Weight of a rock: In a geology course, students are learning to use a balance scale to accurately weigh rocks. One student plans to weigh a rock 20 times and then calculate the average of the 20 measurements to estimate her rock's true weight. A second student plans to weigh a rock 5 times and calculate the average of the 5 measurements to estimate his rock's true weight. The student who weighs his rock 5 times uses the mean to calculate the 95% confidence interval for the rock weight (in grams). His interval is (25.2, 29.1). What does a 95% confidence interval for rock weight tell us in this case? Group of answer choices We are 95% confident that this interval includes the mean of the 5 weight measurements taken by this student. We are 95% confident that most rocks of this type weigh between 25.2 g and 29.1 g. We are 95% confident that the true weight of the rock is between 25.2 g and 29.1 g.

Answer:

28 you have to do it from left to right

Answer:

13-5=8

3x8=24

24-2=22

22+6=28

28 is your answer

Step-by-step explanation:

Answer: This means that the salaries of their marketing professionals are not closely related to their job titles. In further explanation, this shows that a professional with a higher job title, may be paid a lower salary when compared to a professional with a lower job title.

A 0.85 R-Squared shows that the points are far from the trend lines. From this, we can assume that the marketing professionals are paid base on commission on sales, and not base on job position.

Step-by-step explanation: R-Squared is a measure used in statistics, to represent how much proportion of the dependent variables that is explained by the independent variables. A high value of R^2 shows a very low correlation between the dependent and independent variables, while a low value of R^2 shows that the dependent and independent variables are closely related. The R-Squared value are a measure of percentage value.

Answer:

-3/4

Step-by-step explanation:

9/10 ÷ (-6/5)

Copy dot flip

9/10 * -5/6

Rewriting

-5/10 * 9/6

-1/2 * 3/2

-3/4

Answer: -3/4

Step-by-step explanation: Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of that fraction or that fraction flipped.

In other words we can rewrite 9/10 ÷ -6/5 as 9/10 · -5/6.

Before multiplying however, notice that we can cross-cancel

the 9 and 6 to 3 and 2 and the 5 and 10 to 1 and 2.

So we now have 3/2 · -1/2.

Now multiplying across the numerators

and denominators we get -3/4.

Answer:

B,1/5

Step-by-step explanation:

Answer:

the answer would be

B aka your second option

Step-by-step explanation:

i don't really have a step by step but this is the first question i've answered on this app let me know if i am helpful!!

We have been given an image of a trapezoid. We are asked to find the measure of angle M and N.

We know that bases of trapezoid are parallel and the two angles between two parallel lines are supplementary, so we can set an equation as:

[tex]\angle M+\angle N=180[/tex]

[tex](6y-10)+(4y-10)=180[/tex]  

[tex]6y-10+4y-10=180[/tex]

[tex]10y-20=180[/tex]

[tex]10y-20+20=180+20[/tex]

[tex]10y=200[/tex]

[tex]\frac{10y}{10}=\frac{200}{10}[/tex]

[tex]y=20[/tex]

Upon substituting value of y in measure of angle M, we will get:

[tex]m\angle M=6y-10[/tex]

[tex]m\angle M=6(20)-10[/tex]

[tex]m\angle M=120-10[/tex]

[tex]m\angle M=110[/tex]

Therefore, measure of angle M is 110 degrees.

Similarly, we will find the value of angle N as:

[tex]m\angle N=4y-10[/tex]

[tex]m\angle N=4(20)-10[/tex]

[tex]m\angle N=80-10[/tex]

[tex]m\angle N=70[/tex]

Therefore, measure of angle N is 70 degrees.

Answer:

The 98% confidence interval for the population proportion p is (0.4149, 0.6695).

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 = 83, \pi = \frac{45}{83} = 0.5422[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5422 - 2.327\sqrt{\frac{0.5422*0.4578}{83}} = 0.4149[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5422 + 2.327\sqrt{\frac{0.5422*0.4578}{83}} = 0.6695[/tex]

The 98% confidence interval for the population proportion p is (0.4149, 0.6695).

Answer:

2x^2 + x -1

Step-by-step explanation:

-7x + 5 - 2x^2 + 8x -6

2x^2 + x -1

Answer:

[tex]\displaystyle A = \int\limits^{33}_{5} {\frac{1}{x}} \, dx[/tex]

[tex]\displaystyle A = \ln \frac{33}{5}[/tex]

General Formulas and Concepts:

Algebra II

Calculus

Integration

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \frac{1}{x}[/tex]

Bounds: [5, 33]

Step 2: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

Brother read 8 books

Sophia read 32

Step-by-step explanation:

Number of book Sophia and her brother read is 32 and 8.

Given that;

Total number of books = 40 books

Number of book Sophia read = 4[Number of book Sophia's brother read]

Find:

Number of books each person read

Computation:

Assume;

Number of book Sophia's brother read = a

So,

Number of book Sophia read = 4a

So,

a + 4a = 40

5a = 40

a = 8

Number of book Sophia's brother read = 8 books

So,

Number of book Sophia read = 32 books

Find out more information about 'Distribution'.

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THE COMPLETE QUESTION IS:

Which dot plot shows a sample that is most representative of the number of pets in a household?

A. A dot plot going from 0 to 6. There are 3 dots above 0, 5 dots above 1, 4 dots above 2, 3 dots above 3, 2 dots above 4, 0 dots above 5, and 1 dot above 6.

B. Adot plot going from 0 to 6. There are 2 dots above 1, 3 dots above 2, and 1 dot above 5.

C. A dot plot going from 0 to 6. There is 1 dot above 0, 2 dots above 1, 1 dot above 2, 1 dot above 3, 1 dot above 4, 1 dot above 5, 2 dots above 6.

D. A dot plot going from 0 to 6. There is 1 dot above 1, 2 dots above 2, 3 dots above 3, 2 dots above 4, 1 dot above 5.

Answer:

A is the correct option

Step-by-step explanation:

A. A dot plot going from 0 to 6. There are 3 dots above 0, 5 dots above 1, 4 dots above 2, 3 dots above 3, 2 dots above 4, 0 dots above 5, and 1 dot above 6.

A has 3+5+4+3+2+0+1 = 18 dots

The rest are not up to 18.

The best graphical representation of the number of pets in a household is: A dot plot going from 0 to 6. There are 3 dots above 0, 5 dots above 1, 4 dots above 2, 3 dots above 3, 2 dots above 4, 0 dots above 5, and 1 dot above 6.

A graph can be defined as the graphical representation of data (information) on both the horizontal and vertical lines, which are commonly called the x-axis and y-axis respectively.

In Mathematics, there are different types of graph and these include:

A dot plot refers to a type of graph which comprises small data points that are plotted on a simple histogram-like graph. Thus, the number of pets in a household should be represented by using a dot plot with its value ranging from 0 to 6.

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Answer:

Option D is correct.

Rejecting the null hypothesis means that;

There is sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.

The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.

For this question, Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles per gallon in the city. And since this is talking distance covered per gallon of fuel, better means that the new sedan will average more than 32 miles per gallon.

So, the null hypothesis negating this claim would be that there isn't significant evidence to conclude that the average of the new sedan will be better or greater than 32 miles per gallon.

That is, the new average will be less than or equal to 32 miles per hour.

And the alternative hypothesis will confirm the claim that there is significant evidence to conclude that the average of the new sedan will be better or greater than 32 miles per gallon.

Mathematically,

The null hypothesis is represented as

H₀: μ ≤ 32 miles per gallon

The alternative hypothesis is given as

Hₐ: μ > 32 miles per gallon

So, after the hypothesis test has been conducted, rejecting the null hypothesis means accepting the alternative hypothesis and its statement that there is significant evidence to conclude that the average of the new sedan will be better or greater than 32 miles per gallon.

Hence, option D is correct.

Hope this Helps!!!

The conclusion of the hypothesis test indicates that there is sufficient evidence to support the claim that the mean fuel efficiency of the new Libra sedan is greater than 32 miles per gallon.

From the noun hypothesis testing conducted, the conclusion drawn is to reject the null hypothesis. In non-technical terms, rejecting the null hypothesis means that based on the data collected and analyzed, there is sufficient statistical evidence to support the claim that contrary to the null hypothesis, the average (or 'mean') miles per gallon of the new Libra sedan is indeed greater than 32 miles per gallon. These results should confirm Carter Motor Company's assertions about their vehicle's fuel efficiency.

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Answer:

[tex]\huge\boxed{V=576\ ft^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a prism with dimensions}\ l\times w\times h:\\\\V=lwh.\\\\\text{We have}\\\\l=8ft,\ w=6ft,\ h=12ft.\\\\\text{Substitute:}\\\\V=(8)(6)(12)=576(ft^3)[/tex]

Answer:

9

Step-by-step explanation:

it's 9 because you always look in the middle for the mean

Answer:

choose choice C.

Step-by-step explanation:

many vertical lines can cross this graph more than once, which defies the definition of a function.

Answer:

c) A vertical line placed on the graph could intersect more than one point

Step-by-step explanation:

if you did the vertical line test, you would see that there would be more than one point per value.

hope i helped:) !!!

brainliest ??

Answer:

d) All of the above

Step-by-step explanation:

A one way analysis of variance (ANOVA) test, is used to test whether there's a significant difference in the mean of 2 or more population or datasets (minimum of 3 in most cases).

In a one way ANOVA the critical value of the test will be a value obtained from the F-distribution.

In a one way ANOVA, if the null hypothesis is rejected, it may still be possible that two or more of the population means are equal.

This one way test is an omnibus test, it only let us know 2 or more group means are statistically different without being specific. Since we mah have 3 or more groups, using post hoc analysis to check, it may still be possible it may still be possible that two or more of the population means are equal.

The degrees of freedom associated with the sum of squares for treatments is equal to one less than the number of populations.

Let's say we are comparing the means of k population. The degree of freedom would be = k - 1

The correct option here is (d).

All of the above

The correct answer is all of the statements are true in a one-way ANOVA: the test uses the F-distribution, rejecting the null can mean two or more population means are equal, and degrees of freedom for treatment sum of squares is the number of groups minus one.

The correct answer to which statement is true in a one-way ANOVA is d. All of these.

One-way ANOVA is used to determine if there are any statistically significant differences between the means of three or more independent (unrelated) groups. The F statistic in ANOVA is always right-tailed because larger F values fall in the right tail of the F-distribution curve, leading to the rejection of the null hypothesis.

Answer:

m/6-8 =m/58

Step-by-step explanation:

Using the midpoint formula, the coordinates of point B are determined by setting up equations with the known coordinates of point A and midpoint M. Solving these equations yields the x-coordinate of B as -10 and the y-coordinate as 6, making the coordinates of point B (-10, 6).

The question is asking to determine the coordinates of point B if M(-6,8) is the midpoint of AB and A has coordinates (-2,10). To find the coordinates of B, we use the midpoint formula which states that the midpoint M(x,y) is given by M = ((x1 + x2)/2, (y1 + y2)/2) where (x1, y1) and (x2, y2) are the coordinates of points A and B respectively. Since we know the coordinates of A and M, we can set up equations to solve for the coordinates of B.

To find the x-coordinate of B, we set up the equation -6 = (-2 + xB)/2 which yields xB = -10. For the y-coordinate, we use the equation 8 = (10 + yB)/2 which gives us yB = 6. Therefore, the coordinates of point B are (-10, 6).

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Answer:

The point estimate for estimating the true proportion of employees who prefer that plan is 0.436

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

In this problem, we have that:

Lower bound: 0.366

Upper bound: 0.506

Point estimate:

(0.366 + 0.506)/2 = 0.436

The point estimate for estimating the true proportion of employees who prefer that plan is 0.436

Answer:

[tex]\hat p = \frac{0.366+0.506}{2}= 0.436[/tex]

And the point of estimate for the proportion of  employees who prefer plan is on this case 0.436 or 43.6%.

Step-by-step explanation:

We define the parameter of interest as the proportion of employees who prefer plan p and we want to estimate this true parameter

The confidence interval for the this proportion is given by the following formula:  

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

After calculate the 95% confidence interval we got (0.366, 0.506)

We can obtain the best estimate for the proportion of employees who prefer plan like this:

[tex]\hat p =\frac{Upper +Lower}{2}[/tex]

Where Upper and Lower represent the limits for the confidence interval and replacing we got:

[tex]\hat p = \frac{0.366+0.506}{2}= 0.436[/tex]

And the point of estimate for the proportion of  employees who prefer plan is on this case 0.436 or 43.6%.

The margin of error can be estimated using the fact that this confidence interval is symmetrical and we got:

[tex]ME=\frac{Upper-Lower}{2}= \frac{0.506-0.366}{2}=0.07[/tex]

Answer:560

Step-by-step explanation:

Let a be the number of students the school have last year

135% of a=756

135/100 x a=756

135a/100=756

Cross multiplying we get

135a=756 x100

135a=75600

Divide both sides by 135

135a/135=75600/135

a=560

Answer:

  8

Step-by-step explanation:

The lateral area of a cone is ...

  LA = (π/2)ds

where d is the diameter, and s is the slant height.

The area of this tower roof is about ...

  LA = (π/2)(12 ft)(13 ft) = 78π ft² ≈ 245 ft²

About 245/32 = 7.7 bundles of shingles will be required for coverage.

You should buy 8 bundles of shingles to cover the roof.

Answer:

Check the explanation

Step-by-step explanation:

(a) The appropriate test is the matched-pairs test because a student’s score on Try 1 is certainly correlated with his/her score on Try 2. Using the differences, we have xbar =  29 and s = 59.

(b) To test H0: mu=0 vs.  H1 mu > 0, we compute

[tex]t = (29-0)/((59/sqrt(427))=10.16[/tex]

with df = 426. This is certainly significant, with P < 0.0005. Coached students do improve their scores on average

(a) H0: μ1 = μ2 vs. Ha: μ1 > μ2, where μ1 is the mean gain among all coached students and μ2 is the mean gain among uncoached students. H0 and Ha. Using the conservative approach, df = 426 is rounded down to df = 100 in  (t table) and we obtain 0.0025 < P < 0.005. Using software, df = 534.45 and P = 0.004. There is evidence that coached students had a greater average increase.

(b) 8 ± t*(3.0235) where t* equals 2.626 (using df = 100 with (t table) ) or 2.585 (df = 534.45 with software). This gives either 0.06 to 15.94 points, or 0.184 to 15.816 points, respectively.

(c) Increasing one’s score by 0 to 16 points is not likely to make a difference in being granted admission or scholarships from any colleges.

Answer:

-7/2

Step-by-step explanation:

This question is a word problem.

Step 1: interpretation the question

Let's assume the number is x;

X×7 – 1 = X×5 – 8

7x - 1 = 5x - 8

Step 2. Solve the equation for the unknown.

7x - 1 = 5x - 8

Take like terms together

7x - 5x = - 8 +1

2x = -7

Divide both sides by 2

x = -7/2

The answer is -7/2

Answer:

[tex]y=0.259 x +10.447[/tex]

Now we can find the residulls like this:

[tex] e_1 = 17.3 - 17.375 = -0.075[/tex]

[tex] e_2 = 17.1 - 17.052 = 0.049[/tex]

[tex] e_3 = 17.3 - 17.311 = -0.011[/tex]

[tex] e_4 = 17.5 - 17.440 = 0.06[/tex]

[tex] e_5 = 16.9 - 16.922 = -0.022[/tex]

So then we can see that the residuals are not with an specified pattern (alternating sign) so then we can conclude that are distributed normally

Step-by-step explanation:

We have the following data given:

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

We need to find a linear model [tex] y = mx +b[/tex]

For this case we need to calculate the slope with the following formula:

[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]

Where:

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]

So we can find the sums like this:

[tex]\sum_{i=1}^n x_i =130.75[/tex]

[tex]\sum_{i=1}^n y_i =86.1[/tex]

[tex]\sum_{i=1}^n x^2_i =3422.06[/tex]

[tex]\sum_{i=1}^n y^2_i = 1482.85[/tex]

[tex]\sum_{i=1}^n x_i y_i =2252.28[/tex]

With these we can find the sums:

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=3422.06-\frac{130.75^2}{5}=2.95[/tex]

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=2252.28-\frac{130.75*86.1}{5}=0.765[/tex]

And the slope would be:

[tex]m=\frac{0.765}{2.95}=0.259[/tex]

Nowe we can find the means for x and y like this:

[tex]\bar x= \frac{\sum x_i}{n}=\frac{130.75}{5}=26.15[/tex]

[tex]\bar y= \frac{\sum y_i}{n}=\frac{86.1}{5}=17.22[/tex]

And we can find the intercept using this:

[tex]b=\bar y -m \bar x=17.22-(0.259*26.15)=10.447[/tex]

So the line would be given by:

[tex]y=0.259 x +10.447[/tex]

Now we can find the residulls like this:

[tex] e_1 = 17.3 - 17.375 = -0.075[/tex]

[tex] e_2 = 17.1 - 17.052 = 0.049[/tex]

[tex] e_3 = 17.3 - 17.311 = -0.011[/tex]

[tex] e_4 = 17.5 - 17.440 = 0.06[/tex]

[tex] e_5 = 16.9 - 16.922 = -0.022[/tex]

So then we can see that the residuals are not with an specified pattern (alternating sign) so then we can conclude that are distributed normally

Answer:

$390,900

Step-by-step explanation:

Given:

Initial payment = $965

New rapayment = $925 when she decided to refinance her ballon payment with a 30 year mortgage

In this case, a 5/25 ballon mortgage simply means loan repayment for the first 5 years is at a fixed rate.

Which means the total amount she paid in the first five years was=

12 * 5 * $965 = $57,900

When she refinanced the payment with a 30 year mortgage, her total payment = $925 * 12 * 30years = $333,000

Total financed cost Patricia paid =

$57,900 + $333,000 = $390,900

Answer:

The value of the test statistic is [tex]t = 2.67[/tex]

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} = 7.8[/tex]

The alternate hypotesis is:

[tex]H_{1} \neq 7.8[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

In this problem, we have that:

[tex]X = 8.2, \mu = 7.8, \sigma = 0.6, n = 16[/tex]

Then

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \frac{8.2 - 7.8}{\frac{0.6}{\sqrt{16}}}[/tex]

[tex]t = 2.67[/tex]

The value of the test statistic is [tex]t = 2.67[/tex]

Answer:

One solution.

Step-by-step explanation:

A linear line only goes one way, and thus, two lines can only meet at one point.

That is unless, the linear equations are both the same, then they will have infinite solutions.

But what you're asking is if they're different so no, you cannot have two solutions for a system of two linear equations.

Answer:

0

Step-by-step explanation:

Two different solutions means the two equations aren't consistent - there's no unique solution that solves the whole system. Two lines can meet at at most one point, so in this case, no solution to the first equation will be a solution to the second. The system has 0 solutions.

Answer:

h=6

Step-by-step explanation:

the formula for a trapezoid’s area is to multiply the bases (a and b) by the height of the trapezoid, then divide it all by 2.

so typed out, that would look like:

((a+b) h) / 2

and in the case of this problem:

((22) h) / 2 = 66

so just go ahead and solve it algebraically from there and you’re good!

Answer:

B

Step-by-step explanation:

you multiply the numbers and remember the little square is 90

The area of new parallelogram is 78in2

The original parallelogram has a base of 18 inches and a height of 10 inches. Therefore, its area is 18 x10 = 180 square inches.If the height is decreased by 1 inch and the base is decreased by 2 inches, the new base will be 18 - 2 = 16 inches and the new height will be 10 - 1 = 9 inches. So, the area of the new parallelogram will be 16 x 9 = 144 square inches.Therefore, the answer is c. 78in2.

Here's a breakdown of the reasoning for each option:a. 108in2: This is incorrect because it's smaller than the area of the original parallelogram, even though both the base and height are decreased.b. 104in2: 

This is also incorrect because it's still larger than the area of the new parallelogram.c. 78in2: 

This is the correct answer, as calculated above.d. 84 in2: This is incorrect because it's closer to the area of the original parallelogram than the new one.