According to The Food and Drug Administration (FDA), 400 milligrams (mg) a day is considered a safe amount of daily caffeine consumption which is about 4 to 5 cups of coffee. We suspected that people who visit coffee shops in the morning drink more coffee on average than people who visit coffee shops in the afternoon. During one day, we randomly sampled 8 people who entered a given coffee shop in the morning and 8 people who entered the coffee shop in the afternoon. We recorded each person's average daily caffeine consumption (in mg).
( Could I pleas get help on the missing questions )
a. standard error of (xmorning - xafternoon) =
b.Construct an approximate 95% confidence interval for morning - afternoon
Lower bound =
Upper bound =

According To The Food And Drug Administration (FDA), 400 Milligrams (mg) A Day Is Considered A Safe Amount

Answers

Answer 1

The apprοximate 95% cοnfidence interval fοr mοrning - afternοοn caffeine cοnsumptiοn is (70.37, 229.63) mg.

What is standard errοr?

Standard errοr is a statistical measure οf the variability οf a sample mean frοm the true pοpulatiοn mean, representing the precisiοn οf an estimate. It's calculated as the standard deviatiοn οf the sample mean divided by the square rοοt οf the sample size.

a. The standard errοr οf (xmοrning - xafternοοn) can be calculated as fοllοws:

Standard errοr = sqrt[(s₁²/n₁) + (s₂²/n₂)]

b. Tο cοnstruct an apprοximate 95% cοnfidence interval fοr mοrning - afternοοn caffeine cοnsumptiοn, we can use the fοllοwing fοrmula:

(xmοrning - xafternοοn) +/- t(alpha/2, df) * standard errοr

Assuming a twο-tailed test and a significance level οf 0.05, the degrees οf freedοm are 14 (8+8-2).

Let's assume that the sample mean caffeine cοnsumptiοn fοr the mοrning grοup is 500 mg with a sample standard deviatiοn οf 80 mg, and the sample mean caffeine cοnsumptiοn fοr the afternοοn grοup is 350 mg with a sample standard deviatiοn οf 60 mg. Plugging in the values intο the fοrmula, we get:

(xmοrning - xafternοοn) +/- t(alpha/2, df) * standard errοr

= (500 - 350) +/- 2.145 * sqrt[(80²/8) + (60²/8)]

= 150 +/- 79.63

= (70.37, 229.63)

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Related Questions

Please Help ASAP - 100 pts + Brainliest if the answer is correct!

Answers

The sum of the infinite geometric series is: ²/₅

How to find the sum of the infinite geometric series?

The formula for the sum of an infinite geometric series is;

[tex]S_{\infty} = \frac{a}{1 - r}[/tex]

where;

a is first term

r is common ratio

The first term is; a = ⁴/₁₅

Common ratio; r = ⁴/₉ ÷ ⁴/₁₅ = ⁵/₃

r = ²⁰/₂₇  ÷  ⁴/₉ = ⁵/₃

Thus;

[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ (⁵/₃ - 1)

[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ ²/₃

= ²/₅

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Answer:

How to find the sum of the infinite geometric series?The formula for the sum of an infinite geometric series is;S_∞ = a/(1 - r)where;a is first termr is common ratioThe first term is; a = 4/15Common ratio; r = (4/9)/(4/15) = 5/3r = (20/27)/(4/9)  = 5/3Thus;S_∞ = (4/15)/((5/3) - 1)S_∞ = (4/15)/(2/3) = 2/5

PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!

Answers

1) The system of inequalities that models this scenario will be:

6x + 3y ≤ 24

6x + 3y ≥ 4


2)
i) the solution for y is y ≤ 5 - 2x.
ii) the solution for y is y ≥ 3 - x.

3) The graph is attached accordingly.

What is the explanation for the above?

a)
Let's use the variables x and y to represent the number of Mickey pretzels and Mickey bars, respectively, that Mrs. Tobie can buy. We want to ensure that at least four children get one snack each, so the inequality for the total number of snacks should be greater than or equal to 4.

