Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
1. g(y-2)/(y^2-2y+4)
2. f(x) = x^-2inx

The due date of the loan is October 22.

First we need to calculate the number of days between the date it was opened and the date it matures, then add that number of days to the date it was opened.

Given that the loan was opened on January 22, the maturity value of the loan is $15,799, and the interest rate is 9%, we can use the formula:

L = P * (1 + r * t)

where

We can rearrange the formula to find the time in years:

t = (L / P - 1) / r

Substituting the values:

t = ($15,799 / $14,800 - 1) / 0.09 = 0.066 years = 245 days

So, 245 days after January 22 is:

January 22 + 245 days = October 22

Therefore, the due date of the loan is October 22.

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The probability that one girl and two boys are chosen for the team is 0.355 or 35.5%.

The total number of ways to select a team of 3 students from 26 students is:

C(26, 3) = 26! / (3! (26-3)!) = 26! / (6! 20!) = 2600

To select a team of one girl and two boys, we can choose one girl from

the 14 girls and two boys from the 12 boys. So the number of ways to

select a team of one girl and two boys is:

C(14, 1) × C(12, 2) = 14! / (1! 13!) × 12! / (2! 10!) = 14 × 66 = 924

Therefore, the probability of selecting a team of one girl and two boys is:

P(one girl and two boys) = 924 / 2600 = 0.355 or 35.5% (approximate to

one decimal place).

So the probability that one girl and two boys are chosen for the team is

0.355 or 35.5%.

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The surface area of the hemisphere is 254.34 cm^2

To find the surface area of a hemisphere, we first need to find the radius of the hemisphere using the formula for the volume of a hemisphere: V = (2/3)πr^3.

Given the volume of 486π cm³, we can set up the equation:

(2/3)πr^3 = 486π cm³

Solving for r:

r = (486π * 3/(2*π))^(1/3)

r = 9

Now we can use the formula for the surface area of a hemisphere:

A = 2πr^2

Substituting in the value of r that we just found:

A = 2π * 9^2

This gives

A = 254.34 cm^2

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Answer:

161 degrees since 180 - 19 would be 161 since they are supplementary if they are

Step-by-step explanation:

Answer:

x = 4, y = 5.

Step-by-step explanation:

4x-2=3y-1

y+3=3x-4

Rearranging:

4x - 3y =  1       (A)

-3x + y = -7      (B)

Multiply  B by 3:

-9x + 3y = -21   (C)
Adding A and C:

-5x = -20

x = 4

Substitute for x in equation A:

4(4) - 3y = 1

3y = 15

y = 5.

The pencils and erasers that each student have is 14.

From the information, the person has 56 pencils and 42 erasers and wants to make sets of pencils. erasers for her class so that each student has the same number of pencils and erasers.

It should be noted that this has to do with looking for the highest common factor.

The highest common factor for 56 and 42 is 14.

The students will have 14 pencils each.

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Answer:

a) 140 weeks

b) 4 weeks

c) 140 miles

Step-by-step explanation:

a)

1500=10w+100

1400=10w

w=140

b)

10w+100=15w+80

5w=20

w=4

c)

10(4)+100

140

Answer:

The rule of the translation will be:

(x, y) → (x+3, y+5)

Step-by-step explanation:

Translation of an object is basically termed as "sliding" the original. If the image is moved right by the 'c' units, the 'c' unit(s) are added to the x-coordinate and if the image is moved left by the 'c' units, the 'c' unit(s) are subtracted to the x-coordinate.

And If the image is moved up by the 'c' units, the 'c' unit(s) are added to the y-coordinate and if the image is moved down by the 'c' units, the 'c' unit(s) are subtracted to the x-coordinate.

As the point is (4, 2)

The image of the point is (7, 7)

As the coordinates of the image point indicate that 3 units are added to the x-coordinate of the original point, and 5 units are added to the ý-coordinate.

Hence, the image will be move 3 units to the right and 5 units up.

Therefore, the rule of the translation will be:

(x, y)  →  (x+3, y+5)

as

(4, 2) →  (x+3, y+5) = (4+3, 2+5) = (7, 7)

The equivalent expressions to 5(1/3x + 7) - 3(1/2x - 4) include C. 1 2/3x + 35 - 1 1/2x + 12

It should be noted that an expression simply shows the relationship between the variables.

