Help plzz i will give u 15 points if u answer

Sunspots have been observed for many centuries. Records of sunspots from ancient Persian and Chinese astronomers go back thousan

Lunna [17]

Answer:

(a) Null Hypothesis, $H_0$ : $\mu$ $\leq$ 41

Alternate Hypothesis, $H_A$ : $\mu$ > 41

(b) The value of z test statistics is 1.08.

(c) We conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.

Step-by-step explanation:

We are given that in a random sample of 40 such periods from Spanish colonial times, the sample mean is x¯ = 47.0. Previous studies of sunspot activity during this period indicate that σ = 35.

It is thought that for thousands of years, the mean number of sunspots per 4-week period was about µ = 41.

Let $\mu$ = mean sunspot activity during the Spanish colonial period.

(a) Null Hypothesis, $H_0$ : $\mu$ $\leq$ 41 {means that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41}

Alternate Hypothesis, $H_A$ : $\mu$ > 41 {means that the mean sunspot activity during the Spanish colonial period was higher than 41}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean = 47

σ = population standard deviation = 35

n = sample of periods from Spanish colonial times = 40

So, the test statistics = $\frac{47-41}{\frac{35}{\sqrt{40} } }$

= 1.08

(b) The value of z test statistics is 1.08.

(c) Now, the P-value of the test statistics is given by;

P-value = P(Z > 1.08) = 1 - P(Z < 1.08)

= 1 - 0.8599 = 0.1401

Since, the P-value of the test statistics is higher than the level of significance as 0.1401 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.

8 0

3 years ago

The figure below is a right rectangular prism. which expression represents the volume of the prism?

Leviafan [203]

Answer: The expression (equation/formula) for the volume of a:

" right rectangular prism " ; is represented by:

____________________________________________________

→ " V = L * w * h " ;

____________________________________________________

in which: all the dimensions are in the same "units of measurement" (or converted to the same "units of measurement" ;

and in which:

" V " is the "volume" of the right rectangular prism; in the "cubic units" ; or written as: "units³ " ; or, [insert the particular units used}^ ³ " ;

→ that is, [units] raised to the "3rd [third] power" ; assuming these units are the same same "fundamental units of measurement" as the "other 2 (two) values in the expression".

If we are given no specific units of measurement whatsoever, then we use the generic term, "units" as the "units of measurement" ; and we express the "volume; "V" ; of a "right rectangular prism" as: " units ³ " ; or "cubic units" ;

in our answer— if we are asked to solve for the:

"volume; "V"; of a "right rectangular prism" ;

_________________________________________________

and in which:

"L" represents the "length" of a "right rectangular prism" ;

"w" represents the "width" of a "right rectangular prism" ;

"h" represents the "height" of a "right rectangular prism" .

_________________________________________________

To given an example:

Say we have a "right rectangular prism" ; with the given measurements:

width , "w" : w = 2 units;

length, "L" : L = 3 units ;

height, "h" : h = 8 units.

_________________________________________________

We are asked to "find the volume " ; of this "right recentangular prism" .

The formula for the volume; "V" ; of this "right rectangular prism" ;

is:

_________________________________________________

→ Volume = Length * width * height ;

that is:

→ V = L * w * h ;

Solve for the volume; "V" .

_________________________________________________

→ V = L * w * h ; Now plug in the values given:

→ V = (3 units) * (2 units) * (8 units) ;

= 3 * 2 * 8 * (units) * (units) * (units) ;

= 3 * 2 * 8 * units ³ ;

= 48 units ³ .

_________________________________________________

Hope this answer— and explanation—is helpful to you!

Wishing you the best in your academic pursuits

— and within the "Brainly" community!

_________________________________________________

4 0

3 years ago

Read 2 more answers

18 pts plz help.. i tysmm

Furkat [3]

Answer: B

Step-by-step explanation:

5 0

3 years ago

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What is 6+14r-12r+3?

Ugo [173]

6+14r−12r+3

=6+14r+−12r+3

Combine Like Terms:

=6+14r+−12r+3

=(14r+−12r)+(6+3)

Your answer would be:

2r+9

~Good Luck~

5 0

3 years ago

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WILL MARK BRAINLIEST!!! 40 POINTS!! ACTUAL ANSWERS, PLZZZ

steposvetlana [31]

Answer:

Part A:

$\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807$

Part B:

The closure property describes cases when mathematical operations are CLOSED. It means that if you apply certain mathematical operations in a polynomial it will still be a polynomial. Polynomials are closed for sum, subtraction, and multiplication.

It means:

$\text{Sum of polynomials } \Rightarrow \text{ It will always be a polynomial}$

$\text{Subtraction of polynomials } \Rightarrow \text{ It will always be a polynomial}$

$\text{Multiplication of polynomials } \Rightarrow \text{ It will always be a polynomial}$

But when it is about division:

$\text{Division of polynomials } \Rightarrow \text{ It will not always/sometimes be a polynomial}$

Example of subtraction of polynomials:

$(2x^2+2x+3) - (x^2+5x+2)$

$x^2-3x+1$

Step-by-step explanation:

First, it is very important to define what is a polynomial in standard form:

It is when the terms are ordered from the highest degree to the lowest degree.

Therefore I can give:

$x^5-5x^4+3x^3-3x^2+7x+20$

but,

$x^5+3x^3-3x^2+7x+20-5x^4$ is not in standard form.

For this question, I can simply give the answer: $x^5-5x^4+3x^3-3x^2+7x+20$ and it is correct.

But I will create a fifth-degree polynomial using this formula

$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$

Also, note that

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

For $a=x \text{ and } b=7$

$\left(x + 7\right)^{5}=\sum_{k=0}^{5} \binom{5}{k} \left(x\right)^{5-k} \left(7\right)^k$

$\text{Solving for } k \text{ values: } 0, 1, 2, 3, 4 \text{ and } 5$

Sorry but I will not type every step for each value of $k$

The first one is enough.

For $k=0$

$\binom{5}{0} \left(x\right)^{5-0} \left(7\right)^{0}=\frac{5!}{(5-0)! 0!}\left(x\right)^{5} \left(7\right)^{0}=\frac{5!}{5!} \cdot x^5= x^{5}$

Doing that for $k$ values:

$\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807$

8 0

3 years ago