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3 years ago

A school basketball team has an expense account and a fundraising account. After t

1 answer:

3 0

1) the expression that gathers the expenses and the income is the utility function and is defined by U(t) = I(t)-G(t), where I(t) is income and G(t) is expenses, the simplest form that represents the total amount of the balance of the expense account is, for this exercise I(t) = 275+48t and G(t) = 450-70t

PART A

U(t)= 275+48t-(450-70t) ⇒U(t) = 275+48 t-450+70t⇒U(t) = 118t -175

PART B

For f(t) = (275+48t) the total amount (in dollars) after 9 weeks?

it is f(9) = [(450 - 70(9)]= $220

for f(t) =275 +48t ,the total amount in dollars after 9 weeks is f(9) = 275+48(9) = $ 707

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Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.

ycow [4]

This involves quite a lot of arithmetic to do manually.

The first thing you do is to make the first number in row 2 = to 0.

This is done by R2 = -3/2 R1 + R2

so the matrix becomes

( 2 1 1) ( -3 )

( 0 -13/2 3/2) (1/2 )

(5 -1 2) (-2)

Next step is to make the 5 in row 5 = 0

then the -1 must become zero

You aim for the form

( 1 0 0) (x)

(0 1 0) (y)

(0 0 1) ( z)

x , y and z will be the required solutions.

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3 years ago

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It is stated that a quantity varies directly as another if the two quantities always change in the same ratio. So, what would ha

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Answer:

Step-by-step explanation:

Let k is the ratio between two variables or y = kx

when x double, means: y = k (2x) = 2kx quantity y will change with a ratio 2k

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3 years ago

What is the solution to 8 + 9p = 9p - 7?

Norma-Jean [14]

Answer:

15=0 not a real number

Step-by-step explanation:

8+9p=9p-7

+7 +7

15+9p=9p

-9p -9p

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15 one half subtracted by 3 wholes and seventh eights

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15 and one half is 31/2. 3 and seven eighths is 31/8. 31/2 also equals 124/8. Then the answer is 124/8 - 31/8 is 91/8. Hope that helped.

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3 years ago

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Suppose the heights of a population of people are normally distributed with a mean of 65.5 inches and a standard deviation of 2.

kupik [55]

Answer:

a) $P(64.2$

b) 69.764

Step-by-step explanation:

1) 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".

2) Part a

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:

$X \sim N(65.5,2.6)$

Where $\mu=65.5$ and $\sigma=2.6$

We are interested on this probability

$P(64.2$

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:

$P(64.2$

And we can find this probability on this way:

$P(-0.50$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.50$

3) Part b

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

$P(X>a)=0.05$ (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 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

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

$P(X$