The probability that the pink can was chosen because the cookie was a sugar cookie is about 0.282, or about 28.2%.
Why do you think probability?Probability is simply how likely something is to happen. When we are uncertain about the outcome of an event, we can talk about the probability of certain outcomes - how likely they are. The analysis of events driven by probabilities is called statistics.
We can use Bayes' theorem to calculate the probability that the pink can was chosen because the cookie was a sugar cookie. Let P(P) be the probability that the pink jar was chosen, P(S) be the probability that the chosen cookie was a sugar cookie, and P(S|P) be the probability that a sugar cookie was chosen given that the pink one was chosen. Then we have:
P(P|S) = P(S|P) * P(P) / P(S)
We can calculate all these probabilities as follows:
P(S|P) = 9 / (15 9 13) = 9/37
This is the probability of choosing a sugar cookie, given that the pink can was chosen.
P(P) = 1/4
This is the probability of choosing the pink can.
To calculate P(S), we need to consider all possible options for choosing a sugar cookie. We can choose a sugar loaf from a blue, green or pink jar. So:
P(S) = P(S|B) * P(B) P(S|G) * P(G) P(S|P) * P(P)
where P(S|B) is the probability of choosing a sugar cookie from the blue jar, P(G) is the probability of choosing the green jar, and so on. We can calculate all these probabilities as follows:
P(S|B) = 12 / (7 12) = 12/19
P(S|G) = 8 / (6 8 5) = 8/19
P(S|P) = 9 / (15 9 13) = 9/37
P(B) = 1/2
P(G) = 1/4
P(P) = 1/4
So,
P(S) = (12/19) * (1/2) (8/19) * (1/4) (9/37) * (1/4) = 271/444
We can now calculate P(P|S) using Bayes' theorem:
P(P|S) = (9/37) * (1/4) / (271/444) ≈ 0.282
Therefore, the probability that the pink can was chosen because the cookie was a sugar cookie is about 0.282, or about 28.2%.
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Based on the information in the table, what
was the approximate value of this item in
1980?
Answer:
B) 4,700
Step-by-step explanation:
6000 - 4000 = 2000
2000 in 15 year, find how much for each year
2000/ 15 = 133.3333333
133.3333333 estimated = 133
133 approximately for each year
1975 to 1980 is five years
133 x 5 = 665
4000 + 665 = 4665
4665 rounded the the nearest hundred
4700
Is this quadrilateral a parallelogram?
I believe this quadrilateral is a parallelogram.
What is a parallelogram?There are a few ways to choose within the occasion that a quadrilateral may be a parallelogram: Opposite sides are parallel: Within the occasion that inverse sides of a quadrilateral are parallel, at that point it may be a parallelogram.
Inverse sides are said to be consistent: On the off chance that inverse sides of a quadrilateral are consistent, at that point it may be a parallelogram. From the image attached , you can see the both side red are marked equal hence it is a parallelogram
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Five cards are dealt from a standard deck. What is the probability that at least four of them are hearts?
Step-by-step explanation:
To calculate the probability of getting at least four hearts when dealing five cards from a standard deck, we can use the concept of combinations and probability.
There are a total of 52 cards in a standard deck, and 13 of them are hearts (assuming no jokers). So the probability of drawing a heart on the first card is 13/52, or 1/4.
Now, there are two possible scenarios that would result in at least four hearts:
Four hearts and one non-heart: This can happen in C(13,4) * C(39,1) ways, where C(n, k) is the number of combinations of n items taken k at a time. The first part C(13,4) represents choosing 4 hearts out of 13, and the second part C(39,1) represents choosing 1 non-heart out of the remaining 39 cards. The total number of ways to choose 5 cards from 52 is C(52,5).
Five hearts: This can happen in C(13,5) ways, where C(13,5) represents choosing all 5 hearts out of 13.
So, the total number of favorable outcomes is C(13,4) * C(39,1) + C(13,5), and the total number of possible outcomes is C(52,5). Therefore, the probability of getting at least four hearts is:
P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)
Plugging in the values and simplifying, we get:
P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)
= (715 * 39 + 1287) / 2,598,960
= 27,885 / 2,598,960
≈ 0.0107566
So, the probability of getting at least four hearts when dealing five cards from a standard deck is approximately 0.0107566 or about 1.08%.
[tex]1 1/7 - 5/6[/tex]
Which of the points below correctly plots the point (2,7π/4)?
Points are plotted on a polar graph.
Answer: E is correct
Step-by-step explanation:
Remember that the coordinates (2,7π4) tell us the radius r=2 and the angle θ=7π4. So the point should be on the circle labeled 2 and form an angle of 7π4 with the positive x-axis. Point E is the correct point.
4. Which of the following angles is vertical to angle /DEB?
A
C
109°
E
D
B
Answer:
A
Step-by-step explanation:
643 N
5
2
T
-5-4-3-2-1₁-
-2
-3
-4
-5
y
-
2 3 4 5
X
What is the range of the function on the graph?
O all real numbers
Oall real numbers greater than or equal to 0
all real numbers greater than or equal to 1
all real numbers greater than or equal to 2
The range of the function is all real numbers.
What is Function?In mathematics, a function is an expression, rule, or law that specifies a relationship between two variables (the independent variable and the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.
We know,
The x-values (Input values) on the graph define the domain of the function.
and, The y-values (output values) on the graph determine the range of a function.
From the graph attached,
Here the x value start from +1 to ∞.
Thus, the range of the function is all real numbers.
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I REALLY NEED THIS DONE PLS ITS VERY IMPORTANT!!!
Answer: The answer is D
A company sells snow globes made out of glass that are in the shape of hollow
spheres. Khloe measures the outer diameter of a snow globe to be 30 cm. If the glass
has a thickness of 0.35 cm, find the total volume of glass that makes up the globe.
Round your answer to the nearest hundredth if necessary. (Note: diagram is not
drawn to scale.)
The total volume of glass that makes up the snow globe is approximately 1,757.84 cubic centimeters.
What is the inner sphere?
The Inner Sphere is a region of interstellar space surrounding Earth to a radius of roughly 450 - 550 light-years, generally demarcated by the outer borders of the "Great Houses."
The outer sphere has a diameter of 30 cm, so its radius is 15 cm. The volume of the outer sphere is given by the formula:
V outer = (4/3)πr_outer³
V outer = (4/3)π(15 cm)³
V outer ≈ 14,137.17 cm³
The inner sphere has a diameter of 30 cm minus the thickness of the glass on both sides, so its diameter is:
30 cm - 2(0.35 cm) = 29.3 cm
Therefore, the radius of the inner sphere is:
r inner = 29.3 cm / 2 = 14.65 cm
The volume of the inner sphere is given by the formula:
V inner = (4/3)πr_inner³
V inner = (4/3)π(14.65 cm)³
V inner ≈ 12,379.33 cm³
Finally, the volume of glass that makes up the snow globe is the difference between the volumes of the outer and inner spheres:
V glass = V outer - V inner
V glass ≈ 1,757.84 cm³
Therefore, the total volume of glass that makes up the snow globe is approximately 1,757.84 cubic centimeters.
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A BCom graduate bought a small apartment for R151 000.00 with a down payment of R51 000.00. If the graduate secures a mortgage bond with a bank for the balance at 15% per annum, compounded monthly, with a term of 20 years. What are the monthly payments?
The solution of calculate the monthly payments on a mortgage bond, we can use the formula for the present value of an annuity.
what is present value and annuityPresent value (PV) is the current value of a future sum of money, discounted to reflect the time value of money and the risk of non-payment or default.
An annuity is a financial product that pays out a fixed stream of payments to an individual over a specified period of time.
According to the given information:
To calculate the monthly payments on a mortgage bond, we can use the formula for the present value of an annuity:
PV = (PMT / i) x (1 - [tex](1+n)^{-n}[/tex])
Where:
PV = present value (the amount borrowed)
PMT = monthly payment
i = monthly interest rate (15% per annum / 12 months = 1.25%)
n = number of monthly payments (20 years x 12 months per year = 240 months)
First, we need to calculate the present value of the loan, which is the amount borrowed minus the down payment:
PV = R151 000.00 - R51 000.00
PV = R100 000.00
Next, we can plug in the values into the formula:
R100 000.00 = (PMT / 0.0125) x (1 - [tex](1+0.0125)^{-240}[/tex])
Solving for PMT, we get:
PMT = R1,080.80
Therefore, the monthly payments on the mortgage bond will be R1,080.80.
