Assume a jar has five red marbles and three black marbles. Draw out two marbles with and without replacement. Find the requested probabilities. (Enter the probabilities as fractions.) (a) P(two red marbles) with replacement without replacement (b) P(two black marbles) with replacement without replacement (c) P(one red and one black marble) with replacement without replacement (d) P(red on the first draw and black on the second draw) with replacement without replacement
Answers
Answer:
For probabilities with replacement
\(P(2\ Red) = \frac{25}{64}\)
\(P(2\ Black) = \frac{9}{64}\)
\(P(1\ Red\ and\ 1\ Black) = \frac{15}{32}\)
\(P(1st\ Red\ and\ 2nd\ Black) = \frac{15}{64}\)
For probabilities without replacement
\(P(2\ Red) = \frac{5}{14}\)
\(P(2\ Black) = \frac{3}{28}\)
\(P(1\ Red\ and\ 1\ Black) = \frac{15}{28}\)
\(P(1st\ Red\ and\ 2nd\ Black) = \frac{15}{56}\)
Step-by-step explanation:
Given
\(Marbles = 8\)
\(Red = 5\)
\(Black = 3\)
For probabilities with replacement
(a) P(2 Red)
This is calculated as:
\(P(2\ Red) = P(Red)\ and\ P(Red)\)
\(P(2\ Red) = P(Red)\ *\ P(Red)\)
So, we have:
\(P(2\ Red) = \frac{n(Red)}{Total} \ *\ \frac{n(Red)}{Total}\\\)
\(P(2\ Red) = \frac{5}{8} * \frac{5}{8}\)
\(P(2\ Red) = \frac{25}{64}\)
(b) P(2 Black)
This is calculated as:
\(P(2\ Black) = P(Black)\ and\ P(Black)\)
\(P(2\ Black) = P(Black)\ *\ P(Black)\)
So, we have:
\(P(2\ Black) = \frac{n(Black)}{Total}\ *\ \frac{n(Black)}{Total}\)
\(P(2\ Black) = \frac{3}{8}\ *\ \frac{3}{8}\)
\(P(2\ Black) = \frac{9}{64}\)
(c) P(1 Red and 1 Black)
This is calculated as:
\(P(1\ Red\ and\ 1\ Black) = [P(Red)\ and\ P(Black)]\ or\ [P(Black)\ and\ P(Red)]\)
\(P(1\ Red\ and\ 1\ Black) = [P(Red)\ *\ P(Black)]\ +\ [P(Black)\ *\ P(Red)]\)
\(P(1\ Red\ and\ 1\ Black) = 2[P(Red)\ *\ P(Black)]\)
So, we have:
\(P(1\ Red\ and\ 1\ Black) = 2*[\frac{5}{8} *\frac{3}{8}]\)
\(P(1\ Red\ and\ 1\ Black) = 2*\frac{15}{64}\)
\(P(1\ Red\ and\ 1\ Black) = \frac{15}{32}\)
(d) P(1st Red and 2nd Black)
This is calculated as:
\(P(1st\ Red\ and\ 2nd\ Black) = [P(Red)\ and\ P(Black)]\)
\(P(1st\ Red\ and\ 2nd\ Black) = P(Red)\ *\ P(Black)\)
\(P(1st\ Red\ and\ 2nd\ Black) = \frac{n(Red)}{Total} *\ \frac{n(Black)}{Total}\)
So, we have:
\(P(1st\ Red\ and\ 2nd\ Black) = \frac{5}{8} *\frac{3}{8}\)
\(P(1st\ Red\ and\ 2nd\ Black) = \frac{15}{64}\)
For probabilities without replacement
(a) P(2 Red)
This is calculated as:
\(P(2\ Red) = P(Red)\ and\ P(Red)\)
\(P(2\ Red) = P(Red)\ *\ P(Red)\)
So, we have:
\(P(2\ Red) = \frac{n(Red)}{Total} \ *\ \frac{n(Red)-1}{Total-1}\)
We subtracted 1 because the number of red balls (and the total) decreased by 1 after the first red ball is picked.
\(P(2\ Red) = \frac{5}{8} * \frac{4}{7}\)
\(P(2\ Red) = \frac{5}{2} * \frac{1}{7}\)
\(P(2\ Red) = \frac{5}{14}\)
(b) P(2 Black)
This is calculated as:
\(P(2\ Black) = P(Black)\ and\ P(Black)\)
\(P(2\ Black) = P(Black)\ *\ P(Black)\)
So, we have:
\(P(2\ Black) = \frac{n(Black)}{Total}\ *\ \frac{n(Black)-1}{Total-1}\)
We subtracted 1 because the number of black balls (and the total) decreased by 1 after the first black ball is picked.
\(P(2\ Black) = \frac{3}{8}\ *\ \frac{2}{7}\)
\(P(2\ Black) = \frac{3}{4}\ *\ \frac{1}{7}\)
\(P(2\ Black) = \frac{3}{28}\)
(c) P(1 Red and 1 Black)
This is calculated as:
\(P(1\ Red\ and\ 1\ Black) = [P(Red)\ and\ P(Black)]\ or\ [P(Black)\ and\ P(Red)]\)
\(P(1\ Red\ and\ 1\ Black) = [P(Red)\ *\ P(Black)]\ +\ [P(Black)\ *\ P(Red)]\)
\(P(1\ Red\ and\ 1\ Black) = [\frac{n(Red)}{Total}\ *\ \frac{n(Black)}{Total-1}]\ +\ [\frac{n(Black)}{Total}\ *\ \frac{n(Red)}{Total-1}]\)
So, we have:
\(P(1\ Red\ and\ 1\ Black) = [\frac{5}{8} *\frac{3}{7}] + [\frac{3}{8} *\frac{5}{7}]\)
\(P(1\ Red\ and\ 1\ Black) = [\frac{15}{56} ] + [\frac{15}{56}]\)
\(P(1\ Red\ and\ 1\ Black) = \frac{30}{56}\)
\(P(1\ Red\ and\ 1\ Black) = \frac{15}{28}\)
(d) P(1st Red and 2nd Black)
This is calculated as:
\(P(1st\ Red\ and\ 2nd\ Black) = [P(Red)\ and\ P(Black)]\)
\(P(1st\ Red\ and\ 2nd\ Black) = P(Red)\ *\ P(Black)\)
\(P(1st\ Red\ and\ 2nd\ Black) = \frac{n(Red)}{Total} *\ \frac{n(Black)}{Total-1}\)
So, we have:
\(P(1st\ Red\ and\ 2nd\ Black) = \frac{5}{8} *\frac{3}{7}\)
\(P(1st\ Red\ and\ 2nd\ Black) = \frac{15}{56}\)
Related Questions
help pls!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
E - 4,-2
F - 6, -3
G - 1, -4
How many different ways can a race with 7 runners be completed?
Answers
Answer:
as given we have to find number of ways can a race with 7 runners be completed it is completed in 7! = 7*6*5*4*3*2*1 = 5040 ways
Step-by-step explanation: thats a lot of ways
Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?
Answers
Chay can use 3 bags of mulch per flower bed.
Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.
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Consider the following figure.
(Note that the figure is not drawn to scale.)
20°
L
47°
89°
Order the side lengths IK, KL, IJ, IL, and LJ from least to greatest.
Answers
The side lengths from least to greatest as follows:
IK < KL < IJ < IL < LJ
To order the side lengths IK, KL, IJ, IL, and LJ from least to greatest, we can analyze the given figure.
Since the figure is not drawn to scale, we cannot determine the exact lengths of the sides. However, we can make some observations based on the given angles.
Let's analyze the angles:
Angle L: Since angle L is marked as 47°, we know that side KL is the shortest side, as it is opposite to the smallest angle in a triangle.
Angle I: Since angle I is marked as 20°, we can infer that side IJ is longer than side IK, as it is opposite to a larger angle.
Angle LJ: Since angle LJ is marked as 89°, we can conclude that side LJ is the longest side, as it is opposite to the largest angle in the triangle.
Based on these observations, we can order the side lengths from least to greatest as follows:
IK < KL < IJ < IL < LJ
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Johnny uses a wheelbarrow to move planting soil to a delivery truck. The volume of planting soil that fits in the wheelbarrow measures
2
2 feet by
3
3 feet by
1.5
1.5 feet. The delivery truck measures
11
11 feet by
8
8 feet and is
6
6 feet tall. Johnny puts planting soil in the delivery truck until the truck is
70
70% full.
What is the minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is
70
70% full?
Answers
The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled, obtained from the volume of the wheelbarrow and the volume of the truck is about 41 times.
What is the volume of a solid?The volume of a solid is the three dimensional space the solid occupies.
The specified dimensions of the wheelbarrow and truck indicates that the volumes of the wheelbarrow and the truck are;
Volume of the wheelbarrow = 2 ft × 1.5 ft × 3 ft = 9 ft³
Volume of the truck = 11 ft × 8 ft × 6 ft = 528 ft³
70% of the volume of the truck = 70% × 528 ft³ = 369.6 ft³
The number of times Johnny uses the wheelbarrow = 369.6 ft³ ÷ 9 ft³ ≈ 41.0
The number of times Johnny needs to use the wheelbarrow is about 41 times
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Kayla wants to build a fence in her backyard the length of her backyard is 30 feet and the width is 45 feet how many feet of fence will she need to buy?
Answers
Answer:
150
Step-by-step explanation:
30 + 30 + 45 + 45 = 150
What are the solutions to the quadratic equation 4(x + 2)2 = 36 x = −11 and x = 7 x = −7 and x = 11 x = −5 and x = 1 x = −1 and x = 5
Answers
Answer:
c
Step-by-step explanation:
edge2020
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
What is a Quadratic Equation?
Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given that;
4(x + 2)² = 36
4( x(x + 2) + 2(x+2) ) = 36
4( x² + 2x + 2x + 4 ) = 36
4( x² + 4x + 4 ) = 36
4x² + 16x + 16 = 36
4x² + 16x + 16 - 36 = 0
4x² + 16x - 20 = 0
We can further simply ( divide through by 4 )
x² + 4x - 5 = 0
Hence,
a = 1b = 4c = -5x = (-b±√(b² - 4ac)) / (2a)
x = (-4±√(4² - (4 × 1 × -5)) / (2×1)
x = (-4±√(16 - (-20)) / (2)
x = (-4±√(16 + 20)) / (2)
x = (-4±√(36)) / 2
x = (-4±6)) / 2
Hence
x = (-4-6)) / 2 and x = (-4+6)) / 2
x = -10/2 and x = 2/2
x = -5 and x = 1
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
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bedlessnoob is cool, right?
Answers
A 12-ounce sports drink costs $0.99, and a 16-ounce sports drink costs $1.19. Which size is the best buy?
Answers
Answer:
The best buy is the 16-ounce drink
Step-by-step explanation:
here, we see that,
12 ounce = 3/4 (16 ounce)
So, the price should reflect that,
i.e,
price of 12 ounce drink = 3/4 (price of 16 ounce drink)
By this metric,
Price of 12 ounce drink = 3/4 ( 1.19)
Price of 12 ounce drink = $0.8925
So, 12-ounce drink should cost $0.8925 but the actual drink costs $0.99,
So, it is more expensive than it should be,
So, the best buy is the 16-ounce drink
Select the correct answer,
Factor the given expression,
X2 + 16x + 64
O A. (X + 8)(x-8)
OB. (x+ 16)(x + 4)
Oc. (x+4)?
OD. (x+8)?
Answers
Answer:
(x+8)^2
Step-by-step explanation:
x^2 +16x+64
What two numbers multiply to 64 and add to 16
8*8 = 64
8+8 = 16
(x+8)(x+8)
(x+8)^2
A rectangle is 4.2 centimetres wide and each diagonal is 8.6 centimetres long. What is the measure of the angle between a diagonal and the shorter side of the rectangle, to the nearest tenth of a degree?
Answers
Answer:
\( 60.8^\circ \)
Step-by-step explanation:
First, let's check side lengths.
Using the Pythagorean theorem we can find the length of the other side of the rectangle.
a^2 + b^2 = c^2
4.2^2 + b^2 = 8.6^2
b^2 = 56.32
b = 7.5
The other side of the rectangle measures 7.5 cm, so now we know that 4.2 cm is indeed the shorter side of the rectangle.
For the angle in question, the 4.2 cm side is the adjacent leg.
The diagonal of 8.6 cm is the hypotenuse.
The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.
\( \cos \alpha = \dfrac{adj}{hyp} \)
\( \cos \alpha = \dfrac{4.2~cm}{8.6~cm} \)
\( \alpha = \cos^{-1} \dfrac{4.2~cm}{8.6~cm} \)
\( \alpha = 60.8^\circ \)
The total revenue for Jane's Vacation Rentals is given as the function R(x)=400x−0.4x2
, where x is the number of apartments booked. What number of apartments booked produces the maximum revenue?
Answers
The vertex of a quadratic function in the form ax^2 + bx + c can be found using the formula x = -b / (2a).
In this case, a = -0.4, b = 400, and c = 0.
Using the formula, we can calculate the x-coordinate of the vertex:
x = -b / (2a)
= -(400) / (2 * (-0.4))
= -400 / (-0.8)
= 500
Therefore, the number of apartments booked that produces the maximum revenue is 500.
A 9th grade teacher at a local high school wants to know which subject the 9th grade students in the high school like best which group of people should make up a sample that will best answer her question a, other 9th grade teachers in her school
B, parents of 9th graders in her school
C, 9th graders in her school
D,9th graders in her homeroom
Answers
The group of people who should make up a sample that will best answer her question is the 9th graders in her school. The correct option is C.
What are subjects?Subjects are the different sets of information which is studied.
9th graders in her school will be perfect because the question is specifically asking about the opinions of 9th-grade students in the high school, so it makes sense to sample this group directly.
The other options may provide some insights, but they may not be as accurate or representative of the opinions of the 9th-grade students in the school.
Thus, the correct option is C, 9th graders in her school.
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The circle graph shows how a family budgets its annual income. If the total annual income is $100,000, what amount is budgeted for Clothing?
Answers
Answer:
where is the circle graph
For two n by n square matricies A and B,
suppose rankA = rankB = n-1.
Can rank(AB) become less than n-1 ?
(e.g. rank (AB) = n-2)
If so, I humbly ask you for an example.
Thank you very much.
Answers
No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.
According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.
If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.
Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.
However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.
Therefore, if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.
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A tech company bought a number of computers for its employees: 66 costing \$1600$1600 each, 44 costing \$1200$1200 each, and yy costing \$900$900 each, where yy is a positive odd integer. If the median price for all the computers purchased by the company was \$1200,$1200, what is the greatest possible value of yy
Answers
Answer:
5
Step-by-step explanation:
A tech company bought a number of computers for its employees: 6 costing $1600 each, 4 costing $1200 each, and y costing $900 each, where y is a positive odd integer. what is the greatest possible value of y
Solution:
The median of a group of numbers is the middle number when the group of numbers have been arranged either in ascending of descending other. The median of an even group of numbers is the average of the two most middle most numbers while the median of an odd group of numbers is the middle number.
Since there are 6 computers costing $1600, 4 computers costing $1200 each and y computers costing $900 each. Since y is odd, hence y + 6 + 4 would be odd and the median would be the middle number.
Given that the median price = $1200, this means that the middle of the group of numbers is $1200
900, 900, ..., 1200, 1200, 1200, 1200, 1600, 1600, 1600, 1600, 1600, 1600
Since y is odd, for the median price to be $1200, y has to be 3 or 5.
If y = 3:
900, 900, 900, 1200, 1200, 1200, 1200, 1600, 1600, 1600, 1600, 1600, 1600
median = $1200
If y = 5:
900, 900, 900, 900, 900, 1200, 1200, 1200, 1200, 1600, 1600, 1600, 1600, 1600, 1600
Median = $1200
Therefore the greatest possible value of y is 5
By knowing that the median must be $1,200, we will see that the greatest possible value of y is y = 9.
We know that the company bought:
6 computers costing $1,6004 computers costing $1,200y computers costing $900We know that y is a positive odd number.
We also know that the median is $1200, now we want to get the maximum value of y such that the median is $1200. (Remember that the median is the value of the middle element of the set).
Then we will have the distribution:
{ y elements, $1200, the other 3 $1200 computers plus the 6 $1600 computers}
Notice that y (the number of elements at the left of the median) must be equal to the number at the right of the median.
At the right of the median, we have a total of 9 computers, then y must be equal to 9.
The greatest possible value of y is 9.
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Which of the following are more precise than a weight of 1,000 pounds? Check all that apply.
Answers
Give an example of a 2x2 matrix without any real eigenvalues:___________
Answers
Answer:
Step-by-step explanation:
An eigenvalue of n × n is a function of a scalar \(\lambda\) considering that there is a solution (i.e. nontrivial) to an eigenvector x of Ax =
Suppose the matrix \(A = \left[\begin{array}{cc}-1&-1\\2&1\\ \end{array}\right]\)
Thus, the equation of the determinant (A - \(\lambda\)1) = 0
This implies that:
\(\left[\begin{array}{cc}-1-\lambda &-1\\2&1- \lambda\\ \end{array}\right] =0\)
\(-(1 - \lambda^2 ) + 2 = 0\)
\(-1 + \lambda ^2 + 2= 0\)
\(\lambda^2 +1 =0\)
Hence, the eigenvalues of the equation are \(\mathtt{\lambda = i , -i}\)
Also, the eigenvalues can be said to be complex numbers.
if a=1 and b=2 what is the value of a²+b²?
Answers
Answer:
1^2+2^2=5
Step-by-step explanation:
Answer is 5..
HELP!!!!
Question 7 of 25
Does this graph show a function? Explain how you know.
O A. No; there are values that have more than one x-value.
OB. Yes; the graph passes the vertical line test.