Also, Mrs. Tobie has a budget of S24, so the cost of the snacks should be less than or equal to S24. Putting these together, we get:

6x + 3y ≤ 24 (budget constraint)

6x + 3y ≥ 4 (at least four snacks)

So the system of inequalities that models this scenario is:

6x + 3y ≤ 24

6x + 3y ≥ 4


b)

To solve for y in each inequality, we need to isolate y on one side of the inequality sign.

For the first inequality, we have:

x + y ≥ 3

Subtracting x from both sides, we get:

y ≥ 3 - x

So the solution for y is y ≥ 3 - x.

For the second inequality, we have:

6x + 3y ≤ 15

Dividing both sides by 3, we get:

2x + y ≤ 5

Subtracting 2x from both sides, we get:

y ≤ 5 - 2x

So the solution for y is y ≤ 5 - 2x.

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As time, t, passes the value of an investment is modeled by 푉(푡) = 50(0.9)푡. Which of the following statements is supported by the behavior of V(t)?

Answers

The value of the investment modeled by the function V(t) = 50(0.9)^t Decreases at a decreasing rate, starting with an initial value of 50.

We are given the investment value function V(t) = 50(0.9)^t. This function describes the value of an investment over time, t. Let's analyze the behavior of V(t) and find a statement that is supported by this function.

1. The initial value of the investment is V(0) = 50(0.9)^0 = 50(1) = 50. So, the investment starts with a value of 50.

2. The function V(t) contains a term (0.9)^t, which indicates that as time passes, the investment value decreases. This is because 0.9 is between 0 and 1, so raising it to a power of t (as t increases) results in a smaller value.

3. The rate of decrease is not constant, as the function is exponential, not linear. This means the value of the investment decreases at a decreasing rate over time.

Based on the behavior of V(t), the following statement is supported:

As time passes, the value of the investment modeled by the function V(t) = 50(0.9)^t decreases at a decreasing rate, starting with an initial value of 50.

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Which statement describes the relationships between x and y in these two equations?

y = 25x

y = x + 25



Responses

In y = 25x, the value of y is 25 more than the value of x, and in y = x + 25, the value of y is 25 times the value of x.


In y = 25x and y = x + 25, the value of y is 25 more than the value of x.


In y = 25x and y = x + 25, the value of y is 25 times more than the value of x.
In , y, = 25, x, and , y, = , x , + 25, the value of , y, is 25 times more than the value of , x, .

In y = 25x, the value of y is 25 times the value of x, and in y = x + 25, the value of y is 25 more than the value of x.

Answers

That statement that best describes the relationship between x and y in the given equations is: d. In y = 25x, the value of y is 25 times the value of x, and in y = x + 25, the value of y is 25 more than the value of x.

How to Interpret the Linear Relationship Equation?

In the equation y = 25x, the value of y is directly proportional to x and is 25 times greater than x. This means that as x increases, y increases by a multiple of 25. For example, if x = 2, then y = 50 (25 x 2), and if x = 4, then y = 100 (25 x 4).

In the equation y = x + 25, the value of y is equal to the value of x plus 25. This means that y is always 25 greater than x, regardless of the value of x. For example, if x = 2, then y = 27 (2 + 25), and if x = 4, then y = 29 (4 + 25).

The answer is option d.

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The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive given that he or she had the disease.

Answers

The probability of getting someone who tested positive, given that he or she had the disease, is 0.9.

What is probability?

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of getting someone who tested positive, given that he or she had the disease, is equal to the probability that the individual has the disease and tests positive ( P(positive | disease) ).

This can be calculated using the formula P(A|B) = P(A∩B) / P(B)

P(positive | disease) = P(positive ∩ disease) / P(disease)

                    = 141 / (141+16)

                    = 0.898

Therefore, the probability of getting someone who tested positive, given that he or she had the disease, is 0.898, which is 0.9.

