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3 years ago

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each course at college x is worth either 3 or 4 credits. The members of the men's swim team are taking a total of 53 courses tha

t are worth 174 credits. How many 3-credit courses and how many4-credit courses are being taken?

1 answer:

shusha [124]3 years ago

4 0

I can’t figure this one out

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How to do that? Thanks

Vladimir [108]

9) We need to find the limit as x approaches 2 of f(x) - g(x).
When we are approaching a certain value, we are essentially finding values that are infinitesimally approaching x = 2, to the point where we find the exact value when x hits 2.

Thus, by substituting x = 2 into f(x) - g(x), we are finding the value at which the functions' difference hits x = 2.

$\lim_{x \to 2} [f(x) - g(x)] = \lim_{x \to 2}[\frac{3x + 2}{4} - x^{2} + 3]$
$= \frac{3(2) + 2}{4} - 2(2)^{2} + 3$
$= \frac{8}{4} - 8 + 3$
$= 2 - 8 + 3$
$= -3$

Every other question repeats this process, so by applying the above process, your answers should come out smoothly.
Let me know if you need any more assistance, and I can guide you through them.

5 0

3 years ago

Find the solutions to x^2-10+36=0

klemol [59]

Answer:

Only 6

Step-by-step explanation:

We need to factor the equation to find the solution. TO factor we need to find what times what = 36, and what plus what equals -12.

-6 times -6 = 36

and -6 + -6 = -12

So this can be factored into

(x-6)(x-6)=0

We can find the solution by setting each parentheses equal to zero.

x-6 = 0

x = 6

So the only solution is 6

I attached an image that shows an example of factoring.

5 0

3 years ago

4x^-1/2 – 8x^3/2 - 2x ^1/2

Tatiana [17]

Answer:

2x−1 − 4x^3−x

Step-by-step explanation:

3 0

3 years ago

There are two vendors at the fair sleeping snow cones for the same price. If the containers are completely filled and then level

aliya0001 [1]

Answer:

$d = 787.81cm^3$

Step-by-step explanation:

Given

See attachment for the containers

Required

The difference in the amount of snow cone they hold

The amount they hold is determined by calculating the volume of the containers.

The traditional snow cone has the following dimension

Shape: Cone

$r=4cm$ --- radius

$h = 13cm$ --- height

The volume is calculated as:

$Volume = \frac{1}{3} \pi r^2h$

So, we have:

$V_1 = \frac{1}{3} \pi * 4^2 * 13$

$V_1 = \frac{208}{3} \pi$

The snow cone in a cup has the following dimension

Shape: Cylinder

$r=8cm$ --- radius

$h = 5cm$ --- height

The volume is calculated as:

$Volume = \pi r^2h$

So, we have:

$V_2 = \pi *8^2 * 5$

$V_2 = \pi *320$

$V_2 = 320\pi$

The difference (d) in the amount they hold is:

$d = V_2 - V_1$

$d = 320\pi - \frac{208\pi}{3}$

Take LCM

$d = \frac{3*320\pi -208\pi}{3}$

$d = \frac{960\pi -208\pi}{3}$

$d = \frac{752\pi}{3}$

Take $\pi = 22/7$

$d = \frac{752}{3} * \frac{22}{7}$

$d = \frac{752 * 22}{3*7}$

$d = \frac{16544}{21}$

$d = 787.81cm^3$

4 0

3 years ago

One strange phenomenon that sometimes occurs at U.S. airport security gates is that an otherwise law-abiding passenger is caught

valentinak56 [21]

Answer:

c. 0.16

Step-by-step explanation:

For each passenger there are only two possible outcomes. Either they are caught with a gun, or they are not. The probability of a passenger being caught with a gun is independent from other passengers. So we use the binomial probability distribution to solve this question.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 3000000, p = 0.00001$

So

$\mu = E(X) = np = 3000000*0.00001 = 30$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{3000000*0.00001*(1-0.00001)} = 5.48$

What is the probability that tomorrow more than 35 domestic passengers will accidentally get caught with a gun at the airport?

This probability is 1 subtracted by the pvalue of Z when X = 35. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{35 - 30}{5.48}$

$Z = 0.91$

$Z = 0.91$ has a pvalue of 0.8186

1 - 0.8186 = 0.1814.

The closest answer is:

c. 0.16

8 0

3 years ago