The probability that shooting stars are there in the fall is 0.5904.
The probability of not seeing any falling star in that time period of 15 minutes is 1 - 0.2 = 0.8.
In this way, the combined probability of not seeing any of the falling stars in the four-time period is: 0.8 * 0.8 * 0.8 * 0.8 = 0.8⁴ = 0.4096
= 1 - 0.4096 = 0.5904
=P(X = x) = μˣ * e^-μ / x!
Here, the span is of 15 minutes. In this way, the typical number of events in the span is 15λ. The probability of witnessing 0 occasions (i.e X = 0) is:
P(X = 0) = μ⁰ * e^-(15λ) / 0! = 1 / e^(15λ) — — (1)
(1) is equal to 80% as the probability of at least one event happening is 20%.
So, 1 / e^(15λ) = 0.8
or, e^(15λ) = 1.25
or, 15λ = ln(1.25) = 0.2231
= λ = 0.0149 / min
In this way, the typical number of occasions (falling stars) is 0.0149 per minute.
Presently, the typical number of occasions in an hour is:
0.0149 * 60 = 0.8926 / hour
So, the Poisson distribution expression becomes:
P(X = x) = 0.8926ˣ * e^-0.8926 / x! — — (2)
Here, the time span is 60 minutes.
Presently, we should find the probability of not having even a solitary occasion in 60 minutes:
P(X = 0) = 0.8926⁰ * e^-0.8926 / 0! = 0.4096
So, the probability of having at least one event is the complement of the above probability.
So, P(X≥1) = 1 - P(X=0) = 1 - 0.4096 = 0.5904
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Jayce is a taxi driver.
M(n) models Jayce's fee (in dollars) for his nth drive on a certain day.
What does the statement M(10) = K mean?
Choose 1 answer:
A
Jayce's fee for his Kth drive is equal to $10.
(B)
Jayce's fee for his 10th drive is equal to K dollars.
The correct answer is C. Jayce's fee for his 10th drive is equal to K dollars.
Based on the mentioned statements, n refers to the number of drives in a certain day. Additionally, it is mentioned that M(n) models the fee in dollars. As is seen in the equation, M(n) is equal to K. Thus, the fee in dollars is K dollars.
Now, as n is ten, thus the drive is tenth. And the fees for tenth drive is K dollars. So, the third option is correct, which states that Jayce's fee for his tenth drive is equal to K dollars.
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How many dogs could Roscoe groom if he worked for 40 hours?
90
120
220
200
There are 200 dogs Roscoe groom if he worked for 40 hours.
What is working time?
A person's working time is the time they are engaged in paid work. Personal housework, childcare, and pet care are examples of unpaid work that is not included in the definition of the working week.
In most cases, when someone inquires about your working hours, you should first provide the start time before providing the time you leave for home.
From the given graph we can see that for each three hours the number of dogs are increased by 15.
So, for each one hour the number of dogs increased by 5.
For 18 hours the the number of dogs are 90.
After 18 hours to complete 40 hours we need 22 hours.
So, for 22 hours the number of dogs are
22 x 5 = 110.
Therefore, the total number of dogs worked for 40 hours are,
90 + 110 = 220.
Hence, there are 200 dogs Roscoe groom if he worked for 40 hours.
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Pls pls pls help it has to be turned in today!
Using the compound amount formula, the amount after 40 years is 2000(107/100)^40.
In the given question,
Esther got a summer job and decided to set aside $2000 to prepare for retirement without making monthly contribution.
She invests in the US stock market through as index fund that averages a 7% return compounded annually over this 40 year period.
We have to find the total balance in the account after 40 years.
We have to find total balance compounded annually.
The formula of the compound amount is
A = P(1+r/100)^n
where A = Amount
P = Principal Amount
r = interest rate
n = time
From the question we know that
P = $2000, r = 7%, n = 40
Now putting the value in formula
A = 2000(1+7/100)^40
Simplifying
A = 2000(1×100/100+7/100)^40
A = 2000(100/100+7/100)^40
A = 2000((100+7)/100)^40
A = 2000(107/100)^40
You can find the amount after simplifying the amount.
Hence, the amount after 40 years is 2000(107/100)^40.
