solve the simultaneous equations
2x + 5y = -4

Answers

Answer 1

The solution to the system of equations is x = 2 and y = -1.

To solve the system of equations:

2x - 5y = 9 ...(1)

3x + 4y = 2 ...(2)

Multiplying equation (1) by 4 and equation (2) by 5, we can eliminate the variable 'y':

8x - 20y = 36 ...(3)

15x + 20y = 10 ...(4)

Adding equation (3) and equation (4), the 'y' terms cancel out:

(8x - 20y) + (15x + 20y) = 36 + 10

23x = 46

Dividing both sides of the equation by 23, we find:

x = 2

Plugging the value of 'x'

2(2) - 5y = 9

4 - 5y = 9

Subtracting 4 from both sides of the equation:

-5y = 9 - 4

-5y = 5

y = -1

Therefore, the solution to the system of equations is x = 2 and y = -1.

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Related Questions

Factor 6a² - 12a - 5a + 10 by grouping.
O (6a - 5)(a + 2)
(6a - 5)(a - 2)
(6a + 5)(a + 2)
-
O (6a + 5)(a − 2)

Answers

Answer: Therefore, the correct factorization by grouping is (a - 2)(6a - 5).

Step-by-step explanation:

To factor 6a² - 12a - 5a + 10 by grouping, we can group the terms in pairs:

6a² - 12a - 5a + 10

Taking common factors from the first two terms and the last two terms separately:

6a(a - 2) - 5(a - 2)

Now, we can see that (a - 2) is common in both terms, so we can factor it out:

(a - 2)(6a - 5)

Hello!

6a² - 12a - 5a + 10

= 6a² - 17a + 10

= 6a² - 5a - 12a + 10

= (6a² - 5a) + (-12a + 10)

= a(6a - 5) - 2(6a - 5)

= (6a - 5)(a - 2)

A camera has a listed price $859.95 of before tax. If the sales tax rate is 9.5% , find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.

Answers

Answer:

$941.65

Step-by-step explanation:

Salex tax:

We have to find the sales tax of the camera.

tax rate = 9.5%

listed price = $859.95

           [tex]\sf Sales \ tax = tax \ rate * listed \ price[/tex]

                         = 9.5 % * 859.95

                        = 0.095 * 859.95

                        = $81.70

To find the total cost, add the sales tax to the listed price.

Total cost = 859.95 + 81.70

                = $941.65

A bank offers a CD that pays a simple interest rate of 7.0%. How much must you put in this CD now in order to have $4500 for a home-entertainment center in 5 years.
The present value that must be invested to get $4500 after 5 years at an interest rate of 7.0% is $__ (Round up to the nearest cent.)

Answers

Rounding up to the nearest cent, the present value that must be invested in the CD now is approximately $3333.34.

To calculate the present value required to have $4500 after 5 years with a simple interest rate of 7.0%, you can use the formula for simple interest:

Present Value = Future Value / (1 + (Interest Rate × Time))

In this case:

Future Value = $4500

Interest Rate = 7.0%

= 0.07

Time = 5 years

Substituting these values into the formula:

Present Value = $4500 / (1 + (0.07 × 5))

Present Value = $4500 / (1 + 0.35)

Present Value = $4500 / 1.35

Present Value ≈ $3333.33

You may use the simple interest calculation to get the present value necessary to have $4500 after five years with a simple interest rate of 7.0%:

Future Value / (1 + (Interest Rate Time)) = Present Value

In this instance

$4500 is the future value.

Rate of Interest = 7.0% = 0.07

t = 5 years

Substituting these values into the formula:

$4500 / (1 + (0.07 5)) = Present Value

$4500 / (1 + 0.35) equals the present value.

Present Value = $4500 / 1.35

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The present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33

How to find the present value that must be invested to get $4500 after 5 years

Using the formula for calculating the future value of a single sum:

Future Value (FV) = Present Value (PV) + (PV * Interest Rate * Time)

We rearrange the formula to solve for the present value (PV):

PV = FV / (1 + Interest Rate * Time)

Plugging in the given values:

FV = $4500

Interest Rate = 7.0% = 0.07

Time = 5 years

PV = $4500 / (1 + 0.07 * 5)

PV = $4500 / (1 + 0.35)

PV = $4500 / 1.35

PV ≈ $3333.33

Therefore, the present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33 (rounded up to the nearest cent).

