Use Green's Theorem to evaluate F · dr. C (Check the orientation of the curve before applying the theorem.)F(x, y) = y cos(x) − xy sin(x), xy + x cos(x) , C is the triangle from (0, 0) to (0, 8) to (2, 0) to (0, 0)

Answer:

the amount of money Ian invested is P =  £2,500

Step-by-step explanation:

The standard formula for compound interest is given as;

[tex]A = P(1+r/n)^{nt} \\P = \frac{A}{(1+r/n)^{nt}} ...........1\\[/tex]

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case, Given that;

A = £2652.25

t = 2 years

n = 1 (semiannually)

r = 3% = 0.03

substituting the given values into equation 1;

[tex]P = \frac{A}{(1+r/n)^{nt}} ...........1\\P = \frac{2652.25}{(1+0.03)^{2}} \\P = \frac{2652.25}{(1.03)^{2}} \\[/tex]

P =  £2,500

the amount of money Ian invested is P =  £2,500

Answer:

11

Step-by-step explanation:

Answer:

x = 11.

Step-by-step explanation:

9 less than twice a number is the same thing as twice a number minus 9. Let's say that the number is x.

2x - 9 = 13

2x = 22

x = 11

Hope this helps!

Answer:

The Hudson Record Store

1. As a fraction, discount rate = $3/$18 = 0.167

2. As a percentage, discount rate = 16.67%

3. Selling price during 2nd week = $13.50

4. The rate of the new selling price to the old is $13.50/$18 = 75%

Step-by-step explanation:

Selling price of CDs = $18

1st Week, sold CDs at $15

Discount = $3 ($18 - $15)

As a fraction, discount rate = $3/$18 = 0.167

As a percentage, discount rate = 16.67%

2nd Week, sold CDs at $13.50 ($18 - (25% of $18))

Discount = $4.50 ($18 - $13.50)

Price during the second week of the sale = $13.50

The rate of discount = $4.50/$18 = 25%

Step-by-step explanation:

8.x×8-12=50

8x-12=50

9.1/2x>or=100

10.2 whole number5/9-x=31

25/250 = 1/10

I do not know that much english. I an spanish so I might have done it wrong.

the probability that the horse is at least 25 feet away from all boundary lines is 0.5

To calculate the probability that the horse is at least 25 feet away from all boundary lines in an enclosed pasture that is 150 feet by 200 feet, we need to consider the available space for the horse to roam.

The area of the pasture is given by:

Area = Length * Width = 150 feet * 200 feet = 30,000 square feet

Now, let's consider the area where the horse must stay within at least 25 feet away from all boundary lines. We can imagine this as a rectangular strip along the inner boundary of the pasture, with dimensions reduced by 50 feet on each side.

The dimensions of this rectangular strip would be:

Length = 150 feet - 2 * 25 feet = 100 feet

Width = 200 feet - 2 * 25 feet = 150 feet

The area of this rectangular strip is given by:

Area_strip = Length * Width = 100 feet * 150 feet = 15,000 square feet

Therefore, the probability that the horse is at least 25 feet away from all boundary lines is:

Probability = Area_strip / Area = 15,000 square feet / 30,000 square feet = 0.5

The probability is 0.5 or 50%.

Learn more about probability here

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Answer:

C = 150S + 3,500.

$6,050.

Step-by-step explanation:

It costs $3,500 to rent the trucks, so your constant/y-intercept will be $3,500.

It will cost $150 for every ton of sugar, so your slope will be $150.

You then have your equation:

C = 150S + 3,500.

If you were to transport 17 tons of sugar...

C = 150 * 17 + 3,500

C = 2,550 + 3,500

C = $6,050.

Hope this helps!

Answer:

C = $6050

Equation:

To write the equation, we have to remember that C is the total cost, so that means the equation should end in "= C". S is the amount of sugar, so the equation would look something like this:

[tex]3500+150(S)=C[/tex]

3500 is at the beginning since that is the cost for the trucks, and each ton of sugar costs $150, and that would get multiplied by S amount of sugar, to get the total cost, C.

Solving the equation

To solve the equation when S = 17, we simply have to plug in S as 17 into our equation we wrote above.

[tex]3500+150(17)=C[/tex]

150 * 17 is 2550, and 3500 + 2550 is 6050, which is C.

C = $6050

Answer:

Step-by-step explanation:

You have the following function:

[tex]f(x)=-3x+7[/tex]

The y-intercept of the function is given by the independent coefficient, which is 7.

y-intercept = 7

To obtain the x-intercept you equal the function to zero and solve for x, as follow:

[tex]0=-3x+7\\\\3x=7\\\\x=\frac{7}{3}\approx2.33[/tex]

x-intercept = 2.33

Due to the coefficient of x is negative, the slope of the function is negative.

