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2 years ago

Find the slope that is PARALLEL and PERPENDICULAR to the equation of the line y = -1/2x+6.

Mathematics

1 answer:

kifflom [539]2 years ago

3 0

Answer:

parallel: -1/2

perpendicular: 2

Step-by-step explanation:

lines that are parallel have the same slope because they never intersect

lines that perpendicular, have the opposite reciprocal slope.

y = mx + b

where m is the slope

y = -1/2x + 6

-1/2 is the slope.

the slope in the equation given: -1/2

the slope parallel to the line given : -1/2

the slope perpendicular : opposite reciprocal, so the opposite of -1/2 is 1/2 and the reciprocal of 1/2 is 2.

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A multiple-choice examination has 15 questions, each with five answers, only one of which is correct. Suppose that one of the st

Alex

Answer:

0.0111% probability that he answers at least 10 questions correctly

Step-by-step explanation:

For each question, there are only two outcomes. Either it is answered correctly, or it is not. The probability of a question being answered correctly is independent from other questions. 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.

A multiple-choice examination has 15 questions, each with five answers, only one of which is correct.

This means that $n = 15, p = \frac{1}{5} = 0.2$

What is the probability that he answers at least 10 questions correctly?

$P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)$

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

$P(X = 10) = C_{15,10}.(0.2)^{10}.(0.8)^{5} = 0.0001$

$P(X = 11) = C_{15,11}.(0.2)^{11}.(0.8)^{4} = 0.000011$

$P(X = 12) = C_{15,12}.(0.2)^{12}.(0.8)^{3} \cong 0$

$P(X = 13) = C_{15,13}.(0.2)^{13}.(0.8)^{2} \cong 0$

$P(X = 14) = C_{15,14}.(0.2)^{14}.(0.8)^{1} \cong 0$

$P(X = 15) = C_{15,15}.(0.2)^{15}.(0.8)^{0} \cong 0$

$P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.0001 + 0.000011 = 0.000111$

0.0111% probability that he answers at least 10 questions correctly

3 0

2 years ago

you are selling pandesal to raise money for a school field trip. Pandesal with cheese cost 8.00 pesos and ube pandesal cost 9.00

Lera25 [3.4K]

Answer:

Let's define:

C = number of pandesal with cheese that you sell

U = number of pandesal with ube that you sell.

If you sell these numbers of each, the total profit you get is:

C*8.00 pesos + U*9.00 pesos.

And yo want to get at least 180 pesos, then:

C*8.00 pesos + U*9.00 pesos ≥ 180 pesos.

And you also want to sell two of each, then:

C ≥ 2

U ≥2

So the system of inequalities is:

C*8.00 pesos + U*9.00 pesos ≥ 180 pesos.

C ≥ 2

U ≥2

If U is on the x-axis, and C is on the y-axis, then the graph is: (where the region at the right of the vertical line should be shaded)

6 0

2 years ago

Simplify<br> 3x^2+ 13x – 10<br> 9x^2 - 4

svetlana [45]

Answer:

The top one is (3x−2)(x+5)

the bottom one is (3x−2)(3x+2)

Step-by-step explanation:

4 0

2 years ago

5) A rectangular piece of paper is 10cmn long and 5cm broad.find its area,

ivann1987 [24]

Area=L•W
10cm•5cm= 50cm^2

3 0

2 years ago

Each lap around a park is 0.58 miles. Jessica walked 3.25 laps around the park. How many miles did Jessica walk around the park?

xz_007 [3.2K]

0.58x3.25=1.885
c.)1.885 miles

6 0

2 years ago