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Tom buys 5 shirts for $10 total. He also buys shorts for
$4.50 each. What inequality represents the situation?
He only has $50 to spend/

A. 5x + 10 < 50
B. 4.50x + 5 < 10
c. 10+ 4.5x ≤ 50
d. 5x +4.5x < 50

Answers

Answer:

c

Step-by-step explanation:

we know he spends 10$ on shirts but not how much he spends on shorts. Since we know he has $50 to spend, we can buy shorts up to the $50 limit including $50. The only inequality that includes $50 is c

C, 10+ 4.5x ≤ 50

Happy to help, have a great day! :)

7 1 /4 x − x =9 3/ 8

Answers

Answer:

1.5 is the correct answer

(-0.68, 3.02) In y In x (1.07. -1.53) The variables x and y satisfy the equation y Ax-2, where A and p are constants. The graph of In y against In x is a straight line passing through the points (-0.68, 3.02) and (1.07,-1.53), as shown in the diagram. Find the values of A and p.​

Answers

The calculated values of A and p that satisfy the equation y = Ax - 2p are A = -2.6 and p = -0.626

How to calculate the values of A and p

From the question, we have the following parameters that can be used in our computation:

Points = (-0.68, 3.02) and (1.07,-1.53)

The equation is of the form

y = Ax - 2p

Using the given points, we have

3.02 = -0.68A - 2p

-1.53 = 1.07A - 2p

Subtract the eqations

-0.68A - 1.07A = 3.02 + 1.53

So, we have

-1.75A = 4.55

This gives

A = -2.6

Recall that

3.02 = -0.68A - 2p

So, we have

3.02 = 0.68 * 2.6 - 2p

Evaluate

2p = -1.252

Divide by 2

p = -0.626

Hence, the values of A and p are A = -2.6 and p = -0.626

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Question

The variables x and y satisfy the equation y = Ax - 2p, where A and p are constants. The graph of In y against In x is a straight line passing through the points (-0.68, 3.02) and (1.07,-1.53).

Find the values of A and p.​

Convert the rectangular coordinates (–6, 6) to polar coordinates.

Answers

Answer:  A   Polar is (6√2,  [tex]\frac{3\pi }{4}[/tex])

Step-by-step explanation:

Draw a line to point (see image).   You need to find the length of that line and then the angle.   Polar(length, angle)

Using pythagorean theorem

length²  = (6)² + (-6)²

length² = 36 +36

length =√72

length  = [tex]\sqrt{36 *2}[/tex]

length = 6√2

To find angle:

The triangle size is 6-6-6√2  Let's proportionally shrink so we can use unit circle numbers to figure angle.    Becomes: 1-1-√2

So when we do sin x =  opp/adj

sin x = [tex]\frac{1}{\sqrt{2} }[/tex]              >get rid of radical on bottom

sin x  = [tex]\frac{\sqrt{2} }{2}[/tex]             > when is sin = [tex]\frac{\sqrt{2} }{2}[/tex]     This happens at [tex]\frac{\pi }{4}[/tex]   but we are in the 2nd quadrant so the angle is [tex]\frac{3\pi }{4}[/tex]

Polar is (6√2,  [tex]\frac{3\pi }{4}[/tex])

The polar coordinates are (6([tex]\sqrt[]{2}[/tex], 3pi/4).

Rectangular coordinates are in the form of (x, y) and Polar coordinates are expressed in the form of (r, [tex]\theta[/tex]).  

Relation between polar coordinates and rectangular coordinates-

x = r cos([tex]\theta[/tex]), y = r sin([tex]\theta[/tex]) and  x^2 +y^2 =r^2                                       ...(1)

So by using above formulas we can solve our question.

Here , x= -6 and y= 6

r^2 = (-6)^2 +(6)^2

       =72

=>r = 6([tex]\sqrt[]{2}[/tex])

Put the values of x and y in the mentioned formula in eq(1)

-6 =  6([tex]\sqrt[]{2}[/tex] )cos[tex]\theta[/tex]

 6 = 6([tex]\sqrt[]{2}[/tex] )sin([tex]\theta[/tex]),

=>-1/([tex]\sqrt[]{2}[/tex] = cos([tex]\theta[/tex]) , 1/[tex]\sqrt[]{2}[/tex]=  sin[tex]\theta[/tex]

Here cos is negative and sin is positive so it lies in 2nd quadrant

so here [tex]\theta[/tex] lies between [tex]\frac{\pi}{2} \leq\theta\leq\pi[/tex]

[tex]\theta[/tex]= π-π/4

 =3π/4

So,(r, [tex]\theta[/tex]) = ( 6√2, [tex]\frac{3\pi}{4}[/tex] )

divide 16x³+31.6x²-6.8x-12 by x+2​

Answers

Answer:

16x^2 - 1.6x - 5

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

x+2 | 16x^3 + 31.6x^2 - 6.8x - 12

- (16x^3 + 32x^2)

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

-0.4x^2 - 6.8x

+(-0.4x^2 - 0.8x)

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

-6x - 12

+(-6x - 12)

----------

0

Answer:   = 16x²-.4x-6

Step-by-step explanation:

divide 16x³+31.6x²-6.8x-12 by x+2​

Using synthetic division:  Carry first 1 down.  Multiply that by outside -2 and put it under 2nd number.  Add.  Then multiply and repeat until you get to end.

-2    |   16            31.6             -6.8           -12

      |                  -32                  .8             12        

           16              -.4             -6                0

Put back into equation form.  Last number is 0 so remainder is 0

= 16x²-.4x-6

The equation 5/3log4(x)=9 can be written in the form x=2^y for some number y. What is y?

Answers

The value of y is 10.8.

Here, we have,

given that,

The equation is: 5/3log_4(x)=9

or, 5 log₄x = 27

or, log₄x = 27/5

now, we have,

Using the property, x = loga, a = eˣ

we get,

x = 4²⁷/⁵

or, x = 4⁵°⁴

or, x = 2¹⁰°⁸

so, comparing with x=2^y , we get,

y = 10.8

Hence, The value of y is 10.8.

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Heeeeeelp pleaseeeeeeeeee!!!!!!!!!!!!L 3.11.3 Quiz: Comparing and Analyzing Function Types
Question 1 of 10
How would you describe the difference between the graphs of f(x)=2x² and
g(x)=-2x²?
A. g(x) is a reflection of f(x) over the line y = x.
B. g(x) is a reflection of f(x) over the line y = -1.
OC. g(x) is a reflection of f(x) over the y-axis.
D. g(x) is a reflection of f(x) over the x-axis.

Answers

The correct statement regarding the reflection rules in this problem is given as follows:

D. g(x) is a reflection of f(x) over the x-axis.

How to define the reflection?

The functions f(x) and g(x) in the context of this problem are defined as follows:

f(x) = 2x².g(x) = -2x².

The entire function was multiplied by -1, meaning that the signal of the function was exchanged, hence the function was reflected over the x-axis.

As the function was reflected over the x-axis, the correct option in the context of the problem is given by option D.

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Meera can sell 1 jacket for $40, 2 jackets for $35 each, 3 jackets for $30 each, 4 jackets for $25 each, and 5 jackets for $20 each. Her marginal cost of production is constant at $20 for each additional unit (or jacket) produced. If she behaves like a monopolist, what is the number of jackets she will sell?
a. 1
b. 3
c. 4
d. 5

Answers

The number of jackets Meera will sell if she behaves like a monopolist is 3( option B).

To determine the number of jackets Meera will sell if she behaves like a monopolist, we need to compare the marginal revenue (MR) and marginal cost (MC) of producing and selling additional jackets. Meera can sell jackets at various price points depending on the quantity sold, but as she behaves like a monopolist, we consider the revenue and costs associated with a given production level.

From the pricing information given, we can determine her total revenue function, R(x), as follows:

- For 1 jacket, R(1) = 40

- For 2 jackets, R(2) = 70

- For 3 jackets, R(3) = 90

- For 4 jackets, R(4) = 100

- For 5 jackets, R(5) = 100

To determine her marginal revenue function, MR(x), we find the change in revenue from selling an additional jacket. From the data given, we can see that MR is not constant and decreases as the quantity sold increases. Specifically:

- For 1 jacket, MR(1) = 40 - 0 = 40

- For 2 jackets, MR(2) = 35 - 40 = -5

- For 3 jackets, MR(3) = 30 - 35 = -5

- For 4 jackets, MR(4) = 25 - 30 = -5

- For 5 jackets, MR(5) = 20 - 25 = -5

Meera's marginal cost of production is given as a constant $20 for each additional jacket produced, so MC(x) = 20 for all values of x.

