Distance from (3,5) and (-2,-2)

Answer:

We conclude that there is a difference in seat belt use.

Step-by-step explanation:

We are given that of 1,000 drivers 16-24 years old, 79% said they buckle up, whereas 924 of 1,100 drivers 25-69 years old said they did.

Let [tex]p_1[/tex] = population proportion of drivers 16-24 years old who buckle up .

[tex]p_2[/tex] = population proportion of drivers 25-69 years old who buckle up .

So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1-p_2[/tex] = 0      {means that there is no significant difference in seat belt use}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1-p_2\neq[/tex] 0      {means that there is a difference in seat belt use}

The test statistics that would be used here Two-sample z proportion statistics;

                     T.S. =  [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]  ~ N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of drivers 16-24 years old who buckle up = 79%

[tex]\hat p_2[/tex] = sample proportion of drivers 25-69 years old who buckle up = [tex]\frac{924}{1100}[/tex] = 84%

[tex]n_1[/tex] = sample of 16-24 years old drivers = 1000

[tex]n_2[/tex] = sample of 25-69 years old drivers = 1100

So, test statistics  =  [tex]\frac{(0.79-0.84)-(0)}{\sqrt{\frac{0.79(1-0.79)}{1000}+\frac{0.84(1-0.84)}{1100} } }[/tex]  

                              =  -2.946

The value of z test statistics is -2.946.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is a difference in seat belt use.

Answer:

1.5267% probability that he loses AT MOST 3 times

Step-by-step explanation:

For each game that Andy plays, there are only two possible outcomes. Either he wins, or he loses. The probability of winning a game is independent of other games. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The chance of winning a certain game at a carnival is 2 in 5.

So the chance of losing is (5-2) in 5, that is 3 in 5.

So [tex]p = \frac{3}{5} = 0.6[/tex]

12 games:

This means that [tex]n = 12[/tex].

What is the probability that he loses AT MOST 3 times?

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex].

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{12,0}.(0.6)^{0}.(0.4)^{12} = 0.000017[/tex]

[tex]P(X = 1) = C_{12,1}.(0.6)^{1}.(0.4)^{11} = 0.000302[/tex]

[tex]P(X = 2) = C_{12,2}.(0.6)^{2}.(0.4)^{10} = 0.002491[/tex]

[tex]P(X = 3) = C_{12,3}.(0.6)^{3}.(0.4)^{9} = 0.012457[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.000017 + 0.000302 + 0.002491 + 0.012457 = 0.015267[/tex]

1.5267% probability that he loses AT MOST 3 times

Answer:

A. 20

Step-by-step explanation:

look at this step:

4 : 5 = X : 25

X = 4×25/5 = 100/5 = 20

She can assemble 20 boxes.

1. Create a table

# of Boxes                    Time

4                        =>        5 min

x                        =>       25 min

2. Use the table to cross multiply.

5 · x = 4 · 25

5x = 100

5x/5 = 100/5

x = 20

Answer:

[tex] (0.68-0.56) -1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= -0.0263[/tex]

[tex] (0.68-0.56) +1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= 0.2663[/tex]

So then we are 95% confident that the true difference in the proportions is given by:

[tex] -0.0263 \leq p_1 -p_2 \leq 0.2663[/tex]

Step-by-step explanation:

The information given for this case is:

[tex]\hat p_1 = 0.68 , \hat p_2 = 0.56[/tex]

[tex] n_1 = 70, n_2 =100[/tex]

We want to construct a confidence interval for the difference of proportions [tex]p_1 -p_2[/tex] and for this case this confidence interval is given by:

[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1 (1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]

The confidence level is 0.95 so then the significance level would be [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex] if we find the critical values for this confidence level we got:

[tex]z_{\alpha/2}= \pm 1.96[/tex]

And replacing the info we got:

[tex] (0.68-0.56) -1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= -0.0263[/tex]

[tex] (0.68-0.56) +1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= 0.2663[/tex]

So then we are 95% confident that the true difference in the proportions is given by:

[tex] -0.0263 \leq p_1 -p_2 \leq 0.2663[/tex]

The 95% confidence interval is (0.257,-0.017).

To understand the calculations, check below.

The critical value is a cut-off value that is used to mark the start of a region where the test statistic, obtained in hypothesis testing, is unlikely to fall in.

Given that,

[tex]n_1=70\\n_2=100\\\hat{p_1}=0.68\\\hat{p_1}=0.56\\SE=0.07\\\alpha=0.05[/tex]

The critical value is,

[tex]Z_{\frac{\alpha}{2} }=Z_{\frac{0.05}{2} }=1.96[/tex]  (From standard normal probability table)

Therefore, the 95% confidence interval for the difference between population proportions [tex]p_1-p_2[/tex] is ,

[tex](\hat{p_1}-\hat{p_2})\pm Z_{\frac{\alpha}{2} }\times \sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1}+\frac{1}{n_2} ) }\\=(\hat{p_1}-\hat{p_2})\pm Z_{\frac{\alpha}{2} }\times SE\\=(0.68-0.56)\pm 1.96\times 0.07\\=0.12\pm 0.137\\=(0.257,-0.017)[/tex]

Learn more about the topic Critical value:

https://brainly.com/question/1832218

Answer:

Oxford had the highest variability

Step-by-step explanation:

If you put the numbers in order from greatest to least, and get the range 62,55 and 89,55 you get Oxford as the higher variability with a range of 39

Answer:

B. 2-column table with 5 rows. Column 1 is labeled x with entries 60, 61, 63, 67, 69. Column 2 is labeled y with entries negative 20, 0, 3, 8, 8.

C.On a graph, points form a line with negative slope. One point is outside of the line.

Step-by-step explanation:

Answer:

the answer is 1

Step-by-step explanation:

bc if you add -50+51 you get 1

Answer:

uno

Step-by-step explanation

51- 50 =1

Answer:

The expression isTotal number of cupcakes Sean orders=5 boxes (12 cupcakes)+ 3.5 boxes (12 cupcakes)

Step-by-step explanation:

A box= 12 cupcakes

Sean's order

Sister's graduation=5 boxes

Variety show party=3.5 boxes

Total number of cupcakes Sean orders=5 boxes (12 cupcakes)+ 3.5 boxes (12 cupcakes)

Total number of cupcakes Sean orders=5(12)+3.5(12)

=60+42

=102 cupcakes

Answer:

1/25

Step-by-step explanation:

= 5^4/5^6

= 1/5^6-4

= 1/5^2

= 1/25

hope it helps!

Answer:

Here is the answer..

Step-by-step explanation:

It's simple.

look

=5^4/5^6

=1/25

Hope it helps ☺️

We have been given that a right circular cone has a height of 12.2 cm and a base with a circumference of 18.5 cm. We are asked to find the volume of the cone to nearest tenth.

We know that circumference of circle is equal to [tex]2\pi r[/tex].

[tex]2\pi r=18.5[/tex]

[tex]r=\frac{18.5}{2\pi}[/tex]

[tex]r=2.944366[/tex]

Now we will use volume of the cone formula to solve our given problem.

[tex]V=\frac{1}{3}\pi r^2 h[/tex]

[tex]V=\frac{1}{3}\pi (2.944366)^2\cdot (12.2)[/tex]

[tex]V=\frac{1}{3}\pi (8.669291141956)\cdot (12.2)[/tex]

[tex]V=\frac{1}{3}\pi (105.7653519318632)[/tex]

[tex]V=\frac{1}{3}(332.2716526334804752)[/tex]

[tex]V=110.7572175[/tex]

Upon rounding to nearest tenth, we will get:

[tex]V\approx 110.8[/tex]

Therefore, the volume of the given cube would be approximately 110.8 cubic centimeter.

Final answer:

To find the volume of a right circular cone, the base radius is calculated from the circumference, and then the volume is determined using the cone volume formula V = (1/3)πr²h, with the final result being rounded to the nearest tenth. So, [tex]\( V \approx 110.415 \) cm^3[/tex].

Explanation:

To calculate the volume of a right circular cone, we first need to determine the radius of the base which can be found from the circumference. Since the formula for circumference is C = 2πr, where C is the circumference and r is the radius, we can solve for r. For a circumference of 18.5 cm, we have:

18.5 = 2πr => r = 18.5 / (2π)

Now that we have the radius, the volume of the cone can be found using the formula:

V = (1/3)πr²h

Plugging in the radius and height:

V = (1/3) * π * (18.5 / (2π))² * 12.2

After performing the calculation, we can round the result to the nearest tenth to find the volume in cubic centimeters.

Let's calculate it:

1. [tex]\( \frac{18.5}{2\pi} \) \approx \( \frac{18.5}{6.28319} \) \approx 2.942881[/tex]

2. Square the result: [tex]\( (2.942881)^2 \) \approx 8.66347[/tex]

3. Multiply by 12.2: [tex]\( 8.66347 \times 12.2 \)[/tex] ≈ 105.685554

4. Multiply by [tex]\( \frac{1}{3} \) and \( \pi \)[/tex]:

  [tex]\( V = \frac{1}{3} \times \pi \times 105.685554 \)[/tex]

Now, let's calculate \( V \):

[tex]\[ V \approx \frac{1}{3} \times 3.14159 \times 105.685554 \]\[ V \approx \frac{1}{3} \times 3.14159 \times 105.685554 \]\[ V \approx 110.415 \][/tex]

So, [tex]\( V \approx 110.415 \) cm^3[/tex].

Answer:

To figure out if 2 lines are parallel, compare their slopes. You can find the slope of a line by picking 2 points with XY coordinates, then put those coordinates into the formula Y2 minus Y1 divided by X2 minus X1. Calculate the slope of both lines. If they are the same, then the lines are parallel.

Step-by-step explanation:

To figure out if 2 lines are parallel, compare their slopes. You can find the slope of a line by picking 2 points with XY coordinates, then put those coordinates into the formula Y2 minus Y1 divided by X2 minus X1. Calculate the slope of both lines. If they are the same, then the lines are parallel.

Answer:

volume of the larger solid = 686 cm³

Step-by-step explanation:

The solids are similar . A solid is similar if all the corresponding sides are proportional . They are similar if they are the same type of solids and their corresponding sides like height, radius etc are proportional.

The ratio of the surface area of a similar solid is equal to the square of their scale factor.

(a/b)² = 441/225

square root both sides

a/b = √441/√225

a/b = 21/15

The ratio of the volume of a similar solid is equal to the cube of their scale factor.Therefore,

(21/15)³ = a/250

9261 /3375  = a/250

cross multiply

9261 × 250 = 3375a

2315250  = 3375a

divide both sides by 3375

a = 2315250/3375

a = 686  cm³

volume of the larger solid = 686 cm³

Step-by-step explanation:

multiply 2 with the bracket numbers

6x+16=0

6x= - 16

x=-16/6

x= - 8/3

Answer: $612.65, $2,567.45, and increase

Step-by-step explanation:

Answer:

✔ $612.65

was withheld specifically for the tax that is used to pay for a healthcare program.

✔ $2,567.45

was withheld for the payroll tax that specifically supports retired and disabled citizens.

If this individual made more money, the amount withheld for Social Security would

✔ increase

.

Answer:

B. 83

Step-by-step explanation:

Angle in a triangle sum to 180 degrees

-> 25 + 72 + ? = 180

                    ? = 180 - 25 - 72 = 83

Answer:

the answer is B that's it

The polygon which has 7 sides and all its angles inside of the shape is a convex heptagon.

Convex heptagon

A convex heptagon is a type of polygon that has 7 sides and 7 interior angles and 7 vertices.

A polygon that has 7 sides and 7 interior angles and 7 vertices is considered as a convex heptagon.

This means a convex heptagon has 7 sides and all angles go inside of the shape.

So, the polygon which has 7 sides and all its angles go inside of the shape is a convex heptagon.

Learn more about a convex heptagon here-https://brainly.com/question/9949611

#SPJ2

Answer:

A

Step-by-step explanation:

on edge

Answer:

3.8

Step-by-step explanation:

a=3.79 or 3.8km

√(9.4^2 - 8.6^2)

Answer:

The expected amount earned by a waitress per evening is $95.83.

Step-by-step explanation:

At a local restaurant there are six rooms total; 1 is a "high roller" room and other 5 are normal rooms.

There are 6 waitresses working at the local restaurant.

The room assignments are made by fair random selection such that each waitress has an equal probability of being in the "high roller" room.

This implies that a waitress can be assigned any of the six rooms with probability, [tex]\frac{1}{6}[/tex].

The tip earned by the waitress working in the "high roller" room is $200 and that for other rooms is $75.

So, the distribution of tips earned is as follows:

    X: $200    $75    $75    $75    $75    $75

P (X):     [tex]\frac{1}{6}[/tex]          [tex]\frac{1}{6}[/tex]         [tex]\frac{1}{6}[/tex]          [tex]\frac{1}{6}[/tex]         [tex]\frac{1}{6}[/tex]         [tex]\frac{1}{6}[/tex]

The expected value of a random variable is given by:

[tex]E(X)=\sum x\cdot P (X)[/tex]

Compute the expected amount earned by a waitress per evening as follows:

[tex]E(X)=\sum x\cdot P (X)[/tex]

         [tex]=(200\times \frac{1}{6})+(75\times \frac{5}{6})\\\\=\frac{575}{6}\\\\=95.8333\\\\\approx 95.83[/tex]

Thus, the expected amount earned by a waitress per evening is $95.83.

Final answer:

Using the probabilities of being in different rooms and their respective tips, a waitress can expect to make on average approximately $95.83 per evening at this restaurant.

Explanation:

To calculate the average amount a waitress can expect to make per evening, we need to consider the probabilities of the waitress being assigned to the "high roller" room or any other room. Since there are six rooms and assignments are made randomly, each waitress has a 1 in 6 chance of being in the high roller room. Otherwise, she has a 5 in 6 chance of being in a room with a lower tip rate.

We calculate the expected earnings for each scenario and then find the combined average. The expected earnings in the high roller room is $200, while the expected earnings in the other rooms is $75. Using the formula for expected value (EV), we get:

EV = (Probability of High Roller Room) x (Tips in High Roller Room) + (Probability of Other Rooms) x (Tips in Other Rooms)

EV = (1/6) x $200 + (5/6) x $75

EV = $33.33 + $62.50

EV = $95.83

So, on average, a waitress can expect to make approximately $95.83 per evening.

Answer:

a.)Easy to produce, d.)affordable, and e.)abundant

Step-by-step explanation:

i got it correct on the instructions

The correct options are easy to produce, affordable, and abundant​.

A nonrenewable resource is a natural substance that is not replenished with the speed at which it is consumed.

A non-renewable resource is defined as the natural resources which are not readily replaced through natural means and it takes thousands of years for their renewal.

Examples of non-renewable resources include Fossil fuels such as natural gas, oil, and coal.

There are many advantages of non-renewable resources such as:

Hence, the correct options are easy to produce, affordable, and abundant​.

Learn more about the nonrenewable resource here;

https://brainly.com/question/16183007

#SPJ2

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images for the step by step explanation to the question

Answer:

The probability that it was raining on Monday given that Shameel misses his flight is 0.5846.

Step-by-step explanation:

The Bayes' theorem states that the conditional probability of an event E[tex]_{i}[/tex], of the sample space S = {E₁, E₂, E₃,...Eₙ}, given that another event A has already occurred is given by the formula:

[tex]P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{\sum\limits^{n}_{i=1} {P(A|E_{i})P(E_{i})}}[/tex]

Denote the events as follows:

X = it will rain on Monday

Y = Shameel misses his flight.

The information provided is:

[tex]P(X) = 0.19\\P(Y|X)=0.06\\P(Y|X^{c})=0.01[/tex]

Compute the probability that it will not rain on Monday as follows:

[tex]P(X^{c})=1-P(X)\\\\=1-0.19\\\\=0.81[/tex]

Compute the probability that it was raining on Monday given that Shameel misses his flight as follows:

Use the Bayes' theorem:

[tex]P(X|Y)=\frac{P(Y|X)P(X)}{P(Y|X)P(X)+P(Y|X^{c})P(X^{c})}[/tex]

             [tex]=\frac{(0.06\times 0.19)}{(0.06\times 0.19)+(0.01\times 0.81)}\\\\=\frac{0.0114}{0.0114+0.0081}\\\\=\frac{0.0114}{0.0195}\\\\=0.58462\\\\\approx 0.5846[/tex]

Thus, the probability that it was raining on Monday given that Shameel misses his flight is 0.5846.

