as you stop your car at a traffic light, a pebble becomes wedged between the tire tread. when you start off, the distance of the pebble from the pavement in relation to the distance you have traveled can be modeled with a sinusoidal function. assume that the diameter of the wheel is 24 inches. which equation best models this situation?

Answer:

(1, - 1 )

Step-by-step explanation:

x + y = 0 → (1)

5x + y = 4 ( subtract 5x from both sides )

y = 4 - 5x → (2)

substitute y = 4 - 5x into (1)

x + 4 - 5x = 0

4 - 4x = 0 ( subtract 4 from both sides )

- 4x = - 4 ( divide both sides by - 4 )

x = 1

substitute x = 1 into (1) and solve for y

1 + y = 0 ( subtract 1 from both sides )

y = - 1

solution is (1, - 1 )

The percentage of respondents who said the magazine is useful is referred to as the population parameter of interest.

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The symbol replaces the box to make the statement true that 16 ÷ 4 + 12 □ 4 + 24 ÷ 2 is an equal sign, so 16 ÷ 4 + 12 = 4 + 24 ÷ 2.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given expression:

16 ÷ 4 + 12 □ 4 + 24 ÷ 2

Here calculate the first term

16 ÷ 4 + 12 = 4 + 12 = 16

Calculate the second term

4 + 24 ÷ 2 = 4 + 12 = 16

Thus, the equal sign will replace the box,

Therefore, the symbol replaces the box to make the statement true that 16 ÷ 4 + 12 □ 4 + 24 ÷ 2 is an equal sign.

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Answer:

Below

Step-by-step explanation:

Any 5 points you want

pick out 5 values of x      say     -4    -1     0      3   7  

  and calculate the value of the corresponding 'y' using the equation....then plot those points

Answer:

6

Step-by-step explanation:

all are divisible by 6 or can be added by six to get the next number

The required value of the contant of proportionality is given as 1/4.

Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.

Here,

Let G be the number of games and T be the number of tickets,

G ∝ T

So,

G = kT

From the table,

4 = 16k

k = 4/16

k = 1/4

Thus, the required value of the contant of proportionality is given as 1/4.

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The value of m in the triangle XYZ is 16. option D

It is important to note that the sum of angles in a triangle is 180 degrees.

From the information given, we have that;

Then we have that;

Angle MZ + Angle Z = 180

Now, substitute the values into the formula, we have;

(5m - 15) + (7m + 3) = 180°

expand the bracket

5m - 15 + 7m + 3 = 180°

collect like terms

12m - 12 = 180°

12m = 180 + 12

Add the like terms

12m = 192

Make 'm' the subject of formula by dividing both sides by 12, we get;

12m/12 = 192/12

m = 16

The value is 16.

Thus, the value is 16

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The equation (A) 8k-3=12 is not a quadratic equation as it is not in the form ax²+bx+c=0.

A quadratic equation is any algebraic expression that can be expressed in a standard form where x represents an unknown number, a, b, and c represent known values, and where a 0 is true.

The four methods for solving a quadratic issue are factoring, using square roots, completing the square, and the quadratic formula.

Form of a quadratic equation: ax²+bx+c=0

(A) 8k-3=12

Not in form of ax²+bx+c=0.

(B) 9r2 -25 =0

In form of ax²+bx+c=0.

(C) x2 - 5x + 3 = 0

In form of ax²+bx+c=0.

(D) (2x + 5) (x - 1) = - 6​

In form of ax²+bx+c=0.

Therefore, equation (A) 8k-3=12 is not a quadratic equation as it is not in the form ax²+bx+c=0.

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The term used to denote the process that builds a regression equation by testing one variable at a time, starting with the one which is significantly corelated and keeping only the other significant coefficients is known as stepwise regression.

Iteratively building a regression model step by step, stepwise regression entails choosing independent variables to be included in the final model. It entails successively introducing or eliminating putative explanatory factors and assessing statistical significance after each iteration.

Stepwise regression can be accomplished in one of two ways: either by including all potential independent variables in the model and removing those that are not statistically significant, or by attempting each independent variable one at a time and including it in the regression model if it is statistically significant.

