Gayle Miller works 43 hours every week. Her weekly salary is $397.75. How much overtime does Gayle make each week?​

At 95% confidence, the z critical value is roughly z = 1.96

You would use a reference table or calculator to determine this value. Unfortunately it's not something that can be easily/quickly found by hand.

If we're trying to estimate the population mean (mu), then we'll use this margin of error formula

E = z*sigma/sqrt(n)

Or if we want to estimate the population proportion (p), then we use this formula

E = z*sqrt(phat*(1-phat)/n)

The confidence interval then spans from (pointEstimate)-E to (pointEstimate)+E. Where "pointEstimate" represents either xbar or phat depending on the context. Other point estimates are possible. We're focusing on these two for now.

xbar estimates mu

phat estimates p

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An example problem:

A manager at a soda bottling plant wants to know if the contents of the cans are 20 fluid ounces (fl oz) or not. Through past observations, the manager has noted the population standard deviation (sigma) is 1.72 fl oz.

The manager gathers a random sample of 50 cans to test their contents. They find the sample mean is 18 fl oz. Conduct a hypothesis test using a confidence interval at 95% confidence to see if the cans really do have 20 fl oz of drink in them or not.

--------------------------------

Solution:

Null Hypothesis: mu = 20

Alternate Hypothesis: mu ≠ 20

This is a two-tailed test.

E = margin of error

E = z*sigma/sqrt(n)

E = 1.96*1.72/sqrt(50)

E = 0.47676

L = lower boundary of confidence interval

L = xbar - E

L = 18 - 0.47676

L = 17.52324

L = 17.52

U = upper boundary of confidence interval

U = xbar + E

U = 18 + 0.47676

U = 18.47676

U = 18.48

The 95% confidence interval is approximately (17.52, 18.48)

This is equivalent to writing 17.52 < mu < 18.48 in which we are 95% confidence in saying mu is between those endpoints.

But wait, the hypothesized mu = 20 is not in the interval 17.52 < mu < 18.48, which indicates we must reject the null hypothesis and accept the alternate hypothesis.  

The soda cans do not have 20 fl oz of drink. It appears they have slightly less than 20 fl oz.

Answer: 0

Step-by-step explanation:

If the dividend and the divisor are the same, the quotient is always 1. If the dividend is the, then the quotient would always be 0. A division equation with 0 dividend and 0 divisor is not valid.

Answer: All real numbers

Step-by-step explanation: Anything that's being divided by 0, is always going to be 0. For example, 0/7 is always 0.

The addition of w, 9 and 4 is (w+13).

According to the question,

We have the following information:

We need to add w, 9 and 4.

We already know that a variable can only be added or subtracted from the terms having the same variables. For example, 8x can only be added to 5x but not 5y.

So, in this case, w is the variable and it can not be added to any other term because the other two are whole numbers.

Now, the whole numbers can be easily added.

So, we have the following expression:

w+9+4

w+13

Hence, the addition of w, 9 and 4 is (w+13).

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Answer:

22. 2 (-4) = -8

23. (2(-4) + 11) = (-8 + 11) = 3

24. -3 (5 (-4) = -3 (-20) = 60

Answer:

  22.  8

  23.  3

  24.  -60

Step-by-step explanation:

You want the values of the given absolute value expressions when x = -4.

The absolute value function changes the sign to positive, if it isn't already.

  2|-4| = 2(4) = 8

  |2(-4) +11| = |-8 +11| = |3| = 3

  -3|5(-4)| = -3|-20| = -3(20) = -60

A graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
With the help of the vertex and the x-intercept, the equation of the parabola can be formed which helps to graph a quadratic function because the equation of the parabola resembles the quadratic function,

Thus,  a graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.

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Answer: 140 is the answer

Step-by-step explanation: Luis adds 100 to his account  so which makes the account balance 180 and then writes a check so he takes 40 out of his account which means he has 140 left in his account

The types of correlation seen between positive correlation, negative correlation, or no correlation, in the variables is:

One of the main sources of funding for school districts is the property tax charged. This means that increased property taxes will lead to more money being available for teacher salaries which might then increase. There is therefore a positive correlation between the two.

The same is true for the weight of a person and shoe size. This is because the heavier a person is, the larger their shoe size according to research.

There is however no correlation between the height of a person and their attendance of religious services.

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The graph of the function g(x) = -2x - 3 is attached below.

Graph:

Graph refers a diagram that represents the variation of a variable in comparison with that of one or more other variables.

