Suppose you wish to borrow $400 for five weeks and the amount of interest you must pay is $25 per $100 borrowed. What is the APR at which you are borrowing money?

Answers

Answer 1

If we borrowed amount of $400 for 5 weeks, then the APR at which the money is borrowed is 260.71%.

First, we calculate the total interest paid for borrowing $400 for five weeks.

The interest rate is $25 per $100 borrowed, so for $400 borrowed, the interest paid is : $25 × 4 = $100,

So, the total amount that needs to be paid-back is $400 (the original borrowed amount) plus $100 (the interest paid) = $500,

Next, we can use the APR formula to calculate, which is

⇒ APR = (Interest Paid/Amount Borrowed)/(Number of days) × 365 × 100,

In this case, the total interest paid is $100 and the total amount borrowed is $400, and

The number of days amount is borrowed is = 5×7 = 35 days,

Substituting the values,

We get,

⇒ APR = (100/400)/35 ×365 × 100 ≈ 260.71%

Therefore, the APR at which the money is being borrowed is 260.71%.

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Related Questions

Angular speed describes how fast something is turning. Linear speed describes how far it travels while it is turning. Linear speed depends on the circumference of a circle (C = 27r) and the number of revolutions per minute. Vinyl records were not the same size. A 45 rpm record had a diameter of 7 inches, a 33+ a diameter of 12 inches, and a 78 had a diameter of 10 inches. a. If a fly landed on the outer edge of a 45 rpm record, how far would it travel in 1 minute? b. How far if it was perched on the outside edge of a 33 rpm record? c. How far if it was perched on the outside edge of a 78 rpm record?​

Answers

a. On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.

b. On a 33 rpm record (12-inch diameter), the fly would travel 1,245.6 inches in 1 minute.

c. On a 78 rpm record (10-inch diameter), the fly would travel 2,430 inches in 1 minute.

How to solve

Radius of 45 rpm record = 3.5 inches (7/2)

Circumference = 2 * π * r = 2 * π * 3.5 ≈ 22 inches

Distance in 1 minute = Circumference * rpm = 22 * 45 = 990 inches

Thus, it can be seen that On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.


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Mr. Leonard is renting a car for one day. The table below shows the total amount he will be charged for the car based on the number of miles he drivesWhich equation best represents c, the number of dollars Mr. Leonard should be charged for driving m miles?

Answers

Answer:

t = r + cm

Step-by-step explanation:

t = total amount of money spent on rental car

r equals the original payment amount (like how much it cost to even attain tthe car)

c = the number of dollars for every mile

m = amount of miles

You would multiply c and m since every mile the dollars goes up by itself

You need to add the original payment, r, to find the correct total

If there is no original payment then the formula could also just be :

t = cm

total = miles x money per 1 mile

I could provide better explanation if I had the chart you mentioned but hope this helps!

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Express the statement as an inequality Part 6a^2

Answers

Answers:

(c)  [tex]q \le \pi[/tex]

(d)  [tex]2 \ge d \ge 1[/tex]

Explanation:

The "less than or equal to" sign is ≤ which has a "less than sign" placed on top of a single horizontal bar. It can be thought of something like this [tex]\stackrel{ < }{=}[/tex] except there isn't a second horizontal bar.

The "d is between 2 and 1" seems to have a strange order to it. I have a feeling your teacher is wanting 2 ≥ d ≥ 1 because of that order. Normally we would list things from smallest to largest. We involve "or equal to" if we want to include the endpoints.

Part a: q is less than or equal to π: q ≤ π.

Part b: d is between 2 and 1: 1 < d < 2.

Explain about the inequality sign:

Less than (<), more than (>), less than or equal (≤), greater than or equal (≥), and not equal (≠) are the inequality symbols.

Numbers are compared using inequalities to identify the range (or ranges) of values which satisfy the requirements of a certain variable.

Addition, subtraction, multiplication, and division are operations on linear inequalities. Here is a list of the fundamental guidelines for these operations.The inequality sign is unaffected by subtracting the same amount from both sides of the inequality. As an illustration, if a > b, then a - c > b - c.

Part a: q is less than or  equal to π.

In this case:

q < π and q = π

Combining both:

q ≤ π

Part b: d is between 2 and 1

Here values 1 and 2 will not be taken for d.

d < 2 and d > 1

Thus,

1 < d < 2

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Which of the following expressions does cos(x − y) − cos(x + y) simplify to?

