Ask question

Ask question

All categories

3 years ago

6

Andrew is two years older than Beatrice, and Chris is three years younger than Beatrice. The product of Andrew's age and Chris'

age is 66. How old is Beatrice?

1 answer:

stich3 [128]3 years ago

5 0

Answer:

9

Step-by-step explanation:

A = B + 2

C = B - 3

A x C = 66

A = Andrew

C = Chris

B = Beatrice

Multiply A and c together

(B + 2) x (b - 3)

b^2 - 3b + 2b - 6

b^2 -b - 6 = 66

b^2 - b - 72 = 0

factors of -72b^2 that add up to - b are -9b + 8b

b^2 + 8b -9b - 72

b (b + 8) -9(b + 8)

b = 9 or - 8

b = 9

You might be interested in

Jared surf for one third of the nine hours he was at the beach he spent the rest of the time building a sandcastle how many hour

WINSTONCH [101]

9 dived by 3 = 3
so he surfed for 3 hours = 1/3 of 9
and there are 6 hours left

so he spent 6 hours building a sandcastle

8 0

3 years ago

Read 2 more answers

The sum of 3 consecutive integers is 78. What is the integer closest to zero?

vova2212 [387]

Answer:

25

Step-by-step explanation:

Let n be the first integer.

Then the second integer will be (n + 1).

And the third will be (n + 2).

The sum is 78. Therefore:

$n+(n+1)+(n+2)+78$

Solve for n. Combine like terms:

$3n+3=78$

So:

$3n=75$

Therefore:

$n=25$

Therefore, the first integer is 25.

So our sequene is 25, 26, and 27.

The integer closest to zero will thus be 25.

5 0

3 years ago

Read 2 more answers

Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.

dedylja [7]

g(x) is basically transformed f(x). First, let's focus on f(x) graph. Notice how the graph has slope of 1 and intersect y-axis at (0,0).

Which means that our equation for f(x) is:

$\large{f(x) = x}$

Now then we focus on g(x). g(x) is f(x+k). That means if f(x) = x then f(x+k) would mean substitute x = x+k in the equation.

$\large{f(x + k) = x + k }\\ \large{g(x) = x + k}$

Next, we want to find the value of k. In the slope-intercept form or y = mx+b where m = slope and b = y-intercept. Notice the g(x) graph and see that the graph intersects y-axis at (0,4). Therefore k = y-intercept = 4.

$\large{g(x) = x + 4}$

Answer

g(x) = x+4
Therefore the value of k is 4.

3 0

3 years ago

For which value of x must the expression √37x be further simplified?

vekshin1

Answer:

37x

Step-by-step explanation:

Since it has a square root you can square it to get rid of it so your final answer is 37x

5 0

3 years ago

A research study investigated differences between male and female students. Based on the study results, we can assume the popula

garri49 [273]

Using the <u>normal distribution and the central limit theorem</u>, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem:

The mean is of $\mu = 3.5$ .

The standard deviation is of $\sigma = 0.5$ .

Sample of 100, hence $n = 100, s = \frac{0.5}{\sqrt{100}} = 0.05$

The interval that contains 95.44% of the sample means for male students is <u>between Z = -2 and Z = 2</u>, as the subtraction of their p-values is 0.9544, hence:

Z = -2:

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

By the Central Limit Theorem

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

$-2 = \frac{X - 3.5}{0.05}$

$X - 3.5 = -0.1$

$X = 3.4$

Z = 2:

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

$2 = \frac{X - 3.5}{0.05}$

$X - 3.5 = 0.1$

$X = 3.6$

The interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

7 0

2 years ago