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Answer:
Step-by-step explanation:
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Step-by-step explanation:
[tex]{ \tt{ \sqrt{ \frac{3 {a}^{2} }{10 {b}^{6} } } }} = { \tt{ \frac{ {(3a {}^{2}) }^{ \frac{1}{2} } }{ {(10b {}^{6} )}^{ \frac{1}{2} } } }} \\ \\ = { \tt{ \frac{a \sqrt{3} }{ {b}^{3} \sqrt{10} } }} \\ \\ = { \tt{ \frac{a \sqrt{3} }{ {b}^{3} \sqrt{10} } }}[/tex]
Related Questions
Blowlers that score at least 228 point will make it to the next round
Answers
Answer:
p ≥ 228
Step-by-step explanation:
p ≥ 228
This inequality means the Bowlers have to score at least 228 points to move on.
Hope this helped!
I need help. A explanation and how you got the answer would be amazing. Thx
Answers
Answer: What is this equation
Step-by-step explanation:
difference between repeating & terminating decimal
Answers
Answer: If you end up with a remainder of 0, then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.
Step-by-step explanation:
I hope that this helped! :)
Consider the following statement. If a and b are any odd integers, then a2 + b2 is even. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Suppose a and b are any odd integers. By definition of odd integer, a = 2r + 1 and b = 2r + 1 for any integers r and s. By definition of odd integer, a = 2r + 1 and b = 2s + 1 for some integers r and s. By substitution and algebra, a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 +52) + 2(r + s) + 1]. 2r2 + 2s2. Then k is an integer because sums and products of integers are integers. Let k = Thus, a2 + b2 = 2k, where k is an integer. Suppose a and b are any integers. Let k = 2(r2 + 52) + 2(r + 5) + 1. Then k is an integer because sums and products of integers are integers. Hence a2 + b2 is even by definition of even. By substitution and algebra, a2 + b2 (2r)2 + (25)2 = 2(2r2 + 2s2). Proof: 1. ---Select--- 2. ---Select-- 3. ---Select--- 4. ---Select--- 5. ---Select--- 6. ---Select-
Answers
If a and b are any odd integers, then a2 + b2 is even.
And the proof for that we can explain as,
So we have a and b are any odd integers. By definition of odd integer,
a = 2r + 1 and b = 2r + 1 for any integers r and s.
By definition of odd integer,
a = 2r + 1 and b = 2s + 1 for some integers r and s.
By substitution and algebra,
a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 +52) + 2(r + s) + 1]. 2r2 + 2s2.
Then k is an integer because sums and products of integers are integers. Let k = Thus, a2 + b2 = 2k, where k is an integer.
Proof: 1. Suppose a and b are any odd integers.
Proof:2. By definition of odd integer, a = 2r + 1 and b = 2r + 1 for any integers r and s.
Proof:3. By substitution and algebra, a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 + s2) + 2(r + s) + 1].
Proof:4. Let k = 2(r2 + s2) + 2(r + s) + 1. Then k is an integer because sums and products of integers are integers.
Proof:5. Hence a2 + b2 is even by definition of even.
Proof:6. Thus, a2 + b2 = 2k, where k is an integer.
Hence we proved that "If a and b are any odd integers, then a2 + b2 is even".
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A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=−6x ^2 +190x−826
Answers
As a result, in order to make the most money, the widgets must be sold for $15.83, to the nearest cent.
What are a few selling price examples?The cost that consumers pay for a single piece of a good is known as the price at which it is sold. For instance, if a company produces lamps, the sales unit price is indeed the cost to customers of a single lamp. We must identify the x value that maximizes the profitability function y = -6x² + 190x - 826 in order to estimate the selling price for widgets that will yield the highest profit.
Calculus can be used in this process. The critical points, or maximum and lowest values of the function, can be found by taking the derivatives of a profitability function in relation to x and setting it to zero. The derivative test can then be used to assess if the crucial point is indeed a maximum or even a minimum. If we take the profit function's derivative with regard to x, we get:
y' = -12x + 190
By setting y' to zero and figuring out x, we obtain:
-12x + 190 = 0
x = 15.83
The critical value of x is therefore 15.83.
We must compute the second derivative of a profit function with respect to x to determine if this critical point is indeed a maximum or a minimum:
y'' = -12
The critical point at x = 15.83 corresponds to the greatest value of the money demand function since y" is negative. In order to optimize the profit, the widgets must be sold for $15.83, to the nearest cent.
