Gabriel finds some wooden boards in the backyard with lengths of 5 feet, 2.5 feet and 4 feet. He decides he wants to make a triangular garden in the yard and uses the triangle inequality rule to see if it will work.
PLEASE ANSWER IMMEDIATELY Which sums prove that the boards will create a triangular outline for the garden? Select all that apply.
5 + 2.5 > 4
5 + 2.5 < 4
4 + 2.5 > 5
4 + 2.5 < 5
4 + 5 > 2.5
first one to answer will get brainliest

Answer:

b

Step-by-step explanation:

Null hypothesis: mean of valence for all metal song is equal to mean of valence of blues song.

Null hypthesis tests the claim

Altenate hypothesis: mean of valence for all metal songs is not equal to mean of valence of blues song.

Alternate hypothesis rejects the claim.

Answer:

(A) Since Sample 1 comes from the population of Metal songs only and Sample 2 comes from the population of Blue songs only,

The 90% confidence interval for mean valence for Metal songs is (0.2224 , 0.6797)

The 90% confidence interval for mean valence for Blue songs is (0.3063 , 0.8557)

All intermittent and final answers were rounded up to four decimal places.

(B) The option (b) is correct. This is because the question says that the research group suspects a difference between both means, not that one mean is greater or less than the other.

Step-by-step explanation:

(A) Using a 90% confidence level, the true mean is within 1.645 standard deviations of the sample mean

For METAL SONGS,

Lower limit = 0.451 - (1.645)(0.139)

= 0.451 - 0.2287 = 0.2224

Upper limit = 0.451 + (1.645)(0.139)

= 0.451 + 0.2287 = 0.6797

For BLUE SONGS,

Lower limit = 0.581 - (1.645)(0.167)

= 0.581 - 0.2747 = 0.3063

Upper limit = 0.581 + (1.645)(0.167)

= 0.581 + 0.2747 = 0.8557

(B) The null hypothesis is:

Mean valence of Metal songs is equal to the mean valence of Blue songs

Alternative hypothesis:

Mean valence of Metal songs is NOT equal to the mean valence of Blue songs.

As per the given data in the question, Emil's monthly PMI payment is $28.81.

A mortgage is a loan used to finance the purchase or upkeep of a home, land, or other types of rental properties.

The lender agrees to repay the loan over time, usually in regular installments divided into principal and interest. Loans are protected by the property.

To determine Emil's monthly PMI payment, we first need to determine the loan-to-value (LTV) ratio.

Emil is making a 15% down payment on a $175,000 home, which means his loan amount is $148,750. To calculate the LTV ratio, we divide the loan amount by the property value:

LTV ratio = loan amount / property value

LTV ratio = $148,750 / $175,000

LTV ratio = 0.85

Since Emil's LTV ratio is between 85.01% and 90%, his PMI rate for a 15-year fixed-rate loan is 0.23% according to the table.

To calculate Emil's monthly PMI payment, we multiply the loan amount by the PMI rate and divide by 12 (for the 12 months in a year):

Monthly PMI payment = (loan amount x PMI rate) / 12

Monthly PMI payment = ($148,750 x 0.23%) / 12

Monthly PMI payment = $28.81

Therefore, Emil's monthly PMI payment is $28.81.

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Answer:

2y^2+18x

Step-by-step explanation:

4y^2 + 6x -2y^2 + 12x

=4y^2-2y^2+6x+12x

=2y^2+6x+12x

=2y^2+18x

Answer:

2y^2+18x

Step-by-step explanation:

4y^2+6x-2y^2+12x

=4y^2-2y^2 6x+12x

=2y^2+18x

True, True, True, False, True. Without the multiple-choice question options, I can't provide a specific response.

Let's address each question and provide the appropriate response:

1. True/False: "The absolute maximum of a function always occurs where the derivative has a critical function."

  - Answer: False. The absolute maximum of a function can occur at critical points, but it can also occur at endpoints of the domain or other non-critical points.

2. True/False: "Implicit differentiation can be used to find \( \frac{dy}{dx} \) when \( x \) is defined in terms of \( y \)."

  - Answer: True. Implicit differentiation is a technique used to find derivatives of functions that are not explicitly defined in terms of one variable.

3. True/False: "In a related rates problem, there can be more than two quantities that vary with time."

  - Answer: True. Related rates problems involve the rates of change of multiple quantities that are related to each other through an equation or situation.

4. True/False: "A continuous function on an open interval does not have an absolute maximum or minimum."

  - Answer: False. A continuous function on a closed interval always has an absolute maximum and minimum by the Extreme Value Theorem.

5. True/False: "In a related rates problem, all derivatives are with respect to time."

  - Answer: True. Related rates problems involve finding rates of change with respect to time.

Multiple Choice:

6. Since the multiple-choice question is not provided, I can't offer a response. If you have the options, feel free to share them, and I can help you choose the correct one.

Step-by-step explanation:

Here given

6x - 2y = 12

2y = 6x - 12

2y = 6(x - 2)

y = 6( x - 2)

2

y = 3(x - 2)

y = 3x - 6

Comparing with y = mx + c

so slope (m) = 3

Hope it will help you :))

Answer:

B. 19 min 15 sec

B. 13 min 25 sec

Step-by-step explanation:

Door 1 opens every 1 min 45 sec, or 105 sec.

Door 2 opens every 1 min 10 sec, or 70 sec.

Door 3 opens every 2 min 55 sec, or 175 sec.

Door 4 opens every 2 min 20 sec, or 140 sec.

Door 5 opens every 35 sec.

The greatest common factor is 35 seconds, so we can measure the time in units of 35 seconds.

Door 1 opens every 3 units.

Door 2 opens every 2 units.

Door 3 opens every 5 units.

Door 4 opens every 4 units.

Door 5 opens every 1 unit.

The least common multiple of 3, 2, 5, 4, and 1, is 60.  So every 60 units, all five doors will open, and the guard will look down the corridor to check on the prisoner.  Douglas must escape before this time.

In order to escape in the shortest time possible, Douglas should time his escape so that each door opens 1 unit after the door before it.  It takes Douglas 20 seconds to move from one door to another, so he will have enough time to get to the next door before it opens.

Let's say Douglas starts moving when Door 1 opens for the nth time.  In other words, 3n units have passed before he starts moving.  That means Door 2 should open after 3n + 1 units.  Door 3 should open after 3n + 2 units.  Door 4 should open after 3n + 3 units.  And Door 5 should open after 3n + 4 units.

Since Door 2 opens every 2 units, 3n + 1 should be a multiple of 2.

Since Door 3 opens every 5 units, 3n + 2 should be a multiple of 5.

Since Door 4 opens every 4 units, 3n + 3 should be a multiple of 4.

Since Door 5 opens every 1 unit, 3n + 4 should be a multiple of 1.

By trial and error, n = 11.

So Douglas starts moving after 33 units, or 1155 seconds, or 19 min 15 sec.

Douglas clears the fifth door after 37 units, which leaves 23 units to spare, or 805 seconds, or 13 min 25 sec.

Given:

Given that the radius of the circle is 3 units.

The arc length is π.

The central angle is θ.

We need to determine the expression to find the measure of θ in radians.

Expression to find the measure of θ in radians:

The expression can be determined using the formula,

[tex]S=r \theta[/tex]

where S is the arc length, r is the radius and θ is the central angle in radians.

Substituting S = π and r = 3, we get;

[tex]\pi=3 \theta[/tex]

Dividing both sides of the equation by 3, we get;

[tex]\frac{\pi}{3}=\theta[/tex]

Thus, the expression to find the measure of θ in radians is [tex]\theta=\frac{\pi}{3}[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Truly, on a single student level, the Massey method can be applied i.e. problems are ranked according to their level of difficulty for a single student.

Let us say there are 4 problems P1, P2, P3, P4 set in an exam where a student has to solve any two.

Assuming student 1 solves and scores more in P1 than in P2, r1>r2

student 2  more in P1 than P4 r1>r4

student 3 more in P2 than P4 r2>r4

student 4 more in P4 than P3 r4>r3

student 5 more in P2 than P3 r2>r3

and such many more cases.

then the Massey's model can be written as

P1 P2 P3  P4

\begin{bmatrix} 1 &-1 &0 &0\\ 1 &-1 &0 &0 \\ 0 &1 & 0 &-1 \\ 0 & 0 &-1 & 1 \\ 0 & 1 & -1 & 0 \end{bmatrix}.

\times \begin{bmatrix}r1 \\r2 \\r3 \\r4 \end{bmatrix}  =

\begin{bmatrix}y_{1} \\ y_{2} \\ y_{3} \\ y_{4}\\ y_{5}\end{bmatrix}.            

If Pi gives more score than Pj, the entry below Pi shall be 1 and below Pj shall be -1.

The rest of the entries shall be 0.

r1,r2,r3,r4,r5 are ranks .  

There may be more rows depending upon more combination of 2 problems.

Should in case more than one student solve the same combination and get scores in the same order, for instance, 12 students solve P1 and P2, for 7 of them r1>r2, then their scores can be averaged.

Normally, such systems are overdetermined, i.e., more rows than the number of unknowns, then it is solved by the Least square method ., as there shall be no a solution with least error is found out.

The overall ranking, in reverse order, shall give the ranking according to increasing difficulty.

Answer:

The 80% confidence interval for the mean

(4.6199 , 4.7801)

Step-by-step explanation:

Explanation:-

Assuming that the population standard deviation for the number of energy drinks consumed each week is 1

Given the Population standard deviation 'σ' = 1

The study found that for a sample of 256 teenagers the mean number of energy drinks consumed per week is 4.7

given sample size 'n' = 256

mean of the sample 'x⁻' = 4.7

confidence interval for the mean

The 80% confidence interval for the mean is determined by

[tex](x^{-} -Z_{\alpha } \frac{S.D}{\sqrt{n} } , x^{-} + Z_{\alpha }\frac{S.D}{\sqrt{n} } )[/tex]

the z-score of 80% level of significance = 1.282

[tex](4.7 - 1.282\frac{1}{\sqrt{256} } , 4.7 + 1.282\frac{1}{\sqrt{256} } )[/tex]

(4.7 - 0.0801 , 4.7 +0.0801)

(4.6199 , 4.7801)

Conclusion:-

The 80% confidence interval for the mean

(4.6199 , 4.7801)

Answer:

I believe it would be 0.60  cents

Step-by-step explanation:

roll                 5

The cost        3

Divide the 5 by 5 to get 1 and divde 3 by 6 to get 0.60

Answer:

$0.60

Step-by-step explanation:

To work this out you would divide $3 by 5, which is 0.6. This is because we know that $3 is for 5 and so to work out 1 you would divide by 5.

1) Divide 3 by 5.

[tex]3/5=0.6[/tex]

1 roll of paper towels is $0.6.

Answer:

I think the answers are A, C, D, and E

Step-by-step explanation:

Answer:

attached

Step-by-step explanation:

attached

To test the claim that the median titanium content is 8.5%, we use the normal approximation for the sign test. We calculate the observed number of plus differences, the test statistic, and the P-value. We fail to reject the null hypothesis because the P-value is larger than the significance level.

To test the claim that the median titanium content is equal to 8.5%, we can use the normal approximation for the sign test. The sign test is used when the data is not normally distributed. In this case, we have 20 test coupons with titanium content in percent. To calculate the observed number of plus differences (r+), we count the number of values greater than 8.5% and the number of values less than 8.5% in the sample. In this case, there are 7 values greater than 8.5% and 13 values less than 8.5%. Therefore, r+ = 7.

To calculate the test statistic (z0), we use the formula z0 = (r+ - n/2) / sqrt(n/4), where n is the sample size. In this case, n = 20. Plugging in the values, we get z0 = (7 - 20/2) / sqrt(20/4) = -1.5.

