Answer:
x = {9, -3}
Step-by-step explanation:
2| x-3| - 5 = 72| x-3| = 12| x-3| = 6x - 3 = ± 6 ⇒ x= 3+ 6= 9⇒ x= 3 - 6= -3Or it can be shown as:
x= {9, -3}A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
Answer:A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
Step-by-step explanation:
The cylinder is given by A = pi/4 the volume of the prism or π/4 x (4r²h) or π x r² x h
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Area circle is A = πr²
Area square with side s = s²
The side of the square is equal to the diameter of the circle
Area square = D²
A diameter of square is always twice the radius
Area square = (2r)² = 2²r² = 4r²
So , on simplifying , we get
Area circle/Area square = (πr²)/(4r²)
Area circle/Area square = π/4
Now , The volume Prism = Area Square x h
Volume Prism = 4r²h
Volume of Cylinder= Area Circle x h
Volume of Cylinder = π x r² x h
So , Volume Cylinder/Volume Prism = π x r² x h/4r² x h
Volume of Cylinder/Volume of Prism = π/4
Volume of Cylinder = π/4 x Volume Prism
And , The volume of Cylinder = π/4 x (4r²h)
Hence , the volume of cylinder is V = π/4 x (4r²h)
To learn more about cylinder click :
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If ABC~DEF and the scale factor from ABC to DEF is 3/4, what is the length of DF?
Answer:
the length of DF = 3/4 AC
see below for explanation
Step-by-step explanation:
ABC is said to be approximately equal to DEF
The scale factor from ABC to DEF = 3/4
From the question, we can tell the original and new shape is a triangle because the lettering to indicate the vertices for both are 3.
We can deduce from the question, ΔABC was dilated to form ΔDEF
In dilation, the length of each of the corresponding side of the new figure is equal to the multiplication of each of the corresponding sides of the old figure and thee scale factor.
In the absence of cordinates for each vertices and length of each sides, ΔABC has 3 sides :
AB, BC and AC
ΔDEF has 3 sides : DE, EF and DF
If AB corresponds to DE
BC corresponds to EF
AC corresponds to DF
Then:
length DE = scale factor × AB = 3/4 AB
length EF = scale factor × BC = 3/4 BC
length DF = scale factor × AC = 3/4 AC
Therefore, the length of DF = 3/4 AC
A theater is presenting a program on drinking and driving for students and their parents or other responsible adults. The proceeds will be donated to a local alcohol information center. Admission is $6.00 for adults and $3.00 for students. However, this situation has two constraints: The theater can hold no more than 240 people and for every two adults, there must be at least one student. How many adults and students should attend to raise the maximum amount of money?
Answer:
160 adults and 80 students
Step-by-step explanation:
With the information from the exercise we have the following system of equations:
Let x = number of students; y = number of adults
I want to maximize the following:
z = 3 * x + 6 * y
But with the following constraints
x + y = 240
y / 2 <= x
As the value is higher for adults, it is best to sell as much as possible for adults.
So let's solve the system of equations like this:
y / 2 + y = 240
3/2 * y = 240
y = 240 * 2/3
y = 160
Which means that the maximum profit is obtained when there are 160 adults and 80 students, so it is true that added to 240 and or every two adults, there must be at least one student.
Ava is buying paint from Amazon. Ava needs 3⁄4 cup of blue paint for every 1 cup of white paint. Ava has 28 ounces of white paint. How much blue paint does he need?
Answer:
Blue paint=21 ounces
Step-by-step explanation:
3/4 cup=6 ounces
1 cup=8 ounces
3/4 cup of blue paint=6 ounces of blue paint
1 cup of white paint= 8 ounces of white paint
Ava has 28 ounces of white paint
Find the required blue paint
Let the required blue paint=x
Blue paint ratio white paint
6:8=x:28
6/8=x/28
Cross product
6(28)=x(8)
168=8x
x=168/8
x=21 ounces
Hi Folks, l have this Rearranging difficult formulae exercise, l have the answer but l dont understand at all the procedure, the method applied, if someone can explain it to me please will be appreciatted thanks 1/a = 1/b+1/c the procedure is: 1= a/b + a/c (x a) b= a+ ab/c (x b) bc= ac +ab ( x c) b (c-a) = ac b= ac/c-a OR b= - ac /a - c Def l dont understand the method thanks for your help
Step-by-step explanation:
1/a = 1/b + 1/c
Multiply both sides by a.
1 = a/b + a/c
Multiply both sides by b.
b = a + ab/c
Multiply both sides by c.
bc = ac + ab
Subtract ab from both sides.
bc − ab = ac
Factor b.
b (c − a) = ac
Divide both sides by c − a.
b = ac / (c − a)
Answer:
see below
Step-by-step explanation:
1/a = 1/b+1/c
Multiply each side of the equation by a
a( 1/a) =a( 1/b+1/c)
1 = a/b + a/c
Then multiply each side of the equation by b
b*1 =b( a/b + a/c)
b = a + ab/c
Then multiply each side of the equation by c
cb = c( a+ ab/c)
bc = ac + ab
We have gotten rid of the fractions
Now we can solve for a
Factor out a on the right side
bc = a( c+b)
Then divide by c+b on each side
bc / ( c+b) = a ( c+b) / ( c+b)
bc / ( c+b) = a
Now we can solve for b
bc = ac + ab
Subtract ab from each side
bc -ab = ac + ab-ab
bc -ab = ac
Factor out b on the left side side
b( c-a) = ac
Then divide by c-a on each side
b( c-a) / ( c-a) = ac / ( c-a)
b = ac/ ( c-a)
We can factor out -1
b = -ac/( a-c)
People start waiting in line for the release of the newest cell phone at 5\text{ a.m.}5 a.m.5, start text, space, a, point, m, point, end text The equation above gives the number of people, PPP, in line between the hours, hhh, of 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text and 11\text{ a.m.}11 a.m.11, start text, space, a, point, m, point, end text, when the doors open. Assume that 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text is when time h = 1h=1h, equals, 1. What does the 232323 mean in the equation above?
Answer:
There are 23 people in line at 6:00 A.M
Step-by-step explanation:
When you plug in h=1, we get 23 people
h corresponds with the time 6:00 am, as a result there are 23 people in line
The equation represents how many people will come as the hour increases.
23 represents the initial amount of people in line.
(got this from Khan academy too:))
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. VIEW FILE ATTACHED
Answer: see below
Step-by-step explanation:
[tex]P(x)=\dfrac{2}{3x-1}\qquad \qquad Q(x)=\dfrac{6}{-3x+2}\\[/tex]
P(x) ÷ Q(x)
[tex]\dfrac{2}{3x-1}\div \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\times \dfrac{-3x+2}{6}\\\\\\=\large\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]
P(x) + Q(x)
[tex]\dfrac{2}{3x-1}+ \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)+ \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)+6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4+18x-6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{12x-2}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{2(6x-1)}{(3x-1)(-3x+2)}}[/tex]
P(x) - Q(x)
[tex]\dfrac{2}{3x-1}- \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)- \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)-6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4-18x+6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-24x+10}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{-2(12x-5)}{(3x-1)(-3x+2)}}[/tex]
P(x) · Q(x)
[tex]\dfrac{2}{3x-1}\times \dfrac{6}{-3x+2}\\\\\\=\large\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]
EXAMPLE 4 Find ∂z/∂x and ∂z/∂y if z is defined implicitly as a function of x and y by the equation x6 + y6 + z6 + 18xyz = 1. SOLUTION To find ∂z/∂x, we differentiate implicitly with respect to x, being careful to treat y as a constant:
Answer:
see attachment
Step-by-step explanation:
We differentiate implicitly with respect to x taking y as a constant and we differentiate implicitly with respect to y taking x as a constant.
