A pediatrician wants to determine the relation that may exist between a​ child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. Find the residuals from the regression and verify that the residuals are approximately normally distributed. Height​ (inches), x 26.75 25.5 26.5 27 25 Head Circumference​ (inches), y 17.3 17.1 17.3 17.5 16.9

Answer:

Car: Exponential Function

Train: Exponential Function

Step-by-step explanation:

The consecutive differences are quite far from being constant. However, the consecutive ratios are quite close to being constant, being approximately 0.49 for every increase in 2 seconds.Therefore, the speed of the car is best modeled by an exponential function. The consecutive ratios for the trains are quite close to being constant, being approximately 0.56 for every increase in 2 seconds. Therefore, the speed of the train is best modeled by an exponential function.

The data of car is exponential function.

The data of truck is exponential function.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

As, the difference between two consecutive terms is not constant.

but the ratios are quite close to being constant,  approximately 0.49 for every increase in 2 seconds.

The consecutive ratios for the trains are 0.56 for every increase in 2 seconds.

Thus, the speed of the car and truck is an exponential function.

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Using the z-distribution, it is found that the correct option is:

b. is not significantly greater than 50 percent.

At the null hypothesis, it is tested if the proportion is not significantly greater than 50%, that is:

[tex]H_0: p \leq 0.5[/tex]

At the alternative hypothesis, it is tested if the proportion is significantly greater than 50%, that is:

[tex]H_1: p > 0.5[/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]n = 100, \overline{p} = \frac{55}{100} = 0.55, p = 0.5[/tex].

Hence:

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

[tex]z = \frac{0.55 - 0.5}{\sqrt{\frac{0.5(0.5)}{100}}}[/tex]

[tex]z = 1[/tex]

The critical value for a right-tailed test, as we are testing if the mean is greater than a value, using the z-distribution with a significance level of 0.05, is of [tex]z^{\ast} = 1.645[/tex].

Since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that the proportion is greater than 50%, hence, option b is correct.

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Answer:

[tex]f(x)=2x^2-1\\f(5)=2(5)^2-1\\f(5)=2(25)-1\\f(5)=50-1\\f(5)=49[/tex]

Step-by-step explanation:

Answer:

don't bother commenting im a bot

Step-by-step explanation:

Answer:

5/18 I believe

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Since we want to test if it is a right triangle, we can use the Pythagorean Theorem

a^2+b^2=c^2

where a and b are the legs (shortest sides) and c is the hypotenuse (longest side)

We have the sides: 24,18 and 30

24 and 18 are the shortest, therefore they are the legs. 30 is the longest, so it is the hypotenuse.

So, a is 24, b is 18 and c is 30

24^2+18^2=30^2

Evaluate the exponents

576+324=900

Add 576 and 324

900=900

This statement is true, so this is a right triangle

Answer:

Is there any picture ?

Step-by-step explanation:

Option A is the correct answer. That is a nonresponse occurred.

Given that, a hospital did a 10-year study on patients who use his services. 1000 patients were randomly selected and followed over a period of 10 years to determine the average number of visits per year.

An opinion poll, often simply referred to as a poll or a survey, is a human research survey of public opinion from a particular sample.

Look at the explanation given below for the options:

Option A:

We understand that in the span of 10 years, 1000 patients were monitored, and among those were some individuals who had moved. These certain individuals are not responsive anymore, and can not be a source of data, and the poll would be incorrect if the hospital decided to switch out the patients in the midst of the decade. Therefore we are to assume a nonresponse occurred. (To define nonresponse, it is simply a failure to respond, which is indeed what is defined for those who had moved.)

Option B:

It is not B for the two variables have no correlation.

Option C:

It is not C for all patients were at first patrons and the problem did not explicitly state there was missing info.

Option D:

It is incorrect for it said the sample group was selected at random.

Therefore, with the process of elimination, option A would still be the correct answer.

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A hospital did a 10-year study on patients who use his services. 1000 patients were randomly selected and followed over a period of 10 years to determine the average number of visits per year. By the end of the 10 years. Some of the patients had left the area. Identify the problem with the poll.

A) A nonresponse occurred

B) The relationship between two variables implies one causes the other

C) Some of the sample data are missing

D) The conclusion is based on a voluntary response sample

Answer:35 meters

Step-by-step explanation:

Answer:

35 meters

Formula:

a^2+b^2=c^2

12^2+b^2=37^2

Answer:

A. the number of calories consumed and the amount of weight lost by a person.

E. the thickness of the ice on a lake and the likelihood of falling through the ice.

Step-by-step explanation: This is the correct answer on Edge 2021, just did the assignment. Hope this helps ^-^.

An example of negative correlation is;the number of calories consumed and the amount of weight lost by a person.

The term correlation has to do with the way in which two quantities are related. If there is a positive correlation between two quantities, they tend to have a positive slope when plotted.

Two examples of negative correlation are;

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Answer:

its 2,21

Step-by-step explanation:

The only point that is in the circle of radius 5 is option A: (2, √21).

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

The distance between a point (x, y) and the origin is:

d = √(x² + y²).

Of the given options, the only one that meets this condition is the one in option A. (2, √21).

If we find the distance to the origin, we get:

d = √(2² + √21²) = √(4 + 21) = 5.

So that is the correct option.

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Complete question:

Which point is on the circle centered at the origin with a radius of 5 units?

Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot

A. (2, StartRoot 21 EndRoot)

B. (2, StartRoot 23 EndRoot)

C. (2, 1)

D. (2, 3)

Answer:

The probability that a randomly selected monthly cell phone bill is less than $95 is 0.9772

Step-by-step explanation:

The average monthly household cellular phone bill is $73.

[tex]\mu = 73[/tex]

Local monthly household cell phone bills are normally distributed with a standard deviation of $11.

[tex]\sigma = 11[/tex]

We are supposed to find the probability that a randomly selected monthly cell phone bill is less than $95 i.e.P(x<95)

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

[tex]Z=\frac{95-73}{11}[/tex]

Z=2

Refer the z table for p value

So,p value = 0.9772

Hence the probability that a randomly selected monthly cell phone bill is less than $95 is 0.9772

Answer:

r =45.5 units

Step-by-step explanation:

The diameter is twice the radius, or the radius is 1/2 the diameter

r = d/2

r = 91/2

r =45.5 units

Answer: 45.5

Step-by-step explanation: 91/2 because to find the diameter you have to multiply the radius by 2 and now we need to reverse it

Answer:

There is no difference.  Because the mean of Ari's tests equals his median score of his six tests.  mean = 84% median = 84%

Step-by-step explanation:

88%, 73%, 97%, 76%, 90%, 80%

organize by low to high

73%,  76%,  80%, 88%, 90%, 97%

The median here is  (80 + 88)/2 = 84%

let us find the mean

mean = [73% +  76% +  80% + 88% + 90% + 97%  ]/6

mean =  504/6 =  84%

There is no difference.  Because the mean of Ari's tests equals his median score of his six tests.  mean = 84% median = 84%

Answer:

22 millimetres

Step-by-step explanation:

[tex]width \: of \: rectangle \\ = \frac{area}{length} \\ = \frac{198}{9} \\ = 22 \: millimeters \\ [/tex]

Answer:

Jada can do 48 loads of laundry.

Step-by-step explanation:

There are 6 cups of detergent in the bottle. If Jada uses 1/8 cup of detergent each load you would have to find out how many 1/8 cups are in 6 cups. There are 8, 1/8 cups in 1 cup. So you would do 6 time 8, which equals 48 loads.

Answer: I literally gust took the the test and the answer is 112.

Your welcome!!

Answer:

Step-by-step explanation:

Hello!

a)

One of the advantages of assigning the units randomly to the different treatments is to avoid selection bias. An example of selection bias would be selecting the best subjects at the barbell curl to the "encouraged" group and the worst ones to the "not encouraged" group.

Randomization also guarantees independence between the experimental units and treatment groups.

b) (see boxplots in attachment)

Encouraged group:

Box:

Q₁≅ 10

Q₂≅ 30

Q₃= 50

IQD= 50 - 10 = 40

The box seems symmetric, the distance between Q₁-Q₂ and Q₂-Q₃ is the same and the median is exactly in the middle.

Whiskers:

The left whisker is shorter than the right whisker, which is longer.

If you were to look only at the box, the distribution seems symmetrical but adding the whiskers there is a pronounced right asymmetry.

