Find x3 − 2y2 − 3x3 + z4 if x = 3, y = 5, and z = −3.

You need to put your reindeer, Lancer, Prancer, Gloopin, and Bloopin, in a single-file line to pull your sleigh. However, Prance

marysya [2.9K]

Answer:

P43=4!(4–3)!=241=24

Step-by-step explanation:

There are four choices you can make for the lead reindeer. For each possible choice, there are then three remaining you can choose to fly second, making 4×3=12 choices for the lead pair. For each possible choice there are two remaining reindeer to take up the back position, making 12×2=24 choices for the team of three.

This type of problem is called a permutation problem, and we write Pnr for the number of ways of choosing r items from n possibilities when the order of the items matters. In this case we are choosing 3 reindeer from 4 possibilities, and the order they appear in the flying line does matter, so the answer we want is P43. The general formula is Pnr=n!(n−r)!. For the answer we are looking for we therefore have:

P43=4!(4–3)!=241=24

8 0

3 years ago

Read 2 more answers

What is the equation of (4,10),(6,11) in standard form?

SIZIF [17.4K]

ANSWER

The standard form is:

$x - 2y = - 16$

EXPLANATION

The given line passes through (4,10)and (6,11).

The slope of this line is

$m = \frac{11 - 10}{6 - 4}$

$m = \frac{1}{2}$

The equation is given by the formula,

$y-y_1=m(x-x_1)$

We plug in the first point and the slope to get.

$y-10= \frac{1}{2} (x-4)$

$2y - 20 = x - 4$

$x - 2y = - 20 + 4$

$x - 2y = - 16$

The standard form is

$x - 2y = - 16$

7 0

3 years ago

Barbara made a bad investment. Rather than earning interest, her money is decreasing in value by 11% each week! After just one w

pochemuha

Answer: She started with $160.

It will take 6 weeks before she has less than half of what she originally invested.

Step-by-step explanation:

If her money is decreasing in value by 11% each week, it means that the rate at which it is decreasing is exponential.

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the value of the investment after t weeks.

t represents the number of weeks.

P represents the initial value of the investment.

r represents rate of depreciation.

From the information given,

A = $142.40

r = 11% = 11/100 = 0.11

t = 1

Therefore

142.40 = P(1 - 0.11)^1

142.40 = P(0.89)

P = 142.4/0.89

P = 160

For her to have half of what she invested originally, then

80 = 160(0.89)^t

80/160 = (0.89)^t

0.5 = (0.89)^t

Taking log of both sides to base 10

Log 0.5 = log0.89^t = tlog0.89

- 0.3010 = - 0.051t

t = - 0.3010/- 0.051

t = 5.9

Approximately 6 weeks

5 0

3 years ago

Which statement is true about the quadratic equation 8x2 – 5x + 3 = 0?

Artyom0805 [142]

Answer:

c. the leading coefficient is 8

Step-by-step explanation:

4 0

3 years ago

You design a new app for cell phones. Your revenue for x downloads is given by f(x) = 3x Your profit

Snowcat [4.5K]

Answer:

p = 2.7x - 20

p(90) = $223

Step-by-step explanation:

revenue → f(x) = 3x ,where x is the number of downloads.

the statement “Your profit p is $20 less than 90% of the revenue for x downloads”

means

$p=90\% f\left( x\right) -20$

means

$p=\frac{90}{100} \times f\left( x\right) -20$

means

$p=\frac{9}{10} \times (3x) -20$

means

$p=\frac{9}{10} \times (3x) -20$

means

$p=2.7x -20$

………………………………

the profit for 90 downloads :

= p(90)

= 2.7×(90) - 20

= $223

5 0

2 years ago