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Nezavi [6.7K]
3 years ago
5

Find two consecutive even integers whose sum is 14

Mathematics
1 answer:
bagirrra123 [75]3 years ago
5 0
Let x = small number
Let y = large number 
Because they are consecutive even numbers,they must have a difference of 2:
y-x=2
y=2+x

Eqn 1: x+(2+x)=14

Eqn 2: x(2+x)=48

2x+2=14
2x=12
x=6

This means y must be 8 

so your two numbers are 6 and 8 
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What are the factors of 252 .
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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:

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rusak2 [61]

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Each term is 0.8 bigger than the previous one.

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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
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<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>.

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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

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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

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