[tex]\rm \dfrac{\partial z}{\partial x} = - \dfrac{(x^5 + 3yz)}{z^5 + x} \ \ and \ \ \dfrac{\partial z}{\partial y} &= - \dfrac{(y^5 + 3xz)}{z^5 + y}[/tex]
What is an implicit function?When in a function the dependent variable is not explicitly isolated on either side of the equation then the function becomes an implicit function.
The equation is given as [tex]\rm x^6 + y^6 + z^6 + 18xyz = 1.[/tex]
Differentiate partially the function with respect to x treating y as a constant.
[tex]\begin{aligned} \dfrac{\partial}{\partial x} x^6 + y^6 + z^6 + 18xyz &= 0\\\\6x^5 + 0 + 6z^5 \dfrac{\partial z }{\partial x} + 18y(z + x\dfrac{\partial z}{\partial x}) &= 0\\\\x^5 + z^5 \dfrac{\partial z }{\partial x} + 3y(z + x\dfrac{\partial z}{\partial x}) &= 0\\\\\dfrac{\partial z}{\partial x} &= - \dfrac{(x^5 + 3yz)}{z^5 + x} \end{aligned}[/tex]
Similarly, differentiate partially the function with respect to y treating x as a constant.
[tex]\begin{aligned} \dfrac{\partial}{\partial y} x^6 + y^6 + z^6 + 18xyz &= 0\\\\ 0 + 6y^5+ 6z^5 \dfrac{\partial z }{\partial y} + 18x(z + y\dfrac{\partial z}{\partial y}) &= 0\\\\y^5 + z^5 \dfrac{\partial z }{\partial y} + 3x(z + y\dfrac{\partial z}{\partial y}) &= 0\\\\\dfrac{\partial z}{\partial y} &= - \dfrac{(y^5 + 3xz)}{z^5 + y} \end{aligned}[/tex]
More about the implicit function link is given below.
https://brainly.com/question/6472622
pleaseeee helppppp meeeee pleaseeeeee
Answer:
(28/33+28 ) *100
Step-by-step explanation:
(28/33+28 ) *100
(28/61)*100
Answer:
it's 2
Step-by-step explanation:
I did it before
A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 11 students, he found the average time was 4.52 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.1 level of significance. Assume normality. (can you please show how to do this without a calculator or excel i just dont want answer but want to know how to do it).
a) What are the appropriate null and alternative hypotheses?
A) H0: μ = 5 versus Ha: μ < 5
B) H0: μ = 5 versus Ha: μ ≠ 5
C) H0: x = 5 versus Ha: x ≠ 5
D) H0: μ = 5 versus Ha: μ > 5
b) What is the test statistic? Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) What is the appropriate conclusion?
A) Fail to reject the claim that the mean time is 5 minutes because the P-value is larger than 0.01.
B) Reject the claim that the mean time is 5 minutes because the P-value is larger than 0.01.
C) Reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.01.
D) Fail to reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.01.
Answer:
A) Null Hypothesis;H0: μ = 5
Alternative Hypothesis;Ha: μ ≠ 5
B) test statistic = -2.1226
C) p-value = 0.0598
D) Option A is correct
Step-by-step explanation:
We are given;
x = 4.52 minutes
s = 0.75 minutes
μ = 5 minutes
n = 11
degree of freedom = n - 1 = 11 - 1 = 10
A) The hypotheses are;
Null Hypothesis;H0: μ = 5
Alternative Hypothesis;Ha: μ ≠ 5
B) t-statistic = (x - μ)/(s/√n)
(4.52 - 5)/(0.75/√11) = -2.1226
C) From the t-score calculator results attached, the p-value is approximately 0.0598.
D) The P-value of 0.0598 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant. So option A is correct.
What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?
Answer:
13, 21
Step-by-step explanation:
Add 8 to the next number from the left to the right.
Answer:
The next three numbers in the sequence are: 13, 21, 29.
