a) To find y for the given x and Δx values, first calculate x + Δx:
x + Δx = 3 + 0.03 = 3.03
Now, use the function y = f(x) = 9x to find the y values:
y = 9(3) = 27 (for x = 3)
y = 9(3.03) = 27.27 (for x = 3.03)
b) To find dy, we first need to find the derivative of the function (f'(x)). The function is y = f(x) = 9x, and its derivative (using differentiation) is:
f'(x) = 9
c) To find dy for the given x and Δx values, we can now use the formula dy = f'(x)dx:
dy = f'(x)dx = 9(0.03) = 0.27
So, for the given x and Δx values, a) y is 27 and 27.27, b) dy is equal to 9, and c) dy for the given x and Δx values is 0.27.
The charge for a mission to the zoo is $3.25 for each adult and $1.50 for each student. on a day when 400 people paid to visit the zoo, the receipts totaled 1,237. find the number of adult tickets purchased that day
The number of adult tickets purchased that day was 36 if the charge is $3.25 for each adult and $1.50 for each student and 400 people paid $1237
Let the number of adults be x
the number of students be y
Total people = 400
x + y = 400
Total receipts = $1,237
Cost of an adult ticket = $3.25
Cost of a student ticket = $1.50
Cost of x adults tickets = 3.25x
Cost of y student tickets = 1.50y
3.25x + 1.50y = 1237
Multiply the first equation by 1.50
1.50x + 1.50y = 600
Subtract the second and above equation
1.75x = 637
x = 364
364 + y = 400
y = 36
Thus, the number of adult tickets purchased is 36.
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(4,7);y=3x+6
Write an equation passing through the point and parallel to the given line.
The Equation of the line which is parallel to the line "y = 3x + 6", and also passes through (4,7) is "y = 3x - 5".
In order to find an equation of a line which passes through point (4,7) and is parallel to line "y = 3x + 6", we use the fact that parallel lines have the same slope.
The given line ""y = 3x + 6" has a slope of 3,
So, the "parallel-line" we want to find must also have a slope of 3.
Now, by using the "point-slope" form of the equation of a line, which is : y - y₁ = m(x - x₁),
where m is slope and (x₁, y₁) is a point on the line,
So, we substitute "m = 3" and (x₁, y₁) = (4,7) to get:
⇒ y - 7 = 3(x - 4),
⇒ y - 7 = 3x - 12,
⇒ y = 3x - 5
Therefore, the equation of the required line is y = 3x - 5.
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Help with problem in photo
The measures of the arc angle AP is 63° using the Angles of Intersecting Chords Theorem
What is the Angles of Intersecting Chords Theorem
The Angles of Intersecting Chords Theorem states that the angle formed by the intersection of the chords is equal to half the sum of the intercepted arcs, and conversely, that the measure of an intercepted arc is half the sum of the two angles that intercept it.
109° = (AP + RQ)/2
109 = (AP + 155)/2
AP + 155 = 2 × 109 {cross multiplication}
AP + 155 = 218
AP = 218 - 155 {collect like terms}
AP = 63°
Therefore, the measures of the arc angle AP is 63° using the Angles of Intersecting Chords Theorem
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Will give brainliest!
given that the slope of the consecutive sides is -2/3 and 3/2
can you prove that it is a parallelogram or a rectangle.
explain your answer.
A figure with slope of consecutive sides -2/3 and 3/2 is a rectangle and it is not a parallelogram.
To prove that it is a parallelogram or a rectangle, we need to show that the opposite sides are parallel and the adjacent sides are perpendicular.
Let's first check if the opposite sides are parallel. The slope of one side is -2/3, and the slope of the adjacent side is 3/2. For opposite sides to be parallel, the slopes must be equal. However, -2/3 and 3/2 are not equal, so we can conclude that the given figure is not a parallelogram.
