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tekilochka [14]
3 years ago
5

at a garage sale a large bin full of DVDs and CDs are being sold.all the DVDs and all the CDs are the same price. Aaliyah bought

two DVDs for six dollars and the four CDs for eight dollars. Her friend lynn wants to buy four DVDs and two CDs. How much will Lynn have to pay Aaliyah‘s brother Pierre wants to spend $20 on DVDs and CDs what combination of DVDs and CDs could he buy
Mathematics
1 answer:
joja [24]3 years ago
4 0

Answer:

Step-by-step explanation:

$6/(2 DVDs) = $3/DVD, and $8/(4 CDs) = $2/CD

a DVD costs $3

a CD costs $2

Lynn bought 4 DVDs and 2 CDs for 4×$3 + 2×$2 = $16.

Pierre bought d DVDs and c CDs for $20.

d is 0, 2, 4, or 6

c = (20-3d)/2

(d,c) = (0,10), (2,7), (4,4), or (6,1)

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3 years ago
Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = e^5x and z = e^2x. Th
xenn [34]

Answer:

The solutions are linearly independent because the Wronskian is not equal to 0 for all x.

The value of the Wronskian is \bold{W=-3e^{7x}}

Step-by-step explanation:

We can calculate the Wronskian using the fundamental solutions that we are provided and their corresponding the derivatives, since the Wroskian is defined as the following determinant.

W = \left|\begin{array}{cc}y&z\\y'&z'\end{array}\right|

Thus replacing the functions of the exercise we get:

W = \left|\begin{array}{cc}e^{5x}&e^{2x}\\5e^{5x}&2e^{2x}\end{array}\right|

Working with the determinant we get

W = 2e^{7x}-5e^{7x}\\W=-3e^{7x}

Thus we have found that the Wronskian is not 0, so the solutions are linearly independent.

3 0
3 years ago
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nikdorinn [45]

Answer:

Step-by-step explanation:

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3 0
3 years ago
A couple intends to have two children, and suppose that approximately 52% of births are male and 48% are female.
Pachacha [2.7K]

a) Probability of both being males is 27%

b) Probability of both being females is 23%

c) Probability of having exactly one male and one female is 50%

Step-by-step explanation:

a)

The probability that the birth is a male can be written as

p(m) = 0.52 (which corresponds to 52%)

While the probability that the birth is a female can be written as

p(f) = 0.48 (which corresponds to 48%)

Here we want to calculate the probability that over  2 births, both are male. Since the two births are two independent events (the probability of the 2nd to be a male  does not depend on the fact that the 1st one is a male), then the probability of both being males is given by the product of the individual probabilities:

p(mm)=p(m)\cdot p(m)

And substituting, we find

p(mm)=0.52\cdot 0.52 = 0.27

So, 27%.

b)

In this case, we want to find the probability that both children are female, so the probability

p(ff)

As in the previous case, the probability of the 2nd child to be a female is independent from whether the 1st one is a male or a female: therefore, we can apply the rule for independent events, and this means that the probability that both children are females is the product of the individual probability of a child being a female:

p(ff)=p(f)\cdot p(f)

And substituting

p(f)=0.48

We find:

p(ff)=0.48\cdot 0.48=0.23

Which means 23%.

c)

In this case, we want to find the probability they have exactly one male and exactly one female child. This is given by the sum of two probabilities:

- The probability that 1st child is a male and 2nd child is a female, namely p(mf)

- The probability that 1st child is a female and 2nd child is a male, namely p(fm)

So, this probability is

p(mf Ufm)=p(mf)+p(fm)

We have:

p(mf)=p(m)\cdot p(f)=0.52\cdot 0.48=0.25

p(fm)=p(f)\cdot p(m)=0.48\cdot 0.52=0.25

Therefore, this probability is

p(mfUfm)=0.25+0.25=0.50

So, 50%.

Learn more about probabilities:

brainly.com/question/5751004

brainly.com/question/6649771

brainly.com/question/8799684

brainly.com/question/7888686

#LearnwithBrainly

5 0
3 years ago
Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found t
Wittaler [7]

Answer:

a=30 +1.04*8=38.32

So the value of height that separates the bottom 85% of data from the top 15% is 38.32.  

C) 38.32

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) Solution to the problem

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

X \sim N(30,8)  

Where \mu=30 and \sigma=8

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}

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

P(X>a)=0.15   (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 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15

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

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.04

And if we solve for a we got

a=30 +1.04*8=38.32

So the value of height that separates the bottom 85% of data from the top 15% is 38.32.  

C) 38.32

7 0
3 years ago
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