Consider the line segment defined by the points A(0, 1) and B(4,6). How does a


reflection across the x-axis affect AB?


Select all that apply.


A. The x-values of the reflection are the opposite values of the x-values of the


original segment.


B. The y-values of the endpoints become their opposites.


C• The length of the reflection of AB is greater than the length of AB.


DThe length of the reflection of AB is less than the length of AB.


E. The length of the reflection of AB is the same as the length of AB.

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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Answer:

8.2 times 5 is 41

Hello.

Just do a multiplication.

So, the amount of sugar used to make 5 cakes will be 41g.

Att. Isaiasdesign03

Moderator of Brainly BR

From the situation described in the problem, we have that:

a) The system of inequalities is given by: s + a ≤ 800, 4s + 7a ≥ 3400.

b) The solution is graphed at the end of the answer.

c) Yes, the club could meet it's goal.

A system of inequalities is when multiple variables are related in a described situation, and then inequalities are built to find the interval ranges of each variable, according to the relations built.

In the context of this problem, the variables are given as follows:

The auditorium has 800 seats, hence:

s + a ≤ 800.

They have a goal of making at least $3400, hence, considering the price of the tickets, we have that:

4s + 7a ≥ 3400.

The graphical solution of the inequality is given by the painted region on the graph, and since point (200, 475) is inside the region, the club could meet it's goal.

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Answer:

homedogxD: 74 + x + 62 + 55 = 180. So x = -11

Step-by-step explanation:

This is from homedogxD but no one put it as an answer so..................

Using differentiation and area of a rectangle, the dimensions of the poster with the smallest height are 24 cm x 216 cm.

Let x = width of printed material

Total width = printed material width + left margin + right margin

Total width = x + 8 + 8 = x + 16 cm

Total height = printed material height + top margin + bottom margin

Total height = 1536/x + 12 + 12 = 1536/x + 24 cm

The total area of the poster is the product of the width and height:

Total area = Total width * Total height

1536 = (x + 16) * (1536/x + 24)

To find the dimensions of the poster with the smallest height, we can find the minimum value of the total height. To do this, we can differentiate the equation with respect to x and set it to zero:

d(Total height)/dx = 0

Differentiating the equation and simplifying, we get:

1536/x² - 24 = 0

Rearranging the equation, we have:

1536/x² = 24

Solving for x, we find:

x² = 1536/24

x² = 64

x = 8 cm

Substituting this value back into the equations for total width and total height, we can find the dimensions of the poster:

Total width = x + 16 = 8 + 16 = 24 cm

Total height = 1536/x + 24 = 1536/8 + 24 = 192 + 24 = 216 cm

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Answer:

2 cm

Step-by-step explanation:

Answer:

the answer is 2cm

Step-by-step explanation:

Answer: 0.03

Step-by-step explanation:

Answer:

0.03

Step-by-step explanation:

\(\frac{25}{10}\)×\(\frac{12}{1000}\)=

\(\frac{300}{10000}\)=0.03

Answer:

The data table is attached below.

Step-by-step explanation:

The average of a set of data is the value that is a representative of the entire data set.

The formula to compute averages is:

\(\bar x=\frac{1}{n}\sum\limits^{n}_{i=1}{x_{i}}\)

Compute the average for drop 1 as follows:

\(\bar x_{1}=\frac{1}{3}\times[10+11+9]=10\)

Compute the average for drop 2 as follows:

\(\bar x_{2}=\frac{1}{3}\times[29+31+30]=30\)

Compute the average for drop 3 as follows:

\(\bar x_{3}=\frac{1}{3}\times[59+58+61]=59.33\)

Compute the average for drop 4 as follows:

\(\bar x_{4}=\frac{1}{3}\times[102+100+98]=100\)

Compute the average for drop 5 as follows:

\(\bar x_{5}=\frac{1}{3}\times[122+125+127]=124.67\)

The data table is attached below.

The average of the numbers in the data table will be 10, 30, 59.33, 100, and 124.67.

The average for drop 1 will be:

= 1/3 × (10 + 11 + 9)

= 10

The average for drop 2 will be:

= 1/3 × (29 + 31 + 30)

= 30

The average for drop 3 will be:

= 1/3 × (59 + 58 + 61)

= 59.33

The average for drop 4 will be:

= 1/3 × (102 + 100 + 98)

= 100

The average for drop 5 will be:

= 1/3 × (122 + 125 + 127)

= 124.67

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Answer:

D. x<=–7

Step-by-step explanation:

An open circle at the end of an interval means that the end point is not included in the interval, i.e. strictly less than or strictly greater than. A closed circle means the end point is included. Also to know is, what does an open circle mean?

