Using the provided questions with the values of sets A,B and C, Applying the cartesian product, The answer is {(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)} and so on.
What is a mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operations that defines a specific value or a set of values. Examples of mathematical expressions include 2+3, x^2+y^2, and sin(x) + cos(y). These expressions can be evaluated to find a specific numerical value or they can be simplified, rearranged or manipulated using algebraic rules.
What do you mean by cartesian product?In set theory, the Cartesian product of two sets A and B, denoted A x B, is the set of all ordered pairs (a, b) where a belongs to A and b belongs to B. It is the set of all possible combinations of elements from the two sets. For example, if A = {1, 2} and B = {a, b}, then A x B = {(1, a), (1, b), (2, a), (2, b)}. The Cartesian product is a fundamental concept in set theory and is used in many branches of mathematics, including linear algebra, topology, and graph theory. It can be extended to more than two sets, for example, the Cartesian product of three sets A, B, and C is denoted A x B x C and is the set of all ordered triples (a, b, c) where a belongs to A, b belongs to B, and c belongs to C.
1. A = {1,2,3}, B = {4,5,6} C = {a, b}
a. A x B = {(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)}
b. B x C = {(4,a),(4,b),(5,a),(5,b),(6,a),(6,b)}
c. A x C = {(1,a),(1,b),(2,a),(2,b),(3,a),(3,b)}
2. A = (3,6,9), B = (4,5,6)
a. A x B = {(3,4),(3,5),(3,6),(6,4),(6,5),(6,6),(9,4),(9,5),(9,6)}
b. Required relation = {(3,4),(3,5),(3,6)}
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Which package of hot dogs can be divided into 5 equal groups without a remainder?
A 126 B 205 C 79
Answer:
B can
Step-by-step explanation:
126 and 79 are not divisible by 5, only numbers that end in 0 or 5 can
12. Ben has $900 he spends $350 in games and $500 for a pet. How much money he has left explain.
Answer:
$50
Step-by-step explanation:
900 - 350 - 500
50
Which expression represents how much money you will have in one year if 6%is compounded. Quarterly on a 800$ for one year?
The expression that represents how much money that will be in the account is A = 800.00(1 + 0.015)⁴.
How to express compound interest equation?The expression that represents how much money you will have in one year if 6% is compounded quarterly on a 800$ for one year is as follows:
Hence, using the compound interest formula,
A = P + I
where
I = interestP = principalHence,
r = 6/100
r = 0.06 rate per year
Then solve the equation for A
[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]
where
r= ratep = principalt = timeTherefore,
A = 800(1 + 0.06/4)⁴ˣ¹
Therefore, the expression is A = 800(1 + 0.015)⁴
A = $849.09
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Classify the equation 6(x+2)=(5x+7)
Answer:
x = -5
Step-by-step explanation:
6(x+2) = (5x+7)
6x + 12 = 5x + 7
x = -5
Write in standard form if needed, then classify the polynomial.
25-9m^2 -m + 4m^3
The polynomial in the standard form is 4m³ - 9m² - m + 25. Then the polynomial is a cubic polynomial.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The polynomial is given below.
⇒ 25 - 9m² - m + 4m³
Convert the polynomial into its standard form. Then we have
⇒ 25 - 9m² - m + 4m³
⇒ 4m³ - 9m² - m + 25
The degree of the polynomial is 3. Then the polynomial is a cubic polynomial.
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Task 4:
Martin has a triangular garden patch in his backyard, represented by AEXY. He wants to extend the garden by creating a new
border DF that is parallel to XY, where XY = 0.64. The length of XY on the existing border is 16 feet.
DF
EY= (14x-7.5), YF = (6x), and EX = (12x-7).
E
X
O
F
(A) What is the length of DF along the new border? DF =
(B) Solve for the value of x.
X =
(C) What is the length of XD? Do not round.
XD =
Do not round.
Do not round.
Do not round.
The length of DF along the new border is 41 feet. The value of x is 8.5. The length of XD is 95 feet.
What are Similar Triangles?Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.
Triangular garden patch in his backyard, represented by AEXY.
Border DF that is parallel to XY, where XY/DE = 0.64.
The length of XY on the existing border is 16 feet.
EY = (14x-7.5), YF = (6x), and EX = (12x-7).
We can find the length of DF by using the ratio given in the problem. Since XY/DE = 0.64, we have DE = XY / 0.64 = 16 / 0.64 = 25.
Therefore, the length of DF is 25 + 16 = 41 feet.
