Consider the sequence 6, 11, 16, 21 . . . . What is the 50th term in this sequence?

In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsibl

schepotkina [342]

Answer:

$t=\frac{8.19-9.02}{\frac{0.8}{\sqrt{17}}}=-4.28$

The degrees of freedom are given by

$df=n-1=17-1=16$

The p value would be given by this probability:

$p_v =P(t_{(16)}$

Since the p value is lower than the significance level provided of 0.01 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 9.02 cm^3

Step-by-step explanation:

Information given

$\bar X=8.19 cm^3$ represent the sample mean

$s=0.8 cm^3$ represent the sample deviation

$n=17$ sample size

$\mu_o =9.02$ represent the value to verify

$\alpha=0.01$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value

System of hypothesis to check

We want to check if the true mean is less than the normal value of 9.02 cm^3, the system of hypothesis would be:

Null hypothesis: $\mu \geq 9.02$

Alternative hypothesis: $\mu < 9.02$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{8.19-9.02}{\frac{0.8}{\sqrt{17}}}=-4.28$

The degrees of freedom are given by

$df=n-1=17-1=16$

The p value would be given by this probability:

$p_v =P(t_{(16)}$

Since the p value is lower than the significance level provided of 0.01 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 9.02 cm^3

6 0

3 years ago

Given the function f(x) = x2 and k = 3, which of the following represents the graph becoming more narrow?

Bess [88]

Functions A and C and D are translations - this means that they are exactly the same shape as f(x), but are displaced on the axes. A translation in the y-direction by k units is represented by f(x) + k, and a translation in the x-direction by k units is represented by f(x - k). This can be summarised in column vector notation:

A translation of the graph y = f(x), by the vector $\left[\begin{array}{ccc}a\\b\end{array}\right]$ results in the graph defined by y - b = f(x - a). This is done by replacing x with (x - a) and y with (y - b). Finally it is rearranged to make y the subject, as is often the convention: y = f(x - a) + b.

Since the graph needs to change shape, this requires a 'stretch'. A stretch is performed by multiplying x or y by a constant, which here is k.

To stretch in the x-direction by a factor n, replace x with (1/n)x. Similarly to stretch in the y-direction by a factor n, replace y with (1/n)y.

For example to stretch y = f(x) by factor n in the x-direction, it would become y = f((1/n)x).

A simple quadratic graph like y = x^2 behaves slightly differently to most other graphs, in that it can narrowed by a stretch in the x or y direction. This means that a more convenient option is to perform a stretch in the y direction, since the multiplier lies outside the function notation. The stretching factor is 3, so we replace y with (1/3)y:

(1/3)y = f(x)
y = 3f(x)

Since k = 3, this becomes

y = kf(x)

... and hence the correct answer is B

6 0

3 years ago

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Find each of the numbers below. Simplify your answers as much as possible.

puteri [66]

Answer:

a. 4

b. -8

c. -2

Step-by-step explanation:

Take any number x;

Its opposite is -x

The opposite of its opposite is x

Using the above statements, we can solve the following questions

Solving (a): -4

In this case:

$x = -4$

The opposite; -x is

$-x = -(-4)$

$-x = 4$

Solving (b): 8

In this case:

$x = 8$

The opposite; -x is

$-x = -8$

Solving (c): -2

In this case:

$x = -2$

The opposite; -x is

$-x = -(-2)$

$-x = 2$

The opposite; -(-x) is

$-(-x) = -2$

$x = -2$

5 0

3 years ago

If your financial goal is to save at least $40,000 in 10 years, what would be the least

adoni [48]

The least amount of money you would need to invest per month is; $335

The anticipated rate of return on your investments is; 7%

Amount to have been saved at the end of 10 years ≥ $40,000

Number of years of savings = 10 years.

We want to find out the least amount to be invested per month.

There are 12 months in a year. Number of months in 10 years = 10 × 12 = 120 months.

Thus, amount to be saved monthly = 40000/12 = $333.33

Since the minimum amount he wants to save after 10 years is $40000, then we need to approximate the monthly savings in order.

Thus;

Monthly savings ≈ $335

Now, for the anticipated rate of return on the investment, we know from S & P's that the benchmark on good rate of return for investment is a minimum of 7%.

From online calculator, the worth of the investment after 10 years based on 7% rate of return yearly would be $57626.

Read more at; brainly.com/question/9187598

4 0

2 years ago

You Try: True or False: (-8) + 9 = 9+ (-8) Show your work to prove your answer.

poizon [28]

Answer:

true

Step-by-step explanation:

(-8) + 9=1

9+(-8)=9-8=1

4 0

3 years ago

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