Answer each question as stated. Show each line of work for full
solutions. a) How many ways are there to form a lineup of 9
starting players out of 14 players? b) Solve: C(8,3) c) Convert to
Factorial

Answer:

\(174 cm^{2}\)

Step-by-step explanation:

There are two triangles and two rectangles in the figure.

To find the area of the triangles:

6 x 9 = \(54cm^{2}\)

To find the area of the rectangles:

9 x 8 = \(72cm^{2}\)

6 x 8 = \(48cm^{2}\)

Add all of this together for your answer:

54 + 72 + 48 = \(174cm^{2}\)

Answer:

-$0.26

Step-by-step explanation:

Calculation to determine the expected value of playing the game once

Expected value= [18/(18+18+2) x $5)]- [20/(18+18+2) x $5]

Expected value= ($18/38 x $5) - (20/38 x $5)

Expected value= ($2.37-$2.63)

Expected value= -$0.26

Therefore the expected value of playing the game once is -$0.26

Answer:

option A is correct

hope it helps :)

Step-by-step explanation:

The Standard Deviation Rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. It states that

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

Therefore, looking at the options, the true statement id

A) For a normal distribution, 99.7% of the distribution is within 3 standard deviations.

Answer:

y= 4/9x+136/9

Step-by-step explanation:

Write in slope-intercept form, y = mx = b

Answer:

Slope is = 4/9

And your point on the graph is x=0

Step-by-step explanation:

First, you are going to move the -12 to the other side of the equation by adding it to the other side like so...  y=4/9(x+7)+12

Secondly, you would multiply the 4/9 through the parenthesis Causing your answer to look like so... y = 4x/9 + 28/9 +12

Your next and final step is to add 12/1 (which is still equal to 12 it is just written in fraction form) to 28/9 which gives you y = 4x/9 + 118/9  

By following all of these steps you should be able to find that the slope is 4/9 and your point on the graph is x=0

Hope this helps:)

Please tell me if I have made any mistakes, I n=enjoy learning from them:)

Have a great rest of your day!!!

The value of μV is 40 cm³.

Given,The area of bottom of cylindrical container = 10 cm²The height of container = h = Mean height = 4 cm Standard deviation of height = σ = 0.2 cm We are supposed to find the mean volume of fluid in the container.In order to calculate the mean volume, first we need to calculate the volume of fluid in the container.Volume of a cylindrical container = πr²h Where, r is the radius of the base of the container.So, we need to calculate the value of r.The area of the bottom of the container is given as 10 cm².

We know that the area of the base of a cylinder is given as:Area of base of cylinder = πr² We are given that area of the base is 10 cm². So,10 = πr²r² = 10/πr = √(10/π) We can find the volume of fluid using the values we have.Volume of fluid = πr²h = π(√(10/π))² x 4 = 40 cm³We know that mean volume, μV is given as:μV = πr²μh So, we need to calculate the value of μh. We know that standard deviation σh is given as:σh = 0.2 cm So,μh = h = 4 cm So,μV = πr²μh = π(√(10/π))² x 4 = 40 cm³

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Answer:

Add 4x to both sides

Step-by-step explanation:

on Edge

Answer: -15 if I am wrong then -35

Answer:

-15

Step-by-step explanation:

-15 .hwushshshsjwo

The random variable X is the ounces of water in the bottle.

What is a random variable?

The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a sample space of potential outcomes to a measured space, frequently the real numbers.

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable is a numerical representation of the result of an experiment in statistics. Discrete random variables are those that can only take on a finite number or an infinite series of values.

Hence, According to the provided information, it is known that a bottle of water contains 12.05 fluid ounces; hence it is clear that the random variable X will be the ounces of water.

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complete question:

A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words.

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Step-by-step explanation:

I got 47.5 for this, not sure if its right though.

Answer:

slope: (1 ,-3)

y-intercept: -1

y = -3/1 -1

Step-by-step explanation:

hope it helps!

Answer:

16 problems.

