Find the area of a triangle with a base length of 4 units and a height of 5 units.

The 90% confidence interval for the proportion of 8th graders involved in after school activities is c) (0.780, 0.900).

To find the confidence interval, we need to use the formula:

CI = p ± zα/2 * √(p(1-p)/n)

where:

p is the sample proportion (84% or 0.84 in decimal form)

zα/2 is the z-score for the desired confidence level (90% or 1.645 for a two-tailed test)

n is the sample size (100)

Substituting the values, we get:

CI = 0.84 ± 1.645 * √(0.84(1-0.84)/100)

CI = 0.84 ± 0.078

CI = (0.762, 0.918)

Rounding to three decimal places, we get the final answer of (0.780, 0.900) as the confidence interval for the proportion of 8th graders involved in after school activities. Therefore, the correct answer is (c).

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Answer: 5y^2 +3y+12

Step-by-step explanation:

6y^2+3y+1

y^2-11

equals

5y^2+3y+12

The length of the remaining piece of wooden beam after the cut out in terms of polynomial y is 5y² + 3y + 12

Length of the wooden beam = 6y² + 3y + 1

Length cut out from the wooden beam= y² - 11

Length of the remaining piece of beam = Length of the wooden beam - Length cut out from the wooden beam

= (6y² + 3y + 1) - (y² - 11)

= 6y² + 3y + 1 - y² + 11

= 5y² + 3y + 12

Hence, 5y² + 3y + 12 is the remaining length of the wooden beam.

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(1) The probability of getting a soft chicken is 16.67%.

(2) The probability of getting a crunch beef is 16.67%.

(3) The probability of getting a fish  (crunchy or soft) is 33.33%.

The probability of getting a soft chicken is calculated as follows;

total outcome = 6

number of soft chicken = 1

Probability = 1/6 = 16.67%

The probability of getting a crunch beef is calculated as follows;

total outcome = 6

number of crunch beef = 1

Probability = 1/6 = 16.67%

The probability of getting a fish  (crunchy or soft) is calculated as follows;

total outcome = 6

number of soft fish = 1

number of crunch fish  = 1

P(soft or crunch) = 1/6 + 1/6 = 2/6 = 1/3 = 33.33%

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The minimum and maximum heights that the ladder can safely lie against the wall is 6.7 and 6.99 meters.

The minimum and maximum height that the ladder can safely lie against the wall is

sin theta = perpendicular/hypotenuse

Now keeping the each value of theta with hypotenuse to find the perpendicular height.

sin 70 = perpendicular/7.1

Keep the value

Perpendicular = 0.94 × 7.1

Multiply the digits

Perpendicular = 6.7 meters

sin 80 = perpendicular/7.1

Perpendicular = 0.99 × 7.1

Perform multiplication

Perpendicular = 6.99 meters

Thus, minimum and maximum heights are 6.7 and 6.99 meters.

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P1 is 51.9 bpm and P99 is 103.1 bpm.

The probability that a school's average female pulse rate is between 70 and 85 bpm is approximately 1.

a) The distribution of the average pulse rates is expected to follow a normal distribution.

b) To find the percentiles P1 and P99, we can use the z-score formula:

z = (x - μ) / σ

where x is the pulse rate, μ is the population mean (77.5 bpm), and σ is the population standard deviation (11.6 bpm).

