a search committee is formed to find a new software engineer. there are 6666 applicants who applied for the position. 1) how many ways are there to select a subset of 1515 for a short list?

The value of z-stat is -0.6721.

What is z stat?

The relationship between a value and the mean of a group of values is quantified by a Z-stat. The Z-stat is calculated using standard deviations from the mean. When a data point's Z-stat is 0, it means that it has the same score as the mean.

One standard deviation from the mean would be indicated by a Z-stat of 1.0. Z-stats can be positive or negative; a positive value means the score is above the mean, while a negative value means it is below the mean.

Solution Explained:

We use the formula,

[tex]z = \frac{P - \pi }{\sqrt{\frac{\pi (1-\pi )}{200} }}[/tex], where P is the observed proportion, π is the hypothesized proportion

Therefore, P = 42/200 = 0.21 & π = 23/100 = 0.23

Putting the values in

[tex]z = \frac{0.21 - 0.23 }{\sqrt{\frac{0.23 (1-0.23)}{200} }}[/tex]

After calculating, z-stat is therefore equal to -0.6721

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The Total Population after five years will be 13,700 people

What is Compound Interest?

Compound interest is the adding of interest to the principle sum of a loan or deposit, or interest on interest plus interest. It is the outcome of reinvesting interest, or adding it to the lent capital, rather than paying it out or requesting payment from the borrower, so that interest is received on the principle sum plus previously accrued interest in the next month. In finance and economics, compound interest is the norm.

Solution:

To solve the problem mentioned we need to use the concept of compound interest:

Principal = 10,000

Annual Growth Rate = 6.5%

Time = 5 years

Amount = Principal * ((100+Rate)/100)^Time

Total Population after 5 years = 10,000 * (106.5/100)^5

= 10,000 * (1.065)^5

= 10,000 * 1.37008

= 13,700

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The equation of the path to find the dimensions of the patio is x² + (x + 5)² = 841.

Here we have to find the equation of the dimensions of the patio.

Data provided:

the path = 29 meters

length of the path is 5 meters more than the width of the path.

So let us assume that the length of the path is x

with this, the width of the path is x + 5

The formula for the diagonal:

Diagonal²  = length² + width²

Putting the data we have:

29² = x² + (x +5)²

841 = x² + (x+5)²

Therefore we get the equation as x² +(x + 5)² = 841.

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Answer:

Step-by-step explanation:

Let L be the Length and W be the Width of a rectangle.

We are told that:    L = 4W   [the length of a rectangle is four times its width]

Perimeter = 2L + 2W

We learn that P ≤ 130 cm

2L + 2W ≤ 130 cm

Substitute L = 4W:  

2L + 2W ≤ 130 cm

2(4W) + 2W ≤ 130 cm

10W ≤ 130 cm

W ≤ 13 cm

Options:

2w + 2 • (4w) < 130     Not correct since the < sign does not allow for the "at most 130 cm.")

2w + 2 • (4w) > 130      Must be ≤, not >

2w + 2 • (4w) ≤ 130   This option works since the ≤ sign is correct.

Answer:

56.0

Step-by-step explanation:

The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.

Given that,

A marksman has a 0.89 percent chance of hitting the target each time he fires.

We have to find what is the probability that he will only hit the target 13 times out of 15 shots.

We know that,

The probability of getting exactly k successes in n trials is given by the probability mass function that is,

P(X=k)=[tex](\frac{n}{k} )p^{k}(1-p)^{n-k}[/tex]

Where [tex](\frac{n}{k})= n!/k!(n-k)![/tex]

The probability that he hits the target at most 13 times is,

1-[P(he hits 14 times)+P(he hits 15 times)]

So, calculate the probability that he hits a target 14 times as follows:

P(X=14)=[tex](\frac{15}{14} )0.89^{14}(1-0.89)^{1}[/tex]

P(X=14)=15×(0.89)¹⁴×(0.11)

P(X=14)=0.3228

And the probability that he hits a target 15 times is

P(X=15)=[tex](\frac{15}{15} )0.89^{15}(1-0.89)^{0}[/tex]

P(X=15)=1×(0.89)¹⁵×(1)

P(X=15)=0.1741

And the required probability is

=1-[P(he hits 14 times)+P(he hits 15 times)]

=1-[0.3228+0.1741]

=0.5031

Therefore, The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.

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The probability the game lasts less than 4.5 hours is 0.2877.

μ = mean population = 5

σ = standard deviation = 0.9

The probability for the game lasts less than 4.5 hours can be calculated using z test formula.

P(x < 4.5) = P(z < [tex]\frac{x-\mu}{\sigma}[/tex] )

= P(z < [tex]\frac{4.5-5}{0.9}[/tex])

= P(z < -0.56)

Using z table for P(z < -0.56). So,

= 0.2877

Thus, the probability is 0.2877 for the game lasts less than 4.5 hours.