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Jenelle bought a home for $470,000, paying 18% as a down payment, and financing the rest at 5.4% interest
for 30 years. Round your answers to the nearest cent.
How much money did Jenelle pay as a down payment? $
What was the original amount financed? $
What is her monthly payment? $
If Jenelle makes these payments every month for thirty years, determine the total amount of money she
will spend on this home. Include the down payment in your answer. $
Video

Answers

Using percentage, we can find:

1- 84600

2- 385400

3- 20811.6

4- 7576776

What do you mean by percentage?

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage. This percent symbol can always be converted to a fraction or decimal equivalent by "dividing by 100".

Now in the question,

Downpayment = 18% of 470000

= 84600

original amount financed =

470000-84600

= 385400

Monthly payment = 5.4% of 385400

= 20811.6

Total payment in 30 years = 7576776

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What is the greatest number of unit cubes that would fit in a rectangular prism that is 12 units tall, 5 units long, and 7 units wide?

A 420
B 84
C 60
D 7

Answers

Answer:

A or 420

Step-by-step explanation:

Remember Length x Width x Height. 12 * 5 is 60, then 60 * 7 is 420.

will give thanks
trig

Answers

The data in the triangle is not sufficient to find the asked values in the question.

Explain about the sine rule:

The relationship in between sides and angles for non-right (oblique) triangles is known as the Law of Sines. It simply asserts that for all sides and angles of a given triangle, the ratio of the length of a side to the sine angle opposite this side is the same.

You must know between two angles but one side of the triangle (AAS or ASA) either two sides and an angle opposing one of them in order to employ the Law of Sines (SSA).

g/sinG = h/sinH = f/sinF

Where G, H and F are the angles and g, h and f are the angles' opposing sides.

Put the values:

g/sin136 = 13/sinH = 7/sinF

The three pairs of expression are-

HF/sin136 = 13/sinH ;   13/sinH = 7/sinF and g/sin136 = 7/sinF.

HF = 13*sin136/sinH

HF = 10.97/SinH

From the found 3 expression, each has two missing value.

Thus, the angles F and H is not possible to find.

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Examples 1 and 2 1 HOTELS The function y = 100(1.05) represents the cost per night at a hotel that cost $100 when the hotel opened and has been increasing by 5% every year since the hotel opened.
a. Graph the function.​

Answers

Answer:

The graph of the function y = 100(1.05) is shown below.

b. Calculate the cost of the hotel per night after six years.

The cost of the hotel per night after six years is $130.25. This is calculated by plugging in t = 6 into the equation y = 100(1.05)^t and solving for y.

c. What is the overall cost of 7 nights at the hotel in its sixth year of operation?

The overall cost of 7 nights at the hotel in its sixth year of operation is $910.75. This is calculated by multiplying the cost per night after six years ($130.25) by 7 nights.

2 LEARNING RESOURCES

Discuss the advantages of using online learning resources for students.

One of the main advantages of using online learning resources for students is convenience. Online learning resources can be accessed from virtually any location with an internet connection, allowing students to learn from the comfort of their own homes or from mobile devices when they are on the go. Furthermore, online learning resources reduce the need for students to commute to and from a physical school, meaning that students have more time for their studies, hobbies, and other activities.

Another advantage of online learning resources is adaptability. Online learning resources may be tailored to the needs of each individual student and can easily be adjusted should a student’s needs

Find the values of x and y. Write your answers in simplest form.

Answers

Answer:

y = 4

x = 4√2 or 5.66

Step-by-step explanation:

If the △ is a right △ with 1 angle 45o, then the other angle is also 45o. This △ will be isosceles right triangle with y = 4

Pythagorean theorem: c^2 = a^2 + b^2

x^2 = y^2 + 4^2

x^2 = 4^2 + 4^2

x^2 = 32

x = √32 = 4√2 = 5.66

The average height of a boy in the United States, from birth through 60 months, can be modeled by y = 2.9square root of (x) + 20.1 where y is the average height, in inches, of boys who are x months of age. What would be the expected difference in height between a child 49 months of age and a child 16 months of age?

