To make 1 1/2 dozen muffins, a recipe uses 3 1/2 cups of flour.

tatyana61 [14]

Answer:

2x + y = -5 (which is Answer 1).

Step-by-step explanation:

The possible answer choices are all versions of the standard equation of a straight line: Ax + By + C = 0. If A and B are both positive, as they are here, then the slope is negative and has the form m = -A/B. Only the first answer choice passes here: with +2x and +1y, the slope is -2. This automatically eliminates the other possibilities.

Looking at the first answer choice, we see that A must be 2 and B must be 1

so that the slope is m = -2. Writing out this equation: Ax + By + C = 0.

Replace A with 2 and B with 1: 2x + y + C = 0.

Finally, replace x with -1 and y with -3: 2(-1) + (-3) + C = 0.

Solving this for C, we get -2 - 3 + C = 0, or -5 + C = 0, or C = 5.

We end up with 2x + y = -5 (which is Answer 1).

3 0

3 years ago

uppose that an automobile manufacturer advertises that its new hybrid car has a mean gas mileage of 50 miles per gallon. You tak

Harlamova29_29 [7]

Answer:

$t=\frac{47-50}{\frac{5.5}{\sqrt{30}}}=-2.988$

$p_v =2*P(t_{(29)}$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the true mean is significantly different from 50 mpg at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=47$ represent the sample mean

$s=5.5$ represent the sample standard deviation

$n=30$ sample size

$\mu_o =50$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is 50 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 50$

Alternative hypothesis: $\mu \neq 50$

If we analyze the size for the sample is = 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

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

$t=\frac{47-50}{\frac{5.5}{\sqrt{30}}}=-2.988$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=30-1=29$

Since is a two tailed test the p value would be:

$p_v =2*P(t_{(29)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the true mean is significantly different from 50 mpg at 5% of signficance.

4 0

3 years ago

A human heart beats approximately 60 times per minute. If a man lives to the age of 90, how many times will his heart in his lif

makkiz [27]

Answer:

90 Years = 47,304,000 Minutes = 47304000 Minutes.

Step-by-step explanation:

7 0

3 years ago

I wanted to knwo what two to the third power was please help

nikitadnepr [17]

Eight is the answer.