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3 years ago

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Mathematics

1 answer:

klasskru [66]3 years ago

5 0

Answer:

$\frac{y - 18}{x - 1} = \frac{23 - 18}{1.5 - 1} = \frac{5}{0.5} = 10 \\ y - 18 = 10(x - 1) = 10x - 10 \\ y = 10x + 18 - 10 = 10x + 8 \\ \boxed{f(x) = 10x + 8}$

<h2>A. is the right answer.</h2>

hope this helps.

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2n²+3n=27 <br><br>2t²-162=0 <br>find the roots of each equation.

ASHA 777 [7]

Answer:

$n = 3, n=-\frac92; t=9, t=-9$

Step-by-step explanation:

Second one is faster, so let's get rid of it first.

Divide by 2 to make numbers easier, and we get

$t^2-81 = 0$ . You should recognize 81 is 9 squared, and both $-9$ and $+9$ , when squared, give 81, we have our solution.

Now the first. I can't spot any quick trick to solve it, so quadratic formula it is. Let's rememer it: if

$ax^2 +bx+c=0$ then

$x={{-b \pm \sqrt{b^2-4ac}}\over 2a$

Let's bring the first equation in the standard form and calculate the quantity over the square root (usually called with the greek letter delta, $\Delta$ ) to the side.

$2n^2+3n-27 =0\\\Delta = (3)^2 -4(2)(-27) = 9+(8)(3)(9) = 9(1+24)= 9 \cdot25 =(3\cdot5)^2$

now we can apply the formula:

$n={{-3\pm15}\over4}$ Let's split the two cases now

$n= \frac{-3+15}4 = \frac{12}4=3\\n= \frac{-3-15}4 = \frac{-18}4 =-\frac92$

5 0

3 years ago

Wich is greater 42% or 0.44

kakasveta [241]

Since percent means 'over 100', you can put 42 over 100: $\frac{42}{100} = .42$ . Since .42 is less than .44, that means that .44 is your answer.

8 0

3 years ago

Read 2 more answers

Reduce the following fraction to lowest terms: 16/20

UNO [17]

4/5 is the answer to reduce to the lowest of 16/20

5 0

4 years ago

The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra

Snezhnost [94]

Let $X$ denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by $X_1,\ldots,X_{36}$ , each independently and identically distributed with distribution $X_i\sim\mathcal N(26,7.2)$ .

You want to find

$\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)$

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

$\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)$

Recall that if $X\sim\mathcal N(\mu,\sigma)$ , then the sampling distribution $\overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right)$ with $n$ being the size of the sample.

Transforming to the standard normal distribution, you have

$Z=\dfrac{\overline X-\mu_{\overline X}}{\sigma_{\overline X}}=\sqrt n\dfrac{\overline X-\mu}{\sigma}$

so that in this case,

$Z=6\dfrac{\overline X-26}{7.2}$

and the probability is equivalent to

$\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)$
$=\mathbb P(Z>1.481)\approx0.0693$

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3 years ago

Suppose that there are 27 sophomores and 14 juniors in a Physiology class. Two students are chosen at random to participate in a

kolezko [41]

The answer would be 7

6 0

3 years ago

Question is in picture below ​

Question is in picture below