find the slope of the line that passes through points.
(3,5) and (7,2)

Answer:

8.1 miles

Step-by-step explanation:

You have to divide

The probability that the student chosen will be a boy who watched tennis yesterday is 1/8.

Given that 56 students were asked if they watched tennis yesterday, 20 of the students are boys, 17 girls watched tennis yesterday and 32 students did not watch tennis yesterday and out of all these one students is to be chosen at random.

We have to find the probability that the student chosen will be a boy who watched tennis yesterday.

Total number of students is 56.

The total number of girls is 56-20=36

Girls who didn't watch tennis is 36-17=19

Number of the boys who did not watch the game is 32-19=13

Number of boys watching a tennis match is 20-13=7

Now, we will find the probability that the student chosen will be a boy who watched tennis yesterday.

Probability=Number of boys watching a tennis match/Total number of students
Probability=7/56

Probability=1/8

Hence, the probability that the student chosen will be a boy who watched tennis yesterday when 56 students were asked if they watched tennis yesterday is 1/8.

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Step-by-step explanation:

Therefore, the equation that represents line AB is y + 4 = x, which is the fourth option: y + 4 = x - 2.

Answer:

576/18 = 32 miles per gallon

Step-by-step explanation:

For a data set, half of the observations are always greater than the median. The median is the middle value in a set of data when it is arranged in order of increasing or decreasing magnitude.

It is a measure of central tendency that is more robust to outliers than the mean. The median splits the data set in half, with half of the observations being greater than it and half being less than it.

The median is a crucial measure of central tendency that helps us understand the distribution of a data set. It represents the value that separates the top half of the data from the bottom half. The median is often used as an alternative to the mean when the data set contains outliers or extreme values that can skew the mean. The median is easy to calculate and provides a clear picture of the middle of a data set. Therefore, it is a useful tool for statisticians, researchers, and analysts who need to summarize and describe data sets accurately.

In summary, the median is the value that divides a data set into two equal halves, with half of the observations being greater than it and half being less than it. It is a robust measure of central tendency that is widely used in statistics to describe the distribution of data sets.

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To determine the minimum thickness of the iron, we need to calculate the diffusion flux of hydrogen through the iron and equate it to the maximum allowed hydrogen loss.

The diffusion flux (J) of hydrogen through a material can be calculated using Fick's first law of diffusion:

J = -D * (∆C/∆x)

Where:

J is the diffusion flux

D is the diffusion coefficient of hydrogen in iron

∆C is the difference in hydrogen concentration across the thickness (∆C = C1 - C2)

∆x is the thickness of the iron

We are given:

Maximum allowed hydrogen loss = 50 g/cm²/year

Temperature (T) = 400 °C (673 K)

Hydrogen concentration at surface 1 (C1) = 0.05 H atom per unit cell

Hydrogen concentration at surface 2 (C2) = 0.001 H atom per unit cell

First, we need to convert the hydrogen concentrations into a common unit. The atomic mass of hydrogen (H) is approximately 1 g/mol. The number of atoms in a unit cell for BCC iron is 2.

Concentration in g/cm³:

C1 = (0.05 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.025 g/cm³

C2 = (0.001 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.0005 g/cm³

Now, we can calculate the difference in hydrogen concentration across the thickness:

∆C = C1 - C2 = 0.025 g/cm³ - 0.0005 g/cm³ = 0.0245 g/cm³

Next, we need to determine the diffusion coefficient of hydrogen in iron at 400 °C. The diffusion coefficient can be estimated using the following equation:

D = D0 * exp(-Q/RT)

Where:

D0 is the pre-exponential factor

Q is the activation energy for diffusion

R is the gas constant (8.314 J/(mol·K))

T is the temperature in Kelvin

For hydrogen diffusion in iron, typical values are:

D0 = 5 x 10^-7 cm²/s

Q = 40,000 J/mol

Plugging in the values:

D = (5 x 10^-7 cm²/s) * exp(-40000 J/mol / (8.314 J/(mol·K) * 673 K))

D ≈ 2.70 x 10^-12 cm²/s

Now, we can substitute the values into Fick's first law of diffusion and solve for the thickness (∆x):

J = -D * (∆C/∆x)

Rearranging the equation:

∆x = -D * (∆C/J)

Substituting the given values:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year))

Converting the year unit to seconds:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year)) * (1 year / 3.1536 x 10^7 s)

Calculating:

∆x ≈ -0.000347 cm ≈ 3.47 μm

The negative sign indicates that the thickness (∆x) is measured in the opposite direction of the hydrogen diffusion. Thus, the minimum thickness of the iron required to limit the hydrogen loss to no more than 50 g per year through each square cent.

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Answer:

15 cm

Step-by-step explanation:

Use the definition of the area of a square:

\(A=s^2\)

Where s is the side of the square.

Replace the known value in:

\(225 cm^2=s^2\\15cm=s\)

Step-by-step explanation:

Work out 32 as a product of prime factors in index form

First find out the factor for 32

32 can be break into 16 times 2

16 can be break into 8 times 2

8 can be break into 4 times 2

4 can be break into 2 times 2

So, 32 can be written as

\(32=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2\\32=2^5\)

Answer:

The index form of the 32 is

\(2^5\)

Answer:

The answer is x = \(\frac{-5}{3}\).

Step-by-step explanation:

First, we expand the brackets. Therefore:

\(2x+6 = -4x+(-4)\)

\(2x+6 = -4x -4\)

Then, we separate the like terms:

\(2x+4x = -4-6\)

Then we add the like terms up and solve for x:

\(6x = -10\)

Therefore:

\(x = \frac{-10}{6}\)

which, simplified, is:

\(x = \frac{-5}{3}\).

The probability of event A given event B, denoted as P(A | B), is 0.750. The probability of event B given event A, denoted as P(B | A), is 0.900. A and B are not independent events because the conditional probabilities P(A | B) and P(B | A) are not equal to the marginal probabilities P(A) and P(B), respectively.

To find P(A | B), we use the formula:

P(A | B) = P(A ∩ B) / P(B)

In this case, P(A ∩ B) = 0.45 and P(B) = 0.60.

Plugging these values into the formula, we get

P(A | B) = 0.45 / 0.60 = 0.750.

To find P(B | A), we use the formula:

P(B | A) = P(A ∩ B) / P(A)

Here, P(A ∩ B) = 0.45 and P(A) = 0.50.

Substituting the values, we find

P(B | A) = 0.45 / 0.50 = 0.900.

A and B are not independent because the probabilities of A and B are affected by each other. If A and B were independent, then P(A | B) would be equal to P(A), and P(B | A) would be equal to P(B). However, in this case, both P(A | B) and P(B | A) differ from their respective marginal probabilities. Therefore, A and B are dependent events.

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Answer:

The answer is graph D since y int = 3(1)+4 which is 7, that graph crosses y at 7

Answer:

She needs to order 12 cars

Step-by-step explanation:

To find the total number of models, we just need to multiply the number of options for each choice:

body style: 2 options

interior package: 3 options

drive train: 2 options

So the number of different models is:

2 * 3 * 2 = 12 different models

So in order to have all the possible models, she needs to order 12 cars.

it is 1000 because 2 x 5 =10 then just add the extra 2 0s from 20 and 50

Answer:

1,000

Step-by-step explanation:

The specific form of the function G(t) and the limits of integration would depend on the available data or assumptions about gas consumption during the specified months.

To express the average monthly U.S. gas consumption during the part of the year between the beginning of April and the end of September, we can set up an integral to calculate the average value of a function over a specific interval.

Let's denote the gas consumption as a function of time, G(t), where t represents the months from April to September. We'll integrate this function over the interval [April, September] to find the average gas consumption.

The integral that represents the average monthly U.S. gas consumption is:

(1 / (September - April)) ∫[April, September] G(t) dt

In this integral, G(t) represents the gas consumption in a given month, and the integration is taken over the interval from April to September. The average gas consumption is obtained by dividing the integral by the length of the interval (September - April).

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Answer:

y=9

Step-by-step explanation:

im a little confused on what u need help with is that not the answer?

Answer:

∠ 2 = 40°

Step-by-step explanation:

∠ 1 and ∠ 2 are corresponding angles and congruent, thus

∠ 2 = ∠ 1 = 40°

The key features of the polynomials are the vertex, axis of symmetry, x and y intercepts.

1. The degree will help you to find the end behaviour.

2. The vertex shows you where it changes concavity.

3. X and Y intercepts give you a couple of points of reference

4. Axis of symmetry is only applicable to even degree polynomials

Answer:

a) -900 L/min

b) 63000 L

c)  -900t +63000

 d) 7200 L

Step-by-step explanation:

a) You are given two points on the curve of volume vs. time:

(t, V) = (20, 45000) and (70, 0)

The rate of change of volume

= ΔV/Δt = (0 -45000)/(70 -20) = -45000/50 = -900 liters per minute

b) In the first 20 minutes, the change in volume was

(20 min)(-900 L/min) = -18000 L

So, the initial volume was

initial volume - 18000 = 45000

initial volume = 63,000 liters

c) Since we have the slope and the intercept, we can write the equation in slope-intercept form as

 V= -900t +63000.

d) now putting the number in the equation and do the arithmetic.

When t=62, the amount remaining is

= -900(62) +63000 = -55800 +63000 = 7200

Thus, 7200 L remain after 62 minutes.

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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The correct statements are:

There are four ways to choose the committee.

There are three ways to form the committee if person D must be on it.

If persons B and C must be on the committee, there are two ways to form the committee.

It is given that:

A membership committee of three is formed from four eligible members.

1)

There are four ways to choose the committee.

This statement is true.

since we have to choose 3 members out of the 4 members so we can use the method of combination.

2)

There are three ways to form the committee if person D must be on it.

This statement is also true.

since D has to be in the committee, this means we have to choose 2 more people out of the three people to form the committee.

3)

If seven members are eligible next year, then there will be fewer combinations.

This statement is wrong.

Since we have to choose 3 members out of 7 members so the number of possible combinations will be:

i.e. there are 35 combinations possible.

4)

If persons B and C must be on the committee, there are two ways to form the committee.

if B and C have to be in the committee then we have to choose just one person out of the two people left.

Hence, the statement is true.

5)

If persons A and C must be on the committee, then there is only one way to form the committee.

If A and C have to be in the committee then as in last option we have to choose any one of the two person left.

so possible number of ways are 2.

Hence, the statement is false.

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A back tangent with bearing n 24° w meets a forward tangent with a bearing s 79° w. what is the intersection angle. The intersection angle between the back tangent and forward tangent is 175°.

To find the intersection angle between a back tangent with a bearing of N 24° W and a forward tangent with a bearing of S 79° W, we can subtract the two bearings.
First, let's convert the bearings to a common reference. We'll use the North reference.
The bearing N 24° W can be converted to a bearing of N 336°.
The bearing S 79° W can be converted to a bearing of N 161°.
To find the intersection angle, we subtract the two bearings:
336° - 161° = 175°.
Therefore, the intersection angle between the back tangent and forward tangent is 175°.

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Answer:

Slope:  

3 /5

y-intercept:  

− 6

Step-by-step explanation:

Answer:

x = 17°

m∠MKL = 116°

m∠JKL = 159°

Step-by-step explanation:

JKM = 43

MKL = 8x - 20

JKL = 10x - 11

Since JKL is the whole angle, JKM + MKL = JKL

43 + 8x - 20 = 10x - 11

Add 20 to both sides:

43 + 8x = 10x + 9

Subtract 8x from both sides:

43 = 2x + 9

Subtract 9 from both sides:

34 = 2x

x = 17°

MKL = 8(17) - 20

MKL = 116°

JKL = 10(17) - 11

JKL = 159°

And to check 159 - 116 = 43

If my answer is incorrect, pls correct me!

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-Chetan K

The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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The final answers are as follows gross profit $321,600, cost of goods sold of $528,000 and balance due $782,980.

(a) The terms of the sale are 3/10, n/30 which means that if Cullumber Company pays the invoice within 10 days, they will receive a 3% discount on the total invoice amount. However, if they pay within 30 days, they will not receive a discount.

To calculate the amount due if Cullumber Company takes the discount:

$914,000 x 3/100 = $27,420

$914,000 - $27,420 = $886,580

To calculate the gross profit:

$914,000 - $592,400 = $321,600

(b) The return of merchandise means that Cullumber Company is returning $104,600 worth of merchandise and thus the amount due to Marin will be:

$886,580 - $104,600 = $782,980

And the cost of goods sold will be:

$592,400 - $64,400 = $528,000

(c) On March 12, Marin Company received the balance due from Cullumber Company which is $782,980.

This means that the net amount received by Marin Company after the discount and return of merchandise is $782,980.

Therefore, The final answers are as follows gross profit $321,600, cost of goods sold of $528,000 and balance due $782,980.

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Hey! 2 to the power of 5 is 2 x 2 x 2 x 2 x 2 which equals 32.

Answer:

\(2^{5\\}\) so basically 2x2x2x2x2 so 32

Step-by-step explanation:

Based on the triangle midpoint theorem, the statement which must be shown is that: B. the length of GH is half the length of KL.

Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.

Based on the triangle midpoint theorem, we can infer and logically deduce that the statement which must be shown is that the length of GH is half the length of KL.

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Answer:  B. The length of GH is half the length of KL.

Step-by-step explanation:   TRUST ME!  The answer is correct on Edge.  :)

Answer:

NEED HELP

Step-by-step explanation:

I DON'T KNOW?