Your question is incomplete, but most probably your full question was

on average, an american professional football game lasts about five hours, even though the ball is actually in play only 11 minutes. assume that game times are normally distributed with a standard deviation of 0.9 hour. 1. Find the probability that a game lasts less than 4.5 hours.

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Answer:

m = -4

Step-by-step explanation:

2(3m + 1) - 2m = -14

Use distributive property.

6m + 2 - 2m = -14

Combine like terms.

4m + 2 = -14

Subtract 2

4m = -16

Divide by 4.

m = -4

The required relation between independent and dependent variables is y = x/4.

A simple method for considering  independent and dependent variables is, the point at which you're leading an examination, the free factor is what you change, and the reliant variable changes hence. You can likewise consider the autonomous variable the reason and the reliant variable as the impact

The independent variable x is the total number of students in the class.

And the dependent variable y is number of students in each group.

Therefore,

y = x / 4

Here, when we change the value of x then value of y automatically changed.

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Answer:

He rolled a 6, 16 times

He rolled not a 6, 4 times

Brian did not roll 6 in the dice 14 times.

Subtraction is mathematic operation. Which is used to remove terms or objects in expression.

Given, Brian is playing a game of dice. He gets 10 points for each 6 he rolls. He loses 4 points every time he does not roll a 6.

After 20 tries his score is 144 points.

If he rolled 6 each time,

his score would be 200.

Subtracting the number 144 to 200.

200 - 144

= 56

And 56/4

= 14

That means he did not roll 6, 14 times.

Therefore, 14 times he did not roll 6.

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The test hypothesis using 0.05 significance level has the following results:The treatment means differ, The block means do not differ.

A poll or study's findings can be tested using the statistical procedure known as hypothesis testing to see if the findings are significant. By calculating the likelihood that the findings happened by chance, you are basically evaluating if the findings are genuine. If it's possible that your results were a coincidence, the experiment won't be reproducible and won't be of much help.

Hypothesis testing may be one of the most perplexing components for students, mostly because you must first determine what your null is so that you can conduct a test. These challenging word problems that you encounter might sometimes be challenging to understand.

Make a plan for your null hypothesis.

Write down your null hypothesis

Determine the type of test you must do,

How to solve?

Describe the null and alternate treatment hypotheses:

Null hypothesis: No difference in treatment means

Alternative interpretation: The means differ

Indicate the treatment decision-making process:

F(1,2)=18.51 as seen in the table

Reject the null hypothesis if the estimated F exceeds 18.51.

Treatments Calculated F=43.75 > 18.51; hence, the null hypothesis is rejected.

As a result, we find that the treatment means differ.

Write out the null and alternative hypotheses for blocks.

Block means are not different under the null hypothesis.

A different theory There exists at least one pair of distinct meanings.

State the block decision rule as well:

Table F(2,2)=19.0 value

If the estimated F is greater than 19, reject the null hypothesis.

Blocks determined that F=8.14 19.0, thus we did not reject the null hypothesis.

Our conclusion is that the block means are equivalent.

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Answer: 4826

Step-by-step explanation: 8254 - 3248 = 4826

Answer:

2*3

Step-by-step explanation:

divide by smallest number possible

6/2=3

3/3=1

2*3=6

so 2*3

The probability that these events when we randomly select a permutation is  24, 1/2, 1/2, 1/3, 1/4, 1/4

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

P(A) = n(A)/n (S)

The probability of an event "A" is P(A). The number of successful outcomes is n(A). The total number of events in the sample space is denoted by n(S).

1)  From the set we can select 4*3*2*1=24 permutations.

2) There are six permutations that begin with 1, three that begin with 2, three that begin with 3, and no permutations that begin with 4 when 1 comes before 4. So, P1 ={ 6+3+3+0}/{24} = 1/2

3) No permutations begin with 1, three permutations begin with 2, three permutations begin with 3, and six permutations begin with 4, where 4 comes before 1. P2=1/2 

4) There are no permutations that begin with 1, no permutations that begin with 2, no permutations that begin with 2, no permutations that begin with 3, and six permutations that begin with 4, where 4 comes before both 1 and 2. Therefore, P 3 = 1/3

​5) No permutations begin with 1, no permutations begin with 2, no permutations begin with 3, and there are six permutations that begin with 4, where 4 comes before 1, 2, and 3. So, P4= 1/4

​6) There are no combinations that begin with 1, three combinations that begin with 2, no combinations that begin with 3, and three combinations that begin with 4, where 4 comes before 3 and 2 comes before 1. So, P5= 1/4

​

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Answer:

Step-by-step explanation:

hi

Answer:

60

Step-by-step explanation:

she read 60 pages in just 2 days

The probability that it will get to b within 7 hours is approximately 0.014.

Probability:

In math, the favorable way of happening the event is known as probability.

Given,

A frog starts at location a and wants to get to location b that is 500 meters away. starting at a, it sits at a given spot on the path from a to b for a time that is exponentially distributed with parameter 1 (minute). after that, it jumps 1 meter towards b, sits in the new spot for an exponentially distributed time, etc. all the times are independent.

Here we need to find the the probability (approximately) that it will get to b within 7 hours.

While we looking at the given question we have identified that,

starting point = a

ending point = b ( 500 meters)

Time take for one jump = 1 minute

Distance covered in one jump = 1 meter.

Here they also said that the time is independent but the distance remains constant.

So, the probability that it will get to b within 7 hours is calculated as,

=> 7/500

=> 0.014

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The constant of proportionality is 9.5.

The correct option is (a)

Given,

In the question:

The proportional relationship between the price for a certain number of buckets of golf balls at a driving range.

Buckets 3 5 7

Price (dollars) 28. 50 47. 50 66. 50

To determine the constant of proportionality.

Now, According to the question:

We know that:

Proportional relationship equation:

y = kx, where k-constant of proportionality

In the given table, number of buckets represent input values (x) and the price represents output values (y).

We have for the first column:

x = 3, y = 28.50

Find the value of k by plugging in the values of x and y:

28.50 = 3k

k = 28.50/3

k = 9.5

The options are:

a) 9. 5

b) 10. 5

c) 18. 25

d) 28. 5

Hence, The constant of proportionality is 9.5.

So, The correct option is (a).

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a) ∠a = 35

b) ∠b = 40

c) ∠c = 35

d) ∠d = 70

e) When we add all the angles together we get an angle of 360°.

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Given, ∠b =  40  

∠d = 70

∠1 = ∠ a

∠2 = ∠c

∠1 = ∠2

So, ∠1 =∠2 = ∠a = ∠c

70 + 40 + ∠a + ∠2 = 180

110 + 2∠a = 180            

2∠a = 180 - 110

∠a = 70/2

∠a = 35

∠1 =∠2 = ∠a = ∠c = 35

When we add all the angles together we get an angle of 360°

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The points (-10, 0) and (0, 5), on the path of the first boat that can be modeled by a quadratic function and the point (10, 4) on the path of the linear function modelling the second boat, indicates that besides the common starting location, the solution for the point at which the paths of the  boats cross again at (6, 3.2)

The solution to a system of equation is the value of the input variable at which the output of the equations in the system of equations are the same.

Location of the port = (-10, 0)

The vertex of the path of the first boat that can be modeled by a quadratic function = (0, 5)

Point through which the boat that follows a path that can be modeled as a linear function passes = (10, 4)

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

Where;'

(h, k) = The coordinates of the vertex

(h, k) = (0, 5)

Therefore;

y = a·(x - 0)² + 5 = a·x² + 5

When x = -10, y = 0, therefore;

y = 0 = a·(-10)² + 5 = 100·a + 5

0 = 100·a + 5

a = -5/100 = -1/20

a = -0.05

The equation is therefore; y = -0.05·x² + 5

The slope of the straight line path of the other boat is; m = (4 - 0)/(10 - (-10)) = 1/5 = 0.2

The equation is therefore; y - 0 = 0.2·(x - (-10)) = 0.2·x + 2

y = 0.2·x + 2

The point where the two paths cross is therefore;

-0.05·x² + 5 = 0.2·x + 2

-0.05·x² - 0.2·x + 5 - 2

-0.05·x² - 0.2·x + 3 = 0

x = (0.2 ± √((-0.2)² - 4 × (-0.05) × 3))/(2×(-0.05))

Therefore;

x = -10 and x = 6

The x-coordinate of the point the two paths cross, besides the starting location is x = 6

Therefore;

y = 0.2 × 6 + 2 = 3.2

The point besides the common starting location, the paths of the boats cross is; (6, 3.2)

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Answer:

(–6, 3.2)

Step-by-step explanation:

The answer above is correct.

The slope and y-intercept of the given linear equation are [tex]-\frac{5}{4}[/tex] and [tex]5[/tex] respectively. The equation of the given graph is [tex]y=-\frac{5}{4} x+5[/tex]

What is the Slope of a graph?

What is a y-intercept?

Here, from the graph, we can find a line passing through the two points, [tex](4,0)[/tex] and [tex](0,5)[/tex].

