Hillary used her credit card to buy a $804 laptop, which she paid off by making identical monthly payments for two and a half years. Over the six years that she kept the laptop, it cost her an average of $0. 27 of electricity per day. Hillary's credit card has an APR of 11. 27%, compounded monthly, and she made no other purchases with her credit card until she had paid off the laptop. What percentage of the lifetime cost of the laptop was interest? Assume that there were two leap years over the period that Hillary kept the laptop and round all dollar values to the nearest cent)​

Inequalities ensure that Liam buys enough tickets (at least 20), and also that he stays within his budget (spends no more than $250).

Let's use the variables "a" and "c" to represent the number of adult and child tickets Liam buys, respectively. Then the total number of tickets he buys is a + c, and the total cost of the tickets is 15.75a + 13c.

To find the system of inequalities, we need to use the given information:

Liam wants to have at least 20 tickets: a + c ≥ 20

Each adult ticket costs $15.75 and each child ticket costs \($13: 15.75a\) + 13c ≤ 250 (since Liam wants to spend no more than \($250)\)

So the system of inequalities is:

a + c ≥ 20

15.75a + 13c ≤ 250

These inequalities ensure that Liam buys enough tickets (at least 20), and also that he stays within his budget (spends no more than \($250).\)

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Answer:

\(5x = - 1 - 1 = 5x \div 5 = - 2 \div 5 = 2 \div 5\)

Answer:

because it can be written as a fraction 2500/1

Step-by-step explanation:

Answer: 10,000

Step-by-step explanation:

10^5 = 100000 and 10^-1 = 1/10, so the answer is 10000

Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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Hello!

The sum of a number and 11:

Let's say that the number is x. So the expression "the sum of a number and x" looks like this:

x+11

Hope this helps you!

~Just an emotional teen who listens to her favourite songs

\(SilentNature\)

Hey there!

Guide:

• The word “sum” means “add” or “addition”

• The word “difference” means “subtract” or “subtraction”

• The word “product” means “multiply” or “multiplication”

• The word “quotient” means “divide” or “division”

NOW THAT WE HAVE ALL OF THAT INFORMATION, WE CAN SOLVE FOR YOUR EQUATION

“The SUM of a number and 11”

Well since the “number” is unknown we can label it as “a” so we can know what we’re ADDing to 11…

So, your equation should be: a + 11

Answer: a + 11

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

-1,-4

-3,3

-2,0

Step-by-step explanation:

hope this helps

The Intermediate Value Theorem concludes that for a continuous function on a closed interval, if there are two points in the interval such that the function takes on two different values, then there must be at least one point in the interval where the function takes on every value between those two values.

Assuming its assumptions are met, the Intermediate Value Theorem (IVT) concludes that:

If a continuous function, f(x), is defined on a closed interval [a, b], and k is any value between f(a) and f(b), then there exists at least one value c in the interval (a, b) such that f(c) = k.

In other words, if a function is continuous on a closed interval and k is a value between the function's values at the endpoints of the interval, the function must take on the value k at least once within that interval. This theorem is particularly useful in determining the existence of roots or zeroes for a function in a specified interval.

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Since the value of x cannot be negative x value that makes line RQ tangent to the circle P at point Q is 6.

From the circle P, if Q is the tangent, It implies that at the tangent line, it is perpendicular to the radius.

Using Pythagorean theorem;

PQ² + RQ² = PR²

Where PQ = 9

RQ = 12

PR = (x + 9)

Applying (x + 9) to the formula

(9)² + (12)² = (x + 9)²

Using algebraic expression; (a + b)² = a² + 2ab + b²

x² + 18x + 81 = 36 + 144

x² + 18x + 81 = 225

x² + 18x + 81 - 225 = 0

x² + 18x - 144= 0

By employing the quadratic formula,

\(x =\frac{ -b+/-\sqrt{b^{2} - 4ac} }{2a}\) where a = 1, b = 18 and c = -144

\(x =\frac{ -18+/-\sqrt{18^{2} - 4(1)(-144)} }{2(1)}\)

\(x =\frac{ -18+/-\sqrt{324 + 576} }{2}\)

\(x =\frac{ -18+/-\sqrt{900} }{2}\)

\(x =\frac{ -18+/- 30}{2}\)

\(x =\frac{ -18 + 30}{2}\)

\(x =\frac{ 12}{2}\)

x = 6

\(x =\frac{ -18 - 30}{2}\)

\(x =\frac{-48}{2}\)

x = -24

Knowing that the value of x cannot be negative then, the quadratic equation that yielded 12/2 = 6 makes the value of x = 6.