Answers

the expression cos(x − y) − cos(x + y) simplifies to 2sin(x)sin(y).

what is  expression ?

In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.

In the given question,

We can use the trigonometric identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b) to simplify cos(x - y), and cos(a + b) = cos(a)cos(b) - sin(a)sin(b) to simplify cos(x + y).

cos(x - y) = cos(x)cos(y) + sin(x)sin(y)

cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

Therefore,

cos(x - y) - cos(x + y) = (cos(x)cos(y) + sin(x)sin(y)) - (cos(x)cos(y) - sin(x)sin(y))

= cos(x)cos(y) + sin(x)sin(y) - cos(x)cos(y) + sin(x)sin(y)

= 2sin(x)sin(y)

So, the expression cos(x − y) − cos(x + y) simplifies to 2sin(x)sin(y).

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simplify the expressions  cos(x − y) − cos(x + y) ?

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Please help me with #19

Answers

Answer:

a. 1.95 cm.

b. 3920 cm^2.

Step-by-step explanation:

(a) To find the length of the arc that subtends the central angle theta on a circle of diameter d, we can use the formula:

Arc Length = (theta / 360°) x (pi x d)

Substituting the given values, we get:

Arc Length = (1.6 / 360°) x (pi x 140 cm)

Arc Length ≈ 1.95 cm

Therefore, the length of the arc that subtends the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 1.95 cm.

(b) To find the area of the sector determined by the central angle theta, we can use the formula:

Area of Sector = (theta / 2π) x pi x (r^2)

where r is the radius of the circle.

Since the diameter of the circle is given as 140 cm, the radius is half of that, which is 70 cm.

Substituting the given values, we get:

Area of Sector = (1.6 / (2 x pi)) x pi x (70 cm)^2

Area of Sector ≈ 3920 cm^2

Therefore, the area of the sector determined by the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 3920 cm^2.

100 POINTS!! PLS HELP QUICKLY <3 SEE IMAGE FOR DETAILS.
a table of values for Function A and the graph of B are shown

Answers

The equation of the third linear function is:

y = (-1/3)x + (8/3)

How do we calculate?

To find a linear function with a rate of change between Function A and Function B, we need to calculate the rates of change for each function.

For Function A, the rate of change is:

(2 - (-4)) / (6 - (-1)) = 6/7

For Function B, we find the rate of change by selecting any two points on the graph, such as (2, 6) and (-4, 7):

(6 - 7) / (2 - (-4)) = -1/6

So the rate of change for Function A is 6/7, and the rate of change for Function B is -1/6.

To find a linear function with a rate of change between these two values, we can select any value between 6/7 and -1/6. Let's choose a rate of change of -1/3.

We can use the point-slope form of a linear equation to write the equation of the line with a rate of change of -1/3 and passing through the point (2, 6):

y - 6 = (-1/3) * (x - 2)

y = (-1/3)x + (8/3)

In conclusion, the equation of the third linear function is:

y = (-1/3)x + (8/3)

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Find the value of the following expression when x = 5:

8x divided by 4= ?

Answers

Answer:

10

Step-by-step explanation:

Replace X with 5

The new equation should be 8×5 divided by 4

Then you would multiply 8×5, which is 40

Now, divided 40 by 4, which is 10.

Therefore 8×5 divided by 4 is 10.

SORRY IF THIS DIDN'T MAKE SENSE!

10 because if you plug in 5 as the x, your multiplying 5x8 which gives you 40. 40 divided by 4 gives you 10

Two random samples are taken from private and public universities (out-of-state tuition) around the nation. The yearly tuition is recorded from each sample and the results can be found below. Test to see if the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions. Assume unequal variances. Use a 1% level of significance and round answers to 4 decimal places.

Private Institutions (Group 1 )

Public Institutions (Group 2)

43,120

25,469

28,190

19,450

34,490

18,347

20,893

28,560

42,984

32,592

34,750

21,871

44,897

24,120

32,198

27,450

18,432

29,100

33,981

21,870

29,498

22,650

31,980

29,143

22,764

25,379

54,190

23,450

37,756

23,871

30,129

28,745

33,980

30,120

47,909

21,190

32,200

21,540

38,120

26,346

Hypotheses:

H0: μ1 = μ2

H1: μ1 > μ2

Identify the test statistic. Round to 4 decimal places.

t =___

___

Answers

Therefore , the solution of the given problem of test statistic comes out to be 4.0085 is the test statistic for this two-sample t-test.

