Triangle PQR has vertices P(-2, 6), Q(-8, 4) and R(1, -2). It is translated according to the rule (x, y)—> (x, - 2, y -16).
What is the y-value of P’?

a. -18

b. -16

c. -12

d. -10

Answer:

$172.75 is the amount Ahmed has

The probability that of 5 people hired, exactly 2 are from New Jersey is 0.3857.

Given: A company in New Jersey is hiring 5 people for a position. Of the applicants, 7 are from New Jersey, 8 are from New York, and 5 are from Pennsylvania.

The probability formula is given by:

P(E) = n(E)/n(S),

whereP(E) = Probability of Event, n(E) = Number of favorable outcomes, n(S) = Total number of outcomes

Total number of applicants = 7+8+5=20

Number of applicants hired = 5

Since the number of applicants hired is unknown, we will use a combination to solve it.

Exactly 2 are from New Jersey, and 3 from New York and Pennsylvania.

Using the combination, we get 7C2 ways to select two candidates from New Jersey and 13C3 ways to select three candidates from New York and Pennsylvania.

Using the multiplication principle of counting, we get that the total number of favorable outcomes is:

7C2 × 13C3

= (7 × 6)/2! × (13 × 12 × 11)/3!

= 210 × 286

= 60060

Therefore, the probability of exactly 2 people being from New Jersey is:

P = (number of favorable outcomes)/(total outcomes)

P = 60060/15504P

= 0.3857 (approx)

Therefore, the probability that of the 5 people hired, exactly 2 are from New Jersey is 0.3857.

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The dimensions of the tank with minimum  weight  is height= 7 and width and length= 14.

The minimum surface area implies that the tank has minimum weight.

Given that the base is square, its width is equal to its length.

Let x= the base width and length of the tank.

Let h = the height .

We are given the volume of the tank that is 1372 ft^3. The formula is given by

V = hx^2

We're given that V = 1,372 ft^3, so

hx^2 = 1,372

h = 1,372 / x^2  ----------(equation 1)

Surface area can be calculated using the below given formula.

A = x^2 + 4xh

Substituting the value of euation 1, h in A, we get,

A = x^2 + 4x(1,372 / x^2)

= x^2 + 5,488 / x

To get the minimum surface area to get the minimum weight, we need to differentiate  A with respect to x and equate it to zero.

dA/dx = 2x - 5,488 / x^2 = 0

2x^3 - 5,488 = 0

x =\(\sqrt[3]{\frac{5,488}{2} }\)

x= 14

We got the value of x, we substitute the value in equation 1, we get the value of h.

h = 1,372 / 14^2

h= 7

So, the dimensions of the tank with minimum weight are width and length is 14 and height is 7.

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There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

Answer:

(-2,1)

Step-by-step explanation:

Substitute the value of y (x+3) from one equation into the second equation (2x+5)

X+3 = 2x + 5

add -2x to both sides

-x+3=5

add -3 to both sides

-x=2

x=-2

substitute -2 for x in either equation to find y.

y=-2+3

y=1

Check your answer by substituting x and y into either equat to make sure it equals.

y=x+3

1=-2+3

1=1

or

y=2x+5

1=2(-2)+5

1=-4+5

1=1

To obtain Carol's formula for the number of stones needed per set, we simply multiply the binomial formed in part d of task 1 by s. The resulting formula is:

3s^3 + 6s^2 + 3s for the 3 × 3 picture frames

4s^3 + 6s^2 + 2s for the 4 × 4 picture frames

5s^3 + 6s^2 + s for the 5 × 5 picture frames

In part d of task 1, we obtained the binomial expressions for the number of stones needed to cover each picture frame size. To obtain the total number of stones needed for a set, we simply multiply the number of picture frames in the set by the number of stones needed per picture frame.

In this case, the gift shop wants to sell the picture frames in sets of 3, 4, and 5 for the 3 × 3, 4 × 4, and 5 × 5 picture frames, respectively. Thus, we can multiply the binomials obtained in part d of task 1 by s to obtain the formulas for the number of stones needed per set for each picture frame size.

This will give us the total number of stones needed to cover all the picture frames in each set.

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An outlier in a small sample size can have a significant effect on a confidence interval. It can cause the interval to widen, leading to increased uncertainty and decreased precision in estimating the population parameter.

Confidence intervals are statistical ranges used to estimate population parameters based on sample data. In small sample sizes, each data point has a greater impact on the overall result.

An outlier, which is a data point significantly different from the rest of the sample, can distort the calculations used to construct the confidence interval. Since the interval aims to capture the true population parameter with a specified level of confidence, the presence of an outlier can lead to increased variability in the data.

As a result, the confidence interval may need to be widened to account for the potential influence of the outlier, reducing the precision and increasing the uncertainty in estimating the parameter. Therefore, outliers can have a notable effect on confidence intervals based on small sample sizes.

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The correct interpretation is that there is a 99% chance that the true mean number of home fires started by candles each year is between 4785 and 9297.9.

The correct statistical interpretation for the given scenario is:

There is a 99% chance that 4785 < µ < 9297.9 contains the true mean number of home fires started by candles each year.

This statement reflects the interpretation of a confidence interval. A confidence interval provides a range of values within which the true population parameter (in this case, the mean number of home fires started by candles each year) is likely to fall with a certain level of confidence (in this case, 99%).

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This statement is true, as the test statistic represents the number of standard deviations between the observed sample proportion and the claimed value (po) under the null hypothesis.

- The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. This statement is false. A large test statistic implies that the observed data is surprising when the null hypothesis is true, which means there is evidence against the null hypothesis.
- The researcher should fail to reject the null hypothesis. This statement is false. A large test statistic suggests evidence against the null hypothesis, so the researcher should reject the null hypothesis in favor of the alternative hypothesis.

- When the null hypothesis is true, the test statistic comes from a standard normal distribution. This statement is true, as the test statistic follows a standard normal distribution when the null hypothesis is true.
- There is a 4.318% chance that the alternative hypothesis is true. This statement is false. The test statistic does not directly provide the probability of the alternative hypothesis being true. Instead, we can use the test statistic to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

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Answer:

\(\frac{3}{6}=\frac{7}{14}=\frac{29}{58}\)

Step-by-step explanation:

By hit and trial method,

Given series of fractions will be,

\(\frac{3}{6}=\frac{7}{14}=\frac{29}{58}\)

Since, \(\frac{3}{6}=\frac{3\times 1}{3\times 2}\)

             \(=\frac{1}{2}\)

\(\frac{7}{14}=\frac{7\times 1}{7\times 2}\)

    \(=\frac{1}{2}\)

\(\frac{29}{58}=\frac{29\times 1}{29\times 2}\)

    \(=\frac{1}{2}\)

Therefore, \(\frac{1}{2}=\frac{1}{2}=\frac{1}{2}\) is the reduced form of the fractions.

\(\frac{3}{6}=\frac{7}{14}=\frac{29}{58}\) will be the answer.

Answer:

Step-by-step explanation:

30 tens is 30*10=300. 3 tens is 3*10=30 and 3 tenths is 3*0.1. So assuming you mean 30 tens minus 3 tens and 3 tenths, the answer would be 300-30.3 which would equal 269.7

Press fit is calculated by determining the required force to assemble two cylindrical parts, using the interference between them and their material properties.

Press fit is calculated by determining the amount of interference between two cylindrical parts and their material properties. The interference is the difference between the diameter of the shaft (male part) and the diameter of the hole (female part). The required force to assemble the parts is then calculated using the material properties of both parts and the amount of interference. The interference is typically expressed as a percentage of the shaft diameter, and the required force is expressed in pounds or newtons.

Calculating the press fit is important for ensuring that the parts are securely and correctly assembled, and for preventing excessive stress or deformation in either part. Press fit calculations are commonly used in mechanical engineering and manufacturing applications.

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We are given the following function

The real zero of the function is x = 1

The multiplicity of the function is 3

The graph of the function looks like below

As you can see, the function falls to the left and rises to the right.

Since the multiplicity of the function is 3, the end behavior of the function will be

Using the limit notation, we can write

As the value of x grows larger (approaches infinity) the end behavior of the function resembles y = x³

Answer:

2b

Step-by-step explanation:

The greatest common factor is the largest factor shared by the set of terms.

In this case, you will divide 2b from both terms:

\(\frac{8b^2}{2b} = 4b\\ \frac{10b}{2b} = 5 \\\\GCF: 2b\)

Answer:

For the first pic, the path is -4 (A) then 0 (J)  then -2 (P)

The second pics answer is -6/4 > -1.62- in negatives the smaller number is the larger number

The third pics answer is 68%- divide 17/25= 0.68 which is 68%

Step-by-step explanation:

Answer: D

Step-by-step explanation:

A  is a function because  all quadratics are functions because it shows the graph of a parabola.  

B   is also a function because it is a quadratic equation  

C    is a function because it is a linear function    

D which  I don't know about doesn't looks like it represent a function.

Graphically, the intersection of the two lines is the solution of the system of equation. The number of games played is 6 and the number of rides y = 2.

While using the graphical approach to solve simultaneous or systems of equations, we build a graph for each equation and search for the intersection of the two graphs. The answer to the system of equations would be the coordinates of the point of intersection.

There is no solution if the two graphs are parallel, which indicates that they do not intersect.

Let us suppose games = x.

Let us suppose rides = y.

Cost of x games = 1.50x

Cost of y rides = 3y

Given that, Julieta spent $15 altogether:

1.50x + 3y = 15

She played a total of 8 games and rides:

x + y = 8

The system of equation is:

1.50x + 3y = 15........eq 1

x + y = 8........eq2

Plot the graph by substituting different values of x and obtaining the value of y.

Graphically, the intersection of the two lines is the solution of the system of equation.

The graph intersects at (6, 2) hence the value of x = 6 and y = 2.

Hence, the number of games played is 6 and the number of rides y = 2.

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The probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15

For given question,

A research center poll showed that 85 percent of people believe that it is morally wrong to not report all income on tax returns.

so, the probability that someone have this belief is P = 0.85

We know that in probability,

p = 1 - q

where;

p is probability of success

q is probability of failure.

Thus the probability that someone does not have this​ belief would be,

= 1 - P

= 1 - 0.85

= 0.15

Therefore, the probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15

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Answer:

4/18 is closest to 0, my answer got deleted last time.

Step-by-step explanation:

Answer:

Independent.

Step-by-step explanation:

The results of tossing the penny first will have no impact on the result of tossing the nickel. Both can be seen as individual events.

When x = -52 in the equation y = -2x + 74, we can substitute it and solve for y:

y = -2(-52) + 74 = 178

Therefore, when x = -52, y = 178.

To solve for x when y = 79.52 in the equation y = 2.5x - 7.3, we can substitute it and solve for x:

79.52 = 2.5x - 7.3

86.82 = 2.5x

x = 34.728 (rounded to 3 decimal places)

Therefore, when y = 79.52, x = 34.728.

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ANSWER:

500.5 m²

STEP-BY-STEP EXPLANATION:

To know how much artificial grass should be purchased to cover the athletic field, we must calculate the area corresponding to the figure.

The area of a trapezoid has the following formula:

Where b is the small base, B is the large base and h is the height, we substitute and calculate the area, like this:

It is necessary to purchase the amount of 500.5 m² to be able to cover the athletic field

A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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Answer:

You will have $54 by December and here's why:

Step-by-step explanation:

You deposite $4 every month until December, that's 6 months.

so you do $4 × 6 months = 24

So you add 24 and 30

$24 + $30 = $54

The money that will be saved by the end of december is $54.

The amount of money kept for future expenses is known as savings.

Now it is given that,

In June, savings account has a deposit of $30.

Now $4 is monthly deposit until the end of the year.

So, Number of months from June to December = 6

⇒ Amount of money saved till december = 6*$4 = $24

Therefore, Amount of money in the savings account in december = Deposit in savings account + Amount of money saved

⇒ Amount of money in the savings account in december = $30 + $24

⇒ Amount of money in the savings account in december = $54

Thus, the money that will be saved by the end of december is $54.

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The standard error of the sample mean is 1.21.

Given;

Suppose a diet regimen for men results in an average weight loss of between 13. 4 and 18. 3 pounds, according to a 95% confidence interval. These findings were based on a group of 42 men who were classified as overweight at the beginning of the four-month trial.

A 95% confidence interval for a population mean is (13.4, 18.3)

Upper limit = 18.3

Lower limit = 13.4

Since population SD is unknown, this interval is constructed using the t distribution.

n = 42

c = 0.95

∴ α = 1 - c = 1 - 0.95 = 0.05

α/2 = 0.025

Also, d.f = n - 1 = 42 - 1 = 41

∴ ta/2.d.f =  ta/2.n-1  =  t0.025,41  =  2.02 . . . . use t table

Now,

The margin of error = (Upper limit - Lower limit)/2

                                 = (18.3 - 13.4)/2

                                 = 2.45

But,

Margin of error = ta/2.d.f-  * (s / \sqrt{} n)

Margin of error = ta/2.d.f-  * Standard error

2.45 = 2.02 * Standard error

Standard error = 1.2129

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Answer:

n^3-4n^2+5

Step-by-step explanation:

Answer:

8 trips

Step-by-step explanation:

You can solve this by unitary method.

15 kilometers in 5 trips means 1 trip consist of 3 kilometers

Therefore, 24/3 = 8

So the required answer is 8 trips.

Thank you!!

Answer:

0

Step-by-step explanation:

X-X

=0

We need to find the function f(n) whose terms are the same as the series in question. We can then integrate this function from n=1 to infinity and determine if the integral is convergent or divergent. If it is convergent, then the series is convergent. If it is divergent, then the series is also divergent.

To determine whether a series is convergent or divergent using the integral test, we need to first check if the series satisfies three conditions:

1) The terms of the series are positive.

2) The terms of the series are decreasing.

3) The series has an infinite number of terms.

Assuming these conditions are satisfied, we can use the integral test which states that if the integral of the function f(x) from n=1 to infinity is convergent, then the series with terms a_n = f(n) is also convergent. Conversely, if the integral is divergent, then the series is also divergent.

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