5. Rebecca wanted to make bracelets. She bought 9 boxes of beads. Each box contained 40 beads. While carrying the boxes home, 23 beads fell out. How many beads does she have left to make the bracelets?​

Answer:

Step-by-step explanation:

y = abx

a is the y-intercept

y = 16bx

Now substitute 2 for x and 1296 for y

1296 = 16(b)2

81 = b2

b = 9

y = 16(9)x

The function which has range (2, ∞) is,

D) y = 5ˣ + 2

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, For a function: y = 5ˣ

Range is,

⇒ ( 0 , + ∞ )

And, we have:

y = 5ˣ + 2 ,

which is translated 2 units up.

So, the range is ( 2, + ∞ ).

Hence, The function which has range (2, ∞) is,

D ) y = 5ˣ + 2

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Answer:sasa

Step-by-step explanation:

The length of the line segment PQ to the nearest tenth is: 16.5\

The formula for the distance between two coordinates is given by:

D(x, y) = √[(y₂ - y₁)² + (x₂ - x₁)²]

In this question , we are given:

P(-10, 2) and Q(6, 6)

Thus:

PQ = √[(6 - 2)² + (6 + 10)²]

PQ = √(16 + 256)

PQ = √272

PQ = 16.49

To the nearest tenth gives:

PQ = 16.5

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The equation of the hyperbola is [tex](x + 3)^2/16 - (y - 5)^2/36[/tex] = 1.

The collection of all points in a plane such that the distance between any point on the curve and two fixed points (referred to as the foci) is constant is known as a hyperbola. Hyperbolas are a sort of conic section. A hyperbola contains two distinct branches and has the appearance of two curving branches that are mirror reflections of one another. A hyperbola's center, vertices, co-vertices, foci, and asymptotes are some of its most important characteristics. The center, which is the point around which the hyperbola is symmetric, is the midway of the line segment connecting the vertices.

Given that, the co-vertices are (1, 5) and (-7, 5).

Now, using the midpoint formula we have:

center = ((1+(-7))/2, (5+5)/2) = (-3, 5)

Now, the distance between center and vertex is a = 4.

Also, the distance between the center and each co-vertex is b = 6.

Now, the equation of the hyperbola is:

[tex](x - (-3))^2/4^2 - (y - 5)^2/6^2 = 1\\(x + 3)^2/16 - (y - 5)^2/36 = 1[/tex]

Hence, the equation of the hyperbola is [tex](x + 3)^2/16 - (y - 5)^2/36[/tex] = 1.

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Answer: -37.5

Step-by-step explanation: You can simply do this in the calculator by doing 3 times -12.5. the parenthesis is a sign to multiply

Answer:

the answer is -75/2= - 37.5

Answer:

[tex]y=5-2x[/tex]

Step-by-step explanation:

You have to give the equation in the form [tex]y=mx+c[/tex], where m is the gradient and c is the y-intercept (where the line crosses the y-axis).

From the graph, we can see the line crossed the y-axis at (0,5), so the y-intercept is (0,5), which means c is 5.

We can work out the gradient with the two points (2,1) and (1,3) by doing:

[tex]\frac{change in y}{change in x} =\frac{1-3}{2-1}=-2[/tex]
So the gradient of the line, m, is -2.

Thus the equation of the line is [tex]y=5-2x[/tex].

The scale ratio for this map is 0.0000063.

What is scale ratio?

Scale ratio is the ratio between the measurements of an object or distance on a map or drawing and the actual measurements of the object or distance it represents in real life. It allows us to compare and relate the sizes or distances of objects in a drawing or map to their actual sizes or distances in the real world.

