If a = 4 and b = 3, find the
measure of angle B.

diameter=15m

Answer:

Solution given:

diameter [d]=?

Volume of hemisphere=2/3*πr³

896m³=2/3*πr³

r³=896*3/2π

r=\(\sqrt[3]{427.8}=7.5\)

diameter=2r=2*7.5=15m

Radius (r) = ?

Diameter (d) = ?

Volume of hemisphere = 2/3 × πr³

→ 896m³ = 2/3 × πr³

→ r³ = 896 × 3/2π

→ r = ³√427.8

→ r = 7.5

Now,

Diameter (d) = 2r

→ 2 × 7.5

→ 15m is the required answer.

Answer:

\(1)by \: splitting \: middle \: term \\ 2)factorisation \\ .......\)

Both T-statistics and F-statistics are formed using ratios that involve the difference between two means or sums of squares and their respective variances or mean squares. The top part of the equation for both T-statistics and F-statistics represents the difference between the sample means or the sum of squares due to the factor or regression, while the bottom part of the equation contains the standard error or mean square error, which represents the variability or error in the data. The T-statistic is used to test the significance of the difference between two means, while the F-statistic is used to test the overall significance of a linear model or the equality of variances between two or more groups. Therefore, both ratios provide information about the relative magnitude of the difference between groups or the explanatory power of the model, compared to the variability or error in the data.
T-statistics and F-statistics are both formed using ratios, with each ratio serving to compare different sources of variation in the data.

Similarities in form and meaning:
1. Both are used for hypothesis testing.
2. Both ratios have a numerator (top part) and a denominator (bottom part).
3. The resulting values for both are compared to a critical value, which is determined based on a chosen significance level.

For T-statistics, the ratio is formed as follows:
T = (Sample mean - Population mean) / (Sample standard deviation / sqrt(Sample size))

For F-statistics, the ratio is formed as follows:
F = (Between-group variance) / (Within-group variance)

In both cases, the numerator represents the effect or difference of interest, while the denominator represents an estimate of variability or error. In the T-statistic, the top part contains the difference between the sample mean and the population mean, while the bottom part contains the standard error of the mean. In the F-statistic, the top part contains the between-group variance, which represents the variability between different groups, while the bottom part contains the within-group variance, representing the variability within each group.

In summary, T-statistics and F-statistics both use ratios to compare sources of variation in data, with the top part of the equation representing the effect or difference of interest, and the bottom part representing an estimate of variability or error.

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The probability that a student will get 4 or more correct answers just by guessing is d: 11/3^5.

The probability of getting 4 or more correct answers just by guessing in a multiple-choice examination with 5 questions and three alternative answers for each question can be calculated by using the binomial probability formula. The formula is P(X = x) = nCx * p^x * (1-p)^(n-x), where n is the number of questions, x is the number of correct answers, p is the probability of getting a correct answer, and nCx is the binomial coefficient.

For 4 correct answers, the probability is:

P(X = 4) = 5C4 * (1/3)^4 * (2/3)^1 = 5 * (1/81) * (2/3) = 10/243

For 5 correct answers, the probability is:

P(X = 5) = 5C5 * (1/3)^5 * (2/3)^0 = 1 * (1/243) * 1 = 1/243

The total probability of getting 4 or more correct answers is the sum of these two probabilities:

P(X >= 4) = P(X = 4) + P(X = 5) = 10/243 + 1/243 = 11/243

Therefore, the correct answer is d. 11/3^5.

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Answer:

yes

Step-by-step explanation:

The loads carried by an elevator are found to follow a normal distribution with a mean weight of 1812 lbs, and a standard deviation of 105.3 lbs. The answer is c) [1606, 2018].

To answer this question, we need to use the concept of confidence intervals. A 95% confidence interval means that in 95% of all cases, the true population parameter (in this case, the weight of the elevator load) will fall within the interval.

To find the interval centered about the mean, we need to calculate the margin of error first. The formula for margin of error is:

Margin of Error = z*(standard deviation/square root of sample size)

Since we do not have a sample size here, we will use the population standard deviation instead.

