Express 6 h 20 min in seconds.<br> Answer in units of s.

what is the algebraic equation 3 times the sum of a number and 7 is 2 less than five times the number

stealth61 [152]

Let n = number

"3 times the sum of a number and 7" translates to 3(n + 7)

"2 less than five times the number" translates to 5n - 2

The word "is" becomes the equals sign.

3(n + 7) = 5n - 2

I think you already asked this one.

7 0

3 years ago

Forensic scientists can estimate the overall height of an adult male based on the length of the femur bone. A femur bone that is

faust18 [17]

Answer:

h = 1.88f + 32.01

Step-by-step explanation:

To find the linear equation, we first find the gradient of the linear equation from

(y₂ - y₁)/(x₂ - x₁) = m and using the values of the length of femur and overall height respectively, where x₁ = 18 inches and y₁ = 65.85 inches and x₂ = 14 inches and y₂ = 58.33 inches

So, (y₂ - y₁)/(x₂ - x₁) = m

(58.33 - 65.85)/(14 - 18) = m

-7.52/-4 = m

m = 1.88

So, to find the linear equation, we use

(y - y₁)/(x - x₁) = m where f₁ = 18 inches and h₁ = 65.85 inches

So, (y - y₁)/(x - x₁) = m

(y - 65.85)/(x - 18) = 1.88

(y - 65.85) = 1.88(x - 18)

y - 65.85 = 1.88x - 33.84

collecting like terms, we have

y = 1.88x - 33.84 + 65.85

y = 1.88x + 32.01

Given that y = h = overall height of adult male and x = f = length of femur,

h = 1.88f + 32.01

6 0

3 years ago

4- A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produ

galben [10]

Answer:

$\\ \mu = 118\;grams\;and\;\sigma=30\;grams$

Step-by-step explanation:

We need to use z-scores and a standard normal table to find the values that corresponds to the probabilities given, and then to solve a system of equations to find $\\ \mu\;and\;\sigma$ .

<h3>First Case: items from 100 grams to the mean</h3>

For finding probabilities that corresponds to z-scores, we are going to use here a <u>Standard Normal Table </u><u><em>for cumulative probabilities from the mean </em></u><em>(Standard normal table. Cumulative from the mean (0 to Z), 2020, in Wikipedia) </em>that is, the "probability that a statistic is between 0 (the mean) and Z".

A value of a z-score for the probability P(100<x<mean) = 22.57% = 0.2257 corresponds to a value of z-score = 0.6, that is, the value is 0.6 standard deviations from the mean. Since this value is <em>below the mean</em> ("the items produced weigh between 100 grams up to the mean"), then the z-score is negative.

Then

$\\ z = -0.6\;and\;z = \frac{x-\mu}{\sigma}$

$\\ -0.6 = \frac{100-\mu}{\sigma}$ (1)

<h3>Second Case: items from the mean up to 190 grams</h3>

We can apply the same procedure as before. A value of a z-score for the probability P(mean<x<190) = 49.18% = 0.4918 corresponds to a value of z-score = 2.4, which is positive since it is after the mean.

Then

$\\ z =2.4\;and\; z = \frac{x-\mu}{\sigma}$