Answer:
The interval is [tex]0.7187 < p < 2.421[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 100[/tex]
The population proportion is [tex]p = 0.81[/tex]
The confidence level is C = 98%
The level of significance is mathematically evaluated as
[tex]\alpha = 100 -98[/tex]
[tex]\alpha = 2%[/tex]%
[tex]\alpha = 0.02[/tex]
Here this level of significance represented the left and the right tail
The degree of freedom is evaluated as
[tex]df = n-1[/tex]
substituting value
[tex]df = 100 - 1[/tex]
[tex]df = 99[/tex]
Since we require the critical value of one tail in order to evaluate the 98% confidence interval that estimates the proportion of them that are involved in an after school activity. we will divide the level of significance by 2
The critical value of [tex]\frac{\alpha}{2}[/tex] and the evaluated degree of freedom is
[tex]t_{df , \alpha } = t_{99 , \frac{0.02}{2} } = 2.33[/tex]
this is obtained from the critical value table
The standard error is mathematically evaluated as
[tex]SE = \sqrt{\frac{p(1-p )}{n} }[/tex]
substituting value
[tex]SE = \sqrt{\frac{0.81(1-0.81 )}{100} }[/tex]
[tex]SE = 0.0392[/tex]
The 98% confidence interval is evaluated as
[tex]p - t_{df , \frac{\alpha }{2} } * SE < p < p + t_{df , \frac{\alpha }{2} }[/tex]
substituting value
[tex]0.81 - 2.33 * 0.0392 < p < 0.81 +2.33 * 0.0392[/tex]
[tex]0.7187 < p < 2.421[/tex]
Consider the initial value problem y' + 3y = 9t, y(0) = 7.
a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below).
b. Solve your equation for Y(s).
Y(s) = L {y(t)} =
c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t).
y(t) =
Answer:
[tex]y(t) = 3x+8e^{-3x} -1[/tex]
Step-by-step explanation:
Recall that the following laplace transforms
[tex]L(y') = sY(s)-y(0)[/tex]
[tex]L(t) = \frac{1}{s^2}[/tex]
The laplace transform is linear, so, applying the laplace transform to the equation we get
[tex]L(y'+3y) = sY(s)-7+3Y(s) = L(9t) = \frac{9}{s^2}[/tex]
By some algebraic manipulations, we get
[tex] Y(s)(s+3) = \frac{9+7s^2}{s^2}[/tex]
which is equivalent to
[tex] Y(s) = \frac{9+7s^2}{s^2(s+3)} = \frac{9}{s^2(s+3)}+\frac{7}{s+3}[/tex]
By using the partial fraction decomposition, we get
[tex] \frac{9}{s^2(s+3)} = \frac{-1}{s} + \frac{3}{s^2} + \frac{1}{s+3}[/tex]
then
[tex]Y(s) = \frac{-1}{s} + \frac{3}{s^2} + \frac{1}{s+3} + \frac{7}{s+3} = \frac{8}{s+3} + \frac{3}{s^2}-\frac{1}{s}[/tex]
Using that
[tex] L(e^{-ax}) = \frac{1}{s+a}[/tex]
[tex]L(1) = \frac{1}{s}[/tex]
by taking the inverse on both sides we get
[tex] y(t) = L^{-1}(\frac{8}{s+3})+L^{-1}(\frac{3}{s^2})+L^{-1}(-\frac{1}{s}) = 8e^{-3x} + 3x-1[/tex]
a polynomial of degree N has n
Answer:
see explanation
Step-by-step explanation:
According to the Fundamental theorem of Algebra.
A polynomial of degree n has n roots which may be real or complex or both.
Answer:
The Fundamental Theorem of Algebra says that a polynomial of degree n will have exactly n roots
(counting multiplicity)
All help is appreciated! If sin²(32°) +cos² (M) = 1, then M equals?
Answer: M=32°
Step-by-step explanation:
The identity sin²(x)+cos²(x)=1 can help us figure out the value of M. You can see that the problem's format fits exactly the identity. Since x is the same in the identity, we know that M=32°.
CAN SOMEONE HELP ME ASAP
A. 5
B. 53‾√53
C. 10
D. 103√3
Answer:
n = 5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 30 = n/ 5 sqrt(3)
5 sqrt(3) tan 30 = n
5 sqrt(3) * 1/ sqrt(3) = n
5 = n
The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.
(i) 6.9
mPQ = 1
(ii) 6.99
mPQ = 2
(iii) 6.999
mPQ = 3
(iv) 6.9999
mPQ = 4
(v) 7.1
mPQ = 5
(vi) 7.01
mPQ = 6
(vii) 7.001
mPQ = 7
(viii) 7.000
mPQ = 8
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at
P(7, −2).
m = 9
(c) Using the slope from part (b), find an equation of the tangent line to the curve at
P(7, −2).
The equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
For each given value of x, we substitute the coordinates of P and Q into the slope formula to find the slope mPQ.
(i) For x = 6.9:
mPQ = (2/(6 - 6.9) - (-2)) / (6.9 - 7)
= 2.22
(ii) For x = 6.99:
mPQ = (2/(6 - 6.99) - (-2)) / (6.99 - 7)
= 2.020
(iii) For x = 6.999:
mPQ = (2/(6 - 6.999) - (-2)) / (6.999 - 7)
= 2.002002
(iv) For x = 6.9999:
mPQ = (2/(6 - 6.9999) - (-2)) / (6.9999 - 7)
= 2.000200
(v) For x = 7.1:
mPQ = (2/(6 - 7.1) - (-2)) / (7.1 - 7)
= 1.818182
(vi) For x = 7.01:
mPQ = (2/(6 - 7.01) - (-2)) / (7.01 - 7)
= 1.980198
(vii) For x = 7.001:
mPQ = (2/(6 - 7.001) - (-2)) / (7.001 - 7)
= 1.998002
(viii) For x = 7.0001:
mPQ = (2/(6 - 7.0001) - (-2)) / (7.0001 - 7)
= 1.999800
By observing the pattern in the calculated slopes, we can see that as x approaches 7, the slope of the secant line PQ approaches 2.
Using the point-slope form, we have:
y - y₁ = m(x - x₁)
Substituting the values of P(7, -2), we have:
y - (-2) = 2(x - 7)
y = 2x -16
Therefore, the equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
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What’s the difference between the polynomials ?
Answer:
7x^2-4x+3y^2 ( the ^ means the exponent EX: 5^2 is 5 squared. )
Step-by-step explanation:
Remove the parenthesis (a) = a
12x^2-11y^2-13x- (5x^2-14y^2-9x)
-(5x^2 - 14y^2 - 9x)
Distribute parenthesis
-(5x^2) - (14y^2) - (-9x)
Apply minus - plus rules
-5x^2 + 14y^2 + 9x
= 12x^2 - 11y^2 - 13x - 5x^2 + 14y^2 + 9x
Simplify
12x^2-11y^2-13x-5x^2+14y^2+9x
Group like terms
12x^2-5x^2-13x+9x-11y^2+14y^2
Add similar elements
7x^2-13x+9x-11y^2+14y^2
Add similar elements ( - 13x + 9x = -4x )
7x^2-4x-11y^2+14y^2
Add similar elements 11y^2 + 14y^2 = 3y^2
7x^2-4x+3y^2
which of the following is a composite number? 6,1,0,19
Answer:
63
Step-by-step explanation:
A composite number is an integer which can be found by mulitplying 2 smaller integers, 7 and 9 in this case
Which of the following is equivalent to the polynomial given below?
Answer:
[tex](x+(3+\sqrt{11}i)) (x+(3-\sqrt{11}i))[/tex]
Step-by-step explanation:
The first step to this problem is to look at the key features of the initial expression given to us. Namely, the middle term.
Notice that it is just [tex]+6x[/tex]. This indicates that the square root terms cancel out, meaning that their signs need to be opposite, but the threes need to have the same, positive sign. This indicates that our answer is option C, but you should always double check by multiplying the expression out to confirm. Here are the steps:
[tex](x+(3+\sqrt{11}i)) (x+(3-\sqrt{11}i))[/tex]
[tex]x^{2} +(3+\sqrt{11}i)x+(3-\sqrt{11}i)x+(3+\sqrt{11}i)(3-\sqrt{11}i)[/tex][tex]x^{2}+3x+\sqrt{11}ix+3x-\sqrt{11}ix+9+3\sqrt{11}i-3\sqrt{11}i-(\sqrt{11})^{2}(i^{2})[/tex][tex]x^{2}+6x+9-(11)(-1)[/tex]
[tex]x^{2}+6x+9+11[/tex]
[tex]x^{2}+6x+20[/tex]
Therefore as we suspected, the answer is C.
Which is true about all quadratic equations that contain a difference of squares? Only the value of c is a perfect square. Only the value of a is a perfect square. The value b=0. The value |b|=2[tex]\sqrt{a} \sqrt{c}[/tex]
Answer:
b = 0
Step-by-step explanation:
The standard form of a regular quadratic equation is ax² + bx + c and the standard form of the difference of squares is ax² - c. This means that b = 0 because there is no x term.
Suppose the area of a circle is 201.0624 square feet. What's the diameter of the circle? (Use π = 3.1416.)
Answer:
16
Step-by-step explanation:
Area of circle Formula: A = πr²
d = 2r
Simply plug in what you know:
201.0624 = 3.1416r²
64 = r²
r = 8
d = 2(8)
d = 16
Can someone answer these questions dm me or just do it in the comments.
Answer:
1. 8/4+ 3= 5
2. 5/(10/2)= 1
3. 5+10/2=10
4. 8/2+5x5= 29
5. 5+3/15+2= 10.15
6. 30+6x11-11= 25.11
7. 12 + (19+2) / 3 =19
Step-by-step explanation:
---------------------------------------------
Student name : Aparna Guha
Class : 8th
Division : B
School : St. John's Marhauli
Suggested subject : Maths
Work given on : 08 : 07 : 2020
Completed on : 08 : 07 : 2020
Posted on : 08 : 07 : 2020
Topic : Worksheet 1
Teacher's name : Manish Goel
School name : St. John's Marhauli
----------------------------------------------
If a person rolls a six-sided die and then draws a playing card and checks its color, describe the sample space of possible outcomes using 1, 2, 3, 4, 5, 6 for the die outcomes and B, R for the card outcomes.
Answer:
S = {1B, 2B, 3B, 4B, 5B, 6B, 1R, 2R, 3R, 4R, 5R, 6R}
Step-by-step explanation:
The sample space is the set of all possible outcomes in the experiment of rolling a six-sided die and then drawing a playing card and checking its color.
There are 6 possible outcomes for the die roll and two for the color of the card, which yields a total of 12 possible outcomes. The sample space is:
S = {1B, 2B, 3B, 4B, 5B, 6B, 1R, 2R, 3R, 4R, 5R, 6R}
Solving by fractions
Answer: Step 3
Step-by-step explanation:
x = -9 or 1. She flipped the signs.
Hope it helps <3
━━━━━━━☆☆━━━━━━━
▹ Answer
Step 3
▹ Step-by-Step Explanation
Juliet flipped the signs. The final answer should be (-9, 1)
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Translate the following statements into symbolic form using capital letters to representaffirmative English statement.
If Maria Cantwell promotes alternative energy,then if Patty Murray supports wilderness areas, then Dianne Feinstein's advocating gun control implies that Susan Collins does so,too.
Answer:
Step-by-step explanation:
There are two distinct statements but put together, it is:
- If Maria Cantwell (MC) promotes Alternative Energy (AE) and if Patty Murray (PM) supports Wilderness Areas (WA) then Dianne Feinstein (DF) advocating Gun Control (GC), implies that Susan Collins (SC) does so too.
