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3 years ago

Y = 7x - 15 y = 4x - 12

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

3 0

Answer:

Step-by-step explanation:

7x - 15 = 4x - 12

3x - 15 = -12

3x = 3

x = 1

y = 7(1) - 15

y = 7 - 15

y = -8

(1, -8)

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144 coins are divided equally among some

nalin [4]

Answer:

Consider the number of children to be x.

So, 144 coins were divided amongst x children.

For x-3 children, each child would have 16 coins

So, (x-3)*16=144

Solving for x, x-3=144/16

or x-3=9

or x=9+3=12

Answer is 12

3 0

3 years ago

Read 2 more answers

The equation of a line is y = -3x. To which equation is the line parallel to? A. Y = 1 third x minus 4 B. Y = 3x + 10 C. Y = -10

Sergeeva-Olga [200]

Answer:

This line would be parallel to C. y = -10 - 3x

Step-by-step explanation:

This is because parallel lines have the same slope. This means we must see the same coefficient of x in both equations. Both of these two equations have a coefficient of -3 on x.

6 0

3 years ago

Assume that females have pulse rates that are normally distributed with a mean of μ=73.0 beats per minute and a standard deviati

Gennadij [26K]

Answer:

a. the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly selected, the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849

c. D. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Given that:

Mean μ =73.0

Standard deviation σ =12.5

a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 76 beats per minute.

Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.

Then : X $\sim$ N ( μ = 73.0 , σ = 12.5)

The probability that her pulse rate is less than 76 beats per minute can be computed as:

$P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})$

$P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})$

$P(X < 76) = P(Z< \dfrac{3}{12.5})$

$P(X < 76) = P(Z< 0.24)$

From the standard normal distribution tables,

$P(X < 76) = 0.5948$

Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

now; we have a sample size n = 25

The probability can now be calculated as follows:

$P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})$

$P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})$

$P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})$

$P( \overline X < 76) = P(Z< 1.2)$

From the standard normal distribution tables,

$P(\overline X < 76) = 0.8849$

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

In order to determine the probability in part (b); the normal distribution is perfect to be used here even when the sample size does not exceed 30.

Therefore option D is correct.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

5 0

2 years ago

How to integrate sqrt(1+x^3)?

Karolina [17]

First integrate the entire thing by letting multiplying by 1/2 the entire expression raised to exponent 1/2 - 1. That is,
0.5(1 + x³)^-0.5
Then, multiplying this by the derivative of those inside the parentheses. The final answer would be,
(0.5)((1 + x³)^-0.5)(3x²)

8 0

3 years ago

PLEASE HELP MEEEEE!!!!!!!

OverLord2011 [107]

Answer:

Cheese: $4\frac{3}{8}$
Milk: $1\frac{2}{3}$
Pasta: $6\frac{1}{4}$

Step-by-step explanation:

Cheese:

$1\frac{3}{4} = \frac{7}{4}$
Set up a proportion: $\frac{\frac{7}{4} }{4} = \frac{x}{10}$
Cross multiply, then divide: 10 × 7/4 = 17.5, 17.5 ÷ 4 = 4.375
$4.375 = 4\frac{3}{8}$

Milk:

Set up a proportion: $\frac{\frac{2}{3} }{4} = \frac{x}{10}$
Cross multiply, then divide: 10 × 2/3 = $6\frac{2}{3}$ , $6\frac{2}{3}$ ÷ 4 = $1\frac{2}{3}$

Pasta:

$2\frac{1}{2} = \frac{5}{2}$
Set up a proportion: $\frac{\frac{5}{2} }{4} = \frac{x}{10}$
Cross multiply, then divide: 10 × 5/2 = 25, 25 ÷ 4 = 6.25
$6.25 = 6\frac{1}{4}$

I hope this helps!

4 0

3 years ago