Sarah ran 3,682 m yesterday on the track at her school. One time around the track is 263 m. Sarah wants to run 4,222 m today. Which number sentence can be used to calculate how many laps around the track Sarah should run today?

Linear equations are equations that can be written in the form ax + b = c, where a, b, and c are real numbers and a ≠ 0.

The equation can be solved for the variable x by subtracting b from both sides and then dividing both sides by a. This will give the solution for x, which is x = (c - b) / a.

For example, consider the equation 2x + 4 = 10. This is a linear equation since it can be written in the form ax + b = c, where a = 2, b = 4, and c = 10. To solve for x, subtract b from both sides to get 2x = 6, and then divide both sides by a to get x = 3. Therefore, the solution to the equation is x = 3.

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Answer:

The answer is 5⁻¹ or 1/5

Step-by-step explanation:

5²/5³

Here, we know that the base is the same i.e., 5 so, will use the property;

5² ÷ 5³

5² ⁻ ³ = 5⁻¹ = 1/5

Thus, The answer is 5⁻¹ or 1/5

Answer:

x < -18/5

this is the answer of you problem

Vanessa needs to buy 2*(22/7)sqrt(1547/22) + 2 inches of ribbon.

What is the area of circle?

The area of a circle is given by the formula: A = πr^2, where A is the area of the circle, π is a constant (approximately equal to 3.14) and r is the radius of the circle.

Given the area of the circular region is 154 square inches. We can use the formula to find the radius: 154 = πr^2

By substituting π = 22/7 we get:

154 = (22/7)r^2

Solving for r, we get:

r = sqrt(154*7/22)

The circumference of the circle is given by the formula C = 2πr, where C is the circumference and r is the radius.

By substituting the value of r we got before, we get:

C = 2πr = 2*(22/7)sqrt(1547/22)

To be sure she has enough ribbon, Vanessa decides to buy 2 inches more of the ribbon than the original circle's circumference. So she needs to buy:

C + 2 = 2*(22/7)sqrt(1547/22) + 2 inches

Hence, Vanessa needs to buy 2*(22/7)sqrt(1547/22) + 2 inches of ribbon.

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The graph of the function f(x) = -2|x-3|+1 is attached below.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

f(x) = -2|x-3|+1

First |x-3| shows there is horizontal shift by 3 units.

Now, '+1' shows there is Vertical shift by 1 unit.

and, 2|x-3| shows there is Vertical stretch and the negative sign shows reflection over x- axis.

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The dual formula is a formula which we get when we replace the symbol ∨ by ∧ , ∧ by ∨ , T by F  or F by T.

Basically , we can say that it is obtained by replacing tautology by contradiction.

There are certain rules which are to be followed while applying dual formula which are,

S1 is a tautology if and only if S2 is a contradiction.

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three main trigonometry ratios are sin ,cos and tan.

1- Sine or sin θ = perpendicular / Hypotenuse .

2- Cosines or cos θ = base of triangle / Hypotenuse .

3- Tangent or tan θ = perpendicular of triangle / base of triangle.

Trigonometry

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Trigonometric values are based on the angle theta and the values of the sides of triangle in which the theta angle is made.

for example - value of sin theta is equal to the side opposite to the theta angle divided by hypotenuse of the triangle and we will get the values of the sin trigonometric ratio.

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By using the table, each of the items in the lists should be matched as follows:

In Mathematics, a proportion can be defined as an equation which is typically used to represent (indicate) the equality of two ratios. This ultimately implies that, proportions can be used to establish that two ratios are equivalent and solve for all unknown quantities.

Based on the information provided in the table, we can reasonably infer and logically deduce that the variable x represent pounds of butterscotch candy while the variable y represent pounds of peppermint candy.

Additionally, a system of equations that models the information provided in the table is given by;

x + y = 10.                      

2.15x + 2.35y = 22.00.

In conclusion, the total quantity of candies in pounds (lbs.) is equal to 10.

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So, it rained 15/8 inch the day before yesterday.

The total amount of rain that fell in the last three days is 1 inch. We know that 2/8 of an inch fell today, and 3/8 of an inch fell yesterday. We can add these amounts together to find out how much more it rained the day before yesterday.

To add 2/8 and 3/8, we need to convert the fractions to have a common denominator, which is 8.

2/8 = 2/8 * 1 = 2/8

3/8 = 3/8 * 1 = 3/8

Now we can add the fractions:

2/8 + 3/8 = (2+3)/8 = 5/8

Since we know that the total amount of rain that fell in the last three days is 1 inch, we can subtract the amount that fell today and yesterday from the total amount to find out how much more it rained the day before yesterday:

1 inch - (5/8 inch) = 15/8 inch

Therefore, it rained 15/8 inch the day before yesterday.

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If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.

The following formula determines how many combinations of n objects can be taken r at a time: (n,r) = C(n,r)! .

She was a master of both wit and martial arts. The art and science of education blend beautifully. He saw slam poetry as the ideal synthesis of thought, writing, and theater. The desired mix is produced by the computer system (the perfect combination of arabica and robusta).

Five documentaries make up the total.

7 comedies total are available.

Four mysteries are present.

5 horror movies are there.

A total of 14 films, excluding comedies, are available.

If he wants to rent all 7 comedies, there are a total of 9 different combinations that he can do.

1 * (14*13)/2 = 91

If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.

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The number of different North Dakota license plates that can be issued is 17,576,000 plates.

For the first digit, there are 10 possibilities (0 to 9). For the second and third digits, there are also 10 possibilities each. For the first letter, there are 26 possibilities. For the second and third letters, there are also 26 possibilities each.

The total number of different license plates that can be issued is therefore:

= 10 x 10 x 10 x 26 x 26 x 26

= 1, 000 x 17, 576

= 17, 576, 000 different plates

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The unknown angles in the parallel lines are as follows;

x = 28

y = 23

When parallel lines are cut by a transversal line, angle relationships are formed such as linear angles, vertically opposite angles, interior angles, corresponding angles, alternate interior angles, alternate exterior angles etc.

using vertical angles and same side interior angles,

5y - 4 + 3y = 180 (same side interior angles are supplementary)

8y - 4 = 180

8y = 180 + 4

8y = 184

divide both sides by 8

y = 184 / 8

y = 23

Hence,

3y  = 2x + 13(corresponding angles)

corresponding angles are congruent.

Hence,

3(23) = 2x + 13

69 - 13 = 2x

2x = 56

x = 56 / 2

x = 28

Therefore,

x = 28

y = 23

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Answer: 4/5 minus 5/10 can be simplified as:

(4/5) - (5/10)

It can also be re-written as

(4/5) - (1/2)

To subtract these fractions, we need a common denominator, which is 10 in this case.

So it becomes

(4/5)(2/2) - (1/2)(5/5) = 8/10 - 5/10 = 3/10

So the result of 4/5 minus 5/10 is 3/10 on a number line.

Step-by-step explanation:

So, Todd picked 1 apple.

We can use the information given to set up the following equations:

Let x be the number of apples Jack picked, and y be the number of apples Marta picked.

We know that x + y = 16 (Jack and Marta pick a total of 16 apples)

Let y be the number of apples Marta picked, and z be the number of apples Rand picked.

We know that y + z = 15 (Marta and Rand pick a total of 15 apples)

Let z be the number of apples Rand picked, and w be the number of apples Todd picked.

We know that z + w = 13 (Rand and Todd pick a total of 13 apples)

We know that the total number of apples picked is 45, therefore x + y + z + w = 45

We can use the equation x + y = 16 to express x in terms of y:

x = 16 - y

We can substitute this into the other equations

(16 - y) + y = 16

y + z = 15

z + w = 13

We can sum all the equations:

(16 - y) + y + y + z + z + w = 45

16 + 2y + 2z + w = 45

From the equation y + z = 15, we can substitute y = 15 - z

16 + 2(15 - z) + 2z + w = 45

16 + 30 - 2z + 2z + w = 45

46 + w = 45

w = 1

Therefore Todd picked 1 apple.

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Answer:

Trim A

Inches = 36

Feet = 3

Yards = 1

Trim B

Inches = 216

Feet = 18

Yards = 6

Answer:

120

Step-by-step explanation:

3/5 of 200 = 120

This is how the Cluster of sampling technique is best described.

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Answer: -2/3x is the slope and the beginning amount is 5 so the equation would be -2/3x+5.

Step-by-step explanation:

Once you find the slope using the formula rise/run you will get 2/3 but since the slope is going downwards it would be -2/3 which gives you the mx. Now to find the beginning amount look where the line intersects the graph which will give you the equation.

By solving, we see that the product of the polynomials 4 - a and a3 + 7a - 18 is a3 + 3a2 + 46a + 72.

The location on the y-axis where the slope of the line passes is known as the intersection point in mathematics. a point on a line or curve where the y-axis crosses. The equation for the straight line is given as Y = mx+c, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercept form (y=mx+b) are m and b, respectively. There are several equations that can be rewritten to look like slope intercepts. The slope and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0, for example.

given

(4 - a) * ( a3 + 7a - 18 )

= 4a3 + 28a - 72 - a4 + 7a2 + 18 a

= a3 + 3a2 + 46a + 72

By solving, we see that the product of the polynomials 4 - a and a3 + 7a - 18 is a3 + 3a2 + 46a + 72.

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We would require 400 square tiles, each measuring one square foot, to cover the whole surface of the square room.

If the perimeter of the room is 80 feet, we know that all four sides of the square room have the same length. To find the length of each side, we can divide the perimeter by 4: 80 feet / 4 = 20 feet.

Now that we know the length of each side of the room, we can find the area of the room by squaring that measurement: 20 feet x 20 feet = 400 square feet.

To find the number of floor tiles needed to cover the area of the room, we divide the total area of the room by the area of each tile: 400 square feet / 1 square foot/tile = 400 tiles.

So, to cover the entire area of the square room, we would need 400 square tiles of one square foot each.

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The true statement is 6 less than 10

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

(-2) (-3) less greater than equal than 8- (-2)

We start by evaluating each expression

So, we have the following representation

(-2) (-3) = 6

8- (-2) = 10

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

6 less greater than equal than 10

6 is less than 10

So, we have

6 less than 10

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Answer:

y = 3x - 2

Step-by-step explanation:

Using Punnett square we know that 25%of the possible gene combinations result in albino coloring.

The genotypes of a specific cross or breeding experiment are predicted using the Punnett square, a square diagram.

It bears Reginald C. Punnett's name, who developed the method in 1905.

Biologists use the figure to calculate the likelihood that a child will have a specific genotype.

So, there is only one gene combination that could result in albinism.

4 different gene pairings are possible.

The proportion of gene combinations that might result in albinism.

Coloring is, therefore:

Percentage = 1/4 * 100 = 25%

Therefore, using Punnett square we know that 25%of the possible gene combinations result in albino coloring.

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Correct question:

Genetics In deer, the gene N is for normal coloring and the gene a is for albino. Any gene combination with an N results in normal coloring. The Punnett square shows the possible gene combinations of an offspring and the resulting colors when both parents have the gene combination Na.

What percent of the possible gene combinations result in albino coloring?

[tex]-7x < 35[/tex]

Divide both sides by -7:

[tex]\dfrac{-7x}{-7} < \dfrac{35}{-7}[/tex]

Since we are dividing by a negative number, the sign will reverse.

[tex]\fbox{x} > \fbox{-5}[/tex]

The solution to the given inequality is x > -5 which represents a set of all real numbers x that are greater than -5.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question, as follows:

-7x < 35

To solve the inequality -7x < 35, we first need to isolate the variable (x) on one side of the inequality.

We will divide both sides of the inequality by -7 (since -7 is being multiplied by x on the left side).

However, when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality symbol. So the inequality becomes:

x > -5

This inequality can be read as "x is greater than -5." It is the solution set of all real numbers x that is greater than -5.

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Answer:

x = 1

Step-by-step explanation:

Immediately, we will simplify like terms on the left side of the equation. This will give us:

[tex]\sqrt{2x-x-1}[/tex]  = 0

Simplifying gives us:

[tex]\sqrt{x-1}[/tex] = 0

Now, an important thing to note, is that for the square root of a number to be 0, the number has to be 0. Therefore, x - 1 must equal 0. So, x = 1. Checking our work gives us:

[tex]\sqrt{2x - x - 1}[/tex] = 0

[tex]\\\sqrt{2 - 1 - 1}[/tex] = 0

[tex]\sqrt{0}[/tex] = 0

It all checks out.

Hope this helped!

The situation involving coins that is modeled by the system of equations x + y = 24, 0.25x + 0.05y = 4.60 is given as follows:

You have a combination of 24 quarters and cents, and the total you have is of $4.60. How many coins of each type you have.

To obtain the meaning of each of the variables x and y, we look at the second equation, given as follows:

0.25x + 0.05y = 4.60.

This means that:

The result of this sum means that the total amount of money that you have is of $4.60.

The first equation is given as follows:

x + y = 24.

Which means that the total number of coins that you have is of 24.

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The general solution to the given differential equation is y = c₁e⁻t + c₂te⁻t + t².

The given differential equation can be written as y'' - y' - 2y = -2t + 4t², which is a second-order linear differential equation with constant coefficients. To solve this equation, the first step is to solve the associated homogeneous equation, which is y'' - y' - 2y = 0. This homogeneous equation can be solved by using the characteristic equation, r² - r - 2 = 0, which has two roots, r = 2 and r = -1.

The general solution of the homogeneous equation is then y = c₁e²t + c₂e⁻t. To find the particular solution of the non-homogeneous equation, the method of undetermined coefficients is used. Since the non-homogeneous term is 4t², the particular solution of the non-homogeneous equation is yp = t².

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Eight 1/2s are in 4. This can be visualized with pattern blocks, as four triangles (each triangle is 1/2) would be needed to make up a square (4).

Visualization is the process of creating graphical representations of data and information. It can take the form of charts, graphs, diagrams, maps, and other visual representations of data and patterns. Visualization can be used to explore, analyze, and communicate data in an effective and meaningful way, helping to make complex data more accessible and easier to understand. Visualization can also help to uncover trends and relationships that might otherwise be difficult to detect.

b. Three 2/3s are in 2. This can be visualized with pattern blocks, as three hexagons (each hexagon is 2/3) would be needed to make up a rectangle (2).
c. Six 1/6s are in 1. This can be visualized with pattern blocks, as six rhombuses (each rhombus is 1/6) would be needed to make up a hexagon (1).

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