The following 96% confidence interval based on a sample of 32 students was formed to estimate the population mean time that students will require to complete a particular examination: 62.4 ± 12.6 minutes. Which one of the following interpretations is correct for this confidence interval?A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutesB) We are 96% confident that the sample mean time (62.4 minutes) equals the true mean timeC) We are 96% confident that the population mean time required by students who take this test is 62.4 minutesD) We are 96% confident that the sample mean time (62.4 minutes) is correctE) We are 4% confident that an individual student taking this test will require less than 49.8 minutes or more than 75.0 minutes

The measure of angle DCE in this problem is given as follows:

m < DCE = 22.5º.

The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.

The three trigonometric ratios are given as follows:

The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:

cos(38º) = DB/12.2

DB = 12.2 x cosine of 38 degrees

DB = 9.6 cm.

BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:

DE = 1/4 x 9.6

DE = 2.4 cm.

Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:

tan(x) = 2.4/5.8

x = arctan(2.4/5.8)

x = 22.5º

m < DCE = 22.5º.

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Answer:

x = 22.5°

Step-by-step explanation:

Step-by-step explanation:

m and n are parallel so x+18+5x-6 is equal to 180°.

6x+12=180

6x=168

x=28

Answer:

x + 18° + 5x - 6° = 180°

6x = 180° - 12

x = 168/6

x = 28°

ANSWER :- 28°

Step-by-step explanation:

Tag me as brilliant

Answer:

x = 26 degrees

Step-by-step explanation:

Supplementary angles mean that they sum up to be 180 degrees therefore

C + D = 180 degrees

128 degrees + D = 180 degrees

D = 180 degrees - 128 degrees

D = 52 degrees

If the measure of the angle D is two times the value of x then x is...

x = D/2

x = 52 degrees / 2

x = 26 degrees

The break-even point under the old situation is 680000, the break-even point under the proposed situation is 806451 and the birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.

In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even." Although opportunity costs have been paid and capital has obtained the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."

In the given question, last year sales=  birr 100000

net profit= 8% of sales

Fixed costs= birr 170000

Estimated sales increase= 25%

Estimated net profit= birr 30000

Increase in fixed cost due to moving to low-rent warehouse= birr 30000

(a) The break-even point under the old situation (X):

   = 100,000 * a - 170,000

   =1,000,000 * 8%

   a= 25% (net profit)

   X*a= 1170,000

   X=680,000

   That is, the break-even point under the old situation is 680000.

(b) The break-even point under the proposed situation is:

      = 1,250,000 x b - 170,000- 30,000

      = 80,000 + 30,000

      b= 24.8%

      X*b=200,00

      X=806451

      The break-even point under the proposed situation is 806451 and

(c) The birr sales volume must be obtained under the proposed plan to make as much profit as last year is:

        X*b -200,000= 80,000

        X*b = 280,00

        X= 1,129,032

The birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.

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Answer:

B and D

Step-by-step explanation: I got it right

Answer:

y = - 5

Step-by-step explanation:

y = 4 is a horizontal line parallel to the x- axis

A parallel line must therefore be a horizontal line with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (1, - 5) with y- coordinate - 5, thus

y = - 5 ← equation of parallel line

According to the information we can infer that the change between 11 and 12 is 1.3 m/hr

To establish the value of the change in height between 11 and 12 we must look at the values of the y axis. According to this information we can establish that 11 o'clock coincides with 5.2 and 12 o'clock coincides with 3.9. So we must subtract these two values:

According to the above, we can infer that the change between these two hours is 1.3 m/hr.

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The test results' standard deviation is around 33. Standard deviation is a measure of the spread or dispersion of a set of data. It measures how much the individual data points deviate from the mean of the data.

