The lengths that the bolt will be destroyed are given as follows:
Less than 11.8 cm.More than 12.2 cm.How to obtain the lengths?The lengths are obtained applying the proportions in the context of this problem.
Considering the mean length of 12 cm, and the standard deviation of 0.1 cm, the length that is 2 standard deviations below the mean is given as follows:
12 - 2 x 0.1 = 11.8 cm.
The length that is 2 standard deviations above the mean is given as follows:
12 + 2 x 0.1 = 12.2 cm.
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Russell and Valerie start to walk away from the Cafeteria to their classes.
Russell walks 10 yards due West, then turns 40° toward South and walks 5 yards.
Valerie walks 10 yards due East, then turns 60° toward North and walks 5 yards.
Which student is farther from the cafeteria? Explain how you know using a diagram and words.
I need help on question six, pls help me
Answer:
The surface area of the label is 28 squared inches.
Step-by-step explanation:
The dimensions of juice box are length=2 inches, breadth=1.5 inches and height= 4 inches.
The lateral surface area of a cuboid is given by 2(length+breadth)×height.
Now, lateral surface area of juice box = 2(2+1.5)×4
= 2×3.5×4
= 28 squared inches
Answer:
28 square inches
Step-by-step explanation:
Lateral surface of Cuboid:The label covers the lateral surface area of the box.
l = 2 in ; w = 1.5 in ; h = 4 in
[tex]\boxed{\text{\bf lateral surface area of cuboidal box = 2h*(l +w)}}[/tex]
[tex]\sf = 2*4 *( 2 +1.5)\\\\= 2 * 4 * 3.5\\\\ = 28 \ in^2[/tex]
7. Given that 2x² + 4x + 3 = k where k is a constant, find the range of values for k for which the equation has no real roots. (b) The function f is defined on the set R of real numbers by f(x) →kx² + kx + 1, where k is a member of R. Calculate the range of values of k for which the equation f(x) = 0 hasreal roots. Given that k = -2, solve the equation f(x) = 0. 1/2
Answer: (a) The equation 2x^2 + 4x + 3 = k has real roots if and only if its discriminant, which is 4^2 - 4(2)(3), is nonnegative. The discriminant is equal to 0, so the equation has real roots if and only if k = 3.
(b) For the equation f(x) = kx^2 + kx + 1 to have real roots, its discriminant, which is 1 - 4k, must be nonnegative. This gives us k >= 1/4. The range of values of k for which the equation has real roots is k >= 1/4.
(c) When k = -2, the equation f(x) = -2x^2 - 2x + 1 = 0. Solving this equation using the quadratic formula, we get x = (-1 ± √(1 + 8))/4. So, the roots are x = (-1 ± √(9))/4 = (-1 ± 3)/4 = 1/2, -2.
The shape of Tina's kitchen is a rectangle 925 cm long by 485 cm wide.
a) Work out the area of Tina's kitchen in square meters.
Show how to use estimation to check your answers.
Flooring costs $56 per square meter.
It is only sold in whole numbers of square meters.
B) How much does Tina pay to buy flooring for her kitchen floor?
Show how to use inverse operations to check your answer
a) The area of Tina's kitchen is 44.8625 square meters. b) Tina cost $2520 to buy flooring for her kitchen floor.
a) To work out the area of Tina's kitchen in square meters, we need to divide the area in square centimeters by 10,000, which is the number of square centimeters in a square meter:
Area = length x width = 925 cm x 485 cm = [tex]448,625 cm^2[/tex]
Area in square meters =[tex]448,625 cm^2 / 10,000 cm^2/m^2 = 44.8625 m^2[/tex]
b) To find how many whole square meters of flooring Tina needs, we round the area of the kitchen up to the nearest whole number:
Area in square meters rounded up = ceil(44.8625) = [tex]45 m^2[/tex]
The cost of the flooring is $56 per square meter, so Tina pays:
Total cost = [tex]45 m^2 * $56/m^2 = $2520[/tex]
To use inverse operations to check this answer, we can divide the total cost by the cost per square meter to get the number of square meters, and then multiply by the cost per square meter to check that we get back to the total cost:
Number of square meters =[tex]$2520 / $56/m^2 = 45 m^2[/tex]
Total cost = [tex]45 m^2 x $56/m^2 = $2520[/tex] (same as the original answer)
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Trapezoid PQRS with vertices P(-6, 2), Q(-2, -1), R(-2, -3), and S(-6, -6). Reflect in the line x=1
Graph the Trapezoid PQRS with vertices P(-6, 2), Q(-2, -1), R(-2, -3), and S(-6, -6). Reflect in the line x=1.
