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?

Keara has climbed up to 41 feet in the tree.

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

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:

Differences between line plot and box plot:

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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

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

6. The integral converges and its value is 0.

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

The solution of calculate the monthly payments on a mortgage bond, we can use the formula for the present value of an 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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Looking at the table, If Bridget has 10 animals in total with 30 legs, it only means she has 5 chicken.

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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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.

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.

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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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

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.

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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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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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!

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.

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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(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.

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.

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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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.

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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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

The equation of the third linear function is:

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

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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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.

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.

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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The quadratic equation written in vertex form is:

y = (x + 1)^2 - 9

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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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.

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) ?

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:

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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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!