If AB = 2x-16, BC = 3x -19, and AC = 30, find the values of x, AB, and BC.

Using the table your total monthly fixed expenses is 977.43.

Rent payment $953. 20/month

Auto payment $165. 87/month

Telephone $56. 98/month

Auto insurance $714. 36/six months

Once-a-week outing $35. 00/week

= 953.20 + 165.87 + 56.98 + 714.36/6 + (35*4)

= 1435.11

= 2412.54 - 1435.11

=977.43.

An expense is something that calls for the transfer of funds, or fortune in general, from one person or organization to another as payment for a good, service, or other type of cost. Rent is a cost to a tenant. Tuition is a cost to parents or students. Purchasing anything like food, clothing, furniture, or a car is frequently referred to as a cost.

A cost that is "paid" or "remitted" usually in exchange for anything of value is referred to as an expense. "Expensive" refers to something that appears to be very expensive. "Inexpensive" refers to something that appears to be inexpensive. "Expenses of the table" include costs associated with eating, drinking, a feast, etc.

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\(_{12}C_4=\dfrac{12!}{4!8!}=\dfrac{9\cdot10\cdot11\cdot12}{2\cdot3\cdot4}=495\)

The convergence or divergence of the series  Σ \((-4)^n * n^2\) cannot be determined using the Ratio Test alone. Alternating Series Test or Comparison Test, may be needed.

To determine the convergence or divergence of the series Σ \((-4)^n * n^2\) using the Ratio Test, we need to examine the limit of the absolute value of the ratio of consecutive terms:

lim (n→∞)\(|((-4)^(n+1) * (n+1)^2) / ((-4)^n * n^2)|.\)

Simplifying this expression, we have:

lim (n→∞) |\((-4)^(n+1)\) * (n+1)² / \((-4)^n * n^2\)|.

Using the properties of exponents, we can rewrite this expression as:

lim (n→∞) |(-4) * (n+1)² / (-4) * n²|.

Canceling out the common factors, we have:

lim (n→∞) |(n+1)² / n²|.

Expanding the numerator and denominator, we get:

lim (n→∞) |(n² + 2n + 1) / n²|.

As n approaches infinity, the terms 2n and 1 become insignificant compared to n². Therefore, we can neglect them in the limit:

lim (n→∞) |n²/ n²| = lim (n→∞) 1 = 1.

Since the limit is equal to 1, the Ratio Test is inconclusive. The test does not provide definitive information about convergence or divergence.

Therefore, we cannot determine the convergence or divergence of the series Σ \((-4)^n * n^2\) using the Ratio Test alone. Additional tests, such as the Alternating Series Test or Comparison Test, may be necessary to establish convergence or divergence.

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Answer is 41

Hope it help you

Answer:

I dont need

Step-by-step explanation:

what to convert

Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

To find the probability that the mean salary of a person selected at random from Acme Corporation is less than 61,000, we can use the Z-score formula.

First, we need to calculate the Z-score, which measures the number of standard deviations a value is away from the mean. The formula for the Z-score is:

Z = (X - μ) / (σ / √n)

Where:
- X is the value we are interested in (in this case, $61,000)
- μ is the population mean annual salary for Acme Corporation ($63,500)
- σ is the population standard deviation (unknown in this case)
- n is the sample size (unknown in this case)

Since we don't have the population standard deviation or sample size, we cannot calculate the exact Z-score. Therefore, we cannot find the exact probability.

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Based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

The probability of a person selected at random having a salary less than $61,000 can be determined using the z-score and the standard normal distribution.

To calculate the z-score, we need to know the population standard deviation. Since it is not provided, we cannot calculate the exact probability. However, we can use the assumption that the population standard deviation is the same as the sample standard deviation.

Let's assume the sample standard deviation is $5,000.

