help please

In triangle LMN, m∠L = (3c + 66)°. If the exterior angle to ∠L measures 72°, determine the value of c.


c = 72

c = 46

c = 14

c = 2

Answer:

8.35

Step-by-step explanation:

To get absolute value, just make it the opposite

Answer: |-8.35| = 8.35

Step-by-step explanation: |-8.35| = 8.35

To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Example: (2x - 4) x=7 so (2x (x=7) - 4) =18

The total volume of the original mixture is 4 liters.

Given that:

A mixture of 50% alcohol and 50% water has 4 liters of water added to it. It is now 25% alcohol.

Let 'x' be the amount of water and alcohol. Then we have

x / (x + x + 4) = 0.25

x/(x + 2) = 0.5

2x = x + 2

x = 2

The total volume of the original mixture is calculated as,

Total volume = x + x

Total volume = 2 + 2

Total volume = 4 liters

The total volume of the original mixture is 4 liters.

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Answer:

27

Step-by-step explanation:

easy

Answer:

22

Step-by-step explanation:

26=26

-4=4

26-4=22

The equation that represent the number of penguins is (6 ×  4) + (3 × 6) + (3 × 6) = p.

A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.

Therefore, the equation that can be used to find the total number of penguins living in the building is as follows:

Hence,

(6 ×  4) + (3 × 6) + (3 × 6) = p

where

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Answer:

The z-score for this data is Z = -0.26.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

This is based on knowledge that in the U.S., the mean PAL is 1.65 and the standard deviation is 0.55.

This means that \(\mu = 1.65, \sigma = 0.55\)

A study took a random sample of 51 people who lived in low income neighborhoods and found their mean PAL to be 1.63.

This means that \(n = 51, X = 1.63\)

Using a one-sample z test, what is the z-score for this data

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{1.63 - 1.65}{\frac{0.55}{\sqrt{51}}}\)

\(Z = -0.26\)

The z-score for this data is Z = -0.26.

Thus, the scale factor from circle A to circle B is found to be 2.

The ratio between comparable measurements of just an element and a portrayal of that element is known as a scale factor in mathematics. The copy will be larger if the scaling factor is a whole number. A fractional scaling factor means that the duplicate will be smaller.

You must first choose which direction we are scaling in order to determine the scale factor:

The radius of circle A = 2 units

The radius of circle B = 4 units.

So, there is a dilation with the scale factor of 2 units as 2*2 = 4 units.

Thus, the scale factor from circle A to circle B is found to be 2.

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Answer: f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Step-by-step explanation: Using the given recursive formula:

f(1) = 0

f(n) = f(n-1) + 2

We can find the values of f(n) for different values of n:

f(1) = 0

f(2) = f(1) + 2 = 0 + 2 = 2

f(3) = f(2) + 2 = 2 + 2 = 4

f(4) = f(3) + 2 = 4 + 2 = 6

f(5) = f(4) + 2 = 6 + 2 = 8

And so on.

We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:

f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Answer:

19 percent

Step-by-step explanation:

yw

Answer:

The awnser would be 899.5 since she had 300.50 but i think i might be wrong.

Step-by-step explanation:

Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

Answer:

\(\\(x- -1)^{2} + (y- -1)^{2} = 13\)

so, -1, -1 and 13

Answer:

it would take 360 minutes or 6 hours

Step-by-step explanation:

Answer:

6 hours

Step-by-step explanation:

3/4 of an hour is 45 mins, 45 minutes times 8= 360

Convert to hours and you get 6 hours.

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Answer:

The volume of the rectangular prism is 352 ft. The total surface area is 328 ft.

Step-by-step explanation:

Volume:

V = whl

V = 8 x 4 x 11

V = 352 ft

For finding surface area you have to find the lateral surface area: 152 ft, top surface area: 88 ft, and the bottom surface area: 88 ft. Add all that up and you get 328 ft.

Answer:

Step-by-step explanation:

The side opposite the 30 degree angle is always half of the hypotenuse in the 30,60,90 triangle so

h=2(6)

h=12

The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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Step-by-step explanation:

What we'll be using:

The integer rule.

Rule: When a positive number is being subtracted by a negative number, the negative number changes to a positive.

Implying the rule:

\(1 \frac{2}{3} + 5 \frac{2}{3}\)

Add:

\(1 \frac{2}{3} + 5 \frac{2}{3} = 7 \frac{1}{3} \)

Third option is correct.

20.25 square units are enclosed between the two curves.

To find the area enclosed between the two curves, find their intersection points first.

Setting the equations equal to each other:

8x² - x³ + x = x² + 13x

Simplifying and rearranging:

x³ - 7x² - 12x = 0

Factoring out x:

x(x² - 7x - 12) = 0

Solving for x using the quadratic formula:

x = 0, x = 3, x = -4

The two curves intersect at x = 0, x = 3, and x = -4.

Next, determine which curve is on top of the other between these intersection points. We can do this by comparing their y-values for each x:

At x = -4, y = 128

At x = 0, y = 0

At x = 3, y = 27

So, the curve y = 8x² - x³ + x is on top of y = x² + 13x for x in the range -4 ≤ x ≤ 0, and y = x² + 13x is on top of y = 8x² - x³ + x for x in the range 0 ≤ x ≤ 3.

Now find the area between the curves using integration:

∫[from -4 to 0] [(8x² - x³ + x) - (x² + 13x)] dx + ∫[from 0 to 3] [(x² + 13x) - (8x² - x³ + x)] dx

Simplifying:

∫[from -4 to 0] (-x³ + 7x² - 12x) dx + ∫[from 0 to 3] (x³ - 7x² + 12x) dx

Integrating:

[-(1/4)x⁴ + (7/3)x³ - 6x²] from -4 to 0 + [(1/4)x⁴ - (7/3)x³ + 6x²] from 0 to 3

Simplifying:

(64/3) + (81/4) - (27/3) - (64/3) = 20.25

Therefore, the area enclosed between the two curves is 20.25 square units.

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Image transcribed:

(1 point) Find the area of the region that is enclosed between y = 8x² - x³ + x and y = x² + 13x.

The area is

The statement that is true for ΔXYZ and ΔX''Y''Z'' is; 2: ΔXYZ and ΔX''Y''Z'' are congruent

We are told that;

- Triangle XYZ is rotated 90º clockwise about the origin to form triangle X'Y'Z'.

- Thereafter, reflected across the x-axis to form triangle X''Y''Z''

Now, in transformation, Reflection is flipping an object across a line without changing its size or shape while Rotation is rotating an object about a fixed point without changing its size or shape. Thus, it means that the size and shape of the triangle formed is not different from the original one.

Thus, we can say that both triangles are congruent because the shape and size didn't change.

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Answer:

14.75 feet below ground level.

Step-by-step explanation:

90.5-105.25=-14.75

Answer:

its 0.001

Step-by-step explanation:

Hope this helps :)

Answer:

0.001

Step-by-step explanation:

10^-3 = 0.001

You don't multiply since it's a negative power.

Ace

We can write a proportion.

44:3 = 12:m

~Simplify

44m = 36

~Divide 44 to both sides

m = 36/44 or 9/11 minutes

Best of Luck!

Answer: 0.818 minutes

Step-by-step explanation:

You would normally divide 44/3 to see how many plates are washed per minute, but if you reverse it, 3/44 then you will know how much time is spent washing each plate which is 0.068181. Multiply that by 12 and there’s your answer

Answer:

Subtotal 70.00

15% Tip 10.50

Total 80.50  

Step-by-step explanation:

1% 0.70

2% 1.40

3% 2.10

4% 2.80

5% 3.50

6% 4.20

7% 4.90

8% 5.60

% Tip

9% 6.30

10% 7.00

11% 7.70

12% 8.40

13% 9.10

The reason that the point (3, 5) is not a solution to the given inequality is given below.

We are given that;

y > 2x + 1

Now,

The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.

If we have (3,5) as a point, we can see that it lies on the boundary line

y = 2x + 1.

Since the inequality is strict (y >), points on this line are not solutions to the inequality

Therefore, by the inequality the answer will be given above.

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Answer:

Y=2x-5

Step-by-step explanation: