factor out the coefficient of the variable : 2/3j - 2/9
Answer:
j3a3
Step-by-step explanation:
You have 15 marbles in a bag; 5 are red. If you pull out five marbles in a row and don't put
them back in, what are your chances of pulling all 5 red marbles? Decimal answer please.
Step-by-step explanation:
0.33 so says my mother bc she divide
Answer:
The probability of drawing a different marble is 0.25. The probability of drawing a red marble = 0.5
I do not know if this is correct please forgive me if I am wrong.
If I am right hope this helps!
In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y′′+4y′+3y=8te^−t+6e^−t−(9t+6)
with initial values y(0)=2andy′(0)=2.
We're given the ODE,
y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) - (9t + 6)
(where I denote exp(x) = eˣ )
First determine the characteristic solution:
y'' + 4y' + 3y = 0
has characteristic equation
r ² + 4r + 3 = (r + 1) (r + 3) = 0
with roots at r = -1 and r = -3, so the characteristic solution is
y = C₁ exp(-t ) + C₂ exp(-3t )
For the non-homogeneous equation, assume two ansatz solutions
y₁ = (at ² + bt + c) exp(-t )
and
y₂ = at + b
• y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) … … … [1]
Compute the derivatives of y₁ :
y₁ = (at ² + bt + c) exp(-t )
y₁' = (2at + b) exp(-t ) - (at ² + bt + c) exp(-t )
… = (-at ² + (2a - b) t + b - c) exp(-t )
y₁'' = (-2at + 2a - b) exp(-t ) - (-at ² + (2a - b) t + b - c) exp(-t )
… = (at ² + (b - 4a) t + 2a - 2b + c) exp(-t )
Substitute them into the ODE [1] to get
→ [(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c)] exp(-t ) = 8t exp(-t ) + 6 exp(-t )
(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c) = 8t + 6
4at + 2a + 2b = 8t + 6
→ 4a = 8 and 2a + 2b = 6
→ a = 2 and b = 1
→ y₁ = (2t ² + t ) exp(-t )
(Note that we don't find out anything about c, but that's okay since it would have gotten absorbed into the first characteristic solution exp(-t ) anyway.)
• y'' + 4y' + 3y = -(9t + 6) … … … [2]
Compute the derivatives of y₂ :
y₂ = at + b
y₂' = a
y₂'' = 0
Substitute these into [2] :
4a + 3 (at + b) = -9t - 6
3at + 4a + 3b = -9t - 6
→ 3a = -9 and 4a + 3b = -6
→ a = -3 and b = 2
→ y₂ = -3t + 2
Then the general solution to the original ODE is
y(t) = C₁ exp(-t ) + C₂ exp(-3t ) + (2t ² + t ) exp(-t ) - 3t + 2
Use the initial conditions y (0) = 2 and y' (0) = 2 to solve for C₁ and C₂ :
y (0) = C₁ + C₂ + 2 = 2
→ C₁ + C₂ = 0 … … … [3]
y'(t) = -C₁ exp(-t ) - 3C₂ exp(-3t ) + (-2t ² + 3t + 1) exp(-t ) - 3
y' (0) = -C₁ - 3C₂ + 1 - 3 = 2
→ C₁ + 3C₂ = -4 … … … [4]
Solve equations [3] and [4] to get C₁ = 2 and C₂ = -2. Then the particular solution to the initial value problem is
y(t) = -2 exp(-3t ) + (2t ² + t + 2) exp(-t ) - 3t + 2
Jaxon is deciding between two landscaping companies for his place of business. Company A charges $45 per hour and a $150 equipment fee. Company B charges $35 per hour and a $200 equipment fee. Let
A
A represent the amount Company A would charge for
t
t hours of landscaping, and let
B
B represent the amount Company B would charge for
t
t hours of landscaping. Write an equation for each situation, in terms of
t
,
t, and determine the interval of hours,
t
,
t, for which Company A is cheaper than Company B.
Answer
10 hours
Explanation
Step one:
given information
Company A
charges $45 per hour and a $150 equipment fee.
Let A represent the amount Company A would charge for t hours
So, the expression for the total is
A= 45t+150--------------------1
Company B
charges $35 per hour and a $200 equipment fee.
Let B represent the amount Company B would charge for t hours
So, the expression for the total is
B= 35t+200--------------------2
Step two:
equating the two equations above
A=B
45t+150=35t+200
collect like terms
45t-35t= 200-150
5t=50
divide both sides by 5
t=50/5
t=10
When shopping, Joe noticed the prices for the items he purchased; each pen
and pencil (p) cost $0.85 and erasers (e) cost $1.15 each. Determine the amount that Joe spent on his supplies. Show your work:
Joe Spent $________
Answer:$2
Step-by-step explanation:
the uniform distribution over the interval 8.5 to 11.5 gallons per minute. Find the probability that between 9.0 gallons and 10.0 gallons are pumped during a randomly selected minute.
Answer: 1/3
Step-by-step explanation:
Here is the complete question:
machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 11.5 gallons per minute. Find the probability that between 9.0 gallons and 10.0 gallons are pumped during a randomly selected minute.
The Probability of the above question will be calculated as:
= (10-9) / (11.5 - 8.5)
= 1/3
The above is the easier way to solve this
At an arcade, Michael pays $0.50 for each game he plays. proportional or non-proportional?
Answer:
proportional
Step-by-step explanation:
because for each game played, he pays $0.50, meaning equation is 0.50x. That is a proportional equation. The change is constant, at 0.50
please hit the heart button :)
Answer:
That would be proportional
Step-by-step explanation:
If each game is 50 cents then yes it would be proportional
If each thing is worth the same it’s proportional but if not then its not proportional
for example
1 game 50 cents
2 game 1 dollar (becuase 0.5+0.5 is 1)
3 games 1.50
ts proportional
What are the domain and range of the function ? domain: all real numbers range: all real numbers greater than or equal to –5 domain: all real numbers range: all real numbers greater than or equal to –4 domain: all real numbers between –2.5 and 2.5 range: all real numbers domain: all real numbers between –2.5 and 2.5 range: all real numbers greater than or equal to –5
Answer:
Option A Domain: all real numbers between –2.5 and 2.5 range: all real numbers greater than or equal to –5
Step-by-step explanation:
Domain corresponds to the values of x and Range corresponds to the value of y. If sketch the graph on an online calculator we can see that the domain lies between -2.5 and 2.5 for x and the range corresponds to y as in this case
range ≥ -5.
Answer:
a
Step-by-step explanation:
PLEASEE HELP ME!!!!!!!!!!!
Answer:
26%
Step-by-step explanation:
13/50=0.26
0.26x100=26%
- A box contains 7 apples and 5 oranges. The pieces of fruit are taken out of the box, one at a
time and in a random order. What is the probability that the bowl will be empty after the last
apple is taken from the box?
Answer:
The value is [tex]P( O \ and \ A ) = 0.583[/tex]
Step-by-step explanation:
From the question we are told that
The number of apples is [tex]A = 7[/tex]
The number of oranges is [tex]R = 5[/tex]
Generally the probability that the bowl will be empty after the last apple is taken from the box is mathematically represented as
The probability that 5 oranges and 7 apples are drawn in the 1st 11 draws
So
[tex]P( O \ and \ A ) = \frac{(^5 C_5) * (^7 C_6) }{^{12} C_{11}}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
[tex]P( O \ and \ A ) = \frac{(1 * 7 )}{12}[/tex]
=> [tex]P( O \ and \ A ) = 0.583[/tex]
pls help me with this!
Answer:
(25 and 8) = 200
(32,24 and 18) =288
(22 and 4)=44
(14 and 12) = 84
(9,8 and 7)= 504
(27,12 and 36) =108
A varsity boy's basketball team has ratio of seniors and juniors that is 7:4. If the team is made up of only juniors and seniors, what is the ratio of seniors to the total team members?
Answer:
7:11
Step-by-step explanation:
From the question
Seniors : Junior's
7:4
The sum of the proportion = Total team members = 7 + 4 = 11
Hence, the ratio of seniors to total team members =
Senior : Total team members
7 : 11
Noah picked 3 kilograms of cherries. Mai picked half as many cherries as Noah. How many total kilograms of cherries die Mia and Noah pick together?
Group of answer choices
Answer:
cherries picked by Noah =3kg
Mia picked = 1/2*3 = 1.5kg
Total cherries picked together = 3+1.5 = 4.5kg
Step-by-step explanation:
Answer:
4.5 or 4 1/2. Based on the given conditions, formulate: 3 + 3 / 2 Find common denominator and write the numerators. ++++=4.5
Step-by-step explanation:
CORRECT THIS ANSWER MARK A BRAIN LESS
If you know how to do this please help me then will give brainliest
Answer:
The required equation is:
[tex]y=\mathbf{-0.271}x+\mathbf{13.876}[/tex]
Step-by-step explanation:
We have x = Distance of goal posts
y = field Goals made
The data given is:
x y
20 9
25 6
30 7
35 4
40 1
45 2
50 1
We need to find the regression equation y = bx + a
Where [tex]b=\frac{SP}{SS_x} \:and\: a=M_y-bM_x[/tex]
Sum of all values of x = 245
Sum of all values of y = 30
Now, calculating mean using formula: [tex]Mean=\frac{Sum\:of\:all|\:values}{Number\:of\:values}[/tex]
Mean of x (Mₓ) = 35
Mean of y ([tex]M_y[/tex]) = 4.28
Sum of squares (SSₓ) = 700
Sum of products (SP) = -190
Now, finding b:
[tex]b=\frac{SP}{SS_x} \\b=\frac{-190}{700}\\b=-0.271[/tex]
Now, finding a:
[tex]a=M_y-bM_x\\a=4.28-(-0.271*35)\\a=13.786[/tex]
So, the required equation is:
[tex]y=\mathbf{-0.271}x+\mathbf{13.876}[/tex]
There were 6 boys and 9 girls on the camping trip. What was the ratio of boys to girls? 3:2 6:3 6:9 2:3
Answer:
The ratio of boys to girls is 2:3.
Step-by-step explanation:
6:9 = 2:3
Which one of these formulas describes the following sequence?
1,5,12,22,35
We can find a formula for nth term of the given sequence as follows:
1, 5, 12, 22, 35
The 1st differences between terms:
4, 7, 10, 13
The 2nd differences :
3, 3, 3
Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: [tex]a n^2 + b n + c[/tex], where c is a constant. The coefficients a, b, and the constant c can be found.
We can form the following 3 equations with 3 unknowns a, b, c:
[tex]1 = a\cdot1^2 + b\cdot1 + c\\5 = \cdot2^2 + b\cdot2 + c\\12 = a\cdot3^2 + b\cdot3 + c[/tex]
Solving for a, b, c, we get:
a = 3/2, b = -1/2, c = 0
Therefore, the nth term of the given sequence is:
[tex]\boxed{ a_n = \dfrac{3}{2}n^2- \dfrac{1}{2} n}[/tex]
g E. (i). An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. What is the probability that the first strike comes on the third well drilled
Answer:
0.128
Step-by-step explanation:
Given that :
Probability of striking oil = p = 20% = 0.2
Striking occurs on the 3rd well drilled : x = 3
Hence ;
P(x = 3) =?
