what values of x and y are required for the triangles below to be congruent?

Answer:

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Let's denote the cost of one rose bush as r and the cost of one pot of ivy as i.

We can write two equations based on the information provided:

Solve the system by elimination, double the first equation and subtract the second one:

Pot of ivy costs $8.

Find r by substituting 8 for i:

Rose bush costs $12.

So we get the option B provided as a choice.

Option B is correct, the cost of rose bush is $12 and cost of pot of ivy is $8.

Given that Elisa spent $124 on 7 rose bushes and 5 pots of ivy.

7R+5I=124...(1)

Kathryn spent $176 on 14 rose bushes and 1 pot of ivy.

14R+I=176

I=176-14R...(2)

We have to find the cost of rose and pot of ivy

Substitute equation (2) in (1)

7R+5(176-14R)=124

7R+5(176)-5(14R)=124

7R+880-70R=124

880-63R=124

880-124=63R

756=63R

R=$12

Now let us find the cost of I

I=176-14R

I=176-14(12)

I=176-168

I=$8

Hence, option B is correct, the cost of rose bush is $12 and cost of pot of ivy is $8.

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In a boxplot, potential outliers are data points that are more than 1.5 Interquartile Ranges (IQRs) from the edges of the box. A boxplot visually represents the distribution of a dataset, with the box containing the middle 50% of the data and the edges representing the lower and upper quartiles.

To answer your question, potential outliers in a boxplot are points that are more than 1.5 times the interquartile range (IQR) away from the edges of the box. The IQR is the difference between the third quartile (75th percentile) and the first quartile (25th percentile) of the data. The box in a boxplot represents the IQR, with the median (50th percentile) marked by a line inside the box. The whiskers of the boxplot extend to the minimum and maximum values that fall within 1.5 times the IQR from the edges of the box. Any points outside this range are considered potential outliers and are plotted as individual points beyond the whiskers. However, it is important to note that potential outliers do not necessarily indicate errors or incorrect data, and further investigation may be needed to determine their validity. Overall, boxplots are a useful tool for visualizing the spread and distribution of numerical data.

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This limaçon is symmetrical along the y-axis. The horizontal intercepts are (4,0) and (-4,0). The vertical intercepts are (0,-2) and (0,6).

To determine the type of shape, we look at the value of the constant versus the value of the term with the sign.

As 4>2, this is a dimpled limacon.

We have y-intercepts where θ = [tex]\pi/2[/tex] and [tex]3\pi /2[/tex]

Then, our polar equation is r = 4 + 2 sinθ.

r = 4 + 2 sin θ= 6 if θ = [tex]\pi /2[/tex] and

r = 4 + 2 sin θ = 2 if θ = [tex]3\pi /2[/tex]

Therefore, y-intercepts or vertical intercepts are (0,-2) and (0,6)

We have x-intercepts where θ = 0 and [tex]\pi[/tex]

Then

r = 4 + 2sin θ = 4 for θ = 0 and

r = 4 + 2 sin θ = 4

Therefore, x-intercepts or horizontal intercepts are (4,0) and (-4,0)

This is symmetric about the y-axis.

As we already know that sin θ = sin ( [tex]\pi[/tex] - θ) and

cos θ = cos ([tex]\pi[/tex] - θ)

Therefore, we replace θ with [tex]\pi[/tex] - θ, and thus we prove symmetry about the y-axis.

r = 4 + 2sin([tex]\pi[/tex] - θ)= 4 + 2 sin θ

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-5° F represents the change in the temperature of the park city.

Given that the temperature of a park city has been decreased or dropped by 5° F,

We need to represent this as an integer,

So, here dropped means decrease in temperature, that mean whatever was the temperature it is decreased by 5° F.

That mean the change is in negative.

Hence -5° F represents the change in the temperature of the park city.

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the depth perception cue based on the observation that parallel lines converge in the distance is that the depth perception cue based on the observation that parallel lines converge in the distance is known as linear perspective. This is a monocular cue, meaning it can be perceived with just one eye.

When looking at a scene, our brain uses the visual information provided by our eyes to determine depth and distance. Linear perspective is a cue that relies on the way that objects appear to shrink in size and converge towards a vanishing point as they move further away from the viewer. This is why parallel lines, such as the sides of a road or railway tracks, appear to meet at a point in the distance.

Linear perspective is a powerful visual cue that allows us to accurately perceive depth and distance in a scene. It is commonly used in art and architecture to create a sense of depth and realism, and is a crucial component of our visual perception.