First, we calculate the z-score:
    \(z = (x - \mu) / (\sigma / \sqrt n)\)
=> z = (61000 - 63500) / (5000 / √1)
=> z = -2500 / 5000
=> z = -0.5

Next, we find the corresponding area under the standard normal curve using a z-table or a calculator. The area to the left of -0.5 is approximately 0.3085.

Therefore, the probability that a person selected at random will have a salary less than $61,000 is approximately 0.3085 or 30.85%.

In conclusion, based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

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Answer:

C. Points L,J and K are collinear.

Step-by-step explanation:

Collinear points are points that lie on the same line. So in the picture only the points L,J and K are collinear.

Answer:

I think l j and k but I might be wrong.

Step-by-step explanation:

Answer:

-98

Step-by-step explanation:

I hope this help

The cost of x servings of dressing in dollars will be $0.43x.

According to the question,

We have the following information:

Each serving of salad dressing uses 3 tablespoons of olive oil and 1 tablespoon of vinegar.

Cost of 1 tablespoon of olive oil = $0.13

Cost of 1 tablespoon of vinegar = $0.04

So,

The cost of each serving of salad = Cost of 3 tablespoons of olive oil + cost of 1 tablespoon of vinegar

The cost of each serving of salad = 3*0.13 + 0.04

The cost of each serving of salad = $(0.39+0.04)

The cost of each serving of salad = $0.43

Now,

The cost of x servings of salad = $0.43x

(Note that if we have to find the cost of more than 1 product than the number has to be multiplied with the cost of one product.)

Hence, the cost of x servings of salad dressing is $0.43x.

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The derivative of the given function F(x) = x^(4/5) * (x-5)^2

F'(x) = u'v + uv' = (4/5)x^(-1/5)(x-5)^2 + x^(4/5) * 2(x-5)

This is the derivative of the given function.

To find the derivative of the given function F(x), we can use the product rule of differentiation. The product rule states that if we have two functions f(x) and g(x), then the derivative of their product is given by:

(fg)'(x) = f'(x)g(x) + f(x)g'(x)

In this case, we can let f(x) = x^4/5 and g(x) = (x-5)^2. Then, we have:

F(x) = f(x)g(x) = x^4/5 (x-5)^2

Using the product rule, we can find the derivative of F(x) as follows:

F'(x) = f'(x)g(x) + f(x)g'(x)
      = (4/5)x^-1/5(x-5)^2 + x^4/5(2(x-5))
      = 4x^-1/5(x-5)^2 + 2x^9/5 - 10x^6/5

Therefore, the derivative of the given function F(x) is:

F'(x) = 4x^-1/5(x-5)^2 + 2x^9/5 - 10x^6/5

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The mean is 7.50. The median is 8. The mode is 9. The distribution is negatively -skewed.

The sample of scores:

9, 6, 7, 10, 7, 9, 9, 7, 9, 4, 9, 8, 3, 6, 8, 9

The sample contains 16 values. i.e., n = 16.

Sum of the values = 9 + 6 + 7 + 10 + 7 + 9 + 9 + 7 + 9 + 4 + 9 + 8 + 3 + 6 + 8 + 9 =  120

Mean of the sample = sum of the values/n

                                 =  120/16

                                 = 7.50

The median is the middle-most value of the sample of scores arranged in a descending order.

So, 3,4, 6,6,7,7,7,8,8,9,9,9,9,9,9,10 is the ordered sample.

Since there are 16 scores, which is even, the median is the mean of the two middle values.

i.e., Median = 8 +8 /2 = 8

Mode of a sample of values is the most repeated or frequent score in the sample.

Since 9 is repeated 6 times, the mode = 9.

Here, mean is less than median.

So the distribution is negatively-skewed. That is the shape of the distribution will have more than half of  the area to the left.

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Answer:

its 4,000

Step-by-step explanation:

Simon's target number of laps will be 80.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, his coach tells him to swim a target number of laps and Simon swims 45 laps before practice is canceled due to a thunderstorm. Simon still has 35 laps left to reach his target number

Let the target number be x. This will be:

x - 45 = 35

x = 45 + 35

x = 80.

