Consider how the methods of undetermined coefficients and variation of parameters can be combined to solve the given differential equation. Carry out your ideas to solve the differential equation. y'' − 2y' + y = 4x2 − 6 + x−1ex

Step-by-step explanation:

Check the attached file for solution and

simulation screen shot

R-Code:

Sample mean

sd = 60 Population Standard deviation

n = 10 Sample size

conf.level = 0.99 Confidence level

[tex]\alpha = 1-conf.level[/tex]

[tex]z\star = \round(\qnorm(1-\alpha/2),2); z.\star[/tex]

[tex]E = \round(z* \times \sigma/\sqrt(n),2); E[/tex]

[tex]x= c(E,-E)[/tex]

Answer:

[tex](x, y) = \left(\frac{3}{2}, \frac{\sqrt{3}}{2}\right)[/tex]

Step-by-step explanation:

The rectangular coordinates of the point are:

[tex](x,y) = \left(\sqrt{3}\cdot \cos\frac{\pi}{6}, \sqrt{3}\cdot \sin\frac{\pi}{6}\right)[/tex]

[tex](x, y) = \left(\frac{3}{2}, \frac{\sqrt{3}}{2}\right)[/tex]

Answer:

B

Step-by-step explanation:

Answer:

a) We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.3[/tex]  

Alternative hypothesis:[tex]p > 0.3[/tex]  

Right tailed test

b) [tex]p_v =P(z>2.32)=0.0102[/tex]  

c) So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

Step-by-step explanation:

Part a: Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.3[/tex]  

Alternative hypothesis:[tex]p > 0.3[/tex]  

Right tailed test

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

For this case the statistic is given by [tex] z_{calc}= 2.32[/tex]

Part b: Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>2.32)=0.0102[/tex]  

Part c

So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.1[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

The hypothesis test is right-tailed. The P-value should be assessed using a standard normal distribution, and if it is less than the significance level of α0.10, the null hypothesis should be rejected. However, the exact P-value for z=2.32 needs to be determined before a decision can be made.

The test statistic of z=2.32 is obtained when testing the claim that p>0.3. This indicates the hypothesis test in question is right-tailed, as the alternative hypothesis (Ha) suggests that the proportion is greater than 0.3 (p>0.3).

To determine the P-value, we look at the area to the right of our z-test statistic in the standard normal distribution. Given that our z-value is 2.32, the P-value would typically be found using a z-table or statistical software. However, the provided reference states that for a z-test value of 3.32, which seems to be a typo since our z-value is 2.32, the P-value would be 0.0103. We need to correct this and find the P-value for z=2.32, which we would expect to be larger than the P-value for z=3.32 since 2.32 is closer to the mean of the standard normal distribution.

P-value interpretation is critical when deciding whether to reject the null hypothesis (H0). In this case, if we use a significance level of α=0.10, we compare the P-value to this significance level. If the P-value is less than α, we reject H0; if it's greater, we fail to reject H0. Without the exact P-value for z=2.32, we cannot make a definitive decision, but typically, a z-value of 2.32 would result in a P-value less than 0.10, which leads to rejection of H0.

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Answer:

The minimum score required for a letter of recognition is 631.24.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 493, \sigma = 108[/tex]

What is the minimum score required for a letter of recognition

100 - 10 = 90th percentile, which is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 493}{108}[/tex]

[tex]X - 493 = 1.28*108[/tex]

[tex]X = 631.24[/tex]

The minimum score required for a letter of recognition is 631.24.

Answer:

[tex]b=493 +1.28*108=631.24[/tex]

The minimum score required for a letter of recognition would be 631.24

Step-by-step explanation:

Let X the random variable that represent the writing scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(493,108)[/tex]  

Where [tex]\mu=493[/tex] and [tex]\sigma=108[/tex]

On this questio we want to find a value b, such that we satisfy this condition:

[tex]P(X>b)=0.10[/tex]   (a)

[tex]P(X<b)=0.90[/tex]   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find b.

As we can see on the figure attached the z value that satisfy the condition with 0.90 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

[tex]P(X<b)=P(\frac{X-\mu}{\sigma}<\frac{b-\mu}{\sigma})=0.90[/tex]  

[tex]P(z<\frac{b-\mu}{\sigma})=0.90[/tex]

[tex]z=1.28<\frac{b-493}{108}[/tex]

And if we solve for a we got

[tex]b=493 +1.28*108=631.24[/tex]

The minimum score required for a letter of recognition would be 631.24

Answer:

a. 10% - 15%

Step-by-step explanation:

The percentage of a job opening, that gets published, is 15% to 20%,  just since just scarcely any occupations can be seen on a paper, commercials, and employment sheets. A large portion of the employment opportunities can be gotten notification from those representatives that worked inside the organization since there is only two job vacancies.

Answer:

the answer is b

Step-by-step explanation:

Answer:

[tex]t=\frac{12.2-11.5}{\frac{1.6}{\sqrt{34}}}=2.551[/tex]    

[tex] df = n-1=34-1=33[/tex]

[tex]p_v =P(t_{(33)}>2.551)=0.008[/tex]  

Since the p value is less than the significance level of 0.05 we have enough evidence to reject the null hypothesis in favor of the claim

And the best conclusion for this case would be:

b)The p-value is 0.008, indicating sufficient evidence for his claim.

Step-by-step explanation:

Information provided

[tex]\bar X=12.2[/tex] represent the sample mean fould against

[tex]s=1.6[/tex] represent the sample standard deviation

[tex]n=34[/tex] sample size  

represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean is higher than 11.5 fouls per game:  

Null hypothesis:[tex]\mu \leq 11.5[/tex]  

Alternative hypothesis:[tex]\mu > 11.5[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

The statistic is given by:

[tex]t=\frac{12.2-11.5}{\frac{1.6}{\sqrt{34}}}=2.551[/tex]    

P value

The degreed of freedom are given by:

[tex] df = n-1=34-1=33[/tex]

Since is a one side test the p value would be:  

[tex]p_v =P(t_{(33)}>2.551)=0.008[/tex]  

Since the p value is less than the significance level of 0.05 we have enough evidence to reject the null hypothesis in favor of the claim

And the best conclusion for this case would be:

b)The p-value is 0.008, indicating sufficient evidence for his claim.

Answer:

$5,805.92

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 3% into a decimal:

3% -> [tex]\frac{3}{100}[/tex] -> 0.03

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

[tex]A=5,000(1+\frac{0.03}{4})^{4(5)}[/tex]

[tex]A=5,805.92[/tex]

The value of the investment after 5 years will be $5,805.92

Investment value after 5 years, compounded quarterly at 3%, is approximately $5,805.83.

let's calculate step by step.

1. First, let's convert the annual interest rate to decimal form:

 [tex]\[ r = 3\% = \frac{3}{100} = 0.03 \][/tex]

2. Now, let's plug in the given values into the compound interest formula:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

  where:

[tex]- \( P = $5000 \)\\ - \( r = 0.03 \)\\ - \( n = 4 \)\\ - \( t = 5 \)[/tex]

3. Substituting these values into the formula, we get:

[tex]\[ A = 5000 \left(1 + \frac{0.03}{4}\right)^{4 \times 5} \][/tex]

4. Simplifying inside the parentheses:

[tex]\[ A = 5000 \left(1 + 0.0075\right)^{20} \][/tex]

5. Calculating [tex]\( (1 + 0.0075) \):[/tex]

 [tex]\[ 1 + 0.0075 = 1.0075 \][/tex]

6. Now, raise [tex]\( 1.0075 \)[/tex]  to the power of [tex]\( 20 \):[/tex]

[tex]\[ (1.0075)^{20} \][/tex]

  Using a calculator,[tex]\( (1.0075)^{20} \)[/tex] is approximately [tex]\( 1.161166 \).[/tex]

7. Finally, multiply this result by [tex]\( 5000 \):[/tex]

 [tex]\[ A = 5000 \times 1.161166 \]\\ \[ A \approx 5,805.83 \][/tex]

So, the value of the investment in five years, compounded quarterly at a 3% interest rate, would be approximately $5,805.83.

here is complete question:-

"If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in five years?"

