Answer:
[tex]y = 2x + \frac{x^2}{2} - 6[/tex]
Step-by-step explanation:
Solution:-
- We are given the following initial value problem:
[tex]\frac{dy}{dx} = 2 + x , y ( 2 ) = -6[/tex]
- We will first isolate the variables:
[tex]dy = ( 2 + x ).dx[/tex]
- Perform integration for both sides of the equation:
[tex]\int {dy} = \int {( 2 + x )}.dx + c\\\\y = 2x + \frac{x^2}{2} + c\\[/tex]
Where,
c: The constant of integration
- We will solve for the constant of integration by using the initial value y ( 0 ) = -6 as follows:
[tex]-6 = 2(0) + \frac{0^2}{2} + c\\\\c = -6[/tex]
- The final solution can be expressed as follows:
[tex]y = 2x + \frac{x^2}{2} - 6[/tex]
If a person is randomly selected, find the probability that his or her birthday is not on New Year's Day. Ignore leap years.
Answer:
Ignoring leap years, May has 31 days, a year has 365 days. 334 days of the year are NOT in May so the probability of a birthday not being in May = 334/365 = approximately 91.5%
Step-by-step explanation:
The probability of event A which represents that the man's birthday is not on New Year's Day is 0.99.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P(A) = n(A)/n(S)
Given is a person who is randomly selected.
Assume that Event A represents that the man's birthday is not on New Year's Day.
Total number of days in a year = n(S) = 365
Total number of days not on New Year's Day = n(A) = 364
Therefore, the probability that the man's birthday is in May will be -
P(A) = n(A)/n(S)
P(A) = 364/365
P(A) = 0.99
Therefore, the probability of event A which represents that the man's birthday is not on New Year's Day is 0.99.
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The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t), where t is the time in years. When t = 0, the population was 15, and when t = 2, the population increased to 20. Find the population when t = 3.
Answer:
S(3)=22
Step-by-step explanation:
The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t).
[tex]\dfrac{dS}{dt}=k(30-S(t))\\ \dfrac{dS}{dt}+kS(t)=30k\\$The integrating factor: e^{\int k dt}=e^{kt}\\$Multiply all through by the integrating factor\\ \dfrac{dS}{dt}e^{kt}+kS(t)e^{kt}=30ke^{kt}[/tex]
[tex](Se^{kt})'=30ke^{kt} dt\\$Integrate both sides\\ Se^{kt}=\dfrac{30ke^{kt}}{k}+C$ (C a constant of integration)\\Se^{kt}=30e^{kt}+C\\$Divide both sides by e^{kt}\\S(t)=30+Ce^{-kt}[/tex]
When t=0, S(t)=15
[tex]15=30+Ce^{-k*0}\\C=15-30\\C=-15[/tex]
When t = 2, S(t)=20
[tex]20=30-15e^{-2k}\\20-30=-15e^{-2k}\\-10=-15e^{-2k}\\e^{-2k}=\dfrac23\\$Take the natural log of both sides$\\-2k=\ln \dfrac23\\k=-\dfrac{\ln(2/3)}{2}[/tex]
Therefore:
[tex]S(t)=30-15e^{\frac{\ln(2/3)}{2}t}\\$When t=3$\\S(t)=30-15e^{\frac{\ln(2/3)}{2} \times 3}\\S(3)=21.8 \approx 22[/tex]
Please HELP
2^8-10-15\div3=2
8
−10−15÷3=
Answer:
241
Step-by-step explanation:
We want to evaluate the expression:
[tex]2^8-10-15\div3[/tex]
We follow the order of operations: PEMDAS
Since there are no parenthesis(P), we evaluate the exponents(E)
[tex]2^8-10-15\div3=256-10-15\div3[/tex]
Next is Division (D)
[tex]256-10-15\div3=256-10-5[/tex]
We can then simplify since we have only subtraction.(S)
[tex]256-10-5=241[/tex]
Therefore:
[tex]2^8-10-15\div3=241[/tex]
Approximately 12.6% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists Ratkowsky and Martin. (Bitter pit is a disease of apples resulting in a soggy ore, which can be caused either by overwatering the apple tree or by a calcium deficiency in the soil.) Let n be a random variable that represents the first Jonathan apple chosen at random that has bitter pit.(a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.)P(n) = (b) Find the probabilities that n = 3, n = 5, and n = 12. (Use 3 decimal places.)P(3) P(5) P(12) (c) Find the probability that n ≥ 5. (Use 3 decimal places.)(d) What is the expected number of apples that must be examined to find the first one with bitter pit? Hint: Use μ for the geometric distribution and round.
