1. Judy took $20 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each bag of popcorn was $4. The price of each drink was half the price of a bag of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bags of popcorn and the other axis to represent the number of drinks.
(b) Explain your graph.

Answer:

D) six and one third feet

Step-by-step explanation:

To find the total amount of wood that Harry needs, we need to find the total length of the three pieces of wood that are two and three fourths feet long and the total length of the six pieces of wood that are one and one third feet long.

The three pieces of wood that are two and three fourths feet long have a total length of 3 * 2 and 3/4 = 6 and 1/4 feet.

The six pieces of wood that are one and one third feet long have a total length of 6 * 1 and 1/3 = 8 and 2/3 feet.

To find the total length of all the pieces of wood, we need to add the total length of the three pieces that are two and three fourths feet long and the total length of the six pieces that are one and one third feet long. This gives us a total of 6 and 1/4 + 8 and 2/3 = 14 and 7/12 feet.

Therefore, Harry will need a total of 14 and 7/12 feet of wood for the project. This is equivalent to approximately six and one third feet, so the correct answer is d) six and one third feet.

In 84 ways 3 employees can be chosen from the set of 9.

What is combination?

Total 9 employees from that 3 employees can be chosen.

Total number of combination = ⁹C₃

= 9! / (9-3)! 3!

= 9 *8 *7/3*2

=3* 4* 7

= 12 * 7

= 84

Hence, in 84 ways 3 employees can be chosen from the set of 9.

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Answer: 17

Step-by-step explanation: 2 is an even number and 17 is an odd number, therefore it can't be divisible by 2. 17 does not have a 5 or a 0 in it therefore it is not divisible by 5. Any multiple of 5 will always have a 5 or 0 in it. If it doesn't have a zero in it anywhere it is not divisible by 10. A multiple of 10 will always have a zero in it.

The area under the curve r²=50sin2Θ is (15.71)unit square

A parabola is defined as a plane curve that is mirror-symmetrical and approximately U-shaped.

Given:

parabola is r²=50sin 2[tex]\theta[/tex],

where r=5

So, 5²=50 sin 2[tex]\theta[/tex],

Simplifying the equation

25=50 sin 2[tex]\theta[/tex],

sin 2[tex]\theta[/tex] = 1/2

2[tex]\theta[/tex] = [tex]sin^{-1[/tex] 0.5

[tex]\theta[/tex] = 15 degree.

Now, the Area = 22/7 × 5

Area = 15.71 unit²

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The profit function for this problem is defined as follows:

P(x) = 5x - 260.

The profit function is defined as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

In which:

From the image given at the end of the answer, the revenue function and the cost function are given as follows:

Then the profit function is calculated as follows:

P(x) = R(x) - C(x)

P(x) = 3x² + 4x - 60 - (3x² - x + 200).

Combining the like terms, we have that:

P(x) = (3 - 3)x² + (4 + 1)x - 60 - 200

P(x) = 5x - 250.

Meaning that the third option is correct.

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

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The statements that are true are:

π is the area of a circle of radius 1.

π is the circumference of a circle of diameter 1.

π is the constant of proportionality relating the diameter of a circle to its circumference.

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

We have,

Circumference of a circle = 2πr

Area of a circle = πr²

π is the area of a circle of radius 1.

Area = πr² = π x 1 = π

π is the area of diameter 1.

2r = 1

r = 1/2

Area = πr² = π x 1/4 = π/4

π is the circumference of a circle of radius 1.

Circumference of a circle = 2πr = 2 x π x 1 = 2π.

π is the circumference of a circle of diameter 1.

Circumference of a circle = 2πr = 2 x π x 1/2 = π.

π is the constant of proportionality relating the diameter of a circle to its circumference.

Diameter ∝ Circumference

2r = 2πr

2r = π (2r)

π is the constant of proportionality relating the radius of a circle to its area.

r = (πr)r

Thus,

π is the area of a circle of radius 1 is true.

π is the circumference of a circle of diameter 1 is true.

π is the constant of proportionality relating the diameter of a circle to its circumference is true.

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The radius of the given region is calculated as; 19.329 km

We are told that the region is circular and as such the formula for the area of a circle is;

A = πr²

We are told that the population is 44600

Population density is defined as the average number of individuals in a population per unit are.

