Simplify the algebraic expression: x(x + 3) + x(2x - 4) + 6
2 answers:
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Complete question is;
A researcher wants to see if a kelp extract helps prevent frost damage on tomato plants. One hundred tomato plants in individual containers are randomly assigned to two different groups. Plants in both groups are treated identically, except that the plants in group 1 are sprayed weekly with a kelp extract, while the plants in group 2 are not. After the first frost, 12 of the 50 plants in group 1 exhibited damage and 18 of the 50 plants in group 2 showed damage. Let p1 be the actual proportion of all tomato plants of this variety that would experience damage under the kelp treatment, and let p2 be the actual proportion of all tomato plants of this variety that would experience damage under the no-kelp treatment. Is there evidence of a decrease in the proportion of
tomatoes suffering frost damage for tomatoes sprayed with kelp extract? To determine
this, yo u test the hypotheses H0: p1 = p2, Ha: p1 < p2. The p - value of your test is
A) greater than 0.10.
B) between 0.05 and 0.10.
C) between 0.01 and 0.05.
D)between 0.001 and 0.01.
E) below 0.001.
Answer:
B) between 0.05 and 0.10.
Step-by-step explanation:
We are given;
Number of plants in group that exhibited damage = 12
Number of group 1 plants; n₁ = 50
Number of plants in group 2 that exhibited damage = 18
Number of group 2 plants; n₂ = 50
Proportion of plants in group 1 that exhibited damage; p₁^ = 12/50 = 0.24
Proportion of plants in group 2 that exhibited damage; p₂^ = 18/50 = 0.36
Pooled proportion; p¯ = (12 + 18)/(50 + 50) = 0.3
q¯ = 1 - p¯
q¯ = 1 - 0.3 = 0.7
Z-score will be;
z = ((p₁^ - p₂^) - 0)/√((p¯•q¯)×((1/n₁) + (1/n₂))
Plugging in the relevant values;
z = (0.24 - 0.36)/√((0.3 × 0.7) × ((1/50) + (1/50))
z = -0.12/0.092
z = -1.3
From z-distribution table attached, we have;
p-value = 0.0968
Correct answer is option B.
Answer:
The equation of the line is y = x + 2
Step-by-step explanation:
The form of the equation that passes through two points (x1, y1) and (x2, y2) is y = m x + b, where
- m is the slope of the line whose rule is
- b is the y-intercept, you can find it by substituting x, y in the equation by (x1, y1) OR (x2, y2)
Let us solve the question:
∵ The line passes through the points (-3, -2) and (3, 6)
∴ x1 = -3 and x2 = 3
∴ y1 = -2 and y2 = 6
→ Use the rule of m to find it
∵
→ Simplify it by dividing up and down by 2
∴ m =
→ Substitute its value in the form of the equation above
∴ y = x + b
→ To find b substitute x and y by x1 and y1
∴ -2 = (-3) + b
∴ -2 = -4 + b
→ Add 4 to both sides
∴ -2 + 4 = -4 + 4 + b
∴ 2 = b
→ Substitute it in the form of the equation
∴ y = x + 2
∴ The equation of the line is y = x + 2
<u>Answer-</u>
<em>The amount of water is the dependent value.</em>
<u>Solution-</u>
Plotting the graph from the given data points, it comes out to be a straight line with positive slope. So, both the variables i.e amount of rice and amount of water are in a linear relationship. They are directly proportional to each other.
As the amount of rice increases, the water needed to cook the rice also increases. Plotting a graph taking amount of rice in abscissa and amount of water in ordinate, a straight line was obtained.
Here, amount of rice is the independent variable and amount of water is dependent variable as it depends on the amount of rice.