Now, let's check if the adjacent sides are perpendicular. The product of the slopes of the adjacent sides is
(-2/3) x (3/2) = -1, which is the slope of a line perpendicular to both sides. Since the product of the slopes is -1, we can conclude that the adjacent sides are perpendicular.
Therefore, figure is not a parallelogram, but it is a rectangle.
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Lesley needs to spend at least $15 at the grocery store to use a coupon. She buys 1 container of tomatoes and needs to buy some potatoes. One container of tomatoes costs $2. 75 and one pound of potatoes costs $2. 45. How may pounds of potatoes, p, does Lesley need to buy to use the coupon? write your answer using an inequality symbol
Answer: 5
2.75+(2.45x5) = 15
What is the missing value of G if G is two and one-half times smaller than 19. 02 cm? A. 7. 608 cm B. 7. 808 cm C. 8. 608 cm D. 9. 51 cm
Therefore, the missing value of G is 7.608 cm, which is option A.
What is the missing value of G?If G is two and one-half times smaller than 19.02 cm, we can find the value of G by multiplying 19.02 cm by 2/5, since two and one-half is equal to five halves, or 2/5 when expressed as a fraction.
G = (2/5) x 19.02 cm
Simplifying this expression:
G = 7.608 cm
Therefore, the missing value of G is 7.608 cm, which is option A.
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Graph the equation shown below by transforming the given graph of the parent function. 2^3x
The graph of the exponential function [tex]y = 2^{3x}[/tex] is given as follows:
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function in this problem is given as follows:
[tex]y = 2^{3x}[/tex]
Hence the parameter values are:
a = 1, hence when x = 0, y = 1.b = 2, hence when x increases by 1/3, y is multiplied by 2 -> increases by 1/3 due to the horizontal compression with the multiplication by 3 in the domain.More can be learned about exponential functions at brainly.com/question/2456547
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Given two events E and F with Pr(E) = 0. 4, Pr(F) = 0. 5, and Pr(EnF) = 0. 3, a) Pr(E|F) = b) Pr(F|E) = c) Are E and F independent? (Enter YES or NO)
Given two events E and F with Pr(E) = 0. 4, Pr(F) = 0. 5, and Pr(EnF) = 0. 3 then:
a) Pr(E|F) = 0.6
b) Pr(F|E) = 0.75
c) NO, E and F are not independent.
a) To find Pr(E|F), we use the formula: Pr(E|F) = Pr(EnF)/Pr(F). Substituting the given values, we get Pr(E|F) = 0.3/0.5 = 0.6.
b) Similarly, to find Pr(F|E), we use the formula: Pr(F|E) = Pr(EnF)/Pr(E). Substituting the given values, we get Pr(F|E) = 0.3/0.4 = 0.75.
c) We can check for independence by seeing if Pr(E) = Pr(E|F) or Pr(F) = Pr(F|E). However, since Pr(E) ≠ Pr(E|F) and Pr(F) ≠ Pr(F|E), we can conclude that E and F are not independent.
In other words, the occurrence of one event affects the probability of the other event occurring. Specifically, the fact that Pr(EnF) ≠ Pr(E)Pr(F) indicates that the events are dependent.
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69x 10x 6969x 8008x696969696969
BRAIN-COMPATIBLE
Directions: Arrange the sentences in the box to form a problem. Then solve each problem.
Write your answer in your activity notebook.
1. If she leaves home at 6:00 in the morning
What time will she arrive?
Zaira goes to her grandmother's house
She cycles 30 km at a steady speed of 10 km
Problem
Solution
2. I had an average speed of 55 kph for 2 hours in the afternoon
What was the total distance covered by the bus
A bus had an average speed of 65 kph for 1. 5 hours in the morning.
Problem:
Solution:
3 What was the average speed of the train?
The distance between the two stations is 14 km
A train left Station X at 9:00 a. M. And arrived station Y ay 9:30 a. M.
The correct arrangement of problem is explained below and their solution are as follows:
(1) Zaira will arrive at her grandmother's house at 9:00 am.
(2) The total distance covered by bus is 207.5 km.
(3) The average-speed of the train was 28 km/h.
Part (1) : The Problem is : Zaira goes to her grandmother's house. If she leaves home at 6:00 in the morning, she cycles 30 km at a steady speed of 10 km. What time will she arrive?
Solution:
Zaira cycles at a steady speed of 10 km, she will cover the distance of 30 km in 30/10 = 3 hours.
So, she will arrive at her grandmother's house at 6:00 + 3:00 = 9:00 am.
Part (2) : Problem : A bus had an average speed of 65 kph for 1.5 hours in the morning. It had average speed of 55 kph for 2 hours in afternoon. What was total distance covered by bus?
Solution:
The distance covered by the bus in the morning can be calculated as:
Distance = Speed × Time = 65 kph × 1.5 hours = 97.5 km,
The distance covered in the afternoon can be calculated as:
Distance = Speed × Time = 55 kph × 2 hours = 110 km
So, total-distance covered by bus is = 97.5 km + 110 km = 207.5 km.
Part (3) : Problem : A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m. The distance between the two stations is 14 km. What was average speed of train?
Solution:
The time taken by the train to cover the distance of 14 km can be calculated as:
Time = Arrival Time - Departure Time = 9:30 am - 9:00 am = 0.5 hours
The average speed of the train = Distance/Time = 14 km/0.5 hours = 28 km/h;
Therefore, the average speed of the train was 28 km/h.
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The given question is incomplete, the complete question is
Directions: Arrange the sentences in the box to form a problem. Then solve each problem.
(1) If she leaves home at 6:00 in the morning
What time will she arrive?
Zaira goes to her grandmother's house
She cycles 30 km at a steady speed of 10 km
(2) I had an average speed of 55 kph for 2 hours in the afternoon
What was the total distance covered by the bus
A bus had an average speed of 65 kph for 1. 5 hours in the morning.
(3) What was the average speed of the train?
The distance between the two stations is 14 km
A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m.
Edro, Lena, Harriet, and Yermin each plot a point to approximate StartRoot 0. 50 EndRoot.
Pedro A number line going from 0 to 0. 9 in increments of 0. 1. A point is between 0. 2 and 0. 3.
Lena A number line going from 0 to 0. 9 in increments of 0. 1. A point is between 0. 4 and 0. 5.
Harriet A number line going from 0 to 0. 9 in increments of 0. 1. A point is at 0. 5.
Yermin A number line going from 0 to 0. 9 in increments of 0. 1. A point is just to the right of 0. 7.
Whose point is the best approximation of StartRoot 0. 50 EndRoot?
Pedro
Lena
Harriet
Yermin
Yermin's point is the best approximation of the square root of 0.50.
To know whose point is the best approximation of the square root of 0.50 on a number line. We have the points plotted by Pedro, Lena, Harriet, and Yermin.
Step 1: Calculate the square root of 0.50.
[tex]\sqrt{0.50} = 0.707[/tex]
Step 2: Compare the plotted points to the calculated square root value.
Pedro: Between 0.2 and 0.3
Lena: Between 0.4 and 0.5
Harriet: At 0.5
Yermin: Just to the right of 0.7
Step 3: Determine the closest approximation.
Yermin's point (just to the right of 0.7) is the closest to the calculated value of 0.707.
Your answer: Yermin's point is the best approximation of the square root of 0.50.
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A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 19. 1 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 18. 1, 21. 1, 22. 1, 23. 1, 21. 1, 27. 1, and 27. 1 pounds. If α = 0. 200, what is the critical value? The population standard deviation is unknown
Since the population standard deviation is unknown, we use a t-distribution to find the critical value. The degrees of freedom for the t-distribution is n-1, where n is the sample size. In this case, n = 7, so the degrees of freedom is 7-1 = 6. The critical value for a t-distribution with 6 degrees of freedom and a significance level of α = 0.200 (two-tailed) can be found using a t-table or calculator. The critical value is approximately ±1.94.
Write an expression for the sequence of operations described below.
Subtract three from the product of seven and eight
Type x if you want to use a multiplication sign. Type / if you want to use a division sign. Do not simplify any part of the expression.
An expression for the sequence of operations described "Subtract three from the product of seven and eight." is (7 × 8) - 3.
How to evaluate and solve the given expression?In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical expression:
Expression: (7 × 8) - 3
56 - 3
53
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a research methods professor creates a computer tutor to help students understand confounding and obscuring variables. before the second exam in the class, volunteers are randomly assigned to either interact with the computer tutor on the materials or to play angry birds on the computer for an equivalent time (30 minutes). although the students in the tutor group do significantly better on the exam the following day, many of the practice questions from the tutor are exactly the same as those on the exam. what is the main threat to concluding that the tutor was effective?
The main threat to concluding that the tutor was effective in helping students understand confounding and obscuring variables is the issue of 'practice effects'.
Practice effects occur when exposure to specific materials or questions during a study can artificially inflate performance on subsequent measures, such as an exam.
In this case, if the practice questions from the tutor were exactly the same as those on the exam.
Then the students who interacted with the tutor may have had an advantage on the exam .
Due to familiarity with the questions rather than a true understanding of the material.
The use of the same practice questions in the tutor and on the exam .
It represents a potential confounding variable that could affect the interpretation of the results.
It is possible that the tutor may have been effective.
But it is also possible that the practice effect of the repeated questions contributed to the observed improvement in performance.
Future research could use different practice questions in the tutor and on the exam.
Use a different exam altogether to assess performance.
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Given that in an arithmetic series a8 = 1 and a30=-43, find the sum of terms 8 to 30.
The sum of terms 8 to 30 in the arithmetic series is -826.
In an arithmetic series, the nth term is given by the formula an = a1 + (n-1)d, where a1 is the first term and d is the common difference between terms.
We are given that a8 = 1 and a30 = -43. Using the formula above, we can write:
a8 = a1 + 7d = 1 (1)
a30 = a1 + 29d = -43 (2)
Subtracting equation (1) from equation (2), we get:
22d = -44
d = -2
Substituting d = -2 into equation (1) and solving for a1, we get:
a1 = 15
Now we can use the formula for the sum of an arithmetic series to find the sum of terms 8 to 30:
S = (n/2)(a1 + an)
S = (23/2)(15 + (-43))
S = -826
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Find the distance between
the points (4, -3) and (-2, 1)
on the coordinate plane.
Ay
O
X
Answer:no image
Step-by-step explanation:
Can someone please help me ASAP? It’s due tomorrow
Answer:
0.30.400.1Step-by-step explanation:
tried my best as the first two got me stuck
wouldn't recommend trying my answer and Id wait for another answer
Consider the concentration, C, (in mg/liter) of a drug in the blood as a function of the amount of drug given, x, and the time since injection, t For 0 <= x <= 5 and t >= 0 hours, we have C = f(x,t) = 26te^-(5-x) f (3,5) = _____
Using the given function, we can plug in x=3 and t=5 to find the concentration of the drug in the blood:
C = f(x,t) = 26te^-(5-x)
C = f(3,5) = 26(5)e^-(5-3)
C = f(3,5) = 130e^-2
Using a calculator, we can simplify this to:
C = f(3,5) ≈ 32.22 mg/liter
Therefore, the concentration of the drug in the blood 3 hours after injection with a dosage of 5 mg is approximately 32.22 mg/liter.
Hi! To find the concentration C at f(3,5), you'll need to plug in the values for x and t into the given function f(x,t) = 26te^-(5-x).
So, f(3,5) = 26(5)e^-(5-3) = 130e^(-2).
Now, calculate the exponential value: e^(-2) ≈ 0.1353.
