If f={(1, 2), (2, 3), (3,4),(5, 6), (6, 7). what is the range?

If the equation y = 1 3 x + 2 is changed to y = 3x + 2, what will be true about the graph of the equation? A) The graph will shi

MrRa [10]

Answer:

D.

Step-by-step explanation:

The number which multiplies x is the slope of the graph so 13x becoming 3x means the slope of the graph will change.

4 0

3 years ago

) dy 2x<br> ------ = ---------------<br> dx yx2 + y

larisa86 [58]

Step-by-step explanation:

$\dfrac{dy}{dx} = \dfrac{2x}{y(x^2 + 1)}$

Rearranging the terms, we get

$ydy = \dfrac{2xdx}{x^2 + 1}$

We then integrate the expression above to get

$\displaystyle \int ydy = \int \dfrac{2xdx}{x^2 + 1}$

$\displaystyle \frac{1}{2}y^2 = \ln |x^2 +1| + k$

or

$y = \sqrt{2\ln |x^2 + 1|} + k$

where I is the constant of integration.

6 0

2 years ago

Given that x-1 and x+2 are factors of f(x)=x³+px+q where p and q are integers, find p and q. Hence, find the remainder when x³+p

alexandr1967 [171]

Answer:

p = -3
q = 2
remainder = 4

Step-by-step explanation:

We want to find the constants 'a', 'p', and 'q' such that ...

(x -a)(x -1)(x +2) ≡ x³ +px +q

(x -a)(x² +x -2) ≡ x³ +px +q

x³ +x² -2x -ax² -ax +2a ≡ x³ +px +q

This gives rise to three equations:

1 -a = 0 . . . . coefficient of x²

-2 -a = p . . . coefficient of x

2a = q . . . . . constant

The first of these tells us a=1. Then, p=-3 and q=2.

The values of p and q are -3 and 2, respectively.

__

The remainder from division by (x+1) is the value of the cubic for x=-1. That value is ...

(-1)³ -3(-1) +2 = -1 +3 +2 = 4

The remainder from division by (x+1) is 4.

7 0

2 years ago

A distribution of values is normal with a mean of 60 and a standard deviation of 16. From this distribution, you are drawing sam

professor190 [17]

Answer:

The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .