The particular solution that satisfies the given initial condition is y = 1. This is the solution to the given initial-value problem.
To solve this initial-value problem, we must first note that the given differential equation is homogeneous. This means that if y is a solution to the given equation, then so is cy, where c is an arbitrary constant. Thus, the first step in solving this initial-value problem is to find the general solution of the homogeneous equation. To do this, we can use the method of separation of variables.
This method involves separating the variables x and y on opposite sides of the equation, and then integrating both sides with respect to their respective variables. Doing this yields:
∫xy2 dy = ∫(y3 − x3) dx
Integrating both sides of the equation with respect to y yields:
y3x2/3 + C1 = x4/4 + C2
where C1 and C2 are arbitrary constants. Rearranging this equation yields:
y3 = 4x4/3 − 4C2x2/3 + 4C1
Now, we can use the given initial condition, y(1) = 1, to determine the value of the arbitrary constants. Substituting x = 1 and y = 1 into the equation yields:
13 = 4/3 − 4C2/3 + 4C1
Solving for C1 and C2 yields:
C2 = 0, C1 = 3/4
With the arbitrary constants determined, we can now find the general solution of the homogeneous differential equation. Substituting the values of C1 and C2 into the equation yields:
y3 = 4x4/3 − 3/4
This equation is the general solution of the given homogeneous differential equation. To solve the initial-value problem, we must now find the particular solution that satisfies the given initial condition. To do this, we can substitute the initial condition, y(1) = 1, into the general solution to obtain:
13 = 4/3 − 3/4
Solving for y yields:
y = 1
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Answer this quick please
The graph of g is the graph of f translated 3 units right. Option C is the answer
How determine how the graphs of f(x) = 2x + 1, and g(x) = 2(x + 3) + 1 compare?In geometry, a translation is a type of transformation that involves moving a geometric figure from one location to another without changing its size, shape, or orientation.
Remember, in the cartesian plane or graph, the movement in x-axis is either to the left (negative) or right (positive).
Since f(x) = 2x + 1, looking at g(x) = 2(x + 3) + 1, you will notice that 3 is added to the value x. This is a movement in the positive x-axis (right translation) and the translation is by 3 units.
Therefore, the graph of g is the graph of f translated 3 units right
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What is 2/5 of 15? help pls
What is 2/5 of 15?
Answer:
2/5 of 15 is 6.
Answer:
6
Step-by-step explanation:
The word of in math refers to multiplication.
We can convert 15 to a fraction as well so we can use them together (15/1).
[tex]\frac{2}{5}[/tex] x [tex]\frac{15}{1}[/tex]
We can then work diagnolly and reduce the 5 and 15 since they are both divisible by 5- this is also known as the GCF or Greatest Common Factor
[tex]\frac{2}{1}[/tex] x [tex]\frac{3}{1}[/tex]
This is the same as 2 x 3 since both numbers divided by 1 are just themselves.
2x3 = 6
At a constant temperature the volume of a gas is inversely proportional to its mass…
a) The volume of the gas is 0.923 x [tex]10^{-6}[/tex] m³.
b) The pressure of the gas is 0.532 x [tex]10^7[/tex] Pascals.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
3 = 4k is an equation.
We have,
Volume of a gas (V) ∝ 1/ Pressure of a gas (P)
This can be written as,
Volume of a gas = K / Pressure of a gas
K = VP
Now,
P =1.8 x [tex]10^6[/tex] Pascals
V = 2.1 x [tex]10^{-8}[/tex] m³
K = VP = 1.8 x 2.1 x [tex]10^{-2}[/tex]
k = 3.78 x [tex]10^{-2}[/tex] pascal m³
Now,
P = 4.1 x [tex]10^4[/tex] Pascals
V = K/P = 3.78 x [tex]10^{-2}[/tex] Pascal m³ / 4.1 x [tex]10^4[/tex] Pascals
V = 0.923 x [tex]10^{-6}[/tex] m³
Now,
V = 7.1 x [tex]10^{-9}[/tex] m³
P = k/V = 3.78 x [tex]10^{-2}[/tex] Pascal m³ / 7.1 x [tex]10^{-9}[/tex] m³
P = 0.532 x [tex]10^7[/tex] Pascals
Thus,
The volume is 0.923 x [tex]10^{-6}[/tex] m³.