For P1, we want to find the pulse rate such that only 1% of the population has a lower pulse rate. Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 1st percentile is -2.33. Thus,

-2.33 = (x - 77.5) / 11.6

Solving for x, we get:

x = 51.9 bpm

For P99, we want to find the pulse rate such that only 1% of the population has a higher pulse rate. Using the same method as above, we find that the z-score corresponding to the 99th percentile is 2.33. Thus,

2.33 = (x - 77.5) / 11.6

Solving for x, we get:

x = 103.1 bpm

Therefore, P1 is 51.9 bpm and P99 is 103.1 bpm.

c) The mean of a sample of n = 36 female high school seniors is estimated to be the same as the population mean of 77.5 bpm. The standard deviation of the sample is estimated to be:

s = σ / sqrt(n) = 11.6 / sqrt(36) = 1.933 bpm

d) To find the probability that a school's average female pulse rate is between 70 and 85 bpm when the sample size is n = 25, we first need to calculate the standard error of the mean:

SE = s / sqrt(n) = 1.933 / sqrt(25) = 0.387 bpm

Next, we find the z-scores for 70 and 85 bpm:

z1 = (70 - 77.5) / 0.387 = -19.34

z2 = (85 - 77.5) / 0.387 = 19.34

Using a standard normal distribution table or calculator, we find that the area to the left of z1 is essentially 0 and the area to the left of z2 is essentially 1. Therefore, the probability that a school's average female pulse rate is between 70 and 85 bpm is approximately 1.

Shading the area of interest on a normal probability curve would show the entire curve as it represents the entire population of high school female seniors, but the area of interest would be shaded in the middle of the curve.

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To find the critical value for a 99% confidence level, you will need to use the z-table, which lists the z-scores for different confidence levels. Here's a step-by-step explanation:

1. Identify the confidence level: In this case, it's 99%.

2. Calculate the area under the curve: Since the confidence level is 99%, the area under the curve would be 0.99 or 99%. The remaining 1% is split between the two tails of the distribution.

3. Determine the area in one tail: Divide the remaining area by 2 (1% ÷ 2 = 0.005 or 0.5%). This is the area in one tail of the distribution.

4. Use the z-table to find the critical value: Look for the closest value to 0.995 (0.990 + 0.005) in the z-table. This value corresponds to a z-score of 2.576.

5. Round the critical value: Since the question asks for the critical value rounded to two decimal places, the answer would be 2.58. So, the critical value for a 99% confidence level is 2.58.

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Answer:

Math is a broad field that encompasses several branches, each with its own units of measurement. Some examples of units in math include:

In geometry:- Units of length, such as meters, centimeters, and inches

Units of area, such as square meters, square centimeters, and square feet

Units of volume, such as cubic meters, cubic centimeters, and cubic feet- Units of weight or mass, such as kilograms, grams, and pounds - Units of time, such as seconds, minutes, and hours

Units of temperature, such as Celsius and

Fahrenheit

Units of angle measurement, such as degrees and radians

Units of speed or velocity, such as meters per second or miles per hour

Units of frequency, such as Hertz or cycles per second

Units of energy or work, such as joules, calories, and foot-pounds

Units of power, such as watts and horsepower

These are just a few examples of the many units used in math. The type of unit used depends on the specific problem or application.

HOPE IT HELPS

PLEASE MARK ❣️‼️ ME AS BRAINLIEST .

a. i. The circumference of circle A is 128.81 m

ii. The circumference of circle B is 144.53 m

b. The relatonship between the radius and circumference is the same for all circles

The circumference of a circle is the perimeter of the circle.

a.

i. Circumference of circle A

Since circle A has a radius of 21 meters, the circumference is given by C = 2πr where r = radius

So, substituting the values of the variables into the equation, we have that

C = 2πr

= 2π × 21 m

= 41π m

= 41 × 3.142

= 128.81 m

ii Circumference of circle B

Since circle A has a radius of 28 meters, the circumference is given by C = 2πr where r = radius

So, substituting the values of the variables into the equation, we have that

C = 2πr

= 2π × 28 m

= 46π m

= 46 × 3.142

= 144.53 m

b.

The relatonship between the radius and circumference is the same for all circles since the circumference of a circle is always proportional to its radius.

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Answer:

The answer to your problem is, D. If the data is categorical

Step-by-step explanation:

What a pictograph is:

Remember that a pictographs are less useful for comparing change over time or for presenting large sets of numerical data, as they can become cluttered and difficult to read.

