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2 years ago

Statements and reasonings 2(4x+2)=20

Mathematics

1 answer:

Katarina [22]2 years ago

6 0

distribute- 8x+4=20

subtract- 8x=20

divide- 20/8=x

answer- x=2.5

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Find the sum of the first 8 terms of the sequence: -5. 15, -45, 135, .......

MakcuM [25]

Sum of geometric sequence

for the sum where the initial value is a₁ and the common ratio is r and the term is n

$S_n= \frac{a_1(1-r^n)}{1-r}$

common ratio is -3
-5 times -3 is 15, -15 times -3=-45 etc
first term is -5
and we want the 8th term

$S_8= \frac{-5(1-(-3)^8)}{1-(-3)}$
$S_8= \frac{-5(1-6561)}{1+3}$
$S_8= \frac{-5(-6560)}{4}$
$S_8= \frac{32800}{4}$
$S_8= 8200$

the sum is 8200

7 0

1 year ago

Cynthia ran 17.5 laps in 38.5 minutes if she ran each lap at the same pace how long did it take her to run one full lap

marishachu [46]

Answer:

2.2 minutes

Step-by-step explanation:

38.5 ÷ 17.5 = 2.2

4 0

2 years ago

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past

Volgvan

Answer: We reject the null hypothesis, and we use Normal distribution for the test.

Step-by-step explanation:

Since we have given that

We claim that

Null hypothesis : $H_0:\mu\geq 50000$

Alternate hypothesis : $H_1:\mu$

There is 5% level of significance.

$\bar{X}=46800\\\\\sigma=9800\\\\n=29$

So, the test statistic would be

$z=\dfrac{\bar{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{46800-50000}{\dfrac{9800}{\sqrt{29}}}\\\\z=-1.75$

Since alternate hypothesis is left tailed test.

So, p-value = P(z≤-2.31)=0.0401

And the P-value =0.0401 is less than the given level of significance i.e. 5% 0.05.

So, we reject the null hypothesis, and we use Normal distribution for the test.

4 0

2 years ago

Write an exponential function in the form y<br> and (3,72).<br> ab" that goes through points (0,9)

Vikentia [17]

Answer:

$y=9 ( {2}^{x} )$

Step-by-step explanation:

Let the exponential function be

$y = a {b}^{x}$

We substitute (0,9) to get:

$9 = a {b}^{0}$

$9 = a(1)$

$a = 9$

The equation now becomes:

$y = 9 {b}^{x}$

We substitute (3,72) to get:

$72 =9 {b}^{3}$

$8={b}^{3} \\ {2}^{3} = {b}^{3}$

$b = 2$

The equation is therefore

$y=9 ( {2}^{x} )$

3 0

2 years ago

(b) we often read that iq scores for large populations are centered at 100. what percent of these 78 students have scores above

zheka24 [161]

Given that the<span> iq scores for large populations are centered at 100.

To get what percent of these 78 students have scores above 100 we conduct a normal distribution probability of the data.

P(x > 100) = P(z > (100 - 100)/sd) = P(z > 0) = 1 - P(z < 0) = 1 - 0.5 = 0.5 = 50%
</span>

5 0

2 years ago