Step-by-step explanation:
Common Pattern: +8
-27 +8 = -19
-19 + 8 = -11
-3 + 8 = 5
5 + 8 = 13
13 + 8 = 21
21 + 8 = 29
Betty has $33 to buy plants for her greenhouse. Each plant costs $8. How
many plants can she buy? Do not include units in your answer.
Answer:
4 plants
Step-by-step explanation:
If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4
(8 * 4 is 32)
She will have one dollar left but she can't buy another plant since that's not enough.
Answer:
4 plants
Step-by-step explanation:
Take the amount of money she has and divide by the cost per plant
33/8
The amount is 4 with 1 dollar left over
4 plants
Cynthia invested $12,000 in a savings account. If the interest rate is 6%, how much will be in the account in 10 years by compounding continuously? Round to the nearest cent.
Answer:
In 10 years she'll have approximately $21865.4 in her account.
Step-by-step explanation:
When an amount is compounded continuously its value over time is given by the following expression:
[tex]v(t) = v(0)*e^{rt}[/tex]
Applying data from the problem gives us:
[tex]v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4[/tex]
In 10 years she'll have approximately $21865.4 in her account.
Answer:
21,865.43
previous answer left out the last digit
Step-by-step explanation:
The ratio of the legs of a trapezoid is 1:2, and the sum of the angles adjacent to the bigger base is 120°. Find the angle measures of the given trapezoid.
Answer:
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Step-by-step explanation:
A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.
Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:
[tex]2\cdot \alpha = 120^{\circ}[/tex]
[tex]\alpha = 60^{\circ}[/tex]
The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])
[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]
[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]
[tex]\beta = 180^{\circ}-\alpha[/tex]
[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]
[tex]\beta = 120^{\circ}[/tex]
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
assume that when adults with smartphones are randomly selected 42 use them in meetings or classes if 15 adult smartphones are randomly selected, find the probability that "fewer" than 4 of them use their smartphones
Complete Question
Assume that when adults with smartphones are randomly selected 42% use them in meetings or classes if 15 adult smartphones are randomly selected, find the probability that "fewer" than 4 of them use their smartphones
Answer:
The probability is [tex]P[X < 4]= 0.00314[/tex]
Step-by-step explanation:
From the question we are told that
The proportion of those that use smartphone in meeting and classes is p = 0.42
The sample size is [tex]n = 15[/tex]
The proportion of those that don't use smartphone in meeting and classes is
[tex]q = 1- p[/tex]
=> [tex]q = 1- 0.42[/tex]
=> [tex]q = 0.58[/tex]
Now from the question we can deduce that the usage of the smartphone is having a binomial distribution since there is only two outcome
So the probability that "fewer" than 4 of them use their smartphones is mathematically evaluated as
[tex]P[X < 4 ] = P[X = 0] + P[X = 1] +P[X = 2] +P[X = 3][/tex]=
=> [tex]P[X < 4] = [ \left 15} \atop {0}} \right. ] p^{15-0} * q^0 + [ \left 15} \atop {1}} \right. ] p^{15-1 }* q^1 + [ \left 15} \atop {2}} \right. ] p^{15-2 }* q^2 + [ \left 15} \atop {3}} \right. ] p^{15-3 }* q^3[/tex]
Where [tex][\left 15} \atop {0}} \right. ][/tex] implies 15 combination 0 which has a value of 1 this is obtained using a scientific calculator
So for the rest of the equation we will be making use of a scientific calculator to obtain the combinations
[tex]P[X < 4] = 1 * ^{15} * q^0 + 15 * p^{14 }* q^1 + 105 * p^{13 }* q^2 + 455 * p^{12 }* q^3[/tex]
substituting values
[tex]= 1 * (0.42)^{15} * (0.58)^0 + 15 * (0.42)^{14 }* (0.58)^1[/tex]
[tex]+ 105 * (0.42)^{13 }* (0.58)^2 + 455 * (0.42)^{12 }* (0.58)^3[/tex]
=> [tex]P[X < 4]= 0.00314[/tex]
Find the value of annuity if the periodic deposit is $250 at 5% compounded quarterly for 10 years
Answer:
The value of annuity is [tex]P_v = \$ 7929.9[/tex]
Step-by-step explanation:
From the question we are told that
The periodic payment is [tex]P = \$ 250[/tex]
The interest rate is [tex]r = 5\% = 0.05[/tex]
Frequency at which it occurs in a year is n = 4 (quarterly )
The number of years is [tex]t = 10 \ years[/tex]
The value of the annuity is mathematically represented as
[tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex] (reference EDUCBA website)
substituting values
[tex]P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ][/tex]
[tex]P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ][/tex]
[tex]P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ][/tex]
[tex]P_v = \$ 7929.9[/tex]
Help ASAP!!!
