The person is therefore using more water for bathing than for showering, according to the conclusion.
Half of the tub's total water is consumed while taking a bath.
Water used divided by volume equals
[tex]\frac{volume}{2}[/tex]
= [tex]\frac{(5)(3)(2.8)}{2}[/tex]
=[tex]\frac{42}{2}[/tex]
=21 cubic feet.
The following will provide the total amount of water utilized while having a shower:
Total water Equals rate ×time
= 1.52 × 12
= 18.24 gallons.
So, if there are 7.5 gallons in a cubic foot, the amount of water in cubic feet will be amount
=[tex]\frac{18.24}{7.5}[/tex]
=2.432 cubic feet.
The person is therefore using more water for bathing than for showering, according to the conclusion.
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The number of pairs of shoes owned by a sample of seven students are given below. Match the measure to its value.
3, 3, 5, 9, 12, 13, 15
1. range
2. variance
3. standard deviation
12
5
25
According to the solving the given data the values of :
Range = 12
Variance= 25
Standard deviation= 5
What does "variance in statistics" mean?Data points' deviations from the mean are quantified by their variance. Layman defines variance as the degree to which a set of data (numbers) deviates from the mean (average) value. Finding the predicted difference between the deviation from the actual value and the variation.
What do you mean by range?In statistics, range is the distinction between the most and least values in a set. Mathematics' interval, also known as range, is a collection of real numbers that contains all values that fall between any two other values.
According to the given data:Given data: 3, 3, 5, 9, 12, 13, 15
Range = Highest value - lowest value
= 15 - 3
= 12
Mean of the given data:
xi = 3, 3, 5, 9, 12, 13, 15
n = 7
S² = ∑(xi - x)²/(n - 1)
= (30.25 + 30.25 + .25+ 12.25 + 20.25 + 42.25 + 12.25)/6
= 147.75/6
= 24.6
= 25
Finding the standard deviation:
√S² = 25
S = 5
According to the solving the given data the values of :
Range = 12
Variance= 25
Standard deviation= 5
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Nidia cut a rectangle into 2 pieces as shown below.
12 ft
20 ft
20 ft
12 ft
She put the pieces together to form a parallelogram. What is the area of the parallelogram?
The area of the parallelogram is 240 feet.
What is area of parallelogram?A parallelogram's area is the area that it occupies in a two-dimensional plane. A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides. The space bounded by a parallelogram's four sides is known as its area. A parallelogram's area is determined by multiplying its length by its height.
A quadrilateral's interior angles add up to 360 degrees.
The area of a parallelogram can thus be written as :
Area = Base × Height
In this diagram it is given that the Base = 20 feet and the height = 12 feet
Thus the area can be obtained by simply multiplying these two dimensions
So area = 20 × 12 = 240 feet .
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What is the percent change if you paid $1.87 per gallon on February 6th and $1.80 per gallon on February 17th?
The percent change formula is:
[tex]\frac{\text{new price - previous price}}{\text{previous price}}\cdot100[/tex]In this case, the percent change is:
[tex]\frac{1.8-1.87}{1.87}\cdot100=-3.74\text{ \%}[/tex]Find the slope m and y-intercept b. (If an answer is undefined, enter UNDEFINED. If an answer does not exist, enter DNE.)
x = −9
m =
b =
Answer: undefined, DNE
Step-by-step explanation:
This is a vertical line, so there is an undefined slope and no y-intercept.
There is no y-intercept because the line does not pass through the origin.Write the component form of the vector.
Answer:
C , D
Step-by-step explanation:
The component form of a vector is given as < x, y >, where x describes how far right or left a vector is going and y describes how far up or down a vector is going.
The component form of vector C is <1, 5> and the component form of vector D is <8, 2>. The components represent the magnitudes of the vector's displacements in the x and y directions, respectively.
To write the component form of a vector, we simply list its components, which are the numerical values that represent the vector's magnitude and direction in each dimension. In this case, we have vector C with components C<1, 5> and vector D with components D<8, 2>.
