Answer:
17) A(-1,1) B(-1,4) C(5,1)
18) (From origin moving rightwards)
A(0,0) B(a, 0) C(a,a) D(0,a)
Step-by-step explanation:
17) You just count the steps, how many steps left, right, up, or down
18) The first point is at the origin, so 0,0
The second point that lies on the x axis is (a,0) as it is a distance from the origin, 0 because it's on the x-axis.
The third point is (a,a) because it is a distance to the right of the origin AND a distance upwards from the x axis.
The fourth point (0,a) because it is on the vertical line (0) and is a distance above the origin.
Answer:
a) 658008 samples
b) 274050 samples
c) 515502 samples
Step-by-step explanation:
a) How many ways sample of 5 each can be selected from 40 is just a combination problem since the order of selection isn't important.
So, the number of samples = ⁴⁰C₅ = 658008 samples
b) How many samples of 5 contain exactly one nonconforming chip?
There are 10 nonconforming chips in the batch, and 1 nonconforming chip for the sample of 5 be picked from ten in the following number of ways
¹⁰C₁ = 10 ways
then the remaining 4 conforming chips in a sample of 5 can be picked from the remaining 30 total conforming chips in the following number of ways
³⁰C₄ = 27405 ways
So, total number of samples containing exactly 1 nonconforming chip in a sample of 5 = 10 × 27405 = 274050 samples
c) How many samples of 5 contain at least one nonconforming chip?
The number of samples of 5 that contain at least one nonconforming chip = (Total number of samples) - (Number of samples with no nonconforming chip in them)
Number of samples with no nonconforming chip in them = ³⁰C₅ = 142506 samples
Total number of samples = 658008
The number of samples of 5 that contain at least one nonconforming chip = 658008 - 142506 = 515502 samples
Answer:
Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.
Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
- c = 16 miles
- b = 8 miles
- a = 12 miles
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
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Therefore, the angle between their paths is <em>100.8°</em>
Answer:
The number is 92
Step-by-step explanation:
Let x equal the number
It is tripled
3x
Then it is tripled again
3(3x)
That equals 828
3(3x) = 828
9x =828
Divide each side by 9
9x/9 =828/9
x =92
