Find the 60th term of the following sequence.

4, 8, 12,

Using the t-distribution, it is found that:

a)

The null hypothesis is [tex]H_0: \mu = 3.1[/tex]

The alternative hypothesis is [tex]H_1: \mu \neq 3.1[/tex]

b)

c) t = 1.853

d) Since |t| = 1.853 < 2.2, we do not reject the null hypothesis, that is, the sample data does not suggest that there is a difference between the national average and the sample mean of the senior citizens.

Item a:

At the null hypothesis, it is tested if the estimate of 3.1 cups per day is correct, that is:

[tex]H_0: \mu = 3.1[/tex]

At the alternative hypothesis, it is tested if the estimate is not correct, that is:

[tex]H_1: \mu \neq 3.1[/tex]

Item b:

This is a two-tailed test, as we are testing if the mean is different of a value, with 12 - 1 = 11 df and a significance level of 0.05,  hence, the critical value is [tex]t^{\ast} = 2.2[/tex].

Then, the decision rule is:

Item c:

We can find the standard deviation for the sample, hence, the t-distribution is used.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The values of the parameters, with the help of a calculator for the sample mean and standard deviation, are given by: [tex]\overline{x} = 3.425, \mu = 3.1, s = 0.6077, n = 12[/tex]

Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{3.425 - 3.1}{\frac{0.6077}{\sqrt{12}}}[/tex]

[tex]t = 1.853[/tex]

Item d:

Since |t| = 1.853 < 2.2, we do not reject the null hypothesis, that is, the sample data does not suggest that there is a difference between the national average and the sample mean of the senior citizens.

A similar problem is given at https://brainly.com/question/24826023

Answer:

b

Step-by-step explanation:

Answer:

8x-4<-36+4

8x<-32

----

8

x<-4

Answer:x<-4

Step-by-step explanation:

you would have to show your work and do it step by step and and dont stress about it

Answer: 5 inches per hour or 2.5 inches per half an hour

Step-by-step explanation:

Amount of Time Passed: 2 hours 30 minutes

Difference in Candle Height: 12.5 inches

12.5 / 2.5 = 5 inches

5 inches per hour or 2.5 inches per half an hour

If it is incorrect, please let me know.

Answer:

The answer to this is 10 visits.

Step-by-step explanation: For this algebra, take a guess at first, and then you should be able to find an answer from there. All you have to do mathematically, is calculate (using the two starting values), when the prices are the same. For this, the equation would look something like: 5x + 130 and 3x + 150. X represents the unknown number of visits. When x is = 10, the prices are the same, 180 = 180. Edit: Another way you can do this, is graph a line of the two equations, and see what point they intercept. The X value of the point usually is the number of times something occurs until the price is the same, whereas the y value of the point is usually the price.

Answer:

5-8

Step-by-step explanation:

6.5-1.5 = 5

6.5+1.5= 8

Answer:

Step-by-step explanation:

C is right.

5(a + b + c + d)

when you express it it's gonna be 5a + 5b + 5c + 5d

Answer:

The ratio of y to x is the slope

The equation of the graph is y = 1/2x

Step-by-step explanation:

In this scenario, we see that 1/2 of x always equals y, so the y-intercept is 0. This means that the slope is equal to 1/2, and that is the ratio of y to x.

Answer:

a constant is a data item whose value cannot change during the program execution just as its name implies that the value is constant a variable is a data item whose value can change during the program's execution . Thus as its name implies the the value can vary

Answer:

make 90°angle with the help of compase

Answer:

6.15

Step-by-step explanation:

perimeter of a rectangle= 2(Length + width)

perimeter=28.5

length=8.1

28.5=2(8.1+ Width)

28.5=16.2+ 2(Width)

28.5-16.2=2(Width)

12.3=2(Width)

12.3/2=Width

6.15=Width

Answer:

38

Step-by-step explanation:

if you're asking what (-12)-(-50) is the answer is 38 simple method to remember is KCF or KFC same thing just worded differently but it means keep change flip! hope that helped have a great day!!

Answer:

r = -28/9

Step-by-step explanation:

use slope formula of (y₂-y₁) / (x₂-x₁)

5/9 = [r - (-2)] / [-7 - (-5)]

5/9 = (r+2) /-2

cross-multiply to get:

-2(5) = 9(r+2)

-10 = 9r + 18

-28 = 9r

r = -28/9

Answer:

arc PQ = 124°

Step-by-step explanation:

The inscribed angle PRQ is half the measure of its intercepted arc PQ, so

arc PQ = 2 × 62° = 124°

Answer:

  124°

Step-by-step explanation:

Inscribed angle PRQ is half the measure of intercepted arc PQ.

