(c) What is the shortest possible distance between the building and the end of the ramp if the architect redesigns the building so that the doorway is 1.3 feet above the parking lot?

The probability that the orange has a mass of more than 80g is (y/x).

Given is that one of the oranges is chosen at random from the crate of oranges.

Assume that the total number of oranges are {x} and the oranges with a mass of greater than 80 are {y}. So, we can write -

P{E} = y/x

Therefore, the probability that the orange has a mass of more than 80g is (y/x).

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There are 5,760 ways to arrange the books on the bookshelf.

A permutation is an ordered arrangement of objects, and it can be calculated as follows:

ⁿPₓ = n! / (n - x)!

where n is the total number of objects and r is the number of objects that we are arranging.

To determine the total number of ways in which we can arrange the books on a bookshelf, we need to first calculate the total number of possible arrangements. We can do this by using the fundamental principle of counting, which tells us that the total number of possible arrangements is equal to the product of the number of ways in which each book can be arranged.

Therefore, the total number of possible arrangements can be calculated as follows:

Total number of possible arrangements = Number of ways to arrange math books × Number of ways to arrange history books × Number of ways to arrange science books

In our case, we have 4 math books, 5 history books, and 2 science books, so we can calculate the number of permutations for each type of book as follows:

Number of ways to arrange math books = ⁴P₄ = 4! / (4-4)! = 4! / 0! = 24

Number of ways to arrange history books = ⁵P₅ = 5! / (5-5)! = 5! / 0! = 120

Number of ways to arrange science books = ²P₂ = 2! / (2-2)! = 2! / 0! = 2

Now, we can substitute these values in the formula for the total number of possible arrangements:

Total number of possible arrangements = 24 × 120 × 2 = 5,760

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Answer: 19

Step-by-step explanation: 15 x 19 = 285ft^2

Answer: 157.5

To find the volume of the smaller box, we use this equation:

Fitting the dimensions into the equation:

So, the volume of the smaller box is 262.5³.

If the height of the second box is %60 percent bigger, we can use this equation to figure out the new height.

10 × 1.6 = 16

Well, that's a good question! If we were to multiply by 0.6, the box would get smaller, instead of bigger. We add the 1.0 because we have to add the original height, not just the added height.

Now, the equation looks like this:

Now, the second boxes volume is 420³.

To find out the difference between the two volumes, we can subtract.

Therefore, the difference between the two volumes is 157.5.

Answer:

r = 55

Step-by-step explanation:

Sum means addition

r + 18 = 73   Subtract 18 from both sides

r = 55

Answer:

The equation is:

r + 18 = 73

and the result is:

r = 55

Step-by-step explanation:

The  sum of r and 18 is 73, in equation is:

r + 18 = 73

Solve:

r + 18 - 18 = 73 - 18

r + 0 = 55

r = 55

Check:

55 + 18 = 73

Another person named Sarah earns $7.50 per hour, then Reece earns more per hour than Sarah.

If the relationship between the number of hours worked and total earnings for Reece at Fries n More is given by y = 8.25x, where y is total earnings and x is the number of hours worked, then Reece earns $8.25 per hour worked.

To compare Reece's earnings per hour to another person, we would need to know the hourly wage of the other person. For example, if another person named John earns $9.00 per hour, then John earns more per hour than Reece. Conversely, if another person named Sarah earns $7.50 per hour, then Reece earns more per hour than Sarah.

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The difference between rational algebraic expressions and fractions is discussed above.

In mathematics, an expression or mathematical expression is a combination of terms, both variables and constants.

For example → 2x + 3y + z

Given is to explain how is rational algebraic expressions different with fractions.

In a rational algebraic expressions, the expression function in the numerator and denominator both are non - zero polynomials. A fraction is of the form {x/y}, in which it is not necessary that {x} and {y} should be polynomials only. They can be numbers also.

Therefore, the difference between rational algebraic expressions and fractions is discussed above.

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The graph that best models the exponential function is given as follows:

Graph A.

An exponential function is defined as follows:

y = a(b)^x.

In which:

The parameters for this problem are given as follows:

Hence the function is given as follows:

y = 200000(1.06)^x.

The value of the home after 5 years is given as follows:

y = 200000(1.06)^5

y = $267,645.

Which is best approximated by the Graph A.

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The area of the composite figure is equal to 99 mm² square milimetresmetres.

The composite figure can be observed to be made up of two horizontal rectangle, and a vertical rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the bigger horizontal rectangle = 11 mm × 3 mm

area of the bigger horizontal rectangle = 33 mm²

area of the smaller horizontal rectangle = 5 mm × 2 mm

area of the smaller horizontal rectangle = 10 mm

area of the vertical rectangle = 14 mm × 4 mm

area of the vertical rectangle = 56 mm²

total area of the composite figure = 33 mm² + 10 mm² + 56 mm²

total area of the composite figure = 99 mm²

Therefore, the area of the composite figure is equal to 99 mm² square milimetres.

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The ratio tables based on the information will be:

12 16

3 4

36 48

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

This simply indicates that you're dividing the variable A by B. Let us say for instance, the ratio will be 3/10 if A is 3 and B is 10.

Since the ratio is 3:4. When the smaller number is 36, the larger number will be:

= 4/3 × 36.

= 48

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The statement that describes the conversion is To find the weight in pounds, multiply the number of ounce by the unit rate 16 ounces per pound

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

The double number line

On the double number line, we have:

16 ounces = 1 pound

This means that

To find the weight in pounds, multiply the number of ounce by the unit rate 16 ounces per pound

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Answer:

48 residents

Step-by-step explanation:

Let's assume that there are 100 residents in the neighboring house. 64% of the residents subscribe to "Our Football" magazine, so there are 64 residents who subscribe to it. 84% of the residents subscribe to "Top Gear" magazine, so there are 84 residents who subscribe to it. The number of residents who subscribe to both magazines can be calculated by finding the intersection of the two sets, which is equal to the number of residents who belong to both sets. This can be found using the formula:

Number of residents subscribing to both magazines = 100 - (100 - 64) - (100 - 84)

= 100 - 36 - 16

= 48

Therefore, 48 residents of the neighboring house subscribe to both magazines.

List of perfect squares smaller than 10 are: {1, 4, 9}

Subtract 1 from each value to get a new list of {0, 3, 8}

None of these new values are a factor of 12.

The possible answers are: 0, 3, and 8

Answer:

x = 4 twice.

Step-by-step explanation:

x^2-8x+ 16=0

Bring the constant to the other side.

x^2-8x=-16

Half the coefficient of x and square the result. Add to both sides.

x^2-8x+[-8/2]^2=-16+(-8/2)^2

x^2-8x+16= 16-16

x^2-8x+16=0

Now, whenever there's a perfect square constant, take the root of that constant. Since the coeff. of x is negative (-8),

(x-4)(x-4)=0  [-4^2=16 and -4+(-4)=-8]

Therefore, x-4=0 twice.

x=4 twice.

Hope this helps!  :]

Check the picture below.

so the figure is really just a semi-circle, a rectangle and three triangles, let's simply get their area and sum them all up.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ semicircle }{\cfrac{1}{2}\pi (2)^2}~~ + ~~\stackrel{ rectangle }{(4)(5)}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{3})(\underset{h}{2})}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{4})(\underset{h}{1})}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{4})(\underset{h}{2})}} \\\\\\ 2\pi ~~ + ~~20~~ + ~~3~~ + ~~2~~ + ~~4 ~~ \approx ~~ \text{\LARGE 35.28}[/tex]

Answer:

(X-3)5=575

5x-15=575

5x=575+15

5x=590

X= 590:5

X= 118

Based on the conversion factors, the equivalent values are as follows:

1 Tbsp. = 1/16 c

1/4 c. = 4 Tbsp

1 c. = 16 Tbsp

1 c. = 1/2 pint

1/3 c. = 80 mL

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet.

The conversion factor for Tbsp to c is 1/4, which means that 1 Tbsp. is equal to 1/4 c.

The conversion factor for c to mL is 236.6, which means that 1 c. is equal to 236.6 mL (rounded to one decimal place).

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Answer: 46ft

Step-by-step explanation:

Alright so for this you must reference the pythagorean theorem which is:

a^2+b^2=c^2. c^2 is always the diagonal side and a^2 and b^2 the other two sides.

You can therefore set this up like this:

a^2+20^2=50^2 (where a is the side you are looking for- listed as x)

Solve:

a^2=50^2-20^2

a^2=2500-400

a^2=2100

sqrt(a^2)=sqrt(2100)

a= 45.8257569496

Round: a (or x)=46

The absolute value function on the graph is:

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

We know that for an absolute value function with a vertex at (a, b), then the absolute value function is:

f(x) = |x - a| + b

Here we can see that the vertex is at the point (-2, 3)

Then:

a = 2

b = 3

The function will be:

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

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The length of the radius of the circle is 7.5 inches.

The radius formula is easily obtained by halving the circle's diameter. The line segment created when we join a point on a circle's circumference to its exact center is referred to as the ring's radius. The radius of a circle is the separation between its centre and circumference. Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.

Given that the diameter of the circle is 15 inches.

The radius of the circle is half the measure of the diameter.

That is,

R = d/2

R = 15/2

R = 7.5 inches

Hence, the length of the radius of the circle is 7.5 inches.

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The magazine will have 33320 subscribers at the end of 10 years.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Given that, a publishing industry report predicts that magazine

subscriptions will drop by 10% each year.

The problem thus represents an exponential decay problem.

The exponential decay is given as:

[tex]F = P (1 - r)^t[/tex]

Here, F is the future value.

P is the present amount = 98000.

r is the rate of decrease = 10% = 0.1

t is the time = 10 years.

Substituting the values we have:

[tex]F = 98000(1 - 0.1)^{10}\\[/tex]

F = 33320

Hence, the magazine will have 33320 subscribers at the end of 10 years.

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The cost of red grapes per pound is $2.8.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, cost of a large watermelon and 2.4 pounds of red grapes is $7.71.

Let the cost of red grapes be x.

So, the total cost = 7.71+2.4x

Cost of a platter of pre-cut fruit and 1.6 pounds of red grapes is $9.95.

The total cost = 9.95+1.6x

Person and his brother spent same amount of money.

So, 7.71+2.4x=9.95+1.6x

2.4x-1.6x=9.95-7.71

0.8x=2.24

x=2.24/0.8

x=$2.8

Therefore, the grapes cost per pound is $2.8.

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Brand₂ has the highest impact on the price of a smartphone, increasing the price by $80 for each unit increase in that variable.

Regression analysis is a statistical method that helps us understand the relationship between two or more variables.

Based on the regression equation, we can determine which brand increases the price of a smartphone the most. The regression equation is as follows:

Price = 1100 + 50 (Brand₁) + 80 (Brand₂) + 30 (Brand₃) + 20 (Battery Life) + 10 (Camera Resolution)

In this equation, the intercept (1100) represents the average price of a smartphone with all other variables set to zero. The coefficients for each variable represent the change in the price of a smartphone for a one-unit increase in that variable, holding all other variables constant.

Brand₁ and Brand₂ have a lower impact on the price, increasing it by $50 and $30, respectively, for each unit increase in those variables. Battery life and camera resolution have the smallest impact on the price, increasing it by $20 and $10, respectively, for each unit increase in those variables.

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Complete Question:

Can brand, battery life, and camera resolution affect a smartphone's price? Use α= o.05 to perform a regression analysis for the Smartphones01BC dataset and answer the following questions. Solve this problem using Excel and Mega Stat, and write your complete answers in the Response Box so I know that you can interpret the output.

Based on your regression equation, which brand increases the price of a smartphone the most? Use the statistics from your output to explain your answer.

The approximate side length of the largest square envelope that can be placed into the mailbox without bending it is 0.71x.

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles of 90 degrees each. It is a two-dimensional shape that can be represented by a closed polygon with four straight sides and four right angles.

First, we need to measure the size of the mailbox. Let's say that the length of each side of the mailbox opening is "x" inches. We can then set up an inequality to find the maximum size of the side of the square envelope that can fit into the mailbox. The inequality is:

side length of square envelope ≤ x

This inequality tells us that the side length of the square envelope must be less than or equal to the size of the mailbox opening. We want to find the largest possible side length of the square envelope, so we'll use the "less than or equal to" symbol.

To find the largest possible side length of the square envelope, we'll use the value of "x" to set up an equation. We know that the diagonal of the square envelope will be equal to the length of the side of the square envelope multiplied by the square root of 2. Therefore, we can set up the following equation:

diagonal of square envelope = side length of square envelope × √2

We want to find the maximum side length of the square envelope, so we'll use the maximum value of the diagonal of the envelope. We know that the diagonal of the envelope must be less than or equal to the length of the mailbox opening (which is "x"), so we can set up the inequality:

side length of square envelope × √2 ≤ x

We can solve for the side length of the square envelope by dividing both sides of the inequality by the square root of 2:

side length of square envelope ≤ x/√2

To get the largest possible side length of the square envelope, we'll use the maximum value of "x". Therefore, the largest possible side length of the square envelope that can fit into the mailbox without bending is:

side length of square envelope ≤ x/√2 ≈ 0.71x

We can round this value to two decimal places, which gives us:

side length of square envelope ≈ 0.71x

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The function V(r) is representing the volume of basketball when the radius is r.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, the function V(r) =  4/3 πr³, can be used to find the volume of air inside a basketball given its radius (r).

We are asked to find that what does V(r) represents,

Here, V(r) is the function's output is r is the input, the only variable in the formula is r, that means the volume totally depends on the radius of the basket ball. & volume is changes with the radius.

Thus, this function represents the volume of the basketball when radius is r.

Hence, the function V(r) is representing the volume of basketball when the radius is r.

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The degree of the polynomial function represented by the graph is 4 and its leading coefficient is negative

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

The graph

The degree of the polynomial function is the number of times the curve tends to touch or intersect with the graph

In this case, we have

Degree = 4

For the leading coefficient, we have

leading coefficient = negative

This is because the graph opens down

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Answer:

If a = -8 and b = -1 there is exactly one solution to the equation

Step-by-step explanation:

I was unable to find the other one...

Are you sure there are two possible solutions, or did you forget to include one of the options...?

a) The histogram of the data is illustrated below.

b) A cumulative percentage polygon is illustrated on histogram.

c) The cumulative percentage polygon shows us that approximately 66% of calls fall below 240 seconds.

Histograms are a way of representing data visually by dividing it into intervals or bins and plotting the frequency of data points in each bin. In this problem, we will be constructing a percentage histogram and polygon to analyze call duration data.

The call duration data is provided in seconds for 50 customers. To construct a percentage histogram, we need to first determine the bin size or interval. One way to do this is to use the square root rule, which states that the number of bins should be approximately equal to the square root of the sample size. In our case, the sample size is 50, so we can round the square root to 7 and use 7 bins.

Next, we need to determine the range of the data and set the limits for each bin. The range of the data is from 65 to 1141 seconds. We can set the limits for each bin as follows: 60-180, 181-300, 301-420, 421-540, 541-660, 661-780, 781-900, and 901-1020.

To construct the percentage histogram, we need to divide the frequency in each bin by the total sample size and multiply by 100. This gives us the percentage of data points in each bin. We can then plot these percentages as bars of equal width for each bin.

The percentage polygon is constructed by connecting the midpoints of the tops of each bar in the histogram with straight lines. This creates a polygon that represents the distribution of data in the histogram.

In this problem, we are asked to analyze call center performance if a call duration target of less than 240 seconds is set. From the percentage histogram and polygon, we can see that the majority of calls fall within the first three bins, which correspond to call durations of 60-180, 181-300, and 301-420 seconds. Only a small percentage of calls exceed 420 seconds.

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The measure of the missing angle α is 62 degrees.

The sum of angles on the straight line adds up to 180 degrees.

From the diagram;

Since the sum of angles on a straight line adds up to 180 degrees.

Angle 1 + Angle 2 + Angle 3 = 180

Plug in the values

118 + α = 180

Subtract 118 from both sides

118 - 118 + α = 180 - 118

α = 180 - 118

α = 62°

Therefore, the value of angle α is 62 degrees.

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