To find the standard deviation of this data, we first need to calculate the sample mean and variance:

Sample mean, = (290 + 805 + 708 + 606 + 504 + 401 + 302 + 05) / 31 = 56.45

Sample variance, \(s^2 = [(2-56.45)^290 + (80-56.45)^25 + (70-56.45)^28 + (60-56.45)^26 + (50-56.45)^24 + (40-56.45)^21 + (30-56.45)^22 + (0-56.45)^25] / (31-1) = 1080.56\)

To find the standard deviation, we take the square root of the variance:

Standard deviation, \(s = sqrt(s^2) = sqrt(1080.56) = 32.90\\\)

Rounding to the nearest unit, the standard deviation is approximately 33.

Therefore, the standard deviation of the test scores is approximately 33.

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Answer:

max-3925 min-3075

Step-by-step explanation:

Answer:

GIVE BRAINLEIST PLZ Max is 3925 Min is 3075

Step-by-step explanation:

Answer: the value of y is 1

Step-by-step explanation: 6=2 x 1+2

Answer:

d² - 24d + c = (d - 12)² - 144 + c

Answer:

See below.

Step-by-step explanation:

9(n+8)-6

n=5

9(5+8)-6

9(13)-6

117-6

111

A sum is the answer to an addition expression or equation.

When one refers to "less than", they mean the number is "less than" the entirety of the expression or equation.

-hope it helps

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

Step-by-step explanation:

use distributive prop.

3 times q =3Q

3 Times -7 =-21

3Q-21=21

ADD 21 to both sides

3q=42

q=14 .

Given equation 2x + 4y = 4 has infinitely many solutions.

We have been given an equation 2x + 4y = 4

We need to find the number of solutions.

Above equation is a linear equation with two variables.

We know that, a linear equation in two variables has infinitely many solutions.

For any value real value of x we can find corresponding value of y.

Since x can takes infinitely many inputs the output would be infinitely many.

Therefore, given equation 2x + 4y = 4 has infinitely many solutions.

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Answer:

33 degrees

Step-by-step explanation:

31-(-2)=33

\(\:\)

。。。。。。。。。。。。。。。。。。。。。。。。。。。。

\(\frac {7^2}{7^2}\)

\(7^2 ÷ 7^2 \)

\(7^{2-2}\)

\(7^0 \)

\(1 \) ( Opsi C )

。。。。。。。。。。。。。。。。。。。。。。。。。。。。

\(\:\)

Answer:

C. 1

Step-by-step explanation:

7^2/7^2

=1

hope help

To find out when both Bus A and Bus B will arrive at the same stop point, we need to find the time at which they will both have completed an integer number of trips.

Bus A arrives every 15 minutes, so in 1 hour (60 minutes), it will complete 4 trips (60/15=4).

Bus B arrives every 40 minutes, so in 1 hour, it will complete 1.5 trips (60/40=1.5).

To find the time at which both buses will arrive at the same stop point, we need to find the time at which they will have completed an integer number of trips. This means that we need to find the smallest multiple of 15 and 40 that is the same. This is called the least common multiple (LCM) of 15 and 40.

The LCM of 15 and 40 is 120. Therefore, both buses will arrive at the same stop point every 120 minutes or 2 hours.

To find the next time that both buses will arrive at the same stop point, we need to add 2 hours to the current time.

Answer:

5

Step-by-step explanation:

y=mx+b

B is always the y intercept.

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

The critical points of the given function are p = 2 ± √13.

A relation between a collection of inputs and outputs is known as a function.

A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Each function has a range, codomain, and domain.

Critical function:

The key points are locations inside the function's domain where the function's nature changes.

The function stops increasing or decreasing at these places.

The function is: \(h(p)=\frac{p-2}{p^2+9}\)

The derivative test will be applied here:

\(\begin{aligned}& \therefore h^{\prime}(p)=0 \\& \Rightarrow \frac{d}{d p}\left(\frac{p-2}{p^2+9}\right)=0 \\& \Rightarrow \frac{\frac{d}{d p}(p-2)\left(p^2+9\right)-\frac{d}{d p}\left(p^2+9\right)(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{1 \cdot\left(p^2+9\right)-2 p(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{-p^2+4 p+9}{\left(p^2+9\right)^2}=0 \\& \Rightarrow-p^2+4 p+9=0\end{aligned}\)

Then,

\(\begin{aligned}& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{4^2-4(-1) 9}}{2(-1)} \\& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{52}}{-2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm \sqrt{52}}{2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm 2 \sqrt{13}}{2} \\& \Rightarrow p_{1,2}=2 \pm \sqrt{13}\end{aligned}\)

Therefore, the critical points of the given function are p = 2 ± √13.

