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2 years ago

The lines graphed below are perpendicular. The slope of the red line is -1/3. What is the slope of the green line?

Mathematics

1 answer:

Serggg [28]2 years ago

7 0

Answer:

The slope of the green line is 3.

Step-by-step explanation:

<em><u>Definition: </u></em>If the two lines are said to be perpendicular, than the multiplication of their slope is -1.

In other words, the slope of the perpendicular line is the negative reciprocal of the given slope of the line.

Here we are slope of the red line, which is -1/3

Let's take it as "m1"

Let's take "m2" the slope of the green line.

By the above definition,

$m_1 *m_2 = -1$

Given: $m_1 = -\frac{1}{3}$

Now plug m1 value in the above statement, we get

$-\frac{1}{3} *m_2 = -1$

Multiply both sides by reciprocal of -1/3. The reciprocal of -1/3 = -3

$-3*-\frac{1}{3} *m_2 = -3*-1$

$m_2 = 3$

Therefore, the slope of the green line is 3.

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From 2000-2003, students were tested by the state in four major subject areas of math, science, English and social studies. The

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No way to tell . . . . . we can't see the chart below.
It must be WAY down there where the sun don't shine.

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1 year ago

Two rectangular properties share a common side. Lot A is 33 feet wide and 42 feet long.

s344n2d4d5 [400]

Answer:

The width of lot B is 11 feet, so option A is correct.

Step-by-step explanation:

Given:

Two rectangular properties share a common side.

Lot A is 33 feet wide and 42 feet long.

The combined area of the lots = 1,848 square feet.

To find:

How many feet wide is Lot B?

Solution:

we know that, area of a rectangle is length x breadth

Then area of lot A = 33 x 42 = 1386 square feet.

And area of lot B = width x 42

Now, we are given that, total area = 1848

area of lot A + area of lot B = 1848

1386 + width x 42 = 1848

width x 42 = 1848 – 1386

width x 42 = 462

$width =\frac{42}{462}$

width = 11

Hence, the width of lot B is 11 feet, so option A is correct.

7 0

2 years ago

Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order b

Firdavs [7]

Answer:

Ordering a soft drink is independent of ordering a square pizza.

Step-by-step explanation:

20% more customers order a soft drink than pizza, therefore they cannot be intertwined.

Given: P(A)=0.5 & P(B)=.7

P(A∩B) = P(A) × P(B)

= 0.5 × .7

= 0.35

P(A∪B) = P(A) + P(B) - P(A∩B)

= 0.5 + .7 - 0.35

= 0.85

P(AΔB) = P(A) + P(B) - 2P(A∩B)

= 0.5 + .7 - 2×0.35

= 0.5

P(A') = 1 - P(A)

= 1 - 0.5

= 0.5

P(B') = 1 - P(B)

= 1 - .7

= 0.3

P((A∪B)') = 1 - P(A∪B)

= 1 - 0.85

= 0.15

7 0

1 year ago

The net of a triangular prism is shown below. What is the surface area of the prism? A. 128 cm^2 B. 152 cm^2 C. 176 cm^2 D. 304

shtirl [24]

Answer:

B. 152 cm²

Step-by-step explanation:

To find the surface area using a net, do this:

Take apart the figure. We see that there are three rectangles and two triangles. Find the area of each ( $A=l*w$ ) and then add the values together:

The first rectangle on the left is the same as the one on the right.

$5*8=40$

Two measures are 40 cm².

The middle rectangle is:

$6*8=48$

48 cm²

The formula for the area of a triangle is $A=\frac{1}{2}*b*h$ :

$A=\frac{1}{2}*6*4\\\\A=\frac{1*6*4}{2}\\\\A=\frac{24}{2}\\\\ A=12$

The area of the two triangles is 12 cm².

Now add the values:

$40+40+48+12+12=152$

The area of the figure is 152 cm².

:Done

4 0

2 years ago

The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for adm

Nat2105 [25]

Answer:

a) 16% of GMAT scores are 647 or higher.

b) 2.5% of GMAT scores are 647 or higher.

c) 34% of GMAT scores are between 447 and 547.

d) 81.5% of GMAT scores are between 347 and 647.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 547

Standard deviation = 100

a. What percentage of GMAT scores are 647 or higher?

The Empirical rule states that 68% of the scores are within 1 standard deviation of the mean, that is, from 547 - 100 = 447 to 547 + 100 = 647. So 32% of the scores are outside the interval. Since the distribution is symmetric, 16% of them are lower than 447 and 16% of them are higher than 647.

16% of GMAT scores are 647 or higher.

b. What percentage of GMAT scores are 747 or higher (to 1 decimal)?

The Empirical rule states that 95% of the scores are within 2 standard deviations of the mean, that is, from 547 - 2*347 = 347 to 547 + 2*100 = 747. So 5% of the scores are outside the interval. Since the distribution is symmetric, 2.5% of them are lower than 347 and 2.5% of them are higher than 757

2.5% of GMAT scores are 647 or higher.

c. What percentage of GMAT scores are between 447 and 547?

447 is one standard deviation below the mean. The Empirical rule states that 68% of the scores are within 1 standard deviation of the mean, and since the distribution is symmetric, 34% are within one standard deviation below the mean and the mean, and 34% are within the mean and one standard deviation above the mean.

547 is the mean

447 is one standard deviation below the mean

So 34% of GMAT scores are between 447 and 547.

d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)?

The easist way is adding the percentage of scores from 347 to the mean(547) and the mean to 647.

Between 347 and 547

347 is two standard deviations below the mean. The Empirical rule states that 95% of the scores are within 2 standard deviations of the mean, and since the distribution is symmetric, 47.5% are within two standard deviation below the mean and the mean, and 47.5% are within the mean and two standard deviations above the mean.

So 47.5% of the scores are between 347 and 547

Between 547 and 647

447 is one standard deviation above the mean. The Empirical rule states that 68% of the scores are within 1 standard deviation of the mean, and since the distribution is symmetric, 34% are within one standard deviation below the mean and the mean, and 34% are within the mean and one standard deviation above the mean.

So 34% of the scores are between 547 and 647.

Between 347 and 647

47.5 + 34 = 81.5% of GMAT scores are between 347 and 647.

7 0

2 years ago