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4 years ago

find two consecutive even integers such that the smaller added to four times the larger gives a sum of 58.

Mathematics

2 answers:

diamong [38]4 years ago

3 0

10 & 12
There isn't a process beyond estimation and guessing / checking to solve this that I am aware of.

Mice21 [21]4 years ago

3 0

We need to make an equation. We know that the bigger number is 2 more than the smaller number. So let’s set up an equation.
X+2=Y; x is the smaller number and y is the bigger.
The smaller number added to four times the larger number is 58. We need another equation.
4(x+2)+x=58
We need x by itself so we can find one of the numbers. Let’s distribute.
4x+8+x=58
Add like terms
5x+8=58
Subtract 8.
5x=50
Divide.
50/5=10=x
If the smaller number is 10, the numbers are 10 and 12. Let’s check by plugging it into the equation.
4(12)+10=48+10=58

So, the numbers are 10 and 12.

You might be interested in

If the volume of the right prism shown is 27 ft3, then h = __feet.

konstantin123 [22]

Answer:

h=6

Step-by-step explanation:

To find the volume of a right angle prism-

Find area of cross-section, in this case an isoscles triangle so we know that both of the parallel lines are 3ft

To find the area of the cross-section, do:

3 x 3 = 9

9 ÷ 2 = 4.5 (Area of cross-section)

Since we don't know the length of h, we need do:

27^3 ÷ 4.5 = 6

Therefore 6 is h

Hope I explained it okay:)

3 0

2 years ago

A tattoo enthusiast website claims that :

KATRIN_1 [288]

Answer:

The probability that a person is a Millennial given that they have tattoos is 0.5069 (50.69%) or about 0.51 (51%).

Step-by-step explanation:

We have here a case where we need to use Bayes' Theorem and all conditional probabilities related. Roughly speaking, a conditional probability is a kind of probability where an event determines the occurrence of another event. Mathematically:

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

In the case of the Bayes' Theorem, we have also a conditional probability where one event is the sum of different probabilities.

We have a series of different probabilities that we have to distinguish one from the others:

The probability that a person has a tattoo assuming that is a Millennial is:

$\\ P(T|M) = 0.47$

The probability that a person has a tattoo assuming that is of Generation X is:

$\\ P(T|X) = 0.36$

The probability that a person has a tattoo assuming that is of Boomers is:

$\\ P(T|B) = 0.13$

The probability of being of Millennials is:

$\\ P(M) = 0.22$

The probability of being of Generation X is:

$\\ P(X) = 0.20$

The probability of being of Boomers is:

$\\ P(B) = 0.22$

Therefore, the probability of the event of having a tattoo P(T) is:

$\\ P(T) = P(T|M)*P(M) + P(T|X)*P(X) + P(T|B)*P(B)$

$\\ P(T) = 0.47*0.22 + 0.36*0.20 + 0.13*0.22$

$\\ P(T) = 0.204$

For non-independent events that happen at the same time, we can say that the probability of occurring simultaneously is:

$\\ P(M \cap T) = P(M|T)*P(T)$

$\\ P(T \cap M) = P(T|M)*P(M)$

But

$\\ P(M \cap T) = P(T \cap M)$

Then

$\\ P(M|T)*P(T) = P(T|M)*P(M)$

We are asked for the probability that a person is a Millennial given or assuming that they have tattoos or P(M | T). Solving the previous formula for the latter:

$\\ P(M|T)*P(T) = P(T|M)*P(M)$

$\\ P(M|T) = \frac{P(T|M)*P(M)}{P(T)}$

We have already know that

$\\ P(T|M) = 0.47\;P(M) = 0.22\;and\;P(T) = 0.204$ .

Therefore

$\\ P(M|T) = \frac{0.47*0.22}{0.204}$

$\\ P(M|T) = 0.50686 \approx 0.51$

Thus, the probability that a person is a Millennial given that they have tattoos is 0.5069 (50.69%) or about 0.51 (51%).

5 0

4 years ago

Is y = 0.5x - 1 a liner function

Mama L [17]

$\text{Yes, it is a linear function}\\\\\text{The reason why it's a linear function is because there is a constant change}\\\\\text{The constant change would be your slope, and the slope in this case}\\\text{is 0.5}\\\\\text{If you plug this equation in a graph, it would be a straight line forever}\\\\\text{If you want to know if a line is linear, just check the slope to see if it's}\\\text{constant.}$