I need help on this math problem.

Find the area of the region.

Three petals of r = cos(9θ)

Answer:

14 nickels

Step-by-step explanation:

One nickel is worth 5 cents, so find the value of 14 nickels by multiplying 14 by 5:

14(5)

= 70

So, 14 nickels is equal to the 70 cents that she has in her purse.

The correct answer is 14 nickels.

9514 1404 393

Answer:

  Amy: $620

  Tom: $400

Step-by-step explanation:

The pay for 40 hours (1 week) is 40 times the pay for 1 hour:

  Amy: 40 × $15.50 = $620 . . . . Amy's pay for 1 week

  Tom: 40 × $10.00 = $400 . . . . Tom's pay for 1 week

Answers:

The venn diagram is shown below.

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

Explanation:

M = set of people studying math

C = set of people studying chemistry

P = set of people studying physics

Something like the notation n(C) refers to the count of items in set C, aka the number of people who study chemistry. Similar ideas apply to n(M) and n(P) to refer to the counts of math and physics respectively.

Something like n(C and M) is the number of people who study chemistry and math. Same idea applies to something like n(C and P) or n(M and P)

With all that in mind, we have these 7 facts

We'll start with fact 7. This value goes in the very center of the 3 overlapping circles of the venn diagram. Refer to the diagram below.

Since 9 people study all three subjects, and 16 study chemistry and math, this must mean 16-9 = 7 people study chemistry and math without physics involved. We'll write 7 in the region between circles C and M, but outside of circle P.

Since 9 people study all three subjects, and 14 study math and physics, we know that 14-9 = 5 people study only math and physics without chemistry. We'll write 5 in the region between circles M and P, but outside circle C.

Since 9 people study all three subjects, and 18 study chemistry and physics, we know that 18-9 = 9 people study only chemistry and physics without math. We'll write 9 in the region between circles C and P but outside circle M.

If you're lost, then refer the diagram below. So far, we have filled in the very center "9" and the closest three values surrounding it (the 7, 9 and 5).

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

Focus your attention on circle M for now. The values in this circle add to: 7+9+5 = 21

Since n(M) = 41, this must mean the missing value must be 20. This goes in circle M but outside the other two circles.

Note how 7+9+5+20 = 41 when we add everything in circle M. This circle is completely filled out. We'll follow a similar path for the other circles.

Move onto circle C. Adding everything in it so far gets us 9+9+7 = 25. We want to get to n(C) = 48 which means we need to have 48-25 = 23 in circle C but outside the other circles. Circle C is now done.

Lastly, focus on circle P. The values we found so far in this circle add to 9+9+5 = 23. The missing value must be 19 because 42-23 = 19, and n(P) = 42.

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

At this point, all three circles are filled out. The only thing missing is the number outside the circles, but inside the rectangle.

Add up everything in the circles: 23+7+20+9+9+5+19 = 92

This tells us that we have 92 people who studied at least one subject (i.e. one or more subjects). There are 120 people surveyed, meaning that 120-92 = 28 people study neither of these subjects. We write 28 outside the circles.

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

The venn diagram is done by this point. To address the questions, we'll just read from the diagram (and at most do an addition problem).

To find the number of people who study exactly one subject, we will add up the numbers that are in one circle but not in any other circle. Those values are: 23, 20, and 19. So 23+20+19 = 62 people study exactly one subject.

We already found the number of people who study at least one subject, and that was 92 people. This was when we added every number in the circles.

For the last question, we already found this value as well. This answer is 28 people which is found outside all three circles.

The venn diagram is shown below to visually summarize and organize all of the data. Hopefully it clears up any confusion you may have about the previous steps.

Total number of students who exactly one subject is 62

No of students who study at least one subject is 92

No of students who do not study any subject is 28

let us do this problem by set theory.

in the attached figure

three circles have been drawn representing the number of students studying maths, physics and chemistry.

from the diagram

1) Number of students who study exactly one subject=no of students who study maths + number of students who study chemistry+number of students who study physics- 2*[number of students who study both physics and chemistry-number of students who study both physics and maths-number of students who study both maths and chemistry ]+3*number of students who study all three subjects

from the attached figure,

2) Total number of students who exactly one subject = 20+19+23 = 62

3) No of students who study at least one subject will be the sum of each data in the attached figure i.e union of all three sets.

no of students who study at least one subject = 20+7+5+9+19+9+23=92

no of students who do not study any subject = total students- the union of all three sets.

no of students who do not study any subject = 120-92 = 28

therefore,

total number of students who exactly one subject is 62

no of students who study at least one subject is 92

no of students who do not study any subject is 28

to get more about set theory refer to the link,

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Answer:

Here are a few examples.

(30/2 + 1)/2

(26/2 + 3)/2

(28/2 + 2)/2

Answer:

Drawing 4 - 1/10

Drawing odd number - 1/2

Not drawing 3- 9/10

Drawing 5 or 6 -  1/5

Drawing a number greater than 9 - 0

Let me know if this helps!

The following information related to irrigation is as follows:

The gallons of irrigation water per square foot is [tex]326,700\ gallons\ per\ square\ foot[/tex]

For determining the gallons of irrigation water we have to multiply the square foot by the number of gallons in a cubic foot.

Given that,

There are 43,560 square feet in an acre i.e. 1 acre = 43,560.

And, there are 7.5 gallons in a cubic foot i.e. 1 cubic foot = 7.5 gallons.

So, the gallons of irrigation water per square foot is

[tex]= 43,560 \times 7.5\ gallons \\\\= 326,700\ gallons\ per\ square\ foot[/tex]

Therefore we can conclude that the gallons per square foot of irrigation water is [tex]326,700\ gallons\ per\ square\ foot[/tex]

Learn more about per square foot here: brainly.com/question/5991264

Answer:

326,700 gallons

Step-by-step explanation:

1 acre = 43,560 square feet

1 acre-foot of irrigation is an acre irrigated 1 foot deep with water.

Since thee are approximately 7.5 gallons in 1 cubic foot,

1 acre-foot of irrigation = 43,560 * 7.5 gallons

1 acre-foot = 326,700 gallons

This is the number of gallons in one acre-foot, not gallons per square foot.

Answer:

loses  14 cents

- $0.14

Step-by-step explanation:

90%  $0.30   $(0.30)  $(0.27)

9%  $1.00   $0.40   $0.04  

1%  $10.00   $9.40   $0.09  

   $(0.14)

-4 ≤ x ≤ 6

x ≥ -4

3x ≥ -12

3x + 12 ≥ 0

3x + 14 ≥ 2

6 ≥ x

6 - x ≥ 0

1 - x ≥ -5

A. 3x + 14 ≥ 2 and 1 - x ≥ -5

Answer:

first one is correct bro

The correct factorization of x³ - 27 is  (x - 3)(x² + 3x + 9).

a³ + b³ = (a + b)(a² -ab + b²) and a³ - b³ = (a - b)(a² + ab + b²).

If we know the formula of these two we can conclude by observing that

the second option x³ - 27 = (x - 3)(x² + 3x +9) is correct.

As x³ - 27

= x³ - 3³.

= (x - 3)(x² + 3x + 9).

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Answer:

$480

Step-by-step explanation:

Let original price be x

{Original price - discount amount = sale price}

So, x - (x * 35/100) = 312

x - 35x/100 = 312

100x - 35x / 100 = 312

65x/100 = 312

65x = 31200

x = 31200/65

x = $480

So I think the original price of desk was $480

The original price of the desk is $480.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, a desk is being sold for $312.

Let the original price of the desk be x.

Here, x-35% of x =312

x- 35/100 ×x=312

x-0.35x=312

0.65x=312

x=312/0.65

x=480

Therefore, the original price of the desk is $480.

