All categories

3 years ago

The sum of three consecutive integers is 21 larger than twice the smallest integer. find the integers.

1 answer:

7 0

Let the integers be x-1, x, x+1.

Given,

x -1 + x + x + 1 = 21 + 2(x - 1)

3x = 21 + 2x - 2

x = 19

Hence, the three integers are 18, 19 and 20.

You might be interested in

Question 1

12345 [234]

Answer:

A). Surface area = 222 cm²

Volume = 180 cm³

B). Surface area = 375 cm²

Volume = 360 cm³

C). % increase in surface area = 67.57%

% increase in volume = 100%

Step-by-step explanation:

In the figure attached base of a prism has been given.

A). Surface area of the prism = (Perimeter of the base of the prism) × height + 2(area of the base)

Perimeter of the base = 5 + 3 + 2 + 2 + 2 + 3 + 5 + 8

= 30

Area of the base = 8×5 - 2×2 = 36 cm²

Surface area of the prism = 30×5 + 2×(36)= 222 cm²

Volume of the prism = volume of the bigger prism - volume of the smaller prism cut off

= 8×5×5 - 2×2×5

= 200 - 20

= 180 cm³

B). Surface area of the prism if it's height is 10 cm,

Surface area = 30×10 + 2×(36) = 372 cm²

Volume of the prism = 8×5×10 - 2×2×10

= 400 - 40

= 360 cm³

C). Increase in surface area = 372 - 222 = 150 cm²

% increase in the surface area = $\frac{150}{222}\times 100$ = 67.57%

Increase in volume = 360 - 180 = 180 cm³

% increase in volume = $\frac{180}{180}\times 100$ = 100%

4 0

2 years ago

Mary is spending money at the average rate of $5 per day. After 14 days she has $68 left. The amount left depends on the number

Radda [10]

Answer:

A. Y-68=-5(x-14)

Step-by-step explanation:

Mary is spending money at the average rate of $5 per day. After 14 days she has $68 left. The amount left depends on the number of days that have passed. write an equation for the situation

We find the equation using the point slope equation of a line. This is given as:

y - y1 = m(x-x1)

The slope intercept form will be

y = -5x + b

since the amount decreases by $5 per day...

Our slope is -5 so m=-5

We have a point (x1,y1) = (14, 68)

Hence, we have:

y-68 = -5(x-14)

Option A is correct

4 0

3 years ago

The body temperatures of adults are normally distributed with a mean of 98.6degrees° F and a standard deviation of 0.60degrees°

Schach [20]

Answer:

97.72% probability that their mean body temperature is greater than 98.4degrees° F.

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$