Tanner collected 360 cans. This was 40% of what Reggie collected. How many cans did Reggie collect?

So the slope of the scenario is $28 per hour, which indicates that the expense of the tour increases by $28 for every extra hour spent on it.

The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b). For example, the slope of the equation y = 3x - 7 is 3, while the y-intercept is (0, 7).

Here,

In this situation, the slope represents the rate of change in the cost of the tour with respect to the time spent on the tour. The slope of the situation can be calculated as the change in cost divided by the change in time.

Since the one-time fee is a fixed cost, it does not change with respect to the time spent on the tour. Therefore, the slope can be calculated as the rate of change in the cost due to the hourly fee of $28.

The slope can be represented as:

slope = Δcost/Δtime = $28/hour

So, the slope of the situation is $28 per hour, which means that for every additional hour spent on the tour, the cost of the tour increases by $28.

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Answer:

Step-by-step explanation:

To find the speed of a cyclist, divide the distance traveled by the time taken.

In this case, the speed is:

3.75 miles ÷ 0.3 hours = 12.5 miles per hour (mph)

So, the cyclist was traveling at a speed of 12.5 mph.

Answer:

Step-by-step explanation:

Answer should be 12.5 mph.

The simplified expression is equal to 2/3.

        2m⁰ * n⁶ / (3n⁵)

       2 * n⁶ / (3n⁵)

        2 * n / (3n) = 2/3

So the simplified expression is equal to 2/3.

The rules of arithmetic and exponentiation that I used to simplify the expression are general mathematical principles that are applicable to many mathematical problems. However, the specific techniques for simplifying an expression will depend on the particular expression and the context in which it is being used.

For example, there might be additional rules or simplification techniques that are specific to a particular field of mathematics, such as algebra, calculus, or geometry. In these cases, it's important to understand the specific rules and techniques that apply to the problem at hand in order to simplify an expression effectively.

In general, the goal of simplifying an expression is to make it easier to understand and manipulate mathematically, either for further calculations or for understanding the relationships between the variables involved.

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Answer:

b

Step-by-step explanation:

The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²

The probability of getting 2 same colour balls in a row = 41/81

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.

Probability of an event P(E)

= [ No of favorable outcomes ]/ Total No of outcomes

Here we have

There is a bag filled with 5 blue and 4 red marbles.  

Number of balls = 5 + 4 = 9  

Marble is taken at random from the bag,

The probability of getting the red ball = 4/9  

The probability of getting the blue ball = 5/9

The color is noted and then it is replaced.

Another marble is taken at random.  

The probability of getting the red ball 2nd time = 4/9  

The probability of getting the blue ball 2nd time = 5/9    

The probability of getting red ball in 2 attempts = (4/9)(4/9) = 16/81

The probability of getting blue ball in 2 attempts = (5/9)(5/9) = 25/81  

Hence the probability of getting 2 of the same color

= 16/81 + 25/81

= 41/81  

Therefore,

The probability of getting 2 same colour balls in a row = 41/81

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Answer:

No Solution.

Step-by-step explanation:

To solve for x in this equation, we need to simplify both sides of the equation and make them equal.

Starting with the left-hand side:

5 + x - 14 = x - 7

Adding 14 to both sides:

5 + x = x + 7

Subtracting x from both sides:

5 = 7

5 does not equal 7.

Therefore, the value of x is no solution.

Answer:

there is no solution for this, if you solve you will get 0=2 (This is also called a contradiction)

Step-by-step explanation:

5+x-14=x-7

5-14 = -9

-9+x=x-7

x-9=x-7

+9     +9

x=x+2

-x  -x

0 = 2

The point of intersection of the two equations will be ( 0, 3 ). The correct option is C.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the two equations are y= 2x+3 and y=-3x+3. The value of x and y will be calculated as:-

y= 2x+3

y=-3x+3

Equate the equations and solve,

2x + 3 = - 3x + 3

2x +3x = 0

x = 0

The value of y is,

y = 2x+3

y = 2 x 0 + 3

y = 3

Therefore, the two equations points of intersection will be ( 0, 3 ). The right answer is C.

