What is the mode for the following numbers 67 76 67 76 67 23 32 23 32

pishuonlain [190]

Answer:

Step-by-step explanation:

Move 729 to the left side of the equation by subtracting it from both sides. x 3 − 729 = 0 Factor the left side of the equation. Rewrite 729 as 9

3

. x

3

−

9

3

=

0

. Since both terms are perfect cubes, factor using the difference of cubes formula, a

3

−

b

3

=

(

a

−

b

)

(

a

2+ab+b2). Where a

=x and b=9. (x−9)(x2+x⋅9+92)=0

. Simplify. Move 9 to the left of x

. (x−9)(x2+9x+92)=0. Raise 9 to the power of 2

. (x

−9

)(

x

2

+

9

x

+81

)=0

. Set x

−9 equal to 0 and solve for x. Set the factor equal to 0. x−

9=

0. Add 9 to both sides of the equation. x=9

. Set x2+

9

x

+

81 equal to 0 and solve for x

. Set the factor equal to 0

. x2+9x+81=0. Use the quadratic formula to find the solutions. −b±√b2−4(ac) 2a. Substitute the values a=1, b=9, and c=81 into the quadratic formula and solve for x. −9±√92−4⋅ (1⋅81

) 2⋅

1 Simplify. Simplify the numerator. Raise 9 to the power of 2. x=−9±√81−4⋅(1⋅81) 2⋅1. Multiply

81

by

1

.

x

=

−

9

±

√

81

−

4

⋅

81

2

⋅

1

Multiply

−

4

by

81

.

x

=

−

9

±

√

81

−

324

2

⋅

1

Subtract

324

from

81

.

x

=

−

9

±

√

−

243

2

⋅

1

Rewrite

−

243

as

−

1

(

243

)

.

x

=

−

9

±

√

−

1

⋅

243

2

⋅

1

Rewrite

√

−

1

(

243

)

as

√

−

1

⋅

√

243

.

x

=

−

9

±

√

−

1

⋅

√

243

2

⋅

1

Rewrite

√

−

1

as

i

.

x

=

−

9

±

i

⋅

√

243

2

⋅

1

Rewrite

243

as

9

2

⋅

3

.

Tap for fewer steps...

Factor

81

out of

243

.

x

=

−

9

±

i

⋅

√

81

(

3

)

2

⋅

1

Rewrite

81

as

9

2

.

x

=

−

9

±

i

⋅

√

9

2

⋅

3

2

⋅

1

Pull terms out from under the radical.

x

=

−

9

±

i

⋅

(

9

√

3

)

2

⋅

1

Move

9

to the left of

i

.

x

=

−

9

±

9

i

√

3

2

⋅

1

Multiply

2

by

1

.

x

=

−

9

±

9

i

√

3

2

Factor

−

1

out of

−

9

±

9

i

√

3

.

x

=

−

1

9

±

9

i

√

3

2

Multiply

−

1

by

−

1

.

x

=

1

−

9

±

9

i

√

3

2

Multiply

−

9

±

9

i

√

3

by

1

.

x

=

−

9

±

9

i

√

3

2

The final answer is the combination of both solutions.

x

=

−

9

−

9

i

√

3

2

,

−

9

+

9

i

√

3

2

The solution is the result of

x

−

9

=

0

and

x

2

+

9

x

+

81

=

0

.

x

=

9

,

−

9

−

9

i

√

3

2

,

−

9

+

i

√

3

2

7 0

3 years ago

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $.80 A season ski pass costs $300. The

zvonat [6]

Answer:

4

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Calculate a length of a square ground of perimeter 160m

wlad13 [49]

Square Perimetre = Side x 4
So a length of a square ground is 160/4 = 40 (m)

5 0

2 years ago

An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you th

aliya0001 [1]

Answer:

0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 17.42 ppm and a standard deviation of 3.25 ppm.

This means that $\mu = 17.42, \sigma = 3.25$

Sample of 12:

This means that $n = 12, s = \frac{3.25}{\sqrt{12}}$

Find the probability that the mean printing speed of the sample is greater than 18.12 ppm.

This is 1 subtracted by the p-value of Z when X = 18.12.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{18.12 - 17.42}{\frac{3.25}{\sqrt{12}}}$

$Z = 0.75$

$Z = 0.75$ has a pvalue of 0.773.

1 - 0.773 = 0.227

0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.

4 0

3 years ago

2. Solve the following system of equations using substitution.

SOVA2 [1]

First, make sure you convert both equations into standard form. Your two equations would be 2x+2y=38 and -x+y=3. Then multiply the bottom by 2. So your new equations would be 2x+2y=38 and -2x+2y=6. The x would cancel out and you would continue solving for y. y would equal 11 and then you would plug it back into an original equation. When you plug and solve for x, you would get x=8. So your answer would be (8,11)

4 0

3 years ago

What is the mode for the following numbers 67 76 67 76 67 23 32 23 32​

What is the mode for the following numbers 67 76 67 76 67 23 32 23 32