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X (3x + 5)°
(4x)
Y
(8x - 14)°
B
N
Answer:2
Step-by-step explanation:
1+1 es 2
Jerome invested 260000 for 2 years at a rate of 8%p.a. 1)calculate the simple interest 2)calculate the investment at compound interim interest 3)amount at the end of the simple interest 4)amount at the end of compound 5)difference between the amount at simple interest and compound interest
1) Simple interest is $41600, 2) compound interest is $ 43264, 3) Amount at the end of Simple interest is $301600, 4) Amount at the end of Compound interest is $303264, 5) Difference in the amount of simple and compound interest is $ 1664.
Here it is given:
Principle (P) =$ 260000
Time(t) = 2 years
Rate (R) = 8%
1) We have to find the simple interest:
Simple interest(SI) = P× t × R/ 100
= 260000× 2× 8/ 100
= $41600
2) We have to find Compound Interest
Compound interest(CI) =P( 1 + R/100[tex])^{t}[/tex]- P
= 260000( 1 + 8/100[tex])^{2}[/tex]- 260000
= 260000( 27/25[tex])^{2}[/tex] - 260000
= 303264 - 260000
= $43264
3) Amount at the end of simple interest
Amount = P + SI
= 260000 + 41600
=$301600
4) Amount at the end of compound interest
Amount = P + CI
= 260000+ 43264
= $303264
5) Difference between the amount at simple interest and compound interest
Difference = 303264 - 301600
= $1664
Therefore the simple interest is $41600, the compound interest is $43264, the Amount at the end of simple interest is $ 301600, the amount at the end of the compound interest is $303264, and the difference in the amount of simple interest and compound interest is $1664.
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Find the total area for the shape!!
Answer:
56cm²
Step-by-step explanation:
Because this is an irregular shape, you have to split it into two shapes and find the area of each one. Then you can add those two areas together to find the total area of the figure. There are many ways you can split it but the way I did it left me with the equation (12·3)+(4·5). Then all you have to do is multiply and add which will give you a total of 56cm².
To paint a house, a painting company charges
a flat rate of $500 for
supplies, plus $50 for each hour of labor.
a.
How much would the painting company charge to paint
a house that
needs 20 hours of labor? A house that needs 50 hours?
Call the number of hours of labor x.
A flat rate of $500 -> just $500.
$50 for each hour of labor -> 50x (for x hours)
Therefore, we can represent the amount needed for x hours of labor as the function : 500 + 50x.
We substitute :
20 hours of labor = 500 + 50 x 20 = $1500
50 hours of labor = 500 + 50 x 50 = $3000
Jane was asked to solve the equation `2-4=2(-5+1)`. she believes the solution to the equation is `x=\frac{1}{2}` . explain how jane could confirm that her solution is correct
the solution for the given equation is x= 1/2
an equation could be a formula that communicates the balance of two expressions, by interfacing them with the equals sign. Understanding an equation containing factors comprises deciding which values of the factors make the equality true. The factors for which the equation must be fathomed are moreover called unknowns, and the values of the unknowns that fulfill the balance are called solutions of the condition. There are two sorts of equations such as conditional and identities equations. An identity is genuine for all values of the factors. A conditional equation is as it were genuine for specific values of the factors
since the given expression is :
`(2-4)=2(-5+1)x²
so solving for the simple arithmetic expression on both sides :
=>-2 =2(-4)x²
=> -2 = -8x²
=>2/8=x²
=>1/4= x²
=>x= 1/2
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Given the following information about the arithmetic sequence an, find a10. A5=24 a8=39
The 10th term of an arithmetic sequence is found as the 49.
Define the term arithmetic sequence?An ordered group of numbers with a shared difference with each consecutive word is referred as an arithmetic sequence. For particular, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression would be another name for an arithmetic sequence.As per the stated values in question.
Fifth term a5 = 24
8th term a8 = 39.
Let the first term be 'a' and the common difference be 'd'.
Then,
a5 = a + 4d
24 = a + 4d .....eq 1
a8 = a + 7d
39 = a + 7d .....eq 2
Solving eq 1 and 2.
3d = 15
d = 5
a = 4
Now,
a10 = a + 9d
a10 = 4 + (9 x 5)
a10 = 4 + 45
a10 = 49
Thus, the 10th term of an arithmetic sequence is found as the 49.
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Solve for a side in right triangles
Really need help with this one!!
The value of side AC is AC = 3.
What is right triangle?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
The given triangle ΔABC is a right angled triangle.
So, to find the side AC we can use the cosine ratio,
[tex]cosB = \frac{Adjacent side}{Hypotenuse}\\ cos65 = \frac{AC}{AB} \\cos65 = \frac{AC}{7} \\AC = 7(c0s(65)\\AC = 7(0.4226)\\AC = 2.9583[/tex]
AC ≈ 3.
