By the fundamental theorem of calculus,
f(x) = f (0) + ∫₀ˣ f '(t) dt
We're given that the plot of f(x) passes through the point (0, -7), so f (0) = -7, and
f(x) = -7 + ∫₀ˣ (9t ² + 4t - 4) dt
f(x) = -7 + (3t ³ + 2t ² - 4t )|₀ˣ
f(x) = -7 + (3x ³ + 2x ² - 4x)
f(x) = 3x ³ + 2x ² - 4x - 7
Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve.
a) dy/dx = (x − y)/x
b) (x + 1)dy/dx = −y + 20
c) dy/dx = 1/(x(x − y2))
d) dy/dx =(y^2 + y)/(x^2 + x)
e) dy/dx = 5y + y^2
f) y dx = (y − xy^2) dy
g) x dy/dx = ye^(xy) − x
h) 2xyy' + y^2 = 2x^2
i) y dx + x dy = 0
k) (x^2 + 2y/x) dx = (3 − ln x^2) dy
l) (y/x^2) dy/dx + e^(2x^3) + y^2 = 0
Here, we have to classify each differential equation based on their characteristics:
a) dy/dx = (x − y)/xThis is a separable differential equation because the variables can be separated on different sides of the equation.
It's of the form dy/dx = g(x) - f(y)/h(y), where g(x) = x/x and h(y) = 1.
b) (x + 1)dy/dx = −y + 20This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/(x + 1) and Q(x) = 20/(x + 1).
c) [tex]dy/dx = 1/(x(x - y^2))[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
d) [tex]dy/dx = (y^2 + y)/(x^2 + x)[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
e)[tex]dy/dx = 5y + y^2[/tex]This is a Bernoulli differential equation because it is of the form [tex]dy/dx = p(x)y + q(x)y^n[/tex], where p(x) = 0 and q(x) = 5x, n = 2.
f) [tex]y dx = (y - xy^2) dy[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
g) [tex]x dy/dx = ye^{(xy)} - x[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/x and [tex]Q(x) = e^{(xy)} - x^{(-1)[/tex].
h) [tex]2xyy' + y^2 = 2x^2[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -2/x and Q(x) = 2x.
i) y dx + x dy = 0This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
k) [tex](x^2 + 2y/x) dx = (3 - \text ln x^2) dy[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), although it's not immediately obvious what P(x) and Q(x) are.
l) [tex](y/x^2) dy/dx + e^{(2x^3)} + y^2 = 0[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where [tex]P(x) = -1/x^2[/tex] and [tex]Q(x) = -e^{(2x^3)} - y^2[/tex].
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I. Read each question carefully, then write the letter of the correct answer.
1. What is the relationship of the volume between a prism and a pyramid of the same dimensions?
A. the volume of the pyramid is 2/3 of the volume of the prism
B. the volume of the pyramid is 3/3 of the volume of the prism
C. the volume of the pyramid is 1/3 of the volume of the prism
D. the volume of the pyramid is 3/2 of the volume of the prism
2. The volume of a cone is the volume of a cylinder if both are of the same dimensions.
A. double B. thrice
C. twice
D. 4 times
3. How many cones can fill the whole sphere with the same dimension?
A. 1
B. 2
C.3
D.4
4. If the volume of a cylinder is 120 m3, what will be the volume of a cone with the same dimension?
A.180m3
B. 60 m3
C. 40 m3
D. 30 m3
5. What is the length of the edge of a cube if it has a volume of 27 cubic inches?
A. 9 in
B. 6 in
C. 3 in
D. 2 in
Answer:
The answer for number 1 is C
HELP HELPPP!!!у- 3
|
у+
у- 3
3
What is the common denominator of y+
3
in the complex fraction
5 2
9* Зу
?
Зу(у – 3)
у(у – 3)
Зу
О 3
Answer:
The common denominator of [tex]y + \frac{y-3}{3}[/tex] is 3
Step-by-step explanation:
Given
The complex fraction
Required
The common denominator
To solve this, we need not consider the whole complex fraction.
We only consider
[tex]y + \frac{y-3}{3}[/tex]
Take LCM
[tex]y + \frac{y-3}{3} = \frac{3y - (y-3)}{3}[/tex]
Single out the denominator, i.e. 3
Hence, the common denominator of [tex]y + \frac{y-3}{3}[/tex] is 3
bine like terms.
