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3 years ago

I need to solve these two equations using either substitution or elimination

Mathematics

1 answer:

vitfil [10]3 years ago

8 0

Answer:

y = -15

x = -10

Step-by-step explanation:

1/4x - 1/2 = 5 (1)

3x + 2/3y = -40 (2)

Multiply (1) by 4

1/4x - 1/2 = 5

1/4x * 4 - 1/2y * 4 = 5 * 4

4/4x - 4/2y = 20

x - 2y = 20 (3)

Multiply (2) by 3

3x + 2/3y = -40 (2)

3x * 3 + 2/3y * 3 = -40 * 3

9x + 6/3y = -120

9x + 2y = -120 (4)

x - 2y = 20 (3)

9x + 2y = -120 (4)

Using elimination method, Add (3) and (4)

9x + x = -120 + 20

10x = -100

x = -100/10

x = -10

Substitute x = -10 into (3)

x - 2y = 20 (3)

-10 - 2y = 20

-2y = 20 + 10

-2y = 30

y = 30/-2

y = -15

x = -10

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F(h) = 45+ 20 h +0.5 g(h) = 45 + 33(0.5) (h+0.5)

larisa [96]

Steps:

Question 1:

Step 1: Multiply both sides by h+0.5.

Step 2: Factor out variable f.

Step 3: Divide both sides by h^2+0.5h.

Question 2

Let's solve for g.

Step 1: Divide both sides by h.

Answers:

1: f=45h+42.5/h²+0.5h

2: g=16.5h+53.25/h

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3 years ago

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nikdorinn [45]

Answer:

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3 years ago

3.In 1995, the Educational Testing Service in Princeton, New Jersey (which administers SAT exam) re-centered the scores so that

Travka [436]

Answer:

38.22% probability that of 10 randomly selected students, lessthan four will be between 900 and 1,100

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they score between 900 and 1,100, or they score outside this range. The probability of a student scoring between 900 and 1,100 is independent from other students. So we use the binomial probability distribution to solve this question.

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.

About 40 percent of these students’ scores were between 900 and 1,100.

This means that $p = 0.4$ .

a)Based on this estimate, what is the probability that of 10 randomly selected students, lessthan four will be between 900 and 1,100?

This is $P(X < 4)$ when $n = 10$ . So

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

In which

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

$P(X = 0) = C_{10,0}.(0.4)^{0}.(0.6)^{10} = 0.0060$

$P(X = 1) = C_{10,1}.(0.4)^{1}.(0.6)^{9} = 0.0403$

$P(X = 2) = C_{10,2}.(0.4)^{2}.(0.6)^{8} = 0.1209$

$P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.2150$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0060 + 0.0403 + 0.1209 + 0.2150 = 0.3822$

38.22% probability that of 10 randomly selected students, lessthan four will be between 900 and 1,100

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4 years ago

Which equation can be used to find one or more factors of 26

erma4kov [3.2K]

The factors of 26 are one, two, 13 and 26. One and the number itself, in this case 26, are always factors. Since 26 is an even number, which means that it ends in zero, two, four, six or eight, it's evenly divisible by two. Two times 13 equals 26.

No numbers between two and 13 divide evenly into 26, so there are no more factors other than the four listed. Because two and 13 are both prime numbers, which are numbers that are only divisible by one and themselves, the prime factorization of 26 is 2 x 13. The prime factorization of a number refers to the prime numbers that multiply together to make that given number

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4 years ago

Read 2 more answers

Find the sum (4 - n) + 2(-5n + 3)

Assoli18 [71]

Answer:

−11n + 10

Step-by-step explanation:

(4-n) + 2 (-5n+3)

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The answer:-11n+10

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3 years ago