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Serjik [45]
3 years ago
5

Please solve these questions it's important please​

Mathematics
1 answer:
MissTica3 years ago
4 0

<h3>b)</h3>

\frac{3 {a}^{2}  - 9a}{ {a}^{2}  - 9}  =  \frac{3a(a - 3)}{(a + 3)(a - 3)}  =  \frac{3a}{a + 3}

<h3>c)</h3>

\frac{ {y}^{2} - 3yz -4  {z}^{2}  }{3 {y}^{2} - 12yz }  =  \frac{(y + z)(y - 4z)}{3y(y - 4z)}  =  \frac{y + z}{3y}

<h3>d)</h3>

\frac{ {d}^{2} + 4d  + 4}{ {d}^{2}  + 2d}  =  \frac{(d + 2)(d + 2)}{d(d + 2)}  =  \frac{d + 2}{d}

<h3>e)</h3>

\frac{5f - 15}{3 {f}^{2}  - 13f + 12}  =  \frac{5(f - 3)}{(3f - 4)(f - 3)}  =  \frac{5}{3f - 4}

I hope I helped you^_^

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Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. This instructor is about to give t
Lapatulllka [165]

Answer:

P(\bar X >80)=P(Z>2.143)=1-P(z

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Let X the random variable that represent the Student scores on exams given by a certain instructor, we know that X have the following distribution:

X \sim N(\mu=74, \sigma=14)

The sampling distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

The deduction is explained below we have this:

E(\bar X)= E(\sum_{i=1}^{n}\frac{x_i}{n})= \sum_{i=1}^n \frac{E(x_i)}{n}= \frac{n\mu}{n}=\mu

Var(\bar X)=Var(\sum_{i=1}^{n}\frac{x_i}{n})= \frac{1}{n^2}\sum_{i=1}^n Var(x_i)

Since the variance for each individual observation is Var(x_i)=\sigma^2 then:

Var(\bar X)=\frac{n \sigma^2}{n^2}=\frac{\sigma}{n}

And then for this special case:

\bar X \sim N(74,\frac{14}{\sqrt{25}}=2.8)

We are interested on this probability:

P(\bar X >80)

And we have already found the probability distribution for the sample mean on part a. So on this case we can use the z score formula given by:

z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

Applying this we have the following result:

P(\bar X >80)=P(Z>\frac{80-74}{\frac{14}{\sqrt{25}}})=P(Z>2.143)

And using the normal standard distribution, Excel or a calculator we find this:

P(Z>2.143)=1-P(z

6 0
4 years ago
When a number is decreased by 17% the result is 15. what is the original number?
Stels [109]

Answer:

original number is 18.07

Step-by-step explanation:

Let the original number be x

x - 17% of x  = 15

x* (1  - 0.17) = 15

x * 0.83 = 15

x = 15/0.83

x = 18.072289156

Or if your wording meant   17% of a number is 15  then:

x * 17% = 15

x *0.17 = 15

x = 15/0.17 = 88.23529...

but I think you meant  "decreased by 17%"   so I choose  x = 18.07

8 0
3 years ago
Which product is positive a is 2/5 -8/9 -1/3 -2/7 b is -2/5 8/9 -1/3 -2/7 c is 2/5 8/9 1/3 -2/7 d is -2/5 -8/9 1/3 2/7
PIT_PIT [208]

Answer:

(D)

Step-by-step explanation:

A. \frac{2}{5}{\times}\frac{-8}{9}{\times}\frac{-1}{3}{\times}\frac{-2}{7}=\frac{-32}{945} which is a negative number, thus Option A is incorrect.

B. \frac{-2}{5}{\times}\frac{8}{9}{\times}\frac{-1}{3}{\times}\frac{-2}{7}=\frac{-32}{945} which is a negative number, thus Option B is incorrect.

C. \frac{2}{5}{\times}\frac{8}{9}{\times}\frac{1}{3}{\times}\frac{-2}{7}=\frac{-32}{945} which is a negative number, thus option C is incorrect.

D. \frac{-2}{5}{\times}\frac{-8}{9}{\times}\frac{1}{3}{\times}\frac{2}{7}=\frac{32}{945} which is a positive number, thus option D is correct.

7 0
3 years ago
Read 2 more answers
One December day, two spies decide that they must meet to exchange documents. One is in New York City and the other is in Indian
Leto [7]

Answer:

6:00

Step-by-step explanation:

5 0
3 years ago
Suppose Clare labels the books at a constant speed of s books per minute. Write an equation that represents the relationship bet
iragen [17]

Answer:

75 minutes

50 minutes

Number of minutes to finish labelling = Total number of books labelled / Time taken to label them (speed of labelling)

Step-by-step explanation:

Complete question below:

Clare volunteers at a local library during the summer. Her work includes putting labels on 750 books.

How many minutes will she need to finish labeling all books if If she takes no breaks and labels:

a. 10 books a minute

b. 15 books a minute

Suppose Clare labels the books at a constant speed of books per minute. Write an equation that represents the relationship between her labeling speed and the number of minutes it would take her to finish labeling

Solution

a. 10 books a minute

Number of minutes to finish labelling all books at 10 books per minute = Total books / books labelled per minute

= 750 / 10

= 75 minutes

Number of minutes to finish labelling all books at 10 books per minute = 75 minutes

b. 15 books a minute

Number of minutes to finish labelling all books at 15 books per minute = Total books / books labelled per minute

= 750 / 15

= 50 minutes

Number of minutes to finish labelling all books at 15 books per minute = 50 minutes

c. The relationship between her labeling speed and the number of minutes is Total number of books labeled ÷ Time taken to label them

Number of minutes to finish labelling = Total number of books labelled / Time taken to label them (speed of labelling)

7 0
3 years ago
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