Given,

Here we have the function g(x) = -2x - 3

Now, we need to plot the graph of the function.

In order to plot the graph for the given function,

First we have to take some sample values for the given function and then apply it on the given function to generate the table to plot the graph.

Now, we have to take -2, -1, 0, 1, 2 are the samples value for x.

Then we get the value of the function as,

x = -2 => g(-2) = -2(-2) - 3 = 4 - 3 = 1

x = -1 => g(-1) = -2(-1) - 3 = 2 - 3 = -1

x = 0 => g(0) = -2(0) - 3 = 0 - 3 = -3

x = 1 => g(-2) = -2(1) - 3 = -2 - 3 = -5

x = 2 => g(2) = -2(2) - 3 = -4 - 3 = -7

Now, we can get the table like the below

Now, we have to plot the graph through this table, then we get the graph like the following.

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An inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56

In this question we have been given Mrs. Boyer is buying folding chairs that are on sale for $8.

She has $56

We need to find an inequality that can be solved to show the number of chairs c Mrs. Smith can buy.

A price of one chair is $8

So, the price of 'c' number of chairs would be 8c

But she has $56

So, to find the number of chairs she can buy, we need to divide 56 by 8

We can write is as 8c = 56

⇒ c = 7

But she might buy less that 7 chairs.

So, we write above relation in inequality form as,

8c ≤ 56

Therefore, an inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56

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Answer:

1  :  4

Step-by-step explanation:

There are 4 squares and 16 triangles.

That is,

Squares : Triangles

          4  :  16

To write it in its simplest ratio, divide both by 4.

Squares : Triangles

         1  :  4

From the given proof below, we have been able to show that quadrilateral ABCD is a Trapezoid.

A trapezoid is also called a trapezium and it is characterized by four straight sides and one set of parallel sides. The parallel sides are referred to as the base, while the non-parallel sides are referred to as the legs.

We are told that;

O is the point of intersection for the diagonals of quadrilateral ABCD;

where;

AO/BO = CO/DO

This can also be expressed as;

AO/CO = BO/DO

Thus, if we create line OE to be parallel to DC which is OE || DC. Then it means that point E lies on BC.

Using the Basic Proportionality Theory, in ΔBDC, we can say that;

BO/OD = BE/EC ............................1

We are also given that:

AO/CO = BO/DO   ..........................2

Thus, from Equations 1 and 2, we have;

AO/CO = BE/EC

Using the converse form of the Basic Proportionality Theorem, we have;

OE || AB

Therefore, AB || OE || DC.

Therefore we can conclude that ABCD is a Trapezoid.

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Answer:

The answer would be A. (Not sure if its A B C or D question but I will have picture below)

Step-by-step explanation:

Hope this helps you! :))

Answer: 584390

Step-by-step explanation: the r4u819

The sum form of the trigonometric function 2 · sin 2x · sin 2x by product-to-sum formula is 1 - cos 4x.

Herein we find the definition of a trigonometric function defined as a product of trigonometric function, this can be transformed into a sum of trigonometric functions by means of the following product-to-sum formula:

sin α · sin β = [cos (α - β) - cos (α + β)] / 2

First, write the trigonometric function defined in the statement:

2 · sin 2x · sin 2x

Second, use the product-to-sum formula by considering α = β = 2 · x:

2 · [[cos (2x - 2x) - cos (2x + 2x)] / 2]

cos 0 - cos 4x

1 - cos 4x

Third, write the resulting expression:

2 · sin 2x · sin 2x = 1 - cos 4x

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The value of the side CB in the right angled triangle is found as 4√2 units.

For the given question,

The diagram is given;

AB = 7 units.

AG = 3 units.

GB = 7 - 3 = 4 units.

GC = 4 units.

In right angled triangle GCB, apply Pythagorean theorem.

CB² = GB² + GC²

CB² = 4² + 4²

CB² = 2(4)²

Taking square root both side.

CB = 4√2

Thus, the value of the side CB in the right angled triangle is found as 4√2 units.

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Using the distance formula, the distance between the point is √130.

In the given question we have to find the distance between given point in the graph.

From the graph the given points are (4,4) and (-3, -5).

The formula for the distance between point is

Distance = √{x(2)-x(1)}^2+{y(2)-y(1)}^2

From the given points; x(1)=4, y(1)=4, x(2)= -3 and y(2)= -5.

Now putting the value:

Distance = √{-3-4}^2+{-5-4}^2

Distance = √{-7}^2+{-9}^2

Distance = √49+81

Distance = √130

The distance between the point is √130.

