Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the 6 months before the exercise program began and in the 6 months following the exercise program. Following are the results.

Employee Before After
1 8 7
2 7 3
3 8 2
4 8 4
5 6 5
6 7 10
7 6 4
8 8 9

At the 0.050 significance level, can he conclude that the number of absences has declined?

a. Compute the test statistic.
b. Compute the p-value.

In order to achieve $4,000 in three years at 4.5% simple interest, the principal must be equal to $29,629.63.

In Mathematics, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

By substituting the given parameters into the simple interest formula, we have;

4,000 = P × 4.5/100 × 3

4,000 = P × 0.045 × 3

4,000 = 0.135P

Principal, P = 4,000/0.135.

Principal, P = $29,629.63

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Answer:

Draw a picture of Angkor Wat

Note that the angles are found using the principle of the circle theorems.

The angle of the circumference is half of the angle at the center of the circle by an arc.

AB = 78°

∠5 = 39°

Angles intercepted by the same arc are equal.

∠4 = 39°

FE= 105°

∠16 =105°

ED = 27°

∠17 =27°

CD = 42°

∠10 =21°

∠3 =21°

The angle of the semi-circle is 90°.

∠2 =90°

∠8=∠9 = (180-48)/2

∠8= 66°

∠9= 66°

∠7=90°-∠8 = 90°-66°

∠7=24°

∠17 = 180°-∠15-∠16

∠17 = 180°-48°-105°

∠17 =27°

∠6=∠15/2 = 48/2

∠6=24°

∠21 = 180°-∠7-∠16

∠21 = 180°-24°-105°

∠21 =51°

∠19 =51°

∠18 = 180°-∠17-∠6

∠18 = 180°-27°-24°

∠18 = 129°

∠20 = 129°

BC = 60°

∠1 = 60/2

∠1 =30°

∠11=180°-∠1-∠2

∠11=180°-30°-90°

∠11=60°

∠13=60°

∠12=180-∠11

∠12=180°-60°

∠12=120°

∠14=120°

∠15=48°

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The required unit rate is 0.333 products per minute.

What is a product's utilisation rate?

A measurement of how much of a product a user consumes in a certain amount of time; users can be classified as heavy, moderate, or light.

Given that a factory worker can make 15 products in 45 minutes.

We are to find the unit rate.

We will be using the unitary method to solve the given problem.

In 45 minutes, the number of products made by the worker = 15

Therefore, in 1 minute, the number of products made by the worker is given by

= Number of products / Amount of time taken

= 15/45

= 0.333

Thus, the required unit rate is 0.333 products per minute.

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The correct statement regarding the congruence of the two triangles is given as follows:

Yes. We are two right triangles with congruent hypotenuses and a shared congruent side. The triangles are congruent by the HL Triangle Congruence Theorem.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The triangles in this problem have:

Hence, applying the Pythagorean Theorem, the missing side also has the same measure for both triangles, hence they are congruent by the HL Congruence Theorem.

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Answer:

Linear

Step-by-step explanation:

The table represents a consistent function and is therefore linear.

The model is 64.62 inches tall. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." In mathematics, operations like division, multiplication, addition, and subtraction come first, followed by operations like quotient, product, sum, and difference.

We are given that height of tower is 1454 feet and the scale is given as follows:

2 inches = 45 feet

Now, using the division operation, we get

⇒ Height of the model = 1,454 ÷ 45

⇒ Height of the model = 32.31

Now, using the multiplication operation, we get

⇒ Height of the model = 32.31 * 2

⇒ Height of the model = 64.62 inches

Hence, the model is 64.62 inches tall.

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The correct question has been attached below.

Answer:

The formula for the surface area of a cylinder is:

S = 2πrh + 2πr^2

where S is the total surface area, r is the radius of the base, and h is the height.

For one lipstick, the surface area is:

S = 2π(0.6)(2.4) + 2π(0.6)^2

S = 2.88π + 0.72π

S = 3.6π

To wrap 4 lipsticks, we need to multiply this surface area by 4:

S = 4(3.6π)

S = 14.4π

Therefore, the makeup artist will need approximately 14.4π square inches of gift wrap to wrap 4 lipsticks.

Answer:

Step-by-step explanation:

Total surface area of a cylinder = 2πr(r + h)

2 π (.6) (.6 + 2.4)

2 π .6 (3)

1.2π (3)

3.6 π  square inches

Mulitply by four for four lipsticks:

3.6π × 4 = 14.4π sq inches

The effective annual yield of the investment is 0.1501

To find the effective annual yield, we need to use the formula:

(1 + r/n)^n - 1

where r is the annual interest rate and n is the number of times the interest is compounded per year.

In this case, r = 0.14 (14% expressed as a decimal), and n = 52 (since interest is compounded weekly).

Plugging these values into the formula, we get:

(1 + 0.14/52)^52 - 1 = 0.1501

Therefore, the effective annual yield is 0.1501, which is equivalent to 15.01% (rounded to two decimal places).

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Step-by-step explanation:

sin (pi/4)  = sqrt(2) / 2 = .707

  you either just know this after a time or you can use a calculator (in RADIAN mode)

Answer:

sin(π/4) = sin(45°) = 0.707106781186548 ≈ 0.707 (rounded to 3 decimal places)

Step-by-step explanation:

here are the steps:

Convert π/4 to degrees: π/4 * (180/π) = 45°

sin(45°) = opposite/hypotenuse

sin(45°) = opposite/hypotenuse = adjacent/hypotenuse = 1/√2

sin(45°) = 1/√2 * √2/√2 = √2/2

Therefore, sin(π/4) = sin(45°) = √2/2 ≈ 0.707 (rounded to 3 decimal places).

The indefinite integral when evaluated has a solution of 2cot(2x⁵ - 5x) + C

From the question, we have the following parameters that can be used in our computation:

The integral of (10 - 20x⁴)csc²(2x⁵ - 5x)

³

This can be expressed as

∫(10 - 20x⁴)csc²(2x⁵ - 5x) dx

The above is a complex expression

So, we make use of a graphing tool to evaluate the solution

Using a graphing tool, we have

Step 1:

[tex]\frac{4\cos(10x)\sin(4x^5) - 4\sin(10x)\cos(4x^5)}{sin^2(4x^5) - 2\sin(10x)\sin(4x^5) + cos^2(4x5) - 2\cos(10x)\cos(4x5)+ \sin^2(10x) + \cos^2(10x)} + C[/tex]

When simplified, we get

2cot(2x⁵ - 5x) + C

hence, the solution is 2cot(2x⁵ - 5x) + C

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The evaluation of the functions using piecewise function gives:

f(-9) =  8

f(0) =  2

f(6) =  7

f(-6) =  4

f(3) =  4.5

f(9) = -6

To evaluate the functions using piecewise function, we have to the condition they satisfy. That is:

For f(-9), x = -9. Thus, x≤ -6. So use f(x) = (-4/3)x - 4 to evaluate f(-9). That is:

f(-9) =  (-4/3)*(-9) - 4

f(-9) =  8

For f(0), x = 0. Thus, -6 x ≤ 6. So  use f(x) = (5/6)x + 2 to evaluate f(0). That is:

f(0) = (5/6)*0 + 2

f(0) =  2

For f(6), x = 6. Thus, -6 x ≤ 6. So use f(x) = (5/6)x + 2 to evaluate f(6). That is:

f(6) = (5/6)*6 + 2

f(6) =  7

For f(-6), f(x) = (-4/3)x - 4:

f(-6) = (-4/3)*(-6) - 4

f(-6) =  4

For f(3), f(x) = (5/6)x + 2:

f(3) = (5/6)*3 + 2

f(3) =  4.5

For f(9), x = 9. Thus, x > 6. Use f(x) = -2x + 12:

f(9) = -2*9 + 12

f(9) = -6

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Answer: 5,8,6,1

Step-by-step explanation:

math

Answer:

(a) The product xy is negative because one of the factors (x) is negative and the other factor (y) is positive. Therefore, the sign of xy is negative.

(b) The expression x^2y is also negative because x^2 is positive (the square of any real number is positive) and y is positive, so their product is positive. But since x is negative, the overall product is negative.

(c) The expression x/y + x can be written as (x/x)y + x, which simplifies to y + x. Since y is positive and x is negative, the sum y + x could be either positive or negative, depending on which absolute value is greater. If |y| > |x|, then y + x is positive. If |x| > |y|, then y + x is negative.

