A new refrigerator comes packaged in a box shaped like a rectangular prism. The base of the box measures 6 feet by 12 feet. The total surface area of the box is 396 square feet. What is the height of the box in feet?​

Answer:

slope (m) is 4, y-intercept (m) is -3

Step-by-step explanation:

y=4x-3

use y¹-y² over x¹-x² to find slope, then use one of the points to fill in for x and y to find y-intercept

The worm is travelling at a speed of 0.0018 meter per second.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Total distance travelled by the worm = 1.3 m

The worm starts moving at 9 hour 12 minutes and reaches the end of the path at 9 hour 24 minutes.

Total time taken = 24 - 12 = 12 minutes

Speed = Distance / Time

Speed = 1.3 / 12

           = 0.1083 meter / minute

           = 0.0018 meter per second

Hence speed of the worm is 0.0018 meter per second.

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This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.

What is inequality?

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

We can write the first inequality as x + y <= 12

This inequality represents the constraint that Mav can work at most 12 hours in total between both jobs.

The second inequality represents the constraint that Mav must earn no less than $140 in a given week, which can be written as:

15x + 10y >= 140

To graph the system of inequalities, we can plot the lines corresponding to x + y = 12 and 15x + 10y = 140 on the coordinate plane and shade the region that satisfies both inequalities.

The solution to the system of inequalities will be the values of x and y that lie in the shaded region.

One possible solution is x = 4 and y = 8, which means that Mav works 4 hours of lifeguarding and 8 hours of landscaping in a given week, earning a total of 15 * 4 + 10 * 8 = $120.

Hence, This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.

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Answer:

Step-by-step explanation:

You want inequalities, their graph, and a possible solution satisfying Mav's requirement for at most 12 total hours spent lifeguarding at $15 per hour and landscaping at $10 per hour, with an income of at least $140.

The required relations can be written ...

  x + y ≤ 12 . . . . . . . total hours

  15x +10y ≥ 140 . . . . total earnings

The inequalities need to be solved for y to match the answer format requirements.

  inequality 1: y ≤ 12 -x . . . . . . . . . . subtract x

  inequality 2: y ≥ 14 -1.5x . . . . . . divide by 10, subtract 1.5x

The attached graph shows a couple of possible solutions. The solution space is the doubly-shaded area bounded by vertices ...

  (4, 8), (12, 0), and (9 1/3, 0)

Mav will make the most money working 12 hours lifeguarding (x, y) = (12, 0).

She can just meet her income requirements by working 8 hours lifeguarding and 2 hours landscaping (x, y) = (8, 2).

One possible solution is 4 hours lifeguarding and 8 hours landscaping.

The value of x for the similar triangles is given as follows:

x = 40.5.

Similar triangles share these two features:

A bisection divides a triangle into two similar triangles, hence the proportional relationship for the side lengths is given as follows:

x/45 = 18/20

18/20 = 0.9, hence:

x/45 = 0.9

x = 45 x 0.9

x = 40.5.

Meaning that the fourth option is the correct option.

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For the polygon ABCDEFG, the measurement of ∠B is option D: 141°.

What is a polygon?

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides).

The polygon ABCDEFG has angle measurements as -

Measurement of ∠BCD = 148°

Measurement of ∠DEF = 142°

Measurement of ∠EFG = 130°

Measurement of ∠FGA = 129°

Measurement of ∠GAB = 120°

Measurement of ∠CDE = 90°

Let the measurement of ∠ABC be x° .

In a heptagon (or polygon having seven sides) the sum of all angles is 900°.

So, for polygon ABCDEFG the equation will be -

∠BCD + ∠CDE + ∠DEF + ∠EFG + ∠FGA + ∠GAB + ∠ABC = 900°

Substitute the values in the equation -

148° + 90° + 142° + 130° + 129° + 120° + x = 900°

148° + 90° + 142° + 130° + 129° + 120° + x = 900°

759° + x = 900°

x = 900° - 759°

x = 141°

Therefore, the value of x is obtained as 141°.

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Answer:

Step-by-step explanation:

The original price of the hat is $35. Paolo paid $28 for the hat.

So discount for the hat is $(35-28) = $7

$7 is discounted from $35. We have to find the percentage of the discount.