For Susan Collins, she advocates gun control too.
So the symbolic or algebraic representation is:
(SC = DF): (MC ~ AE), (PM ~ WA)
OR
(GC = GC): (MC ~ AE), (PM ~ WA)
Where ":" represents "such that" or "given that"
" ~ " represents "support or promotion of"
It can now be read thus;
Susan Collins has same or equal interest as Dianne Feinstein, given that Maria Cantwell promotes alternative energy and Patty Murray supports Wilderness Areas.
i-Ready
Sofia
The area of a rectangle is 7/9 square feet. The width of the rectangle is 2 1/3 feet. What is the length of the rectangle?
Answer:
1/3 feet.
Step-by-step explanation:
The length = area / width
= 7/9 / 2 1/3
= 7/9 / 7/3
= 7/9 * 3/7
= 3/9
= 1/3 feet,
Determine the slope of the line that has the following coordinates: (5, 9)(11, - 3)
Answer:
[tex] x_1 = 5, x_2 =11, y_1 =9, y_2 = -3[/tex]
The slope can be founded with this formula:
[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m =\frac{-3 -9}{11-5}= -2[/tex]
And the best answer for this case would be :
[tex]m=-2[/tex]
Step-by-step explanation:
For this case we have the following two points given:
[tex] x_1 = 5, x_2 =11, y_1 =9, y_2 = -3[/tex]
The slope can be founded with this formula:
[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m =\frac{-3 -9}{11-5}= -2[/tex]
And the best answer for this case would be :
[tex]m=-2[/tex]
Let ƒ(x) = x + 1 and g(x) = 5x. Evaluate the composition (ƒ ∘ g)(–1). Question 2 options: A) (ƒ ∘ g)(–1) = 6 B) (ƒ ∘ g)(–1) = –4 C) (ƒ ∘ g)(–1) = 4 D) (ƒ ∘ g)(–1) = –6
Answer:
answer B
Step-by-step explanation:
hello,
[tex]f(x)=x+1\\g(x)=5x \ \ so\\(fog)(-1)=f(g(-1))=f(-5)=-5+1=-4[/tex]
so the winner is the answer B
hope this helps
Answer:
D)
(ƒ ∘ g)(–1) = –4
Step-by-step explanation:
Leo takes 15 minutes to cycle to school at an average speed of 12 km/h. What speed will he have if he only takes 12 minutes?
Answer:
15 km/h
Step-by-step explanation:
Leo takes 15 minutes to cycle to school at an average speed of 12 km/h. What speed will he have if he only takes 12 minutes?
15 minutes * (1 hour)/(60 minutes) = 0.25 hour
speed = distance/time
distance = speed * time
distance = 12 km/h * 0.25 hour = 3 km
He cycles a distance of 3 km.
12 minutes * (1 hour)/(60 minutes) = 0.2 hour
speed = distance/time
speed = 3 km/(0.2 hour)
speed = 15 km/h
Uytteday.com, student/dashboard/home
Probability Models - Tutorial - Level G
If we want to know if my shuffler is playing an equal
number of slow jams, dance music, and jazz songs,
what do we need to collect data on exactly?
Answer:
Ima need the answer too
Step-by-step explanation:
Answer:
the genre
Step-by-step explanation:
The population of a town increases by 5 % every five years. Due to a high rate of industrialisation of
the area, the population witnesses a further 5 % increase due to migration from neighbouring places.
Which of the following can be the population of this place, if it is known that the present population of
the place is between 44000 and 45000?
A) 44100
B)44050
C)44200
Answer:
A
Step-by-step explanation:
Because 105%*105%=1.1205
and the only number divisible by that is A
What is the solution to this system of linear equations? x − 3y = −2 x + 3y = 16
Answer:
so x=5 1/3 and
y= -2 2/3
Step-by-step explanation:
x-3y= -2x+3y=16. First we need to move all variables to one side of the equation and whole numbers to the other side of the equation. I see
x-3y+2x-3y=16. -3y-3y equals to -6y. 2x+x=3x. so 3x-6y=16. Lets take out the -6y so our equation would be 3x=16. x would equal 5 1/3. Now lets put back -6y into our equation. Let's now substitute x as 0. 3 times 0 equals 0 so our equation would now be -6y=16 which equals to -2 2/3.
so x=5 1/3 and
y= -2 2/3
Answer: ( x = -32, y = -16 )
Step-by-step explanation:
This can be represented by the three sides of an equilateral triangle.
x - 3y = -2x + 3y , simplify
x + 2x - 3y - 3y = 0
3x - 6y =0
x - 2y = 0 ---------------------- 1
x - 3y. = 16 ---------------------2
Solve using any methods
By elimination
y. = -16.
Substitute for y in any of the equations
x - 2y = 0
x. - 2(-16) = 0
x + 32 = 0
Therefore
x. = -32
Solution is ( -32, -16 )
y = 2x^4 convert to polar form
Answer:
The polar form is sinθ = 2 r³cos⁴θ
Step-by-step explanation:
Explanation:-
Given function y = 2 x⁴
Parametric Form x = r cosθ ....(i)
and y = r sinθ ....(ii)
squaring x² = r² cos ²θ
y² = r² sin²θ
adding x² + y² = r² cos ²θ+r² s in²θ
= r²( cos ²θ+s in²θ)
= r²( 1)
x² + y² = r²
Given function y = 2 x⁴
Now convert into polar form
r sinθ = 2 (r cos θ )⁴
r sinθ = 2 (r )⁴cos θ )⁴
sinθ = 2 r ³cos⁴θ
Please answer this correctly
Answer:
4/5 chance
Step-by-step explanation:
There are 4 numbers that fit the rule, 1, 3, 4, 5, since all of them are either odd or greater than 3. There will be a 4/5 chance of picking one.
Answer:
4/5 is the answer.Step-by-step explanation:
Facts!This is because 5 is odd and greater than 3.
Also. 4 is greater than 3.
After that, the other odd numbers are 1 and 3
So the numbers are 1, 3, 4, and 5.
So 4 out of 5 numbers are counted in the circle.
In this way 4/5 is the answer.
4/5 is the answer.Hope this helped!
Kavitha
Find the measure of angle angle AEB in the figure below. Enter only the number. PLEASE HELP ASAP
Answer:
42°
Step-by-step explanation:
AD is a line
AEC and DEC are both 90°
AEB and CEB make up 90°
AEB+CEB=AEC substitute
AEB+48=90 Next use Subtraction property of equality
AEB=42
Hope this helps, if so please give me brainliest, it helps a lot. :)
Have a good day!
Answer:
∠AEB=42
Step-by-step explanation:
∠AEB and ∠BEC are inside of ∠AEC.
∠AEC is a right angle, Since ∠AEC and ∠CED are on a straight line, they must add to 180 degrees. ∠CED is a right angle (the little square in the corner tell us this), so ∠AEC must also be a right angle. This is because a right angle is 90 degrees (∠CED+∠AEC=180 --> 90+∠AEC=180 --> ∠AEC=90)
Therefore, the 2 angles (AEB and BEC) inside of ∠AEC must add to 90 degrees.
∠AEB+ ∠BEC= 90
We know that ∠BEC=48
∠AEB+48=90
We want to find out what ∠AEB is. We must get ∠AEB by itself. 48 is being added, and the inverse of addition is subtraction. Subtract 48 from both sides.
∠AEB+48-48=90-48
∠AEB=90-48
∠AEB=42
Please answer this correctly
Answer:
40%
Step-by-step explanation:
The numbers that are not even are 5 and 7.
2 numbers out of 5.
