Jordan wrote the following description: Three fewer than one-fourth of x is 12. Write an equation to represent the description.

A superhero is trying to leap over a tall building. The function f(x)=-16x^2+200x gives the superhero's height in feet as a func

Gemiola [76]

Answer:

Since $\bigtriangleup \geq 0$ , the superhero makes it over the building.

Step-by-step explanation:

The height is given by the following function:

$f(x) = -16x^{2} + 200x$

Will the superhero make it over the building?

We have to find if there is values of x for which f(x) = 612.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

If $\bigtriangleup < 0$ , the polynomial has no solutions.

In this question:

$f(x) = -16x^{2} + 200x$

$-16x^{2} + 200x = 612$

$16x^{2} - 200x + 612 = 0$

We have to find $\bigtriangleup$

We have that $a = 16, b = -200, c = 612$ . So

$\bigtriangleup = (-200)^{2} - 4*16*612 = 832$

Since $\bigtriangleup \geq 0$ , the superhero makes it over the building.

7 0

3 years ago

At the end of the day, Mr. Díaz drains the pool. The equation

Charra [1.4K]

Answer: 6 minutes.

Step-by-step explanation: You can use a graphing calculator to see the exact graph, but you're trying to figure out what value of x gives you a y of 0. -50 times 6 is 300, plus 300 equals 0.

7 0

3 years ago

There are eight volunteers at the election. The goal for the evening is to raise $952. If each volunteer raises the same amount,

Stells [14]

Each volunteer has to raise 119 dollars

4 0

3 years ago

Read 2 more answers

suppose X and Y are independent random variables, both with normal distributions. If X has a mean of 45 with a standard deviatio

djyliett [7]

Answer:

0.9772 = 97.72% probability that a randomly generated value of X is greater than a randomly generated value of Y

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question:

$\mu_X = 45, \sigma_X = 4, \mu_Y = 35, \sigma_Y = 3$

What is the probability that a randomly generated value of X is greater than a randomly generated value of Y

This means that the subtraction of X by Y has to be positive.

When we subtract two normal variables, the mean is the subtraction of their means, and the standard deviation is the square root of the sum of their variances. So

$\mu = \mu_X - \mu_Y = 45 - 35 = 0$