  1/2(PQ) = 62°

  PQ = 124° . . . . . . multiply by 2

Answer:

-5/12/ D

Step-by-step explanation:

-9/12 -(-1/3)

turn 1/3 into a fraction with a similar denominator

-9/12-(-4/12)

-(- = addition (+)

-9+4= -5

-5/12

Given two points, the equation of the line may be determined by,

y - y1 = ((y2 - y1) / (x2 - x1))(x - x1)

Substituting the given values,

y - 7 = ((9 - 7) / (6 - 3))(x - 3)

Simplification will yield to an answer of,

y = 2x/3 +5

Therefore, the answer is the second choice.

Answer:

no

Step-by-step explanation:

https://brainly.com/question/18232055

Answer:

Yes!

Step-by-step explanation:

Here, ratios can be rewritten by fractions.

12:6 is [tex]\frac{12}{6}[/tex] which equals to 2,

2:1 is also [tex]\frac{2}{1}[/tex] which is 2.

To get 12 from 2, you multiply by 6.

Multiply the same thing to the denominator(1), and you get 6. So:

12:6 = 2:1

I hope this helps you. Give a like

The x-intercept are x = 0, x = -1.9, x = 0.35, and x = 1.5.

The local minimum is 1.

The function is increasing at the interval (-1.5, 0.5) and (1, ∞).

The function is decreasing at the interval (∞, -1) and (0, 1.5).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

h(x) = [tex]x^4[/tex] - 3x² + x

The x-intercept is when h(x) = 0.

0 = [tex]x^4[/tex] - 3x² + x

From the graph, we see that,

The x-intercept are at x = 0, x = -1.9, x = 0.35, and x = 1.5

Now,

h(x) = [tex]x^4[/tex] - 3x² + x

h'(x) = 4x³ - 6x

h''(x) = 12x² - 6 (positive)

So,

h(x) has a minimum value.  

h'(x) = 0

4x³ - 6x = 0

4x³ = 6x

4x² = 6

x² = 6/4

x² = 3/2

x² = 1.5

x = ±√1.5

x = ±1.22

The minimum values are:

h(1.22) =  [tex]x^4[/tex] - 3x² + x = -1

h(-1.22) =  [tex]x^4[/tex] - 3x² + x = 1

The local minimum is 1.

From the graph, we see that,

The function is increasing at the interval (-1.5, 0.5) and (1, ∞).

The function is decreasing at the interval (∞, -1) and (0, 1.5).

Thus,

The x-intercept are x = 0, x = -1.9, x = 0.35, and x = 1.5.

The local minimum is 1.

Increasing intervals are (-1.5, 0.5) and (1, ∞).

Decreasing intervals are (∞, -1) and (0, 1.5).

Learn more about functions here:

https://brainly.com/question/28533782

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Answer:

85%

Step-by-step explanation:

Add all the numbers together which gives 849. Divide 849 by 10 because there are ten numbers. This gives 84.9. Round it up to 85%

Answer:

Adult tickets = $73.5

Child tickets = $20.5

Step-by-step explanation:

[tex]{ \rm{3x + 5y = 50 - - - \{eqn \: 1 \}}} \\ { \rm{x + 5y = 31 - - - \{eqn \: 2 \}}} \\ [/tex]

• Subtract eqn 2 from eqn 1:

[tex]{ \rm{2x = 21}} \\ { \rm{x = 10.5}}[/tex]

[tex]{ \rm{10.5 + 5y = 31}} \\ { \rm{5y = 20.5}} \\ { \rm{y = 4.1}}[/tex]

Step-by-step explanation:

the description is very difficult to understand with special characters and potential typing errors.

I suspect the definition is

function(x) = 32 - x²

function(-5)function(-5) is then very easily calculated.

we need to calculate function(-5) and then square the result, as function(-5)function(-5) is just a simple multiplication of the function results.

function(-5) = 32 - (-5)² = 32 - 25 = 7

so,

function(-5)function(-5) = 7 × 7 = 49

[tex]x^2 + \dfrac 1{x^2} = \dfrac{x^4 +1}{x^2}[/tex]

Answer:

7.07

Step-by-step explanation:

Angle M is 63 degrees because all 3 angles must add to 180.  

Now use the law of sines:  

sin(90)/x = sin(63)/6.3  

Cross multiply: 6.3 sin (90) = x sin (63)  

Divide by sides by sin (63): (6.3 sin (90))/sin (63) = x  

Use a calculator: 7.07

Answer:

A

Step-by-step explanation:

The slope of the line that is perpendicular to line AB is: 1/2.

Recall:

Given:

A(-1,10)

B(5,-2)

Slope of AB:

[tex]m = \frac{-2 - 10}{5 -(-1)} = \frac{-12}{6} \\\\\mathbf{m = -2}[/tex]

The slope of the line that is perpendicular to line AB will be the negative reciprocal of the slope of AB.

Therefore, the slope of the line perpendicular to AB is: 1/2.

Learn more about slope of a line perpendicular to a line on:

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Answer:

yawa ka ah diyan module tae yan hahaha

don't know sorry mate