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3 years ago

Find three consecutive odd integers such that the sum of the smallest number and

Mathematics

1 answer:

Rudik [331]3 years ago

3 0

Answer:

As the first number is 5, the second will be 7, and the third will be 9.

Step-by-step explanation:

First, let's break down what the information is telling us.

"three consecutive odd integers" means each number is 2 away from each other. So if we were to assign the variable x as the first number, the second would be x + 2 and the third would be x + 4

"sum of the smallest number and twice the middle number" refers to adding the first number and 2 times the second number. So we would write:

x + 2(x + 2)

"is 10 more than the largest number" connects the second part to an equation. This is saying the third number plus 10. So for this, we would write:

(x + 4) + 10

Now we join the information that we have written mathematically into an equation. Since we have an equation, we can solve for the first number, and hence the second and third numbers.

x + 2(x + 2) = (x + 4) + 10

x + 2x + 4 = x + 14

3x + 4 = x + 14

2x = 10

x = 5

As the first number is 5, the second will be 7, and the third will be 9.

The key idea for solving this question is to define a variable and connect it to an equation using the information provided. Try to think about how much information is needed and how many variables need to be defined.

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What is the value of x?

Firlakuza [10]

THIS IS A RIGHT & isosceles triangle: A = 90. B = 45 THEN ANGLE C =45

THEN AB = AC = 4√2

APPLY PYTHAGORAS: BC² =AB² + AC²

===> X² = (4√2)² + (4√2)² ==>16.2 +16.2 = 64
X² 64 & X =√64 ==> X = 8

3 0

3 years ago

Solve equation <br> 3X+2(-2X+3)=50

marta [7]

3x + 2(-2x + 3) = 50 |use distributive property

3x - 4x + 6 = 50

-x + 6 = 50 |subtract 6 from both sides

-x = 44 |change signs

x = -44

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3 years ago

A sample of 900 college freshmen were randomly selected for a national survey. Among the survey participants, 372 students were

Rufina [12.5K]

Answer:

a) $ME=2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.0423$

b) $0.413 - 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.371$

Step-by-step explanation:

1) Data given and notation

n=900 represent the random sample taken

X=372 represent the students were pursuing liberal arts degrees

$\hat p=\frac{372}{900}=0.413$ estimated proportion of students were pursuing liberal arts degrees

$\alpha=0.01$ represent the significance level

z would represent the statistic (variable of interest)

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

p= population proportion of students were pursuing liberal arts degrees

2) Solution to the problem

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

If we replace we have:

$ME=2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.0423$

And replacing into the confidence interval formula we got:

$0.413 - 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.371$

$0.413 + 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.455$

And the 99% confidence interval would be given (0.371;0.455).

We are confident (99%) that about 37.1% to 45.5% of students were pursuing liberal arts degrees.

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3 years ago

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Answer:

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nikklg [1K]

Value of boat per year (up to 10 years)
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4 years= 8132
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6 years= 6848
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8 years= 5564
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10 years= 4280

hope this helps... tell me if anyone of the answers are what you're looking for

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