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Soloha48 [4]
3 years ago
7

Use a proportion to find the missing side length in the following similar figures.

Mathematics
1 answer:
jasenka [17]3 years ago
5 0
D because i did this alreadyyy
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The heights of a random sample of 50 college students showed a mean of 174.5 centimeters and a standard deviation of 6.9 centime
Minchanka [31]

Answer:

Step-by-step explanation:

Hello!

For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.

In this example the variable is:

X: height of a college student. (cm)

There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.

The option you have is to apply the Central Limit Theorem.

The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:

X[bar]~~N(μ;σ2/n)

Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:

98% CI

1 - α: 0.98

⇒α: 0.02

α/2: 0.01

Z_{1-\alpha /2}= Z_{1-0.01}= Z_{0.99} =2.334

X[bar] ± Z_{1-\alpha /2} * \frac{S}{\sqrt{n} }

174.5 ± 2.334* \frac{6.9}{\sqrt{50} }

[172.22; 176.78]

With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].

I hope it helps!

4 0
2 years ago
A principal of $2900 is invested at 4.25% interest, compounded annually. How much will the investment be worth after 7 years?
olga2289 [7]

Let S = Sum after 13 years

     So = amount invested

     t = time in years

     i = annual interest rate = .0325

The S = So(1+i)t = $2,200(1.0325)13 = $3,334.21

4 0
2 years ago
If the two lines 2x + y= 0 and y=3 are plotted on a typical xy coordinate grid, at which point will they intersect?
irina1246 [14]
2x + y = 0
2x + 3 = 0
      - 3  - 3
      2x = -3
       2      2
         x = -1¹/₂
(x, y) = (-1¹/₂, 3)
5 0
3 years ago
Read 2 more answers
Which two numbers add up to be 8 and multiply to be -84
Kisachek [45]
Righ, so negative times positive=negative
negative+positive=positive
thereofr
positive>negative

factor -84 where the negative is smaller ex -12 and 13, not -14 and 10 so

-2 and 42 nope
fast forward
-6 and 14 yes
-6+14=8
so the numbers are -6 and 14
6 0
3 years ago
5700 is compounded semiannually at a rate of 15% for 12 years
Rama09 [41]

Answer:

$32,335.38

Step-by-step explanation:

You are going to want to use the compound interest formula, which is shown below.

P(1+\frac{r}{n} )^{nt}

<em>P = initial balance </em>

<em>r = interest rate </em>

<em>n = number of times compounded annually </em>

<em>t = time</em>

<em />

Now lets plug in the values into the equation:

5,700(1+\frac{.15}{2})^{12(2)} = 32,335.38

Your answer is $32,335.38

4 0
3 years ago
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