Rewraite 3/7 whit a denominator of 28

The Diagram shows the net of a square pyramid and its dimensions

Serjik [45]

<u>Answer:</u>

<u>Explanation:</u>

SA = the area of one side of the pyramid times 4 + the area of the base of the pyramid

Area of a triangle = (height × base)/2

Area of a sqaure = lenght²

given:

h = 4 ft | b = 6 ft | l = 6 ft

SA = 4(h×b×1/2) + l²

SA = 4(4×6×1/2) + 6²

SA = 4×12 + 36

SA = 48 + 36

SA = 84 ft²

3 0

3 years ago

23. A certain type of gasoline is supposed to have a mean octane rating of at least 90. Suppose measurements are taken on of 5 r

Nostrana [21]

Answer:

a) $p_v =P(Z$

b) Since $p_v$ we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.

Because Type I error " is the rejection of a true null hypothesis".

c) $P(\bar X >90)=1-P(Z$

$1-P(Z$

d) For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054

And we can use this formula:

$2.054=\frac{90-89}{\frac{0.8}{\sqrt{n}}}$

And if we solve for n we got:

$n = (\frac{2.054 *0.8}{1})^2=2.7 \approx 3$

Step-by-step explanation:

Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

$\bar X=88.96$ represent the sample mean

$s=1.011$ represent the sample standard deviation

n=5 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 90, the system of hypothesis would be:

Null hypothesis: $\mu \geq 90$

Alternative hypothesis: $\mu < 90$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{88.96-90}{\frac{0.8}{\sqrt{5}}}=-2.907$

Part a

P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=5-1 = 4$

Then since is a left tailed test the p value would be:

$p_v =P(Z$

Part b

Since $p_v$ we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.

Because Type I error " is the rejection of a true null hypothesis".

Part c

We want this probability:

$P(\bar X$

The best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we apply this formula to our probability we got this:

$P(\bar X >90)=1-P(Z$

$1-P(Z$

Part d

For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054

And we can use this formula:

$2.054=\frac{90-89}{\frac{0.8}{\sqrt{n}}}$

And if we solve for n we got:

$n = (\frac{2.054 *0.8}{1})^2=2.7 \approx 3$

7 0

3 years ago

Find S8 for the geometric series 3 + -6 + 12 + -24 +…

kirill115 [55]

I guess you are asking to find the sum of the first 8 terms. If so, then:
Sum = a₁(1-rⁿ)/(1-r), where a₁ is the 1st term, r=common ratio and n=number of terms:
the 1st term a₁ =3
common ratio r = - 2 (since -6/3 = - 2, and 12/-6 = - 2, etc.)

Sum = 3[(1- (-2)⁸]/(1-2) = 3(1- 256)/(1/2)
Sum = -1530

6 0

3 years ago

PLZZZZZZZ NEED HELP!!!!!!!

vivado [14]

The correct answer would be C

4 0

3 years ago

HELP ASAP I WILL GIVE BRAINLIEST!!

Alexxx [7]

Consider the function F(x)= x³ +½x² −2x +3. Use calc and algebra to find any and all stationary points on the graph of the function.Precalc need help ASAP

Solution:

the above function has more than one root or more than one solution. The derivative of the function represents the slope of the tangent line to the curve

F(x)= x³ +½x² −2x +3, F'(x) = 3(x3-1)+(1/2)(2)(x2-1)-2(x1-1)+0

F'(x)=3x2+x-2 is the slope of the tangent line

setting the slope =0 and solving the quadratic equations, you find all the

critical points of interest

3x2+x-2=0, solve by factoring (3x-2)(x+1)=0, then 3x-2=0, x= 2/3

and x+1=0, x=-1 substituting these values of x in the original equation

you get the corresponding values of F(x) such that;

F(x)= x³ +½x² −2x +3, F(x)=(2/3)3+1/2(2/3)2-2(2/3)+3

= 8/27+4/18-4/3+3 = 8/27+2/9-4/3+3/1 = 59/27 and the first point is

(2/3, 59/27)

F(x)= x³ +½x² −2x +3, F(x)=(-1)3+1/2(-1)2-2(-1)+3

= -1+1/2+2+3 = 9/2 and the 2nd point is ( -1, 9/2)

these two points represents points where the slope of the tangent line to the curve is 0 and could be either maximum or minimum points

You can also find the y intercepts where x = 0 F(x)= x³ +½x² −2x +3, setting x = 0, y= F(x)=3 and the point ( 0,3) is a y intercept setting y = 0, then x intercepts can be found upon solving the equation x³ +½x² −2x +3 =0

3 0

2 years ago