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A sandwich shop owner observed the first 100 sandwich orders of the day. The data that the owner obtained is given in the table.
Type of Sandwich Number of Customers
Vegetarian 30
Turkey 20
Ham 35
Chicken 15
Which of the following circle graphs correctly represents the data in the table?
a circle graph with four sections, labeled turkey 30 percent, ham 20 percent, chicken 35 percent, and vegetarian 15 percent
a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent
a circle graph with four sections, labeled chicken 30 percent, vegetarian 20 percent, turkey 35 percent, and ham 15 percent
a circle graph with four sections, labeled ham 30 percent, chicken 20 percent, vegetarian 35 percent, and turkey 15 percent
Question 6(Multiple Choice Worth 2 points)
Answers
The circle graphs which correctly represents the data in the table is "a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent"
The correct answer choice is option B.
Which of the following circle graphs correctly represents the data in the table?Type of Sandwich Number of Customers
Vegetarian 30
Turkey 20
Ham 35
Chicken 15
Total number of customers = 30 + 20 + 35 + 15
= 100
Percentage of each sandwich:
Vegetarian = 30/100 × 100
= 30%
Turkey = 20/100 × 100
= 20%
Ham = 35/100 × 100
= 35%
Chicken = 15/100 × 100
= 15%
Therefore, a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent represents the table.
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A. x/4 +1= -3 B. x +4= -12 How can we get equation b from equation a? A. Add/subtract the same quantity to/from both sides B. Add/subtract a quantity to/from only one side C. Multiply/divide both sides by the same non-zero constant D. Multiply/divide both sides by the same variable expression
Answers
Equation A is converted to equation B by multiplying or dividing both parts by a non-zero constant. Thus, option C is correct.
What are some integers non-constant?If a function accepts more than one value, it is said to be nonconstant (if there is more than one element in its range).
As an illustration, a polynomial with real numbers as its domain and codomain becomes nonconstant. Just observing that and means the function accepts at least two distinct values allows us to demonstrate this.
Starting with the variable solely on a single side of the equation, we can start resolving equation A for x:
[tex]x/4 + 1 = -3\sx/4 = -3 - 1\sx/4 = -4[/tex]
We obtain x = -16 by multiplying both of the equation's sides by 4.
Starting with the variable with one of the equation's equations, we can solve equation B for x:
[tex]x + 4 = -12[/tex]
Therefore, We obtain [tex]x = -16[/tex] by deducting [tex]4[/tex] from both of the equation's components.
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The general form of the equation of a circle is x2 y2 8x 22y 37 = 0. the equation of this circle in standard form is (x )2 (y )2 = . the center of the circle is at the point ( , ).
Answers
The centre οf the circle is (-4, -11).
What is a circle's general equatiοn?We knοw that the general equatiοn fοr a circle is (x - h)² + (y - k)² = r² with (h, k) representing the centre and r representing the radius. Sο multiply bοth sides by 21 tο get the cοnstant term οn the right side οf the equatiοn. Then, fοr the y terms, cοmplete the square.
Tο write a circle equatiοn in standard fοrm, we must cοmplete the square fοr bοth x and y.
Tο begin, cοnsider the fοllοwing equatiοn: x²+ y² + 8x + 22y + 37 = 0.
Let's separate the terms with x frοm the terms with y:
[tex](x^2 + 8x) + (y^2 + 22y) + 37 = 0[/tex]
We add (8/2)² = 16 tο bοth sides tο cοmplete the square fοr x: (x²+ 8x + 16) + (y² + 22y) + 37 = 16
Simplifying the left side οf the equatiοn and cοmbining cοnstants οn the right:
[tex](x + 4)^2 + (y^2 + 22y + 121) = 16 - 37 - 121\s(x + 4)^2 + (y + 11)^2 = 50[/tex]
The equatiοn can nοw be written in standard fοrm:
[tex](x + 4)^2/50 + (y + 11)^2/50 = 1[/tex]
The circle's centre is (-4, -11).
As a result, the standard fοrm οf the circle's equatiοn is (x + 4)²/50 + (y + 11)²/50 = 1, and the circle's centre is (-4, -11).
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QUESTION 5
What portion of a whole does two sevenths of five ninths represent?
