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3 years ago

According to the empirical rule, 68% of 7-year-old children are between _ inches and _ inches tall.

Mathematics

2 answers:

AveGali [126]3 years ago

8 0

Using the empirical rule 68% would fall within one standard deviation of the mean.

The standard deviation is given as 2 inches and the mean is 49 inches.

Since it is only one standard deviation find the lower number by subtracting the standard deviation from the mean and find the higher number by adding the standard deviation to the mean.

49 - 2 = 47

49 + 2 = 51

68% would be between 47 inches and 51 inches tall.

Zepler [3.9K]3 years ago

4 0

Answer:

47 inches and 51 inches tall

Step-by-step explanation:

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3 years ago

Given the function f(x) = 3x, find the value of f−1(81).

Shalnov [3]

Given the function f (x) = 3x, find the value of f-1 (81).
For this case, the first thing you should do is rewrite the function.
We have then:
y = 3 ^ x
From here, we clear the value of x:
log3 (y) = log3 (3 ^ x)
log3 (y) = x
Then, we rewrite the function again:
f (x) ^ - 1 = log3 (x)
Now, we evaluate the inverse function for x = 81:
f (81) ^ - 1 = log3 (81)
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3 years ago

Four times a number added to 3 times a larger number is 31. Seven subtracted from the larger number is equal to twice the smalle

aev [14]

Let the smaller number be x.
Let the bigger number be y.

$\begin{cases} &4x + 3y = 31 \tex{ ----- (1) } \\ &y- 7 = 2x \tex{ ----- (2) } \end{cases}$

Rearrange equation (2):
$\begin{cases} &4x + 3y = 31 \tex{ ----- (1) } \\ &y = 2x + 7 \tex{ ----- (2) } \end{cases}
$

Sub (2) into (1):

$4x + 3(2x + 7 ) = 31$
$4x + 6x + 21 = 31$
$10x + 21 = 31$
$10x = 10$
$x = 1$

Sub x = 1 into (2):

$y = 2x + 7$
$y = 2(1) + 7$
$y= 9$

Answer: The two numbers are 1 and 9.

5 0

3 years ago

Read 2 more answers

According to the empirical rule, 68% of 7-year-old children are between ___ inches and ___ inches tall.

According to the empirical rule, 68% of 7-year-old children are between _ inches and _ inches tall.