Min value ≅ 5

Max value ≅ 75

Range= 75 - 5 = 70

Not encouraged group:

Box:

Q₁≅ 10

Q₂≅ 20

Q₃= 35

IQD= 35 - 10 = 25

The box shows a little skewness to the right (the 2nd Quartile is closer to the first one than the 3rd) and is overall shorter compared to the first group.

Whiskers:

The left whisker is shorter than the right whisker, so in general, this distribution is also right-skewed.

Min value ≅ 0

Max value ≅ 60

Range= 60 - 0 = 60

Compared with the "encouraged" group, the IQD and the Range are shorter, which means that the "not encouraged" group shows less dispersion.

c) and d)

Daniel claims that people perform better in the barbell curl, on average, when being encouraged.

He divided the 29 subjects into two groups and measured their performance, then the study variables are:

X₁: Performance in the barber curl of a subject that was encouraged by his coach.

X₂: Performance in the barber curl of a subject that did not receive encouragement.

Logically, since Daniel wants to study the performance of both groups on average, you'd think that the parameters of interest will be the population means. But to study the average you need the population to have a normal distribution and looking at those boxplots, none of them is near the normal distribution and the size of both samples isn't big enough for an approximation.

The best option is to conduct a non-parametric analysis, for example, the Mann Whitney U-test and instead of comparing the population means, you'll compare the population medians: θ₁ vs. θ₂ ⇒ In the hypothesis of this test, you'll state that both samples come from the same population and if both have the same median, then each observation of the first sample x₁i will have an equal probability of being smaller or greater than each observation of the second sample x₂i (probability 0.5)

Depending of the statistics course, the hypotheses may change, I'm used at working directly with the medians, if they are equal, it will mean that the top 50% and bottom 50% of each population will be the same, which is the same as saying that P(x₁i > x₂i)= 0.5 vs. P(x₁i > x₂i)≠ 0.5

The conditions for the Mann-Whitney U-test are:

1) All observations on both groups should be independent. Check

2) The variables should be continuous or at least ordinal. Check

3) Both variables have the same distribution under the null hypothesis. Check (Looking at the boxplots, both are right-skewed)

4) Under the alternative hypothesis, the values of one of the populations exceed the other. In this case: H₁: θ₁ > θ₂

e)

H₀: θ₁ ≤ θ₂  vs. H₁: θ₁ > θ₂

Using the p-value approach, the decision rule is always the same:

If p-value ≤ α ⇒ Reject the null hypothesis.

If p-value > α ⇒ Do not reject the null hypothesis.

p-value: 0.107 > α: 0.05 ⇒ The decision is to not reject the null hypothesis.

At a 5% significance level, there is no significant evidence to reject the null hypothesis. Both samples seem to be from the same population. He can conclude that encouraging the subjects doesn't change significantly their performance in the barbell curl.

I hope you have a SUPER day!

Answer:

Which set shows greater variability? Set B

Which measure provides greater variability for the set you chose? Range

Answer:

Set B

Range

Step-by-step explanation:

Trust me on this, also can I have brainiest please?

Hope you do well! :D

Answer:

2/10 or simplified, 1/5

Step-by-step explanation:

5 are purple out of 10 flowers so 5/10. 3 are pink so 3/10. That leaves 2/10 left, and depending on what your teacher prefers, the simplified answer is 1/5. I hope this helps.

a) The area of a kite is given by [tex]A=\frac{d_{1}d_{2}}{2}[/tex], where [tex]d_{1}, d_{2}[/tex] are the lengths of the diagonals. So the answer is [tex]\frac{1}{2} (40 \times 60)[/tex].

b) Evaluating the expression from part (a), we get the area to be [tex]\boxed{1200 \text{ cm}^{2}}[/tex]

Answer:

3 would be the initial value so B

Step-by-step explanation:

Answer:

The answer is There were initially 3 bacteria in the culture.

Step-by-step explanation:

Answer:

[tex]a_n = a_o +(n-1) d[/tex]

[tex] 22.5 = 15 +(2-1) d[/tex]

[tex] d = 22.5-15 =7.5[/tex]

The general expression is:

[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]

Step-by-step explanation:

For this case we have the following arithmetic sequence given:

15, 22.5, 30,37.5

In order to fidn the recursive rule for this sequence we need to take in count that the general formula for an arithmetic sequence is given by:

[tex]a_n = a_o +(n-1) d[/tex]

Where [tex]a_n[/tex] is the nth term [tex]a_o[/tex] the initial value for the sequence and d the common difference. For this case we have that [tex]a_o =15[/tex]

And for the first term we have:

[tex] 15= 15 +(1-1)d[/tex]

For the second term we have this:

[tex] 22.5 = 15 +(2-1) d[/tex]

And solving for the value of d we got:

[tex] d = 22.5-15 =7.5[/tex]

And for the 3th term we have:

[tex] a_3= 15 +(3-1)*7.5 =30[/tex]

And for the 4th term

[tex]a_4 =15 +(4-1)*7.5 =37.5[/tex]

So then our expression is correct and would be given by:

[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]

Answer:

The solutions for the equation [tex]x^2\:-\:27=\:67[/tex] are [tex]x=\sqrt{94},\:x=-\sqrt{94}[/tex].

Step-by-step explanation:

To find the solutions for the equation [tex]x^2\:-\:27=\:67[/tex] you must:

[tex]\mathrm{Add\:}27\mathrm{\:to\:both\:sides}\\\\x^2-27+27=67+27[/tex]

[tex]\mathrm{Simplify}\\\\x^2=94[/tex]

[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{94},\:x=-\sqrt{94}[/tex]

Answer:

a) P(4)=0.03

b) P(x≥3)=0.15

c) P(x<3)=0.85

d) µX=1.52

e) σX=1.69

Step-by-step explanation:

The question is incomplete:

The variable X has the following probability distribution:

x  1  2  3  4   5

P(x) 0.7 0.15 0.10 0.03  0.02

a) The probability P(x=4) can be read from the table

[tex]P(4)=0.03[/tex]

b) The probability that there are at least 3 occupants in the car is P(x≥3).

[tex]P(x\geq3)=P(3)+P(4)+P(5)\\\\P(x\geq3)=0.10+0.03+0.02\\\\P(x\geq3)=0.15[/tex]

c) The probability that a car has fewer than 3 occupants (P(x<3)) is:

[tex]P(x<3)=1-P(x\geq3)=1-0.15=0.85[/tex]

d) The mean can be calculated as:

[tex]\mu_x=\sum_{i=1}^5p_i\cdot x_i\\\\\mu_x=0.7*1+0.15*2+0.10*3+0.03*4+0.02*5\\\\\mu_x=0.7+0.30+0.30+0.12+0.10\\\\ \mu_x=1.52[/tex]

e) The standard deviation can be calculated as:

[tex]\sigma_x=\sqrt{\sum_{i=1}^5p_i(x_i-\mu_x)^2}}\\\\ \sigma_x=\sqrt{0.7(1-1.52)^2+ 0.15(2-1.52)^2+ 0.1(3-1.52)^2+ 0.03(4-1.52)^2 +0.02(5-1.52)^2}\\\\ \sigma_x=\sqrt{0.7*0.2704+0.15*0.2304+0.1*2.1904+0.03*6.1504+0.03*12.1104}\\\\\sigma_x=\sqrt{0.18928+0.06912+0.65712+0.738048+1.21104}\\\\ \sigma_x=\sqrt{2.8646}\\\\ \sigma_x=1.69[/tex]

The graph of the probability distribution of X is a bar graph. The mean of X is 1.65 and the standard deviation can be calculated using the variance formula. The probability that a car has at least 3 occupants is 0.12 and the probability that a car has fewer than 3 occupants is 0.85.

Answer:

7.95.

Step-by-step explanation:

Absolute value is the positive version of that number.

Answer:

The team scored 50 points

Step-by-step explanation:

Let the points scored by team be x

We are given that sally was the top scorer woth 30% of the teams points

So, Sally scored points = [tex]30\% \times x[/tex]

Sally scored points = [tex]\frac{30}{100}x[/tex]

We are given that Sally scored 15 points

So, [tex]\frac{30}{100}x=15[/tex]

[tex]30x=1500[/tex]

[tex]x=\frac{1500}{30}[/tex]

x=50

Hence The team scored 50 points

Answer:

1: 20

2: 2020

Step-by-step explanation:

just got it man so ima go yeet

The group will have  290 members in the year 2020

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here, the equation is  y = 14x + 10 and we are required to have 290 members  thus,                     290=14x + 10

                                                 x= 280/14

                                                 x = 20 years

Hence the number of years required to achieve 290 members is equal to 20 years.

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