Finally, multiply this value by 130: 130 * 0.1353 ≈ 17.589.
Thus, f(3,5) = 17.589 mg/liter (rounded to 3 decimal places).
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A rectangular living room measures 6 by 12 feet. At $36 per square yard, how much will it cost to carpet the room?
Answer:
It will cost $288 to carpet the living room at $36 per square yard.
Step-by-step explanation:
First, we need to convert the room dimensions to square yards, since the carpet price is given in square yards.
The area of the living room is:
[tex]\sf:\implies 6\: ft \times 12\: ft = 72\: ft^2[/tex]
To convert this to square yards, we divide by 9 (since there are 9 square feet in a square yard):
[tex]\sf:\implies \dfrac{72\: ft^2}{9} = 8\: yards^2[/tex]
So the living room is 8 square yards in area.
To find the cost of carpeting the room, we multiply the area by the cost per square yard:
[tex]\sf:\implies 8\: yards^2 \times \$36/square\: yard = \boxed{\bold{\:\:\$288\:\:}}\:\:\:\green{\checkmark}[/tex]
Therefore, it will cost $288 to carpet the living room at $36 per square yard.
A shoe store donated a percent of every sale to charity. The total sales were $7,200 so the store donated $144. What percent of $7,200 was donated to charity?
The percentage of $7,200 that was donated to charity would be = 2%
How to calculate the percentage of the total sales that was donated?To calculate the percentage of the total sales that was donated, the following should be carried out.
The total sales at the shoe store = $7,200
The amount of money that was donated = $144
Therefore to calculate the percentage the following is done ;
= 144/7200 × 100/1
= 14400/7200
= 2%
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Each year Wenford Hospital records how long patients wait to be treated in the Accident
and Emergency department.
In 2015 patients waited 11% less time than in 2014.
In 2015 the average time patients waited was 68 minutes.
(a) Work out the average time patients waited in 2014.
Give your answer to the nearest minute.
The average time patients waited in 2014 was approximately 76 minutes, calculated by dividing the 2015 waiting time by 0.89 as patients waited 11% less time in 2015.
Let's call the average time patients waited in 2014 as per Wenford Hospital records "x" (in minutes). According to the problem statement, patients waited 11% less time in 2015 compared to 2014, so,
0.89x = 68
Solving for x,
x = 68 / 0.89
x ≈ 76.4
Therefore, the average time patients waited in 2014 was approximately 76 minutes (rounded to the nearest minute).
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exercise 4.11. on the first 300 pages of a book, you notice that there are, on average, 6 typos per page. what is the probability that there will be at least 4 typos on page 301? state clearly the assumptions you are making.
The probability that there will be at least 4 typos on page 301 is 0.847
To solve this problem, we need to make some assumptions. Let's assume that the number of typos on each page follows a Poisson distribution with a mean of 6 typos per page, and that the number of typos on one page is independent of the number of typos on any other page.
Under these assumptions, we can use the Poisson distribution to calculate the probability of observing a certain number of typos on a given page.
Let X be the number of typos on page 301. Then X follows a Poisson distribution with a mean of 6 typos per page. The probability of observing at least 4 typos on page 301 can be calculated as follows
P(X ≥ 4) = 1 - P(X < 4)
= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
Using the Poisson distribution formula, we can calculate the probabilities of each of these events
P(X = k) = (e^-λ × λ^k) / k!
where λ = 6 and k is the number of typos. Thus,
P(X = 0) = (e^-6 × 6^0) / 0! = e^-6 ≈ 0.0025
P(X = 1) = (e^-6 × 6^1) / 1! = 6e^-6 ≈ 0.015
P(X = 2) = (e^-6 × 6^2) / 2! = 18e^-6 ≈ 0.045
P(X = 3) = (e^-6 × 6^3) / 3! = 36e^-6 ≈ 0.091
Plugging these values into the equation above, we get
P(X ≥ 4) = 1 - (e^-6 + 6e^-6 + 18e^-6 + 36e^-6)
≈ 0.847
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What is the explicit equation for the nth term of the arithmetic sequence 6.3, 3.6, 0.9, –1.8, –4.5, …? an = 6.3 – 2.7n an = 6.3 – 2.7(n – 1) an = 6.3 + 2.7n an = 6.3 + 2.7(n + 1)
The explicit equation for the nth term of the arithmetic sequence is an = 9 - 2.7n.