The preimage's point corresponds to the image's points in the following way:
P(-6, 2) → P'(6, 2)
Q(-2, -1) → Q' (2, -1)
R(-2, -3) → R'(2, -3)
S(-6, -6) → S'(6, -6)
(x,y)→(−x,y)
A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.
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Julia downloaded a 22 MB file in 5 seconds on her tablet. Later she downloaded a 30 MB file on her smart phone in 6 seconds. Are these rates equivalent? Explain your reasoning.
22 MB in 5 seconds
how many MB per second
divide the 5 out
22/5 = 4.4 MBPS
30 MB in 6 seconds
30/6 = 5 MBPS
5 MBPS > 4.4 MBPS
No, they aren't equivalent because one is greater than the other.
Hope this helps,
- Jeron :- )
please help ME EMERGENCY~
The amount that the salesperson will earn in commission from selling the couch is $ 27. 23.
The amount the sale of the couch by the store would get it is $ 467. 77.
How to find the commission ?The commission on the couch can be found by the formula :
= Selling price of couch x Commission to salesperson
= 495 x 5 . 5 %
= $ 27. 23
The money the store will get from the sale of the couch to Lin and her dad is:
= Selling price of couch - Commission to salesperson
= 495 - 27. 23
= $ 467 . 77
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The full question is:
Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5 1/2% of the selling price.
A.How much commission will the salesperson earn by selling a couch for $495?
B.How much money will the store get from the sale of the couch?
In a group, 40% of the items are red. Of all the red items in the group, 30% also have stripes. What percentage of the items in the group are red and have stripes?
Answer:
12% of the items in the group are red and have stripes.
Step-by-step explanation:
Aassume that there is 100 items, 40 items red.
In the 40 items, 30% are striped.
40×(30/100)=12%
12% of the items in the group are red and have stripes. This is found by multiplying the proportion of red items (40%) by the proportion of these red items that also have stripes (30%).
Explanation:We are given that 40% of items in a group are red. This is represented as 40/100, or 0.40. The question mentions that out of these red items, 30% also have stripes. This can be represented as 30/100, or 0.30. The question requires us to find out what percentage of the total items in the group are red and have stripes. To find this, we multiply 0.30 (the proportion of red items that are striped) by 0.40 (the proportion of items that are red).
So, 0.30 x 0.40 = 0.12 or 12%.
Therefore, 12% of the items in the group are red and have stripes.
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Which of the following are equations for the line shown below? Check all that
apply.
(-3,-5)
(3,-2)
A. Y+2=0.5(x-3)
B. Y-5=0.5(x-3)
C. Y+5=0.5(x+3)
D. Y=0.5x-3.5
Answer:
Both C and D are equations for the two given points.
Step-by-step explanation:
A. Y+2=0.5(x-3) NO
(-3,-5): -5+2 = 0.5(-3-3); -3 = 0.5(-6); -3 = -3 YES
(3,2): 2+2 = 0.5(3-3): 4 = 0.5(0); 4 = 0 NO
B. Y-5=0.5(x-3) NO
(-3,-5): -5-5=0.5(-3-3); -10 = -3 NO
(3,-2): -2-5=0.5(3-3); -7 = 0 NO
C. Y+5=0.5(x+3) YES
(-3,-5): -5+5=0.5(-3+3); 0 = 0 YES
(3,-2): -2+5=0.5(3+3); 3 = 3 YES
D. Y=0.5x-3.5 YES
(-3,-5): -5 = 0.5(-3)-3.5; -5 = -5 YES
(3,-2): -2 = 0.5(3)-3.5; -2 = 1.5 - 3.5 YES
use point slope form to write the equation of a line that passes through the point (17,-7) with slope - 1/2
Answer:
y + 7 = -1/2 ( x - 17)
Step-by-step explanation:
y-y₁=m(x-x₁)
[tex]x_{1\\} = 17[/tex]
[tex]y_{1}[/tex] = -7
y - (-7) = -1/2(x - 17)
y + 7 = -1/2(x -17)
Find the value of xx and yy in the parallelogram below.
Answer:
x = 12
y = 11
Step-by-step explanation:
It's a parallelogram, so opposite sides are equal.
4x + 10 = 58
4x = 58 - 10 = 48
x = 48/4 = 12
10y - 6 = 104
10y = 104 + 6 = 110
y = 110/10 = 11
Here are 2 polygons. Select all sequences of translations, rotations, and reflections below that would take polygon P to polygon Q
The sequences of translations, rotations, and reflections bthat would take polygon P to polygon Q will be:
C Translate so that Ais taken to J. Then reflect over line BA
E Reflect over line BAand then translate by directed line segment BA.
What is translation?A function is translated when it is moved from where it was before. In geometry, a function that moves an object a specific distance is referred to as translation. Nothing else is done to change the object.
It is not scaled, reflected, rotated, or refracted. Every point of the object must be translated by the same amount and in the same direction.
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PLEASE HELP WHAT TYPE OF FUNCTION
the given function y = 3(4)ˣ, is an exponential function.
What is a logarithmic function?The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.
Given a function y = 3(4)ˣ
An exponential function is defined by the formula f(x) = a, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = aˣ
therefore, we can say that the given function is an exponential function.
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Y=x+3
3x-3y=9
Solved in substitution
The requried, given system of equations y=x+3 and 3x-3y=9 has no common solution.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
From the first equation, we can solve for y:
y = x + 3
Substitute y = x + 3 into the second equation:
3x - 3(x + 3) = 9
Simplify the right side:
3x - 3x - 9 = 9
-9 = 9 (inconsistent)
Since the equation -9 = 9 is inconsistent, the system of equations has no solution, which means that there are no values of x and y that make both equations true at the same time. It implies the system of equations has no solution.
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Which values are solutions to the inequality below? Check all that apply.
√x <10
A. 100
B. 25
C. -100
D. 105
E. 36
F. 9
Answer:
The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v
Step-by-step explanation:
its E and A
Answer:
The solutions to the inequality are B, E, and F: 25, 36, and 9.
Step-by-step explanation:
The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:
√x < 10
x < 10^2 = 100
So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:
A. 100 (not a solution)
B. 25 (solution)
C. -100 (not a solution)
D. 105 (not a solution)
E. 36 (solution)
F. 9 (solution)
Consider AGHJ in the figure below.
The perpendicular bisectors of its sides are KN, LN, and MN. They meet at a single point N.
(In other words, N is the circumcenter of AGHJ.)
Suppose LN=22, GJ=92, and GN=122.
Find HN, LJ, and GK.
Note that the figure is not drawn to scale.
Answer:
Step-by-step explanation:
32. Solve the equation and check your solution: 3(x + 6) = 18 + 3x
Answer:
4
Step-by-step explanation:
18 = 3x + 6
18 - 6 = 3x
12=3x
12/3 = x
4 = x
Hope this helped, please mark the brainliest if it did! I put a lot of effort into my answers
GARDEN Camila put a frame around a triangular garden in her yard. The two legs of the triangle are 8 feet long each, and the third side is equal to the length of a leg times 2⎯⎯√ . What is the perimeter of the triangle? Give your answer as a simplified radical expression,
The perimeter of the triangle is 16+8√2 feet.
The perimeter of any two-dimensional figure is defined as the distance around the figure. The formula for a closed shape figure's perimeter is typically equal to the length of the figure's outer line.
The perimeter of a triangle will therefore be equal to the sum of its three sides. Consequently, if a triangle has sides a, b, and c,
Here, a= 8 feet
b= 8 feet
c= 8√2 (length of a leg * √2= 8*√2)
Perimeter= Sum of all three sides of the triangle
Perimeter = a + b + c
Perimeter= 8+ 8 +8√2
Perimeter= 16+8√2 feet.
16+8√2 feet is the perimeter of the triangular garden.
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myra can type 70 words in 2 min. how many words can she type in 5 min
Answer:
first convert 2mins to seconds
60sec=1 min
which is 2×60=120sec
then70/120sec=0.583
convert 50mis to sec
5×60=300sec
so therefore 300sec×0.583=174.9words
HOPE IT HELPS
Answer: 175 words
Step-by-step explanation:
First start out by dividing how many amount (5 min) you are looking for by the amount (2 min) that we already know.
5 / 2 = 2.5
This gives us the key to finding our final answer.
Use this new number (2.5) and multiply it by 70 to get our answer.
70 x 2.5 = 175
can someone help me with this
The distances traveled by the car are given as follows:
3 minutes: 3.45 kilometers.5 minutes: 5.75 kilometers.What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The parameters for this problem are given as follows:
v = 1.15 km/min, t = 1 min.
Hence the equation for the distance in km after t minutes is given as follows:
d = 1.15t.
Then after 3 minutes, the distance is of:
d = 1.15 x 3 = 3.45 km.
After 5 minutes, the distance is of:
d = 1.15 x 5 = 5.75 km.
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prove that if a sequence converges it has exactly one limit point. is the converse true? prove it or give a counterexample.
The counterexample proves that the converse of the theorem is not always true, and we have to be careful when making statements about limit points and convergence of sequences.
A sequence is a set of numbers that are generated one after the other in a specific pattern.
The theorem states that if a sequence converges, it will have exactly one limit point. In other words, if a sequence is getting closer and closer to a certain number, there will be only one number that it approaches. This is a fundamental idea in mathematics, and it is important to understand why it is true.
To prove this theorem, let's consider a sequence (a_n) that converges to a limit L. If there were two different limit points, say L1 and L2, then there would be a contradiction. This is because by definition, the sequence (a_n) would be getting closer and closer to L1 and L2 at the same time, which is not possible. Hence, it must be true that the sequence (a_n) has exactly one limit point, L.
The converse of this theorem is not always true. In other words, just because a sequence has exactly one limit point, it doesn't necessarily mean that it converges to that limit. To see why this is the case, let's consider the following sequence:
(2, 3, 4, 5, 6, ...)
In this sequence, the limit point is 6. However, the sequence does not converge to 6 because it is not getting closer and closer to 6 as it goes on. Instead, it is increasing by 1 with each term, and therefore it does not converge.
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Question is in the picture.
The equation is given as y = 4x - 3 , where the slope is m = 4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The value of term 1 = 1 square
The value of term 2 = 5 suqres
The value of term 3 = 9 squares
So , the increment in the number of squares is 4
Let the first point be P ( 1 , 1 )
Let the second point be Q ( 2 , 5 )
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 5 - 1 ) / ( 2 - 1 )
Slope m = 4
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 1 = 4 ( x - 1 )
On simplifying the equation , we get
y - 1 = 4x - 4
Adding 1 on both sides of the equation , we get
y = 4x - 3
Therefore , the value of y is 4x - 3
when x = 1 . y = 4 - 3 = 1
when x = 2 , y = 4 ( 2 ) - 3 = 8 - 3 = 5
Hence , the equation of line is y = 4x - 3
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turn − 5/7 and 8 into a quadratic equation
Answer:
To turn -5/7 and 8 into a quadratic equation, we first need to convert 8 into an equation by adding 8 to both sides. The equation becomes: -5/7 = x^2 + 8. Then, we can expand the right side into a complete square, using the formula (b/2)^2. The equation becomes:
-5/7 = (x^2 + 8) + (4/2)^2
-5/7 = x^2 + 8 + 4
-5/7 = x^2 + 12
Finally, we can rearrange the equation to make the right side equal to 0, and then factor it. The final equation is:
x^2 + 12 + 5/7 = 0
x^2 + 12 + 5/7 = (x + 6/√7)(x + 6/√7) = 0
Step-by-step explanation:
In the first step, we added 8 to both sides to make the equation -5/7 = x^2 + 8. In the next step, we added 4 to the right side to complete the square. The purpose of completing the square is to get a perfect square on the right side, which will make it easier to factor the equation.
Next, we rearranged the equation to make the right side equal to 0, so that we can factor the equation. The equation x^2 + 12 + 5/7 = 0 can be factored as (x + 6/√7)(x + 6/√7) = 0, where (x + 6/√7) is a binomial that satisfies the equation.
Ken is going on a hike with his friends. He brings 8 liters of water for everyone to share. While hiking, they drink 5 of liters.
Answer: If Ken brought 8 liters of water for everyone to share and they drank 5 liters of it, then the remaining amount of water they have is 8 - 5 = 3 liters.
