A small solid metal ball has a weight of 12 g
Another larger ball was made to be
mathematically similar but its diameter is 3 times as big as
the smaller ball.
(3)
What is the weight of the larger
ball?
The surface area of the larger
ball is 108 cm. What is the surface area
of the smaller ball?
(2)
Answers
The weight of the larger ball can be calculated using the principle of similarity. Since the diameter of the larger ball is three times as big as the smaller ball, the volume of the larger ball will be 27 times that of the smaller ball.
As weight is directly proportional to volume, the weight of the larger ball is 27 times the weight of the smaller ball, which is 12 g. Therefore, the weight of the larger ball is 324 g.
To find the surface area of the smaller ball, we can use the formula for the surface area of a sphere. Since the diameter of the larger ball is three times that of the smaller ball, the radius of the larger ball will be three times the radius of the smaller ball. Using the formula for the surface area of a sphere, the surface area of the larger ball is 108 cm². By applying the same principle of similarity, the surface area of the smaller ball is 12 cm².
The weight of an object is directly proportional to its volume. In this case, since the larger ball is mathematically similar to the smaller ball, its volume will be 27 times that of the smaller ball (3^3 = 27). Since the weight of the smaller ball is given as 12 g, the weight of the larger ball will be 27 times that, resulting in a weight of 324 g.
Moving on to the surface area, the formula for the surface area of a sphere is 4πr², where r is the radius of the sphere. As mentioned, the diameter of the larger ball is three times that of the smaller ball, which means the radius of the larger ball is also three times that of the smaller ball. The surface area of the larger ball is given as 108 cm². Applying the principle of similarity, the ratio of the surface areas will be equal to the ratio of the squares of their radii. Therefore, (3r_small)^2 / r_small^2 = 108 / surface area_small. Simplifying this equation gives 9 = 108 / surface area_small, and solving for surface area_small results in 12 cm². Hence, the surface area of the smaller ball is 12 cm².
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Related Questions
Given f(x) = 2x^2+ kx – 9, and the remainder when f(x) is divided by x + 6 is
57, then what is the value of k?
Answers
Given:
The function is
\(f(x)=2x^2+kx-9\)
The remainder when f(x) is divided by x+6 is 57.
To find:
The value of k.
Solution:
According to the remainder theorem, if a polynomial function f(x) is divided by (x-a), then f(a) is the remainder.
The remainder when f(x) is divided by x+6 is 57.
Using remainder theorem, we get f(-6)=57.
Putting x=-6 in the given function.
\(f(-6)=2(-6)^2+k(-6)-9\)
\(57=2(36)-6k-9\)
\(57=72-6k-9\)
\(57=63-6k\)
On further simplification, we get
\(6k=63-57\)
\(6k=6\)
\(k=\dfrac{6}{6}\)
\(k=1\)
Therefore, the value of k is 1.
Answer:
person above lol
Step-by-step explanation:
(-3, 1), (-17, 2) find the slope show the work
Answers
Answer:
1/-14 or -0.071428571428571
Step-by-step explanation
(-3,1) ___ -3 is x1 while 1 is y1
(-17, 2) ___ -17 is x2 while 2 is y2
slope formula is m = y2-y1/x2-x1
plug them in: m = 2-1/-17-(-3), which equals 1/-14 or -0.071428571428571
This figure represents a small doorstop. The plan is to paint 40% of the total surface area, including the bottom face, of the doorstop with blue paint.
How much surface area will be painted blue?
A. 6200 cm²
B. 3720 cm²
C. 2232 cm²
D. 1488 cm²
Answers
The surface area painted blue will be 1,488 square cm.
The correct option is: (D)
What is surface area?Surface area is the amount of space covering the outside of a three-dimensional shape.
We have, The plan is to paint 40% of the total surface area.
