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AnnZ [28]
3 years ago
10

Simplify 5√6 + 3√24 - 6√54 + √150​

Mathematics
2 answers:
jasenka [17]3 years ago
8 0

Answer:

= 3 \sqrt{ 6 + 5 \sqrt{6

= 8 \sqrt{ 6

√54+√150

=√2×3×3×3+√2×5×5×3

=3√6+5√6

=8√6

=8×2. 44

=19. 59

krok68 [10]3 years ago
8 0

Answer:

Step-by-step explanation:

5\sqrt{6}+3\sqrt{6(4)}-6\sqrt{6(9)}+\sqrt{6(25)}\\ \\ \sqrt{6}(5+3\sqrt{4}-6\sqrt{9}+\sqrt{25}\\ \\ \sqrt{6}(5+6-18+5)\\ \\ -2\sqrt{6}

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A survey of 340 randomly chosen US adults found that 60% of the 150 men and 50% of the 190 women ran a five-kilometer race durin
Andrej [43]

Answer:

The p-value is less than the significance level, so we will reject the null hypothesis, and conclude that at 5% significance level, the proportion for women that ran 5 km is more than the proportion of male that ran the 5 km. Thus, women are more likely to run the 5 km race.

Step-by-step explanation:

We are given;

Number of males selected; n₁ = 150

Number of females selected; n₂ = 190

Proportion of the males; p₁ = 0.6

Proportion of females; p₂ = 0.5

Let's define the hypotheses;

Null hypothesis; H0: p₁ ≥ p₂

Alternative hypothesis; Ha: p₁ < p₂

Now, the z score formula for this is;

z = (p₁ - p₂)/√(p^(1 - p^))(1/n₁ + 1/n₂))

Where;

p^ = (p₁ + p₂)/2

p^ = (0.6 + 0.5)/2

p^ = 0.55

Thus;

z = (0.6 - 0.5)/√(0.55(1 - 0.55))((1/150) + (1/190))

z = 0.1/0.0543

z = 1.84

From online p-value from z-score calculator attached, using z = 1.84, significance level = 0.05, one tailed hypothesis, we have;

P-value = 0.033

The p-value is less than the significance level, so we will reject the null hypothesis, and conclude that at 5% significance level, the proportion for women that ran 5 km is more than the proportion of male that ran the 5 km. Thus, women are more likely to run the 5 km race.

Although if we check at 0.01 significance level, we will not have the same answer as the p-value will be greater.

3 0
3 years ago
7r-5r+8=9r+8-r translate to an equation, then solve
pshichka [43]

Answer:

r=0

Step-by-step explanation:

7r-5r+8=9r+8-r

This is already an equation

Combine like terms

2r+8 = 8r+8

Subtract 2r from each side

2r-2r +8 = 8r-2r +8

8 =6r+8

Subtract 8 from each side

8-8 = 6r+8-8

0 = 6r

Divide by 6

0/6 = 6r/6

0 =r

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3 years ago
Question 3 (1 point)
den301095 [7]

Answer: Pay 250 per month until it’s paid off

4 0
3 years ago
A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 50%
IRISSAK [1]

Answer:

a) 0.9

b) Mean = 1.58

Standard Deviation = 0.89

Step-by-step explanation:

We are given the following in the question:

A marketing firm is considering making up to three new hires.

Let X be the variable describing the number of hiring in the company.

Thus, x can take values 0,1 ,2 and 3.

P(x\geq 2) = 50\%= 0.5\\P(x = 0) = 10\% = 0.1\\P(x = 3) = 18\% = 0.18

a) P(firm will make at least one hire)

P(x\geq 2) = P(x=2) + P(x=3)\\0.5 = P(x=2) + 0.18\\ P(x=2) = 0.32

Also,

P(x= 0) +P(x= 1) + P(x= 2) + P(x= 3) = 1\\ 0.1 + P(x= 1) + 0.32 + 0.18 = 1\\ P(x= 1) = 1- (0.1+0.32+0.18) = 0.4

\text{P(firm will make at least one hire)}\\= P(x\geq 1)\\=P(x=1) + P(x=2) + P(x=3)\\ = 0.4 + 0.32 + 0.18 = 0.9

b) expected value and the standard deviation of the number of hires.

E(X) = \displaystyle\sum x_iP(x_i)\\=0(0.1) + 1(0.4) + 2(0.32)+3(0.18) = 1.58

E(x^2) = \displaystyle\sum x_i^2P(x_i)\\=0(0.1) + 1(0.4) + 4(0.32) +9(0.18) = 3.3\\V(x) = E(x^2)-[E(x)]^2 = 3.3-(1.58)^2 = 0.80\\\text{Standard Deviation} = \sqrt{V(x)} = \sqrt{0.8036} = 0.89

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Your answer is .41, hope this helps
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3 years ago
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