One custodian cleans a suite of offices in 3 hrs. When a second worker is asked to join the regular custodian, the job takes only 2 hours. How long does it take the second worker to do the same job alone?
A man divided $9,000 among his wife, son, and daughter. The wife received twice as much as the daughter, and the son received $1,000 more than the daughter. How much did each receive?
If x is the amount the wife received, then which of the following expressions represents the amount received by the son?
Answer:
Step-by-step explanation:
A man divided $9,000 among his wife, son and daughter.
The wife received twice as much as the daughter.
Let the daughter received d amount.
Then the wife received = 2d
and son received $1,000 more than the daughter.
The son received the amount = 1000+d
So the expression will be = d + 2d +(1000+d) = 9,000
3d + (1000+d) = 9000
4d = 9000 - 1000
4d = 8000
d = [tex]\frac{8000}{4}[/tex]
d = 2000
Daughter received $2,000
Wife received 2d = 2 × 2000 = $4,000
Son received 1000 + d = 1000 + 2000 = $3,000
If x is the amount the wife received, then the expression represents the amount received by the son :
S = 1000 + (x/2)
What is the answer to this question?
9/12= 0.75
8.00 * 0.75 = 6.00
the 9" costs $6.00
Rs = 8y + 4 , ST = 4y + 8 , and RT = 36 , find the value of y
The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of 7. What percent of the scores are less than 81?
The probability that an archer hits a target on a given shot is .7 if five shots are fired find the probability that the archer hits the target on three shots out of the five.
The probability that the archer hits the target on exactly three out of five shots is 0.3087, or 30.87%, calculated by using the binomial probability formula.
The probability that an archer hits a target on a given shot is 0.7 and the goal is to calculate the probability that the archer hits the target on exactly three out of five shots. This is a binomial probability problem, as each shot can end in either a success (hitting the target) with a probability of 0.7, or a failure (missing the target) with a probability of 0.3.
To calculate the probability of exactly three successes (hits) out of five, we use the binomial probability formula:
P(X=k) = (n choose k) * (p)^k * (1-p)^(n-k)
Where:
n = total number of trials (5 shots)
k = number of successes (3 hits)
p = probability of success on a single trial (0.7)
Applying the formula, we get:
P(3 hits out of 5) = (5 choose 3) * (0.7)^3 * (0.3)^2
= 10 * (0.343) * (0.09)
= 10 * 0.03087
= 0.3087
Therefore, the probability that the archer hits the target on exactly three out of five shots is 0.3087, or 30.87%.
Simplify Negative 3 over 2 ÷ 9 over 6.
Find the value of each variable. Please help me!!
Evaluate the integral below, where e lies between the spheres x2 + y2 + z2 = 9 and x2 + y2 + z2 = 25 in the first octant.
The student's question involves integrating a function in a region bounded by two spheres in the first octant, implying the use of spherical coordinates and integration over a sphere with a constant radius.
The question pertains to evaluating an integral within the region bounded by two spheres in the first octant. When dealing with spheres and integrals, the use of spherical coordinates is often beneficial. The question suggests using spheres with a constant radius and spherical coordinates (r, θ, φ), where a typical point in space is represented as (r sin(θ) cos(φ), r sin(θ) sin(φ), r cos(θ)). To integrate over the sphere, we consider the bounds given by the radii of the inner and outer spheres, (r = 3 and r = 5, respectively, since the square roots of 9 and 25 are 3 and 5), and the fact that it is within the first octant which further restricts the limits of θ and φ. The rest of the provided excerpts seem to be unrelated specifically to this problem but are examples of standard integrals and applications of integration in physics and potential theory.
The final answer after evaluating the integral is: [tex]\[\frac{49\pi}{3}\][/tex]. This is the value of the integral over the region between the spheres [tex]\( x^2 + y^2 + z^2 = 9 \) and \( x^2 + y^2 + z^2 = 25 \)[/tex] in the first octant.
To evaluate the given integral over the region between the spheres [tex]\( x^2 + y^2 + z^2 = 9 \)[/tex]and [tex]\( x^2 + y^2 + z^2 = 25 \)[/tex] in the first octant, we can use spherical coordinates. In spherical coordinates, the volume element is given by [tex]\( r^2 \sin(\phi) \, dr \, d\theta \, d\phi \),[/tex] where r is the radial distance, [tex]\( \theta \)[/tex] is the azimuthal angle, and [tex]\( \phi \)[/tex] is the polar angle.
The limits for the integral are as follows:
[tex]- \( 3 \leq r \leq 5 \) (limits of the radii for the spheres)\\- \( 0 \leq \theta \leq \frac{\pi}{2} \) (first octant)\\- \( 0 \leq \phi \leq \frac{\pi}{2} \) (first octant)[/tex]
The integral to evaluate is not specified, so let's assume it's a simple function like \( f(x, y, z) = 1 \) for the sake of demonstration. The integral would then be:
[tex]\[\iiint_E 1 \, dV = \int_{0}^{\frac{\pi}{2}} \int_{0}^{\frac{\pi}{2}} \int_{3}^{5} r^2 \sin(\phi) \, dr \, d\theta \, d\phi\][/tex]
Now, let's evaluate this integral step by step:
[tex]\[\int_{0}^{\frac{\pi}{2}} \int_{0}^{\frac{\pi}{2}} \int_{3}^{5} r^2 \sin(\phi) \, dr \, d\theta \, d\phi\][/tex]
[tex]\[= \int_{0}^{\frac{\pi}{2}} \int_{0}^{\frac{\pi}{2}} \left[ \frac{1}{3} r^3 \sin(\phi) \right]_{3}^{5} \, d\theta \, d\phi\][/tex]
[tex]\[= \int_{0}^{\frac{\pi}{2}} \int_{0}^{\frac{\pi}{2}} \left( \frac{125}{3} - \frac{27}{3} \right) \sin(\phi) \, d\theta \, d\phi\][/tex]
[tex]\[= \int_{0}^{\frac{\pi}{2}} \int_{0}^{\frac{\pi}{2}} \frac{98}{3} \sin(\phi) \, d\theta \, d\phi\][/tex]
[tex]\[= \int_{0}^{\frac{\pi}{2}} \left[ \frac{98}{3} \theta \right]_{0}^{\frac{\pi}{2}} \, d\phi\][/tex]
[tex]\[= \int_{0}^{\frac{\pi}{2}} \frac{98}{3} \cdot \frac{\pi}{2} \, d\phi\][/tex]
[tex]\[= \frac{98\pi}{6}\][/tex]
[tex]\[= \frac{49\pi}{3}\][/tex]
So, the value of the integral over the specified region is[tex]\( \frac{49\pi}{3} \).[/tex]
Assume that y varies inversely with x
y = k/x
7=k/-2
k = 7/-2 = -3.5
y =-3.5/7 =-0.5
y=-0.5
A soccer team is having a car wash.the team spent $55 on supplies.they earned $275 including tips.The teams profit is the amount the team made after paying for supplies.Write a sum of integers that repersents the teams profit.
Rewrite with only sin x and cos x. cos 3x
You have $5. If candy bars cost $0.75, what is the greatest number of candy bars you can buy
If (f + g)(x) = 3x2 + 2x – 1 and g(x) = 2x – 2, what is f(x)?
A certain recipe requires 458 cups of flour and 659 cups of sugar. a) If 3/8 of the recipe is to be made, how much sugar is needed?
If the above ingredients are required for one batch, find the amount of flour needed for a double batch.
The sum of a number and -20 is 40.What is the number?
sum means addition
so x +-20 = 40
x = 40 +20 = 60
x=60
You take a three-question true or false quiz. You guess on all the questions. What is the probability that you will get a perfect score?
what is the answer ?
what does it mean to say that's data point has a residual of 0
Answer:
The correct answer is “the point lies directly on the regression line”
Step-by-step explanation:
When you do a regression analysis, then you get a line of regression that best fits it. The data points usually tend to fall in the regression line, but they do not precisely fall there but around it. A residual is the vertical distance between a data point and the regression line. Every single one of the data points had one residual. If one of this residual is equal to zero, then it means that the regression line truly passes through the point.
Help.. :)
Which equation is not equivalent to the formula e = mc?
m equals e over c
c equals e over m
e = cm
m equals c over e
Please help THANKS!
Answer with Step-by-step explanation:
we are given a equation:
e=mc
We have to find which equation is not equivalent to the above formula.
e=mcDividing both sides by c,we get
m=e/c
i.e. m equals e over c
e=mcDividing both sides by m,we get
c=e/m
i.e. c equals e over m
e=mc=cmBut m is not equal to c over eHence, The equation which is not equivalent to e=mc is:
m equals c over e
Find the taylor polynomial t3(x) for the function f centered at the number
a. f(x) = eâ4xsin(2x), a = 0
The Taylor polynomial [tex]T_3(x)[/tex] will be written as [tex]2x-8x^2+\dfrac{44x^3}{3}+......[/tex].
Given:
The given function is [tex]f(x) = e^{-4x}sin(2x)[/tex].
It is required to find the Tylor polynomial [tex]t_3(x)[/tex] centered at a=0.