Final answer:

The probability that it was raining given Shameel misses his flight is approximately 58.46%, calculated using Bayes' theorem with the given probabilities of rain and missing the flight under different weather conditions.

Explanation:

The student is asking about conditional probability related to Shameel missing his flight given that it is raining. We need to use Bayes' theorem to solve this problem. The equation for Bayes' theorem, in this case, is:

P(Rain|Miss) = (P(Miss|Rain) × P(Rain)) / (P(Miss|Rain) × P(Rain) + P(Miss|Not Rain) × P(Not Rain))

Let's plug in the values given:

P(Miss|Rain) = probability that Shameel misses his flight given it is raining = 0.06

P(Rain) = probability that it will rain = 0.19

P(Miss|Not Rain) = probability that Shameel misses his flight given it is not raining = 0.01

P(Not Rain) = probability that it does not rain = 1 - P(Rain) = 1 - 0.19 = 0.81

Substitute all the values into the equation:

P(Rain|Miss) = (0.06 × 0.19) / (0.06 × 0.19 + 0.01 × 0.81)

After calculating:

P(Rain|Miss) = 0.0114 / (0.0114 + 0.0081)

P(Rain|Miss) = 0.0114 / 0.0195 ≈ 0.5846 or 58.46%

So, if Shameel misses his flight, the probability that it was raining is approximately 58.46%.

Answer:

The 92% confidence interval for the actual proportion of all office workers who are able to take every telephone call is (0.3676, 0.4324).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 700, \pi = \frac{280}{700} = 0.4[/tex]

92% confidence level

So [tex]\alpha = 0.08[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.08}{2} = 0.96[/tex], so [tex]Z = 1.75[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.75\sqrt{\frac{0.4*0.6}{700}} = 0.3676[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.75\sqrt{\frac{0.4*0.6}{700}} = 0.4324[/tex]

The 92% confidence interval for the actual proportion of all office workers who are able to take every telephone call is (0.3676, 0.4324).

Answer:

$75,000

Step-by-step explanation:

Given:

Total loaned amount = $200,500

Amount loaned for product Y = y

So, Amount loaned for product X = $50,500 + y

Computation:

Total loaned amount = Amount loaned for product Y + Amount loaned for product X

$200,500 = y + $50,500 + y

$200,500 = 2 y + $50,500

$200,500 - $50,500 = 2 y

$150,000 = 2 y

y = $75,000

Therefore, money loaned for product Y is $75,000

Answer:

opposite angles are congruent

Step-by-step explanation:

thats because if you think about two intersecting lines and draw a circle around the angles you can imagine it as a circle (360 degrees) so whatever value the angles are they have to equal 360

so you may ask the question what does that have to do with anything? well i'm getting to that...the vertical angles are congruent because well one there is a theorem for it (search it up) and two it makes sense if you think of cutting a pizza all the way across and another line intersecting it all the way across. You notice how no matter how you position the two intersecting lines the angle opposite each other look the same. Thats because they are the same exact angle just directly across from each other. I hope this made sense :)

Answer:

The opposite interior angles of the parallelogram have equal measurements.

Step-by-step explanation:

PLATO SAMPLE

Answer:

We conclude that the brown trout's mean I.Q. is greater than four.

Step-by-step explanation:

We are given that the average brown trout's I.Q. is 4. Suppose you believe that the brown trout's mean I.Q. is greater than four.

You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5, 4, 7, 3, 6, 4, 5, 3, 6, 3, 8, 5.