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I need help w this point to right answer
The angle AOB is approximately 98 degrees.
How to find the central angle of a sector?The measure of the angle AOB of the sector can be found as follows:
AOB is the central angle.
Therefore,
length of an arc = ∅ / 360 × 2πr
where
r = radius∅= central angleTherefore,
12 = ∅ / 360 × 2 × 3.14 × 7
12 = 43.96∅ / 360
cross multiply
360 × 12 = 43.96∅
4320 = 43.96∅
divide both sides by 43.96
∅ = 4320 / 43.96
∅ = 98.271155596
Therefore,
∅ = 98 degrees
AOB = 98 degrees
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Help me Help me Help me
Answer:
F
Step-by-step explanation:
First, find the answer to (180 /5 + 4 x 12 - 10) which is 74.
Next, start with solving the possible answers.
Lastly, once you have solves determine which answer is the same, which is F.
Find the number of different arrangements of the 8 letters in the word DECEIVED, in which two Ds are together and the three Es are not all together (i.e. maximum two Es next to each other).
The eight letters in the word DECEIVED may be arranged in 4200 distinct ways, with two Ds grouped together and three Es not all together.
The following approach may be used to determine how many different ways there are for the eight letters in the word DECEIVED to be arranged such that two Ds are together and three Es are not altogether:
Treat the two Ds as a single object, which we can call DD. Now we have 7 objects to arrange: DD, E, E, C, V, I, and E.First, we count the total number of arrangements of these 7 objects, without considering any restrictions. This is simply the number of permutations of 7 objects, which is 7! = 5040.Next, we count the number of arrangements in which the three Es are all together. We can treat the three Es as a single object, which we can call EEE. Now we have 6 objects to arrange: DD, EEE, C, V, I, and an extra E. The number of arrangements of these objects is 6!, since we can treat the EEE as a single object.However, we have overcounted the arrangements in which the two Es are together with the EEE object. To correct for this, we can treat the two Es as a single object, which we can call EE. Now we have 5 objects to arrange: DD, EEE, EE, C, V, and I. The number of arrangements of these objects is 5!, since we can treat the EEE and EE as single objects.Therefore, the number of arrangements in which the three Es are not all together is the difference between the total number of arrangements and the number of arrangements in which the three Es are all together, minus the number of arrangements in which the two Es are together with the EEE object:7! - 6! - 5! = 5040 - 720 - 120 = 4200
Therefore, there are 4200 different arrangements of the 8 letters in the word DECEIVED, in which two Ds are together and the three Es are not all together.
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a rectangular prism is 12 units high and 5 units wide an 10 units long
Answer:
To find the surface area of a rectangular prism, we can use the formula:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
Given that the rectangular prism is 12 units high, 5 units wide, and 10 units long, we can substitute these values into the formula:
Surface Area = 2(10)(5) + 2(10)(12) + 2(5)(12)
Surface Area = 100 + 240 + 120
Surface Area = 460 square units
Therefore, the surface area of the rectangular prism is 460 square units
The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest) 905, 940, 955, 965, 1020, 1040, 1045, 1085, 1090, 1105 Send data to calculator Suppose that one of the people moves. His rent changes from $905 to $ 1055 Answer the following (a) What happens to the mean ? decreases by It increases by s Box It stays the same . (b) What happens to the median ? It decreases by s It increases by It stays the same .
Therefore , the solution of the given problem of mean comes out to be $1055 is more expensive than $1020 it increases by.
What is mean?The total of all values variable divided by all of the values constitutes the outcome of a collection, sometimes referred to as the arithmetic mean. It's one of the key trend indicators that's utilised the most and is typically referred as the "mean." To obtain the answer, multiply the collection's overall number of numbers by each value. Either the raw data or information that has been combined into frequency charts can be used for calculations.
Here,
The average rent is determined by adding up all the rents and dividing by the total number of rents.
This is known as the mean.
Given that the person's rent increased by
=>$150, $1055 - $905 = $150.
The entire sum of all rentals would therefore rise, but the overall number of rents would stay the same at 10.
The mean would therefore rise by
=> $150/10
=> $15.
(b) The median rent at the moment is $1020 because the rents are already arranged from lowest to highest.
The new median would be the middle value of the revised list, which would include the new price of $1055,
if one person's rent increased from $905 to $1055.
The median would rise given that $1055 is more expensive than $1020.
Thus , it increases by.
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HELP RNRNNRNRNRNRNNRNRNRR
Answer:
Step-by-step explanation:
Area= pi times radius²
The radius in the last one is 7, so 7² is 49.
Multiply 3.14 by 49 and you get 153.86. Round it to the nearest tenth and you get 153.9 as the area
Hope this helps!
A force of 350 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 10 centimeters to 40 centimeters?
The work done in stretching the spring from 10 cm to 40 cm is 10,837.5 J.
The work done in stretching a spring is given by the formula:
W = (1/2)k[tex]x^{2}[/tex]
where W is the work done, k is the spring constant, and x is the displacement of the spring from its original position.
To find the spring constant k, we can use the given information:
F = kx
where F is the force applied to the spring. Rearranging this equation, we get:
k = F/x
Substituting the given values, we get:
k = 350 N / 30 cm = 11.67 N/cm
Now, we can find the work done in stretching the spring from 10 cm to 40 cm:
W = (1/2)k([tex](x_{2})^{2} -(x_{1} )^{2}[/tex])
where [tex]x_{1}[/tex] is the initial displacement of the spring (10 cm) and [tex]x_{2}[/tex] is the final displacement (40 cm).
Substituting the values, we get:
W = (1/2) * 11.67 N/cm * ([tex](40 cm)^{2} - (10 cm)^{2}[/tex])
W = (1/2) * 11.67 N/cm * (1600 [tex]cm^{2}[/tex] - 100 [tex]cm^{2}[/tex])
W = (1/2) * 11.67 N/cm * 1500 [tex]cm^{2}[/tex]
W = 10,837.5 joules (J)
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rationalize the denominator [tex]\frac{6}{\sqrt{x} 2\\}[/tex]
The rationalized form of the expression 6/√x is 6√x/x.
Rationalizing the denominatorFrom the question, we have the following parameters that can be used in our computation:
6/√x
To rationalize the denominator of 6/√x, we can multiply both the numerator and denominator by √x.
This gives:
6/√x * √x/√x = 6√x/x
So the rationalized form of 6/√x is 6√x/x.
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if you multiplied a number by 1/2 , the result would be Responses
Answer:
half the number you started with
Step-by-step explanation:
8 times 1/2 would be 4....6 times 1/2 would be 3!
A 3 scoops ice-cream cone cost 4.80. A single Scoop ice-cream cost $2. Which one cost less for each scoop of ice cream ? How much less?
A single scoop is $0.40 cheaper per scoop than a scoop in a 3-scoop cone.
To compare the cost of each scoop of ice cream in a 3-scoop cone and a single scoop, we need to calculate the cost per scoop for each option.
In a 3-scoop cone, the cost of each scoop can be found by dividing the total cost by the number of scoops. Therefore, the cost of each scoop in a 3-scoop cone is:
4.80 ÷ 3 = 1.60
On the other hand, a single scoop of ice cream costs $2. Therefore, the cost of each scoop in a single scoop is:
2 ÷ 1 = 2
Comparing the two options, we can see that a single scoop of ice cream costs less per scoop than a 3-scoop cone. Specifically, a single scoop is $0.40 cheaper per scoop than a scoop in a 3-scoop cone.
Therefore, choosing a single scoop of ice cream over a 3-scoop cone will result in a cost savings of $0.40 per scoop.
In conclusion, when comparing the cost per scoop of ice cream, a single scoop is cheaper than a scoop in a 3-scoop cone. The cost savings per scoop is $0.40.
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PLEASE HELP!!! MIDDLE SCHOOL MATH
Based on the scatter plot below, which is a better prediction for y when x = 74?
