A crayon factory monitored the number of broken crayons per box during the past day.

Broken crayons per box
Stem Leaf
0 0 4 4 9
1 4 6 8 9 9
2 3 8
3 3
4 0 9
5 1 9
6 1
7 1 3
8 2 4 6 8
9 4 9


How many boxes had at least 20 broken crayons but fewer than 60 broken crayons?

Answer:

From the picture,

∠ABC + ∠DBC = ∠ABD

Substituting with data,

x + (3x + 10) = 90

4x + 10 = 90

4x = 90 - 10

4x = 80

x = 80/4

x = 20

Step-by-step explanation:

Answer is down below!

Step-by-step explanation:

5 x2 =`5 xj2

The expression that is equivalent to 6x2y + 2xy^5 include:

2(3x²y + xy^5).

2xy(3x + y⁴)

xy(6x + 2y⁴)

An expression can refer to a variety of things depending on the context in which it is used.

In mathematics and computer programming, an expression typically refers to a combination of numbers, variables, operators, and/or functions that are evaluated to produce a value. For example, "2 + 3" is an expression that evaluates to "5"

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Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.

We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:

r² = x² + y²

r² = (-3)² + 4²

r² = 9 + 16

r² = 25

r = 5

Now we can find the values of sin θ, csc θ, and cot θ:

sin θ = y/r = 4/5

csc θ = r/y = 5/4

cot θ = x/y = -3/4

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.

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The perimeter of the given shape in terms of pi is 22 cm + 25 pi cm.

The circumference of the rectangle is equal to the sum of the lengths of its four sides. It is simple to do this because there are two of each side length; all that is needed is to sum the length and width and multiply the result by two.

By multiplying half of the semicircle's circumference by the diameter's length, one can determine the semicircle's perimeter. Thus, the semicircle's perimeter is as follows:

Perimeter of semicircle = 6 cm + (1/2) x pi x 6 cm

Perimeter of semicircle = 6 cm + 3 pi cm

Each quarter circle has a perimeter that is just one-fourth of its circumference. Consequently, the 14 cm quarter circle's perimeter is as follows:

Perimeter of quarter circle with radius 14 cm = (1/4) x 2 pi x 14 cm

Perimeter of quarter circle with radius 14 cm = 7 pi cm

And, the perimeter of the quarter circle with radius 30 cm is:

Perimeter of quarter circle with radius 30 cm = (1/4) x 2pi x 30 cm

Perimeter of quarter circle with radius 30 cm = 15 pi cm

Therefore, the total perimeter of the given shape is:

Perimeter = Perimeter of semicircle + Perimeter of quarter circle with radius 14 cm + Perimeter of quarter circle with radius 30 cm

Perimeter = (6 cm + 3 pi cm) + (7 pi cm) + (15 pi cm)

Perimeter = 22 cm + 25 pi cm.

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Answer:

30°

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

In a 30°-60°-90° right triangle, the sides are always in the ratio of 1: √3:2, where 1 is the length of the short leg opposite the 30° angle, √3 is the length of the long leg opposite the 60° angle, and 2 is the length of the hypotenuse opposite the 90° angle1234.

In this case, we are given that the long leg is 9√3, so we can use this value to find the other sides by setting up a proportion:

short leglong leg​=13​​

short leg93​​=13​​

Cross-multiplying and solving for the short leg, we get:

short leg=3​93​×1​=9

Similarly, we can use another proportion to find the hypotenuse:

long leghypotenuse​=3​2​

93​hypotenuse​=3​2​

Cross-multiplying and solving for the hypotenuse, we get:

hypotenuse=3​2×93​​=18

Therefore, the measure of the hypotenuse n is 18 and the measure of the short leg m is 9.

a) The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.

b) The number of squares that will fit on the land is 61773.

Explain square

A square is a geometric shape with four sides of equal length and four right angles. It is a type of rectangle, but all of its sides are the same length. Squares are used in mathematics to represent and calculate areas and volumes, and they also have applications in architecture and art.

According to the given information

(a) To find the area of the largest squares that will fit on the land, we need to find the greatest common divisor (GCD) of the dimensions 735 and 756, and then square it.

To find the GCD, we can use the Euclidean algorithm:

GCD(735, 756) = GCD(735, 756 - 735) = GCD(735, 21) = GCD(21, 735 - 21 * 35) = GCD(21, 210) = GCD(21, 210 - 21 * 10) = GCD(21, 90) = GCD(21, 90 - 21 * 4) = GCD(21, 6) = GCD(6, 21 - 6 * 3) = GCD(6, 3) = 3

Therefore, the GCD of 735 and 756 is 3. The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.

(b) To find how many squares will fit on the land, we need to divide the total area of the land by the area of each square. The total area of the land is:

735 * 756 = 555960 square meters

The area of each square is 9 square meters, as we found in part (a). Therefore, the number of squares that will fit on the land is:

555960 / 9 = 61773.333...

Since we can't have a fractional number of squares, we need to round down to the nearest integer. Therefore, the number of squares that will fit on the land is 61773.

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The equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x, is:

y = 98 - 8x

The initial number of soup spoons, 98, is reduced by 8 for each table Lauren sets. Therefore, the number of soup spoons remaining after x tables have been set is 98 - 8x.

Answer: 924 paths

Step-by-step explanation:

Since there is no shorter path, we know that the path must consist of 6 blocks to the north and 6 blocks to the east. Thus, the problem is equivalent to finding the number of ways to arrange 6 N's (for north) and 6 E's (for east) in a sequence such that no two N's are adjacent and no two E's are adjacent.

Let's denote N by 1 and E by 0. Then the problem is equivalent to finding the number of 12-digit binary sequences (i.e., sequences consisting of 0's and 1's) such that there are no consecutive 1's or consecutive 0's.

We can solve this problem using dynamic programming. Let F(n,0) be the number of n-digit binary sequences that end in 0 and have no consecutive 0's, and let F(n,1) be the number of n-digit binary sequences that end in 1 and have no consecutive 1's. Then we have the following recurrence relations:

F(n,0) = F(n-1,0) + F(n-1,1)

F(n,1) = F(n-1,0)

with initial values F(1,0) = 1 and F(1,1) = 1.

Using these recurrence relations, we can compute F(6,0) and F(6,1), and the total number of valid sequences is F(6,0) + F(6,1) = 132. Therefore, there are 132 different paths of length 12 blocks from your apartment to the math class.

1. Axis of symmetry : x= -5            2. Axis of symmetry : x =2

Vertex: (-5, 1)                                                  Vertex: (2, 8)
Domain: (-∞, ∞)                                                Domain  (-∞, ∞)
Ranges:  [1, ∞)                                                   Ranges (-∞, 8]

3. Axis of symmetry : x = 1                4. Axis of symmetry x = -4

Vertex (1, -1)                                                       Vertex = (-4 0)
Domain (-∞, ∞)                                                    Domain (-∞, ∞)
Ranges  [-1, +∞)                                               Ranges (-∞, 0]

For 4. y = -x² - 8x -16

Axis of symmetry

x = -b / (2a)

x = -(-8) / (2 × -1) = 8 / (-2) = -4

Vertex

y = -(-4)² - 8(-4) - 16

= -16 + 32 - 16

= 0  therefore Vertex is (-4, 0)

Therefore range function  (-∞, ∞)

The above answers are for the questions below as seen in the picture

1) y = x² + 10x + 26                    2. y = -2x² + 8x        3. y = x² - 2x

Axis of symmetry :

Vertex
Domain
Ranges

4. y = -x² - 8x -16

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the power tells you how many times the base is multiplied.

1) 3^4 = 3 x 3 x 3 x 3

= 81

It would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.

To solve this problem, we can use the formula for exponential growth:

[tex]A = P * (1 + r)^t[/tex]

where:

A = final amount (in this case, $1,540)

P = principal amount (initial investment, in this case, $840)

r = rate of growth (as a decimal, in this case, the rate at which the money doubles every 10 years, or 1/10 = 0.1)

t = time (in years, which we need to find)

Plugging in the values:

[tex]1,540 = 840 * (1 + 0.1)^t[/tex]

Dividing both sides of the equation by 840:

[tex]1.83333... = (1.1)^tTaking the natural logarithm of both sides:ln(1.83333...) = ln((1.1)^t)Using the property of logarithms that ln(a^b) = b * ln(a), we get:ln(1.83333...) = t * ln(1.1)Finally, dividing both sides by ln(1.1) to solve for t:t = ln(1.83333...) / ln(1.1)[/tex]

Using a calculator, we can find that t ≈ 7.5 (rounded to the nearest tenth of a year).

So, it would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.

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The answers are:

[tex]m \angle1+ m\angle2 + m\angle3=180^o[/tex]  is the sum of interior angles in a triangle.

[tex]m \angle1+ m\angle5 = m\angle AYX[/tex] is Definition of parallel lines.

[tex]m \angle AYX+m\angle 4=180^o[/tex] Definition of a straight angle

[tex]m\angle5=m\angle2[/tex] is Substitution

[tex]m \angle1+ m\angle5 + m\angle4=m \angle AYX+m\angle 4[/tex] Substitution

An angle in geometry is the measurement of the amount of rotation that occurs between two lines, rays, or line segments that have a shared endpoint, or vertex. Angles are expressed in terms of degrees, radians, or other angular measuring units.

A protractor, a tool with a semicircular or circular scale and degree markings, can be used to measure angles. Angles may also be labelled using symbols, such as ∠ABC or ∠PQR, in which the letter in the middle of the symbol designates the vertex of the angle.

An auxiliary line that is parallel to XZ given is the triangle formed by XYZ and AY.

[tex]m\angle 1+m\angle 2+m\angle3=180^o[/tex] Definition of the sum of interior angles in a triangle

[tex]m\angle1=m\angle AYX[/tex] Corresponding angles are congruent (alternate interior angles)

[tex]m \angle 2 = m \angle 4[/tex] Corresponding angles are congruent (alternate interior angles)

[tex]m \angle AYX + m \angle 4 = 180^o[/tex] Definition of a straight angle

[tex]m \angle 1 + m \angle 5 = m \angle AYX[/tex] Definition of parallel lines

[tex]m \angle 5 = m \angle 2[/tex] Substitution

[tex]m \angle 1 + m \angle 2 + m \angle 3 = m \angle 1 + m \angle 5 + m \angle 4[/tex] Substitution

[tex]m \angle 1 + m \angle 5 + m \angle 4 = m \angle AYX + m \angle 4[/tex] Substitution

[tex]m \angle 1 + m \angle 2 + m \angle 3 = m \angle AYX + m \angle 4[/tex] Transitive property of equality

[tex]m \angle 1 + m \angle 2 + m \angle 3 = 180^o[/tex] Substitution

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The function f of the line is f(x) = 2x - 2 and f(-1) = -4.

The slope of a line determines the steepness of the line and is calculated by dividing the vertical change (rise) between any two points on the line by the horizontal change (run) between those same two points. The formula for slope is (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) represent any two points on the line. The slope can be positive, negative, zero or undefined, depending on the direction and steepness of the line. If the line moves up from left to right, it has a positive slope, while a line that moves down from left to right has a negative slope.

From the graph we can take two points on the line (1,0) and (0,-2). Now we can find the equation of the line passing through these points, for that we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is one of the points on the line.

First, we can find the slope:

m = (y₂ - y₁) / (x₂ - x₁) = (-2 - 0) / (0 - 1) = -2/-1 = 2

Next, we can choose either point and substitute the values into the point-slope equation:

y - y₁ = m(x - x₁)

Using point (1,0):

y - 0 = 2(x - 1)

Simplifying:

y = 2x - 2

Therefore, the equation of the line passing through points (1,0) and (0,-2) is y = 2x - 2. That is f(x) = 2x - 2.

f(-1) = 2 × -1 - 2 = -2 -2 = -4.

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The solution set is {(x, y) | x = y + 2}, which represents a straight line with a slope of 1 passing through the point (2, 0).

Therefore, the correct answer is option 2, infinite solutions.

Equations of the form ax2 + bx + c = 0, where a, b, and c are real numbers, and a 0, are known as polynomial equations in the variable x. Any equation that has the formula p(x) = 0, where p(x) is a polynomial of degree 2 with a single variable, is actually a quadratic equation.