The pressure is 0.532 x [tex]10^7[/tex] Pascals.
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Tyler is 8 years old. His sister Olivia is 4 years less than twice his age.
Write a numerical expression for Olivia's age in the box below.
Answer: Olivia is 12 years old.
Step-by-step explanation
Tyler = T
Olivia = O
T=8
O=T*2-4
O=8*2-4
O=16-4
O=12
he lengths of pregnancies in a small rural village are normally distributed with a mean of 260 days and a standard deviation of 15 days. in what range would you expect to find the middle 50% of most pregnancies? between and . if you were to draw samples of size 36 from this population, in what range would you expect to find the middle 50% of most averages for the lengths of pregnancies in the sample? between and . enter your answers as numbers. your answers s
Using the normal distribution, the middle 50% would be expected to be in the range of 250 to 270 days.
Using the central limit theorem, for the samples of 36, the middle 50% would be expected to be in the range of 258 to 262 days.
What is normal distribution theorem?A sort of continuous probability distribution for a real-valued random variable is the normal distribution or the Gaussian distribution.
Normal Distribution of Probabilities
The z-score formula, which for a measure X, in a set with mean and standard deviation, is given by: can be used to address problems with normal distributions.
Z = (X - μ)/σ
The z-score calculates the measure's standard deviation from the mean.
A p-value, or percentile of X, is assigned to each z-score.
Mean (μ) = 260.
Standard deviation (σ)= 15 .
The normal distribution is symmetric, which means that the middle 50% is between the 25th percentile and the 75th percentile.
The 25th percentile is X when Z has a p-value of 0.25, so X when Z = -0.675.
The 75th percentile is X when Z has a p-value of 0.75, so X when Z = 0.675.
Lower bound:
Z = (X - μ)/σ
⇒ -0.675 = (X - 260)/15
⇒ X - 260 = -0.675*15
⇒ X - 260 = -10.125
⇒ X = 260 - 10.125
⇒ X ≈ 250
Upper bound:
Z = (X - μ)/σ
⇒ 0.675 = (X - 260)/15
⇒ X - 260 = 0.675*15
⇒ X - 260 = 10.125
⇒ X = 260 + 10.125
⇒ X ≈ 270
The middle 50% of pregnancies would be in the range of 250 to 270 days.
For sample of 36: By the Central Limit Theorem, the standard deviation of the sampling distribution of sample means of size n is given by .
Sample of 36, thus n=36, s=15/√36
⇒ s=15/6
⇒ s=2.5
Lower bound:
Z = (X - μ)/s
⇒ -0.675 = (X - 260)/2.5
⇒ X - 260 = -0.675*2.5
⇒ X - 260 = -1.69
⇒ X = 260 - 1.69
⇒ X ≈ 258
Upper bound:
Z = (X - μ)/s
⇒ 0.675 = (X - 260)/2.5
⇒ X - 260 = 0.675*2.5
⇒ X - 260 = 1.69
⇒ X = 260 + 1.69
⇒ X ≈ 262
The middle 50% of pregnancies would be in the range of 258 to 262 days.
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Mr. Smith runs 2.7 miles every day of the week. How many miles does he run in one year? : *
Based on the above, Mr. Smith runs approximately 985.5 miles in one year
What is the runTo calculate the number of miles Mr. Smith runs in one year, we can multiply the distance he runs each day by the number of days in a year.
Number of miles Mr. Smith runs in one day: 2.7 miles
Number of days in a year: 365 (assuming a non-leap year)
S, one can calculate the total distance he runs in one year:
Total miles in one year = Distance per day * Number of days in a year
= 2.7 miles x 365 days
= 985.5 miles
Therefore, Mr. Smith runs about 985.5 miles in one year.
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Beth is making gingerbread men. She uses 2 raisins for eyes and 3 raisins for buttons for each gingerbread man. She buys 4 boxes of raisins, each with 120 raisins in it. How many dozens of gingerbread men can she make?