What is test statistics?

The Z-statistic, which confirms the precision of the conventional null hypothesis, is the only strategy that's even remotely close to a Z-test. Consider extrapolating a 2.5 E score in a 2 X y examination with a 0.05 threshold of significance. The p-value connected to this Z-value is 0.0124.

Here,

A two-sample t-test's test statistic is calculated as follows:

The formula for

=> t is (mean1 - mean2) / √((s1 / n1) + (s2 / n2)).

where mean1, mean2 represent the sample means for Group 1 (private institutions) and Group 2 (public institutions), respectively; s12, s22 represent the sample variances for

Groups 1 and 2, and n1, n2 represent the sample sizes for Groups 1 and 2, respectively.

Let's compute the test statistic based on the provided information:

The sample mean (mean1) for private institutions (Group 1) is $43,120.

$1,671,699,489.05 is the sample variance (s12).

Sample (n1) size is 37.

Public Institutions: Sample mean (mean2) = $25,469 (Group 2).

$1,682,553,858.66 is the sample variance (s22).

Number of samples

=>  (n2): 39

=> t = (43,120 - 25,469) / √((1,671,699,489.05 / 37) + (1,682,553,858.66 / 39))

=> t = 4.0085

Therefore, 4.0085 is the test statistic for this two-sample t-test.

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Mariana receives a $20 gift card for downloading music and wants to determine how many songs she can purchase. Each downloaded song costs $1.29. If m represents the number of songs downloaded, which inequality represents the given situation? 20 m greater-than-or-equal-to 1.29 20 m less-than-or-equal-to 1.29 1.29 m less-than-or-equal-to 20 1.29 m greater-than-or-equal-to 20​

Answers

Answer:

The relationship between m number of songs downloaded  and the total cost of $20 Mariana receives will be represented by inequality .

Given,

The value of gift card which Mariana have .

The costs of each downloaded song is .

Since m represents the number of songs downloaded and she has in total , so the inequality represents the given situation is,

.

Hence the required inequality is .

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Step-by-step explanation:

Answer:

The answer should be C

Let A and B be two events such that
P(A) = 1/5 While P(A or B) = 1/2
Let P(B) = P. For what values of P
are A and B independent?​

Answers

We know that if A and B are independent, then the following equation holds true:
P(A and B) = P(A) * P(B)

Let's rewrite P(A or B) as follows:
P(A or B) = P(A) + P(B) - P(A and B)

We can plug in the given values to get:
1/2 = 1/5 + P - P(A and B)

We can simplify this equation to get:
3/10 = P - P(A and B)

Now, we need to find the values of P such that A and B are independent. This means that P(A and B) = P(A) * P(B). Substituting the given values, we get:
P(A) * P(B) = (1/5) * P

And from the above equation, we have:
P(A and B) = P - (3/10)

We can substitute these two equations and solve for P to get:
(1/5) * P = P - (3/10)

Solving for P, we get:
P = 3/4

Therefore, if P = 3/4, then A and B are independent events.

Write a quadratic equation to match this graph.

Answers

The quadratic equation written in vertex form is:

y = (x + 1)^2 - 9

How to write the quadratic equation?

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:

y = a*(x - h)^2 + k

On the graph we can see that the vertex is at (-1, -9), then we have:

y = a*(x + 1)^2 - 9

Now we also can see that the y-intercept is y = -8, then evaluating in zero we should get:

-8 = a*(0 + 1)^2 - 9

-8 = a - 9

-8 + 9 = a = 1

The quadratic equation is:

y = (x + 1)^2 - 9

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regular priced at $85 on sale for 75%
off regular price

Answers

Answer: $21.25

Step-by-step explanation:
This can be solved using the following formula:

discount = (discount rate) x (regular price) sale price = regular price - discountPlugging in the values you provided:discount = (0.75) x (85) discount = 63.75sale price = 85 - 63.75 sale price = 21.25

Therefore, the sale price of the item is $21.25.

A BCom graduate bought a small apartment for R151 000.00 with a down payment of R51 000.00. If the graduate secures a mortgage bond with a bank for the balance at 15% per annum, compounded monthly, with a term of 20 years. What are the monthly payments?

