A preschool has 100 feet of fencing to enclose 3 sides of a rectangular playground. The fourth side is formed by a wall of the school. The function A(x) = 100x − 2x2 represents the possible area of the playground with side length x feet. Which range is appropriate for this situation?

Using proportions and constant of proportionality, the train always move the same distance and the cost is always the same

Proportion can defined as the comparison between two numbers or ratios. Using proportions, when two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The proportional relationship between two numbers can be represented as

y = kx

i)

In this question, let's determine if they have the same constant of proportionality.

y = kx

6 = k(2)

k = 3

12 = k(4)

k = 3

Since they have the same constant of proportionality, the train always go the same distance each minute.

ii)

The time travelled in 10 minutes

y = 3x

y = 3(10)

y = 30

The distance in 10 minutes is 30km

b)

Using constant of proportionality to determine if they have a proportional relationship;

y = kx

21 = k(3)

k = 7

42 = k(6)

k = 7

The equation is y = 7x and the constant of proportionality is 7.

The cost for each person is always the same

ii) From y = 7x

63 = 7x

x = 63 / 7

x = 9

The predicted number for a cost of $63 is 9

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The sale price of the shirt is equal to $12

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We are given that Original price of the shirt = $16

The Sale price = 34% of the original price

If original price = $16, then Sales price will be 34% of original price - original price

= 0.34 × 16 - 16

Apply BODMAS multiply before subtracting;

=16 - 0.34 × 16

=$16 - $4

Sales price = $12

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The complete question is

Shirts are on sale for 34 of the original price. If the original price was $16, what is the sale price?

Answer:

x = 12

y = 4

Step-by-step explanation:

Part B

Gradient

Gradient = (y2 - y1) / (x2 - x1)    

Gradient = (6 - 3) / (10 - 4)

Gradient = 0.5

Line of equation

y - y1 = m (x - x1)

y - 3 = 0.5 (x - 4)

y - 3 = 0.5x - 2

y = 0.5x - 2 + 3

y = 0.5x + 1

f(x) = mx + b ---> f(x) = 0.5x + 1  

m = 0.5

b = 1

Part A

x = 12

y = 4

(Put the values of the graph in the line of equation)

I hope my answer helps you.

Answer:  the area of the rectangle is 456 square millimeters.

Step-by-step explanation:

the perimeter is 88 mm, so if we let L be the length of the rectangle and W be the width, we can write the following equation to find the perimeter:

2L + 2W = 88 mm

Since the base of the rectangle is 38 mm, we know that the width of the rectangle is 38 mm, so we can substitute that value into the equation above to get:

2L + 2(38 mm) = 88 mm

Solving for L, we get:

2L = 88 mm - 2(38 mm)

2L = 88 mm - 76 mm

2L = 12 mm

Therefore, the length of the rectangle is 12 mm. Now that we know both the length and the width, we can find the area by multiplying the length and the width:

Area = L * W

Area = 12 mm * 38 mm

Area = 456 mm^2

Thus, the area of the rectangle is 456 square millimeters.

Answer:

A=228mm

Step-by-step explanation:

What formulas do we know?

Parameter= 2(length)+2(width)

Area= length x width

We can just substitute in values for parameters so,

88=2(length) + 2(38)

88=2L + 78 ------> 12=2L -------> L=6

Now we know width (which is just B) and Length (what we calculated)

Now we use area ----> Area= length x width

Area= (38)(6)-----> 228mm

Answer:

The correct answer would be 5000 x ^108

Step-by-step

The number of pint jar needed to hold 5 gallon of sauce is 40 jars.

Pint and gallons are both units of volume. The number of pint jars needed to hold 5 gallon of sauces can be determined by changing the unit of volume. Conversion of units refers to the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects. According to the conversion of units, 1 gallon is equal to 8 pint. Hence, applying the conversion rate to the total volume of tomato sauce made:

5 gallons = 5*8 = 40 pint

If a jar holds 1 pint of sauce, the number of jars to hold the total volume of sauce is 40 pint jar.

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The difference between the interest compounded daily and the interest compounded annually is $67.13.

To calculate the interest earned by your money annually, you calculate as follows;

To determine the interest, use FV - amount invested

FV = P (1 + r)^n

the above represents,

FV = Future value

P = Present value

R = interest rate

N = number of years

$25,000 (1.0725) = 26,812.50

26,812.50 - $25,000 = $1,812.50

What is the interest earned in your money is compounded on a daily basis?

