3. Sketch the distance-time graphs for the following scenarios.

a. Stand one meter from the sensor, walk
at a constant (steady) slow pace away
from the sensor.

b. Stand one meter from the sensor, walk
away from the sensor changing your
pace from slow to fast.

The statements

(a) If x and y are integers such that 3xy then 3x.

(b) For any integers x, y, and z, if x y and xz, then x(y - z).

(c) If x and y are integers such that x > 1 and if x divides y, then the solution is x(y - 1)

are proved.

The term integers in math is defined as are the collection of whole numbers and negative numbers.

Here we know that x and y are the integers,

Then it takes both positive and negative numbers.

Then we take y=1, then we apply it on the expression then we get,

=> 3x(1) = 3x.

Similarly here we have take that xy|z means xy is a factor of z,

Here we can say xym = z for some integer m.

=> x × ym = z, and ym is an integer by closure hence x is a factor of z such that x|z.

Similarly here we can also y * xm = z, and consider xm is an integer, hence y is a factor of z, i.e. y|z.

Where in the third one, we can take x|y means there exists a constant is written as y = kx

Where as y|x means there exists a constant written as x = cy

When we compare these, then we get,

=> y = kx = kcy

Here we have to true if kc = 1 and since k and c are integers, then we have k = c = 1

Therefore y = kx becomes y = 1*x or y = x

Similarly x = cy becomes x = 1*y or x = y

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Answer:

53.3%

Step-by-step explanation:

14 + 16 = 30

16/30 x 100 = 53.3% are laptops

The mother must drive at a speed of 6 mph to reach Anna in ten minutes.

To find the speed required for the mother to reach Anna in ten minutes, you need to calculate the distance between them and the time it takes to close the gap.

Let x be the speed of the mother's car in mph.

In one hour, Anna will have covered 6 miles.

In ten minutes, the mother will have covered x * 10/60 miles.

The total distance between them is 6 + x * 10/60 miles.

The mother must cover this distance in ten minutes, so:

x * 10/60 = 6 / (10/60)

x = 6 * (10/60) / (10/60)

x = 6 mph

Therefore, the mother must drive at a speed of 6 mph to reach Anna in ten minutes.

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6.93 × 10⁷ dogs were household pets in the U. S. In 2012.

To find the total number of dogs as household pets in the U.S. in 2012, we need to multiply the number of households by the average number of dogs per household.

Number of households = 4.33 × 10⁷

The average number of dogs per household = 1.6

Total number of dogs = (4.33 x 10⁷) × (1.6) = 6.93 × 10⁷

Therefore, approximately 6.93 × 10⁷ dogs were household pets in the U.S. in 2012.

Hence, the correct answer is D.

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Spanish 45 and french 42.5. When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common.

When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common. After that, input how many items are still there in each pair of sets' overlapping zone.

The quantity of each set's leftover pieces should be entered. Lastly, locate any missing numbers using any known totals.

Using a Venn diagram to determine probabilities: The Venn diagram's subset's components should be identified. Figure out the subset's frequency. Work out the larger set's overall frequency.  

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The simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate is $280.

It is the interest calculated on the principal at a given rate for a time period.

We have,

P = $2800

T = 5 years

R = 2%

Now,

The formula for simple interest.

SI = PRT/100

Now,

SI = (2800 x 2 x 5) / 100

SI = 28 x 10

SI = $280

Thus,

Simple interest is $280.

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The slope of the line represented by 4x-7y=62 is 4/7. A line's steepness is measured by its slope. The mathematical expression for slope is "rise over run."

Option A is correct.

In mathematics, a line's slope is the ratio of the change in the y coordinate to the change in the x coordinate. The net change in the y-coordinate and the net change in the x-coordinate, respectively, are denoted by the symbols delta y and delta x.

          We are given equation as 4x-7y=62

First, let's write it in the slope-intercept form .In general, slope-intercept form is                                    y=mx + b

where m is the slope

So, writing the equation in the form, we get

                                    ⇒-7y = 62-4x

                                        ⇒7y = 4x-62

                                          ⇒y = 4x/7-62/7

Now, matching the equation with the general form,

                                          m = 4/7

Hence, the slope of the line represented by 4x-7y=62 is 4/7.

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Answer:

y = x + 7  

Step-by-step explanation:

     [tex]\boxed{(y-y_1)=m(x -x_1)}[/tex]

m = 1

(1 , 8)  ; x₁ = 1  & y₁= 8;

    y - 8 = 1*(x - 1)

    y - 8 = x - 1

          y = x - 1 + 8

          y = x + 7

The expression for the given conditions is Y=10+c

where Y=no. of books Brett has and c=no. of books Erica has.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now

Given No. of books Erica has = 19

and Brett has c more comic books than Erica has

let Y=no. of books Brett has

Hence, the expression will be

          Y=19+c

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12 students do not play any of the games. Number of students who do not play any of the games = 60 - 82 = 12

A group of 60 students, 25 play table tennis, 16 do swimming and 22 play cricket, 8 play table tennis and do swimming, 6 play cricket and do swimming, 5 play table tennis and cricket.

25 play table tennis

16 do swimming

22 play cricket

8 play table tennis and do swimming

6 play cricket and do swimming

5 play table tennis and cricket

Find the number of students who do not play any of the games

Total number of students = 60

Number of students who play any of the games = 25 + 16 + 22 + 8 + 6 + 5 = 82

Number of students who do not play any of the games = 60 - 82 = 12

12 students do not play any of the games.

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By using the property of measure of an arc from the central angle

m(arc MQN) = 225°

m(arc MPN) = 135°

If m(arc KJH) = 312°

m∠1 = 48°

What is the measure of an arc from the central angle?

The measure of an arc from the central angle is the portion of the circumference of a circle that the arc spans. The measure of an arc is typically given in degrees.

In the given figure

by using the property of measure of an arc from the central angle

m(arc MQN) = 225°

m(arc MPN) = 360° - 225° = 135°

In the second figure,
If m(arc KJH) = 312°

m∠1 = 360° - 312° = 48°

Hence, by using the property of measure of an arc from the central angle

m(arc MQN) = 225°

m(arc MPN) = 135°

If m(arc KJH) = 312°

m∠1 = 48°

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Answer:

C. 5/4

Step-by-step explanation:

Let s = the scale factor

4s = 5  divide both sides by 4

s = 5/4

Answer:

Yes, the answers are equivalent.

Step-by-step explanation:

The answers are equivalent because when adding a positive to something it does not change the value of the number. So by adding the + in front of the -1 the value of -1 does not change in the equation.

Hope this helps!!

The number of nickels, x, and the number of dimes y that Harper has are;

8 nickels and 3 dimes

From conversion of coins we know that;

1 nickel = $0.05

1 dime = $0.10

Thus, if she has 5 more nickels than dimes, then;

Let x = the number of dimes Harper has

Let x + 5 = the number of nickels Harper has

Thus;

$0.05(x + 5) + $0.10(x) = $0.70

0.05x + 0.25 + 0.10x = 0.70

0.15x = 0.70 - 0.25

0.15x = 0.45

x = 0.45/0.15

x = 3 dimes

Nickels = 8 nickels

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$97.056 is the total interest accrued after the first month.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating.

The cost of car = 19,725*(1.0475) = 20,661.9375

Down payment = 2,175

So balance amount, P= 20661.9375-2175 = 18,486.9375

So interest for the average rating of a new car = 6.30%

So the interest accrued in first month = 18,486.9375*0.063/12 = $ 97.056

therefore, interest accrued after the first month is $97.056.

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An open circle is at 5 and a bold line starts at 5 and is pointing to the right. Therefore, option B is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -3(2x - 5) < 5(2 - x).

Here, -6x+15<10-5x

Add 5x on both the sides of an inequality, we get

-x+15<10

Subtract 15 on both the sides of an inequality, we get

-x<10-15

-x<-5

Multiply -1 on both the sides of an inequality, we get

x>5

Therefore, option B is the correct answer.

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The Raichu card was made 8 years ago.

To calculate this, we need to take into account the age of the Mewtwo card, the Snorlax card, and the Raichu card.

The Mewtwo card is twice as old as the Snorlax card, so the Mewtwo card is two years old. The Raichu card is five times as old as the Snorlax card, so it must be ten years old.

Since the Raichu card is two years older than the Mewtwo card, it must be eight years old. Therefore, the Raichu card was made eight years ago.

To summarise, the Mewtwo card is two years old, the Snorlax card is one year old, and the Raichu card is ten years old. Therefore, the Raichu card was made eight years ago.

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The order in which they performed be

14 + 16 . . . . add 5 + 9  

30 . . . . . . . add 14 + 16

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. There are four possible math operations here: addition, subtraction, multiplication, and division.

Given: 40/8 + 3² + (15 - 7) × 2

The order of operations instructs you to begin by assessing parenthesized expressions. This is done by deducting 7 from 15.

40/8 + 3² + 8 × 2 . . . . (15 - 7) = 8

Then you evaluate exponential terms.

 40/8 + 9 + 8 × 2 . . . . . 3² = 9

Next, multiply and divide from left to right. In this case, division comes before multiplication.

 5 + 9 + 8 × 2 . . . . . divide 40/8 = 5

 5 + 9 +16 . . . . . . multiply 8 × 2 = 16

The order in which they performed be

14 + 16 . . . . add 5 + 9  

30 . . . . . . . add 14 + 16

The complete question is:

Using the order of operations, what are the steps for solving this expression?

40/8+3^2+(15-7)*2

Arrange the steps in the order in which they are performed.​

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The solution set to the system of linear equations as an ordered pair is (3, -3).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines cross each other (intersect), which is represented as an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.

Note: Each interval on this graph represents 1 unit.

By critically observing the graph of the lines representing the system of linear equations, we can reasonably infer and logically deduce that the correct solution set lies in Quadrant IV and it is denoted by the point of intersection of both the x-coordinate and y-coordinate, which is given by the ordered pair (3, -3).

In conclusion, the ordered pair (3, -3) represents the solution set to the system of linear equations represented by the graph.

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y= -2.6717 + 0.0043(660) + 0.0045(630) = 3.00 is the GPA Score for Bobby Eagle.

A statistical method known as multiple linear regression (MLR), usually referred to as multiple regression, employs a number of explanatory variables to forecast the result of a response variable. One explanatory variable is used just once in multiple regression, an extension of linear (OLS) regression. Financial and econometric inference both make heavy use of MLR.

Score on critical reading = 660

Score on mathematics  = 630

Intercept = -2.6717

Reading(x1) = 0.0043

Mathematics(x2) = 0.0045

Hence, y = -2.6717 + 0.0043(660) + 0.0045(630) is the GPA score for Bobby.

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To meet the goal, the company should adjust the mean and/or standard deviation so that the probability of cans having a volume less than 355ml is less than 2.5%.

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

We can use the z-score formula to find the probability of cans having a volume less than 355 ml.

z-score = (355 - 358.2) / 1.8 = -1.78

Probability of cans having a volume less than 355ml = P(z < -1.78) = 0.0372

The company is not meeting its goal since the probability of cans having a volume less than 355ml is 0.0372 which is greater than 2.5%.

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Tyson has (30-2x) hours left after x days .

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).

A first-degree polynomial is described as the sum of a collection of terms, each of which is the product of a constant and the first power of a variable in a linear equation.

She works out for two hours per day for a total of x days.

She has thus worked for two hours.

She has 30 hours left to accomplish, of which she has already worked for two of them.

She now has 30 2 hours to finish the task.

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Answer:32/5

Step-by-step explanation:

32/5

Answer:

Solution: 6.4% as a fraction is 32/5.

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

you divide the intergert and div8de its easy

Answer: 70

Step-by-step explanation:

No hay solución para la ecuación algebraica 3 · x + 15 = 3 · x + 10.

En este problema tenemos el caso de una ecuación algebraica con una variable única y es nuestra labor determinar su solución, en caso de existir, por métodos algebraicos. Primero, escriba la ecuación algebraica correspondiente:

3 · (x + 5) = 3 · x + 10

Segundo, halle la solución por propiedades algebraicas:

3 · x + 15 = 3 · x + 10

15 = 10 (CRASH!)

La ecuación algebraica 3 · x + 15 = 3 · x + 10 no tiene solución.

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A linear equation giving the value of the equipment in terms of the time t is calculated to be v = 117000 - 16714.3t.

The value of the colour printer is 117000 $ and machine has no value after 7 years.

As it is given that the machine has no value after 7 years. That mean rate is decreasing every year. So, the decreasing rate is, 117000/7 = 16714.3.

Let us assume v is the value of the machine and t is the time. Then, the linear equation for the given problem is, v = 117000 - 16714.3t

Thus, the required linear equation is v = 117000 - 16714.3t.

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Step-by-step explanation:

To solve this problem, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and an angle C opposite side c,

c² = a² + b² - 2abcos(C)

In this problem, we can consider the man's starting point as the origin, and the distance he travels in the first leg as the first side of the triangle (a = 4km). The distance he travels in the second leg is the second side of the triangle (b). The angle between the two legs is the angle opposite side c, which is 90 degrees since the man changes direction from due west to southwest.

Therefore, we can use the law of cosines to find the distance he traveled in the second leg:

c² = a² + b² - 2abcos(90)

c² = 4² + b²

c = √(4² + b²)

c = √(16 + b²)

We know that the bearing of the second leg is 197 degrees, which is equivalent to a bearing of -163 degrees, since bearing measurements are taken clockwise from due north.

So we can use the law of cosines to find the distance he traveled in the second leg:

b = √(c² + a² - 2ac cos (-163))

We can now plug in the values we know:

b = √(c² + 4² - 24c*cos(-163))

We can now solve for c:

c = √(b² + 16 - 8bc)

The man is then southwest of his starting point, so the distance from his starting point to the final point is c.