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2 years ago

(x-2)(x+2)(x²+4)-(x²+3)(x²-3)+2022

Mathematics

1 answer:

torisob [31]2 years ago

3 0

The simplified form of the given expression is 2015

<h3>Simplifying expressions </h3>

The given expression is (x-2)(x+2)(x²+4)-(x²+3)(x²-3)+2022

The expression can be simplified as shown below

(x-2)(x+2)(x²+4) - (x²+3)(x²-3) + 2022

x(x+2)-2(x+2)(x²+4) - x²(x²-3) +3(x²-3) + 2022

(x²+2x-2x-4)(x²+4) - (x⁴-3x²+3x²-9) + 2022

(x²-4)(x²+4) - (x⁴-9) + 2022

x²(x²+4) -4(x²+4) - (x⁴-9) + 2022

(x⁴+4x²-4x²-16) - (x⁴-9) + 2022

(x⁴-16) - (x⁴-9) + 2022

x⁴ -16 -x⁴ +9 + 2022

x⁴ -x⁴ -16 +9 +2022

= 2015

Hence, the simplified expression is 2015

Learn more on Simplifying an expression here: brainly.com/question/723406

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In ACME PUBLISHING SWEEPSTAKES, the chance of winning a car is 1 in 1,000. What percent of tickets to ACME PUBLISHING SWEEPSTAKE

Yuri [45]

Answer:

0.1% of tickets to ACME PUBLISHING SWEEPSTAKES win a car

Step-by-step explanation:

Given :The chance of winning a car is 1 in 1,000.

To Find : What percent of tickets to ACME PUBLISHING SWEEPSTAKES win a car?

Solution:

The chance of winning a car is 1 in 1,000.

The percent of tickets to ACME PUBLISHING SWEEPSTAKES win a car:

= $\frac{1}{1000} \times 100$

= $\frac{1}{10}$

= $0.1\%$

Hence 0.1% of tickets to ACME PUBLISHING SWEEPSTAKES win a car.

8 0

3 years ago

Fowle Marketing Research Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean tim

sergejj [24]

Answer:

a) Null hypothesis: $\mu \leq 15$

Alternative hypothesis: $\mu > 15$

b) $t=\frac{17-15}{\frac{4}{\sqrt{35}}}=2.958$

c) $p_v =P(t_{34}>2.958)=0.0028$

d) 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, so we can conclude that the true mean is higher than 15 at 1% of signficance.

Step-by-step explanation:

Data given and notation

The sample mean is given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation is:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=17$ represent the sample mean

$s=4$ represent the sample standard deviation

$n=35$ sample size

$\mu_o =15$ 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)

Part a State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less or equal than 15, the system of hypothesis would be:

Null hypothesis: $\mu \leq 15$

Alternative hypothesis: $\mu > 15$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Part b Calculate the statistic

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

$t=\frac{17-15}{\frac{4}{\sqrt{35}}}=2.958$

Part c P-value

The degrees of freedom are given by:

$df = n-1= 35-1=34$

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

$p_v =P(t_{34}>2.958)=0.0028$

Part d Conclusion

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, so we can conclude that the true mean is higher than 15 at 1% of signficance.

7 0

3 years ago

Pearl's Biking Company manufactures and sells bikes. Each bike costs £40 to make, and the company's fixed costs are £5000. In ad

____ [38]

Answer:

R(x) =300·x - 2·x²

C(x) = £5000 + £40 × x

The break even points are 23.47 and 106.53 or 23 and 107 bikes

Step-by-step explanation:

Given that the price function P(x) = 300 -2·x

Cost per bike = £40

The revenue function R(x) is given by bike price × total number of bikes manufactured and sold

∴ R(x) = P(x)×x = (300 - 2·x)×x = 300·x - 2·x²

The company's cost function, C(x) is Fixed cost + cost to produce each bike × total number of bikes produced

∴ C(x) = £5000 + £40 × x

The break even point is given by the relation;

Total revenue - total cost = 0

That is, break even point is R(x) - C(x) = 0

300·x - 2·x² - (5000 + 40·x) = 0

-2·x²+260·x-5000 = 0 or 2·x²- 260·x + 5000 = 0

Factorizing, we have;

(x - (65 -5√69))(x - (65 +5√69))

Solving gives x = 23.47 or 106.53

Therefore, the break even points are 23.47 and 106.53.

That is the company is profitable when they produce less than 23 bikes or more than 107 bikes.

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3 years ago

(x+40)(x+40) show steps

pishuonlain [190]

(x + 40) * (x + 40) =

(x + 40)² =

x² + 80x + 1600

6 0

3 years ago

7/8 - 6/7. what is the answer.???

lesantik [10]

Answer:

0.0178 is the answer

6 0

2 years ago