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mojhsa [17]
3 years ago
8

In the xy-plane, the line x + y=k, where k is a constant, is tangent to the graph of y=x^2+3x+1. What is the value of k?

Mathematics
1 answer:
Talja [164]3 years ago
4 0
Slope of tangent line = dy/dx = 2x+3
k is y_intercept of tangent line

2x+3 = -1
x = -2
y = (-2)^2+3(-2)+1 = -1

tangent line passes through point (-2,-1)

k = x+y

k = -2 -1

k = -3

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The standard IQ test has a mean of 97 and a standard deviation of 17. We want to be
densk [106]

Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97.  But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,

μ = 97

Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions.  This means the standard deviation of the average x is

σ = 17/√n

We want to be 95% certain

97 - 5 ≤ x ≤ 97 + 5

By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that

μ - 2σ ≤ x ≤ μ + 2σ

Comparing to what we want, that's means we have to solve

2σ = 5

2 (17/√n) = 5

√n = 2 (17/5)

n = (34/5)² = 46.24

We better round up.

Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean

6 0
3 years ago
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ser-zykov [4K]
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3 0
2 years ago
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3 0
2 years ago
Solve the unknown angle measure?<br><br>Help Any1 ASAP! Will Mark Brainliest!
zlopas [31]

Answer:

X=40°

X=30°

X=50°

Step-by-step explanation:

Let our unknown angles be denoted by X

Part I

We are given the sum of the angles as 70°, the known as 30° and the unknown as X;

To find X, we subtract the known angle from the sum as:

X=70°-30°=40°

Hence X= 40°

Part II

We are given the sum of the angles as 70°, the known as 40° and the unknown as X;

To find X, we subtract the known angle from the sum as:

X=70°-40°=30°

Hence X= 30°

Part III

We are given the sum of the angles as 80°, the known as 30° and the unknown as X;

To find X, we subtract the known angle from the sum as:

X=80°-30°=50°

Hence X= 50°

3 0
3 years ago
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