Answer:
8 (see work)
14. 2x^2 -4x^2 +3
Step-by-step explanation:
There's attached work for explanation
Answer:
C) 13/4
Step-by-step explanation:
The slope can easily be identified if put into y=mx+b. The equation given to you is not in that format, however, we can rearrange a few variables to make it so.
As a reminder, y=mx+b, m is the slope and b is the y-intercept.
<u>Convert into y=mx+b form</u>
<u />
<u />
Now, as you can see, 13/4 is in place of m, which means this is the slope.
The answer is 450 <span>Bananas </span> don't now is that helps but
Answer:
1. 64.0
2. 88°
Step-by-step explanation:
1. By the cosine rule,
![MN^2=NL^2+ML^2-2ML\cdot NL\cdot \cos\angle L,\\ \\MN^2=36^+47^2-2\cdot 36\cdot 47\cdot \cos 100^{\circ},\\ \\MN^2=1296+2209-3384\cos100^{\circ}\approx 4092.625433,\\ \\MN\approx 63.97\approx 64.0.](https://tex.z-dn.net/?f=MN%5E2%3DNL%5E2%2BML%5E2-2ML%5Ccdot%20NL%5Ccdot%20%5Ccos%5Cangle%20L%2C%5C%5C%20%20%5C%5CMN%5E2%3D36%5E%2B47%5E2-2%5Ccdot%2036%5Ccdot%2047%5Ccdot%20%5Ccos%20100%5E%7B%5Ccirc%7D%2C%5C%5C%20%5C%5CMN%5E2%3D1296%2B2209-3384%5Ccos100%5E%7B%5Ccirc%7D%5Capprox%204092.625433%2C%5C%5C%20%5C%5CMN%5Capprox%2063.97%5Capprox%2064.0.)
2. Use the cosine rule,
![UV^2=UT^2+VT^2-2UT\cdot VT\cdot \angle T,\\ \\8.1^2=4.2^2+7.1^2-2\cdot 4.2\cdot 7.1\cdot \cos \angle T,\\ \\65.61=17.64+50.41-59.64\cos \angle T,\\ \\\cos \angle T=\dfrac{65.61-17.64-50.41}{-59.64}=\dfrac{2.44}{59.64}\approx 0.0409,\\ \\\angle T\approx 88^{\circ}.](https://tex.z-dn.net/?f=UV%5E2%3DUT%5E2%2BVT%5E2-2UT%5Ccdot%20VT%5Ccdot%20%5Cangle%20T%2C%5C%5C%20%5C%5C8.1%5E2%3D4.2%5E2%2B7.1%5E2-2%5Ccdot%204.2%5Ccdot%207.1%5Ccdot%20%5Ccos%20%5Cangle%20T%2C%5C%5C%20%5C%5C65.61%3D17.64%2B50.41-59.64%5Ccos%20%5Cangle%20T%2C%5C%5C%20%5C%5C%5Ccos%20%5Cangle%20T%3D%5Cdfrac%7B65.61-17.64-50.41%7D%7B-59.64%7D%3D%5Cdfrac%7B2.44%7D%7B59.64%7D%5Capprox%200.0409%2C%5C%5C%20%5C%5C%5Cangle%20T%5Capprox%2088%5E%7B%5Ccirc%7D.)
Answer:
Probability that at least 490 do not result in birth defects = 0.1076
Step-by-step explanation:
Given - The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count the number not resulting in a defect. Assume the births are independent.
To find - If 500 births were observed rather than only 5, what is the approximate probability that at least 490 do not result in birth defects
Proof -
Given that,
P(birth that result in a birth defect) = 1/33
P(birth that not result in a birth defect) = 1 - 1/33 = 32/33
Now,
Given that, n = 500
X = Number of birth that does not result in birth defects
Now,
P(X ≥ 490) =
=
+ .......+
= 0.04541 + ......+0.0000002079
= 0.1076
⇒Probability that at least 490 do not result in birth defects = 0.1076