To find the value of x, we can use the equations given in the problem. We are told that EY = 14x - 7.5 and YF = 6x, so adding these equations gives us the length of EF = EY + YF = 14x - 7.5 + 6x = 20x - 7.5.
We are also told that EX = 12x - 7, so adding this to EF gives us the length of FX = EX + EF = 12x - 7 + 20x - 7.5 = 32x - 7.5.
We know that FX is the same as DF, so 32x - 7.5 = 41.
Solving this equation for x gives us x = 8.5.
Finally, to find the length of XD, we can use the equation EX = 12x - 7. Substituting in the value of x that we found above, we get :
EX = 12(8.5) - 7 = 102 - 7 = 95.
Therefore, the length of XD is 95 feet.
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0.5 (-2 + 4d) -13 for d
Step-by-step explanation:
-13 x 4 = -52
-52 x 0.5 = -25
-2 x 0.5 = -1
-1 + -25 = -26
pat has of feneing to enclose three identical stalls behind the barn. as shown. what dimensions will produce a maximum area for each stall? a) label correctly the given diagram at the side with chosen yariables that must be identified. use let statements. b) express the area of the stalls as a function of its width. c) determine the domain and range of this area function. show your work. domain: range: d) determine the dimensions th
The maximum area for each stall can be achieved when the width and length are equal, so the dimensions must be any value greater than 0.
a) Let x = width of each stall, y = length of each stall
b) Area of each stall = xy
c) Domain: x > 0, y > 0
Range: all real numbers
d) To maximize the area of each stall, we must maximize the product of x and y. Taking the derivative of xy with respect to both x and y, we get y = x. Therefore, the maximum area will be achieved when the width = length = x. Therefore, the dimensions that will produce the maximum area for each stall is x = x = any value greater than 0 so the dimensions must be any value greater than 0.
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The complete question is
pat has of feneing to enclose three identical stalls behind the barn. as shown. what dimensions will produce a maximum area for each stall? a) label correctly the given diagram at the side with chosen variables that must be identified. use let statements. b) express the area of the stalls as a function of its width. c) determine the domain and range of this area function. show your work. domain: range: d) determine the dimensions thst would produce a maximum area for each stall.
xavier is chopping 60 tomatoes for dinner. it took him 3 minutes to chop the first 15.what percent of the tomatoes has he chopped so far
The percentage he has chopped is 25%
How to determine the percentage he has choppedFrom the question, we have the following parameters that can be used in our computation:
Total number of tomatoes = 60
Total number of chopped tomatoes = 15
The percentage he has chopped is then calculated as
Percentage = Total number of chopped tomatoes/Total number of tomatoes * 100%
Substitute the known values in the above equation, so, we have the following representation
Percentage = 15/60 * 100%
Evaluate
Percentage = 25%
Hence, the percentage is 25%
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Answer, please?
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 80.2° is added to the data, how does the range change?
The range stays 47°.
The range decreases to 47°.
The range stays 48°.
The range increases to 50°.
Question 7(Multiple Choice Worth 2 points)
(Effects of Changes in Data MC)
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 58° is changed to 101°, which of the following measures changes the most and what is the new value?
Median 86.5°
Mean 84°
Range 48°
IQR 32°
The range of a data-set is given by the difference between the highest value of the data-set by the smallest value of the data-set.
The highest and smallest high temperatures for the city are given as follows:
Smallest: 57º.Highest: 105º.Hence the range is obtained as follows:
105 - 57 = 48º.
80.2º would be neither the highest nor the smallest value in the data-set, which would then remain constant.
What is the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
As it involves all values, it would be changed the most by changing the value of 58º to 101º, and would then assume a value of 84º.
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OB Susan's Lawn Care $20 Number of Hours Worked 2 3 7 Amount Charged (dollars) 48 11 72 168 Amount Charged (dollars) 1 2 3 4 5 6 Number of Hours Worked What is the difference between Susan's and Jim's lawn-care businesses in the amounts they charge for 10 hours of work? OA. $16 264 140 120 100 80 60 40 20 0 Jim's Lawn Care Jim charges for lawn Previous Next →
Jim's and Susan's lawn care businesses charge different rates for a 10-hour shift; the difference is $40.
How should a number be read?The groupings of numbers include ones, tens, scores, tens, millions, and so forth. Ones, tens, or hundreds are the three subgroups that make up each group. When printing or reading a huge number, start with both the largest group on the left and work your way right.
work done = force × distance. W = F s. When the amount of work (W) is expressed in joules.
It will be Susan's Charge for ten hours.
= 168 + 72 $
= 240 $
while Jim Charges was for 10 hours
= 120 + 80 $
= 200$
The rates Susan and Jim charge during 10 hours of labor in their respective lawn care businesses are as follows:
= 240 - 200 $
= 40$
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The figure above represents a square sheet of cardboard with side length 40 inches. The sheet is cut and pieces are discarded. When the cardboard is folded, it becomes a rectangular box with a lid. The pattern for the rectangular box with a lid is shaded in the figure. Four squares with side length xx and two rectangular regions are discarded from the cardboard. Which of the following statements is true? (The volume V of a rectangular box is given by V=lwh).
A. When x = 20 inches, the box has a minimum possible volume.
B. When x = 20 inches, the box has a maximum possible volume.
C. When x = 20/3 inches, the box has a minimum possible volume.
D. When x = 20/3 inches, the box has a maximum possible volume.
When the square sheet of cardboard is cut and folded to create a rectangular box with a lid, the maximum possible volume is achieved when x = 20 inches. All other values will result in a smaller volume for the box.
1. Calculate the side lengths of the box and lid:
Box: 40 inches - 2x = 40 - 2x
Lid: 2x
2. Calculate the volume of the box with a lid when x = 20 inches:
Box Volume:
(40 - 2x) x (40 - 2x) x (40 - 2x) = (40 - 2*20) x (40 - 2*20) x (40 - 2*20) = (20) x (20) x (20)
= 8000 in^3
Lid Volume: 2x x 2x x 2x = 2*20 x 2*20 x 2*20
= 8000 in^3
Total Volume: 8000 in^3 + 8000 in^3 = 16000 in^3
3. Calculate the volume of the box with a lid when x = 20/3 inches:
Box Volume: (40 - 2x) x (40 - 2x) x (40 - 2x) = (40 - 2*20/3) x (40 - 2*20/3) x (40 - 2*20/3) = (33 1/3) x (33 1/3) x (33 1/3)
= 7157.7 in^3
Lid Volume: 2x x 2x x 2x = 2*20/3 x 2*20/3 x 2*20/3
= 1365.3 in^3
Total Volume: 7157.7 in^3 + 1365.3 in^3
= 8523 in^3
4. Comparison: When x = 20 inches, the box has a minimum possible volume of 16000 in^3, while when x = 20/3 inches, the box has a volume of 8523 in^3. Therefore, the statement is true
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A friend proposes a game: Spin the spinner twice and if the sum is even, then you win. Let's say my spinner lands on 2 for the first spin, and then lands on 3 for the second spin.
My calculated sum would then be 5. However, if the sum is odd, then your friend wins. Is this a fair game?
The probability to know of it is a fair game depends on how the spinner is designed.
How to illustrate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events.
It depends on how the spinner is designed and the probability of landing on each number. If the spinner is fair and each number is equally likely to be spun, then the probability of winning is 1/2, or 50%.
This means that over the long run, you would be expected to win half of the games you play. If you and your friend agree that these are the rules of the game and you both understand the probability of winning, then the game could be considered fair.
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For a frequency polygon to display the distribution of data accurately, intervals of equal width must be used.
a) Explain why, using examples.
b) Can some of the data be left out of the frequency polygon? Justify your answer.
a. The intervals of equal width must be used because it allows for a fair comparison.
b. Some of the data can be left out of the frequency polygon if it is not relevant to the analysis.
How to explain the polygon?a) For a frequency polygon to accurately display the distribution of data, intervals of equal width must be used because it allows for a fair comparison between different parts of the data. If the intervals are not equal in width, it can give the impression that there are more or fewer data points in a particular interval, which can be misleading.
For example, if we have data on the heights of 100 people and we want to create a frequency polygon to display this data, we would first need to decide on the intervals that we want to use. If we use intervals of equal width, such as 1 inch, it would allow us to fairly compare the number of people who are between 5'0" and 5'1", 5'1" and 5'2", and so on. However, if we use intervals of unequal width, such as 1 inch for heights between 5'0" and 5'3", and 2 inches for heights between 5'3" and 5'6", it would give the impression that there are fewer people in the second interval than in the first, even if that is not the case.
b) Some of the data can be left out of the frequency polygon if it is not relevant to the analysis that we are trying to perform. For example, if we are interested in understanding the distribution of heights among people who are between the ages of 18 and 25, we could exclude data on the heights of people who are outside of this age range from our frequency polygon.