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Leontief input output model (technology matrix) is an economic model that shows the quantitative relationship and sectorial interdependency in a national economy

The responses with  regards to the question are;

(i) The technology matrix for the economy is presented as follows;

[tex]\mathbf{ A} =\left[\begin{array}{ccc}Agric&&Textile\\0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] \begin{array}{ccc}\mathbf{Per \ Unit}\\Agriculture\\\\Textile\end{array}\right][/tex]

(ii) The required gross production of each industry to meet the desired surplus are;

50 units of agriculture and 250 units of textile

The reason the above values are correct is as follows:

(i) The given parameters are;

The industries in the economy = Agricultural industry and textile industry

Units of agricultural input required per unit of agricultural output = 0.4

Units of textile input required per unit of agricultural output = 0.1

Units of agricultural input required per unit of textile output = 0.1

Units of textile input required per unit of textile output = 0.2

Let X represent agriculture, and let Y represent textile, we have;

[tex]Agric \ for \ agric = \dfrac{0.4 \ units \ of \ agriculture}{1\ unit \ of \ agric \ produced} \times X \ Agric \ produced= 0.4 \cdot X[/tex]

[tex]Agric \ for \ textile = \dfrac{0.1 \ units \ of \ agriculture}{1\ unit \ of \ textile \ produced} \times Y \ textile \ produced= 0.1 \cdot Y[/tex]

We also have;

Textile for agriculture = 0.1·X

Textile for textile = 0.2·Y

Therefore;

X = 0.4·X + 0.1·Y

Y = 0.1·X + 0.2·Y

Therefore;

The technology matrix for the economy is presented as follows;

[tex]\mathbf{Technology \ matrix, A} =\left[\begin{array}{ccc}Agric&&Textile\\0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] \begin{array}{ccc}\mathbf{Per \ Unit}\\Agriculture\\\\Textile\end{array}\right][/tex]

(ii)  Let P represent the production vector, and let d represent the demand vector, we have;

[tex]P = \left[\begin{array}{c}X \\Y\end{array}\right][/tex], [tex]d = \left[\begin{array}{c}5 \\195\end{array}\right][/tex]

P = A·P + d

∴ P - A·P = d

Therefore;

[tex]P = \mathbf{ \dfrac{d}{(I - A)}}[/tex]

Where I = The 2 by 2 identity matrix

We get;

[tex]I - A =\left[\begin{array}{ccc}1&&0\\&&\\0&&1\end{array}\right] - \left[\begin{array}{ccc}0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] = \mathbf{\left[\begin{array}{ccc}0.6&&-0.1\\&&\\-0.1&&0.8\end{array}\right]}[/tex]

With the use of a graphing calculator, we have;

[tex]P =\left[\begin{array}{c}X \\Y\end{array}\right] = \dfrac{\left[\begin{array}{c}5 \\195\end{array}\right]}{\left[\begin{array}{ccc}0.6&&-0.1\\&&\\-0.1&&0.8\end{array}\right]} = \left[\begin{array}{ccc}50\\\\\ 250\end{array}\right][/tex]

The required gross product of agriculture, X = 50 units

The required gross product of textile, Y = 250 units

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We have that he technology matrix for this economy and the  the gross production of each industry are

a)    [tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]

b)    [tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]          

From the Question we have told that

Each unit of agricultural output requires 0.4 unit of agricultural input

Each unit of agricultural output requires 0.1 unit of textiles input.

Each unit of textiles output requires 0.1 unit of agricultural input

Each unit of textiles output requires 0.2 unit of textiles input.

Generally the technology matrix for this economy is given below

With

X =Agricultural industry Gross output

Y= Textile industry Gross Output

Therefore

[tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]

b)

From the Question we are told that

Surpluses of 5 units of agricultural products and 195 units of textiles are desired.

Therefore, we have Desired surplus matrix of

[tex]D= \begin{vmatrix}5\\195\end{vmatrix}[/tex]

Generally the Technology equation is mathematically given as

[tex](I-X)\phi=D[/tex]

Where

X =Agricultural industry Gross output

I=A Unit matrix

\phi=Matrix of gross production

Therefore

[tex]\begin{vmatrix}1 & 0\\0 & 1\end{vmatrix}-(\begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}))\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}5\\195\end{vmatrix}[/tex]

[tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]

In conclusion

The technology matrix for this economy and the  the gross production of each industry are

[tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]

[tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]         Respectively

In conclusion

https://brainly.com/question/16863924

5

Answer:

1050

Step-by-step explanation:

Natural Numbers are positive whole numbers. They aren't negative, decimals, fractions. We can just divide 5 into 100 to find how many natural numbers go up to 100 and just add them but that is just to much.