The function is a straight line, then, its domain all all real numbers and its range are all real numbers.

The graph of the function is attached in the image below.

Answer:

1/36

Step-by-step explanation:

the fair die has 6 equal parts which means its the total

the probability of rolling a 6 is 1/6

the probability of rolling another 6 is 1/6

so u multiply 1/6 times 1/6 which is 1/36

hope this helps

Hey there

Find attached to this answer the diagram of the Quadrilateral

Question:

If ABCD is a parallelogram, AD = 14, EC = 11, m∠ABC = 64°, m∠DAC = 71°, and m∠BDC = 25, find each measure.

a) BC =

b) AC =

c) m∠DAB =

d) m∠ABD =

e) m∠ACD =

f) m∠ADB =​

Answer:

a) BC = 11

b) AC = 22

c) m∠DAB = 116°

d) m∠ABD = 39°

e) m∠ACD = 45°

f) m∠ADB =​ 25°

Step-by-step explanation:

a) BC

In the question above, EC = 11

We can see that EC and BC are equal sides of a diagonal line that has been divided into two equal parts in a Quadrilateral.

Hence, In a quadrilateral ABCD,

EC = BC

Hence BC = 11

b) AC

AC is one of the diagonal lines that divided parallelogram ABCD

AC = BC + EC

AC = 11 + 11

AC = 22

c) m∠DAB

m∠ABC = 64°

m∠ADC = 64°

For the two angles above, a diagonal bisects through those angles.

Also the sum of angles in a triangle = 180°

Hence,

180° = 1/2m∠ABC + 1/2m∠ADC +

m∠DAB

m∠DAB = 180° - ( 1/2 (64) + 1/2(64))

m∠DAB = 180 ° - 64°

m∠DAB = 116°

d) m∠ABD

Since,

m∠ABC = 64° and m∠BDC = 25

m∠ABC = m∠BDC + m∠ABD

64 = 25+ m∠ABD

m∠ABD = 64° - 25°

m∠ABD = 39°

e) m∠ACD

In the above question,

m∠ABC = 64°,

m∠ADC = m∠ABC, this is because, opposite angles in a quadrilateral are congruent and equal to each other.

Hence, m∠ADC = 64°

m∠DAC = 71°,

In a triangle , all the angles in a triangle = 180°

Hence,

180° = m∠DAC + m∠ADC + m∠ACD

180° = 71° + 64 ° + m∠ACD

m∠ACD = 180° -(71 + 64)°

m∠ACD = 180° - 135°

m∠ACD = 45°

f) m∠ADB

Since

m∠DAB = 116°

m∠ABD = 39°

The sum of angles in a triangle = 180°

180° = m∠ABD + m∠DAB + m∠ADB

180° = 39 ° + 116° + m∠ADB

m∠ADB = 180° - ( 116 + 39)°

m∠ADB = 25 °

a) BC = 11

b) AC = 22

c) m∠DAB = 116°

d) m∠ABD = 39°

e) m∠ACD = 45°

f) m∠ADB =​ 25°

Given : AD=14 , EC=11, m∠ABC= 64°, m∠DAC=71° and m∠BDC=25°

To find:  BC =?  , AC =? , m∠DAB =?, m∠ABD =?  ,m∠ACD =?  ,m∠ADB =​?

Consider the figure given below ABCD is a parallelogram

To find a) BC

Given, EC = 11

As seen in figure that EC and BC are equal sides of a diagonal line that has been divided into two equal parts in a Parallelogram.

Hence, In a Parallelogram ABCD,

EC = BC

Hence BC = 11

To find b) AC

AC is one of the diagonal lines that divided parallelogram ABCD

AC = BC + EC

AC = 11 + 11

AC = 22

To find c) m∠DAB

Given, m∠ABC = 64°

m∠ADC = 64°

(For the two angles above, a diagonal bisects through those angles)

Also From Angle sum property;

Hence,

180° = 1/2m∠ABC + 1/2m∠ADC +  m∠DAB

m∠DAB = 180° - ( 1/2 (64) + 1/2(64))

m∠DAB = 180 ° - 64°

m∠DAB = 116°

To find d) m∠ABD

Since,

m∠ABC = 64° and m∠BDC = 25  

m∠ABC = m∠BDC + m∠ABD

64 = 25+ m∠ABD

m∠ABD = 64° - 25°

m∠ABD = 39°

To find e) m∠ACD

Given,  m∠ABC = 64°;

m∠ADC = m∠ABC, this is because, opposite angles in a quadrilateral (here parallelogram) are congruent and equal to each other

Hence, m∠ADC = 64°

m∠DAC = 71°,

In a triangle , all the angles in a triangle = 180°(Angle sum property)

Hence,

180° = m∠DAC + m∠ADC + m∠ACD

180° = 71° + 64 ° + m∠ACD

m∠ACD = 180° - (71 + 64)°

m∠ACD = 180° - 135°

m∠ACD = 45°

To find f) m∠ADB

Since  ,m∠DAB = 116°  and m∠ABD = 39°

From Angle sum property;

180° = m∠ABD + m∠DAB + m∠ADB

180° = 39 ° + 116° + m∠ADB

m∠ADB = 180° - ( 116 + 39)°

m∠ADB = 25 °

Learn more:

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Answer:

See below

Step-by-step explanation:

The statement that can be written for 4p = 8 is:

=> Four times a certain number equals eight.

so you have the amount.

amount: 1200

then you have the ratio

ratio: 3:5

you have the count.

count: 2

and then you have the shares

shares: 8

and the amount per share is 150.00

so the total amount of shares is the sum of each person's ratio so,

so 1:5:2:3:9 = 1 + 5 + 2 + 3 +9 = 20 shares.  hope that helps you..

Answer:

y = 4/3x+2

Step-by-step explanation:

We can use the slope intercept form of the equation

y = mx+b

Where m is the slope and b is the y intercept

y= 4/3 x +b

Substitute the point into the equation

6 = 4/3(3) +b

6 = 4 +b

Subtract 4 from each side

2 = b

y = 4/3x+2

Answer:

Step-by-step explanation:

You can let c, b, s represent the investments in CDs, bonds, and stocks, respectively.

  c + b + s = 170000 . . . . . . total invested

  0.0325c +0.038b +0.067s = 7745 . . . . . . . annual income

  -c + b = 60000

You can solve this set of equations using any of a number of methods, including on-line calculators, graphing calculators, scientific calculators, Cramer's Rule, substitution, elimination, and more. The solution is ...

  c = 30,000

  b = 90,000

  s = 50,000

Maricopa's Success invested $30,000 in CDs, $90,000 in bonds, and $50,000 in stocks.

Answer:

352.8 ft

Step-by-step explanation:

m∠A = 180° − 102.9° − 18.6° = 58.5°

AB = c and BC = a.

Use law of sines:

c / sin C = a / sin A

c / sin 18.6° = 943 / sin 58.5°

c = 352.8

Answer:

B. The company should have 8 production runs each year.

Step-by-step explanation:

From the given information:

A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer

It costs $4 to store one can of paint for one year

$500 to set up the plan for production of the primer

Let x be the number of cans of paint produced during each production run

Let y be the number of production runs.

If the total storage and setup cost is C = 500y + 2c

and cy = 16000

Then c = 16000/y

From;

C = 500y + 2c

Replacing c with 16000/y,  we have;

C = 500y + 2(16000/y)

C = 500y + 32000/y

in order to minimize the total storage and setup costs  [tex]C_{min} = C[/tex]

Therefore [tex]\dfrac{dc}{dy}=0[/tex]

⇒ 500 - 32000/y² =0

y² = 32000/500

y² = 320/5

y² = 64

y = (√64)

y = 8

Therefore; The company should have 8 production runs each year in order to minimize the total storage and setup costs

Answer:

25 and 30

Step-by-step explanation:

Let the smaller consecutive multiples of 5 be x. Therefore, other consecutive multiples will be x + 5.

Now as per statement the sum of two consecutive multiples of 5 is 55. To find the multiples. Thus

x + x + 5 = 55

2x + 5 = 55

2x = 55 - 5

2x = 50

x = 50/2

x = 25

This the smaller consecutive multiples of 5 is 25, the other consecutuve multiple is x+ 5, 25 + 5 = 30.

The consecutive multiple numbers of 5 are 25 and 30

Answer the two consecutive multiples of 5 are 25 and 30

Answer:

25 and 30.

Step-by-step explanation:

Let the smaller consecutive multiple of 5 be 'x'. So, the other multiple will be x + 5.

Now, the statement is the sum of two consecutive multiples of 5 is 55. To find the multiples, we must simplify as below.

x + x + 5 = 55

2x + 5 = 55

2x = 55 - 5

2x = 50

x = 50/2

x = 25

We observe that the smaller consecutive is 25, so the other multiple is x+ 5, 25 + 5 = 30.

(Hope this helps and please mark as the brainliest)

Answer:

14.16 miles further.

Step-by-step explanation:

Campbell to Summerfield

9.52mi + 4.62 mi + 10.08 mi = 24.24 mi

Princeton to summerfield

is 10.08 mi

Therefore difference is 24.24mi - 10.08mi = 14.16 mi

Hope this helps.

Answer:

y = -1/2x - 3

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Determine known variables

Slope = -1/2 (m = -1/2)

y-intercept - (0, -3), so b = -3

Step 2: Write in known variables

y = -1/2x - 3

Answer:

y = -1/2 - 3

Step-by-step explanation:

Well slope intercept is y = ax + b

ax is the slope which is given,

b is the y intercept which is -3 because the point (0,-3)

doesn’t have a x coordinate meaning if the line goes through that point it touches the y intercept at -3.

Thus,

the equation in slope-intercept is y = -1/2 - 3.

Hope this helps :)

Answer:

90 degree EFC. and. BMC

across fc/ma

across ec/ab

Answer: Sample mean [tex](\overline{x})[/tex]

Step-by-step explanation:

Given: A study was conducted to determine the average birth weight (in ounces) of babies born in hospitals in a five county area of a given state.

i.e. The parameter of the study is [tex]\mu[/tex] . (Population mean).

A Simple Random Sample of Recent birth records at the local hospitals were selected and the confidence interval was calculated to be (117.89 ounces, 124.91), at a 95% level of confidence.

Since a measure of sample is a statistic , and this case statistic is sample mean denoted by [tex]\overline{x}[/tex].

Hence, the statistic is appropriate for this confidences interval : [tex]\overline{x}[/tex]

1

Step-by-step explanation:

p(x≤20)=p(x=-10) +p(x=-5)+p(X=0) +p(x=5) +p(x=10)+ p(X=15)+p(X=20)

This, p(X≤20)=0.20+0.15+0.05+0.1+0.25+0.1+0.15

=1

Answer:

-52, and the opposite of this is 52.

Step-by-step explanation:

If we are losing 52 pounds, then our number is -52 since we are losing 52 pounds (adding a negative number to a positive number is the same as subtracting that number).

The opposite of a number is when we negate the number, or multiply it by -1.

A negative number times a negative number is a positive number.

[tex]-52\cdot-1 = 52\cdot1 = 52[/tex]

Hope this helped!

Answer:

Hey there!

Loss of 52 pounds, -52

Opposite, 52

Hope this helps :)

Answer:

The highest number on a die is 6. when we roll out two die the total sum cannot be more that 12. and each sum having the same probability of showing up.

The outcome of our experiment can be 2,3,4,5,6,7,9,10,11 or 12.

Step-by-step explanation:

Statistical experiment can be simply stated as the likelihood of an an event to occur or not.

Answer:

Step-by-step explanation:

Easy way to solve

5^4 = 625.

5^12=244140625.

Thus, 625m=244140625.

Divide both sides by 625/

m=390625, or 5^8.

Better way to solve

When dividing by exponents [tex]x^{4}/x^{2} =x^{4-2}=x^2[/tex]

Thus, simply do 12-4=8 to know that m=5^8.

Hope it helps <3

Answer:

Step-by-step explanation:

(5⁴)m = 5¹²

Divide both sides by 5⁴

((5⁴)m)/5⁴ = 5¹²/5⁴

m = 5⁸

Answer:

Winning odd = 3.4

Loosing odd = 4.3.

Step-by-step explanation:

So, from this particular Question or problem we have the following data or information or parameters which is going to aid or help us in solving this particular Question;

=> Given 6 of hearts and the 8 of diamonds.

We know that there are 8 types of cards.

Also, we know that the total number of the cards is equal to fifty-two(52).

From cards of six(6) to ten(10) a bust will surely occur.

Therefore, 8 × 4 / 52= 32/52 = 0.62.

If an ace is pulled, then the chance of winning bis surely 4 out of 52 deck of cards.

Giving you a Winning odd = 3.4 and a

Loosing odd = 4.3.

Answer:

Mean = 16.5

Variance = 35.55

Step-by-step explanation:

           x      P(x)        x. P(x)     x²            x². P(x)

          6      0.10          0.6      36            3.6

         12     0.35          4.2       144           50.4

        18     0.25           4.5       324            81

        24     0.30          7.2        576         172.8

                  ∑x P (x)  16.5         ∑x² P (x) 307.8

The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.

Mean is given by  E(X)=  ∑x P (x) =  16.5

Similarly the variance is also calculated using the expected value of X and X².

Variance is given= E(X)²-  [E(X)]²= 307.8- (16.5)²=  307.8-272.25 = 35.55

Answer:

Probability distribution

Step-by-step explanation:

Probability distribution is the function which describes the likelihood of possible values assuming a random variable. Alternative hypothesis is a statement which we accept or reject based on the null hypothesis. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

Answer:

Dang shes rich, but what is the question?

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

im not too sure

Answer:

[tex]\boxed{x<20}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2} x<10[/tex]

Multiply both sides by 2.

[tex]x<20[/tex]