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3 years ago

Someone please help me and show work

Mathematics

1 answer:

Feliz [49]3 years ago

4 0

Answer:

Step-by-step explanation:

The Total Cost formula for the Dealership is

$24 + ($99/hr)h, where h represents the number of hours of labor performed.

That for the Local Mechanic is

$45 + ($89/hr)h

We equate these two formulas so as to determine h, the number of hours elapsed so that the total costs are the same:

24 + 99h = 45 + 89h

Combining like terms, we get:

21 = 188h

Solve for h by dividing both sides by 188:

h = 188/21 = 8.95

The two bills would be equal 8.95 hours after commencement of the work.

Part b:

Dealership: $24 + ($99/hr)h. Evaluate this at 8.95 hrs: $910.05.

The dealership's bill would be more expensive AFTER 8.95 hours, because the rate of change ($99/hr) is greater in that case.

The local mechanic's total bill would be less up until the time that the car has been worked on for 8.95 hours.

$24 + ($99/hr)(8.95 hr) =

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Why do scientist collect data

julsineya [31]

As scientists conduct their research, they make observations and collect data. The observations and data often lead them to ask why something is the way it is. Scientists pursue answers to these questions in order to continue with their research.

5 0

3 years ago

The function C(x)=−20x+1681 represents the cost to produce x items. What is the least number of items that can be produced so th

Reptile [31]

Answer:

The least number of items to produce is 41

Step-by-step explanation:

Average Cost

Given C(x) as the cost function to produce x items. The average cost is:

$\displaystyle \bar C(X)=\frac{C(x)}{x}$

The cost function is:

$C(x) = -20x+1681$

And the average cost function is:

$\displaystyle \bar C(X)=\frac{-20x+1681}{x}$

We are required to find the least number of items that can be produced so the average cost is less or equal to $21.

We set the inequality:

$\displaystyle \frac{-20x+1681}{x}\le 21$

Multiplying by x:

$-20x+1681 \le 21x$

Note we multiplied by x and did not flip the inequality sign because its value cannot be negative.

Adding 20x:

$1681 \le 21x+20x$

$1681 \le 41x$

Swapping sides and changing the sign:

$41x \ge 1681$

Dividing by 41:

$x\ge 41$

The least number of items to produce is 41

8 0

3 years ago

(4x + 4)(ax – 1) – x2 +4

Oksana_A [137]

Answer:

b=-3

Step-by-step explanation:

If the expression simplifies to bx that means the $x^{2}$ terms and the constant terms must be cancel out.

Simplify it first.

$(4x+4)(ax-1)-x^{2} +4\\=(4ax^{2} -4x+4ax-4)-x^{2} +4\\=4ax^{2} -x^{2} -4x+4ax-4+4\\=4ax^{2} -x^{2} -4x+4ax$

We know –4 + 4 will cancel out. If we simplify this expression to only an x term, then the $x^{2}$ terms should be cancelled. Therefore, we say that 4ax^2 – x^2 = 0.

$4ax^{2} -x^{2} =0\\x^{2} (4a-1)=0\\4a-1=0\\4a=1\\a=\frac{1}{4}$

If we put a = ¼, then we can find the value of b:

$=4(\frac{1}{4} )x^{2} -x^{2} -4x+4(\frac{1}{4} )x\\=x^{2} -x^{2} -4x+x\\ (cancel out x^{2} terms)\\$

$=-3x$

$bx=-3x\\$ if the expression is equivalent to bx

Therefore, b = –3.

8 0

3 years ago

Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the number of arrivals in a minute follows the

Black_prince [1.1K]

Answer:

a) P(2)=0.270

b) P(X>3)=0.605

c) P=0.410

Step-by-step explanation:

We know that customers arrive at a grocery store at an average of 2.1 per minute. We use the Poisson distribution:

$\boxed{P(k)=\frac{\lambda^k \cdot e^{-\lambda}}{k!}}$

a) In this case: $\lambda=2.1$

$P(2)=\frac{2.1^2 \cdot e^{-2.1}}{2}\\\\P(2)=0.270$

Therefore, the probability is P(2)=0.270.

b) In this case: $\lambda=2\cdot 2.1=4.2$

$P(X>3)=1-P(X\leq 3)\\\\P(X>3)=1-\sum_{x=0}^3 \frac{4.2^x \cdot e^{-4.2}}{x!}\\\\P(X>3)=1-0.395\\\\P(X>3)=0.605$

Therefore, the probability is P(X>3)=0.605.

c) We know that two customers came in in the first minute. That is why we calculate the probability of at least 5 customers entering the other 2 minutes.

In this case: $\lambda=2\cdot 2.1=4.2$

$P(X\geq 5)=1-P(X$