To find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis, we can use the method of cylindrical shells.

First, let's determine the limits of integration. The region is bounded by x = 1 and x = 5, so our limits of integration will be from x = 1 to x = 5.

Next, we consider a small vertical strip at an arbitrary x-value within this interval. The height of the strip is given by the difference between the y-values of the two curves: y = 5/x and y = 0. Thus, the height of the strip is h = 5/x - 0 = 5/x.

The circumference of the strip is 2πr, where r is the x-value. Therefore, the circumference is 2πx.

Now, we can calculate the volume of the strip by multiplying the height, the circumference, and a small width dx. Hence, the volume of the strip is dV = 2πx * (5/x) * dx = 10π dx.

To find the total volume, we integrate the expression for dV from x = 1 to x = 5:

V = ∫(1 to 5) 10π dx.

Integrating, we get:

V = [10πx] (from 1 to 5)

= 10π(5 - 1)

= 40π.

Therefore, the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 5/x, y = 0, x = 1, and x = 5 about the x-axis is 40π cubic units.

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Answer:

1440

Step-by-step explanation:

hope this helps.......

Answer:

D.

Step-by-step explanation:

I took the test.

Answer:

answer d or chose 4

Step-by-step explanation:

i did unit test on edg.

The probability is P(a | b) = 0.5, P(b | a) = 0.1667, P(a' ∩ b') = 0.3, P(a' | b') = 0.375.

Using the formula for conditional probability, we have:

P(a | b) = P(a ∩ b) / P(b) = 0.1 / 0.2 = 0.5

P(b | a) = P(a ∩ b) / P(a) = 0.1 / 0.6 = 0.1667

P(a' ∩ b') = 1 - P(a ∪ b) = 1 - (P(a) + P(b) - P(a ∩ b)) = 1 - (0.6 + 0.2 - 0.1) = 0.3

P(a' | b') = P(a' ∩ b') / P(b') = 0.3 / 0.8 = 0.375

Therefore:

P(a | b) = 0.5

P(b | a) = 0.1667

P(a' ∩ b') = 0.3

P(a' | b') = 0.375

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Lydia earns $52.5 more than Gabrielle after 3 years.

percentage, a relative value indicating hundredth parts of any quantity.

we can use the formula for compound interest:

\(A = P(1 + r/n)^n^t\)

where A is the final amount,

P is the principal (initial investment),

r is the annual interest rate (as a decimal),

n is the number of times the interest is compounded per year, and

t is the number of years.

For Lydia (n=365)

A=1000(1+0.0525/365)¹⁰⁹⁵

A=1115.7

For Gabrille, we use the same formula but with n = 2 (compounded semi-annually):

A = 1000(1 + 0.0525/2)⁶

A = 1000(1.0265625)⁶

A = 1168.2

To find the difference in the amounts earned, we subtract Gabrielle's amount from Lydia's:

1168.2- 1115.7 = 52.5

Hence, Lydia earns $52.5 more than Gabrielle after 3 years.

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Answer: The slope is -5/7

Step-by-step explanation:

Slope is rise/run

The rise is -5, and the run is 7

This is why the slope is -5/7

Answer:

The rise is 6 and the run is 7 6/7

She could only solve 24 * 25 if the array has 24 rows and 25 columns or vice versa

From the question, we have the following parameters that can be used in our computation:

Product expression = 24 * 25

An array is a set of items that has rows and columns

The array is not given

However, the true statement is that: for Rosie to evaluate the expression using an array, then the array must be a 24 x 25 array or 25 x 24 array

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Answer:8

Step-by-step explanation:

We can expect 8 of the next 16 people to have black hair, based on the given information.

It is a branch of mathematics that deals with the occurrence of a random event.

Since 2 out of the total number of people who have already taken their seats at the seminar have black hair

we can assume that the probability of a person having black hair is 2 out of the total number of people who have taken their seats.

The probability of a person having black hair can be expressed as:

P(black hair) = 2/(2+2) = 1/2

This means that out of the total number of people who have already taken their seats, half of them have black hair.

If we assume that the next 16 people to take their seats are chosen randomly and independently from the population,

we can use the expected value formula to calculate the number of people with black hair we would expect among those 16 people:

Expected value = total number of people x probability of having black hair

Expected value = 16 x (1/2)

Expected value = 8

Therefore, we can expect 8 of the next 16 people to have black hair, based on the given information.

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Answer:

a) 83,b) -4,c) 48,d) 16,e) 8

Answer:

For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3).

Here using the length of square, it is obtained that

Annie walked 14 blocks in total.

What is a square?

Square is a two dimensional four sided figure.

Here,

Length of each side of one square = 1 block

From Annie's home to the supermarket, Annie will have to walk 1 block

From Supermarket to pet store, Annie will have to walk 1 block straight and then 2 blocks to the left

From pet store to the fruit vendor, Annie will have to walk 1 block straight and then 2 blocks to the left

Total number of blocks walked by Annie from home = 1 + 1 + 2+ 1 + 2

                                                                                        = 7 blocks

Total number of blocks walked by Annie while returning  home

                                                                                        = 1 + 1 + 2+ 1 + 2

                                                                                        = 7 blocks

Total number of blocks walked by Annie = 7 + 7 = 14 blocks

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Complete Question

The figure has been attached

Answer:

7 is the answer :> mark brainliest <3

the edges of a cube increase at a rate of 5 centimeters per second. The surface area is changing at a rate of 150 cm²/sec.

To calculate the rate at which the surface area of a cube is changing when each edge is 10 cm long, we first need to calculate the surface area of the cube. The surface area of a cube can be calculated by multiplying the length of one edge cubed by 6. In this case, the length of one edge is 10 cm, so the surface area of the cube is 600 cm². Since the edges of the cube are increasing at a rate of 5 cm/sec, the rate at which the surface area of the cube is changing is equal to the surface area multiplied by the rate of increase, or 600 cm² * 5 cm/sec = 300 cm²/sec.

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To calculate the present value of a zero-coupon bond, we can use the formula: Present Value = Future Value / (1 + Interest Rate)^n

where Future Value is the par value of the bond, Interest Rate is the annual market interest rate, and n is the number of years. In this case, the Future Value is $2,000, the Interest Rate is 10% (or 0.10), and the number of years is 5. Using Excel, we can calculate the present value as follows:
1. In cell A1, enter the Future Value: 2000
2. In cell A2, enter the Interest Rate: 0.10
3. In cell A3, enter the number of years: 5
4. In cell A4, enter the formula for calculating the present value: =A1 / (1 + A2)^A3
5. Press Enter to get the result.

The present value of the 5-year zero-coupon bond with a $2,000 par value and an annual market interest rate of 10% is $1,620.97.

The formula for present value calculates the current worth of a future amount by discounting it back to the present using the interest rate. In this case, the future value is $2,000, and we divide it by (1 + 0.10)^5 to account for the effect of compounding over 5 years. The result is the present value of $1,620.97, which represents the amount that is considered equivalent to receiving $2,000 in 5 years at a 10% interest rate.

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Answer:

4 hours

Step-by-step explanation:

2×6=3x

12÷3= 4

x=4 so 4 hours.

Answer:

540km/hr

Step-by-step explanation:

8.4km/min×60min/km

=8.4/60

=540km/hr

a. MRS = √(W/B)
b. Optimal bundle and total utility.
c. Adjusted income for constant utility.

a. The marginal rate of substitution (MRS) of walnuts for bananas is the rate at which you are willing to give up walnuts in exchange for one additional pound of bananas while keeping the utility constant. In this case, the MRS is equal to the ratio of the marginal utility of walnuts to the marginal utility of bananas. Since the utility function is U = √(W * B), the MRS can be calculated as MRS = √(W/B).

b. Using the Lagrangian approach, we can set up the following optimization problem: maximize U = √(W * B) subject to the constraint 2W + B = I, where W represents the pounds of walnuts, B represents the pounds of bananas, and I represents income. By solving the Lagrangian equation and the constraint, we can find the optimal consumption bundle and income level.

c. If the price of bananas doubles to $2 per pound, we need to determine the income required to maintain the same level of utility. With the new price, the constraint becomes 2W + 2B = I. By solving the Lagrangian equation again and substituting the new constraint, we can find the income level required to maintain the same level of utility.

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To find the surface area of the figure, we need to consider the individual surfaces and add them together.

First, let's identify the surfaces of the figure:

The lateral surface area of the larger prism (excluding the base)

The two bases of the larger prism

The lateral surface area of the smaller prism (excluding the base)

The two bases of the smaller prism

The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.

The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.

To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.

Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.

Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.

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