In this question, the population density is given as 388 people per sq. km

Thus;

Area = Population/population density

πr² = 44600/388

r² = 44600/388π

r² = 373.595

r = 19.329 km

We conclude that is the radius

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Answer: x=9, excluded value x≠5

Step-by-step explanation:

1. add 3 to both sides -> 16/x-5 = 4

2. then multiply both sides by x-5 -> 16=4(x-5) -> 16=4x-20

3. add 20 to both sides -> 36=4x

4. divide both sides by 4 to solve for x -> 9=x

the excluded value is whatever would make the denominator of the fraction equal to 0. You can't divide by 0. Therefore in this case, x can't equal 5 because 5-5=0

48 is the number does not belong in the following series 1, 2, 5, 10, 13, 26, 29, 48

The series is formed by following the sequence that is:

1, 2, 5, 10, 13, 26, 29, 48

Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.

The first number is multiplied by 2 and the next number should be added by 3 to the previous number.

The first number is 1 and it should be multiplied by 2

1 × 2 = 2

Then the next number should be added by 3

2 + 3 = 5

The series will be continued:

5 × 2 = 10

10 + 3 = 13

13 × 2 = 26

26 + 3 = 29

but 29 × 2 = 58 ≠ 48.

Therefore the number 48 does not belongs to the given series.

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The total amount of interest that Maria will owe on her unsubsidized loan = $113.63

In this question we have been given Maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.05%

We need to find the total amount of interest that Maria will owe on her unsubsidized loan.

Using simple interest formula,

I = P * t * r

where P - the principal

r - the interest rate,

and t - time period

Maria  begins making payments 6 months after graduation, this means there are 12 - 6 = 6 months between graduation and the start of payments.

so, t = 6 months

i.e., t = 0.5 year

Here, R = 5.05%, P = $4500

Now we convert R percent to r a decimal

r = R/100

 = 5.05%/100

 = 0.0505 per year,

Using the formula of simple interest,

I = 4500 * 0.0505 * 0.5

I = $113.63

Therefore, the interest amount is $113.625

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The complete question is:

At the beginning of her senior year maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.05%. if maria begins making payments on her loans 6 months after graduation, how much interest will she owe to the nearest dollar?

The required equation of the line is y = 4x + 1.

The Slope-intercept form of a line is given by

Where m is the slope of the line and c is the y-intercept

Note:

The product of slopes of perpendicular lines = -1

Here we have

y = -1/4x + 6 Line (1)  

Here slope of the line m₁ = -1/4

Let y = m₂x + c Line (2)

Assume that Line (2) is the perpendicular line to Line

As we know The product of slope of two perpendicular lines is -1  

=> m₁m₂ = -1        [∵ Line (1) and Line (2) perpendicular lines ]

=> -1/4(m₂) = -1     [ ∵ m₁ = -1/4  ]

=>  m₂ = 4

The line (2) => y = 4x + c  

Given that the line passes through (2, 9)

=> 9 = 4(2) + c

=> c = 9 - 8

=> c = 1

Therefore,

The required equation of the line is  y = 4x + 1

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Convert the radicals as follows:

The simplification of the expression are;

[tex]\sqrt[6]{25^3}[/tex] = 5

[tex]\dfrac{1}{\sqrt[3]{5^4} } =\dfrac{1}{5^{4/3}} }[/tex]

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

We are given the expression as;

[tex]\sqrt[6]{25^3}[/tex]

Convert the radicals as follows:

[tex]\sqrt[6]{25^3}\\\\= \sqrt[6]{(5^2)^3}\\\\= \sqrt[6]{5^6}\\\\=5^{6/6}\\=5^1=5[/tex]

Now,

[tex]\dfrac{1}{\sqrt[3]{5^4} } =\dfrac{1}{5^{4/3}} }[/tex]

Here this cannot be further simplified.

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Answer:

answer on the picture. Let me know if I am right!

On average, for every hour spent on clinical care two hours is spent on the EHR documenting care.

According to a new survey, physicians spend slightly over 16 minutes every patient visit examining electronic health records(EHR). For every hour of clinical care two hours are spend on EHR documentation. According to the study published in the Annals of internal medicine this accounts for a large percentage of a physician's day.

An Electronic Health Record (EHR) is an electronic version of a patients medical history, that is maintainrd by the provider over time, and may include all of the key administrative clinical data relevent to that persons care under a particular provider. It helps providers better manage care for patients and provide better health care.

