Draw a graph for f(x)= 2^x-3

a) Let x denote the quality rating and y denote the meal price.

b. From the above table, the marginal density function of x is 1.94

c. From the probability table, the marginal density function of y is 2.09

The probability distribution table for quality and meal price is obtained by dividing each and every frequency by the total frequency of 300 is attached in the image.

The probability distribution is obtained in the attached image below.

The expected value of x is,

1 x 0.28  + 2 x 0.50 + 3 x 0.22

= 1.94

To find the marginal density function of y

1 x 0.26  + 2 x 0.39 + 3 x 0.35

= 2.09

Given that var(x+y)=1.6691

var(x)=0.4964 and var(y)=0.6019

var(x+y) =1.6691

var(x) + var(y) +2* cov(x,y)=1.6691

0.4964+0.6019+ 2 *cov(x,y) =1.6691

1.0983+ 2 * cov(x,y) =1.6691

2 * cov(x,y) =1.6691-1.0983

2* cov(x,y)=0.5708

cov(x,y) =(0.5708)/2

cov(x,y)= 0.2854

Thus, the covariance of x and y is, 0.2854.

Here, the covariance of x and y is positive.

Thus, the relationship between quality and meal price is positive.

If the quality of the meal increases then the meal price also increases.

Yes, the expected result is positive because if the quality of the meal is good then meal price increases.

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The solution is, radius: 23 inches.

Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (a segment of a circle). In simple words, the distance that runs through the curved line of the circle making up the arc is known as the arc length.

here, we have,

Formula: ∅r = arc length

Here the ∅ is 2 rads and arc length is 46 inches.

using the formula:

2*r = 46

r = 23 inches

The solution is, radius: 23 inches.

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A claw arcade machine contains stuffed animals and mystery boxes.

A claw arcade machine is a popular type of game machine found in many arcades and amusement parks. It typically consists of a glass cabinet that contains a variety of stuffed animals and other prizes, such as mystery boxes, that can be won by using a mechanical claw.

The player inserts a designated amount of money and then uses the joystick to position the claw over the desired prize. Once the player is satisfied with the claw's position, they press a button to make the claw descend and attempt to grab the prize. If the claw is successful in grabbing the prize, it will lift it up and drop it into the prize chute, where the player can then collect it.

The prizes in a claw machine can vary from small plush toys to larger stuffed animals, and even mystery boxes that contain unknown items or a chance to win a bigger prize. The claw's strength and grip are adjustable, which can make winning a prize more difficult or easier depending on the machine's settings.

Claw machines are a popular form of entertainment for all ages, and the thrill of successfully grabbing a coveted prize can be a source of excitement and satisfaction for players.

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The cost of the burger and the cost of an order of fries to Lynn would be :

From the problem, we know that Lynn spent $20.00 and purchased 4 hamburgers and 5 orders of fries. Similarly, we know that Ricardo spent $41.20 and purchased 10 hamburgers and 7 orders of fries, which gives us the equations:

4h + 5f = 20

10h + 7f = 41.20

Using substitution, we can express h in form of f to be :

4h + 5f = 20

4 [ ( 3 f + 1. 20 ) / 2] + 5 f = 20

6 f + 2 . 40 + 5 f = 20

11 f = 17. 60

f = $ 1. 60

We can then find the cost of hamburgers using the first equation :

4h + 5f = 20

4h + 5 ( 1. 60 ) = 20

4h + 8 = 20

4h = 12

h = $ 3

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According to the statement, the Ship must move at an average pace of 150 meters per hour.

The variable under examination is lessened when the gradient is "downhill" (negative). When used as a gauge of how well things are doing, "downhill" denotes a downward trend. Yet, if this indicates trouble or some other unpleasant quality, the situation is improving.

The chess player Carissa walks very, very slowly. She actually moves at speeds of 100 meters per hr upward, 150 meters per hr on flat terrain, and 200 meters every hour on downhill terrain.

Here,

Carissa traverses Boston on foot from a coffeehouse to a boba store before returning over the same path.

Total distance walked = 2 [200 + 100 + 150] = 900 meter

Total time = 2 [1 + 1 + 1] = 6 hour

Average speed is calculated as distance divided by time (900 / 6 = 150 m/s),

As a result, the needed Carissa average speed is 150 meters per hr.

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The value for the expression 1/3x² for x = 6 is 1/108. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often known as "arithmetic operations," are said to allow every real number to be stated, according to mathematicians. Divide, multiply, add, and subtract are the four mathematical operations that result in quotient, product, sum, and difference, respectively.

We are given an expression as  1/3x².

We need to find its value for x = 6.

Substituting this in the expression, we get

⇒1/3(6)²

⇒1/3(36)

⇒1/108

Hence, the value for the expression 1/3x² for x = 6 is 1/108.

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The solution is,  if depreciation is involved it will NEVER be greater than the amount the car was. $16464

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

30000(1+ -.012/4) ^4*5

Use the compounded continuously formula

A= intial amount

Pe^rt

A=30000e

the small e means euler

r= rate

t= t

A= 30000e ^(-0.12x5)

=$16464

the answer is 16,464

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Answer:

Step-by-step explanation:

is -2(-12y+5)+4=8(3y+2)-22 a conditional equation an identity or a contradiction

-2(-12y + 5) + 4 - 8(3y - 2) + 22 = 0

24y - 10 + 4 - 24y - 16 + 22 = 0

-6 - 16 + 22

- 22 + 22 = 0

0 = 0   (All real numbers are solutions.)

Answer:

19/28

Step-by-step explanation:

1/4 = 7/28

3/7 = 12/28

Then:

1/4 + 3/7 = 7/28 + 12/28 = (7+12)/28

= 19/28

Answer:

Step-by-step explanation:

To find the third year value of the deposit, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money after t years, P is the principal (the initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

For the first year, we have:

P = $500

r = 0.05

n = 1 (compounded annually)

t = 1

So, the amount after the first year is:

A1 = $500(1 + 0.05/1)^(1*1) = $525

For the second year, we have:

P = $525 (the amount after the first year)

r = 0.06

n = 1

t = 1

So, the amount after the second year is:

A2 = $525(1 + 0.06/1)^(1*1) = $556.50

For the third year, we have:

P = $556.50 (the amount after the second year)

r = 0.07

n = 1

t = 1

So, the amount after the third year is:

A3 = $556.50(1 + 0.07/1)^(1*1) = $594.64

Therefore, the third year value of the deposit is $594.64.

Answer:

No real solutions

Step-by-step explanation:

If lines are parallel, it means that they will never meet each other indicating that there are no real solutions.

Answer: To graph this system of inequalities, we can first graph each inequality separately and then find the region where they overlap.

Starting with the first inequality, x - y ≥ 7, we can rearrange it to y ≤ x - 7 and graph the line y = x - 7. Since the inequality includes the line, we will use a solid line to represent it, and shade below the line to show the region where y is less than or equal to x - 7.

Next, for the second inequality, x + 2y < 5, we can rearrange it to y < (-1/2)x + 5/2 and graph the line y = (-1/2)x + 5/2. Since the inequality excludes the line, we will use a dashed line to represent it, and shade below the line to show the region where y is less than (-1/2)x + 5/2.

Now we can combine the two shaded regions to find the overlapping region where both inequalities are satisfied. This region is shown in the graph below:

     |          /

     |        /

     |      /

     |    /  

     |  /    

     |/      

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

The point that represents a solution to the system is the point where the two lines intersect. To find this point, we can solve the system of equations:

y = x - 7

y = (-1/2)x + 5/2

Substituting the first equation into the second, we get:

x - 7 = (-1/2)x + 5/2

Simplifying this equation, we get:

(3/2)x = 19/2

x = 19/3

Substituting this value of x into either of the original equations, we get:

y = 19/3 - 7 = 2/3

So the point that represents a solution to the system is (19/3, 2/3).

Step-by-step explanation:

450, 46, 12

46, 12, 10

450, 10, 12

46,450,10

Step-by-step explanation:

The mixture of any three would be the possibilities

450, 46, 12

46, 12, 10

450, 10, 12

46,450,10

Answer: C) (1, -1)

Step-by-step explanation:

[tex]\boldsymbol{\sf{\underline{\diamond System \ of \ equations \ by \ the \ reduction \ method:} }}[/tex]

   [tex]\boldsymbol{\sf{We\:have\:the\:system\:of\:equations \ --\to \ \left \{ {{x+2y=1 \ } \atop {2x-3y=5 }} \right. }}[/tex]

Multiply the first equation by 2, and the second equation by -1, then both equations must be added.