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The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total time required to finish building the transmission if Jose and Luis works together be = A

Now , the equation will be

The time required by Jose to build a transmission = 10 hours

The time required by Luis to build a transmission = 8 hours

If it takes one person 10 hours to build a transmission and another person 8 hours to build the same transmission , working together they could build the transmission even quicker

So ,

If Jose builds the transmission is 10 hours , he builds 1/10th of the transmission in one hour

If Luis builds the transmission in 8 hours , he builds 1/8th of the transmission in one hour

And ,

Together they build the transmission in

1/A = 1/10 + 1/8

where A is the total time required to finish building the transmission if Jose and Luis works together

So , the equation is

1/A = 1/10 + 1/8

1/A = 18/80

Taking reciprocals on both sides of the equation , we get

A = 80/18

A = 40/9

On simplifying the equation , we get

A = 4.44 hours

Therefore , the value of A is 4.44 hours

Hence , The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours

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The number of songs that he transferred per minute is 1 5/7 songs per minute (option B).

In order to determine the number of songs he can transfer in one minute, divide the number of songs transferred in 1 2/3 by the number of minutes.

Division is the process of determining the quotient of two or more numbers. It entails grouping a number into equal groups using another number. The sign that is used to represent division is ÷

Number of songs they want to transfer per minute = 2 6/7 ÷ 1 2/3

20 /7 ÷ 5/3

20/7 x 3/5 = 12/7 = 1 5/7 songs per minute

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The solution to each of the given algebraic expressions are;

1) 2n - 2 = 10

2) 12n - 1 = 17

3) 4 * 9 = 36

4) 23 - 8 = 15

5) (3 * 7) + 1 = 22

6) ¹/₆ * 42 = 7

7) 3n - 6 = 70

8) y - 2 = 9

9) x = 5 * 12

10) -48 = -4 * 12

11) -32/-8 = 4.

12) (15 - 3)n = 2

13) (5 + 8)n = 42

14) (12 + 6)/2 = 9

15) -4 = -2(5 - 3)

16) x + (x + 1) = 25

17) (x) + (x + 1) = -3

18) 11 - x = -1

1) Two less than twice a number is equal to 10 is expressed as;

2n - 2 = 10

2) 17 is one more than twice a number;

2n - 1 = 17

3) Four times 9 is 36;

4 * 9 = 36

4) Eight less than 23 is fifteen;

23 - 8 = 15

5) One more than 3 times 7 is 22;

(3 * 7) + 1 = 22

6) One sixth of forty two is seven;

¹/₆ * 42 = 7

7) Six less than 3 times a number is equal to seventy;

3n - 6 = 70

8) Two dollars off the regular price of a calculator is $9;

y - 2 = 9

9) A number is equal to five times 12;

x = 5 * 12

10) Negative 4 is a product of the opposite of four and 12;

-48 = -4 * 12

11) Four is the quotient of -32 and -8;

-32/-8 = 4.

12) When 15 minus 3 is multiplied by a number, the product is 2;

(15 - 3)n = 2

13) A number times the sum of five and 8 is 42;

(5 + 8)n = 42

14) 9 is the quotient when 12 + 6 is divided by 2;

(12 + 6)/2 = 9

15) -4 = -2(5 - 3)

16) x + (x + 1) = 25

17) (x) + (x + 1) = -3

18) 11 - x = -1

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The answer is 106 since it is 26 more than twice the number and 4 less than 5 times a number.

Step-by-step explanation:

The number multiplied by 3 and subtracted by 2 equals 40 is 14.

The Equation that is used to find an unknown value is known as Linear Equation. To find an unknown value or quantity, first form a linear equation according to the conditions that are given the problem, here we use variables like x, y, etc. to represent the unknown value.  

Here we have

A Number is multiplied by 3 and subtracted by 2 equals 40

Let the number be x

Given that 'x' is multiplied by 3 (3x); subtracted by 2 (3x-2) equals to 40

=> 3x - 2 = 40

Add 2 on both sides

=> 3x - 2 + 2 = 40 + 2

=> 3x = 42

Divide by 3 into both sides

=> 3x/3 = 42/3

=>  x = 14

Therefore,

The number multiplied by 3 and subtracted by 2 equals 40 is 14.

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Answer:

1.1 hectares

Step-by-step explanation:

6.93/6.3 = 1.1

He can plant 1.1 hectares of land.

Answer:

Step-by-step explanation:

The surface area of solid cylinder = 231 cm²

and curved surface area = 2/3 * 231 cm² = 154 cm²

Now, 2πrh = 154 ...........(i)

2πrh+2πr² = 231

Subtracting, 2πr² =  231 - 154 = 77

⇒2 * 22/7 * r² = 77

⇒r² = 77*7/2*22 ⇒ 49/4 ⇒ (7/2)²

so, r = 7/2 cm

Now, from (i),

2 * 22/7 * 7*h/2 = 154

⇒22h = 154 ⇒ 154/22 = 7

and volume = πr²h = 22/7 * 7/2 * 7/2 * 7cm³ ⇒ 539/2 = 269.5 cm²

Using Pythagoras theorem If sin tetha = x/4, then cos tetha = √(16-x²)/4

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

The sides of this triangle have been named Perpendicular, adjascent and Hypotenuse. If sin (tetha) = x/4, this means

x = opposite and

4 = hypotenuse

From hypotenuse² = opposite² + adjacent²

4² = x²+y²

y² = 16-x²

y = √ ( 16-x²)

cos (tetha) = adjacent/ hypotenuse

cos (tetha) = √(16-x²)/4

Therefore the value of cos (tetha) = √(16-x²)/4

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The boat's distance and bearing from the port regions are as follows;

The boat is located around 157.15 kilometers from the harbor on a bearing of 150°.

In mathematics, a bearing is an angle measured clockwise from the north or y-axis direction.

The Coast Guard cutter travels at a speed of 30 kno

Angelica, a Coast Guard cutter, has a bearing of 95 degrees.

The coast guard goes for 2 hours in the first direction.

The shift in direction of the Coast Guard cutter = 185°

Travel time in the new direction = 2 hours

30 knots equals 55.56 km/hr

The distance traveled in the first direction = 55.56 km/hr = 111.12 km in 2 hours

Distance traveled in the other direction = 55.56 km/hr 2 hours = 111.12 km

According to the accompanying graphic, the figure produced by the Coast Guard cutter's course is an isosceles triangle.

The Pythagorean theorem gives the distance from the port to the position of the boat as l = √(111.122^2 + 111.122^2) ≈ 157.15.

The boat is roughly 157.15 kilometers away from the port.

An isosceles right triangle has 45° base angles.

As a result, the bearing is 95° + 45° = 150°.

The angle between the port and the boat is 150°.

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Therefore, Gracie will earn $61600 if she waits until December 21. However, she will earn bank discount $61132.87 on November 12.

A bank discount is interest that the bank deducts beforehand in the basic discount note. The maturity value less the bank discount equals the amount owed. The total of the principle and interest due at the conclusion of the time period is the maturity value.

Date of note = 14th July

Face value = $60000

Length of note = 160 days,

Interest rate = 6%

Calculating the interest and maturity value:

Interest  = Principal × interest × time

= 60000 × 0.06 × 160/360

= 1600

So the maturity value MV = Face value + interest

= 60000 + 1600

= 61600

2. Calculating discount period:

Note discounted on 12th November

Time till 12th November = 315 days

Time till 14th July = 194 days

So days before note is discount = 315 - 194= 121 days

Length of note = 160 days,

So the discount period = 160 - 121 = 39 days

3 - Bank discount:

Bank discount = MV × Bank discount rate × number of days bank waits till due date

= 61600 × 0.07 × 39/360

= 467.133

4 - Proceeds from bank: Proceeds = MV - Bank discount

= 61600 - 467.133

= 61132.87

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The required coordinate pair for W" is (2,-3)

When a point is reflected over axes, its position changes and sign of coordinates also change.

Given that, Point W is located at (-2, 3) on a coordinate plane. Point W is reflected over the x-axis to create point W'. Point W' is then reflected over the y-axis to create point W".

When a point is reflected over the x-axis, then we know,

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

W(-2,3) = W (−2,−3)

And,

When a point is reflected over the y-axis, then we know,

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

Therefore, W'(-2,-3) = W" (2,-3)

Hence, the coordinates of the point W" are (2,-3)

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Answer:

Slope:  - 4/3

Point (4,1)

Step-by-step explanation:

hope this helps

The hot air balloon travels 40 miles against the wind in the same amount of time that it travels 200 miles with the wind. Therefore, the rate of the hot air balloon against the wind is 40 miles/200 miles x 20 mph = 8 mph.

1. Calculate the ratio of the distance traveled against the wind compared to the distance traveled with the wind: 40 miles/200 miles = 0.2

2. Multiply the ratio by the speed of the wind: 0.2 x 20 mph = 4 mph

3. The speed of the hot air balloon against the wind is 8 mph.

The hot air balloon is able to travel at a speed of 20 mph when the wind is in its favor. However, when the wind is not in its favor, the hot air balloon must travel against the wind, drastically decreasing its speed. In the same amount of time, the hot air balloon was able to travel 40 miles against the wind while it was able to travel 200 miles with the wind. To calculate the speed of the hot air balloon against the wind, we can use the following formula: Speed = (Distance against the wind/Distance with the wind) x Speed of the wind. In this case, the ratio of the distance traveled against the wind compared to the distance traveled with the wind is 40 miles/200 miles = 0.2. When we multiply this ratio by the speed of the wind, which is 20 mph, we get 4 mph. Therefore, the rate of the hot air balloon against the wind is 8 mph.

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It will take 5.625 hours for both Darryl and Valerie to paint the room if they work together .

In the question ,

it is given that ,

Darryl can paint the room in 9 hours .

So , in 1 hour Darryl can paint 1/9 of the room .

Valerie can paint the room in 15 hours .

So , in 1 hour Valerie can paint 1/15 of the room .

So , the time taken to paint the room together can be calculated using ,

1/t = 1/9 + 1/15

1/t = 5/45 + 3/45

1/t = 8/45

Simplifying further ,

we get ,

t = 45/8

t = 5.625

Therefore , the time taken will be 5.625 hours .

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Answer:

Area = 600

Step-by-step explanation:

The area formula for rectangles is length x width. In this equation, the length is 20 and the width is 30, multiplying them together gets us the area of 600.

Answer:

20

Step-by-step explanation:

h=hypotenuse. s1=side 1. s2=side 2

h^2 = (s1)^2 + (s2)^2  ==> hypotenuse formula

h^2 = 12^2 + 16^2  => plug in known values

h^2 = 144 + 256  

h^2 = 400  ==> simplify

[tex]\sqrt{h^2 = 400}[/tex]  ==> take the square root on both sides to remove the power

[tex]\sqrt{h^2}[/tex] = [tex]\sqrt{400}[/tex]

h = 20

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Aggregates is distorts the effectiveness of charting data points. So the option d is correct.

In the given question, we have to select which of the following, when included, distorts the effectiveness of charting data points.

Charts are a quick and efficient way to communicate information to your audience. If the charts are properly created, that is.

A lot goes into creating the ideal visual material, and it's simple to let some components slip. Charts that are hurriedly created are frequently more detrimental than beneficial.

We've compiled a list of useful do's and don'ts to bear in mind while building your own data representations, whether they take the shape of straightforward bar charts and graphs or more intricate interactive visualizations, in order to help you prevent this.

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The rate of change or the speed of the different sections and the distance answers are below;

1) 2 m/s

2) 0 m/s

3) 3 m/s

4) Section C

5) Section A

1) The formula for the slope is;

Slope = (y₂ - y₁)/(x₂ - x₁)

Taking two coordinates in section A, we can find the slope which gives us the speed;

Speed = (50 - 0)/(25 - 0)

Speed = 2 m/s

2) Section B shows that the speed is constant and as such the rate of change of speed 0 m/s

3) Rate of change of section C is;

Speed = (80 - 50)/(70 - 60)

Speed = 3 m/s

4) The section that the person was moving at the highest speed is 3 m/s which is section C.

5) The section that the person travelled the farthest is section A which was 50 meters.

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The amount of the investment at maturity is $2443.341

Compound interest is the interest on the initial principal plus the interest which has been accumulated.

Given,

Principal amount (P)=  $1500

Rate of interest(R)= 5% = 5/100 = 0.05%

Time(T)= 10 years

The formula for annual compound interest is as follows:

FV = P (1+ r/m)^mt

Where:

FV - the future value of the investment, in our calculator it is the final balance

P - the initial balance (the value of the investment)

r - the annual interest rate (in decimal)

m - the number of times the interest is compounded per year (compounding frequency)

t - the number of years the money is invested for

FV = 1500*(1+0.05/1)^(10*1) = 2443.341

The value of the investment after 10 years will be $2443.341.

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Answer:

The answer is in the image I attached to this response. Let p = the cost of 1 pencil, and let r = the cost of 1 ruler.

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The 3 combinations of coins with the value of 30% of a dollar are 2 dimes + 1 Nickel + 5 Pennies, 1 dime + 2 Nickels + 10 Pennies, 3 Nickels + 1 dime + 5 Pennies.

How many types of coins are there?

There are 4 types of coins. They are Quarter, Nickel, dime, and Penny.

1 Quarter = 25 cent

1 dime = 10 cents

1 Nickel = 5 cents

1 penny = 1 cent

Now calculate 30 percentage of a dollar.

1 dollar = 100 cents.

30% of 100 cents = (30/100) × 100 = 30 cents.

2 dimes + 1 Nickel + 5 Pennies = 20 cents + 5 cents + 5 cents = 30 cents

1 dime + 2 Nickels + 10 Pennies = 10 cents + 10 cents + 10 cents = 30 cents

3 Nickels + 1 dime + 5 Pennies = 15 cents + 10 cents + 5 cents = 30 cents

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