The scale ratio can be found by dividing the distance on the map by the corresponding distance in reality:

scale ratio = distance on map / distance in reality

In this case, the distance from Wellspring to Red Creek is 4 inches on the map and 10 miles in reality. So the scale ratio is:

scale ratio = 4 inches / 10 miles

To simplify this ratio, we need to convert the units so that they are the same. Let's convert inches to miles:

1 mile = 63,360 inches

So, we can convert the inches on the map to miles as follows:

4 inches * (1 mile / 63,360 inches) = 0.000063 miles

Now we can rewrite the scale ratio as:

scale ratio = 0.000063 miles / 10 miles

Simplifying this ratio by canceling out the units of miles, we get:

scale ratio = 0.0000063

Therefore, the scale ratio for this map is 0.0000063.

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If you are given a sample percentage of 43%, you would need to know the sample size in order to convert this percentage to a proportion.

The conversion formula is proportion = percentage/100. However, the proportion alone does not give information about the sample size, which is necessary for inference and hypothesis testing. The other statements are not true.

The test statistic is not affected by the sample size, but its value can be used to determine the significance of a hypothesis test. A larger p-value indicates weaker evidence against the null hypothesis, not stronger evidence. Finally, we assume the null hypothesis is true until we have sufficient evidence to reject it.

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Using probability, there is only one outcome that represents rolling an odd number and landing on blue.

What exactly is probability?

Probability is a measure of the possibility or chance that an event will occur. It is represented by a number between 0 and 1, with 0 representing an improbable occurrence and 1 representing a certain event. A given event's probability is estimated by dividing the number of favourable outcomes by the total number of potential possibilities. Probability theory is frequently used to analyse and forecast the likelihood of occurrences in domains such as statistics, physics, economics, and finance.

Now,

The probability of rolling an odd number is 3/6, which can be simplified to 1/2. The probability of landing on blue= 1/3. Since the events of rolling an odd number and landing on blue are independent, we can multiply the probabilities to find the probability of both events occurring:

(1/2) × (1/3) = 1/6

So, there is only one outcome that represents rolling an odd number and landing on blue. The answer is 1.

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The graphical representation that is best and most appropriate for the data is Box plot, because the median can easily be determined from the large set of data. That is option A.

The box plot is a type of graphical representation of data that gIves more than one detail about the data set such as;

Box plots allow you to compare multiple data sets better than others dues to the above listed features that it has.

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a) The zero rates for the five maturities are: 1 year is 2.01%, 2 years is 2.48%, 3 years is 2.77%, 4 years is 1.73%, and 5 years is 4.32%.

b) The price of the security is $128.31.

a) To find the zero rates for all 5 maturities, we can use the formula for the present value of a bond:

PV = C / [tex](1+r)^n[/tex]

where PV is the present value,

C is the coupon payment,

r is the zero rate, and

n is the number of years to maturity.

We can solve for r by rearranging the formula:

r = [tex](C/PV)^{(1/n) }[/tex]- 1

Using the bond data given in the question, we can calculate the zero rates for each maturity as follows:

For the 1-year bond, PV = 98 and C = 0, so r = 2.01%.

For the 2-year bond, PV = 101, C = 2.48, and n = 2, so r = 2.48%.

For the 3-year bond, PV = 103, C = 2.91, and n = 3, so r = 2.77%.

For the 4-year bond, PV = 101, C = 2, and n = 4, so r = 1.73%.

For the 5-year bond, PV = 103, C = 5, and n = 5, so r = 4.32%.

Alternatively, we can use linear algebra to find the zero rates. We can write the present value equation in matrix form:

PV = A × x

where A is a matrix of coefficients, x is a vector of unknowns (the zero rates), and PV is a vector of present values.

To solve for x, we can use the equation:

x = ([tex]A^{-1}[/tex]) x PV

where ([tex]A^{-1}[/tex]) is the inverse of matrix A.