Answers
Answer:
10/63
Step-by-step explanation:
Equation: 2/7 * 5/9
Multiply the numerators: 2*5=10
Multiply the denominators: 7*9=63
Your answer: 10/63
How can I use the compound angle formula to write sin 165degrees as surds?
Answers
We may approximate the sin 165 angles using trigonometric formulas as: tan 165°/(1 + tan2(165°)) (1-cos2(165°))...
Trigonometric identities enable the expression of sin 165° as,
Sin (15°) = sin(180° - 165°)
(-sin 180 + -sin 165) = -sin 345
cos(-75°) = cos(-90° - 165°)
(90 + 165)/255 = -cos 255
Explanation: We know that cos(165) is negative and sin(165) is positive because 165 is in QII. We will use 330 with in half angle formulae because 165=3302.
165 degrees are somewhere between 90 and 180 degrees. Hence, it has an acute angle.
Hence, the 165° angle's addition is 15°. Q. Below are a few angles' measurements.
525 is a positive number of interactions angle, while 195 is a negative coterminal angle.
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how does the graph of the function g(x) = 2x – 3 differ from the graph of f(x) = 2x?
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Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)
the national football league (nfl) records a variety of performance data for individuals and teams. to investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 nfl teams for one full season.
Answers
The National Football League (NFL) is an American football league that is based in the United States. The NFL records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 NFL teams for one full season.The data collected by the NFL shows that passing has a significant impact on the percentage of games won by a team. Teams that have a higher average number of passing yards per attempt tend to win more games than those with a lower average. Additionally, teams that have a lower number of interceptions thrown per attempt also tend to win more games than those with a higher number of interceptions thrown per attempt.The data also shows that the conference a team plays in does not have a significant impact on the percentage of games won by a team. This means that a team's conference is not a good indicator of its performance.The NFL should continue to record data on passing to help teams improve their performance. Coaches can use this data to identify areas for improvement and develop strategies to help their teams win more games.
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the number of students using the cafeteria's healthy lunch line can be found by solving the inequality 1/5s - 51 < 20. How many students use this lunch line?
Select the answers from the drop-down list to correctly complete the sentence
There are ___ students ___ that use this lunch line
1. 142
2. 62
3. 36
4.35
1. or more
2. or fewer
PLEASE HELP NEEDED!!!
Answers
The answer of the given question based on the the number of students using the cafeteria's healthy lunch line can be found by solving the inequality 1/5s - 51 < 20, the correct answer is (1) 142 , (1) or more.
What is Equation?An equation is mathematical statement that shows equality of two expressions, typically separated by equal sign. Equations are used to express relationships between variables and to solve problems in various fields of mathematics, science, and engineering. In essence, an equation is representation of real-world scenario or problem in mathematical terms.
The variables in equation can take on different values, and equation remains true regardless of the values chosen for variables. Solving equation means finding values of the variables that make equation true.
Equations can be linear, quadratic, polynomial, exponential, logarithmic, or trigonometric, among other types. They are fundamental tool in mathematics and have numerous applications in fields like physics, engineering, economics, and finance.
There are 155 students or more students that use this lunch line.
The correct answer is 1. or more.
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Michaela holds her state high school record for the 500-meter freestyle swimming event. She can swim the event in 4 minutes and 50 seconds. At this same rate, how far will she swim in 10 minutes?
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Answer: To solve the problem, we need to use the given time to find Michaela's swimming rate in meters per second, and then use that rate to calculate the distance she will swim in 10 minutes.
1 minute = 60 seconds
4 minutes and 50 seconds = 4 x 60 + 50 = 290 seconds
So, Michaela's rate is:
distance / time = x / 290 seconds
where x is the distance she can swim in 290 seconds.
Simplifying the equation:
x = distance = (time x distance) / time = (290 seconds x distance) / 290 seconds = distance
We know that Michaela can swim 500 meters in 290 seconds:
500 meters / 290 seconds = 1.724 meters per second
Therefore, in 10 minutes (600 seconds), she will swim:
distance = rate x time = 1.724 meters/second x 600 seconds = 1034.4 meters
So, Michaela will swim 1034.4 meters in 10 minutes.
Step-by-step explanation:
Peter buys 30 apples at R5. 00 each. He sell each apple for R7. 0. How much profit does he makes?
Answers
Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.
