Which equation represents an exponential function with an initial value of 500?

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.

We have been given that Maria put trim around a banner that is the shape of a triangle. Each side is 21 inches long.

The amount of trim will be equal to perimeter of triangle. The perimeter of given triangle will be 3 times each side length that is [tex]3\times 21=63[/tex] inches.

Now we need to convert 63 inches into feet.  

12 inches = 1 feet

63 inches = [tex]\frac{63}{12}[/tex]  feet = 5.25 feet.

We are also told that Maria has [tex]\frac{3}{4}[/tex] foot of trim left, so total length of trim would be trim used plus trim left that is [tex]5.25+\frac{3}{4}=5.25+0.75=6[/tex] feet.

Since we need to find length of trim in yards, so we will convert 6 feet into yards.

3 feet = 1 yard

6 feet = [tex]\frac{6}{3}[/tex] yards = 2 yards

Therefore, the length of the trim was 2 yards.

Answer:

[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]

Step-by-step explanation:

In statistics, the standard deviation is a measure about the amount of variation of a dataset.

The variation is measured through comparison between each data and the mean of the dataset. This way, we could get a numerical information about how far are those values form the mean (which represents the central value).

The formula to find the standard deviation of a sample is

[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]

Where [tex]\mu[/tex] is the sample mean and [tex]N[/tex] is the total number of values there are.

In the formula you can notice the difference between each value ([tex]x_{i}[/tex]) and the mean ([tex]\mu[/tex]), That's why the standard deviation is commonly use to measure variation.

Therefore, the answer is

[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]

Answer:

87

Step-by-step explanation:

The expected value is the product of the probability and the outcome.

E = 0.98 (89)

E = 87.22

Rounded to the nearest integer, the expected number of classes is 87.

Answer:

Given:

mean, u = 6.2

sample size, n = 180

Sample mean, X' = 6.3

s.d [tex] \sigma [/tex] = 0.9

Significance level = 0.05

The null and alternative hypothesis will be:

H0 : u = 6.2

H1 : u > 6.2

Degree of freedom = 180 - 1 = 179

Using t table, the t critical value,

t> t(0.05, 179) = 1.6534

The test statistic:

[tex] t = \frac{X' - u}{\frac{\sigma}{\sqrt{n}}} [/tex]

[tex] T = \frac{6.3 - 6.2}{\frac{0.9}{\sqrt{180}}} = 1.4907 [/tex]

Since the test statistic(t calculated value) 1.4907 < t critical value (1.6534), we fail to reject the null hypothesis H0.

To find the expected number of white marbles in future pulls, calculate the probability of pulling a white marble from the current results, then multiply this probability by the number of new pulls.

To solve this problem, we will first identify the probability of pulling a white marble out of the bag based on Maria's results. Then, we will multiply this probability by the number of new marbles being pulled out (20) to determine the expected number of white marbles.

Note: Since the outcomes are being replaced, the probabilities don't change after each pull.

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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: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:

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:

4x + 7 = x + 10: x = 1!

Step-by-step explanation:

Not sure if you wanted me to solve as well; but I figured I would do it just in case!

To solve this, use the following steps!:

[tex]4x+7=x+10\\-7\\4x=x+3\\-x\\3x=3\\x=1![/tex]

x = 1 Should be the correct answer!

The sum of four times a number and seven is ten more than the number can be express as follows:

4x - 3

let

the number = x

Therefore,

Four times the number = 4x

Seven is ten more than the number is as follows:

Therefore, the sum of four times a number and seven is ten more than the number is as follows:

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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:

-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.

Angle 3 = 60°

Angle 4 = 60°

Step-by-step explanation:

To find angle 3 we have to use the straight angle that is formed with angle C. Angle C is the same value as angle 2 (120°) so all we have to do now is make an equation by subtracting angle C (120°) from 180°. 180°-120°=60°. So 60° is the value of angle 3.

Angle 4 is also 60° because it is the same angle as angle 3. So the value of angle 4 is 60°.

Another way to solve this problem (shown in the picture) is using the value of angle 1 (60°) and when you have the value 60° and there are triangles formed within the angle (highlighted in the picture) you know that all the angles within the triangle are going to be 60° because all angles within a triangle add up to 180°. So if we were to use this rule the equation would look like 60°+60°+60°=180°. Angle 3 in the green triangle would be equal to 60° because of the fact that one angle was already confirmed as being 60° so because of that all the angles in the triangle have to add up to 180° so the all the angles must be 60°. Angle 4 in the red triangle would also be equal to 60° for the same reason mentioned above.

So therefore the answer to this question is Angle 3 = 60° and Angle 4 = 60°

Hope this helps! If you have any more questions or you need further clarification please comment down below or message me! Good luck!

Answer: It should be used 2 for type-A and 3 for type-B to minimize the cost.

Step-by-step explanation: As it is stipulated, x relates to type-A and y to type-B.