For a 95% confidence level, the z-value is 1.96. So, plugging in the values we have:

Margin of Error = 1.96*(105.3/square root of 1)

Margin of Error = 205.97

Now, we can find the interval by adding and subtracting the margin of error from the mean:

Interval = [1812 - 205.97, 1812 + 205.97]

Interval = [1606.03, 2017.97]

Therefore, the answer is c) [1606, 2018].

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The given function is f(x) = -3x^2 + 2x + 3.

The interval(s) over which the function f(x) = -3x^2 + 2x + 3 is continuous is: x ∈ (-∞, ∞)

Steps to find the interval notation of continuous function:

For a given function, check if it has any discontinuities such as a vertical asymptote, a jump discontinuity, or a removable discontinuity.

If the function does not have any such discontinuities, then the function is continuous for all real values of x.

Write the answer using interval notation.

The given function is a polynomial function and does not have any vertical asymptotes, jump discontinuities, or removable discontinuities. Therefore, the function is continuous for all real values of x, and the interval notation for the continuous function is x ∈ (-∞, ∞).

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The solution to the expression 4+(−634) is -630

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

4+(−634)

Rewrite the expression properly

So, we have the following representation

4 + (−634)

Remove the bracket in the above expression

This gives

4 + (−634) = 4 - 634

Evaluate the difference

4 + (−634) = -630

Hence, the solution is -630

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Answer:

D

Step-by-step explanation:

The range of the function is all possible y-values of an function or an output.

Answer:

- 12 and - 187

Step-by-step explanation:

To evaluate f(- 7) substitute x = - 7 into f(x)

f(- 7) = 2(- 7) + 2 = - 14 + 2 = - 12

Similarly for g(- 4)

g(- 4) = 3(- 4)³ + 5 = 3(- 64) + 5 = - 192 + 5 = - 187

Answer:

\(given \: that \: it \: is \: issoscless \: triangl e \\ so \: the \: third \: side \: must \: be \: 2 \\ thank \: you\)

The standard score value of a observed X value, where mean, μ = 88.2 and standard deviations, σ = 89.4, is equals to the 0.02.

In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the population or sample mean value. Formula for Standard score is, Z-score = (X - μ)/σ

where, μ --> mean of values

σ --> standard deviations

X --> observed value

Z --> Standard score

Now, we have, mean, μ = 88.2

Standard deviation, σ = 89.4

Observed value, X = 89.7

Using Z-score formula, Z = (X - μ)/σ

Subsritute all known values in above formula,

= 89.7 - 88.2 / 89.4

= 1.5 / 89.4

= 0.02

Z = 0.02

Hence, required standard score value is 0.02.

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The equation of the line that passes through (3,7) and is parallel to the line passing through (4,5) and (0,1) is y = x + 4.

To find an equation of the line that passes through the point (3,7) and is parallel to the line passing through (4,5) and (0,1), we first need to determine the slope of the line passing through (4,5) and (0,1), which is the same as the slope of the parallel line we are trying to find.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be found using the slope formula:

m = (y₂ - y₁) / (x₂ - x₁)

Applying this formula to the points (4,5) and (0,1), we get:

m = (1 - 5) / (0 - 4) = -4 / -4 = 1

Therefore, the slope of the line we are trying to find is 1.

Using the point-slope form of the equation of a line, we can write the equation of the line passing through (3,7) with a slope of 1 as:

y - 7 = 1(x - 3)

Simplifying the equation, we get:

y = x + 4

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Step-by-step explanation:

Here, slope= 4/5 , As y= mx+c

according to formula, y-y1= m(x-x1)

y-6= 4/5(x+6)

5/4 (y-6)= x+6

5/4y - 15/2= x+6

x- 5/4y + 27/2 =0

Answer:

11

Step-by-step explanation:

13×13 = 169

17 × 17 = 289

289 - 169 = 120

Square root of 120 is 10.95

Round answer to 11

8) The percent of people that said that Pinocchio was their favorite Disney Movie is of: 28%.

9) The percent of people that said that Pinocchio or Cars was their favorite Disney movie is of: 39%.

10) The two movies that about half the people say were their favorite is of: Pinocchio and Toy Story.

From the pizza graph, the sum of all the percentages must be of 100%, hence the Pinocchio percentage is obtained as follows:

10 + 11 + 14 + 15 + 22 + P = 100

72 + P = 100

P = 100 - 72

P = 28%.

Then the percentage for Pinocchio or Cars is of:

28 + 11 = 39%.

The percentage for Pinocchio or Toy Story is of:

28 + 22 = 50%.

(about half).

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Answer: 29/8 of 3.625

Step-by-step explanation:

6 1/8- 2 1/2= 29/8 or 3.625

Answer: 29/8

Step-by-step explanation:

Answer:

There are a total of eight factors of 24, they are 1, 2, 3, 4, 6, 8, 12 and 24.

Step-by-step explanation:

Answer: I think yes.

Step-by-step explanation: Why not poll the other passengers in economy? Just because their rich doesn't mean they have life stories

Answer:

4. d = 4

5. d = 8.8

6. d = 6

7. d = 10

8. d = 3

9. d = 1

Step-by-step explanation:

4. (-5, 2), (-5, 6)

    (x₁, y₁)  (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-5 - (-5))² + (6 - 2)²

d = √(-5 + 5)² + (4)²

d = √(4)²

d = √16

d = 4

5. (4.5, -3.3), (4.5, 5.5)

       (x₁, y₁)      (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(4.5 - 4.5)² + (5.5 - (-3.3)²

d = √(0)² + (5.5 + 3.3)²

d = √(8.8)²

d = √77.44

d = 8.8

6. ((5(1/2), (-7(1/2)) and ((5(1/2), (-1(1/2))

         (x₁,     y₁)                   (x₂,     y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(11/2) - (11/2)² + (-3/2) - (-15/2))²

d = √(d)² + ((-3/2) + (15/2)²

d = √(6)²

d = √36

d = 6

7. (-2(1/4)), -8) and (7(3/4), -8)

        (x₁,   y₁)               (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(31/4) - (-9/4))² + (-8 - (-8))²

d = √(31/4) + (9/4))² + (-8 + 8)²

d = √(10)²

d = √100

d = 10

8. (5(1/4)), (-3(1/4) and ((5(1/4), (-6(1/4))

         (x₁,     y₁)                    (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(21/4) - (21/4))² + (-25/4) - (-13/4))²

d = √(-25/4) + (13/4))²

d = √(-3)²

d = √9

d = 3

9. (-1(1/2)), (-6(1/2) and ((-2(1/2), (-6(1/2))

          (x₁, y₁)                        (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-5/2) - (-3/2))² + (-13/2) - (-13/2))²

d = √(-5/2) + (3/2))²

d = √(-1)²

d = √1

d = 1

I hope this helps!

The sample standard deviation is 0.89

In the given statement is:

A sample n = 5 scores which means that there are 5 sample having m = 20 which is the arithmetic mean (A.M.)of these samples, and \(s^{2}\) = 4 is the variance of these samples.

Let us know the :

What is meant by Sample Standard deviation?

The sample standard deviation (s) is the square root of the sample variance and is also measure of the spread from the expected values.

Standard deviation is the square root of the variance.

Therefore, \(s^{2}\) =4 => s = 2

(Where, s denotes sample standard deviation ,σ)

Also, Standard error of the sample S(E) = Sample standard variance / \(\sqrt{number of samples}\)

= σ /\(\sqrt{n}\) = 2/\(\sqrt{5}\)

and, root 5 = 2.24

put the value of root 5

=2 / 2.24

= 0.89

Hence, The sample standard deviation is 0.89

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x = 7

hope it helps...!!!

Answer:

The curve meets the coordinate axes at the points A(0, 1 – k) and 1 B(. ) ... 2x + 1. (d) Find the value of k. (4). (Total 12 marks). 7. –5. 5 x y. O. M (2, 4).Step-by-step explanation:

The polynomial function is P(n) = n(3n - 1)/2 and the sequence is 1, 5, 12, 22 and 35

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

Sequence of five figurate numbers

An instance of a sequence of figurate numbers is the pentagonal numbers

This is represented as

P(n) = n(3n - 1)/2

For the terms of the sequence, we have

P(1) = 1 * (3 *1 - 1)/2 = 1

P(2) = 2 * (3 *2 - 1)/2 = 5

P(3) = 3 * (3 *3 - 1)/2 = 12

P(4) = 4 * (3 *4 - 1)/2 = 22

P(5) = 5 * (3 *5 - 1)/2 = 35

Hence, the polynomial is P(n) = n(3n - 1)/2

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Answer:

\(\frac{-(-14)+\sqrt{(-14)^2-4.1.0 } }{2.1}\) = \(\frac{14+\sqrt{196-0} }{2}\) = \(\frac{14+14}{2}\) = 14

Step-by-step explanation:

The solution of the given system of equations is as follows:

x = x y = y z = -4/3x - 10/9y + 68/27

w = -1/147

Let's solve the given system of equations:

4x + 12y - 7z - 20w = 263x + 9y - 5z - 28w = 36

Divide the first equation by 4 and the second equation by 3 we have:

x + 3y - 7/4z - 5/2w = 26/43x + 3y - 5/3z - 28/3w = 12

Now, multiply the first equation by 3 and subtract from the second equation:

3(1x + 3y - 7/4z - 5/2w = 26/4)3x + 3y - 21/4z - 15/2w = 39/4- (3x + 3y - 5/3z - 28/3w = 12)1/3z + 11/3w = 7/4

Now, solve for z:

z = 21w - 28/3By substituting the value of z in terms of w in the first equation we get:

1x + 3y - 7/4(21w - 28/3) - 5/2w = 26/4x + 3y - 147/4w + 7 = 13/2

Multiply both sides by 2, and we get:2x + 6y - 147/2w + 14 = 13

Therefore,2x + 6y - 147/2w = -1/2

Now, solving for w:{147}/{2w}= {-1}/{2}

w = -1/147

By substituting the value of w in the equation x + 3y - 7/4z - 5/2w = 26/4, we get:

1x + 3y - 7/4z - 5/2(-1/147) = 26/4x + 3y - 7/4z + 5/294 = 13/12

Multiplying both sides by 12, we get:12x + 36y - 21z + 5 = 39

Now, solve for z:

z = -{4}/{3}x - {10}/{9}y + {68}/{27}

Hence, the solution of the given system of equations is as follows:x = x y = y z = -4/3x - 10/9y + 68/27w = -1/147

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Lauren's accounting profit can be calculated by subtracting her total expenses (rent, labor costs, and overhead expenses) from her total revenue.

To determine Lauren's accounting profit, we need to subtract her total expenses from her total revenue. Her total revenue for the year was $145,000. Her total expenses include rent ($12,000), labor costs ($65,000), and overhead expenses ($15,000).

To calculate her accounting profit, we subtract the total expenses from the total revenue:

Accounting Profit = Total Revenue - Total Expenses

Accounting Profit = $145,000 - ($12,000 + $65,000 + $15,000)

Accounting Profit = $145,000 - $92,000

Accounting Profit = $53,000

Therefore, Lauren's accounting profit for the year is $53,000. This represents the amount of interests left after deducting all the expenses from the total revenue. It is important to note that accounting profit does not take into account other factors such as opportunity costs or non-cash expenses, but it provides a basic measure of the profitability of the business based on the given information.

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Answer:

11 hours

Step-by-step explanation:

270/18=15 per hour

so 165/15 = 11

Answer:

11 hours

Step-by-step explanation:

270:18 simplified is 15:1

165/15 = 11

Hope this helps!