4. Find the Area of the trapezoid.

Answer:

y= 3x+4

Step-by-step explanation:

standard form is always y equals first

Answer:

the particular solution is

Y_{p}= C +D\sin 5t +E\cos 5t + F\exp 4t + G\exp -2t

the differential operator that annihilate the non homogeneous differential equation is

D(D^2+5)

Step-by-step explanation:

hello,

i believe the non homogeneous differential equation is

[tex]U^{''} - 2U^{'} - 8= \cos 5x + 7[/tex]

the homogeneous differential equation of the above is

[tex]u^{''} -2u^{'} -8 =0[/tex]

the differential form of the above equation is

[tex]D^2-2D-8=0[/tex]

[tex](D-4)(D+2)=0[/tex]

thus the roots are 4 and -2.

thus the solution of the homogenous differential equation is given as

[tex]Y_{h} (t)= A\exp{4t} + B\exp{-2t}[/tex]

the differential operator of the non homogeneous equation is given as

[tex](D-4)(D+2)(u)=\cos 5x +7[/tex]

the differential operator [tex]D^2 +5[/tex] annihilates [tex]\cos 5x[/tex] and the differential operator D annihilates 7

applying [tex]D(D^2+5)[/tex] to both sides of the differential equation we have;

(D-4)(D+2)(u)=\cos 5x +7

[tex]D(D^2+5)(D-4)(D+2)=D(D^2+5)(\cos5x+7)[/tex][tex]D(D^2+5)(D-4)(D+2)=0[/tex]

the roots of the characteristic polynomial of the diffrential equation above are [tex]0, \cmplx 5i, -\cmplx 5i, 4, -2[/tex]

thus the particular solution is

[tex]Y_{p}= C\exp{0}+D\sin 5t +E\cos 5t + F\exp {4t} + G\exp {-2t}[/tex]

this gives us the particular solution

[tex]Y_{p}= C +D\sin 5t +E\cos 5t + F\exp 4t + G\exp -2t[/tex]

To use the annihilator method for the differential equation [tex]\(u'' - 2u' - 8 = \cos(5x) + 7\),[/tex] the operator [tex]\(D^3 + 25D\)[/tex] will annihilate the nonhomogeneous part [tex]\(\cos(5x) + 7\).[/tex] This operator reduces the nonhomogeneous function to zero. The differential operator combines the annihilation of both the cosine and constant terms.

To determine the form of a particular solution for the given differential equation[tex]\(u'' - 2u' - 8 = \cos(5x) + 7\),[/tex] we first identify a differential operator that annihilates the nonhomogeneous part [tex]\(\cos(5x) + 7\).[/tex]

For [tex]\(\cos(5x)\)[/tex] , the appropriate annihilator is [tex]\(D^2 + 25\)[/tex], where [tex]\(D\)[/tex] represents differentiation with respect to [tex]\(x\)[/tex].

This is because applying [tex]\(D^2 + 25\)[/tex]  to [tex]\(\cos(5x)\)[/tex] will yield zero:

For the constant term 7, the annihilator is simply [tex]\(D\)[/tex], since the derivative of a constant is zero:

Combining these, the overall differential operator that will annihilate [tex]\(\cos(5x) + 7\)[/tex] is:

The differential operator [tex]\( D^3 + 25D \)[/tex] will annihilate the nonhomogeneous part [tex]\( \cos(5x) + 7 \),[/tex] reducing it to zero.

We can set up a proportion since we know the ratio between the # of purple marbles and the # of green marbles.

A ratio is a way to compare two different values: for every 8 purple marbles there are 5 green marbles

Complete Question:

The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April, 1 2, 201 2). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries. State the null and alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries

Answer:

Null hypothesis, H₀ : μ = 24.57

Alternative hypothesis, [tex]H_{a}[/tex] :  μ ≠ 24.57

Step-by-step explanation:

The mean hourly wage for the goods producing industry = $24.57

Since we want to see  if the mean of hourly wage for the manufacturing industry is equal to $24.57( The mean f hourly wage for the good producing industry)

Therefore the, null hypothesis will be that there is no significant difference between the means of the hourly wages of both the goods producing and the manufacturing industries, while the alternative hypothesis will be that the means of their hourly wages are significantly different

Null hypothesis, H₀ : μ = 24.57

Alternative hypothesis, [tex]H_{a}[/tex] :  μ ≠ 24.57

Answer:

The height of the tower is 245 m

Step-by-step explanation:

The complete question in English is

Find the height of the tower with the data provided by the engineering team. Value of the segment ab= 50 m. The length between the child and the tip of the tower is 250 m

