Find two consecutive even integers whose sum is 14

Naya [18.7K]

Answer:

252 is a composite number.

Prime factorization: 252 = 2 x 2 x 3 x 3 x 7, which can be written 252 = (2^2) x (3^2) x 7

The exponents in the prime factorization are 2, 2, and 1. Adding one to each and multiplying we get (2 + 1)(2 + 1)(1 + 1) = 3 x 3 x 2 = 18. Therefore 252 has 18 factors.

Factors of 252: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

Factor pairs: 252 = 1 x 252, 2 x 126, 3 x 84, 4 x 63, 6 x 42, 7 x 36, 9 x 28, 12 x 21, or 14 x 18

Taking the factor pair with the largest square number factor, we get √252 = (√7)(√36) = 6√7 ≈ 15.875

Step-by-step explanation:

4 0

3 years ago

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Complete the series 1.5, 2.3, 3.1, 3.9, whats next

rusak2 [61]

4.7

Each term is 0.8 bigger than the previous one.

4 0

3 years ago

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The perpendicular bisectors of two sides of a triangle meet at point that belongs to the third side. Prove that this is a right

devlian [24]

<h3>Step-by-step explanation:</h3>

The point of intersection of the perpendicular bisectors of a triangle is the circumcenter, the center of the circle that contains the three triangle vertices.

If that center is on one side, that side must be a diameter of the circle. The diameter cuts the circle into two arcs, each of which measures 180°.

The third vertex of the triangle and its two legs form an inscribed angle that subtends an arc of 180°. The measure of that angle is half the measure of the arc, so the angle measures 90° and is a <em>right angle</em>.

A triangle with a right angle is a right triangle. QED

3 0

3 years ago

Plz help me i dont know the answer

mario62 [17]

Answer:

D) log₁₀20x⁵-1 and E) log₁₀(2x⁵)

Step-by-step explanation:

5log₁₀x+log₁₀20-log₁₀10

5log₁₀x+log₁₀20-1

log₁₀x⁵+log₁₀20-1

log₁₀20x⁵-1 (Option D)

5log₁₀x+log₁₀20-log₁₀10

log₁₀20x⁵-log₁₀10

log₁₀(20x⁵/10)

log₁₀(2x⁵) (Option E)

4 0

3 years ago

A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is current

vladimir2022 [97]

Answer:

$z=\frac{7.1-7.4}{\frac{1.2}{\sqrt{36}}}=-1.5$

Since is a left sided test the p value would be:

$p_v =P(z$

Comparing the p value and the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and the true mean is significantly lower than 7.4 minutes at 10% of significance

Step-by-step explanation:

Data given and notation

$\bar X=7.1$ represent the sample mean

$\sigma=1.2$ represent the population standard deviation

$n=36$ sample size

$\mu_o =7.4$ represent the value that we want to test

$\alpha=0.1$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean i lower than 7.4, the system of hypothesis would be:

Null hypothesis: $\mu \geq 7.4$

Alternative hypothesis: $\mu < 7.4$

The statistic is given by

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

Calculate the statistic

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

$z=\frac{7.1-7.4}{\frac{1.2}{\sqrt{36}}}=-1.5$

P-value

Since is a left sided test the p value would be:

$p_v =P(z$

Conclusion

Comparing the p value and the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and the true mean is significantly lower than 7.4 minutes at 10% of significance

6 0

3 years ago