Here is a little example, if you want to show how the population of a city has changed over the years, a line graph or a bar graph would be a better choice than a pictograph

Thus the answer to your problem is, D. If the data is categorical

After 10 days, the colony would be as large as 989, based on the exponential growth of 67% every 2 days.

An exponential growth refers to a constant rate or percentage of growth in the number or value of some variables.

Exponential growth can be modeled using the exponential growth function and used to determine the future quantity or amount of the variables.

Initial number of the bacteria microorganisms = 55

Growth rate = 67% every 2 days

Daily growth rate = 33.5% (67% ÷ 2)

The number of days involved, t = 10 days

The ending number of the bacteria microorganisms = Future Amount = 55(1 + 33.5%)^t

= 55(1.335)^10

= 989

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Answer:

55 0.67 ^5

Step-by-step explanation:

The future amount = ? micro organisms

Answer:

Step-by-step explanation:

Key March Highlights: Travel spending totaled $93 billion in February—5% above 2019 levels and 9% above 2022 levels. Leisure travel demand does not appear to be abating with America’s excitement to travel at record highs and more than half (55%  Data Question 2 The following table shows the number of visitors to a park from January to April: Month January

The solution of the given inequality is x less than 3/23.

The given inequality is 8>23x+5.

Subtract 5 on both the sides of an inequality, we get

8-5>23x+5-5

3>23x

Divide 23 on both the sides of an inequality, we get

3/23>x

x<3/23

Therefore, the solution of the given inequality is x less than 3/23.

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a) Yes, it is reasonable to use t-distribution to perform a test about average gas price. (b) There is evidence that average gas price on August 8, 2012 was higher than national average at 5% significance level. (c) 95% confidence interval lies between $3.813 and $4.137.

a) Yes, it is reasonable to use the t-distribution to perform a test about the average gas price since the sample size n = 10 is small and the population standard deviation is unknown.

b) To test for the evidence, we can perform a one-sample t-test.

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (3.975 - 3.63) / (0.2266 / sqrt(10))

t = 2.728

Using a t-table the critical t-value is 1.833 which is less than calculated t-value (2.728) ), therefore, we reject the null hypothesis and conclude that there is evidence that the average gas price was significantly higher than the national average at the 5% significance level.

c) The standard error can be calculated as:

standard error = sample standard deviation / sqrt(sample size)

standard error = 0.2266 / sqrt(10)

standard error = 0.0717

Using a t-table, the t-value is 2.262. Therefore, the 95% confidence interval is:

(sample mean) ± (t-value * standard error)

3.975 ± (2.262 * 0.0717)

3.975 ± 0.162

(3.813, 4.137)

So we can be 95% confident that the true mean gas price in Illinois on August 8, 2012 lies between $3.813 and $4.137.

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To find a root-finding method with a third order of convergence, consider using the "Halley's method." Halley's method is an iterative numerical technique used for finding roots of a function. It has a third-order convergence, meaning the number of correct digits approximately triples with each iteration, resulting in a faster convergence rate compared to methods with lower orders of convergence.

Here's a step-by-step explanation of Halley's method:

1. Choose an initial guess x_0 for the root of the function f(x).

2. Calculate the first and second derivatives of the function f(x), denoted as f'(x) and f''(x), respectively.

3. Update the guess using the formula:
  x_(n+1) = x_n - (2 * f(x_n) * f'(x_n)) / (2 * (f'(x_n))^2 - f(x_n) * f''(x_n))

4. Check for convergence by comparing the difference between consecutive guesses (x_(n+1) - x_n) to a predefined tolerance level.

5. If the convergence criterion is not met, repeat steps 3 and 4 until convergence is achieved or a maximum number of iterations is reached.

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The given statement "Quantitative Easing was used extensively in the aftermath of the(the late 1990s/2000s) dot com crisis is false because Quantitative Easing was not used extensively in the aftermath of the dot com crisis in the late 1990s/2000s.

Quantitative easing (QE) was not used extensively in the aftermath of the dot-com crisis in the late 1990s and early 2000s. In fact, QE as a monetary policy tool gained prominence after the global financial crisis of 2008. The dot-com crisis primarily affected the technology sector, causing a stock market downturn, but it did not lead to a widespread financial crisis that would have necessitated the use of QE.

Therefore, the given statement is false.

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The actual distance between two cities is 70 miles when 1 inch is equal to 20 miles

Given that Daniel is planning to drive from City X to City Y.

The distance between two cities is [tex]3\frac{1}{2}[/tex] inches

Given that 1 inch = 20 miles

We have to find the actual distance between two cities in miles

[tex]3\frac{1}{2}[/tex]  = 3.5

Now multiply 3.5 with 20 to find distance in miles

3.5×20

70 miles

Hence, the actual distance between two cities is 70 miles when 1 inch is equal to 20 miles

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The probability that a customer will have to wait more than 2 minutes is 0.0099.

(a) Since the waiting time at the supermarket is assumed to be exponentially distributed, the probability density function is given by:

f(x) = (1/B)e^(-(x/B)) for x ≥ 0

= 0 elsewhere

where B is the mean waiting time. In this case, the mean waiting time is 19 seconds. Therefore, the probability density function of waiting time at the supermarket is:

f(x) = (1/19)e^(-(x/19)) for x ≥ 0

= 0 elsewhere

(b) To find the probability that a customer will have to wait between 15 and 30 seconds, we need to find the area under the probability density function between x=15 and x=30. This can be calculated using the cumulative distribution function (CDF) of the exponential distribution:

P(15 ≤ x ≤ 30) = ∫15^30 f(x)dx = ∫15^30 (1/19)e^(-(x/19)) dx

Using integration by substitution, let u = -(x/19), then du/dx = -1/19 and dx = -19 du:

P(15 ≤ x ≤ 30) = ∫-(15/19)^-(30/19) e^udu = e^(-(15/19)) - e^(-(30/19))

P(15 ≤ x ≤ 30) ≈ 0.2462 (rounded to four decimal places).

Therefore, the probability that a customer will have to wait between 15 and 30 seconds is 0.2462.

(c) To find the probability that a customer will have to wait more than 2 minutes, we need to find the area under the probability density function for x > 120 seconds (2 minutes). This can be calculated using the CDF of the exponential distribution:

P(x > 120) = ∫120^∞ f(x)dx = ∫120^∞ (1/19)e^(-(x/19)) dx

Using integration by substitution, let u = -(x/19), then du/dx = -1/19 and dx = -19 du:

P(x > 120) = ∫-(120/19)^-∞ e^udu = e^(-(120/19))

P(x > 120) ≈ 0.0099 (rounded to four decimal places).

Therefore, the probability that a customer will have to wait more than 2 minutes is 0.0099.

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Answer:

2nd and 4th

Step-by-step explanation:

In the second quadrant, the x-coordinate is negative and the y-coordinate is positive. If we let the x-coordinate be -a, then the y-coordinate will be a. Therefore, the point will have the form (-a, a), and the y-coordinate will be the opposite of the x-coordinate.

In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative. If we let the x-coordinate be a, then the y-coordinate will be -a. Therefore, the point will have the form (a, -a), and again, the y-coordinate will be the opposite of the x-coordinate.

Answer:

Step-by-step explanation:

Given right angle XOV and 30° angle XOW, you want to know the measure of angle WOV. You also want to find the measure of angle YOZ, which is opposite angle VOW, where XOY is a right angle, and WOZ is a straight angle.

The angle addition theorem tells you that ...

  ∠XOW +∠WOV = ∠XOV

Angle XOV is given as a right angle, and angle XOW is shown as 30°, so we have ...

  30° +∠WOV = 90°

  ∠WOV = 60° . . . . . . . . . subtract 30° from both sides

Angle WOV is 60° using the angle addition theorem.

Rays OY and OV are opposite rays, as are rays OZ and OW. This means angles YOZ and VOW are vertical angles, hence congruent.

  ∠YOZ = ∠WOV = 60°

Angle YOZ is 60° using the congruence of vertical angles.

As in part 2, angle WOZ is a straight angle, so measures 180°. The angle addition theorem tells you this is the sum of its parts:

  ∠ZOY +∠YOX +∠XOW = ∠ZOW

  ∠ZOY +90° +30° = 180°

  ∠ZOY = 60° . . . . . . . . . . . . . subtract 120° from both sides

Angle YOZ is 60° using the measure of a straight angle.

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Answer:

x = 5

Step-by-step explanation:

o find the equation of the line that is perpendicular to line G, we need to find the slope of line G first. The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

Using the points (-8, 3) and (7, 3) on line G, we get:

slope of line G = (3 - 3) / (7 - (-8)) = 0

Since the line we want to find is perpendicular to line G, its slope will be the negative reciprocal of the slope of line G. That is:

slope of perpendicular line = -1 / slope of line G = undefined

An undefined slope means that the line is vertical. Therefore, the equation of the line that is perpendicular to line G and passes through the point (5, -3) is simply:

x = 5

Answer:

To find the distance between two points, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the two points are (3, 4) and (6, 8), so we have:

d = sqrt((6 - 3)^2 + (8 - 4)^2)

d = sqrt(3^2 + 4^2)

d = sqrt(9 + 16)

d = sqrt(25)

d = 5

Therefore, the distance between the points (3, 4) and (6, 8) is 5 units.

It's worth noting that the values 5√22 and √7 do not match the above

If S is the substance of M4(R) consisting of all lower triangular matrices, then dim S = 10.
To find the dimension of S, we need to count the number of linearly independent matrices in S. A lower triangular matrix in M4(R) has the form:

[ a 0 0 0 ]
[ b c 0 0 ]
[ d e f 0 ]
[ g h i j ]
where a, b, c, d, e, f, g, h, i, and j are real numbers.

Since S consists of all lower triangular matrices, we can choose the entries of the matrices in S freely, subject to the constraint that the upper diagonal entries must be 0. Therefore, we have 10 free parameters (a, b, c, d, e, f, g, h, i, and j) that we can choose independently, and the remaining entries are determined by the fact that the matrix is lower triangular. Therefore, the dimension of S is 10.

(b) If S is the subspace of M5(R) consisting of all matrices with trace 0, then dim S = 20.

To find the dimension of S, we need to count the number of linearly independent matrices in S. A matrix in M5(R) with trace 0 has the form:

[ a b c d e ]
[ f g h i j ]
[ k l m n o ]
[ p q r s t ]
[ u v w x y ]

where a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, and y are real numbers and a + g + m + s + y = 0. Since there is one constraint on the entries of the matrix, we have 24 free parameters that we can choose independently. However, there is also a linear dependence between the entries of the matrix, since the trace is 0. Specifically, we have the constraint a + g + m + s + y = 0. Therefore, we have 23 free parameters, and the remaining entries are determined by the trace constraint. Therefore, the dimension of S is 23 - 1 = 22.

(a) If S is the substance of M4(R) consisting of all lower triangular matrices, then dim S = 10.

Explanation:

In the set of all 4x4 lower triangular matrices, the elements on and below the main diagonal can have non-zero values, while the elements above the main diagonal must be zero. There are a total of 4+3+2+1=10 elements in the lower triangular part. Since these 10 elements can be any real numbers, the dimension of S (the substance of M4(R) consisting of all lower triangular matrices) is 10.

(b) If S is the subspace of M5(R) consisting of all matrices with trace 0, then dim S = 24.

