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Cloud [144]
3 years ago
15

Given the equation 2x +4 = 4x -2, select the reasoning that correctly solves for x.

Mathematics
2 answers:
valkas [14]3 years ago
7 0

A is the correct answer.

  1. 2x+4=4x-2
  2. 2x+4+2=4x-2+2
  3. 2x+6=4x
  4. 2x-2x+6=4x-2x
  5. 6/2=2x/2
  6. 3=x

padilas [110]3 years ago
3 0
<span>The correct answer is A, as you add two to both sides, giving 2x +6=4x, then subtract 2x from both sides, giving 6=2x, and then divide both sides by 2, giving 3=x.</span>
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In one college, 67 students made the dean's list. If this was 33.5% of the student body, what was the total number of students i
poizon [28]

Answer:

Total number of students in the college = 200 student

Step-by-step explanation:

Given:

Number of student make dean's list = 67 student

Percentage of student make dean's list = 33.5% of all student

Find:

Total number of students in the college

Computation:

Total number of students in the college = Number of student make dean's list / Percentage of student make dean's list

Total number of students in the college = 67 / 33.5%

Total number of students in the college = 67 / 0.335

Total number of students in the college = 200 student

3 0
3 years ago
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Step-by-step explanation:

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2 years ago
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Solve for all values of x by factoring.<br> x^2-11x+10=0
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Answer:

x= 10, x=1

Step-by-step explanation:

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A researcher collected data on the hours of TV watched per day from a sample of five people of different ages. Here are the resu
frozen [14]

Answer:

1. The least squares regression is y = -0.1015·x + 6.51

2. The independent variable is b) age

Please see attached table

Step-by-step explanation:

The least squares regression formula is given as follows;

\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y}  \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}}

We have;

\bar x = 24

\bar y = 4

\Sigma (x_i - \bar x) (y_i - \bar y) = -79

\Sigma (x_i - \bar x)^2 = 778

\therefore \hat \beta =\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y}  \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}} = \frac{-79}{778} = -0.1015

The least squares regression is y = -0.1015·x + α

∴ α = y  -0.1015·x = 6 - (-0.1015 × 5) = 6.51

The least squares regression is thus;

y = -0.1015·x + 6.51

2. The independent variable is the age b)

3. Steps to create an ANOVA table with α = 0.05

The overall mean = (43  + 30  + 22  + 20  + 5  + 1  + 6  + 4  + 3  + 6 )/10 = 14

There are 2 different treatment = df_{treat} = 2 - 1 = 1

There are 10 different treatment measurement = df_{tot} = 10 - 1 = 9

df_{res} = 9 - 1 = 8

df_{treat} + df_{res} = df_{tot}

The estimated effects are;

\hat A_1 = 24 - 14 = 10

\hat A_2 = 4 - 14 = -10

SS_{treat} = 10^2 \times 5 + (-10)^2 \times 5 =1000

\sum_{i}\SS_{row}_i = \sum_{i}\sum_{j} (y_{ij} - \bar y)= [(1 - 4)^2 + (6 - 4)^2 + (4 - 4)^2 + (3 - 4)^2 + (6 - 4)^2] = 18

\sum_{i} S S_{row}_i = \sum_{i}\sum_{j} (y_{ij} - \bar y) ^2= [(43 - 24)^2 + (30 - 24)^2 + (22 - 24)^2 + (20 - 24)^2 + (5 - 24)^2] = 778

S S_{res} = \sum_{i} S S_{row}_i = 778 + 18 = 796

SS_{tot} = (43  - 14)² + (30  - 14)² + (22  - 14)² + (20  - 14)² + (5  - 14)² + (1 - 14)1² + (6  - 4 )² + (3  - 14)² + (6  - 14)² = 1796

MS_{treat} = \dfrac{SS_{treat} }{df_{treat} } = \dfrac{1000}{1} = 1000

MS_{res} = \dfrac{SS_{res} }{df_{res} } = \dfrac{796}{8} = 99.5

F- value is given by the relation;

F = \dfrac{MS_{treat} }{MS_{res} } = \frac{1000}{99.5} = 10.05

We then look for the critical values at degrees of freedom 1 and 8 at α = 0.05 on the F-distribution tables 5.3177

Hence; F = 10.05 > F_{1,8}^{Krit}(5\%) = 5.3177, we reject the null hypothesis.

7 0
3 years ago
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