Directions: Evaluate the following combinations and determine the value of the
unknown. Write the complete solutions in your answer sheet.
1. nCs = 126
2. 10Cr= 252
3. C(n, 5) + 8 = 9
4. C(n+1, 7) = 01
5. C(6r, 6-1) = 12 + C(4,2)




what is the answer with solution po​

Answer:

C) 3.61 units

Step-by-step explanation:

5 - 3 = 2

7 - 4 = 3

distance²  = 2² + 3³ = 4 + 9 = 13

distance = √13 = 3.61

Answer:

x=5

Step-by-step explanation:

Area of triangle=1/2 * b * h

In this case b=10, h=x, and A=25

By substituting values in we can say:

[tex]A=\frac{1}{2} * b *h\\25=\frac{1}{2} * 10 * x\\25=5x\\x=5[/tex]

Answer:

0.0625

Step-by-step explanation:

Hope this helps :)

Have a nice day <3

Answer:

1/16

Step-by-step explanation:

Just multiply all numerators and all denominators: 1x1x1x1/2x2x2x2. That gives you your total of 1/16.

Answer:

To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.

Step-by-step explanation:

Answer:

10 hours (I am not positive)

Step-by-step explanation:

We first want to find the volume of pool which is 30 x 18 x 4 = 2160.

Then you are going to divide by 216 to find how many hours it takes to drain the whole pool. (I'm not that big of an expert)

Answer:

-5 cos (2x)

Step-by-step explanation:

Reflection over x axis just means "multiply by -1" so the answer is

f(x) = 5 cos (2x)

g(x) = -5 cos (2x)

Answer:

c. 42°

Step-by-step explanation:

two interior angles= one exterior angle

let x be the other interior angle

90° + x=132°

x=132-90

x=42°

Answer:

the last one

Answer:

1 cubic inch

Step-by-step explanation:

For rectangular prism:

[tex]l = 4 \times \frac{1}{2} = 2 \: in \\ \\ w= \frac{1}{2} \: in \\ \\ h = 2 \times \frac{1}{2} = 1 \: in \\ \\ volume \: of \: prism = lbh \\ = 2 \times \frac{1}{2} \times 1 \\ = 1 \: {in}^{3} [/tex]

Answer: The volume is 1 cubic inch.

Step-by-step explanation:

Volume of 1 cube

V= l*w*h

V= 1/2*1/2*1/2

V= 1/8 or 0.125

Volume of Prism

8*1/8= 1

This is a 30-60-90 right triangle.

In this special triangle, opposite 60 degrees = sqrt{3}. Thus, x = sqrt{3}.

Answer:

B) A herd of lions whose numbers triple every decade.

Step-by-step explanation:

Situations that can be modeled by exponential functions:

A situation can be modeled by exponential functions when the change is a multiplication or a division, not a sum or subtractions.

In this question:

In option A, C and D the measures are a sum or subtractions, as the rate of change is always the same. So it rests option B as the answer, as tripling is multiplying by 3.

Answer: there is a correlation between a number of songs downloaded. there may or may not be causation. further studies would ave to be done to determine this.

Step-by-step explanation:

Answer:

There is a correlation between number of CDs purchased and number of songs downloaded. There may or may not be causation. Further studies would have to be done to determine this.

Step-by-step explanation:

A music store conducted a survey. It showed that the number of CDs purchased by a shopper decreases with the number of songs she downloaded. What can we likely say?

Answer:

it is likely because the majority of the outcomes are in your favor

Answer:

A

Step-by-step explanation:

Impossible, did it on usatestprep

Answer:

-4

Step-by-step explanation:

Answer:

B. $104.95

Step-by-step explanation:

$160.45-$55.50=$104.95

Answer:

If you think numbers with fractions are annoying, consider transforming the number into fractions!

Step-by-step explanation:

7 1/2 is (14+1)/2, and 3 1/8 is (24+1)/3. Not you have 15/2 miles for 25/3 days and by dividing them you get 0.9 miles a day

Answer:

(x - 2) (x^2 + 3)

Step-by-step explanation:

x^3-2x^2+3x-6

Factor by grouping

Answer:

Factor by grouping

Step-by-step explanation:

[tex]x^{3}-2x^{2} +3x-6[/tex]

[tex]x^{2} (x-2) + 3 (x-2)[/tex]

[tex](x^{2} +3)(x-2)[/tex]

Answer:

C,D,E

Step-by-step explanation:

Answer:

25π or 78.5mm²

Step-by-step explanation:

[tex]A=3.14*5^{2} \\ =3.14*25\\ =78.5[/tex]

Answer:

Step-by-step explanation:

The formula for the area of a circle is

A = π*r²

Now we can rewrite with the radius. *Note* I am using 3.14 for pi to make it easier*

A = π*5²

Solve

5² = 25

25 * 3.14 = 78.5

Now since the measurements were done in millimeters, we will add mm to the end.

Also since it is area, we need to add ²

78.5 mm²

Answer:

108

Step-by-step explanation:

Answer:

Mean x¯¯¯ 5.8888888888889

Median x˜ 6

Mode 7

Range 3

Minimum 4

Maximum 7

Count n 9

Sum 53

Quartiles Quartiles:

Q1 --> 5

Q2 --> 6

Q3 --> 7

Interquartile

Range IQR 2

hope i helped:) can u plz mark me brainlest

Answer:

the mean is 5.88888888889

Step-by-step explanation:

to find the mean, add all the data results together and divide by how many results you have.  

for example:  5+4+5+7+7+7+5+7+6= 53

53 divided by 9= 5.88888888889

have a good day

Answer:

G) y ≥ 1

Step-by-step explanation:

Range is all the y-values seen on the graph.

Since it starts at (0, 1), the lines just keep increasing so:

y ≥ 1

Answer: c

Step-by-step explanation:

9514 1404 393

Answer:

  (x1, x2) = (3, -4)

Step-by-step explanation:

As with any 2-step linear equation, subtract the constant, then multiply by the inverse of the coefficient of the variable.

  [tex]\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]+\left[\begin{array}{c}1\\2\end{array}\right]=\left[\begin{array}{c}2\\-3\end{array}\right]\\\\\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}1\\-5\end{array}\right]\\\\\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{5}\left[\begin{array}{cc}5&-2\\-5&3\end{array}\right]\left[\begin{array}{c}1\\-5\end{array}\right][/tex]

Performing the multiplication of the matrix by the vector gives the solution.

  x = ((5)(1) +(-2)(-5))/5 = 15/5 = 3

  y = ((-5)(1) +(3)(-5))/5 = -20/5 = -4

Using your variables, x1, x2, the solution is ...

  (x1, x2) = (3, -4)

Answer:

1/12

Step-by-step explanation:

He has a 1/4 pan left and wants to divide that into 3 equal pieces. So in night he will eat 1/3 of what he has left from the 1/4 pan. To figure out how much one slice is from an entire pan:

1/4 * 1/3  = 1/12

Answer:

Step-by-step explanation:

Answer:

x=16, y=-4

Step-by-step explanation:

-1(x-y=12)

x+7y=-20

-x+y=-12

x+7y=-20

8y=-32

y=-4

x-4=12

x=16

Answer:

x= 8, y= -4

Step-by-step explanation:

You can subtract one equation by another to eliminate x

(x-y)-(x+7y)=12-(-20)

-8y = 32

y= -4

Substitute y =  -4 in the first equation:

x-(-4) = 12

x =8

Answer:

122

Step-by-step explanation:

122 + 58 = 180

Answer:

x=122°

Step-by-step explanation:

58° and x form a straight angle, which is 180°.

x+58°=180°

x=180°-58°=122°

Answer:

The pvalue of the test is 0.0784 > 0.01, which means that at this significance level, we do not reject the null hypothesis that the percentage of blue candies is equal to 29%.

Step-by-step explanation:

The candy company claims that the percentage of blue candies is equal to 29%.

This means that the null hypothesis is:

[tex]H_{0}: p = 0.29[/tex]

We want to test the hypothesis that this is true, so the alternate hypothesis is:

[tex]H_{a}: p \neq 0.29[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.29 is tested at the null hypothesis:

This means that [tex]\mu = 0.29, \sigma = \sqrt{0.29*0.71}[/tex]

Suppose that in a random selection of 100 colored candies, 21% of them are blue.

This means that [tex]n = 100, X = 0.21[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.21 - 0.29}{\frac{\sqrt{0.29*0.71}}{\sqrt{100}}}[/tex]

[tex]z = -1.76[/tex]

Pvalue of the test:

The pvalue of the test is the probability of the sample proportion differing at least 0.21 - 0.29 = 0.08 from the population proportion, which is 2 multiplied by the pvalue of Z = -1.76.

Looking at the z-table, z = -1.76 has a pvalue of 0.0392

2*0.0392 = 0.0784

The pvalue of the test is 0.0784 > 0.01, which means that at this significance level, we do not reject the null hypothesis that the percentage of blue candies is equal to 29%.