Hence, the length of side AC is 3.
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the weight of bags of all purpose flour is normally distributed with expected value 10 pounds and standard deviation 0.2 pounds. the heaviest 2.5% of the bags packaged by the flour company are labeled as overweight. what is the probability that of 10 randomly chosen bags of flour at least 2 are overweight?
The probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68.
Given, that the weight of bags of all purpose flour is normally distributed with expected value 10 pounds and standard deviation 0.2 pounds.
As, we know that
P(X) = (1/s√2π)exp(-1/2((X-m)/s)^2)
where, m is the expected value
and s is the standard deviation.
Now, we have Expected value 10 pounds
and Standard Deviation 0.2 pounds
So, the probability that of 10 randomly chosen bags of flour at least 2 are overweight be
P(X=0) + P(X=1) = (1/0.2√2π)exp(-1/2((0-10)/0.2)^2) + (1/0.2√2π)exp(-1/2((1-10)/0.2)^2)
P(X=0) + P(X=1) = 0.32
So, Required Probability be 0.68.
Now, the probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68
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The variable p represents number of presents. If it takes 10 feet of ribbon to make 1 bow on a present and 3 feet is used to practice trying the bow, the expression 10p + 3 can be used. If there are 7 presents, how much ribbon is needed? Ribbon is sold in 15 feet packages. How many do you need to buy?
The number of ribbons that is needed for 7 presents is 73 ribbons.
She needs 5 packages.
What is an expression?An expression is simply used to illustrate the relationship between the variables.
In this case, it takes 10 feet of ribbon to make 1 bow on a present and 3 feet is used to practice trying the bow, the expression 10p + 3 can be used.
The ribbons needed for 7 presents will be:
= 10p + 3
= 10(7) + 3
= 70 + 3
= 73
Since it's sold in 15 feet packages, the number needed will be:
= 73 / 15
= 5
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Which equation represents a line that is parallel to the line y = -2/3x + 5? Pls Hurry :/
The equation of the line parallel to the equation y = - 2 / 3 x + 5 is 2x - 3y = 21
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Lines are parallel when they have the same slope.
Using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = - 2 / 3 x + 5.
The slope of the equation is - 2 / 3.
Hence, let's find the equation that has the same slope as - 2 / 3. First, we will have to represent the equation in slope intercept form.
2x - 3y = 21
add 2x to both sides of the equation
2x + 2x - 3y = 21 + 2x
- 3y = 2x + 21
divide both ides by - 3
- 3y / - 3 = 2x / -3 + 21 / - 3
y = - 2 / 3 x - 7
Therefore, the slope is - 2 / 3 , the equation is 2x - 3y = 21
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work out the minimum number of hikers who could have walked between 6 miles and 17 miles work out the maximum number of hikers who could have walked between 6 miles and 17 miles
The maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
We need to find the maximum number of hikers who could have walked between 6 miles and 17 miles.
What is meant by minimum and maximum value?When the derivative equals 0, rearrange the function using elementary algebraic principles to find the value for x. The x-coordinate of the function's vertex, which is where the maximum or lowest will occur, is provided in this answer. the solution back into the original function to determine the minimum or maximum.
From the table, we can see
Between intervals 5≤x<10 there are 2 hikers
Between intervals 10≤x<15 there are 9 hikers
Between intervals 15≤x<20 there are 8 hikers
So, total number of hikers = 2+9+8
= 19
Hence, the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
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Suppose we want to choose 4 letters, without replacement, from 17 distinct letters. How many ways can this be done, if the order of the choices is not taken into consideration
Thus, the number of ways in which to choose 4 letters, without replacement, from 17 distinct letters is 57,120.
Define the term permutation?The term permutation applies to a mathematical computation of a number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something can be organized or arranged.Total distinct letters are 17.
There are 17 alternatives for the initial letter if there are 17 letters.
There are just 16 alternatives left once you remove the letter.
Each time you remove a letter, the bag contains one fewer letter.
Number of ways = 17 x 16 x 15 x 14
Number of ways = 57,120
Thus, if the sequence of the alternatives is irrelevant, there are 57,120 options.
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If Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.
The time taken to label 750 books if Clare labels books at 15 books per minute is 50 minutes.
How to calculate the time used?In this situation, Clare volunteers at a library during the summer and has to label 750 books and she labels books at 15 books per minute and she takes no breaks.
Let the time taken to label the 750 books be represented by x.
This will be illustrated as:
1/x = 15/750
Cross multiply
(15 × x) = (750 × 1)
15x = 750
Divide
x = 750 / 15
x = 50
The time is 50 minutes.
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Complete question
Clare volunteers at a library during the summer and has to label 750 books. Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.
Rhino poaching is a serious problem and has resulted in rhinos, particularly the black rhino, becoming an endangered species. Statistics suggest that there were 60 500 black rhinos at the beginning of 1970, but only 4 000 remained at the end of 2011. Determine the annual rate of depreciation that these statistics represent.
The annual percentage rate of depreciation of the number of rhinos represented by the statistics is approximately 6.41 %
What is a rate of depreciation?The rate of depreciation is the rate at which the number or value of an item reduces within each specified period.
The initial number of black rhinos in 1970 = 60,500
The number of black rhinos remaining in 2011 = 4,000
The annual rate of depreciation can be found using the formula;
[tex]FV = PV \cdot \left(1+\dfrac{r}{100} \right)^n[/tex]Where;
FV = The future value = 4,000
PV = The present value = 60,500
r = The annual depreciation rate
n = The number of years
[tex]4,000 = 60,500 \times \left(1+\dfrac{r}{100} \right)^{(2011-1970)}=60,500 \times \left(1+\dfrac{r}{100} \right)^{41}[/tex]
[tex]\left(1+\dfrac{r}{100} \right)^{41} = \dfrac{4000}{60500} = \dfrac{8}{121}[/tex]
[tex]r = 100\times \left(\sqrt[41]{ \dfrac{8}{121}} - 1\right) \approx -6.41[/tex]
The annual rate of depreciation is approximately 6.41%
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which contours are usually drawn darker than the other contours? group of answer choices index contours largest (max) value contour contour interval smallest (min) value contour
Index contours are usually drawn darker than the other contours.
Index Contours are darker and wider than the other regular contour lines for ease of identification. They are labeled with elevation and also have their altitude value mentioned on the dark lines and these values represent the altitudes of the particular contours. Index contours appears after every fifth contours. If the number with contours will increase then its elevation will also increase and similarly if the number associated with contours starts to decrease then its elevation also decreases.
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PLS ANSWER THIS Solve the following system of equations for all three variables.
The values of x, y and z are 4, 1 and - 6 respectively.
What is the general equation of a Straight line? What is a system of equations in two or three variable.The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied
We have the following equations -
8x + y + 4z = 9
4x - 3y + z = 7
8x - 4y + 5z = - 2
We have -
4x - 3y + z = 7
z = 7 - 4x + 3y
We can write -
8x + y + 4z = 9
as -
8x + y + 4(7 - 4x + 3y) = 9
8x + y + 28 - 16x + 12y = 9 ...Eq[1]
and we can write -
8x - 4y + 5z = - 2
8x - 4y + 5(7 - 4x + 3y) = -2
8x - 4y + 35 - 20x + 15y = - 2 ...Eq[2]
Plot the graph of equation [1] and [2]. We will will get -
x = 4
y = 1
Now -
z = 7 - 4x + 3y
z = 7 - 16 + 3
z = - 6
Therefore, the values of x, y and z are 4, 1 and - 6 respectively.
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a 61 mg of a vaccine is given to a patient to prevent measles. the vaccine leaves the body at a rate of 6.1% per hour. define a function g that gives the mass of the vaccine remaining in the body, v, in terms of the number of hours, n since the vaccine was administered. how much of the vaccine remains in the body 24 hours after it was administered? mg use your graphing calculator to determine how many hours passed before there were only 5mg of the vaccine remaining in the body.
The linear equation that represent the amount vaccine that remain is g = 61 - 0.061n. The vaccine remains in the body 24 hours after it was administered 59.536 mg. There were only 5mg of the vaccine remaining in the body after 918.033 hours.
What is rate?
A rate is a unique ratio where the two words are expressed in several units.
Given that the amount of vaccine is 61 mg.
The vaccine leaves the body at a rate of 6.1% per hour.
After 1 hour the body will consume 6.1% = 6.1/100 = 0.061 mg.
After n hour the body will consume 6.1%× n = 0.061n mg.
The remaining amount of vaccine is (61 - 0.061n).
The required linear equation that represent the remaining amount of vaccine is g = 61 - 0.061n.
Putting n =24 in the equation:
g = 61 - 0.061×24
g = 59.536 mg
The vaccine remains in the body 24 hours after it was administered 59.536 mg.