The Target number is 80

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Answer:

architect because they need to determine the length, width, and height of objects, they need to use area to see if there's enough space for what they want to build, etc.

Step-by-step explanation:

Answer:

12:00 am midnight

Step-by-step explanation:

Given;

I can read a 336-page book in 6 hours.

My rate r1 = 336/6 pages per hour = 56 pages per hour

Jayne can read a 144-page book in 3 hours.

Jayne rate r2 = 144/3 = 48 pages per hour

If I start reading a 5000-page book at noon and Jayne starts reading the same book at 10 AM

Taking 10 am as the reference time.

Let x represent the time from 10 am at which they would both be on the same page.

For me;

Since i started by noon; 2 hours after 10 am

Time t1 = x-2

For Jayne;

She started by 10 am

Time t2 = x

For them to be on the same page they must have read the same number of pages;

Number of pages read = rate × time

r1(t1) = r2(t2)

Substituting the values;

56(x-2) = 48(x)

56x - 112 = 48x

x(56-48) = 112

x = 112/(56-48)

x = 14 hours

Since 10 am is the reference, the time would be;

=10 am + x = 10 am + 14 hours

= 24:00

= 12:00 am midnight

Answer:

4x+10

Step-by-step explanation:

3x *4x=12x²,so you can know the next

Answer:

h = 4x+10

Step-by-step explanation:

a = b(h)

h = a/b

Sub:

a = 12x^2 + 38x + 20

b = 3x + 2

12x^2 + 38x + 20 = 3x + 2 * h

Rewrite:

h = 12x^2 + 38x + 20 / 3x + 2

Solve:

2(3x+2)(2x+5)  / 3x+2

2(2x+5) = 4x + 10

Answer:

Step-by-step explanation:

The slope is 2 so rise / run = 2 / 1, or up two right one.

There are 848 different combinations of games that you can attend if you want to go to at least 4 games out of the 10 scheduled games.

If you want to attend at least 4 games out of the 10 scheduled games, there are several different combinations that you can attend.

To calculate the total number of combinations, we can use the combination formula

nCr = n! / r! × (n-r)!

where n is the total number of games (10), and r is the number of games you want to attend (4).

First, let's calculate the number of combinations of attending exactly 4 games

10C4 = 10! / 4! × (10-4)! = 210

This means that there are 210 different combinations of attending exactly 4 games out of the 10 scheduled games.

Next, let's calculate the number of combinations of attending 5, 6, 7, 8, 9, or all 10 games

10C5 = 10! / 5! × (10-5)! = 252

10C6 = 10! / 6! × (10-6)! = 210

10C7 = 10! / 7! × (10-7)! = 120

10C8 = 10! / 8! × (10-8)! = 45

10C9 = 10! / 9! × (10-9)! = 10

10C10 = 10! / 10! × (10-10)! = 1

So the total number of different combinations of attending at least 4 games is

210 + 252 + 210 + 120 + 45 + 10 + 1 = 848

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Answer:

hypotenuse —>26

Legs —> 10 and 24

Step-by-step explanation:

Generally ,the hypotenuse is the longest side .

So in our triangle the hypotenuse is of length 26.

Consequently, the legs are of lengths 24 and 10.

Also ,we can verify that this is right triangle using the Pythagorean theorem:

26^2 = 676

24^2+10^2 = 676

Then

26² = 24²+10².

Using it's concept, it is found that the vertical asymptotes of the function \(f(x) = \frac{x + 2}{x^2 - 3x - 4}\) are given by:

In this problem, the function is:

\(f(x) = \frac{x + 2}{x^2 - 3x - 4}\)

The denominator is \(x^2 - 3x - 4\), which is a quadratic function with coefficients \(a = 1, b = -3, c = -4\), hence, it's roots are found as follows.

\(\Delta = b^2 - 4ac = (-3)^2 - 4(1)(-4) = 25\)

\(x_{1} = \frac{-(-3) + \sqrt{25}}{2} = 4\)

\(x_{2} = \frac{-(-3) - \sqrt{25}}{2} = -1\)

Hence, the asymptotes are x = 4 and x = -1.

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Answer:

x=4 and x=-1

Step-by-step explanation: hope this helps

To compute the z-score for each observation, we need to standardize the data using the formula z = (x - μ) / σ, where x is the individual observation, μ is the mean of the sample, and σ is the standard deviation of the sample.

Given the sample observations: 16, 11, 13, 22, 15, and 19, we can calculate the z-score for each observation as follows:

Calculate the mean (μ) of the sample:

μ = (16 + 11 + 13 + 22 + 15 + 19) / 6 = 16

Calculate the standard deviation (σ) of the sample:

Step 1: Calculate the squared deviations from the mean for each observation:

(16 - 16)², (11 - 16)², (13 - 16)², (22 - 16)², (15 - 16)², (19 - 16)²

0, 25, 9, 36, 1, 9

Step 2: Calculate the variance:

Variance = (0 + 25 + 9 + 36 + 1 + 9) / 6 = 80 / 6 ≈ 13.33

Step 3: Calculate the standard deviation:

σ = √(Variance) = √13.33 ≈ 3.65

Calculate the z-score for each observation:

z = (x - μ) / σ

For 16: z = (16 - 16) / 3.65 = 0 / 3.65 = 0

For 11: z = (11 - 16) / 3.65 = -5 / 3.65 ≈ -1.37

For 13: z = (13 - 16) / 3.65 = -3 / 3.65 ≈ -0.82

For 22: z = (22 - 16) / 3.65 = 6 / 3.65 ≈ 1.64

For 15: z = (15 - 16) / 3.65 = -1 / 3.65 ≈ -0.27

For 19: z = (19 - 16) / 3.65 = 3 / 3.65 ≈ 0.82

The z-scores for the given sample observations are: 0, -1.37, -0.82, 1.64, -0.27, and 0.82.

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Answer:

Infinity

Step-by-step explanation:

Look it up, its how it works. 0 can go into 3.2 infinity times.

Answer:

5 dollars a week

Step-by-step explanation:

18-3=15

15/3=5

La ecuación de la recta es y = 1.2x + 0, o simplemente y = 1.2x. Y el precio en euros de 10 dólares es de 12 €.

La ecuación de la recta que nos da el precio en euros, y, de x dólares se puede hallar utilizando la fórmula de la pendiente de una recta, que es m = (y2 - y1) / (x2 - x1). En este caso, los puntos dados son (3, 3.6) y (7, 8.4).

Primero, calculamos la pendiente de la recta:
m = (8.4 - 3.6) / (7 - 3)

m = 4.8 / 4

m = 1.2

Luego, utilizamos la fórmula de la ecuación de la recta, y = mx + b, para encontrar el valor de b. Podemos utilizar cualquiera de los puntos dados para esto. Usaremos el punto (3, 3.6).

3.6 = 1.2(3) + b
3.6 = 3.6 + b
b = 0

Por lo tanto, la ecuación de la recta es y = 1.2x + 0, o simplemente y = 1.2x.

Esta ecuación nos da el precio en euros, y, de x dólares. Si queremos encontrar el precio en euros de una cierta cantidad de dólares, simplemente sustituimos el valor de x en la ecuación y resolvemos para y. Por ejemplo, si queremos encontrar el precio en euros de 10 dólares, sustituimos x = 10 en la ecuación:

y = 1.2(10) = 12

Por lo tanto, el precio en euros de 10 dólares es de 12 €.

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Answer:

65

Step-by-step explanation:

5% = 0.05

0.05 x 1300 = 65

Answer:

LCM = 27,720

Step-by-step explanation:

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