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3 years ago

What is the ninth term of the arithmetic sequence defined by the rule A(n)= -14+(n-1)(2)

1 answer:

3 0

If you start counting from 0, you ninth term will be 8. Replace n=8 and calculate:
A(8) = -14 + (8-1)(2) = -14 + (7)(2) = -14 + 14 = 0

If you start counting from 1, your ninth term will be 9. Replace n=9 and calculate:
A(9) = -14 + (9-1)(2) = -14 + (8)(2) = -14 + 16 = 2

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13/2 divided by 3/4

Juliette [100K]

Answer: 26/3

Step-by-step explanation: When dividing by a fraction, we can change

the division sign to multiplication and flip the second fraction.

So 13/2 ÷ 3/4 means the same thing as 13/2 · 4/3.

So when dividing by a fraction, we can just multiply

by the reciprocal of that fraction or that fraction flipped.

Next we cross-cancel.

4 and 2 reduce to 2 and 1.

Multiplying across the numerator and denominators we have 26/3.

5 0

3 years ago

Which quadratic function has a wider graph than y=2x^2?

Trava [24]

Answer:

y = 1/2 x²

Step-by-step explanation:

The coefficient of the first term in a quadratic, in our case here, x², will tell us how the graph stretches. This is akin to the slope within the linear graph. Similar to the slope, the smaller the coefficient value, or value of slope m, the shallower the angle.

When discussing quadratics, the larger the coefficient of our x² term, the steeper, and skinnier the graph. If we want to look for a graph that is wider than y = 2x², then we need to find a graph with a coefficient that is less than 2.

Our only option then is

y = 1/2 x²

8 0

3 years ago

A study was conducted and two types of engines, A and B, were compared. Fifty experiments were performed using engine A and 75 u

USPshnik [31]

Answer:

a) -6 mpg.

b) 2.77 mpg

c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Gas mileage A: Mean 36, standard deviation 6, sample of 50:

$\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485$

Gas mileage B: Mean 42, standard deviation 8, sample of 50:

$\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314$

Distribution of the difference:

Mean:

$\mu = \mu_A - \mu_B = 36 - 42 = -6$

Standard error:

$s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142$

A. Find the point estimate.

This is the difference of means, that is, -6 mpg.

B. Find the margin of error

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = zs = 1.96*1.4142 = 2.77$

The margin of error is of 2.77 mpg

C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)

The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg

The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg

The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

8 0

3 years ago

This one number 4<br><br> What to do

Readme [11.4K]

Answer:

231/8 simplified is 28 7/8

Step-by-step explanation:

first you have to convert all mixed fractions into improper fractions so 8 1/4 will become 33/4 and 3 1/2 will become 7/2 and then just multiply and you get 231/8 which simplified is 28 7/8

5 0

2 years ago

Help how do and is help?

Dimas [21]

Answer:

x = 12

Step-by-step explanation:

The total of all the angle is 180 degrees so just divide 180 by the total number of x's which is 5+4+3+2+1 = 15

180/15 = 12

If you wanted to know how much each angle is just plug in 12 for x.

So first angle is just X so it is 12 degrees.

Second angle is 2X so 2x12 = 24 degrees.

and so on for all the angles.

6 0

3 years ago