Using a geometric probability function :
p(x = x) = (1 - p)^(x - 1) * p
P(x = 3) = (1 - 0.2)^(3 - 1) * (0.2)
P(x = 3) = 0.8^2 * 0.2
P(x = 3) = 0.64 * 0.2
P(x = 3) = 0.128
After a baby was born, she began to gain weight at a rate of 2 pounds per month. The weight of the baby at birth was 8 pounds. Write an equation
Answer:
W x T = 8 or 2w x t = 8
Step-by-step explanation:
Answer:
After a baby was born, she began to gain weight at a rate of 2 pounds per month. The weight of the baby at birth was 8 pounds. how much did the baby way a 12 months
Step-by-step explanation:
8 x 2 =16 16 x 12= 192 so the baby will be 19 pounds and 2 ounces at 12months
PLEASE HELP WILL MARK BRAINLIEST!!!!! +20 POINTS
only answer number 25.
Answer:
the one up: 21
the one down: 16
4x + 6y = 16
x = –8
Solve for x, y
I think the answer is yes=8
You wonder if one's age is independent of whether or not one's willingness to wear masks in public. You ask 100 people whether they are wearing masks in public or not and whether they are under 20 years old, between 20 and 39, between 40 and 59, or 60 or above. Using your data, you calculate a test statistic of 16.5. Using a critical value of 7.82, what is your statistical conclusion
Answer:
One's age is not independent of one's willingness to wear masks in public.
Step-by-step explanation:
The hypothesis for the study can be defined as follows:
H₀: One's age is independent of one's willingness to wear masks in public.
Hₐ: One's age is not independent of one's willingness to wear masks in public.
It is provided that the test statistic value is, t = 16.5.
And the critical value of the test is, c = 7.82.
t = 16.5 > c = 7.82
Since the test statistic value is more than the critical value, the null hypothesis will be rejected.
Thus, concluding that one's age is not independent of one's willingness to wear masks in public.
which of the following expression eqaul to -4x^2-36
Answer:
2hole square and six whole square (a+b) (a-b) finish...
Helppppppppppppppppppppppppp
Answer:
Option A
Step-by-step explanation:
We know that for an eqn. [tex]ax^{2} +bx+c=0[/tex] , the quadratic formula is =
[tex]x = \frac{-b+\sqrt{b^{2}-4ac } }{2a} or \frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
So using quadratic eqn. for [tex]x^{2} -6x-5=0[/tex]
[tex]x =\frac{-(-6)+\sqrt{(-6)^{2}-4*1*(-5) } }{2*1}or\frac{-(-6)-\sqrt{(-6)^{2}-4*1*(-5) } }{2*1}[/tex]
[tex]=> x = \frac{6+\sqrt{36+20} }{2} or\frac{6-\sqrt{36+20} }{2}[/tex]
[tex]=>x = \frac{6+\sqrt{56} }{2} or\frac{6-\sqrt{56} }{2}[/tex]
hard 9th grade work pls help
The length of a rectangle exceeds the width by 2 cm . If the diagonal is 10 cm long , find the width of the rectangle .
Q: In an examination 14% of the students failed and 559 students passed. Find
the number of students who failed?
This is a puzzle can someone solve it
Answer:
Xavier, Yeoman, and Zenger
Step-by-step explanation:
He spoke to them multiple times during the given time period while he only spoke to Osborn once.
What is the quotient of 2 ÷2/3 plz help
Answer:
3
Step-by-step explanation:
2/(2/3)=(2/1)/(2/3)=(2/1)(3/2)=6/2=3
Answer:
3, I think (hope this helps)
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words.
Renee and David plan to file taxes as married filing jointly. They have a combined taxable income of $51,325. Use the table to determine the amount of tax due, and calculate their effective tax rate, rounding to the nearest tenth.
Answer:
the answer is 6766 and the percent is 13.2
Step-by-step explanation:
100 on the plato test
AJKL and ALMN are shown.
Answer:
mLNM=63
Step-by-step explanation:
triangle JKL is isocelese so mKJL and KLJ are the same
180-72=108
108/2=54
so both mKLJ and mMLN are equal
and since triangle LMN is an isoceles then mLNM and mLMN are equal to each other
so 180-54=126
126/2=63
mLNM=63