Answers

Answer:

Step-by-step explanation:

To find the expected difference in height between a child 49 months of age and a child 16 months of age, we need to first find the average height of each child and then find the difference between them.

For a child who is 49 months old, the average height can be found by substituting x = 49 in the given equation:

y1 = 2.9sqrt(49) + 20.1 = 42.7 inches

For a child who is 16 months old, the average height can be found by substituting x = 16 in the given equation:

y2 = 2.9sqrt(16) + 20.1 = 28.9 inches

Therefore, the expected difference in height between the two children would be:

y1 - y2 = 42.7 - 28.9 = 13.8 inches

So we can expect the child who is 49 months old to be, on average, 13.8 inches taller than the child who is 16 months old.

The length of a rectangle is 7 inches more than its width. The area of the rectangle is equal to 2 inches more than 2 times the perimeter. Find the length and width of the rectangle.

Answers

The width of the rectangle is x = 6 inches and the length of the rectangle is 13 inches.

What is area of a rectangle?

The region contained inside the rectangle's perimeter is referred to as the area of the rectangle. In other terms, the area of a rectangle is the whole area that a rectangle encloses. Depending on the provided dimensions, this may be determined using the area of rectangle formula and a number of other techniques.

Let us suppose the width = x.

Then, length is given as:

l = x + 7

The area of the rectangle is:

A = lw

Substituting the values:

A = (x + 7)x

The perimeter of the rectangle is:

P = 2(l + w)

P = 2(x + 7 + x)

P = 2(2x + 7)

P = 4x + 14

Also, we have:

A = 2P

Substituting the values of area and perimeter:

4x + 14 = (x + 7)x

Simplifying the expression:

x^2 + 7x = 8x + 30

x^2 - x - 30 = 0

(x-6)(x+5) = 0

Since, width cannot be negative value we have:

x = 6.

l = 7 + 6 = 13 inches.

Hence, the width of the rectangle is x = 6 inches and the length of the rectangle is 13 inches.

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PLEASE HELP
I bought a pie. It cost somewhere between £1.30 and £2.99. I gave a 24% tip, and the total price was still an exact number of a pence. When I paid with a £5 note I received five coins in my change (the fewest I could have been given for that amount). What were the two possible amounts of change I could have been given?

Answers

The two possible amounts of change are 3 x £1 + 1 x 50p + 1 x 10p and 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p, which simplify to £3.60 and £3.25 respectively.

What is combination ?

Combination refers to the number of ways a selection of items can be made from a larger set of items without regard to their arrangement. In other words, combinations are a way to calculate the total number of possible groups of items that can be formed, regardless of the order in which the items are selected. The formula for calculating the number of combinations is nCr, where n is the total number of items and r is the number of items being selected.

According to the question:
Let's start by finding the possible prices of the pie. Since the price must be an exact number of pence, we can convert the price range to pence by multiplying each value by 100:

£1.30 = 130 pence

£2.99 = 299 pence

We know that the price plus the 24% tip must be an exact number of pence. If we let x be the price of the pie in pence, then we can write this as:

x + 0.24x = 1.24x

Since 1.24 is not divisible by 5 (which we'll need for the change), we need to find two values of x that differ by a multiple of 5. One way to do this is to start with the lower bound and add multiples of 5 until we get a valid value:

x = 130: 1.24x = 161.2

x = 135: 1.24x = 167.4

x = 140: 1.24x = 173.6 (valid)

x = 145: 1.24x = 179.8

x = 150: 1.24x = 186.0 (valid)

x = 155: 1.24x = 192.2

x = 160: 1.24x = 198.4

So the possible prices of the pie are 140p and 150p. To find the possible amounts of change, we need to subtract each price from 500p (the value of the £5 note) and express the result as a combination of coins. For example:

Price = 140p, change = 360p = 3 x £1 + 1 x 50p + 1 x 10p

Price = 150p, change = 350p = 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p

Therefore, the two possible amounts of change are 3 x £1 + 1 x 50p + 1 x 10p and 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p, which simplify to £3.60 and £3.25 respectively.

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Use the diagram below to answer the questions.





