The expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased and multiplying by x gives the total revenue from selling x units at that price.
What is revenue?
Revenue can be defined as the total amount of income generated by the sale of goods and services related to the primary operations of the business.
The revenue (R) from a particular distributor that buys x units can be calculated using the following function statement:
R(x) = (4000 - 0.03x) * x
Where
4000 is the original list price per unit 0.03 is the discount per unit per unit purchased x is the number of units purchasedThe expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased, and multiplying by x gives the total revenue from selling x units at that price.
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A picture of a family crest is 5.1 inches wide. The family needs a reduced copy for the front page of the family
newsletter. The copy must fit in a space 1.3 inches wide. What scale factor should be used on the copy machine to
adjust the size of the picture of the crest?
Answer:
0.255 or 25.5%
Step-by-step explanation:
You want the scale factor that reduces 5.1 inches to 1.3 inches.
Scale factorThe scale factor is the ratio of the image size to the original size:
1.3/5.1 ≈ 0.254902 ≈ 0.255 = 25.5%
__
Additional comment
A scale factor of 0.255 would give an image of 1.3005 inches. That's probably close enough. Rounding to the nearest percent, it would be 25%, which would give an image size of 1.275 inches.
Jade and Juliette are riding their bikes across the country to promote autism awareness. They rode their bikes 45.4 miles on the first day and 56.3 miles on the second day. From now on, Jade and Juliette plan to ride their bikes 62 miles per day. If the entire trip is 2,878 miles, how many more days do they need to ride?
Write a short script that could be used to make a video about this cross-country bike trip. Provide a short character description, dialogue (conversation between characters), and directions for the actors, but keep the script simple
Jade and Juliette 44.7days more days to complete their trip.
How to calculate the number of days to complete the tripTo calculate how many more days Jade and Juliette need to ride, we can use the equation:
Total distance = Distance on first day + Distance on second day + Distance on remaining days
We know the first and second day distances, and the daily distance for the remaining days, so we can substitute those values in the equation:
2878 = 45.4 + 56.3 + 62x
where x is the number of remaining days they need to ride.
Simplifying the equation:
2878 - 101.7 = 62x
2776.3 = 62x
Dividing both sides of the equation by 62
x = 44.7
hence, Jade and Juliette need to ride for 44.7 more days to complete their trip.
Say that a certain stadium for professional football has 70,000 seats. What is the shape of the
supply curve for tickets to football games at that stadium? Explain.
Answer: The shape of the supply curve for tickets to football games at the stadium with 70,000 seats is upward-sloping. This means that as the price of tickets increases, the quantity of tickets supplied also increases.
The reasoning behind this is simple: when the price of tickets is high, there is more incentive for the sellers (e.g. the stadium, ticket resellers, etc.) to sell more tickets. They have the ability to supply more tickets as the demand for tickets at the high price is likely to be higher, thus increasing their profits.
However, it is important to note that the upward slope of the supply curve is not necessarily linear. The supply curve for tickets to football games is likely to be more elastic in the higher price range, meaning that as the price continues to increase, the quantity supplied may increase at a slower rate. This is because at some point, even if the price continues to rise, there will be a limit to how many tickets can actually be sold due to a decrease in demand.
Overall, the upward-sloping shape of the supply curve for tickets to football games at the stadium with 70,000 seats reflects the basic principle of supply and demand: as the price increases, the quantity supplied will also increase, but at some point, the increase in price will lead to a decrease in demand, limiting the quantity supplied.
Step-by-step explanation:
What are the domain and range of the real-valued function f(x) = -3-√√4x - 12?
The domain of the real valued function as required is; [3, infinity).
The range of the function as required is; (-infinity, -3].
What is the domain of the function?By observation of the given function; the domain is the set of all real numbers except those for which;
4x - 12 < 0
4x < 12
x < 3.
Hence, the domain of the function is; [3, infinity).
The range as observed in the task content has a maximum value of; -3. Hence, the range of the function as required is; (-infinity, -3].