Peter buys 30 apples at a value of R5.00 every, for a total price of R150.00. He then sells every apple at R7.00, for a complete sales of R210.00.
To calculate his earnings, we subtract his price from his revenue.
profit = revenue - cost
In this case, his income is R210.00 - R150.00 = R60.00. this means that Peter makes a profit of R60.00 from selling 30 apples.
Consequently, Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.
The earnings made with the aid of Peter is the distinction between the sales generated via the income and the price of buying the apples. with the aid of subtracting the cost from the revenue, we are able to see the earnings he has made. This easy calculation can be used by organizations to decide their earnings and to make choices approximately pricing and stock.
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One little cat can eat a bag of treats in 15 minutes while another cat can eat the same bag of treats in 10 minutes. What part of the bag can they eat together in the given time? 1 minute. 2 minute, and 3 min
Answers
Answer:
1 minute = 1/6
2 minutes = 1/3
3 minutes =1/2
Step-by-step explanation:
one can eat a bag in 15 minutes so in 1 minute this cat can eat 1/15 of a bag
the other cat can eat a bag in 10 minutes so in 1 minute the cat can eat 1/10 of the bag
to find how much they can eat in 1 minute, add 1/10 and 1/15 which gives you 1/6. to find 2 and 3 minutes just multiply by 1/6 by 2 or 3
stuck on this question need some help
Answers
Answer:
1. The graphs of f(x) and h(x) are both quadratic functions with a minimum point. However, the minimum point of f(x) is located at (6,0), while the minimum point of h(x) is located at (2,3).
2. The graphs of g(x) and h(x) both open upwards and are quadratic functions. However, the vertex of g(x) is located at the origin (0,0), while the vertex of h(x) is located at (2,3).
3. The graph of g(x) is a simple parabola that opens upwards, while the graphs of f(x) and h(x) are more complex parabolas with a minimum point and an upward opening. The graph of f(x) is centered at (6,0), while the graph of h(x) is centered at (2,3).
(a)
A Chinese restaurant offers 10 different lunch specials. Each weekday for one week, Fiona goes to the restaurant and selects a lunch special. How many different ways are there for her to select her lunches for the week? Note that which lunch she orders on which day matters, so the following two selections are considered different.
One possible selection:
Mon: Kung pao chicken
Tues: Beef with broccoli
Wed: Kung pao chicken
Thurs: Moo shu pork
Fri: Beef with broccoli
A different selection:
Mon: Beef with broccoli
Tues: Kung pao chicken
Wed: Kung pao chicken
Thurs: Moo shu pork
Fri: Beef with broccoli
(b)
Now suppose that in addition to selecting her main course, she also selects between water or tea for her drink. How many ways are there for her to select her lunches?
Answers
There are 6 ways for the student to select her lunch when she chooses from the given main course selection and chooses between water or tea for her drink selection. 3 × 2 = 6 ways.
The problem is about counting the number of ways that can be possible to select the meal for the student.
The student selects one main course and one drink. The main course consists of one of the following:
beef with broccoli, moo shu pork, or chicken with cashew. She can select water or tea for her drink. Therefore, the total number of ways that can be possible to select her lunch is obtained by multiplying the number of options for each course.For instance, there are three options for main course selection, and two options for drink selection. Therefore, the total number of ways that she can select her lunch
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sebi rides his bike at a constant rate of 10 mph by a linear equation to represent how far he travels
Answers
The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.
what is linear equation ?The basic form of a linear equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. Many real-world situations, such as the connection between a product's price and the number of sales, or the relationship between a person's age and height, can be modelled using linear equations.
given
Let t be the number of hours and d be the number of miles that Sebi goes. Since Sebi consistently travels at 10 mph on his bicycle, we can apply the following equation:
Distance is determined by rate and duration.
When we change the numbers, we obtain:
d = 10t
The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.
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A champion race horse can run 10 000 metres in 60 minutes. What is the average speed in km/h 10,000.show working out.
a champion racehorse runs 10000 metres in 60 minutes what is the average speed in km/h show working out
Answers
Answer: We have one km being covered in one minute. So how many km do we cover in one hour? Remember, there are 60 minutes in one hour. Do you think it might be 60 km in one hour? Can you say that a different way, say number of km in one hour? 60 km in one hour. Close. Very good. Now let’s clean up your answer and just say 60 km per hour or 60 ``````````````````````.
Help me please
For problems 4-9,find the circumference.Round your answer to the nearest hundredth.Use 3.14 for п
Answers
The circumference of circle has the formula 2xPixr
where, r = radius of circle.
The relation between radius (r) and diameter (d) of the circle is d = 2r
Circumference = pi x diameter = 3.14 x 25m = 78.5m
Circumference = 2 x pi x radius = 2 x 3.14 x 4.5cm = 28.26cm
Circumference = 2 x pi x radius = 2 x 3.14 x 28in = 175.84in
Circumference = pi x diameter = 3.14 x 19ft = 59.66ft
Circumference = 2 x pi x radius = 2 x 3.14 x 3mm = 18.84mm
Circumference = 2 x pi x radius = 2 x 3.14 x 35in = 219.8in
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Andrew can row his boat downstream 15 miles in the same amount of time as it takes him to row upstream 8 miles. If the current in the river is 2 mph, how fast can Andrew row in still water? (round to the tenth)
hint: t=d/t
Answers
The time that Andrew can use to row his boat in still waters would be = 5.75 hrs.
How to calculate the speed of the boat in still water?The speed can be defined as the scalar quantity that shows that amount of distance that is covered with respect to time.
The formula that can be used to calculate speed = distance/time.
The speed of the current in the river = 2 mph
The distance covered downstream = 15miles
The distance covered upstream = 8
average distance = 15+8/2 = 11.5 miles
Given 2 miles = 1 HR
11.5 miles = X
Make X the subject of formula;
X = 11.5×1/2
= 5.75 hrs
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A.14.5 square inches
B.29 square inches
c.20.5 square inches
d.32 square inches
Answers
Answer:
d. 32 in.²
Step-by-step explanation:
Bottom face: 6 in. × 0.5 inch
Side faces: 2 × 5 in. × 0.5 in.
Front and back faces: 2 x 6 in. × 4 in. / 2
surface area = 3 in.² + 5 in.² + 24 in.²
surface area = 32 in.²
If a matrix A is 5 x 3 and the product AB is 5 x 7, what is the size of B?
Answers
The size of the the matrix B if a matrix A is 5x3 and the product AB is 5x7 is B =[3x7].
Two matrices can only be multiplied if the first matrix has the same number of columns as the second matrix has. If the first matrix has dimensions of a x b and the second matrix has dimensions of c x d, then b = c and their product will have dimensions of a x d.
Let A is a 3 x 5 matrix and B is a 5 x 7 matrix
We know that matrix multiplication of A and B is possible if
Number of columns of A = Number of rows of B
Since in the given problem
Number of columns of A = Number of rows of B = 5
So the product is possible
Now the product AB is a matrix of order 3 × 7
Now the order of the product AB is 3 × 7
If a 3 x 5 matrix is multiplied by a 5 x 7 matrix then their product is a matrix of order 3 × 7.
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what 52,437 rounded to the nearest hundred
Answers
Answer: 52,400
Step-by-step explanation:
help me fast please I need good grades
Answers
A smaller sample size can offer a good estimate of the mean. The expressions population of working adults is not too vast to estimate the mean of the entire group using a sample.
What is expression ?An expression in mathematics is a collection of numbers, variables, and complex mathematical (such as addition, subtraction, multiplied, division, multiplications, and so on) that express a quantity or value.
Expressions might be as basic as [tex]"3 + 4"[/tex] or as complicated as [tex]"(3x2 - 2) / (x + 1)"[/tex] . They may also contain functions like "sin(x)" or "log(y)".
Expressions can indeed be evaluated by swapping values for the variables and performing the algebraic calculations in the order specified.
If [tex]x = 2[/tex] , for example, the formula [tex]"3x + 5"[/tex] equals [tex]3(2) + 5 = 11[/tex] . Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
If Fran chooses a random sample of the working adult population in her town, the mean for that group will most likely be close to the mean for the entire group.
Therefore, A smaller sample size can offer a good estimate of the mean. The population of working adults is not too vast to estimate the mean of the entire group using a sample.
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Mrs. Murphy by balloons garlands paper lanterns and banners to decorate a school party she got three times as many bags of balloons as paper lanterns seven more garlands than paper lanterns and for banners she paid $5. 25 for each banner $6. 50 for each paper lantern five dollars for each bag of balloons and $3. 50 for each garland how many of each kind of decoration did she purchase if she paid $145. 50
Answers
She purchased 4 Paper Lanterns, 12 Bags of Balloons, 11 Garlands, and 4 Banners if she paid $145. 50.
The cost of lanterns is $6.50
Mrs Murphy bought 4 lanterns
Multiply the cost of one lantern ($6.50) by the number of lanterns bought (4) 6.50 multiplied by 4 equals 26
The cost of banners is $5.25
Mrs Murphy bought 4 banners
Multiply the cost of one banner ($5.25) by the number of banners bought (4) 5.25 multiplied by 4 equals 21
Mrs Murphy bought 3 times as many balloons as she did lanterns
So, you multiply the number of lanterns bought (4) by 3
This gives 12
We then multiply the cost of each balloon ($5.00) by the number of balloons bought (12)
5.00 multiplied by 12 equals 60
Mrs Murphy bought 7 more garlands as she did lanterns
So, we add 7 to the number of lanterns bought (4)
7 plus 4 equals 11
To find the cost of the total garlands bought
We multiply the cost of each garland ($3.50) by the number of garlands bought (11)
3.50 multiplied by 11 equals 38.5
Now we can add up the costs of all the items
26+21+60+38.5=145.50
145.50 was the total amount she spent so we know it is the correct answer.
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Sophie bikes at the speed of s mph. Her friend rana is slower, her biking speed is only r mph. Today both girls went on 20 mile trip. Each girls was biking at there usual speed. How long did Sophie wait for rana at the finish line
Answers
The amount of time Sophie waited for Rana at the finish line can be calculated as 20/r - 20/s, where r is Rana's biking speed in mph and s is Sophie's biking speed in mph.
To find out how long Sophie waited for Rana at the finish line, we need to calculate the time it takes for each of them to complete the 20 mile trip. The time taken can be calculated using the formula: time = distance / speed.
Sophie's time to complete the trip can be calculated as follows:
time taken by Sophie = distance / speed of Sophie
time taken by Sophie = 20 / s
Similarly, Rana's time to complete the trip can be calculated as:
time taken by Rana = distance / speed of Rana
time taken by Rana = 20 / r
Since Sophie waits for Rana at the finish line, she would have to wait for the amount of time it takes for Rana to finish the trip. Therefore, the total waiting time would be the time taken by Rana to complete the trip minus the time taken by Sophie to complete the same trip:
waiting time = time taken by Rana - time taken by Sophie
waiting time = 20/r - 20/s
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A rectangular pyramid has a volume of 100 cm? What is the volume of a rectangular prism in cubic centimeters with the same dimensions?
Answers
The volume of the rectangular prism with the same dimensions as the rectangular pyramid is 300 cubic centimeters.
What is rectangular prism?A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional solid shape with six rectangular faces, where each pair of opposite faces are congruent (i.e., have the same dimensions) and parallel to each other.
The rectangular prism is defined by three dimensions: length, width, and height. The length is the longest dimension of the prism, the width is the second-longest dimension, and the height is the shortest dimension, perpendicular to both length and width. The volume of a rectangular prism is given by the formula: V = l * w * h.
In the given question,
Let's assume that the rectangular pyramid has a rectangular base with length l, width w, and height h. The formula for the volume of a rectangular pyramid is given by:
V_pyramid = (1/3) * base_area * height
where base_area = l * w is the area of the rectangular base of the pyramid.
We know that the volume of the rectangular pyramid is 100 cm^3, so we can write: 100 = (1/3) * l * w * h
Simplifying this equation, we get:
l * w * h = 300
Now, let's find the volume of the rectangular prism with the same dimensions. The formula for the volume of a rectangular prism is given by: V_prism = base_area * height
where base_area = l * w is the area of the rectangular base of the prism.
Since the rectangular prism has the same dimensions as the rectangular base of the pyramid, its volume is given by: V_prism = l * w * h
Substituting the value of l * w * h from the equation we derived earlier, we get: V_prism = 300
Therefore, the volume of the rectangular prism with the same dimensions as the rectangular pyramid is 300 cubic centimeters.
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design a context-free grammar (cfg) for the following language (20 points). if your grammar has multiple variables, please briefly describe the strings derived by each variable of your grammar (5 points, please see the lecture notes on cfg design for examples). l
L={aibi| 3i=0, j >=0}
Answers
Answer: 67
Step-by-step explanation:67 x1