sharon earns a base pay of $14 h she also earns time and a half for overtime. overtime is any hours beyond 40 h the goal of the question is to write an equation to model the situation then use the equation to determine how many hours sharon worked if she earned $749

Answers

Answer 1

Sharon worked 49 hours to earn $749.

To solve this problem, we need to write an equation that models Sharon's earnings based on her base pay and overtime pay. The equation is as follows:

Earnings = (Base pay x Regular hours) + (Overtime pay x Overtime hours)

Since Sharon earns a base pay of $14 per hour and time and a half for overtime, her overtime pay is $14 x 1.5 = $21 per hour. We can plug these values into the equation:

$749 = ($14 x 40) + ($21 x Overtime hours)

Solving for the overtime hours, we can rearrange the equation and isolate the variable on one side:

$749 - $560 = $21 x Overtime hours

$189 = $21 x Overtime hours

Overtime hours = 9

Therefore, Sharon worked 9 hours of overtime in addition to her regular 40 hours, for a total of 49 hours.

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Related Questions

need some help with this problem. I don't understand it but I would like if someone could help give me a good explanation. Thanks

Answers

Answer: Triangle 1: -6x + 105      Triangle 2: 20x - 30        Triangle 1 would have a greater perimeter if x = 5

Step-by-step explanation:

The perimeter of a shape is the sum of all the sides. (Add them together)

Triangle 1:

17 + 6x + 4(-3x + 22)

Simplify:

17 + 6x -12x + 88

Perimeter = -6x + 105

Triangle 2:

24 + 5x + 3(5x - 18)

Simplify:

24 + 5x + 15x - 54

Perimeter = 20x - 30

If x = 5: (Plug in 5 for x)

Triangle 1:

If x = 5: (Plug in 5 for x)

-6(5) + 105

-30 + 105 = 75

Triangle 2:

20(5) - 30

100 - 30 = 70

75 > 70

Triangle 1 would have a greater perimeter if x = 5

Hope this helps!

Determine the formula for an exponential function f(x) = a -bpasses through the points (1,4.5) and (-1,0.5); i.e., determine the values of a and b, and write the equation for the associated exponential function

Answers

The equation for the exponential function is f(x) = (4.5)((0.5/4.5)-1/2)x. The equation for an exponential function is f(x) = abx, where a and b are constants.

To determine the values of a and b, we can use the two points given in the question, (1,4.5) and (-1,0.5).

Let's substitute the point (1,4.5) into the equation.

f(1) = a*b1
4.5 = a*b

Now let's substitute the point (-1,0.5) into the equation.

f(-1) = a*b-1
0.5 = a*b-1

We can now solve for a and b.

a = 4.5 / b
b-1 = 0.5 / a
b-1 = 0.5 / (4.5/b)
b-1 = 0.5b/4.5
b-2 = 0.5/4.5
b = (0.5/4.5)-1/2

Thus, the equation for the exponential function is f(x) = (4.5)((0.5/4.5)-1/2)x

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Which value of x makes the equation true?
2x - 22 = 12
Group of answer choices
A. 30
B. -6
C. 17
D. 6

Answers

Answer: C (17)

Step-by-step explanation: We need to make the equation true so we take

2x times 17 to get 34  and so 34-22=12

The answer is C. 17

2(30)-22 = 38
2(-6)-22 = -34
2(17)-22 = 12
2(6)-22 = -10

The table for the quadratic functions f(x) and g(x) are given. x f(x) g(x) −2 4 8 −1 1 2 0 0 0 1 1 2 2 4 8 Determine the type of transformation and the value of k.


g(x) = f(2x)

g(x) = 2f(x)

g of x equals f of one half times x

g of x equals one half times f of x


please ASAP!!

Answers

Using the scale factors obtained the values are -

The value of k is 8, since g(−2) = 8.

The value of k is 8, since g(−2) = 8.

The value of k is 8, since g(−2) = 1.

The value of k is 4, since g(−2) = 2.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

For each part, we can use the given table to determine how the transformation affects the function values -

g(x) = f(2x)

This transformation is a horizontal compression by a factor of 2.

To see this, notice that when we evaluate g at x = -1, we get the same value as f evaluated at x = -2.

Similarly, when we evaluate g at x = 0, we get the same value as f evaluated at x = 0.

And so on. In other words, the function values of g(x) are the same as the function values of f(x) at every other point (starting with x = -2).

So, g(x) is a compressed version of f(x) horizontally by a factor of 2.

Therefore, the value of k is 8, since g(−2) = 8 = f(2×(-2)).

g(x) = 2f(x)

This transformation is a vertical stretch by a factor of 2.

To see this, notice that every value of g(x) is twice the corresponding value of f(x).

So, g(x) is a stretched version of f(x) vertically by a factor of 2.

Therefore, the value of k is 8, since g(−2) = 2f(−2) = 2×4 = 8.

g(x) = f(x/2)

This transformation is a horizontal stretch by a factor of 2.

To see this, notice that when we evaluate g at x = -2, we get the same value as f evaluated at x = -4.

Similarly, when we evaluate g at x = -1, we get the same value as f evaluated at x = -2.

And so on. In other words, the function values of g(x) are the same as the function values of f(x) at every other point (starting with x = -4).

So, g(x) is a stretched version of f(x) horizontally by a factor of 2.

Therefore, the value of k is 8, since g(−2) = f(−1) = 1.

g(x) = (1/2)f(x)

This transformation is a vertical compression by a factor of 2.

To see this, notice that every value of g(x) is half the corresponding value of f(x).

So, g(x) is a compressed version of f(x) vertically by a factor of 2.

Therefore, the value of k is 4, since g(−2) = (1/2)f(−2) = (1/2)×4 = 2.

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The table shows the dimensions of three cylinders.
Cylinders
Radius (inches)
Cylinder
W
X
Y
3
4
4.5
Height (inches)
9
2
6
Which two cylinders have the same lateral surface area in square
inches? Answer in capital letters and put them in alphabetical
order.

Answers

Cylinders X and Y have the same lateral surface area in square inches.

Natalie mowed 3 lawns in 18 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.

Answers

Answer: See attached.

Step-by-step explanation:

     First, we will find the unit rate by dividing.

18 hours / 3 lawns = 6 hours per lawn

     Then, we can fill out the other values using this unit rate.

1 lawn * 6 hours = 6

12 hours / 6 hours = 2

       Lastly, we will use these two equivalent ratios we found above to fill out the table and then plot the points. See attached.

Consider the following mathematical function. Сп f(x) = = a cos (2x) + (1 – a) sin (7x). An electronical engineer is willing to understand the behavior of this function. Build a line plot of this function for all a € (0.25k: 1 ks 3,k e Z+), and x € {x € R:-15x 1), where b=2.5, C = 1.6 by creating 15000 rational numbers from (-1,1) interval. In our graphical representation use black, red and blue colors for respective k values. Provide the code and graphical output in your answer sheet

Answers

15000 rational numbers from (-1,1) interval using black

Answer: Code for the given mathematical function# Python code for plotting sine and cosine functions import matplotlib.py plot as plt import numpy as npa = [0.25, 1, 3] # given set of valuesx = np.linspace(-15, 1, 15000) # from (-1, 1) interval and 15000 rational numbersb = 2.5c = 1.6fig, ax = plt.subplots()# Plotting the graph with different colorsplt.plot(x, a[0]*np.cos(b*x)+ (1-a[0])*np.sin(c*x), color='black', label='a=0.25')plt.plot(x, a[1]*np.cos(b*x)+ (1-a[1])*np.sin(c*x), color='red', label='a=1')plt.plot(x, a[2]*np.cos(b*x)+ (1-a[2])*np.sin(c*x), color='blue', label='a=3')# Adding labels and titlesplt.xlabel('x-axis')plt.ylabel('y-axis')plt.title('Plot of given mathematical function')plt.legend()# Displaying the plotplt.show()Graphical output for the given mathematical function:Here, the above code gives a line plot of the given mathematical function for all a € (0.25k: 1 ks 3,k e Z+), and x € {x € R:-15x 1), where b=2.5, C = 1.6 by creating 15000 rational numbers from (-1,1) interval using black, red, and blue colors for respective k values.

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Multiply: (3w)/(55c^(2))*(11c^(4))/(6w^(2)) (Assume all denominators are nonzero )

Answers

(3w/55c6w2)*(11c4/6w2) = 33c4/330c6w4.

To multiply fractions, we first need to express the fractions in the same denominator. To do this, we need to find the least common denominator (LCD) of the two fractions. In this case, the LCD is 55c6w2. Once we have the LCD, we can then rewrite the fractions with that as the denominator.

So the first fraction will be (3w/55c6w2) and the second fraction will be (11c4/6w2). Now that the fractions have the same denominator, we can multiply the numerators of the fractions and keep the same denominator.

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Coach Kidd goes shopping on Monday for water to sell at the ball game. She has $30.00. After buying 15 water bottles, she had $7.50 left. How much did each water bottle cost?

Answers

Answer:

Step-by-step explanation:

based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number

Answers

The solution is:  standard deviation. So, correct option is C.

Here, we have,

Explanation:

However, note that the mean of a sample from a normal population (that is, a type of "standard deviation" known as "standard deviation from a sample mean", is an "unbiased estimator" of the "population mean".

We shall represent the "sample mean" as:  X  ;

              (pronounced: "x-bar"; that is; "ex-bar"); this is the usual symbol                                                                                                              used;

We shall represent the sample size as "n" ;

                                                (This is the usual variable used; note that

                                                                               "n" is a numeric value).

The standard deviant from the sample mean:

(n *  X)  / (n + 1) is a "biased estimator of the mean" that becomes "unbiased" as the sample size increases; since as "n" increases in values; the value of the entire entire expression becomes smaller (i.e the standard deviation becomes smaller.

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Complete question:

Which biased estimator will have a reduced bias based on an increased sample size? mean median standard deviation range

Find the values of x such that the angle between the vectors < 2, 1, -1 > , and < l,x,0 > is 45 degree.

Answers

The values of x that satisfy the equation are (l + sqrt(11)l)/10 and (l - sqrt(11)l)/10.

To find the values of x such that the angle between the vectors < 2, 1, -1 > and < l,x,0 > is 45 degrees, we can use the formula for the dot product of two vectors:

= |u||v|cos(theta)

Where  is the dot product of the vectors u and v, |u| and |v| are the magnitudes of the vectors, and theta is the angle between them. Plugging in the values from the question, we get:

< 2, 1, -1 > . < l,x,0 > = |< 2, 1, -1 >||< l,x,0 >|cos(45)

Simplifying the dot product, we get:

2l + x = sqrt(6)sqrt(l^2 + x^2)/sqrt(2)

Squaring both sides and rearranging, we get:

4l^2 + 4lx + x^2 = 6l^2 + 6x^2

2l^2 + 2lx - 5x^2 = 0

Using the quadratic formula, we can solve for x:

x = (-2l +/- sqrt(4l^2 - 4(2l^2)(-5)))/(2(-5))

x = (-l +/- sqrt(l^2 + 10l^2))/(-10)

x = (-l +/- sqrt(11)l)/(-10)

x = (l +/- sqrt(11)l)/10

Therefore, the values of x that satisfy the equation are (l + sqrt(11)l)/10 and (l - sqrt(11)l)/10.

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2(3a+2b−7) what is the equivalent expression to the given expression?