The components of a vector represent its position or displacement along the coordinate axes. In a two-dimensional Cartesian coordinate system, the first component represents the displacement along the x-axis (horizontal direction), and the second component represents the displacement along the y-axis (vertical direction).
For vector C, the component form is written as <1, 5>, where the first component is 1 and the second component is 5. This means that vector C has a displacement of 1 unit in the x-direction and 5 units in the y-direction.
Similarly, for vector D, the component form is <8, 2>, indicating a displacement of 8 units in the x-direction and 2 units in the y-direction.
Therefore, the component form of vector C is <1, 5> and the component form of vector D is <8, 2>. The components represent the magnitudes of the vector's displacements in the x and y directions, respectively.
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Find the area of a parallelogram that is 6m height 7m length
Answer:
Area (A) = 42m²
Step-by-step explanation:
A = b·h = 6·7 = 42m²
f(x) = 8x + 1, g(x) = 4x - 2
Find (fg)(x).
f(g(x)) for the given equation f(x)=8x+1 and g(x)=4x-2 is 32x-15 using substitution method of solving the equation.
What is equation?An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. It is a formula that expresses the connection between two expressions on each side of a sign.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
given,
f(x)=8x+1
g(x)=4x-2
f(g(x))=8(4x-2)+1
=32x-16+1
f(g(x))=32x-15
Hence, this is required f(g(x)) for the given two equations.
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I’m struggling on question number 16, me and friend are getting VERY different answers and I would like to get a good grade in this class!
Solution:
Given a sphere of diameter, d, 2.5ft.
To find the volume, V, of the sphere, the formula to apply is
[tex]V=\frac{4}{3}\pi r^3[/tex]Where, the radius, r, is
[tex]\begin{gathered} r=\frac{d}{2}=\frac{2.5}{2}=1.25ft \\ r=1.25ft \end{gathered}[/tex]Substitute for r into the formula to find the volume of a sphere above
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\times\pi\times1.25^3 \\ V=8.18123\text{ ft}^3 \\ V=8.2\text{ ft}^3\text{ \lparen nearest tenth\rparen} \end{gathered}[/tex]Hence, the volume, V, of the given sphere is 8.2 ft³ (the nearest tenth)
determine the volume of each rectangular prism.. round to the nearest tenth if necessary
The volume of a rectangular prism is given by the formula:
[tex]V=\text{length}\times\text{width}\times\text{height}[/tex]Given the length is 7 cm
Width is 3 cm
Height is 3 cm
Substituting into formula, we find the volume:
[tex]\begin{gathered} V=7\times3\times3 \\ V=63\operatorname{cm}^3 \end{gathered}[/tex]Which of the following is equivalent to −2(4x + 8y) − 5(3q + 6p)?
−8x + 8y − 15q + 6p
−8x + 16y − 15q + 30p
−8x − 16y − 15q − 30p
−10(4x + 8y − 3q + 6p)
Answer:
-8x + 16y -15q - 30p
Step-by-step explanation:
your just expanding brackets here
Answer: -8x - 16y - 15q - 30p Is the correct answer
I hope this helps!
I need help with this problem
)
2) So, let's begin with the lower-left product of matrices:
[tex]\begin{gathered} \begin{pmatrix}-2 & 12 \\ -1 & -3\end{pmatrix}\times\begin{pmatrix}2 & 1 \\ 4 & 2\end{pmatrix}= \\ \begin{pmatrix}\left(-2\right)\cdot \:2+12\cdot \:4&\left(-2\right)\cdot \:1+12\cdot \:2\\ \left(-1\right)\cdot \:2+\left(-3\right)\cdot \:4&\left(-1\right)\cdot \:1+\left(-3\right)\cdot \:2\end{pmatrix} \\ \begin{pmatrix}44&22\\ -14&-7\end{pmatrix} \end{gathered}[/tex]Now for the next pair of matrices in the middle:
[tex]\begin{gathered} \begin{pmatrix}2 & 0 \\ 1 & 0\end{pmatrix}\times\begin{pmatrix}3 & -1 \\ 2 & 2\end{pmatrix}= \\ \begin{pmatrix}2\cdot \:3+0\cdot \:2&2\left(-1\right)+0\cdot \:2\\ 1\cdot \:3+0\cdot \:2&1\cdot \left(-1\right)+0\cdot \:2\end{pmatrix} \\ \begin{pmatrix}6&-2\\ 3&-1\end{pmatrix} \end{gathered}[/tex]Notice that each row is multiplied by each correspondent column.
And finally, the pair on the lower-right:
[tex]\begin{gathered} \begin{pmatrix}5&-2\\ \:\:\:4\:&-3\end{pmatrix}\times \begin{pmatrix}2&-1\\ \:\:3&1\end{pmatrix} \\ \begin{pmatrix}5\cdot \:2+\left(-2\right)\cdot \:3&5\left(-1\right)+\left(-2\right)\cdot \:1\\ 4\cdot \:2+\left(-3\right)\cdot \:3&4\left(-1\right)+\left(-3\right)\cdot \:1\end{pmatrix} \\ \begin{pmatrix}4&-7\\ -1&-7\end{pmatrix} \end{gathered}[/tex]) Thus, the se are theanswers .
Stella signed up for a streaming music service that costs $9 per month. The service allows Stella to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $1.25 per song. How much total money would Stella have to pay in a month in which she downloaded 40 songs? How much would she have to pay if she downloaded ss songs?
The money would Stella have to pay in a month in which she downloaded 40 songs is $59.
The amount that she has to pay if she downloaded ss songs is 9 + 1.25s.
How to illustrate the information?From the information, Stella signed up for a streaming music service that costs $9 per month and the service allows Stella to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $1.25 per song.
The money would Stella have to pay in a month in which she downloaded 40 songs is:
= 9 + 1.25s
where s = number of songs
= 9 + 1.25s
= 9 + 1.25(40)
= 9 + 50
= $59.
The amount that she has to pay if she downloaded s songs is:
= 9 + 1.25(s)
= 9 + 1.25s
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Please help with the following question:
Using the combination formula, it is found that:
a) There are 210 distinct ways to choose the problems.
b) The probability is of 0.1667 = 16.67%.
c) The probability is of 0.3333 = 33.33%.
What is the combination formula?[tex]C_{n,x}[/tex] gives the number of different combinations of x objects from a set of n elements, according by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The order in which the problems are chosen is not important, which is the reason for the use of the combination formula in this problem.
4 problems are chosen from a set of 10, hence the number of ways to choose the problems is given by:
[tex]C_{10,4} = \frac{10!}{4!6!} = 210[/tex]
The number of ways to choose 4 problems that she can solve is:
[tex]C_{7,4} = \frac{7!}{4!3!} = 35[/tex]
Hence the probability is:
p = 35/210 = 0.1667 = 16.67%.
For item c, the desired outcomes are as follows:
0 problems is not possible, as she knows 7 out of 10 and 4 will be chosen.1 problem: 7 x C(3,3) = 7.2 problems: C(7,2) x C(3,2) = 21 x 3 = 63.Hence the probability is:
p = (7 + 63)/210 = 70/210 = 0.3333.
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A rectangular tabletop has an area of 28 1/8 sqaure feet length of 6 1/4 feet what is the width of the tabletop
If a rectangular tabletop has an area of [tex]28\frac{1}{8}[/tex] square feet and the length of [tex]6\frac{1}{4}[/tex] feet, then the width of the tabletop is [tex]4\frac{1}{2}[/tex] feet
The area of the tabletop = [tex]28\frac{1}{8}[/tex] square feet
Convert the mixed fraction to simple fraction
[tex]28\frac{1}{8}[/tex] square feet = 225/8 square feet
The length of the tabletop = [tex]6\frac{1}{4}[/tex] feet
Convert the mixed fraction to simple fraction
[tex]6\frac{1}{4}[/tex] feet = 25/4 feet
Area of the rectangle = Length × width
Width of the rectangle = Area of the rectangle ÷ Length of the rectangle
Substitute the values in the equation
Width of the rectangle = 225/8 ÷ 25/4
= 225/8 × 4/25
= 9/2 feet
Convert the simple fraction to mixed fraction
9/2 feet = [tex]4\frac{1}{2}[/tex] feet
Hence, if a rectangular tabletop has an area of [tex]28\frac{1}{8}[/tex] square feet and the length of [tex]6\frac{1}{4}[/tex] feet, then the width of the tabletop is [tex]4\frac{1}{2}[/tex] feet
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3) Travis International has a one-time expense of $1.13 million that must be paid two years from today. The firm can earn 4.3 percent annually, compounded monthly, on its savings. How much must the firm save each month to fund this expense if the firm starts investing equal amounts each month starting at the end of this month?
A) $38,416.20
B) $45,172.02
C) $51,300.05
D) $47,411.08
E) $53,901.15
Find the volume of this rectangular pyramid Be sure to include the correct unit in your answer
Okay, here we have this:
Considering the provided rectangular pyramid, we are going to calculate the requested volume, so we obtain the following:
Then, we are going to use the following formula to find the volume of this rectangular pyramid:
V=(abH)/3
Replacing:
V=(abH)/3
V=(5cm*6cm*7cm)/3
V=(210cm^3)/3
V=70 cm^3
Finally we obtain that the volume of the rectangular prism is 70 cm^3.
help meeeeeeeeee
12 Answer:
Evaluate the expression: 8-6+4
13 Answer:
Evaluate the expression: 16÷(4-2)-3
14 Answer:
Check whether the given number is a solution of the equation:
3x + 5 = 17; x=2
a. solution is correct
b. solution is incorrect
15 Answer:
Check whether the given number is a solution of the equation:
4y - 7 = 3y - 4; y=3
a. solution is correct
b. solution is incorrect
16 Answer:
Check whether the given number is a solution of the inequality:
2m - 3 < 4; 2
a. number is a solution
b. number is not a solution
17 Answer:
Check whether the given number is a solution of the inequality:
5 + 2n ≥ 12; 0
a. number is a solution
b. number is not a solution
Answer:
Step-by-step explanation:
13) 8 - 6 + 4 = 2 + 4 = 6
14) 16÷(4-2)-3 = 16÷2 - 3 = 8 - 3 = 5
15) 3x + 5 = 17
3x = 17 - 5
3x = 12
x = 4 ≠ 2
b. solution is incorrect
16)4y - 7 = 3y - 4
4y - 3y = -4 + 7
y = 3
a. solution is correct
17) 2m - 3 < 4
2m < 4 + 3
2m < 7
m < 3.5
2 < 2.5, so a. number is a solution
18 ) 5 + 2n ≥ 12
2n ≥ 12 - 5
2n ≥ 7
n ≥ 3.5
0 is not greater than equal to 3.5, so b. number is not a solution
In the game, your score grew by 200 points each time you scored. Two expressions below represent your echoes after 12 hits. Find both.
A) 200 + 200 + - - - + 200 +200
—————————————————
12times
B) 200 ⚫️ 200 ⚫️ - - - ⚫️ 200 ⚫️ 200
—————————————————
12times
C) 200 ⚫️ 12
D) 200 + 12
Answer: A and C
Sample Answer: Multiplication is a short way to write repeated addition. So 200 •12 means the same as 200 + 200 + . . . + 200.
Answer:
b
Step-by-step explanation:
A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. If the number of defective bulbs is 1 or less, the lot passes inspection. Suppose 10% of the bulbs in the lot are defective. What is the probability that the lot will pass inspection? Round your answer to four decimal places
May I please get help with this. For I have tried multiple times but still could not get the correct answers for them or even plot it on the graph 90 degrees clockwise
To rotate the figure 90 degrees clockwise about a point, every point (x, y) will rotate to (y, -x):
[tex](x,y)\to(y,-x)[/tex]The vertices of the triangle have the following coordinates:
[tex]\begin{gathered} 1=(-5,-1) \\ 2=(-1,-2) \\ 3=(-3,-4) \end{gathered}[/tex]Applying the transformation rule, we have the new coordinates to be:
[tex]\begin{gathered} 1\to(-1,-(-5))=(-1,5) \\ 2\to(-2,-(-1))=(-2,1) \\ 3\to(-4,-(-3))=(-4,3) \end{gathered}[/tex]The transformed image is shown below (the black triangle):
Gina is driving 76 miles to her brother's house. If she stops for gas after driving 34 miles, how many miles does she have to go before she gets to her brother's house?
Answer:
42
Step-by-step explanation:
76-34
Members of the marching band line up in 6 rows of 8.
Answer: 6x8
Ur answers should be 48 and again we did repeated addition so
6+6+6+6+6+6+6+6 or we can do 12+12+12+12 or 24+24 which we should know use 48
Step-by-step explanation:
please help me to do this problem.
3 is dividing on the right, then it will multiply on the left
B is multiplying on the right, then it will divide on the left
[tex]\frac{V\cdot3}{B}=h[/tex]Please Help me solve this
The value of f'(x) at x = 1 is 1 for first order derivative of x^x^3.
A derivative in calculus is the rate of change of a quantity y with respect to another quantity x. It is also termed the differential coefficient of y with respect to x. Differentiation is the process of finding the derivative of a function.
Given that, x^x^3 and we have to find the first order derivative with respect to x and then find the value at x = 1.
Let's proceed to solve this question accordingly.
let f(x) = x^x^3
The first order derivative = f'(x) = d/dx(x^x^3)
First apply the generalized power rule, then we have
= x^x^3.d/dx(ln(x)x^3)
Applying the power rule, we get
= x^x^3 (d/dx(x^3).ln(x)+x^3.d/dx(ln(x)))
= x^x^3 (3x^2 ln(x) +x^3.1/x)
= x^x^3 (3x^2ln(x) +x^2)
On simplifying, we will get
= x^x^3+2(3ln(x)+1)
f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1)
Now, at x = 1, we get
f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1) = 1
Therefore, f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1) = 1 is the required answer.
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15) A sample of 4 different calculators IS randomly selected from a group
containing 46 that are defective and 26 that have no defects. What is the
probability that all four of the
calculators selected are defective? Round to four
decimal places.
A) 0.1021
B) 0.1586
C) 0.1666
D) 10.9154
Answer:
C) 0.1666
Step-by-step explanation:
The probability of selecting a calculator that is defective can be defined as: [tex]\frac{46}{46+26}[/tex]
The 46 in the numerator is the number of calculators that are defective in the group. The 46 + 26 represents the total amount of calculators since 46 are defective and 26 are not defective and assuming a calculator can only be defective or not defective then these are the total number of calculators in the group.
This gives you a probability of approximately: [tex]\frac{46}{72}[/tex] or approximately 0.638889
We can multiply independent events to find the combined probability of these events occurring. So we have to assume you put the calculator back into group after selecting one.
If this is the case we simply multiply 46/72 * 46/72 * 46/72 * 46/72 or (46/72)^4 to get an approximate probability of: 0.1666
b(x)=18-0.5x 6 and 18
The solution of B(x) = 18 - 0.5x with x being -2, 0, 5 is 19, 18 and 15.5.
How to evaluate functions?Finding the value of f(x) =... or y =... that corresponds to a certain value of x is what it means to evaluate a function. Simply swap out all instances of x with the value of x to do this. For example, if we are requested to evaluate f(4), then the value 4 has been given to x.Given:
B(x) = 18-0.5x
x = -2, 0, 5
Putting the values of x to find the result of the function.
B(-2) = 18 - 0.5 × (-2) = 18 + 1 = 19
The required solution of the function at x = -2 is f(-2) = 19.
B(0) = 18 - 0.5 × (0) = 18
The required solution of the function at x = 0 is f(0) = 18.
B(5) = 18 - 0.5 × (5) = 18 - 2.5 = 15.5
Thus, the required solution of the function at x = 5 is f(5) = 15.5.
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The complete question is :"How do you solve B(x) = 18-0.5x with x being -2, 0, 5."
a(1)= -13
a(n)= a(n-1)+4
Find the 2nd term in the sequence
The second term of the arithmetic sequence is:
a₂= -9
How to find the second term in the sequence?Here we have an arithmetic sequence, such the the recursive formula is:
aₙ = aₙ₋₁ + 4
So to get each term, we need to add 4 to the previous one.
We know that the first term is:
a₁ = -13
Then the second term will be:
a₂ = a₁ + 4 = -13 + 4 = -9
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The balance on a credit card, that charges a 15.5%
APR interest rate, over a 1 month period is given in
the following table:
Days 1-3: $200 (initial balance)
Days 4-20: $300 ($100 purchase)
Days 21-30: $150 ($150 payment)
What is the finance charge, on the average daily
balance, for this card over this 1 month period?
finance charge = $ [?]
Round to the nearest hundredth.
Enter
4
Finance charge = $93.00
What is finance charge of credit card?The interest you'll pay on a loan is defined as a finance charge, and it's most commonly used in the context of credit card debt. A financing fee is computed by taking your annual percentage rate, or APR, the amount you owe, and the time period into account.
Given that,
Interest rate = 15.5%
Date: 1-3 (3 days)
Average daily balance = amount paid × days
= $200 × 3 = $600
Date: 4-20 (17 days)
Average daily balance = amount paid × days
= $300 × 17 = $5100
Date: 21-30 (10 days)
Average daily balance = amount paid × days
= $150 × 10 = $1500
So, total average daily balance for the month
= $(600+5100+1500)
= $7200
Now, the finance charge = $7200 × (15.5÷12)
= $93.00
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provide the correct reason for the statement in line 4. (please help)
The property that completes the proof is the transitive property
How to determine the statement that represents the reason in the proof?From the question, we have the following parameters
The point C is the midpoint of AE
BC = CD
The above implies that
AC = CE
And it also means that:
The line segment BC and the line segment CD have equal lengths
According to the transitive property of equation, we have:
If A = B and B = C, then A = C
This can also be represented as
If A + B = C + D and C + D = E + F, then A + B = E + F
Using the above as a guide, we have (in step 3)
AB + BC = AC
CD + DE = CE
This implies that
AB + BC = CD + DE
Hence, the statement that represents the reason 4 in the proof is (b) transitive property
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Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
If one order is selected, find the probability of getting an order that is not accurate or is from Restaurant C. Are the events of selecting an order that is not accurate and selecting an order from Restaurant C disjoint events?
The probability is 0.334 and the events are not disjoint events
How to determine the probability?The table of values represents the given parameters
The probability to calculate is given as
The probability of getting an order that is not accurate or is from Restaurant C
This can be represented as
P(Not accurate or Restaurant C)
This is calculated as
P(Not accurate or Restaurant C) = [n(Not accurate) + n(Restaurant C) - (Not accurate and Restaurant C)]/Total
So, we have
P(Not accurate or Restaurant C) = (37 + 52 + 34 + 19 +237 + 34 - 34)/(330 + 276 + 237 + 150 + 37 + 52 + 34 + 19)
Evaluate the sum and the difference
P(Not accurate or Restaurant C) = 379/1135
Evaluate the quotient
P(Not accurate or Restaurant C) = 0.334
Lastly, the events of selecting an order that is not accurate and selecting an order from Restaurant C are not disjoint events
This is so because it is possible to select an order from restaurant C that is not accurate
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