A firm produces a commodity and receives $100 for each unit sold. The cost of producing and selling x units is 20x 0.25x 2 dollars. Find the number of units the company should produce in order to maximize profit, and find the maximum profit.

Answer:

385 ways

Step-by-step explanation:

Given;

7 red balls

10 white balls

In how many ways can 4 balls be selected if there are more than 2 red balls.

Selecting 4 balls which must contain more than 2 red balls, will be 3 red balls and 1 white ball to make it 4 in total, or all the 4 balls selected will red balls.

= 3 red balls and 1 white ball  OR 4 red balls

= 7C₃ x 10C₁  + 7C₄

[tex]= \frac{7!}{4!3!} *\frac{10!}{9!1!} \ \ + \ \frac{7!}{3!4!} \\\\= (35*10) \ + \ 35\\\\= 350 \ + 35\\\\= 385 \ ways[/tex]

Therefore, there are 385 ways of selecting 4 balls, if there are more than 2 red balls.

Answer:

[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is 0.98 and the significance is [tex]\alpha=1-0.98 =0.02[/tex] and [tex]\alpha/2 =0.01[/tex] and the critical value using the table is:

[tex]z_{\alpha/2}= 2.326[/tex]

And replacing we got:

[tex] ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex]\sigma = 425[/tex] represent the population deviation

[tex] n =22[/tex] the sample size

[tex]\bar X =1520[/tex] represent the sample mean

We want to find the margin of error for the confidence interval for the population mean and we know that is given by:

[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is 0.98 and the significance is [tex]\alpha=1-0.98 =0.02[/tex] and [tex]\alpha/2 =0.01[/tex] and the critical value using the table is:

[tex]z_{\alpha/2}= 2.326[/tex]

And replacing we got:

[tex] ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76[/tex]

Answer:

€113.67

Step-by-step explanation:

£3 = €4

£85.40 is €x

Cross multiply.

[tex]4 \times 85.4=3x[/tex]

[tex]3x=341.6[/tex]

[tex]\frac{3x}{3}=\frac{341.6}{3}[/tex]

[tex]x=113.86666...[/tex]

Answer:

Step-by-step explanation:

From the question; we are given the following inclusive frequency distribution information

Class                Frequency f

1.1-1.5                           18

1.6-2.0                         27

2.1-2.5                         31

2.6-3.0                        40

3.1-3.5                         56

3.6-4.0                        55

4.1-4.5                          23

Convert the above inclusive frequency distribution to exclusive frequency distribution with respect of the upper and lower class limit ; we have:

Class                             Frequency f

1.05 - 1.55                             18

1.55 - 2.05                           27

2.05 - 2.55                          31

2.55 - 3.05                          40

3.05 - 3.55                          56

3.55 - 4.05                          55

4.05 - 4.55                          23

Class                             Frequency f                     cf

1.05 - 1.55                             18                              18            

1.55 - 2.05                           27                               45

2.05 - 2.55                          31                               76

2.55 - 3.05                          40                               116

3.05 - 3.55                          56                               172

3.55 - 4.05                          55                               227

4.05 - 4.55                          23                               250

                                       n = 250

To determine the daily sales; we can derive that from estimated Mode by using the relation :

Estimated Mode = L + fm − fm-1(fm − fm-1) + (fm − fm+1) × w

here:

L  = the lower class boundary of the modal group

fm-1 =  the frequency of the group before the modal group

fm = the frequency of the modal group

fm+1 = the frequency of the group after the modal group

w  = the group width

However;

It is easier now to determine  the modal group (i.e the group with the highest frequency), which is 3.05 -3.55

L = 3.05

fm-1 =40

fm =56

fm+1 = 55

w = 0.5

∴[tex]mode = 3.05 + \dfrac{56 - 40 }{(56 - 40) + (56 -55)} * 0.5 \\ \\ mode = 3.05 + 0.4705 \\ \\ mode = 3.5205[/tex]

To find Median Class ; we use the formula;

Median Class = value of (n / 2)th observation

Median Class  = value of (250 / 2)th observation  

Median Class = value of 125th observation

From the column of cumulative frequency cf,

we will see that the 125th observation lies in the class 3.05-3.55.

∴ The median class is 3.05-3.55.

