sry for the awful picture but i couldnt get it as a file

Step-by-step explanation:

5.

xnew = 205 = 2×xold + 5

200 = 2×xold

xold = 100

the old city machine can produce 100 copies per hour.

6.

2 cups of milk relate to 6 1/4 cups of flour.

such recipes represent a direct dependency of one variable on the other. one variable is always the other variable multiplied by a constant factor.

m = cups of milk

f = cups of flour

m = n×f

2 = n×(6 1/4) = n×(6×4 + 1)/4 = n×25/4

8 = 25n

n = 8/25

now, f = 43 3/4 = (43×4 + 3)/4 = 175/4

so,

m = 8/25 × 175/4 = (8×175)/(25×4) = 2×7 = 14

you will need 14 cups of milk.

The picoseconds that are there in 6 minutes is 3.6 × 10^14.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

In this case, picosecond is one trillionth of a second. If one trillionth = 1 × 10^12

The seconds in 6 minutes will be:

= 60 × 6

= 360 seconds

= 3.6 × 10^2

The picoseconds in 6 minutes will be:

= 1 × 10^12 × 3.6 × 10^2

= 3.6 × 10^14

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The values of the variables as represented in the right triangle are; (8√15)/3 and s = (4√15)/3.

It follows from the task content that the values of the variables in the right triangle are to be determined.

It follows from trigonometric ratios that;

Sin (∆) = opposite / hypothenuse

Cos (∆) = adjacent / hypothenuse

Tan (∆) = opposite / adjacent

It therefore follows from the attached image that;

Sin (60) = 4√5 ÷ p

p = 4√5 ÷ √3/2

p = (8√15)/3.

Also;

Tan (60) = 4√5 ÷ s

s = 4√5 ÷ √3

s = (4√15)/3

Therefore, the value of the variables are; p = (8√15)/3 and s = (4√15)/3.

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The revolution per minute done by the wheel of a bicycle is 16.9 rev/min.

Velocity is the rate at which a moving object's direction changes as perceived from a certain vantage point and measured by a particular unit of time. Kinematics, the area of special relativity that investigates how bodies move, starts with the fundamental idea of speed.

In order to be explained, the scientific vector quantity known as velocity needs to have both a magnitude and a direction.

As per the given information in the question,

Diameter of wheel = 20 inch

Radius, r = 10 inch

The velocity of the bicycle, v = 13 mi/h.

Revolution, R = v²/r

R = 13²/10

R = 16.9 rev/min

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If the value of R² in the regression equation is 0.810, the value of R is 0.9

From the question, we have the following parameters that can be used in our computation:

Regression equation: y = -2.6x + 10

Value of R2 = 0.810

Rewrite the above parameters properly

So, we have the following representation

y = -2.6x + 10

R² = 0.810

The variable r² represents the coefficient of determination

Recall that

R² = 0.810

This gives

r² = 0.810

Take the square roots of both sides

r = 0.9

Hence, the value of r is 0.9

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The measure of the angle 1, angle 2, angle 3 is 68°, 94°, 25° respectively.

What is angle?

An angle is created where two straight lines or rays meet at a single point. The point from where two lines converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which meaning "corner."

Let's firstly find angle 1,

We  know that, the sum of the all three angles of a triangle is 180°.

So,

18° + 94° + angle 1 = 180°

112° + angle 1 = 180°

angle 1 = 180° - 112°

angle 1 = 68°

Now, we know that, opposite angle are always equal

Therefore,

angle 2 = 94°

Now, again applying the property of triangle that sum of all three angles are equal:

Therefore,

angle 3 + angle 2 + 61° = 180°

angle 3 + 94° + 61° = 180°

angle 3 = 25°

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If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.

What do you mean by traversal line?

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.

What do you mean by angle?

An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.

From the figure,

x + 1 = 180°

y + 2 = 180°

Adding above equations,

x + y + 1 + 2 = 360°

Given ,

x + y = 1 +2

x + y + x + y = 360°

2(x + y) = 360°

x + y = 180°

Angles made on same side of transversal is supplementary . So the lines are parallel.

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The slope is 5 and the y-intercept is -2000.

(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.

(c) The situation can be modeled as y = 5x -200. Here, y= profit per week and x= number of customers per week.

(d) If the state world roller rink reached a maximum capacity of 2,500 customers per week then the weekly profit will be $10,500.

In order to make the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) immediately apparent, a line's equation must be written in the slope-intercept form. This version is frequently known as y = mx + b. the equation of a straight line in the form of y = mx + b, where m is the line's slope and b is its y-intercept. The slope intercept formula y = mx + b is used when you know the line's slope and the provided point is also the line's y-intercept (0, b).  y = mx + b, where m represents the line's slope, is the slope-intercept form of a line.

(a) Consider two points

(x₁, y₁) = (400, 0)

(x₂, y₂) = (500, 500)

The slope is given as

m = (y₂ - y₁)/ (x₂ - x₁)

= (500-0)/(500-400)

= 500/100

= 5

To find y- intercept put (x, y) = (400,0) in y= mx+b (slope-intercept form of a line)

0 = 5(400)+b

0 = 2000 + b

b= - 2000

(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.

(c) Let the number of customers per week = x

And the profit per week = y

Then, the situation can be modeled using slope-intercept form as

y = 5x -200

(d) Put x= 2500 in y = 5x -200

y = 5(2500)-2000

= 12,500-2000

= 10,500

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The value of y is,  [tex]y = \frac{tan^-^1(-x) + \pi n}{x}[/tex].

What is tangent function?

One of the primary six trigonometric functions, the tangent function is typically expressed as tan x. When considering the angle in a right-angled triangle, it is the ratio of the opposite side to the adjacent side.

Consider, the given function

x + tan(xy) = 0

Subtract x from both sides,

x + tan(xy) - x = -x

          tan(xy) = -x

Apply tan inverse on both sides,

[tex]xy = tan^-^1(-x) + n\pi[/tex]                      (Tangent function is a periodic function)

Divide both sides by x,

[tex]y = \frac{tan^-^1(-x)}{x} + \frac{n\pi }{x}[/tex],         x ≠ 0

Hence, the value of y is, y = [tex]y = \frac{tan^-^1(-x)}{x} + \frac{n\pi }{x}[/tex].

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The solution of the geometric equation is x = 1/2 or x = 1

An equation is a mathematical expression that shows the relationship between variables.

A geometric series is the sum of a geometric sequence.

Since the equation 0 = ( 1 - X - X²-...) (2 - X - X²-...). To solve this, let the series x + x² + ... = p

So, 0 = ( 1 - X - X²-...) (2 - X - X²-...).

0 = (1 - [X + X²+...) (2 - [X + X²+...).

Substitute x + x² + ... = p. So,

0 = (1 - [X + X²+...) (2 - [X + X²+...).

0 = (1 - p)(2 - p).

So, (1 - p) = 0 or (2 - p) = 0

p = 1 or p = 2

Since x + x² + ... = p, the left side of the equation is the sum to infinity of a geometric series.

The sum to infinity of the geometric series is given by

S = a/(1 - r) where

For the given series,

So, S = a/(1 - r)

= x/(1 - x)

Since S = p, we have that

x/(1 - x) = 1 or x/(1 - x) = 2

So, x = 1 - x or x = 2 - x

x + x = 1 or x + x = 2

2x = 1 or 2x = 2

x = 1/2 or x = 2/2

x = 1/2 or x = 1

So, the solution is x = 1/2 or x = 1

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Step-by-step explanation:

To purchase $12,200 worth of restaurant equipment for her business, Linda made a down payment of $1600 and took out a business loan for the rest. After 3 years of paying monthly payments of $322.48, she finally paid off the loan.

(a) What was the total amount Linda ended up paying for the equipment

(including the down payment and monthly payments)?

How much on loan:

12,200 - 1,600 = $10,600 loan amount

How much paid on loan:

$322.48 * 3 years * 12 months = $11,608.28 amount paid on loan

Total paid:

= loan amount + amount paid on loan

$10,600 + $$11,608.28

= $22,208.28 paid overall

________________________________________

(b) How much interest did Linda pay on the loan?

= loan amount - amount  paid on loan

= $11,608.28 - $10,600

= $1,009.28 paid in interest

12 ounces of water.

Total mass of the solution: 30 ounces.

Total mass of salt (solute): (30*0.07)= 2.1 ounces.

Total mass of water (solvent): (30*0.93) 27.9 ounces.

