What is the fourth term in the binomial expansion of (2x – y) 7?

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Let's think of our original price ($P) as 100%. This is also the same thing as 1 because 100% is one whole thing.

Now, we see that he got a 15% off discount. Now, we just subtract 15% from 100% to see what percent he actually payed.

100%-15%=85%

This means that $R is 85% of $P (100%).

Answer A is not correct because 0.85% is less than 1%, which is not 85%.

Answer B is not correct either because 0.15% is also less than 1%.

Answer C is correct because $R is 85% of the original cost.

I hope that this helps! Have a wonderful day!

Answer:

x = -1

Step-by-step explanation:

32(-1)+20=28(-1)-16(-1)

-32+20=-28+16

-12=-12

Answer:

it is option A bro

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Answer:

Step-by-step explanation:

Given

height of the pine cone above the ground can be modelled by

[tex]h=-16t^2+40[/tex]

When pine cone reaches the ground [tex]h=0[/tex]

[tex]\Rightarrow 0=-16t^2+40[/tex]

[tex]\Rightarrow 40=16t^2[/tex]

[tex]\Rightarrow t=\sqrt{\frac{40}{16}}[/tex]

[tex]\Rightarrow t=\frac{\sqrt{40}}{4}[/tex]

[tex]\Rightarrow t=\frac{2\sqrt{10}}{4}[/tex]

[tex]\Rightarrow t=\frac{\sqrt{10}}{2}[/tex]

[tex]\Rightarrow t=1.58\ s[/tex]

Thus cone take 1.58 s to reach ground

Answer:

13/50; 13/50

Step-by-step explanation:

a): Theoretical=# of favorable outcomes/# of total outcomes

To find the total, add 21+26+25+28, which is 100

A has a frequency of 26.

That would be 26/100, which is also 13/50

b): Experimental probability is based on the amount of times the spinner is spun. Since A is the only vowel in "MATH", we would take that fraction and multiply it by 100, or the number of times.

13/50*100=13*2=26

Put that over 100, which would be 26/100, which is also 13/50.

Hope this helped! Have a good rest of your day!

Answer:

The value of the intercept is a=216.

Step-by-step explanation:

We define "s" as the number of scarecrows and "C" the number of crops eaten.

The farmer finds the linear regression equation:

[tex]C=a-0.8s[/tex]

We have a linear function, for which we only know the slope (m=0.8) and a point within it (when s=20, C=200).

We can find a replacing the variables C asn s with the known point (20, 200):

[tex]C=a-0.8s\\\\C(20)=a-0.8(20)=200\\\\a=200+0.8*20=200+16\\\\a=216[/tex]

The value of the intercept is a=216.

Answer:

Project B is preferable solely from the standpoint of expected monetary return.

Step-by-step explanation:

Calculations of Expected Returns:

Project A:

Net Profits             Probability          Expected Returns:

GHȼ 20,000.00    0.2                      GHȼ 4,000

GHȼ 30,000.00    0.4                      GHȼ 12,000

GHȼ 50,000.00    0.4                      GHȼ 20,000

Total Expected Returns                   GHȼ 36,000

Project B:

Net Profits             Probability          Expected Returns:

GHȼ 100,000         0.5                      GHȼ 50,000

GHȼ 0.00               0.5                      GHȼ 0.00

Total Expected Returns                   GHȼ 50,000

Expected Returns are the returns or income which have been weighed with their probabilities of occurrence.  It is used to determine the best outcome given events that have different probabilities of occurring.   It is an important measure of returns which helps in deciding the best investment option to pursue.

Answer:

x>108

Step-by-step explanation:

Answer:

The number of students who attend music club only is 13.

Step-by-step explanation:

The three different types of clubs are:

D = drama club

M = music club

S = sports club

The information provided is:

n (M) = 39

n (D) = 35

n (Exactly 2 clubs) = 26

Consider the Venn diagram attached.

From the Venn diagram it is clear that 13 students attended the Music club only.

Thus, the number of students who attend music club only is 13.

Answer & Step-by-step explanation:

First, we will multiply 5 by 28 to find out the total number of ages in the room.

5 * 28 = 140

Now, we will multiply 6 by 29 to find out the total number of ages in the room after the new person comes in.

6 * 29 = 174

Now, in order for us to find the age of the new person, then we will subtract 140 from 174.

174 - 140 = 34

So, the person that entered the room is 34 years old.

Answer:

34

Step-by-step explanation:

Answer:

need more info

Step-by-step explanation:

need more info

Answer:

64

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

A = 1/2 (16) *8

A =64

Answer:

[tex]64[/tex]

Step-by-step explanation:

[tex]area \\ = \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times 16 \times 8 \\ = 64[/tex]

hope this helps

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Answer:

Check the explanation

Step-by-step explanation:

a) Probability that Box #1 is empty is computed here as:

= Number of ways to distribute each of the the n balls in remaining (n - 1) boxes / Total ways to distribute n balls into n boxes

= [tex]\frac{(n-1)^n}{n^n} = (1 - \frac{1}{n})^n[/tex]

This is the required probability here.

b) Probability that only 1 box is empty is computed here as:

= Number of ways to choose one of the remaining (n - 1) boxes such that it will have 2 balls * Number of ways to select 2 balls of that box* permutation of remaining (n - 2) balls into (n - 2) boxes / Total ways to distribute n balls into n boxes

= [tex]\frac{\binom{n-1}{1}\binom{n}{2}(n-2)!}{n^n}[/tex]

= [tex]\frac{(n-1)n!(n-2)!}{2n^n}[/tex]

= [tex]\frac{n!(n-1)!}{2n^n}[/tex]

This is the required probability here.

c) Probability that only 1 box is empty is computed here as:

= Number of ways to select a box which would be empty * Probability that only that box would be empty ( from previous part)

= [tex]\frac{n*n!(n-1)!}{2n^n}[/tex]

= [tex]\frac{(n!)^2}{2n^n}[/tex]

This is the required probability here.

d) Given that box #1 is empty, probability that only 1 box is empty is computed here as:

= Probability that only box 1 is empty / Probability that box 1 is empty

We will use the answers from parts a) and b) here to get:

=[tex]\frac{ \frac{n!(n-1)!}{2n^n}}{\frac{(1 - n)^n}{n^n}}[/tex]

= [tex]\frac{n!(n-1)!}{2(1-n)^n}[/tex]

This is the required probability here.

e) Given that only 1 box is empty, probability that box #1 is empty is computed here as:

= 1/n as each box is equally likelt to be empty

Therefore 1/n is the required probability here.

Answer:

4,8,12,16,24,32,36.......

Step-by-step explanation:

Answer:

The answer to the question is A

Adding the negative value in front of x flips the graph lacrosse the Y axis and compressed it vertically.

The answer is C.

Answer:

C. The graph of G(x) is the graph of F(x) flipped over the y-axis and compressed vertically.

Step-by-step explanation:

The negative in front of the 2 made the function flip over the y-axis. While the 2, compressed the function a little, making it so the function touched 2, vertically.

Answer:

-x+3

Step-by-step explanation:

hope this helps

Answer:

Question 1:

A) Parallelogram

B) Right Angled Triangle

Question 2:

Using parallelogram to use properties of parallel lines. To find whether a quadrilateral is parallelogram, first we will write it's coordinates. After writing coordinates, we find slope of each line by slope formula. After this , we compare the slope of equal lines through which we come to know whether they are parallel to eachother or not. After that, if two pairs of lines are parallel, then the given quadrilateral is a parallelogram.

Answer:

Step-by-step explanation:

Bring to one side

x^2-12x+y^2-8y+27=0

Complete the square

(x^2-12x+A)+(y^2-8y+B)=-27

Answer:

First option is the correct answer

The equation of the circle is: [tex](x-6)^2+(y-4)^2= 25[/tex]

The center is at (6, 4), and the radius is 5 units.

Step-by-step explanation:

[tex]x^{2} -12x+27=-y^2 +8y\\\\x^{2} -12x+27+y^2 -8y=0\\(x^{2} -12x+36)-36+27+(y^2 -8y +16)-16=0\\(x^{2} -12x+6^2)+(y^2 -8y +4^2)-25=0\\(x-6)^2+(y-4)^2= 25\\(x-6)^2+(y-4)^2= 5^2\\Equating\: it \: with\\(x-h)^2+(y-k)^2= r^2\\we\:find:\\Center = (h,\:k) = (6,\:4)\\Radius \:(r) = 5[/tex]

Answer:

Null hypothesis:[tex]\mu \geq 6[/tex]

Alternative hypothesis:  [tex] \mu <6[/tex]

For this case after conduct the one lower tail test we got the following p value:

[tex] p_v = P(t <-1.68) = 0.0465[/tex]

And for this case if we want to conduct a bilateral test or two sided the sytem of hypothesis are:

Null hypothesis:[tex]\mu = 6[/tex]

Alternative hypothesis:  [tex] \mu \neq 6[/tex]

And for this case the p value can be calculated like this:

[tex] p_v = 2* P(t <-1.68) =2* 0.0465= 0.0930[/tex]

Step-by-step explanation:

For this case we are trying to proof the following system of hypothesis:

Null hypothesis:[tex]\mu \geq 6[/tex]

Alternative hypothesis:  [tex] \mu <6[/tex]

For this case after conduct the one lower tail test we got the following p value:

[tex] p_v = P(t <-1.68) = 0.0465[/tex]

And for this case if we want to conduct a bilateral test or two sided the sytem of hypothesis are:

Null hypothesis:[tex]\mu = 6[/tex]

Alternative hypothesis:  [tex] \mu \neq 6[/tex]

And for this case the p value can be calculated like this:

[tex] p_v = 2* P(t <-1.68) =2* 0.0465= 0.0930[/tex]

Answer:

We conclude that the true average percentage of Silicon Dioxide is smaller than 5.5.

Step-by-step explanation:

We are given that the desired percentage of Silicon Dioxide (SiO2) in a certain type of aluminous cement is 5.5.

16 independently obtained samples are analyzed and a sample mean of 5.25 was obtained. Suppose that the percentage of SiO2 in a sample is normally distributed with a sigma of 0.3.

Let [tex]\mu[/tex] = true average percentage of Silicon Dioxide.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 5.5     {means that the true average is greater than or equal to 5.5}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 5.5     {means that the true average is smaller than 5.5}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

                            T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean percentage of Silicon Dioxide = 5.25

            σ = population standard deviation = 0.3

            n = sample size = 16

So, the test statistics  =  [tex]\frac{5.25-5.5}{\frac{0.3}{\sqrt{16} } }[/tex]

                                      =  -3.33

The value of z test statistics is -3.33.

Now, the P-value of the test statistics is given by;

                P-value = P(Z < -3.33) = 1 - P(Z [tex]\leq[/tex] 3.33)

                              = 1 - 0.9996 = 0.0004

Since, the P-value of the test statistics is less than the level of significance as 0.0004 < 0.01, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the true average percentage of Silicon Dioxide is smaller than 5.5.

Answer:

The true average percentage of Silicon Dioxide (SiO2) is less than 5.5.

Step-by-step explanation:

In this case we need to test whether the true average percentage of Silicon Dioxide (SiO2) in a certain type of aluminous cement is smaller than 5.5.

The hypothesis can be defined as follows:

H₀: The true average percentage of Silicon Dioxide (SiO2) is 5.5, i.e. μ = 5.5.

Hₐ: The true average percentage of Silicon Dioxide (SiO2) is less than 5.5, i.e. μ < 5.5.

The information provided is:

[tex]\bar x=5.25\\\sigma=0.30\\n=16\\\alpha =0.01[/tex]  

As the population standard deviation is provided, we will use a z-test for single mean.

Compute the test statistic value as follows:

 [tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{5.25-5.5}{0.30/\sqrt{16}}=-3.33[/tex]

The test statistic value is -3.33.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

[tex]p-value=P(Z<-3.33)=0.00043[/tex]  

*Use a z-table for the probability.

The p-value of the test is 0.00043.

p-value = 0.00043 < α = 0.05

The null hypothesis will be rejected at 5% level of significance.

Thus, it can be concluded that the true average percentage of Silicon Dioxide (SiO2) is less than 5.5.

Answer:

Center = (5, 0)

Radius = 9

Step-by-step explanation:

Look at the picture

The radius of the circle is 9units and the center of the circle is at (5, 0)

The standard equation of a circle is expressed as:

(x-a)^2+(y-b)^2 = r^2

where

r is the radius of the circle

(a, b) is the centre of the circle

GIven the equation is (x – 5)² + y² = 81.

Compare both equations

a = 5, b = 0

r^2 = 81

r = 9units

Hence the radius of the circle is 9units and the center of the circle is at (5, 0)

Learn more on equation of circle here: https://brainly.com/question/14150470

Answer: the men’s of this set of numbers is 60

Step-by-step explanation:

Add all the numbers together and then divided but the amount of numbers in the set

Answer:

Step-by-step explanation:

Hello!

Full text

In a national survey college students were​ asked, "How often do you  wear a seat belt when riding in a car driven by someone​ else?" The response frequencies appear in the table to the right.​ (a) Construct a probability model for​ seat-belt use by a passenger.​ (b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone​ else?

Response , Frequency  

Never  102

Rarely  319

Sometimes  524

Most of the time  1067

Always  2727

n= 102+319+524+1067+2727= 4739

​(a) Complete the table below.

Response

Probability  To calculate the probability for each response you have to divide the frequency of each category by the total of people surveyed:

Never P(N)= 102/4739= 0.0215

​(Round to the nearest thousandth as​ needed.)

Rarely P(R)= 319/4739= 0.0673

​(Round to the nearest thousandth as​ needed.)

Sometimes P(S)= 524/4739= 0.1106

​(Round to the nearest thousandth as​ needed.)

Most of the time  P(M)= 1067/4739= 0.2252

​(Round to the nearest thousandth as​ needed.)

Always  P(A)= 2727/4739= 0.5754

​(Round to the nearest thousandth as​ needed.)

​(b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone​ else?

A.

​No, because there were 102  people in the survey who said they never wear their seat belt. Incorrect, an event is considered unusual if its probability (relative frequency) is low, you cannot know if it is usual or unusual just by looking at the absolute frequency of it.

B.

​Yes, because ​P(never) < 0.05. Correct

C.

​No, because the probability of an unusual event is 0.    Incorrect, the probability of unusual events is low, impossible events are the ones with probability zero

D.

​Yes, because 0.01 < ​P(never) <  0.10. Incorrect, by the definition an event is considered unusual when its probability is equal or less than 5%.

I hope this helps!

Answer:

the number 6 is in the millions place

Step-by-step explanation:

the millions place is the sixth digit in the number family

and it also has six numbers after the number

Answer: The answer is 606060.

Step-by-step explanation: Its pretty simple all you do is add like this and you will get the answer you are needing. If this helped leave a like and try to respond. ❤

Answer:

606060.

Step-by-step explanation:

Answer:

$ 7.9

Step-by-step explanation:

Amount of bill = $52.87 = $52.9

Amount of tip = 15% of $52.9

[tex] = \frac{15}{100} \times 52.9 \\ \\ = 0.15 \times 52.9 \\ = 7.935 \\ = \$ \: 7.9 \\ [/tex]

Answer:

y=x-2

Step-by-step explanation:

y=2^x and y=x-2 have the same domain. Any x-values work for both functions. The domain is all real numbers.

If this answer is correct, please make me Brainliest!