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Andrei [34K]
3 years ago
5

1

Mathematics
1 answer:
Leona [35]3 years ago
7 0

Given:

The inequality is:

y>5x+3

To find:

The y-intercept, slope and type of line (solid or dotted).

Solution:

The slope intercept form of a line is:

y=mx+b            ...(i)

Where, m is the slope and b is the y-intercept.

We have,

y>5x+3

The relation equation is:

y=5x+3             ...(ii)

On comparing (i) and (ii), we get

m=5

b=3

It means the slope is 5 and the y-intercept is 3.

The sign of the inequality in the given inequality is ">". It means the boundary line is not included in the solution set. So, the boundary line is a dotted line.

Therefore, the slope is 5, the y-intercept is 3 and the line is a dotted line.

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Darlene has 59 pages to type. so far she gas type 23 pages. what fraction of the job is finished ​
coldgirl [10]

Answer:

\frac{23}{59}

Step-by-step explanation:

A fraction can be found be taking the current amount over the total amount:

\frac{current}{total}=\frac{23}{59}

Since Darlene has only typed 23 pages out of 59, her fraction is 23 over 59.  Fractions must always be in simplest form, which means that both the numerator and denominator can no longer be divided by the same factor.  Since the numbers 23 and 59 are both prime and have no other factors other than 1 and themselves, the fraction 23/59 is in simplest form.

4 0
3 years ago
Psychologist Michael Cunningham conducted a survey of university women to see whether, upon graduation, they would prefer to mar
bagirrra123 [75]

Answer:

A.The probability that exactly six of Nate's dates are women who prefer surgeons is 0.183.

B. The probability that at least 10 of Nate's dates are women who prefer surgeons is 0.0713.

C. The expected value of X is 6.75, and the standard deviation of X is 2.17.

Step-by-step explanation:

The appropiate distribution to us in this model is the binomial distribution, as there is a sample size of n=25 "trials" with probability p=0.25 of success.

With these parameters, the probability that exactly k dates are women who prefer surgeons can be calculated as:

P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{25}{k} 0.25^{k} 0.75^{25-k}\\\\\\

A. P(x=6)

P(x=6) = \dbinom{25}{6} p^{6}(1-p)^{19}=177100*0.00024*0.00423=0.183\\\\\\

B. P(x≥10)

P(x\geq10)=1-P(x

P(x=0) = \dbinom{25}{0} p^{0}(1-p)^{25}=1*1*0.0008=0.0008\\\\\\P(x=1) = \dbinom{25}{1} p^{1}(1-p)^{24}=25*0.25*0.001=0.0063\\\\\\P(x=2) = \dbinom{25}{2} p^{2}(1-p)^{23}=300*0.0625*0.0013=0.0251\\\\\\P(x=3) = \dbinom{25}{3} p^{3}(1-p)^{22}=2300*0.0156*0.0018=0.0641\\\\\\P(x=4) = \dbinom{25}{4} p^{4}(1-p)^{21}=12650*0.0039*0.0024=0.1175\\\\\\P(x=5) = \dbinom{25}{5} p^{5}(1-p)^{20}=53130*0.001*0.0032=0.1645\\\\\\P(x=6) = \dbinom{25}{6} p^{6}(1-p)^{19}=177100*0.0002*0.0042=0.1828\\\\\\

P(x=7) = \dbinom{25}{7} p^{7}(1-p)^{18}=480700*0.000061*0.005638=0.1654\\\\\\P(x=8) = \dbinom{25}{8} p^{8}(1-p)^{17}=1081575*0.000015*0.007517=0.1241\\\\\\P(x=9) = \dbinom{25}{9} p^{9}(1-p)^{16}=2042975*0.000004*0.010023=0.0781\\\\\\

P(x\geq10)=1-(0.0008+0.0063+0.0251+0.0641+0.1175+0.1645+0.1828+0.1654+0.1241+0.0781)\\\\P(x\geq10)=1-0.9287=0.0713

C. The expected value (mean) and standard deviation of this binomial distribution can be calculated as:

E(x)=\mu=n\cdot p=25\cdot 0.25=6.25\\\\\sigma=\sqrt{np(1-p)}=\sqrt{25\cdot 0.25\cdot 0.75}=\sqrt{4.69}\approx2.17

4 0
2 years ago
A store sells rope by the meter. The equation p=0.8L represents the price p(in dollars) of a piece of nylon rope that is L meter
Margaret [11]

Answer:

1. $0.80 or 80 cents

2. 1.25 meters

Step-by-step explanation:

The equation p=0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long.

1. To find how much the nylon costs per meter, take L = 1 (this means you are calculating the price of a piece of nylon rope that is 1 meter long):

L=1,\\ \\p=\$0.8\cdot 1=\$0.80

2. To find how long a piece of nylon rope that costs $1.00 is, substitute into the equation p = 1:

p=1,\\ \\1=0.8L\\ \\L=\dfrac{1}{0.8}=\dfrac{10}{8}=\dfrac{5}{4}=1.25\ meters

5 0
3 years ago
Which property was used to simplify the expression?
Vadim26 [7]

Answer:

commutative property

Step-by-step explanation:

Either order or way you put the numbers, it will be the same answer.

5 0
2 years ago
What's the horizontal asymptote of f(x)=x-3/x+2
jasenka [17]

Answer:

y=1

Step-by-step explanation:

4 0
2 years ago
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