2. Find an equation that relates amount of water and percentage of salt.

Since we know that the amount of salt is 2.1 ounces, and it has to remain constant, we have to create a function such that the variable is the amount of water and it gives us the percentage of solution we are looking for. The function should look like this:

[tex]\frac{2.1}{x} =0.05[/tex]; where x is the mass of the water in the solution.

Side note: The number "0.05" is 5% converted into a decimal.

[tex]\frac{2.1}{x} =0.05\\ \\\frac{x}{2.1} =\frac{1}{0.05} \\ \\x=\frac{2.1}{0.05} \\ \\x=42[/tex]

42 would be the total amount of ounces the solution should have in order to be a 5% solution. Therefore, 12 ounces (42-30) have to be added.

12 ounces of water have to be added to this solution in order to make it a 5% solution, where 2.1 ounces is salt and 39.9 is water.

The percentage of computers not working is 10%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that there are three of the 30 computers are out of service.

The percentage of the computers which are out of service will be calculated as,

P = 3 / 30

P = 0.1

P = 0.1x 100

P = 10%

Therefore, the percentage of computers not working is 10%.

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1. The table of values for Dianely's salary can be represented for 4 years as follows:

Year         Salary

1            $40,000

2           $42,500

3           $45,000

4           $47,500

2. The equation that models Dianely's salary after n years is S = 40,000 + 2,500n.

An equation is a mathematical statement stating that two mathematical expressions are equivalent or equal.

For instance, given the number of years, one can claim that Dianely's salary will be a given amount based on the above equation.

Equations involve variables, numbers, and the use of the equation sign (=) with some mathematical operands.

Initial salary = $40,000

Salary raise per year = $2,500

Disney's salary after n years in equation form, S = 40,000 + 2,500n.

Table of Values for Dianely's Salary:

Year         Salary

1            $40,000

2           $42,500 (40,000 + 2,500)

3           $45,000 (42,500 + 2,500)

4           $47,500 (45,000 + 2,500)

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Considering the definition of an equation and the way to solve it, the equation is y +(-3)=-8 and the solution is -5.

An equation is an algebraic equality in which letters appear with unknown value.

In an equation appears:

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true. To solve an equation, keep in mind:

Being "y" a number, and knowing that sum of a number and -3 is -8, the equation in this case is:

y + (-3)= -8

Solving:

y -3= -8

y= -8 +3

y= -5

Finally, the number "y" is -5.

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Using the multiplication operation, the greatest number of people who could be in the 380 rooms with space for 6 persons at the same time is 2,280.

Multiplication operation is one of the basic mathematical operations, including subtraction, addition, and division.

A multiplication operation involves applying the multiplier to the multiplicand to result in a product.

The total number of rooms in the resort = 380

The number of people per room = 6

380 x 6 = 2,280

Thus, by multiplication, if 6 persons occupy each of the 380 rooms, the resort will have 2,280 persons at a time.

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Answer:

j=24

Step-by-step explanation:

j/8 - 2 = 1

j/8 - 2 + 2 = 1 + 2

j/8 = 3

8 * j/8 = 8 * 3

j=24

Answer:

Karen is waiting for a pot of soup to cool off before serving it. After 4 min the soup has cooled from 100°C to 78°C. What was the average change in temperature each minute?

✓ Answer:It went down 5.5°C a minute.Step-by-step explanation:You have to look for the difference of 100 and 78, which is …

The numbers are plotted in the attached graph.

A number line is a representation of real numbers in the form of a graded straight line.

Note that 5/3 is approximately equal to 1.7.

Similarly, -5/3 is approximately equal to -1.7.

Now, use the number line to mark the points -1.7 and 1.7, the numbers lie near -2 and 2 respectively.

The numbers are plotted in the attached graph.

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With the help of subtraction we can say that the answer is =21/15

Acc to the question-

Hence,The answer is = 21/15

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Answer:

21/15

Step-by-step explanation:

Given problem,

→ (32/15) - (11/15)

Let's solve the given problem,

→ (32/15) - (11/15)

→ (32 - 11)/15

→ 21/15

Hence, the answer is 21/15.

Answer:

y=3x+2

Step-by-step explanation:

Divide by 5 on all sides.

3x-y=-2

Step-by-step explanation:

Answer:

the answer is down there