The equation for the slope formula is given as, [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Using the slope formula, we get the slope of the given graph as,

[tex]m=\frac{ 5-0 }{0-4 }\\\implies m=-\frac{5}{4}[/tex]

The y-intercept (c) is the value of y when x equals zero.

The line is passing through the point [tex](0,5)[/tex]

Here, the value of x is equal to 0 and the value of y is equal to 5.

So, the y-intercept of the given graph, [tex]c=5[/tex]

We know that the equation of a straight line is expressed as, [tex]y=mx+c[/tex]

Substituting the values of m and c in the straight line equation form, we get the equation of the given line as,

[tex]y=-\frac{5}{4} x+5[/tex]

Therefore, the slope of the given graph, [tex]m=-\frac{5}{4}[/tex] and the y-intercept, [tex]c=5[/tex].

Also, the equation of the given line is [tex]y=-\frac{5}{4} x+5[/tex]

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Answer:

2,632 copies

Step-by-step explanation:

32100× 0.082= 2632.2

About 2,632

The GPA of the student who scored 63 in the performance test is 2.394.

Given, a researcher analyzed data using linear regression correlating a performance test and GPA and calculated a slope of 0.028 and y-intercept of 0.63.

we have find the GPA of a student who scored 63 in the performance test.

Let the score of the student in performance test be, x

and the GPA of the student be, y

So, y = mx + c

as, m = 0.028 and c = 0.63

y = 0.028x + 0.63

at x = 63

y = 0.028×63 + 0.63

y = 2.394

So, the GPA of the student who scored 63 in the performance test is 2.394.

Hence, the GPA of the student who scored 63 in the performance test is 2.394.

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The quadratic equation 15[tex]x^{2}[/tex]-22x -7 = 0 has solution x = 1.7355 or -0.26886

In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as

a[tex]x^{2}[/tex] + bx + c =0

where x represents an unknown value, and a, b, and c represent known numbers. One supposes generally that a ≠ 0; those equations with a = 0 are considered degenerate because the equation then becomes linear or even simpler. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can be factored into an equivalent equation

given that

5(x-1)3x = 7(x+1)

15[tex]x^{2}[/tex]-15x = 7x +7

15[tex]x^{2}[/tex]-22x -7 = 0

x = -b ± [tex]\sqrt{b^{2}-4ac }[/tex]/2a

x = -(-22) ± [tex]\sqrt{(-22)-4(15)(-7)}[/tex] /2(15)

x = 1.7355 or -0.26886

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Answer: x = 12

Step-by-step explanation:  

Distribute the parenthesis on both sides of the equation

5x - 5 + 3x = 7x + 7

8x - 5 = 7x + 7 ( subtract 7x from both sides )

x - 5 = 7 ( add 5 to both sides )

x = 12

Therefore, your answer is: x = 12

Answer:Answer:

D.

{(-9,8), (-5,-8), (-7,8), (-6,-8)}

Step-by-step explanation:

The simplification that explains the statement is [tex](9^{\frac{1}{2} })^{2} = (9^{\frac{1}{2} } )(9^{\frac{1}{2} } ) = 9^{\frac{1}{2} + \frac{1}{2} } = 9^{\frac{2}{2} } = 9^{1} = 9[/tex]

The law of indices(exponent) can be used to explain the following statement:

[tex]\sqrt{9} = 9^{\frac{1}{2} }[/tex]

Therefore, using the law of indices.

[tex](a^{x}) (a^{y} ) = a^{x+y}[/tex]

Hence, applying this law of exponents.

Exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent:

[tex](9^{\frac{1}{2} })^{2}[/tex]

[tex](9^{\frac{1}{2} } )(9^{\frac{1}{2} } )[/tex]

[tex]9^{\frac{1}{2} + \frac{1}{2} }[/tex]

[tex]9^{1}[/tex]

9

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On solving the provided question, we got -  0.001 is a stronger significance level,

any of a product's characteristics taken into account in respect to a certain characteristic. especially: a term's constant component as opposed to its variable. a value that represents a quality or attribute by a number (as of a substance, device, or process)

Whenever a variable is multiplied, a coefficient is used. In this case, "z" is a variable, making 6 a coefficient. 6z stands for 6 times z. Coefficient 1 applies to variables without a value.

0.001 is a stronger significance level, It means that the probability of error for the statistic is greater than 5 in 100, therefore the researchers concluded that the research is not statistically significant.

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Answer:

Segment CE is 12 units.

Step-by-step explanation:

CD and DE add together to make CE. See image.

Use this idea to write an equation. Combine like terms and solve for x. Use the x value you find to calculate the length of CE. See image.

Answer: 144a^14 b^8

Step-by-step explanation:

(-4a^(5)b^(3))^(2)* (-3a^(2)b)^(2) = 144a^14 b^8