In 1992, a postage stamp cost $0.25. In 2004, a postage stamp cost $0.37. What is the average rate of change in postage cents per year?

In order for the ratio of AP to PB to be 3/2, the coordinates of point P along the directed line segment AB are (14/5, -1).

The section formula returns the coordinates of a point that divides the line connecting two points in a ratio, either internally or externally.

Section formula is given as follows:

[tex](\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})[/tex]

It is given that the coordinates of the points A and B are A(-2, -4), B(6, 1) and   AP/PB = 3/2

Let the coordinates of the point P be (a, b).

By using section formula,

(a, b) = [tex](\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})[/tex]

(a, b) =  [tex](\frac{3(6)+2(-2)}{3+2} , \frac{3(1) +2(-4)}{3+2} )[/tex]

(a, b) = [tex](\frac{18 - 4}{5} , \frac{3-8}{5})[/tex]

(a, b) = [tex](14/5, -5/5)[/tex]

(a, b) = [tex](14/5, -1)[/tex]

Therefore, the coordinates of the point P along the directed line segment AB so that the ratio of AP to PB is 3/2 are (14/5, -1).

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Option (C) is correct which is the equation 4 w + ( − 4 p ) = 8 . 00 is the result of subtracting the second equation in the system from the first equation.

Mai and Tyler are selling items to earn money for their elementary school.

Mai sells 14 wreaths and 3 potted plants and the school earns $70.50. Mathematically we can write,

14 w + 3 p = 70.50                          equation 1

Tyler sells 10 wreaths and 7 potted plants and the school earns $62.50. Mathematically we can write,

10 w + 7 p = 62.50                           equation2

equation 1 - equation 2 , we get

4 w + ( - 4 p ) = 8.00

which is the required equation.

We can conclude that the equation 4 w + ( − 4 p ) = 8 . 00 is the result of subtracting the second equation in the system from the first equation

So, option (C) is correct.

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Answer: cosφ=-3/5

Step-by-step explanation:

[tex]\displaystyle\\sin\phi=\frac{4}{5} \ \ \ \ \ 90^0 < \phi < 180^0\\\\sin^2\phi+cos^2\phi=1\\\\\cos^2\phi=1-sin^2\phi\\\\cos^2\phi=1-(\frac{4}{5})^2\\\\ cos^2\phi=1-\frac{16}{25} \\\\cos^2\phi=\frac{1(25)-16}{25}\\\\ cos^2\phi=\frac{25-16}{25} \\\\cos^2\phi=\frac{9}{25} \\\\cos\phi=б\sqrt{\frac{9}{25} } \\\\cos\phi=б\sqrt{\frac{3^2}{5^2} }\\\\cos\phi=б\sqrt{(\frac{3}{5})^2} \\\\cos\phi=б\frac{3}{5} \\\\90^0 < \phi < 180^0\\\\Hence,\ \\\\cos\phi=-\frac{3}{5}[/tex]

Answer:

$74.00

Step-by-step explanation:

Two tickets at $37 apiece, we cal calculate a total by adding 37 + 37,

OR by multiplying

2×37

Either way, the total works out to be $74

Answer:

x=110

Step-by-step explanation:

You can set the equation up like this:

100=x-10

Make x by itself

x=110

The largest possible number of red socks in the drawer that is consistent with this data is 990.

To solve the given question, we will form equations according to the given data including a known and an unknown variable.

Let r be the number of socks that are red, and t be the total number of socks.

We get,

2(r(r-1)+(t-r)(t-r-1))=t(t-1)

Expanding the left hand side and the right hand side

we get,

4r^2-4rt+2t^2-2t = t^2-t

moving the terms, we will get that

4r^2-4rt+t^2 = t

We notice that the left side is a perfect square.

(2r-t)^2 = t

Thus t is a perfect square.

And, the higher t is, the higher r will be. So, we should set

t = 44^2

= 1936

we see, 2r-1936 = 44

We will use the positive root, to get that

2r-1936 = 44,

2r = 1980

r = 990

Therefore, we can conclude that the largest possible number of red socks in the drawer that is consistent with this data is 990.

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15x + 25 y = 230 and x - y = 2 is a system of equations that could be used to calculate the number of hours Mamadou worked and Brianna worked.

Given:

Mamadou can iron 15 shirts in one hour, whereas Brianna can do 25. Mamadou put in two more hours of work than Brianna, and the two of them combined to iron 230 shirts.

Let y be the number of hours Brianna, works, and x be the number of hours Mamadou  works.

In y hours, Brianna would iron 25y shirts.

In x hours, Mamadou would iron 15x shirts.

Combining total number of shirts,

15x + 25 y = 230

Since, Mamadou put in two more hours of work than Brianna.

x = y +2

x - y = 2

Therefore, for the number of hours Mamadou and Brianna worked, a system of equations 15x + 25 y = 230 and x - y = 2 could be utilised.

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Answer:

15x + 25 y = 230 and x - y = 2

Step-by-step explanation:

Table A doesn't represent the constant of proportionality.

Table B doesn't represent the proportional relationship.

Treat the values in table as (x,y) values. The result is a linear function

For A, 85/5 = 17 while 79 / 10 = 7.9. This doesn't illustrate a constant.

For B, 1.49/16 and 1.59/20 have different values. In this case, 1.49/16 = 0.093 and 1.59/20 = 0.0795.

Therefore. they don't have a constant of proportionality. This was because the values that were gotten for both A and B aren't equal.

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Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?

1. How loud a sound is depending on how far away you are

5 85

10 79

20 73

40 67

b. The fountain drinks at hot dog hut.

16 1.49$

20 1.59$

30 1.89$

The inequality for the expression will be represented by n > 5.

The parameters present shows a geometric sequence. A Geometric sequence is the one in which the ratio between the consecutive terms remains constant. The constant ratio is called common ratio. The nth term of geometric sequence is represented by Tₙ = arⁿ⁻¹ where n is the number of terms, r is common ratio and a is the first term. Here, a = 15 and r = 3. Now, for the people to be more than 3000 the inequality can be written as

arⁿ⁻¹ > 3000

15 (3)ⁿ⁻¹ > 3000

3ⁿ⁻¹ > 200

Taking log on both sides

log 3ⁿ⁻¹ > log 200

(n - 1) > log 200/log 3

n - 1 > 4.82

n > 5.82

Rounding off we get

n > 5 which is required inequality.

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The probability that a sample of 10 items will contain at most 1 defective item is 0.7361

Consider X to denote the number of defective items which follows binomial distribution with sample size, n equals to 10.

The probability p of an item produced by a certain machine will be defective is 0.1.

Therefore, the probability q of an item produced by a certain machine will not be defective is:

(1−0.1)

=0.9

The probability of at most one defective item can be calculated as follows:

[tex]P(X\leq 1)=P(X=0)+P(X=1)\\[/tex]

[tex]=^{10} C_{0} p^{0} (1-p)^{10} +^{10} C_{1} p^{1}(1-p)^{9}[/tex]

[tex]=(0.9)^{10} +10(0.1)(0.9)^{9}[/tex]

[tex]=0.7361[/tex]

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Answer:

  y +7 = 3(x +4)

Step-by-step explanation:

You want the point-slope equation of the line with slope 3 through point (-4, -7).

The point-slope equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

For m=3 and (h, k) = (-4, -7), this is ...

  y -(-7) = 3(x -(-4)) . . . . . substitute for m, h, k

  y +7 = 3(x +4)

The length of the building in the scale drawing is; 31. 25 Inches

From the given, we have that Scale drawing was used 0. 25 inches represents 2 feet

The length of the building = 250 feet

Then, 0. 25 inches = 2 feet

Then, x inches = 250 feet

Now cross multiply

x × 2 = 0. 25 × 2500

Multiply through, we have;

2x = 62. 5

Make 'x' the subject by dividing both sides by 2

2x/2 = 62. 5/ 2

x = 31. 25 Inches

Thus, the length of the building in the scale drawing will be; 31. 25 Inches.

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Answer:

W

Step-by-step explanation:

9 + 7 = 16 and P is the 16th letter of the English Alphabet

4 + 1 = 5 and E is the 5th letter of the English Alphabet

15 + 8 = 23 and W is the 20th letter of the English Alphabet

You can see the three points where the result is equal to an integer in the photo below. Good luck!

If the children sold 50 cups of lemonade one the first day and 90 cups on the second day. then the percentage increase in the number of lemonade cups sold 80%

The number of cups of lemonade sold on first day =  50 cups

The number of cups of lemonade sold on second day = 90 cups

The percentage increase = (New value - Old value)/Old value × 100

Substitute the values in the equation

The percentage increase in the number of lemonade cups sold

= [tex]\frac{90-50}{50}[/tex]×100

= 0.8×100

= 80%

Hence, if the children sold 50 cups of lemonade one the first day and 90 cups on the second day. then the percentage increase in the number of lemonade cups sold 80%

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Answer:

90-50/50 = P/100

Step-by-step explanation:

This is the correct answer on T4L!

Converting each of the question mentioned decimal into fractions in their simplest form, we get,

(i) 0.6 with 6 recurring = (2/3)

(ii) 3.405 with (405) recurring = (378/37)

(iii) 0.75 with (75) recurring = (25/33)

(iv) 0.3 with 3 recurring = (1/3)

As per the question statement and the attached reference along with the question, we are provided with four recurring decimal values.

We are required to convert each of the decimal values into fractions in their simplest form.

Starting with (i), 0.6 with 6 recurring = 0.66666...

Now, let [x = 0.6666...]

Or, [10x = 6.6666...]

Or, [(10x - x) = (6.6666...) - (0.6666...)]

Or, (9x = 6)

Or, [x = (6/9)]

Or, [x = (2/3)]

Or, [0.6666... = (2/3)]

Similarly for (ii), 3.405 with (405) recurring = 3.405405405405...

Now, let [x = 3.405405405...]

Or, [1000x = 3405.405405405...]

Or, [(1000x - x) = (3405.405405405...) - (3.405405405...)]

Or, (999x = 3402)

Or, [x = (3402/999)]

Or, [x = (378/37)]

Or, [3.40540405... = (378/37)]

Coming to (iii), 0.75 with (75) recurring = 0.757575...

Now, let [x = 0.757575...]

Or, [100x = 75.757575...]

Or, [(100x - x) = (75.757575...) - (0.757575...)]

Or, (99x = 75)

Or, [x = (75/99)]

Or, [x = (25/33)]

Or, [0.757575... = (25/33)]

Finally coming to (iv), 0.3 with (3) recurring = 0.333...

Now, let [x = 0.333...]

Or, [10x = 3.333...]

Or, [(10x - x) = (3.333...) - (0.333...)]

Or, (9x = 3)

Or, [x = (3/9)]

Or, [x = (1/3)]

Or, [0.333... = (1/3)]

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Answer:

slope = [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = C (1, 3 ) and (x₂, y₂ ) = B (4, 7 )

m = [tex]\frac{7-3}{4-1}[/tex] = [tex]\frac{4}{3}[/tex]

Answer:

5.5 oz

Step-by-step explanation:

154÷28

By solving a linear equation we will see that the value of x is x = $4.00

We know that a store owner mixes 2 Ib of candy that costs x dollars per pound with 3 Ib of candy that costs $1.50 per pound. She sells the mix for $2.50

The total amount of the mix is:

2lb + 3lb = 5lb, now, the total cost at the beginning must be the same as the final cost, so we can write the equation:

2*x + 3*$1.50 = 5*$2.50

Now we can solve this linear equation for x:

2*x = 5*$2.50 - 3*$1.50 = $8.00

x = $8.00/2 = $4.00

The cost of the candy is 4 dollars.

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⇒Logically we know that to find the  [tex]3^{rd}[/tex] term we use [tex]T_{3} =a+2d[/tex]

⇒From

[tex]T_{3} =a+(3-1)d\\T_{3}=a+2d[/tex]

⇒And the [tex]4^{th}[/tex] is equal [tex]T_{4} =a+3d[/tex] from the same method I used above from the general equation of finding the [tex]n^{th}[/tex] term.

⇒It is said the sum of [tex]T_{3}[/tex] and [tex]T_{4}[/tex] is -2  meaning

[tex]T_{3} +T_{4} =(a+2d)+(a+3d)\\-2=a+2d+a+3d\\-2=a+a+2d+3d\\-2=2a+5d[/tex]

⇒It is also said that [tex]T_{2}[/tex] is 2 and we know at this point that

[tex]T_{2} =a+d\\2=a+d[/tex]

⇒Then we can use the simultaneous equations technique to find the value of d.

I will use the substitution method by deriving the third equation from the second equation 2=a+d

a=2-d  is the [tex]3^{rd}[/tex] equation that I will substitute in the  equation

In the place of a it means I will plug in  2-d in the place of a.

[tex]-2=2a+5d\\-2=2(2-d)+5d\\-2=2(2)+2(-d)+5d\\-2=4-2d+5d\\-2-4=3d\\\\3d=-6\\\\[/tex]

[tex]\frac{3d}{3} =\frac{-6}{3} \\d=-2[/tex]

NOTE if you were also asked to find the value of a you can use the equations above to find the value of a which is the first term. the difference represented by letter d is -2.

GOODLUCK!!

Given:

If you borrow $100, you will have an interest of $10.

Asked: How much do you owe at the end of four weeks?

Solution:

To solve this problem, we need to find the rate, r.

According to the given, we can get the rate by:

$100 x rate = $10

rate = $10/$100

rate = 0.10

Now, if you borrow $1100, you will pay at the end of four weeks the amount of:

$1100 x 0.10 = $110

Total amount = $1100 + $110 = $1210

ANSWER: You will owe $1210 at the end of four weeks.

Answer:

You will owe $1210 at the end of four weeks.

Answer:

2.7 feet

Step-by-step explanation:

S = a²

S = 7.29

a = sqrt(7.29) = 2.7

Answer:

2.7

Step-by-step explanation:

Area is [tex]side^{2}[/tex]

a= [tex]s^{2}[/tex]

[tex]\sqrt{7.29}[/tex] = 2.7

2.7 x 2.7 = 7.29

The expression 5xy - x²t + 2xy + 3x²t has a value of 7xy + 2x²t

From the question, the expression is given as

5xy - x squared t + 2xy + 3x squared t

Rewrite the above expression properly

This is represented as

5xy - x²t + 2xy + 3x²t

Next, we collect the like terms in the above expression

So, we have the following equation

5xy - x²t + 2xy + 3x²t = 5xy + 2xy - x²t  + 3x²t

Evaluate the like terms in the above expression

So, we have the following equation

5xy - x²t + 2xy + 3x²t = 7xy + 2x²t

The equation cannot be further simplified

Hence, the value of 5xy - x²t + 2xy + 3x²t is 7xy + 2x²t

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The value of q in the given equation is 0.

This is a problem from an algebraic equation, we can solve this problem by following a few steps.

The given equation is,

8(q-2) = 44+5(2q-12)

Let's simplify the equation.

8(q-2) = 44+5(2q-12)

Or, 8q- 16= 44+ 10q- 60

Now, we have to organize the equation.

8q- 10q= 44- 60+ 16

Or, -2q = 0

Or, q = 0/2        ( dividing both side by 2 )

Or, q = 0

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The complete question is:

Find the value in the given equation,

8(q-2) = 44+5(2q-12)

Answer: y=-1/8x

Step-by-step explanation:

Choose a point that the perpendicular line will pass through.

(0,0)

Use the slope-intercept form to find the slope.

m=8

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

perpendicular

m= −1/8

Find the equation of the perpendicular line using the point-slope formula.

y+0=−1/8⋅(x+0)

Write in

y=mx+b

form.

y=−1/8x

Hope this helps

The equivalent ratios of 2:6 can be 4:12, 6:18, 8:24, etc.

According to the question,

We have the following ratio:

2:6

Now, we have to find its equivalent ratios.

We know that equivalent ratios mean that when we compare any obtained ratio with the given ratio it should be same. So, to find equivalent ratios, we need to multiply both the numbers in the ratio by the same number.

In this case, we will find the three equivalent ratios. We will multiply both the numbers by 2, 3 and 4.

The given ratio = 2:6

Multiplying by 2:

4:12

Multiplying by 3:

6:18

Multiplying by 4:

8:24

Hence, the equivalent ratios of 2:6 are 4:12, 6:18 and 8:24.

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The graph of the quadratic function y = x² - 2x + 3 is shown in attached figure.

What is Quadratic equation?

An equation is called a quadratic equation if the highest power of variable of the equation is 2.

Given that;

The quadratic equation is,

y = x² - 2x + 3

Now,

The graph of the quadratic function y = x² - 2x + 3 has vertex (1, 2).

Thus,

The graph of the quadratic function y = x² - 2x + 3 is shown in attached figure with vertex (1, 2).

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B = 47°

a = 10.9

b = 11.7

How are the angles and sides of the right triangle calculated?

a) Finding B

We know that ,the sum of every angles of a triangle = 180°

So, B + 90° +43° = 180°

     B+ 133° = 180°

     B = 180° - 133°

        =47°

b) Finding a

We know,

[tex]sin\theta =\frac{opposite}{hypotenuse} \\\\sin 43^{\circ} =\frac{a}{16} \\\\a= 16(sin 43^{\circ})\\\\a = 16 (0.681)\\\\a=10.9[/tex]

c) Finding b

We know,

[tex]cos\theta = \frac{adjacent}{hypotenuse} \\\\cos 43^{\circ} =\frac{b}{16} \\\\b = (cos 43^{\circ})16\\\\b= (0.731) 16\\\\b= 11.7[/tex]

What is a right triangle?

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