7 – 64 – 5x3 – 1 + x3 – 7 – 2y
PLS HURRY
Answer:
-4x³ - 8y - 1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
7 - 6y - 5x³ - 1 + x³ - 7 - 2y
Step 2: Simplify
[Addition] Combine like terms (x³): -4x³ + 7 - 6y - 1 - 7 - 2y[Subtraction] Combine like terms (y): -4x³ - 8y + 7 - 1 - 7[Subtraction] Combine like terms: -4x³ - 8y - 1Construct a frequency polygon that represents the following data regarding the selling prices of houses sold in 2006 for a particular neighborhood find the midpoint
Class Frequency
78787 – 98786 9
98787 – 118786 8
18787 – 138786 9
138787 – 158786 4
158787 – 178786 8
Answer:
See attachment for polygon
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Class} & {Frequency} & 78787 - 98786 & 9 &98787 - 118786 & 8 & 118787 - 138786 & 9 & 138787 - 158786 & 4 & 158787 - 178786 & 8 \ \end{array}[/tex]
Required
The frequency polygon
First, we calculate the midpoint of each class.
This is the average of the class limits
So, we have:
[tex]x_1 = \frac{78787 + 98786}{2} = \frac{177573}{2} = 88786.5[/tex]
[tex]x_2 = \frac{98787 + 118786}{2} = \frac{217573}{2} = 108786.5[/tex]
----
--
-
[tex]x_5 = \frac{158787 + 178786}{2} = \frac{337573}{2} = 168786.5[/tex]
(138787 + 158786)/2
So, the table becomes:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {x} &78787 - 98786 & 9 & 88786.5 & 98787 - 118786 & 8 & 108786.5 & 118787 - 138786 & 9 & 128786.5 & 138787 - 158786 & 4 & 148787.5 & 158787 - 178786 & 8 & 168786.5\ \end{array}[/tex]
See attachment for frequency polygon
After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only four women among the last 19 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.
Help her address the charge of gender discrimination by finding the probability of getting four or fewer women when 19 people are hired, assuming that there is no discrimination based on gender.
(Report answer accurate to 8 decimal places).
P(at most four) =
Answer:
P(at most four) = 0.00960541
Step-by-step explanation:
For each employee hired, there are only two possible outcomes. Either it is a women, or it is not. The probability of an employee being a women is independent of any other employee, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
19 new employees.
This means that [tex]n = 19[/tex]
Approximately equal number of qualified men as qualified women.
This means that [tex]p = 0.5[/tex]
Probability of getting four or fewer women when 19 people are hired
This is:
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{19,0}.(0.5)^{0}.(0.5)^{19} = 0.00000191[/tex]
[tex]P(X = 1) = C_{19,1}.(0.5)^{1}.(0.5)^{18} = 0.00003624[/tex]
[tex]P(X = 2) = C_{19,2}.(0.5)^{2}.(0.5)^{17} = 0.00032616[/tex]
[tex]P(X = 3) = C_{19,3}.(0.5)^{3}.(0.5)^{16} = 0.00184822[/tex]
[tex]P(X = 4) = C_{19,4}.(0.5)^{4}.(0.5)^{15} = 0.00739288[/tex]
Then
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.00000191 + 0.00003624 + 0.00032616 + 0.00184822 + 0.00739288 = 0.00960541[/tex]
So
P(at most four) = 0.00960541
A crew clears brush from 1/3 acre of land in 2 days. How long will it take the same crew to clear the entire plot of 2 1/ 2 acres?
Answer:
15 days
Step-by-step explanation:
Given that :
Time taken to clear 1/3 acre = 2 days
This means that, they will be able to clear ;
1/3 ÷ 2 = 1/3 * 2 /1 = 1/6 acre in one day
1/6 acres per day :
Hence, the number of days it will take to clear 2 1/2 acres will be :
2 1/2 acres ÷ 1/6
5 / 2 ÷ 1/ 6
5/2 * 6 /1 = (5*6) / (2*1) = 30/2 = 15
Hence, it will take 15 days to clear 2 1/2 acres
The interarrival time of nuclear particles in a Monte Carlo simulation of a reaction is designed to have a uniform distribution over an interval from 0 to 0.5 milliseconds. Determine the probability that the interarrival time between two particles will be:
Answer:
Incomplete question, but you can use the formulas given to solve it.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Uniform distribution over an interval from 0 to 0.5 milliseconds
This means that [tex]a = 0, b = 0.5[/tex]
Determine the probability that the interarrival time between two particles will be:
Considering [tex]a = 0, b = 0.5[/tex], and the question asked, you choose one of the three formulas above.