Answers

For an expression 2(3a+2b−7), an equivalent expression is 6a + 4b - 14

The correct answer is an option (D)

Consider an expression 2(3a+2b−7)

We simplify this expression.

2(3a+2b−7)

To simplfy this expression, multiply each term of (3a+2b−7) by 2

2(3a+2b−7)

= 2 × (3a + 2b - 7)

= (2 × 3a) + (2 × 2b) - (2 × 7)

= 6a + 4b - 14

So, we get 2(3a+2b−7) = 6a + 4b - 14

Therefore, 6a + 4b - 14 is an equivalent expression to 2(3a+2b−7)

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The complete question is:

Which expression is equivalent to the given expression? 2(3a+2b−7) ​

A 5a+4b−5

B 6a+2b−7

C 6a+4b−7

D 6a+4b−14

The diagram shows a quarter circle of radius 12 cm
12 an
Work out the area of the shape,
Answer
Not drawn
accurately
cm²
[2 marks]

Answers

In response to the supplied query, we may state that Therefore, the area of the circle is approximately 113.1 cm² (rounded to one decimal place).

What is circle?

A circle is created in the plane by each point that is a specific distance from another point (center). Hence, it is a curve made up of points that are separated from one another by a defined distance in the plane. Moreover, it is rotationally symmetric about the centre at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "centre." A circular symmetry line is made by drawing a line through the circle. Moreover, it is rotationally symmetric about the centre at every angle.

We must make certain assumptions because the diagram was not created precisely. Assume that the quarter circle is a perfect quarter circle and that its radius is 12 cm (as given in the question).

A = r2, where r is the radius, is the formula for calculating a circle's surface area. Due to the fact that we only have a quarter of a circle, we must divide the outcome by 4. Hence, the quarter circle's area is:

[tex]A = (1/4)\pi r^2\\A = (1/4))\pi(12^2)\\A = (1/4))\pi(144)\\A = 36)\pi[/tex]

Therefore, the area of the shape is approximately 113.1 cm² (rounded to one decimal place).

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Isλ=4an eigenvalue of​32−4​033​2−26​​? If so, find one corresponding eigenvector. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. Yes,λ=4is an eigenvalue of​32−4​033​2−26​​. One corresponding eigenvector is (Type a vector or list of vectors. Type an integer or simplified fraction for each matrix element.) B. No,λ=4is not an eigenvalue of​32−4​033​2−26​​

Answers

The correct option is A. Yes, λ=4 is an eigenvalue of the matrix.

To find the corresponding eigenvector, we need to solve the equation (A - λI)x = 0, where A is the given matrix, λ is the eigenvalue, I is the identity matrix, and x is the eigenvector.
First, we subtract λI from A:
A - λI = 3-4 -4 0 0 3-4 3 2-4 -2 6
= -1 -4 0 0 -1 3 2 -2 2
Next, we set the equation (A - λI)x = 0 and solve for x:
(-1 -4 0) (x1) = 0
(0 -1 3) (x2) = 0
(2 -2 2) (x3) = 0
Simplifying the equations gives us:
-x1 - 4x2 = 0
-x2 + 3x3 = 0
2x1 - 2x2 + 2x3 = 0
We can solve this system of equations to find the eigenvector. One possible solution is x1 = 2, x2 = 1, x3 = 1/3. Therefore, one corresponding eigenvector is (2, 1, 1/3).
So the correct answer is A. Yes, λ=4 is an eigenvalue of the matrix. One corresponding eigenvector is (2, 1, 1/3).

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It costs an appliances company an initial flat rate of $25.70 to
request a shipment of products, with an additional $2.30 charged
per item. Write an equation in slope-intercept form where x
represents the number of items manufactured, and y represents the
total cost of the appliances.

Answers

Answer: The flat rate cost is $25.70 and the cost per item is $2.30, so the total cost (y) can be represented as:

y = 2.30x + 25.70

This is in slope-intercept form, where the slope is 2.30 and the y-intercept is 25.70.

Step-by-step explanation:

(73) If you insert number of arithmetic means between - 65 and 125 and the twelveths mean = - 113 , then the number of means = .. (a) 12 (b) 13 (c) 14 (d) 15 ​

Answers

The number of means is 13. Option B

How to find the number of means

We can use the formula for the nth term of an arithmetic sequence to solve the problem. Let d be the common difference and n be the number of terms between -65 and 125.

Then we have:

a + (n-1)d = 125 (1)

a + nd = -113 (2)

Subtracting equation (2) from equation (1), we get:

(n-1)d + 238 = 0

Solving for d, we get:

d = -238/(n-1)

Using the formula for the twelfth term, we have:

a + 11d = -113

Substituting the expression for d, we get:

a - 11(238/(n-1)) = -113

Multiplying both sides by n-1, we get:

a(n-1) - 11(238) = -113(n-1)

Substituting a = -65 and simplifying, we get:

n = 13

Therefore, the number of means is 13

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Rewrite the expression in terms of ln 3 and ln 4.
ln(144)

Answers

ln(144) can be written in terms of ln(3) and ln(4) as:

ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)

We can use the logarithmic property that states that ln(a * b) = ln(a) + ln(b) to rewrite ln(144) in terms of ln(3) and ln(4).

First, we can find the prime factorization of 144:

[tex]144 = 2^4 * 3^2[/tex]

Using the property above, we can rewrite ln(144) as:

[tex]ln(144) = ln(2^4 * 3^2) = ln(2^4) + ln(3^2)[/tex]

Now, we can use another logarithmic property that states that ln(aᵇ) = b * ln(a) to simplify ln(2⁴) and ln(3²):

ln(144) = 4 ln(2) + 2 ln(3)

Therefore, ln(144) can be written in terms of ln(3) and ln(4) as:

ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)

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what two situations involving rational exponents or radicals will never result in a negative real soltution

Answers

Answer:

There are two situations involving rational exponents or radicals that will never result in a negative real solution:

Even-indexed roots: If we take the square root, fourth root, sixth root, etc. of a non-negative real number, the result will always be non-negative. For example, the square root of 9 is 3, and the fourth root of 16 is 2, both of which are non-negative. This is because even-indexed roots always produce a non-negative result, regardless of the sign of the original number.

Exponents with even denominators: If we raise a non-negative real number to an exponent with an even denominator, the result will always be non-negative. For example, (4^2/4) is equal to 4, which is non-negative. This is because any negative base raised to an even power results in a positive number, and any positive base raised to an even power also results in a positive number. Therefore, any exponent with an even denominator will always produce a non-negative result, regardless of the sign of the original number.

-70÷ (-1)
How do i get the solution??​

Answers

ANSWER: 70

Any expression divided by -1 equals its opposite, turning -70 into positive 70.

Answer:

70

Step-by-step explanation:

-70 / -1

= 70 / 1

= 70

What is the solution to the inequality x-41 <3?

Answers

This can be solved through steps!

1. Rewrite the problem

x - 41 < 3

Rewriting the problem helps to stay organized.

2. Add 41 to both sides

x - 41 + 41 < 3 + 41

x < 44

3. Answer Recap

Now that we have the variable isolated, we have our answer to the inequality: x < 44.

4. For the system of equations \[ \begin{array}{r} 2 x_{1}-2 x_{2}+5 x_{3}+7 x_{4}=0 \\ x_{1}+5 x_{2}+6 x_{3}+9 x_{4}=0 \\ x_{1}+17 x_{2}+13 x_{3}+20 x_{4}=0 \\ 3 x_{1}-2 x_{2}+4 x_{3}=0 \end{array} \

Answers

$x_1 = \frac{7}{2}, \ x_2 = \frac{11}{2}, \ x_3 = -\frac{1}{2}, \ x_4 = \frac{9}{2}$.

To solve this system of equations, first use the array method to organize the equations.

Array Method:

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 1 & 5 & 6 & 9 & 0 \\ 1 & 17 & 13 & 20 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Now, use row operations to solve the system. Begin by combining the first and third equations by adding them together.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 1 & 5 & 6 & 9 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Next, combine the second and fourth equations by subtracting the fourth equation from the second equation.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 7 & 2 & 9 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Then, combine the second and third equations by adding the second equation to the third equation.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 0 & 14 & 36 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Now, combine the first and third equations by subtracting the third equation from the first equation.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 0 & 14 & 36 & 0 \\ 0 & 0 & -2 & -9 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Finally, use back substitution to solve for the variables. Starting with $x_4$, use the fourth equation to solve for it:

$x_4 = \frac{9}{2}$

Then, use the third equation to solve for $x_3$:

$x_3 = -\frac{1}{2}$

Continuing this process, we can also solve for $x_2 = \frac{11}{2}$ and $x_1 = \frac{7}{2}$.

Therefore, the solution to the system is:

$x_1 = \frac{7}{2}, \ x_2 = \frac{11}{2}, \ x_3 = -\frac{1}{2}, \ x_4 = \frac{9}{2}$.

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1. A graduate student from the Catholic University of Puerto Rico carried out a research project on how the adult population in Puerto Rico communicates with the objective of estimating the percentage of adults who prefer postal mail to electronic mail. She started with a survey that she mailed to 600 of the adults she knew. She asked them to send her the answer to this question: Do you prefer to use email or the postal service? Upon receiving the responses, 250 adults indicated their preference for the postal service. After completing her study, the student concludes that 48% of adults in Puerto Rico prefer the postal service to email.
a. the variable
b.population
c.population
d.parameter
e. sample

Answers

a. The variable is the type of communication preference: postal service or email.

b. The population is the adult population in Puerto Rico.

c. The parameter being estimated is the percentage of adults who prefer postal mail to electronic mail.

d. The parameter being estimated is the percentage of adults who prefer postal mail to electronic mail.

e. The sample is the 600 adults that the graduate student surveyed.

a. The variable in this research project is the preferred method of communication for adults in Puerto Rico (postal mail or email).

b. The population in this research project is the adult population in Puerto Rico.

c. The sample in this research project is the 600 adults that the graduate student surveyed.

d. The parameter in this research project is the percentage of adults in Puerto Rico who prefer postal mail to email.

e. The statistic in this research project is the 250 adults who indicated their preference for the postal service out of the 600 adults surveyed. This statistic was used to estimate the parameter of 48% of adults in Puerto Rico preferring the postal service to email.

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A sales manager wants to know if display at point of purchase helps in increasing the sales of his product. He has taken note on sales before the display and after the display for a randomly selected 11 shops. The mean of the differences in sales between after display and before display was found to be 300 with SD=314.8. Is there sufficient evidence to conclude that display at point of purchase helps in increasing the sales of his product ? Use 1 % significance level. Also make your decision based on 99% CI for true difference.

Answers

Yes, there is sufficient evidence to conclude that display at point of purchase helps in increasing the sales of the product. This is because the mean difference in sales after display (300) is greater than the standard deviation (314.8), which indicates that there is a significant difference between the two groups.

To further support this conclusion, we can use a 99% confidence interval (CI) for the true difference. The formula for a 99% CI is:

CI = mean difference ± (t-value)(SD/sqrt(n))

Where n is the sample size, t-value is the critical value for a 99% CI, and SD is the standard deviation. For a sample size of 11 and a 99% CI, the t-value is 3.106. Plugging in the values, we get:

CI = 300 ± (3.106)(314.8/sqrt(11))

CI = 300 ± 294.6

CI = (5.4, 594.6)

Since the 99% CI does not include 0, we can conclude that there is sufficient evidence to support the claim that display at point of purchase helps in increasing the sales of the product. In other words, we can be 99% confident that the true difference in sales between after display and before display is between 5.4 and 594.6, which supports the claim that display at point of purchase helps in increasing sales.

True difference in sales lies between -162 and 662

Yes, there is sufficient evidence to conclude that display at point of purchase helps in increasing the sales of the product. The mean of the differences in sales between after display and before display was found to be 300 with a standard deviation of 314.8. This indicates that, on average, the display helped to increase sales by 300.

Furthermore, with a 99% confidence interval, the true difference in sales lies between -162 and 662, which is statistically significant. Therefore, the display at point of purchase has a statistically significant effect on sales and should be implemented.

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z_(3)+(2z_(3)+i)^(x)=4-6i Find Z_(3), giving your answer in the form a+b i where a,binR

Answers

z3 = 6 - 2xz3x + 4 in the form a + b i, where a,b in R.

=> z3 + (2z3 + i)x = 4 - 6i

Expand the bracket:

z3 + 2xz3x + ix = 4 - 6i


Subtract 4 from both sides:

z3 + 2xz3x + ix - 4 = - 6i


Rearrange and set ix = -1:

z3 + 2xz3x - 4 = 6


Subtract 2xz3x from both sides:

z3 - 4 = 6 - 2xz3x


Solve for z3:

z3 = 6 - 2xz3x + 4


Therefore, z3 = 6 - 2xz3x + 4 in the form a + b i, where a,b in R.

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Only datasets having a linear relationship between variables can be assessed using regression analyses. A. True B. FALSE

Answers

The statement, "Only datasets having a linear relationship between variables can be assessed using regression analyses" is False, because Non-Linear relationships also can be assessed, the correct option is (b)False.

The Regression Analysis can be used to assess the relationship between variables, including non-linear relationships.

There are various types of regression models that can capture non-linear relationships, such as polynomial regression, exponential regression, and logarithmic regression.

The interpretation of the regression coefficients and other statistics may be different in non-linear regression models compared to linear regression models.

Therefore, the given statement is (b)False.

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A train leaves a station every 8 minutes. (1) A bus leaves the station every 10 minutes. A bus and a train both leave the station at 3.50pm. Find the next time when a train and a bus leave the station

Answers

The next time when a train and a bus leave the station together is 4:30pm.

The next time when a train and a bus leave the station together will be the least common multiple (LCM) of the two intervals, 8 minutes and 10 minutes.

To find the LCM of 8 and 10, we can list the multiples of each number until we find a common multiple:
8: 8, 16, 24, 32, 40
10: 10, 20, 30, 40

The LCM of 8 and 10 is 40. This means that a train and a bus will leave the station together every 40 minutes.

Since the train and bus both leave the station at 3:50pm, the next time they will leave together will be 40 minutes later, at 4:30pm.

Therefore, the next time when a train and a bus leave the station together is 4:30pm.

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58. If G is a non-Abelian group, prove that G has an automorphism that is not the identity.

Answers

If G is a non-Abelian group, it has an automorphism that is not the identity. This is proven by constructing a map φ that is a bijective homomorphism but not the identity, using an element a that is not in the center of G.

An automorphism is a bijective homomorphism of a group onto itself. If G is a non-Abelian group, we need to prove that there is an automorphism that is not the identity.

To prove this, we can use the following steps:

1. Let G be a non-Abelian group.
2. Choose an element a ∈ G that is not in the center of G. This means that there exists an element b ∈ G such that ab ≠ ba.
3. Define a map φ: G → G by φ(x) = axa⁻¹ for all x ∈ G.
4. We can prove that φ is a homomorphism by showing that φ(xy) = φ(x)φ(y) for all x, y ∈ G.
5. We can also prove that φ is bijective by showing that it has an inverse map φ⁻¹: G → G defined by φ⁻¹(x) = a⁻¹xa for all x ∈ G.
6. Since φ is a bijective homomorphism, it is an automorphism of G.
7. However, φ is not the identity, because φ(b) = aba⁻¹ ≠ b.
8. Therefore, G has an automorphism that is not the identity.

In conclusion, if G is a non-Abelian group, it has an automorphism that is not the identity. This is proven by constructing a map φ that is a bijective homomorphism but not the identity, using an element a that is not in the center of G.

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Which polynomial function has zeros of x=-2 with a multiplicity of 2,x=1 with a multiplicity of 1 , and a y-intercept of 2 ?

Answers

The polynomial function has zeros of x=-2 with a multiplicity of 2, x=1 with a multiplicity of 1 , and a y-intercept of 2 is y = (x+2)^2(x-1) + 2.

To find out which polynomial function has zeros of x=-2 with a multiplicity of 2, x=1 with a multiplicity of 1, and a y-intercept of 2, we can use the factored form of a polynomial function.

This is given by:

f(x) = a(x - r₁)^n₁(x - r₂)^n₂ ... (x - rₖ)^nₖ where a is a constant, r₁, r₂, ..., rₖ are the zeros of the function, and n₁, n₂, ..., nₖ are their respective multiplicities.

Using the given zeros and multiplicities, we can write the factored form of the polynomial as:

f(x) = a(x + 2)²(x - 1) where the y-intercept is 2. To find the value of a, we can substitute the y-intercept, (0, 2), into the function:

f(0) = a(0 + 2)²(0 - 1) = -4a

Since the y-intercept is 2, we have:

f(0) = 2-4a = 2 => -4a = 0 => a = 0

Therefore, the polynomial function is:

f(x) = a(x + 2)²(x - 1) = 0(x + 2)²(x - 1) = 0

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1 and 2 are complementary. if 1 is x + 4 and 2 is 23 + 2 x, find the measure of 1 and 2​

Answers

Answer:

Step-by-step explanation:

x + 4 + 2x + 23 = 90

3x + 27 = 90

3x = 63

x = 21

x + 4 = 21 + 4 = 25 for <1

2(21) + 23  = 42 + 23 = 65 for <2

Perform long division, please clearly show work of remainders
and arrows, where numbers pass down.
Thanks
1. 32.156 / 100
2. 174.787 / 0.01

Answers

There are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.

To perform long division, we need to follow these steps:

Set up the long division problem with the dividend on the inside and the divisor on the outside of the division symbol.
Determine how many times the divisor can go into the first digit or group of digits of the dividend.
Write the result above the division symbol and multiply it by the divisor.
Subtract the result from the first digit or group of digits of the dividend.
Bring down the next digit or group of digits from the dividend and repeat the process until there are no more digits to bring down.
The final result is the quotient with any remainders.

For the first problem, 32.156 / 100, we can set it up like this:

```
100 | 32.156
```

Since 100 cannot go into 32, we need to bring down the next group of digits, which is 156. Now we have:

```
100 | 3215.6
```

100 can go into 3215 a total of 32 times, so we write 32 above the division symbol and multiply it by 100:

```
32
100 | 3215.6
  -3200
   -----
     15.6
```

Now we bring down the next group of digits, which is 6:

```
32.1
100 | 3215.6
  -3200
   -----
     156
```

100 can go into 156 a total of 1 time, so we write 1 above the division symbol and multiply it by 100:

```
32.16
100 | 3215.6
  -3200
   -----
     156
    -100
   -----
      56
```

Since there are no more digits to bring down, we are left with a remainder of 56. So the final result is 32.156 with a remainder of 56.

For the second problem, 174.787 / 0.01, we can set it up like this:

```
0.01 | 174.787
```

Since 0.01 cannot go into 174, we need to bring down the next group of digits, which is 787. Now we have:

```
0.01 | 17478.7
```

0.01 can go into 17478 a total of 1747800 times, so we write 1747800 above the division symbol and multiply it by 0.01:

```
1747800
0.01 | 17478.7
   -17478
    -----
        0.7
```

Since there are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.

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