three potential employees took an aptitude test. each person took a different version of the test. the scores are reported below. kaitlyn got a score of 74.5 ; this version has a mean of 68.5 and a standard deviation of 12 . kiersten got a score of 244.8 ; this version has a mean of 210 and a standard deviation of 29 . rebecca got a score of 7.24 ; this version has a mean of 6.7 and a standard deviation of 0.3 . if the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?

Answer:

Option i

(Last Image)

Step-by-step explanation:

rational Numerus And irrational Numbers form real Numbers

Irrational Numbers = real Numbers

Rational Numbers can include whole Numbers natural Numbers integers

Irrational Numbers are Separate.

"The mean will be higher than the median in any distribution that" ;

has a positively skewed distribution

A positively skewed distribution is one in which the majority of data values are clustered towards the lower end of the range, while the rest of the values are spread out towards the higher end of the range. As a result, the mean (the average of all the data values) will be higher than the median (the middle value of the data set).

This is because the mean is affected by the higher values in the distribution, while the median is not.

Positively skewed distributions are common in real-world data sets and are often seen in income distributions, stock market returns, and other economic data.

For example, a distribution of incomes may have a few very high earners pushing up the mean, while the majority of people make much lower amounts, resulting in a median that is lower than the mean.

Similarly, stock market returns may have a few very large returns that pull the mean up, while the majority of returns are much lower, resulting in a median that is lower than the mean.

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A residual in regression refers to the difference between the observed value and the predicted value of the dependent variable. It represents the unexplained portion of the data that the regression model fails to capture.

In regression analysis, the goal is to build a model that can predict the value of a dependent variable based on one or more independent variables. The model estimates the relationship between the independent variables and the dependent variable by fitting a line or curve through the data points. However, due to inherent variability or noise in the data, the model may not perfectly predict the observed values of the dependent variable.

Residuals are used to measure the accuracy of the regression model. They represent the vertical distance between the observed values and the corresponding predicted values on the regression line. A positive residual indicates that the observed value is higher than the predicted value, while a negative residual indicates the opposite. By calculating the residuals for each data point and examining their distribution, we can assess how well the regression model fits the data.

Analyzing the residuals can guide model improvements, such as identifying outliers, heteroscedasticity, or nonlinear relationships, and can also be used to assess the statistical assumptions of the regression model, such as independence, normality, and constant variance.

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Step-by-step explanation:

the dimensions could be:

1) the height = 6 cm and the width = 9 cm

or

2) the height = 12 ft and the width = 18 ft

#1

\(\\ \sf{:}\dashrightarrow \dfrac{3}{4.5}=\dfrac{3(2)}{4.5(2)}=\dfrac{6}{9}\)

#2

\(\\ \sf{:}\dashrightarrow 1(\dfrac{3}{4.5})=\dfrac{3}{4.5}\)

we have a 18 -gon

Its a regular polygon with 18 congruent sides and 18 congruent angles

step 1

Find the measure of each interior angle

we know that

the sum of the interior angles in any regular polygon is equal to

where

n is the number of sides

so

for n=18

substitute

Divide by the number of sides n

the measure of each interior angle is 160 degrees

Step 2

Find the measure of each exteriior angle

Remember that the sum of the interior angle and the exterior angle is equal to 180 degrees

therefore

the measure of each exterior angle is equal to 20 degrees

Translation of the Ax=0 solution set yields the Ax-b solution set since Ax-b is consistent. The Ax = b solution set is therefore a single vector if and only if the Ax = 0 solution set is a single vector, which occurs if and only if Ax 0 has only the trivial solution.

Finding the solution to an equation is like finding the solution to a puzzle. A mathematical equation proves the equality of two algebraic expressions. Determine the values of the variables that make the equation a true statement in order to solve an equation. An equation's solution is any value that causes the equation to be true.

given

Let's suppose that there is a solution to the equation ax = b.

Now, we want to demonstrate that the trivial solution exists for the equation ax = b when ax = 0.

Ax = 0 is homogeneous.

In the event that this equation was true for b, we define

To be a set of vectors with the form ax = b

w = m + gh

The subscript "h"

A solution to ax = 0 is gh.

Ax=b is in the form of w= m+gh based on the information we know had.

with

m = ax=solution b's

Soulution of gh = ax=0

Only a simple solution, ax = 0, exists.

gh = 0

where gh = 0

The relationship between ax=b and w=m

Ax = b thus has no alternative solutions.

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The system having equations y=3x-4 and 3y=-x-6 is consistent.

Given that system has equations y=3x-4 and 3y=-x-6.

We are required to find whether the system is consistent,inconsistent or neither.

The system which has atleast one solution is known as consistent.

We have to first find the solution of the equations.

Equation is like the relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c.

We have been given linear equations.

y=3x-4----------1

3y=-x-6---------2

Use the value of y from 1 in 2.

3(3x-4)=-x-6

9x-12=-x-6

9x+x=-6+12

10x=6

x=6/10

x=3/5

Since,it has one solution,so it is consistent.

Hence the system having equations y=3x-4 and 3y=-x-6 is consistent.

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Answer:

Please check the formatting in the problem.

Step-by-step explanation:

As written, "p−m ÷ p−n" is only p - m/p - n. None of the answer options comes close. Is the expression witten correctly?

The Answer Options are also unusual:

a) p−m − (−n) is just p-m+n

b) p−m − n

c) p−m(−n) is just p +mn

d) p−m ÷ n is p = (m/n)

Answer:

 5/13 and Cos(x) = 12/13 and so Sin(x) + Cos(x) =

5/13 + 12/13 = 17/13. Simple really.

Step-by-step explanation:

By using Permutation, The number of ways in which 4 distinct prizes be awarded is 5,040.

Number of Contestants = 10

Number of distinct prizes = 4

We will use permutation to evaluate the number of ways in which 4 distinct prizes be awarded,

The first prize can be given in 10 ways

The second prize can be given in 9 ways

The third prize can be given in 8 ways

The fourth prize can be given in 7 ways

Now, Total number of ways 4 prizes can be awarded = 10 * 9 * 8* 7 = 5,040

Thus, the number of ways in which 4 distinct prizes be awarded is 5,040

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Answer:

Tolerance is needed in all spheres of life, and on every level and in every stage because it plays a vital role in establishing peace and love in all the units of society, from the smallest up to the highest. Lack of tolerance leads to violence, and finally it destroys the peace and security of society.

Step-by-step explanation:

Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

Answer:

5⁻² = 1 / 5² = 1/25 and 2³ = 2 * 2 * 2 = 8 so the answer is 1/25 / 8 = 1/200.

The set A {a,b,c}  that is neither symmetric nor antisymmetric is option D)  {(a, b), (b, a),(a, c)} on {a,b,c}

We are looking for a relation on the set A that is neither symmetric nor antisymmetric. Here are the given options:
A. the empty set on {a, b, c}
B. {(a, b), (b, a), (a, a), (a, a)} on {a, b, c}
C. {(a, b), (b, a)} on {a, b, c}
D. {(a, b), (b, a), (a, c)} on {a, b, c}

A relation R on set A is symmetric if for all (x, y) in R, (y, x) is also in R. It is antisymmetric if for all (x, y) in R, (y, x) in R implies x = y.

Let's examine each option:

A. The empty set has no elements(null set), so it is both symmetric and antisymmetric, which does not satisfy the required condition.

B. {(a, b), (b, a), (a, a), (a, a)}: Since (a, b) and (b, a) are in the relation, it is symmetric.

However, (a, a) makes it not antisymmetric, as (a, a) does not imply a = b.

Thus, this option is symmetric and does not satisfy the condition.

C. {(a, b), (b, a)}: This relation is symmetric since (a, b) and (b, a) are both in the relation, but it is not antisymmetric. Therefore, this option does not satisfy the condition.

D. {(a, b), (b, a), (a, c)}: This relation is neither symmetric nor antisymmetric. It is not symmetric because (a, c) is in the relation but (c, a) is not.

It is not antisymmetric because (a, b) and (b, a) are both in the relation but a ≠ b. Thus, this option satisfies the required condition.

Hence the relation on the set A that is neither symmetric nor antisymmetric is D. {(a, b), (b, a), (a, c)} on {a, b, c}.

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Answer:

A. \(4^3*6^3\)

Step-by-step explanation:

First, you solve the given equation.

\((4*6)^3\\\\=24^3\\=13824\)

You solve the multiple choice afterwards. Since choice A was given first, we managed to find the answer.

\(4^3 * 6^3\\\\=64 * 216\\=13824\)

Choice A has the same answer as the given equation, making them equivalent.

option B.

Calculations ↓

First, let's think of two numbers so that :

These numbers are :

4 and 1

Plug these numbers here :

(x+4) (x+1)

So the correct factored form of this expression is

Option B) (x+4)(x+1)

\(\footnotesize\text{hope\:helpful~}}\)

The slopes of the figures 1 , 2 & 3 are 0 , 1 & 1/3 respectively.

Given, two figures with the lines passing through different points

we have to find the slopes of different figures.

Now, in figure 1 curve passes through (0 , -1)

as, 2x + 2yy' = 0

y' = -x/y

y' = -(0)/-1

y' = 0

Now, in figure 2 curve passes through (-2 , 2)

as, y ' = -x/y

y' = -(-2)/2

y' = 1

In figure 3 curve passes through (1 , -3)

as, y' = -x/y

y' = -1/-3

y' = 1/3

So, the slopes of the figures 1 , 2 & 3 are

0 , 1 & 1/3 respectively.

Hence, the slopes of the figures 1 , 2 & 3 are 0 , 1 & 1/3 respectively.

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Step-by-step explanation:

5b²+39b=8

<=> 5b²+39b-8=0

(5b-1)(b+8)=0

b = ¹/5 or b = -8

b=-8 and b=1/5.

Answer:

Solution given:

5b²+39b=8

5b²+39b-8=0

try to do middle term factorization.

it needs 40 while multiplication and 39 when subtraction.

it is 40-1 and 40*1

now

doing middle term factorization

5b²+(40-1)b-8=0

5b²+40-b-8=0

take common from each 2 term

5b(b+8)-1(b+8)=0

again take common and keep remaining in another brackets

(b+8)(5b-1)=0

either

b=-8

or

b=1/5

Answer:

2/3

Step-by-step explanation:

its the only possible answer looking at the chart since it's the only answer above zero and below one

The surface area of a sphere with a radius of 4.18 meters is approximately 219.57 square meters. The area of a right triangle with side lengths of 8.55 meters and 2.13 meters is approximately 9.10 square meters.

To find the surface area of a sphere, we use the formula: A = 4πr^2, where A represents the surface area and r is the radius of the sphere. Substituting the given radius of 4.18 meters into the formula, we get A = 4π(4.18)^2. Evaluating this expression, we find that the surface area of the sphere is approximately 219.57 square meters.  

For the right triangle, we can use the formula for the area of a triangle, which is A = (1/2)bh, where A represents the area, b is the base, and h is the height of the triangle. In this case, the base is 8.55 meters and the height is 2.13 meters. Substituting these values into the formula, we have A = (1/2)(8.55)(2.13), which simplifies to A ≈ 9.10 square meters. Therefore, the area of the right triangle is approximately 9.10 square meters.

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Answer:46

Step-by-step explanation:

C! Just got the question and turned in the test, it’s C!!

The horse's average speed for the race in units of kilometers per hour will be 178.06.

The winning horse in a recent race covered the 5.50-furlong distance in 22.37 seconds.

The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.

We know that the average speed formula is given as,

Average speed = Total distance / Total time

The conversion is given as,

1 furlong = 0.201168 km

5.50-furlong = 0.201168 x 5.5 km

5.50-furlong = 1.10642 km

1 second = 1/3600 hour

22.37 seconds = 22.37/3600 hour

22.37 seconds = 0.0062 hour

The average speed is calculated as,

Average speed = 1.10642 / 0.0062

Average speed = 178.06 km per hour

The horse's average speed for the race in units of kilometers per hour will be 178.06.

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The bit pattern 1001001 represents the letter I. The letter represented by the decimal value 73 in ASCII is the uppercase letter "I".

The ASCII value for the letter A is indeed 65 in decimal. To find the letter represented by the bit pattern 1001001, we need to convert this binary value to decimal.

Step 1: Write down the binary value:
1001001

Step 2: Identify the position of each digit (starting from right to left):
2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6

Step 3: Multiply the binary digit by its corresponding position value:
(1*2^6) + (0*2^5) + (0*2^4) + (1*2^3) + (0*2^2) + (0*2^1) + (1*2^0)

Step 4: Calculate the decimal value:
(64) + (0) + (0) + (8) + (0) + (0) + (1) = 73

The decimal value for the binary number 1001001 is 73. Now, we can find the ASCII character that corresponds to this decimal value.

The letter represented by the decimal value 73 in ASCII is the uppercase letter "I".

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Answer:

Use " m-a-t-h-w-a-y " for this.

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

1 + 11 = 12, so x = 12. hope this helps

The unit tangent vector t(t) is (3, 4t, 2t) / sqrt(9 + 20t^2), and the unit normal vector n(t) is (3, 4, 2t) / sqrt(25 + 4t^2).

The unit tangent vector t(t) of the given vector function r(t) = (3t, 1 + 2t^2, t^2) is obtained by dividing the derivative of r(t) by its magnitude. The derivative of r(t) is (3, 4t, 2t), and the magnitude of this vector is sqrt(9 + 20t^2). Therefore, t(t) = (3, 4t, 2t) / sqrt(9 + 20t^2).

The unit normal vector n(t) can be obtained by dividing the derivative of t(t) by its magnitude. The derivative of t(t) is (3, 4, 2t), and the magnitude of this vector is sqrt(25 + 4t^2). Thus, n(t) = (3, 4, 2t) / sqrt(25 + 4t^2).

These unit vectors t(t) and n(t) represent the direction of motion and the direction of the curve's curvature at each point t, respectively, providing valuable information about the behavior of the vector function r(t).

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Answer:

35.57 degrees

Step-by-step explanation:

tan x = 108/151

tan x = 0.71523

x = 35.57 degrees