Find the distance between the two points in simplest radical form.
(-2,-1) and (-8,7)

Answer:

I understand there is a typo, so Belly and Billy are the same person. His age is represented as B, and Suzy's as S.

S = 19

B = 9

Step-by-step explanation:

Suzy is ten years older than Belly:

(1)  S = B + 10

the next year she will be twice as old as Billy

(2)  S + 1 = 2 (B + 1)

solving the system of equation (1) and (2):

Making (2) - (1):  

1 = 2 (B + 1) - B - 10 => 1 = 2 B + 2 - B - 10  => 1 = B - 8 => B = 9

replacing in (1) S = 19

Answer:

babysitting = $9

working at coffeehouse = $12

x = hours for babysitting

y = hours at coffeehouse

minimum = ≥

9x + 12y ≥ 240

Step-by-step explanation:

just a short note on which symbol you should use when you see these words in inequality questions:

i) use ≥

-more than or equal to

-not less than

-at least

-minimum

ii) use >

-more than

-greater than

iii) use ≤

-less than or equal to

-not more than

-at most

-maximum

iv) use <

-less than

The inequality 9x + 12y ≥ 240 represents that Rachael wants to earn a minimum of $240 if she earns $9 per hour babysitting, and she earns $12 per hour working at the coffee-house.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Rachael earns $9 per hour babysitting, and she earns $12 per hour working at the coffee-house.

x is the number of hours babysitting.

y is the number of hours at the coffee-house.

9x + 12y ≥ 240

Because, Rachael wants to earn a minimum of $240.

Thus, the inequality 9x + 12y ≥ 240 represents that Rachael wants to earn a minimum of $240 if she earns $9 per hour babysitting, and she earns $12 per hour working at the coffee-house.

Learn more about the inequality here:

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Answer:

-300

Step-by-step explanation:

z = -21/0.07

z = -300

Answer:

-300

Step-by-step explanation:

Divide -21 by 0.07 to get -300

here's the answer.....I hope it would work

Answer:

3/17

Step-by-step explanation:

Substitute the given values for the variables.

[tex]\frac{12}{5+9(7)}[/tex]

Simplify

[tex]\frac{12}{5+63}[/tex]

[tex]\frac{12}{68}[/tex]

[tex]\frac{3}{17}[/tex]

Answer:

Option (a) [tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]

Step-by-step explanation:

The given expression is :

[tex]\dfrac{3}{1{\cdot} 2}+\dfrac{3}{2{\cdot} 3}+\dfrac{3}{3{\cdot} 4}+\dfrac{3}{4{\cdot} 5}+....[/tex]

We need to rewrite the sum using sigma notation.

The numerator is 3 in all terms.

At denominator, in first term (1)(2), in second term (2)(3) and so on.

A general term for the denominator is k(k+1).

Sigma notation is :

[tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]

Hence, the correct option is (A).

Answer:

24

Step-by-step explanation:

[tex]\sqrt{25^2-7^2}\\\\=\sqrt{(25-7)(25+7)}\\\\=\sqrt{18(32)}\\\\=\sqrt{9*2*2^5}\\\\=\sqrt{3^2\cdot 2^6}\\\\=\sqrt{(3\cdot2^3)^2}\\\\=3\cdot2^3\\\\=3\cdot8\\\\=24[/tex]

Answer:

24

Step-by-step explanation:

First we compute the number under the radical.

We have 25² = 625 and 7² = 49, so 25² - 7² = 625 - 49 = 576.

Thus, √25² - 7² = √576 = √24², which is 24.

Answer:

the answer is D

Step-by-step explanation:

√-9 ≠ -3

-3 ≠ √-9

(-3)² ≠ -9 ( proven )

9 ≠ -9

The value √-9 ≠ -3², option D is correct answer.

An imaginary number is a number that, when squared, has a negative result.

Given an expression, √-9

√-9 ≠ -3

-3 ≠ √-9

(-3)² ≠ -9

9 ≠ -9

Hence, √-9 ≠ -3²

For more references on imaginary number, click;

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Answer:

Step-by-step explanation:

Let s be the surface area and r be the radius

Then according to given statement

s∝r²

Removing the proportionality symbol introduces k, the constant of proportionality

[tex]s = kr^2[/tex]

Now

A soap bubble with a  0.75 in. radius has a surface area of approximately 7.07 square inches.

Putting in the equation

[tex]7.07 = k (0.75)^2\\7.07 = k * 0.5625\\k = \frac{7.07}{0.5625}\\k = 12.5688..\\k = 12.57[/tex]

The euqation beomes

[tex]s = 12.57r^2[/tex]

Putting s = 113.1 in the equation

[tex]113.1 = 12.57r^2\\r^2 = \frac{113.1}{12.57}\\r^2 = 8.99761...\\\sqrt{r^2} = \sqrt{8.9976..}\\r = 2.9996..[/tex]

Hence,

Answer:10

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

the second to last one

Step-by-step explanation:

Sorry if it is incorrect!

Answer:

what?????????????????

Step-by-step explanation:

how do you want me to solve with a fraph or sometging else

Step-by-step explanation:

Use the slope-intercept form

y=mx+b

to find the slope m and y-intercept b

Slope: 5/4

y-intercept: (0,-4)

Answer: 32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Inside the parentheses, we see 5+3, which equals 8. Now, do 8x4, which equals 32!

Answer:

- 5/6

Step-by-step explanation:

turn it into an improper fraction.

1 and 2/3 = 5/3

2 and 1/2 = 5/2

5/3 - 5/2 = 10/6 - 15/6

= -5/6

Answer:

First you have to change both of the mixed numbers to improper fractions. To do this you would multiply the denominator and the whole number then add the numerator.

1 2/3 = 5/3

-2 1/2 = -5/2

Find the least common denominator (LCM). Add the numerator, and keep the denominator the same.

The LCM for these two fractions would be 6 so to get to six you would multiply 5/3 by 2/2 and -5/2 by 3/3.

5/3 = 10/6

-5/2 = -15/6

Add the numerators (10 + -15 = -5), and keep the denominator the same (6). Therefore, the answer would be -5/6.

Answer:

68 degrees

Step-by-step explanation:

1 & 6 have to equal 180. Therefore, if 1 is 112 then you take 180-112. Then you get 68 degrees.

Answer:

Angle 6 would be 68 degrees

Step-by-step explanation:

Angles 1, 3, 5, and 7  all equal 112. you would subtract 112 from 180 to get the measurement for angles 2, 4, 6, and 8

Answer:

1778.68 I think

Step-by-step explanation:

Answer:

605

I just got confused sorry.

Answer:

4

Step-by-step explanation:

I am pretty sure its that one

Answer:

i) Assigning women at random ensures that the two groups are comparable.

iv) A control group provides a baseline for comparisons to determine treatment effects.

Step-by-step explanation:

(a)

It is pertinent that there two comparable groups. In light of the fact that it will help in making better decisions since there will be some people who have blood pressure as a result of uncontrolled physical characteristics such as anger, positive attitude, lower blood pressure. etc Thus, there is a need to consider two equivalent groups.

(b)

A control group is used as a benchmark for determining the cause and effect of a treatment on a given experimental group. This may be in regard to the social aspect of meeting other individuals involved that make up the physical changes.

Answer:

x = 1.25

y = 1.75

Step-by-step explanation:

Since, the line that is 8 units long is parallel to the line that is ten units long.

Therefore, both the triangles are similar by AA postulate.

Corresponding sides of of the similar triangles are in proportion.

Therefore,

[tex] \frac{5}{x + 5} = \frac{7}{y + 7} = \frac{8}{10} \\ \\ \implies \frac{5}{x + 5} = \frac{8}{10} \\ \\ 5 \times 10 = 8(x + 5) \\ \\ 50 = 8x + 40 \\ \\ 50 - 40 = 8x \\ \\ 10 = 8x \\ \\ \frac{10}{8} = x \\ \\ x = 1.25 \\ \\ \\ \frac{7}{y + 7} = \frac{8}{10} \\ \\ 7 \times 10 = 8(y + 7) \\ \\ 70 = 8y + 56 \\ \\ 70 - 56 = 8y \\ \\ 14 = 8y \\ \\ \frac{14}{8} = y \\ \\ y = 1.75[/tex]

Answer:

I think it might be 16 or 24.

Step-by-step explanation:

Pardon if I'm wrong.

Answer:

9/6

Steps:

5/6 - (-2 x 2)

____. = 9/6

3 x 2

Answer:

Approximately [tex]0.012[/tex] (that's approximately [tex]1.2\%[/tex].)

Step-by-step explanation:

The question did not specify the exact distribution of the size of those images. However, the sample size [tex]n = 80[/tex] is a rather large number. Assume that:

If both assumptions are met, the central limit theorem would apply. This theorem would suggest that the sum of the sizes of these [tex]80[/tex] image (a random variable) will approximately follow a normal distribution. The mean of that sum would be approximately [tex]n\cdot \mu= 80 \times 0.5[/tex]. The standard deviation of that sum would be approximately [tex]\sigma\, \sqrt{n} = 0.2\times \sqrt{80}[/tex].

Let [tex]\displaystyle \Sigma X[/tex] denote the sum of these eighty sizes.

Under these assumption, [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left(n\, \mu,\, \sigma\,\sqrt{n}\right)[/tex].

That is: [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left({80\times 0.5},\, \left(0.2\times \sqrt{80}\right)^2}\right)[/tex].

The question is asking for the probability [tex]P(49 \le \Sigma X \le 53)[/tex]. Therefore, calculate the [tex]z[/tex]-score that corresponding to [tex]\Sigma X = 49[/tex] and [tex]\Sigma X = 53[/tex]:

Make use of a [tex]z[/tex]-table to find these two probabilities:

Calculate the probability that this question is asking for:

[tex]\begin{aligned}& P(49 \le \Sigma X \le 53) \\ &= P(\Sigma X < 53) - P(\Sigma X < 49) \\ & \approx 0.99942 - 0.98778 \approx 0.012 = 1.2\%\end{aligned}[/tex].

Answer:

The decision rule is  

Reject the null hypothesis  

Step-by-step explanation:

From the question we are told that

    The population mean is [tex]\mu = 5.6 \ pounds/inch^2[/tex]

     The  sample size is  n =  160

      The sample mean is  [tex]\= x = 5.7 \ pounds/ inch^2[/tex]

     The variance is [tex]\sigma ^2 = 0.25[/tex]

       The level of significance is  [tex]\alpha = 0.01[/tex]

The null hypothesis is  [tex]H_o : \mu = 5.6[/tex]

The alternative hypothesis is [tex]H_a : \mu > 5.6[/tex]

Generally the standard deviation is mathematically represented as

           [tex]\sigma = \sqrt{\sigma ^2 }[/tex]

=>         [tex]\sigma = \sqrt{0.25 }[/tex]  

=>         [tex]\sigma = 0.5[/tex]  

Generally the test statistics is mathematically represented as

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

=>     [tex]z = \frac{5.7 - 5.6 }{ \frac{0.5 }{\sqrt{ 160 } } }[/tex]  

=>     [tex]z = 2.53[/tex]

From the z table  the area under the normal curve to the left corresponding to  2.53   is

        [tex]p-value = P(Z > 2.53 ) =0.0057[/tex]

From the value obtained we see that the [tex]p-value < \alpha[/tex] hence

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to conclude that the believe  that the valve performs above the specifications is true

Answer:

False

Step-by-step explanation:

As of 2017, 5 states (Alaska, Delaware, Montana, New Hampshire and Oregon) do not levy a statewide sales tax. California has the highest base sales tax rate, 7.25%. Including county and city sales taxes, the highest total sales tax is in Arab, Alabama, 13.50%.