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3 years ago

Level 3 Solve: |x + 2|– 5 = -1

Mathematics

1 answer:

leonid [27]3 years ago

6 0

Answer:

x=−6

x=2

Step-by-step explanation:

Combine like terms and use the properties of equality to get the variable on one side of the equal sign and the numbers on the other side. Remember to follow the order of operations.

∣x+2∣−5=−1

Add 5 to both sides of the equation.

∣x+2∣=4

Use the definition of absolute value.

x+2=4

x+2=−4

Subtract 2 from both sides of the equation.

x=2

x=−6

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The Blair family was one of the first to come to the original 13 colonies (now part of the USA). They had 4 children. Assuming t

Mumz [18]

Answer:

31.25% probability that the Blair family had at least 3 girls

Step-by-step explanation:

For each children, there are only two possible outcomes. Either it was a girl, or it was not. The probability of a child being a girl is independent of any other children. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

They had 4 children.

This means that $n = 4$

The probability of a child being a girl is 0.5

This means that $p = 0.5$

Probability of at least 3 children:

$P(X \geq 3) = P(X = 3) + P(X = 4)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{4,3}.(0.5)^{3}.(0.5)^{1} = 0.25$

$P(X = 4) = C_{4,4}.(0.5)^{4}.(0.5)^{0} = 0.0625$

$P(X \geq 3) = P(X = 3) + P(X = 4) = 0.25 + 0.0625 = 0.3125$

31.25% probability that the Blair family had at least 3 girls

3 0

3 years ago

Pam works a 52 hours in a week. Considering that a normal work week is 40 hours and paid at $1470 per hour and overtime is paid

Bezzdna [24]

Step-by-step explanation:

they way it is written, she has one of the best paying jobs in the world : $1470 per hour ...

but I guess it is really $14.70 per hour, right ?

that is then her basic wage : $14.70 per hour for 40 hours = 14.7 × 40 = $588.

her overtime rate is then 14.7×1.25 (one time and a quarter) = 18.375 ≈ $18.38

and she gets that rate for all hours beyond the basic 40 hours, so, 52-40 = 12 hours.

12×18.38 = $220.56

or if you need it totally precise

12×18.375 = $220.50

in total, her gross wage for that week is then

588 + 220.56 = $808.56

or totally precise with unrounded hourly rates

588 + 220.5 = $808.50

which would create a mean hourly rate

808.56/52 = $15.54923077... per hour ≈ $15.55 per hour

808.5/52 = $15.54807692... per hour ≈ $15.55 per hour

many payroll systems do the rounding of the hourly rates and then calculate the total amount (as the first option here). some others keep the full decimal positions in the calculation and then only round the total (as the second option here).

so, it is the question what your teacher expects here. I cannot tell from the description.

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2 years ago

Can you find the midpoint of AB

Masteriza [31]

Use the distance formula for the 2 points and then halve the answer

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2 years ago

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ipn [44]

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3 years ago

The ratio of teachers needs to be 1:30. If there were 120 students, how many teachers would be needed?

mezya [45]

Answer:

4:120

Step-by-step explanation:

for 120 student they would be 4 teacher needed per 30 student

4:120

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3 years ago