O C. Yes, there are no values that have more than one x-value.
O D. No; the graph fails the vertical line test.
SUBMIT
Answers
Answer:
B. Yes; the graph passes the vertical line test.
Step-by-step explanation:
If a vertical line can intersect the graph at more than one point the graph is not a function.
Answer: B, the graph passes the vertical line test
Step-by-step explanation:
What is the length of the base of a right triangle with an area of 15 square meters and a height of 3 meters? A. 5 m B. 10 m C. 30 m D. 45 m
Answers
Answer:
B.10
Step-by-step explanation:
15=1/2b(3)
30=3b
10= base
Quickkkkkkk pleaseee
Answers
Answer:
x=4.2. If you divide 12.6 by 3, you get 4.2
Answer: =6 hope that helps
PLEASE HELP ME WORTH ALOT OF POINTS
Answers
Am not sure though
One brand of cola co fizz is sold in packs of 4*500ml for 2.50 another brand colo is sold in packs of 10 330mlfo $2 which brand is more expensive
Answers
Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.
To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.
For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.
For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.
Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.
Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.
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how much will a person pay for 4.5 pounds of bananas at a price of $1.25 per pound
Answers
Answer:
$5.62 it could also possibly be $5.63 if you have to round up.
Step-by-step explanation:
Answer: $5.63
Step-by-step explanation: multiply 4.5 by the price per pound.
Marta recorded the temperature at 8 p.m. as 56°F and the temperature at 8 a.m. the next morning as 36°F. Marta assumed the temperature changed at a constant rate. She wrote an equation to find the number of degrees the temperature dropped each hour, h, of the night. Which equation did Marta write?
Answers
Answer: 5h/3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
Answer:
5h 3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
Joanna's vegetable garden covers an area of 16 of a square mile. If the garden is 14 mile wide, how long does the garden stretch?
112 mile
1 over 12 mile
512 mile
5 over 12 mile
23 mile
2 thirds mile
34 mile
Answers
The length of the rectangular garden given the area and width is 8/7 miles
Area of rectangleA rectangle is a form of quadrilateral having opposing sides parallel and four right angles. The area of a rectangle can be calculated by multiplying the length by width.
Width of the rectangular garden = 14 mileLength of the rectangular garden = x mileArea of the garden = 16 square milesArea of a rectangular garden = length × width
16 = x × 14
16 = 14x
divide both sides by 14x = 16 / 14
x = 8/7 miles
Therefore, the length of the rectangular garden given the area and width is 8/7 miles.
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PLEASE HELP!
A game board with 17 spaces. Start, green, green, star, quesiton mark, question mark, star, question mark, green, cat town, green, green, star, question mark, green, green, star, green, end.
You are playing a board game and your playing piece begins the game at START. You roll a single number cube numbered 1 to 6 to find out how many spaces you can move.
What is the theoretical probability of landing on a question mark space on your first roll.
A 1/6
B 1/4
C 1/3
D 1/2
Answers
Answer:
C 1/3
Step-by-step explanation:
out of the 6 possible moves you have the possibility of landing on question mark twice. 2/6 -> 1/3
Help please geometry
Answers
The area of the shaded region = 30.903 in²
From the attached figure we can observe that the radius of the circle R is r = 6 in.
Using the forula for the area of circle, the area of circle R would be,
A₁ = πr²
A₁ = π × 6²
A₁ = 36π
A₁ = 113.097 in²
So, the diameter would be d = 6 × 2 = 12 in.
The circle R is inscribed in a square.
So, the side length of square is equal to the diameter of the circle.
This means the side length 'a' os square = 12 in.
Using the formula of the area of square,
A₂ = side²
A₂ = a²
A₂ = 12²
A₂ = 144 in²
so, the area of the shaded region would be,
A = A₂ - A₁
A = 144 -113.097
A = 30.903 in²
This is the required area.
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How do you simplify (a3b2)2
Answers
Answer:
a^6b^4
Step-by-step explanation:
(a³b²)²
a^6b^4
9514 1404 393
Answer:
a⁶b⁴
Step-by-step explanation:
The relevant rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
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These let us simplify the expression as follows:
\((a^3b^2)^2=(a^3)^2(b^2)^2=a^{3\cdot2}b^{2\cdot2}=\boxed{a^6b^4}\)
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Additional comment
It might be helpful to remember that an exponent signifies repeated multiplication.
a·a·a = a³ . . . . . . 'a' is a factor 3 times, so the exponent is 3.
Similarly, ...
(a³)² = (a³)·(a³) = (a·a·a)·(a·a·a) = a⁶