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3 years ago

Which number line is the correct solution to y z l?

Mathematics

1 answer:

Svet_ta [14]3 years ago

8 0

9514 1404 393

Answer:

Step-by-step explanation:

These state exam questions are checking that you know certain things about linear equations and inequalities, and how to solve and graph them. It is also checking that you now the meanings of certain math terms and can translate those meanings to relationships between numbers.

1. The "slope-intercept form" of a linear equation is ...

y = mx + b . . . . . . where m is the slope and b is the y-intercept

Note that the left side is "y =", eliminating the last two answer choices.

The problem tells you the slope is m = 2, and the y-intercept is b = 5. Then the equation is ...

y = 2x + 5 . . . . matches A

2. The picture is fuzzy, but we think it says y ≥ 1. The little bar in the comparison symbol means "or equal to", so you're looking for a graph that shows numbers greater than or equal to 1. The "or equal to" means the end dot on the graph will not be an open circle, but will be a solid dot. The "greater than" means the shaded part of the line is to the right of that dot.

graph C is the appropriate representation

3. The picture is fuzzy, but we think it says 126 < -7x. For this sort of inequality, you are expected to know that multiplying or dividing by a negative number will reverse the inequality symbol.

126 < -7x . . . . given

126/-7 > x . . . . divide both sides by the coefficient of x, -7

-18 > x . . . . . matches D

4. This is a vocabulary question. Angles are "complementary" when their sum is 90°. The sums of the given angle pairs are ...

A: 90° . . . . the correct answer choice

B: 100°

C: 180°

D: 185°

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Daily high temperatures in St. Louis for the last week were as follows: 95, 92, 93, 92, 95, 90, 90 (yesterday). a) The

hichkok12 [17]

Answer:

a) T = 91.7 degrees

b) T = 90 degrees

c) MAD = 1.9

d) MSE = 5.05

Step-by-step explanation:

Given:

- Daily high temperatures in St. Louis for the last week were as follows:

95, 92, 93, 92, 95, 90, 90

Find:

a) Forecast the high temperature today, using a 3-day moving average.

b) Forecast the high temperature today, using a 2-day moving average.

c) Calculate the mean absolute deviation based on a 2-day moving average, covering all days in which you can have a forecast and an actual temperature.

d) The mean squared error for the 2-day moving average

Solution:

- The set of 3 day moving average is as follows:

4. (95 + 92 + 93) ÷ 3 = 93.33⁰C

5. (92 + 93 + 92) ÷ 3 = 92.33⁰C

6. (93 + 92 + 95) ÷ 3 = 93.33⁰C

7. (92 + 95 + 90) ÷ 3 = 92.33⁰C

8. (95 + 90 + 90) ÷ 3 = 91.667⁰C

- Now use these points on excel sheet to forecast the temperature for today. The line of best fit is given:

T = 91.7 degrees

- The set of 2 day moving average is as follows:

3. (95 + 92) ÷ 2 = 93.5⁰C

4. (95 + 93) ÷ 2 = 92.5⁰C

5. (93 + 92) ÷ 2 = 92.5⁰C

6. (92 + 95) ÷ 2 = 93.5⁰C

7. (95 + 90) ÷ 2 = 92.5⁰C

8. (90 + 90) ÷ 2 = 90⁰C

- Now use these points on excel sheet to forecast the temperature for today. The line of best fit is given:

T = 90 degrees

Error Error^2

3. 93.5⁰C 0.5 0.25

4. 92.5⁰C 0.5 0.25

5. 92.5⁰C 2.5 6.25

6. 93.5⁰C 3.5 12.25

7. 92.5⁰C 2.5 6.25

8. 90⁰C

- The mean absolute deviation as follows:

MAD = Sum of all errors / 5

MAD = (0.5+0.5+2.5+3.5+2.5) / 5

MAD = 1.9

- The mean squared error deviation as follows:

MSE = Sum of all error^2 / 5

MSE = (0.25+0.25+6.25+12.25+6.25) / 5

MSE = 5.05

4 0

3 years ago

Graph a line with a slope of -3 that contains the points (4,-2)

Lera25 [3.4K]

Answer:

see below for a graph

Step-by-step explanation:

To draw a graph on a grid, locate the point (4, -2) and use the slope to find another point. One such point will be 1 to the left and up 3*, at (3, 1). With two points, you can draw the line through them to complete the graph.

For a graphing tool that requires an equation, the point-slope form of the equation can be used:

y -k = m(x -h) . . . . . a line of slope m through point (h, k)

For the given slope and point, the equation of the line is ...

y +2 = -3(x -4)

y = -3x +10

_____

* The slope is "rise" over "run". The slope of -3 means that a run of +1 will result in a rise of -3. The given point is already below the x-axis, so we don't really want to find more points farther down. In order to go up on a line with negative slope, we must choose a point to the left of the given one.