$25,000x (1 + 0.0725 /365)^365 = 26,879.63

26,879.63 - $25,000 = $1879.63

What is the difference in interest?

$1879.63 -  $1,812.50 = $67.13

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The logical statement [tex]$(a \wedge b) \rightarrow(b \vee c)$[/tex] is a tautology. Hence, Option B  and Option C is the most appropriate answer to the given question.

A tautology is a logical statement where the conclusion is always equivalent to the premise. No matter what the individual parts are, the result is always a true statement; i.e. a tautology is always true. The opposite of tautology is either a contradiction or a fallacy.

say, "x=y or x≠y".

Similarly, "either the ball is red, or the ball is not red" is always true, irrespective of the color of the ball.

Here, checking the truth tables of each of the options

we can conclude that the truth values of (P v Q)→Q and P v (P→Q) are always true.

So, (P V Q) →Q and P v (P→Q) are tautology statements.

Hence, option B and option C are the correct choices for this question.

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Answer: 0.03 pounds

Step-by-step explanation:

To determine how much trail mix went in each bag, you need to divide the total amount of trail mix by the number of bags.

In this case, you would divide 3 pounds of trail mix by 10 bags to find that each bag contained 0.3 pounds of trail mix.

You can also express this amount in ounces. Since there are 16 ounces in a pound, each bag contained 4.8 ounces of trail mix (0.3 pounds * 16 ounces/pound = 4.8 ounces).

X is an algebraic variable which has no defined value. X is kind of universe variable taken in most of the equations.

The value of x in the solution set of - 5x - 15 > 10 + 20x is x < - 1 and the required value from the solution set is -2.

Solution:

Given: - 5x - 15 > 10 + 20x

Let us solve the inequality by isolating the variable x.

Add 5x on both sides

- 5x - 15 + 5x > 10 + 20x + 5x

- 15 > 10 + 25x

Subtract 10 from both sides

- 15 - 10 > 10 - 10 + 25x

- 25 > 25x

Divide both sides by - 25

-1 > x

x < - 1

The value of x in the solution set of - 5x - 15 > 10 + 20x is x < - 1 and the required value from the solution set is -2.

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Answer:

-2

Step-by-step explanation:

i did it

Answer:

It will cost $86.00 for the care to be towed 7 miles.

Step-by-step explanation:

C(x) = 3x + 65  Substitute in 7 for x

C(7) = 3(7) + 65

C(x) = 21 + 65

C(x) = 86

Answer

86 Dollars

Step-by-step explanation:

It is given that

[tex]c(x) = 3x + 65 \\ [/tex]

Since,x is the number of miles the car is towed which in this case is 7

So, If we input 7 in the function C(x)

[tex]c(7) = 3 \times 7 + 65[/tex]

We know through BODMAS that multiplication is done before addition.

Thus,

[tex]c(7) = 21 + 65 \\ because \: 3 \times 7 = 21 \\ [/tex]

and so,

[tex]c(7) = 86 \\ because \:21 + 65 = 86[/tex]

and so,

c(7) = 86

We also know that C(x) is the cost of having the car towed which is equal to 86 for the case of towing the car 7 miles

Thus,The cost of having the car towed 7 miles is 86 Dollars

Answer:

nth term = a+(n-1)d

Step-by-step explanation:

where a=first term

n=nth term

d=common difference=2nd term - 1st term=5

The Probability of getting less than 555 orders = x<555/ccc

Suppose we discuss about two events which can be occurred at any time but the occurrence of one event is not dependent on other event. In such case the probability of occurring each event is called independent probability.

The probability of two independent events is calculated by the formula

probability of one event × probability of another event

If A and B are two events occurred independently

    probability of happening two events = P(A)×P(B)

In our problem, order for cake over telephone is one event

         order for cake manually is another event

10 percent order get over telephone

So, percent of probability to get order from phone = 10/100 = 1/10

She got total ccc cake order in a month before getting order over phone

let. X is a number of orders she got before getting her first telephone order.

Therefore, the probability that it takes fewer than 555 orders for Lilyana to get her first telephone order = X<555/ccc

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A significant relationship between x and y is  b. large p-value for the estimated slope.

Simple linear regression is used to estimate the connection among  quantitative variables. You can use easy linear regression whilst you need to know: How robust the connection is among variables (e.g., the connection among rainfall and soil erosion). The fee of the established variable at a positive fee of the impartial variable (e.g., the quantity of soil erosion at a positive stage of rainfall). Simple linear regression is used to version the connection among  non-stop variables. Often, the goal is to are expecting the fee of an output variable (or response) primarily based totally at the fee of an input (or predictor) variable.

Thus, option b is the correct choice.

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64 observations were randomly selected at random from a population of 500. the population standard deviation is 16.The standard deviation of the sample mean is 4 (16/√64).

The standard deviation of the sample mean is calculated by dividing the population standard deviation (16) by the square root of the sample size (64).

Consequently, the sample mean's standard deviation is

16/√64 = 4.

This means that the expected spread of the sample means is 4, which is less than the population standard deviation of 16. This is because the sample is smaller than the population, so the sample standard deviation will be smaller than the population standard deviation.

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Answer:

8) y = 4

9) y = x

Step-by-step explanation:

8) Parallel = Same slope

y = mx + b

m = 0

4 = - 4(0) + b

4 = b

y = 4

9) y = x + b

7 = 7 + b

b = 0

The primary eight candles or oil lamps must be on a plane that is higher or lower than the shamash.

A nine-branched candelabrum known as a Hanukkah menorah, also known as a hanukkiah, is lighted during the eight-day Jewish festival of Hanukkah. Eight of the nine branches are held up by lights (candles or oil lamps), which stand throughout the eight nights of the festival. One additional light is lighted each night until all eight branches are illuminated on the last night. The candle on the ninth branch, known as the shamash (Arabic for "helper" or "servant"), is used to light the other eight branches.

The seven-branched menorah used in the first Temple in Jerusalem is commemorated by the Hanukkah menorah, which is separate from it. It's one of the most commonly manufactured pieces of Jewish ritual art, along with the Star of David and the menorah with seven branches.

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The result of the multiplication of  (√2x³ +√12x)(2√10x³ + √6x²) is

[tex]2\sqrt{20}x^6 + \sqrt{12}x^5 + 2\sqrt{120}x^4 + \sqrt{72}x^3[/tex]

What is multiplication?

Multiplication is a mathematical operation in which one number is multiplied by another. It is usually used to calculate the product of two or more numbers. It is an important operation in mathematics and is used in a variety of ways, including calculating the area of a rectangle, the volume of a cube, and the total cost of items purchased at a store. Multiplication is often represented by the multiplication symbol, which is usually an 'x' or an asterisk (*). When two numbers are multiplied, the result is called the product. For example, if two numbers are multiplied together, the product is the answer to the question "what is the result of multiplying these two numbers together?" The answer is the product of the two numbers.

Here the multiplication given is

(√2x³ +√12x)(2√10x³ + √6x²)

[tex]2\sqrt{20}x^6 + \sqrt{12}x^5 + 2\sqrt{120}x^4 + \sqrt{72}x^3[/tex]

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The present ages of the father and his son are 50 and 30 years respectively.

An algebraic expression can be defined as an expression made up of constants, variables, terms, coefficients, and factors.

These expressions are also made up of mathematical or arithmetic operations, which includes;

From the information given;

Let the son's age be x

Let the father's age be x + y

x + x + y = 80

2x + y = 80

Then, 2x - y = 40

From equation (1), make 'y' the subject

y = 80 - 2x

Substitute the value

2x - (80 - 2x) = 40

2x - 80 + 2x = 40

collect like terms

4x = 120

x = 30

y = 80- 2(30)

y = 20

Hence, their ages are 30 years and 50 years

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With the mentioned area of fabric, the five person in group will get 6.47 ft² of fabric per person.

Firstly converting the area of fabric from mixed fraction to fraction.

The area of fabric = (32×3 + 1)/3

Performing multiplication and addition on Right Hand Side of the equation

The area of fabric = 97/3 ft²

Amount of fabric each person gets = (97/3)/5

Performing division on Right Hand Side of the equation

Amount of fabric each person gets = 97/(3×5)

Amount of fabric each person gets = 97/15

Amount of fabric each person gets = 6.47 ft²

Thus, each person will get the fabric of area 6.47 ft².

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The equation of line that would graph his salary over time will be;

⇒ y = 1/685x - 38.89

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

After 4 years, he makes $56,785; after 9 years, he makes $60,210.