What is the implicit equation?
An implicit equation is an equation in which the variables are not explicitly expressed in terms of each other. In other words, the equation does not give a direct formula for one of the variables in terms of the other(s), but rather relates the variables through some function or equation.
What is the explicit equation?
An explicit equation is an equation in which one variable is expressed directly in terms of the other(s). In other words, the equation gives a formula for one of the variables in terms of the other(s).
According to the given information:
the first term of the sequence is a1 = 6.3, and the common difference between consecutive terms is d = -2.7 (since we subtract 2.7 from each term to get to the next term). Therefore, the explicit equation for the nth term of the sequence is:
an = 6.3 + (n - 1)(-2.7)
Simplifying this expression, we get:
an = 6.3 - 2.7n + 2.7
an = 9 - 2.7n
So the correct equation for the nth term of the arithmetic sequence 6.3, 3.6, 0.9, -1.8, -4.5, ... is:
an = 9 - 2.7n
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Suppose the length of voicemails (in
seconds) is normally distributed with a mean
of 40 seconds and standard deviation of 10
seconds. Find the probability that a given
voicemail is between 20 and 50 seconds.
10
20
30
40
50
60
P = Г?1%
Hint: Use the 68 - 95 - 99.7 rule
70
Enter
The probability that a given voicemail is between 20 and 50 seconds is 0.8185, or 81.85%.
How to find the the probability that a given voicemail is between 20 and 50 seconds.To find the probability that a voicemail is between 20 and 50 seconds, we need to standardize the values and use a standard normal distribution table.
First, we find the z-scores for 20 seconds and 50 seconds:
z1 = (20 - 40) / 10 = -2
z2 = (50 - 40) / 10 = 1
Using a standard normal distribution table, we can find the area to the left of each z-score:
Area to the left of z1 = 0.0228
Area to the left of z2 = 0.8413
To find the probability between 20 and 50 seconds, we subtract the area to the left of z1 from the area to the left of z2:
P(20 < x < 50) = P(-2 < z < 1)
= 0.8413 - 0.0228
= 0.8185
Therefore, the probability that a given voicemail is between 20 and 50 seconds is 0.8185, or 81.85%.
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Please help me with this math problem!! Will give brainliest!! It's due tonight and it's the last problem!!! :)
part a.
the percentage of eggs between 42 and 45mm is 48.48%
part b.
The median width is approximately (42+45)/2 = 43.5mm.
The median length is approximately (56+59)/2 = 57.5mm.
part c.
The width of grade A chicken eggs has a range of about 24mm.
part d.
I think its impossible to determine because we don't have the value for the standard deviation.
The second option should be correct.
What is a histogram?A histogram is described as an approximate representation of the distribution of numerical data.
part a.
From the histogram, we see that the frequency for the bin that ranges from 42 to 45mm is 4 and we have a total of 33 eggwe use this values and calculate the percentage of eggs between 42 and 45mm is 48.48%.
part b.
we have an estimation that the median of the width is 48mm and the median of the length is around 60mm.
part c.
Also from the histogram, we notice that the smallest value is around 36mm and the largest value is around 66mm, hence the width of grade A chicken eggs has a range of about 24mm.
In a histogram, the range is the width that the bars cover along the x-axis and these are approximate values because histograms display bin values rather than raw data values.
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Mohal is a waiter at a restaurant. Each day he works, Mohal will make a guaranteed wage of $25, however the additional amount that Mohal earns from tips depends on the number of tables he waits on that day. From past experience, Mohal noticed that he will get about $15 in tips for each table he waits on. How much would Mohal expect to earn in a day on which he waits on 16 tables? How much would Mohal expect to make in a day when waiting on
�
t tables?
Answer:
If Mohal waits on 16 tables, he can expect to earn $25 wages + ($15 tips x 16 tables) = $265 in a day.
If Mohal waits on 1 table, he can expect to earn $25 wages + ($15 tips x 1 table) = $40 in a day.
All the 4-digit numbers you could make using seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8
Using the seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8, we can make 1260 different 4-digit numbers.
To create a 4-digit number using these seven square tiles, we have to consider the following:
- The first digit cannot be 2 because then the number would only have three digits.
- We can choose any of the remaining six tiles for the first digit, which means there are 6 choices.
- We can choose any of the seven tiles for the second digit, which means there are 7 choices.
- We can choose any of the remaining six tiles for the third digit, which means there are 6 choices.
- We can choose any of the remaining five tiles for the fourth digit, which means there are 5 choices.
Therefore, the total number of 4-digit numbers we can make is:
6 x 7 x 6 x 5 = 1260
So, using the seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8, we can make 1260 different 4-digit numbers.
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1. In Circle O shown below, with a radius of 12 inches, a sector has been defined by two radii oB and o4 with a central angle of 60° as shown. Determine the area of shaded sector.
B
Step 1: Determine the area of the entire circle in terms of pi.
Step 2: Determine the portion (fraction) of the shaded sect in the circle by using the central angle value.
Step 3: Multiply the area of the circle with the portion (fraction) from step 2.
The area of the shaded sector of the given circle would be = 42,593.5 in²
How to calculate the area of a given sector?To calculate the area of the given sector the formula that should be used is given as follows;
The area of a sector =( ∅/2π) × πr²
where;
π = 3.14
r = 12 in
∅ = 60°
Area of the sector = (60/2×3.14)b × 3.14× 12×12
= 94.2× 452.16
= 42,593.5 in²
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Write a function to model the volume of a rectangular prism if the length is 26cm and the sum of the width and height is 32cm. what is the maximum possible volume of the prism?
To model the volume of a rectangular prism with length 26cm and width w and height h such that the sum of the width and height is 32cm, we can use the following function:
V(w, h) = 26wh
subject to the constraint:
w + h = 32
We can solve for one of the variables in the constraint equation and substitute it into the volume equation, giving us:
w + h = 32 => h = 32 - w
V(w) = 26w(32 - w) = 832w - 26w^2
To find the maximum possible volume, we can take the derivative of this function with respect to w and set it equal to zero
dv/dw= 832 - 52w = 0
Solving for w, we get:
w = 16
Substituting this value back into the constraint equation, we get:
h = 32 - w = 16
Therefore, the maximum possible volume of the prism is:
V(16, 16) = 26(16)(16) = 6656 cubic cm
So the function to model the volume of the rectangular prism is V(w) = 832w - 26w^2, and the maximum possible volume is 6656 cubic cm when the width and height are both 16cm.
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Question 3 Part C (3 points): Tami has two jobs and can work at most 20 hours each week. She works as a server and makes $6 per hour. She also tutors and makes $12 per hour. She needs to earn at least $150 a week. Review the included image and choose the graph that represents the system of linear inequalities.
The expression of linear inequalities that represents Tami's earnings is as follows: 6x + 12y ≥ 150.
What is linear inequality?A linear inequality is a mathematical expression that involves a linear function and a relational operator such as <, >, ≤, ≥, or ≠ and it can be used to compare two expressions or values. It defines a range of values that satisfy inequality.
For the scenario painted above, we see that Tani is meant to earn a minimum of $150 Thus, the greater than or equal to symbol ≥ should be used for the expression. $6 per hour and $12 per hour are also well represented in the equation.
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