Answer: 96
Step-by-step explanation: This is how to solve:
120 * 4
= 480
3 + 2 = 5
480 / 5
= 96
First, you need to multiply the boxes bought by the total amount inside the box. (120 * 4)
The, we need to find how many raisins she uses IN TOTAL for each gingerbread man. So, we need to add 3 + 2
This equals 5
So, 120 * 4 = 480
So, in total, she buys 480 raisins. So, to find how much gingerbread she can make, we need to divide 480 by 5. This would get you 96. I hope this helps ;)
a roof has a 5:12 pitch and the roof is 175" horizontally from the ridge to the edge , what is the height of the roof from the lowest point to the highest point?
When a roof has a pitch of 5 : 12 and the roof is 175'' horizontally the height of the roof from the lowest point to the highest point is solved to be 73''
How to determine the roof's heightThe idea of the slope is represented in the form 5: 12 when calculating the height of the roof.
This indicates that there is a 5 increase for every 12 units.
The rise is equal to 5, and the run is 12.
The vertical is the ascent, and the run is the horizontal.
It is possible to compare using the provided ratio as follows.
Let x represent the rise so that
x / 175" = rise / run = 5 / 12
x / 175" = 5 / 12
cross multiplying
175 * 5 = 12x
12x = 875
x = 875 /12
x = 72.92 ''
The height of the roof, measured from its lowest to its highest point, is calculated to be 73 inches.
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For a concert, 19 boys and 22 girls bought tickets from the music club. The total cost of the tickets was $256. This total cost includes a $10 tax. What was the cost of each ticket, not including the tax?
Part A
Which of the following steps are needed to solve this problem? Select all that apply.
A.
Subtract 19 from 22 to find out how many more girls than boys went to the concert.
B.
Add 19 and 22 to find the total number of students who attended the concert.
C.
Add $10 to $256 to find the total cost of the tickets without the tax.
D.
Subtract $10 from $256 to find the total cost of the tickets without the tax.
E.
Divide $256 by 10 to find the total cost of the tickets without the tax.
Part B
What was the cost of each ticket, not including the tax?
A.
$4
B.
$5
C.
$6
D.
$7
A) First we need to subtract the tax, the correct option is D.
B) by dividing the total cost without the tax by the number of people, we wiill see that each ticket costs $6, the correct option is C.
Which is the first step?We want to find the total cost of each ticket not including the tax, then the first thing that we need to doo is take the total cost ($256) and subtract the $10 of the tax, we will ge:
$256 - $10 = $246
Then the correct option is D
"Subtract $10 from $256 to find the total cost of the tickets without the tax."
Part B:
Now we can divide that amount by the number of people so we get how much each ticket costs:
19 + 22 = 41
We will get:
$246/41 = $6
Then the correct option is C.
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Can someone help??
Answers:
A. 1 cm and 5 cm
B. 8 cm and 15 cm
C. 3 cm and 4 cm
D. 5 cm and 17 cm
Answer:
A. 1 cm and 5 cm
Step-by-step explanation:
Let me know if my work makes sense!
Corey is making a wall-mounted bookshelf. It has 2 shelves, with a third piece of wood intersecting them. To support the shelves, Corey orders some L-brackets to put between the shelves
and the crosspiece. He measures angle 6. How many brackets should he order to have one for every angle that is congruent to angle 6? Explain.
O
2
34
5
6
7 8
A. 2; 27 is congruent to 26.
B. 2; 23 is congruent to 26.
C. 3; 27, 23 are both congruent to 26.
OD. 4; 27, 22, 23 are all congruent to 26.
k
Answer:
B / 2; <3 is congruent to <6
Step-by-step explanation:
To find a congruent angle you must find what can fit inside the giving number the best. If we compare all of the answer is wouldn't make sense, since 7 is greater than 6 it would be wrong. So, A is Incorrect.
C is about 3 and 7. C would fit but 7 wouldn't. So, C is incorrect.
D has both 2 and 3 but also have 4 and 7 which wouldn't match. So, D is incorrect.
( THIS IS WHAT I THINK IS IT)
Answer:
B
Step-by-step explanation:
for a generic a→b, what quantity, when graphed versus time, will yield a straight line?
A graph [tex]\frac{1}{A_{t}}[/tex] and time yields a straight line for a second order reaction. The positive slope of the straight line is rate constant k for second order.
For a second order reaction A→B.