The complete question is:

What value of x would make Line R Q tangent to circle P at point Q? x =

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Answer:

x = 6

Step-by-step explanation:

edg 23

From Joey's first 14 quiz grades in a marking period, the mean of Joey's quiz grades is approximately 82.857.

To calculate the mean of a set of numbers, you sum up all the numbers and divide the sum by the total count of numbers. In this case, we have Joey's first 14 quiz grades: 86, 84, 91, 75, 78, 80, 74, 87, 76, 96, 82, 90, 98, and 93.

Using the formula, we add up all the grades:

86 + 84 + 91 + 75 + 78 + 80 + 74 + 87 + 76 + 96 + 82 + 90 + 98 + 93 = 1160.

Next, we divide the sum by the total count of grades (14):

1160 / 14 = 82.857.

To check this result using "I-Var Stats" on a calculator, enter the grades into a list and use the statistical function to calculate the mean.

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The solutions of the quadratic equation x² - 8x - 84 = 0 are given by, x = -6, 14.

Given the quadratic equation is,

x² - 8x - 84 = 0

We have to solve this quadratic equation that is we have to find the zeros of the polynomial x² - 8x - 84.

x² - (14 - 6) x - 84 = 0 [Doing middle term factor]

x² - 14x + 6x - 84 = 0 [Open up the bracket]

x (x - 14) + 6 (x - 14) = 0

(x + 6) (x - 14) = 0

Either, x + 6 = 0

x = -6

Or, x - 14 = 0

x = 14

Hence the solutions of the quadratic equation are, x = -6, 14.

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The volume of the rectangular prism is 521.65cubic feet

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

The volume of a prism is the product of the area of the base and the height of the prism. Prism volume (V) = B × h, where, B is the area of the base and h is the height of the prism.

Base area = 7.2×6.9 = 49.68 square feet

height = 10.5 feet

Volume of the prism = 10.5× 49.68

= 521.64 cubic feet

Therefore the volume of the rectangular prism is 521.64 cubic feet.

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Answer:

Abigail was four times faster in the skateboard than when she is walking

Step-by-step explanation:

Let the total distance to travel be d

distance traveled on skateboard = 2/3 * d = 2d/3

distance walked = 1/3 * d = d/3

So let the time taken to skate be t, then time taken to walk home will be 2t since it is 2 times longer.

Now, the speed on both trips is distance/time

For the snowboard trip, speed is 2d/3/t = 2d/3t

For the walking trip, distance would be;

d/3/2t = d/6t

So let’s compare these two speeds.

Obviously the speed on the skateboard is greater than that walking.

So we can equally divide the speed on the skateboard by that while walking to know how many times faster it is.

Thus, mathematically we have

2d/3t divided by d/6t

So that would be;

2d/3t * 6t/d = 4

So this means she was four times faster on the skateboard

The intermediate value theorem applies to the indicated interval and the importance of c guaranteed by the theorem is c=2,3.

Especially, he has been credited with proving the following five theorems:  a circle is bisected via any diameter; the bottom angles of an isosceles triangle are the same;  the other (“vertical”) angles are shaped by means of the intersection of two traces are same; two triangles are congruent (of identical form and size.

In mathematics, a theorem is an announcement that has been proved or may be proved. The evidence of a theorem is a logical argument that makes use of the inference guidelines of a deductive system to set up that the concept is a logical result of the axioms and formerly proved theorems.

In line with the Oxford dictionary, the definition of the concept is ''a rule or principle, especially in arithmetic, that may be proved to be true''. For example, in arithmetic, the Pythagorean theorem is a  theorem and is maximum extensively used in the domain of science.

2-1and interval = [4]

since function text is continuous in a given interval. And also

+(4) = 42+4 = 4-1

20 = 6667

$(5/4) = ($145/2

stone-1

= 5.833

simple, f(4) > $(5/2), hence Intermediate

Theorem & applies to the indicated proved.

Now,

= 6 C-1

C-5c +6 = 0

C=2 or c=3

1=3 or

C= 2, 3

<= 2

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Answer:

-2

Step-by-step explanation:

Answer: 34990

Step-by-step explanation:

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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Hey there! I'm happy to help!

Let's call the length and width L and W respectively.

L=2W+8

2W+2L=124

We plug our value of L into the second equation and solve for W.

2W+2(2W+8)=124

We undo the parentheses with the distributive property.

2W+4W+16=124

Combine like terms.

6W+16=124

Subtract 16 from both sides.

6W=108

Divide both sides by 6.

W=18

We plug this W value into the first equation to solve for L.

L=2(18)+8

L=36+8

L=44

So, the length is 44 feet and the width is 18 feet.

Have a wonderful day! :D

To perform a hypothesis test on the proportion of people who subscribe to a cable television service versus others, we need to check the following conditions:

1. Random Sampling: Ensure that the sample is randomly selected, which means each person has an equal chance of being selected. This is important to avoid biases and ensure the sample is representative of the population.

2. Independence: If sampling without replacement, the sample size (n) should be less than 10% of the population size (N) to assume independence. This is called the 10% Rule. Independence is important because the outcome of one person's choice should not affect another person's choice.

3. Normality: We need to ensure that the sampling distribution of the sample proportion (p-hat) is approximately normal. This can be checked using the success-failure condition, which states that both np and n(1-p) should be greater than or equal to 10. This ensures that the distribution is sufficiently normal to apply the z-test.

To help the student, remind them to:

1. Verify that the sample is random.
2. Check the independence condition by confirming the sample size is less than 10% of the population size.
3. Check the normality condition by calculating np and n(1-p) and making sure both values are greater than or equal to 10.

It is crucial to check these conditions because if they are not met, the hypothesis test's results may not be valid or reliable. Meeting these conditions ensures that the statistical methods applied are appropriate and provide accurate results for making conclusions.

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Answer:

3161 meters

Step-by-step explanation:

i added the numbers

Answer:

GH = MN

Step-by-step explanation:

Same as last posted question

The minimum cost to meet the minimum requirements is $1280.

To determine the minimum cost, we need to calculate the number of platters required to meet the minimum requirements for each item (hamburgers, hot dogs, and chicken wings) and then multiply it by the cost of each platter.

Let's calculate the number of platters required for each item:

For hamburgers:

80 hamburgers / 1 burger per platter = 80 platters

For hot dogs:

95 hot dogs / 1 hot dog per platter = 95 platters

For chicken wings:

380 chicken wings / 5 chicken wings per platter = 76 platters

Now, let's calculate the cost:

For Platter A:

80 platters * $16 per platter = $1280

For Platter B:

95 platters * $20 per platter = $1900

The minimum cost would be the lower of the two costs, which is $1280. Therefore, the minimum cost to meet the minimum requirements is $1280.

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Complete Question:

The Very Possible Foods Company makes vegan versions of hamburgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of 1 burger, 3 hot dogs, and 5 chicken wings, which costs $16. Platter B consists of 2 burgers, 1 hot dog, and 8 chicken wings, which costs $20.

A barbecue organizer requires 80 hamburgers, 95 hot dogs, and 380 chicken wings. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost (in dollars)?

The upper bοund fοr the 30th truncatiοn errοr fοr the series Σ (−1)n n² frοm n = 1 tο infinity is 810000/899.

Theοrem 9.17 states that if the series Σ |an| cοnverges, then the remainder Rn = Σ |an| frοm n+1 tο infinity satisfies the inequality |Rn| ≤ |an+1| + |an+2| + ... fοr all n.

In this case, we have the series Σ (−1)n n² frοm n = 1 tο infinity. Tο find an upper bοund fοr the 30th truncatiοn errοr, we need tο determine the remainder term R30.

First, let's rewrite the series as Σ |an| = Σ n² fοr n = 1 tο infinity. Since the terms in the series are pοsitive, we can drοp the absοlute value signs.

The 30th truncatiοn errοr can be expressed as R30 = Σ n² frοm n = 31 tο infinity.

Nοw, we want tο find an upper bοund fοr R30 using Theοrem 9.17. Tο dο this, we need tο determine a bοund fοr the terms |an+1|, |an+2|, and sο οn.

Lοοking at the series Σ n², we οbserve that the terms are increasing as n increases. Therefοre, we can find an upper bοund fοr the remainder term by cοnsidering the sum οf the terms beyοnd n = 30.

Since n² is a quadratic functiοn, we knοw that it grοws faster than linear functiοns such as n οr \(n^{1/2\). Sο, fοr all n ≥ 30, we can apprοximate the terms as |an| ≥ 30² = 900.

Therefοre, we have |R30| = Σ |an| frοm n = 31 tο infinity ≤ Σ 900 frοm n = 31 tο infinity.

Tο find an upper bοund fοr this sum, we can cοnsider an infinite geοmetric series with a cοmmοn ratiο less than 1. Let's denοte the sum as S.

S = 900/(1 - 1/900) = 900/(899/900) = 900 * (900/899) = 810000/899.

Thus, we have |R30| ≤ S = 810000/899.

Therefοre, the upper bοund fοr the 30th truncatiοn errοr fοr the series Σ (−1)n n² frοm n = 1 tο infinity is 810000/899.

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Answer:

A

Step-by-step explanation:

Plug the values into the equation

Option A is the correct answer.

If you look at the x and y values in table D, you’ll see that the change in y values is +2, while the change in x values is +1. Thus, the slope is 2/1 or 2.

Another way to look at it is by solving for the slope:

Using coordinates: (3, 5) (4 ,7):

Let x1 = 3

x2 = 4

y1 = 5

y2 = 7

\(m = \frac{(y_{2} - y_{1}) }{(x_{2} - x_{1}) }\)

\(m = \frac{7 - 5}{4 - 3} = \frac{2}{1} = 2\)

Therefore, the slope (m) = 2.

For the y-intercept, (b): it is the value of y when x = 0.

Let x = 0:

y = mx + b

y = 2(0) -1

y = -1

Therefore, the y-intercept is -1, which is also included in the given equation.

Answer: The critical points of g(t) occur at t = ±sqrt(-d/2) if d < 0. If d ≥ 0, then dg(t)/dt is always greater than or equal to zero, so g(t) has no critical points.

Step-by-step explanation:

To find the critical points of g(t), we need to find the values of t where the derivative dg(t)/dt is equal to zero or does not exist.

Using the given information, we have:

dg(t)/dt = 4ct^3 + 2dct

Setting this equal to zero, we get:

4ct^3 + 2dct = 0

Dividing both sides by 2ct, we get:

2t^2 + d = 0

Solving for t, we get:

t = ±sqrt(-d/2)

Therefore, the critical points of g(t) occur at t = ±sqrt(-d/2) if d < 0. If d ≥ 0, then dg(t)/dt is always greater than or equal to zero, so g(t) has no critical points.

Note that we also need to assume that c is nonzero, since if c = 0, then dg(t)/dt = 0 for all values of t and g(t) is not differentiable.

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Answer:

-9 is the correct answer

The mean of the sample (D) none of these alternatives is correct.

Therefore, the mean of the sample (D) none of these alternatives is correct.

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The correct question is given below:

The mean of the sample

a. is always smaller than the mean of the population from which the sample was taken

b. can never be zero

c. can never be negative

d. None of these alternatives is correct.