Type-A has 60 deluxe cabins and B has 80. It is needed a minimum of 360 deluxe cabins, so:

60x + 80y ≤ 360

For the standard cabin, there are in A 160 and in B 120. The need is for 680, so:

160x + 120y ≤ 680

To calculate how many of each type you need:

60x + 80y ≤ 360

160x + 120y ≤ 680

Isolating x from the first equation:

x = [tex]\frac{360 - 80y}{60}[/tex]

Substituing x into the second equation:

160([tex]\frac{360 - 80y}{60}[/tex]) + 120y = 680

-3200y+1800y = 10200 - 14400

1400y = 4200

y = 3

With y, find x:

x = [tex]\frac{360 - 80y}{60}[/tex]

x = [tex]\frac{360 - 80.3}{60}[/tex]

x = 2

To determine the cost:

cost = 42,000x + 51,000y

cost = 42000.2 + 51000.3

cost = 161400

To keep it in a minimun cost, it is needed 2 vessels of Type-A and 3 vessels of Type-B, to a cost of $161400

Answer:

The 90% confidence interval for the population proportion of all train travelers who do not buy a ticket is (0.08, 0.16).

Step-by-step explanation:

The (1 - α)% confidence interval for the population proportion is:

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

The information provided is:

n = 200

X = 24

Confidence level = 90%

Compute the value of sample proportion as follows:

[tex]\hat p=\frac{X}{n}=\frac{24}{200}=0.12[/tex]

Compute the critical value of z for 90% confidence level as follows:

[tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]

Compute the 90% confidence interval for the population proportion of all train travelers who do not buy a ticket as follows:

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

     [tex]=0.12\pm 1.645\times\sqrt{\frac{0.12(1-0.12)}{200}}\\\\=0.12\pm0.038\\=(0.082, 0.158)\\\approx (0.08, 0.16)[/tex]

The 90% confidence interval for the population proportion of all train travelers who do not buy a ticket is (0.08, 0.16).

The 90% confidence interval (0.08, 0.16) for the population proportion of all train travelers who do not buy a ticket implies that there is a 0.90 probability that the true proportion lies in this interval.

Or if 100 such intervals are computed then 90 of those intervals will consist of the true proportion.

Rectangle square rhombus

Step-by-step explanation:

Answer:

18.66

Step-by-step explanation:

2.41 + 15.8 + 0.45

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:16

Step-by-step explanation:

prime factors of 16=2x2x2x2

Prime factors of 48=2x2x2x2x3

Their greatest common factor is:2x2x2x2=16

The greatest common factor of 16 and 48 is determined by listing the factors of each number and identifying the largest factor they share. In this case, the GCF of 16 and 48 is 16.

The greatest common factor (GCF) is the highest number that divides exactly into two or more numbers. To find the GCF of 16 and 48, you can list the factors of each number and find the highest factor they share.

The factors of 16 are 1, 2, 4, 8, 16. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest number that appears in both lists is 16. Therefore, the GCF of 16 and 48  is 16.

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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 production level that will maximize the revenue is 1800 (in thousands of phones produced), that is, production of 1,800,000 phones will maximize the revenue.

Step-by-step explanation:

The price per unit of phone is given as

p = 45 - 0.0125x

where x is in thousands of phones produced

Revenue = (price per unit) × (number of units)

Revenue = (45 - 0.0125x) × x

= (45x - 0.0125x²)

To find the maximum revenue, we need to obtain the maximum value of the revenue function.

R(x) = (45x - 0.0125x²)

At maximum point, (dR/dx) = 0 and (d²R/dx²) < 0

R(x) = (45x - 0.0125x²)

(dR/dx) = 45 - 0.025x

at maximum point, (dR/dx) = 0

(dR/dx) = 45 - 0.025x = 0

0.025x = 45

x = (45/0.025) = 1800

Hence, the production level that will maximize the revenue is 1800 (in thousands of phones produced)

That maximum revenue is thus

R(x) = (45x - 0.0125x²)

R(1800) = (45×1800) - (0.0125×1800²)

= 40,500

Hope this Helps!!!

To find the production level that will maximize revenue, we need to find the critical point of the revenue equation and determine if it is a maximum or minimum. Then we can find the corresponding production level.

To find the production level that will maximize revenue, we need to find the value of x that maximizes the revenue equation R(X)=X*p. The revenue equation can be written as R(X) = X*(45 - 0.0125x). To maximize revenue, we can find the x-value where the derivative of the revenue equation is equal to zero. After finding this critical point, we can check if it is a maximum or minimum by analyzing the second derivative. Finally, we can substitute this x-value back into the original equation to find the corresponding production level.

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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:

9

Step-by-step explanation:

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

Answer:

116

Step-by-step explanation:

8.2 / 2 = 4.1

a = [tex]\sqrt{7^{2}-4.1^{2} } = 5.6736[/tex]

0.5 x 8.2 x 5.6736 = 23.2618

23.2618 x 5 = 116.309 = 116

Answer:

2 1/4 hours

Step-by-step explanation:

Each night, he read for 3/4 hours = 3*60/4 = 45 minutes.

He read for 3 days.

So in total, he read for:

3*45 = 135 minutes.

135 minutes is 2 hours and 15 minutes. 15 minutes is 1/4 of an hour.

So the correct answer is:

2 1/4 hours

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:

3 x 12 = 36

Step-by-step explanation:

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

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