Step-by-step explanation:

100% divided by 20 questions.

100/20 is equal to 5, therefore each question is worth 5 points.

Grade of 80% divided by points per question.

80/5 is 16 so the student answered 16 questions correctly.

Answer:

The equation is; A student got a grade of 80% on a test that has 20 problems.

1/20 = 5%

2/20 = 10%

3/20 = 15%

4/20 = 20%

5/20 = 25%

6/20 = 30%

7/20 = 35%

8/20 = 40%

9/20 = 45%

10/20 = 50%

11/20 = 55%

12/20 = 60%

13/20 = 65%

14/20 = 70%

15/20 = 75%

16/20 = 80%

As your final answer, as shown above, 16 is your final answer!

Step-by-step explanation:

I found out the answer by using fractions!

Hope this helps! :D      

(Can you mark me brainliest? It is greatly appreciated!)  

- ❤ 7272033Alt ❤

Answer:

-12-(-12) = (-12) + (-12)

Step-by-step explanation:

The best order of integration for the given double integral is integrating with respect to y first and then with respect to x. The result of the integral will be 60xy.

The given double integral is 60x. To determine the best order of integration, we need to evaluate the integral using both the row-first order and the column-first order and compare the results.

Let's first consider integrating with respect to x first and then with respect to y. The limits of integration for x will depend on the outer integral with respect to y. Since there is no information provided about the limits of integration, we cannot proceed with this order.

Now, let's consider integrating with respect to y first and then with respect to x. The limits of integration for y will depend on the outer integral with respect to x. However, since the given function is 60x, the integral with respect to y will yield 60x times the integral of 1 with respect to y, which simplifies to 60xy.

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12 km / 3 hours = 4 km in 1 hour

1 hour / 4 km = 1/4 hour per km

Answer: 1/4 hour to run 1 km

Answer:

1/4 hours=0.25 hours

Step-by-step explanation:

Ntate runs 12 km in 3 hours.

Ntate runs 1 km in 3/12=1/4 hours.

The increase in price (8.20%) is less than the interest she would have paid (12 payments of $7125), it seems that postponing her purchase and saving money was a good trade-off for Dorothy.

The APR (Annual Percentage Rate) for Dave's loan can be calculated

using the formula:

APR = ((Total interest + Service charge) / Principal) * 100

In this case, the total interest is $44.90 and the service charge is $6.40.

The principal is $600. Plugging these values into the formula:

APR = (($44.90 + $6.40) / $600) * 100

Simplifying the equation:

APR = ($51.30 / $600) * 100

APR = 8.55%

For Dorothy, if she bought the dishwasher on credit, the total cost would

be $855.00 after making 12 monthly payments of $7125.

However, if she saved $70.00 a month for one year, she would have

$898.80 in deposits plus interest.

When she goes back to the store, the dishwasher now costs $908.88,

which is an increase of 8.20%.

Since the increase in price (8.20%) is less than the interest she would

have paid (12 payments of $7125), it seems that postponing her purchase

and saving money was a good trade-off for Dorothy.

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Problem 1

Answers: Choice A, choice D

The formula you use is

a & c/d = (a*d+c)/d

To convert from mixed number form to improper fraction form.

So,

6 & 2/3 = (6*3+2)/3 = (18+2)/3 = 20/3

And also,

8 & 1/5 = (8*5+1)/5 = (40+1)/5 = 41/5

===============================================

Problem 2

Answer: Reflection

Think of how mirrors cause a reflection and this should help you remember the term better. If we reflect point A over some line L, to get point A', then the distance from A to L is the same from A' to L also.

Answer:

A=35, B=55, and C=25

Step-by-step explanation:

Angle A and the angle next to it are linear pairs, so you can subtract 145 from 180.

if you already know Angle A, and that the other angle is 90 degress, you can add 90+35 and subtract it from 180 to get Angle B

Angle C is paired with the angle across from it (I forgot what the term is called) so it is 25 degrees.

The pair of lines that are perpendicular to one another are Y=2/3x+4 and y=2/3x

Any point on this line will be a point on the perpendicular transversal that intersects the line y=4/3x+1/3 at a right angle.

Let's take the example of the two lines given in the question: Y=2/3x+4 and y=2/3x-8. We can rewrite these equations in the slope-intercept form y=mx+b, where m is the slope and b is the y-intercept.

The slope of the first line is 2/3, and the slope of the second line is also 2/3. To determine if they are perpendicular, we need to find the product of their slopes:

(2/3) x (2/3) = 4/9

Since the product of their slopes is not equal to -1, these two lines are not perpendicular.

To find the slope of the perpendicular line, we need to use the fact that the product of the slopes of two perpendicular lines is -1. Therefore, the slope of the perpendicular line will be the negative reciprocal of the slope of the parallel line:

slope of parallel line = 4/3

slope of perpendicular line = -3/4

Now we can use the point-slope form of the equation of a line to find the equation of the perpendicular transversal. We are given a point Q(5,1) that is on the perpendicular transversal, and we know the slope of the line is -3/4. Therefore, the equation of the perpendicular transversal is:

y - 1 = (-3/4) (x - 5)

Simplifying this equation gives:

y = (-3/4)x + (19/4)

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The limit 9/4 is greater than 1, the series

\(\(\sum_{n=1}^{\infty} \frac{9^{n}}{(n+1) 4^{2 n+1}}\)\)  diverges by the Ratio Test.

To determine the convergence or divergence of the series,

\(\(\sum_{n=1}^{\infty} \frac{9^{n}}{(n+1) 4^{2 n+1}}\)\), we can use the Ratio Test.

The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. If the limit is greater than 1 or infinite, then the series diverges. If the limit is exactly 1, the test is inconclusive.

Let's denote aₙ as the nth term of the series:

\(\[a_n = \frac{9^n}{(n+1)4^{2n+1}}\]\)

Now, let's calculate the limit of the ratio

\(\(\lim _{n \rightarrow \infty} \frac{a_{n+1}}{a_n}\):\)

\(\[\lim _{n \rightarrow \infty} \frac{a_{n+1}}{a_n} = \lim _{n \rightarrow \infty} \frac{\frac{9^{n+1}}{(n+2)4^{2(n+1)+1}}}{\frac{9^n}{(n+1)4^{2n+1}}}\]\)

Simplifying the expression:

\(\[\lim _{n \rightarrow \infty} \frac{9^{n+1}}{(n+2)4^{2(n+1)+1}} \cdot \frac{(n+1)4^{2n+1}}{9^n}\]\)

\(\[\lim _{n \rightarrow \infty} \frac{9^{n+1}}{(n+2)9^n} \cdot \frac{(n+1)4^{2n+1}}{4^{2(n+1)+1}}\]\)

\(\[\lim _{n \rightarrow \infty} \frac{9^n \cdot 9}{(n+2)9^n} \cdot \frac{(n+1)4^{2n+1}}{4^{2n+2} \cdot 4}\]\)

\(\[\lim _{n \rightarrow \infty} \frac{9}{n+2} \cdot \frac{n+1}{4 \cdot 4} = \frac{9}{4} \lim _{n \rightarrow \infty} \frac{n+1}{n+2}\]\)

As n approaches infinity, the limit becomes:

\(\[\frac{9}{4} \cdot 1 = \frac{9}{4}\]\)

Therefore, the series is divergent.

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Complete Question:

Use the Ratio Test to determine whether the series is convergent or divergent.\(\(\sum_{n=1}^{\infty} \frac{9^{n}}{(n+1) 4^{2 n+1}}\)\) and evaluate the following limit \(\(\lim _{n \rightarrow \infty} \frac{a_{n+1}}{a_n}\):\)

Answer:

M(3/2, -1)

Step-by-step explanation:

\((\frac{x_1+y_1}{2},\frac{x_2+y_2}{2})\\ \\(\frac{-8+11}{2},\frac{-7+5}{2})\\\\(\frac{3}{2},\frac{-2}{2})\\\\(\frac{3}{2},-1)\)

Therefore, the midpoint between P(-8, -7) and K(11,5) is M(3/2, -1)

Answer: 16,384

Step-by-step explanation:

The seven marbles have different colours, so we can differentiate them.

Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.

For the first marble, we have 4 options ( we have 4 jars)

For the second marble, we have 4 options.

Same for the third, for the fourth, etc.

Now, the total number of combinations is equal to the product of the number of options for each selection.

We have 7 selections and 4 options for each selection, then the total number of combinations is:

C = 4^7 = 16,384

Answer:

the answer is 16384

Step-by-step explanation:

have a nice day.

The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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Answer:

i think its A cs its the most reasonable one

Step-by-step explanation:

sorry if its wrong

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Sample mean(x) = 23500

Sample standard deviation (sd) = 3900

Sample size (n) = 20

Population mean (m) = 20,000

Null hypothesis : m = 20000

H1: m > 20000

To obtain the z-score :

(population mean - sample mean) / (sample standard deviation /√sample size)

(x - m) / (sd/√n)

(23500 - 20000) / (3900 / √20)

3500 / (3900 /4.4721359)

3500 / 872.06651

= 4.0134

Get the P value to know if to reject or accept the null:

P(z > 4.0134) = 1 - P(z < 4.0134)

P(z < 4.0134) = 1

1 - P(z < 4.0134) = 1 - 1 =0

Since P value is < alpha, we reject the null.

Hence average is > 20000

The exponential functions for the two scenarios given are -

a) \(y = 12500 (0.91)^x\), Price of car after 5 years is $7800.40.

b) \(y = 50 (1.03)^x\), Price of baseball card after 5 years is $57.96.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The exponential function is in the form -

\(y=ab^x\)

Here y is the function, a is the constant base value, b is the rate of growth/depreciation and x is the time in years.

The first statement is -

A $12,500 car depreciates 9% each year.

The value for base is a = $12,500.

The value for rate is 9% = 0.09

Since, the price is depreciating the value for b is b = (1 - 0.09)

The exponential function is -

\(y = 12500 (1 - 0.09)^x\)

\(y = 12500 (0.91)^x\)

The value of car after 5 years can be obtained by substituting x = 5.

\(y = 12500 (0.91)^5\\y = 12500(0.6240)\\y=7800.40\)

Therefore, the equation is \(y = 12500 (0.91)^x\) and the value of car is $7800.40.

The second statement is -

A baseball card brought for $50 increases 3% in value each year.

The value for base is a = $50.

The value for rate is 3% = 0.03

Since, the price is increasing the value for b is b = (1 + 0.03)

The exponential function is -

\(y = 50 (1+0.03)^x\)

\(y = 50 (1.03)^x\)

The value of baseball card after 5 years can be obtained by substituting x = 5.

\(y = 50 (1.03)^5\\y = 50 (1.1592)\\y =57.96\)

Therefore, the equation is \(y = 50 (1.03)^x\)and the value of baseball card is $57.96.

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Answer:this is for part c I think?

Step-by-step explanation:

David walks 10 dogs, because if he earns a dollar for each dog he walked that means he walked 10 to earn 10 dollars. I’m not good with sentences so I’m sorry if you do not understand.

The juice is 27 and the tornadoes are 21.

An equation is a mathematical statement that shows that two expressions are equal by using an equal sign (=). Equations are used to find the value of an unknown variable or to show the relationship between variables.

We know that the number of the juice and the tornadoes can be x and y

We then have that;

5x + 3y = 24 ----- (1)

4x + 2y = 30 ----- (2)

Multiply equation 1 by 4 and equation 2 by 5 we have that;

20x + 12y = 96 ---- (3)

20x + 10y = 150 ----- (4)

Subtract (3) from (4)

-2y =54

y = -27

Then;

5x + 3(-27) = 24

x = 21

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