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2 years ago

Please help me with this problem Evaluate (-½·3)³

Mathematics

1 answer:

-Dominant- [34]2 years ago

3 0

Answer: -27/8

Step-by-step explanation:

$\left(-\frac{1}{2}\cdot \:3\right)^3$

$\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=-a^n,\:\quad \mathrm{if\:}n\mathrm{\:is\:odd}$

$\left(-\frac{1}{2}\cdot \:3\right)^3=-\left(\frac{1}{2}\cdot \:3\right)^3$

$=-\left(\frac{1}{2}\cdot \:3\right)^3$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n$

$\left(\frac{1}{2}\cdot \:3\right)^3=\left(\frac{1}{2}\right)^3\cdot \:3^3$

$=-\left(\frac{1}{2}\right)^3\cdot \:3^3$

$=-\frac{1}{8}\cdot \:3^3$

$=-\frac{1}{8}\cdot \:27$

$=-\frac{27}{8}$

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Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday morning. She has asked them both in case

olga nikolaevna [1]

Answer:

(a) The probability that both Dave and Mike will show up is 0.25.

(b) The probability that at least one of them will show up is 0.75.

Step-by-step explanation:

Denote the events as follows:

<em>D</em> = Dave will show up.

<em>M</em> = Mike will show up.

Given:

$P(D^{c})=0.55\\P(M^{c})=0.45$

It is provided that the events of Dave of Mike showing up are independent of each other.

(a)

Compute the probability that both Dave and Mike will show up as follows:

$P(D\cap M)=P(D)\times P (M)\\=[1-P(D^{c})]\times [1-P(M^{c})]\\=[1-0.55]\times[1-0.45]\\=0.2475\\\approx0.25$

Thus, the probability that both Dave and Mike will show up is 0.25.

(b)

Compute the probability that at least one of them will show up as follows:

P (At least one of them will show up) = 1 - P (Neither will show up)

$=1-P(D^{c}\cup M^{c})\\=P(D\cup M)\\=P(D)+P(M)-P(D\cap M)\\=[1-P(D^{c})]+[1-P(M^{c})]-P(D\cap M)\\=[1-0.55]+[1-0.45]-0.25\\=0.75$

Thus, the probability that at least one of them will show up is 0.75.

(c)

Compute the probability that neither Dave nor Mike will show up as follows:

$P(D^{c}\cup M^{c})=1-P(D\cup M)\\=1-P(D)-P(M)+P(D\cap M)\\=1-[1-P(D^{c})]-[1-P(M^{c})]+P(D\cap M)\\=1-[1-0.55]-[1-0.45]+0.25\\=0.25$

Thus, the probability that neither Dave nor Mike will show up is 0.25.

6 0

3 years ago

Read 2 more answers

Please assist me in my time of need.

vaieri [72.5K]

Answer:

I shall assist thee.

Step-by-step explanation:

Being me, I would say the answer is A. or B. But i'd prolly go with A tbh.

And oofers on me if this ain't what you need.

4 0

3 years ago

If you run for 0.4 hours at 7 mph, how fast should you walk during the next 0.8 hours to have the average speed of 5 mph?

Fantom [35]

Answer:

4 mph

Step-by-step explanation:

The average speed of an object is given by the total distance covered by the time taken:

$v=\frac{d}{t}$

where

d is the total distance covered

t is the time taken

in the first part, the person runs for 0.4 hours at a speed of 7 mph, so the distance covered in the 1st part is

$d_1 = v_1 t_1 = (7)(0.4)=2.8 mi$

Then the distance covered in the second part is $d_2$ , so the total distance is

$d=2.8+d_2$ (1)

The total time elapsed is 0.4 hours (first part) + 0.8 hours (second part), so

$t=0.4+0.8=1.2 h$

So we can write the average speed as

$v=\frac{2.8+d_2}{1.2}$ (1)

We want the average speed to be 5 mph,

v = 5 mph

Therefore we can rearrange eq.(1) to find d2:

$d_2 = 1.2v-2.8 = (1.2)(5)-2.8=3.2 mi$

And therefore, the speed in the second part must be

$v_2=\frac{d_2}{t_2}=\frac{3.2}{0.8}=4 mph$

4 0

3 years ago

Please help FAST I need the answer along with you explaining the steps so I can get it thanks! I’ll give Brainlist also!

kupik [55]

Answer:

The equation of required line is: $\mathbf{5x-8y+34=0}$

Step-by-step explanation:

We need to write equation in the form Ax+By+C=0 of the line parallel to $5x-8y+12=0$ and through the point (-2,3)

First we need to find slope and y-intercept of the required line.

Using equation of line $5x-8y+12=0$ to find slope.

Since the given line and required lines are parallel there slope is same.

Writing equation in slope intercept form: $y=mx+b$ where m is slope.

$5x-8y+12=0 \\-8y=-5x-12\\\frac{-8y}{-8y}=\frac{-5x}{-8}-\frac{12}{-8}\\y=\frac{5}{8}x+\frac{3}{4}$

So, the slope m = 5/8

The slope of required line is $m=\frac{5}{8}$

Now finding y-intercept using slope $m=\frac{5}{8}$ and point(-2,3)

$y=mx+b\\3=\frac{5}{8}(-2)+b\\3=\frac{-5}{4}+b\\b=3+\frac{5}{4}\\b=\frac{3*4+5}{4}\\b=\frac{12+5}{4}\\b=\frac{17}{4}$

So, the equation of required line having slope $m=\frac{5}{8}$ and y-intercept $b=\frac{17}{4}$

$y=mx+b\\y=\frac{5}{8}x+\frac{17}{4}\\y=\frac{5x+17*2}{8}\\y= \frac{5x+34}{8} \\8y=5x+34\\5x-8y+34=0$

So, The equation of required line is: $\mathbf{5x-8y+34=0}$

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2 years ago

Determine whether y=4(7)^x represents an exponential function.

gtnhenbr [62]

B
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