Based on the information marked in the diagram , ABC and DEF must be congrent true or false
2 answers:
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Answer:
$75
Step-by-step explanation:
Joni currently earns $300 per week (given)
To find how much more she will earn each week, write an expression adding the original pay and the raise amount.
$300 + 25%
Find 25 as a decimal for multiplication
25% = 25/100 = 0.25
Write an expression to represent the scenario
Expression example 1:
$300 + 0.25(300)
This expression adds the original pay and the new raise together.
Expression example 2:
$300 (1.25)
This expression already takes the new pay into account by finding 125% of the original pay.
Simplify both expressions
Expression 1:
$300 + 0.25(300)
$300 + $75
$375
Expression 2:
$300 (1.25)
$375
Both expressions represent the same scenario and therefore come out to the same result. Now that we know how much Joni made after the raise, we need to find how much more money she will earn in a week with the following equation.
New amount - original amount = amount increase
Substitute known values into the equation
$375 - $300
Simplify
$75
Joni will earn $75 more each week.
Let me know if you have any questions!
Answer:
(1) (c) <u>5.30 years</u>.
(2) (b) <u>0.289</u>.
(3) (b) <u>0.80</u>.
(4) (d) <u>0.50</u>.
(5) (a) <u>5.25 years</u>.
Step-by-step explanation:
Let <em>X</em> = age of the children in kindergarten on the first day of school.
The random variable <em>X</em> follows a continuous Uniform distribution with parameters <em>a</em> = 4.8 years and <em>b</em> = 5.8 years.
The probability density function function of <em>X</em> is:
(1)
The expected value of a Uniform random variable is:
Compute the mean of <em>X</em> as follows:
Thus, the mean of the distribution is (c) <u>5.30 years</u>.
(2)
The standard deviation of a Uniform random variable is:
Compute the standard deviation of <em>X</em> as follows:
Thus, the standard deviation of the distribution is (b) <u>0.289</u>.
(3)
Compute the probability that a randomly selected child is older than 5 years old as follows:
Thus, the probability that a randomly selected child is older than 5 years old is (b) <u>0.80</u>.
(4)
Compute the probability that a randomly selected child is between 5.2 years and 5.7 years old as follows:
Thus, the probability that a randomly selected child is between 5.2 years and 5.7 years old is (d) <u>0.50</u>.
(5)
It is provided that a randomly selected child is at the 45th percentile.
This implies that:
P (X < x) = 0.45
Compute the value of <em>x</em> as follows:
Thus, the age of the child at the 45th percentile is (a) <u>5.25 years</u>.