Answer:
Step-by-step explanation:
Let n be a random variable that represents the first Jonathan apple chosen at random that has bitter pit.
a) P(X = n) = q(n-1)p, where q = 1 - p.
From the information given, probability if success, p = 12.6/100 = 0.126
b) for n = 3, the probability value from the geometric probability distribution calculator is
P(n = 3) = 0.096
For n = 5, the probability value from the geometric probability distribution calculator is
P(n = 5) = 0.074
For n = 12, the probability value from the geometric probability distribution calculator is
P(n = 12) = 0.8
c) For n ≥ 5, the probability value from the geometric probability distribution calculator is
P(n ≥ 5) = 0.58
d) the expected number of apples that must be examined to find the first one with bitter pit is the mean.
Mean = 1/p
Mean = 1/0.126 = 7.9
Approximately 8 apples
simplify 4x/7-x/21 find
The answer is 11x/21
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex] \frac{11x}{21} [/tex]
Step-by-step explanation:
[tex] \frac{4x}{7} - \frac{x}{21} \\ = \frac{12x - x}{21} \\ = \frac{11x}{21} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
In a game of rolling a die. If the number showing is even, you win $3, if the number showing is 1 you win $3 and if the number showing is either 3 or 5 you win nothing. Let x be the amount you win,
i. list the probability distribution of x.
ii. What is the amount of dollar you expect to win?
Answer:
(a)
[tex]\left|\begin{array}{c|c|c}---&---&---\\x&\$0&\$3\\---&---&---\\P(x)&\dfrac13&\dfrac23\\---&---&---\\\end{array}\right|[/tex]
(b)$2
Step-by-step explanation:
In the given game of rolling a die. these are the possible winnings.
If the number showing is even(2, 4, or 6) or 1, you win $3.If the number showing is either 3 or 5 you win $0.There are 6 sides in the die.
[tex]P($obtaining a 1,2,4 or 6)=\dfrac46=\dfrac23\\P($obtaining a 3 or 5)=\dfrac26=\dfrac13[/tex]
(i)The probability distribution of x.
Let x be the amount won
Therefore:
Probability distribution of x.
[tex]\left|\begin{array}{c|c|c}---&---&---\\x&\$0&\$3\\---&---&---\\P(x)&\dfrac13&\dfrac23\\---&---&---\\\end{array}\right|[/tex]
(ii) Expected amount of dollar won
Expected Amount
[tex]=\sum x_iP(x_i)\\=(0*\dfrac13)+(3*\dfrac23)\\=\$2\\[/tex]
You would expect to win $2.
what two decimals are equivalent to 4.400
Answer:
4.4
4.40
Step-by-step explanation:
These two decimals above are equivalent to 4.400 because no matter the amount of zeroes, the numbers are the same. For example, 4.400 is also equivalent to 4.400000000000000000000000000000000. As long as the "4's" maintain the same place (ones place and tens place), the decimals will be congruent to one another.
Maths Fractions Questions! How to do? Will mark the BRAINLIEAST!
Answer:
1. 5 packets
2. 3/8
1. 4/5 to 16/20
1/4 to 5/20
1/10 to 2/20
16- (2*5)= 16-10= 6
6/2 = 3 packets
2 pack.+3 pack.= 5 packets
2. 1/2= .5
.5*3/4=.375
.375=3/8
which interval describes the range of this function?
Answer:
Range. The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values
Step-by-step explanation:
One t-shirt is sold for every 5 people who attend a concert.what is one way to write the unit rate in words?
1 T-Shirt for every 5 people
First of all, B & C are wrong, because they say 5 T-shirts for one person.
Next, we will look at A & D. A is more grammatically correct, and so you should use A.
OR
Answer:
The last one
What is 0.03% written as a decimal?
O A. 0.3
O B. 0.0003
O C. 0.003
O D. 0.03
The percentage 0.03% when it is written as a decimal is equivalent to 0.0003.
What are decimals?
A decimal is a number that is made up of integers and non-integers. The whole numbers are separated from numbers that are not whole number by a decimal point.
0.03% is equal to 0.03/100.
0.03/100 is equal to 0.0003
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The “line of best fit” for a scatterplot is the line that __________.
Answer:
Scatter plots are used to plot data points on a horizontal and a vertical axis in the attempt to show how much one variable is affected by another. Each row in the data table is represented by a marker whose position depends on its values in the columns set on the X and Y axes
Step-by-step explanation:
A researcher wishes to estimate the proportion of left-handed people among a certain population. In a random sample of 820820 people from the population, 22.722.7% are left-handed. Find the margin of error for the 95% confidence interval for the population proportion. Round to four decimal places.
Answer:
The margin of error for the 95% confidence interval for the population proportion is of 0.0287.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Find the margin of error for the 95% confidence interval for the population proportion.
We have that [tex]n = 820, p = 0.227[/tex]
So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.227*0.773}{820}} = 0.0287[/tex]
The margin of error for the 95% confidence interval for the population proportion is of 0.0287.
Figure 2 was constructed using figure 1. For the transformation to be defined as a rotation, which statements must be true? Select three options. The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2). The transformation is rigid. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2. Segment CP is parallel to segment CP'. If figure 1 is rotated 180° about point C, it will be mapped onto itself.
Answer:
all but the last two
Step-by-step explanation:
Rotation is a rigid transformation that moves every point of a figure through the same rotation angle about the center of rotation. Each point has the same distance from the center it had before the rotation. Hence the following are true:
The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2). The transformation is rigid. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.__
Statements that do not apply are ...
- Segment CP is parallel to segment CP'. (A segment to the center of rotation will only be parallel to the corresponding segment on the image if the rotation is a multiple of 180°.)
- If the figure is rotated 180° about C, it will be mapped to itself. (This will be true in general only if C is a center of rotational symmetry of even order.)
Answer:
A,B,C
Step-by-step explanation:
I'm sure cause I got it right depends what your Edgenu is, mine is 2020
I Really Need Help with this not good with graphs
Answer:
D
Step-by-step explanation:
The one dot that is a lot farther away from the rest of the points is an outlier so the answer is D.
rudo is making pizzas he needs 3/4 cup of cheese to make one whole pizza. he has 2/8 cup of cheese
Answer: He can make 1/3 of pizza.
Step-by-step explanation: Divide 2/8 by 3/4. When you divide fractions you need to keep the first number exactly as it is and change the sign to multiplication and flip the second number. It is going to be 2/8 times 4/3. Which is 8/24 and if you simplify it, divide 8 and 24 by 8, and the answer is 1/3.
The required solution is 1/3.
It is required to find the remaining part to make one whole pizza.
What is fraction?A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.
Given:
He has 2/8 cup of cheese.
Divide 2/8 by 3/4.
When you divide fractions you need to keep the first number exactly as it is and change the sign to multiplication and flip the second number. It is going to be 2/8 times 4/3. Which is 8/24 and if you simplify it, divide 8 and 24 by 8, and the answer is 1/3.
Therefore, the required solution is 1/3.
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~Help me with this please! I will mark as BRANLIEST and if you answer correctly there would be a 55 point question for you!!!
Answer:
Simply here we use system of 2 equations.
Step-by-step explanation:
Let x be the cost of one small shirt and let y be that of one large shirt.
(4x +14y =210) (-3)
12x +11y =110
-12x - 42y= -630 note:cross 12x and - 12x
12x +11y =110
__________
-42y +11y = - 630 +110
-31y = -520
Y=520/31
Replace y in second equation:
12x +11y =110
12x +11(520/31) =110
12x +5720 =110
12x =110 - 5720/31
X= - 385/62
So one small shirt costs - 385/62 $
And a large one costs 520/31 $
Though I think there's something wrong in this problem since i verified my answer using calculator the same prices are obtained and as u see the cost of a small shirt is negative which is unbelievable.. So plz make sure from anyone else. I tried my best to help.
Which of the following are true? If false, explain briefly.
​a. A very high​ P-value is strong evidence that the null hypothesis is false. ​
b. A very low​ P-value proves that the null hypothesis is false. ​
c. A high​ P-value shows that the null hypothesis is true.
d. A​ P-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.
Answer:
The correct options are;
a. False
b. True
c. True
d. False
Step-by-step explanation:
We look at each of the options as follows
a. A very high p-value is strong evidence that the null hypothesis is false;
The above statement is false because the p-value indicates the likelihood of the null hypothesis being correct, therefore, a high p-value is indicative of the correctness (truth) of the null hypothesis
b. A very low p-value shows that the null hypothesis is false
The above statement is true
c. A high p-value shows that the null hypothesis is true
The above statement is true
d. A P-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.
The above statement is false as the p-value below which we reject the null hypothesis is dependent on the value of the significance level, α.
In a science class, 40% of the students received a grade of A, 30% received a grade of B, and 20% received a grade of C on a project. The others fell short of a passing grade. a. If 12 students received an A, how many students were in the science class? b. How many students received a failing grade?
Answer:
30 students are in the science class and 3 students recieved a failing grade.
Answer:
30, 3
Step-by-step explanation:
a. Let's call the total students x. If 40% x = 12, 0.4x = 12, x = 12/0.4 = 30 students.
b. We know that 100 - 40 - 30 - 20 = 10% of all students failed. This is 10% * 30 = 0.1 * 30 = 3 students.
~Help me with this please it’s a math test answer correctly and I will mark as BRANLIEST and I will give you 55 points!!
Answer:
the weight of 1 textbook is 2 pounds
the weight of 1 game is about 0.5 pounds
Step-by-step explanation:
1/2 of 2 = 0.5 pounds
0.5 times 8 (games) = 4
22 - 4 = 18
18 divided by 9 (textbooks) = 2 pounds
Answer:
Each game is 0.5 pounds and each textbook is 2 pounds.
Step-by-step explanation:
If x represents games and y represents textbooks you can use the equation
6x + 9y = 21
we know that if the box was 21 pounds and she adds two games and it's now 22 pounds that each game is 0.5 pounds so x = 0.5
after plugging in the x value the equation is:
3 + 9y = 21
Combine like terms and it's 9y = 18
Divide 18 by 9 and you get:
Y= 2
Hope this helps! Good luck on your test.
The coordinates of the points below represent the vertices of a rectangle.
P (2, 2) Q (6, 2) R (6, 5) S (2, 5)
What is the perimeter, in units of rectangle PQRS?
Answer:
18 units
Step-by-step explanation:
5+5=10
4+4=8
8+10=18 units
Answer:
14
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of the 4 sides of a rectangle. Since in a rectangle opposite sides are congruent, you just need to find the lengths of any two adjacent sides because adjacent sides cannot be opposite. Then add them and multiply the sum be 2 to account for the opposites sides.
Two find the distance between any two points, you can use the distance formula. If the two points lie on the same vertical line (both points have the same x-coordinate), or if the two points lie on the same horizontal line (both points have the same y-coordinate), then just subtract the different coordinates and take the absolute value.
PQ = |2 - 6| = |-4| = 4
QR = |2 - 5| = |-3| = 3
perimeter = 2(length + width)
perimeter = 2(4 + 3)
perimeter = 2(7)
perimeter = 14
Solve the quadratic equation 3x²+2x-4=0
Answer:
Step-by-step explanation:
Hello,
[tex]\Delta = 2^2-4*3*(-4)= 4+48=52[/tex]
so the two solutions are
[tex]\dfrac{-2+2\sqrt{13}}{2*3}=\dfrac{\sqrt{13}-1}{3}=0.87\\\\\dfrac{-2-2\sqrt{13}}{2*3}=-\dfrac{\sqrt{13}+1}{3}=-1.54\\\\[/tex]
g(-2) for
g(x)=2x^3 3x^2 =4
PLEASE ANSWER THIS YOU WILL GET 20 POINTS I NEED HELP ASAP THANK YOU SO MUCH
Answer:
g(-2)
g(x)=2x^3 3x^2 =4
i'm not exactly sure what you are asking for but if its something like
g(x)=2x^3+3x^2-4 and then g(-2)
then you just have to multiply
2(-2)^3=-16
+3(-2)^2-4=8
=-8
2(-2)^3=-16
2(-2)^3-+3(-2)^2-4
=-32
In ΔGHI, the measure of ∠I=90°, IG = 6.8 feet, and HI = 2.6 feet. Find the measure of ∠G to the nearest degree.
Answer:
[tex]\angle G=20.8\approx 21^{\circ}[/tex]
Step-by-step explanation:
Given: In ΔGHI, [tex]\angle I[/tex]=90°, IG = 6.8 feet, and HI = 2.6 feet
To find: [tex]\angle G[/tex]
Solution:
Trigonometry defines relationship between the sides and angles of the triangle.
For any angle [tex]\theta[/tex],
[tex]tan\theta[/tex] = side opposite to [tex]\theta[/tex]/side adjacent to [tex]\theta[/tex]
In ΔGHI,
[tex]tan G=\frac{HI}{GI}[/tex]
Put [tex]HI=2.6 \,\,feet\,,\,GI=6.8\,\,feet[/tex]
So,
[tex]tan G=\frac{2.6}{6.8}=0.38[/tex]
Therefore, [tex]\angle G=20.8\approx 21^{\circ}[/tex]
Answer:
G=24.6236≈24.6
I need the answer here is the question:
Write the fraction in simplest form . And the picture ☝
Answer:
i need points sorry
Step-by-step explanation:
nfefgrn
Help me please thanks
Answer:
7
Step-by-step explanation:
Work backwards:
(37-9)÷4=input
28÷4=input
input=7
The input was 7
A box contains 2 red marbles, 3 white marbles, 4 green marbles, and 1
blue marble. Two marbles, one after the other, are drawn at random
WITHOUT replacement. Find the probability of: selecting a green marble
on the second draw if the first marble is blue *
1/6
2/13
4/9
1/9
Answer:
Solution is 4/9
Explanation:
A box contains:
2 red marbles,
3 white marbles,
4 green marbles,
1 blue marble.
=> Total: 2 + 3 + 4 + 1 = 10
After selected a blue one without replacement, the remaining number: 10 - 1 = 9
=> Probability of drawing a green one: P = 4/9.
Hope this helps!
:)
a =
2
4
b =
(3
-2
Work out 3a + b as a column vector.
Answer:
As a column vector 3a +b = (9,10)
Step-by-step explanation:
A =
(2
4)
b =
(3
-2)
3a = 3*2 = 6
3*4= 12
3a + b = 6. + 3
12. +(-2)
3a +b = 9
10
As a column vector 3a +b = (9,10)
Please answer this correctly
Answer:
1570f³t
Step-by-step explanation:
V=πr²h
V=3.14×10²×5
V=3.14×100×5
V=314×5
V=1570
simplify the equation below and find the value of x
4/2x-5)= 20
Answer:
x=13/5
Step-by-step explanation:
