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2 years ago

6(a)If the gradient of the straight line

Mathematics

1 answer:

tensa zangetsu [6.8K]2 years ago

5 0

Answer:

(i) k =1

(ii) y-intercept is 7

Step-by-step explanation:

Given line:

ky = kx + x + 7

Divide all terms by k to get slope-intercept form of the line

y = (1 + 1/k)x + 7/k

Since the gradient (slope) of the line is 2:

1 + 1/k = 2
1/k = 1
k = 1

The equation is now:

y = 2x + 7

y - intercept is found when x = 0

x = 0 ⇒
y = 2*0 + 7
y = 7

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Nine percent of americans say they are well informed about politics in comparison to most people. You randomly sample 200 americ

Arada [10]

Answer:

Step-by-step explanation:

Using normal distribution

z = (x - mean) / standard deviation

Nine percent of americans say they are well informed about politics in comparison to most people.

That means probability of success is p =9/100 = 0.09,

then probability of failure is

q = 1-p =1 -0.09= 0.91

n = number of sample = 200

x=(8% of 200) = 0.08×200 =16

mean = np = 200×0.09= 18

Standard deviation = npq = 200×0.09×0.91= 16.38

We are looking for the probability that less than 8% of the people sampled will answer yes to the question

8% of 200 = 16

P (x greater than 16) =P(x lesser than/equal to 15)

z = 15-18 /16.38 = -3/16.38

= -0.18

Looking at the normal distribution table

P(x greater than 16) = 0.5714

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3 years ago

3 / m + 4 - 4 / m = 6 (i) Show that this equation can be written as 6m^2 + 25m+16= 0

Evgen [1.6K]

Answer:

Proved Below

Step-by-step explanation:

$\sf \frac{3}{m+4} - \frac{4}{m} = 6\\LCM = m(m+4)\\Multiplying \ both \ sides \ by\ m(m+4)\\3m - 4(m+4) = 6m(m+4)\\3m-4m-16 = 6m^2+24m\\-m-16 = 6m^2+24m\\Adding\ m\ to\ both\ sides\\-16 = 6m^2+24m+m\\-16 = 6m^2+25m\\Adding \ 16 \ to \ both \ sides\\0 = 6m^2+25m+16\\OR\\6m^2+25m+16 = 0$

Hence, Proved that $\sf \frac{3}{m+4} - \frac{4}{m} = 6$ is equivalent to $\sf 6m^2+25m+16 = 0$ .

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3 years ago

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Out of 18 people in a room, 2 have red hair. What is the probability that a person picked at random from the room does NOT have

Mariana [72]

Answer :

Total number of people in the room = 18

Number of people with red hair = 2

Number of people not with red hair = 18 - 2 = 16

Probability of picking a person who doesn't have red hair = $\sf\dfrac{Number\:of\:favourable\:outcomes}{Total\:outcomes}$

Probability = 16/18

Reduce the fraction with 2

Probability = 8/9

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2 years ago

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denis23 [38]

Answer:

Step-by-step explanation:

5.70 divided by 3

witch would be $1.90

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3 years ago

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How many solutions does an equation have when you isolate the variable and it equals a constant?

OLEGan [10]

1 solution is available when variable equals a constant.

Answer: Option B.

Explanation:

You will be able to determine if an equation has one solution (which is when one variable equals one number), or if it has no solution (the two sides of the equation are not equal to each other) or infinite solutions (the two sides of the equation are identical).

The ordered pair that is the solution of both equations is the solution of the system. A system of two linear equations can have one solution, an infinite number of solutions, or no solution. If a consistent system has exactly one solution, it is independent.

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3 years ago