(d) The expression y-x is positive because y is greater than x and y is positive while x is negative. So the difference y-x is positive.

The x-coordinates of all the points on the graph of f(2x) are half the x-coordinates of the corresponding points on the graph of f(x), which results in a horizontal compression or shrinking of the graph.

What is a graph?

In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).

The transformation f(2x) stretches the graph of f(x) horizontally by a factor of 1/2. In other words, the graph of f(2x) will be compressed horizontally compared to the graph of f(x).

To see why this is the case, consider the effect of replacing x with 2x in the expression for f(x). If we think of f(x) as a set of points in the xy-plane, then each point (x,y) on the graph of f(x) is transformed into the point (2x,y) on the graph of f(2x).

Therefore, this means that the x-coordinates of all the points on the graph of f(2x) are half the x-coordinates of the corresponding points on the graph of f(x), which results in a horizontal compression or shrinking of the graph.

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Answer:

no

Step-by-step explanation:

to check if (-1,-10) is a solution to the system of equations y = -8x + 7 and y = 6x + 5, we substitute x=-1 and y=-10 into both equations and check if both equations hold true.

y = -8x + 7 -10 = -8(-1) + 7 -10 = 8 + 7 -10 ≠ 15

y = 6x + 5 -10 = 6(-1) + 5 -10 = -1

Since (-1,-10) does not satisfy both equations simultaneously, it is not a solution to the system of equations.

The function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3).

In mathematics, a function is a relation between two sets that associates each element of the first set, called the domain, with a unique element of the second set, called the range. In other words, a function maps each input value to a unique output value.

The notation used to represent a function is f(x), where f is the name of the function and x is the input value. The output value is then given by the expression f(x).

Functions can be represented in various ways, such as tables, graphs, equations, and verbal descriptions. They are used to model real-world phenomena, analyze data, and solve problems in various fields, including science, engineering, economics, and finance.

To find the intercepts of the rational function, we set the numerator equal to zero and solve for x:

2/(2x² - x - 3) = 0

2 = 0 (there is no solution for x that makes the numerator zero)

Therefore, the rational function has no x-intercepts.

To find the y-intercept, we set x = 0:

f(0) = 2/(2(0)² - 0 - 3) = -2/3

Therefore, the y-intercept is (0, -2/3).

To find the vertical asymptotes, we set the denominator equal to zero and solve for x:

2x² - x - 3 = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 24))/4

x = (1 ± 5)/4

x = -3/2, 1

Therefore, the rational function has vertical asymptotes at x = -3/2 and x = 1.

To describe the behavior at the vertical asymptotes, we can use limits. Let's consider the vertical asymptote at x = -3/2:

lim x → -3/2+ f(x) = 2/(2(-3/2)² - (-3/2) - 3) = -∞

lim x → -3/2- f(x) = 2/(2(-3/2)² - (-3/2) - 3) = +∞

This means that as x approaches -3/2 from the right, the function approaches negative infinity, and as x approaches -3/2 from the left, the function approaches positive infinity. Therefore, the function has a vertical asymptote at x = -3/2 with a vertical (or infinite) discontinuity.

Let's now consider the vertical asymptote at x = 1:

lim x → 1+ f(x) = 2/(2(1)² - (1) - 3) = +∞

lim x → 1- f(x) = 2/(2(1)² - (1) - 3) = -∞

This means that as x approaches 1 from the right, the function approaches positive infinity, and as x approaches 1 from the left, the function approaches negative infinity. Therefore, the function has a vertical asymptote at x = 1 with a vertical (or infinite) discontinuity.

To analyze and draw the graph of the rational function, we can use the intercepts, asymptotes, and behavior at the vertical asymptotes that we found earlier. We can also find the horizontal asymptote by looking at the degree of the numerator and denominator:

Degree of numerator = 0

Degree of denominator = 2

Therefore, the horizontal asymptote is y =0

As we can see from the graph, the function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3). The behavior at the vertical asymptotes is a vertical (or infinite) discontinuity.

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The complete question is:

Answer:

Volume = (1/2)(7)(24)(22) =

1,848 cubic meters

Surface area = 2(1/2)(7)(24) + 7(22) + 22(24) + 22(25) = 1,400 square meters

The mean of the given set of numbers is 21.8. and median is 25.