What are two other names for line WQ?
QW
What is another name for plane V?

What are three points that are collinear? What is a fourth point that is not collinear with those three points?

What is a point that is not coplanar with R, S, and T?

Answers

Answer:

Step-by-step explanation:

b-y=55

How to multiply polynomials

Answers

Answer:

To multiply polynomials, you can follow these steps:

Distribute each term of the first polynomial to each term of the second polynomial.

Combine like terms.

Simplify the resulting expression.

Here is an example:

(2x + 3)(x - 4)

Distribute:

2x(x - 4) + 3(x - 4)

Combine like terms:

2x^2 - 8x + 3x - 12

Simplify:

2x^2 - 5x - 12

So, (2x + 3)(x - 4) = 2x^2 - 5x - 12.

Step-by-step explanation:

quick Math Answer ok ​

Answers

Answer:

See below.

Step-by-step explanation:

For this problem, we are asked to find x, the hypotenuse.

There are a few ways to find the hypotenuse, but an easy way is to use the Pythagorean Theorem.

Represented as;

[tex]a^2 + b^2 = c^2\\(Short \ Leg)^2 + (Long \ Leg)^2 = (Hypotenuse)^2.[/tex]

We have 2 given values, the short leg and the long leg. We can begin solving for the hypotenuse.

Substitute:

[tex]40^2+42^2=c^2[/tex]

[tex]3364 = c^2[/tex]

Square Root the Equation:

[tex]\sqrt{3364} = \sqrt{c^2}[/tex]

[tex]c = 58.[/tex]

The Hypotenuse is 58. Our final answer is Letter D.

In​ 1940, the average size of a privately owned farm in a particular country was 170 acres. In a recent​ year, the average size of a privately owned farm in the country had increased to 432 acres. What is this percent​ increase?

Answers

Answer:

154%

Step-by-step explanation:

First, we need to calculate the increase in size of the privately owned farm:

increase = new value - old value

increase = 432 - 170

increase = 262

Next, we can use the formula to calculate the percent increase:

percent increase = (262 / 170) x 100%

percent increase = 1.54 x 100%

percent increase = 154%

Therefore, the percent increase in the size of privately owned farms in the country is 154%.

Use the graphs of f and g to find (fg)(−2).

Answers

In this the point (-2,3) on the graph of f multiplied by the corresponding point (-2,2) on the graph of g yields the product (-2,6), which is equal to -8.

What is a coordinate plane?

A coordinate plane is a two-dimensional surface composed of two number lines, one horizontal (x-axis) and one vertical (y-axis). It is used to graph points, lines, and other shapes. Each point is identified by a pair of numbers which indicate its position along the x and y axes. The x and y axes intersect at the origin and divide the plane into four quadrants.

The graph of fg can be found by first graphing both f and g on the same coordinate plane. From there, the graph of fg can be found by taking each point on the graph of f and multiplying it by the corresponding point on the graph of g. In this example, the point (x,y) on the graph of f is multiplied by the corresponding point (x,y) on the graph of g to form a new point (x,yz). This new point is then placed on the graph of fg.

Using the graphs of f and g provided, we can determine that (fg)(-2) = -8. To find this, first locate the point (-2,3) on the graph of f. Then, locate the corresponding point (-2,2) on the graph of g. The product of these two points is (-2,6). This means that (fg)(-2) = -8.

In summary, to find (fg)(-2) using the graphs of f and g, first graph both f and g on the same coordinate plane. Then, take each point on the graph of f and multiply it by the corresponding point on the graph of g. In this example, the point (-2,3) on the graph of f multiplied by the corresponding point (-2,2) on the graph of g yields the product (-2,6), which is equal to -8.

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Consider the function
f(t)=1−2t+4t2.
Give the largest value of t such that the percentage rate of change equals 100. Give your answer to one decimal place.

Answers

Answer:

The percentage rate of change of a function f(t) is given by:

(Δf / f) x 100

where Δf is the change in f and f is the original value of the function.

To find the largest value of t such that the percentage rate of change equals 100, we need to find the value of t for which:

(Δf / f) x 100 = 100

Simplifying, we get:

Δf / f = 1

This means that the change in f is equal to the original value of f.

So, we need to solve the equation:

f(t + Δt) - f(t) = f(t)

where Δt is the change in t.

Substituting the given function, we get:

[1 - 2(t + Δt) + 4(t + Δt)^2] - [1 - 2t + 4t^2] = 1 - 2t + 4t^2

Simplifying, we get:

-8tΔt + 8Δt^2 = 1

Since we are interested in the largest value of t, we can assume that Δt is a small positive number, such that Δt << t.

Ignoring the term Δt^2, we get:

-8tΔt = 1

Solving for Δt, we get:

Δt = -1 / (8t)

Substituting this value of Δt back into the equation -8tΔt + 8Δt^2 = 1, we get:

-8t(-1 / (8t)) + 8(-1 / (8t))^2 = 1

Simplifying, we get:

1 / t^2 = 1

Solving for t, we get:

t = 1

Therefore, the largest value of t such that the percentage rate of change equals 100 is t = 1.

She is exactly correct

In a grocery store, a $12 case of soda is discounted 20%. How much will you save?

Answers

Answer: 9.60

Step-by-step explanation:

Labeled price = $ 12

Discount = 20% of labeled price = 12 x 20%

= 12 x 2 / 10 = 24 / 10 = $ 2.4

Sale price = Labeled price - Discount.

Sale price = $ 12 - $ 2.40 = $ 9.60

Thus the sale price of the case of soda is 9.60 $

Solve for x. Round to the nearest tenth, if necessary.
x=

Answers

Step-by-step explanation:

For RIGHT  triangles the cos of an angle = adjacent LEG / hypotenuse

 so for THIS triangle   cos 55°  = x / 9.3

    re-arrange to    9.3 * cos 55° = x    

       use calculator to find x = ~ 5.3 units   (rounded)

Answer:

x = 5.3

Step-by-step explanation:

As triangle XYZ is a right triangle, and we have been given angle X, the side adjacent the angle, and the hypotenuse, we can use the cosine trigonometric ratio to solve for x.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given:

θ = 55°A = xH = 9.3

Substitute the given values into the formula and solve for x:

[tex]\implies \cos 55^{\circ}=\dfrac{x}{9.3}[/tex]

[tex]\implies x=9.3 \cos 55^{\circ}[/tex]

[tex]\implies x=5.3342608...[/tex]

[tex]\implies x=5.3\; \sf (nearest\;tenth)[/tex]

Therefore, the value of x is 5.3 to the nearest tenth.

Type the correct answer in each box. Use numerals instead of words. Consider function g. g ⁡ ( x ) = { 6 , - 8 ≤ x < - 2 0 , - 2 ≤ x < 4 - 4 , 4 ≤ x < 10 What are the values of the function when x = - 2 and when x = 4 ? g ⁡ ( - 2 ) = g ⁡ ( 4 ) =

Answers

After addressing the issue at hand, we can state that Therefore, function  g(-2) = 0 and g(4) = -4.

what is function?

Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.

When x = -2, g(x) = 0.

When x = 4, g(x) = -4.

Therefore, g(-2) = 0 and g(4) = -4.

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Write the equation of the line that has a slope of 4 / 3 and passes through the point ( 0, - 3 ).

Answers

Answer: y = 4/3x -3

Step-by-step explanation:

Help with math problems

Answers

Answer:

in absolute value you consider both the positive and negative side of the expression in the absolute bar.

Assume that the data has a normal distribution and the number of observations is
greater than fifty. Find the critical z value used to test a null hypothesis.
a = 0.05 for a two-tailed test.
O±2.575
O±1.764
O±1.645
O±1.96

Answers

-1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.

A null hypothesis is what?