The picture in the attached figure

we know that

In the right triangle ABC

Applying the Pythagorean Theorem

[tex]AC^2=AB^2+BC^2[/tex]

we have

[tex]AB=50\ m\\AC=250\ m[/tex]

substitute

[tex]250^2=50^2+BC^2[/tex]

[tex]BC^2=250^2-50^2[/tex]

[tex]BC^2=60,000\\BC=245\ m[/tex]

Answer:

Triangle

Step-by-step explanation:

I got done taking the quiz and it wasn't oval For k12 people this is the answer. Hope this helps

Answer:

Step-by-step explanation:

An eccentric philanthropist undertakes to give away $100,000. He is eccentric because he insists that each of his gifts be a number of dollars that is a power of two, and he will give no more than one gift of any amount. How does he distribute the money?

To solve this problem, we will simply write 1,00,000 in base 2.

2^17 gives 131072, 2^16 gives 65536.

So, the first gift is 65536, we then need to repeat this process for  34,464 ((100,000-65536 = 34,464), to get all gifts in succession.

6 gifts in all: one each of $32, $128, $512, $1024, $32768, and $65536.

Answer:

78.52% probability that the sample mean is greater than 320 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 330, \sigma = 80, n = 40, s = \frac{80}{\sqrt{40}} = 12.65[/tex]

What is the likelihood the sample mean is greater than 320 minutes?

This is 1 subtracted by the pvalue of Z when X = 320. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{320 - 330}{12.65}[/tex]

[tex]Z = -0.79[/tex]

[tex]Z = -0.79[/tex] has a pvalue of 0.2148

1 - 0.2148 = 0.7852

78.52% probability that the sample mean is greater than 320 minutes

Answer:

Step-by-step explanation:

You can start by recognizing 19/12π = π +7/12π, so the desired sine is ...

  sin(19/12π) = -sin(7/12π) = -(sin(3/12π +4/12π)) = -sin(π/4 +π/3)

  -sin(π/4 +π/3) = -sin(π/4)cos(π/3) -cos(π/4)sin(π/3)

Of course, you know that ...

  sin(π/4) = cos(π/4) = (√2)/2

  cos(π/3) = 1/2

  sin(π/3) = (√3)/2

So, the desired value is ...

  sin(19π/12) = -(√2)/2×1/2 -(√2)/2×(√3/2) = -(√2)/4×(1 +√3)

Comparing this form to the desired answer form, we see ...

  A = 2

  B = 3

Answer:4

Step-by-step explanation:

The equation of motion for the given scenario, involving a 1-slug mass attached to a spring, an applied external force and a damping force, is determined by formulating a differential equation from Newton's 2nd law, incorporating the spring's force and the damping force. (a) The final equation is: d²x/ dt² + 2(dx/dt) + 5x = (16 cos 2t + 4 sin 2t).

The given scenario relates to the field of physics, specifically harmonic motion and dampening force. Harmonic motion can be studied in the context of a mass attached to a spring, such as in this question. Here, it's specified that we have a 1-slug mass attached to a spring with a spring constant of 5lb/ft, and that an external force, f(t) = 16 cos 2t + 4 sin 2t, is applied.

To find the equation of motion, you can use the general formula from Newton's 2nd law, F=ma. Given that the movement takes place in a medium providing a damping force numerically equal to two times the instantaneous velocity, the force equation of the damped harmonic oscillator becomes relevant.

The damping force can be represented as - 2v and the spring force represented as - 5x (as F= -kx). Hence, the differential equation F=ma can be represented as: m* d²x/ dt² = -2v * dx/dt – 5x + f(t), translating to: d²x/ dt² + 2(dx/dt) + 5x = (16 cos 2t + 4 sin 2t). This equation represents the equation of motion for the given conditions.

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Answer:

b

Step-by-step explanation:

Option D: 15-year fixed, 20% down at a fixed rate of 5.5% would result in the lowest monthly payment for the Johnsons.

Based on the options given, the loan option that would result in the lowest monthly payment for the Johnsons would be Option D: 15-year fixed, 20% down at a fixed rate of 5.5%. To determine this, we need to compare the monthly payments for each option.

By calculating the monthly payments for each option, it is found that Option D has the lowest monthly payment for the Johnsons.

Answer:

[tex]\displaystyle \frac{7}{8}[/tex].

Step-by-step explanation:

If two events are complements, then the sum of their probabilities should be [tex]1[/tex].

This question suggests that the following two events are complements:

As a result:

[tex]\begin{aligned}& P(\text{at least one child is female}) \\ &= 1 - P(\text{all three children are male})\end{aligned}[/tex].