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Answer:

Large box: 18.5 kg

Small box: 13.75 kg

Step-by-step explanation:

Let  L represent a large box, and S represents a small box

We have the equation

3L + 2S = 83 kg

5L + 6S = 175 kg

We time the first equation by -3

-9L - 6S = - 249 kg

5L + 6S = 175 kg

Now Let's find the large box weighs first

Add both equation and we get

-4L = -74 kg

L = 18.5 kg

Now put 18.5 in for the L to find the weight of the small box

5(18.5) + 6S = 175 kg

92.5 + 6S = 175 kg

6S = 82.5 kg

S = 13.75 kg

Answer:

x as large; y as small

3 large + 2 small = 83    (1st equation)

5 large + 6 small = 175    (2nd equation)

3x + 2y = 83   (multiply by -5)

5x + 6y = 175   (multiply by 3)

-15x - 10y = -415

15x + 18y = 525      (simplify)

8y = 110

y = 13.75       (small box weight)

3x + 2y = 83       (substitute the value of y)

3x + 2(13.75) = 83

3x + 27.5 = 83

3x = 55.5

x = 18.5       (large box weight)

3x + 2y = 83

3(18.5) + 2(13.75) = 83

55.5 + 27.5 = 83

83 = 83          (1st equation is proven right)

5x + 6y = 175

5(18.5) + 6(13.75) = 175

92.5 + 82.5 = 175

175 = 175           (2nd equation is proven right)

therefore, large box weight is 18.5kg and the small box weight is 13.75kg.

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Step-by-step explanation:

Answer:

B. Same-side interior angles

Step-by-step explanation:

Same Side interior angles are angles that are on the same side and add up to 180 degrees. So, the answer is B

The complete table of values of the proportional relationship is

A= 8, 24, 40

B= 3, 9, 15

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

A= 8, _, 40

B= 3, 9, _

Calculate the constant of proportion using

constant = B/A

Substitute the known values in the above equation, so, we have the following representation

constant = 3/8

Substitute constant = 3/8 in constant = B/A

3/8 = B/A

So, we have

3A = 8B

When B = 9, we have

3A = 8 * 9

This gives

A = 24

When A = 40, we have

3 * 40 = 8B

This gives

B = 15

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Complete question

Complete the table such that a and b represent a proportional relationship

A= 8, _, 40

B= 3, 9, _

Given A = rolling a number lower than 2

A six- sided bones has possible issues and 6. We also note that the only outgrowth lower than 2. probability of both issues is equal i.e. 50 or 1/2.

So, the probability of an event is Favorable issues Total number of issues. It's denoted with the gap i.e. P( Event) The possibility of the result of any arbitrary event is known as probability. This expression refers to determining the liability that any given circumstance will do. What are the chances of entering a head, for case, when we toss a coin in the air? The number of issues that could do is the base for the response to this question. The outgrowth in this case might be either head or tail. thus, there's a 50 chance that the result will be a head. The probability serves as a hand for how probably an event is to do. It gauges how likely an event is. The probability formula is as follows P( E) is equal to the rate of favourable issues to overall issues.

P( E) = n( E)/ n( S)

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The dimension is d and d<n. Thus maximum number of linearly independent vectors that can draw from the set V1, V2....Vn is d.

First note that for "any vector space V, basis B of V is maximal linearly independent set in V". That is there is no other any linearly independent set which contains more than |B| number of elements on B. Let us consider this statement as 1. Two or greater vectors are stated to be linearly independent if none of them may be written as a linear mixture of the others. On the contrary, if at the least certainly considered one among them may be written as a linear mixture of the others, then they may be stated to be linearly dependent. Now here dimension is d and d<n. Thus maximum number of linearly independent vectors that can draw from the set V1, V2....Vn is d.

Thus, the maximum number = d

Therefore, statement is true hence proved.

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The mixed number between 2 and 10. I am nearer to 8 than 10 is 6 1/9, it  is an entire quantity, and a right fraction represented together.

A mixed fraction is an entire quantity, and a right fraction represented together. It commonly represents a range of among any  complete numbers. Look on the given image, it represents a fragment this is extra than 1 however much less than 2. It is thus, a mixed fraction. A fraction represented with its quotient and the rest is a combined fraction. For example, 2 1/three is a combined fraction, wherein 2 is the quotient, 1 is the the rest. So, a combined fraction is a aggregate of an entire quantity and a right fraction.

Thus, the mixed number if 6 1/9.

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Answer: 5x and 3x

Step-by-step explanation:

5x and 3x are like terms because they both have the same variable being multiplied to them which is x.

The elevation of this mountain in feet is 28,169 feet. This gives us the original number of 9,417 yards, confirming that our answer is correct.

To convert yards to feet, we simply need to multiply the number of yards by 3. There are 3 feet in a yard, so to convert 9,417 yards to feet, we multiply 9,417 by 3.

This gives us the total of 28,169 feet as the elevation of this mountain. To check our answer, we can also convert 28,169 feet back to yards by dividing 28,169 by 3.

This gives us the original number of 9,417 yards, confirming that our answer is correct.

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The total distance Renaldo could travel on his trip when he starts from Atlanta goes to London and  Newyork city, and return to Atlanta is 15502 miles.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The distance between Atlanta and London = 4281 miles,

The distance between London to Newyork city  = 3470 miles,

Write the trip blue plan as shown below,

Renaldo start from Atlanta → London → Newyork city →  London → Atlanta

Calculate the total distance as shown below,

The total distance = 4281 + 3470 + 3470 + 4281

The total distance = 2 (4281 + 3470)

The total distance = 2 × 7751

The total distance = 15502 miles

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If f(4) = 7 then the inverse of the function f⁻¹(7) is 4.

Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

The given function is,

f(4) = 7

According to inverse function property,

if f(x) = y, then f⁻¹(y) = x

The inverse of function,

f⁻¹(7) = 4

The inverse of the function f(4) = 7 is f⁻¹(7) = 4.

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Answer:

Step-by-step explanation:

in x intercepts y is equals to 0

10x = 8

x = 8/10

x = 4/5

in y intercepts x is equals to 0

y = 8

Answer: (x - 6)(x + 6)

Step-by-step explanation:

To factor this, recall the difference of squares

[tex]a^{2} - b^{2} = (a-b)(a+b)[/tex]

And because 36 is [tex]6^{2}[/tex], that means

[tex]x^{2} - 36 = x^{2} - 6^{2} = (x-6)(x+6)[/tex]

[tex] \bold{(x-6)(x+6)}[/tex]

To simplify this equation, quadratic factoring patterns should be used. These patterns are the following:

[tex] \bold{a^2-b^2=(a-b)(a+b)}[/tex]

This pattern works because if one distributes the terms in the parentheses by multiplying each term in one of the parentheses by each term in the other, the result is the original equation:

[tex] \bold{36=6^2}[/tex]

So it can be applied to the given equation:

[tex] \bold{x^2-36}[/tex]

[tex] \bold{ \bold{\boxed{(x-6)(x+6)}}}[/tex]

The factored form of the expression is [tex]\bold{(x-6)(x+6)}[/tex]

96 minimum sample size required to have 95% confidence that the variance of the sample is within 20% of the variance of the population.

Given that,

We have to determine the minimal sample size required to have 95% confidence that the variance of the sample is within 20% of the variance of the population.

We know that,

Confidence Interval is CI=95%

Variance is σ²=20%

We have

n=(Z/M.E)²

n=(1.96/0.20)²

n=(9.8)²

n=96.04

Therefore, 96 minimum sample size required to have 95% confidence that the variance of the sample is within 20% of the variance of the population.

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Answer:

(3, 9)

Step-by-step explanation:

You start on (0, 0), and try and remember the term, "you run before you can jump(x before y, (x, y)) when working with coordinates.

X axis: so you "run" 3 units to the right, as it's not a negative number. so now your on (3, 0) (dark blue arrows)

Y axis: now you do the "jumping" portion of this, so you jump up six units as it's a negative, so now your on (3, 6) (red arrows)

Y: axis: but now you have to move down 1 unit, so you essentially "fall" 1 unit down, (3, 5) (pink arrow)

Y axis:  you have to "jump" 4 units up now, so now your at (3, 9) (green arrows)

you haven't moved along the X axis so you keep the 3, you only moved the Y axis.

So your asnwer is (3, 9)!

Hope this helped!! (picture help as well!)

On solving the provided question, we can say that - Level significance  = 0.05, Z = 1.96, Margin of error= 0.0349

A well-known statistical theory called the null hypothesis asserts that there is no statistical connection between two sets of observable data and measurable phenomena for a given set of observed variables. A null hypothesis is a kind of statistical hypothesis that asserts that a certain collection of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. A scientific hypothesis is a prediction of what researchers will discover via their investigation. A statistical hypothesis, however, states what a statistician does not anticipate. The null hypothesis is so named because of this.

Null hypothesis,

Sample size, n = 570

Sample portion, P’ = 135/579 = .2368

At 95% confidence,

Level significance  = 0.05

Z = 1.96

Margin of error= 0.0349

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The probability that the next chew that Jamar removes from the bag will be an apple chew is of:

0.9 = 90%.

In the context of an experiment, a probability is calculated as the division of the number of desired outcomes in the context of the problem by the number of total outcomes in the context of the experiment.

In this problem, the outcomes are given from the previous experiments, hence we have an experimental probability.

The outcomes are given as follows:

Then the probability that the next chew that Jamar removes from the bag will be an apple chew is calculated as follows:

p = 53/59 = 0.9 = 90%.

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

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