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3 years ago

(a 3 - 2a + 5) - (4a 3 - 5a 2 + a - 2)

Mathematics

2 answers:

boyakko [2]3 years ago

8 0

Answer:

The simplified form is

$-3a^3+5a^2-3a+7$

Step-by-step explanation:

Given the expression

$(a^3-2a+5)-(4a^3-5a^2+a-2)$

we have to simplify the above expression.

$(a^3-2a+5)-(4a^3-5a^2+a-2)$

Step 1: Opening the brackets

$a^3-2a+5-4a^3+5a^2-a+2$

Step 2: Combining like terms

$(a^3-4a^3)+5a^2-(2a+a)+(5+2)$

$-3a^3+5a^2-3a+7$

which is required simplified form

rosijanka [135]3 years ago

5 0

(a^3 - 2a + 5) - (4a^3 - 5a^2 + a - 2)
=a^3 - 2a + 5 - 4a^3 + 5a^2 - a + 2
= -3a^3 + 5a^2 - 3a + 7

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You work in the HR department at a large franchise. you want to test whether you have set your employee monthly allowances corre

ra1l [238]

Answer:

1) Null hypothesis: $\mu \leq 500$

Alternative hypothesis: $\mu > 500$

$z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90$

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:

$z_{crit}= 2.33$

For this case we see that the calculated value is higher than the critical value

Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level

2) Since is a right tailed test the p value would be:

$p_v =P(z>5.90)=1.82x10^{-9}$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1

Step-by-step explanation:

Part 1

Data given

$\bar X=640$ represent the sample mean

$\sigma=150$ represent the population standard deviation

$n=40$ sample size

$\mu_o =500$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Step1:State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is higher than 500, the system of hypothesis would be:

Null hypothesis: $\mu \leq 500$

Alternative hypothesis: $\mu > 500$

Step 2: Calculate the statistic

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

We can replace in formula (1) the info given like this:

$z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90$

Step 3: Calculate the critical value

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:

$z_{crit}= 2.33$

Step 4: Compare the statistic with the critical value

For this case we see that the calculated value is higher than the critical value

Step 5: Decision

Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level

Part 2

P-value

Since is a right tailed test the p value would be:

$p_v =P(z>5.90)=1.82x10^{-9}$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1

7 0

3 years ago

PLEASE HELP!!!

vovangra [49]

Answer:

<em>Michael drove faster than Jordan.</em>

Step-by-step explanation:

<u>Speed</u>

The speed is the ratio between the distance d traveled by an object and the time t it took to move. In terms of a mathematical equation, it's expressed as:

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

Michael drove 210 miles in 3 and one-half hours. The parameters to calculate the speed are: d= 210 miles, t = 3.5 hours. The speed of Michael is:

$\displaystyle v_M=\frac{210}{3.5}=60\ mi/h$

Jordan drove 330 miles in 6 hours, thus his speed is:

$\displaystyle v_J=\frac{330}{6}=55\ mi/h$

It's clear that Michael drove faster than Jordan.

8 0

3 years ago

Use signed numbers to solve. A helicopter descended 1200 feet, rose 800 feet, and then descended 450 feet. What was the net gain

sergey [27]

The rise or an increase in altitude is represented by positive sign and a decend or decrease in altitude is represented by negative sign.

First the helicopter descended 1200 feet. So the change in altitude will be -1200 feet.

Then the helicopter rose by 800 feet. So the change in altitude will be 800 feet.

Finally the helicopter descended by 450 feet. So the change in altitude will be -450 feet.

The net change in altitude will be the sum of all the above 3 changes.
Change in altitude = -1200 + 800 - 450 = -850 feet

The negative sign indicates a descend i.e. loss in altitude. So the net change in altitude was a loss of 850 feet.

3 0

3 years ago

-3/4x>12 solve for x

Ad libitum [116K]

Answer:

$\Huge\boxed{\mathsf{\rightarrow X$

Step-by-step explanation:

$\Large\boxed{\mathsf{SUBJECT: MATH}}$

Isolate x on one side of the equation.

Find the value of x.

First, multiply -1 from both sides.

(-3/4x)(-1)<12(-1)

Solve.

12(-1)=-12

3/4x<-12

Next, multiply 4 from both sides.

4*3/4x<4(-12)

Solve.

Multiply the numbers from left to right.

4(-12)=-48

3x<-48

Then, divide by 3 from both sides.

3x/3<-48/3

Solve.

Divide the numbers from left to right.

-48/3=-16

X<-16

$\Large\boxed{\Rightarrow \mathsf{X$

The correct answer is x<-16.

6 0

3 years ago

I need an answer ASAP!!! Tyyyy

patriot [66]

Part A

x = amount of money she starts with

(4/9)x = cost of the dress

(5/9)x = amount of money leftover after buying the dress

note that 4/9 and 5/9 add to 1 to represent 100% of her money

(3/4)*(5/9)x = (15/36)x = (5/12)x = amount spent on shoes

We see that she spent 5/12 of her original amount of money on shoes.

-----------------------

We can look at a more concrete example if the previous section does not make sense.

Let's multiply the denominators 9 and 4 to get 9*4 = 36. Doing this trick will mean that the later steps won't involve decimal values.

Let's say she starts off with $36

Multiply that with 4/9 to get (4/9)*36 = 16. So in this hypothetical situation, the dress costs $16 and she's left with 36-16 = 20 dollars.

Multiply that 20 by 3/4 to get (3/4)*20 = 15

In this situation, the shoes cost $15

We'll then divide the cost of the shoes (15) over the original amount of money she started with (36)

15/36 = (3*5)/(3*12) = 5/12

-----------------------

<h3>Answer: 5/12</h3>

=======================================================

Part B

From the first section in part A, we found that:

(4/9)x = amount of money spent on the dress
(5/12)x = amount of money spent on shoes

Add those two expressions

(4/9)x + (5/12)x = (16/36)x + (15/36)x = (31/36)x

This indicates that buying the dress and shoes will cost (31/36)x dollars, where x is the original amount of money Jing has to start with.

The amount left over is (5/36)x because 5/36 adds with 31/36 to get 1.

Take 1/3 of this to get:

(1/3)*(5/36)x = (5/108)x

Then set this equal to 18 and solve for x

(5/108)x = 18

5x = 18*108

5x = 1944

x = 1944/5

x = 388.80

--------------------

Let's check the answer

If she starts with 388.80 dollars, then the dress costs (4/9)*388.80 = 172.80

She's left with 388.80 - 172.80 = 216 dollars after buying the dress.

She then spends the remaining 3/4 of that on shoes. So (3/4)*216 = 162 dollars is spent on the shoes.

Jing now has 216 - 162 = 54 dollars left over.

1/3 of which is spent on the shoe bag, meaning it costs (1/3)*54 = 18 dollars

This confirms our answer.

--------------------

<h3>Answer: $388.80</h3>

8 0

2 years ago