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Answer:

no

Step-by-step explanation:

because Kira ordered 5 pieces of crab while Marcy has ordered 6 pieces of crab

60 minutes will be taken by the older computer to send out the email on its own.

Two or more expressions with an Equal sign is called as Equation.

one computer takes x minutes and the other takes 3x minutes

in 1 minute, they send (1/x) and (1/3x) of the total message

together, (15/x)+(15/3x)=1, the full message

multiply by 3x to clear fractions

45+15=3x

60=3x

Divide both sides by 3

20=x

So for older computer  60 minutes  it take to send out the email on its own.

Hence, 60 minutes will be taken by the older computer to send out the email on its own.

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Answer:

Step-by-step explanation:

Answer: 13.9

Step-by-step explanation:

17.140 rounded to the nearest tenth is 17.1

03.179 rounded to the nearest tenth is 3.2

17.1 - 3.2 = 13.9

Answer:

  f(x) = x² -2x -35

Step-by-step explanation:

You want a quadratic function that has zeros 7 and -5.

Each zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).

  f(x) = (x -7)(x +5)

  f(x) = x² -2x -35

__

Additional comment

You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.

  sum: 7-5 = 2

  product: (7)(-5) = -35

  quadratic: f(x) = x² -2x -35

By using the concept of set operation, the result obtained is

[tex]n(A \cap B) = 2[/tex]

What is a set?

Set is a well defined collection of distinct objects. The members of a set are called elements of a set. Set can be empty as well as non empty.

Set can be finite as well as infinite.

The number of elements inside a set is known as cardinal number of the set

Operations on set are union, intersection, set difference and symmetric difference

Concept of set operation has been used here

n(A)=5 n(B)=7 and n(AUB)= 10

[tex]n(A \cap B) = n(A) + n(B) - n(A \cup B)[/tex]

[tex]n (A \cap B) = 5 + 7 -10\\n(A \cap B ) =2[/tex]

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The different ways to make groups of 4 based on the napkins given is 6 ways.

Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Thus can be illustrated by nCr

Combination formula

nCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time

In this case, Elijah has red and yellow napkins. He must set out napkins for 4 people. This will be:

= n! / ((n – r)! r!)

= 4! / (4 - 2)! 2!

= 4! / 2!2!

= 4 × 3/2

= 6

Therefore, there are 6 ways.

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Answer:

Add up all the numbers and divide the product of that by the numbers there are.

7+6+12+5+7+6+13 = 56

There are 7 numbers in these set of numbers hence we divide the product (56) by 7.

56/7 = 8

The answer is 8; The average of all these numbers is 8.

Step-by-step explanation:

Step-by-step explanation:

9)=

By the question:-

x + y = 130-i

x - y = 34-ii

Now,

Add i and ii,

x + y + x -y = 164

or, 2x = 164

so, x = 82

Now,

x -y = 34

or, 82 - y = 34

so, y = 48

The numbers are 82 and 48.

10) =

Let adults ticket be x and childs ticket be y.

x + y = 800

x = 800 - y - eqn i

4.5x + 6y = 4500

Substituting x's value from eqn i,

4.5(800-y) + 6y = 4500

or, 3600 - 4.5y + 6y = 4500

or, 1.5y = 900

so, y = 600

Now,

x + y = 800

or, x + 600 = 800

so, x = 200

Hence, 600 adult tickets were sold and 200 child tickets were sold.

11)=

Let cost of one small box be x and one medium box be y.

So,

4x + 2y = 54-eqn i

x + 2y = 33-eqn ii

subtracting eqn i from ii,

x + 2y - 4x - 2y = - 21

or, -3x = - 21

so, x = 7

Now,

x + 2y = 33

or, 2y = 33 - 7

or, y = 26/2

so, y = 13

So, cost of one small box is $7 and medium box is $13.

Answer:

6x=24-12y

x=24-12y/6

x=4-12y

Answer: C

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!

From the proportional relationship graphed, it is found that:

A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0, meaning that the relationship passes through the origin.

When the two variables x and y are direct proportional, the output variable y is obtained multiplying the input variable x by the constant of proportionality k, according to the rule presented follows:

y = kx.

From point (2,16) in this problem, the constant is given as follows:

k = 16/2 = 8.

Hence the equation is:

y = 8x.

Meaning that her rate is of:

8 miles per hour.

If she ran faster, the slope = constant would increase, as it represents the velocity.

The problem is given by the image at the end of the answer.

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father age 46.5

daughter age 15.5

46.5 - 15.5 = 31