Now, the expansion of the function [tex]e^{-4x}[/tex] can be written as,
[tex]e^{-4x}=\sum\dfrac{(-4x)^n}{n!}\\e^{-4x}=1+(-4x)^1+\dfrac{(-4x)^2}{2!}+\dfrac{(-4x)^3}{3!}+.....\\e^{-4x}=1-4x+\dfrac{16x^2}{2}-\dfrac{64x^3}{6}+.....\\e^{-4x}=1-4x+8x^2-\dfrac{32x^3}{3}+.....[/tex]
Similarly, the expansion of the function [tex]sin(2x)[/tex] will be,
[tex]sin(2x)=\sum\dfrac{(-1)^n(2x)^{2n+1}}{(2n+1)!}\\=\dfrac{2x}{1!}+\dfrac{-(2x)^3}{3!}+.....\\=2x-\dfrac{4x^3}{3}+......[/tex]
So, the function [tex]f(x) = e^{-4x}sin(2x)[/tex] will be written as,
[tex]f(x) = e^{-4x}sin(2x)\\f(x)=(1-4x+8x^2-\dfrac{32x^3}{3}+.....)(2x-\dfrac{4x^3}{3}+......)\\f(x)=2x-8x^2+16x^3-\dfrac{4x^3}{3}+.......\\f(x)=2x-8x^2+\dfrac{(48-4)x^3}{3}+......\\f(x)=2x-8x^2+\dfrac{44x^3}{3}+......[/tex]
Therefore, the Taylor polynomial [tex]T_3(x)[/tex] will be written as [tex]2x-8x^2+\dfrac{44x^3}{3}+......[/tex].
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can someone solve this for me
Which of the following is the radical expression of a to the four ninths power
Answer:
[tex]\sqrt[9]{a^{4}}[/tex]
Step-by-step explanation:
To convert a fraction form into a radical form you need to know that the denominator will be the root index and the numerator will be the exponent into the root. For the case of four ninths:
[tex]a^{\frac{4}{9}} = \sqrt[9]{a^{4}} .[/tex]
is 5.21 a rational number
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)= 120t-16t^2 . What is the maximum height that the ball will reach? Do not round
The answer is: 225.
To find the maximum height that the ball will reach, we need to determine the vertex of the parabola described by the function [tex]\( h(t) = 120t - 16t^2 \)[/tex]. The vertex form of a parabola is[tex]\( h(t) = a(t - h)^2 + k \)[/tex], where [tex]\( (h, k) \)[/tex] is the vertex of the parabola. The value of [tex]\( k \)[/tex] will give us the maximum height.
The given function can be rewritten in the form [tex]\( h(t) = -16(t^2 - \frac{120}{16}t) \)[/tex]. To complete the square, we take the coefficient of [tex]\( t \)[/tex], divide it by 2, and square it. This value is then added and subtracted inside the parentheses:
[tex]\( h(t) = -16(t^2 - \frac{120}{16}t + (\frac{120}{32})^2 - (\frac{120}{32})^2) \)[/tex]
[tex]\( h(t) = -16((t - \frac{120}{32})^2 - (\frac{120}{32})^2) \)[/tex]
Now, we expand the squared term and multiply through by -16:
[tex]\( h(t) = -16(t - \frac{120}{32})^2 + 16(\frac{120}{32})^2 \)[/tex]
[tex]\( h(t) = -16(t - 3.75)^2 + 16(3.75)^2 \)[/tex]
The maximum height [tex]\( k \)[/tex] is the constant term when the equation is in vertex form:
[tex]\( k = 16(3.75)^2 \)[/tex]
[tex]\( k = 16 \times 14.0625 \)[/tex]
[tex]\( k = 225 \)[/tex]
Therefore, the maximum height that the ball will reach is 225 feet.
What is the value of x in the equation below?
1+2e^x+1=9
Answer:
X = In4-1 C on edge, just took the test
The value of a car decreases by 20 percent per year. Mr. Sing purchases a $22,000 automobile. What is the value of the car at the end of the second year?
22,000 - 20% = 17,600
17,600 - 20% = 14,080
$14,080 at the end of the second year .
What is the property of 16+31=31
We have the equation here is
16 + 31 = 31
When we simplify the equation to the understandable form, we move all terms or numbers to right and on left side zero will be left.
0 = 31-16-31
We get, 0 = -16
Now we see that both sides of equations are not equal, it means there is no solution so it is an invalid equation.
Which of the following represents the linear equation 3x =12 - 2y in standard form?
A: y=-2/3x-2
B: y=-2/3x-6
C: y=-3/2x+6
D: y= 2/3x-17/3
Five individuals, including a and b, take seats around a circular table in a completely random fashion. suppose the seats are numbered 1, . . . , 5. let x = a's seat number and y = b's seat number. if a sends a written message around the table to b in the direction in which they are closest, how many individuals (including a and
b.would you expect to handle the message?
The number of individuals you would expect to handle the message is 2.5.
Joint probability distributionLet Z represent the number of individuals that handle the message
Table for the possible joint value of X and Y
Z Y
1 2 3 4 5
X 1 - 2 3 3 2
2 2 - 2 3 3
3 3 2 - 2 3
4 3 3 2 - 2
5 2 3 3 2 -
Each cell contain=1/4×1/5=1/20
Hence:
Number of individual=10×2×1/20+10×3×1/20
Number of individual=20×0.05+30×0.05
Number of individual=2.5
Therefore the number of individuals you would expect to handle the message is 2.5.
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