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Simplify (5 square root 2) * ( 3 square root 2 )

Answers

Answer 1

Answer:

The solution is : the simplification of 5√2 × 3 √2 is: 30.

Here, we have,

given that,

5√2 × 3 √2

now, we need to simplify this, i.e. we have to multiply this.

so, we get,

multiply 5 x 3 and we get 15

then multiply the roots and we also get 2

i.e. √2 ×√2 = 2

so then you have to multiply 15 and 2 to get 30.

i.e. 15 * 2 = 30

so, we have,

5√2 × 3 √2

= 5 × 3 × √2 ×√2

=15 × 2

=30

Hence, The solution is: the simplification of 5√2 × 3 √2 is: 30.

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Answer 2

Answer:

Answer:

Step-by-step explanation:

multiply 5 x 3 and you get 15 then multiply the roots and you also get 2 so then you have to multiply 5 and 2 to get 30.

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there are four pizzas which each have 12 slices. these pizzas will be divided between 15 people. how many slices does each person get if they are split evenly
The white "Spirit" black bear (or Kermode) Ursus americanus kermodei, differs from the ordinary black bear by a single amino acid change in the melanocortin 1 receptor gene (MC1R). In this population, the gene has two forms (or alleles): the "white" allele b and the "black" allele B. The trait is recessive: white bears have two copies of the white allele of this gene (bb), whereas a bear is black if it has one or two copies of the black allele (Bb or BB). Both color morphs and all three genotypes are found together in the bear population of the northwest coast of British Columbia. If possessing the white allele has no effect on growth, survival, reproductive success, or mating patterns of individual bears, then the frequency of individuals with 0, 1, or 2 copies of the white allele (b) in the population will follow a binomial distribution. To investigate, Hedrick and Ritland (2011) sampled and genotype 87 bears from the northwest coast:42 were BB 24 were Bb 21 were bb Assume that this is a random sample. A formal hypothesis test was carried out to compare the observed and expected frequencies of genotypes. The procedure obtained P = 0.0001. 1. "The frequency distribution of genotypes has a binomial distribution in the population" is the________ hypothesis, whereas "The frequency distribution of genotypes does not have a binomial distribution" is the _________ hypothesis. 2. The degrees of freedom for the test statistic are __________. Say whether the each of the following statements is true or false solely on the basis of these results: 3. The difference between the observed and expected frequencies is statistically significant.________4. The test statistic exceeds the critical value corresponding to α = 0.05. ___________5. The test statistic exceeds the critical value corresponding to α = 0.01. ____________
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Answers

$(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) = sin \alpha - cos \alpha$

Solution:

Given that we have to simplify:

$(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha)$ ---- eqn 1

We know that,

$sin^2 x = 1 - cos^2 x$

Substitute the above identity in eqn 1

$(2\left(1-\cos ^(2) \alpha\right)-1)/(\sin \alpha+\cos \alpha)$

Simplify the above expression

$(2-2 \cos ^(2) \alpha-1)/(\sin \alpha+\cos \alpha)$

$(1-2 \cos ^(2) \alpha)/(\sin \alpha+\cos \alpha)$ ------- eqn 2

By the trignometric identity,

$(sin x + cos x)(sin x - cos x) = 1-2cos^2 x$

Substitute the above identity in eqn 2

$((\sin \alpha+\cos \alpha)(\sin \alpha-\cos \alpha))/(\sin \alpha+\cos \alpha)$

Cancel the common factors in numerator and denominator

$((\sin \alpha+\cos \alpha)(\sin \alpha-\cos \alpha))/(\sin \alpha+\cos \alpha)=\sin \alpha-\cos \alpha$

Thus the simplified expression is:

$(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) = sin \alpha - cos \alpha$

Q 3.28: To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off a certain percent from each tail. Indicate what percent of values must be chopped off from each tail for a 97% confidence level. A : We keep the middle 97% of values by chopping off 1.5% from each tail. B : We keep the middle 1.5% of values by chopping off 97% from each tail. C : We keep the middle 3% of values by chopping off 97% from each tail. D : We keep the middle 3% of values by chopping off 1.5% from each tail. E : We keep the middle 97% of values by chopping off 3% from each tail.

Answers

Answer:

A : We keep the middle 97% of values by chopping off 1.5% from each tail.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = (1-0.97)/(2) = 0.015$

This means that for a 97% confidence interval, 1.5% of each tail is removed, while the middle 97% of values are kept.

So the corect answer is:

A : We keep the middle 97% of values by chopping off 1.5% from each tail.

The mean breaking strength of a ceramic insulator must be at least 10 psi. The process by which this insulator is manufactured must show equivalence to this standard. If the process can manufacture insulators with a mean breaking strength of at least 9.5 psi, it will be considered equivalent to the standard. A random sample of 50 insulators is available, and the sample mean and standard deviation of breaking strength are 9.32 psi and 0.21 psi, respectively. a. State the appropriate hypotheses that must be tested to demonstrate equivalence.

Answers

Answer:

H0: u ≥ 9.5

Ha: u < 9.5

Step-by-step explanation:

The null hypothesis and the alternate hypothesis are reverse of each other.

The claim is either set as the null or alternate hypothesis

The null hypothesis is : H0: u ≥ 9.5 the mean breaking strength of a ceramic insulator is at least 9.5 which is considered equivalent to the standard.

The alternate hypothesis is: Ha: u < 9.5 the mean breaking strength of a ceramic insulator is less than 9.5 which is not considered equivalent to the standard.

HELPP!!! BRAINLYESTTTTT!!!!!!

GRAPH THE FUNCTION:

Answers

Answer:

Step-by-step explanation:

We are given the function f(x) = -3/4(x) +6.

We know that the slope intercept form of a line is y = mx + b

Here, the slope m = -3/4.

The y-coordinate of the y intercept is b = 6 so the y-intercept is at the point (0,6) [x is always 0 at the y-intercept]

If you have to points you can graph the line, we only have the point (0,6).

To find the second point we use the slope.

We add the bottom point of the slope to the x coordinate of the y-intercept and we add the top part of the slope to the y coordinate of the y-intercept, so our second point is (0 + 4, 6 +(-3)) = (4, 3).

You then plot the points we have: (0,6) and (4,3) and draw the line through them.

Solve for x: 4x/5= -20

Answers

Answer:

x = -25

Step-by-step explanation:

Get x by itself by multiplying both sides by 5: 4x = -100

Get x by itself by dividing both sides by 4: x = -25

You are going to play mini golf. A ball machine that contains 23 green golf balls, 24 red golf balls, 18 blue golf balls, and 24 yellow golf balls, randomly gives you your ball. What is the probability that you end up with a red golf ball?

Answers

Answer:

$(24)/(89)$ chance or ≈27% chance or 0.27

Step-by-step explanation:

P of getting a red golf ball: $(24)/(23+24+18+24) =(24)/(89)$

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