Median of 8, 10, 12, 14

Answer: The slope of the line passing through the points (-3, 5) and (4, -1) is -6/7.

Step-by-step explanation:   To find the slope of a line given two points, you can use the formula:

slope = (y2 - y1) / (x2 - x1)

Using the points (-3, 5) and (4, -1), we can substitute the values into the formula:

slope = (-1 - 5) / (4 - (-3))

= (-6) / (4 + 3)

= (-6) / 7

Therefore, the slope of the line passing through the points (-3, 5) and (4, -1) is -6/7.

Answer:  

\(Slope=-\frac{6}{7}\)

Step-by-step explanation:

\(m= \frac{y2-y1}{x2-x1} \\\\m=\frac{-1-5}{4-(-3)} \\\\m=\frac{-6}{7} \\\\Slope= -\frac{6}{7}\)

The probability that this batter will hit a home run on this pitcher's next pitch is approximately 0.074, or 7.4%.

To determine the probability that the batter will hit a home run on the pitcher's next pitch,

we need to consider the probabilities of the pitcher throwing a fastball and a curveball, as well as the probabilities of hitting a home run on each type of pitch.

Given that the pitcher throws fastballs 80% of the time and curveballs 20% of the time, we can calculate the probability of the batter facing each type of pitch:

- Probability of facing a fastball = 80% = 0.8
- Probability of facing a curveball = 20% = 0.2

Now, we need to determine the probability of hitting a home run on each type of pitch:

- Probability of hitting a home run on a fastball = 8% = 0.08
- Probability of hitting a home run on a curveball = 5% = 0.05

To find the overall probability of hitting a home run on the pitcher's next pitch, we can use the following formula:

Overall probability = (Probability of facing a fastball * Probability of hitting a home run on a fastball) + (Probability of facing a curveball * Probability of hitting a home run on a curveball)

Plugging in the values we have:

Overall probability = (0.8 * 0.08) + (0.2 * 0.05)
Overall probability = 0.064 + 0.01
Overall probability = 0.074

Therefore, the probability that this batter will hit a home run on this pitcher's next pitch is approximately 0.074, or 7.4%.

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The actual nominal rate of return is approximately 6.68%. None of the provided answer options exactly match this value, but the closest option is 6.77%.

To calculate the actual nominal rate of return, we use the Fisher equation:

Nominal Rate = (1 + Real Rate) * (1 + Inflation Rate) - 1

Given:

Real Rate = 3.87% (0.0387 as a decimal)

Inflation Rate = 2.75% (0.0275 as a decimal)

Now, let's plug in the values:

Nominal Rate = (1 + 0.0387) * (1 + 0.0275) - 1

Nominal Rate = 1.0387 * 1.0275 - 1

Nominal Rate = 1.0668 - 1

Nominal Rate = 0.0668 or 6.68% (rounded to two decimal places)

So, the actual nominal rate of return is approximately 6.68%. None of the provided answer options exactly match this value, but the closest option is 6.77%.

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The cost of  each piece of trim is $1.63

To find the cost of one piece of trim, we can use the unitary method, which involves dividing the total cost by the number of pieces. In this case, we can use the following formula

Cost of one piece of trim = Total cost / Number of pieces

We know that Kevin bought 4 pieces of trim for a total of $6.52, so we can substitute these values into the formula

Cost of one piece of trim = $6.52 / 4

Simplifying this expression, we get

Cost of one piece of trim = $ 1.63

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The probability is approximately 0.000008155 or 0.0008155%.

To compute the probability of winning the million-dollar prize in the lottery, we need to determine the number of favorable outcomes (matching all six numbers) and the total number of possible outcomes.

The number of favorable outcomes is 1 because there is only one combination of six numbers that matches the numbers on your ticket.

The total number of possible outcomes can be calculated using the formula for combinations. Since there are 48 balls in the machine and 6 balls are drawn, the total number of possible outcomes is given by:

C(48, 6) = 48! / (6!(48-6)!) = 48! / (6!42!) = 12271512

Therefore, the probability of winning the million-dollar prize with a single lottery ticket is:

P(win) = favorable outcomes / total outcomes = 1 / 12271512 ≈ 0.00000008155

The complete question is:

In a certain lottery, 48 balls numbered 1 through 48 are placed in a machine and six of them are drawn at random. If the six numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. If in this lottery, the order the numbers are drawn in does matter, compute the probability that you win themillion-dollar prize if you purchase a single lottery ticket.

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Answer:

(-6,0) and (3,0)

Step-by-step explanation:

This function has two x intercepts: (-6,0) and (3,0)

Answer:

(- 6, 0) and (3, 0)

Step-by-step explanation:

Whenever a question mentions the x-intercept, the y intercept is 0 and vice versa.

Now, putting the equation equal to 0, we get:

= x + 6 = 0 and x - 3 = 0

= x = - 6 and x = 3

So the point is (- 6, 0) and (3, 0)

Hope this helps, and please mark me brainliest if it does!

Answer:

C) Y > -7

-Y < 7        given

0 < 7 + Y       add Y to both sides

-7 < Y            subtract 7 from both sides

The particular antiderivative that satisfies the given condition is: C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000

To find the particular antiderivative (or integral) of the given derivative \(C''(x) = 4x^2 - 3x\)  that satisfies the condition C(0) = 2000, we need to integrate the given function twice.

First, we integrate C''(x) to find C'(x):

\(C'(x) = ∫ (4x^2 - 3x) dx\)

To find the antiderivative of \(4x^2\), we use the power rule for integration: the power of x increases by 1 and is divided by the new power. Similarly, the antiderivative of -3x is \(-(3/2)x^2\).

\(C'(x) = ∫ (4x^2 - 3x) dx = (4/3)x^3 - (3/2)x^2 + K1\)

Here, K1 is the constant of integration. Next, we integrate C'(x) to find C(x):

\(C(x) = ∫ (C'(x)) dx = ∫ ((4/3)x^3 - (3/2)x^2 + K1) dx\)

To find the antiderivative of \((4/3)x^3\), we again use the power rule for integration. Similarly, the antiderivative of \(-(3/2)x^2\) is \(-(3/2)(1/3)x^3\).

The constant of integration K1 will also be integrated with respect to x, resulting in another constant of integration, K2.

\(C(x) = (1/3)(4/3)x^4 - (1/2)(3/2)x^3 + K1x + K2\)

Simplifying further, we have:

\(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + K2\)

Now, we can apply the initial condition C(0) = 2000 to find the particular solution for K2:

\(C(0) = (4/9)(0)^4 - (9/8)(0)^3 + K1(0) + K2 = 2000\)

Since all the terms involving x become zero when x = 0, we have:

K2 = 2000

Therefore, the particular antiderivative that satisfies the given condition is: \(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000\)

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Pattern: The pattern is to start with the number 2 and repeatedly multiply each number by 2 and then add 1 until we have a sequence of 5 numbers.

Start with the number 2.

Multiply the starting number by 2: 2 * 2 = 4.

Add 1 to the result from step 2: 4 + 1 = 5. We now have the first number in our sequence.

Multiply the previous number (5) by 2: 5 * 2 = 10.

Add 1 to the result from step 4: 10 + 1 = 11. We now have the second number in our sequence.

Repeat the process: multiply the previous number by 2 and then add 1.

Multiply the previous number (11) by 2: 11 * 2 = 22.

Add 1 to the result from step 6: 22 + 1 = 23. We now have the third number.

Repeat steps 6 and 7 two more times to obtain the fourth and fifth numbers:

Fourth number: (23 * 2) + 1 = 47.

Fifth number: (47 * 2) + 1 = 95.

Thus, the pattern generates the sequence: 2, 5, 11, 23, 47, 95.

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Answer:

.066 = 6.6 percent chance

Step-by-step explanation:

1 in 5 chance to get 6, so that is .20 multiply .20 and .33 and you get .066

Answer:

  (c)  x² -64

Step-by-step explanation:

The factoring of the difference of squares is one of the special forms we use in the study of polynomials. It tells you ...

  a² -b² = (a +b)(a -b)

__

You have a factor (x +8), so a=x, b=8, and the "expanded" form is ...

  a² -b² = x² -8² = x² -64

Answer:

x^2-64

Step-by-step explanation:

just did the test

Answer:

Below in bold.

Step-by-step explanation:

81^2/3

= 81^2 = 6561

6561^1/3

= ∛(6561)

= 18.72

√18.72

= 4.33 to nearest hundredth.

Answer:

Your equation would be:
(x + 6)² + (y - 5)² = 29

Step-by-step explanation:

Have a great rest of your day
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Step-by-step explanation:

\( \sqrt{} 4(m - 1) ^{2} = \sqrt{} 4 \)

Answer:

4(m-1)^2=4

(2(m-1))^2=2^2

2(m-1)=2

2m-2=2

2m=4

m=2

Answer:

n = 4.

Step-by-step explanation:

-3(n + 2) - 5 = -23

Distribute the -3.

-3n - 6 - 5 = -23

Combine like terms.

-3n - 11 = -23

Add 11 to both sides.

-3n = -12

Divide both sides by -3.

n = 4

Single Sampling Plan: AQL = 0, LTPD = 3.41, AOQ = 1.79 Double Sampling Plan: AQL = 0, LTPD = 2.72, AOQ = 1.48

The values for the ASN (Average Sample Number) curves for the given single sampling plan and double sampling plan are:

Single Sampling Plan (n=80, c=3):

ASN curve values: AQL = 0, LTPD = 3.41, AOQ = 1.79

Double Sampling Plan (n1=50, c1=1, r1=4, n2=50, c2=4, r2):

ASN curve values: AQL = 0, LTPD = 2.72, AOQ = 1.48

The ASN curves provide information about the performance of a sampling plan by plotting the average sample number (ASN) against various acceptance quality levels (AQL). The AQL represents the maximum acceptable defect rate, while the LTPD (Lot Tolerance Percent Defective) represents the maximum defect rate that the consumer is willing to tolerate.

For the single sampling plan, the values n=80 (sample size) and c=3 (acceptance number) are used to calculate the ASN curve. The AQL is 0, meaning no defects are allowed, while the LTPD is 3.41. The Average Outgoing Quality (AOQ) is 1.79, representing the average quality level of outgoing lots.

For the equally effective double sampling plan, the values n1=50, c1=1, r1=4, n2=50, c2=4, and r2 are used. The AQL and LTPD values are the same as in the single sampling plan. The AOQ is 1.48, indicating the average quality level of outgoing lots in this double sampling plan.

These ASN curve values provide insights into the expected performance of the sampling plans in terms of lot acceptance and outgoing quality.

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Answer:

the answer is roational symmetry.

Step-by-step explanation:

Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

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We will use the first principle of differentiation, to prove the function.

y = f(x) with respect to its variable x. If this limit exists and is finite, then we say that: Wherever the limit exists is defined to be the derivative of f at x.

Given function cosec x

d(cscx)dx = d(1/sinx)dx

= limh→0 1/sin(x+h)-1/sinx / (x+h)-x

= limh→0 sinx - sin(x + h)/sinxsin(x + h) /h

= limh→0 sinx - sin(x + h) / h sinx sin(x + h)

= limh→0 -(sin(x + h) - sinx)/h sinx sin(x + h)

= limh→0 - (sin(x + h) - sinx)h × 1/limh→0 sinx sin(x + h)

= -cosx × 1/sin2x

= -cosx/sinx × 1/sinx

= -cotx cscx

Therefore, proved the derivative of cosec x to be -cot x cosec x using the first principle of differentiation.

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The system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

Given that,  Six of the orchestra's 111 musicians hold driving licenses for big, multi-passenger vehicles. 25 people can fit on a bus, but renting one is far more expensive. 12 persons can fit in a passenger van.

The system of equations to find the smallest number of busses the orchestra can rent is,

The total number of buses :

b + v ≤ 6

The total number of passengers.

25b + 12v ≥ 111 - - - - (2)

Thus, the system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.

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Answer:

2(13+36) = 98

Answer:

P= side a*2+ side b*2

= 13*2 + 36*2

= 26+72

= 98 cm

The coordinates of the vertex of the quadratic functions are (-10, 0)

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.