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-(3x+1)+7=4-(3x + 2)
Show work
Answer:
no solution
Step-by-step explanation:
- (3x + 1) + 7 = 4 - (3x + 2) ← distribute parenthesis on both sides
- 3x - 3 + 7 = 4 - 3x - 2
- 3x + 4 = 2 - 3x ( subtract 4 from both sides )
- 3x = - 2 - 3x ( add 3x to both sides )
0 = - 2 ← false statement
this false statement indicates the equation has no solution
-(3x+1)+7=4-(3x + 2)
-3x-1+7=4-3x-2
-3x+6=-3x+2
-3x+3x=-4
0=-4
no solution
Hasten plans to choose a book from the section of the store where everything is 25% off he likes expression D -0.25 days to find the sale price of the book it if there is a YZ dollars below correctly write another expression 0.7 5D that will also find the surprise of the book if the original price is de dollars
Another form of representing the cost of the book is (75/100)×D.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know, Percentages and decimals are related.
10% in decimal form is equivalent to (10/100) - 0.1 in decimal.
An expression that represents the sale day book price is 0.75D.
Another expression that would represent the cost of the book priced 'D' would be,
= (75/100)×D.
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See attached image and answer questions.
The properties of the polynomial are
Degree = oddLeading coefficient = NegativeOdd multiplicity = 3Even multiplicity = 1How to determine the properties of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -5A root of multiplicity 1 at x = -2A root of multiplicity 2 at x = 1A root of multiplicity 1 at x = 4y-intercept = 2Using the above as a guide, we have the following:
Degree = sum of multiplicities
Degree = 1 + 1 + 2 + 1
Degree = 5
The leading coefficient is negative
This is so because the graph opens down
There are 3 zeros with odd multiplicities and 1 zero with even multiplicity
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Can the following fraction be simplified or expressed in a different form -
(5x-1)/x+4
Answer:
= 9x - 1
Step-by-step explanation:
[tex] \frac{(5x - 1)}{x} + 4 \\ = x \times \frac{5x - 1}{x} + 4(x) \\ = 5x - 1 + 4x \\ = 5x + 4x - 1 \\ = 9x - 1[/tex]
Reactive Power VARS Apparent Power VA CD True Power W
a. Reactive power is the power lost in the inductive or capacitive load in an AC electrical circuit.
b. Apparent power is the power is the total power delivered to an AC electrical circuit
c. True power is the power lost in a resistive load in an AC electrical circuit.
What is power?Power is the rate at which work is done.
a. What is reactive power VARS?Reactive power is the power lost in the inductive or capacitive load in an AC electrical circuit. The reactive power is given by
P' = IVsinФ where
I = current in circuit, V = voltage in circuit and Ф = load angleb. What is apparent power VA?Apparent power is the power is the total power delivered to an AC electrical circuit. The apparent power is given by
S = IV where
I = current in circuit, V = voltage in circuit c. What is true power W?True power is the power lost in a resistive load in an AC electrical circuit. The true power is given by
P' = IVcosФ where
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13. Landon is 6 ft. tall and measures his shadow to
be 8.3 ft. long. At the same time of day, he
measures a tree's shadow to be 17.6 ft. long. How
tall is the tree?
Answer: 12.72 ft.
Step-by-step explanation:
[tex]\frac{6}{8.3} = \frac{x}{17.6} \\\\ 8.3x= 105.6\\\\x= 12.72[/tex]
Write the equation of the graph shown below in factored form
The equation of the polynomial is P(x) = -4(x + 1)(x - 1)(x - 2)^2
How to determine the equation of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -1A root of multiplicity 1 at x = 1A root of multiplicity 2 at x = 2y-intercept = -12A polynomial is represented as
P(x) = a * (x - zero)^multiplicity
Using the above as a guide, we have the following:
P(x) = a * (x + 1)(x - 1)(x - 2)^2
The y-intercept is -12
So, we have
a * (0 + 1)(0 - 1)(0 - 2)^2 = -12
This gives
a = -4
Hence, the expression is P(x) = -4(x + 1)(x - 1)(x - 2)^2
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create a table of values to represent the total cost if ben orders 1 or 2 books or spends 41$, $65 OR $125
The table to represents the total cost for the different numbers of books ordered is:
Number of books Spending Total cost
1 $41 $44
2 $65 $71
3 $125 $134
What is an expression?An expression is written with one or more terms with addition, subtraction, multiplication, and division.
Example:
2.2 + 3x + 4y = 7 is an expression.
3 + 5x = 9 is an expression.
We have,
The book cost = $3
Now,
Spendings = $41, $65, or $125
Now,
Table:
Number of books Spending Total cost
1 $41 41 + 3 = $44
2 $65 65 + 6 = $71
3 $125 125 + 9 = $134
Thus,
The table for the total cost is given above.
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Suppose you have $200 with which you can buy shares of stock from two companies:
ABC Hot Chocolate Company and XYZ Lemonade. Each company's stock currently sells for $100 per share. If the temperature next year is lower than average, the stock price for ABC will increase by $20, and the stock price for XYZ will not change.
If the temperature next year is higher than average, the stock price for XYZ will increase by $20, and the stock price for ABC will not change. There is a 50% chance that it will be colder than average next year, and a 25% chance that it will be warmer than average.
If you purchase two shares of ABC stock and no shares of XYZ stock, there is a _____ chance that your gain will be $40. Otherwise, your gain will be _____.
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
The chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and if it is not $40 the gain is:
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
So, the option (4) 50%, $20 is the correct option.
The given question is asking what the chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and what the gain will be if it is not $40.
Mathematically, this can be broken down as follows:
There is a 50% chance that the temperature will be lower than average, in which case the stock price for ABC will increase by $20. Thus, the expected gain from investing in ABC is 50% x $20 = $10.
There is a 25% chance that the temperature will be higher than average, in which case the stock price for XYZ will increase by $20. Since you are not investing in XYZ, your expected gain from this is 0.
Therefore, the expected gain from investing in ABC and not investing in XYZ is 50% x $10 + 25% x $0 = $10 + $0 = $10.
Since you are investing in two shares of ABC stock, your expected gain is 2 x $10 = $20. Thus, there is a 50% chance that your gain will be $40, and otherwise your gain will be $20.
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For a particular 4 leaf clover, the highway had to be compacted on the south side making the circles two different sizes. The two circles on the north of the highway have a radius of 128 feet and the two on the south side have radius of 102 feetCalculate the total area of grass seed needed for these four circles
The total area of the two circles will be 168316.9 square feet.
What is a circle?The circle is defined as a two-dimensional figure having a fixed point and the number of the points is traced around the curved path at an equal distance from the fixed point. The overall figure is called a circle.
The area of the circle is calculated by the formula:-
Area = πr²
Given that the south side of the highway needed to be compacted in order to create two circles of various sizes for a specific four-leaf clover. The two circles on the north side of the road have a 128-foot radius, whereas the two on the south side have a 102-foot radius.
The total area will be calculated as:-
Area = 2 x π x 128² + 2 x π x 102²
Area = 102943.25 + 65370.25
Area = 168316.9 square feet
Hence, the total area will be 168316.9 square feet.
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Help!!! I can’t even find the answer for this question
Answer:
<1 and <2
Step-by-step explanation:
Adjacent means angles that are next to each other. This is not the only pair, but <1 and <2 are adjacent.
In the diagram, ACDF∼VWYZ
. Find the value of y.
The value of the variable y is 3
How to determine the valueFrom the information given, we have that;
ACDF∼VWYZ
Given that the lengths are;
A= 12CD = 9YW = 6VZ = 3y -1Since the diagrams are equivalent, then,
A/VZ = CD/YW
substitute the values, we have;
12/3y - 1 = 9/6
cross multiply
3y - 1 = 12(6)/9
divide the values
3y - 1 = 8
collect like terms
3y = 9
Make 'y' the subject
y =3
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wer:
My number is a 2-digit multiple of 9. The ratio of its units digit to its tens digit is 1:2.
What is my number?
Let's call the tens digit "x" and the units digit "y". We know that the number is a multiple of 9, so:
x + y = 9
and the ratio of the units digit to the tens digit is 1:2, so:
y = 2x
Substituting the second equation into the first, we get:
x + 2x = 9
3x = 9
x = 3
So the tens digit is 3 and the units digit is 2 times that, or 6. The number is 36.
Answer:
63
Step-by-step explanation:
___________________
First, let's list all the 2-digit multiples of "9":
______________________________________________________
18, 27, 36, 45, 54, 63, 72, 81, 90, 99.
______________________________________________________
From this list, the only answer that has a ratio in which its "units digits to its tens digits" is "1:2" is: "63" . "3:6" = "1:2" .
The polynomial of degree 4,
P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at x=0 and x = - 4. It goes through the point (5,144). Find a formula for P(x).