Using this method, we can solve for the zero rates as follows:

[2.01% ]

[2.48% ]

[2.77% ] = x

[1.73% ]

[4.32% ]

PV = [tex]A^{-1}[/tex] x  [98]

                   [101]

                   [103]

                   [101]

                   [103]

PV =   [-0.0201]

          [ 0.0248]

          [ 0.0277]

          [-0.0173]

          [ 0.0432]

b) To find the price of the security which pays cash flows of $10 in one year, $25 in two years, and $100 in four years, we can use the formula for the present value of a series of cash flows:

PV = [tex]C1/(1+r)^1 + C2/(1+r)^2 + C3/(1+r)^4[/tex]

where PV is the present value, C1, C2, and C3 are the cash flows, r is the zero rate, and the exponents correspond to the number of years until each cash flow is received.

Using the zero rates calculated in part (a), we can calculate the present value of each cash flow:

PV1 = $10 /(1+2.01 % [tex])^1[/tex] = $9.80

PV2 = $25/(1+2.48%[tex])^2[/tex] = $22.15

PV3 = $100/(1+1.73%[tex])^4[/tex] = $81.36

Then, the price of the security is the sum of the present values:

PV = $9.80 + $22.15 + $81.36 = $128.31

Therefore, the price of the security is $128.31.

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The volume of Preston's new step in rectangular prism shape with given length , width, and height is equals to 2,376 cubic inches

Let us consider l be the length, w is the width, and h is the height.

The volume of a rectangular prism is equal to,

V = l × w × h

In this case,

The length (l) is equals to 11 inches,

The width (w) is equals to 36 inches,

The height (h) is equals to 6 inches.

So, we can plug in these values and calculate the volume,

V = l × w × h

⇒ V = 11 inches × 36 inches × 6 inches

⇒ V = 2,376 cubic inches

Therefore, the volume of Preston's new step for given dimensions is 2,376 cubic inches.

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1. x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.

2. x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.

1. Which function reaches 50 first?

To answer this, we need to solve for x in each function when the output is 50:

For f(x): 50 = 10x + 3

47 = 10x

x = 4.7

For g(x): 50 = 2x

x = 25

Since x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.

2. Which function reaches 100 first?

Similarly, we'll solve for x in each function when the output is 100:

For f(x): 100 = 10x + 3

97 = 10x

x = 9.7

For g(x): 100 = 2x
x = 50

Since x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.

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Answer:

p = 3, q = 1

Step-by-step explanation:

well, let's think about what (x - p)² actually is.

let's do the multiplication (what a square is) :

(x - p)(x - p) = x² - px - px + p² = x² - 2px + p²

now, we compare the theoretical equation to the actual equation :

x² - 6x + 8 = 0

x² - 2px + p² = q

x² = x² check

-6x = -2px

-6 = -2p

p = -6/-2 = 3

that gives us

x² - 6x + 9 = q

compare this to

x² - 6x + 8 = 0

we subtract the second equation from the first

x² - 6x + 9 = q

- x² - 6x + 8 = 0

------------------------

0 0 1 = q

there you have it.

The volume of the basketball is approximately 4.2x³.

a. The formula for the volume of a sphere is:

V = (4/3)πr³

where r is the radius of the sphere. In this case, the radius is given as x, so we have:

V = (4/3)πx³ ≈ 4.2x³

Therefore, the volume of the basketball is approximately 4.2x³.

b. The volume of a cube is given by:

V = s³

where s is the length of one of its sides. Since the basketball touches all of the sides of the case, the length of one of its sides is equal to the diameter of the basketball plus the length of a side of the basketball. This is equal to 2x + 2x = 4x. Therefore, we have:

V = (4x)³ = 64x³

Therefore, the volume of the box is 64x³.

c. The volume of air in the box is equal to the volume of the box minus the volume of the basketball. We can substitute the formulas we obtained in parts (a) and (b) to get:

V_air = V_box - V_basketball = 64x³ - 4.2x³ = 59.8x³

Therefore, the volume of air in the box is approximately 59.8x³.

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The height of the monitor using Pythagoras theorem is: 13.3 inches

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

We are given:

Diagonal = 27 inches

Length = 23.5 inches

Thus:

Height is:

h = √(27² - 23.5²)

h = 13.3 inches

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Answer: Of the two numbers you provided, +3 is greater than -7. So, +3 is the most upper of the two numbers.

