Answer:
(i) 11 years old
(ii) 30 years old
Step-by-step explanation:
K is x
In four years, he will be x+4 and his mother will therefore be 3(x+4)
Six years ago, he was x-6 and his mother was 7(x-6).
In 10 years his mother went from 7(x-6) to 3(x+4)
so their difference is 10
7x-42+10=3(x+4), since 7x-42 is 10 years less than 3x+12
7x-32=3x+12
4x=44
x=11 age of K now
in 4 years he will be 15 and his mother 45.
Six years ago he was 5 and his mother 35
Therefore, his mother was 30 when he was born.
She is now 41.
Imran is currently 10 years old. His mother's current age is 34 years old and she was 24 years old when Imran was born.
Explanation:The question involves a system of equations based on the relationship between Imran and his mother's ages. We can define Imran's current age as i and his mother's current age as m. From the problem we have the following two equations:
In four years' time, his mother will be three times as old as him: m + 4 = 3 * (i + 4)Six years ago, his mother was seven times as old as him: m - 6 = 7 * (i - 6)
By solving this system of equations, we can determine that Imran's current age (i) is 10 years old and his mother's current age (m) is 34 years old. To find the age of Imran's mother when he was born, we would subtract Imran's age from his mother's, i.e., 34 - 10, so Imran's mother was 24 years old when Imran was born.
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a positive integer with exactly eight positive divisors, two of
which are 21 and 33
21 = 3 · 7
33 = 3 · 11
If 21 and 33 are two divisors, then so are 3, 7, 11, and 77. And 1 and the number itself are always divisors.
So, we have 1, 3, 7, 11, 21, 33, 77, and the number. That's eight divisors.
So the number is 3·7·11 = 231, the product of only the prime divisors of the number.
Find X, Y, and Z.
TEACHING TEXTBOOKS GEOMETRY
The required values of x, y and z are 58°, 29° and 60°
What is an angle?An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Given are two triangles with unknown angles, we are asked to find, value of x, y and z.
Since, the lines are given parallel,
Therefore,
2y = 58° [alternate interior angles]
y = 29°
Now,
2y = x [alternate interior angles]
x = 58°
Since, we know that, the sum of interior angles of a triangle is 180°
Therefore,
x + z + 62° = 180°
58° + 62° + z = 180°
z = 180° - 120°
z = 60°
Hence, the required values of x, y and z are 58°, 29° and 60°
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Work out the value of x.
Answer:
x = 4 . . . cm
Step-by-step explanation:
You want the measure of the segment CE from external point C to circle O, given several other dimensions of chords and segments in the circle.
Crossing chordsAs in the attachment, we can extend segment DO across the circle to make diameter DX. Then we can use the relation for chord lengths to find the radius of the circle (r).
Segments of crossing chords have the same product:
FA·FE = FD·FX
7·4 = 2·(2r -2) . . . . . use given segment values
14 = 2r -2 . . . . . . divide by 2
16 = 2r . . . . . . . add 2
r = 8 . . . . . . . divide by 2
The radius of the circle is 8 cm.
SecantsWe can also extend radius EO across the circle to make diameter EY, as shown in the attachment.
The relation involving the product of secant segments can be used to find x:
CE·CY = CB·CA
x(x +16) = 5(5+4+7)
x² +16x = 80 . . . . . . . . simplify
x² +16x +64 = 144 . . . . . . . add 64 to complete the square
(x +8)² = 12² . . . . . . . . . write as squares
x +8 = 12 . . . . . . . . positive square root
x = 4 . . . . . . . . subtract 8
The value of x is 4.
__
Additional comment
The attachment is accurately drawn.
OK I need this answer quick A model of Seattle, Washington space Needle is 20 inches tall The actual Space Needle is approximately 600 feet tall
a: what does the 1 inch represent in the model? what is the scale?
b: what is the scale factor model ?
it would mean a lot if someone could answer this!!
a. The representation of 1 inch in the model is 30 feet.
ii. The scale is 1:30.
b. The scale factor of the model is 1:360.
What is a scale factor?A scale factor is also referred to as a representation fraction which is the rate of length on drawing to that of the original length.
i.e. scale factor = length on drawing/ original length
Given that Washington space Needle is 20 inches tall. And the actual space Needle is approximately 600 feet tall, then;
a. 1 inch in the model = 600 feet/ 20 inch
= 30 feet / inch
i. The representation of 1 inch in the model is 30 feet.
ii. The scale is 1:30 i.e. 1 inch on the drawing is equal to 30 feet on the actual model.
b. The scale factor of the model is;
1 feet = 12 inches
600 feet = x
x = 7200 inches
scale factor = 20 / 7200
= 1/ 360
The scale factor is 1:360. i.e. 1 inch on the drawing is equivalent to 360 inches on the actual model.
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What type of solutions does this equation have?
y² = 0
one real solution
two imaginary solutions
two real solutions
no solutions
Answer:
the last one
Step-by-step explanation:
Answer: One real solution (0)
Step-by-step explanation:
The only thing square which equals 0 is 0 itself.
Kris is making cookies.
He has 4/3 cups of sugar.
He needs 2/3 cup of sugar to make one whole batch of cookies.
Use the drop-down menus to complete the statements below about the cookies that Kris can make.
Answer: With 4/3 cups of sugar, Kris can make (4/3) / (2/3) = 2 batches of cookies.
Step-by-step explanation:
if there are 240 boys in a school with a total of 960 students, then what percent of the students are girls?
Answer
60%
Step-by-step explanation:
Answer: 75% of students are girls.
Step-by-step explanation: First, you divide 960 by 100 to get 9.6. Then you do 960-240 to get the amount of girls (720), then you divide 720 by 9.6 to get 75.
A shop assistant sells goods to the value of $3400 during a certain week. If she is
paid 7.5% commission on these sales, calculate the amount of commission earned.
If she is paid a basic wage of $450, calculate her total wage for that week.
Answer:
$705
Step-by-step explanation:
($3400)(0.075) = $255 commission earned
Total wage for that week = $450 + $255 = $705
note: this answer assumes that $450 is the weekly basic wage, not daily
Simplify the rational expression. x2 – 5 x + 5 –x – 5
The answer is -1(x - 5)(x + 1)
To simplify the rational expression x^2 - 5x + 5 - x - 5, we can combine like terms and factor out the greatest common factor of the numerator and denominator.
Step 1: First, we can combine like terms in the numerator to get x^2 - x - 5
Step 2: Next, we can factor out the greatest common factor of -1 from the numerator to get -1(x^2 - x - 5)
Step 3: Now we can factor the expression in the parenthesis:
-1(x - 5)(x + 1)
So the simplified form of the given rational expression is: -1(x - 5)(x + 1)
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Answer:
-6x+x^2
Step-by-step explanation:
To start off the equation you want to make everything have the same symbol:
x^2+-5x+5+-x+-5
next, you can rearrange the symbols to combine terms:
5+-5+-x+-5x+x^2
Now we combine:
-6x+x^2
the 5 cancels out. The -x plus the -5x gets you -6x. and the x^2 can not be combined.
Your answer:
-6x+x^2
g(x)=1/2x-3 find g (12)
Answer:
g(12) = 3
Step-by-step explanation:
g(12) means to put 12 in place of x.
g(x) = 1/2x - 3
g(12) = 1/2(12) - 3
Mulitply 1/2 and 12.
= 6 - 3
subtract.
= 3
g(12) = 3
a bakery needs to make 10 batches of bagels before opening in 6 hours ech batch of bagels takes 3/4 of an hour to make will the bakery have enough time to bake 10 bagels
The bakery will not have enough time to bake 10 batches of bagels in 6 hours.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
Given that,
There is a time limit of 6 hours to make 10 batches of bagel.
Time needed to make 1 batch of bagel = 3/4 hour
Time needed to make 10 batches of bagel = 10 × (3/4)
= 30 / 4
= 7.5 hours
Hence at least 7.5 hours is needed to make 10 batches of bagel.
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put -x+3y<6 into cordinates
The inequality -x+3y < 6 passes through the points (-6, 0) and (0, 2).