The graph represents that there were only 5mg of the vaccine remaining in the body after 918.033 hours.
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The value of function is positive so the function have maximum value at x=3.
In the given question we have to find the maximum or the minimum value of a function.
The given function is
f(x) = -3x^2+18x+3
To find the maximum or minimum value we firstly find the value of f'(x).
f'(x) = -6x+18
Now put f'(x)=0
-6x+18=0
Subtract 18 on both side we get
-6x=-18
Divide by -6 on both side we get
x = 3
Now finding the value of function at x=3
f(3)= -3*(3)^2+18*3+3
f(3)= -3*9+54+3
f(3)= -27+54+3
f(3)= 30
Since the value of function is positive so the function have maximum value at x=3.
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Write a unit rate for the situation.
Situation: 87 students in 3 classrooms
Unit rate:
students per classroom
The unit rate for the given situation is 29 students per classroom.
What is the unit rate?
A unit rate is described as a ratio comparing the first quantity to one unit of the second quantity.
Given situation is 87 students in 3 classrooms.
So, the unit rate [tex]= \frac{87}{3}[/tex] students/classroom
[tex]= 29[/tex] students per classroom
Hence, the unit rate for the given situation is 29 students per classroom.
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The graphing calculator screen below represents time on the horizontal axis and the speed of an object on the vertical axis.
The data graphed on the screen indicates which of the following about an object?
The object was at rest, then began moving, and then stopped.
O The object moved at a constant speed, then sped up, and then stopped.
O The object was at rest, then began moving, and then slowed down.
O The object moved at a constant speed, then sped up, and then moved at a constant speed again.
Check the picture below.
I really need help on this one.The amount of milk needed for each of 5 recipes is shown on the line plot.What is the total amount of milk needed for the recipes?
The total amount of milk needed for the recipes, considering the line plot, is of:
5.25 cups.
How to obtain the total amount of milk needed for the recipes?The total amount of milk needed for the recipes is obtained adding all the measures of the line plots.
The measures of the line plot given by the image at the end of the answer are given as follows:
Two measures of 1/4 cups = 0.25 cups, which is half the distance between 0 and 1/2.One measure of 1.25 cups, which is the value at the midpoint between 1 and 1.5.One measure of 1.5 cups.One measure of 2 cups.The total amount is given by the sum of all these measures, hence:
2 x 0.25 + 1.25 + 1.5 + 2 = 5.25 cups.
Missing InformationThe line plot is given by the image at the end of the answer.
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David picked 15 pears. Jenna picked p fewer pears than David. Write an expression that shows how many pears Jenna picked.
Answer:
15-p
Step-by-step explanation:
15-p
2x+y=4 1x-y=11 adding subtracting equations to solve systems.
By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3
What is meant by an equation?An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.
An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.
Given,
2x+y=4
x-y=1
By solving above two equations we get,
2x+y=4
x-y=1
3x=5
x=5/3
y=-1+x
y=(5/3)-1
y=2/3
Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3
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Help with this please (ASAP)
2x + 3x equals to 20x find the value of x.
Answer:
Here,
2x+3x=20x
or,5x=20x
or,5x-20x=0
or,15x=0(divide both sides by -15)
hence,x=0
PLEASE HELP
In November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems. In March's Math Meet, they solved $\frac23$ of the problems. (There might be different numbers of problems asked in November and March.)
In total, the Little Monsters solved $13$ of $30$ problems over both Math Meets. How many problems were asked at March's Math Meet?
The number problems solved by the little Monsters of Beast Academy in March's meet is 15.
How to determine the number of problems solved in March meetThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
let the number of questions solved by little Monsters of Beast Academy in
March's meet be xNovember's meet be yIn November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems = y/5
In March's Math Meet, they solved $\frac23$ of the problems = 2x/3
Hence:
y/5 + 2x/3 = 12
x + y = 30
solving the equation gives
x = y = 15
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what is 56/60 as a percentage
Answer:
93.33%
Step-by-step explanation:
56/60 as a percentage:
56/60 = 0.93333
0.93333 as a percent:
0.93333 * 100 = 93.33%
The value of solution for a number 56/60 into a percentage is,
⇒ 93.33%
We have to given that,
To change a number 56/60 into a percentage.
Since, A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Hence, We can write as,
⇒ 56/60 × 100%
⇒ 5600/60
⇒ 93.33%
Therefore, The value of solution for a number 56/60 into a percentage is,
⇒ 93.33%
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