Now,

Since, After 4 years, he makes $56,785; after 9 years, he makes $60,210.

Hence, The equation of line passes through the points (56,785, 4) and

(60,210, 9).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (9 - 4) / (60210 - 56785)

m = 5 / 3425

m = 1/685

Thus, The equation of line with slope 1/685 is,

⇒ y - 4 = 1/685 (x - 56,785)

⇒ y - 4 = 1/685x - 42.89

⇒ y = 1/685x - 42.89 + 4

⇒ y = 1/685x - 38.89

Therefore, The equation of line that would graph his salary over time will be;

⇒ y = 1/685x - 38.89

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the time it takes to preform a task has a continuous uniform distribution between 43 min and 57 min. 0.1875 is the the probability it takes between 54.7 and 56 min. round to 4 decimal places.

The probability of any event occurring is given by the formula P(x) = (x-a)/(b-a). In this case, the probability of the task taking between 54.7 and 56 minutes is (56-54.7)/(57-43) = 0.1875. This probability is equal to the area under the uniform distribution graph between 54.7 and 56 minutes. As the graph is a rectangle, the area is simply the width multiplied by the height, so 0.1875. Rounding to 4 decimal places, the probability is 0.1875.

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The number of coach tickets is; 3 coach tickets

The number of first class tickets is; 8 first class tickets

We are told that she took 11 people on the trip.

Let the number of first class tickets be f

Let the number of coach tickets be c

Thus;

c + f = 11  -----(1)

She was able to purchase coach tickets for $180 and first class tickets for $1200. She used her total budget for airfare for the trip, which was $10,140. Thus;

180c + 1200f = 10140   -----(2)

Make c the subject in eq 1 to get;

c = 11 - f

Put 11 - f for c in eq 2 to get;

180(11 - f) + 1200f = 10140

1980 - 180f + 1200f = 10140

1020f = 8160

f = 8

Thus;

c = 11 - 8

c = 3

So, 3 coach tickets and 8 first class tickets were bought

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To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, we need to first solve the system of equations to find the value of x and y that satisfy both equations.

To solve the system of equations, we can first solve the first equation for y:

y = −3x + 1

Next, we can substitute this expression for y into the second equation and solve for x:

2y = −6x + 2

2 * (−3x + 1) = −6x + 2

−6x + 2 = −6x + 2

0 = 0

Since the two equations are equivalent, the system of equations is consistent and dependent, meaning that there is only one possible solution (x = 0, y = 1) that satisfies both equations.

The percentage represented is 72%, and the decimal is 0.72

First lets find the decimal, it will be equal to the quotient between the total number of shaded squares and the total number of squares.

There are 200 squares in total, and of these 200, there are 144 shaded ones, then the decimal is:

d = 144/200  = 0.72

To find the percentage, you only need to multiply the decimal by 100%, we will get:

p = 100%*0.72 = 72%

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The two linear equations can be written as:

y = 2*x + 1

y = x + 2

Remember that a general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

First, we know that one of the lines has an y-intercept at y = 1, then:

y = a*x + 1

And the line passes through (1, 3), replacing these values we get:

3 = a*1 + 1

3 - 1 = a

2 = a

That line is y = 2*x + 1

The other line has a y-intercept at y = 2, then:

y = a*x + 2

This line also passes through (1, 3), then:

3 = a*1 + 2

3 = a + 2

3 - 2 = a

1 = a

The line is:

y = a*x + 2

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The variables x, y, z associated to the parallelogram are equal to 60, respectively.

A parallelogram is a quadrillateral formed by two pairs of parallel sides. The figure shows a parallelogram since the following relationships are met: BC ║ AD, AB ║ CD. We need three equations to determine the values of x, y and z and this can be obtained by means of parallelogram properties:

y = x

y + (x + y) = 180°

z + (x + y) = 180°

First, substitute x on the second and third equations:

3 · y = 180°

z + 2 · y = 180°

Second, find y:

y = 180° / 3

y = 60

Third, find z:

z = 180° - 2 · y

z = 180° - 2 · 60

z = 180° - 120°

z = 60

Fourth, find x:

x = 60

The values of variables x, y, z are 60, respectively.

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Answer:

x = 145°

Step-by-step explanation:

x and 35° are a linear pair and sum to 180° , then

x + 35° = 180° ( subtract 35° from both sides )

x = 145°