Thus;,  

L=lower boundary point of median class =3.05

n=Total frequency =250

cf=Cumulative frequency of the class preceding the median class =116

f=Frequency of the median class =56

c=class length of median class =0.5

[tex]Median M=L+n2-cff- c \\ \\ =3.05+125-11656⋅0.5 \\ \\=3.05+0.08036 \\ \\ =3.13036[/tex]

hence median sales = $3130.36

Answer:

[tex]x=-10[/tex]

Step-by-step explanation:

[tex]\frac{x}{2}=-5\\\mathrm{Multiply\:both\:sides\:by\:}2\\\frac{2x}{2}=2\left(-5\right)\\Simplify\\x=-10[/tex]

Answer:

A-8

Step-by-step explanation:

Any other higher number plugged in makes the equation false

Answer:

Equilateral, acute

Step-by-step explanation:

Equilateral triangles have all sides the same length (all sides are 4 ft in this triangle, so it is equilateral).

Acute triangles have no angles that are greater than or equal to 90 degrees (all angles are 60, which is less than 90, so it is acute).

Functions

Vertical Line Test

Let's see what we are given.

We are given a graph of an inverse of a function.

We need to figure out whether the graphed inverse function is a function or not.

By the definition of a function, we know that every x input must correlate with one y output. In layman's terms, each respective x input has its own specific y output.

This definition builds the foundation of the Vertical Line Test. We can use this simple "tool" to verify whether or not a given graph is a function or not.

When we apply the Vertical Line Test to the graphed inverse function, we can see that every x input has only one specific y output.

∴ we can conclude that the graphed inverse function is indeed a function.

The answer to the question would be A. True.

___

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___

Topic: Algebra I

Unit: Functions

The value of X is 4

please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

All real numbers greater than or equal to -3

Step-by-step explanation:

First look at graph where the line points to which direction of the graph

And look for any closed or open circles in the graph

Since in the graph has a close circle at (-3,-2) meaning it includes that x-value for its domain.

With the graph going to positive infinity it states that the domain is all real numbers.

So in conclusion it has a domain of all real numbers greater than or equal to -3

Answer:

So we can use geometric progression each time multiplying by 0.0475

so thats (275*0.0475)*10

So that means that we would get

130.625 so we subtract that from 275

275-130.625=144.375

That would be

Step-by-step explanation:

Answer:

c of what im sure about

Step-by-step explanation:

Answer:

We conclude that the mean age of Canadian businesswomen has increased.

Step-by-step explanation:

We are given that according to a report released by CIBC entitled "Women Entrepreneurs: Leading the Charge," the average age for Canadian businesswomen in 2008 was 41.

The researchers randomly sample 97 Canadian businesswomen and ascertain that the sample mean age is 43.4. From past experience, it is known that the population standard deviation is 8.95.

Let [tex]\mu[/tex] = mean age of Canadian businesswomen.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 41      {means that the mean age of Canadian businesswomen has decreased or remained same}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 41     {means that the mean age of Canadian businesswomen has increased}

The test statistics that would be used here One-sample z-test statistics because we know about population standard deviation;

                               T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean age of Canadian businesswomen = 43.4

             [tex]\sigma[/tex] = population standard deviation = 8.95

             n = sample of Canadian businesswomen = 97

So, the test statistics  =  [tex]\frac{43.4-41}{\frac{8.95}{\sqrt{97} } }[/tex]

                                     =  2.64

The value of z test statistic is 2.64.

Also, P-value of the test statistics is given by;

             P-value = P(Z > 2.64) = 1 - P(Z < 2.64)

                           = 1 - 0.99585 = 0.00415

Now, at 1% significance level the z table gives critical value of 2.33 for right-tailed test.

Since our test statistic is more than the critical value of z as 2.64 > 2.33, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean age of Canadian businesswomen has increased.

Answer:

Finding 1/5 of something is the same as dividing that number by 5. Since 24 isn't divisible by 5, 24 / 5 is not an integer. Since you can't have 4.8 species of animals the answer to (a) is no.

For (b), 1/3 * 24 = 8 and 24 - 8 = 16.

Answer:

10

Step-by-step explanation:

First multiply 9 by 2.5

Then divide 225 by 22.5

The answer is B..........

Answer:

B. 1

Step-by-step explanation:

If it was more than one it wouldn't be a triangle.

