The probability of number of times we draw a card is 3.
The probability of drawing a heart or a face card on any given draw.
There are 16 such cards in the deck (4 kings, 4 queens, 4 jacks, and 4 hearts), out of a total of 52 cards. So the probability of drawing a heart or a face card on any given draw is 16/52, which simplifies to 4/13.
Now, to calculate the expected number of draws until we get a heart or a face card, we can use the formula:
Expected number of draws = 1/P(event)
where P(event) is the probability of the event happening. In this case, the event is drawing a heart or a face card, so:
Expected number of draws = 1 / (4/13) = 13/4 = 3.25
So on average, we would expect to draw a card 3.25 times before getting a heart or a face card. However, since we cannot draw a fraction of a card, the actual number of draws will either be 3 or 4.
Hence, the expected number of times we draw a card is 3 (or 4, if the last card drawn is not a heart or a face card).
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can someone help me with this please asap? thank you so much
Answer:
[tex]\\\cos B =\dfrac{8\sqrt{79}}{79}[/tex]
Step-by-step explanation:
How do we find cosine of an angle in a right triangle?
In a right-angled triangle, if one of the angles is θ, then the cosine of θ is the length of the side adjacent to θ, divided by the length of the hypotenuse .
Here we are trying to find cos B
The side adjacent to B is BC with a length of [tex]8[/tex]
The hypotenuse is BD with a length of [tex]\sqrt{79}[/tex]
[tex]\therefore\\\cos B = \dfrac{8}{\sqrt{79}}\\[/tex]
[tex]79[/tex] is a prime number so it cannot be factored
To express in simplest radical form, we have to remove [tex]\sqrt{79}[/tex] from the denominator by multiplying the numerator and denominator by [tex]\sqrt{79}[/tex]
[tex]\therefore\\\cos B = \dfrac{8}{\sqrt{79}} \times \dfrac{\sqrt{79}}{\sqrt{79}} \\\\= \dfrac{8\sqrt{79}}{79}[/tex]
Rory works a different number of hours each week. To cover his rent, bills and food costs he needs to a mean average of £268 per week. Week 1 £307. 50, Week 2 £235. 75, Week 3 £287. Rory this he has earned 10% more than the average over the last 4 weeks. Is he correct?
Since his total earnings are £1072, which is greater than £294.80, we can conclude that Rory's claim is correct.
To see if Rory's assertion is correct, we must compute the mean average of his wages for the last four weeks.
By adding up the earnings for each week, the total earnings over the last four weeks may be calculated:
Total earnings = £307.50 + £235.75 + £287 + x (week 4 earnings)
We know that Rory's wages over the last four weeks should have averaged £268, thus we can solve the following equation:
(£307.50 + £235.75 + £287 + x) / 4 = £268
Simplifying this equation, we get:
£830.25 + x = £1072
x = £1072 - £830.25
x = £241.75
As a result, Rory's earnings for week 4 should be £241.75, for a total of £268 for the last four weeks.
Rory now claims to have earned 10% more than the average over the last four weeks. The average wages over the last four weeks are £268, so 10% extra would be:
£268 + 10% of £268 = £268 + £26.80 = £294.80
Rory's earnings for the last four weeks are as follows: £307.50 + £235.75 + £287 + £241.75 = £1072
To see if he made 10% more than the average, we can take 10% of the average and multiply it by the average to get the expected value:
£268 + 10% of £268 = £268 + £26.80 = £294.80
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Please help me with this homework
Answer:
A = 4 cm^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 ( 4) (2)
A = 4 cm^2
Answer:
[tex]4 {cm}^{2} [/tex]
Step-by-step explanation:
Formula for the area of a triangle= 1/2*base*height
[tex] \frac{1}{2} \times 4 \times 2 \\ = 4[/tex]
[tex]therefore \: the \: area \: = 4 {cm}^{2} [/tex]
Find the area of the shaded region.
Answer:
13 units²
Step-by-step explanation:
Find the area of the shaded region.Area = L x W
Area = 3 1/4 x 4 (3 1/4 = 3.25)
Area = 3.25 x 4
Area = 13
or
Area = L x W
Area = 3 1/4 x 4
Area = 13
you train a ridge regression model, you get a r^2 of 1 on your training data and you get a r^2 of 0 on your validation data; what should you do?
In case of different values of cofficient of determination, r² during training and validation represents our regression model is overfitting, so increase the parameter alpha. So, option(a) is right.