To find the percentage we have to divide the discount amount by the original price and then have to multiply it by 100.

So the discount percentage =

((7/35)×100) %

We can simplify 7/35 by dividing 7 and 35 both by 7. So we will get 1/5 after simplifying.

((1/5) ×100) %

(100/5)% = 20%

So the hat was discounted by 20%.

Answer:

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The circumference of a circle with a diameter of 11 inches using  π as 22/7 is 34.86 inches.

To find the circumference of a circle, we can use the formula:

C = πd

where C is the circumference, π is a mathematical constant (approximately 22/7), and d is the diameter of the circle.

The diameter of a circle is a straight line that passes through the center of the circle and touches two points on the edge of the circle. In this problem, we are given that the diameter of the circle is 11 inches.

To find the circumference, we can substitute this value for d in the formula:

C = πd = π(11 inches)

We can simplify this by using the approximation π ≈ 3.14 (or more precisely, π ≈ 22/7), to get:

C ≈ (3.14)(11 inches) = 34.54 inches

or

C ≈ (22/7)(11 inches) = 34.86 inches

So the circumference of the circle is approximately 34.54 inches or 34.86 inches, depending on which approximation of π is used.

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Answer:

FG = 18

Explanation:

There is a simpler solution:

It has to do with the interior angle bisector theorem. (the illustration with the angle marks and the line show that it is being bisected)

Which will divide the opposite side into segments whose lengths have the same ratio as the adjacent sides of the bisected angle.

x / 24 = x + 10 / 54 →

54x = 24(x + 10) →

54x = 24x + 240 →

30x = 240 →

x = 8.

Since the expression x + 10 represents the length of FG, it's length must be 18.

Answer:

The average rate of change of a function over an interval is a measure of how the function's value changes over that interval, given by the ratio of the change in the function's value to the change in the independent variable. To find the average rate of change of a function over an interval, we need to know the function's values at two points in the interval.

In the case of the function f(x) = x^2, the interval is -4 ≤ x ≤ 0. To find the average rate of change, we need to find the difference in the function's value between two points in this interval, and divide that by the difference in the x-values.

For example, if we compare the values of the function at x = -4 and x = 0, we have:

f(-4) = (-4)^2 = 16

f(0) = 0^2 = 0

The difference in the function's value is f(0) - f(-4) = 0 - 16 = -16.

The difference in the x-values is x2 - x1 = 0 - (-4) = 4.

So the average rate of change over this interval is the difference in the function's value divided by the difference in the x-values, or -16 / 4 = -4.

In other words, the average rate of change of the function f(x) = x^2 over the interval -4 ≤ x ≤ 0 is -4, meaning that for every 4 units of change in x, the function value decreases by 16 units.

Step-by-step explanation:

If one marble is drawn from a bag containing three red ones and one white one , then probability that it is a red one is 3/4 .

Total number of marbles in the jar is = 4 marbles ;

the number of red marbles in the jar is = 3 marbles ;

the number of white marbles in the jar is =  1 marble ;

The probability of drawing a red marble from the jar can be calculated as the number of red marbles divided by the total number of marbles in the jar:

⇒ P(red marble) = number of red marbles / total number of marbles

⇒ 3/4

⇒ 0.75

⇒ 75%

Therefore, the probability of drawing a red marble from the jar is 0.75 or 75%.

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The given question is incomplete , the complete question is

A jar contains four marbles: three red ones and one white ones , if one marble is drawn from the jar , find the probability that it is a red one ?

The difference 6.96 - 0.04 is greater than 7.

Given that 10 bottles were bought for a total amount of $12, the price per bottle of sport drink is $1.20.

$12 divided by ten bottles equals $1.20.

By dividing the total amount paid ($12) by the quantity of bottles bought, the price per bottle of sport drink was determined (10). As a result, each bottle cost $1.20. According to the computation, the price of 10 bottles of sport drink came to a total of $12. The cost of individual goods or greater quantities of bottles can then be determined using this cost per bottle. The price per bottle can be used to compare the costs of various sport drink brands or sizes. Customers can choose and buy sport drinks with more knowledge if they are aware of the price per bottle.

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The correct answer is "It takes 15 pattern block trapezoids to create 5 hexagons."

Pattern block trapezoids are a type of geometric shape commonly used in math education. They are one of several shapes that can be used to create tessellations, or repeating patterns, on a flat surface. Pattern block trapezoids come in different sizes and are made of different colored plastic or foam, with each color representing a different size and shape. In addition to their use in creating tessellations, pattern block trapezoids are often used to teach geometry concepts such as area, perimeter, and angles. They can also be used to help students develop spatial reasoning skills and problem-solving abilities. The most common set of pattern blocks includes six shapes: the trapezoid, hexagon, square, parallelogram, rhombus, and triangle. These shapes can be combined in a variety of ways to create different patterns and designs, making them a versatile and useful tool for math education.

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Answer:

[tex]10^{\circ}[/tex]

Step-by-step explanation:

Supplementary angles have measures that add to [tex]180^{\circ}[/tex].

The hypotenuse of the right triangle with legs measuring 18 in and 26 in is 31.6 in, rounded to the nearest tenth. This is calculated by using the Pythagorean Theorem, which states that a2 + b2 = c2 and plugging in the values for a and b.

The hypotenuse of a right triangle is the longest side of the triangle and is always opposite of the right angle. To calculate the length of the hypotenuse, you need to use the Pythagorean Theorem. The theorem states that a2 + b2 = c2, where a and b are the legs of the triangle and c is the hypotenuse. In this case, a is 18 inches and b is 26 inches, so the equation would be 182 + 262 = c2. Plugging in the values, we get 324 + 676 = c2, which simplifies to 1000 = c2. To find the length of the hypotenuse, we need to take the square root of 1000, which is 31.6 inches. Rounded to the nearest tenth, the hypotenuse of the right triangle with legs measuring 18 in and 26 in is 31.6 in.

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The solution is, point (5,4) will correspond to (5,8).

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

1) To find that the corresponding points, let'-s plug it into that formula:

(5,4)

If we plug 5 and we have output the number 4,

then f(x) is y=x-1

now,

2f(x-3)+4  is the function f(x) with a horizontal shift of 3 units to right, a vertical stretch 4, a reflection.

2) y=2(5-3)+4 then y=2(2)+4

y=8

So point (5,4) will correspond to (5,8)

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The S = 37.2^0

Below has been attached a diagram with the meaning of this problem. So we have a right triangle whose Opposite side (s) measures 18.9 and whose Adjacent side (r) measures 24.9. So, these two sides are related in the following form:

[tex]tan(S)=\frac{\text{Opposite side}}{\text{Adjacent side}} =\frac{s}{r} \\\\tan(S)=\frac{18.9}{24.9} \\\\tan(S)=0.76\\\\S=arctan(0.76)\\\\S=37.23^o\\\\\text{Roundding off:}\\\\\boxed{S=37.2^o}[/tex]

Therefore, the S = 37.2^0

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Answer:

60 sopomores

Step-by-step explanation:

Let X denote the event prefer amusement park on a field trip

The probability that a sophomore will opt for a class trip to an amusement park would be 8/20 = 2/5 based on survey results

P(X) = 2/5

Based on this probability, if the number of sophomores is 150 then expected number of sophomores who prefer the amusement park trip

E(X) - P(X) x N where N is the total number of sophomores

E(X) = 2/5 x 150 = 60

The appropriate methods are

y = x + 8 and y = 4x + 2 - Substitution method

2x + 6y = 18 and x + 5y = 13 - Elimination method  

y = 3x + 3 and y = x + 7  - Substitution method

4x + 7y = 10 and -3x + y = -1 - Elimination method  

In this approach, the equation in one variable is obtained by either adding or subtracting the equations. We can add the equation to delete a variable if its coefficients are the same and have the opposite sign from the other variables.

Similarly to this, we can subtract the equation to get the equation in one variable if the coefficients of one of the variables are the same and their signs are the same.

From the given options, the system of equations

2x + 6y = 18 and x + 5y = 13  

4x + 7y = 10 and -3x + y = -1    

Can be solved using the Elimination method  

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

From the given options, the system of equations  

y = x + 8 and y = 4x + 2

y = 3x + 3 and y = x + 7

Can be solved by using the Substitution method

Therefore,

The appropriate methods are

y = x + 8 and y = 4x + 2 - Substitution method

2x + 6y = 18 and x + 5y = 13 - Elimination method  

y = 3x + 3 and y = x + 7  - Substitution method

4x + 7y = 10 and -3x + y = -1 - Elimination method  

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The constant of proportionality is 180.

One example is 70:2. In the case of any non-zero number, this is a ratios of the form 35*k/k.

An set of points of numbers “ a ” and  “ b", represented as a / b, is a ratio if b is not equal to 0. The proportion is an expression that sets two ratios at the same value. If there are two boys and five girls, for instance, you may express the ratio as 2:5.

We got the word "ratio" directly from the Latin word, which is also called "suitable ratio." The mathematics and English ratios were derived from the Latin ratio, which had multiple meanings, ranging from "cause" to "calculated" to "proportion."

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The side which corresponds to QS is VU, and the scale factor is 2.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that, the figure on the right is a scaled copy of the figure on the left.

We need to find the corresponding side of QS and scale factor,

The figure is 90° counterclockwise rotated,

Therefore,

The corresponding sides are:

PR ~ TW

RQ ~ VT

QS ~ UV
PS ~ WU

∵ the measure of QS = 4 units and the measure of UV = 2 units

∴ scale factor = 4/2 = 2

Hence, the side which corresponds to QS is VU, and the scale factor is 2.

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The question do not contain figure, the similar question is solved.

The point equidistant from the three sides of a triangle is (c) Incenter .

The Circumcenter of a triangle is defined as a point where perpendicular bisectors of  sides of triangle intersect. It is also equidistant from  3 vertices of triangle .

The Centroid is defined as a point where 3 medians of the triangle intersect.

The Incenter is defined as a point where  angle bisectors of the triangle intersect. It is equidistant from the three sides of the triangle, and is the center of the inscribed circle of the triangle .

The Orthocenter is defined as a point where the 3 altitudes of the triangle intersect.

So , by the definition of the Incenter , the correct option is (c) Incenter .

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The given question is incomplete , the complete question is

The point equidistant from the three sides of a triangle is

(a) Circumcenter

(b) Centroid

(c) Incenter

(d) Orthocenter

According to the above statement, she has a 1/6 chance of rolling a 7 on the dice.

A possibility is a ratio that expresses the possibility or likely that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

When using two six-sided dice, there are 36 possibilities that might occur.

By using two dice, there are six ways to arrive to the sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), & (6, 1).

The likelihood of rolling a 7 is thus 6/36 = 1/6.

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The equation -6(x+1)+8x=2(x-3) has all real numbers as solutions, meaning that any value of x will make the equation true. The equation does not have a single unique solution for x.

What is the equation in one variable?

An equation in one variable is a mathematical expression that contains a single variable, typically represented by x. The goal of solving an equation in one variable is to determine the value of the variable that makes the equation true.

To solve the equation -6(x+1)+8x=2(x-3), we can simplify the left-hand and right-hand sides of the equation and then solve for x. Here are the steps:

Distribute the -6 and 2 to the terms inside the parentheses: -6x - 6 + 8x = 2x - 6

Combine like terms on each side of the equation: 2x - 6 = 2x - 6

Subtract 2x from both sides of the equation: -6 = -6

At this point, we have a true statement (-6 = -6), but there is no variable present. This means that the equation has infinitely many solutions, and every real number is a solution to the equation.

Hence, the equation -6(x+1)+8x=2(x-3) has all real numbers as solutions, meaning that any value of x will make the equation true. The equation does not have a single unique solution for x.

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The measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

We shall first evaluate for the angle m∠B as follows:

m∠A + m∠B + m∠C = 180° {sum of interior angles of a triangle}

49° + B + 90° = 180°

B + 139° = 180°

B = 180° - 139° {subtract 139° from both sides}

m∠B = 41°

12.7/sin90° = a/sin41

a = (12.7 × sin49)/sin90° {cross multiplication}

a = 9.5848

12.7/sin90° = b/sin49

b = (12.7 × sin49)/sin90 {cross multiplication}

b = 8.3319

Therefore, the measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.

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Answer:

taking your points

Step-by-step explanation: