If it takes 1 printer 14 minutes to print a batch of leaflets, how long would it
take 2 printers to print the same number of leaflets?

The number will x=17 and y=-3 as the sum of two numbers is 14 and the difference between the numbers is 20.

The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators. One operand is added to the other in addition. On the provided operands, the operator is accustomed to performing mathematical operations like addition, subtraction, multiplication, division, modulus, etc. Examples of arithmetic operators include: 5 + 3 = 8, 5 - 3 = 2, 2 * 4 = 8, etc.

Here,

x+y=14

x-y=20

subtract equation,

2y=-6

y=-3

x+y=14

x-3=14

x=17

The result will be x=17 and y=-3 because the sum of the two numbers is 14 and their difference is 20.

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Answer: 667

Step-by-step explanation:

14.50 x 46

Linda' number of questions has an expected value of 11.3

The given parameters in the question are:

8 questions with probability 0.6,

15 questions with probability 0.3

20 questions with probability 0.1

The expected value is then calculated as

E(x) = Sum of (number of questions * probability)

Substitute the known values in the above equation, so, we have the following representation

E(x) = 8 * 0.6 + 15 * 0.3 + 20 * 0.1

Evaluate

E(x) = 11.3

Hence, the expected value  is 11.3

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The types of variation and their constants are;

1) Direct variation with constant of variation as -1/4

2) Direct variation with constant of variation as ³/₂

A variation is defined as a relation that exists between a set of values of one variable and then a set of values of other variables.

In variation, if the variables change proportionately that is they either increase together or decrease together, then they are said to vary directly.

1) We are given the equation;

4y = -x

Now, y is the output while x is the input and so we make y the subject to get; y = -¹/₄x

Now, writing the relationship between y and x as a variation, we will have; y ∝ x

For this to be equal, there has to be a constant of proportionality which means; y = kx

Comparing with our equation tells us that;

This is a direct variation with constant of variation as -1/4

2) We are given the equation;

3x = 2y - 7

Rearranging gives;

2y = 3x + 7

y = ³/₂x + 7

Now, the greater the value of x, the greater the value of y and as such this is also a direct variation with the constant of variation being 3/2.

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[tex]39 + \frac{1}{7}r[/tex] when r = -1/2

[tex]39 + \frac{1}{7}*\frac{-1}{2} \\\\39 + \frac{-1}{14}\\\\[/tex]

= 38.92857 (in decimal form)

= 545/14 (in fractional form)

The required time that would it takes to reach the flames is 2.78 sec.

Given that,
A helicopter drops a bucket of water onto a forest fire from 38 meters above the blaze how long it takes the water to fall and reach the flames is to be determined.

Here,
According to the question,
The initial velocity of the water is u = 0, and s = 38
Speed gain by the water is due to the acceleration due to gravity g = 9.8.
The time for water to reach to the ground is given by the second equation of motion.
s = u²t + 1/2gt²
Substitute the values in the above equation,
38 = 1/2(9.8)t²
(9.8)t² = 76
t = √(76/9.8)
t = 2.78 sec.

Thus, the required time that would it takes to reach the flames is 2.78 sec.

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Any number between -7 and 7 can be located in the number line.

The number line is a horizontal line that has equally spread number increments.

Given a number line, suppose we plot -5 on it, which is between -7 and 7

Then, its position will be 5 units left of 0 on the number line.

Hence, -5 is the point between -7 and 7 on the number line, which is 5 units left on 0.

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Answer:

(A∩B)={1,15}

Step-by-step explanation:

R₀, 270° is the rule that describes the transformation

Rotation simply means turning. In a cartesian plane, if a point P, whose position vector is (x,y), is rotated through θ° about the origin, the position of the image P' is

a. (-y, x) for θ = 90°

b. (-x, -y) for θ = 180°

c. (y, -x) for θ = 270°

Given the: Triangle RST with vertices R(2, 0), S(4, 0), and T(1, -3). And the image of triangle RST after a rotation has vertices R'(0, -2). S'(0, -4), and T(-3, -1)

From the given vertices it is obvious that the relation between preimage and image is defined as

(x, y) => (y, -x)

Therefore, the rule that describes the transformation is (y, -x) for θ = 270° (i.e. when the figure rotates 270° counterclockwise). So the third option (R₀, 270° ) is the answer.

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The value after 11 years with annual compounding is $11,389.79

The value after 11 years with quarterly compounding is $11,552

The value after 11 years with monthly compounding is $11,589.68

The value after 11 years with continous compounding is $70,080.78.

