Sequence: 10, 21, 32, 43, 54, ... Find the 75th term.

Answer:

2.5 or 5/2

Step-by-step explanation:

The formula for the area of a triangle is \dfrac{bh}{2}, where b represents the length of the base and h represents the length of the height. With this in mind, you can set up the following equation:

[tex]\dfrac{15}{8}=\dfrac{1.5b}{2}[/tex]

[tex]\dfrac{15}{4}=1.5b[/tex]

b=2.5 or [tex]\frac{5}{2}[/tex]

Hope this helps!

Answer:

10

Step-by-step explanation:

3+2=5+26=31+9=40/4=10

Step-by-step explanation:

When finding mean, you have to add up all of the number and divide that answer by the number of numbers used.

3 + 2 + 26 + 9 = 40

Now, we will divide 40 by 4 because there are 4 numbers.

40 / 4 = 10

So, the mean of the set is 10.

g(x) = ⅞x - ½

g(7) = ⅞(7) - ½

= 49/8 - ½

= 49/8 - 4/8

= 45/8

= 5 ⅝

So, the value of g(7) for that function is 5 ⅝

Hope it helpful and useful :)

The value of the given function for g(7) is 45/8.

The given function is [tex]g(x)=\frac{7}{8}x-\frac{1}{2}[/tex].

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

We need to find the value of g(7)

Substitute x=7 in the given function and simplify, we get

[tex]g(7)=\frac{7}{8}(7)-\frac{1}{2}[/tex]

= 49/8 - 1/2

= 49/8 - 4/8

= 45/8

Hence, the value of the given function for g(7) is 45/8.

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Answer:

Jo : μ ≤ 64.

Jo : μ > 64.

Step-by-step explanation:

From the question, the Important information to solve this question is that; ''the speed limit on this portion of Interstate 95 is 64 mph''.

The question wants us to find the fact that the average speed is greater or more than the speed limit.

Therefore, In order to solve this question, the formula to use is the ''null and alternative" hypothesis. It states that;

Jo : μ ≤ 64.

Jo : μ > 64.

The above expression is the competing hypotheses in order to determine if the average speed is greater than the speed limit.

Answer:

The 20th of May

Step-by-step explanation:

I made a chart like a calendar and started on the 5th of may and counted every 5 days for the swimming lessons and every 3 days. Then I saw when she had both swimming and driving lessons and the first time after the 5th is the 20th.

Answer:

Bridget will have both swimming and diving lessons on the 15th.

Answer:

     3x^2 + 18x + 27 = 0

<=> 3(x^2 + 6x + 9) = 0

<=> 3(x + 3)^2 = 0

<=> x = -3

Hope this helps!

:)

Answer:

 0 days 3 hours 40 minutes 0 seconds

- 0 days 1 hours 55 minutes 0 seconds

= 0 days 1 hours 45 minutes 0 seconds

= 0.0729167 days

= 1.75 hours

= 105 minutes

= 6,300 seconds

Step-by-step explanation:

Final answer:

To calculate the difference between given times, convert them into minutes and subtract. The result will be the time difference in minutes.

Explanation:

Compute: 3:40 - 1:55

To compute the difference between 3:40 and 1:55, you need to subtract the two times. First, convert both times into minutes: 3:40 = 3 x 60 + 40 = 180 + 40 = 220 minutes, and 1:55 = 1 x 60 + 55 = 60 + 55 = 115 minutes. Then, subtract 115 from 220 to get the result.

The difference between 3:40 and 1:55 is 105 minutes.

Answer:

1 year

Step-by-step explanation:

8 + 7x = 2 + 13x

Move the 2 to the other side by subtracting 2 from both sides.

6 + 7x = 13x

Move the 7x to the other side by subtracting both sides by 7x.

6 = 6x

Divide both sides by 6.

1 = x

Therefore, x equals 1 and it will take 1 year for both trees to reach the same height.

