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3 years ago

Which of the following statements best describes the graph of x + y = 4?

Mathematics

1 answer:

joja [24]3 years ago

5 0

Answer: The correct option is, It is a line joining the points whose x and y coordinates add up to 4.

Step-by-step explanation:

The given equation is, $x+y=4$

when we take x = 1 then

$1+y=4$

$y=3$

when we take x = 2 then

$2+y=4$

$y=2$

From this we conclude that the sum of 'x' and 'y' coordinates is always equal to 4.

Hence, the correct answer is, It is a line joining the points whose x and y coordinates add up to 4.

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Please help with these? thank you

Burka [1]

The answer is the second one; 15y^2–11y

5 0

3 years ago

a bookstore took in$ 167 on the sale of 5 copies of a new cookbook and 3 copies of a new novel the next day it took in $ 89 on t

PSYCHO15rus [73]

I am going to use C to represent cookbook and N to represent N. I find that easier to remember which is which.

Day 1: 5C + 3N = 167

Day 2: 3C + 1N = 89

We need to solve one of these equation for either the C or N. I always choose the easiest one! Day 2 looks like the one.

3C + 1N = 89 (I am doing to solve for N because we won't have a fraction)

1N=89-3C

N=89-3C

Now we take this solution for N and put it into our first equation.

5C + 3(89-3C) = 167 (We need to distribute)

5C + 267 - 9C = 167 (Use subtraction to move C values to the right and numbers to the left)

267-167 = 9C-5C

100 = 4C

25 = C $25 for the Cookbooks.

Now, we have to go back and solve for N by putting $25 in for C in the second equation.

N=89-3(25)

N=89-75

N=14 dollars for each novel.

Check by putting both back into the first equation:

5C + 3N = 167

5(25) + 3(14) = 167. It checks out!

3 0

3 years ago

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three op

Rashid [163]

Answer:

I will assume the equation is supposed to be f(x) = x^2 – 5x + 12 since it is said to be a quadratic equation.

Step-by-step explanation:

See attached graph.

The value of f(–10) = 82 False

f(-10) = (-10)^2 - 5*(-10) + 12

f(-10) = (100) +50 + 12

f(-10) = 162

The graph of the function is a parabola. True

The graph of the function opens down. False

The graph contains the point (20, –8). False

The graph contains the point (0, 0). False

8 0

2 years ago

Imagine an experiment having three conditions and 20 subjects within each condition. The mean and variances of each condition ar

xxTIMURxx [149]

Answer:

1. Mean square B= 5.32

2. Mean square E= 16.067

3. F= 0.33

4. p-value: 0.28

Step-by-step explanation:

Hello!

You have the information of 3 groups of people.

Group 1

n₁= 20

X[bar]₁= 3.2

S₁²= 14.3

Group 2

n₂= 20

X[bar]₂= 4.2

S₂²= 17.2

Group 3

n₃= 20

X[bar]₃= 7.6

S₃²= 16.7

1. To manually calculate the mean square between the groups you have to calculate the sum of square between conditions and divide it by the degrees of freedom.

Df B= k-1 = 3-1= 2

Sum Square B is:

∑ni(Ÿi - Ÿ..)²

Ÿi= sample mean of sample i ∀ i= 1,2,3

Ÿ..= general mean is the mean that results of all the groups together.

General mean:

Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ 3 = (3.2+4.2+7.6)/3 = 5

Sum Square B (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (3.2 - 5)² + (4.2 - 5)² + (7.6 - 5)²= 10.64

Mean square B= Sum Square B/Df B= 10.64/2= 5.32

2. The mean square error (MSE) is the estimation of the variance error (σ $_{e}^2$ → $S_{e} ^{2}$ ), you have to use the following formula:

Se²= (n₁-1)S₁² + -(n₂-1)S₂² + (n₃-1)S₃²

n₁+n₂+n₃-k

Se²= 19*14.3 + 19*17.2 + 19*16.7 = 915.8 = 16.067

20+20+20-3 57

DfE= N-k = 60-3= 57

3. To calculate the value of the statistic you have to divide the MSB by MSE

$F= \frac{Mean square B}{Mean square E} = \frac{5.32}{16.067} = 0.33$

4. P(F $_{2; 57}$ ≤ F) = P(F $_{2; 57}$ ≤ 0.33) = 0.28

I hope you have a SUPER day!

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3 years ago

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nika2105 [10]

Answer:

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3 years ago