Casper had some money.He spent$180

The profit function for a product is given by p(x)=-x^3+3x^2+900x-2100, where x is the number of units produced and sold and P i

nalin [4]

Answer:

x = 30 and x = 3 both solve the equation correctly. See work below.

Step-by-step explanation:

The very first step is to realize that p(x) is in hundreds of dollars and that the given number is not. 60000 is not in hundreds of dollars. It is in dollars. 60000 dollars = 60000/100 = 600 hundreds of dollars.

Make the polynomial = 600

-x^3+3x^2+900x-2100 = 600 Subtract 600 from both sides

-x^3+3x^2+900x-2100 - 600 = 0 Combine

-x^3+3x^2+900x- 2700 = 0 Group the first and second term and the Thrid and fourth terms.

(-x^2 + 3x^2) + (900x - 2700) = 0 Bring out the common factors from both groups.

-x^2(x - 3) + 900(x - 3) = 0 Factor out x - 3 on both sides of the plus sign

(- x^2 + 900)(x - 3) = 0 Reverse -x^2 + 900 to 900 - x^2

(900 - x^2)(x - 3) = 0 factor (900 - x^2) using the difference of squares

(30 - x)(30 + x) (x - 3) = 0

The two answers that work are

30 - x = 0 Solve

- x = - 30 Divide by - 1

-x/-1 = -30/-1 Combine

x = 30

============

x - 3 = 0

x = 3

===========

There are two values that will work to give p(x) = 600. There is no way to account for why both values work.

The graph below confirms both answers.

3 0

3 years ago

A soccer team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium fo

lesya692 [45]

Answer:

45 premium tickets were sold

Step-by-step explanation:

p = premium

d = deluxe

r = regular

p+d+r = 273

6p+4d + 2r = 836

118+d = r

Replace r with 118+d

p+d+118+d = 273

p +2d = 273-118

p+2d = 155

6p+4d + 2(118+d) = 836

6p+4d + 236+2d = 836

6p +6d = 836-236

6p + 6d = 600

Divide by 6

p+d = 100

d = 100-p

Replace d in p +2d= 155

p +2(100-p) = 155

p+200-2p = 155

-p = 155-200

-p =-45

p =45

45 premium tickets were sold

3 0

3 years ago

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How do I divide 178.8 by 24?

Doss [256]

<span>7.45 is the final answer

178.8/ 24 = about 7.45</span>

4 0

2 years ago

Using traditional methods, it takes 10.1 hours to receive a basic driving license. A new license training method using Computer

Law Incorporation [45]

Answer:

We need to conduct a hypothesis in order to check if the technique performs differently than the traditional method, the system of hypothesis would be:

Null hypothesis: $\mu =10.1$

Alternative hypothesis: $\mu \neq 10.1$

$t=\frac{10.5-10.1}{\frac{1.4}{\sqrt{12}}}=0.990$

$p_v =2*P(t_{(11)}>0.990)=0.343$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can't conclude that the technique performs differently than the traditional method at 10% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=10.5$ represent the sample mean

$s=1.4$ represent the sample standard deviation

$n=12$ sample size

$\mu_o =10.1$ represent the value that we want to test

$\alpha=0.1$ 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 technique performs differently than the traditional method, the system of hypothesis would be:

Null hypothesis: $\mu =10.1$

Alternative hypothesis: $\mu \neq 10.1$

If we analyze the size for the sample is < 30 and 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:

$t=\frac{10.5-10.1}{\frac{1.4}{\sqrt{12}}}=0.990$

P-value

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

$df=n-1=12-1=11$

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

$p_v =2*P(t_{(11)}>0.990)=0.343$

Conclusion

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can't conclude that the technique performs differently than the traditional method at 10% of signficance.

7 0

3 years ago

Find the total surface area of the figure below:

kow [346]

Answer:

95

Step-by-step explanation:

Formula -

Triangle Area - 1/2bh

Square - l x w

Triangle - 5 x 7 = 35/2 = 17.5

Since there are four triangle, we will multiply 17.5 x 4 which is equal to 70

Square - 5 x 5 = 25

Now we add both 70 and 25 which is 95

So the total surface area is 95

8 0

2 years ago

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