             [tex]\boldsymbol{\sf{\star \ 2(x+2y=-1) }}\\ \boldsymbol{\sf{\star -1(2x-3y=5) }}[/tex]

We add these equations to eliminate x.

             [tex]\boldsymbol{\sf{\star \ 7y=-7 }}[/tex]

Then we solve 7y=-7 for y (divide by 7).

               [tex]\boldsymbol{\sf{\star \ \dfrac{7y}{7}=\dfrac{-7}{7} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ y=-1}}}[/tex]

We place the found value of y, in one of the original equations y to solve for x.

                  [tex]\boldsymbol{\sf{\star \ x+2y=-1}} \\ \\ \boldsymbol{\sf{\star \ x+2(-1)=-1}}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}[/tex]

Simplify (We add x to both sides.)

                  [tex]\boldsymbol{\sf{\star \ 0+(x)=-x+1+(x) }}\\ \\ \boldsymbol{\sf{\star \ x=1}}\\ \\ \boldsymbol{\sf{\star -2=-1-x}}[/tex]

Add (2) to both sides.

                   [tex]\boldsymbol{\sf{\star \ -2+(2)=-x-1+(2) }}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}[/tex]

We divide by 1.

                      [tex]\boldsymbol{\sf{\star \ \dfrac{x}{1}=\dfrac{1}{1} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ x=1}}}[/tex]

                                     [tex]\underline{\bf{ \ \ x,y \ answer\ \ \ \ }}\\\boxed{\boldsymbol{\sf{x=1,y=-1 }}}[/tex]

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Percentage of amount paid towards principal = 70.37%

Percentage of amount paid towards interest = 29.63%

APR is abbreviation Annual Percentage Rate. APR is estimate cost over a year of borrowing, It is expressed in percentage of the money borrowed. The higher it is, the more expensive to borrow. The lower it is, the cheaper it'll be to borrow.

Given,

Principal amount (P) = $95000

APR (R) = 5% = 0.05

Time (T)= 25 years

Amount paid monthly $450 for 25 years

There are 12 payments every year for 25 years

No. of payments,

12 × 25 = 300.

Total amount paid

3000 × $450 = $135000.

Amount paid toward Principal = $95,000

In percentage

= (95000/135000)×100

= 70.37%

Toward Interest = $135000 - $95000 = $40000

In percentage

= (95000/135000)×100

= 29.63%

Hence, 70.37% of amount is paid toward principal and 29.63% is paid for interest.

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Answer:

Step-by-step explanation:

To determine what percentage of the total amount paid is applied towards the principal and interest, we first need to calculate the total amount paid over the 25-year term.

The monthly payment can be calculated using the formula for a loan payment:

P = (r(PV)) / (1 - (1+r)^(-n))

where P is the monthly payment, r is the monthly interest rate (APR / 12), PV is the present value of the loan (or the amount borrowed), and n is the total number of payments (25 years * 12 months/year = 300).

Plugging in the given values, we get:

P = (0.05/12 * $95,000) / (1 - (1+0.05/12)^(-300)) = $536.82

This means that the total amount paid over the 25-year term is:

Total amount paid = 300 * $536.82 = $161,046

The amount borrowed (or the principal) is $95,000. Therefore, the amount of interest paid over the 25-year term is:

Total interest paid = $161,046 - $95,000 = $66,046

To find the percentage of the total amount paid that is applied towards the principal, we can divide the principal by the total amount paid and multiply by 100:

Percentage of total amount paid towards principal = ($95,000 / $161,046) x 100% = 59.03%

To find the percentage of the total amount paid that is applied towards interest, we can divide the interest paid by the total amount paid and multiply by 100:

Percentage of total amount paid towards interest = ($66,046)

The magnitude of the earthquake, as measured on the Richter Scale, is 2.5.

What is Richter Scale ?

The Richter Scale is a logarithmic scale used to measure the magnitude of earthquakes. It was developed by seismologist Charles Richter in the 1930s and is named after him.

The Richter Scale measures the amplitude of the seismic waves produced by an earthquake, which are detected by seismographs. The amplitude is a measure of the size of the earthquake, and is related to the amount of energy released by the earthquake.

Given by the question:
The Richter Scale equation for the magnitude (R) of an earthquake is:

R = log(A/A0)

where A is the amplitude of the earthquake and A0 is a standard wave amplitude.

We are given that the earthquake amplitude (A) is 288 times as great as the standard wave amplitude (A0):

A = 288 A0

Substituting this into the Richter Scale equation, we get:

R = log(288 A0 / A0)

R = log(288)

Using a calculator or a logarithm table, we can evaluate the logarithm of 288 to get:

R = 2.46

Rounding this to one decimal place, we get:

R ≈ 2.5

Therefore, the magnitude of the earthquake, as measured on the Richter Scale, is 2.5.

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Answer:

Let M be the minimum monthly payment and A be the additional monthly payment of $30. Let B be the balance on the store credit card.

From the problem, we have:B = M * 58 (if only minimum payments are made)

B = (M + A) * 24 (if an additional $30 is paid each month)

Simplifying these equations, we get:M = B / 58

M + A = B / 24

Substituting the first equation into the second equation, we get: B / 58 + A = B / 24

Solving for A, we get:A = B / 24 - B / 58

A = B * (58/24 - 1/58)

Simplifying, we get:A = B * 0.08275862

To find the percent of time that Haddad will save by paying the extra $30 per month, we need to find the difference in time between the two scenarios and divide by the longer time (58 months).

The time it takes to pay off the balance with only the minimum payments is 58 months, while the time it takes to pay off the balance with the additional $30 each month is 24 months.

The difference in time is:58 - 24 = 34

So Haddad will save 34 / 58 = 0.5862, or 58.62% of the time by paying the extra $30 per month.

please see the picture I but the answer on the top and the explanation in the bottom.

To match the terms to their correct definitions, we have:

A quadrilateral refers to a two-dimensional shape that has four sides, four vertices, and four angles.

There are different categories of quadrilaterals, such as trapezium, kite, parallelogram, rectangle, rhombus, and square.

The sides of a quadrilateral can be of different lengths and the angles can be of different measures.

Some types of quadrilaterals such as squares, rectangles, rhombus, etc. are special with some of their sides and angles being equal.

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Finally, we can solve for y by dividing both sides by (A + 3):

y = 18 / (A + 3)

Therefore, the solution for y is y = 18 / (A + 3).

By connecting two expressions with an equal sign, a mathematical statement known as an equation is produced. An equation is something like 3x - 5 = 16. The answer of this equation, which indicates that the value of the variable x is 7, is 7.

To solve for y in the equation Ay + 3y + 9 = 27, we need to isolate y on one side of the equation. We can do this by first combining the like terms on the left-hand side of the equation, and then subtracting 9 from both sides to get:

Ay + 3y = 18

Next, we can factor out the y term on the left-hand side:

y(A + 3) = 18

Finally, we can solve for y by dividing both sides by (A + 3):

y = 18 / (A + 3)

Therefore, the solution for y is y = 18 / (A + 3).

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Answer:

36 green marbles

Step-by-step explanation:

If 60% of the 60 marbles in the bag are green, then the number of green marbles can be calculated as:

Green marbles = 60% x 60 marbles

To simplify this calculation, we can convert 60% to a decimal by dividing by 100:

Green marbles = 0.60 x 60 marbles

Green marbles = 36 marbles

Therefore, Rudy received 36 green marbles.

Answer: 36

Step-by-step explanation:

60 is 6/10 of 100 so if you are taking a percent of 60 just multiply the percentage by 6/10. 6/10 of 60 is 36

Answer:

Step-by-step explanation:

Let's start by defining our variables:

a = number of student tickets sold

y = number of adult tickets sold

To write the system of inequalities, we need to take into account the given conditions:

The auditorium can hold no more than 85 people, so the total number of tickets sold cannot exceed 85:

a + y ≤ 85

The drama club must make no less than $690 from ticket sales:

7a + 10y ≥ 690

They must sell a minimum of 10 student tickets and at least 55 adult tickets:

a ≥ 10

y ≥ 55

To solve this system of inequalities graphically, we can plot the lines representing each inequality on the same graph and shade the feasible region. The feasible region is the area that satisfies all the inequalities.