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
We have an inequality,
-x+3y < 6.
The graph of the inequality is given in the attached image.
And inequality passes through the points (-6, 0) and (0, 2).
Therefore, the graph of the inequality is given in the attached image.
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How do I do it? I’m unsure and would like to achieve the answer
The equivalent ratio where the amount of stock is 100 mL is 80 mL
How to an equivalent ratio?
An equivalent ratio is a ratio that is equal to another ratio, but with the terms in a different order or with different values.
Since the recipe calls for 350 mL of Dashi in order to make a smaller batch using 280 mL of Dashi. Thus, we can say:
equivalent ratio = 280/350
Thus, an equivalent ratio where the amount of stock is 100 mL will be:
280/350 = x/100
0.8 = x/100
x = 0.8 × 100
x = 80 mL
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y = -5x - 21
-4x + y = 6 Solve each system of equations. Show all your work.
The solution of the system of equations:
y = -5x + 21-4x + y = 6is (-3, 6)
How to solve the system of equations?
Here we want to solve the system of equations below:
y = -5x + 21
-4x + y = 6
We can use the elimination method to solve this if we take the difference between the two equations, we will get:
y - (-4x + y) = -5x - 21 - 6
4x = -5x - 27
Now we can solve this for x.
4x + 5x = -27
9x = -27
x = -27/9 = -3
And the value of y is given by:
y = -5x - 21 (we need to evaluate that on x = -3)
y = -5*-3 - 21
y = 15 - 21 = 6
The solution is (-3, 6).
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Answer: Elimination : (-3,-6) Substitution : (5/3,38/3)
Step-by-step explanation: Elimination : y = -5x + 21;-4x + y = 6 y - (-4x + y) = -5x - 21 - 6 4x = -5x - 27 4x + 5x = -27 9x/9 = -27/9 x = -3 y = -5x - 21 y = (-5) (-3) - 21 y = 15 - 21 y = -6 (-3,-6) Substitution : y = -5x + 21;-4x + y = 6 −4x + −5x + 21 = 6 −9x + 21 - 21 = 6 - 21 -9x/-9 = -15/-9 x = 5/3 y = −5x + 21 y = −5 (5/3) + 21 (-25) (1) + (21) (3) / (3) (1) -25/3 + 63/3 y = 38/3 (5/3,38/3)
Find the value of x, y, and z in the rhombus below.
104°
(10y+6)°
(z+7)
(-x-10)°
The value of x, y, and z in the rhombus are -114, 7 and 59 respectively
How to find the value of x, y, and z in the rhombus?Since the opposite angles of a rhombus are equal to each other. We can write:
(-x-10)° = 104°
-x-10 = 104
-x = 104 + 10
x = -114
Since the adjacent angles in rhombus are supplementary. We have:
114 + (z + 7) = 180
121 + z = 180
z = 180 -121
z = 59
104 + (10y + 6) = 180
110 + 10y = 180
10y = 180 - 110
10y = 70
y = 70/10
y = 7
Thus, the value of x, y, and z are -114, 7 and 59
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I need help quickly Pleasee
The volume of a pyramid with a base area of 15 square inches and a height of 7 inches will be 35 cubic inches.
What is the volume of the pyramid?Suppose the base of the pyramid has length = L units and width = W units, slant height = K units, and the height of the pyramid is of H units.
Then the volume of the pyramid will be
V = (L × B × H) / 3
V = (Base area x H) / 3
The volume of a pyramid varies jointly with the base area of the pyramid and its height.
The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.
Then the volume of a pyramid with a base area of 15 square inches and a height of 7 inches will be
V = (15 x7) / 3
V = 35 cubic inches
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L
6cm
10cm
X
if the shaded area is 112 cm²,
then the length x in the figure is 口。
cm.
If the shaded area is 112 cm², then the length x in the figure is 7cm.
What is Area of Rectangle?The area of Rectangle is length times of width.
Split the shape into two rectangles:
then you have two areas:
x×10 and x×6
the shaded area is given as 112cm²
10x+6x=112
Add the like terms
16x=112
Divide both sides by 16
x=112/16
x=7 cm
Hence, if the shaded area is 112 cm², then the length x in the figure is 7cm.
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Find x and y.
65°
40°
to
Answer:
x 23 y 60
Step-by-step explanation:
Statistics Help! Will give Brainliest!
The probability that a teenage boy has a cholesterol level greater than 200 is 0.33: Option D
What is probability?It is the chance of occurrence of an event E
To solve this problem you must first find the z-score associated with a cholesterol level greater than 200.
The general formula for a z score is:
z = (x-µ)/σ
Where z is the z score, x is the data point, µ is the mean, and σ is the standard deviation. With your numbers that would become:
z = (200-170)/30
z = 1.833
If you are using a graphing calculator, such as the TI-83 Plus, you can then go to 2nd vars, and the second option is normalcdf
To use normalalcdf enter normalcdf (lower z score, upper z score) in your case normalcdf (1.833, 1E99) to get the probability that a teenage boy has a cholesterol level greater than 200 Which will give you .0337.
If you are using a z table, find the probability associated with your z score of 1.83, and subtract that from 1. You subtract from 1 because a z table gives you the probability of a score being below the one you obtained.
This implies therefore that the probability is 0.337
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A recipe for sparkling grape juice calls for 1 quarts of sparkling water and
quart of grape juice.
a. How much sparkling water would you need to mix with 9 quarts of grape juice?
18
b. How much grape juice would you need to mix with quarts of sparkling water?
c. How much of each ingredient would you need to make 100 quarts of sparkling
grape juice?
Please answer all no need for a step by step I just need the answers thanks :)
a. 9 quarts of sparkling water
b. 1 quart of grape juice
c. 50 quarts of sparkling water and 50 quarts of grape juice
What is the rational behind these values?The rationale behind the values above are as explained below:
a. If the recipe calls for 1 quart of sparkling water to be mixed with 1 quart of grape juice, then to mix with 9 quarts of grape juice, you would need 9 quarts of sparkling water.
b. If the recipe calls for 1 quart of sparkling water to be mixed with 1 quart of grape juice, then to mix with 1 quart of sparkling water, you would need 1 quart of grape juice.
c. To make 100 quarts of sparkling grape juice, using the 1:1 ratio in the recipe, you would need 50 quarts of sparkling water and 50 quarts of grape juice.
Therefore, the correct answers are as given above
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3. Suppose that your goal is to build a credit history by establishing a FICO score. How should
you approach payments on a long-term loan, such as an auto loan?
OPay the minimum amount required each bill.
OMake multiple small payments toward each bill.
OSkip payments occasionally.
OPay as much as you can afford each bill.
Suppose that your goal is to build a credit history by establishing a FICO score. you should approach payments on a long-term loan, such as an auto loan by: A. pay the minimum amount required each bill.
What is credit history?Credit history can be defined as the record that help to show a creditworthiness of a person which is the ability to pay back a loan.
FICO score on the other hand is as well used to determine the creditworthiness of a borrower based on the fact that this score help to show whether a borrower used to pay the amount loan to him/her on time or delay it.
Therefore the correct option is A.
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A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
A. The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.
B. The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.
C. The confidence interval from the first simulation is (0.191, 0.233), and the confidence interval from the second simulation is (0.213, 0.257). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.191 and 0.233. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.213 and 0.257.
D. The confidence interval from the first simulation is (0.191, 0.233), and the confidence interval from the second simulation is (0.213, 0.257). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.191 and 0.233. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.213 and 0.257.
The correct option regarding the 95% confidence interval for this problem is given as follows:
A. The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for the first simulation are given as follows:
[tex]n = 1000, \pi = \frac{212}{1000} = 0.212[/tex]
Hence the lower bound of the interval is of:
[tex]0.212 - 1.96\sqrt{\frac{0.212(0.788)}{1000}} = 0.187[/tex]
The upper bound is of:
[tex]0.212 + 1.96\sqrt{\frac{0.212(0.788)}{1000}} = 0.237[/tex]
For the second simulation, the parameters are given as follows:
[tex]n = 1000, \pi = \frac{235}{1000} = 0.235[/tex]
Hence the lower bound of the interval is of:
[tex]0.235 - 1.96\sqrt{\frac{0.235(0.765)}{1000}} = 0.209[/tex]
The upper bound is of:
[tex]0.235 + 1.96\sqrt{\frac{0.235(0.765)}{1000}} = 0.261[/tex]
This means that option A is the correct option.
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An 8 feet tall stop sign creates a shadow that is 2.5 feet long. At the same time, a utility pole creates a shadow that is 10 feet long. How tall, in feet, is the utility pole?
The height of the utility pole casting a shadow 10 ft is 32 feet.
What is the height of the utility pole?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
Given that;
Height of stop sign = 8ftShadow of stop sign = 2.5ftShadow of utility pole = 10ftHeight of utility pole = xRatio of height of utility pole and its shadow = x / 10
Ratio of height of sign post and its shadow = 8/2.5
Equate to determine the height of the utility pole.
x/10 = 8/2.5
Solve for x
x × 2.5 = 8 × 10
2.5x = 80
x = 80 / 2.5
x = 32 ft
Therefore, the height of the utility pole is 32 ft.
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Modeling Real Life A train ride from Chicago to Emeryville, California, is 2,438 miles. It is about 8 times as long as a train ride from Chicago to Port Huron, Michigan. About how long is the train ride from Chicago to Port Huron?
As per the given ratio between distance, The Train ride from Chicago to Port Huron is 304.375 miles.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, A train ride from Chicago to Emeryville, California, is 2,438 miles.
Since It is about 8 times as long as a train ride from Chicago to Port Huron, Michigan.
Thus,
The train ride from Chicago to Port Huron = 2438/8
The Train ride from Chicago to Port Huron = 304.375 miles
Therefore, The Train ride from Chicago to Port Huron is 304.375 miles.
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Hank bought a four family residence for a rental property he put 20% down on 300,000 rental unit how much will he be able to depreciate using the class recovery period for residential rental. Properties each year
The amount he will be able to depreciate using the class recovery period for a residential rental property each year is D. $10,909.09.
The term depreciation defines as an accounting method used to allocate the cost of a tangible or physical asset over its useful life.
It also represents how much of an asset's value has been used, and allows companies to earn revenue from the assets they own by paying for them over a certain period of time.
Using this formula:
Depreciation=Rental unit amount/ MACRS residential rental property recovery period
Where:
Rental unit amount=$300,000
MACRS Residential rental property recovery period=27.5 years
Let's plug in the formula
Depreciation=$300,000/27.5
Depreciation=$10,909.09
In conclusion, the amount he will be able to depreciate using the class recovery period for a residential rental property each year is: D. $10,909.09
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Incluc trip. She was able to purchase coach tickets for $200 and first class tickets for $1290. She used her total bud $11,720. How many first class tickets did she buy? How many coach tickets did she buy?n took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 15 people took the She was able to purchase coach tickets for $200 and first class tickets for $1290. She used her total budget for airfare for the trip, which was $11,720. How many first class tickets did she buy? How many coach tickets did she buy?
6 coach tickets and 9 first-class tickets were bought, totaling the number of tickets purchased.
Explain about the expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
A mix of operators, constants, and variables make up an expression. An expression can yield a value by using one or more operands and one or more operators.
An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
The algebraic expression that results from multiplying two variables, x and y, is xy.
Let's say that x coach tickets were purchased.
And y is the total number of first-class tickets bought.
Now,
15 people in total, including Sarah, made the journey.
Thus,
x + y = 15(1)
Coach and first-class tickets are priced at $200 and $1290, respectively.
The trip's total spending for air travel is $11,720.
Therefore,
200x + 1290y = 11720
20x + 129y = 1172
We obtain by resolving both equations.
x = 6
y = 9
Consequently, 6 coach tickets and 9 first-class tickets were acquired, making up the total number of tickets.
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Each of the s swimmers on the relay team swam an equal number of the 8 laps in a race. Write an expression that shows how many laps each swimmer swam.
Answer: If each of the s swimmers on the relay team swam an equal number of the 8 laps in a race, the expression that shows how many laps each swimmer swam would be 8/s.
This expression shows that each swimmer swam 8 laps, divided by the total number of swimmers on the team, s.
So, if there are 's' swimmers on the relay team, each swimmer swam 8/s laps.
Step-by-step explanation:
let the sum of a set of numbers be the sum of its elements. let $s$ be a set of positive integers, none greater than 15. suppose no two disjoint subsets of $s$ have the same sum. what is the largest sum a set $s$ with these properties can have?
No S with sum greater than 61 is possible and 61 is indeed the maximum.
By using the greedy algorithm, we obtain 61, with S={15,14,13,11,8}.
We must now prove that no such set has sum greater than 61. Suppose such a set [tex]$S$[/tex] existed. Then [tex]$S$[/tex] must have more than 4 elements, otherwise its sum would be at most 15+14+13+12=54.
S can't have more than 5 elements. To see why, note that at least.
[tex]$\left(\begin{array}{l}6 \\ 0\end{array}\right)+\left(\begin{array}{l}6 \\ 1\end{array}\right)+\left(\begin{array}{l}6 \\ 2\end{array}\right)+\left(\begin{array}{l}6 \\ 3\end{array}\right)+\left(\begin{array}{l}6 \\ 4\end{array}\right)=57$[/tex] of its subsets have at most four elements (the number of subsets with no elements plus the number of subsets with one element and so on), and each of them have sum at most 54. By the Pigeonhole Principle, two of these subsets would have the same sum. If those subsets were disjoint, we would directly arrive at a contradiction; if not, we could remove the common elements to get two disjoint subsets.
Thus, [tex]$S$[/tex] would have to have 5 elements. [tex]$S$[/tex] contains both 15 and 14 (otherwise its sum is at most 10+11+12+13+15=61.
It follows that [tex]$S[/tex] cannot contain both a and a-1 for any [tex]$a \leq 13$[/tex], or the subsets {a,14} and {a-1, 15} would have the same sum. So now [tex]$S$[/tex] must contain 13 (otherwise its sum is at most 15+14+12+10+8=59, and S cannot contain 12, or the subsets, {12,15} and {13,14} would have the same sum.
Now the only way [tex]$S$[/tex] could have sum at least 62=15+14+13+11+9
would be if S={15,14.13,11.9}. But the subsets {9,15} and {11,13} have the same sum, so this set does not work.
Therefore, no S with sum greater than 61 is possible and 61 is indeed the maximum.
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Use the equation to answer the question.
12a+9b=k(2a+32b)
Which value of k makes the equation true?
a. 6
b. 2
c. 4
d. 3
The value of k that makes the equation true is given as follows:
a. 6.
How to obtain the value of k?The equation for this problem is defined as follows:
12a + 9b = k(2a + 3/2b).
The equation will be true is both sides are equal.
Applying the distributive property to the right side, we have that:
12a + 9b = 2ak + 3kb/2.
Taking one of the terms, the value of k is obtained as follows:
2ak = 12a
k = 12a/2a
k = 6.
Meaning that the correct option is given by option A.
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Ben decides to build a rabbit to keep his children rabbits in. The run will be a rectangular with a width of 4cm. He has a maximum of 34m of fencing to use but wants the area to be greater than 50msquared. Find the range of values for the length of the run using inequalities
For the given case, the the range of values for the length of the run using inequalities is 4 < l < 8.5.The equation for the area of a rectangle is A = w x l, where w is the width and l is the length.
To find the range of values for the length of the run, we need to set up an inequality equation. We know the width is 4cm, so A = 4l > 50m2. This can be rearranged to 4l > 50m2, and then divided by 4 to get l > 50/4m2, which gives us l > 12.5m. This means that the length of the run must be greater than 12.5m.
We also know that Ben has a maximum of 34m of fencing to use, so l < 34/4m, which gives us l < 8.5m. This means that the length of the run must be less than 8.5m. Therefore, the range of values for the length of the run using inequalities is 4 < l < 8.5m.
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