The surface area is :
Surface Area = (17 + 17 + 18 + 30 + 18) x 24 + 8 x 30 + 2 x 30 x 18
Surface Area = 100 x 24 + 8 x 30 + 60 x 18
Surface Area = 2400 + 240 + 1080
Surface Area = 3720 square cm
Blue paint will be applied to 40% of the overall surface area of the doorstop, including the bottom face then
= 0.40 x 3720
= 1488 square cm
Therefore, the surface area painted blue will be 1,488 square cm.
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for the region rr below, write ∬rfda∬rfda as an iterated integral in polar coordinates.
Answers
No function f(r,θ) is given, we cannot evaluate the integral further.
To write ∬rfda as an iterated integral in polar coordinates for the given region rr, we need to determine the limits of integration for r and θ.
Let's first look at the region rr. From the given graph, we can see that the region is bounded by the circle with radius 3 centered at the origin. Therefore, we can express the region as:
r ≤ 3
To determine the limits for θ, we need to examine the region rr more closely. We can see that the region is symmetric about the x-axis, which means that the limits for θ are:
0 ≤ θ ≤ π
Now, we can write the iterated integral as:
∬rfda = ∫₀³ ∫₀ᴨ f(r,θ) r dθ dr
where f(r,θ) is the integrand function and r and θ are the limits of integration. Note that r is integrated first, followed by θ.
In this case, since no function f(r,θ) is given, we cannot evaluate the integral further.
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Michelle is giving away prizes at one of her meetings. The prizes include 4 stress balls, 3 notepads, 2 gift cards and 7 sticky notes. She picks prizes without replacement. What is the probability of her giving out a stress ball and then a gift card? A. 6 31 B. 1 30 C. 5 16 D. 1 8
Answers
We need to use probability and combinations. The answer to the question is D. 1/8.
There are a total of 16 prizes that Michelle is giving away (4 stress balls + 3 notepads + 2 gift cards + 7 sticky notes = 16). The probability of her first picking a stress ball is 4/16, or 1/4. Since she doesn't replace the prize, there are now only 15 prizes left, so the probability of her picking a gift card is 2/15. To find the probability of both events happening, we need to multiply their probabilities: (1/4) x (2/15) = 1/30.
The probability of Michelle giving out a stress ball and then a gift card can be found by calculating the probability of each event happening independently and then multiplying them together. There are a total of 16 prizes (4 stress balls, 3 notepads, 2 gift cards, and 7 sticky notes). First, let's find the probability of her giving out a stress ball. There are 4 stress balls and 16 total prizes, so the probability is 4/16. Next, we need to find the probability of her giving out a gift card after a stress ball. Since the stress ball was not replaced, there are now 15 total prizes left (1 stress ball is already given away). There are 2 gift cards, so the probability is 2/15.
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(1 point) find as a function of if ‴−6″ 8′=15,
Answers
The function of "if ‴−6″ 8′=15" is f(x) = c1 + c2e^(2x) + c3e^(4x).
How to find the functionTo find the function of "if ‴−6″ 8′=15," we need to first understand what the notation means.
The triple prime symbol (‴) indicates the third derivative of a function, while the double prime (″) indicates the second derivative and the prime (') indicates the first derivative.
So, we can rewrite the equation as follows: f‴(x) - 6f″(x) + 8f'(x) = 15
Now, we can use techniques from differential equations to solve for f(x).
First, we can find the characteristic equation:
r^3 - 6r^2 + 8r = 0
Factorizing out an r, we get: r(r^2 - 6r + 8) = 0
Solving for the roots, we get: r = 0, r = 2, r = 4
Therefore, the general solution to the differential equation is:
f(x) = c1 + c2e^(2x) + c3e^(4x)
where c1, c2, and c3 are constants determined by initial or boundary conditions.
In summary, the function of "if ‴−6″ 8′=15" is f(x) = c1 + c2e^(2x) + c3e^(4x).
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Integrate f(x,y,z)=x+sqrt(y)-z^4 over the path from (0,0,0) to (1,1,1) given by
C1: r(t)=ti+(t^2)j, between t=0 and 1
C2: r(t)=i+j+tk, between t=0 and 1
Answers
The line integral of the given function over the two paths is (5/6) + (2/3) √2 - (1/5).
To evaluate the line integral of the given function over the path C1, we first parameterize the function in terms of t as f(r(t)) =\(t + √(t^2) - (t^4)^2\)= t + t - \(t^8.\) Then, we calculate the derivative of the parameterization with respect to t, which is dr/dt = i + 2tj. Substituting these values in the line integral formula ∫C f(r(t)) dr/dt dt, we get:
∫0^1 [2t -\(t^8\)] √(1 +\(4t^2)\) dt
We can simplify this integral using substitution t^2 = u, which gives:
(1/2) ∫\(0^1 [1/u^3 - 2/u^(7/2)] du\)
Evaluating this integral gives us the line integral over C1 as (5/6) + (2/3)\(\sqrt{2}\).To evaluate the line integral over C2, we parameterize the function as f(r(t)) = 1 + √1 - t^2 - t^4, and the derivative of the parameterization is dr/dt = kt. Substituting these values in the line integral formula, we get:
∫\(0^1 [1 + √1 - t^2 - t^4]\) k dt
Since k = 1, this simplifies to:
∫\(0^1 [1 + √1 - t^2 - t^4]\) dt
Using substitution t^2 = u, we get:
(1/2) ∫0^1 [1 + √1 - u - u^2] du
Evaluating this integral gives us the line integral over C2 as -(1/5). Therefore, the total line integral over both paths is (5/6) + (2/3) \(\sqrt{2}\) - (1/5).
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a ____ is a procedure performed for definitive treatment rather than diagnostic purposes.
Answers
A therapeutic procedure is a procedure performed for definitive treatment rather than diagnostic purposes.
A procedure performed for definitive treatment rather than diagnostic purposes is a therapeutic procedure. These procedures are aimed at treating or curing a particular condition, disease, or illness. Therapeutic procedures are used to relieve pain, restore function, improve mobility, or even save a patient's life. Unlike diagnostic procedures that are performed to identify a problem, therapeutic procedures involve actually treating the problem. Examples of therapeutic procedures include surgeries, chemotherapy, radiation therapy, and immunotherapy. These procedures are often more invasive than diagnostic procedures and may require anesthesia or sedation. The goal of a therapeutic procedure is to improve the patient's health and well-being, and they are an essential part of modern medical care.
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What would the approximate amperage setting be if a welder were set to the high range (150 to 350 amps) and the fine adjustment knob were painting at 5 on a 10 point scale
Answers
On solving the provided question, we can say that the approximate amperage setting be if a welder were set to the high range would be 350 amps.
What is range?The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.The solution provides the list's range.
here,
the approximate amperage setting be if a welder were set to the high range would be 350 amps
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find slope of the altitude on each side of triangle ABC (d) A(-2,-3), B(3,6), C(-5,5)letter d) question 3)
Answers
Graphing the points that make up the triangle you have
Now, to obtain the slope of each side of the triangle you can use the slope formula, that is,
\(\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}\)So, the slope of segment AB will be
\(\begin{gathered} A=(x_1,y_1)=(-2,-3) \\ B=(x_2,y_2)=(3,6) \end{gathered}\)\(\begin{gathered} m=\frac{6-(-3)}{3-(-2)} \\ m=\frac{6+3}{3+2} \\ m=\frac{9}{5} \end{gathered}\)The slope of segment BC will be
\(\begin{gathered} B=(x_1,y_1)=(3,6) \\ C=(x_2,y_2)=(-5,5) \\ m=\frac{5-6}{-5-3} \\ m=\frac{-1}{-8} \\ m=\frac{1}{8} \end{gathered}\)The slope of segment AC will be
\(\begin{gathered} A=(x_1,y_1)=(-2,-3) \\ C=(x_2,y_2)=(-5,5) \\ m=\frac{5-(-3)}{-5-(-2)} \\ m=\frac{5+3}{-5+2} \\ m=\frac{8}{-3} \\ m=-\frac{8}{3} \end{gathered}\)Therefore, the slope of each side of the triangle ABC is
\(\begin{gathered} \text{ The slope of segment AB is }\frac{9}{5} \\ \text{ The slope of segment BC is }\frac{1}{8} \\ \text{ The slope of segment AC is }\frac{-8}{3} \end{gathered}\)
I need help with this question I need to write a equation for this
how old am I if 300 reduced by 3 times my age is 138?
Answers
Answer:
54 years old
Step-by-step explanation:
Equation: 138=300-3x
Subtract 300 from each side: -162=-3x
Divide each side by -3: x=54
A line passing through the point(-10,-5) and has a slope of -1/2
Answers
ex : -10 is x, -5 is y, -1/2 is slope
y = mx + b, m is slope, solving for b (y-intercept)
-5 = -1/2(-10)+b
-5 = 5 + b
try to get b by itself, so minus the positive 5
-5-5 = b, so -10 = b
which leads to y = -1/2x - 10
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> ⌒ヽ
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/ / ＼＼ or CORONA WILL NEVER Live
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( (ヽ
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Answers
Answer:
Wow u good and thanks for the points and I love your profile picture
Step-by-step explanation:
Answer:
wE nEeD cRoNa tO DiE
Step-by-step explanation:
How would you describe the slice that created the rectangular
cross-section on this cake?
A-perpendicular to
the base
B. diagonal to the
base cutting off
exactly 1 vertex
C. diagonal to the
base cutting off
exactly 1 edge
D. parallel to
the base
Answers
Answer:
The answer is perpendicular to the base.
Step-by-step explanation:
Answer:
The answer is perpendicular to the base.
Step-by-step explanation:
Took the quiz! :)
Althea has $100. She divides it evenly among her 4 children. Her oldest child, Raul, spends $15 of the amount he receives. How much money does Raul have left after he spends $15?
Which statements about this word problem are true? Check all that apply.
O This is an example of a part-whole problem.
O This is an example of a comparison problem.
O Addition then multiplication can be used to solve the problem.
O Division then subtraction can be used to solve the problem.
O Division then multiplication can be used to solve the problem.
Answers
Answer:
Division then subtraction
Step-by-step explanation:
You divide the $100 to 4 people, which means they each get $25. Then you subtract $15 from $25
Not sure about the other one
Answer:
Division then subraction can be used and example of a part whole problem
Step-by-step explanation:
The Owens family has saved up $50,000 for a down pay
saved up $50,000 for a down payment on a house. They are
going to use this money as the 10% down payment their lender is req
make to purchase the house. What is the price of the ne
eune house. What is the price of the house that the Owens family
is buying?
Answers
Answer:
Step-by-step explanation:
Let the price of the house be P .
10 % of P is demanded as down payment
10 % of P = P x 10 / 100
= P / 10
This down-payment = 50000
P / 10 = 50000
P = $5,00,000 .
Price of house = $5,00,000
3.12 If h(t)= [u(t-1)- u(t - 4)] and x(t) = t[u(t)- u(t-2)], obtain graphically the response y(t). For what value of t does y(t) reach its maximum value?
Answers
The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:
Plotting h(t):
The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].
The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:
For t < 1, h(t) = [0 - 0] = 0
For 1 ≤ t < 4, h(t) = [1 - 0] = 1
For t ≥ 4, h(t) = [1 - 1] = 0
So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.
Plotting x(t):
The function x(t) is defined as x(t) = t[u(t) - u(t-2)].
For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.
For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.
For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.
So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.
Obtaining y(t):
To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.
In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.
The convolution y(t) = h(t) * x(t) can be written as:
y(t) = ∫[1,4] h(τ) x(t - τ) dτ
For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).
For 1 ≤ t < 2, the convolution integral simplifies to:
y(t) = ∫[1,t+1] 1(0) dτ = 0
For 2 ≤ t < 4, the convolution integral simplifies to:
y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ
Evaluating this integral, we get:
\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4
For t ≥ 4, y(t) will be 0 again.
Maximum value of y(t):
To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.
Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.
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Factor this equation 144x2-49
Answers
We have the following equation
\(144x^2-49\)We must factor this, in this case with the fourth case factorization.
The solution is the following:
\((12x+7)(12x-7)\)Please help me answer these
Answers
Answer:
98
Step-by-step explanation:
b(c(3))
b(3(3)-2)
2(3(3)-2)^2
2(9-2)^2
2(7)^2
2(49)
98
Two events are ________ if the occurrence of one is related to the probability of the occurrence of the other.
Answers
Answer:
Dependent
Step-by-step explanation:
Two events are said to be dependent when the outcome of the first event is related to the other.
When two events, A and B are dependent, the probability of occurrence of A and B is:
P(A and B) = P(A) · P(B|A)
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Two events are dependent if the occurrence of one is related to the probability of the occurrence of the other.
A probability-dependent event is an event whose occurrence affects the probabilities of others. Suppose you have 3 red balls and 6 green balls in your pocket. Two balls are drawn one after the other from the bag. A dependent event is an event that depends on what happened before. These events are affected by previously occurring results.In other words, two or more intedependent events are called dependent events. A random change in one event can deviate from another.If two events A and B depend on each other, then the probability of A and B occurring is
P(A and B) = P(A) P(B|A)
Two events are dependent if the occurrence of one is related to the probability of the occurrence of the other.
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Given A(-1, 2), B(-4, r) and C(8, -8), if the slope
Answers
Answer:
to be honest i dont even knoq
Jim Goodman, an employee at Walgreens, earned $42,000, an increase of 17.4% over the previous year. What were Jim's earnings the previous year? Note: Round to the nearest cent.
Answers
Answer:
$35,775.13
Step-by-step explanation:
You want the amount that results in $42,000 when it is increased by 17.4%.
MultiplierA value that is increased by a fraction (p) is effectively multiplied by 1+p.
In this case, we have ...
(previous salary) · (1 +17.4%) = $42000
SolutionDividing by the coefficient of (previous salary), we have ...
previous salary = $42000/1.174 = $35,775.13
Jim's earnings the previous year were $35,775.13.
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7² ft
7. A billboard has the
given dimensions.
42
Using exponents, write two equivalent
expressions for the area of the rectangle.
Answers
How can these models be used to find the sum 2.42 + 1.9?
Enter your answers in the boxes.
The models show a total of 3 wholes,
tenths, and
hundredths. After regrouping 10 tenths into 1 whole, there are
wholes,
tenths, and
hundredths. Therefore, the sum of the numbers is
. pls hurry 100 points
Answers
Answer:
4 wholes, 3 tenths and 2 hundredthsor
4.32Step-by-step explanation:
According to the model we have:
2.42 = 2 wholes, 4 tenths and 2 hundredths1.9 = 1 whole and 9 tenthsSum up:
2 + 1 = 3 wholes4 + 9 = 13 tenths = 1 whole and 3 tenths2 hundredthsRegroup the wholes to get:
3 + 1 = 4 wholes, 3 tenths and 2 hundredthsIn decimal form it is:
4.32answer the following, Round final answer to 4 decimal places. a.) Which of the following is the correct wording for the randon variable? r×= the percentage of all people in favor of a new building project rv= the number of people who are in favor of a new building project r N= the number of people polled r×= the number of people out of 10 who are in favor of a new building project b.) What is the probability that exactly 4 of them favor the new building project? c.) What is the probabilitv that less than 4 of them favor the new building project? d.) What is the probabilitv that more than 4 of them favor the new building project? e.) What is the probabilitv that exactly 6 of them favor the new building project? f.) What is the probability that at least 6 of them favor the new building project? 8.) What is the probabilitv that at most 6 of them favor the new building project?
Answers
In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.
a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.
b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.
c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.
d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).
e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.
f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).
g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).
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let f and g be two real self-adjoint linear maps f, g : rn → rn. prove that if f and g have nonnegative eigenvalues (f and g are positive semidefinite) and if f 2 = g2, then f = g
Answers
To prove that f = g, we need to show that for any vector x in rn, f(x) = g(x).
We know that f and g have nonnegative eigenvalues, which means that there exist real numbers λ1, λ2, ..., λn such that:
f(x) = λ1x1v1 + λ2x2v2 + ... + λnxnv_n,
g(x) = μ1x1w1 + μ2x2w2 + ... + μnxnw_n,
where v1, v2, ..., vn and w1, w2, ..., wn are orthonormal bases of eigenvectors corresponding to the eigenvalues λ1, λ2, ..., λn and μ1, μ2, ..., μn respectively.
Since both f and g are positive semidefinite, we know that λi and μi are nonnegative for all i. We also know that f^2 = g^2, which means that (f^2 - g^2)(x) = 0 for all x in rn.
Expanding this equation using the expressions for f(x) and g(x) above, we get:
(λ1^2 - μ1^2)x1v1 + (λ2^2 - μ2^2)x2v2 + ... + (λn^2 - μn^2)xnvn = 0.
Since the vectors v1, v2, ..., vn form an orthonormal basis, we can take the inner product of both sides with each vi separately. This gives us n equations of the form:
(λi^2 - μi^2)xi = 0,
which implies that λi = μi for all i, since λi and μi are both nonnegative.
Now, since λi = μi for all i, we have:
f(x) = λ1x1v1 + λ2x2v2 + ... + λnxnv_n = μ1x1w1 + μ2x2w2 + ... + μnxnw_n = g(x),
which shows that f = g.
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HELP I WILL PUT U AS BRAINLIEST
Find g(2)
g(x) = x^2 - 4x
Answers
Answer:
-4
Step-by-step explanation:
g(2) means x=2
\(2^{2}-4(2) = -4\)
Which expression is equivalent to
(3x^2 + 2x - 4) + (5x^2 - 4x + 5) ?
8x^2 + 6x + 9
8x^2 + 2x + 1
8x^2 - 2x + 1
8x^2 + 6x + 9
Answers
Answer:
8x^2-2x+1
explaniationfirst remove the bracket 3x^2+2x-4+5x^2-4x+5then collect like term3x^2+5x^2+2x-4x-4+5 then the answer will be 8x^2-2x+1 thank you!!!!!An automatic machine in a manufacturing process is operating groperly if the iengths of an important subcomponent are normally distributed with a mean of izal cri and a otandard deviation of 5.6 cm. A. Find the probability that one selected subcomponent is longer than 122 cm, Probability = B3. Find the probability that if 3 subcomponents are randomly selected, their mean length exceeds 122 cm. Probability win C. Find the probabilify that if 3 are randomly selected, ail 3 have lengths that exceed 122 cm. Probability =
Answers
A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.
z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)
Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.
B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.
The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.
Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm
Now we can calculate the z-score for a mean length of 122 cm:
z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)
Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.
C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.
Probability = (0.9999)^3 ≈ 0.9997
Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.
Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.
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Mateo is making bookmarks with different colored ribbon.The amount of color he has is shown in the table.Each bookmark will be 1/6 yard long.How many more orange bookmarks can he make than aqua bookmarks.
color length(yd)
Aqua 3/4
orange 9/10
yellow 15/16
use reciprocals pls
Answers
The orange bookmarks that Mateo can make than aqua bookmarks is 1.
How to calculate the number of bookmark?Based on the information given, let x = number of aqua bookmarks
(1/6) × x = 3/4
x = (3/4) × (6/1)
x = 18/4
x = 4.5
Rounding down shows that we can make 4 aqua bookmarks.
y = number of orange bookmarks
(1/6)y = 9/10
y = (9/10)*(6/1)
y = 54/10
y = 5.4
This rounds down to 5 orange bookmarks.
Therefore, Mateo can make 5-4 = 1 extra orange bookmark compared to aqua.
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Mateo is making bookmarks with different colored ribbon. The
amount of each color he has is shown in the table. Each bookmark
will be yard long. How many more orange bookmarks can he make
than aqua bookmarks?
Table:
Color: Length (yd):
———————————-
Aqua. 3/4
Orange. 9/10
Yellow. 15/16