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Answer:

[tex]3=e[/tex]

Step-by-step explanation:

I know this might be late but I can help if you still need it

So in the equation [tex]2=e-1[/tex], we need [tex]e[/tex] by itself. To do that we need to add [tex]1[/tex] to each side. We do this because the side that [tex]e[/tex] is on, the [tex]1[/tex] is being subtracted and we need to do the opposite of subtraction which is addition.

[tex]2=e-1[/tex]

[tex]+1[/tex]     [tex]+1[/tex]

So the new equation:

[tex]3=e[/tex]

Hope this helped!
Stay safe and have a great day/night! (:

The vertex form of quadratic equation is y = a(x - 0)² + 7 and the standard form of quadratic equation is y = 0x² + 7

The vertex form of a quadratic equation is an equation written in the form:

f(x) = a(x - h)² + k,

where (h, k) is the vertex of the parabola represented by the equation. The variable x represents the input value, f(x) represents the output value, a represents the coefficient of the x² term, h represents the x-coordinate of the vertex, and k represents the y-coordinate of the vertex. The vertex form of a quadratic equation is useful for easily identifying the location and shape of the parabola represented by the equation, especially if the parabolic function has a vertex that is not at (0,0).

The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

To find the vertex form of this equation, we need to find the vertex first. To do this, we can average the x-values of the maximum and minimum points in the table, which gives us the x-coordinate of the vertex. In this case, the maximum and minimum points are (1, 7) and (-1, -9), so the x-coordinate of the vertex is (1 + -1)/2 = 0.

Next, we can find the y-coordinate of the vertex by evaluating f(0), which gives us 7.

So, the vertex of the parabola is (0, 7).

Using this information, we can write the vertex form of the equation:

y = a(x - 0)² + 7

To find the standard form of the equation, we need to expand the vertex form and simplify.

y = a(x² - 0x) + 7

y = ax² + 7

We can then find the value of a by using any one of the points in the table. Let's use the point (1, 7):

7 = a(1²) + 7

7 = a + 7

a = 0

So, the standard form of the equation is:

y = 0x² + 7

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Answer: The team's time on the final run can be found by successively multiplying their first time by (1 - 0.512) twice:

First run time: 4.85 minutes

Second run time: 4.85 * (1 - 0.512) = 2.37 minutes

Third run time: 2.37 * (1 - 0.512) = 1.15 minutes (rounded to the nearest hundredth)

So the team's time on their final run was 1.15 minutes.

Step-by-step explanation:

The expression that can represent how many more cans were collected is 8n - 7 > 6n + 3, which is in fact an inequality.

An inequality in math is an algebraic expression that represents, well, inequality. It shows a relationship between two values or expression, which aren't equal to each other. It is used to compare two values/expression, showing if one is greater than, less than, or simply not equal to another. Thus, we would use a mathematical symbol of <, >, ≤, ≥, or ≠ to express an inequality.

Since students in Mr. Juarez's homeroom collected more cans than students in Ms. Wade's homeroom do, you can use the symbol > in your inequality. The number of cans collected in Mr. Juarez's homeroom is 8n − 7, while the number of cans collected in Ms. Wade's homeroom is 6n + 3. Therefore, your inequality would be 8n - 7 > 6n + 3.

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Answer:

To make the smallest number with the cards 3, 2, 4, and 7, you can arrange them as 2, 3, 4, 7 to get the number 237.

To make the number closest to 5000, arrange the cards as 7, 4, 2, 3 to get the number 7243.

Step-by-step explanation:

The equation we get for the amount of bacteria with  with time T

T(t)=15×2ⁿ where n is the number of hours.

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here: A certain type of bacteria doubles every hour

Now number of hours between 9-12 pm

is 15 hours

if at 9 a.m the amount of bacteria is x then we have in 15 hours

at t=1 we have the number of bacteria was

T=2×15

=30

Similarly we have for t=15 we get

T=15×2¹⁵

Hence, The equation we get for the amount of bacteria with  with time T

T(t)=15×2ⁿ where n is the number of hours.

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The length of the line segment is approximately 12.04 units. This formula calculates the distance between two points, (x1, y1) and (x2, y2), on the line segment. The formula is as follows: d = √((x2 - x1)^2 + (y2 - y1)^2)

The length of a line segment in a two-dimensional x-y coordinate plane can be found using the distance formula. This formula calculates the distance between two points, (x1, y1) and (x2, y2), on the line segment. The formula is as follows:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the line segment extends from the point (2, 8) to the point (12, 2). By plugging these values into the formula, we find that:

d = √((12 - 2)^2 + (2 - 8)^2) = √(100 + 36) = √136 = 12.04

So, the length of the line segment is approximately 12.04 units. This formula is useful for finding the distance between any two points in a two-dimensional plane and can be used in various fields such as geometry, physics, and engineering. The formula is based on the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

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Complete question:

What is the length of the line segment in the first quadrant of an x-y coordinate plane that extends from (2, 8) to (12, 2)?

Answer:

its D 136

Step-by-step explanation:

khan

The summation of the series ¹³∑ₙ₎ ₁ (3n - 1) is 260.

Given the summation in the question;

¹³∑ₙ₎ ₁ (3n - 1)

First, we split the summation into smaller summations that fits the summation rule.

¹³∑ₙ₎ ₁ (3n - 1) = 3 ¹³∑ₙ₎ ₁ (n) + ¹³∑ₙ₎ ₁ (- 1)

Now, lets evaluate 3 ¹³∑ₙ₎ ₁ (n).

Using the formula for the summation of a polynomial with degree 1

ⁿ∑ₐ₎ ₁ (a) = n( n + 1 ) / 2

Plug in the values

3 ¹³∑ₙ₎ ₁ (n) = (3) (( 13(13+1))/2)

3 ¹³∑ₙ₎ ₁ (n) = (3) (( 13(14))/2)

3 ¹³∑ₙ₎ ₁ (n) = (3) (182/2)

3 ¹³∑ₙ₎ ₁ (n) = (3) (91)

3 ¹³∑ₙ₎ ₁ (n) = 273

Next, evaluate ¹³∑ₙ₎ ₁ (- 1)

Using the formula for the summation of a constant

ⁿ∑ₐ₎ ₁ (c) = cn

Plug in the values

¹³∑ₙ₎ ₁ (- 1) = (-1)(13)

¹³∑ₙ₎ ₁ (- 1) = -13

Now, we add the results of the summation.

273 - 13

260

Therefore, the sum of the series is 260.

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The number of 10-digit numbers with unique digits from 1 to 9 such that the first five digits form an increasing series and the last five digits form a decreasing series is 15, 120 * 15, 120 = 227, 528, 000.

For the first five digits to form an increasing series, we can choose the first digit in 9 ways (it can't be 0), the second digit in 8 ways, the third digit in 7 ways, the fourth digit in 6 ways, and the fifth digit in 5 ways. So, there are 9 × 8 × 7 × 6 × 5 = 15, 120 ways to choose the first five digits.

For the last five digits to form a decreasing series, we can choose the sixth digit in 9 ways (it can't be 0), the seventh digit in 8 ways, the eighth digit in 7 ways, the ninth digit in 6 ways, and the tenth digit in 5 ways. So, there are 9 × 8 × 7 × 6 × 5 = 15, 120 ways to choose the last five digits.

Therefore, the number of 10-digit numbers with unique digits from 1 to 9 such that the first five digits form an increasing series, and the last five digits form a decreasing series is 15, 120 * 15, 120 = 227, 528, 000.

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The two sequences of transformations of ΔABC that exhibit the congruence between the two triangles include the following:

A. a rotation of 180° about the origin and a translation of 1 unit left.

E. a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit left.

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y)                  →     (-x, -y)

Point A = (-6, 2)  →  Point A' = (-(-6), -(2)) = (6, -2).

By translating the pre-image of triangle A'B'C' horizontally left by 1 unit, the coordinate A" of the image of triangle A'B'C' include the following:

(x, y)                               →                  (x - 1, y - 7)

Coordinate A' = (6, -2)   →    Coordinate A'' (6 - 1, -2) = (5, -2)

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As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.

The biggest integer that is able to divide two or more quantities is known as the highest common factor (HCF) or greatest common factor. Highest refers to the biggest or greatest number. The sharing a common meaning of two or more integers. Feature is an integer that can be used to divide a whole number (a divisor). Write each integer as the sum of one's main characteristics in step one.  Step 3: The HCF of said given integers is the greatest number that can be found among the common factors.

given

1. It is assumed that when Helen thinks of two numbers, they have corresponding HCF and LCM values of 5 and 12.

2. The smallest common multiple shared by two numbers is referred to as the least common number.

LCM of 4 and 6 is 12, for instance.