Có 7 cây hãy trồng thành 6 hàng, mỗi hàng 3 cây?
Answer:
Step-by-step explanation:
Bạn vẽ 1 tức giác ABCD lồi sau đó nối AB và CD cắt nhau tại E, AD và BC cắt nhau tại F, AC và BC cắt nhau tại G. Trồng 7 cây vào các điểm ABCDEFG l. Ta có sáu hàng là ABE, DCE, BCF, ADF, ACG, BDG
I need help resolving this please
27x^6 = 387420489
You want something similar but cubed.
[tex]\sqrt[3]{387420489}[/tex] = 729
YOUR ANSWER: 729x^3 = 387420489
Step-by-step explanation:
PLS HELP
the simplest form of this product has a numerator of
x + 2
x - 2
( x - 2 ) ( x - 2 )
( x + 2 ) ( x - 2 )
and a denominator of
x - 5
( x - 5 ) ( x - 1 )
x - 1
( x + 5 ) ( x + 1 )
the expression has an excluded value of x
- 5
2
-1
5
(x+2)(x-2) / (x-1)(x-5) this is the simplified form of the expression.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.
x²-3x-10/x²-6x+5 • x-2/x-5
We can factor the numerator and denominator of the first fraction as follows: (x-5)(x+2) / (x-5)(x-1)
Notice that there's a common factor of x-5 in both the numerator and denominator. We can cancel them out, leaving: (x+2) / (x-1)
Now let's simplify the second fraction:
x-2 / x-5
We can't simplify this fraction any further, so we leave it as is.
Putting it all together, we get:
(x+2) / (x-1) * (x-2) / (x-5)
Multiplying the two fractions, we get:
(x+2)(x-2) / (x-1)(x-5)
This is the simplified form of the expression.
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Ivy is competing in a 400 m race.
She runs at a constant speed of 5.4 m/s for the first 150 m, then 4.5 m/s for 40 seconds.
The remainder of the race takes her 34 seconds to complete.
What is Ivy's average speed for the entire race to 1 dp?
Answer:
4.5m/s
Step-by-step explanation:
4.5x40=180
180+150=330
400-330=70
70/34=2.05882352941
(2.05882352941x70)+(5.4x150)+(4.5x180)=1791.11764706
1791.11764706/400=4.47779411765
4.47779411765=4.5
4.5m/s
Answer:
Average speed = 3.9 m /s
Step-by-step explanation:
Total distance = 400m
First 150m = 5.4m/s
[tex]speed = \frac{distance}{time} \\\\time = \frac{distance}{speed} = \frac{150}{5.4} = 27.78 \ s[/tex]
Second part :
S = 4.5m/s for 40s
[tex]Distance = speed \times time = 4.5 \times 40 = 180 \ m[/tex]
Third part :
Remaining distance = 400 - 150 -180 = 70m
Time taken to cover it = 34s
[tex]speed = \frac{distance}{time} = \frac{70}{34} = 2.05 \[/tex]
Speed = 2.05m/s
Find average speed
[tex]Average\ speed = \frac{total \ distance }{total \ time \ taken } \\\\Average \ speed = \frac{400}{101.78} = 3.93 \ mps[/tex]
Round to 1 dp => average speed = 3.9m /s
Write the phrase as an algebraic expression and simplify if possible. Let x represent the unknown number
Three times a number, decreased by five
(Simplify your answer.)
To express the phrase "Three times a number, decreased by five" as an algebraic expression, we can use the variable x to represent the unknown number: 3x - 5
Now, let's simplify this expression: Given that the unknown number is represented by x, we can substitute it into the expression above. Substituting x into the expression, we have: [tex]3(x) - 5 3x - 5[/tex] Therefore, the algebraic expression representing "Three times a number, decreased by five" is [tex]3x - 5.[/tex] At this point, there is no further simplification possible since the expression is already in its simplest form.