Answer:
Step-by-step explanation:
Since the polynomial has a root of multiplicity 2 at x = 3, it can be written as (x - 3)^2 times another polynomial Q(x). Also, since it has roots of multiplicity 1 at x = 0 and x = -4, it can be written as (x - 3)^2 * (x - 0) * (x + 4) * Q(x).
Next, we can use the fact that the polynomial goes through the point (5, 144) to find the formula for Q(x). The polynomial P(x) must satisfy P(5) = 144, so we can write:
(5 - 3)^2 * (5 - 0) * (5 + 4) * Q(5) = 144
4 * 9 * 9 * Q(5) = 144
36 * Q(5) = 144
Q(5) = 4
So, the polynomial P(x) can be written as:
P(x) = (x - 3)^2 * (x - 0) * (x + 4) * 4
= 4 * (x - 3)^2 * (x - 0) * (x + 4)
= 4 * (x^2 - 6x + 9) * x * (x + 4)
= 4x^4 - 84x^3 + 378x^2 - 648x + 576
This is the formula for P(x).
Which shows the expression x^2-1/x^2-x
in simplest form?
Answer:
x+1/x
Step-by-step explanation:
An international company has 21,800 employees in one country. If this represents 32.2% of the company's employees, how many employees does it have in
total?
Round your answer to the nearest whole number.
employees
X
Español
?
D
Answer:
Step-by-step explanation:
The international company has 21,800 employees in one country, which represents 32.2% of the company's total employees. We can use this information to find the total number of employees by solving for the missing value.
Let's call the total number of employees in the company "X".
If the 21,800 employees in one country represent 32.2% of the total employees, we can write an equation to represent this relationship:
0.322 * X = 21,800
Next, we'll isolate X by dividing both sides of the equation by 0.322:
X = 21,800 / 0.322
Using a calculator, we can find that:
X = 68,062.5
Rounding to the nearest whole number, the company has 68,063 employees in total.
So, that's how you can use a percentage to find the total number of employees in the company. By knowing the number of employees in one country and the percentage that this represents of the total, we can find the total number of employees in the company.
Please help me I’m confused
Answer:
Below
Step-by-step explanation:
Here is what the graph should look like ...you can see that he will have 0 fence left to paint ( 0 = y ) when time = 3 hrs
Put a decimal point in the number 26583 so that the 5 has a value of
100
50
The number as decimal is 26583.0
How to rewrite the number as decimalFrom the question, we have the following parameters that can be used in our computation:
Number = 26583
Also, we have the required value of 5 to be
Required = 100
Using the above as a guide, we have the following:
The number 5 must have a value of 100 in the new number i.e. 500
So, we have
Number = 26583
Rewrite as
Number = 26500 + 83
This means that we add 5 at the end
So, we have
Number = 26583.0
Hence, the new number is 26583.0
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In simple terms, please explain to me what is the difference between horizontal shrink and vertical stretch.
Answer:
see attached
Step-by-step explanation:
You want the difference between horizontal shrink and vertical stretch.
Horizontal shrinkA horizontal shrink compresses a graph horizontally. In the attached figure, the original graph is the red circle. The blue ellipse is that circle shrunk horizontally by a factor of 3. It retains the same height, but is compressed sideways.
Vertical stretchA vertical stretch expands the graph vertically. The green ellipse in the attached figure is the original circle stretched vertically by a factor of 3. The horizontal dimension remains unchanged.
InterchangeableYou will notice that replacing a variable x by x/k effectively accomplishes a stretch by a factor of k in that variable's direction. Similarly, replacing a variable x by kx accomplishes a compression by a factor of k.
Your question suggests that you have noticed the similarities between vertical stretch and horizontal compression. For some figures, there is basically no difference.
Here are a couple of examples of that:
line y = x. Vertical stretch by 2: y/2 = x, or y = 2x. Horizontal compression by 2: y = 2x. These equations are identical.
parabola y = x². Vertical stretch by 4: y/4 = x² or y = 4x². Horizontal compression by 2: y = (2x)² = 4x². These equations are identical.
DifferencesThe differences between stretch in one direction and compression in the other direction are more apparent for figures with multiple reversals of direction. The second attachment shows the sine function (red) vertically stretched (blue) and horizontally compressed (green).
100 points!!!!!!!!