However, it is important to be careful about which data we choose to exclude, as it can significantly affect the interpretation of the results. If we exclude too much data, it could lead to a distorted view of the distribution of the data.
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9) The population of rabbits (P) in a pet store is a function of time, (t) measured
in days. It can be modeled with the following equation: (3 pts)
P(t)=18(2)4
a) How many rabbits will be present after 30 days?
b) When will the population reach 10,000 rabbits?
There will be approximately 1.9 billion rabbits after 30 days. It will take approximately 9.8 days for the population of rabbits to reach 10,000.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
a) To find the number of rabbits after 30 days, we can substitute 30 for t in the equation [tex]P(t) = 18(2)^t[/tex]:
[tex]P(30) = 18(2)^{30}[/tex]
= 18 × 1073741824
= 1934917632
So there will be approximately 1.9 billion rabbits after 30 days.
b) To find the time it takes for the population to reach 10,000 rabbits, we need to solve the equation P(t) = 10,000 for t. We can do this by first dividing both sides of the equation by 18 to get:
(1/18)P(t) = (1/18)(10,000)
[tex](2)^t = (10,000/18)[/tex]
We can then take the logarithm of both sides of the equation with base 2:
t = log₂((10,000/18))
= log₂(555.56)
= 9.8
Therefore, tt will take around 9.8 days for the rabbit population to reach 10,000.
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In the solid figure below, what is the volume of the top section of the figure? 20 cm 3 10 cm 3 9 cm 3 40 cm 3
The volume of the top section of the figure is 16 cm³.
What is the volume?The volume of a body is a three - dimensional region, enclosed by a two - dimensional curve. Mathematically, we can write volume as → Vₙ = ∫∫∫(V{x, y, z}dx dy dz.The volume of cuboid is given by → V = l x b x hGiven is the solid cuboidal figure as shown in the image.
The volume of the top cuboidal figure will be -
V = L x B x H
V = 2 x 2 x 4
V = 4 x 4
V = 16 cm³
Therefore, the volume of the top section of the figure is 16 cm³.
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A pair of shoes usually sells for $67. If the shoes are 40% off, and sales tax is 5%, what is the total price of the shoes, including tax?
After the discount and the tax is applied, the final cost of the shoes is $42.21
What is the final price of the shoes?Remember that if the original price is P, and we have a discount of X, the new price will be:
P' = P*(1 - X/100%)
If instead we have an increase, like a tax, the new price will be:
P' = P*(1 - x/100%)
Here the original price is $67, first we apply a discount of 40% so we get:
P' = $67*(1 - 40%/100%)
P' = $67*(1 - 0.4)
P' = $67*(0.6)
And now we apply a tax of 5%, then the final price will be:
P'' = $67*(0.6)*(1 + 5%/100%)
P'' = $67*(0.6)*(1.05) = $42.21
The final cost of the shoes is $42.21
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In Quadrilateral ABCD, AB || CD and m<2=35 degrees
What is m<5?
Since AB || CD and m∠2 = 35° in Quadrilateral ABCD, the measure of angle 5 (m∠5) is equal to 35°.
What is the Alternate Interior Angles Theorem?In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
Additionally, these angles are generally referred to as alternate interior angles. In this scenario, we can logically deduce the following information and parameters from Quadrilateral ABCD:
Lines AB and CD are the parallel lines.Line BD represents a transversal line. Angle m∠5 = Angle m∠2 (alternate interior angles).Therefore, we can logically deduce and conclude that m∠5 in Quadrilateral ABCD is equal to 35 degrees in accordance with the Alternate Interior Angles Theorem.
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4. The table below shows the number of basketball games and the total points scored by three
teammates.
Number of
Games Played
Total Points
Scored
Kiara 25 175
Cecilia 20 120
Kayleigh 15 105
a. Determine the ratio of total points scored to games played for each player.
b. Determine which two players’ points scored to games played ratios are proportional. Show
all work to justify your answer
The ratio of total points scored to games played for each player are Kiara 7:1, Cecilia = 6:1, and Kayleigh= 7:1. (b) The ratios of Kiara and Kayleigh are proportional
How to determine proportional ratio?You should know that two ratios are proportional to each other if they are equal. also, you should be aware that ratios show the number of times a number appears in another number when divided.
The parameters that will guide us to get these ratios are
Players Number of games Total points Ratios
Kiara 25 175 1:7
cecilia 20 120 1:6
Kayleigh 15 105 1:7
Therefore from the table shown above, the ratios of Kiara and Kayleigh are proportional with 1:7 respective.
