Water has a density of 1.0 g/cm3. What is the mass of 10.0 cm3 of water?
2 answers:
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The given line is y = x - 4, and the given point is (-4, 2).
The slope of the given line is 1, and its y-intercept is (0, -4).
Part a.
The slope of a line parallel to the given line is 1.
Part b.
Let the equation of a line parallel to the given line be
y = x + c
Let (x,y) be a point on a parallel line which passes through (-4,2).
Then, in point-slope form,
(y - 2)/(x + 4) = 1
That is,
y - 2 = x + 4
y = x + 6
If x = 0, then
y - 2 = 0 + 4
y - 2 = 4
y = 6
Therefore the point (0, 6) is one of many points that lies on this line.
Part c.
The slope of a line perpendicular to the given line is -1.
The product of the slopes of perpendicular lines is -1.
Let (x,y) be a point on the perpendicular line which passes through (-4,2).
In point-slope form, its equation is
(y - 2)/(x + 4) = -1
That is,
y - 2 = -x - 4
y = -x - 2
Wneh x = 0, then y = -2.
A point on the perpendicular line that passes through (-4,2) is (0, -2).
Answers:
1. The slope is 1.
2. The point (0, 6) falls on the parallel line passing through (-4, 2).
3. The slope of a perpendicular line is -1.
4. The point (0, -2) falls on the perpendicular line passing through (-4, 2).
The slope of the given line is 1, and its y-intercept is (0, -4).
Part a.
The slope of a line parallel to the given line is 1.
Part b.
Let the equation of a line parallel to the given line be
y = x + c
Let (x,y) be a point on a parallel line which passes through (-4,2).
Then, in point-slope form,
(y - 2)/(x + 4) = 1
That is,
y - 2 = x + 4
y = x + 6
If x = 0, then
y - 2 = 0 + 4
y - 2 = 4
y = 6
Therefore the point (0, 6) is one of many points that lies on this line.
Part c.
The slope of a line perpendicular to the given line is -1.
The product of the slopes of perpendicular lines is -1.
Let (x,y) be a point on the perpendicular line which passes through (-4,2).
In point-slope form, its equation is
(y - 2)/(x + 4) = -1
That is,
y - 2 = -x - 4
y = -x - 2
Wneh x = 0, then y = -2.
A point on the perpendicular line that passes through (-4,2) is (0, -2).
Answers:
1. The slope is 1.
2. The point (0, 6) falls on the parallel line passing through (-4, 2).
3. The slope of a perpendicular line is -1.
4. The point (0, -2) falls on the perpendicular line passing through (-4, 2).
Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.5 inches. a baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less than 2.5 inches. the heights (in inches) of 20 randomly selected players are shown in the table.
72 74 71 72 76
70 77 75 72 72
77 72 75 70 73
74 75 73 74 74
What are the correct hypotheses for this test?
The null hypothesis is H₀?: ____ 2.5
The alternative hypothesis is H₁?: ____ 2.5
Calculate the value of the test statistic.
x² = _____ (Round to three decimal places)
Answer:
Null hypothesis, H₀: σ = 2.5
Alternative hypothesis, Hₐ: μ<2.5
Test statistic = 12.920
Step-by-step explanation:
Given Data shows that:
men between the ages of 20 and 29 in a general population have a mean height of 69.3 inches, with a standard deviation of 2.5 inches
We consider a random sample of 20 selected baseball players.
Therefore;
The Null and Alternative hypothesis are as follows:
The Null hypothesis is the standard deviation of the heights of major league baseball players is not less than 2.5 inches.
Null hypothesis, H₀: σ = 2.5
On the other hand: The Alternative hypothesis is the standard deviation of the heights of major league baseball players is less than 2.5 inches.
Alternative hypothesis, Hₐ: μ<2.5
The Mean Calculation is:
The sample standard deviation is:
The test statistics is now determined as :
Answer:
311 students prefer sushi
Step-by-step explanation:
Let
x------> the number of students who prefer pizza
y -----> the number of students who prefer sushi
we know that
-----> equation A
-----> equation B
Substitute the equation B in equation A and solve for y