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The probability that a randomly sampled household has more than $16,000 in credit card debt is approximately 0.4726 or 47.26%.

The question asks us to find the probability that a randomly sampled household has more than $16,000 in credit card debt, given that the distribution of household debt is somewhat right skewed with a mean of $15,355 and a standard deviation of $10,000.

To solve this problem, we can use the standard normal distribution, which allows us to calculate probabilities for any normal distribution by standardizing the variable of interest (in this case, credit card debt) to a standard normal distribution with a mean of 0 and a standard deviation of 1.

To standardize the value of $16,000, we use the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, σ is the standard deviation, and z is the corresponding z-score. Substituting the given values, we get:

z = (16000 - 15355) / 10000 = 0.0655

This means that $16,000 is 0.0655 standard deviations above the mean. To find the probability that a randomly sampled household has more than $16,000 in credit card debt, we need to find the area to the right of this z-score under the standard normal curve. We can use a standard normal table or calculator to find this probability, which is approximately 0.4726.

It's important to note that this probability is based on the assumptions made about the distribution of household debt, and may not accurately reflect the true probability in practice. Additionally, credit card debt is influenced by a variety of factors beyond just household income and spending habits, so it's important to consider the limitations of this analysis when interpreting the results.

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A box of 30 pieces of chocolate candies contains approximately 424.11 cubic units of chocolate.

The volume of a sphere can be calculated using the formula:

V = (4/3) * π * r^3

where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.

Since the diameter of each candy is 3, the radius is half of that, or 1.5. We can plug this value into the formula to find the volume of one piece of candy:

V = (4/3) * π * r^3

V = (4/3) * 3.14 * 1.5^3

V ≈ 14.137

So one piece of candy has a volume of approximately 14.137 cubic units. To find the total amount of chocolate in a box of 30 candies, we can simply multiply the volume of one candy by the number of candies in the box:

Total volume = 14.137 * 30

Total volume = 424.11

Therefore, a box of 30 pieces of chocolate candies contains approximately 424.11 cubic units of chocolate.

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The correct options for the parts of the circle are:

A circle is a spherical plane figure whose edge is made up of points spaced equally apart from a fixed point.

The fixed point from which every point on the circle's edge is equally distant is the center of the circle.

The parts of a circle include the following:

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The notations and the terms that correctly defines them is matched below:

1.)GCB = Major arc. Option I.

2.)CE = Chord. Option B.

3.)AB= Radius. Option C.

4.)CB= Minor arc. Option A.

5.)BAD= central angle. Option F.

6.)A = Center. Option J.

7.)DGC = Minor arc. Option A.

8.)CD = Diameter. Option G.

The circle has the following parts with their various properties described below;

Major arc: This is part of the circle that has an angle which measures more that 180°.

Minor arc: This is part of the circle that has an angle which measures less than 180°.

Diameter: This is defined as the distance across a circle which must pass through its central point.

Radius: This is defined as half the diameter of a circle.

Chord:. This is defined as the line that joins two point on the circumference of a circle.

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The standard deviation of the sampling distribution of sample means is 2.5.

The standard deviation of the sampling distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:

σM = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size, and σM is the standard deviation of the sampling distribution of sample means.

Substituting the given values, we get:

σM = 20 / sqrt(64) = 20 / 8 = 2.5

Therefore, the standard deviation of the sampling distribution of sample means is 2.5.

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Based on the pattern of increasing numbers in the table, a reasonable value for the missing cell would be option c, 9.

Looking at the table, we can see that each number is increasing by approximately the same amount from left to right and from top to bottom. Specifically, each row and each column increases by a consistent value of 1.2. For example, the first row increases from 4.4 to 5.6 to 6.8, and the second row increases from 5.6 to 6.8 to 8.0.

Using this pattern, we can estimate the value of the missing cell by looking at the corresponding row and column. The missing cell is in the third row, so we can estimate it by adding 1.2 to the previous cell in the row, which is 7.2. This gives us an estimate of 8.4.

However, none of the answer choices include 8.4, so we need to consider which of the given options is closest to this estimate. Option c, 9, is the closest option, and it is also the option that makes the most sense given the pattern of increasing numbers in the table. Therefore, a reasonable value for the missing cell is option c, 9.

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what is a reasonable value for the missing cell, if each number is increasing?

a. 8 b. 8.8 c. 9 d. 9.1

The given series converges to 4/3.

The given series is:

4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ...

We can rewrite this series as:

4(1/5 - 1/7 + 1/9 - 1/11 + 1/13 - ...)

Now, we can use the alternating series test, which states that an alternating series converges if the absolute values of its terms decrease monotonically to zero.

In this case, the absolute values of the terms are:

|4/5|, |4/7|, |4/9|, |4/11|, |4/13|, ...

These terms do decrease monotonically to zero, so we can apply the alternating series test. Therefore, the series converges.

To find the sum of the series, we can use the formula for the sum of an alternating series:

S = a - a1 + a2 - a3 + ...

where S is the sum of the series, a is the first term, and ai is the ith term.

In this case, a = 4/5 and the common difference d = -2/5, since we are subtracting 2/5 from each term to get the next one. So, we have:

S = 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ...

S = a/(1 + d) = (4/5)/(1 - 2/5) = 4/3

Therefore, the given series converges to 4/3.

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The  distance John would have to walk to get from point A to point B without going through the pond is 60.84 meters.

Since, John walks 36 m south and 49 m east which covered the distance equal to the hypotenuse of a right triangle

Using the Pythagorean theorem

c² = a² + b²

c² = 36² + 49²

c² = 1296 + 2401

c² = 3697

c = √3697

c = 60.84 m

Thus, the distance is 60.84 meters.

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To solve the expression -25 x (84/21) + (-3) x (-6), follow these steps:

Step 1: Perform the division inside the parentheses.
(84/21) = 4

Step 2: Replace the terms and rewrite the expression.
-25 x (4) + (-3) x (-6)

Step 3: Perform the multiplications.
-25 x 4 = -100
-3 x -6 = 18

Step 4: Rewrite the expression and perform the addition.
-100 + 18

Step 5: Calculate the final result.
-100 + 18 = -82

Your answer is -82.

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We cannot find the correlation coefficient between x and y for this bivariate distribution.

To find the correlation coefficient between x and y, we need to first calculate the expected value of x, denoted E(x), the expected value of y, denoted E(y), and the expected value of xy, denoted E(xy).

Using the given distribution, we can calculate:

E(x) = ∑x * p(x,y) = ∑x * 0.5(x y) = 0.5(1+2+3+...) = ∞ (diverges)

E(y) = ∑y * p(x,y) = ∑y * 0.5(x y) = 0.5(1+2+3+...) = ∞ (diverges)

E(xy) = ∑x*y * p(x,y) = ∑x*y * 0.5(x y) = 0.5(1*1 + 2*1 + 2*2 + 3*1 + 3*2 + 3*3 + ...) = ∞ (diverges)

Since the expected values of both x and y diverge, we cannot use the formula for the correlation coefficient that involves standard deviations. Instead, we can use the formula:

[tex]\rho = [E(xy) - E(x)E(y)] / [(E(x^2) - E(x)^2) * (E(y^2) - E(y)^2)]^{(1/2)}[/tex]

Since E(x²) and E(y²) also diverge, we cannot use this formula either.

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a. The standard error of the mean can be determined using the formula:

Standard error of the mean = population standard deviation / square root of sample size

Plugging in the given values, we get:

Standard error of the mean = 25 / square root of 250
Standard error of the mean = 25 / 15.8114
Standard error of the mean = 1.579 (rounded to 3 decimal places)


The standard error of the mean measures the amount of variability or error that is expected in the sample mean when compared to the true population mean. It is calculated by dividing the population

by the square root of the sample size. In this case, the standard error of the mean is 1.579, indicating that the sample mean of 20 is expected to be off by around 1.579 units from the true population mean.

c. To determine the 95% confidence interval for the population mean, we can use the formula:

Confidence interval = sample mean +/- (critical value) x (standard error of the mean)

The critical value can be obtained from a t-distribution table with n-1 degrees of freedom, where n is the sample size. For a 95% confidence interval and 249 degrees of freedom, the critical value is 1.96.

Plugging in the given values, we get:

Confidence interval = 20 +/- (1.96) x (1.579)
Confidence interval = 20 +/- 3.095
Confidence interval = (16.905, 23.095) (rounded to 3 decimal places)


The confidence interval is a range of values that is expected to contain the true population mean with a certain degree of confidence. In this case, we are 95% confident that the true population mean falls within the range of 16.905 to 23.095. This means that if we were to repeat this sampling process many times, 95% of the resulting confidence intervals would contain the true population mean.

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To determine whether the linear transformation T is one-to-one, onto, or neither, we need to analyze the rank and nullity of the transformation.

The rank of T is the dimension of the image space, which is the span of the columns of the transformation matrix. To find the matrix, we can write T(X, Y, Z, W) = (V, W, X, Z) as a matrix equation:

|V|   |0 0 1 0||X|
|W| = |0 1 0 0||Y|
|X|   |1 0 0 0||Z|
|Z|   |0 0 0 1||W|

From this matrix, we can see that the columns are linearly independent, so the rank of T is 4.

The nullity of T is the dimension of the kernel, which is the set of all solutions to the equation T(X, Y, Z, W) = (0, 0, 0, 0). We can set up the augmented matrix for this equation:

|0 0 1 0 0|
|0 1 0 0 0|
|1 0 0 0 0|
|0 0 0 1 0|

Row-reducing this matrix gives:

|1 0 0 0 0|
|0 1 0 0 0|
|0 0 1 0 0|
|0 0 0 1 0|

The only solution is the trivial one, so the nullity of T is 0.

Since the rank of T is equal to the dimension of the domain and the codomain, T is onto. And since the nullity of T is 0, T is also one-to-one. Therefore, the correct answer is "one-to-one and onto".
Hi! To determine whether the linear transformation T: R4 → R4, T(X, Y, Z, W) = (V, W, X, Z) is one-to-one, onto, or neither, let's analyze the properties of this transformation.

1. One-to-one: A linear transformation is one-to-one if different input vectors produce different output vectors.

In this case, T(X, Y, Z, W) = (V, W, X, Z). Observe that every input vector (X, Y, Z, W) uniquely determines the output vector (V, W, X, Z). Thus, this transformation is one-to-one.

2. Onto: A linear transformation is onto if every output vector can be produced by some input vector.

For this transformation, T(X, Y, Z, W) = (V, W, X, Z), every output vector (V, W, X, Z) can be produced by the input vector (X, Y, Z, W). So, the transformation is onto as well.

In conclusion, the linear transformation T: R4 → R4, T(X, Y, Z, W) = (V, W, X, Z) is both one-to-one and onto.

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The volume of the solid generated when the region r is revolved about the x-axis is 4π (5^(1/4) - 3^(1/4) + 1/5^(1/4) - 1/3^(1/4)).

To find the volume of the solid generated when the region r is revolved about the x-axis, we can use the method of cylindrical shells.

First, we need to determine the limits of integration. The region r is bounded by the curves y=e^(x/2) , y=e^(-x/2), x=ln3, and x=ln5. Since we are revolving the region about the x-axis, we need to integrate with respect to x. The lower limit of integration is ln3 and the upper limit is ln5.

Next, we need to find the radius of each cylindrical shell. The radius is the distance from the x-axis to the curve. For this region, the radius is e^(x/2) - e^(-x/2).

Finally, we need to find the height of each cylindrical shell. The height is the differential dx.

Thus, the integral that gives the volume of the solid is:

V = ∫[ln3, ln5] 2π (e^(x/2) - e^(-x/2)) dx

Simplifying the integrand:

V = 2π ∫[ln3, ln5] (e^(x/2) - e^(-x/2)) dx

Evaluating the integral:

V = 2π (2e^(x/2) + 2e^(-x/2)) |[ln3, ln5]

V = 4π (e^(ln5/2) - e^(ln3/2) + e^(-ln5/2) - e^(-ln3/2))

V = 4π (5^(1/4) - 3^(1/4) + 1/5^(1/4) - 1/3^(1/4))

Therefore, the volume of the solid generated when the region r is revolved about the x-axis is 4π (5^(1/4) - 3^(1/4) + 1/5^(1/4) - 1/3^(1/4)).

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The inequality is solved to give the value of x as x≤ 4

Inequalities are defined as those expressions with unequal comparison of numbers, expressions, variables or even terms.

It is important to note the different signs of inequalities. They are;

From the information given, we have that;

9-7.25x ≤-20

Now, collect the like terms, we have;

-7. 25 ≤ - 20- 9

subtract the values given, we get;

-7.25x ≤ -29

Divide both sides by the coefficient of x, we get;

x ≤ - 29/7.25

Divide the values, we get;

x ≤ 4

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All three options are relevant questions to consider when effectively using statistics in a speech.