Given is a quadratic function, y = (x+10)², we need to find the vertex coordinates,

y = (x+10)²

y = x²+100+20x

For x coordinate,

x = -b/2a

x = -20/2

x = -10

Put x = -10 in equation, to find the y coordinate,

y = (-10+10)²

y = 0

The coordinates are (-10, 0)

Hence, the coordinates of the vertex of the quadratic functions are (-10, 0)

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The equations that can be used to solve for y , the length of the room are , y² – 5y = 750     ,   750 - y(y-5) = 0 and (y+25)(y-30)=0  , the correct options are (b) , (c) and (e) .  .

In the question ,

it is given that

the area of the rectangular room is 750 square feet ,

and the width of the room is 5 feet less than the length of the room .

let the length of the room be "y" feet .

so , the width of the room become "y-5" feet .

So , the area of the rectangular room = 750 square feet

we know that area of rectangle = length\(\times\)width

So, on substituting the values i   the area formula ,

we get

750 = y * (y-5)        

750 - y(y-5) = 0      ...(2)

750 - y²+5y = 0

y² - 5y -750 =0           ....(1)

y² +25y -30y -750 = 0

y(y+25)-30(y+25)=0

(y+25)(y-30)=0   ....(3)

From equation (1), (2) , (3) , we can conclude that

the equations to solve y are  750 = y * (y-5)    ,   750 - y(y-5) = 0 and (y+25)(y-30)=0  .

Therefore , The equations that can be used to solve for y , the length of the room are , y² – 5y = 750     ,   750 - y(y-5) = 0 and (y+25)(y-30)=0  , the correct options are (b) , (c) and (e) .

The given question is incomplete , the complete question is

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.

(a) y(y + 5) = 750

(b) y² – 5y = 750

(c) 750 – y(y – 5) = 0

(d) y(y – 5) + 750 = 0

(e) (y + 25)(y – 30) = 0

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The algebraic expression of the statement given as the difference of 27 and 5​ is 27 - 5

The statement is given as:

the difference of 27 and 5​

Difference means minus.

The minus sign is represented as -

This means that the statement given as: the difference of 27 and 5​

Can be represented as

27 minus 5

So, have

27 - 5

Hence, the algebraic expression of the statement given as the difference of 27 and 5​ is 27 - 5

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Answer:

John has a sheet of paper that is 8 feet long. He cuts the length of paper into eighths, and then cuts the length of each of these \(\frac{1}{8}\) pieces into fourths. How many pieces does he have? How many inches long is each piece?

Step-by-step explanation:

The height of Jeremy is 159 cm.

To find the height of Jeremy:

So,

Then, Jeremy = 135 + 24 = 159 cm.

Therefore, the height of Jeremy is 159 cm.

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Answer:

y=mx+b is the equation for a line, x and y being coordinates, m as your slope and b as your y intercept. Slope is rise over run.

Step-by-step explanation:

According to the conversation we can infer that the information focused on the conversation of two people; one of them is studing for an exam.

To identify what is the conversation about we have to consider who is talking and what are the ideas that they share. In this case, we can infer that the main idea of this conversation is that one of them is studying for an exam this week.

Also, the second person is apologizing because he considered that he is distracting the other person. So, the correc information about de conversation is a short conversation about study.

Note: This question is incomplete. Here is the complete information:

Conversation:
Hello

Hello, How are you?

I am fine, and you?

i am fine too, What are you doing?

I am studing for an exam this week.

Oh, sorry I won´t distract you.

Don´t worry.

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Answer:

x² + y² = 34

Formula:

Here find the radius using distance formula:                → origin : (0, 0)

Thus the equation of circle:

Answer:

H.  \(x^2+y^2=34\)

Step-by-step explanation:

Equation of a circle (in standard form)

\((x-h)^2+(y-k)^2=r^2\)

(where (h, k) is the center and r is the radius of the circle)

Given center = (0, 0):

\(\implies (x-0)^2+(y-0)^2=r^2\)

\(\implies x^2+y^2=r^2\)

As the circle passes through point (3, 5):

\(\implies 3^2+5^2=r^2\)

\(\implies r^2=34\)

Final equation

\(x^2+y^2=34\)