a fair coin is tossed three times. the random variable x is defined to be 2ℎ , where h is the number of flips that come up heads. for example, x(hht)

The tax rate given as a percentage, can be used to find out the amount

to be paid as tax.

Correct response:

The given parameters are;

Susan Wong's taxable income last year = $52,915

The income tax rate = 2%

Required:

Susan Wong's tax last year

Solution:

The tax rate is given as a percentage of the taxable income.

The amount payable as tax = The tax rate × The taxable income

Therefore;

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ANSWER

EXPLANATION

To reflect the triangle over the x-axis, the x-coordinates of the vertices remain the same, and the y-coordinates change to their opposites. Thus, to draw the image, we have to draw auxiliary vertical lines across each vertex of triangle LMN and graph the image of each vertex at the same distance from the x-axis on the opposite side,

Answer:

Step-by-step explanation:

If you leave π as π, it should be 169π square feet

If you do π as 3.14, it should be 530.66 square feet.

If you do π as 22/7, it should be 531 1/7 square feet.

Hope that helps! :)

Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.

To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.

The present value of an annuity formula is given by:

P = A * [(1 - (1 + r)^(-n)) / r],

where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:

196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].

Simplifying the expression inside the brackets:

196,000 = A * (1 - 0.469091).

196,000 = A * 0.530909.

Dividing both sides by 0.530909:

A = 196,000 / 0.530909.

A ≈ 369,238.68.

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The volume of the ice cube is 35.937 mm^3

We know that for a cube of side length L, the volume is defined as:

V = L^3

Here, we do know that each side of our ice cube measures 3.3 mm, so we have:

L = 3.3mm

Then the volume of the cube is just:

V = (3.3 mm)^3 = 35.937 mm^3

We can conclude that the volume of the ice cube is 35.937 mm^3

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Answer:

She spent 51 dollars on pants and 22 on t-shirts so she bought 4 shirts

Step-by-step explanation:

Therefore, the compound inequality for the diameter of the washers is: 3.150 ≤ d ≤ 3.240.

In mathematics, an inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or equal to the other. The symbols used to represent inequalities are:

">" which means "greater than"

"<" which means "less than"

"≥" which means "greater than or equal to"

"≤" which means "less than or equal to"

Inequalities can be solved by applying algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides of the inequality by the same number. The solution to an inequality is a range of values that satisfy the inequality.

Here,

The formula for the circumference of a circle in terms of its diameter is:

C = πd

where π (pi) is approximately 3.14.

We are given that the acceptable range for the circumference of the washer is 9.9 ≤ C ≤ 10.2 centimeters. Substituting C = 3.14d into this inequality, we get:

9.9 ≤ 3.14d ≤ 10.2

Dividing all sides of the inequality by 3.14, we obtain:

3.15 ≤ d ≤ 3.24

Rounding to three decimal places, the corresponding interval for the diameters of the washers is:

3.150 ≤ d ≤ 3.240

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Answer:

x = 7.2 , y = 57 , z = 10.8

Step-by-step explanation:

the sum of the 3 angles in the outer triangle = 180° , that is

y + 88 + 35 = 180

y + 123 = 180 ( subtract 123 from both sides )

y = 57

------------

the outer and inner triangles are similar ( AA postulate ) then the ratios of corresponding sides are in proportion, that is

\(\frac{x}{12}\) = \(\frac{9}{9+6}\) = \(\frac{9}{15}\) ( cross- multiply )

15x = 108 ( divide both sides by 15 )

x = 7.2

and

\(\frac{z}{18}\) = \(\frac{9}{15}\) ( cross- multiply )

15z = 162 ( divide both sides by 15 )

z = 10.8

The survey will be conducted with the selected schools, and the results will be analyzed to identify the schools that will participate in the new physical education program.

To select a sample for a survey to identify and describe the schools that will participate in a new physical education program, the following steps need to be followed:

Step 1: Create a List of Schools in the Province. The first step is to make a comprehensive list of all the schools in the province. This list should include all the schools in the province, including both public and private schools.

Step 2: Random Sampling. To ensure that the sample is representative of the population, we must use random sampling. In this case, we will use a simple random sampling technique to select the schools for the survey.

Step 3: Determining the Sample Size. To determine the sample size, we must consider several factors such as the population size, margin of error, and confidence level. In this case, we want to select 25 schools from the population of schools in the province.

Step 4: Contacting the Schools. Once the sample has been selected, the schools will be contacted to participate in the survey. The schools that agree to participate in the survey will be included in the final sample.

Step 5: Conducting the Survey. The survey will be conducted with the selected schools, and the results will be analyzed to identify the schools that will participate in the new physical education program.

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Answer:

a. 0 ≤ t ≤ 3.4 s. b. 0 ≤ y ≤ 50 ft. c. i. -∞ ≤ t ≤ +∞. ii. -∞ ≤ y ≤ 50

Step-by-step explanation:

a. What is the practical domain of the function?

Since the toy rocket lands on the ground 3.4 seconds later, if the time it starts to fly in the air is time t = 0 and the time it lands is time t = 3.4 s, the practical domain of the function is 0 ≤ t ≤ 3.4 s.

b. What is the practical range of the function?

Since the rocket reaches a maximum height of 50 ft, if the maximum height of the toy rocket is y = 50 ft and it lands on the ground at y = 0, the practical range of the function is 0 ≤ y ≤ 50 ft.

c. How would the theoretical domain and range of the function differ from the practical domain and range of the situation?

i. The theoretical values of t is from is from t = -∞ to t = +∞. So, the theoretical domain is -∞ ≤ t ≤ +∞.

ii. Since the maximum value of the function is y = 50, and it also decreases to y = -∞. So, the theoretical domain is from y = -∞ to y = 50. So, the theoretical range is -∞ ≤ y ≤ 50

Answer:a-20miles

b-5miles

C-35 miles

Step-by-step explanation:

Answer:

45 meters

Step-by-step explanation:

graph the equation and find the y-intercept

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer:

The third option is wrong becuase x isn't a defined variable, and they specified that the book must be at least 250 pages, which means that it can't be less.

Answer:

First u get the Y by itself then you read the less than or equal to or greater than or equal to.

Step-by-step explanation:

hope it helps

The mean of the 32 numbers is 12.375. To calculate the mean, we can consider the sum of all the numbers and divide it by the total count.

Given that the mean of 10 numbers is 15, their total sum is 10 multiplied by 15, which equals 150. Similarly, the mean of 20 numbers is 11, so their total sum is 20 multiplied by 11, resulting in 220. We know that the last two numbers are both 10, so their sum is 10 plus 10, which equals 20.

To find the mean of all 32 numbers, we need to calculate the total sum by adding the sums of the three groups: 150, 220, and 20. This gives us a total sum of 390. Finally, we divide this sum by the total count of numbers, which is 32. Therefore, the mean of the 32 numbers is 390 divided by 32, which equals approximately 12.375.

In summary, by calculating the mean of the given groups of numbers and considering the last two numbers as 10, we find that the mean of all 32 numbers is approximately 12.375.

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Elise is correct in Part A, as the IQR is an appropriate measure of spread for data sets with a normal distribution. Lia is correct in Part B, as the standard deviation is a suitable measure of spread for data sets with a normal distribution.

In Part A, the data set provided (1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15) exhibits a normal distribution. For normally distributed data sets, the interquartile range (IQR) is a reliable measure of spread. The IQR measures the range between the 25th and 75th percentiles, capturing the middle 50% of the data. It is particularly useful for identifying the spread of data in the presence of outliers. In Part B, the data set (0, 10, 20, 25, 55, 60, 390) does not follow a normal distribution, as it contains an outlier (390) that significantly deviates from the other values. In such cases, the standard deviation is a more appropriate measure of spread. The standard deviation quantifies the average deviation of data points from the mean, providing a measure of how spread out the data is. It is suitable for both normally and non-normally distributed data sets, helping to assess the overall variability.

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The measure of the vertex angle is 92°

Here,

The triangle is isosceles and one base angle of an isosceles triangle has a measure of 44°

We have to find the measure of the vertex angle.

What is Isosceles triangle?

A triangle is said to be isosceles if there is any two corresponding sides are equal and there angle are equal.

Now,

The triangle is isosceles triangle.

Hence, there corresponding sides and there angles are equal.

So, Both base angles of a triangle are equal.

And, Sum of angles of a triangle are 180°

Let the measure of the vertex angle is x°

Hence,

⇒ 44° + 44° + x° = 180°

⇒ x° = 180° - 88°

⇒ x° = 92°

Therefore, The measure of the vertex angle is 92°

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Answer:

Earthquakes of this magnitude are very unlikely to trigger a tsunami.

Step-by-step explanation:

Although earthquake magnitude is one factor that affects tsunami generation, there are other important factors to consider. The earthquake must be a shallow marine event that displaces the seafloor. Thrust earthquakes (as opposed to strike slip) are far more likely to generate tsunamis, but small tsunamis have occurred in a few cases from large (i.e., > M8) strike-slip earthquakes.

Answer:

B

Step-by-step explanation:

took the assignment

The ellipse is obtained by slicing the cone at an angle. Then the correct option is B.

A shape made up of a surface and a round cone intersecting. A conic section is sometimes a circle, an ellipse, a parabola, or a hyperbola, based on the direction of the surface with regard to the conical.

The ellipse is obtained by slicing the cone at an angle that passes through the surface of the cone.

Then the correct option is B.

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Answer:

\( m \angle \: 3 = 94 \degree\)

Step-by-step explanation:

\(m \angle \: 3 + 86 \degree = 180 \degree \\(linear \: pair \: \angle s) \\ \\ m \angle \: 3 = 180 \degree - 86 \degree \\ \\ m \angle \: 3 = 94 \degree \\ \\ \)

The total number of apples, oranges, and tangerines in the fruit basket is in the ratio 10 or 10x

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.

We know that : the ratio of apples : oranges : tangerines = 3 : 2 : 5.

The total number of apples, oranges, and tangerines in the fruit basket is the total number of ratio, that is 3 + 2 + 5 = 10.

Because of the question is not contain information about the number of pieces, we can describe the dividend with x (or unknown value). So, the total number of apples, oranges, and tangerines in the fruit basket with ratio, that is 10 or 10x.

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The distance between the third traffic light from the second traffic light is 35 yards.

Three traffic lights on a street span 120 yards.

If the second traffic light is 85 yards away from the first.

Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.

This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.

Thus, the distance between the third traffic light from the second traffic light is 35 yards.

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Given,

out of 402 students 24%have attended a different school at some time before.

= 402×24

1 100

= 201×24

1 50

= 201×12

1 25

=2412

25

=96.48

Answer:

a)  26 tickets

b)  £5

c)  chips, pastie and a soft drink

Step-by-step explanation:

Given:

Part (a)

Greatest number of tickets = total available to spend ÷ cost of one ticket

                                             = 200 ÷ 7.5

                                             = 26.66666...

                                             = 26 tickets

(We can't round up, as 27 tickets would cost £202.50)

Part (b)

Money left = Total available spend - cost of 26 tickets

                  = 200 - (26 × 7.50)

                  = 200 - 195

                  = £5

Part (c)

Cost of 3 items = £10 - change

                         = £10 - £4.70

                         = £5.30

One of the items can't be a burger, as £5.30 - £3.50 = £1.80
and £1.80 is not enough to buy 2 items.

If he buys chips, he has: £5.30 - £2.40 = £2.90 left to spend on the other 2 items.

Pastie + Soft Drink = £1.60 + £1.30 = £2.90

So he can buy: chips, pastie and a soft drink

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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This is a table of values of three functions at selected values of x.

It is asking for h(f(-2))

Its saying, take f(-2), and take whatever you get from that and put it into h(x)

So, find f(-2).

Find x = -2, then see what f is there.

f(-2) = -1

So, find h(-1)

h(-1) = 0

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Answer:

1) 2           2) -5

Step-by-step explanation:

1.

It's positive 3 PLUS negative 1 which can be written as 3 - 1. That is 2.

2.

It's negative 3 PLUS negative 2 which can be written as -3 - 2. That is -5.

Answer:

1) 2

2) -5

Step-by-step explanation:

It's always a great idea to use a number line when you are solving problems like these. In the first problem we are starting at positive 3, so go to the number 3 on the number line. Then we are adding a negative 1, so we need to go back 1 on the number line. If we added a positive 1 we would need to go forward 1, but since this is a negative 1 we need to go backwards.

When you go back 1 from 3, you should get 2! Try this method for any other problem as well.