1. "Are my numbers from reliable sources?" - It is crucial to use reliable and accurate data sources to ensure that your speech presents trustworthy information.
2. "Do I use statistics to quantify ideas?" - Using statistics can help support your arguments and make your points more concrete, making your speech more persuasive and engaging.
3. "Do I relate the statistics to the audience?" - Relating statistics to the audience helps make the data more relevant and understandable, allowing listeners to better grasp the importance of the information.

To effectively use statistics in a speech, you should ensure that you use reliable sources, use statistics to quantify your ideas, and relate the statistics to your audience.

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Answer:

Set your calculator to degree mode.

tan B = 5/2

B = tan^-1 (5/2) = 68.20°

Riemann sum with right endpoints and n = 8 is -93

We can divide [0,4] into 8 subintervals with right endpoints

The widths of those smaller intervals is 0.5

We get the following right subinterval endpoints: 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0

Remember, this is a right Riemann sum.

Now we evaluate the function x²- 5x at those right endpoints and we get the heights of our 8 little rectangles of -2.25, -4.00, -5.25, -6.00, -6.25, -6.0,-5.25, -4.00

f(x) = x²- 5x when x = 0.5

f(x) = (0.5)² - 5(0.5)

f(x) = -2.25

f(x) = x²- 5x when x = 1.0

f(x) = (1)² - 5(1)

f(x) = -4

f(x) = x²- 5x when x = 1.5

f(x) = (1.5)² - 5(1.5)

f(x) = -5.25

f(x) = x²- 5x when x = 2

f(x) = (2)² - 5(2)

f(x) = - 6

f(x) = x²- 5x when x = 2.5

f(x) = (2.5)² - 5(2.5)

f(x) = -6.25

f(x) = x²- 5x when x = 3

f(x) = (3)² - 5(3)

f(x) = -6

f(x) = x²- 5x when x = 3.5

f(x) = (3.5)² - 5(3.5)

f(x) = -5.25

f(x) = x²- 5x when x = 4

f(x) = (4)² - 5(4)

f(x) = -4

To find the area we multiply the width of each rectangle times its height and we get the areas of our 8 rectangles:

Area = L × B when L = 0.5 B = -2.25

Area = - 1.125

Area = L × B when L = 1 B = - 4

Area = - 4

Area = L × B when L = 1.5 B = - 5.25

Area = -7.875

Area = L × B when L = 2.0 B = -6

Area = -12

Area = L × B when L = 2.5 B = -6.25

Area = -15.625

Area = L × B when L = 3.0 B = -6

Area = -18

Area = L × B when L = 3.5 B = -5.25

Area = - 18.375

Area = L × B when L = 4 B = -4

Area = - 16

By adding all the values we get our desired Reimann sum of -93

This is an approximation to the integral of the same function with the same limits which is the limit of Riemann sum if we let delta_x go to 0 and the number of rectangles therefore approach infinity.

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Answer:31.4

Step-by-step explanation: tan=oppisite/adjacent, so just plug it in.
tan e=square root 22/square root 59
tan^-1=(square root 22/square root 59) < Use arc tan to find the missing angle.

M<E= 31.4

The second plan would be more cost-effective for Chris if he drives less than 300 miles over the weekend.

Chris will rent a car for the weekend and can choose between two plans. The first plan has an initial fee of $60 and costs an additional $0.60 per mile driven, while the second plan has no initial fee but costs $0.80 per mile driven.

Let's say Chris plans to drive a total of m miles over the weekend.

Under the first plan, the total cost, C1, would be:

C1 = 60 + 0.60m

Under the second plan, the total cost, C2, would be:

C2 = 0.80m

To determine which plan is more cost-effective for Chris, we can set the two expressions for cost equal to each other and solve for m:

60 + 0.60m = 0.80m

60 = 0.20m

m = 300

So, if Chris drives more than 300 miles over the weekend, the second plan would be more cost-effective, and if he drives less than 300 miles, the first plan would be more cost-effective.

For example, if Chris plans to drive 250 miles over the weekend, the total cost under the first plan would be:

C1 = 60 + 0.60(250) = $210

And under the second plan, the total cost would be:

C2 = 0.80(250) = $200

Therefore, the second plan would be more cost-effective for Chris if he drives less than 300 miles over the weekend.

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The number of students enrolled at a college is 16,500 and grows by 4% each year. To determine the growth rate of the number of students over a certain period, the formula for compound interest can be used. This information can be useful for college administrators in terms of planning and budgeting.

The compound interest formula can be used to calculate the growth rate of the number of students at the college. The formula is A = P(1 + r/n)^nt,

where A is the final amount,

P is the initial principal,

r is the interest rate,

n is the number of times the interest is compounded per year, and

t is the number of years.

