All categories

3 years ago

The sum of 5 consecutive integers is 120. what is the third number in this sequence?

Mathematics

1 answer:

guapka [62]3 years ago

5 0

Answer:

The third number in the sequence is 24.

Step-by-step explanation:

Sum of five consecutive numbers is 120.

Let the numbers be represented by x,x+1,x+2,x+3,x+4

So the relevant equation for the sum of the numbers is represented as:

x + (x+1) + (x+2) + (x+3) + (x+4) = 5x + (1+2+3+4) = 5x+10

=> 5x + 10 = 120

=> 5x = 120-10

=> 5x = 110

=> x= 110/5 = 22

So the 5 consecutive numbers are 22, 22+1, 22+2, 22+3 , 22+4

In other words the required numbers are 22,23,24,25,26

The third number in the sequence is 24.

You might be interested in

Need answer quickly ;D

Strike441 [17]

Answer:

I think it is the last one

7 0

3 years ago

If you can help that would be great!!!!

Mila [183]

Answer:

1 and four

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

two ferries start moving toward each other from opposite riverbanks, a and b. when they pass each other for the first time, the

Usimov [2.4K]

Let 'x' be the distance from THE far bank where 700 is the distance to the NEAR bank

boat one has travelled 700 (rate = 700/unit time) boat two has travelled x rate = x / unit time

boat one then travels x + 400 more and boat two travels 700 + (700+x -400) more when they meet

The time is the same rate x time = distance distance/rate = time equate the distances divided by the respective rates

(700 + x + 400)/700 = ( x + 700 + (700+x-400) )/x

1100x + x^2 = 1400x + 700000

x^2-300x -700000 = 0 quadratic formula yields x = 1000

One boat travels 700 the other 1000 whe they first meet.....width of river = 700+ 1000 = 1700 m

3 0

3 years ago

In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly d

____ [38]

Complete question is;

In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.

Answer:

P(has diabetes | positive) = 0.442

Step-by-step explanation:

Probability of having diabetes and being positive is;

P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)

We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.

Thus;

P(positive & has diabetes) = 0.08 × 0.95 = 0.076

P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)

P(negative & has diabetes) = 0.004

P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)

We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease

Thus;

P(positive & no diabetes) = 0.92 × 0.1 = 0.092

P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)

P(negative &no diabetes) = 0.828

Probability that a person selected having diabetes actually has the disease is;

P(has diabetes | positive) =P(positive & has diabetes) / P(positive)

P(positive) = 0.08 + P(positive & no diabetes)

P(positive) = 0.08 + 0.092 = 0.172

P(has diabetes | positive) = 0.076/0.172 = 0.442

8 0

3 years ago

Given that A, O & B lie on a straight line segment, evaluate acute

Luba_88 [7]

If the value of x is 10. Then the measure of angle ∠COB will be 56°.

<h3>What is an angle?</h3>

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

Given that A, O, and B lie on a straight line segment.

Then they make a linear angle that is 180 degrees.

Then we have

∠AOC + ∠COD + ∠DOB = 180

(3x + 94) + (x + 30) + (2x - 4) = 180

6x + 120 = 180

6x = 60

x = 10

Then the measure of angle ∠COB will be

∠COB = ∠COD + ∠DOB

∠COB = (x + 30) + (2x - 4)

∠COB = (10 + 30) + (20 - 4)

∠COB = 40 + 16

∠COB = 56°

More about the angled link is given below.

brainly.com/question/15767203

#SPJ1

5 0

2 years ago