Pavel and Sarah are knitting hats to sell. Pavel spends
£20 on wool and Sarah spends £80. They sell all the hats for a total of
£1000. Is it fair that they get £500 each? Explain your answer.

Answer:

D

Step-by-step explanation:

[tex]\frac{7-i}{3+i}[/tex]

rationalise the denominator by multiplying the numerator and denominator by the conjugate of the denominator

the conjugate of 3 + i is 3 - i

note that i² = - 1

= [tex]\frac{(7-i)(3-i)}{(3+i)(3-i)}[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{21-7i-3i+i^2}{9-3i+3i-i^2}[/tex]

= [tex]\frac{21-10i-1}{9-i^2}[/tex]

= [tex]\frac{20-10i}{9+1}[/tex]

= [tex]\frac{20-10i}{10}[/tex]

= [tex]\frac{20}{10}[/tex] - [tex]\frac{10i}{10}[/tex]

= 2 - i

After substituting the given values of x and y in the equation, all that can apply are (0, 2), (3, 0), and (6, -2).

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

here, we have,

As per the given information in the question,

The given equation is,

y=-2x+6

Now, substitute the corresponding points and check,

The points are,

(1 ,4) ⇒ 4= -2*1+6

⇒4=4

This is correct.

(2, 3)  ⇒ 3 = -4+6

This is not correct.

(-1, 8)  ⇒ 8= 2+6

This is correct.

(10, -15) ⇒ -15=-20+6

This is not correct.

(0, 3)  ⇒ 3=6

This not correct.

(3,0)  ⇒ 0 = -6+6

This is correct.

(7, -8)  ⇒ -8= -14+6

This  is correct.

(-6,17)  ⇒ 17 = 12+6

This is not correct.

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The value of the quadratic function f(x) = 2x² + 5x  - 17 at x = - 1 will be - 20.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = 2x² + 5x  - 17

The value of the function at x = - 1, is calculated as,

f(-1) = 2(-1)² + 5(-1)  - 17

Simplify the equation, then we have

f(-1) = 2(-1)² + 5(-1)  - 17

f(-1) = 2 - 5  - 17

f(-1) = 2 - 22

f(-1) = - 20

The value of the quadratic function f(x) = 2x² + 5x  - 17 at x = - 1 will be - 20.

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Answer:

2.88 markup per rose

Step-by-step explanation:

12.24/12 = 1.02 per rose

46.8/12 = 3.9 per rose

3.9 - 1.02 = 2.88 markup per rose

[tex]\it P(A)=\dfrac{n^o\ de\ casos\ favorables\ de\ A}{n^o\ total\ de\ casos\ posibles}\\ \\ \\ n^o\ total\ de\ casos\ posibles=100\\ \\ n^o\ de\ casos\ favorables=50+30=80\\ \\ P(A)=\dfrac{\ 80^{(20}}{100}=\dfrac{4}{5}[/tex]

In 37 years and 6 months, Jacob will be 1.5 years older than his uncle Todd.

In 37 years and 6 months, Jacob will be 1.5 years older than his uncle Todd.

Hello, using the information provided, write an equation to get the answer to this question:

33 years old Todd

12 years old Jacob

So, Jacob's age plus the amount of years asked equals 1.5 Todd's age (1.5 x 33).

(12+x)

12 +x = 1.5 (33) (33)

working out x

12 +x = 49.5

x= 49.5 -12

: x = 37.5 years

Given that 12 months make up a year, 0.5 years is equal to half a year.

12 times 0.5 years equals 6 months.

In 37 years and 6 months, Jacob will be Todd's age by a factor of 1.5.

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On solving the provided question, we can say that he equation is

[tex]40/2000=32/X = > X=1600\\[/tex]

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation is

[tex]40/2000=32/X \\40X=32*2000\\40X=64000\\X=64000/40\\X=1600\\[/tex]

IS THE PROJECTED INCREASE FROM 1860 TO 1892.

THUS THE TOTAL POPULATION IS EXPECTEDTO BE 22000+1600=23600.

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Expressions that perform similarly but differ in appearance are said to be equivalent expressions.

When the same value(s) for the variable are entered, two algebraic expressions that are equivalent will have the same value (s).

It is comparable to perform 3+2minus, 3, plus, 2, and 2 3 232, minus, 3. Despite being in opposite sequence, the numbers add out to 1 less than 1.

Each of the fractions 1 start fraction, 1 divided by, 2 end fraction, and 5 10 10 5 start fraction, 5 divided by, 10 end fraction, is identical. Despite the difference in the numerals, they both add up to 5.

Algebraic expressions 2 + 2 2x+22, x, plus, 2 and 2(x+1)2, left parenthesis, x, plus, 1 and right parenthesis, are equal. All xx values have the same value according to the expression:

x     2(x + 1 )                  2x + 2

0     2(0 - 1 ) = 2            2(0) + 2 = 2

1      2(1 + 1 ) = 4             2(1) + 2 = 4

2      2(2 + 1 ) = 6           2(2) + 2 = 6

3      2(3 + 1 ) = 8           2(3) + 2 = 8.

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The ratios 25/45 and 15/27 are proportional.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Ratios = 25/45 and 15/27

Now, simplifying the ratios we get

25/45

= 5/9  

and, 15/27

= 5/9

Hence, the ratio are proportion.

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The length of AB is AB = 8 units.

What is distance between two points?

The length of a straight line in the coordinate plane that connects two points in space is what is referred to as their distance. We use the absolute value to calculate the distance between any two points because it is impossible for this distance to be negative.

Consider, the given points A (-4, -3), B (4, -3), C (4, -7), D (-4, -7).

We have to find the length of AB.

Consider, the distance formula,

[tex]d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

where,

[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the points.

Here,

[tex](x_1, x_2) = (-4, -3)\\(x_2, y_2) = (4, -3)[/tex]

Plug these values in the above formula,

[tex]d = \sqrt{(4-(-4))^2+(-3-(-3))^2} \\d = \sqrt{8^2 +0^2} \\d = \sqrt{8^2} \\d = 8[/tex]

Hence, the length of AB is AB = 8 units.

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The average rate of change of filling the water heater is solved to be

The results indicate that 1 1/3 is the ratio of the rate of change of water height to time.

The average rate of change for the points t = 3 and t = 6  is solved using the formula

m = (y₀ - y₁) / (x₀ - x₁)

m = (3 - 7) / (3 - 6)

m = (-4) / (-3)

m = 4/3

m = 1 1/3

The values means that the rate of change of of height of water to time it takes is equal to 1 1/3

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The specified dimensions of the interior and exterior walls, indicates that the dimensions of the building is 28 feet 10 5/8 inches

The dimensions of a building includes the lengths, height, and width of the building.

The wall measurements for the building are;

The thickness of the interior walls = 2 × 4 (3 1/2'')

The thickness of the sheetrock on both sides of the interior walls = 1/2''

The dimensions of the exterior walls = 2 × 6(5 1/2'')

The thickness of the sheet rock on the interior of the interior walls = 1/2''

The thickness of the sheeting on the exterior of the exterior walls = 7/16''

The thickness of the brick on the exterior of the exterior wall = 3 5/8''

The specified dimension of one of the rooms = 11' 3''

The dimension of the second room = 15'7''

The outside dimension of the house, D, is therefore;

D = The sum of the dimensions of the rooms + The dimension of the inner wall + 2 × The thickness of the outer wall

Therefore;

D = 11'3'' + 15'7'' + 3 1/2'' + 1/2'' + 1/2'' + 2 × (5 1/2'' + 1/2'' + 7/16'' + 3 5/8'')

D = 11'3'' + 15'7'' + 4 1/2'' + 20 1/8'' = 28' 10 5/8''

The dimension of the building, D = 28 feet 10 5/8 inches

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Answer:

Step-by-step explanation:

8. ( - 3, 6 )

10. ( - 7, 9 )

Answer:

Number of republicans = 207 Number of democrats = 245

Step-by-step explanation:

Here you go

(x + 38) + x = 452 x + 38 + x = 452 2x = 452 - 382x = 414x = 414 / 2 x = 207

On average, each family member ran 6 km in the relay race.

What is the mean distance?

The extent or amount of space between two things, points, lines, etc. the state or fact of being apart in space, as of one thing from another; remoteness. a linear extent of space: Seven miles is a distance too great to walk in an hour. an expanse; area: A vast distance of water surrounding the ship.

To find the mean distance, you need to add up all the distances run by each family member and divide by the number of family members.

The total distance run by all the family members is:

11 + 4 + 8 + 2 + 5 = 30

So the mean distance is:

30 km / 5 family members = 6 km/family member

Hence, on average, each family member ran 6 km in the relay race.

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Answer: To calculate the number of attendees after 4 years, we can use the formula:

Attendance = 1200 * (1 - 0.5%)^4

Where 0.5% is the decimal equivalent of the percentage decrease.

In this case:

Attendance = 1200 * (1 - 0.005)^4

Attendance = 1200 * 0.995^4

Attendance = 1200 * 0.9450625

Attendance = 1134

So, after 4 years, the attendance will be 1134 people.

Step-by-step explanation:

The PCR in terms of t is 6,912in3t, rounded to the nearest hundredth.

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Answer:

hellooooooooooooooooiiiiioo hi

The 10,000 loan has 132.56 in monthly payments, and the loan's total interest is 5363.27.

Until the loan is repaid in full at the conclusion of its term, the principle and interest that make up each level payment are shown on a loan amortisation schedule, which is the whole table of periodic loan payments.

The formula for monthly payments for the loan is,

[tex]$M . P .=\frac{P(r / n)}{1-(1+r / n)^{-n t}}$[/tex]

where, P is the initial amount

r is the rate

n is the period in a year

is the number of years

Now it is given that,

Principle amount borrowed P =  10,000

Rate of interest, r = 7% = 0.07

Monthly Payment, so n = 12

Time, t = 4 years

Thus, Monthly payment of the loan is given as,

[tex]M . P .=\frac{P(r / n)}{1-(1+r / n)-n t}[/tex]

Putting the values we get,

[tex]\text { M.P. }=\frac{10,000(0.07 / 12)}{1-(1+0.07 / 12)-12 * 4}[/tex]

Simplifying we get,

[tex]\text { M.P. }=\frac{(70 / 12)}{1-(12.07 / 12)^{-48}}[/tex]     or,

[tex]\text { M.P. }=\frac{5.833}{1-(1.005)^{-48}}[/tex]

Thus, we get

[tex]\text { M.P. }=\frac{5.833}{1-0.756}[/tex]    or,

[tex]\text { M.P. }=\frac{5.833}{0.244}[/tex]

Solving we get,

[tex]\text { M.P. }=\$ 132.56[/tex]

This is the loan's needed monthly payment.

The difference between the total amount of monthly payments made and the original sum will now be the total amount of interest paid.

Thus,

Total interest of the loan = T.M.P - P

Therefore,

Total Monthly Payments = M.P x t x n

Putting the values we get,

Total Monthly Payments = 132.56 x 4 x 12

⇒ Total Monthly Payments = $6363.27

Therefore,

Total interest of the loan = 6363.27 - 10,000

⇒ Total interest of the loan = $5363.27

As a result, the 10,000 loan's monthly payment is 132.56, and its overall interest cost is 5363.27.