Answer:

[tex] t = \frac{42.56-35.375}{\sqrt{\frac{6.327^2}{9} +\frac{4.34^2}{8}}}=2.755[/tex]

The degrees of freedom are given by:

[tex] df=n_1 +n_2-2 =9+8-2= 15[/tex]

Since we have a two tailed test the p value can be calculated like this:

[tex] p_v=2* P(t_{15} >2.755) = 0.0147[/tex]

And since the p value is lower than the significance lvel given of 0.05 we have enough evidence to conclude that we have significant differences between the two groups on this case.

Step-by-step explanation:

We have the following data given:

Business  Travelers

42 31 37 45 49 52 43 39 45

Leisure  Travelers

32 29 35 40 38 34 42 33

For this case we need to begin finding the sample mean and deviations for each group with the following formulas:

[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex] s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And we got:

[tex] \bar X_1 = 42.56[/tex] represent the sample mean for the Business travelers

[tex]s_1 = 6.327[/tex] represent the sample deviation for the Business travelers

[tex]n_1= 9[/tex] the sample size for the Business travelers

[tex] \bar X_2 = 35.375[/tex] represent the sample mean for the Leisure travelers

[tex]s_2 =4.34[/tex] represent the sample deviation for the Leisure travelers

[tex]n_2= 8[/tex] the sample size for the Leisure travelers

The system of hypothesis for this case are:

Null hypothesis: [tex] \mu_1 =\mu_2[/tex]

Alternative hypothesis: [tex] \mu_1 \neq \mu_2[/tex]

The statistic for this case is given by:

[tex] t =\frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}[/tex]

And replacing we got:

[tex] t = \frac{42.56-35.375}{\sqrt{\frac{6.327^2}{9} +\frac{4.34^2}{8}}}=2.755[/tex]

The degrees of freedom are given by:

[tex] df=n_1 +n_2-2 =9+8-2= 15[/tex]

Since we have a two tailed test the p value can be calculated like this:

[tex] p_v= 2*P(t_{15} >2.755) = 0.0147[/tex]

And since the p value is lower than the significance lvel given of 0.05 we have enough evidence to conclude that we have significant differences between the two groups on this case.

Answer:

The usual number of yellow eggs in samples of 45 eggs is 14.4.

Step-by-step explanation:

For each egg, there are only two possible outcomes. Either they are yellow, or they are not. The probability of an egg being yellow is independent of other eggs, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

32% of the eggs are yellow

This means that [tex]p = 0.32[/tex]

45 eggs

This means that [tex]n = 45[/tex]

What is the usual number of yellow eggs in samples of 45 eggs

[tex]E(X) = np = 45*0.32 = 14.4[/tex]

The usual number of yellow eggs in samples of 45 eggs is 14.4.

In a random sample of 45 dragon eggs on planet Pern, we would typically expect around 14 to 15 eggs to be yellow, based on the given probability of an egg being yellow (which is 32%).

The subject of the question relates to probabilities in statistics. Here, we are given that the chance a dragon's egg on planet Pern is yellow is 32% or 0.32 in decimal form. We are then asked to predict the number of yellow eggs in a group of 45 eggs.

To solve this, we simply multiply the total number of eggs by the notation of the probability:

45 eggs * 0.32 = 14.4

However, you can't have 0.4 of an egg, so we have to round this number to 14 or 15 eggs. Therefore, in a random sample of 45 dragon eggs, we would typically expect around 14 to 15 of them to be yellow assuming that the probability remains constant.

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Answer:

Mia needs to subtract another 6 square feet

Step-by-step explanation:

Guessed it and got it right

Answer:

needs to subtract another 6 ft

Step-by-step explanation:

Answer:

The conditions for use of the normal model to represent the distribution of sample proportion are not met. He should increase the sample size until the conditions are met.

If the test is done anyway, the null hypothesis failed to be rejected.

The conclusion is taht there is not enough evidence to support the claim that the percentage is lower in this district.

Step-by-step explanation:

The conditions for use of the normal model to represent the distribution of sample proportion are not met, as the affirmative responses are less than 10.

[tex]np=80*0.1=8<10[/tex]

If the test of hypothesis is done as if the conditiones were met, we know that the claim is that  the percentage is lower in this district.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.173\\\\H_a:\pi<0.173[/tex]

The significance level is 0.05.

The sample has a size n=80.

The sample proportion is p=0.1.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.173*0.827}{80}}\\\\\\ \sigma_p=\sqrt{0.001788}=0.042[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.1-0.173+0.5/80}{0.042}=\dfrac{-0.067}{0.042}=-1.578[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]P-value=P(z<-1.578)=0.057[/tex]

As the P-value (0.057) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that  the percentage is lower in this district.

Answer: D

H0: μ=522

H1: μ>522

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

So, for this case;

The null hypothesis is that the mean score equals to 522

H0: μ=522

The alternative hypothesis is that the mean score is greater than 522.

H1: μ>522

The correct answer is D. [tex]Upper H_0: = 522, Upper H_1 > 522[/tex].

In this scenario, the math teacher is claiming that her review course increases the scores of students on the math portion of a college entrance exam. Therefore, the null hypothesis [tex](H_0)[/tex]  should represent the claim that there is no increase in the mean score, which would be that the mean score is equal to the population mean of 522. The alternative hypothesis [tex](H_1)[/tex]   should represent the teacher's claim that the mean score has increased, which would be that the mean score is greater than 522.The null hypothesis is a statement of no effect or no difference and serves as the baseline for testing. The alternative hypothesis is what we aim to support; it is a statement that there is an effect or a difference. In this case, we are testing whether the mean score of students after taking the review course is greater than the population mean.Therefore, the correct hypotheses are:- Null Hypothesis [tex](H_0): = 522[/tex] , indicating no increase in the mean score.- Alternative Hypothesis [tex](H_1): > 522[/tex] , indicating an increase in the mean score.This is a one-tailed test because we are only interested in whether the mean score has increased, not whether it has changed at all (which would require a two-tailed test).

Answer:

The test statistic value is 1.474.

Step-by-step explanation:

In this case we need to determine whether the plant is making a higher than expected number of irregular t-shirts.

If more than 8% of the t-shirts manufactured at a plant are classified as irregular, the manager has to do an investigation to try to find the source of the increased mistakes in the manufacturing process..

The hypothesis for this test can be defined as follows:

H₀: The proportion of irregular t-shirts is 8%, i.e. p = 0.08.

Hₐ: The proportion of irregular t-shirts is more than 8%, i.e. p > 0.08.

The information provided is:

n = 100

X = number of irregular t-shirts = 12

Compute the sample proportion as follows:

[tex]\hat p=\frac{X}{n}=\frac{12}{100}=0.12[/tex]

Compute the test statistic as follows:

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

  [tex]=\frac{0.12-0.08}{\sqrt{\frac{0.08(1-0.08)}{100}}}\\\\=1.47441\\\\\approx 1.474[/tex]

Thus, the test statistic value is 1.474.

Answer:

1

Step-by-step explanation:

3(x+2)-10=4x-6+x

3x+6-10=5x-6

2x=2

x=1

This is the only solution to this equation, meaning that there is only one solution to the equation. Hope this helps!

The equation 3(x + 2) - 10 = 4x - 6 + x has one solution, which is x = 1. After simplifying the equation and solving for x, we confirm that substituting x = 1 back into the equation results in an identity, indicating that this is the correct solution.

To determine how many solutions the equation 3(x + 2) \\- 10 = 4x \\- 6 + x has, we must first simplify the equation and solve for x.

Let's simplify both sides of the equation:

Distribute the 3 on the left side: 3x + 6 \\- 10 = 4x \\- 6 + x.

Combine like terms on the right side: 3x \\- 4 = 5x \\- 6.

Get all the x terms on one side and constants on the other: 3x \\- 5x = \\-6 + 4.

Simplify the equation: \ -2x = \\-2.

Divide both sides by \\-2 to solve for x: x = 1.

So, the solution to the equation is x = 1. To verify that this is the solution, we can substitute x = 1 back into the original equation and check that it holds true, which would confirm that the equation is an identity. In this case, the substitution leads to an identity, confirming that x = 1 is the correct and only solution to the equation.

Answer:

They have a 85% chance of winning their next game.

Step-by-step explanation:

100÷20 = 5

17×5=85

So, they have a 85% chance of winning their next game.

Hope This helped!!!!! :)

Answer:

D. the sample means is equal to the expected distribution based on theory/knowledge of the population.

Step-by-step explanation:

The Chi square goodness-of-fit test is used in statistical analysis to determine if the observed value in a collection of data, is significantly different from the expected value. Theoretical distribution which could be classified as normal, binomial, or poisson, are compared against the empirical distribution.To run a chi square goodness-of-fit test, we first formulate the null and alternate hypothesis. The degrees of freedom are then observed from the data given and the hypothesis is tested.

The null hypothesis assumes that the observed frequencies are equal to the expected frequencies. If there is a considerable difference, then the null hypothesis is rejected.

Answer:

$6.74

Step-by-step explanation:

Subtract 15.49 and 8.75

Answer: 6.74.

Step-by-step explanation: I took the quiz before!

Hope this helps! (✪ ω ✪)

Answer: is their any picture? or an example?

Answer:

0.8 or 80%

Step-by-step explanation:

To easily find percents, divide the numerator with the denominator. Or, first you can simplify the fraction first.

20/25 can be divided by 5. Which is 4/5.

4/5=0.8

So, the answer is 80%

Answer:

80%

Step-by-step explanation:

[tex]\frac{20}{25} = \frac{4}{5}[/tex]

To find the percentage, multiply by 100:

[tex]\frac{4}{5} * 100 = 80[/tex]

Answer:

2 is an initial value

tell me if its right because i garuntee it is

The solid figure that is shown by the net would be a Rectangular prism.

The number of vertices would be 8 vertices.

A rectangular prism is a 3D shape with six faces, eight vertices, and twelve edges. It is a type of polyhedron, which is a solid figure with flat faces and straight edges.

The net given is a rectangular prism because the dashed lines show that the sides would fold up along with the triangles to form a rectangular prism.  

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Answer:

$159075.84

Step-by-step explanation:

100-7.6=92.4

1721.60*92.4=$159075.84

Answer:

Population, all chicken meat; parameter, minimum temperature of 170 degrees Fahrenheit; sample, four random thermometer readings; statistic, minimum sample reading of 180 degrees Fahrenheit

Step-by-step explanation:

Answer:

$18206.5

Step-by-step explanation:

Considering,  r = interest rate

    n = number of intervals

    t = duration of the payment

    A = monthly installment  

   PV = Present Value

   FV = Final Value

Using the formula

FV=PV (1+ r/n[tex])^{nt-1[/tex] + a((1+ r/n[tex])^{nt[/tex]-1/[tex]\frac{r}{n}[/tex])

FV=6000[tex](1+ \frac{0.03}{12} )^{(12)(4)-1} +225\frac{(1+0.03/12)^{(12)(4)}-1 )}{0.03/12}[/tex]

FV= 6747 + 11459.5

FV=18206.5

Her balance in 4 years is $18206.5

Answer:

D. This scenario should be analysed using paired data because the groups are dependent and have a natural pairing.

Step-by-step explanation:

Paired Data can be defined as data set, when sample units of one data set are related to sample units in other data set.

Research Study about spouses number of hours of sleep each night is paired data. As, each man in the male sample group is related to a corresponding woman (his wife) in the female sample group. So, they have a natural paring & they, their sleep schedules are dependent on each other.

Based on the information given, this scenario should be analyzed using paired data because the groups are dependent and have a natural pairing.

In conclusion, the correct option is D.

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Answer:

Probability of even = 0.5

Step-by-step explanation:

Probability of even = total number of even numbers/ total number

Total number of Eve number = [ 2,4,6] = 3

Total numbers = [ 1,2,3,4,5,6] = 6

Probability of even = 3/6

Probability of even = 1/2

Probability of even = 0.5