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4 years ago

Simplify (3 - √7)(5 + √7)

2 answers:

6 0

(3-√7)(5+√7)
FOIL
F-Multiply the First to numbers 3×5=15
O-Multiply the Outter two numbers 3×√7=3√7
I-Multiply the Inner two numbers -√7×5=-5√7
L-Multiply the last two numbers -√7×√7=-7
Put it together and you get
15+3√7-5√7-7
Combine the like terms 15-7=8 and 3√7 - 5√7=-2√7
And you get 8-2√7

MaRussiya [10]4 years ago

3 0

You can use F.O.I.L. for this, which if you don't know stands for first outer inner last, so multiply the first in each parentheses, then the outer, then the inner, then the last. yours would be 3*5+3*√7+(-√7)*5+(-√7)*√7 => 15+3√7-5√7-7 => 8-2√7
Final answer:
8-2√7
Hope I could help :)

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Consider the sequence below

GalinKa [24]

Answer: option D is the correct answer

Step-by-step explanation:

In the given sequence, the consecutive terms differ by a common difference.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = - 351

d = - 343 - - 351 = - 343 + 351

d = 8

Therefore, the explicit function which defines the sequence is

f(n) = - 351 + 8(n - 1)

f(n) = 8n - 8 - 351

f(n) = 8n - 359

5 0

3 years ago

For the hypothesis test H0: μ = 10 against H1: μ >10 and variance known, calculate the Pvalue for each of the following test

Basile [38]

Answer:

a) $p_v =P(Z>2.05)=1-P(z$

b) $p_v =P(Z>-1.84)=1-P(z$

c) $p_v =P(Z>0.4)=1-P(z$

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis: $\mu=10$

Alternative hypothesis: $\mu >10$

If the random variable is distributed like this: $X \sim N(\mu,\sigma)$

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

$z_o=\frac{\bar X -\mu}{\sigma}$

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

$p_v =P(Z>2.05)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

$p_v =P(Z>-1.84)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

$p_v =P(Z>0.4)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say $\alpha=0.05$ . For part a the $p_v$ so then we can reject the null hypothesis at this significance level.