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Answer:

            4  to  1

Step-by-step explanation:

                                                Tablespoon of cocoa   to Tablespoon of sugar

                                                                          8             :                2

                                                                          [tex]\frac{8}{2}[/tex]              :                [tex]\frac{2}{2}[/tex]

                                                                          4             to                1

When recipe is doubled:                             ( 8 x 2)         to        (2 x 2)

                                                                         16             :              4

                                                                         [tex]\frac{16}{4}[/tex]             :               [tex]\frac{4}{4}[/tex]

                                                                          4           to              1

It can be observed that the ratio remains the same

Answer:

12j + 6

Step-by-step explanation:

You have to multiplied this polynomial expression in order to expand it:

2(6j + 3)

12j + 6

Answer:

12j + 6

a(b+c) = ab + bc

2(6j+3)

2*6 = 12

12j

2*3 = 6

12j + 6

Answer:

1 and 1/4

Step-by-step explanation:

Each piece of tomato is a unit fraction of 1/4 of a whole tomato. The equation representing the total number of quarters of a whole tomato is 2 x (1/4) = 2/4. The multiplication shown in the image is 2 x (1/4) = 2/4. As a mixed number, this would be represented as 1 and 1/4.

Addison's purple paint will be bluer.

To determine the percent of blue paint in Arturo's mixture, divide the amount of blue paint (11 cups) by the total amount of paint (11 cups + 5 cups) and multiply by 100. This gives you 68.75%.

To determine the percent of blue paint in Addison's mixture, divide the amount of blue paint (8 cups) by the total amount of paint (8 cups + 3 cups) and multiply by 100. This gives you 72.73%. Since 72.73% is greater than 68.75%,

Therefore, the correct answer is as given above. It can then be concluded that Addison's purple paint will be bluer.

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Answer: 4z² - 10z + 6

Step-by-step explanation:

The expression -(-4z² + 10z − 6) can be simplified by applying the rule that -(-a) = a. So, -(-4z² + 10z − 6) = 4z² - 10z + 6. The negative signs before the 4z² and 10z have been eliminated, leaving only one negative sign before the last term 6. The simplified expression is 4z² - 10z + 6.

Answer: hopefully this should work out!

The fine for a book that is n days overdue can be represented by the following number sentence:

f = 0.25 + (0.10 x n)

This equation shows that the fine for an overdue book is $0.25, plus an additional $0.10 for each day the book is overdue. So if a book is overdue for n days, the fine would be $0.25 + ($0.10 x n) dollars.

Step-by-step explanation:

The rate of change of function A is greater than the rate of change of function B. This is the statement which best compares the rate of change of the two functions.

What is rate of change?

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.

The formula for rate of change is:

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

The points for first function A are

(7,21) and (8,24).

So, the rate of change is:

[tex]m=\frac{24-21}{8-7}[/tex]

m= 3/1 = 3

The points for second function B are

(2,4) and (3,6).

So, the rate of change is:

[tex]m=\frac{6-4}{3-2}[/tex]

m= 2/1 = 2

The rate of change of function A is 3, while the rate of change of function B is 2.

Hence, the rate of change of function A is greater than the rate of change of function B.

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Answer:

2 miles / half-hour

Step-by-step explanation:

You will notice that the y intercepts the x at every half-hour interval

Ex: 2 at 30 min, 4 at one hour, 6 at one hour 30 minutes...

a) The percentage of shoppers that have computer access at home is given as follows: 44%.

b) The percentage of shoppers that do not have an e-mail account is given as follows: 66%.

A percentage is obtained as a proportion, dividing the number of desired outcomes by the number of total outcomes, and then multiplying this amount by 100%.

Out of 150 shoppers, 48 + 18 = 66 have computer access at home, hence the percentage is given as follows:

66/150 x 100% = 44%.

Out of 150 shoppers, 18 + 81 = 99 do not have an e-mail, hence the percentage is given as follows:

99/150 x 100% = 66%.

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Answer:

7/8

12.5%

Step-by-step explanation:

Two calculations that she can do to find the cost are:

Remember that if we have a value A, and we want to apply a discount X (where X is a percentage) then the value after the discount is:

A' = A*(1 - X%/100%)

Here we know that the initial value of the pants is c dollars, and the discount is of the 15%, then the expression that we need to solve is:

cost = c*(1 - 15%/100%)

Now we can simplify that expression to get:

cost = c*(1 - 0.15)

cost = c*0.85

These the calculations that she needs to do.

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