Let the density function of a continuous random variable X be f(x) = 0 if x<0 . 2x/bc if 0≤x≤c
. 2(b-x)/b(b-c) if c≤x≤b
. 0 if x>b
​
a) Find the CDF of X
b) Find E[X]
c) Find Var(X)
d) What is the range of X?

The value of the x is 8.94.

What is the median?

The median is the middle number. Since there is no number “in the middle” you find the mean of the two numbers in the middle.

In a right triangle, the length of the median drawn from the vertex of the right angle equals half the length of the triangle’s hypotenuse.

here we have given a triangle let's say ABC in this A is a right angle which is divided by the median AD

So, AD = 1/2 * BC

= 1/2 * 8 = 4

Now, we need to find the value of the x, which hypotenuse of the new triangle that is the ADC

SO, AC² = AD² + DC²

x² = (4)² + (6)²

x = √(16+64)

= √(80)

x =8.94

Hence, the value of the x is 8.94.

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The amount of felt in the compound shape for the art project is: 313cm².

A compound shape is a 2D shape made up of two or more simpler shapes, often with different sizes and orientations, combined together. When computing the dimensions of a compound shape, the first thing to do is to fragment the shape into regular shapes.

Having fragmented the above given shape (art project) there are:

The required amount of felt for the art project will the sum of the areas of these shapes. The dimensions are given:

We derived 6cm by removing 11cm, 5cm and 3cm from 25cm. That is:

25 - 11 - 5 - 3 = 6cm

We derived 8cm - the height of the right angled tringle by removing 9cm from 17cm. That is:

17cm - 9cm = 8cm.

Areas of the following shapes are given as follows:

1) Area of the rectangle with dimensions 17cm x 5cm:                                  Area = length x width = 17cm x 5cm = 85 square cm

2)  Area of the rectangle with dimensions 17cm x 9cm:

    Area = length x width = 17cm x 9cm = 153 square cm

3) Area of the rectangle with dimensions 17cm x 3cm:

Area = length x width = 17cm x 3cm = 51 square cm

4) Area of the right-angle triangle with base 6cm and height 8cm:

Area = 1/2 x base x height = 1/2 x 6cm x 8cm = 24 square cm

Sum of the areas of all four shapes:

85 + 153 + 51 + 24 = 313 square cm

So the amount of felt required in the shape for the art project is: 313cm².


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Full Question:

Although part of your question is missing, you might be referring to this full question: See the attached images.

The solution to the inequality 13x|20 is all real numbers, as any value of x, no matter how small or large, will make the statement true.

The way to address inequity Using only real values, 13x|20. This means that there is no single solution to this inequality. The inequality is essentially asking what values of x will make the statement true. In this case, any value of x, no matter how small or large, will make the statement true. This is because the absolute value of x is being taken, which means that the value of x is being evaluated regardless of the sign--whether it is positive or negative. For example, if x is -1, then 13x|20 would be 13(-1)|20, which simplifies to -13|20, or 20. This means that no matter what the value of x is, it will always make the statement true. Therefore, the solution to the inequality is all real numbers.

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The radius of the fifth sphere  or the value of r is 14.14

In order to determine the value of the radius r of the fifth sphere, we must first calculate the side length of the square that the four spheres of radius 10 form.

Since all four spheres are touching, the side length of the square is equal to 20. Thus, the area of the square is equal to 400. Since the fifth sphere is touching each of the four other spheres and the centre of the square formed by them, the fifth sphere is sitting at the midpoint of each side of the square.

Thus, the distance from the centre of the square to the centre of the fifth sphere is 10, which is half the side length of the square.  Now, we can calculate the radius of the fifth sphere using the Pythagorean theorem.

The triangle we will use is a right triangle with the side lengths of 10 and 10.

Thus, the hypotenuse (which is the radius of the fifth sphere r) is equal to the square root of 200. Therefore, the radius of the fifth sphere is approximately 14.14.

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Based on the given parameters, the calculated value of the probability that it will not rain is 2/3

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

P(Rain) = 1/3

The probability it will not rain is the complement of the probabilty it will rain

This means that

If the probability of rain tomorrow is 1/3, then the probability of not raining tomorrow is 1 - 1/3 = 2/3.

This can be expressed as

Probability = 0.67 or 67%

Hence, the probability that it will not rain tomorrow is 2/3 or approximately 0.67 (or 67%).

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a. Mean: 85.4; Standard deviation: 12.1

b. Five-number summary: 60, 78, 88, 95, 98

c. The test scores appear to form a normal distribution. The data points form a symmetric pattern about the mean of 85.4, indicating that the majority of the test scores are concentrated near the mean and gradually become less common as you move away from the mean.

d. The mean of 85.4 and standard deviation of 12.1 indicate that most of the test scores are clustered in the middle, with a few outliers on both the higher and lower end. This suggests that the test was neither too easy nor too difficult for the students, as it was not too difficult to achieve a higher score nor too easy to achieve a low score.

Standard deviation is a measure of how spread out data points are from the mean. It is calculated by taking the square root of the variance and can be used to measure the volatility of a data set. By looking at the standard deviation, one can determine the amount of variability in a given set of data.

The mean of the test scores is 85.4, which is calculated by adding the scores together and dividing by the total number of scores (13). The standard deviation of the scores is 12.1, which is calculated by taking the square root of the variance (217.8). The five-number summary of the test scores is 60, 78, 88, 95, and 98. This means that the minimum score is 60, the first quartile is 78, the median is 88, the third quartile is 95, and the maximum score is 98. This type of distribution is a right-skewed distribution, meaning that most of the scores are closer to the upper end of the range and there are fewer scores near the lower end. This is evident from the five-number summary, where the median is lower than the mean and the third quartile is close to the maximum score.

From this distribution, it is possible to infer that the test was likely a hard test for these students. This is because the mean score of 85.4 is much lower than the maximum score of 98, indicating that not many students were able to achieve the highest score. Additionally, the standard deviation of 12.1 is relatively large, indicating that there is a wide range of scores. This is further evidence that the test was difficult for the students.

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Answer:

28

Step-by-step explanation:

Because you're decreased the number, you'll subtract the percentage from 100%. Then , use ratio.

100% : 56

100% - 50% ( 50%) : ?

= 50/100 ×56

= 1/2 × 56

= 56/2

= 28

The vertex represents the minimum value of the function. The vertex, in this case, is (-4, 7), which is the point where the function reaches its minimum value of 7.

The vertex represents the minimum value of the function because the coefficient of the squared term is positive, which means that the parabola opens upwards, and the vertex is the lowest point on the curve.

To find the vertex of the parabola, we can use the formula x = -b/2a, where a is the coefficient of the squared term, b is the coefficient of the linear term, and c is the constant term. In this case, a = 1, b = 8, and c = 23, so x = -8/2 = -4.

Substituting x = -4 into the function g(x) gives us g(-4) = (0)^2 + 7 = 7. Therefore, the vertex of the parabola is (-4, 7), which is the point where the function reaches its minimum value of 7.

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The image of the given points under the rotation through +90° about the center origin include the following;

A' (-5, 4).

B' (-3, -2).

C' (5, -3).

D' (1, 4).

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of each figure, the coordinates of the vertices of the image are as follows:

(x, y)    →       (-y, x)

A (4, 5) = A' (-5, 4).

B (-2, 3) = B' (-3, -2).

C (-3, -5) = C' (-(-5), 3) = (5, -3)

D (4, -1)​ = D' (-(-1), 4) = (1, 4)

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Answer:

The interior angles of a triangle add up to 180 degrees, so Angle E = 70 degrees.

Therefore, the open box with the largest volume has a length  of [tex]20” - 2(4”) = 12”[/tex], and a height of 4”. The volume of the resulting box is 0 x 12 x 4 = 0 cubic inches.

The resulting box with the largest volume can be created by cutting out 4 squares with the same dimensions from each corner of the 8-inch by 20-inch cardboard. After cutting the squares, the sides can be bent up to form an open box. The dimensions of the box with the largest volume can be calculated using the formula for the volume of a rectangular prism, [tex]V = L x W x H.[/tex]

In this case, L = 8” - 2x, W = 20” - 2x, and H = x, where x is the length of each side of the square cut from each corner. The volume of the resulting box will be maximized when x is the greatest value that still produces a box with the given dimensions. Solving the equation, 8” - 2x = x, yields x = 4”.

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Answer:

they are not similiar

Step-by-step explanation:

..........

(a)   3/4

(b)   F(x) = ∫f(x)dx = ∫0^x f(t)dt, where x ≥ 0

(c)   1

(a) Using the definition, we can calculate P r(1 < x < 3) as follows:
P r(1 < x < 3) = ∫1^3f(x)dx = ∫1^2 (x/4)dx + ∫2^3 (4-x)/4dx
= [x^2/8]1^2 + [(4x - x^2/2]2^3
= 1/4 + 5/4 = 3/4

(b) The distribution function of X is F(x) = ∫f(x)dx = ∫0^x f(t)dt, where x ≥ 0.

(c) To find µ = E(X), σ2 , σ for X, we need to use the definition of expected value and variance, respectively:
µ = E(X) = ∫-∞^∞xf(x)dx = ∫0^2 x^2/8 dx + ∫2^4 (4x - x^2/2)dx
= [x^3/24]0^2 + [(4x^2 - x^3/3]2^4
= 0 + 7 = 7

σ2 = Var(X) = ∫-∞^∞(x - µ)^2f(x)dx
= ∫0^2(x - 7)^2(x/4)dx + ∫2^4 (x - 7)^2(4-x)/4dx
= [x^3/24 -14x^2/3 +98x/3]0^2 + [(4x^3 -14x^2 +98x]2^4
= 7 + 36 = 43

σ = √σ2 = √43 ≈ 6.55
a) We have to calculate P r(1 < x < 3) using the definition of the probability density function. f(x) = ( x/4 for 0 < x ≤ 2 (4−x)/4 for 2 < x < 4) ∫f(x)dx = ∫(x/4)dx for 0 < x ≤ 2 ∫f(x)dx = ∫((4−x)/4)dx for 2 < x < 4 = ∫(x/4)dx | from 1 to 2 + ∫((4−x)/4)dx | from 2 to 3= (x^2/8) | from 1 to 2 + [(4x-x^2)/8] | from 2 to 3 = (2-1)/8 + (12-8-2+4)/8= 1/8= 0.125 The probability of 1 < x < 3 is 0.125. b) The distribution function for X is: F(x)=0 for x ≤ 0∫f(x)dx for 0 < x ≤ 2= (x^2/8) + C1 for 0 < x ≤ 2∫f(x)dx for 2 < x < 4= (x/4-2) + C2 for 2 < x < 4= 1 for x ≥ 4c) We have to find µ = E(X), σ2, and σ for X using the definition of the probability density function. µ = E(X) = ∫xf(x)dx from 0 to 4 ∫f(x)dx for 0 < x ≤ 2= ∫((x^2)/16)dx for 0 < x ≤ 2 = (x^3/48) | from 0 to 2= 2/3 ∫f(x)dx for 2 < x < 4= ∫((4x−x^2)/16)dx for 2 < x < 4 = [(2x^2−(x^3)/12)/16] | from 2 to 4= (16−16−(16−8))/48= 1/3 ∴µ= (2/3) + (1/3)= 1 E(X) = 1 σ^2 = V(X) = E(X^2)- (E(X))^2=E(X^2)- µ^2 ∫x^2f(x)dx from 0 to 4 ∫f(x)dx for 0 < x ≤ 2= ∫((x^3)/16)dx for 0 < x ≤ 2 = (x^4/64) | from 0 to 2= 2 ∫x^2f(x)dx from 0 to 4 ∫f(x)dx for 2 < x < 4= ∫((4x^2-2x^3+x^4)/16)dx for 2 < x < 4 = [(2x^3-3x^4+(x^5)/5)/80] | from 2 to 4= (128−240+32−8−64/5+24/5)/80= 8/15 σ^2 = E(X^2)- (E(X))^2=2−1=1 σ = sqrt(σ^2)= 1

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The amount that Instant Meals spends on postage to mail out 188 samples is: 19458 cents

The parameters are given as:

W = 64 oz

Total quantity = 188 samples

Charge = 36 cents per 1.5 pounds

Thus converting pounds tp oz, we have;

Charge = 36 cents per 24 oz

Required:

Total amount to pay the parcels

Solution:

Multiply W to 188 samples,

Total weight = 69 oz. (188)

Total weight = 12,972 oz.

Use the charge as an conversion factor,

Total price to pay:

P = 12,972 oz. (36 cents / 24 oz.)

P = 19458 cents

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(a)  The probability of getting a face card or a number card is:P(face card or number card) = (12/52) + (40/52) = 52/52 = 1

(b)  The probability of drawing a black and a Queen is:P(black and a Queen) = (26/52) × (2/26) = 2/52 = 1/26

(c) The probability of drawing a black and a face card is:P(black and a face card) = (26/52) × (6/26) = 6/52 = 3/26.

(d) The probability of drawing a Queen and a 3 is 0.

(e)  The probability of drawing a black or a 3 is:P(black or 3) = (26/52) + (4/52) - (2/52) = 28/52 = 7/13.

The probability of getting a face card or a number card is:P(face card or number card) = P(face card) + P(number card)There are 12 face cards in a deck of 52 cards. There are 4 Kings, 4 Queens, and 4 Jacks.There are 52 - 12 = 40 cards which are not face cards. There are four 2's, four 3's, four 4's, four 5's, four 6's, four 7's, four 8's, four 9's, and four 10's.Therefore, the probability of getting a face card or a number card is:P(face card or number card) = (12/52) + (40/52) = 52/52 = 1

The probability of drawing a black and a Queen is:P(black and a Queen) = P(black) × P(Queen given black)The probability of drawing a black card is 26/52 since there are 26 black cards in a deck of 52 cards. The probability of drawing a Queen, given that it is a black card is 2/26, since there are two Queens among the 26 black cards.Therefore, the probability of drawing a black and a Queen is:P(black and a Queen) = (26/52) × (2/26) = 2/52 = 1/26

The probability of drawing a black and a face card is:P(black and a face card) = P(black) × P(face card given black)The probability of drawing a black card is 26/52 since there are 26 black cards in a deck of 52 cards. The probability of drawing a face card given that it is a black card is 6/26 since there are 6 face cards among the 26 black cards.Therefore, the probability of drawing a black and a face card is:P(black and a face card) = (26/52) × (6/26) = 6/52 = 3/26

The probability of drawing a Queen and a 3 is:P(Queen and 3) = 0Since there are no 3's among the Queens, the probability of drawing a Queen and a 3 is 0.

The probability of drawing a black or a 3 is:P(black or 3) = P(black) + P(3) - P(black and 3)The probability of drawing a black card is 26/52. The probability of drawing a 3 is 4/52. There are two 3's which are black cards.Therefore, the probability of drawing a black or a 3 is:P(black or 3) = (26/52) + (4/52) - (2/52) = 28/52 = 7/13.

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[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =140 \end{cases}\implies n140=180n-360 \\\\\\ 140n+360=180n\implies 360=40n\implies \cfrac{360}{40}=n\implies 9=n \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ their~sum }{(9)(140)}\implies \text{\LARGE 1260}[/tex]

Answer:

To find the area of the reduced triangle, we need to know the length of the base and the height of the triangle after the scaling.

Since the triangle has been reduced by a scale of 0.4, the length of each side has been multiplied by 0.4. Therefore, the base of the reduced triangle is:

10 cm × 0.4 = 4 cm

To find the height of the reduced triangle, we can use the fact that the ratio of corresponding sides in similar triangles is the same. Since the triangle has been scaled down by a factor of 0.4, the ratio of the corresponding sides is 0.4. Therefore, the height of the reduced triangle is:

30 cm × 0.4 = 12 cm

Now that we know the base and the height of the reduced triangle, we can calculate its area using the formula:

Area = (1/2) × base × height

Area = (1/2) × 4 cm × 12 cm

Area = 24 cm²

Therefore, the area of the reduced triangle is 24 cm².

Step-by-step explanation:

Answer: volume (cubic units) diameter of base (units) area of base (square units) height (units)

4 1.60 0.785 10

6 2.17 3.54 6

63π 10.03 79 1

Step-by-step explanation:

The standard matrix of the linear transformation T is [1/2 0 ; √3/2 0].

The transformation T: R2 => R2 rotates points clockwise through π/3 radians and then projects each point onto the x1 axis. Here, we are supposed to find the standard matrix of the linear transformation T.To find the standard matrix of the linear transformation T, we need to find out the standard matrix of each step involved in the transformation.

Then the standard matrix of the transformation T can be found out by taking the product of the standard matrices of each step. Let A be the standard matrix of the linear transformation that rotates points clockwise through π/3 radians, and B be the standard matrix of the linear transformation that projects each point onto the x1 axis.

The standard matrix of the linear transformation that rotates points clockwise through π/3 radians can be found out by using the formula that is given below.cosθ  −sinθsinθcosθHere, θ = π/3 cos (π/3) = 1/2, sin (π/3) = √3/2The standard matrix of the linear transformation that rotates points clockwise through π/3 radians is A.

A = (1/2)  −√3/2√3/2 1/2= [1/2  -√3/2 ; √3/2 1/2]The standard matrix of the linear transformation that projects each point onto the x1 axis is B.B = [1 0 ; 0 0]The standard matrix of the linear transformation T can be found out by taking the product of the standard matrices A and B.T = AB= [1/2  -√3/2 ; √3/2 1/2][1 0 ; 0 0]= [1/2 0 ; √3/2 0]

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The area of the container can be calculated by multiplying its width, height, and length together ,the area of the container is 1,920 square feet.

The area of a container can be calculated by multiplying its width, height, and length. In order to find the area of the container in this problem, the width of 8 feet, the height of 12 feet, and the length of 24 feet must be multiplied together. Mathematically, this can be expressed as A = 8 × 12 × 24. Solving the equation yields a result of 1,920 square feet.

To calculate the area of the container in square feet, begin by multiplying the width, height, and length together. 8 × 12 × 24 = 1,920. This result can be written as 1,920 square feet. Therefore, the area of the container is 1,920 square feet.

Using basic algebra, the area of the container can be found by multiplying its width, height, and length. 8 × 12 × 24 = 1,920 square feet. This can be written as A = 8 × 12 × 24, where A represents the area of the container in square feet. Solving the equation yields a result of 1,920 square feet. This result can be interpreted to mean that the area of the container is 1,920 square feet.

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The total cost for watching 4 movies in a month would be:

4 x $10 = $40.

Analysis is, broadly speaking, the process of approximating certain mathematical objects—like integers or functions—by other, simpler objects. For example, if you want to write pi as the limit of a series of numbers that you already know how to calculate, you should do so. This will allow you to discover the first few decimals of pi. Or here's a case that works the other way around: Although the sequence of factorials n! has a pleasing aesthetic quality, calculations frequently require an estimate of n! that more clearly illustrates its growth order; this approximation is provided by the classical Stirling formula.

We need to analyze the overall cost of each choice to decide if Ms. Espiritu should purchase a monthly pass or pay each time she visits the theatre.

Assume that each movie ticket is $10 and that a monthly pass is $30. It would be less expensive for Ms. Espiritu to get a monthly pass if she intends to watch more than three films in a month. This is why:

If she purchases each movie ticket individually, the total price for four movie viewings in a month would be:

4 x $10 = $40

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Choosing a sampling method that changes each time you take a sample is not the meaning of sampling variation.

The correct meaning of sampling variation is the fact that different samples taken from the same population will mostly produce different sample statistics due to random sampling error.

This means that there is a difference in the estimations gotten from different samples, even if the samples are drawn from the same population using the same sampling method.

The other options given are also not correct definitions of sampling variation. selecting a large sample size can help to reduce the amount of sampling variation by increasing the estimates obtained from the sample.

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a)  The p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that μ1 < μ2.

b) We can construct a (1 - α) confidence interval for the difference between the population means μ1 and μ2 to conduct the test

c) The power of the test is approximately 0.012 when μ1 is three units less than μ2.