To calculate the P-value, we need to find the probability of observing a test statistic as extreme as -1.5 or more extreme in a standard normal distribution. We can use a statistical table or software to find the P-value. In this case, the P-value is 0.133, calculated using a standard normal distribution table.

Since the P-value (0.133) is larger than the significance level α (0.05), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the median titanium content is different from 8.5%.

Answer:

[tex]t=\frac{30.8-30}{\frac{1.5}{\sqrt{32}}}=3.017[/tex]    

[tex]p_v =2*P(t_{(31)}>3.017)=0.0051[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the treu mean is different from 30 minutes at 1% of significance

Step-by-step explanation:

Data given and notation  

[tex]\bar X=30.8[/tex] represent the sample mean

[tex]s=1.5[/tex] represent the sample standard deviation

[tex]n=32[/tex] sample size  

[tex]\mu_o =30[/tex] represent the value that we want to test

[tex]\alpha=0.01[/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)  

1) State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is equal to 30 minutes, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 30[/tex]  

Alternative hypothesis:[tex]\mu \neq 30[/tex]  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

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

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

2) Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{30.8-30}{\frac{1.5}{\sqrt{32}}}=3.017[/tex]    

3) P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=32-1=31[/tex]  

Since is a two sided hypothesis test the p value would be:  

[tex]p_v =2*P(t_{(31)}>3.017)=0.0051[/tex]  

4) Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the treu mean is different from 30 minutes at 1% of significance

Answer:

[tex]z=\frac{0.556 -0.5}{\sqrt{\frac{0.5(1-0.5)}{836}}}=3.238[/tex]  

[tex]p_v =2*P(z>3.238)=0.0012[/tex]  

The p value is a reference value and is useful in order to take a decision for the null hypothesis is this p value is lower than a significance level given we reject the null hypothesis and otherwise we have enough evidence to fail to reject the null hypothesis.

Step-by-step explanation:

Data given and notation

n=836 represent the random sample taken

[tex]\hat p=0.556[/tex] estimated proportion of interest

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

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

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 ture proportion is equal to 0.5 or no.:  

Null hypothesis:[tex]p=0.5[/tex]  

Alternative hypothesis:[tex]p \neq 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{0.556 -0.5}{\sqrt{\frac{0.5(1-0.5)}{836}}}=3.238[/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 next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z>3.238)=0.0012[/tex]  

The p value is a reference value and is useful in order to take a decision for the null hypothesis is this p value is lower than a significance level given we reject the null hypothesis and otherwise we have enough evidence to fail to reject the null hypothesis.

The ratio 3:x equivalent to 1:9 results in x being equal to 27.

To find the number that makes the given ratio equivalent to 1:9 we can set up a proportion using the information given which is a ratio of 3 to an unknown number (let's call it x).

First we write down the two ratios as fractions and set them equal to each other to find x:

1/9 = 3/x

We then cross-multiply to solve for x:

1 × x = 9 × 3

This gives us:

x = 27

So, the number that makes the ratio equivalent to 1:9 when compared to 3 is 27.

Answer:

The​ p-value for this​ test is 0.22065.

Step-by-step explanation:

We are given that a national study report indicated that​ 20.9% of Americans were identified as having medical bill financial issues.

A news organization randomly sampled 400 Americans from 10 cities and found that 90 reported having such difficulty.

Let p = proportion of Americans who were identified as having medical bill financial issues in 10 cities.

SO, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 20.9%   {means that % of Americans who were identified as having medical bill financial issues in these 10 cities is less than or equal to 20.9%}

Alternate Hypothesis, [tex]H_A[/tex] : p > 20.9%   {means that % of Americans who were identified as having medical bill financial issues in these 10 cities is more than 20.9% and is more severe}

The test statistics that will be used here is One-sample z proportion statistics;

                                  T.S.  = [tex]\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of 400 Americans from 10 cities who were found having such difficulty =  [tex]\frac{90}{400}[/tex] = 0.225 or 22.5%

            n = sample of Americans = 400

So, test statistics  =  [tex]\frac{0.225-0.209}{{\sqrt{\frac{0.225(1-0.225)}{400} } } } }[/tex]

                               =  0.77

Now, P-value of the test statistics is given by the following formula;

         P-value = P(Z > 0.77) = 1 - P(Z [tex]\leq[/tex] 0.77)

                                            = 1 - 0.77935 = 0.22065

Testing the hypothesis, using the information given, it is found that the p-value is of 0.2148.

At the null hypothesis, it is tested if the proportion for these cities is of 20.9% = 0.209, hence:

[tex]H_0: p = 0.209[/tex]

At the alternative hypothesis, it is tested if the proportion for these cities is greater than 0.209, hence:

[tex]H_1: p > 0.209[/tex].

The test statistic is given by:

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

In which:

For this problem, the parameters are: [tex]p = 0.209, n = 400, \overline{p} = \frac{90}{400} = 0.225[/tex].

Then, the value of the test statistic is:

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

[tex]z = \frac{0.225 - 0.209}{\sqrt{\frac{0.209(0.791)}{400}}}[/tex]

[tex]z = 0.79[/tex]

The p-value for this test is the probability of finding a sample proportion above 0.225, which is 1 subtracted by the p-value of z = 0.79.

Looking at the z-table, z = 0.79 has a p-value of 0.7852.

1 - 0.7852 = 0.2148.

The p-value for this test is of 0.2148.

A similar problem is given at https://brainly.com/question/24166849

Answer:

400nanometers

Step-by-step explanation:

Based on Margot measurement, the distance for 6wavelengths of visible light is 2400nanometers. To calculate the resulting distance for 1wavelength we have:

6wavelength = 2400nanometers

1wavelength = x

6wavelength × x = 2400nanometers × 1wavelength

x = 2400nanometres/6

x = 400nanometres

Answer:

1. Yes.

2. No.

3. Yes.

Step-by-step explanation:

Consider the following subsets of Pn given by

1.Let W1 be the set of all polynomials of the form [tex]p(t)=at^2[/tex], where a is in ℝ.

2.Let W2 be the set of all polynomials of the form [tex]p(t)=t^2+a[/tex], where a is in ℝ.

3. Let W3 be the set of all polynomials of the form [tex]p(t)=at^2+at[/tex], where a is in ℝ.

Recall that given a vector space V, a subset W of V is a subspace if the following criteria hold:

- The 0 vector of V is in W.

- Given v,w in W then v+w is in W.

- Given v in W and a a real number, then av is in W.

So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.

- First property:

Note that for W2, for any value of a, the polynomial we get is not the zero polynomial. Hence the first criteria is not met. Then, W2 is not a subspace of Pn.

For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.

- Second property:

W1. Consider two elements in W1, say, consider a,b different non-zero real numbers and consider the polynomials

[tex]p_1 (t) = at^2, p_2(t)=bt^2[/tex].

We must check that p_1+p_2(t) is in W1.

Note that

[tex]p_1(t)+p_2(t) = at^2+bt^2  = (a+b)t^2[/tex]

Since a+b is another real number, we have that p1(t)+p2(t) is in W1.

W3. Consider two elements in W3. Say [tex]p_1(t) = a(t^2+t), p_2(t)= b(t^2+t)[/tex]. Then

[tex]p_1(t) + p_2(t) = a(t^2+t) + b(t^2+t) = (a+b) (t^2+t)[/tex]

So, again, p1(t)+p2(t) is in W3.

- Third property.

W1. Consider an element in W1 [tex] p(t) = at^2[/tex]and a real scalar b. Then

[tex] bp(t) = b(at^2) = (ba)t^2)[/tex].

Since (ba) is another real scalar, we have that bp(t) is in W1.

W3. Consider an element in W3 [tex] p(t) = a(t^2+t)[/tex]and a real scalar b. Then

[tex] bp(t) = b(a(t^2+t)) = (ba)(t^2+t)[/tex].

Since (ba) is another real scalar, we have that bp(t) is in W3.

After all,

W1 and W3 are subspaces of Pn for n= 2

and W2 is not a subspace of Pn.  