The integrated rate law is
-d[n]/dt = k[A]^{r}
where, k = rate constant of second order reaction and
[A]^{r} = concentration of [A]
-[tex]\int^{A_{t}}_{A_{0}}\frac{d[A]}{[A]^{r}} = k\int^{t}_{t_{0}}dt[/tex]
where, [tex]A_{t}[/tex] = concentration of A at time t
[tex]A_{0}[/tex] = concentration of A at time t=0
[tex]\frac{1}{A_{t}}-\frac{1}{A_{0}}=kt[/tex]
Adding [tex]\frac{1}{A_{0}}[/tex]on both side, we get
[tex]\frac{1}{A_{t}}=kt+\frac{1}{A_{0}}[/tex]....................(1)
On comparing the equation 1 by the equation y = mx+c, we get that the plot of [tex]\frac{1}{A_{t}}[/tex] and plot of time t will be in the straight line with the positive slope k.
The plot is given below:
Hence, a graph [tex]\frac{1}{A_{t}}[/tex] and time yields a straight line for a second order reaction. The positive slope of the straight line is rate constant k for second order.
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The complete question is given below:
pls do this asap its important
Answer:
3.1 mm
Step-by-step explanation:
as 1mmx3.14=3.14mm
And then correct it to 1 decimal place =3.1
Which one of the following is arithmetic sequence? 15, 12, 9, 6 … 15, 30, 60, 120 … 1, 4, 9, 16 … 1, 8, 27, 64 …
An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed number, called the common difference, to the previous term. For example, the sequence 15, 12, 9, 6, … is an arithmetic sequence because each term is obtained by subtracting 3 from the previous term, which is the common difference. On the other hand, the sequence 15, 30, 60, 120, … is not an arithmetic sequence because the difference between each consecutive pair of terms is not constant. The same is true for the sequences 1, 4, 9, 16, … and 1, 8, 27, 64, …. Therefore, the only arithmetic sequence among the given options is 15, 12, 9, 6, ….
finish the question
the value of decreasing of 15% from £1200 is equal to....
Answer: The final value is £1,020
Step-by-step explanation: In order to find the final value, the first step in the process is to multiply 1,200 by 0.15 in order to find out what 15% of 1,200 is. After doing obtaining the answer, which is 180, subtract that from the original answer in order to find out what the final value will be.
The final value is then equal to £1,020
PLS HELP ALMOST DUE AND REALLY IMPORTANT.
What is the constant of proportionality for the data in the table? Time (weeks) 2 5 10 Trees Planted 130 325 650 k= 70 k = 130 k = 65 k = 195
The constant of proportionality for the data in the table is 65. This can be determined by dividing the number of trees planted by the number of weeks for each data point in the table. For example, for the first data point where 2 weeks have passed, 130 trees have been planted, which means the constant of proportionality is 65 (130 / 2 = 65). This value is the same for all of the data points in the table, which means it is the constant of proportionality for the data.
Which of the following choices lists the values of the side lengths of an isosceles triangle with a hypotenuse = 8?
8,8, and 16
2, 4, and 8
4√2, 4√2, and 8
None of these choices are correct.
The set of the values of the side lengths of an isosceles triangle that has a hypotenuse that is 8 units long is: C. 4√2, 4√2, and 8.
What is an Isosceles Triangle?An isosceles triangle is a type of triangle that has two sides that are of the same length, while the third side has a different length.
What is the Hypotenuse of a Triangle?The hypotenuse is found in a triangle that has a right angle. This means the triangle is a right triangle, and therefore, according to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the other legs of the triangle.
Considering the definition given above, it means the right triangle we are looking for must be a right triangle is isosceles, which hast two equal sides and an hypotenuse that is 8 units long.
The values of the set of lengths, 2, 4, and 8 cannot be the isosceles triangle because they have three different side lengths.
8,8, and 16 do not conform to the Pythagorean Theorem because:
16² ≠ 8² + 8²
4√2, 4√2, and 8 conform to the Pythagorean Theorem because:
8² = (4√2)² + (4√2)²
64 = 64
Therefore, the values of side lengths are: C. 4√2, 4√2, and 8.
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please help will give brainliest
The polygon for the given data will be a square. The correct option is E.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
A square is a quadrilateral having all the sides equal and all the angles congruent to each other. The value of all the angles is 90 degrees and the sum of the angles of the square is 360 degrees.