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Keisha is going to the airport. It is 5:31 PM right now. Keisha's flight will depart in 3 hours 48 minutes. What is the departure time of her flight?
Answer:
9:37
Step-by-step explanation:
right!
Answer:
8:19
Step-by-step explanation:
Find the equation of the exponential function
Sebastian observed the number of minutes his dormmates spent on social media sites while they were at the library. he reported his data in the following list.
13, 0 , 14 , 36, 18, 9
Find the mean absolute deviation (mad) of the data set. ___ minutes
The mean absolute deviation (MAD) of the data set is equal to 180.625.
The mean absolute deviation of a data set is to find the average distance of each observation of the data set and the mean of the data set.
Mean absolute deviation = 1/n ∑ absolute value of (xi - x bar)
x bar =average value of the given data set
n= total number of data set
xi = data value in a given set
According to the question,
x bar = sum of all the data set / total number of the data set
x bar = 2052/16 = 128.25
Substitute the value in the formula, we have
Mean absolute deviation = 2890/16 = 180.625
Hence, the Mean absolute deviation of the data set is equal to 180.625.
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As per the given data, the Mean absolute deviation (MAD) of the data set is equals to 17.5
The term Mean absolute deviation in math is defined as the average distance of each observation of data set and the mean of the data set.
Here we have given the following data.
=> 13, 0 , 14 , 36, 18, 9
Then the mean of the data is calculated as,
=> (13 + 0 + 14 + 36 + 18 + 9)/6
=> 90/6
=> 15
Now, we have to the Substitute the value in the formula, we have
And then the Mean absolute deviation is calculated as,
=> (90 + 15)/6
=> 105/6
=> 17.5
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PLEASE HELP!!!
Use this information for questions 9 to 11.
Question 9: What is ∠2? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.
Question 10: What is ∠4? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.
Question 11: With the given information and what you are able to determine, can you conclude that a ll b? If they are not parallel, explain why they are not. If they are parallel, what theorem can be used to prove them parallel? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.
Step-by-step explanation:
p and q are parallel.
let's first only look at a and it's intersections with p and q.
based on the rules of intersecting lines (the angles of intersecting lines are the same in both sides of any of the lines, they are only left-right mirrored) and then parallel lines at that (the intersecting angles of a line with parallel lines are the same with every parallel line, otherwise they are not parallel).
angle 2 = angle 5 = angle 10 = angle 13
therefore,
8x + 14 = 10x - 10
14 = 2x - 10
24 = 2x
x = 24/2 = 12
angle 2 = 8×11 + 14 = 88 + 14 = 102°
because of the same rules of intersecting lines and parallel lines. it is also clear that
angle 4 = angle 7 = angle 12 = angle 15
therefore,
13y + 19 = 15y + 5
19 = 2y + 5
14 = 2y
y = 14/2 = 7
angle 4 = 13y + 19 = 13×7 + 19 = 91 + 19 = 110°
if a and b would be parallel too, then the principle of the same angles would be true not only top-down (as for the pervious 2 problems) but also left-right.
and then angle 2 would be equal to angle 4.
but they are not.
although the difference is small, it means a and b will intersect somewhere.
and they are therefore not parallel.
35. Identify a pair of alternate interior angles given that g || h.
<3 and <6
<8 and <9
<2 and <4
<5 and <7
A pair of alternate interior angles given that g || h include the following: D. <5 and <7.
What are parallel lines?In Mathematics, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
What is the Alternate Interior Angles Theorem?The Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent. Additionally, these angles are generally referred to as alternate interior angles.
In this scenario, we can logically conclude that angle 5 and angle 7 forms a pair of alternate interior angles because line g is parallel to line h.
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Find at least ten solutions to the linear equation 1/2x + y = 5, and plot the points on a coordinate plane. What shape is the graph of the linear equation taking?
The solutions of the linear equation is
x y
-8 9
-6 8
-4 7
-2 6
0 5
2 4
4 3
6 2
8 1
10 0
the graph is a straight-line graph
How to find the solutions of the linear equationThe solutions of the linear equation is the found by substituting an x value and solve for y
the given equation 1/2x + y = 5, rearranging the equation gives
y = 5 - 1/2 x
For x = -8, y = 5 - 1/2 * -8 = 9
For x = -6, y = 5 - 1/2 * -6 = 8
For x = -4, y = 5 - 1/2 * -4 = 7
For x = -2, y = 5 - 1/2 * -2 = 6
For x = 0, y = 5 - 1/2 * 0 = 5
For x = 2, y = 5 - 1/2 * 2 = 4
For x = 4, y = 5 - 1/2 * 4 = 3
For x = 6, y = 5 - 1/2 * 6 = 2
For x = 8, y = 5 - 1/2 * 8 = 1
For x = 10, y = 5 - 1/2 * 10 = 0
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212 divided by 18 estimate
The estimated answer for 212 divided by 18 is 12.