2/5 = 0.4
P(not even) = 40%
Answer:
[tex]40\%[/tex]
Step-by-step explanation:
5 and 7 are not the numbers
There are 5 numbers in the spinner
[tex]p = \frac{2}{5} \\ = \frac{2 \times 20}{5 \times 20} \\ = \frac{40}{100} \\ = 40\%[/tex]
PLEASE HELP! Two complementary angles measure (12x - 18) and (5x +23). What is the measure of the smaller angle? (1) 5 (2) 42 (3) 48 (4) 90
Answer:
5
Step-by-step explanation:
firstly, what are complementry angles.complementary angles are angles that su
m up to 90°
(12x-18)+(5x+23)=90
collecting like terms
12x+5x+23-18=90
17x-5-90=0
17x-95=0
17x=95
divide through by 17
x=5
The measure of the smaller angle when complementary angles are given is 42 degree.
Complementary AnglesWhat are complementary angles?Complementary angles are two angles whose total is 90 degrees in geometry. In other terms, complimentary angles are two angles whose sum is 90 degrees. 60° and 30°, for instance.
Calculation for the value of x in the given angles:The first angle of the triangle is (12x - 18).
The measure of the second angle of the triangle is (5x + 23).
As both angles are complementary, their sum would be equal to 90 degree.
(12x - 18) + (5x + 23) = 90
12x - 18 + 5x + 23 = 90
17x = 85
x = 5
Calculation for the angles.Substitute the value of x = 5 in the given angles.
(1) 12x - 18 = 12×5 - 18
= 42 degrees
(2) 5x + 23 = 5×5 +23
= 48 degrees
Therefore, the smaller angle is found to be 42 degrees.
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I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer: L = 20.25
Step-by-step explanation:
[tex]T=2\pi \sqrt{\dfrac{L}{32}}[/tex]
Given: T = 5, π = 22/7
[tex]5=2\bigg(\dfrac{22}{7}\bigg)\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{5}{2}\bigg(\dfrac{7}{22}\bigg)=\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{35}{44}=\sqrt{\dfrac{L}{32}}\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\bigg(\sqrt{\dfrac{L}{32}}\bigg)^2\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\dfrac{L}{32}\\\\\\32\bigg(\dfrac{35}{44}\bigg)^2=L\\\\\\\large\boxed{20.25=L}[/tex]
a.) The perimeter of a rectangular field is 354 m. If the length of the field is 95m, what is its width? b.) The area of a rectangular painting is 8439 cm^2. If the width of the painting is 87cm, what is its length?
Answer:
a) 82
b) 97
Step-by-step explanation:
a) 354 - (95+95)
354 - 190
164
164 ÷ 2 = 82
(82+82+95+95=254)
b) 8439 cm^2 = 87x
8439 cm^2 ÷ 87 = 87x ÷ 87
97 = x
Find the measure of the indicated angle to the nearest degree please. Thanks.
Answer:
? = 35°Step-by-step explanation:
Let the angle be x
To find the indicated angle we use sine
sin ∅ = opposite / hypotenuse
From the question
7 is the hypotenuse
4 is the opposite
sin x = 4/7
x = sin-¹ 4/7
x = 34.85
x = 35° to the nearest degree
Hope this helps you
You own 13 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?
Answer:
1/154440
Step-by-step explanation:
To calculate the probability it would be the quotient between 1 and the number of ways to choose 5 out of 13, but in this case the order matters, so it would be the permutation 13P5, therefore:
We know that:
nPr = n! / (n-r)!
we replace and we have:
13P5 = 13! / (13-5)! = 154440
The probability that the rack ends up in alphabetical order is 1/154440
The probability that the rack ends up in alphabetical order is 1/154440
This is a question relating to permutation and combination. In order to calculate the probability, it would be the permutation 13P5, and this will be:
nPr = n! / (n-r)!
13P5 = 13! / (13-5)!
= 13! / 8!
= 13 × 12 × 11 × 10 × 9
= 154440
Therefore, the probability that the rack ends up in alphabetical order is 1/154440.
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