The given data is that all the sides are congruent and all the angles are congruent so the given figure is square.
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What place value is this
18 thousands x 10 = ?
given the vector a⃗ =3.0i^+1.5j^, find a vector b⃗ that is perpendicular to a⃗ .
1.5i^- 3j^ is the perpendicular vector to the vector 3.0i^+1.5j^
What is perpendicular vector?Whenever there is a 90 degree angle between two vectors, they are said to be perpendicular. Two perpendicular vectors dot product is zero. and dot product is scaler product of 2 vectors.
Let b = xi^+ yj^ be the perpendicular vector to a vector
and we know that 2 vectors are perpendicular if thier dot product is 0
so it implies that
b.a(dot product) =0
=> (3i^+1.5j^) . (xi^+yj^)=0
=> 3xi^.i^+ 3y i^.j^ +1.5xj^.i^+1.5yj^j^=0
=>3x+1.5y=0 ----(i)
becaus i^.j^=0 and j^.i^0
=> x= 1.5 and y=-3 satisfies equation (i).
so the perpendicular vector is 1.5i^- 3j^
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Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 18)(0,18) and (3, 6174)(3,6174).
The exponential function in the form y = ab^x is y = 18(7)^x
How to determine the exponential function in the formFrom the question, we have the following parameters that can be used in our computation:
Points: (0, 18) and (3,6174).
The above can be represented as
(x, y) = (0, 18) and (3,6174).
An exponential function is represented as
y = ab^x
Where
a = y when x = 0
This means that
a = 18
So, we have
y = 18b^x
At (3,6174), we have
6174 = 18b^3
So, we have
343 = b^3
Take the cube root of both sides
b = 7
This means that
y = 18(7)^x
Hence, the function is y = 18(7)^x
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Solve this please .
b/24= -6 for b
Answer:
b = -144
Step-by-step explanation:
b/24 = -6
Multiple 24 on both sides since it's being divided.
b = -144
Answer:
[tex] \sf \: b = - 144[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of b.
The equation is,
→ b/24 = -6
Then the value of b will be,
→ b/24 = -6
→ b = (-6) × 24
→ [ b = -144 ]
Hence, the value of b is -144.
what is the coefficient of x in -3 / 7 x
Answer:5103
Step-by-step explanation:We only care about 7xy6, cause it's the only term involving x In your example y = −3, thus 7(−3)6x = 7 ⋅ 729x = 5103x The coefficient of x is 5103
It’s a hot summer day. Darius is babysitting and has promised his sweet little sister that he will fill her wading pool. He plans to soak his feet in the water as he sips a cool soda and watch little sister as she plays in the water. Sounds great, right? All he needs to do is get the pool filled. Unfortunately, little sister is impatient and starting to whine. Darius has a hose ready in the backyard to fill the pool, but he decides he will also drag the hose from the front-yard, so the two hoses can work together to fill the pool faster. Nobody wants their darling little sister to be unhappy!
Darius knows from experience that if he only uses one hose at a time, the front-yard hose takes 10 minutes longer to the fill the pool than the back-yard hose. With the two hoses working together, the pool is filled in 12 minutes. Once Darius is comfortable with his toes dangling in the water, he starts to wonder how long it would have taken to fill the pool if he had only used one of the hoses.
Darius thinks, “Hmmm. Usually when I think about how long it takes to do something I have to think about the rate it is going.”
5. Write a function, R(x), that models the combined rate of the two hoses in terms of the time that it takes for the backyard hose to fill the pool alone.
6.a. What is the entire domain of this function, if the context is not considered?
6.b. What is the domain of this function in the context of filling Darius’ pool? Explain your thinking after you submit.
7. Graph R(x). Label all important features and describe them.
Answer: I can’t help you
Step-by-step explanation:
Can someone help me answer this please?
Answer:
B
Step-by-step explanation:
When zero is our denominator the graph is undefined at that point. In the case of b, when x = 1 The denominator is o. That is why there is a striped line at x = -1
Marcia made 10 bracletes for 5 friends. Jen made 1 braclets for 4 friends.Are these ratios/rates equivalent.
The fraction or ratio for the bracelet aren't equivalent.
Are these fractions equivalent?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
Here Marcia made 10 bracletes for 5 friends. This will be:
= 10/5
= 2:1
Jen made 1 braclets for 4 friends. This will be:
= 1/4.
= 1:4
The fraction or ratio aren't equivalent.
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450 kid and chaperone total go to a field trip to the zoo. Each bu hold 80 paenger; how many bue will be needed to tranport all the paenger?
With 450 kids and chaperone there are 451 passengers to be transported, Using simple unitary method, The answer is 6 buses.
What do you mean by unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
What do you mean by arithmetic operators?The arithmetic operator is used to carry out mathematical operations on the provided operands, including addition, subtraction, multiplication, division, and modulus.
total members to be transported = 451
each bus hold = 80
Number of bus needed = 451/80 = 5.63
So, We need 6 buses in total.
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it would take charlene and gina 18 minutes to organize charlene’s comic book collection if they work together. if gina works alone, it would take her 15 minutes longer than it would take charlene working alone. when x represents the number of minutes it takes charlene to organize the comic book collection working alone, the situation is represented by this equation: 1/x + 1/x + 15 = 1/18which value is a solution of the rational equation that must be discarded because of the context?a. x = 0 b. x = -9 c. x = -15 d. x = -30
The value that is a solution of the rational equation that must be discarded because of the context is B. x = 9.
How to illustrate the equation?From the information, it would take Charlene and Gina 18 minutes to organize charlene’s comic book collection if they work together. if gina works alone, it would take her 15 minutes longer than it would take charlene working alone.
The equation can be illustrated as:
1/x + 2/(x + 15) = 1 / 18
The objective is to determine the value which nullify the context. The option will be -9. This is illustrated as:
1 / -9 = 1 / -9 + 15 = 1 / 18
The correct option is B.
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miae is baking .the recipe uses 3/4 cup sugar.miae wants to make 1/2 of a batch .how many cups of sugar does she need
To answer the question, Miae needs 3/8 cup of sugar for 1/2 of a batch, it is important to understand the concept of fractions. miae is baking .the recipe uses 3/4 cup sugar.Miae needs 3/8 cup of sugar for 1/2 of a batch.
To answer the question, Miae needs 3/8 cup of sugar for 1/2 of a batch, it is important to understand the concept of fractions. A fraction is a part of a whole, it is represented by a numerator and denominator, the numerator represents the number of parts and the denominator represents the total number of parts. In this question, the recipe calls for 3/4 cup of sugar for the entire batch, so to get 1/2 of the batch, Miae needs to divide the fraction by 2. To do this, we can either divide the numerator and denominator by 2, or multiply the fraction by 1/2. In this case, 3/4 multiplied by 1/2 is 3/8, so Miae needs 3/8 cup of sugar for 1/2 of a batch.
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Seems to me like a lot of little boys have the name 'Jack' lately. Let's assume it's one in every ten.
What's the probability that my daughter will have at least one Jack on her co-ed soccer team of 12
players, 6 of whom are boys?
O 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10
O 1/10 x 1/10 x 1/10 x 1/10 x 1/10 x 1/10
O 1-(9/10 x 9/10 x 9/10 x 9/10 x 9/10 x 9/10)
O 1/6+1/6 + 1/6 + 1/6 + 1/6 + 1/6
O 6/12 x 5/11 x 4/10 x 3/9 x 2/8 x 1/7
The probability of at least one boy named Jack is (c) 1 - (9/10 x 9/10 x 9/10 x 9/10 x 9/10 x 9/10)
How to determine the probability of at least one boy named JackFrom the question, we have the following parameters that can be used in our computation:
P(Jack) = 1/10
Number of boys = 6
Using the complement rule of probabilities, we have
P(At least one Jack) = 1 - P(No jack)
Where
P(No jack) = (1 - P(Jack))⁶
So, we have
P(No jack) = (1 - 1/10)⁶
Evaluate
P(No jack) = (9/10)⁶
Substitute the known values in the above equation, so, we have the following representation
P(At least one Jack) = 1 - (9/10)⁶
Evaluate
P(At least one Jack) = 1 - (9/10 x 9/10 x 9/10 x 9/10 x 9/10 x 9/10)
Hence, the probability is (c) 1 - (9/10 x 9/10 x 9/10 x 9/10 x 9/10 x 9/10)
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