For example, let's assume the unknown number x is 7. We can plug in this value to evaluate the expression: [tex]3(7) - 5 = 21 - 5 = 16[/tex] Similarly, if x is -2, the calculation would be: [tex]3(-2) - 5 = -6 - 5 = -11[/tex] In conclusion, the algebraic expression 3x - 5 represents the phrase "Three times a number, decreased by five."
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1.) If I am selling a dozen at $3, how much would each egg cost?
2.) If each egg costs that amount of money, how much would an 18 pack be?
I'm trying to figure this out because this is a real-life problem, and I'm trying to sell eggs to my teacher.
Answer:
1.$3÷12=0.25
each egg would cost 25 cents
2.12×18=216
216×25=5,400
What are the 2 \ 3 parts of a right angle in a whole wheel?
Answer:
[tex]\frac{2}{3} \ part \ of \ right \ angle \ is \ \frac{1}{6} \ part \ of \ a \ whole \ wheel.[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} \ of \ a \ right \ angle \ = \frac{2}{3} \times 90^{\circ} = 60^{ \circ}\\\\A \ whole \ wheel \ is \ = 360^ {\circ}\\\\[/tex]
Now to find what part of 360 is 60 :
[tex]Let \ it \ be \ x\\\\x \times 360 = 60 \\\\x = \frac{60}{360} = \frac{1}{6}[/tex]
Therefore ,
[tex]\frac{2}{3} \ part \ of \ right \ angle \ is \ \frac{1}{6} \ part \ of \ a \ whole \ wheel.[/tex]
write the other side of this equation so its true for all values of x: 1/2(6x-10)-x=
9514 1404 393
Answer:
2x -5
Step-by-step explanation:
Any equivalent expression can be used. It is perhaps easiest just to simplify the given expression.
1/2(6x -10) -x = 3x -5 -x = 2x -5
Putting 2x-5 on the right will give an equation true for all x.
1/2(6x -10) = 2x -5
Which function is increasing and has a domain of (1,∞ )
The graph of a square root function has a domain of (0, ∞) and range of [1, ∞).
Answer:
f(x)=log(x-1)+2
Step-by-step explanation:
I did the test on plato and got it right.
ppose we are testing a new shampoo to see if it makes hair grow faster. We knowthat the average rate of hair growth is 0.5 inches per month. The hypothesis are as follows:H0:m0:5vs.H1:m>0:5. Suppose that the null hypothesis is not rejected and that thereal truth is that the shampoo actually does make hair grow faster. What type of error, if any,occurred?
Answer:
Type II error occurred
Step-by-step explanation:
It is given that a new shampoo is being tested to determine whether the hair grows faster by using this shampoo.
It is known that hair grow at 0.5 inches per month at average.
The hypothesis are,
Null hypothesis, [tex]$H_0: \mu=0.5$[/tex]
Alternate hypothesis, [tex]$H_1: \mu>0.5$[/tex]
But it is known that :
Type [tex]$I$[/tex] error occurs when rejecting the null hypothesis when the null hypothesis is true actually.
Type [tex]$II$[/tex] error occurs [tex]\text{when we fail reject the null hypothesis}[/tex] when the null hypothesis is actually false.
Now here since the null hypothesis is not been rejected, type [tex]$II$[/tex] error had occurred.
please help steps thx
Answer:
240 cubic metres
Step-by-step explanation:
I'm not really sure for Q17 but I do know Q18.
Q18. Volume of cuboid = Length×Breadth×Height
=12×4×5
=240 cubic metres
hope it helps!!!
look at attachment below
An educational psychologist wondered whether there was a relationship between the amount of academic pressure a high school student felt and their plans for college. They surveyed a random sample of 300 high school students throughout the country about their college plans and whether they felt academic pressure. Here are the responses and partial results of a chi-square test (expected counts appear below observed counts):
Chi-square test:
Planned years of college vs. feeling academic pressure now
O years Up to 4 years Up to 4 years More than 4 years Total
Yes 31 48 161 240
31.2 48 160.8
No 8 12 40 60
7.8 12 40.2
Total 39 60 201 300
They want to use these results to carry out a xạ test of independence. Assume that all conditions for inference were met. What are the values of the test statistic and P-value for their test?
What are the values of the test statistic and P-value for their test?
A. x² = 0.002;
0.001 < P-value < 0.0025
B. x² = 0.002;
P-value > 0.25
C. x² = 0.007;
0.005 < P-value < 0.01
D. x² = 0.007;
P-value > 0.25
Answer:
D. x² = 0.007;
P-value > 0.25
Step-by-step explanation:
The observed and expected values are given below :
Yes____31 48 161 ____240
______31.2 48 160.8
No ____ 8 12 40_____ 60
______7.8 12 40.2
Total __ 39 60 201 ___300
The Chisquare statistic, χ²:
Σ(Observed - Expected)²/ Expected
Chi-Squared Values:
0.00128205 __ 0 __ 0.000248756
0.00512821 __ 0 __ 0.000995025
(0.00128205 + 0 + 0.000248756 + 0.00512821 + 0 + 0.000995025 )
= 0.007654041
The degree of freedom = (row - 1) * (column - 1)
Degree of freedom = (2-1)*(3-1) = 1*2= 2
The Pvalue = 0.9962
Pvalue > 0.25
There is a bag filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?
Answer:
its a three in seven chance, since there are seven total outcomes and there is only one favorable outcome. Hope that helps.
Step-by-step explanation:
I need help with this!
Answer:
1. y=5 x=1
2. y=4 x=4/5
3. y=2 x=2/5
Step-by-step explanation:
Plug the y-values in for y:
1. 5=5x
2. 4=5x
3. 2=5x
Then solve for x:
1. x=1
2. x=4/5
3. x= 2/5
Hope this helps!
Expand, and simplify the following expressions a. (2x+y)(x+y) + (2x-y)(x+y)
Step-by-step explanation:
2x²+2xy+yx+y²+2x²+2xy-yx+y²
2x²+2x²+2xy+2xy+yx-yx+y²+y²
2x²+2x²+2xy+2xy
4x²+4xy
Your Answer is in the above image.
Hope this solution may help you
What is 15 5/7 - 6 4/5
Answer:
8.9
Step-by-step explanation:
15.71428571-6.8=8.914285714
We round of to one significant figure because its addition n the lowest is 6.8
Answer:
[tex]8\frac{32}{35}[/tex]
Step-by-step explanation:
Cómo chica quiere armar sus propios lindos para una galería de arte los cuadros deben ser de forma cuadrada así que todos los lados deben de medir los mismos y una amiga le donó dos trozos de madera de 128 cm y 224 cm respectivamente qué tan grande es podrían ser los lados sin que sobre madera?
I need help I’ll mark u as brainlest
Answer:
105 in³
Step-by-step explanation:
Volume of triangular prism = base area * height
here
base area = (10*7)/2 = 35
height = 3
Volume = 35* 3 = 105
A man, 1.5m tall, is on top of a building. He observes a car on the road at an angle of 75°. If the building is 30m, how far is the car from the building?
Answer:
The answer to this question is 8.44 m.
Step-by-step explanation:
This problem is best illustrated in the photo below.
First, we must know that the angle stated in the problem is the angle of depression. Angle of depression is the angle between the horizontal and the line of sight of the observer. On the other hand, if the observer is looking upward, then the angle between the horizontal and his line of sight is called the angle of elevation.
Since we have the given angle of depression, we must use its complementary angle to solve for the distance of the car from the building.
Let x = complementary angle of 75°
y = distance of the car from the building
To solve for x,
To solve for y, we need to use a trigonometric function that will relate the adjacent of 15° and the opposite of 15°. Let us look at the mnemonics
SOH: Sine =
CAH: Cosine =
TOA: Tangent =
Therefore we must use the tangent function to solve for y.
what is 1+1+3+4+6+2+6+3+5=+8+2+5
Answer:
16
Step-by-step explanation:
baámmáy tính
a bag contains 16 red coins , 8 blue coins , and 8 green coins. A player wins by pulling a red coin from the bag. Is this game fair? Justify your answer
Answer:
Step-by-step explanation:
there are a total of 16+8+8=32 coins in bag
16 out of 32 are red
player wins by pulling a red coin
assume it is a single pull, the winning probability = 16/32 = 1/2
so it is 50/50 chance n hence a fair game
Step-by-step explanation:
yes it is a fair game because any one don't know what the coin will get, it is based on luck