Find sin(c). Round to the nearest hundredth if necessary.
A: 0.38
B: 0.92
C:0.42
D:1.08
Answer:
The answer is option A
0.38Step-by-step explanation:
sin ∅ = opposite / hypotenuse
Since we are finding sin (c)
From the question
The opposite is BA
The hypotenuse is AC
So we have
sin c = BA/ AC
BA = 5
AC = 13
sin c = 5/13
sin c = 0.384615
sin (c) = 0.38 to the nearest hundredth
Hope this helps you
Answer:
[tex]\boxed{Sin C = 0.38}[/tex]
Step-by-step explanation:
Sin C = opposite/hypotenuse
Where opposite = 5, hypotenuse = 13
Sin C = 5/13
Sin C = 0.38
3 solutions for x<-2
Answer:
-3,-4,-5
Step-by-step explanation:
those are all numbers less than -2! your welcome! please give me brainliest!
Answer: -3, -16, and -642,000
Step-by-step explanation: In this problem, we're asked to state three solutions for the following inequality, x < -2.
The inequality x < -2 means that any number
less than -2 is a solution to the inequality.
For example, -3 is a solution because -3 is less than -2.
Another solution would be -16 because -16 is less than -2.
One other solution would be -642,000 because it's less than -2.
It's important to understand that these are only 3 possible
answers and there are many answers to choose from.
Verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a power x2n + 1 let k = n + 1.] y = (-1) nx2n, (1 + x2)y' + 2xy = 0
Answer:
The given power series [tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex] is a solution of the differential equation (1+x^2)y' + 2xy = 0
Step-by-step explanation:
This is a very trivial exercise, follow the steps below for the solution:
Step 1: Since n = 0, 1, 2, 3, 4, ........, Substitute the values of n into equation (1) below.
[tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex].....................(1)
[tex]y = 1 - x^2 + x^4 - x^6 + x^8.........[/tex]
Step 2: Find the derivative of y, i.e. y'
[tex]y' = -2x + 4x^3 - 6x^5 + 8x^7 .............[/tex]
Step 3: Substitute y and y' into equation (2) below:
[tex](1+x^2)y' + 2xy = 0\\\\(1+x^2)(-2x + 4x^3 - 6x^5 + 8x^7......) + 2x(1 - x^2 + x^4 - x^6 + x^8.......) = 0\\\\-2x+ 4x^3 - 6x^5 + 8x^7........ - 2x^3 +4x^5 - 6x^7 + 8x^9 ......+ 2x - 2x^3 + 2x^5 - 2x^7 + 2x^9...... = 0\\\\0 = 0[/tex]
(Verified)
Since the LHS = RHS = 0, the given power series [tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex] is a solution of the differential equation (1+x^2)y' + 2xy = 0
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's standard deviation
Answer:
15
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
30 hcchxfifififififfud7dd7d
Solve: 5x=110. (Round to three decimal places.)
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In equations, letters like x or y are called variables. They represent a number that we do not know yet, or they can almost be seen as a question mark in an equation. For example, 1+?=2. We know that this ? represents the number 1, and the same would go if you put a variable in there. If you have 1+x=2, you can figure out that x=1!
