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3 years ago

3√12•√6please show a step by step explanation

Mathematics

1 answer:

Oduvanchick [21]3 years ago

5 0

Answer: $18\sqrt{2}\\\\$

This is the same as saying 18*sqrt(2) or you could say 18√2

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Explanation:

We'll be using this square root rule: $\sqrt{A}*\sqrt{B} = \sqrt{A*B}$

So we could have this as our steps:

$3\sqrt{12}*\sqrt{6}\\\\3\sqrt{12*6} \ \text{ ... Apply the rule mentioned}\\\\3\sqrt{72}\\\\3\sqrt{36*2}\\\\3\sqrt{36}*\sqrt{2} \ \text{ ... Apply the rule again, but in reverse}\\\\3*6*\sqrt{2}\\\\18\sqrt{2}\\\\$

Therefore, $3\sqrt{12}*\sqrt{6} = 18\sqrt{2}$

The basic idea is to first combine the roots using that rule. From there, we factor the radicand such that we pull out the largest perfect square factor. This will allow us to break the root apart and fully simplify it.

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A woman starts out walking due north for 2 miles, and then she turns due west and continues for another 2 miles. How far from he

Mrac [35]

For this case we can model the problem as a rectangle triangle.
We have:
Length of the sides of the triangle.
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$d = \sqrt{2 ^ 2 + 2 ^ 2} 

d = \sqrt{4 + 4} 

d = \sqrt{8} 

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3 years ago

Suppose a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%. A cell phon

leva [86]

Answer:

We conclude that the actual percentage of households is equal to 30%.

Step-by-step explanation:

We are given that a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%.

Their marketing people survey 150 households with the result that 43 of the households have three cell phones.

Let p = proportion of households that have three cell phones NOT known.

So, Null Hypothesis, $H_0$ : p = 30% {means that the actual percentage of households is equal to 30%}

Alternate Hypothesis, $H_A$ : p $\neq$ 30% {means that the actual percentage of households different from 30%}

The test statistics that would be used here One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of households having three cell phones = $\frac{43}{150}$ = 0.29

n = sample of households = 150

So, the test statistics = $\frac{0.29-0.30}{\sqrt{\frac{0.30(1-0.30)}{150} } }$

= -0.27

The value of z test statistic is -0.27.

Also, P-value of the test statistics is given by;

P-value = P(Z < -0.27) = 1 - P(Z $\leq$ 0.27)

= 1 - 0.6064 = 0.3936

Now, at 1% significance level the z table gives critical value of -2.58 and 2.58 for two-tailed test.

Since our test statistic lies within the range of critical values of z, 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 actual percentage of households is equal to 30%.

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3 years ago

Algebra Graph each line. y = 3x + 4

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I created this using a graphing calculator website called Desmos! You can use this to further explore slopes and lines and graphing in general :)

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3 years ago

Sindi borrowed an amount of money from his father to open the Salon. The loan will be paid back by means of payments of R25 000

amm1812

The present value of the loan will be = R36,250

<h3>Calculation of the present value</h3>

The principal capital (P) = R25 000

Interest rate for the payment (R)= 7.5%

Time for the payment (T)= 6 years

Therefore simple interest = P×T×R/100

= 25,000×6×7.5/100

= 250×6×7.5

= R11,250

The present value of the loan will be;

= 25,000 + 11,250

= R36,250

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2 years ago

Americans receive an average of 20 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with

soldier1979 [14.2K]

The distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.

<h3>Probability</h3>

a. Distribution

X ~ N (20 , 6)

b. P(x ≤24)

= P[(x - μ ) / σ (24 - 20) / 6]

= P(z ≤0.67)

= 0.74857

=0.7486

Hence:

Probability = 0.7486

c. P(21 < x < 26)

= P[(21 - 26)/ 6) < (x - μ ) / σ < (24 - 20) / 6) ]

= P(-0.83 < z < 0.67)

= P(z < 0.67) - P(z < -0.)

= 0.74857- 0.2033

= 0.54527

Hence:

Probability =0.54527

d. Using standard normal table ,

P(Z < z) = 66%

P(Z < 0.50) = 0.66

z = 0.50

Using z-score formula,

x = z× σ + μ

x = 0.50 × 6 + 20 = 23

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Therefore the distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.

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2 years ago

3√12•√6please show a step by step explanation ​

3√12•√6please show a step by step explanation