In this case, the value of the expression illustrated will be:

5(1/3x + 7) - 3(1/2x - 4)

= 5/3x + 35 - 3/2x + 12

= 5/3x - 3/2x + 35 + 12

= 10/6x - 9/6x + 47

= 1/6x + 47.

Therefore, the equivalent expressions to 5(1/3x + 7) - 3(1/2x - 4) will be 1 2/3x + 35 - 1 1/2x + 12. This was illustrated based on the information given as it has the final value of 1/6x + 47.

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The following parts can be solved by the concept of Area.

1. The area of the sprinkled lawn is 9π square feet, where π is approximately 3.14.

2. The area that the storm will affect is 113.1 square miles, where the value of π is approximately 3.14.

1. To find the area of the sprinkled lawn, we need to find the area covered by the sprinkler in one rotation and then multiply it by the number of rotations. The sprinkler sprays water 3 feet in every direction, so it covers a circular area with a radius of 3 feet. The area of a circle with a radius of 3 feet is given by the formula A = πr^2, where r is the radius of the circle.

Therefore, the area covered by the sprinkler in one rotation is 9π square feet (A = π x 3^2 = 9π). If the sprinkler rotates n times, then the total area covered by the sprinkler is n times the area covered in one rotation.

2. To find the area that the storm will affect, we need to find the area of the circle with a radius of 6 miles. The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. Therefore, the area that the storm will affect is 36π square miles (A = π x 6^2 = 36π). To get a numerical value, we can use the approximation of π as 3.14, which gives us an area of approximately 113.1 square miles (A = 3.14 x 36 = 113.1).

Thus, the storm will affect an area of approximately 113.1 square miles.

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Answer:

115 degrees

Step-by-step explanation:

We know that angle y is 45 degrees and angle z is 70 degrees so to find x, you do 180-45-70 to get 65 degrees.

Because W plus X has to equal 180 degrees, 180-65=115, so the answer is 115 degrees

Answer:

choice 3) W = 115 degrees

Step-by-step explanation:

all triangle interior angles add up to 180 degrees

180 = 45 + 70 + X

X = 65 degrees

Angle W is supplemental to angle X (angle W and angle X add up to 180 degrees.)

W = 180 - 65 = 115 degrees

The composite method for determining the location of the center of gravity of a composite body requires integration.

So, the answer is A.

The center of gravity is the point at which the entire weight of a body appears to act when the body is in equilibrium.

The concept of a center of gravity is used to calculate the behavior of a body when subjected to external forces. The composite method for determining the location of the center of gravity of a composite body involves integration.

The center of gravity is found by dividing the sum of the products of individual masses with their corresponding distance from an arbitrary reference line by the total mass of the system. When there is more than one weight distribution involved, the composite method is employed.

Hence, the answer of the question is A.

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Answer:

12.17634

Step-by-step explanation:

Answer: $1,544.40

Step-by-step explanation: It just is

To find the area of triangle ABD, we can use the formula for the area of a triangle: A = (1/2)bh, where b is the base of the triangle and h is the height.

First, we need to find the length of BD. We can use the Pythagorean theorem to do this:

BD^2 = AB^2 - AD^2

BD^2 = 12^2 - 12^2

BD^2 = 144 - 144

BD^2 = 0

BD = 0

This means that D is actually the midpoint of AC, and BD is a height of triangle ABD.

So, the base of triangle ABD is AB = 12, and the height is BD = 0. Therefore, the area of triangle ABD is:

A = (1/2)bh

A = (1/2)(12)(0)

A = 0

The area of triangle ABD is 0 because BD, the height of the triangle, is 0.

Answer:

The area is \(32\sqrt{5}\) or 71.5542 units²

Step-by-step explanation:

Segment AD is a 12 units, and so is segment AB. This makes triangle ABD and isosceles triangle (a triangle with 2 equal side lengths)

The equation for area of an isosceles triangle given only the base and a side length s is

\(A = \frac{1}{2} b \sqrt{s^2-\frac{b^2}{4} } \\\)

\(A = \frac{1}{2} * 16 * \sqrt{12^2-\frac{16^2}{4} } \\A = 8 * \sqrt{144-64} \\A = 8\sqrt{80} \\A = 32\sqrt{5}\)

The area of Triangle ABD is \(32\sqrt{5}\) units², or 71.5542 units² in decimal form.

Answer: 25 or 30-60

Step-by-step explanation:

Vote me for branliest Have a great day or night everyone!!!

\(\displaystyle \Large \boldsymbol{} a) \ \underline{x^2-3x}+\underline{2x-6}-\underline{xy+3y}=\\\\\\x(x-3)+2(x-3)-y(x-3)=\boxed{(x-3)(x-y+2)} \\\\\\b) \ mn-mx-n+x=m(n-x)-(n-x) =\boxed{ (m-1)(n-x)}\)

n = 37, and tenth term = 18

Given progression,

36, 34, 32, ...

The sum of the first n terms is 0

First term(a1) = 36

The common difference (d)= 34-36 = -2,

The formula of the sum of the first n term is,

\(Sn = \frac{n}{2} [2a_{1} + (n - 1)d]\)

substitue the values Sn= 0, a1= 36, d= -2 in the above equation to find n

\(0\)= \(\frac{n}{2} [2(36) + (n-1) (-2)]\)

\(0 = \frac{n}{2}[72- 2n+ 2]\)

\(0 = \frac{n}{2}[74 - 2n]\)

\(74 - 2n = 0\)

\(2n = 74\)

\(n = \frac{74}{2}\)

\(n = 37\)

n = 37

The formula for finding the nth term(10th term):

\(a_{n} = a1 + (n - 1)d\)

n = 10, a1 = 36, d = -2

\(a_{10} = 36 + (10-1)(-2)\)

\(a_{10} = 36 + 9(-2)\)

\(a_{10} = 36 - 18\)

\(a_{10} = 18\)

\(a_{10}\) = 18

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Answer:

Third choice, 147

Step-by-step explanation:

Look at the bottom right angle, a straight line is 180 degrees, the line separating going on the line is at a 90 degree angle as there's a square that represents a right angle for the outer angle, the inner angle is also 90 as 90+90=180. A triangle is 180 degrees, all the equations plus 90 equals 180 so:

8x + 1 + 5x - 2 + 90 = 180

add like terms

13x + 89 = 180

subtract 89 from both sides

13x = 91

divide by 13

x = 7

Replace the equation the x in 5x - 2 to find angle 1, a straight line is 180 degrees so:

5x - 2 + ∠1 = 180

5(7) - 2 + ∠1 = 180

35 - 2 + ∠1 = 180

33 + ∠1 = 180

subtract 33 from both sides

∠1 = 147

Answer:

147

Step-by-step explanation:

(8x+1)+(5x-2)+90=180

add 5x + 8x and 1-2

13x-1+90=180

combine -1 and 90

13x+89=180

subtract 89 from both sides

13x=91

91÷13

=7

Then you want to solve for (5x-2)

plug in x (7)

5(7)-2

35-2

33

then subtract 33 from 180 to get angle one

180-33

=147

The lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches.

To find the total length of the two boards, you need to add their individual lengths together.

Step 1: Identify the length of each board. The first board is 234 inches long, and the second board is 246 inches long.

Step 2: Add the lengths of the boards together.

234 (length of first board) + 246 (length of second board) = 480

So, the total length of the two boards on the shelf is 480 inches. This means that if you were to place the two boards end-to-end, they would cover a distance of 480 inches.

In summary, by identifying the lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches. This calculation helps us understand the total amount of space the boards would occupy if placed side by side.

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Answer:

Distance ≈ 14.8

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 4, 6) and (x₂, y₂ ) = (3, - 7)

Hope this helps!!!!

Answer:

The answer is 648 miles.

Step-by-step explanation:

936miles= 13 hours

? = 9 hours

936/ 13 = 72

72miles in 1 hour

72 x 9 = 648

648 miles in 9 hours

A] 1/3

B] \(\frac{5}{10}\)×\(\frac{5}{9\\}\)=\(\frac{25}{90}\)=\(\frac{5}{18}\)

Answer:

2 + 6 + 2x + 6 > 74

x > 9

there are 312 cubic inches of wood left after cutting out a square hole with side lengths of 5 inches from a cube-shaped block with side lengths of 8 inches.

How to find the volume ?

To find the volume of the remaining wood, first find the volume of the cube-shaped block. To find the volume of a cube use V = s³ where s is the side of the cube. In this case, s = 8 inches, so V = 8³ = 512 cubic inches.

Then, find the volume of the hole using the side lengths of the hole and the same depth as the cube, which is 8 inches. The hole has side lengths of 5 inches, so its volume is V = 5² * 8 = 200 cubic inches.  

To find how much wood is left after cutting out the hole, subtract the volume of the hole from the volume of the cube:

512 - 200 = 312 cubic inches

Therefore, there are 312 cubic inches of wood left after cutting out a square hole with side lengths of 5 inches from a cube-shaped block with side lengths of 8 inches.

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Answer:

No

Step-by-step explanation:

22,54,8 and 112 aren't prime numbers.

The probability that a five-card poker hand does not contain the queen of hearts is 47/52.

We have been given that,

Total card to choose = 5

Total cards in a deck = 52

We need to find the probability that a five-card poker hand does not contain the queen of hearts.

The total ways of choosing 5 cards from a deck of 52 cards = \(^{52}C_5\)

The number of queens of hearts in a deck = 1

The number of cards excluding queens of hearts = 52 - 1

                                                                                  = 51

The total ways of choosing 5 cards from 51 cards = \(^{51}C_5\)

Now we find the required probability.

\(\Rightarrow P= ^{51}C_5 \times ^{52}C_5\\\\\Rightarrow P=\frac{51!}{5!(51-5)!} ~\times \frac{52!}{5!(52-5)!}\\\\\Rightarrow P=\frac{47}{52}\)

Therefore, the probability that a five-card poker hand does not contain the queen of hearts is 47/52.

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The correct formula for finding the present value of an investment is given by option D) PV = FV x 1/(1 + r)^n.

The present value (PV) of an investment is the current value of future cash flows discounted at a specified rate. The formula for calculating the present value takes into account the future value (FV) of the investment, the interest rate (r), and the number of periods (n).

Option D) PV = FV x 1/(1 + r)^n represents the correct formula for finding the present value. It incorporates the concept of discounting future cash flows by dividing the future value by (1 + r)^n. This adjustment accounts for the time value of money, where the value of money decreases over time.

In contrast, options A), B), and C) do not accurately represent the present value formula and may lead to incorrect calculations.

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There is enough proof to indicate that the percentage of newsletter readers who possess a Rolls Royce is less than 69%.

The null hypothesis is that p = 0.69, meaning that 69% of the newsletter readers own a Rolls Royce. The alternative hypothesis is that p < 0.69, meaning that less than 69% of the newsletter readers own a Rolls Royce.

We can use a one-tailed z-test to test the hypothesis. Assuming a sample size of n = 100, if we observe fewer than 69 Rolls Royces in our sample, we can reject the null hypothesis.

Using a z-test, we can calculate the z-score by using the formula:

z = (p' - p) / sqrt(p * (1 - p) / n)

where p' is the sample proportion, p is the hypothesized proportion, and n is the sample size.

At a significance level of 0.10, the critical z-value is -1.28. If the calculated z-score is less than -1.28, we can reject the null hypothesis.

If we conduct a survey of 100 newsletter readers and find that 58 of them own a Rolls Royce, the sample proportion would be p' = 0.58. Calculating the z-score, we get:

z = (0.58 - 0.69) / sqrt(0.69 * 0.31 / 100) = -1.83

Since -1.83 is less than -1.28, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that fewer than 69% of the newsletter readers own a Rolls Royce.

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Answer:

32 gallons of water

Step-by-step explanation:

If the total tank can hold up to 80 gallons of water, it is considered full when it contains 80 gallons. When the tank is 40% full, it has 40% of 80 gallons in the tank. 40% of 80 is 40/100*80=8*4=32 gallons of water.