Write 2 equations needed to solve this problem

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:

4

Step-by-step explanation:

Answer:

189

Step-by-step explanation:

Also can you make me brainliest please

Answer:

Step-by-step explanation:

A. 40:80

B: 80/40

C; 40: 120

D: 80:120 ;)

Answer:

you didn't post the graph but (0,0) is the origin

Answer:

ok

Step-by-step explanation:

twenty thousandddd

20k

Answer:

twenty thousand

Step-by-step explanation:

Because you just have to spell it out spell twenty and then thousand.

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:

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:

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:

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:

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%.

Answer:

the second to last one

Step-by-step explanation:

Sorry if it is incorrect!

Answer:

The answer is D. the gas mileage after the additive is used

Step-by-step explanation:

I got 100% on edg!

Answer:

d

Step-by-step explanation:

edge2o2o

Answer:

9/6

Steps:

5/6 - (-2 x 2)

____. = 9/6

3 x 2

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]

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:

I think it might be 16 or 24.

Step-by-step explanation:

Pardon if I'm wrong.

Answer:10

Step-by-step explanation:

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:

4

Step-by-step explanation:

I am pretty sure its that one

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]

Method 1: A pure algebraic approach

The unknown in this problem is the percent of decrease. A percent of decrease is the percentage of the original price that was deducted from the original price to obtain the sale price. We could write a "word equation" for this process like this:

original price - (percent of decrease)(original price) = sale price

Since the percent of decrease is the unknown in this problem, we'll call the percent of decrease x%.

Here's what we know so far:

The original price was $200

The sale price was $170

The percent of increase was x%

Putting this information in our word equation gives us an algebraic equation:

200 - (x%)(200) = 170

What do we do with the percent sign in this equation? "Percent" means "out of 100", so x% means x out of 100, or . Now we have this:

200 - (200) = 170

Now we'll solve our equation:

200 - (200) = 170

200 - 2x = 170

-2x = -30

x = 15

So the percent of decrease is 15%

Method 2: A method involving pure arithmetic.

If we know the original price and the sale price, we can find the percent of decrease in two steps:

Find the amount of decrease

Divide the amount of decrease by the original amount

This will give us the percent of decrease (written as a decimal number). We can then write the decimal as an equivalent percent to find our final answer.

Let's use method 2 on the same problem:

Frank bought a new television set on sale. If the TV's original price was $200 and Frank paid $170 for the TV, what was the percent of decrease?

First, let's find the amount of decrease:

Amount of decrease = 200 - 170 = 30

So the price decreased by $30.

Next, we'll find the percent of decrease, and rewrite the decimal answer as a percent:

Percent of decrease =  = = .15 = 15%

So the percent of decrease is 15%

Before we leave the problem, let's check our answer:

Original price = $200

Price reduced by 15% of original price = 200(.15) = $30

Sale price would then be = $200 - $30 = $170

Our answer checks. We're done!    Me not know if correct.

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:

Step-by-step explanation:

4• (7 • y) is equivalent to all of the following:

28 • y

4 · 7y or (4 · 7) · y

(7 · 4) · y

Note that 4 • 7 + 4 • Y is absolutely wrong, since the original expression has no " + " sign

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,