All categories

2 years ago

The sum of three consecutive even integers is 486. Find all three integers.

Mathematics

1 answer:

Salsk061 [2.6K]2 years ago

8 0

Answer:

161 + 162 + 163 = 486

Step-by-step explanation:

(X) + (X + 1) + (X + 2) = 486

X + X + 1 + X + 2 = 486

3X + 3 = 486

3X + 3 - 3 = 486 - 3

3X = 483

3X/3 = 483/3

X = 161

You might be interested in

Hamburger buns come in packages of 8. Hamburger patties come in packages of 10.

Vadim26 [7]

Answers/Step-by-step explanation:

A. LCM

B. Greatest Common Factor(GCF) shows the largest whole number, in this case patties and buns, would be a part of the whole that matches both numbers. Neil is unable to buy parts of packages because that not how most stores do business. Least common multiple(LCM) is the number that is both closest in value to the original number while being equal for all numbers. in that case, Neil is buying whole packages so it would work.

C. Neil would buy 4 packages of hamburger patties and 5 packages of hamburger buns. He could make 20 burgers.

3 0

3 years ago

A red die is tossed and then a green die is tossed what is the probability that the red die shows a six or the green die shows a

Dovator [93]

The red die would be 1/6 and the green die would be 1/6 but when you combine them you get the awnser 2/12.

6 0

3 years ago

There are three power plants [X, Y, Z] that at any given time each one either generates electricity or idles. Event A is that pl

insens350 [35]

We're told that

$P(A\cap B)=0.15$

$P(A\cup B)^C=0.06\implies P(A\cup B)=0.94$

$P(B\mid A)=P(B^C\mid A)=0.5$

where the last fact is due to the law of total probability:

$P(A)=P(A\cap B)+P(A\cap B^C)$

$\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)$

$\implies 1=P(B\mid A)+P(B^C\mid A)$

so that $B\mid A$ and $B^C\mid A$ are complementary.

By definition of conditional probability, we have

$P(B\mid A)=P(B^C\mid A)$

$\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}$

$\implies P(A\cap B)=P(A\cap B^C)$

We make use of the addition rule and complementary probabilities to rewrite this as

$P(A\cap B)=P(A\cap B^C)$

$\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)$

$\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)$

$\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]$

$\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]$

$\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C$

$\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)$

By the law of total probability,

$P(B)=P(A\cap B)+P(A^C\cap B)$

$\implies P(A^C\cap B)=P(B)-P(A\cap B)$

and substituting this into $(*)$ gives

$2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]$

$\implies P(B)=P(A\cup B)-P(A\cap B)$

$\implies P(B)=0.94-0.15=\boxed{0.79}$

8 0

3 years ago

Jay traveled from Miami to Jacksonville, a distance of 320 miles. He left Miami at 8:00 AM, stopped for lunch for 30 minutes, an

fredd [130]

Distance Rate times Time
320= R 5.25
R= 60.9
R= 61 mph

5 0

3 years ago

Find the value of x y and z below !

ehidna [41]

Answer:

$x=67, y=121, z=65$

Step-by-step explanation:

One property of parallelogram is that opposite angles have the same measure, so we can write down:

$(y-9)=112\\y=121$

Another property is that two adjacent angles are supplementary (meaning that they add up to 180 degrees). Thus, the following equations are true:

$(z+3)+112=180\\(x+1)+112=180$

Solve the equations:

$(z+3)+112=180\\z+115=180\\z=65\\(x+1)+112=180\\x+113=180\\x=67$

To check, add up all 4 angles and check if they sum up to 360 degrees:

$x=67, y=121, z=65\\(y-9)+(x+1)+(z+3)+112=360\\(121-9)+(67+1)+(65+3)+112=360\\112+68+68+112=360\\360=360$

And please ignore the fact that I cannot insert the degree sign :(

8 0

3 years ago

The sum of three consecutive even integers is 486. Find all three integers.​

The sum of three consecutive even integers is 486. Find all three integers.