Answer: +3

Step-by-step explanation: Positive 3 is greater than negative 7. Therefore, +3 is the greater value.

An airline passenger is planning a trip with three connecting flights from airports A, B, and C.

The least total amount of time the passenger must spend between flights, assuming all flights keep to their schedules, is 55 minutes.

This occurs when the passenger takes the first flight from airport A at 8:00 a.m., arriving at airport B at 10:30 a.m., catches the second flight from airport B at 10:40 a.m., arriving at airport C at 11:50 a.m., and then takes the third flight from airport C at 12:45 p.m.

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The most appropriate statistical procedure to answer this research question would be a two-sample t-test for means.

In this particular case, the research question is related to a Star Trek scenario, where two groups of people have different levels of experience with the franchise.

The most appropriate statistical procedure to answer this research question would be a two-sample t-test for means.

This is because the two-sample t-test for means is used when two independent samples are compared to determine if there is a significant difference between the means of the two samples.

This is useful in this scenario, as it will allow us to compare the levels of experience between the two groups and determine if there is a statistically significant difference between them.

The two-sample t-test for means is the most appropriate statistical procedure for this task, as it allows us to compare the means of two independent samples and determine if there is a statistically significant difference between them.

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Given statement "We conduct a test of hypothesis by assuming that ha is correct, since that is the hypothesis we are trying to show is true." is true. Because we start by assuming that the null hypothesis is correct, not the alternative hypothesis, when conducting a test of the hypothesis.

When conducting a test of hypothesis, we do not assume that Ha (the alternative hypothesis) is correct.

Instead, we begin by assuming that the null hypothesis (H0) is true.

The null hypothesis typically represents a statement of "no effect" or "no difference" between two groups or variables.

The alternative hypothesis (Ha) represents the statement we are trying to prove or gather evidence for but we must start with the assumption that the null hypothesis is correct.

State the null hypothesis (H0) and the alternative hypothesis (Ha).

The null hypothesis typically represents the status quo or a baseline assumption, while the alternative hypothesis represents the claim you want to prove or gather evidence for.

Determine the level of significance (α), which is the probability of rejecting the null hypothesis when it is actually true. Common significance levels are 0.05, 0.01, and 0.001.

Select an appropriate test statistic, which depends on the type of data and the hypothesis being tested. Examples include the t-test, chi-square test, and ANOVA.

Collect data and calculate the value of the test statistic based on the data.

Compare the calculated test statistic value to the critical value for the chosen level of significance.

If the test statistic is more extreme than the critical value, we reject the null hypothesis in favor of the alternative hypothesis.

Otherwise, we fail to reject the null hypothesis.

Hence, the statement is false.

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The number of batches of pancakes made by Hugo using 3 cups of milk is equal to 9 batches.

Number of cups of milk used by Hugo for each batch =  1/3 cup of milk ,

The total amount of milk used for b batches would be,

Total milk = (1/3) × b

The total milk used was 3 cups,

Substitute the value in the equation we have,

⇒ (1/3) × b = 3

Solve for b we get,

Multiply both sides of the equation by the reciprocal of 1/3,

Reciprocal of ( 1/3 ) = 3/1 or simply 3

⇒ (1/3) × b × 3 = 3 × 3

⇒ b = 9

Therefore, Hugo made 9 batches of pancakes.

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The above question is incomplete, the complete question is:

Hugo made a bunch of batches of pancakes for his summer camp. For each batch, Hugo used 1/3 cup of milk. Hugo used a total of 3 cups of milk. Let b represent the number of batches Hugo made . Find the value of b?

Answer:

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.

In this case, the diameter of the circle is given as 12.5 cm.

Substituting this value into the formula, we get:

C = π(12.5)

C = 39.25 cm

Therefore, the circumference of the circle is 39.25 cm.

Hence, the answer is 39.25 cm.

