H(t) = – 16t2 + 48t + 28

Answers

Answer 1
Answer:

Answer:

-4(2t+1)(2t-7)

Step-by-step explanation:

First factor out the common term -4

Then factor out -4^2

Answer 2
Answer:

Answer:

the answer is( -42t+1)(2t-7)


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A bank credit card charges interest at the rate of 24% per year, compounded monthly. If a senior in college charges $1,500 to pay for college expenses, and intends to pay it in one yewhat will he have to pay? (Round your answer to the nearest cent.)

$

Answers

Answer: 1902.36

Step-by-step explanation:

When interest is compounded monthly , the formula to find the accumulated amount is

A=P(1+(r)/(12))^(12t) , where P = principal value , r = rate of interest , t = time.

As per given,

r= 24% =  0.24

P= $1500

t= 1 year

Put all value in formula , we get

A= 1500(1+(0.24)/(12))^(12* 1)\n\n=1500(1+0.02)^(12)\n\n=1500(1.02)^(12)\n\n=1500(1.26824179456)\approx1902.36

Hence, he need to pay $1902.36.

The filling variance for boxes of cereal is designed to be .02 or less. A sample of 41 boxes of cereal shows a sample standard deviation of .16 ounces. Use α = .05 to determine whether the variance in the cereal box fillings is exceeding the design specification.

Answers

Answer:

\chi^2 =(41-1)/(0.02) 0.0256 =51.2

p_v =P(\chi^2_(40) >51.2)=0.1104

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(51.2,40,TRUE)"

If we compare the p value and the significance level provided 0.05 we see that p_v >\alpha so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 0.02, so there is no a violation of the specifications.

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

n=41 represent the sample size

\alpha=0.05 represent the confidence level  

s^2 =0.16^2 =0.0256 represent the sample variance obtained

\sigma^2_0 =0.02 represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance specification is higher than the standard of 0.02, so the system of hypothesis would be:

Null Hypothesis: \sigma^2 \leq 0.02

Alternative hypothesis: \sigma^2 >0.02

Calculate the statistic  

For this test we can use the following statistic:

\chi^2 =(n-1)/(\sigma^2_0) s^2

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

\chi^2 =(41-1)/(0.02) 0.0256 =51.2

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case df = 41-1=40. And since is a right tailed test the p value would be given by:

p_v =P(\chi^2_(40) >51.2)=0.1104

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(51.2,40,TRUE)"

Conclusion

If we compare the p value and the significance level provided 0.05 we see that p_v >\alpha so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 0.02, so there is no a violation of the specifications.

The owner of a construction company buys cement in bulk. He recently paid $600.00 for 6 tons of cement. How much did he pay per pound? (1 ton = 2,000 lbs.)$0.05 per pound
$0.30 per pound
$0.50 per pound
$100.00 per pound

Answers

Final answer:

The owner of the construction company paid A) $0.05 per pound for the cement.

Explanation:

To figure out how much the owner of the construction company paid per pound, we need to convert tons to pounds. We know that 1 ton is equal to 2,000 pounds, so 6 tons is equal to 6 * 2,000 = 12,000 pounds. Now we can calculate the price per pound by dividing the total cost of $600 by the number of pounds, which is $600 / 12,000 = $0.05 per pound.

Learn more about Cost per pound for cement

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Answer: $100.00 per pound

A fire ranger stands atop an observation tower 70 feet above the ground and sees a fire in the distance. She measures the angle of depression from where she is to the fire and finds it to be 34° How far away from the base of the tower is the fire?​

Answers

Answer:

103.78\:\mathrm{ft}

Step-by-step explanation:

We can form a right triangle where the distance between the ranger's current position and fire is the hypotenuse of the triangle. In a right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse.

Therefore, we have:

\tan 34^(\circ)=(70)/(x), where x is the distance between the base of the tower and the fire.

Solving, we get:

x=(70)/(\tan 34^(\circ))=103.779267796\approx \boxed{103.78\:\mathrm{ft}}

How to convert from point slope form to slope intercept form

Answers

Answer:

y=mx+(y_1-mx_1), b=y_1-mx_1

Step-by-step explanation:

The point slope form of the equation of a line is given as:

y-y_1=m(x-x_1)

The slope-intercept form of the equation of a line is given as:

y=mx+b

where: m=slope, b=y-intercept.

To convert from the point slope form to slope intercept form, follow these steps:

Step 1: Distribute the right hand side

y-y_1=m(x-x_1)\ny-y_1=mx-mx_1

Step 2: Isolate the y variable

y=mx-mx_1+y_1\ny=mx+(y_1-mx_1)

This is the slope-intercept form. We can evaluate y_1-mx_1 $ given values for $(x_1,y_1)$ and slope, m

What is the slope of the line represented by the equation y = - 1/2x + 1/4

Answers

Answer:

The slope is -1/2

Step-by-step explanation:

-1/2 is a negative slope. Down 1 to the right 2