The 12th term of 2, 8, 14 ....

A leaf is falling from the top of a tree. The height of the leaf in feet, y, can be found using the function y = -3.5x + 28, whe

Bess [88]

Answer:

It took 8 seconds for the leaf to reach the ground.

Step-by-step explanation:

The height of the leaf in feet can be found using the function:

y = -3.5*x + 28

where x is the time in seconds the leaf has been in the air.

You want to know how long it took for the blade to reach the ground. That is, the time it took for the blade to reach a height of 0 feet. So, replacing this value in the expression:

0= -3.5*x + 28

and solving you get:

-28= -3.5*x

(-28)÷ (-3.5)=x

8=x

<u><em> It took 8 seconds for the leaf to reach the ground.</em></u>

5 0

3 years ago

An automobile manufacturer claims that its car has a 33.7 miles/gallon (MPG) rating. An independent testing firm has been contra

Gnoma [55]

Answer:

$z=\frac{34-33.7}{\frac{1.6}{\sqrt{120}}}=2.05$

And the p value would be given by:

$p_v= 2*P(z>2.05) = 0.0404$

And since the p value is higher than the significance level we have enough evidence to fail to reject the null hypothesis.

Step-by-step explanation:

Data given and notation

$\bar X=34$ represent the sample mean

$\sigma=\sqrt{2.56}= 1.6$ represent the population standard deviation

$n=120$ sample size

$\mu_o =33.7$ represent the value that we want to test

$\alpha=0.02$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

System of hypotheses.

We need to conduct a hypothesis in order to check if the true mean is 33.7 mpg or no, the system of hypothesis would be:

Null hypothesis: $\mu =33.7$

Alternative hypothesis: $\mu \neq 33.7$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{34-33.7}{\frac{1.6}{\sqrt{120}}}=2.05$

And the p value would be given by:

$p_v= 2*P(z>2.05) = 0.0404$

And since the p value is higher than the significance level we have enough evidence to fail to reject the null hypothesis.

6 0

3 years ago

a company can make 5000 crayons in 6 minutes how many crayons can be made in 3 hours. please show the steps!

Sloan [31]

6 mins goes into 60 mins ten times.
so, first do
$5000 \times 10 = 50000$
now 50000 crauons are being made in 1 hour but your are trying to find how many crayons are being made in 3 hours
so, you multiply
$50000 \times 3 = 150000$
150000 is how many crayons are made in 3 hours.

7 0

3 years ago

Gradient of the line 3y-12x+7=0

Nata [24]

The gradient of the line 3y-12x+7=0 is; 4.

According to the question;

We are responsible to determine the gradient of the line 3y-12x+7=0.

To do this; we must rewrite the equation 3y-12x+7=0 in the slope-intercept form as follows;

3y-12x+7=0

3y = 12x - 7

y = 4x -7/4

By comparison with; y = mx + c;

where, gradient/slope is m;

The gradient/slope of the line 3y-12x+7=0 is; 4.