W1 is a subspace of ℙn, W2 is not a subspace of ℙn, and W3 is a subspace of ℙn.

For a set to be a subspace of ℙn, it must satisfy three conditions: the zero vector must be in the set, the set must be closed under addition, and the set must be closed under scalar multiplication.

To determine if W1 is a subspace of ℙn, we check if it satisfies the three conditions:

Therefore, W1 is a subspace of ℙn.

Therefore, W3 is a subspace of ℙn.

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Answer:

[tex]430-1.943\frac{26.9}{\sqrt{7}}[/tex]    

[tex]430+1.943\frac{26.9}{\sqrt{7}}[/tex]    

And the best option would be:

e. 430 ± 1.943 (26.9/√7)

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".

[tex]\bar X=430[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=26.9 represent the sample standard deviation

n=7 represent the sample size  

Solution to the problem

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

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=7-1=6[/tex]

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,6)".And we see that [tex]t_{\alpha/2}=1.943[/tex]

Now we have everything in order to replace into formula (1):

[tex]430-1.943\frac{26.9}{\sqrt{7}}[/tex]    

[tex]430+1.943\frac{26.9}{\sqrt{7}}[/tex]    

And the best option would be:

e. 430 ± 1.943 (26.9/√7)

For 90 percent confidence interval for the mean weight of all baby orca whales is,

[tex]430\pm1.943\dfrac{26.9}{\sqrt{7} }[/tex]

Thus option e is the correct option.

Given-

Mean [tex]X[/tex] of the random sample is 430 pounds.

Standard deviation [tex]s[/tex] of the sample is 26.9 pounds.

Confidence interval is 90 percent.

The degree of freedom is sample size n-1. Thus,

[tex]D_f=7-1[/tex]

[tex]D_f=6[/tex]

The critical value for 90 percent confidence level is,

[tex]t_{\frac{a}{2} }=1.943[/tex]

The confidence interval of a mean can be given by,

[tex]X\pm t_{\frac{a}{2}}\dfrac{s}{\sqrt{n} }[/tex]

Put the value in above equation we get,

[tex]430\pm1.943\dfrac{26.9}{\sqrt{7} }[/tex]

Taking positive sign,

[tex]430+1.943\dfrac{26.9}{\sqrt{7} }[/tex]

Taking negative sign,

[tex]430-1.943\dfrac{26.9}{\sqrt{7} }[/tex]

Hence, For 90 percent confidence interval for the mean weight of all baby orca whales is,

[tex]430\pm1.943\dfrac{26.9}{\sqrt{7} }[/tex]

Thus option e is the correct option.

For more about the confidence interval, follow the link below-

https://brainly.com/question/2396419

Answer:

18

Step-by-step explanation:

Answer:

23400 cm

Step-by-step explanation:

30 cm x 30 cm x 26 cm = 23,400 cm

The population of deer will double when the growth rate exceeds the mortality rate, and the net effect is a 4% growth rate. It will take approximately 17.3 years for the population to double.

The population of deer will double when their growth rate exceeds the mortality rate and the net effect is a 4% growth rate. We can calculate the time it takes for the population to double using the formula for exponential growth:

https://brainly.com/question/16013460

#SPJ11

Answer:

The equation of the circle is [tex](x+3)^2+(y-5)^2 = 17[/tex]

Step-by-step explanation:

The complete question is

If the coordinates of the endpoints of a diameter of the circle are​ known, the equation of a circle can be found.​ First, find the midpoint of the​ diameter, which is the center of the circle. Then find the​ radius, which is the distance from the center to either endpoint of the diameter. Finally use the​ center-radius form to find the equation.

Find the center-radius  form of the circle having the points (1,4) and (-7,6) as the endpoints of a diameter.

Consider that, if both points are the endpoints of a diameter, the center of the circle is the point that is exactly in the middle of the two points (that is, the point whose distance to each point is equal). Given points (a,b) and (c,d), by using the distance formula, you can check that the middle point is the average of the coordinates. Hence, the center of the circle is given by

[tex](\frac{1-7}{2}, \frac{4+6}{2}) = (-3,5)[/tex].

We will find the radius. Recall that the radius of the circle is the distance from one point of the circle to the center. Recall that the distance between points (a,b) and (c,d) is given by [tex]\sqrt[]{(a-c)^2+(b-d)^2}[/tex]. So, let us use (1,4) to calculate the radius.

[tex] r = \sqrt[]{(1-(-3))^2+(4-5)^2} = \sqrt[]{17}[/tex].

REcall that given a point [tex](x_0,y_0)[/tex]. The equation of a circle centered at the point [tex](x_0,y_0)[/tex] is

[tex](x-x_0)^2+(y-y_0)^2 = r^2[/tex]

In our case, [tex](x_0,y_0)=(-3,5)[/tex] and [tex] r=\sqrt[]{17}[/tex]. Then, the equation is

[tex](x-(-3))^2+(y-5)^2 = (x+3)^2+(y-5)^2 = 17[/tex]

Answer:

11.20 is maybe the answer

Answer:

70

Step-by-step explanation:

Assume the unknown value is 'Y'

28 = 40% x Y

28 = 40/100 x Y

Multiplying both sides by 100 and dividing both sides of the equation by 40 we will arrive at:

Y = 3 x 100/40

Y = 70%

Final answer:

The probability that a randomly chosen student from the Algebra 2 class plays basketball or baseball is 13/22, which is approximately 0.59 or 59% when calculated using the principle of inclusion and exclusion in probability.

Explanation:

To calculate the probability that a student chosen randomly from the Algebra 2 class plays basketball or baseball, you need to use the principle of inclusion and exclusion in probability theory. The total number of students in the class is 22. There are 5 students who play basketball and 11 who play baseball, but since 3 students play both sports, these students have been counted twice in the total of 5+11=16. Therefore, the correct number of students who play at least one of the sports is 5+11-3=13.

The probability that a randomly chosen student plays either basketball or baseball is hence the number of students who play either one or both sports divided by the total number of students in the class. This gives us 13/22. To convert this fraction to a decimal, we can divide 13 by 22, which gives us approximately 0.59. Therefore, the probability that a student chosen randomly from the class plays basketball or baseball is approximately 0.59, or 59%.

Step-by-step explanation:

Given a builder makes drainpipes that drop 1 cm over a horizontal distance of 30cm to prevent clogs. The ratio of the vertical drop to the horizontal distance covered is [tex]\frac{1}{30}[/tex] cm.

The angle of inclination,

tan(θ) = [tex]\frac{1}{30}[/tex]

θ = 1.9º

By trignometric ratio,

cos(θ) = [tex]\frac{horizontal distance}{length of the drainpipe}[/tex]

length of the drainpipe = [tex]\frac{700}{cos(1.91)}[/tex] = [tex]\frac{700}{0.999}[/tex]

length of the drainpipe = 700.7 cm

Answer:

The correct Answer for Khan Academy is 700.4

Step-by-step explanation:

Answer:

24 cm

Step-by-step explanation:

Answer:

$5.04

Step-by-step explanation:

Answer:

In Math, she scored in the 93rd percentile, which is higher than the French percentile. So she did better on the Math exam as compared with the other incoming college students

Step-by-step explanation:

Z-score:

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.

On which exam did she do better as compared with the other incoming college students?

On the exam for which she had the higher z-score.

Franch:

Scored 85.

Mean 72, SD = 12. So

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

[tex]Z = \frac{85 - 72}{12}[/tex]

[tex]Z = 1.08[/tex]

[tex]Z = 1.08[/tex] has a pvalue of 0.8810, so her French score is in the 88th percentile.

Math:

Scored 80

Mean 68, SD = 8. So

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

[tex]Z = \frac{80 - 68}{8}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a pvalue of 0.9332.

In Math, she scored in the 93rd percentile, which is higher than the French percentile. So she did better on the Math exam as compared with the other incoming college students

Answer:

See the attached file for the answer.

Step-by-step explanation:

See the attached file for the explanation.