Explanation:

In a 5x5 matrix, there are a total of 5x5=25 elements. The trace of a matrix is the sum of its diagonal elements. If a 5x5 matrix has a trace of 0, then the sum of its diagonal elements must be 0. This means that we have freedom to choose any real values for 24 elements (the other 20 off-diagonal elements and 4 of the diagonal elements), and the last diagonal element is determined by the other 4 diagonal elements to ensure the trace is 0. Therefore, the dimension of S (the subspace of M5(R) consisting of all matrices with trace 0) is 24.

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The equivalent expression for -4/7-8/9+4/7+9/8 is given by option C. -8/9 + 9/8 and option D. - (4/7+ 8/9 ) + 4/7 + 9/8.

The expression is equals to,

-4/7-8/9+4/7+9/8

Verify  all attached options using property of addition.

-4/7- (8/9+4/7 )+9/8

Open the parenthesis as plus minus is minus we get,

- 4/7 - 8/9 - 4 /7 + 9/8

It is not equivalent to -4/7-8/9+4/7+9/8.

Incorrect option.

- ( 4/7-8/9+4/7 ) + 9/8

Open the parenthesis as (+)( - )is minus  and ( - ) ( - ) is plus we get,

- 4/7  + 8/9 - 4 /7 + 9/8

It is not equivalent to -4/7-8/9+4/7+9/8.

Incorrect option.

-8/9 + 9/8

= 0 -8/9 + 9/8

= -4/7 + 4/7  -8/9 + 9/8

Rearrange terms we get,

-4/7-8/9+4/7+9/8

It is equivalent to -4/7-8/9+4/7+9/8

Correct option.

- (4/7+ 8/9 ) + 4/7 + 9/8

Open the parenthesis as plus minus is minus we get,

-4/7 -8/9 + 4/7 + 9/8

It is equivalent to -4/7-8/9+4/7+9/8

Correct option.

0

Incorrect option.

Therefore, for the given expression equivalent terms are option C. -8/9 + 9/8 and option D. - (4/7+ 8/9 ) + 4/7 + 9/8.

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The above question is incomplete, the complete question is:

-4/7-8/9+4/7+9/8

Which of the following expressions are equivalent to

Attached options.

Suppose that foreign citizens decide to purchase more U.S. pharmaceuticals and U.S. citizens decide to buy stock in foreign corporations. Other things being the same, these actions would lead to an increase in demand for U.S. pharmaceuticals and a decrease in demand for U.S. stocks, leading to changes in the relative prices of these assets.

An increase in demand for U.S. pharmaceuticals would lead to higher prices for these products, assuming that the supply of pharmaceuticals remains constant. This increase in demand could benefit U.S. pharmaceutical companies, as they would be able to charge higher prices for their products, resulting in increased revenues and profits. However, higher prices could also result in reduced affordability and access to these products for U.S. consumers.

On the other hand, a decrease in demand for U.S. stocks could lead to lower prices for these securities, assuming that the supply of foreign stocks remains constant. This decrease in demand could negatively impact U.S. investors who hold these stocks, as the value of their holdings would decline. However, it could also lead to increased investment in foreign corporations, potentially benefiting these companies and the economies in which they operate.

Overall, the actions of foreign and U.S. citizens can significantly affect the prices of different assets and the performance of various industries and economies. Understanding these relationships and dynamics is important for investors and policymakers in making informed decisions about investment and trade.

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Answer:

The volume of a cone is given by the formula:

V = (1/3)πr^2h

where r is the radius of the base, h is the height, and π is the constant pi (approximately 3.14).

Plugging in r = 6 and h = 15, we get:

V = (1/3)π(6^2)(15) = 540π cubic feet

Rounding to the nearest hundredth, we get:

V ≈ 1696.63 cubic feet

Therefore, the volume of the cone is approximately 1696.63 cubic feet.

