1. Interpret the domain restrictions on the demand and the supply functions. What do they represent in context of the scenario?
2. Suppose that in her first month Yaseen is able to create 15 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work.
3. In her first month of business, Yaseen sells out of her kits in 3 days. In her second month of business, she decides to supply 60 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work.
4. If Yaseen creates 60 kits in her second month of business and offers them for sale at $66 each, do you think she will sell all of them? Why or why not?
5. What family of functions do f(x) and g(x) belong to? How do you know?
6. If you were to graph two quadratic functions on the same xy-plane, how many intersection points could there be? Use examples to explain your thinking.
7. Use algebraic methods to find where Yaseen’s demand and supply functions intersect. What does this point(s) represent in context of this problem? Show all your work.
8. Confirm your answer from question 7 by using Desmos to create a single graph that shows both () and () with their domain restrictions. Provide a screenshot of your graph with the intersection point(s) marked.
Answers
According to Yaseen's demand function, if she can produce 60 kits, the function cost per kit should be set at:
[tex]p = 30 - 0.5q\s60 = q = > p = 30 - 0.5(60) (60) > p = $15[/tex]
What is function?Probability theory is an area of mathematics that deals with calculating the likelihood that an event will occur or a proposition will be true. A risk is a number between 0 and 1, where 0 represents the possibility of an event occurring and 1 represents certainty.
Probability is a mathematical expression of the possibility that an event will occur. The proportion of equally plausible options that actually occur relative to all potential outcomes when an event happens is known as the probability, and it may also be written as an integer between 0 and 1.
According to Yaseen's supply function, if she can produce 15 kits, the cost per kit she should charge is:
[tex]p = 10 + 0.5q[/tex]
[tex]p = 10 + 0.5(15) (15)[/tex]
[tex]p = $17.50[/tex]
According to Yaseen's demand function, if she can produce 15 kits, the cost per kit she should charge is:
[tex]p = 30 - 0.5q\sp = 30 - 0.5(15) (15)[/tex]
[tex]p = $22.50[/tex]
According to Yaseen's supply function, if she can provide 60 kits, the cost per kit should be as follows: [tex]p = 10 + 0.5q 60 = q p = 10 + 0.5 (60)[/tex]
[tex]p = $40[/tex]
According to Yaseen's demand function, if she can produce 60 kits, the cost per kit should be set at:
[tex]p = 30 - 0.5q\s 60 = q[/tex]
[tex]p = 30 - 0.5(60) (60)[/tex]
[tex]p = $15[/tex]
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Answer:
Step-by-step explanation:
1. Demand- 0<=x<=85 / Supply- 0<=x<=100
The company is estimating that no more then 85 kits will be demanded each month. The company can supply no more then 100 kits per month.
2. x=15
S(15)=0.01(15)^2+0.5(15)=9.75
D(15)=0.02(15-100)^2=144.5
3. x=60
S(60)=0.01(60)^2+0.5(60)=66
D(60)=0.02(60-100)^2=32
4. The supply in question 3 is larger then the demand. Supply>Demand- No, because the demanding price is much lower.
5. X^2- Quadratics because in math the quadratic equation of degree 2 is the highest exponent of the equation with the standard as y=ax^2+bx+c
6. See attachment
7. f(x)=0.02(x-100)^2 g(x)=0.01x^2+0.5x
They intersect on the graph at (50, 50) so the products is 50.
8. See Attachment
f(x)=0.02(x-100)^2
g(x)=0.01x^2+0.5x
Related Questions
What does the residual plot tell you about the line of best fit?
Answers
The residual plot tell you about the line of best fit, the closer a data point's residual is to 0, the better the fit.
A residual value is a measure of how much a retrogression line vertically misses a data point. Retrogression lines are the stylish fit of a set of data. You can suppose of the lines as pars; a many data points will fit the line and others will miss.
A residual plot has the Residual Values on the perpendicular axis; the vertical axis displays the independent variable.
A residual plot is generally used to find problems with retrogression. Some data sets aren't good campaigners for retrogression, including
Heteroscedastic data( points at extensively varying distances from the line).Data that's non-linearly associated.Data sets with outliers.Learn more about Residual Plot:
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Compare the function g(x) = 4^3√x + 2 -5 to the cube root parent function f(x)=^3√x. How has the function been transformed from the original parent function?
PLEASE SHOW ALL WORK FOR BRAINLIEST!!
Answers
The transformations from the parent cube root function to generate function g(x) are given as follows:
Vertical stretch by a factor of 4.Shift left by 2 units.Shift down by 5 units.What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.For this problem, the transformations are given as follows:
Multiplication by 4: vertical stretch by a factor of 4.x -> x + 2: shift left 2 units.y -> y - 5: shift down 5 units.More can be learned about translations at brainly.com/question/28174785
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A restaurant serves pancakes that are made from a powdered pancake mix there is a proportional relationship between the number of scoops and powdered pancake mix and the amount of water needed to make them for every four scoops of mix 1/2 quart of water is needed in for every 10 scoops of mixed one and 1/4 quarts of water are needed per day find the constant of proportionality show every step of your work part be right in equation that represents the relationship show every step of your work part Siri describe how you would grab the relationship use complete sentences party how many quarts of water are needed for 12 scoops of pancake mix (I NEED HELP FAST!!)
Answers
Nvm. I got it wrong me self. Srry:(
What is change in demand and change in quantity demanded?
Answers
Answer:
Step-by-step explanation:
Change in demand refers to a shift in the entire demand curve, either to the right or to the left, resulting in a higher or lower demand for a good or service, respectively. It can be caused by a variety of factors, such as changes in consumer preferences, changes in the price of related goods, changes in income, changes in the population, or changes in consumer expectations.
Change in quantity demanded, on the other hand, refers to a movement along the demand curve, resulting from a change in the price of a good or service, without any change in the underlying demand for the good or service. For example, if the price of a good decreases, the quantity demanded of that good will increase, and vice versa. This relationship between price and quantity demanded is known as the law of demand.
In summary, change in demand represents a shift in the demand curve, while change in quantity demanded represents a movement along the demand curve.
Please i need hhelp tysm!!
Answers
Answer:
The answer is 4×7×8 units³
Step-by-step explanation:
This is a really easy question. All you have to do is take a look at the prism and you see the height of 4 units, the width of 8 units, and the length of 7 units. To find the volume of a cube you have to multiply the Length, Width, and Height. Therefore, 7×8×4. Also, it doesn't matter the order of the numbers to multiply. Hope this helps!!
How do you write an inequality in a word problem?
Answers
To indicate that one value is greater than, less than, or equal to another, an inequality in a word problem is written using mathematical symbols like, >, or.
Determine the values that the inequality will compare before using the correct mathematical symbol to express the relationship between them in a word problem. Once the values have been determined, represent the relationship between them using the proper mathematical symbol. For instance, the inequality would be phrased as "x > 5" if the problem stated that "x is greater than 5". Other possible symbols for inequalities are (less than), (less than or equal to), and (more than) (greater than or equal to). It is crucial to always use the appropriate mathematical symbols when creating an inequality since they are needed to indicate the direction of the comparison. Moreover, make sure to incorporate all essential components, including the values being compared, the mathematical symbol, and the equals sign, if required. These procedures can be used to effectively write an inequality in a word problem.
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eric reads an article that says 15 out of 25 adults use their computer everyday. He collects data from a random sample of adults. Out of 1,270 adults, estimate the number of adults who use their computer every day. Please show your work!
Answers
we can estimate that 762 adults in Eric's sample use their computer every day.
What is random sample?Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.
According to question:We can use the proportion from the article to estimate the number of adults who use their computer every day in Eric's sample.
The proportion of adults who use their computer every day from the article is:
15/25 = 0.6
This means that 60% of adults use their computer every day.
To estimate the number of adults who use their computer every day in Eric's sample, we can multiply the proportion by the sample size:
0.6 x 1,270 = 762
So we can estimate that 762 adults in Eric's sample use their computer every day.
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A museum roomcircular in shape, has 5 equally spaced sensors on its walls. There are no dead or overlapping spots along the perimeter of the roomEach sensor has the same angle of detection What is the detection angle of each sensor ? Enter your answer in the box plsss help asap
Answers
Answer: 108 degrees.
Step-by-step explanation:
I think this is how you solve it:
A circle has a total of 360 degrees.
Having 5 equally placed sensors with a certain detection angle means that the sensors form a regular pentagon.
Finding the measure of the interior angles of a regular pentagon can be found using the formula
(180(n-2))/n, with n being the number of vertices of the polygon.
180(5-2)/5 ; 180(3)/5 ; 540/5 = 108
I think this means the detection angle is 108 degrees. Hope this helps!
If you get it wrong I'm terribly sorry T-T
Solve for x
Urgent help pleaseee
Show proofs
Answers
Using the geometric mean theorem, the value of x is approximately 8.2.
What is the Geometric Mean Theorem or Altitude of a Right Triangle Theorem?The right triangle altitude theorem, also known as the geometric mean theorem, is a basic concept in geometry that connects the altitude of a right triangle to the two line segments it creates on the hypotenuse. According to the theorem, the altitude is equal to the geometric mean of the two line segments.
Using the theorem, we have:
14 = √(x * 24)
14² = 24x
196 = 24x
x = 196/24
x ≈ 8.2
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-7 1/7 * (3 2/5)+6 3/5*(-71/7)=x
Answers
Answer:
x = -91 8/35
Step-by-step explanation:
Challenging, but lets take it step by step. We have two sets each of complex fractions being multiplied, and then added. As per PEDMAS, do the multiplication first and then add. [I changed the -71/7 as per your note in the comment section.]
[-7 1/7 * (3 2/5)] + [6 3/5*(-7 1/7)] = x
Convert the two numbers into fractions. Eg., 7 1/7 becomes 50/7 and 3 2/5 becomes 17/5. 6 3/5 becomes 33/5 and 7 1/7 becomes 50/7.
[-50/7 * (17/5)] + [33/5*(-50/7)] = x
Now multiply the numerators and denominators.
[-850/35] + [-2343/35] = x
Now we can add the two fractions since they have the same denominator.
-(3193/35) = x
x = -91 8/35
Are All Fixed Costs Considered Sunk Costs?
Answers
No, not all fixed costs are considered sunk costs. Sunk costs are costs that have already been incurred and cannot be recovered, regardless of any future actions.
Fixed costs, on the other hand, are costs that do not vary with changes in output or sales, such as rent or salaries. While some fixed costs may be sunk costs (such as a non-refundable deposit for a lease), other fixed costs may still be recoverable or avoidable with different decisions, and therefore are not considered sunk costs. Sunk costs are only relevant in decision making to the extent that they cannot be recovered and should not be factored into future decisions.
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Jen’s phone uses a simple algorithm to count the number of strides she takes.
The algorithm looks at the phone’s accelerometer measurements, and counts a
stride each time the acceleration goes from below to above 3 g. Based on the
number of strides counted in the 20-second window shown here, and assuming
that Jen travels 140 cm per stride, what was Jen’s average walking speed, in
meters per second, over the 20-second window? Express your answer as a
decimal to the nearest hundredth.
Answers
Using the relationship between speed, distance and time, Jen's average walking speed was approximately 1.75 meters per second over the 20-second window.
What is Jen's average walking speedTo find Jen's average walking speed, we need to first find the total distance that she walked in 20 seconds. We can do this by multiplying the number of strides she took by the distance of each stride, which is given as 140 cm.
From the graph provided, we can see that Jen took 25 strides in the 20-second window. Therefore, the total distance she walked is:
distance = number of strides * distance per stride = 25 * 140 cm = 3500 cm
To convert this to meters, we divide by 100:
distance = 3500 cm / 100 = 35 meters
Finally, we can find Jen's average walking speed by dividing the total distance by the time it took her to walk it, which is 20 seconds:
average speed = distance / time = 35 meters / 20 seconds ≈ 1.75 meters per second
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Answer: 1.33 m/s
Step-by-step explanation:
We need meters per second, not centimeters per second, so convert the stride of 140 cm to meters:
140 cm times 1 m/100 cm = 1.4 meters.
The number of pulses going above the dashed line for the 3 g threshold to
count as strides are 19. Therefore, a total assumed distance of $19 times 1.4 meters is covered in 20 seconds, making the average speed
19 times 1.4/20 = 19 times 0.07 = 1.33m/s.
let abc~def and the ratio of the respective altitude is 1:3. if the measure of the sides of abc are 3cm,5cm,and 7cm. Then find the measures of the sides of the larger triangle.
Answers
Answer:
Since the ratio of the altitudes of the two triangles ABC and DEF is 1:3, we can say that the altitude of triangle DEF is three times that of triangle ABC.
Let's assume the altitude of triangle ABC is h, then the altitude of triangle DEF is 3h.
Now, we know that the area of a triangle is given by the formula:
Area = (1/2) * base * height
Let's apply this formula to both triangles:
Area of triangle ABC = (1/2) * base * altitude
= (1/2) * 7cm * h
= 3.5h cm^2
Area of triangle DEF = (1/2) * base * altitude
= (1/2) * 7cm * 3h
= 10.5h cm^2
Since the two triangles are similar, their areas are proportional to the squares of their corresponding sides. That is:
Area of triangle ABC / Area of triangle DEF = (AB / DE)^2
Substituting the values, we get:
3.5h / 10.5h = (AB / DE)^2
1/3 = (AB / DE)^2
Taking the square root of both sides, we get:
AB / DE = 1 / sqrt(3)
AB = (1 / sqrt(3)) * DE
Now, we know that the sides of triangle ABC are 3cm, 5cm, and 7cm.
Let's assume that the sides of triangle DEF are a, b, and c.
Since the sides of the two triangles are proportional, we can write:
a / 3 = b / 5 = c / 7 = 1 / sqrt(3)
Solving for a, b, and c, we get:
a = 3 / sqrt(3) = sqrt(3) cm
b = 5 / sqrt(3) = (5 * sqrt(3)) / 3 cm
c = 7 / sqrt(3) = (7 * sqrt(3)) / sqrt(3) = 7 cm
Therefore, the measures of the sides of triangle DEF are sqrt(3) cm, (5 * sqrt(3)) / 3 cm, and 7 cm.
Ex 2: Matt bowled games of 162, 170, and 148. What must he bowl in the next game to
have an average of 155?
Answers
Mat must bowl 140 in the next game.
What is Average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Given:
Matt bowled games of 162, 170, and 148.
Average = 155
let the score on fourth game be x.
So, (162 + 170 + 148 + x)/4 = 155
480 + x= 620
x= 140
Thus, he must bowled 140.
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Suppose you grow, arrange, and sell flowers. If it costs $2,300 to arrange 500 bouquets,
and it costs $3,100 to arrange 600 bouquets, what is your marginal cost in this range?
Answers
Answer:
The marginal cost in this range is $0.50 per bouquet. This can be calculated by finding the difference in total cost of arranging 500 bouquets and 600 bouquets, which is $800, and dividing that by the difference in quantity of bouquets, which is 100. This gives a marginal cost of $0.50 per bouquet.
In ΔRST, r = 530 cm, s = 530 cm, and t=950 cm. Find the measure of ∠T to the nearest 10th of a degree.
Answers
The measure of angle ∠T found in the triangle ΔRST found using the law of cosines is 127.3°.
What is meant by the law of cosines?
The law of cosines, commonly referred to as the cosine formula or cosine rule, is a relation in trigonometry that links the lengths of a triangle's sides to the cosine of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.
If ABC is a triangle, then as per the statement of the law of cosines, we have:
c = [tex]\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}[/tex]
where,
c = length of side c
a = length of side a
b = length of side b
γ = angle opposite c
Given a triangle, ΔRST
The length of side r = 530 cm
The length of side s = 530 cm
The length of side t = 950 cm
According to the law of cosines,
t² =s² + r² - 2.s.r . cos T
950² = 530² + 530² - 2 * 530 * 530 * cos T
902500 = 280900 + 280900 - 561800 * cos T
cos T = -0.6064
m∠T = 127.3°
Therefore the measure of angle ∠T found using the law of cosines is 127.3°.
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In figure below, l || m. Find x.
Answers
Answer:
70
The top line should add up to 180 and both sides other than x are 55 so since 55+55=110 180-110=70
Write a function where y should vary directly with x, then give a real world example for it.
Answers
The function to represent a direct variation relationship between y and x is y = kx.
How to write a function where y should vary directly with x?A direct variation relationship is one where the ratio of two quantities is always constant. In mathematical terms, if y varies directly with x, then there is a constant k such that y = kx.
Below is a function to represent a direct variation relationship between y and x:
y = kx
where k is the constant of proportionality.
A real world example of a direct variation relationship is the relationship between the distance traveled by a vehicle and the time it takes to travel that distance.
If a car travels at a constant speed, then the distance it travels is directly proportional to the time it takes to travel that distance. In mathematical terms, we can write:
distance = rate × time
where the constant of proportionality (rate) is the speed of the car.
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There are 80 people in a choir.
Half of the people in the choir are women
The number of men in he choir is one quarter of the number of women
the number of children in the choir : the number of men in the choir = n:1
Work out the value of n.
You must show how you get your answer.
Answers
Answer:
We know that half of the choir members are women, which means:
Number of women = 80/2 = 40
We also know that the number of men is one-quarter of the number of women, which means:
Number of men = 40/4 = 10
Now, we're given that the ratio of children to men in the choir is n:1. Let's call the number of children in the choir "c".
So, we have:
c : 10 = n : 1
We can cross-multiply to get:
c = 10n
Since we know that the total number of people in the choir is 80, we can set up another equation:
40 (women) + 10 (men) + c (children) = 80
Substituting c = 10n, we get:
40 + 10 + 10n = 80
Simplifying the left side, we get:
50 + 10n = 80
Subtracting 50 from both sides, we get:
10n = 30
Dividing both sides by 10, we get:
n = 3
Therefore, the value of n is 3
3^3x=9^9
Find the answer for x in the following equation...............................
Answers
Answer:
x= 6
Step-by-step explanation:
3^3x = 9^9
3^3x = 3^(2×9)
3^3x = 3^18
3x = 18
3x/3 = 18/3
x = 6
Select the correct phrase to make the statement about 96 multiplied by 11/8
is true.
The product is between 1/8 and 96
Answers
The statement that is true regarding "96 multiplied by 11/8" is: G. The product is greater than 96.
How to Find the Product of Two Numbers?To find the product of 96 and 11/8, we can multiply these two numbers:
96 x 11/8 = (96/1) x (11/8)
= 1056/8
= 132
So the product is 132.
Now we can check which statement is true:
F. The product is less than 11/8. This statement is false, since 132 is greater than 11/8.
G. The product is greater than 96. This statement is true, since 132 is greater than 96.
H. The product is between 11/8 and 96. This statement is false, since 132 is greater than both 11/8 and 96.
I. The product is equal to 96. This statement is false, since we have calculated that the product is actually 132.
The statement that is true is G. The product is greater than 96.
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At the corner store, you can buy 5 super-size granola bars for $10. How much does a single super-size granola bar cost?
Answers
Answer:
3
Explanation:
Based on the given conditions, formulate: 3
Cross out the common factor: 3
get the result:3
Answer: 3
Answer:
2$
Step-by-step explanation:
10/5=2
Are 5 2 13 5 and -5 2 13 -5 inverses? Why or why not?
Answers
Yes multiplying the matrices shows that it is inverse matrix
How to find if they are inversesThe inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix.
Using multiplication of matrices product is sort as follows
Row 1 column 1
= 5 * - 5 + 2 * 13 = -25 + 26 = 1
Row 1 column 2
= 5 * -2 + 2 * 5 = -10 + 10 = 0
Row 2 column 1
= 13 * -5 + 5 * 13 = -65 + 65 = 0
Row 2 column 2
= 13 * 2 + 5 * -5 = 26 + -25 = 1
The identity matrix is
Row 1 column 1 Row 1 column 2 1 0
Row 2 column 1 Row 2 column 2 0 1
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A random sample of 20 seventh graders found that 14 participate in a local contest making duct-tape wallets. Complete parts a through c.
a. If there are 500 seventh graders, write a proportion to estimate the number of seventh graders, n, who participate in the contest.
The proportion
14 n
20 500
=
can be used to estimate the number of seventh graders who participate in the contest.
b. Solve the proportion to estimate the number of seventh graders who participate in the contest.
About seventh graders participate in the contest.
(Type a whole number.)
Answers
Answer:
350
Step-by-step explanation:
Using the proportion from part (a):
14/n = 20/500
Cross-multiplying, we get:
20n = 14 × 500
Dividing both sides by 20, we get:
n = 14 × 500 / 20 = 350
Therefore, about 350 seventh graders participate in the contest.
Can you help me answer this
Answers
Answer: C
Step-by-step explanation:
Jimmy, Jimbo and Jim Bob are all GT Algebra II students. It takes Jimmy 8 minutes to solve a 3-variable substitution problem without a calculator. Together, it takes Jimbo and Jim Bob 6 minutes to solve a 3-variable substitution problem without a calculator. If Jim Bob can solve a problem by himself in 14 minutes, how long would it take Jimbo to solve a problem alone?
It would take Jimbo
Question Blank 1 of 1
type your answer...
minutes to solve a problem alone.
Answers
Jimbo approximately 5.09 minutes to solve the problem by himself.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The amount of time it takes Jimbo to solve the problem by himself = x.
The amount of time Jimmy takes to solve the problem.
= 8 minutes
The amount of time it takes Jimmy to solve the problem by himself.
= 1/8
Jimbo and Jim Bob together can solve the problem in 6 minutes, so their combined rate of work is 1/6 of the problem per minute.
The amount of time it takes Jim Bon to solve the problem by himself.
= 1/14
Now,
We can make an equation:
1/8 + 1/x + 1/14 = 1/6
We can solve for x to find the amount of time it would take Jimbo to solve the problem by himself.
1/8 + 1/x + 1/14 = 1/6
Multiply both sides by 168x.
We get,
21x + 168 + 12x = 28x
33x = 168
x = 168/33
x = 5.09
Thus,
Jimbo approximately 5.09 minutes to solve the problem.
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A contact center provides incentives based on the number of sales achieved by its
representatives. Ross made 27 sales in 3 days. His colleague, Mona secured 49 sales in
one week. Who achieved a higher sales target per day? HELPP
Answers
Ross achieved a higher sales target.
What is a fraction?A fraction is a number which represents the part of a whole or collection of objects. It is in the from of [tex]\frac{a}{b}[/tex] where a represents the numerator part and the b represents the denominator parts.
A contact center provides incentives based on the number of sales achieved by its representatives.
Ross made 27 sales in 3 days.
Sales per one day =[tex]\frac{27}{3}=9.[/tex]
Mona secured 49 sales in one week
Sales per day =[tex]\frac{49}{7}=7[/tex]
Therefore, in one day sale of Ross is 9 and sale of Mona is 7.
Hence, Ross achieved a higher sales target.
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a basketball court is 46 feet wide and 84 feet long. the court has a border that is 10 feet wide. the cost of a hardwood floor is $9 per square foot. how much will it cost to put a new floor on both the court and its border?
Answers
The total cost to put a new floor on both the court and its border is; $61776
How to solve Algebra Word problems?The parameters given are;
Initial length = 84 ft
Initial Width = 46 ft
Now, since the court has a border that is 10 ft wide, it means that we will add 20 ft to the initial length and width to get the new measurements. Thus;
New length = 84 + 20 = 104 ft
New Width = 46 + 20 = 66 ft
Thus;
Area = 104 * 66
Area = 6864 sq.ft
Thus;
Total Cost = 6864 * 9
= $61776
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write 5x10^3 x 9x10^7in stanadred form
Answers
Answer:
Step-by-step explanation:
5 x 10^3 x 9 x 10^7 can be written as follows in standard form:
5 x 10^3 = 5 x 10^3 x 1 = 5 x 10^3
9 x 10^7 = 9 x 10^7 x 1 = 9 x 10^7
So,
5 x 10^3 x 9 x 10^7 = (5 x 10^3) x (9 x 10^7) = 45 x 10^(3 + 7) = 45 x 10^10 = 4.5 x 10^11
In standard form, the coefficient (45) is written as a number between 1 and 10, and the exponent (10) gives the number of places the decimal point must be moved. So, 4.5 x 10^11 is written in standard form as 4.5 x 10^11.
Answer:
Step-by-step explanation:
45*10^10=4.5*10^11
Write (5-√5)² in the form a + b√5, where a and b are intergers
Answers
The required expression is 30 - 10√5 which is in the form a + b√5, where a = 30 and b = -10.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression is given in the question, as follows:
(5-√5)²
Expanding the above expression,
(5)² + (√5)² - 2 × 5 × √5
25 + 5 - 10√5
30 - 10√5
Compare the above expression to the form a + b√5, and we get
a = 30 and b = -10
Thus, the required expression is 30 - 10√5.
Learn more about Expressions here :
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