How much change will stacy get if she buys two cds and two books and gives the clerk two $20 bills?

Find the max/min value of f(x) = 2x2 + 3x - 5

Lelechka [254]

Answer:

The minimum value is $(-\frac{3}{4},-\frac{49}{8})$ or $(-0.75,-6.125)$

Step-by-step explanation:

we have

$f(x)=2x^{2}+3x-5$

This is the equation a vertical parabola open upward

The vertex represent a minimum

The general equation in vertex form is

$f(x)=a(x-h)^2+k$

where

(h,k) is the vertex

Convert the given function in vertex form

$f(x)=2x^{2}+3x-5$

Factor 2

$f(x)=2(x^{2}+\frac{3}{2}x)-5$

Complete the square

$f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-5-\frac{9}{8}$

$f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-\frac{49}{8}$

Rewrite as perfect squares

$f(x)=2(x+\frac{3}{4})^{2}-\frac{49}{8}$

The vertex is the point $(-\frac{3}{4},-\frac{49}{8})$

8 0

3 years ago

Let X equal the number of flips of a fair coin that are required to observe

Nataliya [291]

Answer:

(a) I attached a photo with the diagram.

(b) $f(x) = \big( \frac{1}{2} \big)^{x-1}$

(c) 1/4

(d) 4

(e) $k^2/2$

Step-by-step explanation:

(a) I attached a photo with the diagram.

(b) The easiest way to think about this part is in terms of combinatorics. Think about it like this.

To begin with, look at the three each level of the three represents a possible outcome of throwing the coin n-times. If you throw the coin 3 times at the end in total there are 8 possible outcomes. But The favorable outcomes are just 2.

1 - Your first outcome is HEADS and all the others are different except the last one.

2 - Your first outcome is TAILS and all the others are different except the last one.

Therefore the probability of the event is

$f(x) = P(X=x) = \frac{2}{2^x} = \frac{1}{2^{x-1}} = \big( \frac{1}{2} \big)^{x-1}$

(c)

P(X = 0) = 0 because it is not possible to have two consecutive tails or heads.

$E(X > 4) = 1 - P(X \leq 3) = 1 - ( P(X = 0 ) + P(X = 1) + P(X = 2) + P(X = 3))\\= 1 - ( \frac{1}{2} + \frac{1}{4} ) = \frac{1}{4}$

(d)

Remember that this is a geometric distribution therefore

$E[X] = p/(1-p)$ , in this case $p = 1/2$ so $E[X] = 1$ and

$E[X+1]^2 = ( E[X] +1 )^2 = (1+1)^2 = 2^2 = 4$

Also

(e)

This is a geometric distribution so its variance is

$Var(X) = \frac{1-p}{p^2} = 1/2 / 1/4 = 1/2$

And using properties of variance

$Var(kX - k ) = Var(kX) = k^2 var(X) = k^2 /2$

3 0

4 years ago

Plz Help ASAP!!! Will mark BRAINLIEST!!

Solnce55 [7]

Answer:5

Step-by-step explanation:

8 0

4 years ago

What is the square root of 450

RUDIKE [14]

Answer:

$15\sqrt{2}$ or 21.2132

Step-by-step explanation:

$\sqrt{450}$

$\sqrt{15^{2} }$ <em> </em>(root of a product is equal to the product of the roots of each factor)

$\sqrt{15^{2} } \sqrt{2}$ (simplify)

$15\sqrt{2}$ or ≈ 21.2132

4 0

4 years ago

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Write all the properties for a kite

Andrew [12]

Answer:

Kite properties include (1) two pairs of consecutive, congruent sides, (2) congruent non-vertex angles and (3) perpendicular diagonals. Other important polygon properties to be familiar with include trapezoid properties, parallelogram properties, rhombus properties, and rectangle and square properties.

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers