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3 years ago

The sum of four consecutive integers 130 what is the third number in the sequence

1 answer:

8 0

If x is the first number in the sequence, you can represent the next consecutive number using (x+1), the one after with (x+2), etc. We can set up an equation like this:

x + (x+1) + (x+2) + (x+3) = 130

This can be simplified to:

4x + 6 = 130

Now subtract 6 from each side:

4x = 124

Next we divide each side by 4:

x = 31

We have the first number in the sequence, but we need the THIRD number. Since we've already established that (x+2) would be the third number, we can just plug in x.

31 + 2 = 33

The third number in this sequence is 33.

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Combine like terms<br><br> 4y^2+4(7y^2-8)=<br><br> please show your work

kirza4 [7]

Answer:

32y^2-32

Step-by-step explanation:

4y^2+4(7y^2-8)

4y^2+28y^2-32

32y^2-32

if you need extra steeps explaining then plz let me know and I will help :)

8 0

3 years ago

the weight M of an object on Mars varies directly as it’s weight E on Earth. A person who weighs 95 lb on Earth weighs 38 lb on

lorasvet [3.4K]

Answer:

A 100 lb person will weight 40 lb on Mars

Step-by-step explanation:

Given:

Weight on Mars directly varies as its weight on earth.

Let weight on Mars be = $M$

Let weight on Earth be = $E$

Its known that:

$M$ ∝ $E$

Thus

$M=kE$

where $k$ is constant of proportionality.

when $E=95\ lb$ , then $M=38\ lb$

thus, we have

$38=k(95)$

dividing both sides by 95.

$\frac{38}{95}=\frac{k(95)}{95}$

∴ $k=\frac{38}{95}$

Thus when $E= 100$ , $M$ would be calculated as

$M=\frac{38}{95}\times 100$

$M=\frac{3800}{95}$

∴ $M=40\ lb$ (Answer)

∴ A 100 lb person will weight 40 lb on Mars.

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3 years ago

This year the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot,

Vlad [161]

Using conditional probability, it is found that there is a 0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.

Conditional Probability

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this problem:

Event A: Person has the flu.

Event B: Person got the flu shot.

The percentages associated with getting the flu are:

20% of 30%(got the shot).

65% of 70%(did not get the shot).

Hence:

$P(A) = 0.2(0.3) + 0.65(0.7) = 0.515$

The probability of both having the flu and getting the shot is:

$P(A \cap B) = 0.2(0.3) = 0.06$

Hence, the conditional probability is:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.515} = 0.1165$

0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.

To learn more about conditional probability, you can take a look at brainly.com/question/14398287

7 0

2 years ago

What is always true about a linear pair?

kicyunya [14]

Answer:

Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.

Step-by-step explanation:

3 0

3 years ago

The endpoints of one diagonal of a rhombus are (0, -8) and (8, -4). If the coordinates of the 3 rd vertex are (1, 0), what are t

atroni [7]

You can answer this problem using the midpoint formula, but we can work out the 4th vertex by just logically thinking it through by first drawing out the rhombus on an x-y coordinate plane. I wrote the answer out on paper since it is easier than typing. Let me know if you have any questions.

6 0

3 years ago