A null hypothesis is a statistical hypothesis that presupposes that there is no link between two variables in a population or that there is no meaningful difference between two populations. It serves as the beginning point of a statistical hypothesis test and is typically marked as H0. A null hypothesis serves as a reference point against which the alternative hypothesis may be compared. The alternative hypothesis is accepted if there is sufficient evidence from the data to reject the null hypothesis. The null hypothesis is not rejected if there is insufficient evidence in the data to support it.

Using a significance threshold of 0.05, we may use a conventional normal distribution table or calculator to get the essential z value. The value that corresponds to the 0.025 percentile is the crucial z value (or the 0.975 percentile, depending on the direction of the alternative hypothesis).

The z value for the 0.025 percentile, as determined by a typical normal distribution table, is -1.96.

Hence, -1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.

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A block of wood with dimensions 10 in. by 10 in. by 6 in. has a 2 in. by 2 in. square hole cut through the square face, as shown.

A top view of a square block shows the square face with sides 10 inches long. A square hole near the right side has sides 2 inches long. A side view shows that the square cut goes through the block, from the top face to the bottom.
Top View Side View
What is the volume of the resulting block of wood?
Responses

24 in3
24 in3

576 in3
576 in3

600 in3
600 in3

624 in3
624 in3

Answers

The volume of the resulting block of wood is 576 in³. The correct option is the second option 576 in³

Calculating the volume of the resulting block of wood

From the question, we are to determine the volume of the resulting block of wood.

From the given information,

The dimensions of the block of wood is 10 in. by 10 in. by 6 in.

First, we will calculate the original volume of the block of wood.

The original block of wood has a volume of

V = 10 x 10 x 6

V = 600 in³

Now, we will determine the volume og the hole that was cut through

The dimensions of the hole is 2 in. by 2 in. by 6 in.

Volume of the hole = 2 x 2 x 6

Volume of the hole = 24 in³

The resulting block would have a volume of

Volume of resulting block = 600 - 24

Volume of resulting block = 576 in³

Hence, the volume is 576 in³.

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What is the perimeter and area of ​​a right triangle, which has the measures of its sides, the horizontal 4m, the vertical 3m, and the diagonal 5m?

a) 12m and 6m²
b) 12m and 10m²
c) 21m and 21m²
d) 6m and 12m²
e) 6m and 7.5m²

Answers

Answer:

the answer is c because every side of a triangle sides are he same so c is your answer

Anjali borrow 19000 rupees at 6% interest for 2 years at the end of 2 years she pays 15000 rupees and a gold ring to the money lender. What is the value of the gold ring

Answers

Answer:

Gold ring = 6180

Step-by-step explanation:

Gold ring = ?

I = prt

= 19000 x 6% x 2

= 2180

Amount to be paid= 19000 + 2180

= 21180

gold ring = 21180 - 15000

= 6180

Question Content Area
At the beginning of the period, the Cutting Department budgeted direct labor of $37,260 and supervisor salaries of $43,370 for 4,140 hours of production. The department actually completed 4,500 hours of production.

Determine the budget for the department assuming that it uses flexible budgeting.

Answers

Answer:

To determine the flexible budget for the Cutting Department, we need to use the information provided to adjust the original budget for the actual level of production.

First, we need to calculate the variable cost per hour of production:

Variable cost per hour = Direct labor / Hours of production

Variable cost per hour = $37,260 / 4,140 hours

Variable cost per hour = $9

Next, we can use this variable cost per hour to calculate the flexible budget for the actual level of production:

Flexible budget = (Variable cost per hour x Actual hours of production) + Fixed costs

Flexible budget = ($9 x 4,500 hours) + $43,370

Flexible budget = $40,500 + $43,370

Flexible budget = $83,870

Therefore, the flexible budget for the Cutting Department, based on the actual level of production of 4,500 hours, is $83,870.

If the quotient of 3/8 and 1/4 is subtracted from the product of 2 1/4 and 1 1/7 what is the difference

Answers

Answer:

Step-by-step explanation:

(9/4 * 8/7) - (3/8*4/1) =

(72/28) - (12/8)

18/7 - 3/2

36/14 - 21/14

15/14 = 1 1/14

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