The equation has the following form: ax2 + bx + c = 0, where x is the unknown variable and a, b, and c are constants, with "a" not equal to 0.

Numerous strategies, including factoring, completing the square, and the quadratic formula, can be used to solve quadratic equations.

To solve the system of equations:

x - y = 2 ---(1)

-3x + 3y = -6 ---(2)

We can use the first equation to isolate x in terms of y:

x = y + 2

-3(y + 2) + 3y = -6

Simplifying the equation, we get:

-3y - 6 + 3y = -6

Solving for y, we get:

0 = 0

For all values of y this equation is true-

So,the equations has infinite solutions.

To find the solution set, we can substitute the value of y into the expression for x:

x = y + 2

x = y + 2, for all values of y

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Assume that adults have IQ scores that are normally distributed with a

mean of μ = 100 and a standard deviation o= 15. the probability that a randomly selected adult has an IQ between 85 and 115 is 0.6826.

Let Z represent  the standard normal random variable

Z = (X - μ) / σ

where:

X = IQ score

μ=  mean (100)

σ= standard deviation (15).

In order to determine the probability  we have to find the  area

P(85 < X < 115) = P[(85 - 100) / 15 < Z < (115 - 100) / 15]

= P(-1 < Z < 1)

= Φ(1) - Φ(-1)

Where;

Φ=  Cumulative distribution function

Using a standard normal distribution table

Φ(1) = 0.8413

Φ(-1) = 0.1587

So,

P(85 < X < 115) =0.8413 - 0.1587

= 0.6826

Therefore the probability is 0.6826.

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The quadratic equation in standard form can be written as:

y = x² - 10

Remember that for a quadratic equation whose solutions are x₁ and x₂, the quadratic can be written as:

y = (x - x₁)*(x - x₂)

Here the solutions are:

x = √10

x = -√10

Then we can write:

y = (x+  √10)*(x - √10)

Expanding that we will get:

y = x² + √10x - √10x + √10*-√10

y = x² - 10

That is the quadratic.

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To find the value of a6, we need to first determine the value of a2, a3, a4, and a5 using the given recurrence relation:

a1 = 6

a2 = 5a1 = 5(6) = 30

a3 = 5a2 = 5(30) = 150

a4 = 5a3 = 5(150) = 750

a5 = 5a4 = 5(750) = 3750

Now, we can find a6 using the recurrence relation:

a6 = 5a5 = 5(3750) = 18750

Therefore, the value of a6 is 18750.

The point (1, 8) would then represent that the babysitter charges $8 per hour

The point (1, 8) in this situation could mean that the babysitter charges $8 for one hour of work.

In general, when working with a fee-per-hour situation, we can use the slope-intercept form of a linear equation, y = mx + b,

If we assume that the initial fee is $0, then the equation for the babysitter's fee would be y = mx, where m is the hourly rate.

The point (1, 8) would then represent that the babysitter charges $8 per hour, since when x = 1 (one hour of work), y = 8 (the fee for one hour).

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The correct answer is not listed among the options. The correct answer is E. 1/x.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find f'(x), we need to differentiate the function f(x) with respect to x. Since we are given k(x) = 3x, we can use the chain rule to differentiate f(x) = ln(k(x)) = ln(3x) as follows:

f'(x) = d/dx [ln(3x)]

= 1/(3x) * d/dx [3x] (applying the chain rule)

= 1/(3x) * 3

= 1/x

Therefore, the correct answer is not listed among the options. The correct answer is E. 1/x.

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Answer: 11 Cookies

Step-by-step explanation:

let C be cookies

17($3.25) + 1.60C = $72.85

$55.25 + 1.60C = $72.85

1.60C = $17.60

C=11

She sells 11 cookies

Answer:

11

Step-by-step explanation:

To be able solve, you need to do 17 x 3.25, which would give you 55.25. Then you need to subtract 72.85 by 55.25, which is 17.60. Now divide 17.60 by 1.60. This should give you 11. Therefore, she sold 11 cookies.

I AM SO SORRY IF THIS DIDN'T MAKE SENSE!