According to the question,

[tex]\displaystyle P(\text{all three children are male}) = \frac{1}{8}[/tex].

Therefore,

[tex]\begin{aligned}& P(\text{at least one child is female}) \\ &= 1 - P(\text{all three children are male}) \\ &= 1 -\frac{1}{8} \\ &= \frac{7}{8}\end{aligned}[/tex].

In this Mathematics problem of probability, the calculation required was for the probability of 'at least one child being female'. This is a complementary event to 'all three children being male', enabling us to solve it by using the formula P(at least one child is female) = 1 - P(all three children are male). Hence, the answer equals 7/8.

The subject of the question is probability, which is a branch of Mathematics. Looking at the question, the probability of having all three children as males has been given as 1/8. We are required to find the probability of having 'at least one female child'. This event is complementary to having 'all three children as males', so we can find the solution using the formula you stated. As P(all three children are male) = 1/8, therefore P(at least one child is female) = 1 - 1/8 = 7/8.

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Answer:

one solution

Step-by-step explanation:

X-9=0

Add 9 to each side

X-9+9=0+9

x = 9

There is one solution

Answer:

1/4(1-3x)

Step-by-step explanation:

Answer: The expected utility is 0.59.

Step-by-step explanation:

Since we have given that

[tex]U(c)=\sqrt{c}[/tex]

Probability that he will be injured = 0.1

Probability that he will not be injured = 0.9

If Billy is not injured this season, he will receive an income of 25 million dollars.

and

If he is injured, his income will be only 10,000 dollars.

According to question, the expected utility is given by

[tex]E[x]=0.9\times \sqrt{(0.01)}+0.1\times \sqrt{25}\\\\E[x]=0.9\times 0.1+0.1\times 5\\\\E[x]=0.09+0.5\\\\E[x]=0.59[/tex]

Hence, the expected utility is 0.59.

Final answer:

To calculate Billy's expected utility, we need to multiply his utility function by the probability of each outcome and sum the results. His expected utility is approximately 3333.33.

Explanation:

To calculate Billy's expected utility, we need to multiply his utility function by the probability of each outcome and sum the results. In this case, Billy's utility function is U(c) = c^(1/2), where c represents his income. If Billy is not injured, his income will be $25 million, and if he is injured, his income will be $10,000. The probability of being injured is 0.1, and the probability of not being injured is 0.9.

Expected utility = U(income if not injured) * P(not injured) + U(income if injured) * P(injured)

Expected utility = U($25 million) * 0.9 + U($10,000) * 0.1

Expected utility = (25 million)^(1/2) * 0.9 + (10,000)^(1/2) * 0.1

Solving this equation, we find that the expected utility for Billy is approximately 3333.33.

Answer:

2 out of 6

Step-by-step explanation:

Answer: 2 out of 6

Step-by-step explanation:

Answer:

P(B)=0.30

Step-by-step explanation:

Out of 1000 Voters, 30% favor Jones.

Event S=Favors Jones on First Trial

Event B=S occurs on Second Trial

P(S)=0.30

P(S')=1-0.30=0.70

Event B could occur in two ways

Therefore,

P(B)=P(SS)+P(S'S)

=(0.3X0.3)+(0.7X0.3)

=0.09+0.21

=0.3

Therefore, the probability of event B(that event S occurs on the second trial), P(B)=0.30.

Answer:

1.One proportion

2. Proportions from Dependent Samples

3. Two Independent Proportions

4. One Mean

5. Means from Dependent Samples

6. Two Independent Means

Step-by-step explanation:

What proportion of Americans believe in climate change? - One proportion

From the above information, there is only one sample and the question is about proportion. So, we must use "One proportion".

Do college students change their view on climate change as they go through college? One hundred freshman are asked if they believe in climate change. The same students are asked four years later if they also believe in climate change. - Proportions from Dependent Samples

From the information given, there are two samples and samples are dependent ( that is same students are asked four years later). Furthermore, the question is about proportion, we must use " Proportions from dependent samples ".



Is there a difference in the proportion of men and women who believe in climate change? - Two Independent Proportions

From the information given, there are two independent samples and they are asking about proportion, we must use "Two independent proportions".

What is the average amount of time that Americans spend watching or reading the news a day? - One Mean

From the information, there is only one sample and they are asking about mean. Therefore, we must use ". One mean".

Is there a difference in the amount of time that college students spend reading or watching the news as they go through college? One hundred students were asked as freshmen and as senior how many minutes a day they spent reading or watching the news? - Means from Dependent Samples

There are two samples and samples are dependent ( the same students are asked four years later). Also, they are asking about mean, we must use "Means from dependent samples ".

Is there is a difference in the amount of time that Republicans and Democrats spend watching or reading the news? - Two Independent Means

From the information given, there are two independent samples and they are asking about mean, we must use "Two independent means".

The statistical tests required are a hypothesis test for a proportion for the questions on proportions of Americans' beliefs, a paired t-test for examining changes in the same group over time, an independent t-test for comparing means of different groups and measures of central tendency (mean) for assessing averages.

The various questions posed require different types of statistical tests. Proportions are evaluated using a hypothesis test for a proportion. So, the question 'What proportion of Americans believe in climate change?' and 'Is there a difference in the proportion of men and women who believe in climate change?' would utilize this test.

For questions where the same group is measured at two different times, a paired t-test is appropriate. Hence, the question 'Do college students change their view on climate change as they go through college? One hundred freshman are asked if they believe in climate change. The same students are asked four years later if they also believe in climate change.' would require a paired t-test.

When comparing the means of two independent groups, an independent t-test should be used. This would apply to the questions 'Is there a difference in the amount of time that Republicans and Democrats spend watching or reading the news?' and 'Is there is a difference in the amount of time that college students spend reading or watching the news as they go through college?'

Finally, to measure an average or central tendency, a mean is used – therefore, the question 'What is the average amount of time that Americans spend watching or reading the news a day?' would require the calculation of a mean.

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Answer:

[tex]z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=0.6[/tex]  

[tex]p_v =P(z>0.6)=0.274[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of people who prefer Pepsi is not higher than 0.5 or 50%

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

X=53 represent the people who prefer Pepsi

[tex]\hat p=\frac{53}{100}=0.53[/tex] estimated proportion of people who prefer PEsi

[tex]p_o=0.5[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

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

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.5.:  

Null hypothesis:[tex]p\leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

When we conduct a proportion test we need to use the z statistic, 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  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=0.6[/tex]  

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 significance level provided [tex]\alpha=0.05[/tex]. 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>0.6)=0.274[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of people who prefer Pepsi is not higher than 0.5 or 50%

To determine if more than 50% of people prefer Pepsi to Coca-Cola, conduct a one-sample proportion test using the given data and a significance level of 0.05.

To conduct a hypothesis test to determine if more than 50% of people prefer Pepsi to Coca-Cola, you can use a one-sample proportion test. The null hypothesis, denoted as H0, is that the proportion of people who prefer Pepsi is equal to 50%. The alternative hypothesis, denoted as H1, is that the proportion is greater than 50%. Using the given data, you would calculate the test statistic and compare it to the critical value or p-value associated with a significance level of 0.05. If the test statistic falls in the rejection region, you would reject the null hypothesis and conclude that more than 50% of people prefer Pepsi.

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Answer:

53

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

[tex](14 - 8) \ast8 + 5 \\ =6 \ast8 + 5 \\ = 48 + 5 \\ = 53 \\ \\ \red{ \boxed{\bold {\therefore \: (14 - 8) \ast8 + 5 = 53}}}[/tex]

Answer:

OptionB

Step-by-step explanation:

Answer:

0.826%

Step-by-step explanation:

The Rydberg constant = 2.178 × [tex]10^{-18}[/tex] J.

students record = 2.16 x [tex]10^{-18}[/tex]J.

error = 0.018 x [tex]10^{-18}[/tex]J.

Percentage error = [tex]\frac{error}{actual measurement}[/tex] x 100

  = [tex]\frac{ 0.018 * 10^{-18} }{2.178 * 10^{-18} }[/tex] x 100

  = 0.826%

Answer:

[tex]0.72 - 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.696[/tex]

[tex]0.72 + 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.744[/tex]

The 85% confidence interval would be given by (0.696;0.744)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

The estimated proportion for this case is [tex]\hat p =\frac{700}{972}=0.720[/tex]

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 85% of confidence, our significance level would be given by [tex]\alpha=1-0.85=0.15[/tex] and [tex]\alpha/2 =0.075[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.44, z_{1-\alpha/2}=1.44[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

If we replace the values obtained we got:

[tex]0.72 - 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.696[/tex]

[tex]0.72 + 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.744[/tex]

The 85% confidence interval would be given by (0.696;0.744)

Answer:

The first one is 16.0 and the second one is 22.5

Answer:

The first one is 16.0 and the second one is 22.5

Answer:

Correct option:

(1) the eastern gray squirrels that live in New York City's Central Park

Step-by-step explanation:

A population in Statistical analysis represents the set of all possible values a random variable, X can assume. For example, all the registered voters of the United States form a population, the weight of all the newborn babies in the country form a population.

All the mammals living in the region of Boulder, Colorado cannot form a population. This is because the set consists of n different species in the region.

And the gray squirrels and fox squirrels are two different species. So, together they cannot form a population.

The red foxes found east of the Mississippi River in the United States and in eastern Europe cannot form a population because the red foxes selected are from two different regions.

The eastern gray squirrels that live in New York City's Central Park can form a population because the set consists of one one species, i.e. the eastern gray squirrels from a particular region, i.e. New York City's Central Park.

Thus, the example of a population is "the eastern gray squirrels that live in New York City's Central Park."

The correct example of a population is all the mammals living in the region of Boulder, Colorado.

An example of a population is all the mammals living in the region of Boulder, Colorado. This includes all species of mammals in that specific geographic area. Population refers to a group of individuals of the same species living in a specific area at a given time.

In this case, the population would include various mammals such as deer, rabbits, bears, and others. It does not include the specific populations of eastern gray squirrels in Central Park or red foxes across different regions.

Therefore, the correct option representing an example of a population is: all the mammals living in the region of Boulder, Colorado.

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Answer:

Step-by-step explanation:

Given the equation of the hyperbola

[tex]\dfrac{(x+2)^2}{144}-\dfrac{(y-4)^2}{81} =1[/tex]

Since the x part is added, then

[tex]a^2=144; b^2=81\\a=12,b=9[/tex]

Also, this hyperbola's foci and vertices are to the left and right of the center, on a horizontal line paralleling the x-axis.

From the equation, clearly the center is at (h, k) = (–2, 4). Since the vertices are a = 12 units to either side, then they are at (-14,4) and (10,4).

From the equation

[tex]c^2=a^2+b^2=144+81=225\\c=15[/tex]

The foci, being 15 units to either side of the center, must be at (–17, 4) and (13, 4)

The appropriate null and alternative hypotheses for the consumer watch group's hypothesis test on the hypnosis program's success rate are:

option a) H0: p = 0.57 vs. Ha: p < 0.57

The Null Hypothesis (H0):The success rate of the hypnosis program is 57%.

Alternative Hypothesis (Ha): The success rate is less than 57%.

We use a one-tailed test because we have a directional hypothesis (suspecting a lower success rate).

If we suspected a higher or different rate, we'd use a two-tailed test.

The consumer watch group is challenging the claim of a 57% success rate by testing if the actual success rate is lower than 57%. This setup allows for a focused investigation into the program's effectiveness.

The complete question is :A hypnosis program designed to help individuals quit smoking claims a 57% success rate. A consumer watch group suspects that this claim is high and randomly selects 50 individuals who have completed the program in order to conduct a hypothesis test. What are the appropriate null and alternative hypotheses?

a) H0: p = 0.57 vs. Ha: p < 0.57

b) H0: p = 0.57 vs. Ha: p > 0.57

c) H0: p = 0.57 vs. Ha: p ≠ 0.57

d) H0: p < 0.57 vs. Ha: p > 0.57

Answer:

Step-by-step explanation:

In physics, Work is defined as the energy needed to move certaing object through a certain distance. Specifically, the work done is directly proportional to the force exerted and the distance.

It's important to know that a change of point is needed to have actually work done, physically speaking. This means if the object doesn't move, then there's no work done.

Mathematically, the work is defined

[tex]W= F \times d[/tex]

Isolating the force

[tex]F=\frac{W}{d}[/tex]

So, notice that the distance is inversely proportional to the force needed, which means the less distance, more force we need.

Now, the problem is giving wides and slopes, which we can use to find heights. And we know already that the less distance we have, the greater force we need, or the most distance, the least force.

Let's find which wedge has the greatest vertical distance.

[tex]m=\frac{y}{x}[/tex]

[tex]5=\frac{y}{2} \implies y=10[/tex]

[tex]8=\frac{y}{4} \implies y=32[/tex]

[tex]9=\frac{y}{3} \implies y=27[/tex]

[tex]10=\frac{y}{5}\\ y=50[/tex]

Notice that the last wedge has greater vertical distance, that means Wedge Z requires least amount of force to do a job.

Answer:

The correct answer is Y not Z.

Step-by-step explanation:

Answer:

  classification is based on the measure of the largest angle

Step-by-step explanation:

Every triangle will have angle measures that add up to 180°. The classification as to acute, right, or obtuse is based on the largest angle.

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If the largest angle is less than 90°, the triangle is acute.

If the largest angle is equal to 90°, the triangle is right.

If the largest angle is greater than 90°, the triangle is obtuse.

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Because you know the angle sum is always 180°, you can generally figure out what kind of triangle it is from the sum of two of the angles. If both are less than 90° and their sum is more than 90°, then the triangle will be acute, for example.