The cardholder will pay an additional $1,471.66 in interest by making monthly payments of $200 until the balance is paid off instead of paying off the current balance in full.

First, we need to calculate the total interest that will accrue on the current balance of $4,528.34. We can do this using the formula

Interest = Balance x (APR/12)

where APR is the annual percentage rate and is divided by 12 to get the monthly interest rate. Plugging in the values, we get:

credit card Interest = $4,528.34 x (22.99%/12) = $87.80

So the total interest that will accrue on the current balance is $87.80.

Next, we need to calculate how long it will take to pay off the balance by making monthly payments of $200. We can use a credit card repayment calculator to do this, but we'll use a simplified formula here

Months = -log(1 - (Balance x (APR/12))/Payment) / log(1 + (APR/12))

where Payment is the monthly payment amount. Plugging in the values, we get

Months = -log(1 - ($4,528.34 x (22.99%/12))/$200) / log(1 + (22.99%/12)) = 29.6 months

So it will take about 30 months (or 2.5 years) to pay off the balance by making monthly payments of $200.

Finally, we can calculate how much more the cardholder will pay in total by subtracting the current balance from the total amount paid over 30 months

Total amount paid = $200 x 30 = $6,000

Total interest paid = $6,000 - $4,528.34 = $1,471.66

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If Alice has $50 and spends 4/5 of her money, she spends $40.

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. Fractions are commonly represented using two numbers separated by a horizontal line, where the top number is called the numerator and the bottom number is called the denominator.

Alice spends 4/5 of her money, which is equivalent to 0.8 of her money.

To find out how much Alice spends, we can multiply her total money ($50) by 0.8

= $50 x 0.8

Multiply the numbers

= $40

Therefore, Alice spends $40.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Alice has $50 and spends 4/5 of her money. How much does Alice spend?

Sue works 5 out of 7 days a week, which implies that she has two days off. We need to discover how numerous conceivable plans there are for her to work on Tuesday or Friday or both.

There are two cases to consider:

1. Sue works on Tuesday as it were, Friday as it were, or both Tuesday and Friday.

2. Sue does not work on Tuesday or Friday.

For the primary case, there are three conceivable outcomes:

1. Sue works on Tuesday as it were and has Friday off.

2. Sue works on Friday as it were and has Tuesday off.

3. Sue works on both Tuesdays and Fridays.

For the moment case, there are two conceivable outcomes:

1. Sue works on one of the other 5 days of the week and has both Tuesday and Friday off.

2. Sue has Tuesday and Friday off.

In this manner, there are added up to 3 + 2 = 5 conceivable plans for Sue to work on Tuesday or Friday or both. 

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1.  The radius of V is approximately 14.04 meters.2.The circumference of V is approximately 88.24 meters. 3.mST arc is  26.85 degrees. 4.the length of ST arc is approximately 6.61 meters. 5.34.69 meters. 6.88.24m.

In geometry, a sector is a part of a circle enclosed by two radii and an arc. Essentially, a sector is a slice of a circle. The two radii that form the sector are equal in length and share a common endpoint, which is the center of the circle. The arc of the sector is a portion of the circumference of the circle and its length is proportional to the measure of the central angle that it subtends.

We can use the given information to solve for the following:

1. Radius of V:

The area of a circle is given by the formula A = πr². We are given the area of V as 624.36 square meters, so we can solve for the radius r as:

A = πr²

624.36 = πr²

r² = 624.36/π

r ≈ 14.04 meters

Therefore, the radius of V is approximately 14.04 meters.

2. Circumference of V:

The circumference of a circle is given by the formula C = 2πr. Using the radius we just found, we can solve for the circumference of V as:

C = 2πr

C = 2π(14.04)

C ≈ 88.24 meters

Therefore, the circumference of V is approximately 88.24 meters.

3. mST arc:

The area of the sector SVT is given as 64.17 square meters. The area of a sector is given by the formula A = (θ/360)πr², where θ is the central angle of the sector in degrees. We are not given the value of θ, but we can solve for it as:

A = (θ/360)πr²

64.17 = (θ/360)π(14.04)²

θ ≈ 26.85 degrees

Therefore, the central angle of the sector SVT is approximately 26.85 degrees, and mST arc is also 26.85 degrees.

4. Length of ST arc:

The length of an arc of a circle is given by the formula L = (θ/360)C, where θ is the central angle of the arc in degrees, and C is the circumference of the circle. We can use the values we have already calculated to solve for the length of ST arc as:

L = (θ/360)C

L = (26.85/360)(88.24)

L ≈ 6.61 meters

Therefore, the length of ST arc is approximately 6.61 meters.

5. Perimeter of shaded region (sector):

The perimeter of a sector is the sum of the length of the arc and the lengths of the two radii that form the sector. Using the values we have already calculated, we can solve for the perimeter of the shaded sector as:

Perimeter = L + 2r

Perimeter = 6.61 + 2(14.04)

Perimeter ≈ 34.69 meters

Therefore, the perimeter of the shaded region (sector) is approximately 34.69 meters.

6. Perimeter of unshaded region (remaining circle part):

The perimeter of a circle is given by the formula C = 2πr. Using the radius we previously calculated, we can solve for the perimeter of the unshaded region as:

Perimeter = 2πr

Perimeter = 2π(14.04)

Perimeter ≈ 88.24 meters

Therefore, the perimeter of the unshaded region (remaining circle part) is approximately 88.24 meters.

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Answer:

  $9.50

Step-by-step explanation:

You want Suzie's hourly rate on Saturday if she babysat for 3.5 hours on Friday, earning 8.50 per hour, and for 4.5 hours on Saturday, earning a total of 72.50 from both jobs.

For (hours, rates) of (h1, r1) and (h2, r2), Suzie's total earnings for the two jobs are ...

  earnings = h1·r1 +h2·r2

Filling in the known values, we can find r2:

  72.50 = 3.5·8.50 +4.5·r2

  72.50 = 29.75 +4.5·r2 . . . . . . . simplify

  42.75 = 4.5·r2 . . . . . . . . . . . subtract 29.75

  9.50 = r2 . . . . . . . . . . . . divide by 4.5

Suzie earned $9.50 per hour on Saturday.

__

Additional comment

The steps of the "multistep" problem are ...

Effectively, these are the steps to solving the equation we wrote.

The total amount of interest she will have to pay for this month considering her APR is 18.75% is $362.5. therefore the correct option is Option D

In order to calculate the credit card interest we have to divide the annual percentage rate by 12.

the formula for evaluating the interest on the given credit card is

Interest = ( balance x APR)/12

here,

balance = outstanding balance

APR = annual percentage rate

Given,

Sasha had a balance of $3200 from which a purchase of $300 was made the remaining balance is to be paid later.

then, Sasha's

outstanding balance = $2900

APR = 18.75%

therefore, Sasha's monthly interest is

18.75/12 => 1.5625%

now, calculating the interest on the given credit card

Interest = (2900 x 1.5625) /12

Interest = $362.5

The total amount of interest she will have to pay for this month considering her APR is 18.75% is $362.5

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The complete question is

In the month of January, Sasha had a balance of $3200 on her credit card. She made a payment of $300 and left the remaining balance to be paid later. How much interest will she pay this month if her APR is 18.75%? Round to the nearest cent.

a) $35. 10

b) $543. 75

c) $46. 19

d) $362.5

Answer:

4x²( x¹0 - 16)

Therefore, the expression 4x¹0-64x² can be rewritten as 4x²(x¹0 - 16) by factoring out the greatest common factor.

4x²(x^8 - 16)

Then, we can use the difference of squares formula to factor x^8 - 16, which gives:

4x²(x^4 + 4)(x^2 + 2)(x^2 - 2)

Therefore, the fully factored form of 4x¹0-64x² is 4x²(x^4 + 4)(x^2 + 2)(x^2 - 2).