The profit on a teddy bear can be found by using the function P(x) = - 2x2 + 35x - 99 where x is the price of the bear.Calculate the price that maximizes profit.

Answers

Answer 1

Answer:

Answer:

x=8.75

Step-by-step explanation:

The price x that maximizes profit is the maximum value of the function, and the maximum value of the function is located at a point where the first derivative of the function is equal to zero. The first derivative is:

$P(x) = - 2x^2+35x-99\nP'(x)=-2(2)x^((2-1))+35(1)-0\nP'(x)=-4x+35$

Using P'(x)=0:

$0=-4x+35\n4x=35\nx=35/4\nx=8.75$

The minimum value of the function is also at a point where the first derivative of the function is equal to zero. To differentiate if x=8. is a minimum or a maximum obtain the second derivative and evaluate it at x=8.75 if the value P''(x)>0 x is minimum and if P''(x)<0 x is a maximum.

$P'(x)=-4x+35\nP''(x)=-4(1)\nP''(x)=-4$

Evaluating at x=8.75:

$P''(8.75)=-4$

Therefore, x=8.75 is the maximum value of the function and it is the price that maximizes profit.

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. What would be the new coordinates if (-2,-4) is translated 5 units up and7 units to the left.

Answers

Answer:

(-9, 1)

Step-by-step explanation:

translating UP is to increase on the y axis, so -4+5=1

translating to the LEFT is to subtract on the x axis so-2-7=-9

-9, 1 I think is the correct answer

A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of five cars form this company have an average gas mileage of 25.2 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?

Answers

Answer with explanation:

Let $\mu$ be the population mean.

Null hypothesis : $H_0:\mu\geq26$

Alternative hypothesis : $H_1:\mu<26$

Since the alternative hypothesis is left tailed, so the test is a left-tailed test.

Sample size : n=5 <30 , so we use t-test.

Test statistic: $t=\frac{\overline{x}-\mu}{(\sigma)/(√(n))}$

$t=(25.2-26)/((1)/(√(5)))\approx-1.79$

Critical t-value for t= $t_(n-1, \alpha)=t_(4,0.06)=1.9712$

Since, the absolute value of t (1.79) is less than the critical t-value , so we fail to reject the null hypothesis.

Hence, we have sufficient evidence to support the company's claim.

A stone which is dropped into a dry well hits the bottom in 2.2s how deep is the well. take g=10m/s

Answers

Answer:

23.7m

Step-by-step explanation:

Given parameters:

Time taken = 2.2s

Acceleration due to gravity = 10m/s

Unknown:

Depth of the well = ?

Solution:

To solve this problem, we simply apply one of the motion equations;

S = ut + $(1)/(2)$ gt²

where S = depth of the well

u = initial velocity

t = time taken

g = acceleration due to gravity

Input the parameters and solve for S;

Note initial velocity = 0;

S = $(1)/(2)$ x 9.8 x 2.2²

S = 23.7m

Simplity 1-5(3 + 2-3)?

Answers

Answer:

-9

Step-by-step explanation:

1 - 5 (3 + 2 - 3)

1 − 5 (5 − 3)

1 - 5 x 3

1 - 10

-9

Use pemdas

3+2 -3 = 2
1-5 = -4
-4 x 2 = -8
I hope that helps!

At the zoo there were 5 times as many tigers as lion Tom counted a total of 54 tigers and lions how many.tigers were there?

Answers

Answer:

5x=54

Step-by-step explanation:

5x=54

divide 5 by both sides

x=10.8

sorry if I am wrong but I tried my best

Daryl invested $2,200 for 3 years. He received interest of $264. What was the interest rate?

Answers

Answer:

Step-by-step explanation:

264 interest/3 years=88 interest/year

principal x interest rate =interest/year

2200 x interest rate =88

interest rate =88/2200

interest rate =.04 or 4%

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