To maximize her profits, Meera should produce and sell jackets up to the point where MR(x) = MC(x), which represents the level of production that equates the revenue from selling an additional jacket with the cost of producing that jacket. This happens at the output level of 3, where MR(3) = -5 = MC(3) = 20.(option-b)

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MARKING AS BRAINLIST PLEASE HELP!!

Answers

The correct probability that either event will occur is 0.533.

What is probability?

A measure of the likelihood of an event to occur.

P(A or B) = P(A) + P(B).

Probability = Number of favorable outcomes/Total number of outcomes

P(A) = 1/5 = 0.3

P(B) = 1/3 = 0.33

P(A) + P(B) = 1/5 +1/3

                 = 0.533

Probability = 0.533.

Therefore, the probability that either event will occur is 0.533.

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Based on the W2 form above, how much money did Jane Doe get to take home after taxes in 2017?

Question 9 options:

$48,500


$6,835


$50,000


$725

Answers

The amount of money that Jane Doe get to take home after taxes in 2017 is A. $48500

How to calculate the amount

Based on the W-2 form above, Jane Doe's gross pay was $50,000. She had $6,835 in federal income tax withheld, $725 in state income tax withheld, and $1,000 in FICA taxes withheld. This means that her net pay was $48,500.

Net pay = Gross pay - Total taxes withheld

Net pay = $50,000 - ($6,835 + $725 + $1,000)

Net pay = $48,500

Therefore, amount of money that Jane Doe get to take home after taxes in 2017 is A. $48500

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David and Ken took part in a cycling race. Both of them did not change their speed throughout the race. David completed the race in 5 hours while Ken took 7 hours. Ken's average speed was 9.8 km/h less than David's average speed.
A) What was David average speed
B)What was the distance of the cycling race?

Answers

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.[tex][/tex]

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

[tex]\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}[/tex]


This distance for the cycling race can now be used to determine David's average speed:

[tex]\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}[/tex]

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.


Define the term "surplus"in this context​

Answers

In this context, "surplus" refers to the excess or additional amount beyond the ideal diameter of 24 inches that the actual diameter of the cake possesses.

It represents the difference between the actual diameter and the desired or expected diameter, taking into consideration the specified margin of error.

When a chef aims to purchase a cake with a margin of error of 3 inches, the surplus indicates the extent to which the cake's diameter surpasses the desired size.

It is a measure of how much larger the cake is compared to the ideal diameter, considering the acceptable range within the margin of error.

The surplus can be positive or negative, depending on whether the actual diameter is larger or smaller than the ideal diameter.

If the actual diameter is greater than 24 inches, the surplus will be a positive value, indicating the excess size of the cake.

Conversely, if the actual diameter is smaller than 24 inches, the surplus will be a negative value, representing the shortfall in size.

By quantifying the surplus, the chef can assess the degree to which the actual cake deviates from the ideal size and make an informed decision based on their specific requirements and preferences.

The surplus helps ensure that the cake's dimensions align with the desired specifications and meets the chef's expectations within the specified margin of error.

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A car rental company charge $50 a day and 20 cents per mile for renting a car. Let y be the total rental charge (in dollar) for a car for one day and x be the miles driven. The equation for the relationship between x and y is y = 50 + 20x How much will a person pay who rents a car for one day and drives it 100miles​

Answers

Answer:$2050.

Step-by-step explanation:

To find out how much a person will pay for renting a car for one day and driving it 100 miles using the given equation, you can substitute x = 100 into the equation y = 50 + 20x and solve for y:

y = 50 + 20x

y = 50 + 20(100)

y = 50 + 2000

y = 2050

Therefore, a person who rents a car for one day and drives it 100 miles will pay $2050.

HII PLEASE FILL OUT THE CROSSWORD PUZZEL FOR ME

Answers

Answer:

what is all that?!

Solve for the exact solutions in the interval [0,2]
List your answers separated by a comma, if it has no real solutions, enter DNE.

Answers

The solutions to the trigonometric equation in this problem are given as follows:

θ = π/6.θ = 5π/6.θ = 7π/6.θ = 11π/6.

What are complementary angles?

Two angles are said to be complementary angles when the sum of their measures is of 90º.

For complementary angles, we have that the sine of one of the angles is the cosine of the other angle, hence in this problem we have that 2θ and θ are complementary angles.

Then the value of θ is obtained as follows:

2θ + θ = 90

3θ = 90

θ = 30º.

θ = π/6.

The equivalent angles, which are also solutions to the equation, are given as follows:

θ = 5π/6. -> second quadrant.θ = 7π/6. -> third quadrant.θ = 11π/6. -> fourth quadrant.

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Help please, I need to get through geometry recovery class

Answers

To prove ∠AOW = 45°

Given,

∠WOZ = 90°

∠ZOB = 45°

Now,

∠XOA +∠AOW = 90°............(1)

∠XOA = ∠ZOB ( Vertically opposite angle  )

∠XOA = 45°

Substitute in (1),

45° +  45° = 90°

Now,

∠WOX = ∠XOA +∠WOA

So,

∠WOA + ∠WOZ + ∠ZOB = 180°( Linear pair )

∠WOA + 90° + 45° = 180°

∠WOA = 45°

Hence proved.

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Name at least ONE method a person can use to send money to another person who does not have a bank account.​

Answers

Answer:

One method that a person can use to send money to another person who does not have a bank account is through a money transfer service like Western Union or MoneyGram. These services allow individuals to send money to recipients who can then collect it in cash from designated locations. The sender can visit a local agent or use an online platform to initiate the transfer, providing the recipient's name and other required details. The recipient can then go to a nearby agent location with proper identification to receive the cash. This method provides a convenient way to send money to individuals who may not have access to traditional banking services.

Step-by-step explanation:

Person 1 takes money out of wallet, gives money to person 2.

BOOM!

Prior to June 30, a company has never had any treasury stock transactions. The company repurchased 185 shares of its $1 par common stock on June 30 for $42 per share. On July 20, it reissued 90 of these shares at $46 per share. On August 1, it reissued 70 of the shares at $40 per share. What is the journal entry necessary to record the reissuance of treasury stock on July 20?

Answers

On July 20, the journal entry to record the reissuance of treasury stock is: Debit Cash for $4,140 and credit Treasury Stock for $4,140.

To record the reissuance of treasury stock on July 20, the company needs to make the following journal entry:

Date: July 20

Account Debit Credit

Cash $4,140

Treasury Stock $4,140

Explanation:

Debit to Cash ($46 per share * 90 shares) to record the cash received from the reissuance of 90 shares of treasury stock: $46 * 90 = $4,140.

Credit to Treasury Stock to remove the cost of the 90 reissued shares from the treasury stock account.

This journal entry reflects the cash inflow from the reissuance of treasury stock and reduces the balance in the treasury stock account, indicating a reduction in the number of shares held by the company as treasury stock.

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QUESTION 1
A credit card has a balance of $1,400. The APR is 25% and the minimum payment is 3% of the balance. You will pay the minimum balance this month. If you do not use the card again then how much
should the balance be next month?
QUESTION 2
A credit card with an APR of 18% has a balance of $2500 on it. You make a $1400 payment that posts on the 11th day of a 31-day month. How much interest will you be charged for the month?
QUESTION 3
Suppose we have a card with an APR of 25%. The minimum payment is 7% of the balance Suppose we have a balance of $350 on the credit card. We decide to stop charging and to pay it off by making
the minimum payment each month.
Calculate the new balance after the first minimum payment is made.
Calculate the minimum payment that is due the next month.
QUESTION 4
Your credit card has a balance of $2500 and an interest rate of 21%. The credit card requires a minimum payment of 3%
Lennors

Answers

Answer:

Q1: $1,360, Q2: $30.83, Q3: $325.50, Q4: $75

Step-by-step explanation:

QUESTION 1:

If the minimum payment is made and no additional charges are made, the balance next month should be $1,400 minus 3% of $1,400, which is $1,360.

QUESTION 2:

To calculate the interest charged for the month, we need to determine the average daily balance. Assuming no other transactions, the average daily balance would be (($2,500 * 20) + ($1,100 * 10)) / 31 = $2,032.26. Multiply this by the APR of 18% and divide by 365 to get the daily interest rate. The interest charged for the month would be approximately ($2,032.26 * 0.18) / 365 * 31 = $30.83.

QUESTION 3:

After making the first minimum pyment, the new balance would be $350 minus 7% of $350, which is $325.50.

