This area model represents the product 27 and another number . What is the other number

Write the following as a mixed number 65/18 user: perform the operation and write the answer in simplest form 4/7 * 3/11

sesenic [268]

65/18 = 3 11/18

4/7 * 3/11 = 12/77

5 0

4 years ago

At NC State University, 16.4% of the undergraduate classes have more than 50 students. If a random sample of 200 undergraduate c

Lena [83]

Answer:

We need to check the conditions in order to use the normal approximation.

$np=200*0.164=32.8 \geq 10$

$n(1-p)=200*(1-0.164)=167.2 \geq 10$

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The mean is given by:

$p =0.164$

And the deviation is given by:

$\sigma_{p}= \sqrt{\frac{0.164*(1-0.164)}{200}}= 0.0262$

So then the correct options for this case are:

The sampling distribution will be approximately normal.

The mean of the sampling distribution will be 16.4%.

The standard deviation of the sampling distribution will be 0.0262.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=200, p=0.164)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=200*0.164=32.8 \geq 10$

$n(1-p)=200*(1-0.164)=167.2 \geq 10$

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The mean is given by:

$p =0.164$

And the deviation is given by:

$\sigma_{p}= \sqrt{\frac{0.164*(1-0.164)}{200}}= 0.0262$

So then the correct options for this case are:

The sampling distribution will be approximately normal.

The mean of the sampling distribution will be 16.4%.

The standard deviation of the sampling distribution will be 0.0262.

6 0

3 years ago

Kylie Matsumoto is a set designer. Her annual salary is $ 45,320. Kylie's semi-monthly salary is $ _________. (Round to the near

ivanzaharov [21]

The answer to this question would be: $1888.33/semi-month

To answer this question you need to convert the annual into semi-monthly. Annual mean every 1 year or every 12 months. Semi-monthly mean two times a month. Then the equation would be: $45,320 / year x (1 year/12month) x (1 month/2 semi-month) = $1888.33/semi-month

3 0

3 years ago

Which of the following is the solution to the inequality below?

irakobra [83]

Answer:1/3

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

3/2*(x-1/3)-(-5*x)>0

Step by step solution :

STEP

1

:

1

Simplify —

3

Equation at the end of step

1

:

3 1

(— • (x - —)) - -5x > 0

2 3

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 3 as the denominator :

x x • 3

x = — = —————

1 3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • 3 - (1) 3x - 1

——————————— = ——————

3 3

Equation at the end of step

2

:

3 (3x - 1)

(— • ————————) - -5x > 0

2 3

STEP

3

:

3

Simplify —

2

Equation at the end of step

3

:

3 (3x - 1)

(— • ————————) - -5x > 0

2 3

STEP

4

:

Equation at the end of step

4

:

(3x - 1)

———————— - -5x > 0

2

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 2 as the denominator :

-5x -5x • 2

-5x = ——— = ———————

1 2

Adding fractions that have a common denominator :

5.2 Adding up the two equivalent fractions

(3x-1) - (-5x • 2) 13x - 1

—————————————————— = ———————

2 2

The equation at the end of step

5

:

13x - 1

——————— > 0

2

STEP

6

:

6.1 Multiply both sides by 2

6.2 Divide both sides by 13

x-(1/13) > 0

Solve Basic Inequality :

6.3 Add 1/13 to both sides

x > 1/13

7 0

3 years ago

If Q(x,3) is a point on the line y= -2x+3. what are the coordinates of point Q?

cupoosta [38]

The point Q will satisfy the equation y=-2x+3 if the coordinates are plugged into the equation, so we plug in our known coordinate of the point Q (y = 3) and then we solve for x:
3 = -2x + 3
subtract 3 from both sides
0 = -2x
divide both sides by -2
x = 0
so the coordinate Q is (0,3)

7 0

3 years ago