There is a easier method.

E.g: Natural Numbers that are divisible by a Nth Number. is the same as adding the Nth Numbers to a multiple of that Nth Term. For example, let say we need to find numbers divisible by 2. We know that 4 is divisible by 2 because 4/2=2. We can add the Nth numbers which is 2 to 4. 4+2=6. And 6 is divisible by 2 because 6/2=3. We can call this a arithmetic series. A series which has a pattern of adding a common difference

Back to the problem, we can use the sum of arithmetic series formula,

[tex]y = x( \frac{z {}^{1} + {z}^{n} }{2} )[/tex]

Where x is the number of terms in our sequence. Z1 is the fist term of our series. ZN is our last term. And y is the sum of all of the terms

The first term is 5, the numbers of terms being added is 20 because 100/5=20. The last term is 100.

[tex]y = 20( \frac{5 + 100}{2} )[/tex]

[tex]y = 20( \frac{105}{2} )[/tex]

[tex]y = 1050[/tex]

Answer:

100000

Step-by-step explanation:

100000x80=8m

Answer:

2.592 x 10^5

Step-by-step explanation:

1st step: Calculate for 1 day.

if 1 hour = 3.6 X 10³

24 hrs = (3.6 x 10³) X (2.4 x 10¹)

= 3.6 x 2.4 X 10⁴

= 8.64 x 10⁴

2nd Step: Calculate for 3 days;

if 1 day = 8.64 x 10⁴

3 days = (8.64 x 10⁴) X (0.3 x 10¹)

= 8.64 x 0.3 x 10^5

= 2.592 x 10^5

Answer:

3y=x+5

Step-by-step explanation:

The slope of the line is (1/3). The equation of the line is y=(1/3)x+5/3 or 3y=x+5

Answer:

Y=Srt(12xs^2/z^2)

Step-by-step explanation:

Firstly

We multiply both sides with 1/x^2

We get

Y^2=12/z^2*1/x^2

Y^2=12x^2/z^2

Next: introduce a srt root

We have

Y=srt(12x^2/z^2)

Hi,

AxB = 0 means A=0. or B=0

so 2 solutions :

4x-3= 0

4x=3

x = 3/4

and x+2 = 0.

x= -2

solutions are : -2 +and 3/4

2 answers

1) -2

2) -3/4

Answer:

Rs. 11132

Step-by-step explanation:

formula for depriciation= P(1-R/100)^T

p= principal, r=rate, t=time

Answer:

15162

Step-by-step explanation:

after 1 year= 16800*95%= 15960

after 2 year= 15960*95%= 15162

Answer:

207m

Step-by-step explanation:

(17+5)*6=132

(15*5)=75

132+75=207

Step-by-step explanation:

A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone wrong in the manufacturing process, at most 7 chips each lot would be defective, but if something does go wrong, there could be far more defective chips. If something goes wrong with a given lot, they discard the entire lot. It would be prohibitively expensive to test every chip in every lot, so they want to make the decision of whether or not to discard a given lot on the basis of the number of defective chips in a simple random sample. They decide they can afford to test 100 chips from each lot. You are hired as their statistician.

There is a tradeoff between the cost of eroneously discarding a good lot, and the cost of warranty claims if a bad lot is sold. The next few problems refer to this scenario.

Problem 8. (Continues previous problem.) A type I error occurs if (Q12)

Problem 9. (Continues previous problem.) A type II error occurs if (Q13)

Problem 10. (Continues previous problem.) Under the null hypothesis, the number of defective chips in a simple random sample of size 100 has a (Q14) distribution, with parameters (Q15)

Problem 11. (Continues previous problem.) To have a chance of at most 2% of discarding a lot given that the lot is good, the test should reject if the number of defectives in the sample of size 100 is greater than or equal to (Q16)

Problem 12. (Continues previous problem.) In that case, the chance of rejecting the lot if it really has 50 defective chips is (Q17)

Problem 13. (Continues previous problem.) In the long run, the fraction of lots with 7 defectives that will get discarded erroneously by this test is (Q18)

Problem 14. (Continues previous problem.) The smallest number of defectives in the lot for which this test has at least a 98% chance of correctly detecting that the lot was bad is (Q19)

(Continues previous problem.) Suppose that whether or not a lot is good is random, that the long-run fraction of lots that are good is 95%, and that whether each lot is good is independent of whether any other lot or lots are good. Assume that the sample drawn from a lot is independent of whether the lot is good or bad. To simplify the problem even more, assume that good lots contain exactly 7 defective chips, and that bad lots contain exactly 50 defective chips.

Problem 15. (Continues previous problem.) The number of lots the manufacturer has to produce to get one good lot that is not rejected by the test has a (Q20) distribution, with parameters (Q21)

Problem 16. (Continues previous problem.) The expected number of lots the manufacturer must make to get one good lot that is not rejected by the test is (Q22)

Problem 17. (Continues previous problem.) With this test and this mix of good and bad lots, among the lots that pass the test, the long-run fraction of lots that are actually bad is (Q23)

Answer:

?

How did you simplify

Answer:

6 pies

Step-by-step explanation:

For 60 - 89 cherries there are 10 pies

For 90 -119 cherries there are 4 pies

10 -4 = 6

There are 6 more pies in the 60 -89 cherries category than in the 90-119 category

Let on of the angle be x

ATQ

97 + x = 180

x = 180 - 97 (Angles on same line adds upto 180°) (Linear pair cuz 2 angles)

x = 83

The unknown angle is 83°

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Question: -4 + 5x -7 = 10 + 3x -2x

⇒ 5x -11 = 10 + x

⇒ 5x - x = 10+11

⇒ 4x = 21

⇒ x = 21/4

Answer is Option D

x = 21/4

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Answer:

Step-by-step explanation:

Answer:

8 =x

Step-by-step explanation:

- 18 = -3x + 6

Subtract 6 from each side

-18-6 = -3x+6-6

-24 = -3x

Divide each side by -3

-24/-3 = -3x/-3

8 =x

Answer:

x= 8

Step-by-step explanation:

[tex]\sf{}[/tex]

=> -3x+6 = -18

=> -3x+6-6= -8-6

=> -3x= -24

=> x= 8

Answer:

10.9

Step-by-step explanation:

[tex]a^2+b^2=c^2[/tex]

[tex]9.1^2+6^2=c^2[/tex]

[tex]82.81+36=c^2[/tex]

[tex]c^2=118.81[/tex]

[tex]c=\sqrt{118.81} =10.9[/tex]

I assume A ∆ B denotes the symmetric difference of A and B, i.e.

A ∆ B = (B - A) U (A - B)

where - denotes the set difference or relative complement, e.g.

B - A = {b ∈ B : b ∉ A}

It can be established that

A ∆ B = (A U B) - (A ∩ B)

so that

n(A ∆ B) = n(A U B) - n(A ∩ B) = 10 - 3 = 7

Not sure what you mean by p(A ∆ B), though... Probability?

Answer:

sec^2(x)

Tell me if I'm correct or wrong. If I'm correct, plz mark me brainliest!

Step-by-step explanation:

Recall that

[tex]\sin (\frac{\pi}{2} - x) = \cos x[/tex]

[tex]\cos (\frac{\pi}{2} - x) = \sin x[/tex]

So we can rewrite the given expression as

[tex]\dfrac{\cos^2 x}{\sin^2 x} + (\sin^2 x + \cos^2 x)[/tex]

[tex]\Rightarrow \dfrac{\cos^2 x}{\sin^2 x} + 1[/tex]

or

[tex]\dfrac{\cos^2 x + \sin^2 x}{\sin^2 x} = \dfrac{1}{\sin^2 x} = \csc^2 x[/tex]