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Answer:

f(–5)=–4

Step-by-step explanation:

as it is defined

Answer:

n ≤ 1 or n ≥ 7

Step-by-step explanation:

solve each part separately

86n + 13 ≤ 99 ( subtract 13 from both sides )

86n ≤ 86 ( divide both sides by 86 )

n ≤ 1

n + 90 ≥ 97 ( subtract 90 from both sides )

n ≥ 7

solution is n ≤ 1 or n ≥ 7

Answer:

27

Step-by-step explanation:

The area of this parallelogram is its base times height. 6x4.5 is 27.

Hope this helps! (please mark me brainliest)

Answer:

closing costs

Step-by-step explanation:

Answer:

For the box that you did not fill out the area of that shape is 190 sq units

Step-by-step explanation:

10 x 5 = 50 ÷ 2 = 25

10 x 15 = 150

10 x 3 = 30 ÷ 2 = 15

25 + 150 + 15 = 190

Answer:

36

190

72

Step-by-step explanation:

have a good day

Here is the correct format for the question.

\(x'_1 = 7x_1 +4x_2+ 12x_3 , \ \ x'_2 = x_1 + 2x_2 + x_3 , \ \ x'_3 = -3x_1 -2x_2 -5x_3\) . Then find the solution that satisfies  \(x \limits ^{\to} = \left[\begin{array}{c}0\\1\\-2\end{array}\right]\)

Answer:

\(\mathbf{c_1 = -3, c_2 = 2, c_3 = 2}\)

Step-by-step explanation:

From the figures given above:

the matrix can be computed as,

\(\left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right] x \limits ^{\to} = \left[\begin{array}{c}x_1\\x_2\\x_3\end{array}\right] = x \limits ^{\to} = \left[\begin{array}{c}x_1'\\x_2'\\x_3'\end{array}\right]\)

The first thing we need to carry out is to determine the eigenvalues of A,

where:

\(A = \left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right]\)

\(|A-rI|=0\)

\(\begin {vmatrix} 7-r&4&12\\1&2-r&1\\-3&-2&-5-r \end {vmatrix}=0\)

the eigenvalues are r = 0, 1, 3

However, the eigenvector correlated to each eigenvalue can be calculated as follows.

suppose  r = 0

(A - rI) x = 0

\(\left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right] \left[\begin{array}{c}x_1\\x_2\\x_3\end{array}\right] = \left[\begin{array}{c}0\\0\\0\end{array}\right]\)

now the eigenvector is \(\left[\begin{array}{c}-4\\1\\2\end{array}\right]\)

However, for eigenvalue = 1, we have :  \(\left[\begin{array}{c}-4\\1\\2\end{array}\right]\)

for eigenvalue = 3, we have:\(\left[\begin{array}{c}-2\\-1\\1\end{array}\right]\)

The solution now can be computed as :

\(x(t)= c_1 \left[\begin{array}{c}-4\\1\\2\end{array}\right] + c_2e^t \left[\begin{array}{c}-4\\3\\1\end{array}\right]+ c_3e^{3t} \left[\begin{array}{c}-2\\-1\\1\end{array}\right]\)

Similarly, the fundamental matrix solution is:

\(\left[\begin{array}{ccc}-4&-4e^t&-2e^{3t}\\1&3e^t&-e^{3t}\\2&e^t&e^{3t}\end{array}\right]\)

\(-4c_1 -4c_2-2c_3 =0 \\ \\ c_1 + 3c_2 -c_3 = 1\\ \\ 2c_1+c_2 +c_3 = -2\)

Solving the above equation, we get:

\(\mathbf{c_1 = -3, c_2 = 2, c_3 = 2}\)