Answer:

[tex]n=(\frac{1.960(80)}{25})^2 =246.73 \approx 247[/tex]

So the answer for this case would be n=247 rounded up to the nearest integer

Step-by-step explanation:

We know that the standard deviation is :

[tex]\sigma = 80[/tex] represent the deviation

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution and the critical value would be [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.960(80)}{25})^2 =246.73 \approx 247[/tex]

So the answer for this case would be n=247 rounded up to the nearest integer

Answer:

Step-by-step explanation:

Random sampling is a procedure for sampling from a population in which (a) the selection of a sample unit is based on chance and (b) every element of the population has a known, non-zero probability of being selected.

Answer:

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

I hope this helped...

Answer:

answer d) 20

Step-by-step explanation:

Because the two lines are parallel two by two, the figure is a parallelogram.

In a parallelogram the opposite corners are identical.

Given:

opposite corner1 = 130°

opposite corner2= (6a + 10)°

Because corner1 = corner2 we now have:

(6a + 10) = 130

6a + 0 = 130 -10

6a = 120

a = 20

Which is answer d).

Answer:

2 liters of paint.

Step-by-step explanation:

First we nned to know to total area of the wall by using the formula A = lw

A = 4*5 = 20m²

then we given 1 liter cover 10 m², 20 m² = 2 liters of paint.

Answer:

C............PAC-MAN

Step-by-step explanation:

Answer:

E. 400

Step-by-step explanation:

So this is how we set this up, and how we solve

[tex]0.25x=100\\x=100/0.25\\x=400[/tex]

Hope this helps!

So you are solving for circumference of a quarter circle: [tex]\frac{1}{4}2 \pi r[/tex]

r= 28

[tex]\pi=3.14[/tex]

[tex]\frac{1}{4}2(87.92)=\\43.96[/tex]

Answer:

Answers below

Step-by-step explanation:

a. Is x​ (approximately) a binomial random​ variable?

b. Give the probability distribution for x as a formula.

c. Find p(x = 2).

d. Find P(x <= 1).

Answer: Biased sample

Step-by-step explanation:

This is a biased sample because only students with strong opinions are likely going to volunteer or show interest in representing the school at the board meeting. This sample is a voluntary type sample, and at such the conclusion is not valid. This sample is biased because a group or population of students have a higher or lower sampling probability.

Answer:[tex]y=-\frac{3}{2} x+12[/tex]

Step-by-step explanation:

Perpendicular lines have inversely proportional slopes. So make the slope negative and switch it to its reciprocal.

2/3x would change into -3/2x

Lets write that down for a starting point for our perpendicular line.

y = -3/2x + b

We were given the x and y value via the coords. x = 12 and y = -6

Now we have -6 = -3/2(12) + b. Multiply -3 and 12 to get -36, then divide by 2 to get -18.  Now it's -6 = -18 + b. Solve for b by adding 18 to both sides to get b = 12

Answer:

the answer is 6!!!!!!

Step-by-step explanation:

The missing value in the table is 5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

An intravenous fluid is infused at the rate shown in the table

Minutes         Milliliters

3                            4

?                             12

2.                            3

?                             6

3                             9

9                             24

Slope=24-9/9-3

=15/3

=5

Now 5=12-4/x-3

5=8/x-3

5x-15=8

5x=23

x=23/5

x=4.6

x=5

The missing number is 5.

Hence, the missing value in the table is 5

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Answer:

C.

Step-by-step explanation:

[tex]\frac{1}{5} +\frac{5}{6}[/tex] ≈ 1

5 + 8 + 1 = 14

Answer: 4/3

Step-by-step explanation:

As you know this graph is a lemniscate

[tex]4\int\limits^1_0 {x\sqrt{1-x^{2} } \, dx =\frac{4}{3} =1.33$[/tex]

Answer:

[tex]31400\mu m^2[/tex]

Step-by-step explanation:

We are given that

Diameter of egg,d=[tex]100\mu m[/tex]

We have to find the  surface area of egg in [tex]\mu m^2[/tex].

Radius of egg,r=[tex]\frac{d}{2}=\frac{100}{2}=50\mu m[/tex]

Surface area of sphere=[tex]4\pi r^2[/tex]

Where [tex]\pi=3.14[/tex]

Using the formula

Surface area of egg=[tex]4\times 3.14(50)^2[/tex]

Surface area of egg=[tex]31400\mu m^2[/tex]

Hence, the surface area of the egg=[tex]31400\mu m^2[/tex]

Answer:

A

Step-by-step explanation:

(2,1) - only one in the table. Remember (x,y)