Let the length of the long leg equal x. How can the length of the short leg 10 points

Which two shapes are equivalent fractions?

malfutka [58]

Answer:

B. 1 and 3

Step-by-step explanation:

7 0

3 years ago

This is the question

Sonja [21]

Answer:

The first option: As the x-values go to positive infinity, the function's values go to negative infinity.

Step-by-step explanation:

Let's focus on the right part of the graph. Notice that at x = 1, the line is on the negative y-axis. The same thing happens to when we locate x = 2, it still continues to go down approaching negative infinity.

5 0

3 years ago

Lagrange Multiplier Million Dollar question. Anybody please Use the method of Lagrange multipliers to find the max and min value

jekas [21]

We are given the equation: g(s,t) = t^2 e^s

Which is subject to the constraint: s^2 + t^2=3

The points (x,y) that will maximize g(s,t) will be the points that will satisfy the equation ∇f(x, y, z) = λ∇g(x, y, z), therefore:

2 t e^s = λ (2 t), so e^s = λ --> 1

t^2 e^s = λ (2 s) --> 2

s^2 + t^2 = 3 -->3

To solve this problem, note that λ cannot be zero by equation 1 since e^s can never be zero. Therefore plug in equation 1 to 2:

t^2 e^s = (e^s) (2 s)

t^2 = 2 s --> 4

Plug in equation 4 to 3:

s^2 + 2s = 3

By completing the square:

s^2 + 2s + 1 = 4

(s + 1)^2 = 4

s + 1 = ±2

s = -3, 1

Calculating for t using equation 4:

when s = -3

t^2 = 2(-3)

t = sqrt(-6)

Since t is imaginary, therefore s=-3 is not a solution

when s = 1

t^2 = 2(1)

t = sqrt(2) = ±1.414

Therefore the maxima and minima points are at:

(1, -1.414) and (1, 1.414)

g(1, -1.414)=(-1.414)^2 e^(1) = 5.434

g(1, -1.414)=( 1.414)^2 e^(1) = 5.434

5 0

3 years ago

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5

masya89 [10]

Answer:

$z= \frac{3.44-2.54}{0.45}=2$

$P(X>3.44) = P(Z>2) = 0.025$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the grade points avergae of a population, and for this case we know the following properties

Where $\mu=2.54$ and $\sigma=0.45$

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

So we can find the z score for the value of X=3.44 in order to see how many deviations above or belowe we are from the mean like this:

$z= \frac{3.44-2.54}{0.45}=2$

So the value of 3.44 is 2 deviations above from the mean, so then we know that the percentage between two deviations from the mean is 95% and on each tail we need to have (100-95)/2 = 2.5% , because the distribution is symmetrical, so based on this we can conclude that:

$P(X>3.44) = P(Z>2) = 0.025$

5 0

4 years ago

Help please. i really need this answer

VladimirAG [237]

Answer:

$\displaystyle y = 5x - 92\:or\:y + 12 = 5[x - 16]$

Step-by-step explanation:

−12 = 5[16] + b

80

$\displaystyle -92 = b \\ \\ y = 5x - 92$

To write this in Point-Slope Formula now, $\displaystyle y - y_1 = m[x - x_1],$ you simply plug the coordinate into the formula with their CORRECT SIGNS because all negative symbols give the OPPOSITE terms of what they really are:

$\displaystyle y + 12 = 5[x - 16]$

* Parallel lines have SIMILAR <em>RATE OF CHANGES</em> [<em>SLOPES</em>], so 5 remains the way it is.

I am joyous to assist you anytime.

5 0

3 years ago