To calculate the minimum payment due the next month, we take 7% of the new balance, which is 7% of $325.50, equal to $22.79 (rounded to the nearest cent).

QUESTION 4:

The minimum payment required on a balance of $2,500 would be 3% of $2,500, which is $75.

determine the value of

(



)
P(A∩B), rounding to the nearest thousandth, if necessary.

Answers

The probability of the intersection P(A∩B) is 0

What is the probability of the intersection P(A∩B)

From the question, we have the following parameters that can be used in our computation:

Event A = 18

Event B = 12

Intersection = 0

Other Events = 6

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 12 + 6

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 12/36

For the intersection events, we have

P(A∩B) = 0/36

Evaluate

P(A∩B) = 0

Hence, the probability of P(A∩B) is 0

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Ryan is building two gardens.
The flower garden is 6 feet long
and 4 feet wide. The vegetable
garden is the same length as the
flower garden. The area of the
flower garden is half the area of
the vegetable garden. What is the
width of the vegetable garden?

Answers

The width of the vegetable garden is 8 feet.

To determine the width of the vegetable garden.

Given information:

Flower garden length = 6 feet

Flower garden width = 4 feet

Vegetable garden length = Flower garden length

Area of the flower garden = half the area of the vegetable garden

To find the width of the vegetable garden, we need to find the area of both gardens.

Area of the flower garden = length × width

Area of the flower garden = 6 feet × 4 feet

Area of the flower garden = 24 square feet

Since the area of the flower garden is half the area of the vegetable garden, we can set up the following equation:

24 square feet = (1/2) × Area of the vegetable garden

To solve for the area of the vegetable garden, we multiply both sides of the equation by 2:

2 × 24 square feet = Area of the vegetable garden

48 square feet = Area of the vegetable garden

Now that we know the area of the vegetable garden is 48 square feet, we can find the width.

Area of the vegetable garden = length × width

48 square feet = 6 feet × width

To solve for the width of the vegetable garden, we divide both sides of the equation by 6:

48 square feet / 6 feet = width

8 feet = width

Therefore, the width of the vegetable garden is 8 feet.

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Phi can be determined for Cable 2 from
O cos^-1 (Fy/Fx)
sin^-1 (Fy/Fx)
O tan^-1 (Fy/Fx).

Answers

Phi (Φ) can be determined for Cable 2 from:

[tex]tan^-1 (Fy/Fx).[/tex]

In trigonometry, [tex]tan^-1 (Fy/Fx)[/tex] represents the inverse tangent function, also known as arctan or atan.

This function is used to find the angle whose tangent is equal to the ratio of the y-component (Fy) to the x-component (Fx) of a vector.

By calculating the ratio Fy/Fx and applying the inverse tangent function, we can determine the angle phi (Φ) for Cable 2.

The value obtained from [tex]tan^-1 (Fy/Fx)[/tex] will represent the angle in radians.

It's important to note that the resulting angle phi (Φ) will provide information about the direction or inclination of Cable 2 based on the given vector components Fy and Fx.

In summary, to determine the angle phi (Φ) for Cable 2, we use the inverse tangent function, represented as[tex]tan^-1 (Fy/Fx),[/tex] which calculates the angle whose tangent is equal to the ratio of the y-component to the x-component of the vector.

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Abiodun walks 5km due north,then12km due east.How far ia he from the starting point?

Answers

13 km
do you need the explanation too?

The following cylinder has a volume of 20π cm3 and a height of 5 cm

What is the diameter of the cylinder? Remember, the diameter of a circle is two times its radius

Answers

Answer:

Step-by-step explanation:

To find the diameter of the cylinder, we can use the formula for the volume of a cylinder:

Volume = π * radius^2 * height

Given:

Volume = 20π cm^3

Height = 5 cm

We can rearrange the formula to solve for the radius:

radius^2 = Volume / (π * height)

radius^2 = (20π) / (π * 5)

radius^2 = 4

radius = 2

Now, we can find the diameter by multiplying the radius by 2:

diameter = 2 * radius

diameter = 2 * 2

diameter = 4

Therefore, the diameter of the cylinder is 4 cm.

NO LINKS!! URGENT HELP PLEASE!!!

