Fleur is making 8 identical thank-you cards for her teachers. each card requires 2.5 sheets of yellow paper and some red paper. she uses a total of 30 sheets of paper. a. write an equation that can be used to determine the number of red sheets, r, required for each card. __

The probability that x < y is 1/8 or 0.25 .

What is probability of an event?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.

Given, the vertices of the rectangle are (0, 0), (4, 0), (4, 1), (0, 1).
On carefully analyzing and plotting the vertices roughly, we get that the given rectangle has a width of 4 units and a height of 1 unit.
Therefore, the area of the given rectangle = Width*Height = 4*1 = 4 units²
Also, it can be assessed that the line x = y passes through the points of the rectangle at (0, 0) and (1, 1).
Thus, the area for which x < y will be an isosceles triangle with side length of 1 units and co-ordinates of vertices as (0, 0), (0, 1) and (1, 1).
The area of the isosceles triangle thus assumed = 0.5 × 1² = 0.5 units²
Probability that x < y is P(E): 0.5/4 = 1/8 = 0.25
Therefore, the probability that x < y is 1/8 or 0.25 .

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The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:

= 48π + 42

The area of a circle, A, is calculated using the formula A = pi * r2, where r is the circle's radius. Since we already know that a semicircle is half of a circle, we can easily divide that equation by two to determine the area of a semicircle. As a result, A = pi * r2/2 is the formula for calculating the area of a semicircle.

With the aid of the following formula, we can determine a semicircle's perimeter: The semicircle's perimeter is equal to r + 2r units, where r is the radius of the semicircle.

Diameter of the semi-circle = 84cm

Now,

the circumference of the semi-circle  =  πr + 2r

Substituting the value of r in the given formula:

the circumference of the semi-circle  =  πr + 2r

                                                              = πr + 2r

                                                               = 48π + 42

The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:

= 48π + 42

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Answer:

I hope this is right

TG = 34 TG=34  inches

From the figure

            PQR is a triangle

            PS, QT are medians of the triangle  

            G is the centroid

Step 1: Calculate the segment of the median (TG = ? )

              We know that

              Each median is divided into segments with a 2:1 ratio by the triangle centroid.

                    \therefore \frac{TG}{GQ} = \frac{2}{1} ∴

GQ/TG = 1/2

​

                          TG = 2 GQ TG=2GQ

                          TG = 2 * 17 TG=2∗17

                          TG = 34 TG=34

               Hence, segment of the median  TG = 34  inches

We have an absolute value function that opens upwards. The interval where it is decreasing only is:

(-∞, 2)

All absolute value equations of the form:

y = |x - a| + b

have graphs that open upwards, and a vertex in the point (a, b).

While ones of the form:

y = -|x - a| + b

have graphs that open downwards, and again, a vertex in the point (a, b).

In this case we have one that open upwards:

h(x)=|x-2|+6

With a vertex at (2, 6)

The function will be decreasing on the left side of the vertex, so the interval where the function is only decreasing is:

(-∞, 2)

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Answer:

15 weeks.

Step-by-step explanation:

Answer:

I can use the given (algebraic expression) 24c+12 to find the total cost of the order

The expression has two (terms). They are 24c and 12

In 24c the number 24 is the (coefficient) and the letter c is the (variable).

The term 24c represents a (product)

To find the total cost of the order I can (evaluate) the given expression

I have to (substitute) the given value for the variable then I can follow the (order of operations) to simplify the expression

24c+12

24(6)+12

144+12

156

The total cost is 156

Hope this helps :)

As per the reference attachment attached thereby along with the question statement, to prove the triangles ABC and ADC are congruent by SAS property, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will suffice.

In the reference attachment attached thereby along with the question statement, we are provided with two triangles, (ADC and ABC),

And as per the question statement, we are required to determine the relation between the corresponding sides or angles of the concerned triangles which we will need to prove over the information already provided in the figure, to ascertain that triangles ABC and ADC are congruent by SAS property.

Now, for two triangles to be congruent by SAS property, they will need to have two pairs of equal corresponding sides, and one set of equal corresponding angles.

Among our concerned triangles, ΔABC and ΔADC, already given that,

(∠DAC = ∠BCA), i.e., one set of equal corresponding angles,

And, (AC) is a common side to both ΔABC and ΔADC, i.e., one set of equal corresponding sides.

At this point, for ΔABC and ΔADC to be congruent, we will need to prove another set of corresponding sides to be equal, to complete SAS property.

Therefore, proving either of (AB ≅ CD), (AB ≅ DC) or (AD ≅ BC) will complete the second set of corresponding sides being equal, and  (ΔABC and ΔADC) can be proved to be congruent triangles.

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The equation to represent the expression is C ( b ) = 2.25b , where C ( b ) is the cost of b number of chocolate bars

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of b chocolate bars be = C

Let the cost of 1 bar of chocolate bar be = $ 2.25

Let the number of chocolate bar be = b

Now , the equation to find the cost of b number of chocolate bars is ,

The cost of b number of chocolate bar =
cost of 1 bar of chocolate bar x number of chocolate bar

So , the equation is

The cost of b number of chocolate bar = 2.25b

So , the equation to find the cost of b number of chocolate bars is ,

Cost of b chocolate bars C = cost of b number of chocolate bar

C ( b ) = 2.25b

Therefore , the expression is C ( b ) = 2.25b

Hence , The equation to represent the expression is C ( b ) = 2.25b , where C ( b ) is the cost of b number of chocolate bars

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The ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint 4:9.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint.

So, the ratio of gallons of blue paint to gallons of yellow paint is

= 5 to 9  or 5:9

Now, ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint

= 1- 5/9

=4/9

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The total cost for an order of 30 copies is $17.50.

So, calculate the total cost as follows:

We have:

Here, x implies a number of orders of copies and in question, it says the order of 30 copies.

So, Substitute x=30 in equation 1,

Hence, the total cost for an order of 30 copies is $17.50.

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Answer:

Is this an arithmetic sequence?

Yes.

Is there a common difference and if so, what is it?

Yes, there is a common difference : 1

The common difference is 1

The domain of the graph is (d) all set of real values

The graph represents the given parameter

This graph represents a function

Say the graph represents the function f(x)

The x values represent the domain

i.e domain = Set of all x values

On the graph, we can see that the graph extends across the x-axis till infinity on both sides

This means that

Domain = All set of real values

Hence, the domain of the relation is (d) all set of real values

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Part A

The equation that shows the statement is

2N + 20 = 4N - 40

Part B

The value of N = 30

The number that he is thinking = N

Twice (N+10) = 2(N+10)

= 2N + 20

Four times (N-10) = 4(N - 10)

= 4N - 40

Twice (N+10) is the same as four times (N-10)

The equation that represent the given statement is

2N + 20 = 4N - 40

Part B

Solve the equation

2N + 20 = 4N - 40

4N - 2N = 20 + 40

2N =  60

N = 60/2

Divide the terms

N =30

Hence,

Part A

The equation that shows the statement is

2N + 20 = 4N - 40

Part B

The value of N = 30

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Answer:

the answer is 9/14

Step-by-step explanation:

2/7× 2 1/4 = 2/7× 9/4

= 2 × 9 / 7 × 4

= 18/28

= 9/14

the figure for m3 in the above question is 50

Answer:

Q1 = 6.45f/s

Q2 = 0.633 times

Q3 = 0.107 miles

Step-by-step explanation:

Q1: Since

4.4 miles = 1 hour

and

1 mile = 5,280 feet

1 hour = 3600 seconds

Then 4.4 miles

= 5,280 feet × 4.4

= 23,232 feet / 3600 seconds

= 6.453f/s

= 6.45f/s

Q2: Wing beat per minute

= 38 ÷ 60

= 0.633 times

Q3: Miles per minute

Since 6.4 miles = 1 hour,

6.4 miles = 1 × 60

6.4 miles = 60 minutes

x miles = 1 minute

= 6.4/60

= 0.107 miles

The 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)

Given the equation that models the situation expressed as:

4x + 6y = 48

We are to find 4 possible solutions for x and y. Note that the values of x and y must be integers.

If there are no cars i.e. at when x = 0

4(0) + 6y = 48

0 + 6y = 48

6y = 48

y = 48/6

y = 8

One of the solution is (0, 8)

If there are 3 cars, i.e. at when x = 0

4(3) + 6y = 48

12 + 6y = 48

6y = 48 - 12

y = 36/6

y = 6

The second solution will be (3, 6)

If there are 6 cars, i.e. at when x = 6

4(6) + 6y = 48

24 + 6y = 48

6y = 48 - 24

y = 24/6

y = 4

The third solution will be (6, 3)

If there are 9 cars, i.e. at when x = 9

4(9) + 6y = 48

36 + 6y = 48

6y = 48 - 36

y = 12/6

y = 2

The fourth solution will be (9, 2)

Hence the 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)

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Answer:

0.000065 km

Step-by-step explanation:

To get from cm to km you need to divide 6.5 by 0.000001 which equals 0.000065km

The coordinates of G' after the rotation = (6, 5)

In this question we have been given a point G, located at (-5, 6) is rotated 270° counterclockwise.

We need to find the coordinates of G' after the rotation.

a point (-5, 6) is located in the second quadrant.

First 90° counterclockwise rotation gives (-6, -5)  because x & y are interchanged and in Quadrant III both coordinates will be negative.

Second 90° counterclockwise rotation yields (5,-6) because x & y are interchanged and in Quadrant IV the y coordinate will be negative.

Last 90° counterclockwise rotation yields (6, 5) because x & y are interchanged and in Quadrant I both coordinates will be positive.

Therefore, the coordinates of G' after the rotation = (6, 5)

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With the help of angles we can say that ∠HJI=∠FJG.

Acc to our question-

Hence, ∠HJI≅∠FJG are equal and congruent.

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Answer:

  45,000

Step-by-step explanation:

Given a 30 minute sample of a constant stream shows 2250 people entered the gate, you want an estimate of the total number of people through the gate in 10 hours.

A half-hour period is 1/20 of the 10-hour period the gate was open. The rate is assumed constant, so the 2250 people entering in that half-hour period is presumed to be 1/20 of the total attendance.

  20 · 2250 = 45000

The estimated festival attendance is 45,000 people.

Step-by-step explanation:

so, after clarification from your side, we know

f(x) = 12500 × (0.82)^x

so, with every new year we are multiplying the value of the previous year by 0.82.

in other words

f(n) = f(n-1) × 0.82

with f(0) = 12500

because anything to the power of 0 equals 1.

A

so, the price is decreasing every year, because any multiplication with a positive value smaller than 1 decreases the original number.

multiplying an amount by a decimal number like 0.82 creates exactly 82% of the original amount because 1 represents 100%.

that means the value decreases every year by 100 - 82 = 18% compared to the value of the previous year.

B

1 5600

2 3136

3 1756.16

4 983.45

remember, Part A showed always an 18% decrease over the previous year.

from 5600 to 3136, this was a change of

100% = 5600

1% = 100%/100 = 5600/100 = $56

the price difference was 5600 - 3136 = 2464

how many % was that decrease ?

as many as how often 1% fits into 2464 :

2464 / 56 = 44%

that was much more than Part A.

from 3136 to 1756.16, this was a change of

100% = 3136

1% = $31.36

the price difference was 3136 - 1756.16 = $1,379.84

how many %

1,379.84 / 31.36 = 44%

again.

from 1756.16 to 983.45, this was a change of

100% = 1756.16

1% = $17.5616

the price difference was 1756.16 - 983.45 = 772.71

hire many %

772.71 / 17.5616 = 43.99997722...%

and again 44% (just a little rounding uncertainty).

so, product B recorded a much greater percentage change in value over the previous year than product A :

44% to 18%

Time taken by bus to travel from Las Vegas to salt lake city is 6.41 hours.

Here it is given that bus travel from La to Lv in 4 hours and the distance between them is 265 miles.

We have to find the time taken to travel from Las Vegas to salt lake city whose distance between them is 425 miles.

Formula to find the speed is:

Speed = Distance / Time

Distance = 265 miles

Time = 4 hours

Speed = 265/4

= 66.25 miles/ hour

From this, we can find the time taken to travel from Las Vegas to salt lake city.

Distance = 425 miles

Speed = 66.25 miles/ hours

Speed = Distance/time

Time = Distance / Speed

= 425/ 66.25

= 6.41 hours

Therefore the time taken is 6.41 hours.

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Answer:

The number to the ration

Step-by-step explanation:

Answer:

82 and 2/4 (if it was 30 days)

Step-by-step explanation:

you turn the fraction into a decimal and multiply it by the certain number of what you need to figure out.

The value of x in the equation is $55 and this represents the cost of the expensive book

The variable x is not defined in the question

So, we represent x as the more expensive book and y to represent the less expensive book

Also, from the question we understand that

The above statements can be interpreted to the following equations

x = 4 + 3y

x + y = 72

Substitute x = 4 + 3y in the equation x + y = 72

So, the equation x + y = 72 is represented as

4 + 3y + y = 72

Evaluate the like terms in the above equation

4 + 4y = 72

Collect the like terms in the above equation

4y = 72 - 4

Evaluate

4y = 68

Divide both sides by 4

So, we have

y = 17

Substitute 17 for y in the equation x = 4 + 3y to solve for x

x = 4 + 3 * 17

Evaluate the products

x = 4 + 51

Evaluate the sum

This gives

x = 55

Hence, the cost of the more expensive book is $55

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Answer:

4

Step-by-step explanation:

12÷3=4

Answer: 92

Step-by-step explanation:

The value of y is 11.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given that Parallelogram ABCD is a rectangle.

Consider that AC and BD are opposite sides. In a parallelogram, we know that opposite sides are congruent which means:

AC = BD

2y + 7 = 3y - 4

Solving;

2y - 3y = -4 - 7

-y = -11

y = 11

Hence, the value of y is 11.

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Answer:

x=10

Step-by-step explanation:

-3+x=7

Add 3 to both sides.

7+3=10

x=10

Answer:

x=10

Step-by-step explanation:

-3+x=7

You have to add 3 to both sides to cancel out the -3

x=10

That leaves you with x=10