Julia needs to make a box in the shape of a rectangular prism with a height of 3 inches and a volume of 243 cubic inches. The dimensions, in inches, must be whole numbers greater than 1. Julia claims that the length and the width must be equal.
Part A: What dimensions would support Julia's claim about the length and with of the box?
Part B: What dimensions would not support Julia's claim about the length and width of the box.
Part A length =______________
Part A width=_____________________.
Part B length_________________
Part B Width=_____________________.

The probability that Jessica picks a yellow pencil is 80%.

What exactly is probability?

Probability is a measure of an event's possibility or chance of occurring. It is stated as a number ranging from 0 to 1, or as a percentage ranging from 0% to 100%, where 0 indicates an impossible occurrence and 1 (or 100%) represents a certain event.

Now,

The probability of picking a yellow pencil =  the number of yellow pencils / total number of pencils:

Probability of picking a yellow pencil = Number of yellow pencils / Total number of pencils

In this case, there are 8 yellow pencils out of a total of 10 pencils:

Probability of picking a yellow pencil = 8 / 10

Simplifying the fraction by dividing both the numerator and denominator by 2, we get:

Probability of picking a yellow pencil = 4 / 5

Probability of picking a yellow pencil = 4 / 5 x 100%

Probability of picking a yellow pencil = 80%

Therefore, the probability that Jessica picks a yellow pencil is 80%.

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Therefore, the common difference of the arithmetic sequence is 1.5.

To find the common difference of an arithmetic sequence, you need to know at least two consecutive terms of the sequence. The common difference is the constant amount by which each term increases or decreases from the previous term.

If you have the first term (a1) and the second term (a2) of an arithmetic sequence, you can find the common difference (d) using the formula:

[tex]d = a_2 - a_1[/tex]

For example, consider the arithmetic sequence: 3, 7, 11, 15, ...

Here, a1 = 3 and a2 = 7. Substituting these values in the formula, we get:

[tex]d = a_2 - a_1 = 7 - 3 = 4[/tex]

So, the common difference of this sequence is 4.

Let the first term of the arithmetic sequence be "a", and let the common difference be "d".

Then the seventh term would be:

[tex]a + 6d = 10.2[/tex]

And the twelfth term would be:

[tex]a + 11d = 17.7[/tex]

Now we have two equations with two variables. We can solve for "a" and "d" using these equations.

First, we can subtract the first equation from the second equation:

[tex](a + 11d) - (a + 6d) = 17.7 - 10.2[/tex]

Simplifying this equation, we get:

[tex]5d = 7.5[/tex]

Dividing both sides by 5, we get:

[tex]d = 1.5[/tex]

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Answer:

a. To find the number of diagonals in an n-sided polygon, we need to count the number of pairs of vertices that can be connected by a diagonal, while excluding the sides of the polygon. Any pair of vertices that are adjacent or separated by only one vertex are already connected by a side of the polygon, so we need to consider pairs of vertices that are separated by at least two vertices.

We can choose two vertices out of n vertices in the polygon in nC2 ways. However, any pair of vertices that are separated by only one vertex defines a side of the polygon, so we need to subtract n from this count to exclude the n sides of the polygon. Therefore, the number of diagonals in an n-sided polygon is:

nC2 - n = (n * (n-1))/2 - n = (n^2 - 3n)/2

b. The above expression gives the number of diagonals for any polygon, not just a convex one. However, for a convex polygon, any pair of vertices separated by only one vertex defines a side of the polygon, so we need to exclude these diagonals as well.

For an n-sided convex polygon, there are n sides and n vertices, so we have to exclude n diagonals (one diagonal for each vertex). Therefore, the number of diagonals in an n-sided convex polygon is:

(n^2 - 3n)/2 - n = (n^2 - 5n)/2

Step-by-step explanation:

The five number summary, based on the given box plot would be:

Minimum value is the left-most point or the left end of the left whisker of the box plot. In the box plot, the minimum value is 1. Q1 is the left edge of the box. It represents the value below which 25% of the data falls.

Median is the line inside the box that divides it into two parts. It represents the value below which 50% of the data falls, or the 50th percentile. The median is 7. Q3 is the right edge of the box. It represents the value below which 75% of the data falls. In your given summary, Q3 is 9.

Maximum value is the right-most point or the right end of the right whisker of the box plot.

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The given function is not one-to-one.

To determine whether the function y = 2(x+1)²-4 is one-to-one, we need to check whether each unique value of x produces a unique value of y.

Let's begin by assuming that two different values of x, say x1 and x2, produce the same value of y, i.e., y(x1) = y(x2).

Then we have:

2(x1+1)²-4 = 2(x2+1)²-4

Simplifying this equation, we get:

(x1+1)² = (x2+1)²

Taking the square root of both sides, we get:

x1+1 = ±(x2+1)

We can now solve for x1 in terms of x2 as follows:

x1 = -(x2+1)±1

Since there are two possible values for x1 corresponding to a given value of x2, the function is not one-to-one.

Therefore, the given function is not one-to-one.

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The probability of selecting a blue spool is 14% greater than the probability of selecting an orange spool.

Probability is a branch of mathematics that deals with the study of random events or phenomena. It involves the calculation of the likelihood or chance of an event occurring, based on the available information or data.

Percent is a mathematical concept used to represent a part of a whole as a fraction of 100.

To calculate the probability of selecting a blue spool or an orange spool, we need to first find the total number of spools and the number of blue and orange spools.

The total number of spools is: 8+5+7+10+3+6+4+7 = 50

The number of blue spools is: 10

The number of orange spools is: 3

Therefore, the probability of selecting a blue spool is: 10/50 = 0.2 or 20%

The probability of selecting an orange spool is: 3/50 = 0.06 or 6%

The difference in probability is: 20% - 6% = 14%

Therefore, the probability of selecting a blue spool is 14% greater than the probability of selecting an orange spool.

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The minimum mοnthly payment fοr May is $831.48.

A percentage is a figure οr ratiο that can be stated as a fractiοn οf 100 in mathematics. If we need tο cοmpute the percentage οf a number, divide it by the whοle and multiply by 100. As a result, the percentage denοtes a part per hundred. The term % refers tο οne hundred percent. It is denοted by the sign "%".

The minimum mοnthly payment fοr May is the greater οf $500 οr 4.5% οf the credit card bill.

Tο find οut which is greater, we can calculate 4.5% οf the credit card bill:

4.5% οf $18,477.26 = 0.045 x $18,477.26 = $831.48

Since $831.48 is greater than $500, the minimum mοnthly payment fοr May is $831.48.

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The statement represented by the given box plot is Option C The maximum value of the rainfall in April is equal to the median rainfall in March.

A box plot, sometimes referred to as a box-and-whisker plot, is a graphical depiction of a collection of numerical data that demonstrates the distribution of the data along a number line. It is frequently used to condense and contrast the distribution of data among several groups or samples.

Two whiskers plus a box make up a box plan. The data's interquartile range (IQR), or the space between the first and third quartiles, is depicted in the box (Q1 and Q3, respectively). The minimum and highest values of the data that aren't deemed outliers are covered by the whiskers that extend from the box.

From the given box plot we observe that the maximum value of the rainfall in April is equal to the median rainfall in March.

Hence, the statement represented by the given box plot is Option C The maximum value of the rainfall in April is equal to the median rainfall in March.

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Answer:

[tex]1216 = 64 \times 19[/tex]

64 is 4 cubed, and 19 is a prime number between 10 and 20.

Step-by-step explanation:

If Julian and two of his friends are going to share 1/4 of a pizza, then they will be sharing the pizza equally among three people. To find out how much each person will get, you need to divide the 1/4 of the pizza by 3, which gives:

1/4 ÷ 3 = 1/4 × 1/3 = 1/12

So each person will get 1/12 of the pizza.

Answer:Quadrant 1

Only in Quadrant 1, the both y and x-axis is positive. So (10, 15) is in quadrant 1.

an employee's overtime rate is 1.5 times their regular rate, but this can vary depending on the company and jurisdiction. Once the overtime rate is known

what is regular rate?

Regular rate refers to the standard hourly wage that an employee receives for their regular, non-overtime work. This is the base rate of pay that an employer agrees to pay an employee for their normal working hours

In the given question,

In order to determine how much Ashley made in overtime, we would need to know her overtime rate and the number of overtime hours she worked. Without this information, it is not possible to calculate the amount she earned in overtime.

Typically, an employee's overtime rate is 1.5 times their regular rate, but this can vary depending on the company and jurisdiction. Once the overtime rate is known, we could multiply the overtime rate by the number of overtime hours worked to determine the amount earned in overtime.

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The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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The midline of the function is the horizontal line: y = -0.9

What is Graph ?

A graph is a visual representation of data or a mathematical function that shows the relationship between different variables. Graphs can take many forms, but some common types of graphs include line graphs, bar graphs, scatter plots, and pie charts.

The midline of a trigonometric function is the horizontal line that is equidistant from the maximum and minimum points of the function. For a sine or cosine function, the midline is given by the equation:

y = a

where a is the vertical displacement of the graph (i.e., the distance between the horizontal axis and the center of the graph).

In this case, the function has a minimum point at (2, -0.9) and an amplitude of 3. The amplitude is the distance between the maximum and minimum points of the function, which is equal to half the distance between the maximum and minimum y-values. Therefore, the maximum y-value is:

y_max = -0.9 + 3 = 2.1

Similarly, the minimum y-value is:

y_min = -0.9 - 3 = -3.9

The center of the graph is the average of the maximum and minimum y-values, which is:

a = (y_max + y_min) ÷ 2

a = (2.1 - 3.9)÷ 2

a = -0.9

Therefore, the midline of the function is the horizontal line: y = -0.9

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Yes, we can find the area of the regular polygon when only given the apothem. The given polygon area is 753.093 in²

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

      To create a closed figure, a minimum of three line segments must be connected end to end. As a result, a polygon with at least three sides is known as a triangle and is also known as a 3-gon. An n-gon is a polygon with n sides.

   Apothem is the distance of a perpendicular line from any side of the polygon to its center.

               Area = [tex]Area =\frac{1}{2} (ap)\\Area=\frac{1}{2} (bh)*(n)[/tex]

                n= no of sides of polygon

               b= side of the polygon

               h= height of polygon / (apothem)

                Area= [tex]\frac{1}{2} (16.7354 * 15 * 6 )\\[/tex]

                        = 125.5155 * 6

                        = 753.093 in²

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Both of these equations correctly represent the verbal sentence "A variable is ten more than thrice another variable. "

A variable is a symbol or a letter that represents a value that can change or vary. It is usually denoted by a letter from the alphabet, such as x, y, z, a, b, c, etc. Variables are used to represent unknown or unspecified values, as well as to express relationships between quantities.

For example, in the equation[tex]y = mx + b[/tex], x and y are variables, where x represents the input variable and y represents the output variable. The values of x and y can change depending on the specific problem being considered.

Variables can also be used in formulas, functions, and other mathematical expressions to represent a quantity that may vary or depend on other factors. In algebra, variables are commonly used to solve equations and express mathematical relationships.

Let's assume that the first variable is represented by x and the second variable is represented by y.

According to the verbal sentence, we know that:

The first variable is ten more than thrice the second variable, which can be written as:

[tex]x = 3y + 10[/tex]

Alternatively, we can also express the same equation as:

[tex]y = (x-10)/3[/tex]

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Answer: Sorry meant to send this*

Step-by-step explanation:

Answer:

10m²

Step-by-step explanation:

A=b×h/2=4×5/2=20/2=10m²

Hope this helps!

Answer:

1.03

Step-by-step explanation:

3÷100= 0.03

to multiply add 1

multiply by 1.03

Answer:

1.03

Step-by-step explanation:

original value is 3/100

if our value is 1 then increased by 3%  = 1 + 3/100

we then increase the value of our original, 3%= 1+ 0.03

then again, 3%= 1.03

1.03

The net dollar advantage or disadvantage of accepting the outside supplier's offer is a disadvantage of $50,937.50.

cost typically refers to the amount of resources, such as time, money, or effort, that is required to perform a particular task or to acquire a certain item or quantity. Cost can be represented numerically and is often expressed in terms of currency or other units of measurement. In some contexts, cost may also refer to the negative consequences or drawbacks associated with a particular action or decision.

To calculate the net dollar advantage or disadvantage of accepting the outside supplier's offer, we need to compare the total cost of producing 42,500 units of part S-6 with the cost of purchasing 37,500 units from the outside supplier and renting out the facilities.

Total cost of producing 42,500 units of part S-6:

Direct materials: $4.75 x 42,500 = $201,875

Direct labour: $10.75 x 42,500 = $457,375

Variable overhead: $3.75 x 42,500 = $159,375

Fixed overhead: $9.75 x 42,500 = $414,375

Total cost: $1,233,000

Cost per unit: $1,233,000 / 42,500 = $29.00

Total cost of purchasing 37,500 units from the outside supplier:

Cost per unit: $25.75 x 37,500 = $965,625

Cost of renting out the facilities: $94,000

Total cost: $965,625 + $94,000 = $1,059,625

Avoided fixed overhead: 30% x $414,375 = $124,312.50

Net dollar advantage or disadvantage: Total cost of producing - Total cost of purchasing - Avoided fixed overhead

= $1,233,000 - $1,059,625 - $124,312.50

= -$50,937.50

The net dollar advantage or disadvantage of accepting the outside supplier's offer is a disadvantage of $50,937.50.

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Answer:

$24.5

Step-by-step explanation:

Given info:

Kaitlin bought 6 games which are $3.30 each and 1 DVD which cost $4.70

Now to find out the cost of all 6 games multiply 6 by the cost of each one, $3.30

$3.30*6 = $19.8

Now add the price of the DVD to it to find the total price

19.8+ 4.70= $24.5

So thus, the total cost of Kaitlin's items was $24.5

The x-intercepts are (4,0)(5,0) of the following graph.

In the context of a graph, an x-intercept is a point where a curve or line crosses the x-axis. It is the point at which the value of y is zero. In other words, the x-intercept is the value of x when the function or equation crosses the x-axis.

To find the x-intercepts of a function, you can set y equal to zero and solve for x. The resulting values of x will be the x-intercepts.

In the context of a graph, a y-intercept is a point where a curve or line crosses the y-axis. It is the point at which the value of x is zero. In other words, the y-intercept is the value of y when the function or equation crosses the y-axis.

To find the y-intercept of a function, you can set x equal to zero and solve for y. The resulting value of y will be the y-intercept.

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Answer:

  a) $975

  b) growth

  c) 0.3% per month

  d) 6 months: $992.68; 12 months: $1010.68

  e) 8.5 months

Step-by-step explanation:

Given the formula for the monthly balance in a savings account is b = 975(1.003^m), you want the initial deposit, the monthly growth rate, the balance after 6 and 12 months, and the time until the account has a value of $1000.

The general form of an equation for exponential growth is ...

  value = (initial value) × (growth factor)^(time periods)

     where (growth factor) = 1 + growth rate per time period

Comparing this form to the given equation, we can identify the parts:

  value = b, the monthly balance

  initial value = 975, the amount Michael opened the account with

  growth factor = 1.003 per month; time periods are months

  growth rate = 0.003 = 0.3% per month

From our analysis of the equation, we see that the opening deposit is $975.

The growth rate is positive, so this is a case of exponential growth.

The growth rate per month is 0.3%. The monthly interest rate is 0.3%.

We can find the balance after 6 and 12 months by evaluating the formula for those values of m.

To find the time it takes for the balance to reach 1000, we must solve the equation for m. Since m is an exponent, logarithms are involved.

  1000 = 975(1.003^m)

  1000/975 = 1.003^m . . . . . . divide by 975

  log(1000/975) = m·log(1.003) . . . . take logarithms

  m = log(1000/975)/log(1.003) . . . . . divide by the coefficient of m

  m ≈ 8.5 . . . . months

It will take about 8.5 months for the account balance to be $1000.

__

Additional comment

The relevant rule of logarithms is ...

  log(a^b) = b·log(a)

Logarithms were invented for the purpose of transforming multiplication problems into addition problems. When exponents are involved, that means exponential problems are transformed to linear problems. That's what we're doing here.

We have left log(1000/975) as a log expression. We could have replaced it with a number. That might better help you see the simplicity of the equation for m:

  0.0109954 = 0.00130093·m

As with all such equations, you find the value of the variable by dividing both sides by its coefficient.

You need to be careful with precision. These numbers are rounded to 6 significant figures. Their ratio is good to 4 significant figures. We let the calculator figure the value from the log expressions so we get the best possible accuracy.

Therefore, it will cost $8400 to build a floor in the storage house with dimensions 12 feet wide, 10 feet long, and 8 feet high.

Square feet (often abbreviated as sq ft or ft²) is a unit of area commonly used in the United States and other countries that measures the area of a two-dimensional space. One square foot is equal to the area of a square with sides that are each one foot long. For example, a room that measures 10 feet by 12 feet has an area of 120 square feet (10 x 12 = 120). Square feet are commonly used to measure the size of houses, apartments, and commercial spaces, as well as outdoor areas such as yards or gardens.

To calculate the cost of building a floor in the storage house, we need to first determine the area of the floor.

The area of the floor is simply the product of the length and width of the storage house. Therefore:

[tex]Area of floor = Length * Width = 12 ft *10 ft = 120 sq ft[/tex]

To calculate the cost of building the floor, we can multiply the area of the floor by the cost per square foot:

Cost of building floor = Area of floor × Cost per square foot

[tex]Cost of building floor = 120 sq ft * $70/sq ft = $8400[/tex]

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Answer:

Step-by-step explanation:

the vertices of the rectangle lie on the circumference of the circle

We know that our diameter of the circle is equal to 13 cm, radius of the circle is half the diameter

the radius of the circle = 1/2 (13) = 6.5 cm

1. 3.14 × (6.5)²  = 132.67 cm²

2. 12 × 5 = 60 cm²

3. 132.67 - 60 = 72.67 cm²

The lengths of the legs of the triangle cannot be determined by

[tex]x^2 + (x + 2)^2 = 100[/tex]. Thus, option D is correct.

Three vertices when joined with a straight line make up a triangle, a

three-sided polygon. The angles of triangle are formed by a point,

where each of the three sides are joined end to end.

The three angles  add up to make a triangle, sum of angles is a total of 180 degrees. The equations that can be used to find the lengths of the legs of triangle are:

[tex]0.5 (x) (x + 2) = 24\\x(x + 2) = 24\\x^2 + 2x -24 = 0[/tex]

Therefore, 4, [tex]x^2 + (x + 2)^2 = 100[/tex], is not an equation to find the

lengths of the legs of a triangle. It is a different equation that involves

the value of x and y that satisfy the equation of a circle with a center

[tex](-2, 0)[/tex] and radius of  [tex]10[/tex] .

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A.  ∠XAE and ∠EAY form a linear pair.

A linear pair refers to two adjacent angles formed when two lines intersect. The angles are said to be "linear" because they are positioned along the same line, and together they add up to 180 degree

Mathematically, we can express the relationship between the angles as:

∠A + ∠B = 180 degrees

As the ∠XAE + ∠EAY =180 degrees

so  ∠XAE and ∠EAY form a linear pair.

Two angles are said to be complementary if their sum is equal to 90 degrees. In other words, if ∠A and ∠B are two angles, and ∠A + ∠B = 90°, then ∠A and ∠B are complementary angles.

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