Answers

The solution of calculate the monthly payments on a mortgage bond, we can use the formula for the present value of an annuity.

what is present value and annuity

Present value (PV) is the current value of a future sum of money, discounted to reflect the time value of money and the risk of non-payment or default.

An annuity is a financial product that pays out a fixed stream of payments to an individual over a specified period of time.

According to the given information:

To calculate the monthly payments on a mortgage bond, we can use the formula for the present value of an annuity:

PV = (PMT / i) x (1 - [tex](1+n)^{-n}[/tex])

Where:

PV = present value (the amount borrowed)

PMT = monthly payment

i = monthly interest rate (15% per annum / 12 months = 1.25%)

n = number of monthly payments (20 years x 12 months per year = 240 months)

First, we need to calculate the present value of the loan, which is the amount borrowed minus the down payment:

PV = R151 000.00 - R51 000.00

PV = R100 000.00

Next, we can plug in the values into the formula:

R100 000.00 = (PMT / 0.0125) x (1 - [tex](1+0.0125)^{-240}[/tex])

Solving for PMT, we get:

PMT = R1,080.80

Therefore, the monthly payments on the mortgage bond will be R1,080.80.

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Use the word factor product quotient in sum to describe the parts of five minus M divided by N -2-8 times M plus N

Answers

The parts of the expression in terms of factor, product, quotient, and sum are:

Factor- (5 - M)/(N - 2)

Product- 8 * M

Quotient- (5 - M)/(N - 2)

Sum- (5 - M)/(N - 2) + N - 8 * M - 2

Explain expression

An expression is a mathematical phrase that contains numbers, variables, and/or mathematical operations. It can be simplified or evaluated using mathematical rules and principles.

What is meant by quotient?

The quotient is the result obtained when one quantity is divided by another, usually represented as a whole number, fraction, or decimal. It is a fundamental concept in mathematics.

According to the given information

The given expression is:

(5 - M)/(N - 2) - 8 * M + N

We can break it down into the following parts using the words factor, product, quotient, and sum:

Factor: (5 - M)/(N - 2)

Product: 8 * M

Quotient: (5 - M)/(N - 2)

Sum: (5 - M)/(N - 2) + N - 8 * M - 2

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Kelly is making a bubble mixture for kids to play with at a backyard party. She adds 1/4 of a cup of corn syrup to 6 cups of soap and water.

She wants to make more bubble mixture and has 18 cups of the soap and water mixture to use.

How much corn syrup does she need to add?

A. 2/3 of a cup of corn syrup
B. 3 cups of corn syrup
C. 3/4 of a cup of corn syrup
D. 3 1/4 cups of corn syrup

Answers

Answer: C. 3/4 of a cup of corn syrup

Step-by-step explanation:

    We will set up a proportion to help us solve.

[tex]\displaystyle \frac{1/4\text{ cup corn syrup}}{6\text{ cups of soap and water}} =\frac{x\text{ cups corn syrup}}{18\text{ cups of soap and water}}[/tex]

    Next, we will cross-multiply.

1/4 * 18 = 6 * x

9/2 = 6x

    Lastly, we will divide both sides of the equation by 6.

x = 3/4 of a cup of corn syrup

                       C. 3/4 of a cup of corn syrup

ms george baked 2 cakes of equal size each of her 12 guests at the same amount of cake, and no cake was left over.

a What fraction of a cake did each guest eat

b. How do you think ms george cut the cakes into equal pieces? Explain

Answers

ANSWER TO A: each guest got 1/6 of a cake. To solve, you divide 2/1 by 12/1.
To do so, you do keep (keep the 2/1 the same) change, (change the division symbol to multiplication) and flip (1/12)
So now you multiply 2/1 • 1/12 which would get you 2/12. 2/12 is equivalent to 1/6. Therefore each guest gets 1/6 of a cake.

ANSWER TO B: Ms George cut each cake into 6 equal pieces (or a total of 12) She did this because there are 12 people, who each need a slice out of 2 cakes. You would have to divide 2 into 12, which would give you 6 slices per cake.

I AM SO SORRY IF THIS DID NOT MAKE SENSE!

Question attached below:

Answers

The probability that Frank gets a head and a tail in any order is 2/5.

We have,

The sample space of tossing two coins.

= {HT} x {HT}

= {HH, HT, TH, TT}

So,

The table is filled as:

First coin   Second coin

  Head         Head

  Head         Tail

  Tail             Head

   Tail             Tail

Now,

The probability that Frank gets a head and a tail in any order.

= Number of required outcomes / Total outcomes

{HT, TH} = 2

{HH, HT, TH, TT} = 5

So,

= 2/5

Thus,

The probability that Frank gets a head and a tail in any order is 2/5.

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15 Points 15 Points 15 Points

(Diversifying Portfolios MC)



Name of Stock Symbol High Low Close

Stock A A 105.19 103.25 103.38

Stock B B 145.18 43.28 144.05



Last year, an investor purchased 120 shares of stock A at $90 per share and 35 shares of stock B at $145 per share. What is the difference in overall loss or gain between selling at the current day's high price or low price?


A The difference in overall gain is $299.30.

B The difference in overall loss is $299.30.

C The difference in overall gain is $293.90.

D The difference in overall loss is $293.90.

Answers

the answer is option C: The difference in overall gain is $293.90.

How to solve the question?

To calculate the difference in overall loss or gain, we need to calculate the current value of the investor's portfolio for both high and low prices and then compare the two values.

First, let's calculate the current value of the investor's holdings for stock A:

High price: 120 shares x $105.19 per share = $12,623.80

Low price: 120 shares x $103.25 per share = $12,390.00

Next, let's calculate the current value of the investor's holdings for stock B:

High price: 35 shares x $145.18 per share = $5,080.30

Low price: 35 shares x $43.28 per share = $1,514.80

Now we can calculate the total current value of the investor's portfolio:

High price: $12,623.80 + $5,080.30 = $17,704.10

Low price: $12,390.00 + $1,514.80 = $13,904.80

The difference between the two values is:

High price: $17,704.10 - ($120 x $90) - ($35 x $145) = $299.30

Low price: $13,904.80 - ($120 x $90) - ($35 x $145) = $293.90

Therefore, the answer is option C: The difference in overall gain is $293.90.

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Classify the solid.

Explain your reasoning.

Image below.

Answers

The solid displayed in the image is a trapezoidal prism.

What is a trapezoidal prism?

A trapezoidal prism is a three-dimensional solid with two parallel trapezoids as its bases, and rectangular or parallelogram sides connecting them. The top and bottom faces are identical, and the side faces are parallelograms.

To classify the solid, look at its properties. The solid has two parallel trapezoids as its bases, and the side faces are parallelograms. Therefore, it is a prism.

Since the bases are not identical rectangles or squares, it is not a rectangular or square prism. However, since the bases are trapezoids, it is a trapezoidal prism.

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TREE CLIMBING Keara climbs a tree and looks down at her friend through a pair of range finders. According to the range finders, the distance from Keara to her friend is 55 feet. If the angle of depression from Keara to her friend is 40°, how high has Keara climbed in the tree? Round to the nearest tenth of a foot. feet

Answers

Keara has climbed up to 41 feet in the tree.

How to round off a value to the nearest tenth?

Rounding off a value to the nearest tenth means finding the closest multiple of 0.1 to the given value. To do this, you need to look at the digit in the hundredths place. If the digit is 5 or greater, you round the tenths place up by 1. If the digit is less than 5, you leave the tenths place unchanged. For example, to round the value 3.874 to the nearest tenth, you would look at the digit in the hundredths place, which is 7. Since 7 is greater than 5, you round up the tenths place to 8, and the rounded value is 3.9. Rounding to the nearest tenth is often used when working with measurements or values that require a certain level of precision.

According to the range finders, the distance from Keara to her friend is 55 feet and the angle of depression from Keara to her friend is 40°.

From this the following diagram can be drawn.

Now, we need to find the length of AB which will denote how high Keara climbed.

We can use the trigonometric sine function to find the length of AB,

Sin 40° = opposite side / hypotenuse = AB/ BC = AB/ 55

Hence AB = 55 × Sin 40° ≈ 40.981

That is she would have climbed approximately 41 feet.

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Suppose a golfer took 70 shots to finish his or her round on this course. What integer represents this​ score?

Answers

In golf, lower scores are better, so a score of 70 is considered to be a good score for a round of golf, especially on a challenging course.

What is integer?

An integer is a whole number that can be either positive, negative or zero, and does not have a fractional or decimal part. Integers can be represented on a number line, with positive integers located to the right of zero and negative integers located to the left of zero.

According to question:

an integer is a whole number that does not have a fractional or decimal part. In golf, a player's score for a round is determined by counting the number of strokes they took to complete the course.

So, if a golfer took 70 shots to finish his or her round on a golf course, the integer that represents this score is simply 70. This is because 70 is a whole number and there are no fractional or decimal parts involved in the score.

In golf, lower scores are better, so a score of 70 is considered to be a good score for a round of golf, especially on a challenging course.

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graph math pls help me!!!!

Answers

Looking at the table, If Bridget has 10 animals in total with 30 legs, it only means she has 5 chicken.

What are the missing values in the table?

Based on the information on the table,

For the number of chicken legs, we say

9 x 2 = 18       3 x 2 = 6          7 x 2= 14       14 x 2 = 28

If we sum these number to the total number of legs in each row, it would be;  4 + 18 = 22   8+6 = 14   12 + 14 = 26     16+28 = 44

This means that all the values provided so far does not give us the accurate number of legs of the animals.

If 5p = 20L the number of hen should be 30- 20 = 10/2 = 5

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The model below represents the division problem 2\frac{1}{5}\div\frac{4}{5}2
5
1

÷
5
4

.

Answers

The equivalent value of the fraction is A = 11/4

Given data ,

Let the fraction be represented as A

Now , let the first fraction be p = 2 1/5

Let the second fraction be q = 4/5

Now , A = p/q

On simplifying the equation , we get

A = ( 2 1/5 ) / 4/5

A = ( 11/5 ) / ( 4/5 )

On further simplification , we get

A = ( 11/5 ) x ( 5 / 4 )

A = 11/4

Therefore , the value of A is 11/4

Hence , the fraction is A = 11/4

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What is the equation of the graphed line written in standard form?

a. 2x - y = -4
b. 2x - y = 4
c. y = 2x - 4
d. y = 1/2x - 4

Answers

Answer:

answer is

c. y = 2x - 4

Step-by-step explanation:

y=mx+b is standard, b is also correct but not in standard form, hope this helps

Give an example of data you would put in a line plot, histogram, and box plot. Explain why you chose each type of representation. How is a line plot similar to and different from a box plot
Please, I need now

Answers

Let's say we have a dataset representing the heights (in inches) of 30 students in a class.

How to represent the data in line plot, histogram and box plot?

Here's an example of data and how we can represent it using a line plot, histogram, and box plot:

Line Plot:

Data: Heights of 30 students (in inches): 60, 62, 61, 63, 64, 65, 63, 62, 64, 63, 61, 60, 61, 63, 62, 64, 65, 64, 63, 62, 61, 63, 65, 64, 63, 62, 61, 60

A line plot would be suitable for visualizing this dataset, as it provides a simple and clear representation of individual data points along a number line. A line plot is useful for showing the distribution of data points and identifying any patterns or trends in the dataset.

Histogram:

Data: Heights of 30 students (in inches): 60, 62, 61, 63, 64, 65, 63, 62, 64, 63, 61, 60, 61, 63, 62, 64, 65, 64, 63, 62, 61, 63, 65, 64, 63, 62, 61, 60

A histogram would be suitable for visualizing this dataset, as it provides a graphical representation of the distribution of data points in different intervals or bins. The heights of the students can be grouped into bins, such as 60-62, 62-64, 64-66, etc., and the frequency of data points falling into each bin can be represented by the height of bars.

Box Plot:

Data: Heights of 30 students (in inches): 60, 62, 61, 63, 64, 65, 63, 62, 64, 63, 61, 60, 61, 63, 62, 64, 65, 64, 63, 62, 61, 63, 65, 64, 63, 62, 61, 60

A box plot, also known as a box-and-whisker plot, would be suitable for visualizing this dataset, as it provides a summary of the data's distribution, including measures of central tendency and variability. The box in the plot represents the interquartile range (IQR), which contains the middle 50% of the data, with the line inside the box representing the median.

Similarities between line plot and box plot:

Both line plot and box plot provide a visual representation of the distribution of data points.Both line plot and box plot can show individual data points or values.

Differences between line plot and box plot:

Line plot displays data points along a number line, while a box plot summarizes data using quartiles and displays them in a box-and-whisker form

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Match each inequality on the left with its correct solution on the right.


Some answer choices on the right will be used more than once.

Answers

Answer:

4x + 2 > 10 and -3x-1 > 5 : No solution

| 3x | + 4< 10:  -2 < 2 x < 2

| x+2 | + 4< 3: No solution

|2x+4 | +2 > 4: x > -1 or x < -3

Step-by-step explanation:

Two buses leave a station at the same time and travel in opposite directions. One bus travels 20 mi/h faster than the other. If the two buses are 576 miles apart after 4 hours, what is the rate of each bus?

Answers

The first bus would be going 54 MPH, and the second bus would be going 66 MPH!

Brad Harrington bought 31 shares of one stock for $9 3/4 per share and 26 shares of another stock for $11 5/8 per share. How much did he pay?

Answers

Answer:

  $604.50

Step-by-step explanation:

You want to know the total paid for 31 shares at $9 3/4 and 26 shares at $11 5/8.

Total paid

The total paid is computed the same as for any other purchase. It is the sum of the products of quantity and price each.

  total = (31)(9 3/4) +(26)(11 5/8) = 604.50

Harrington paid $604.50 for the stock.

A number cube with the numbers 1 through 6 is rolled. What is the probability of the number cube showing a 3 or an odd number?

Answers

There are three odd numbers on a number cube, which are 1, 3, and 5. Since 3 is already an odd number, we don't need to count it twice when finding the probability of rolling an odd number. So, there are a total of four numbers that meet the requirement of being a 3 or an odd number. That means the probability of rolling a 3 or an odd number is 4/6, or 2/3.

Help with the following 2 problems please

Answers

2. The solution to the integral is: -2cot(x) - 4ln|sin(x)| - 3x + C

6. The integral converges and its value is 0.

How did we get these values?

2. To solve this integral using partial fractions, we need to rewrite the integrand as a sum of simpler fractions. We first rewrite the integrand as follows:

(2cos(x)/sin²(x) - 4 sin(x) - 5) = 2/sin(x)² - 4sin(x) - 5

Now we need to express the first term 2/sin(x)² as a sum of two fractions with different denominators. To do this, we let:

2/sin(x)² = A/sin(x) + B/sin(x)²

Multiplying both sides by sin(x)², we have:

2 = A sin(x) + B

Next, we need to determine the values of A and B. To do this, we can substitute two different values for x that make sin(x) ≠ 0, such as x = 0 and x = π/2.

Substituting x = 0, we get:

2 = A(0) + B

2 = B

Substituting x = π/2, we get:

2 = A(1) + B

2 = A + B

2 = A + 2

Therefore, A = 0.

So we have:

2/sin(x)² = B/sin(x)²

B = 2

Substituting these values back into our original expression, we get:

(2cos(x)/sin²(x) - 4 sin(x) - 5) = 2/sin(x)² - 4sin(x) - 5

= 2/sin(x)² - 4sin(x)/sin(x) + 2sin(x)/sin(x) - 5

= 2/sin(x)² - 4cot(x) + 2 - 5

= 2/sin(x)² - 4cot(x) - 3

Now we can integrate each term separately:

∫2/sin(x)² dx = -2cot(x) + C1

∫-4cot(x) dx = -4ln|sin(x)| + C2

∫-3 dx = -3x + C3

So the solution to the integral is:

∫(2cos(x)/sin²(x) - 4 sin(x) - 5) dx = -2cot(x) - 4ln|sin(x)| - 3x + C

where C = C1 + C2 + C3 is the constant of integration.

6. We can solve this integral by using the substitution u = x - 2, which gives us du = dx. We can then rewrite the integral as:

∫₁ (1/(x-2)²) dx = ∞

∫-∞ (1/u²) du

Now, we can evaluate this integral as:

∫-∞ (1/u²) du = [-1/u]∞

= [0 - (-1/(-∞))]

= 0 - 0

= 0

Therefore, the integral converges and its value is 0.

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The text format of the questions:

2. Use the method of partial fractions to find the integral:

∫(2cos(x)/sin²(x) - 4 sin(x) - 5) dx

6. State whether the integral converges or diverges. If it converges give the value it converges to.

∫₁ (1/(x-2)²) dx

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