Our equation is 5x=110. When you see a number next to a variable, that number is called the coefficient. It is a number that multiplies a variable. So, our coefficient is 5. This means that five is multiplied by x to equal 110.
5·x=110
What if we don't know off the top of our heads what we multiply 5 by to get to 110? It was easy with 1+1=2, but this is trickier. Here's how to figure it out.
We want to get the x all by itself on one side of the equation. Then, we will see what x equals.
To do this, we use inverse operations. I will show you below with our 1+x=2 example.
1+x=2
We have a positive one plus an x equals two. We could visualize this like this.
+1+x=2
What we want to do is move the 1 to the other side of the equation so that x is by itself. So, what's the opposite of adding? Subtracting!
However, we don't just subtract the 1 from the left side, but we do it from the right side! You have to do the inverse operation on both sides to find the answer.
So, let's subtract 1 from both sides.
+1+x-1=2-1
x=1
We see that x equals 1, and if we plug this into the equation 1+x=2, we see that it is correct.
Now, with our problem, we need to divide, because that is the opposite of multiplication. We need to divide both sides by 5 to isolate the x. Let's do it!
5x÷5=110÷5
x=22
We see that 5×22 is equal to 110, so this is correct! Now you can solve for variables in equations!
Have a wonderful day!
ANSWER ASAP. Which number line correctly shows –3 – 1.5? A number line going from negative 4.5 to positive 4.5. An arrow goes from 0 to negative 3 and from negative 3 to negative 4.5. A number line going from negative 4.5 to positive 4.5. An arrow goes from 0 to 3 and from 3 to 4.5. A number line going from negative 4.5 to positive 4.5. An arrow goes from negative 3 to negative 1.5 and from 0 to negative 3. A number line going from negative 4.5 to positive 4.5. An arrow goes from negative 1.5 to 1.5 and from 0 to negative 1.5.
Answer:
An arrow goes from 0 to negative 3 and from negative 3 to negative 4.5
Step-by-step explanation:
Start at 0 and move 3 units to the left since it is negative
Move 1.5 units to the left since we are subtracting
We end up at - 4.5
Answer:
An arrow goes from 0 to negative 3 and from negative 3 to negative 4.5
Step-by-step explanation:
-3 is also 0-3
arrow goes from 0 to -3 backwards.
arrow goes from -3 to -4.5 because -3-1.5=-4.5
Assume that IQ scores are normally distributed, with a standard deviation of 16 points and a mean of 100 points. If 60 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points
Answer:
The probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points is 0.67
Step-by-step explanation:
Please check attachment for complete solution and step by step explanation
A restaurant gat an average of 14 calls in a 2 hr time period. What is the probability that at most 2 calls in 45 min period
Answer:
0.10512
Step-by-step explanation:
Given the following :
Mean number of calls(μ) in 2 hours = 14
2 hours = 60 * 2 = 120 minutes
Average number of calls in 45 minutes :
= (45 / 120) * 14
= 0.375 * 14
= 5.25
Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)
Using the poisson probability formula:
P(x, μ) = [(e^-μ) * (μ^x)] / x!
Where :
e = euler's constant
μ = 5.25
x = 0, 1, 2
Using the online poisson probability calculator :
P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)
P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512
A city's population is currently 50,000. If the population doubles every 70 years, what will the population be 280 years from now?
Answer:
200,000
Step-by-step explanation:
The current population: 50,000
Doubling time:70
Population after 280 years=?
280/70=4
50,000*4=200,000
Hope this helps ;) ❤❤❤
Answer: 800,000
Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.
The graph of f*x)=2^(x+3) shifts 10 units to the right when it is replaced with the graph of f(x)=2^(x-k). What is the value of k?
Answer:
7
Step-by-step explanation:
f(x) = 2^(x + 3)
Shifted 10 units to the right:
f(x) = 2^(x + 3 − 10)
f(x) = 2^(x − 7)
Therefore, k = 7.
volume= (can someone explain please, im not really understanding this)
Not the greatest picture; I think it's trying to be a house, an A frame with a rectangular base.
This is a prism with a side 3 equilateral triangle at the end and a length of 6.
The area of the triangle is
[tex]\Delta = \dfrac{\sqrt{3}}{4} s^2[/tex]
The volume is area times length,
[tex]V = L \Delta = \dfrac{\sqrt{3}}{4} s^2 L[/tex]
[tex]V = \dfrac{\sqrt{3}}{4} (3^2) 6 = \dfrac{27}{2} \sqrt{3}[/tex]
Answer: (27/2) √3
Need help ASAP! Will give brainliest if you tell me how to do this!
Answer:
A
Step-by-step explanation:
The syntax is binomcdf(trials, probability, value). There are 100 trials, and the probability is 0.5. binomcdf will return the probability that there is at most n successes. So, in this case we want 45 or less successes, so n is 45. So, the answer is binomcdf(100, 0.5, 45).
Hope this makes sense! Please give brainliest!
The following table shows the number of innings pitched by each of the Greenbury Goblins' starting pitchers during the Rockbottom Tournament. Pitcher Calvin Thom Shawn Kris Brantley Number of innings pitched 11 1111 12 1212 7 77 3 33 ? ?question mark If the mean of the data set is 8 88 innings, find the number of innings Brantley pitched. innings
Answer:
The number of innings Brantley pitched is 7.
Step-by-step explanation:
We are given that the table shows the number of innings pitched by each of the Greenbury Goblins' starting pitchers during the Rockbottom Tournament below;
Pitcher Number of innings pitched
Calvin 11
Thom 12
Shawn 7
Kris 3
Brantley x
Let the number of innings Brantley pitched be 'x'.
The mean of the following data set is given by the following formula;
Mean = [tex]\frac{\text{Sum of all data values}}{\text{Total number of observations}}[/tex]
[tex]8 = \frac{11+12+7+3+x}{5}[/tex]
[tex]8\times 5 =33+x[/tex]
[tex]40 = 33+x[/tex]
x = 40 - 33 = 7
Hence, the number of innings Brantley pitched is 7.
Answer:
7
Step-by-step explanation:
Khan Academy
i need these THREE questions ANSWERED please!!!! please i really need these done!!!
Step-by-step explanation:
8. As the name implies, a box-and-whisker plot looks like a box with two whiskers. The box is the middle 50%. The whiskers are the bottom 25% and the top 25%.
First, we need to sort the numbers from smallest to largest. Starting with Set A:
Set A = {56, 57, 62, 68, 71, 82, 84, 92, 97, 101, 103, 106}
Now we find the median of the set, or the middle number. Set A has 12 data points. Since 12 is an even number, the median will be the average of the 6th and 7th numbers.
M = (82 + 84) / 2 = 83
Next, we find the median of the lower half. There are 6 numbers in the lower half, so the median is the average of the 3rd and 4th numbers.
Ml = (62 + 68) / 2 = 65
Now we find the median of the upper half. Again, there are 6 numbers in the upper half, so the median will be the average of the 3rd and 4th numbers.
Mu = (97 + 101) / 2 = 99
So the left whisker is from 56 to 65.
The box is from 65 to 99.
The right whisker is from 99 to 106.
Don't forget to mark the median, 83.
Repeat for Set B.
Set B = {36, 37, 42, 46, 48, 56, 58, 63, 69, 72, 75, 78}
M = (56 + 58) / 2 = 57
Ml = (42 + 46) / 2 = 44
Mu = (69 + 72) / 2 = 70.5
So the left whisker is from 36 to 44.
The box is from 44 to 70.5.
The right whisker is from 70.5 to 78.
The median is 57.
By graphing both on the same number line, we can easily compare them.
9. To make a dot plot, draw a number line starting from the smallest number and ending at the largest number. For each number, draw a dot every time the number appears in the set. For example, the number 3 appears twice in Set A, so draw two dots on 3. You may find it helpful to sort the data first.
10. Draw a dot plot of the set to determine the shape.