When an amount is compounded annually, it increases in value once a year. When an amount is compounded quarterly, it increases in value four times a year. When an amount is compounded monthly, it increases in value twelve times a year. When an amount is compounded continuously, it increases continuously over the investment period.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

Value after 11 years with annual compounding: $6,000 x (1.06)^11 = $11,389.79

Value after 11 years with quarterly compounding: $6,000 x (1 + 0.06 /4)^(11 x 4) = $11,552

Value after 11 years with monthly compounding: $6,000 x (1 + 0.06 /12)^(11 x 12) = $11,589.68

The formula for calculating future value when there is continuous compounding is : A x e^r x N

Where:

Value after 11 years: 6,000 x (2.718^0.06) x 11 = $70,080.78

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The expressions (5 + 9 - 2³) and (4² - 6) are not equal (≠) to each other. Then the correct option is B.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The numerical expressions are given below.

(5 + 9 - 2³) and (4² - 6)

Simplify the expression, then we have

(5 + 9 - 2³) = 5 + 9 - 8 = 6

(4² - 6) = 16 - 6 = 10

The expressions (5 + 9 - 2³) and (4² - 6) are not equal (≠) to each other. Then the correct option is B.

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The completion of the trend analysis for sales with 2010 as the base year is as follows:

                               2013           2012           2011           2010

Sales               $ 158,000   $ 615,000   $ 280,000   $ 500,000

Trend Analysis       32%           123%           56%           100%

Trend analysis uses observed historical data to predict future developments and monitor performances about a particular topic.

Undertaking a trend analysis for sales, which is a technical analysis, involves setting a base year.  The sales figure for the base year is set to 100% and used to check changes during the review periods.

The other years' sales results, in percentages, are compared to the base year by dividing each year's sales by the base year.

2013 (D) = 32% ($158,000/$500,000 x 100)

2012 (C) 123% ($615,000/$500,000 x 100)

2011 (B) 56% ($280,000/$500,000 x 100)

2010 (A) = 100% ($500,000/$500,000 x 100)

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Answer:

3

Step-by-step explanation:

√83-√35 = 3.1943537960446828393782978131270521416836379374706155296172187959...

Step-by-step explanation:

we need to remember the squared numbers of the baud integers :

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

so, what squared integers are closest to 83 and 35 ?

well, 81 (9²) and 36 (6²).

so, the result has to be closest to 9 - 6 = 3.

83 is larger than 81 than 35 is smaller than 36. so, 3 is less than sqrt(83) - sqrt(35).

therefore, the correct answer is indeed 3.

The vertical asymptote of a given function is x = -2 and x = -3.

What is the vertical asymptote of a function?

A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. It appears at the x-value that is outside the domain of the function, therefore the graph can never cross it.

To find the vertical asymptotes, set the denominator equal to zero and solve for x.

For the given function,

                           [tex]F(x) = \frac{1}{7(x+2)(x+3)}[/tex]

To find the vertical asymptote, equate the denominator to zero.

                            7(x + 2)(x + 3) = 0

                              (x + 2)(x + 3) = 0

                  x + 2 = 0           (or)         x + 3 = 0

                  x = -2                (or)         x = -3

Hence, The vertical asymptote of the given function is x = -2 and x = -3.

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The total amount Jaxon should paid for the apples is 12 dollars which is 1200 cents.

Given,

The quantity of apple bought by Jaxon = 10 2/3 pounds

The cost of one pound of apple = $1.80

We have to find the total amount Jaxon should paid for the apples, in dollars and cents;

Here,

Total amount Jaxon should paid = Quantity of apple bought by Jaxon × Cost of one pound of apple

Total amount Jaxon should paid = 10 2/3 × 1.80

Total amount Jaxon should paid = 12 dollars

1 dollar is equal to 100 cents

Then,

12 dollars = 12 x 100 = 1200 cents.

Therefore,

The total amount Jaxon should paid for the apples is 12 dollars which is 1200 cents.

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Using simple mathematical operations, David's overall loss is -5.8.

So, the overall gain/loss of David is:

Now, calculate loss/gain as follows:

Therefore, using simple mathematical operations, David's overall loss is -5.8.

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Answer:  The correct answer is x = 50

Step-by-step explanation:

The sum of angles in a triangle = 180 degrees

This is a right-angled triangle, so one of the angles is 90 degrees + x +y

Therefore: 90 + y + x = 180

Substitute the variables:

90 + 40 + x = 180

130 + x =180

Subtract 130 from each side:

(-130) 130 + x =180 (-130)

x = 50

The correct statement about the model, using proportions, is given as follows:

The model shows that there are 4 pieces that are each 0.75 ft long.