In this case, P is 16,500, r is 4%, n is 1 (since the interest is compounded annually), and t is the number of years. For example, if we want to find the number of students after 5 years, the formula would be A = 16,500(1 + 0.04/1)^(1*5) = 20,221.

This means that the number of students will have grown by 3,721 over a period of 5 years.

This information can be useful for college administrators in terms of planning and budgeting. They can use this data to project the number of students that will be enrolled in future years and make decisions about staffing, resources, and facilities accordingly.

For example, if they know that the number of students will be increasing, they may need to hire more faculty and staff, or build new classrooms and dormitories. On the other hand, if the number of students is projected to decrease, they may need to make cuts in certain areas to balance the budget. Overall, understanding the growth rate of the number of students at a college is an important factor in effective planning and decision-making.

The number of students enrolled at a college is 16,500 and grows 4% each year. Based on this information we can determine the following

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The correct answer is C) rectangular prism trash can by $0.50.

To determine which trash can design will cost the company less to manufacture, weneed to calculate the cost of material for each design.

For the rectangular prism-shaped trash can:

The base dimensions are 1.5 ft and 2.0 ft, which gives a base area of 1.5 ft * 2.0 ft = 3.0 sq ft.

The total volume is given as 7.85 cubic ft.

To find the height of the rectangular prism, we divide the total volume by the base area:

Height = Total volume / Base area = 7.85 cubic ft / 3.0 sq ft = 2.617 ft

The cost of material for the rectangular prism-shaped trash can is the product of the base area and the cost per square foot:

Cost = Base area * Cost per square foot = 3.0 sq ft * $3.60/sq ft = $10.80

For the cylindrical trash can:

The base area is given as 3.14 sq ft.

To find the height of the cylindrical trash can, we divide the total volume by the base area:

Height = Total volume / Base area = 7.85 cubic ft / 3.14 sq ft ≈ 2.5 ft

The cost of material for the cylindrical trash can is the product of the base area and the cost per square foot:

Cost = Base area * Cost per square foot = 3.14 sq ft * $3.60/sq ft = $11.30

Comparing the costs, we can see that the rectangular prism-shaped trash can costs $10.80, and the cylindrical trash can costs $11.30. Therefore, the rectangular prism-shaped trash can design will cost the company less to manufacture.

The cost difference is:

$11.30 - $10.80 = $0.50

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Hi!
You make $15 per day.
60 divided by 4 (The number of days you work per month since you work once weekly.) is 15.

Hope this helps!

The investment with the greater amount of interest is Investment X which earns $50.40 more.

Hence the correct option for first position is (A) and for second position is option (C).

For Investment X:

Given that the principle amount of investment (P) = $ 6000

Time period (t) = 2 years

Rate of Interest (r) = 4.5% (simple interest rate)

So the interest gained over 2 years = (6000*2*4.5)/100 = $540.

For Investment Y:

Given that the principle amount of investment (P) = $ 6000

Time period (t) = 2 years

Rate of Interest (r) = 4% (compound interest rate)

so the amount after 2 years is given by

= 6000(1 + 4/100)²

= 6000*(1.04)²

= $6489.6

so the interest gained over 2 years = 6489.6 - 6000 = $489.6

So the difference between the interests = 540 - 489.6 = $50.40

Hence the Investment X gives greater interest.

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Answer:

22

Step-by-step explanation:

As we know the basic rule to solve an expression is BODMAS, the full form is Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

So first, we will solve the first bracket, and as we know if we multiply a negative integer with another negative integer then the result is a positive value ( - * - =  + ), and the expression becomes

-4(-8)+(-10) = 32+(-10)

Now we solve another bracket, and as we know positive multiplied by negative results in a negative sign ( + * - = - ), and the expression becomes

32+(-10) = 32 - 10

And now we subtract 10 from 32, so our final answer is

32 - 10 = 22

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The total discount value percentage the customer is getting is A = 32.5 %

Given data ,

Let the cost of the toaster be x

Now , the customer is getting a discount of 25 % by salesperson

So , the price of the toaster = 0.75x

Now , the customer is getting another 10 % off on new price of toaster

So , price of toaster = 0.75x - 0.075x

The final price of toaster = 0.675x

And , the percentage discount the customer is getting is A

A = x - 0.675x

A = 32.5 %

Hence , the discount percentage is 32.5 %

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