Calculate the Zscore of $80

1 answer:

3 0

The Z-score (z) is calculated according to the formula: z = (x - μ) / σ

Where: x is the raw score value, μ is the mean of the population, σ is the standard deviation of the population.

x = 80, μ = 5, σ = 4

z = (80 - 5) / 4

z = 75 / 4 = 18.7500

Z-score is 18.7500

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Given: ∆ABC ≅ ∆DEF<br> Find: AB and m∠F

Sindrei [870]

AB = 14

m∠F = 39°

Well the explanation here is simple.

Since the given states that the two triangles, ΔABC and ΔDEF, are congruent, they must have congruent/corresponding parts.

So AB is the same as DE which measures 14, so therefore AB must measure 14.

The same explanation goes to m∠F, ∠C is congruent to ∠F so it must measure 39° too.

3 0

2 years ago

sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project

alukav5142 [94]

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

$\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min$