To check, we can use the formula for the volume of a cone to calculate the volume using different methods. For example, we can use the fact that the cone is one-third the volume of a cylinder with the same base and height. The cylinder has radius 6 feet and height 15 feet, so its volume is:

V_cylinder = π(6^2)(15) = 540π cubic feet

Dividing by 3, we get:

V_cone = (1/3)V_cylinder = (1/3)(540π) = 180π cubic feet

Rounding this to the nearest hundredth, we get:

V_cone ≈ 565.49 cubic feet

This is reasonably close to our previous answer of 1696.63 cubic feet, so we can be confident that our calculation is correct.

Step-by-step explanation:

The series after solving the following term f(x) = [tex]e^{-2x}[/tex] is given as:

[tex]e^{-2x}[/tex] = 1 - 2x + 2x² - 4/3x³ + 2/3x⁴ - 4/15x⁵+....|x| < ∞.

The fundamental concepts in mathematics are series and sequence. A series is the total of all components, but a sequence is an ordered group of items in which repeats of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.

By using the formulae to solve issues, one may gain a deeper understanding of the principles. The main distinction between them and sets is that in a sequence, certain terms might appear again in different locations. A series can be finite or infinite in length and has length equal to the number of terms.

Given f(x) = [tex]e^{-2x}[/tex], center x = 0

f(x) = [tex]e^{-2x}[/tex] = [tex]1 - 2x + \frac{(2x)^2}{2!} +\frac{(2x)^3}{3!} +\frac{(2x)^4}{4!} +\frac{(2x)^5}{5!} +.....|x|[/tex]

[tex]e^{-2x}[/tex] = 1 - 2x + 4([tex]\frac{x^2}{2}[/tex]) - 8([tex]\frac{x^3}{6}[/tex]) + 16([tex]\frac{x^4}{24}[/tex]) - 35([tex]\frac{x^5}{100}[/tex])+.....|x| < ∞

[tex]e^{-2x}[/tex] = 1 - 2x + 2x² - 4/3x³ + 2/3x⁴ - 4/15x⁵+....|x| < ∞

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We have shown that A is a subset of B and that B is not a subset of A, we can conclude that A and B are not equal, i.e., A ≠ B.

a. To prove that A is a subset of B, we need to show that every element in A is also in B. Let n be an arbitrary element in A. Then, we have to show that n is also in B, i.e., n = 10r + 2 for some integer r. Since n is in A, we know that n = 5q + 2 for some integer q. We can rewrite this as:

n = 10q + 2q + 2

= 10q + 2(q + 1)

= 10r + 2

where r = q + 1. Since r is an integer, we have shown that n is in B. Therefore, A is a subset of B.

b. To disprove that B is a subset of A, we need to find at least one element in B that is not in A. Let m = 5s + 3 for some integer s be an arbitrary element in B. We need to show that m is not in A, i.e., m ≠ 10r + 2 for any integer r. Suppose for the sake of contradiction that m = 10r + 2 for some integer r. Then we have:

5s + 3 = 10r + 2

5s = 10r - 1

s = 2r - 1/5

Since s and r are both integers, this is a contradiction. Therefore, there is no integer r that satisfies the equation above, and m is not in A. Thus, we have shown that B is not a subset of A.

c. Since we have shown that A is a subset of B and that B is not a subset of A, we can conclude that A and B are not equal, i.e., A ≠ B.

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Answer: 87

Step-by-step explanation:

To find the volume of Tammy's storage shed, which is in the shape of a rectangular prism, we need to use the formula: Volume = Length × Width × Height.

Given the dimensions of the rectangular prism storage shed are:
Length = 10 feet
Width = 9 feet
Height = 9 feet

We can calculate the volume as follows:

Step 1: Multiply the length, width, and height.
Volume = 10 × 9 × 9

Step 2: Perform the multiplication.
Volume = 810 cubic feet

So, Tammy's storage shed has a volume of 810 cubic feet.

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