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3 years ago

How many solutions does the system have?

Mathematics

1 answer:

marishachu [46]3 years ago

3 0

Answer:

{x,y} = {-2,2}

Step-by-step explanation:

Solve equation [2] for the variable y

7y = 7x + 28

y = x + 4

Plug this in for variable y in equation [1]

-8x + 4•(x +4) = 24

-4x = 8

Solve equation [1] for the variable x

4x = - 8

x = - 2

By now we know this much :

x = -2

y = x+4

Use the x value to solve for y

y = (-2)+4 = 2

Solution :

{x,y} = {-2,2}

and this intersects at only one point so your answer is A

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Radius = circumference/2(3.14)
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What are the coordinates of the point on the directed line segment from (-4,1) to (1,6) that partitions the segment into a ratio

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Answer:

a segment is partitioned at a ratio of 1:3, then the point is one-fourth of the distance from (-4,-1) to (2,7).

To compute the x-coordinate of that point, you will need to compute one-fourth of the x-distance between 2 and -4 then add it to -4: (2--4)/4 = 1.5; 1.5 + -4 = -2.5.

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1 year ago

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3 years ago

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A study showed that 25% of the students drive themselves to school. Based on the suggested probability, in a class of 18 student

Gwar [14]

Answer:

B) 0.283

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

25% of the students drive themselves to school.

This means that $p = 0.25$

Class of 18 students

This means that $n = 18$

What would be the probability that at least 6 students drive themselves to school?

This is

$P(X \geq 6) = 1 - P(X < 6)$

In which

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{18} = 0.006$

$P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{17} = 0.034$

$P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{16} = 0.096$

$P(X = 3) = C_{15,3}.(0.25)^{3}.(0.75)^{15} = 0.17$

$P(X = 4) = C_{15,4}.(0.25)^{4}.(0.75)^{14} = 0.213$

$P(X = 5) = C_{15,5}.(0.25)^{5}.(0.75)^{13} = 0.199$

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.006 + 0.034 + 0.096 + 0.17 + 0.213 + 0.199 = 0.718$

$P(X \geq 6) = 1 - P(X < 6) = 1 - 0.718 = 0.282$

Closest option is B, just a small rounding difference.

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3 years ago

In 2000, 54% of the residents in a large city regularly used newspapers for getting news and this has decreased at an average r

Anika [276]

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y=percentage of residents (still) reads newspapers for information
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slope = increase each year = -1.7% (because it is a decrease)
the slope intercept form of the equation is therefore:
y=slope(x)+initial value, or
y=-1.7x+54 (in %)

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2 years ago