What translation is made from f(x) = x to f(x) = (x + 3).

Tenacious ran 12 miles in 2 hours. then he ran 36 miles in 3 hours. by how much did his rate increase

Lyrx [107]

ANSWER

$6mph$

EXPLANATION

At first Tenacious ran 12 miles in 2 hours.

The rate at which he ran is the same as his speed.

$= \frac{12}{2} mph$
$= 6mph$

Now Tenacious ran 36 miles in 3 hours,

His new rate is

$= \frac{36}{3} mph$

$= 12mph$

Tenacious' rate increased from 6mph to 12mph.

Hence his rate increased by 6mph

7 0

4 years ago

Read 2 more answers

Use the normal distribution to find a confidence interval for a difference in proportions p1-p2 given the relevant sample result

9966 [12]

Answer:

a) $\hat p_1 -\hat p_2= 0.2-0.35= -0.15$

b) $ME= 2.58 \sqrt{\frac{0.2(1-0.2)}{60} +\frac{0.8(1-0.8)}{100}} =0.169$

c) $(0.2-0.35) - 2.58 \sqrt{\frac{0.2(1-0.2)}{60} +\frac{0.8(1-0.8)}{100}} =-0.319$

$(0.2-0.35) + 2.58 \sqrt{\frac{0.2(1-0.2)}{60} +\frac{0.8(1-0.8)}{100}} =0.0185$

And the 99% confidence interval would be given (-0.319;0.0185).

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_1$ represent the real population proportion 1

$\hat p_1=0.2$ represent the estimated proportion 1

$n_1=60$ is the sample size required 1

$p_2$ represent the real population proportion for 2

$\hat p_2 =0.35$ represent the estimated proportion 2

$n_2=100$ is the sample size required for Brand B

$z$ represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_2)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}$

Part a

The best estimate is given by:

$\hat p_1 -\hat p_2= 0.2-0.35= -0.15$

Part b

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The margin of error is given by:

$ME= 2.58 \sqrt{\frac{0.2(1-0.2)}{60} +\frac{0.8(1-0.8)}{100}} =0.169$

Part c

And replacing into the confidence interval formula we got:

$(0.2-0.35) - 2.58 \sqrt{\frac{0.2(1-0.2)}{60} +\frac{0.8(1-0.8)}{100}} =-0.319$

$(0.2-0.35) + 2.58 \sqrt{\frac{0.2(1-0.2)}{60} +\frac{0.8(1-0.8)}{100}} =0.0185$

And the 99% confidence interval would be given (-0.319;0.0185).

4 0

4 years ago

Graph the line with the slope 1/3 that contains the point (-4, -3)

forsale [732]

Answer:

So, 1 point is on (-4, -3)

Other point is on (-4, -7)

Step-by-step explanation:

Slope = y/x - y1/x1

=> -3 / -4 - ? = 1/3

=> -3 / -4 - 1/3 = ?

=> -3 -1 / -4 - 3

=> -4 / -7

So, -3 / -4 - (-4 / -7)

=> -3 +4 / -4 + 7

=> 1/3

So 1 point is on (-4 , -3)

Other point is on (-4, -7)

4 0

3 years ago

Read 2 more answers

- 6(x + 2) + 2x - 4 = 8(x - 2) + 8<br> does this have a solution if do why

kobusy [5.1K]

Answer:

Yes, there is a solution: - 2/3

Step-by-step explanation:

Step 1:

- 6 ( x + 2 ) + 2x - 4 = 8 ( x - 2 ) + 8

Step 2:

- 6x - 12 + 2x - 4 = 8x - 16 + 8

Step 3:

- 4x - 16 = 8x - 8

Step 4:

- 16 = 12x - 8

Step 5:

- 8 = 12x

Step 6:

- 8/12 = - 2/3

Answer:

- 2/3

Hope This Helps :)

6 0

3 years ago

Read 2 more answers

Which of the following is equivalent to 16/3

Neko [114]

Answer:

C

Step-by-step explanation:

6÷3=2

9÷3=3

combined that is 15/3

so the extra 1 goes back into the fraction

giving us 5 1/3

6 0

2 years ago