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2 years ago

A company pays $20 per hour for up to 7 hours of work, and $30 per hour for

Mathematics

1 answer:

katovenus [111]2 years ago

3 0

Answer:

Step-by-step explanation:

current total of hours work earnings (7hrs): $140

total earnings: $980 per week

49 hours work per week (no overtime)

immagine you're working another 4 hours for overtime payment everyday:
current total of hours work earnings (11hrs): $280 including 4 hours overtime ($120)

total working hours: 77 hours per week

total earnings: $1,960 per week

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Which inequality represents all the solutions of -2(3x + 6) ≥ 4(x + 7)?

svet-max [94.6K]

B. x < -4

-2(3x + 6) > 4(x + 7)

-6x - 12 > 4x + 28

-10x > 40

X < -4

7 0

2 years ago

3xy + x = -29 Literal Equations! Solve for X. Show solution please! Thanks in advance!

frosja888 [35]

3xy+x=-29
-3xy -3xy
x= -3xy-29

4 0

3 years ago

The article "Monte Carlo Simulation—Tool for Better Understanding of LRFD" (J. Structural Engr., 1993: 1586–1599) suggests that

Sedaia [141]

Answer:

a) $P(X$

And we can find this probability using the normal standard distribution or excel and we got:

$P(z$

b) $P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)$

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

$P(z>3.78)=1-P(Z$

c) $z=0.674$

And if we solve for a we got

$a=43 +0.674*4.5=46.033$

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(43,4.5)$

Where $\mu=43$ and $\sigma=4.5$

Part a

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard distribution or excel and we got:

$P(z$

Part b

$P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)$

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

$P(z>3.78)=1-P(Z$

Part c

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X$