What is Estimation?Estimation means approximating a quantity to the required accuracy.
This is obtained by rounding off the numbers involved in the calculation and getting a quick and rough answer. It is used to find a value that is close enough to the right answer.
Estimation in math is done by rounding off the numbers to their closest whole value to get a quick and simple rough answer. It saves time and effort.
Dividing 212 by 18
= 212/18
= 11.77777
Estimated to be 12
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PLs help!!Frances and Muriel are picking peaches. Frances has 17 beaches, which is 2more than 3 times the number of peaches that Muriel has. Write an equation that could be used to find the number of peaches p Muriel has? PLS HElp thank u so much due
The equation that can be used to find the number of peaches Muriel has is; 2 + 3·x = 17
What is an equation?A mathematical equation is a statement that has two expressions, joined by the equals to, '=' sign.
The number of peaches Frances has = 17
Let x represent the number of peaches Muriel has
Therefore;
The number of peaches Frances has = 2 + 3·x
Which indicates through substitution property, that we get;
17 = 2 + 3·x
The equation that can be used to find the number of peaches Muriel has, x is; 17 = 2 + 3·x
Solving for x in the above equation, we get;
17 = 2 + 3·x
3·x = 17 - 2 = 15
x = 15 ÷ 3 = 5
The number of peaches Muriel has, x = 5 peaches
The 17 peaches Frances has and the indication that Frances has 2 more than 3 times the number of peaches Muriel has, indicates that the equation that could be used to find the the number of peaches Muriel has is; 17 = 2 + 3·x
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Divisor = 5
Dividend = 3075
Quotient =
According to the given statement if Divisor = 5, Dividend = 3075 then The quotient is 615.
What is division?Division is an arithmetic operation that is the inverse of multiplication. It is used to determine how many times one number, called the divisor, is contained within another number, called the dividend. The result of the division is called the quotient.The three most widely discussed are the Commutative, Associative, and Distributive Laws.
The quotient is 615.
You can find this by dividing the dividend (3075) by the divisor (5) using long division or by using the formula: Quotient = Dividend / Divisor
In this case, 3075 / 5 = 615
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Evaluate the expression.
Simplify if possible
-4 5/6 + (-1 2/3)
Give your answer as a mixed number. Enter the number that
goes in the green box.
Evaluating and simplifying -4 5/6 + (-1 2/3) gives the value of = 6 1/2
How to evaluate the equationThe equation involves -4 5/6 + (-1 2/3) addition of fraction
The fraction required are:
-4 5/6 and -1 2/3
converting the mixed numbers to improper fractions
= -29/6 + (-5/3)
making the numbers have similar denominator by multiplying by 2/2
= -29/6 - 5/3 * 2/2
= -29/6 - 10/6
The addition is done by
= (-29 - 10) / 6
= -39/6
simplifying gives
= -39/6
= -13/2
= 6 1/2
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Kathy has 5 red cards and 5 green cards. She shuffles the 10 cards and lays out 5 of the cards in a row in a random order. She will be happy if and only if all the red cards laid out are adjacent and all the green cards laid out are adjacent. For example, card orders RRGGG, GGGGR, or RRRRR will make Kathy happy, but RRRGR will not. The probability that Kathy will be happy is m/n where m and n are relatively prime positive integers. Find m +n
m+n = 8. The probability that Kathy will be happy is 3/8. This can be seen by counting the total number of possible arrangements of red and green cards that would make her happy (6). There are a total of 8 arrangements, so the probability is 3/8.
There are 6 possible arrangements of red and green cards that would make Kathy happy:
RRRRR, GGGGG, RRGGG, GGRRR, GRRRG, and RGGGR.
There are a total of 10 cards and 5 of them are laid out in a row, so the total number of arrangements is
10C5 = 10!/5!(10-5)!
= 10*9*8*7*6/5*4*3*2*1
= 10*9*8/5*4*3
= 8*9
= 72.
The probability that Kathy will be happy is the number of arrangements that make her happy (6) divided by the total number of arrangements (72). Therefore, the probability is
6/72
= 3/8.
Therefore, m+n = 8.
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