PLEASE LOOK AT THE PICTURE!!!!!!!!!!!!!!
The better prediction for y, when x = 74, based on the scatter plot, can be found to be 57.
How to find the better prediction ?Looking at the scatter plot, the better prediction of y when the value of x is 74 can be found by looking for the values of y that have a value of x that is around 74.
From the scatter plot, we see that the value of x of 74, would correspond with the value of y of 57. We can therefore infer that y = 57 is the better prediction for x = 74.
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Brad Harrington bought 31 shares of one stock for $9 3/4 per share and 26 shares of another stock for $11 5/8 per share. How much did he pay?
Answer:
$604.50
Step-by-step explanation:
You want to know the total paid for 31 shares at $9 3/4 and 26 shares at $11 5/8.
Total paidThe total paid is computed the same as for any other purchase. It is the sum of the products of quantity and price each.
total = (31)(9 3/4) +(26)(11 5/8) = 604.50
Harrington paid $604.50 for the stock.
I need help with this Regression question!
A quadratic model for the data is y = -0.0076x² + 0.6915x + 14.711.
The fuel economy at 80 mph is 21.39.
How to determine the linear regression equation and correlation coefficient?In this scenario, the speed (x) would be plotted on the x-axis of the scatter plot while the fuel economy (y) would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the relationship between the speed (x) and fuel economy (y), a quadratic model for the line of best fit is given by:
y = -0.0076x² + 0.6915x + 14.711
When the speed (x) = 80 mph, the fuel economy (y) is given by;
y = -0.0076(80)² + 0.6915(80) + 14.711
y = 21.39
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Find the area
Round to nearest tenth
The total surface area to paint is 22000 sq. ft.
What is surface area?Surface area is the measurement of the outer surface of an object. It is often used to calculate the area of a three-dimensional object, such as a cube, cylinder, or sphere, and is also used to calculate the area of the faces of a solid object. Surface area is measured in square units such as square centimeters (cm2), square meters (m2), or square inches (in2).
Surface Area = 2(lw + lh + wh)
Surface Area = 2((100' x 50') + (100' x 40') + (50' x 40'))
Surface Area = 2(5000' + 4000' + 2000')
Surface Area = 2(11000')
Surface Area = 22000 sq. ft.
Answer: The total surface area to paint is 22000 sq. ft.
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Is (9,8) a solution to this system of equations?
6x - 5y = 16
X = 9
yes
no
Entries for Sale of Fixed Asset
Equipment acquired on January 8 at a cost of $212,000 has an estimated useful life of 15 years, has an estimated residual value of $14,000, and is depreciated by the straight-line method.
a. What was the book value of the equipment at December 31 the end of the fifth year?
b. Assume that the equipment was sold on April 1 of the sixth year for $105,800.
1. Journalize the entry to record depreciation for the three months until the sale date.
2. Journalize the entry to record the sale of the equipment.
The journal entry to record the sale of the equipment would be:Cash $105,800,Loss on Sale of Equipment $35,650,Equipment $212,000
Accumulated Depreciation $66,000
How to solve the question?
a. To calculate the book value of the equipment at December 31 of the fifth year, we need to determine the accumulated depreciation for the first five years. The annual depreciation expense is calculated as follows:
Depreciation Expense = (Cost - Residual Value) / Useful Life
Depreciation Expense = ($212,000 - $14,000) / 15
Depreciation Expense = $13,200 per year
The accumulated depreciation for five years is therefore:
Accumulated Depreciation = Depreciation Expense x Number of Years
Accumulated Depreciation = $13,200 x 5
Accumulated Depreciation = $66,000
The book value of the equipment at December 31 of the fifth year is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - $66,000
Book Value = $146,000
b.
To record depreciation for the three months until the sale date, we need to calculate the depreciation expense for the sixth year. The annual depreciation expense remains the same at $13,200, but since the equipment was sold on April 1, we need to prorate the depreciation for the first three months of the year.
Depreciation Expense for the Sixth Year = Depreciation Expense x (Months Remaining / 12)
Depreciation Expense for the Sixth Year = $13,200 x (9 / 12)
Depreciation Expense for the Sixth Year = $9,900
The journal entry to record depreciation for the three months until the sale date would be:
Depreciation Expense $9,900
Accumulated Depreciation $9,900
To record the sale of the equipment, we need to compare the sale price to the book value of the equipment at the time of the sale.
The book value of the equipment at the time of the sale is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - ($13,200 x 5.25)
Book Value = $141,450
Since the sale price of $105,800 is less than the book value of $141,450, we need to record a loss on the sale of the equipment. The journal entry to record the sale of the equipment would be:
Cash $105,800
Loss on Sale of Equipment $35,650
Equipment $212,000
Accumulated Depreciation $66,000
The cash received from the sale is debited, and the difference between the sale price and the book value is recorded as a loss on the sale of the equipment. The equipment and its accumulated depreciation are removed from the books.
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so can u help me guys
Thus, 715,000 = 7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.
Explain about the scientific notations:The number of times that decimal point must be moved to obtain a number between 1 and 10 is the exponent in scientific notation. The decimal point is shifted to the left in order to represent this number in scientific notation.
The main goal of scientific notation is to simplify computations using numbers that are abnormally large or small. With scientific notation, every digit counts because zeros are just no longer used to denote the decimal point.
Given expression:
715,000 __ 7.15 x 10⁵
LHS = 715,000
Take the RHS value :
= 7.15 x 10⁵
This, can be simplifies as:
= 7.15 x 100,000
Now multiply the two values,
= 715,000 (RHS values)
as, LHS = RHS
LHS = 715,000
715,000 (RHS values)
Thus, 715,000 = 7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.
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The halt-lime performance of a marching band includes a performance in which the band members form a circle with point J at the center. This formation can he modeled by the equation 2° +1? + 10z 12y - 83 = 0.
The required values are as follows:
Center = (-5, 6), Radius = 12, Domain: x ∈ (-17, 7), Range: y ∈ (-6, 18)
Given equation: x² + y² + 10x - 12y - 83 = 0
To convert it into standard form, complete the square for both the x and y terms:
(x² + 10x) + (y² - 12y) = 83
(x² + 10x + 25) + (y² - 12y + 36) = 83 + 25 + 36
(x + 5)² + (y - 6)² = 144
Comparing this with the standard form, we have:
Center (h, k) = (-5, 6)
Therefore, the coordinates for the point J are (-5, 6).
The radius represents the distance from each band member to the center of the circle. In this case, the radius of the circle is the square root of the constant term on the right side of the standard form equation:
Radius = √144 = 12
The domain of the circle is the set of all possible x-values that lie on the circle. Since the circle is centered at (-5, 6) and has a radius of 12, the domain can be expressed as:
Domain: x ∈ (-5 - 12, -5 + 12) or -17 ≤ x ≤ 7
The range of the circle is the set of all possible y-values that lie on the circle. Using the same information, the range can be expressed as:
Range: y ∈ (6 - 12, 6 + 12) or -6 ≤ y ≤ 18
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if 3+1=34
2+2=44
2+3=65
5+3=158
7+2=?
Answer:
7 + 2 = 149 here.
7 × 2 = 14, and 7 + 2 = 9.
NO LINKS!!! URGENT HELP PLEASE!!!!
Express the statement as an inequality. Part (2a^2)
d. c is between 1/7 and 1/5
1. 1/5 ≥ c ≥ 1/7
2. 1/7 < 1/5 < c
3. c < 1/7 < 1/5
4. 1/7 < c < 1/5
5. 1/7 ≤ c ≤ 1/5
e. p is not greater than -6
1. p ≤ -6
2. p < -6
3. p ≥ -6
4. p > -6
5. p = -6
f. The negative of m is not less than -2
1. m ≤ -2
2. m < 2
3. -m < -2
4. m < -2
5. -m ≥ -2
Answer:d. The inequality that represents "c is between 1/7 and 1/5" is:
1/7 ≤ c ≤ 1/5
e. The inequality that represents "p is not greater than -6" is:
p ≤ -6
f. The inequality that represents "the negative of m is not less than -2" is:
-m ≥ -2
Note that we need to flip the inequality when we multiply or divide both sides by a negative number, which is the case in part (f).
Step-by-step explanation: