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3 years ago

Y = x + 2 5x - 4y = -3 Solving systems by equations

Mathematics

1 answer:

Lunna [17]3 years ago

6 0

Answer: x = 5, y = 7

Step-by-step explanation:

First, put the variables together/rearrange:

y - x = 2 & 5x - 4y = -3

Cancel out variable x by multiply the first equation by 5:

5y - 5x = 10 & 5x - 4y = -3

Add equations:

y = 7

Then determine x by plugging y back into the first equation y = x + 2:

x = 5

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According to a recent Census Bureau report, 12.7% of Americans live below the poverty level. Suppose you plan to sample at rando

larisa [96]

Answer:

a) $P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928$

b) $P(X \leq 10) = 0.2614$

c) $(1-0.127)^7 (0.127) =0.0491$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=100, p=0.127)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

a. What is the probability that you count exactly 10 in poverty?

For this case we want this probability P(X=10)

$P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928$

b. What is the probability that you count 10 or less in poverty? .2614

For this case we want this probability $P(X=\leq10)$

$P(X\leq10)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)$

And we can find the individual probabilities like this:

$P(X=0)=(100C0)(0.127)^{0} (1-0.127)^{100-0}=1.263x10^{-6}$

$P(X=1)=(100C1)(0.127)^{1} (1-0.127)^{100-1}=1.837x10^{-5}$

$P(X=2)=(100C2)(0.127)^{2} (1-0.127)^{100-2}=0.000132$

$P(X=3)=(100C3)(0.127)^{3} (1-0.127)^{100-3}=0.000629$

$P(X=4)=(100C4)(0.127)^{4} (1-0.127)^{100-4}=0.00222$

$P(X=5)=(100C5)(0.127)^{5} (1-0.127)^{100-5}=0.00620$

$P(X=6)=(100C6)(0.127)^{6} (1-0.127)^{100-6}=0.0143$

$P(X=7)=(100C7)(0.127)^{7} (1-0.127)^{100-7}=0.0279$

$P(X=8)=(100C8)(0.127)^{8} (1-0.127)^{100-8}=0.0471$

$P(X=9)=(100C9)(0.127)^{9} (1-0.127)^{100-9}=0.0701$

$P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928$

And then repplacing we got:

$P(X \leq 10) = 0.2614$

c. What is the probability that you start taking the random sample and you find the first person in poverty on the 8th person selected? .0491

For this case we need after 7 people , 1 in poverty so we can find this probability like this:

$(1-0.127)^7 (0.127) =0.0491$

7 0

3 years ago

A Grocery store offers a cheese sampler that includes a pepper cheddar cheese that cost $15 per kilogram and Pennsylvania jack t

Len [333]

Answer:

1.5 kg of pepper cheddar cheese and 4.5 kg of Pennsylvania jack was used in the mixture.

Step-by-step explanation:

Pepper Cheddar cheese = $15 per kilogram

Pennsylvania jack = $11 per kilogram

The cheese sampler includes a Pepper Cheddar cheese and a Pennsylvania jack that cost $15 per kilogram and $11 per kilogram respectively.

The mixture = 6 kg

Let

a = kg of the pepper cheddar cheese

b = kg of the Pennsylvania jack

a + b = 6............(i)

Rate

15a + 11b/6 = 12

15a + 11b = 72.............(ii)

Combine the equation

a + b = 6............(i)

15a + 11b = 72.............(ii)

a = 6 - b

15(6 - b) + 11b = 72

90 - 15b + 11b = 72

90 - 72 = 15b - 11b

18 = 4b

divide both sides by 4

b = 18/4

b = 4.5 kg

insert the value of b in equation (i)

a + b = 6............(i)

a = 6 - 4.5

a = 1.5 kg

1.5 kg of pepper cheddar cheese and 4.5 kg of Pennsylvania jack was used in the mixture.

4 0

3 years ago

Find the value of x. *<br> I think I’m a little off

DiKsa [7]

Answer:

x = 44

Step-by-step explanation:

3x - 5 is complementary to y° so their sum is 180°

The angle with measure 127° is also complementary with y°

127 + y = 180

y = 53°

53 + 3x - 5 = 180

3x + 48 = 180

3x = 132

x = 44

6 0

3 years ago

Katerina runs 15 miles in 2.5 hours

shusha [124]

Answer:

We have that The average number of minutes it takes her to run 1 mile

From the Question we are told that

Katerina runs 15 miles in 2 1/2 hours

Average number of minutes it takes her to run 1 mile

Generally

Therefore

The average number of minutes it takes her to run 1 mile

In conclusion

The average number of minutes it takes her to run 1 mile

Step-by-step explanation:

3 0

3 years ago

They are a pencils and a package pillion how many packages will be needed for 28 children if each child gets 4 the pencil

svet-max [94.6K]

7 packages
28 ÷ 4 = 7

4 0

3 years ago

Read 2 more answers