Let [tex]\mu[/tex] = the brown trout's mean I.Q.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 4       {means that the brown trout's mean I.Q. is smaller than or equal to four}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 4       {means that the brown trout's mean I.Q. is greater than four}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                          T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean I.Q. of brown tout =  [tex]\frac{\sum X}{n}[/tex]  = 4.92

            s = sample standard deviation =  [tex]\sqrt{\frac{\sum (X- \bar X)^{2} }{n-1} }[/tex]  = 1.62

            n = sample of brown trout = 12

So, the test statistics  =  [tex]\frac{4.92-4}{\frac{1.62}{\sqrt{12} } }[/tex]  ~ [tex]t_1_1[/tex]

                                     =  1.967

The value of t test statistics is 1.967.

Now, at 5% significance level the t table gives critical value of 1.796 at 11 degree of freedom for right-tailed test.

Since our test statistic is more than the critical value of t as 1.967 > 1.796, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the brown trout's mean I.Q. is greater than four.

To conduct a hypothesis test, compare the sample mean IQ of 12 brown trout to the hypothesized mean of 4 using a one-sample t-test at a 0.05 significance level.

To conduct a hypothesis test of the belief that the brown trout's mean IQ is greater than four, we can use a one-sample t-test. The null hypothesis (H0) is that the mean IQ of brown trout is equal to four. The alternative hypothesis (Ha) is that the mean IQ is greater than four.

Using a proper significance level of 0.05, we can compare the sample mean IQ of the 12 brown trout to the hypothesized mean of four. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence to support the belief that the brown trout's mean IQ is greater than four.

https://brainly.com/question/34171008

#SPJ11

Answer:

35

Step-by-step explanation:

The way I know is because I memorized every square up to 33.

BUT that's probably not helpful to you.

Remember that every perfect square has an odd number of factors. I'm not going to list them all out, but the factors of 35 are 1, 5, 7, and 35, giving it an even number of factors. All the rest have an odd number of factors because of the property of a perfect square: a number times itself gives a perfect square, but that number only counts as 1 factor.

Answer:

25

Step-by-step explanation:

Step-by-step explanation:

the equivalent of 3/8 is 6/16

Answer:

[tex]\frac{6}{16} = \frac{9}{24} =\frac{12}{32} =\frac{15}{40}[/tex]

Step-by-step explanation:

There are infinitely many equivalent fractions of [tex]\frac{3}{8}[/tex] but here are a few:

[tex]\frac{6}{16} = \frac{9}{24} =\frac{12}{32} =\frac{15}{40}[/tex]

Answer:

Central angle = θ = 2.5 radians

Step-by-step explanation:

The radian measure of central angle is given by

[tex]\theta = \frac{s}{r}[/tex]

Where s is the arc length, r is the radius of circle and θ is angle in radians

We are given an arc length of 5 units

[tex]s = 5[/tex]

We are given radius of 2 units

[tex]r = 2[/tex]

Therefore, the central angle in radians is

[tex]\theta = \frac{5}{2}\\\\\theta = 2.5 \: rad[/tex]

Bonus:

Radian is a unit which we use to measure angles.

1 Radian is the angle that results in an arc having a length equal to the radius.

Degree is another unit that we use to measure angles.

There are 360° in a circle.

There are 2π radians in a circle.

Answer:

  [tex]a_k=\left|\dfrac{k^2-3}{k^2+4}\right|;\text{ is nondecreasing for $k>2$}[/tex]

  [tex]\lim\limits_{k \to \infty} a_k =1[/tex]

  The series does not converge

Step-by-step explanation:

Given ...

  [tex]S=\displaystyle\sum\limits_{k=2}^{\infty}{x_k}\\\\x_k=(-1)^k\cdot\dfrac{k^2-3}{k^2+4}\\\\a_k=|x_k|[/tex]

Find

  whether S converges.

Solution

The (-1)^k factor has a magnitude of 1, so the magnitude of term k can be written as ...

  [tex]\boxed{a_k=1-\dfrac{7}{k^2+4}}[/tex]

This is non-decreasing for k>1 (all k-values of interest)

As k gets large, the fraction tends toward zero, so we have ...

  [tex]\boxed{\lim\limits_{k\to\infty}{a_k}=1}[/tex]

Terms of the sum alternate sign, approaching a difference of 1. The series does not converge.