In mathematics and statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing by the total number of values. The mean is also known as the arithmetic mean or average.

To find the mean and median of the given set of numbers, we can follow these steps:

Arrange the numbers in order from smallest to largest: 2, 5, 25, 35, 42.

To find the mean, add up all the numbers and divide by the total number of numbers:

Mean = (2 + 5 + 25 + 35 + 42) / 5

= 109 / 5

= 21.8

Therefore, the mean of the given set of numbers is 21.8.

To find the median, we need to find the middle number in the ordered list. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

In this case, there are 5 numbers, so the median is the middle number, which is 25.

Therefore, the median of the given set of numbers is 25.

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(a) The vertex is (6, 144),(b) When the fireworks are launched at time x = 0 and return to the earth at time x = 12 seconds, respectively, these times are denoted by zeros in the function,.(c) this is the quadratic function that represents the situation f(x) = -4 + 144.

a. To find the zeros and vertex of the quadratic function, we need to first write it in the standard form:

[tex]f(x) = ax^2 + bx + c[/tex]

where a, b, and c are constants.

The vertex of the function is given by:

x = -b/2a

Since the quadratic function is symmetrical around the vertex, we know that the time it takes to reach the maximum height is halfway between the launch time and the time it hits the ground again. So, the time to reach maximum height is (4 + 8)/2 = 6 seconds.

Therefore, we can set up a system of equations using the information given:

f(4) = 0 (the firework is launched from the ground)

f(6) = 256 (the firework reaches its maximum height)

f(12) = 0 (the firework hits the ground again)

Plugging in the values of x and f(x), we get:

16a + 4b + c = 0

36a + 6b + c = 256

144a + 12b + c = 0

Solving this system of equations, we get:

a = -4

b = 48

c = 0

Therefore, the quadratic function that represents the situation is:

[tex]f(x) = -x^2 + 48x[/tex]

The zeros of the function can be found by setting f(x) = 0:

[tex]f(x) = -4x^2 + 48x[/tex]

0 = x(-4x + 48)

x = 0 (the firework is launched from the ground)

x = 12 (the firework hits the ground again)

The vertex can be found using the formula:

x = -b/2a = -48/(-8) = 6

So the vertex is (6, 144).

b. Using the zeros and vertex, we can sketch a graph of f(x):

The quadratic function's graph

Considering the function's primary characteristics in light of the circumstances:

The peak height of the fireworks, which occurs at x = 6 seconds and f(6) = 256 feet, is represented by the function's vertex.

The firework is at ground level at x = 0 (launch time) and x = 12 seconds (when it reaches the ground again), which are represented by zeros in the function.

The graph's form suggests that the firework rises before falling again, which is consistent with the scenario given.

c. The quadratic function that represents the situation is:

[tex]f(x) = -4x^2 + 48x[/tex]

This function can be simplified by factoring out -4:

[tex]f(x) = -4( x^2- 12x)[/tex]

Completing the square:

[tex]f(x) = -4( x^2- 12x + 36 - 36)[/tex]

[tex]f(x) = -4( (x^2-6)- 36)[/tex]

[tex]f(x) = -4(x^2-6) + 144[/tex]

This form of the function shows that the vertex is (6, 144), and that the maximum height is 144 feet.

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Answer: 20a +5,600 < 21,000

move the content to the right

20a < 21,000 -5600

calculate

20a<15400

20a <15400
divide both sides of the inequality by 20

a<770

From the graph we can conclude that the x-intercept is (-2.0) and the y-intercept is (0, -4).

The graph is a logical representation of the data, to put it simply. It makes it easier for us to comprehend the facts. The numerical information gleaned via observation is referred to as data.

"Data" is derived from the Latin term datum, which means "something given."

Data are gradually gathered through observation after creating a study question. The data is then summarised, categorised, sorted, and graphically presented.

A variety of objectives are served by data and information: Data is the source of all information, whereas information can be inferred from data.

Here in the question,

From the graph we can see that the line intersects x-axis and y-axis at one point each.

So, the points where they intersect:

x-intercept is (-2.0).

y-intercept is (0, -4).

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The complete question is:

Finding intercepts of a nonlinear function give

The graph of a function is given below.

Give all y-intercepts and x-intercepts shown.

(a) y-intercept(s):

(b) x-intercept(s):

If there is more than one answer, separate them with commas.

To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

The experimental probability of tossing a 3 is 22% ( option D).

Experimental probability, which is also known as Empirical probability, is based on actual experiments and adequate recordings of the occurring of events. An experiment can be repeated a fixed number of times and each repetition is known as a trial. The formula for the experimental probability is defined by;

Probability of an Event P(E) = Number of times an event occurs / Total number of events

From the table it is visible that the occurrence of tossing 3 is 11 times.

So by the definition of experimental probability the possibility is 11/50

As the table given is the result for tossing a number cube 50 times.

In 50 times the possibility is 11

In 1 time the possibility is 11/50

In 100 times the possibility is (11×100)/50

                                              = 22

Hence, the experimental probability of tossing a 3 is 22%.

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Answer: 924 paths

Step-by-step explanation:

Since there is no shorter path, we know that the path must consist of 6 blocks to the north and 6 blocks to the east. Thus, the problem is equivalent to finding the number of ways to arrange 6 N's (for north) and 6 E's (for east) in a sequence such that no two N's are adjacent and no two E's are adjacent.

Let's denote N by 1 and E by 0. Then the problem is equivalent to finding the number of 12-digit binary sequences (i.e., sequences consisting of 0's and 1's) such that there are no consecutive 1's or consecutive 0's.

We can solve this problem using dynamic programming. Let F(n,0) be the number of n-digit binary sequences that end in 0 and have no consecutive 0's, and let F(n,1) be the number of n-digit binary sequences that end in 1 and have no consecutive 1's. Then we have the following recurrence relations:

F(n,0) = F(n-1,0) + F(n-1,1)

F(n,1) = F(n-1,0)

with initial values F(1,0) = 1 and F(1,1) = 1.

Using these recurrence relations, we can compute F(6,0) and F(6,1), and the total number of valid sequences is F(6,0) + F(6,1) = 132. Therefore, there are 132 different paths of length 12 blocks from your apartment to the math class.

Answer:

Option D) 400π cubic units.

Step-by-step explanation:

GIVEN :

TO FIND :

USING FORMULA :

[tex]\quad\star{\underline{\boxed{\sf{V_{(Cylinder)} = \pi{r}^{2}h}}}}[/tex]

SOLUTION :

Substituting all the given values in the formula to find the volume of cylinder :

[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{r}^{2}h}}}[/tex]

[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{(5)}^{2}16}}}[/tex]

[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{(5 \times 5)}16}}}[/tex]

[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{(25)} \times 16}}}[/tex]

[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi \times 25\times 16}}}[/tex]

[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi \times 400}}}[/tex]

[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = 400 \pi}}}[/tex]

[tex]\quad\star{\underline{\boxed{\sf{\pink{V_{(Cylinder)} = 400 \pi \: {units}^{3}}}}}}[/tex]

Hence, the volume of cylinder is 400π cubic units.

A simplification of the fractions (-5/8) ÷ (-3/4) is equal to: B. -20/24.

The step in which Johnetta made her error include the following: A. step 1.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, the division can be calculated as follows;

Fraction = (-5/8) ÷ (-3/4)

Fraction = -5/8 × (-4/3)

Fraction = -20/24

For Johnetta, we have:

Fraction = 7/9 ÷ 3/8

Fraction = 7/9 × 8/3

Fraction = 56/27

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Answer:

Step-by-step explanation:

The angle of elevation of the ladder is approximately 71.6 degrees.

To find the angle of elevation of the ladder, we can use trigonometry. The ladder forms a right triangle with the ground and the tree.

The base of the triangle is 4 feet, the height is 12 feet, and the hypotenuse is the length of the ladder.

Using the trigonometric function tangent (tan), we can write:

tan(angle) = opposite/adjacent

In this case, the opposite side is the height of the tree (12 feet) and the adjacent side is the base of the triangle (4 feet).

Therefore, we can calculate the angle of elevation as follows:

tan(angle) = 12/4

angle = arctan(12/4)

Using a calculator or a trigonometric table, we can find that arctan(12/4) is approximately 71.6 degrees.

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