The regression model using the normal L₁ technique is called Lasso Regression, and the model using L2 is called Ridge. Ridge regression reduces all regression coefficients to zero. We have a ridge regression training model, during data training, regression coefficient R² = 1
during data validation, regression coefficient R² = 0
R-squared is a suitable measure for linear regression models. This analysis shows the percentage of variance in the variable that the independent variables explain together. Here, R² = 1, shows model is good to fit but R² = 0, shows model is not fit to good. If the R²(test) ≪R²(training), then it indicates that your model does not generalize well. Then we can say model is overfitting state. So, option (b) represents right step to do.
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Complete question:
you train a ridge regression model, you get a R^2 of 1 on your training data and you get a R^2 of 0 on your validation data; what should you do?
a) Your model is underfitting, so increase the parameter alpha.
b) Your model is overfitting, so increase the parameter alpha
c) Your model is under fitting; so perform a polynomial transform
d) Nothing, your model performs flawlessly on your validation data
Juan weighs 185 pounds. Water makes up 68% of his body weight. How much does the water in his body weight
The requried water in Juan's body weight is 57.13 kilograms or 117.13 pounds
To find out how much water is in Juan's body weight, we need to multiply his body weight by the percentage of his weight that is water:
Water weight = Body weight × Percentage of body weight that is water
First, we need to convert Juan's weight from pounds to a more convenient unit for the calculation, such as kilograms:
185 pounds = 84.09 kilograms
Now we can calculate the water weight:
Water weight = 84.09 kg x 68/100 = 57.13 kg
Therefore, the water in Juan's body weight is 57.13 kilograms or 117.13 pounds
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Divide. Write your answer in simplest terms. 2/5 / 7/8
Answer:
The answer to your problem is, [tex]\frac{16}{35}[/tex]
Step-by-step explanation:
= [tex]\frac{2}{5} / \frac{8}{7}[/tex]
= [tex]\frac{2*8}{5*7}[/tex]
= [tex]\frac{16}{35}[/tex]
Thus the answer to your problem is, [tex]\frac{16}{35}[/tex]
Hope this is as simple you can get.
a telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the south and the northeast. the representative's belief is based on the results of a survey. the survey included a random sample of 620 southern residents and 720 northeastern residents. 35% of the southern residents and 50% of the northeastern residents reported that they were completely satisfied with their local telephone service. find the 98% confidence interval for the difference in two proportions.
For a sample of two proportions, the 98% confidence interval for the difference in two proportions is equals to ( 0.087, 0.211).
We have a random sample of customers completely satisfied with their local telephone service. Number of southern residents in sample, [tex] n_1[/tex] = 620
Number of northeastern residents in sample, [tex] n_2[/tex] = 720
The first proportion of southern residents who are completely satisfied with their local telephone service, [tex] \hat p_1[/tex] = 35% = 0.35
The second proportion of northeastern residents who are completely satisfied with their local telephone service , [tex] \hat p_2[/tex]= 50% = 0.50
We have to determine the 98% confidence interval for the difference in two proportions.
Confidence level = 98%
Level of significance = 1 - 0.98 = 0.02 or a/2 = 0.01
Now, using the distribution table value of z-score for 98% or 0.01 confidence level is equals 2.326. The confidence interval formula, [tex]CI = ( \hat p_1 - \hat p_2) ± z^* \sqrt{ \frac{\hat p_1( 1 - \hat p_1)}{n_1} + \frac{ \hat p_2( 1 - \hat p_2)}{n_2}} \\ [/tex]
Substitute all known values in above formula, [tex]CI = ( 0.35 - 0.50 ) ± (2.326)\sqrt{ \frac{0.35( 1 - 0.35)}{620} + \frac{0.50( 1 - 0.50)}{720}} \\[/tex]
[tex] = ( -0.15) ± (2.326)\sqrt{ \frac{0.35( 0.65)}{620} + \frac{0.50( 10.50)}{720}} \\ [/tex]
[tex]= ( -0.15) ± 2.326×0.027 \\ [/tex]
= ( 0.087, 0.211)
Hence, required value is ( 0.087, 0.211).
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a couple plans to have children until they have a girl. suppose that they set no limit on the number of children. each child has probability 0.49 of being a girl and 0.51 of being a boy. simulate 25 repetitions, using table a of random digits, starting at line 101. what is your estimate of the expected number of children?
The estimate of the expected number of children is 2.88.
To pretend the process of having children until the couple has a girl, we can use the following algorithm:
Start with an empty list of children.
Repeat the following until a girl is born:
1. Firstly create an arbitrary digit from Table A.
2. Then if the digit is 0, 1, 2, 3, 4, or 5, then add a girl to the list of children.
3. Now, if the digit is 6, 7, 8, or 9, add a boy to the list of children.
After this count total number of children present.
We can repeat this process 25 times using Table A, starting at line 101, and record the number of children in each simulation. Then we can calculate the average number of children as our estimate of the expected number of children.
They are the results of 25 simulations:
9, 3, 3, 7, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1
The average number of children in these simulations is:
(9 + 3 + 3 + 7 + 1 + 1 + 1 + 3 + 3 + 3 + 3 + 3 + 3 + 5 + 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 5 + 1) / 25
= 2.88
thus, our estimate of the anticipated number of children until the couple has a girl is roughly 2.88.
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How many real and imaginary zeros does f(x) = 3x^5 - 12x^4 + 20x³ - 180x² + 120x+81
Answer:
Step-by-step explanation:
To find the number of real zeros of a polynomial, we can use Descartes' rule of signs. According to this rule, the number of positive real zeros of a polynomial is equal to the number of sign changes in the coefficients of the polynomial, or is less than that by a multiple of 2. Similarly, the number of negative real zeros is equal to the number of sign changes in the coefficients of f(-x), or is less than that by a multiple of 2.
For f(x) = 3x^5 - 12x^4 + 20x³ - 180x² + 120x+81, there are 2 sign changes in the coefficients, so the number of positive real zeros is either 2 or 0. To find the number of negative real zeros, we can substitute -x for x in f(x) and simplify:
f(-x) = 3(-x)^5 - 12(-x)^4 + 20(-x)³ - 180(-x)² + 120(-x)+81
= -3x^5 - 12x^4 - 20x³ - 180x² - 120x + 81
There are 3 sign changes in the coefficients of f(-x), so the number of negative real zeros is either 3 or 1. Therefore, f(x) has either 2 or 0 positive real zeros, and either 3 or 1 negative real zeros.
To find the number of imaginary zeros, we can use the complex conjugate root theorem, which states that if a polynomial with real coefficients has a+bi as a root (where a and b are real numbers and i is the imaginary unit), then its conjugate a-bi is also a root. Since the coefficients of f(x) are all real, any non-real roots must occur in conjugate pairs.
Since f(x) has degree 5, it has 5 complex roots (counting multiplicities). If all the real zeros are distinct, then there are 5 distinct complex roots, and hence 5 imaginary zeros (again, counting multiplicities). If there are any repeated real zeros, then there are fewer than 5 distinct complex roots, and hence fewer than 5 imaginary zeros.
In summary, the number of real zeros of f(x) is either 2 or 0 positive zeros and either 3 or 1 negative zeros. The number of imaginary zeros is at most 5 (counting multiplicities).
Graph the image of J(7, 8) after a translation 9 units left.
The image of the translated point is A' ( -2 , 8 )
Given data ,
To perform a translation of 9 units left, we need to subtract 9 from the x-coordinate of the point J(7, 8):
New x-coordinate = 7 - 9 = -2
y-coordinate remains the same: y = 8
So the image of J(7, 8) after a translation 9 units left is the point (-2, 8).
To graph this, we start by plotting the original point J(7, 8) on the coordinate plane:
Hence , the translated point is A' ( -2 , 8 )
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The answer is 68°, but I need to know the steps..
Solve for x.
The measure of the angle ∠SQR is 34°. Then the measure of arc RQ will be 68°.
Given that:
arcYQ = 80°
∠RQY = 106°
The central angle is double the angle at the periphery that was subtended by the same chords.
∠RQY + ∠RSY = 180°
106° + ∠RSY = 180°
∠RSY = 74°
∠QSY = 1/2 arc QT
∠QSY = 1/2 x 80°
∠QSY = 40°
∠SQR + ∠QSY = ∠RSY
∠SQR + 40° = 74°
∠SQR = 34°
arc RQ = 2 x ∠SQR
arc RQ = 2 x 34°
arc RQ = 68°
The measure of the angle ∠SQR is 34°. Then the measure of arc RQ will be 68°.
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Ms. Leverenz is doing an art project with her class. She has a 3 foot piece of ribbon. If she gives each student an eighth of a foot of ribbon, will she have enough for her class of 22 students? I need help asap
Answer: she will have enough for 22 students.
Step-by-step explanation:
How many ribbons can she give out if she gives each student 1/8th of a foot of ribbon?
3 divided by 1/8 = 24
She can give out 24 ribbons.
24>22.
So, she will have enough for 22 students.
the mean of a normal probability distribution is 320; the standard deviation is 18. a. about 68% of the observations lie between what two values?
Approximately 68% of the observations fall between the values 302 and 338 where the mean of a normal probability distribution is 320; the standard deviation is 18.
For a standard probability distribution with mean μ and standard deviation σ, about 68% of the observations lie within one standard deviation of the mean, between μ - σ and μ + σ.
In this case, the mean is 320 and the standard deviation is 18. therefore,
μ - σ = 320 - 18 = 302
μ + σ = 320 + 18 = 338
Therefore, approximately 68% of the observations fall between the values 302 and 338.
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The goalpost on a football field is 12.5 feet tall. At the same time, Coach Collins, who is 6 feet tall, casts a shadow that is 14.4 feet long. What is the length of the shadow of the goalpost?
The length of the shadow of the goalpost is 30 feet long
What is proportion?Proportion can be described as an equation in which there are two different ratios that are set equal to each other.
From the information given, we have that;
The goalpost is 12. 5 feet tall
The Coach is 6 feet tall
The coach casts a shadow that is 14. 4 feet lone.
Then,
if 6 feet = 14. 4 long
Then, 12. 5 feet = x
cross multiply the values
x = 180/6
Divide the values
x = 30 feet long
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the dot plot below represents how long it takes students in a 7th grade math class to get to school every morning. commute time commute time minutes what was the mean commute time? minutes
For a Dot plot of time taken in math class by students in a 7th grade, the mean commute time is equal to the 23.75 minutes.
Mean is a statistical measures. It is calculated by the addition of all data values divided by number of data values. It is denoted by [tex]\bar X[/tex].
That is [tex]\bar X = \frac{ \sum X_i}{ n}[/tex], where
Xᵢ --> different data valuesn --> total number of valuesWe have a Dot plot which represents time it takes students in a 7th grade math class to get to school every morning. We have to determine mean of compete time in minutes. See the above figure carefully, and concluded the value,
Time students
5 4
10 0
15 4
20 4
25 2
30 2
35 5
40 2
45 1
Using above mean formula, [tex]\bar X = \frac{ (4×5+ 0 ×10+ 15×4 + 20×4 + 25×2 + 30×2 + 35×5 + 40×2 + 45× 1)}{24}[/tex]
= 23.75
Hence, mean value is 23.75 minutes.
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Complete question:
The above figure complete the question
the dot plot below represents how long it takes students in a 7th grade math class to get to school every morning. commute time commute time minutes what was the mean commute time? minutes
Question 2 of 10
The graph of F(x), shown below, has the same shape as the graph of
G)-2. Which of the following is the equation of F(X)?
OA. F(X)=4-22
B. F(x)=-4
C. F(X)=x²+4
D. F(X)=22²
FM)=7
The required equation of the graph is f(x) = x²- 4. Option B is correct.
Given information,
The graph of F(x), shown, has the same shape as the graph of g(x) = x².
In the graph, it can be seen clearly that the graph is obtained by the trasformation of the graph g(x) by 4 units down. So the equation of the graph shown is given as:
f(x) = g(x) - 4
f(x) = x²- 4
Thus, the required equation of the graph is f(x) = x²- 4. Option B is correct.
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.
when constructing a table with metric variables, you should absolutely include the average(s). true false
It is true that when constructing a table with metric variables, you should absolutely include the average(s).
When constructing a table with metric variables, it is important to include the measures of central tendency such as the mean, median, and mode. The average or mean is particularly important as it provides a summary measure of the data set and is often used as a benchmark for comparison with other values. By including the average, the table can convey information about the typical or expected value of the metric variable.
The mean, or average, is a commonly used measure of central tendency. It is calculated by summing all of the values in the data set and dividing by the number of observations. The mean is useful because it is sensitive to all of the values in the data set and provides a benchmark for comparison with other values.
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HELP GEOMETRY SHOW WORK WILL GIVE BRAINLIEST!!!!!
The surface area of the pyramid is determined as 435.60 mm².
What is the surface area of the pyramid?The surface area of the pyramid with pentagon base is calculated as follows;
S.A = 5/2 b(a + s)
where;
b is the base of the pyramids is the slant heighta is the apothemThe slant height is calculated as follows;
l = √(15.4² + 7.2²)
l = 17 mm
The surface area of the pyramid is calculated as follows;
S.A = 5/2 x 7.2 (7.2 + 17)
S.A = 435.60 mm²
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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 29 liters
per minute. There are 300 liters in the pond to start.
Let W represent the total amount of water in the pond (in liters), and let 7 represent the total number of
minutes that water has been added. Write an equation relating W to T. Then use this equation to find the
total amount of water after 11 minutes.
so after solving, Hence, after 11 minutes, there are 619 litres of water in equation the pond overall.
What is equation?A assertion that charged objects are equal is known as an equation. Normally, two expressions are connected by the equality symbol (=). A mathematical tool for representing relationships between a number of variables or quantities is an equation. By identifying particular asset(s) of the indeterminate factors that make the equation true, equation may be utilized to solve issues. Many aspects of daily life as well as numerous fields of science, engineering, maths, or other disciplines use equations.
This question is similar to the pipe and cistern problem. The amount of water in the pond (W) after T minutes can be represented by the following equation:
W = 29T + 300
where 29T represents the amount of water added in T minutes and 300 represents the initial amount of water in the pond.
We may simplify the equation by adding T = 11 and finding the total volume of water in the pond after 11 minutes:
W = 29(11) + 300
W = 319 + 300
W = 619
Hence, after 11 minutes, there are 619 litres of water in the pond overall.
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The total amount of water in the pond after 11 minutes of adding water at a rate of 29 liters per minute is 619 liters.
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b.
The equation that relates W (total amount of water in the pond) to T (time in minutes) is:
W = 29T + 300
where 29T represents the amount of water added in T minutes (at a rate of 29 liters per minute) and 300 represents the initial amount of water in the pond.
To find the total amount of water after 11 minutes, we substitute T = 11 into the equation:
W = 29(11) + 300
W = 319 + 300
W = 619
Therefore, the total amount of water in the pond after 11 minutes of adding water at a rate of 29 liters per minute is 619 liters.
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Determine the different possibilities for the number of positive negative and non-real complex zeros for the following function.
Using Descartes rule of signs, the number of negative zeros is 2, the number of positive zeros is 2 and the number of complex zeros is 3
What is the different possibilities for the numbers of positive, negative and normal complex zeros for the following function?To determine the different possibilities for the numbers of positive, negative and normal complex zeros in the given function;
f(x) = x⁵ + 3x⁴ - x³ + 3x + 7
Using Descartes rule of signs, we can find the positive, negative and normal complex zeros;
f(x) has two or 0 positive real zero
Let's find f(-x)
f(-x) = (-x)⁵ + 3(-x)⁴ - 3(-x) + 7
f(-x) = -x⁵ + 3x⁴ + 3x + 7
This shows that f(x) has 2 or 0 negative real zeros
Let's subtract the number of real zeros from degree of f(x) to determine the complex zeros
complex zeros = 5 - 2 = 3
This shows we have 2 positive zeros, 2 negative zeros and 3 complex zeros
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Nicole has a standard deck of 52 cards. A standard deck has 4 suits: 13 red hearts, 13 red diamonds, 13 black clubs, and 13 black spades. Each suit has the numbers 2-10, Ace, Jack, Queen, and King. She is going to pull out one card, replace it, then pull another card again. Find the probability she pulls a spade, then pulls a red queen.
Without using a calculator, order the following expressions from least to greatest.
The ascending order of the expressions are π/3 , √8/3 , √4/2
Given data ,
Let the expression be represented as A
Now , the value of A is
A = π/3 , √8/3 , √4/2
On simplifying , we get
Now , π > √8
So , the value of π/3 is greater than √8/4 since they have the same denominator
And , the value of √4/2 = 1
Hence , the ascending order is √4/2 , √8/3 , π/3
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659,470. 53 Is the 100%, if you have only 321,034. 21 of it, whats the percentage?
Answer:48.6805998746%, you can round this.
Step-by-step explanation:
In order to solve this, you need to divide the smaller number by the larger number, creating a fraction. This will give you a decimal number. In order to get the percent, you need to take the decimal, and move the decimal point 2 digits TO THE RIGHT. This will give you 48.6805998746%.
To check this, you can use the answer, and use a calculator such as desmos to calculate 48.6805998746% of 659470.53
This provides you with 321034.21, which means that this is the correct percent. You can round this to get something like 48.7%
pls pls help if you get it right ill mark you brainilest
Answer:
triangle is it
Step-by-step explanation:
C goes to C'
(5,-6) goes to (-6,-5) this is a 90 degree rotation clockwise
( x, y) changed to (y,-x) <====== clockwise rotation 90 degrees
Please help!!!
The lengths of three metal rods, A, B and C, are such that length of A : length of B = 3 : 2 and
length of A : length of C = 2 : 5
The difference in length between the longest rod and the shortest rod is 55 cm. Find the total length of the three rod in metres,
The lengths of the three rods are given as follows:
Rod A: 30 cm.Rod B: 20 cm.Rod C: 75 cm.How to obtain the lengths of the rods?The lengths of the rods are obtained applying the proportions in the context of the problem.
The ratio of A to B is:
A/B = 3/2.
Hence:
A = 3B/2.B = 2A/3, thus A > B.The ratio of A to C is:
A/C = 2/5.
Hence:
A = 2C/5.C = 5A/2 -> C > A.Thus the order, from least to greatest, is:
B, A, C.
The difference in length between the longest rod and the shortest rod is 55 cm, hence the length of rod A is obtained as follows:
C - B = 55
2.5A - 0.6666A = 55
A = 55/(2.5 - 0.6666)
A = 30 cm.
Then the lengths of B and C are given as follows:
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A tennis racquet is on sale for 20% off. The sale price of the tennis racquet is ($60)
What is the original price of the tennis racquet?
A $20
B $40
C $65
D $75
multiple polynomials to find area
Stephanie borrowed $35,000 on August 6 with an interest due on December 14. If the interest rate is 6%, find the interest on the loan using exact interest and ordinary interest. What is the difference between the 2 interest amounts?
a. $8.24
b. $11.24
c. $9.86
d. $10.38
a) The interest on the loan using exact interest and ordinary interest is as follows:
Exact Interest = $747.95Ordinary Interest = $758.33.b) The difference between exact interest and ordinary interest amounts is d. $10.38.
What is the difference between exact interest and ordinary interest?Exact Interest is interest based on a period of 365 days.
Ordinary interest is interest based on a period of 360 days.
Loan amount = $35,000
Loan period = August 6 to December 14 (130 days)
Interest rate = 6%
Exact Interest:Interest = $35,000 x 6% x 130/365
= $747.95
Ordinary Interest:Interest = $35,000 x 6% x 130/360
= $758.33
Difference = $10.38 ($758.33 - $747.95)
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In order to earn money in her new studio, Monica uses her knowledge, experience and expertise to set up a recording studio where she rents studio space to new clients and charges by the hour. She charges her clients
$
50
for each hour of time in the studio and pays
$
2
,
500
per month for her overhead costs to run the studio.
The profit earned by Monica per month for the overhead cost of $2,500 is equal to $3,700.
Amount charged by Monica for each hour of time in the studio = $50
Amount paid by Monica per month for her overhead costs to run the studio = $2500
Monica's revenue for the month,
= Multiply the number of hours each client spends in the studio by the hourly rate she charges.
Substitute the values for each client we have,
Client A,
28 hours x $50/hour = $1,400
Client B,
16 hours x $50/hour = $800
Client C,
20 hours x $50/hour = $1,000
Client D,
36 hours x $50/hour = $1,800
Client E,
24 hours x $50/hour = $1,200
Total revenue for the month
= $(1400 + 800 + 1,000 + 1,800 + 1,200 )
= $6,200
Monica's profit for the month
= subtract her overhead costs from her revenue.
This implies,
Profit = Revenue - Overhead Costs
⇒Profit = $6,200 - $2,500
⇒Profit = $3,700
Therefore, Monica's profit for the month is $3,700.
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The above question is incomplete, the complete question is:
In order to earn money in her new studio, Monica uses her knowledge, experience and expertise to set up a recording studio where she rents studio space to new clients and charges by the hour. She charges her clients $50 for each hour of time in the studio and pays $2,500 per month for her overhead costs to run the studio.
Clients Hours per month in studio
A 28 hours in studio
B 16 hours in studio
C 20 hours in studio
D 36 hours in studio
E 24 hours in studio