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of the problem.

The application of proportions in this problem is to find the length of each piece, which is obtained as the division of the total length of the model by the number of pieces, hence:

Length of each piece = Total length/number of pieces.

The measures are given as follows:

Hence the length per piece is given by:

3 ft / 4 = 0.75 ft.

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Answer:

answer is 3/4!!! hope this helped

The ratio of the areas of the similar figures is given as follows:

225/16.

Similar figures are figures that share these two features:

The ratio of the side lengths of the similar figures can be represented as follows:

(b/a).

The side length is measured in units, while the area is measured in units squared, hence the ratio of the areas of the similar figures is represented as follows:

(b/a)² = b²/a².

From the image of the right triangle shown at the end of the answer, the ratio of the side lengths is:

15/4.

Hence the ratio of the areas of the figures is given as follows:

(15/4)² = 225/16.

The figures are given by the image at the end of the answer.

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Answer:

true

Step-by-step explanation:

5^ -2

(1/5)^2

1/25

Answer:

That's true :

5^-2= 1/5^2= 1/25

so yes : 5^-2=1/25

Step-by-step explanation:

A. The data modeling the relation is an exponential function.

B. The function is: y = 2^x.

C. The rate of change from x = 2 to x = 4 is of 4.

The definition of an exponential function is presented as follows:

[tex]y = ab^x[/tex]

In which the variables of the function are listed as follows:

From this data-set, when x increases by one, y is multiplied by 2, hence the rate of change is:

b = 2.

When x is increased by n, the rate of change is:

b^n = 2^n.

Hence, when x is increased by 2, from 2 to 4, in item c, the rate of change is:

2² = 4.

When x = 1, the output is the output at x = 0 multiplied by 2, hence the coefficient a of the function is given as follows:

a = 2/2 = 1.

Then the exponential function is:

[tex]y = 2^x[/tex].

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It is true that when you add an integer to +3, a negative sum or postive sum is possible. An example is 2 + 3 = 5 and -4 + 3 = -1

It should be noted that from the information,we want to prove that addition of +3 to an integer can either be negative or positive.

This will be:

= 2 + 3

= +5

In this case, it gives a positive number.

Also, -4 + 3

= -1

This gives a negative number.

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Answer:

2/3

Step-by-step explanation:

The gradient is found by doing rise/run. If you go to a point on the line you can then rise 2 squares and run 3 to the right. This means that the gradient is 2/3. It is not negative as the line is going up.

The fraction of the patients that have a waiting time of more than 7 minutes found by using the area under the curve is 269/312

A fraction indicates the quantitative comparison showing the number of times one quantity is contained in another quantity.

The area under the frequency curve is found as follows;

Dividing the area into composite shapes of a rectangle, triangle and trapezoid, we get;

(9.2 - 5.5) × 4 + (4 + 2)×3/2 + (2.5 + (9.2 - 5.5)) × 1/2 + (2.5 + 1.2) × 2/2 + 1.2 × 1/2 = 31.2

The area for those that have a waiting time of more than 7 minutes is therefore;

(9.2 - 5.5) × 4 + (4 + 2)×3/2 + (2.5 + (9.2 - 5.5)) × 1/2 = 26.9

The fraction that have a waiting time of more than 7 minutes is therefore;

26.9/31.2 = 269/312  ≈ 0.862

The fraction of the patients that have a waiting time of more than 7 minutes is 269/312

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If the distance from P to R is 3 units, then the distance from Q to S is; 3 units

We are told that quadrilateral PQRS is a scaled copy of quadrilateral ABCD. Thus, this means that;

P → A

Q → B

R → C

S → D

We are also told that the length of PR = 3 units.

Now, from the given image, we see that;

AC = 6 and BD = 6

We also know that;

AC corresponds to PR

BD corresponds to QS

Due to the fact that AC and BD have the same side lengths, then it means that PR and QS will have the same side lengths.

Therefore, the value of QS is: QS = 3

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Complete question is;

Here is Quadrilateral ABCD.

Quadrilateral PQRS is a scaled copy of Quadrilateral ABCD Point P corresponds to A.

Q to B. R to C. and S to D.

1. If the distance from P to R is 3 units, what is the distance from Q to S?

Answer:

124 km

Step-by-step explanation:

Wanda walked 43.4 km in 14 days. At this rate, how far would she walk in 40 days? She would walk__km in 40 days.

First, figure km per day:

43.4/14 = 3.1 km per day

3.1 * 40 = 124 km

She would walk 124 km in 40 days.