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3 years ago

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A certain company's main source of income is selling cloth bracelets. The company's annual profit (in thousands of dollars) as a

function of the price of a bracelet (in dollars) is modeled by: P(x)=-2x^2+16x-24. What is the maximum profit that the company can earn?

2 answers:

larisa86 [58]3 years ago

7 0

Answer:

8

Step-by-step explanation:

tester [92]3 years ago

6 0

Answer:

8 thousand dollars

Step-by-step explanation:

The company's annual profit (in thousands of dollars) as a function of the price of a bracelet (in dollars) is modeled by: P(x)=-2x^2+16x-24

To find maximum profit , we need to find out the vertex

x coordinate of vertex formula is -b/2a

$P(x)=-2x^2+16x-24$

a=-2 and b = 16

$x= \frac{-b}{2a}= \frac{-16}{2(-2)} = 4$

Now we plug in 4 for x and find out P(4)

$P(x)=-2(4)^2+16(4)-24$ = 8

So the maximum profit the company can earn is 8 thousand dollars when price = $4

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Complete Question

In a study of the accuracy of fast food drive-through orders, one restaurant had 32 orders that were not accurate among 367 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is equal to 10%. Does the accuracy rate appear to be acceptable?

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to show that the rate of inaccurate orders is equal to 10%

Step-by-step explanation:

Generally from the question we are told that

The sample size is n = 367

The number of orders that were not accurate is $k = 32$

The population proportion for rate of inaccurate orders is p = 0.10

The null hypothesis is $H_o : p = 0.10$

The alternative hypothesis is $H_a : p \ne 0.10$

Generally the sample proportion is mathematically represented as

$\^ p = \frac{k}{n}$

=> $\^ p = \frac{32}{367}$

=> $\^ p = 0.0872$

Generally the test statistics is mathematically represented as

$z= \frac{ \^ p - p }{ \sqrt{ \frac{ p(1 - p)}{ n} } }$

=> $z= \frac{ 0.0872 - 0.10 }{ \sqrt{ \frac{ 0.10 (1 - 0.10 )}{367} } }$

=> $z= -0.8174$

From the z table the area under the normal curve to the left corresponding to -0.8174 is

$P(z < -0.8173 ) = 0.20688$

Generally the p-value is mathematically represented as

$p- value = 2 * 0.20688$

=> $p- value = 0.4138$

From the value obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to show that the rate of inaccurate orders is equal to 10%

4 0

2 years ago

The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)

Lemur [1.5K]

Answer:

Cardiac output: $F=0.055 L\s$

Step-by-step explanation:

Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.

To Find : Find the cardiac output.

Solution:

Formula of cardiac output: $F=\frac{A}{\int\limits^T_0 {c(t)} \, dt}$ ---1

A = 3 mg

$\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt$

Do, integration by parts

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}$

Substitute the value in 1

Cardiac output: $F=\frac{3}{54.49}$

Cardiac output: $F=0.055 L\s$

Hence Cardiac output: $F=0.055 L\s$

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3 years ago