Answer: 8/10 or 4/5

Step-by-step explanation:

10/10 - 2/10 = 8/10

Answer:

Since 10 - 2 = 8

The fraction of the remaining oceans would be 8/10

And if you simplify both 8 and 10 by 2

Meaning you divide them by two

8 ÷ 2 = 4

10 ÷ 2 = 5

Our new fraction is 4/5

~DjMia~

Answer:

H0 : mu1 = mu2

Ha : mu1 ≠ mu2

Which means

Null hypothesis H0; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is the same/equal

Alternative hypothesis Ha; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is different (not equal)

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean(i.e it tries to prove that the old theory is true). While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

Therefore, for the case above;

H0 : mu1 = mu2

Ha : mu1 ≠ mu2

Which means

Null hypothesis H0; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is the same/equal

Alternative hypothesis Ha; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is different (not equal)

The answer is c

Step-by-step explanation:

Answer:

answwr is c and i got it right

Step-by-step explanation:

Answer:

 We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .

Step-by-step explanation:

Given -

The sample size is large then we can use central limit theorem

n = 50 ,  

Standard deviation[tex](\sigma)[/tex] = 7.1

Mean [tex]\overline{(y)}[/tex] = 110

[tex]\alpha =[/tex] 1 - confidence interval = 1 - .98 = .02

[tex]z_{\frac{\alpha}{2}}[/tex] = 2.33

98% confidence interval for the mean caffeine content for cups dispensed by the machine = [tex]\overline{(y)}\pm z_{\frac{\alpha}{2}}\frac{\sigma}\sqrt{n}[/tex]

                     = [tex]110\pm z_{.01}\frac{7.1}\sqrt{50}[/tex]

                      = [tex]110\pm 2.33\frac{7.1}\sqrt{50}[/tex]

       First we take  + sign

   [tex]110 + 2.33\frac{7.1}\sqrt{50}[/tex] = 112.34

now  we take  - sign

[tex]110 - 2.33\frac{7.1}\sqrt{50}[/tex] = 107.66

 We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .

Final answer:

A 98% confidence interval for the mean caffeine content of cups dispensed by the machine is calculated using the sample mean, the standard deviation, and the Z-score for a 98% confidence level, leading to an interval of (107.72 mg, 112.28 mg). We can be 98% confident that the true mean caffeine content lies within this range.

Explanation:

To construct a 98% confidence interval for the mean caffeine content of cups dispensed by the machine, we use the provided sample mean (μ), which is 110 mg, and the standard deviation (s), which is 7.1 mg, of the 50 cups sampled. Since the sample size is 50, which is more than 30, we can use the Z-distribution as an approximation of the T-distribution for this confidence interval as the Central Limit Theorem suggests that the distribution of sample means will be normally distributed if the sample size is large enough. Using a Z-score for 98% confidence, which typically is approximately 2.33 (you would obtain the exact value from a Z-table), the margin of error (E) can be calculated using the formula E = Z * (s/√n), where n is the sample size (50 in this case).

The margin of error is then 2.33 * (7.1/√50), which equals approximately 2.28 mg. The 98% confidence interval is therefore the sample mean plus or minus the margin of error, which is 110 mg ± 2.28 mg or (107.72 mg, 112.28 mg).

The interpretation of this confidence interval is that we can be 98% confident that the true mean caffeine content of all cups of coffee dispensed by the machine falls between 107.72 mg and 112.28 mg.

Answer:

[tex]\Delta A = 5.9\,cm^{2}[/tex]

Step-by-step explanation:

The area of an rectangle is given by the following formula:

[tex]A = w\cdot h[/tex]

Where:

[tex]w[/tex] - Width, in centimeters.

[tex]h[/tex] - Height, in centimeters.

The differential of the expression is derived hereafter:

[tex]\Delta A = \frac{\partial A}{\partial w} \cdot \Delta w + \frac{\partial A}{\partial h}\cdot \Delta h[/tex]

[tex]\Delta A = h \cdot \Delta w + w \cdot \Delta h[/tex]

[tex]\Delta A = (31\,cm)\cdot (0.1\,cm) + (28\,cm)\cdot (0.1\,cm)[/tex]

[tex]\Delta A = 5.9\,cm^{2}[/tex]

Using differentials the maximum error in the calculated area of the rectangle wi’ould be 5.9 cm

The area formular of a rectangle is :

Maximum error can be defined thus :

Δmax = (L × Δe) + (W × Δe)

Δmax = (31 × 0.1) + (28 × 0.1)

Δmax = 3.1 + 2.8

Δmax = 5.9 cm

Hence, the maximum error in the calculated area value is 5.9 cm.

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Answer:

The answer is B.

Step-by-step explanation:

The example given in the question uses the null hypothesis versus the alternative hypothesis. Null hypothesis is the statement that is tested to be true or not and if it is not true, then the alternative hypothesis is accepted.

In the example, it is stated that the hypothesis test for the null hypothesis failed which means that the statement given on the percentage of students who read the book is false.

Then the option b is going to be interpreted which claims that the null hypothesis is false and there is not enough evidence to say that less than 55% of students read the textbook.

I hope this answer helps.

Final answer:

When a hypothesis test does not reject the null hypothesis with a p-value greater than the alpha level of 0.05, it indicates that there is not sufficient evidence to support the claim being tested, in this case, that less than 55% of students read the textbook.

Explanation:

If a hypothesis test is performed and fails to reject the null hypothesis, the interpretation depends on the results related to the alpha level and the p-value. In this case, where the claim is that less than 55% of students read the textbook and the p-value is greater than the alpha level (0.05 or 5%), the correct interpretation is that there is not sufficient evidence to support the claim that less than 55% of students read the text. This means that the sample data does not provide strong enough evidence to infer that the proportion of students who read the textbook is less than 55% for the entire population of students.

Therefore, the correct answer is:

b. There is not sufficient evidence to support the claim that less than 55% of students read this text.

Answer:

C

Step-by-step explanation:

A cube has 6 faces

Each face is a square of area:

5² = 25

Surface area: 6 × 25

= 150 in²

Answer:

150 in^2

Step-by-step explanation:

The surface area of a cube is given by

SA = 6 s^2 where s is the side length

SA = 6 (5)^2

    = 6 * 25

    = 6*25

    = 150 in^2

Answer:

Probability that it wins at least 3 of its final 5 games = .02387

Step-by-step explanation:

Given -

The probability of win the weekend game = 0.5

The probability of loose  the weekend game = 0.5

If he wins the game this weekend then it will play its final 5 games in the upper bracket of its league

In this case,  probability of success is (p) = 0.3

probability of failure is (q) = 1 - p = 0.7

Let X be number of game won out of last five games

probability that it wins at least 3 of its final 5 games

( 1 )

[tex]P(X\geq3)[/tex] = [tex]P(X\geq3/first\; game\; won)[/tex] ( probability of first game won )

               =   [tex]0.5\times[/tex]P( X =3 ) + [tex]0.5\times[/tex]P( X =4) + [tex]0.5\times P(X = 5)[/tex]

                =  [tex]0.5\times\binom{5}{3}(0.3)^{3}(0.7)^{2} + 0.5\times\binom{5}{4}(0.3)^{4}(0.7)^{1}[/tex] + [tex]0.5\times\binom{5}{5}(0.3)^{5}(0.7)^{0}[/tex]

                 = [tex]0.5\times\frac{5!}{(3!)(2!)}\times(0.3)^{3}\times(0.7)^{2} + 0.5\times\frac{5!}{(4!)(1!)}\times(0.3)^{4}\times(0.7)^{1}[/tex] + [tex]0.5\times\frac{5!}{(5!)(0!)}\times(0.3)^{5}\times(0.7)^{0}[/tex]= = .065 + .014 + .001215  = .080

If he loose the game this weekend then it will play its final 5 games in the lower bracket of its league

In this case,  probability of success is (s) = 0.4

probability of failure is (t) = 1 - s = 0.6

( 2 )

[tex]P(X\geq3/first\; game\; lost)[/tex] ( probability of first game lost )

= [tex]0.5\times P(X = 3) + 0.5\times P(X = 4)[/tex] + [tex]0.5\times P(X=5)[/tex]

= [tex]\binom{5}{3}(0.4)^{3}(0.6)^{2} + 0.5\times\binom{5}{4}(0.4)^{4}(0.6)^{1}[/tex]+ [tex]0.5\times\binom{5}{5}(0.4)^{5}(0.6)^{0}[/tex]

= [tex]0.5\times\frac{5!}{(3!)(2!)}\times(0.4)^{3}\times(0.6)^{2} + 0.5\times\frac{5!}{(4!)(1!)}\times(0.4)^{4}\times(0.6)^{1}[/tex] + [tex]0.5\times\frac{5!}{(5!)(0!)}\times(0.4)^{5}\times(0.6)^{0}[/tex] = = .1152 + .0384 + .00512 = .1587

Required probability = ( 1 ) + ( 2 ) = .02387

Answer:

4.49

Step-by-step explanation:

Answer:

4.49

Step-by-step explanation:

*Imagine it as money, you have $4.25 and you find $0.24

1) 4.25 + 0.24= 4.49

You now have $4.49

Hoped that helped ;)

Answer:

80 meters (8*10=80)

Answer:

80

Step-by-step explanation:

10 times 8= 80

to find the area is always lenght × height × weight

to find the perimeter is always lenght × lenght × heigth × heigth

example...

a house with the height of 5 and the lenght of 1 .find the perimeter

5+5+1+1= 12

Answer:

Step-by-step explanation:

He invested $41,000 more than 4 times the amount at 9%.

Total Annual Interest Earned = $35,260

Therefore, Time=1 year

Simple Interest[tex]=\frac{Principal X Rate X Time}{100}[/tex]

Therefore, his total interest

=Interest from Investment 1 + Interest from Investment 2

[tex]35260=\left(\frac{x*5*1}{100} \right)+\left(\frac{4x+41000*9*1}{100} \right)\\35260=0.05x+(0.36x+3690)\\35260-3690=0.05x+0.36x\\31570=0.41x\\\text{Divide both sides by 0.41}\\x=\$77000[/tex]

Therefore:

The amount invested at 5%=$77,000

The amount invested at 9%=$(4*77,000+41000)=$349,000

Answer:

2%

Step-by-step explanation:

You do 12÷6×1=2

I used PEMDAS

Final answer:

The probability that Lue will roll a sum of 12 on two rolls of a standard six-sided die is 1/36 or about 2.78%, as only the combination (6,6) results in the sum of 12.

Explanation:

Probability of Rolling a Sum of 12

To calculate the probability that Lue will roll a sum of 12 on two rolls of a six-sided die, we need to consider all the possible combinations that can result in a sum of 12. These combinations are (6,6). Since each die is independent, we calculate the probability for one die and then square it for two dice, because there is only one way to get a six on a die, and there are six faces. Therefore, the probability of rolling a six is:

1/6

To find the probability of rolling two sixes, we multiply the probabilities of each independent event:

(1/6) × (1/6) = 1/36

So, the probability that Lue will roll a sum of 12 in two rolls is 1/36, or approximately 2.78%.

Answer:

1. y + 10 - 3/2y = -y/2 + 10

2. 2r+ 7r-r - 9 = 8r - 9

3.  7 + 4p-5+p+2q = 2 + 5p + 2q

Step-by-step explanation:

basically you can add terms that have the same variable

integers can be added together, Xs can be added, Zs, Ys, As, Bs, Cs, you get the point

1. y + 10 - 3/2y = -y/2 + 10

2. 2r+ 7r-r - 9 = 8r - 9

3.  7 + 4p-5+p+2q = 2 + 5p + 2q (do not add different variables p and q ) together

try 4-6 on your own to get this skill down, if you need help with those just let me know

To find the annual interest rate of Nadia’s account, we use the simple interest formula I = PRT. By rearranging the formula and plugging in the known values, we determine that the interest rate is 5.5%.

To determine the interest rate of Nadia’s account, we can use the formula for simple interest I = PRT, where I is the interest earned, P is the principal amount deposited, R is the annual interest rate in decimal, and T is the time in years. In Nadia's case, we know that she earned $990 in interest (I), deposited $3000 (P), over 6 years (T).

We need to solve for R.

The formula thus becomes: $990 = $3000 × R × 6

To find R, we divide both sides of the equation by $3000 × 6:

R = $990 / ($3000 × 6)

R = $990 / $18000

R = 0.055 or 5.5%

Therefore, the annual interest rate Nadia received on her account was 5.5%.

Answer:

Step-by-step explanation:

Each rotation is 360° or 2π radians. So, 36.7 rotations is ...

  36.7×360° = 13,212°

or

  36.7×2π = 73.4π radians

Answer:

##  Profit/Loss = [tex]14x-400[/tex]

##  29 tickets

Step-by-step explanation:

Profit/Loss is Revenue - Cost

For the fundraisers:

Revenue comes from tickets sold at $14 each

x tickets sold, means the revenue is:

14x

Now, cost is what they are going to give out, that is $400 TV Set, so the cost is:

400

Hence, Profit/Loss would be:

Profit/Loss = [tex]14x-400[/tex]

Raffle sales equaling the cost of prize is basically when we break-even, or when profit/loss is equal to 0. So we solve the equation:

Profit/Loss = 14x - 400

0 = 14x - 400

14x = 400

x = 28.57

We can't sell fractional tickets, so we have to sell 29 tickets in order to break even

At a 5 percent significance level and with a p-value of 0.023, we reject the null hypothesis, concluding that more than 20% of cars are speeding.

The question involves determining whether to reject the null hypothesis based on a p-value from a statistical test concerning the true proportion of cars that are speeding on a highway. Since the p-value of 0.023 is less than the alpha level of 0.05, we would reject the null hypothesis (H0: p = 0.20). At the 5 percent significance level, there is sufficient evidence to conclude that more than 20% of cars are speeding on the highway.

Since the p-value is less than the alpha level of 0.05, we reject the null hypothesis. Therefore, the police department should consider installing the speed sensor and traffic camera.

To determine if the police department should install a speed sensor and traffic camera based on a significance test, we need to examine the hypotheses:

H0: p = 0.20 (the true proportion of cars speeding is 20%)

H1: p > 0.20 (the true proportion of cars speeding is greater than 20%)

Given that in a random sample of 100 cars, 28 were speeding, the test resulted in a p-value of 0.023. At the alpha level of 0.05, since the p-value (0.023) is less than alpha (0.05), we reject the null hypothesis.

In conclusion, at the 5 percent significance level, there is sufficient evidence to conclude that the true proportion of cars speeding is greater than 20%, justifying the installation of the speed sensor and traffic camera.

Answer:0.6 sec

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.6 is the answer just took the test

Answer:

-1.39

Step-by-step explanation:

Revenue and cost as a function of units sold are [tex]u(x) = 9x-2x^{2}[/tex]and[tex]c(x)=x^{3}-3x^{2}+4x+1[/tex]  respectively.

we are have to know for which value or input units are these functions at maximum which translates to for how many units is the revenue maximum and for how many same units is our cost minimum.

Answer:

55

Step-by-step explanation:

Combinations formula is used to make choice of 'R' out of 'N' options =

N(C)R = N ! / [ R ! . (N-R)! ]

Total choices to choose 4 out of 8 friends = 8C4

= 8! / (4! 4!)  

= 70

Choices for calling them 2 together = 2C2 x 6C2

= 1 x [ 6! / (2! 4!)]

= 15

So : Number of choices that the 2 friends are not called together = Total choices - choices they are called together

= 70 - 15 = 55