle ADC and AEB such that it make line EB parallel to line DC is given by to option d. 36.

To make line EB parallel to line DC,

Ensure that triangle AED and triangle ABC are similar triangles.

This can be achieved by having the corresponding sides of the triangles in proportional lengths.

Let us find the value of AB that would make line EB parallel to line DC.

In triangle AED, we have AE = 51 and ED = 17.

In triangle ABC, we have BC = 12.

If the triangles are similar, then the ratio of corresponding sides should be equal.

This implies,

AB/BC = AE/ED

Plugging in the values we get,

⇒ AB/12 = 51/17

Cross-multiplying and get the value ,

⇒ AB × 17 = 12 × 51

⇒ AB = (12 × 51) / 17

⇒ AB = 36

Therefore, the value of AB that would make line EB parallel to line DC is equal to option d. 36.

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The above question is incomplete, the complete question is:

Which value of AB would make line EB parallel to line DC?

Attached diagram.