The length of the rectangle is 15.9 inches. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often known as "arithmetic operations," can be used to explain any real number. Operations like quotient, product, sum, and difference come after operations like division, multiplication, addition, and subtraction in mathematics.

We are given that the perimeter of a rectangle is 42.4 inches and the length is three times its width.

Let the width be 'x'.

So, length will be 3x.

From this, we get

⇒ Perimeter = 2 (length + width)

⇒ 42.4 = 2 (3x + x)

⇒ 42.4 = 2 (4x)                             (Using addition operation)

⇒ 42.4 = 8x                                  (Using multiplication operation)                

⇒ x = 5.3                                      (Using division operation)

So,

⇒ Length = 3 * 5.3

⇒ Length = 15.9 inches

Hence, the length of the rectangle is 15.9 inches.

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Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.

A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.

The area of the rectangular patio is given by multiplying its length by its width, so the area is:

A = (1 + 2x)(2 - 3x)

Now using distributive property we get,

A = 2 - 3x + 4x - 6x²

Simplifying further, we get:

A = -6x² + x + 2

Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.

To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:

P = 2(1 + 2x) + 2(2 - 3x)

Simplifying this expression, we get:

P = 2 + 4x + 4 - 6x

P = 6 - 2x

Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.

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In Linear equation, The of sales/month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

Let x be # sales/month:

Plan A:  $2500 + 6%•x

Plab B:  $3000 + 4%•x

For Plan A to be better than Plan B:  Plan A > Plan B

So inequality would be: $2500 + 6%•x > $3000 + 4%•x, then solve for x:

2%•x > $500 or x > $500/0.02

x > 25,000

Therefore, the of sales/month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.

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In Linear equation, The of sales of the month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.

What is  linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b.

To solve this system of linear equations, we can use the method of elimination or substitution.

Let x be sales of the month:

Plan A:  $2500 + 6% × x

Plan B:  $3000 + 4% × x

For Plan A to be better than Plan B:  Plan A > Plan B

So inequality would be: $2500 + 6%×x > $3000 + 4%×x

then solve for x:

=> 2500+0.06x > 3000+0.04x

=> 0.06x-0.04x > 3000-2500

=> 0.02x > 500

=> x > 500/0.02

=> x > 25000

Therefore, the of sales of the month (x) has to exceed 25,000 units for Plan A to be superior to Plan B.

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Answer:

127.5

Step-by-step explanation:

multiply 15 and 17 divide by 2 and boom

The proportional relationship between x and y is shown by the table:

x   7  14  28   35

y  1     2    4     5

A connection among two factors that changes proportionally is referred to as a proportional relationship. If y=kx, where k is just the proportionality constant, can be used to represent two quantities, x and y, then they are said to be proportional.

From the given options, consider the table:

x   7  14  28   35

y  1     2    4     5

As per proportional relationship.:

y=kx

k = y/x (must be same in all cases)

k = 1/7

k = 14/2 = 1/7

k = 4/28 = 1/7

k = 5/35 = 1/7

As all the k value for the given values of x and y are found equal.

Thus, the proportional relationship between x and y is shown by the table:

x   7  14  28   35

y  1     2    4     5

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The mean of the given set of numbers is 21.8. and median is 25.

In mathematics and statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing by the total number of values. The mean is also known as the arithmetic mean or average.

To find the mean and median of the given set of numbers, we can follow these steps:

Arrange the numbers in order from smallest to largest: 2, 5, 25, 35, 42.

To find the mean, add up all the numbers and divide by the total number of numbers:

Mean = (2 + 5 + 25 + 35 + 42) / 5

= 109 / 5

= 21.8

Therefore, the mean of the given set of numbers is 21.8.

To find the median, we need to find the middle number in the ordered list. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

In this case, there are 5 numbers, so the median is the middle number, which is 25.

Therefore, the median of the given set of numbers is 25.

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The surface area of the trapazoid based prism is 289.6 ft². The right option is b. 289.6 ft².

A prism is a solid shape that is bound on all its sides by plane faces.

To calculate the surface area of the trapazoid based prism, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is b. 289.6 ft².

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