First, let's plot the line a + y = 85. To do this, we can find the intercepts:

a + y = 85

a = 0 ⇒ y = 85

y = 0 ⇒ a = 85

Plotting these points and connecting them with a straight line, we get:

     |

   85|       /

     |       /

     |     /

     |   /  

     | /    

     |/______

          85    

Next, let's plot the line 7a + 10y = 690. To do this, we can find the intercepts:

7a + 10y = 690

a = 0 ⇒ y = 69

y = 0 ⇒ a = 99

Plotting these points and connecting them with a straight line, we get:

     |

   85|      /

     |      /

     |    /

     |  /  

     |/

     |______

          99

Finally, we need to shade the feasible region. We know that a ≥ 10 and y ≥ 55, so we can shade the region above the line a = 10 and to the right of the line y = 55.

markdown

Copy code

     |

   85|        /\

     |         /   \

     |       /       \

     |     /          \

     |    /             \

      /_________\

          99    55

This shaded region represents all the possible solutions that satisfy all three inequalities. We can now find one possible solution by picking any point within this region. For example, the point (20, 65) represents selling 20 student tickets and 65 adult tickets, which meets all the conditions and generates a total revenue of 720 + 1065 = $690.

Answer:

x = 10

Step-by-step explanation:

We know that it's a right triangle and it's two sides, which are 6 and 8

So we can find the third side, the Hypotenuse or x, using the Pythagoras Theorem

6² + 8² = Hypotenuse ²

36 + 64 = Hypotenuse²

100 = Hypotenuse²

Hypotenuse = root100

Hypotenuse = 10

Therefore x = 10

The equation for the given statement can be written as:

-95x - 14 = -70 - x

To solve for x, we can rearrange the equation and combine like terms:

-95x + x = -70 + 14

-94x = -56

Next, we can divide both sides by -94 to isolate x:

x = -56/-94

Finally, we can simplify the fraction to get our answer:

x = 28/47

Therefore, the solution to the equation is x = 28/47.

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The annual interest rate for the given compound interset is 6%

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.  

Given that, Rs.2250 is deposited for 2 years in an account, it amounts to Rs.2560 compounded annually.

A = P(1+r)ⁿ

2560 = 2250(1+r)²

2560 / 2250 = (1+r)²

1.13 = (1+r)²

Taking roots,

1+r = √1.13

r = 0.06

r = 6%

Hence, the annual interest rate for the given compound interset is 6%

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Based on the given information, we can make the following conclusions: Both means are shorter than their respective medians. The median-to-mean increase is greater in the case of bypass surgery

In statistics, the median is a measure of central tendency that represents the middle value of a dataset when the data is arranged in ascending or descending order. It is the value that separates the lower 50% of the data from the upper 50% of the data. To find the median of a dataset, the data is first arranged in order. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values. The median is a useful measure of central tendency because it is less sensitive to outliers than the mean, which makes it a better indicator of the typical or central value of a dataset when the data is skewed or contains extreme values.

Here,

1. Both means are shorter than their respective medians, suggesting that both distributions are skewed to the right. This means that there are some patients who wait for a very long time, causing the right tail of the distribution to be longer.

2. The fact that the median is greater for angioplasty and the mean is greater for bypass surgery tells us that the median-to-mean increase is greater in the case of bypass surgery, suggesting that the skewness is more pronounced for bypass surgery than for angioplasty. This means that there are relatively more patients who wait for a very long time for bypass surgery compared to angioplasty, which is reflected in the longer right tail of the distribution for bypass surgery.

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The average is 9.99, the very first percentile is 8.01, as well as the upper quartile is 13.33 as a result.

From smallest to highest number, 25% is the first quartile. Second quartile: 25.1% to 50% (till median) 51% to 75%, third quartile (above the median) 25% of the biggest values are in the fourth quartile.

The data must first be arranged in ascending order before we can calculate the median or quartiles of the provided data:

5.24, 6.02, 6.67, 7.30, 7.59, 7.99, 8.03, 8.35, 8.81, 9.45, 9.61, 10.37, 10.39, 11.86, 12.22, 12.71, 13.07, 13.59, 13.89, 15.42

There are a total of 20 data points, and the median is calculated as that of the average of a 10th and 11th pieces of data:

(9.61 + 10.37) / 2 = 9.99; median

The very first quartile (Q1) must be determined in order to determine.

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