The number of laps that Swimmer A swam was 50 laps.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Let we suppose that:
Swimmer A swam x laps
Swimmer B swam y laps.
Then, according to the given data, we have:
x + y = 175 laps
y = 25 + 2x
(25 more than twice of laps of A is the number of laps of B).
Thus, we get a system of two equations:
x + 25 + 2x = 175
3x + 25 = 175
3x = 175 - 25 = 150
x = 50
As x is the number of laps Swimmer A swam, thus, the number of laps that Swimmer A swam was 50 laps.
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Determine whether the successive probabilities are independent or dependent events.
15) The probability of getting 4 tails in a row when flipping a coin?
a) Independent
b) Dependent
16) The probability of drawing 2 Queens in a row from a deck of cards?
a) Independent
b) Dependent
Answer:
15) a) independent 16) b) Dependent Step-by-step explanation:
15) let T1 be the event : “get a tail in the first flip”
let T2 be the event : “get a tail in the second flip”
p(T1 ∩ T2) = 1/4
p(T1) = 1/2
p(T2) = 1/2
Then
p(T1) × p(T2) = (1/2)(1/2 = 1/4
Since ,p(T1 ∩ T2) = 1/4 = p(T1) × p(T2)
Then the events are independent.
16) These events are dependent since we don’t replace the Queen before the second draw.
The two Events are dependent because the probability that we draw a Queen in the first draw affect the probability that we draw a Queen in the second draw.
13. Figure QRSP is a rectangle.
Q.
100°
What is the measure of angle RPS?
A. 40 degrees
C. 80 degrees
B. 50 degrees]
Answer:
b 50 degrees bavaggagshdd
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,128 was collected on the sale of 1,336 tickets. How many of each type of ticket were sold?
Answer:
Adults = 448
Students = 888
Step-by-step explanation:
Write equations with info given
A = Adult tickets
S = Student tickets
5A+1S=3,128
A+S=1336
Subtract equations from each other
4A=1792
Solve for A
A=448
Plug A into second equitation
448+S=1336
Solve for S
S=888
Solve the quadratic equations by completing the square.
x^2-4x=-1
Answer:
2 ± √3
Step-by-step explanation:
Solving quadratic equation by completing squares:x² - 4x = -1
Divide the coefficient of x by 2.4 ÷ 2 = 2
Now, square the result and add that to both sides of the equation.2² = 2* 2 = 4
x² - 4x + 4 = -1 + 4
x² - 4x + 4 = 3
x² - 2 * x * 2 + 2² = 3
Compare it with a² - 2ab + b² . Now , a = x and b = 2(x - 2)² = 3
Take square root both sidesx - 2 = ±√3
x = 2 ± √3
Solutions: x = 2 +√3 ; 2 - √35 yrs ago, Nuri was thrice as old as Sonu. 10 yrs later, Nuri will be twice as old Sonu. How old are Nuri n Sonu?
Answer:
Answer will be 50
Step-by-step explanation:
Let us suppose, present age of Nuri be ‘x’ years and present age of Sonu be ‘y’ years.
Now, it is given that five years ago, Nuri was thrice old as Sonu. Hence,
Five years ago,
Nuri’s age = x-5 years
Sonu’s age = y-5 years
And relation between ages can be given as
Nuri’s age = 3×sonu’s age or
x-5 = 3(y-5)
x-5 = 3y-15
x-3y+10 = 0 ………..(i)
Another relation is given in the problem that ten years later, Nuri is twice as old as Sonu.
So, ten years ago,
Nuri’s Age = x+10
Sonu’s Age = y+10
And relation between ages can be written as
x+10 = 2(y+10)
x+10 = 2y+20
x-2y-10 = 0 …………..(ii)
Now we can solve the equation (i) and (ii) to get values of x and ‘y’ or present ages of Nuri and Sonu.
Value of ‘x’ from equation (i) be
x = 3y-10 ……….(iii)
Putting value of ‘x’ from equation (iii) in equation (ii) we get,
3y-10-2y-10 = 0
y = 20
Now, from equation (iii) value of ’x’ can be given as,
x= 3(20)-10
x = 50
Hence, the present ages of Nuri and Sonu are 50 years and 20 years respectively.
Is anyone able to solve this equation? It’s urgent
Answer:
1500
Step-by-step explanation:
You can find the complete solution in the given attachment
Math work class rell
Answer:
The answer is D. infinite.
Answer:
infinte
Step-by-step explanation:
→ For any value of x which is substituted you will get that value
G.MG.3 Beth is going to enclose a rectangular area in back of her house. The house wall will form one of the four sides of the fenced in area, so Beth will only need to construct three sides of fencing. Beth has 48 feet of fencing. She wants to enclose the maximum possible area.
The maximum area of the rectangular path is when the length is 24 feet and the width is 12 feet.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the length and y represent the width. Hence:
There is 48 feet of fencing:
x + 2y = 48
x = 48 - 2y (1)
The area (A) is:
A = xy = y(48 - 2y)
A = 48y - 2y²
The maximum area is at A' = 0, hence:
48 - 4y = 0
y = 12
x = 48 - 2(12) = 24
The maximum area of the rectangular path is when the length is 24 feet and the width is 12 feet.
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Finding the relationship of two lines
[tex]Explanation[/tex]
This is very basic all you have to look at is the 2x because whenever the number has a variable with [tex]x[/tex] it means its the slope and the slope will tell you whether they are parallel or perpendicular.
so as you can see the slopes are alike because they are both 2x
Thus, the answer is Parallel
//-carry on learning-//
If the scale factor is three and the center of origin is (1,1) dilate the coordinates A(-5,-7) B(-6,-5) C(-2,-3)
ZA=C
Round your answer to the nearest hundredth.
C
B
6
8
A
?
Answer:
? = 41.41°
Step-by-step explanation:
The known side length is adjacent to the angle we need to find hence we will use cosine
cosx = adjacent /hypotenuse
cos(?) = 6 / 8
simplify fraction, cos(?) = 3 / 4
? = arccos(3 / 4)
What is the probability of rolling a two on the first die and a three on the second die?
Answer:
a dice has 1 two and 1 three
1/6 *1/6 =1/36
alex has a box of 250 nails. he uses 80 nails. then he loses 35 nails. how many nails does alex have left? what is the hidden question
I need the answer for this question please
The sum of √30 + √50 lies between 12 and 13.
What is the sum of the numbers?The square root of a number can be described as number that when multiplied with itself yields that number.
√30 = 5.48
√50 = 7.07
5.48 + 7.07 = 12.55
The consecutive integers are 12 and 13
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How should this model be completed to represent 1,881 ÷ 33?
Answer:
Check the attached image below
Find the area of a regular polygon with 7 sides that has a side length of 6 inches and an apothem of 8 inches.
Area = [?]in2
Answer:
see the attachment photo!
Convert (728), to base 10
Answer:
2D8
Step-by-step explanation:
To convert decimal number 728 to hexadecimal, follow these steps:
step 1 =Divide 728 by 16 keeping notice of the quotient and the remainder.
step 2 =Continue dividing the quotient by 16 until you get a quotient of zero.
step 3 =Then just write out the remainders in the reverse order to get hexadecimal equivalent of decimal number 728.
Using the above steps, here is the work involved in the solution for converting 728 to hexadecimal number:
728 / 16 = 45 with remainder 8
45 / 16 = 2 with remainder 13 (D)
2 / 16 = 0 with remainder 2
Then just write down the remainders in the reverse order to get the answer, The decimal number 728 converted to hexadecimal is therefore equal to :
2D8
What is k equal to if StartFraction 7.6 over 2 EndFraction = StartFraction 9.5 over k EndFraction?
1.6
2.5
3.8
4.8
In algebra, there are lots of rules and properties to remember. The good news is that once you understand them, you can apply them in lots of different orders and combinations. Give an example of a mathematic problem that can be solved in multiple ways by applying properties of algebra differently. Explain your reasoning.
Algebraic properties can be applied in any mathematical equation.
How to explain the algebraic property?There are several algebraic properties; they include:
Distributive propertyAdditive propertyInverse propertyCommutative propertyAnd so onAll these properties can be applied in a mathematical equation.
An instance is as follows:
3(x + 2) = 18
Method 1
Apply the distributive property
3x + 6 = 18
Apply the subtraction property of equality
3x = 12
Apply the division property of equality
x = 4
Method 2
Apply the division property of equality
x + 2 = 6
Apply the subtraction property of equality
x = 4
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1. Solve the quadratic function by graphing. x²-3x - 18 - 0
Answer:
that's easy all you have to do is find out what is the value of x then divided by 2 once you divide by 2 subtract 3x 18 and 0
round your final answer to the nearest degree
Answer:
The correct answer is 37°
A(n) ___ function is the function that sometimes results when the independent variable of a function is exchanged with the dependent variable.
The A(n) is inverse function is the function that sometimes results when the independent variable of a function is exchanged with the dependent variable.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We know that the inverse of a function, sometimes known as an anti function, is a function that can be reversed into another.
In other words, if a function "f" converts x to y, the inverse of the same function will convert y to x. The inverse function is denoted by f⁻¹ or F⁻¹ if the function is denoted by 'f' or 'F'.
Thus, the A(n) is inverse function is the function that sometimes results when the independent variable of a function is exchanged with the dependent variable.
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8.92 x 10^6 in scientific notation
Answer:
8.92 * 10^10
Step-by-step explanation:
1. Convert to decimal notation
[tex]8.92*10^6[/tex]
The exponent is 6, making it 10 to the power of 6. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 6 time(s):
8.92 -> [tex]8920000[/tex]
2. Final result
[tex]8920000[/tex]
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
8.92 * 10^10
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Why learn thisScientific notation, or standard form, makes things easier when working with very small or very big numbers, both of which come up frequently in the fields of science and engineering. It is used in science, for example, to convey the mass of the heavenly bodies: Jupiter’s mass is [tex]1.898*10^{27}[/tex]kg, which is easier to comprehend than writing the number 1,898 followed by 24 zeroes. Scientific notation also makes solving problems that use such high or low numbers more straightforward.
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Terms and topicsScientific NotationScientific notation is also referred to as scientific form or standard index form, or in the UK, standard form.
Is 12/19 rational or irrational?
Answer:
irrational
Step-by-step explanation:
ASAP!!!
Alicia found $1.90 on the beach. Her brother found three times as much money. How much money did Alicia and her brother find in total?
Please be accurate!
Answer: The correct answer is $7.60.
Step-by-step explanation: First, you multiply 1.90 and 3. This gives you 5.7. Then, you add 1.9. This gives you $7.60.
Answer:
£7.60
Step-by-step explanation:
Alicia found £1.90, we can give this the value x
Her brother found triple the amount, or 3x
In total they found 4x
If £1.90 is x, 4x is £7.60
Solve for x to the nearest tenth.
Can someone help me? Multi-Step Diagrams
Answer:
Step-by-step explanation:
a bicycle wheel has a diameter of 65cm what is the length of one revolution of the wheel PLEASE HELP
AnswerAnswerAnswerAnswer: C = πd = 65π = 204.2 cm
Step-by-step explanation: C = pi*d
where d is the diameter.
First we get the circumference, then we multiply it by the number of revolutions, which is 20:
C = 3.14 * 65
C = 204.1 cm (this is only equal to 1 revolution)
Therefore, total distance travelled in after 20 revolutions is
204.1 * 20 = 4082 cm
A school wants 2 chaperones for every 25 students on a field trip. There are 100 students going on the field trip. How many chaperones does the school need?
A
4
B
8
C
108
D
50
Using proportions, it is found that the number of chaperones that the school needs is given by:
B. 8.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, 2 chaperones are needed for every 25 students. How many are needed for 100 students? The rule of three is given by:
2 chaperones - 25 students
n chaperones - 100 students
Applying cross multiplication:
25n = 2 x 100
n = 200/25
n = 8.
Hence option B is correct.
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At a cake stall , muffins cost $2 each & cookies cost $1 each. The cake stall earned $146. If 2 more cookies than muffins were sold, how many muffins were sold?
Answer:
48 muffins were sold
Step-by-step explanation:
Represent the number of muffins by m and the number of cookies by c.
Then the revenue from the sales of muffins was ($2/muffin)m and that from the sales of cookies ($1/cookie)c. Remembering that c = m + 2, we obtain the following equation:
($2/muffin)m + ($1/cookie)(m + 2) = $146, so that:
2m + 1m + 2 = 146, or 3m + 2 = 146, or 3m = 144.
Dividing both sides of this result by 3, we get m = 48
Thus, 48 muffins were sold.
A survey indicated that 4 out of 6 doctors used brand X aspirin. If 3600 doctors were surveyed, how many used brand X?
Answer: 2,400 doctors used brand X aspirin.
Step-by-step explanation: The question notifies us that 3,600 total doctors were surveyed. This automatically lets us know that 6/6 doctors = 3,600 doctors. We can find the unit rate from this point by dividing 3,600 by 6. We will find that 600 doctors represents 1/6 doctors. We can multiply our unit rate by 4 to find that 4 out of 6 doctors, or 2,400 doctors, use brand X aspirin. 4/6 of 3,600 is 2,400, so 2,400 doctors used brand X aspirin. Hope this helps!
Answer:
1200 doctors
Step-by-step explanation:
60% of doctors use brand X aspirin.
So, what is 60% of 2000?
(0.6) (2000) = 1200
1200 out of the 2000 use brand X.