4. Use the theorems for interior and exterior angles of a polygon to find:

a. The sum of the interior of a 73-gon.

b. The number of sides of a regular polygon if the sum of the interior angles is 2700°

c. The number of sides of a reguluar polygon if the exterior angle is 7.2°

Answers

Answer:

see explanation

Step-by-step explanation:

a

the sum of the interior angles of a polygon is calculated as

sum = 180° (n - 2) ← n is the number of sides

here n = 73 , then

sum = 180° × (73 - 2) = 180° × 71 = 12,780°

b

here sum of interior angles = 2700° , then

180° (n - 2) = 2700° ( divide both sides by 180° )

n - 2 = 15 ( add 2 to both sides )

n = 17

number of sides is 17

c

the sum of the exterior angles of a polygon = 360°

given the polygon is regular then each exterior angle is congruent , so

number of sides = 360° ÷ 7.2° = 50

 

Answer:

a)  12870°

b)  17

c)  50

Step-by-step explanation:

Part a

The Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.

The number of sides of a 73-gon is n = 73. Therefore, the sum of its interior angles is:

[tex]\begin{aligned}\textsf{Sum of the interior angles of a 73-agon}&=(73-2) \cdot 180^{\circ}\\&=71 \cdot 180^{\circ}\\&=12870^{\circ}\end{aligned}[/tex]

Therefore, the sum of the interior angles of a 73-gon is 12870°.

[tex]\hrulefill[/tex]

Part b

The Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.

Given the sum of the interior angles of a regular polygon is 2700°, then:

[tex]\begin{aligned} \textsf{Sum of the interior angles}&=2700^{\circ}\\\\\implies (n-2) \cdot 180^{\circ}&=2700^{\circ}\\n-2&=15\\n&=17\end{aligned}[/tex]

Therefore, the number of sides of the regular polygon is 17.

[tex]\hrulefill[/tex]

Part c

According the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.

Therefore, to find the number of sides of a regular polygon given its exterior angle is 7.2°, divide 360° by the exterior angle.

[tex]\begin{aligned}\textsf{Number of sides}&=\dfrac{360^{\circ}}{\sf Exterior\;angle}\\\\&=\dfrac{360^{\circ}}{7.2^{\circ}}\\\\&=50\end{aligned}[/tex]

Therefore, the number of sides of the regular polygon is 50.

A group of ten students recorded the number of minutes they spent on one math homework problem. The
mean amount of time was 9 minutes, but the MAD was 7 minutes.
Draw a dot plot to represent a data set that matches this description. Be sure to include a title and label
your axis.

Answers

1. Create a horizontal axis labeled "Time Spent on Homework Problem (Minutes)."

2. Choose an appropriate scale for the axis, such as labeling every other unit of time from 0 to 18.

3. Plot a dot for each student's data point along the horizontal axis.

4. Arrange the dots in order from smallest to largest time spent on the problem.

5. Title the dot plot to reflect the data set being represented, such as "Math Homework Problem Time Spent: Mean 9 Minutes, MAD 7 Minutes."

6. Include a legend or key if needed to clarify the meaning of the dot plot.(The dot plot is attached below)

To draw a dot plot representing a data set where the mean amount of time spent on one math homework problem is 9 minutes and the MAD is 7 minutes for a group of ten students, we can follow these steps:

The resulting dot plot may show a spread of data between 2 and 16 minutes, with more dots around the center or mean of 9 minutes and fewer dots at the tails. The MAD of 7 minutes suggests a relatively high degree of variability in the data, with some students spending significantly less or significantly more time on the math homework problem. The dot plot can help to visualize these differences and identify any potential outliers in the data.

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The endpoints of segment XY are X(-2,3) and Y(7,4). The segment is translated along the vector <-3,1> and then rotated 90 degrees. What is the coordinate of X"?

Answers

The coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees is X" (4, 5).

To find the coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees, we need to follow these steps:

Translation: Add the components of the translation vector <-3, 1> to the coordinates of point X(-2, 3) to get the new coordinates of X'.

X' = (-2 + (-3), 3 + 1) = (-5, 4)

Now, we have the translated endpoint X'.

Rotation: To rotate the point X' by 90 degrees, we need to swap the x and y coordinates and negate the new x coordinate.

X" = (y-coordinate of X', -x-coordinate of X')

X" = (4, -(-5))

X" = (4, 5)

Therefore, the coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees is X" (4, 5).

In summary, we first translate point X(-2, 3) along the vector <-3, 1> to get X' (-5, 4). Then, we rotate X' by 90 degrees to obtain X" (4, 5).

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