3. The highest number that divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.

HCF of 6 and 8 is 2, for instance.

4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.

5.The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values other than 5. 60 and 120 have an HCF of 60, but not 5.

As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.

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Using Pythagorean theorem and the vertices given, the two triangle are similar

Two triangles are similar if and only if the ratios of their corresponding sides are equal. So, to determine if triangle ABC is similar to triangle XYZ, we need to compare the ratios of corresponding sides.

One way to do this is to calculate the lengths of the sides in both triangles and compare the ratios. For example, the length of side AB in triangle ABC can be found using the Pythagorean theorem:

AB = √((0-(-3))^2 + (10-6)^2) = √(3^2 + 4^2) = √25 = 5

Similarly, the length of side XY in triangle XYZ can be found:

XY = √((2-(-1))^2 + (7-3)^2) = √(3^2 + 4^2) = √25 = 5

Next, we can compare the ratios of corresponding sides AB and XY, BC and YZ, and AC and XZ. If the ratios are equal for all corresponding sides, then the triangles are similar.

In this case, we find that the ratios of corresponding sides AB and XY, BC and YZ, and AC and XZ are all equal, so triangles ABC and XYZ are similar.

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The correct answer is option A. 2 1/8 when reduced to the lowest terms.

To subtract 3 1/4 - 1 1/8, we need to convert the fractions to a common denominator. The common denominator for 3 1/4 and 1 1/8 is 8. To convert 3 1/4 to 8, we multiply both the numerator and denominator by 2, resulting in 6/8. To convert 1 1/8 to 8, we multiply both the numerator and denominator by 8, resulting in 8/8.

Now we have two fractions with a common denominator of 8. To subtract them, we subtract the numerators and keep the same denominator. We have 6/8 - 8/8, which is -2/8. To reduce this fraction to the lowest terms, we divide the numerator and denominator by the greatest common factor (GCF), which is 2. -2/8 divided by 2 is -1/4. Finally, we add -1/4 to 1 1/8 to get the answer 2 1/8.

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The measures of the angles in the right triangle formed by the two regular pentagons are 18 degrees and 72 degrees.

The interior angles of a regular pentagon measure 108 degrees each. Therefore, if we have two regular pentagons, the right triangle formed by the two pentagons will have two angles that are equal to 108 degrees each.

These two angles are the complement of each other, meaning they add up to 90 degrees. Therefore, one of the angles in the right triangle formed by the two pentagons is 72 degrees, and the other is 18 degrees.

So, the measures of the angles in the right triangle formed by the two regular pentagons are 18 degrees and 72 degrees.

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Answer:

This question is asking for a construction problem, which involves using a pair of compasses and a ruler to draw the triangle DEF and then measure certain aspects of the triangle, such as the length of DF, the height of XF, and the locus of a point 2cm from E. It also requires bisecting the angle D.

Step-by-step explanation:

a. To construct the triangle DEF, use the compasses to draw arcs with radii of 3cm and 7cm from points D and E respectively, so that the arcs intersect. Then, connect the points of intersection with a straight line to form the side DE. Next, use the compasses to draw an arc with a radius of 8cm from point F and intersect it with the previous arcs. Connect the points of intersection with a straight line to form the side DF. Finally, use the ruler to connect the points D, E, and F to form the triangle. To draw the perpendicular line at X, draw a line segment parallel to DE passing through the midpoint X, and then use the compasses to draw arcs centered at X and intersecting the sides DE and DF. Connect the points of intersection to form the perpendicular line at X.

b. Measure the length of DF using a ruler.

c. Measure the height of the triangle XF by measuring the distance from X to DF.

d. The locus of the point that is 2cm from E can be found by drawing an arc with a radius of 2cm centered at E and intersecting the sides DE and DF. The points of intersection represent the points that are 2cm from E.

e. To bisect the angle D, use the compasses to draw two arcs centered at D that intersect the sides DE and DF. Connect the points of intersection to form the bisector of angle D.

It is important to note that these steps are only a general guide and may need to be adjusted slightly depending on the specifics of the problem.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Area of a rectangle is given by :

[tex]\qquad \sf  \dashrightarrow \: area = l \times b[/tex]

[ l = Length, and b = width ]

[tex]\qquad \sf  \dashrightarrow \: x {}^{2} + 3x = (x + 3)(b)[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = \dfrac{ {x}^{2} + 3x }{x + 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: b = \dfrac{ {x(}x^{} + 3) }{x + 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: b = x[/tex]

Next problem ~

[tex] \textsf{Number of stoppers fixed per minute = 25 } [/tex]

[tex] \textsf{1 stopper is fixed in = 1/25 minutes} [/tex]

[tex] \textsf{2250 stoppers are fixed in = 1/25 × 2250 = 90 minutes } [/tex]

Now, convert it into hours~

[tex]\qquad \sf  \dashrightarrow \:60 \: \: min = 1 \: \: hr[/tex]

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: min = \dfrac{1}{60} \: \: hrs[/tex]

[tex]\qquad \sf  \dashrightarrow \: 90 \: \: min = \dfrac{1}{60} \times 90 \: \: hrs[/tex]

[tex]\qquad \sf  \dashrightarrow \: 90 \: \: min = \dfrac{3}{2} \: \: hrs[/tex]

[tex]\qquad \sf  \dashrightarrow \: 90 \: \: min = 1.5 \: \: hrs[/tex]

So, in total it would take 1.5 hours to fix stoppers on 2250 bottles.

Step-by-step explanation:

(g–f)

multiply by nine

9(g–f)or 9g–9f

1) 2x + 5y = 17

+ 6x – 5y = -9

────────

8x = 8

divide both sides by 8 :

Answer : x = 1 (one solution)

2) (3x – y = 0) * 4

(4x + 2y = 14) * 3

12x – 4y = 0

- 12x + 6y = 14

────────
-10y = -14

Divide both sides by -10

Answer : y = 1.4 (one solution)

3) 6x + 5y = 39

- 3x + 5y = 27

────────
3x = 12

Divide both sides by 3

Answer : x = 4 ( one solution )

4) 4x – 7y = 3

+ x – 7y = -15

────────
5x = -12

Divide both sides by 5

Answer : x= -2.4 (one solution)

Answer:

£ 3125

Step-by-step explanation:

Tax amount on  £ 2665 = 20% of 2665

                                       = 0.2 * 2665

                                       =  £ 533

Rest amount = 3672 - (972 + 2665)

                     = 3672 -3637

                     =  £ 35

Tax amount of  £ 35 = 40% * 35

                                 = 0.4 * 35

                                 = 14

Total tax = 533 + 14

               =  £ 547

Money left after paying tax = 3672 - 547

                                              =  £ 3125

Because of this, we apply a variety of equality characteristics, such as the multiplication, subtraction, and division properties.

A relationship of two expresses or integers that is neither equal in mathematics is referred to as an inequality. Furthermore, inequity results from imbalance. In math and science, an inequalities establishes the connection between two ou alors elements. Egality and inequality are not the same. Use the not equal symbol most frequently when two quantities are not equal (). Values of any size can be examined using a variety of inequalities. By changing the two sides until only the variables are left, many straightforward inequalities can be solved. However, a number of factors support inequality: Both sides' 0 are split or added. Exchange the left and the right.

given

2(x- 9 ) = -10   ( given )

= 2x - 18 = -10   ( multiplication property )

= 2x = -10 + 18  ( subtraction property )

2x = 8 ( division property )

x = 4

Because of this, we apply a variety of equality characteristics, such as the multiplication, subtraction, and division properties.

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Answer:

Below

Step-by-step explanation:

Slope of BLACK line = rise/run =   9  / 3 = m =  3  

  y intercept = b = 2       Line eq =  y = mx+ b    y = 3x +2

Slope of BLUE line   similarly is  9 / -3  = m = -3

   and b = 8

     y = mx + b      y = -3x + 8

Answer:

XZ=65

Step-by-step explanation:

so half of the circle would be 180

we need XZ and we know that YW+WX+XZ= 180

we also know that WX and YZ are parallel

WX=50

YW=XZ

YW+XZ=2XZ

WX+2XZ=180

50+2XZ=180

2XZ=130

XZ=65

Answer:

25

Step-by-step explanation:

diameter YZ = 50

OZ = OX = 25

thus, mXZ= 25