Step-by-step explanation:
(3+4x-2)4 2/7
please help or my mom said she was going to put me up for adoption which i don't care for i just want to get this work done
The value of x in expression is -1/8.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
(3+4x-2)4 2/7=0
(3+4x-2)16/7=0
48+64x-32=0
x=-1/8
Therefore, the answer of given algebra problem will be -1/8.
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Which equation represents the line that passes through the point (1,5) and has a slope of -2?
Use this for question 6 to 8:
Four machines A, B, C and D produce respectively 30%, 30%, 15% and 25% of the total number of
items from a factory. The percentage of defective output from these machines are 1%, 1.5%, 3% and
2% respectively. Given that an item is to be selected at random from the total output.
6: Find the probability that the item will be defective.
(a) 0.105
(2 marks)
(b) 0.017
(c) 0.007
(d) 0.170
7: If an item selected at random is found defective, what is the probability that it is produced by
machine A
(2 marks)
(2 marks)
(d) 0.007
(a) 0.018
(b) 0.015
(c) 0.111
8: Find the probability that the item is produce by machine D
(a) 0.294
(b) 0.034
(c) 0.118
(d) 0.253
The probability that the item will be defective is 0.017, the probability that an item selected at random is defective is 0.018 and the probability that an item is produced by machine D is 0.25
What is the probability that the item will be defectiveUsing the formula of probability distribution to solve the given problem;
6: The probability that the item will be defective is the sum of the probabilities of a defective item from each machine:
(1% * 30%) + (1.5% * 30%) + (3% * 15%) + (2% * 25%) = 0.017
So the answer is b
7: If an item is selected at random and found to be defective, the probability that it was produced by machine A is the probability of a defective item from machine A divided by the overall probability of a defective item:
(1% * 30%) / 0.017 = 0.018
The answer is option a
8: The probability that the item was produced by machine D is the probability of a non-defective item from machine D divided by the overall probability of a non-defective item:
(25% * 98%) / (100% - 0.017) = 0.25 * 0.98 / 0.895 = 0.25
So the answer is (d) 0.253
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The surface of the area of a cylinder is 372pi square centimeters the radius is 6 cm what is the height of the cylinder
If the surface of the area of a cylinder is 372π square centimeters. Then the height of the cylinder is 31 centimeters.
What is the surface area of a right circular cylinder?Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,
SA = 2πrh square units
The surface of the area of a cylinder is 372π square centimeters the radius is 6 cm. Then the height of the cylinder is given as,
SA = 2πrh
372π = 2π x 6 x h
h = 372 / 12
h = 31 centimeters
The height of the cylinder is 31 centimeters.
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Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era, and find the correct solution
Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era, and find the correct solution
The students divided the number ‘n’ by 3 instead of dividing (n-5) by 3.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: Given, Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era wrote an algebraic expression for “5 less than a number n divided by 3” as (n/3) - 5.
We have to find the error made by the students.
5 less than a number n = n - 5
5 less than a number n divided by 3 = (n - 5)/3
Correct expression = (n - 5)/3
Expression written by student = (n/3) - 5
Therefore, the students divided the number ‘n’ by 3 instead of dividing (n-5) by 3.
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What’s the Error? A Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era wrote an algebraic expression for “5 less than a number n divided by 3” as (n/3) - 5. What error did the they make?
Charlie has a utility function U(A, B) = AB, the price of apples is $1, and the price of bananas is $2. If Charlie’s income were $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint? * 1 point a. 30 b. 15 c. 60 d. 6 e. 90
Charlie's utility function is given by U(A, B) = AB, where A is the number of apples he consumes and B is the number of bananas he consumes. The price of apples is $1, and the price of bananas is $2.
If Charlie's income is $120, he has a budget constraint given by:
1A + 2B = 120
To maximize his utility subject to this budget constraint, Charlie must use his income to purchase the combination of apples and bananas that gives him the greatest value of U(A, B).
The solution to this problem can be found by using the method of Lagrange multipliers. From the budget constraint, we can solve for A in terms of B:
A = 120 - 2B
Substituting this into the utility function, we have:
U(B) = (120 - 2B)B = 120B - 2B^2
To maximize U(B), we must find the value of B that maximizes this expression. Taking the derivative of U(B) with respect to B and setting it equal to zero, we find that:
dU/dB = 120 - 4B = 0
Solving for B, we find that:
B = 30
Thus, if Charlie chose the bundle that maximizes his utility subject to his budget constraint, he would consume 30 units of bananas. The answer is therefore a. 30.
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