The test statistic for this hypothesis test is:

t = (x1 - x2) / √(s1²/n1 + s2²/n2)

Plugging in the given values, we get:

t = (6.2 - 7.8) / √(4/15 + 6.25/15) = -2.72

Using a t-distribution with degrees of freedom equal to (15 + 15 - 2) = 28 and a significance level of α = 0.05, we find the critical value to be -1.701. Since the test statistic is less than the critical value, we reject the null hypothesis.

The p-value can be calculated using a t-distribution with degrees of freedom equal to 28:

p-value = P(T < -2.72) = 0.0068

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that μ1 < μ2.

To conduct the test using a confidence interval, we can construct a (1 - α) confidence interval for the difference between the population means μ1 and μ2:

(x1 - x2) ± t(1-α/2, n1+n2-2) * √(s1²/n1 + s2²/n2)

Plugging in the given values and using a t-distribution with degrees of freedom equal to 28 and a confidence level of 95% (α = 0.05), we get:

(6.2 - 7.8) ± 2.048 * √(4/15 + 6.25/15)

-2.168 < μ1 - μ2 < -0.232

Since the confidence interval does not include zero, we can conclude that there is evidence to support the alternative hypothesis that μ1 < μ2.

The power of a hypothesis test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. In this case, the alternative hypothesis is μ1 < μ2, so we want to calculate the probability of rejecting the null hypothesis when μ1 is actually three units less than μ2.

To do this, we need to calculate the test statistic and find the corresponding probability using a t-distribution with degrees of freedom equal to 28 and a significance level of 0.05.

The test statistic for this case is:

t = (x1 - x2 - Δ) / √(s1²/n1 + s2²/n2) = (6.2 - 7.8 - 3) / √(4/15 + 6.25/15) = -4.14

Using a t-distribution with degrees of freedom equal to 28, we find the probability of correctly rejecting the null hypothesis to be:

power = P(T < -t_crit) = P(T < -1.701 - (-4.14)) = P(T > 2.439) ≈ 0.012

Therefore, the power of the test is approximately 0.012 when μ1 is three units less than μ2. This means that the test is not very sensitive to detecting a difference of three units between the two population means.

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After 15 years, $412.5 will joy have earned in interest than Rico as he had an interest rate of 4%.

The simple interest is the rate at which you borrow or give money. When a user receives funds from a lender, the lender receives additional funds in return. The principal refers to the borrowed funds that are granted for a particular time period. Interest is the additional sum that must be returned to the provider for the use of the borrowed funds.

The principal quantity is multiplied by the number of periods and interest rate to determine simple interest. You do not have to pay interest on interest, and simple interest does not increase. In the case of simple interest, the contribution is applied to the current month's interest and the remaining sum is deducted from the principal.

We know that Rico put $5,500 in an account with 3.5 interest rate, which gives us a total amount of $8,387.5 and Interest Earned $2,887.5

We also know that Joy put $5,500 in a bank account with a 4% simple interest rate, which gives us a total amount of $8,800 and Interest Earned $3300.

To find the amount of money joy have earned in interest than Rico:

3300 - 2887.5 = 412.5

Therefore, we can say that after 15 years, $412.5 will joy have earned in interest than Rico as he had an interest rate of 4%.

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Answer:

the volume is 5 to the next power which is 3 u end up with multiplication which mean u multiply 5 with 3 to get ur units

We can say that after answering the offered question Therefore, the Pythagorean theorem model dimension of the bicycle wheel diameter is 120 inches.

The Pythagorean Theorem is the foundational Euclidean geometry connection that exists between the three sides of the right triangle. According to this rule, the area of either a cube with the length x side is equal to the total of the regions of triangles shared by its other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the perfect angle is the combined squares that spanned its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.

multiplying it by 12 and then multiplying by 5 to get the model dimension in inches:

[tex]$2\text{ ft} \times 12\text{ in/ft} \times 5 = 120\text{ in}$[/tex]

Therefore, the model dimension of the bicycle wheel diameter is 120 inches.

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