Martina is playing a carnival game. She is blindfolded while she throws a dart at a board of 12 balloons, as shown below. Each balloon is labeled "S" for small,
"M" for medium, "L" for large, or "XL" for extra-large. The board has 5 small balloons, 1 medium balloon, 4 large balloons, and 2 extra-large balloons. She hits one of the balloons at random and wins a stuffed animal of that size.
(a)Find the odds in favor of Martina winning a medium stuffed animal.
(b) Find the odds against Martina winning a medium stuffed animal.
Answer:
(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.
(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.
Answer:
(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.
(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.
Help please I don’t understand it at all
Answer:
Both of them are correct.
Step-by-step explanation:
Let's review both of their methods and check their validity.
Kaylee's Method:This method is the most straight forward and seems to be correct as we're simply calculating the total value of each, and then subtracting the difference. We can write the expression as: [tex]2.25(4.25)-2.25(2.85)[/tex] and this should give us the difference assuming the prices and math is done correctly.
Ariel's Method:While this method is a bit difference, it actually does work! Think of this way, we first calculate the difference in the prices and then for each pound we increase it by, the difference also increases by this amount. It also helps to look at our original expression: [tex]2.25(4.25)-2.25(2.85)[/tex], notice how we have a factor of 2.25 on both sides? Well we can just factor that out to get: [tex]2.25(4.25 - 2.85)[/tex] and this is essentially what Ariel's method is. This should give us the difference in prices and is likely easier than Kaylee's method as we do less multiplication and with smaller numbers.
2/3 of the students in Mrs. Gracie’s class are boys . If there are 27 students in the class, how many of them are girls?
Answer:
9
Step-by-step explanation:
divide 27 by 3
It equals 9
9 x 2 = 18 boys
27-18= 9 girls
Please help me answer this
The given expression can be written in a single radical as q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]. The solution has been obtained by solving the radical expressions.
What are radical expressions?
An expression which contains a square root is referred to as a radical expression. The 'V'-shaped portion of the radical sign will have a superscript number when it is used to represent any root other than a square root.
We are given √q³ [tex]\sqrt[3]{q^{8} }[/tex].
On simplifying the expression, we get
⇒√q² . q [tex]\sqrt[3]{q^{3} . q^{3} . q^{2} }[/tex]
⇒q . √q . q² . [tex]\sqrt[3]{ q^{2} }[/tex]
⇒q³ . √q [tex]\sqrt[3]{ q^{2} }[/tex]
⇒q³ . [tex]\sqrt[]{ q^{\frac{1}{2} + \frac{2}{3} } }[/tex]
⇒q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]
Hence, the given expression can be written in a single radical as q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex].
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Claudia is interested in knowing which figure skater competing in the
Olympic Games is most favored to win a gold medal. To sample the
students in her school, she prepares a list of all of the boys and girls in the
school and randomly chooses a sample from each group so that the size of
each group is proportional to the number of boys and girls in the school.
Which sampling method did Claudia use?
OA) simple random sampling
OB) stratified random sampling
OC) systematic random sampling
OD) simple non-random sampling
OD) Is simple non-randon sampling
Step-by-step explanation:
because Claudia randomly choose a sample from each group.
Choose all of the values that are solutions to inequality x < -2
Answer:
The solution to the inequality x < -2 is all real numbers that are less than -2. This means that any number that is less than -2 will satisfy the inequality, but any number that is greater than or equal to -2 will not.
So, the solution set for x < -2 is all real numbers that are less than -2. This solution set can be expressed as (-∞, -2).
Therefore, the values that are solutions to the inequality x < -2 are:
• all real numbers less than -2, such as -3, -4, -5, etc.
Note that -2 itself is not part of the solution set, since it is not less than -2.
please, help with this one
r log a + y log c
The required r log a + y log c is equivalent to the expression as [tex]r log a + y log c = log (a^r c^y)[/tex].
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The expression r log a + y log c can be simplified using logarithmic properties. Specifically, we can use the rule that says:
[tex]log a^b = blog a[/tex]
Using this rule, we can write the expression as:
[tex]r log a + y log c = log a^r + log c^y[/tex]
Now we can use the rule that says:
log a + log b = log ab
to combine the two logarithms:
[tex]log a^r + log c^y = log (a^r c^y)[/tex]
Therefore, the expression r log a + y log c simplifies to:
[tex]r log a + y log c = log (a^r c^y)[/tex]
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