27POINTS A parallelogram has an area of 14 cm 2. If the dimensions of the parallelogram are doubled, what will the new area be?

A.14 cm 2
B.28 cm 2
C.56 cm 2
D.112 cm 2

The average of the combined list of 400 students is 71.9 and the standard deviation is 13.1.

To find the average and standard deviation of the combined list of 400 students, you can use the following formulas:

Average of combined list = (Average of one class * Number of students in one class + Average of another class * Number of students in another class) / Total number of students

Standard deviation of combined list = sqrt(((SD of one class)^2 * (Number of students in one class - 1) + (SD of another class)^2 * (Number of students in another class - 1) + ((Average of one class - Average of another class)^2 * Number of students in one class * Number of students in another class)) / Total number of students)

Applying the values from the given information:

Average of combined list = (67 * 75 + 72 * 325) / 400 = 71.9

Standard deviation of combined list

= sqrt(((12^2 * 74) + (15^2 * 324) + ((67 - 72)^2 * 75 * 325)) / 400)

= 13.1

Answer: 1001

B/c i said so

If the measure of angle ACB = 30 and the measure of angle A = 80, the measure of angle B is 70 degrees.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

If the measure of angle ACB = 30 and the measure of angle A = 80, To find the measure of angle B

We know that the angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

∠ACB + ∠A + ∠B = 180

30 + 80 + ∠B = 180

∠B = 180 - 110

∠B = 70

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The altitude of the top of the hill is 274 feet.

To find how much lower Checkpoint 1 is than Checkpoint 5, we subtract the elevation of Checkpoint 1 from the elevation of Checkpoint 5:

Difference = Elevation at Checkpoint 5 - Elevation at Checkpoint 1

Difference = (-57) - (-188)

Now, simplify the expression:

Difference = -57 + 188

Difference = 131 feet

So, Checkpoint 1 is 131 feet lower than Checkpoint 5.

Next, to find the altitude of the top of the hill, we add the rise of the hill to the elevation at Checkpoint 1:

Altitude of the top of the hill = Elevation at Checkpoint 1 + Hill rise

Altitude = (-188) + 462

Now, calculate the sum:

Altitude = 274 feet

The altitude of the top of the hill is 274 feet.

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Answer:

The correct option is 1. The area of cross section area is 48 mm².

Step-by-step explanation:

From the find it is noticed that the cross section is a rectangle with length 4 mm and width is 12 mm.

The area of a rectangle is the product of its dimensions.

[tex]A=l\times w[/tex]

Where, l is length of the rectangle and w is width of the rectangle.

The area of cross section is

[tex]A=4\times 12[/tex]

[tex]A=48[/tex]

Therefore the area of cross section area is 48 mm². Option 1 is correct.

The quotient Q(x) is found to be x² - 4x - 11 and the remainder R is 4.

The question involves using synthetic division to find the quotient Q(x) and the remainder R when the polynomial P(x) = x³ − 2x² − 3x + 18 is divided by (x + 2).

To perform synthetic division, we first write down the coefficients of P(x): 1, -2, -3, and 18. The divisor is (x + 2), so we use -2 for the synthetic division.

Write the coefficients of P(x): 1, -2, -3, 18.

Write the root of the divisor (x + 2) = -2 on the left side of the synthetic division setup.

Bring down the first coefficient (1).

Multiply -2 by 1, place the result (-2) under the second coefficient (-2), and add the two numbers yielding -4.

Repeat the multiplication and addition process for the rest of the coefficients.

The results of the synthetic division process give us the coefficients of the quotient Q(x) and the remainder R.

In performing the synthetic division, we find that the quotient Q(x) is x² - 4x - 11 and the remainder is R = 4.

Jeffery's monthly loan payments for the loan will be $515.19.

To calculate the monthly loan payments for Jeffrey, we can use the formula for calculating the monthly payment of a loan. The formula is:

Monthly Payment = (Principal * Monthly Interest rate) / (1 - (1 + Monthly Interest rate) ^ (-n))

In this case, Jeffrey's principal is $30,000, the annual interest rate is 5.2%, and the loan term is 6 years. Since Jeffrey will graduate in 4 years, we need to adjust the loan term accordingly. The monthly interest rate can be calculated by dividing the annual interest rate by 12, and the number of monthly payments will be multiplied by 4.

Using these values in the formula, we can calculate the monthly loan payment for Jeffrey.

Monthly Payment = (30000 * 0.052/12) / (1 - (1 + 0.052/12) ^ (-24))

Monthly Payment = $515.19

Answer:

Height=6in

Step-by-step explanation:

Took test and got it correct

Answer:

8 in.

Step-by-step explanation:

Let's find the rhombus's length...

cosine =  [tex]\frac{adjacent}{hypotenuse}[/tex]

cosine = ° = 54°

adjacent =  = 4.5 in

Length of Rhombus = Hypotenuse

So...

cos54 = [tex]\frac{9}{x}[/tex]

x = [tex]\frac{4.5}{cos 54}[/tex]

x = 7.6558... about 8 inches

The two ships are sailing in opposite sides, Hence, the resultant speed is given by 15+5 = 20 km/hr.

Therefore, from the below triangle, we have

[tex]\frac{dx}{dt} = 20 \text{  km/hr}[/tex]

Let the distance between the ships is y. On applying Pythagorous theorem, we have

[tex]y^2=x^2+60^2\\ \text{On differentiating, we get}\\ 2y\frac{dy}{dt} =2x\frac{dx}{dt}\\\frac{dy}{dt}= \frac{x}{y} \frac{dx}{dt}[/tex]

On substituting the value of y as [tex]y=\sqrt{60^2+x^2}[/tex]

[tex]\frac{dy}{dt} =\frac{x}{\sqrt{60^2+x^2}} \frac{dx}{dt}[/tex]

Since, the at noon the ship is 60 km to each other. Hence, for 4 PM, i.e. t=4, we have

[tex]x=4 \times \frac{dx}{dt} \\ x= 4 \times 20 \\x=80[/tex]

On substituting the value in above, we get

[tex]\frac{dy}{dt} =\frac{80}{\sqrt{60^2+80^2}} (20[/tex]

[tex]\frac{dy}{dt} = 16.0 \text{ km/hr}[/tex]

Therefore,  the distance between the ships changing at a rate of 16 km/hr at 4:00 pm

Answeeeeeerrrrr

0.2861

Using the mode concept, according to the stem-and-leaf plot, the missing value is of 71.

It is the value that appears the most times in the data-set. When it's unique, the mode is the value that appears the most often in a data set and it can be used as a measure of central tendency, like the median and mean.

Here, we have,

In this problem, following the key format of the stem-and-leaf plot, disconsidering the missing value, the values 71 and 64 each appear 3 times.

However, the mode is 71, meaning that is should appear more times than 64, which means that the missing value is of 71.

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complete question:

This Stem-and-Leaf Plot is missing one data item. If the mode of the data set is 71, what is the value of the unknown data item?

Answer:

the answer is D

Step-by-step explanation:

Using the hypergeometric distribution, it is found that there is a 0.0923 = 9.23% probability that 4 CPAs will be selected.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, there are 15 accountants, 9 are CPAs and 4 will be selected, hence N = 15, k = 9, n = 4.

The probability that 4 CPAs will be selected is P(X = 4), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,15,4,9) = \frac{C_{9,4}C_{6,0}}{C_{15,4}} = 0.0923[/tex]

0.0923 = 9.23% probability that 4 CPAs will be selected.

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