among a group of 97 students who are studying either discrete math or calculus or both, 62 are studying discrete math. of those 62, 33 are also studying calculus. how many students are studying calculus?
Answers
The number of students studying calculus is 68.
This question is based on a formula in set theory and venn diagrams. This is given by-
(A U B) = A +B – (A∩B)
Or n (A U B) = n(A) + n(B) – n(A∩B).
Now, here the given values are –
n (A U B) = 97 , n(A)= 62, n(B)= x and n(A∩B)=33
where A is the set of students studying discrete maths, B of Calculus and A∩B of studying both of them and (A U B) is the set of students studying either one of them or both.
On applying this formula, we get-
97=62+ x- 33
97= 29-x
And then x=68. Where x are the number of students studying calculus.
Hence, the final answer is 68.
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Related Questions
f(x) = x, g(x) = 2x
combining functions
Answers
Answer:
f(x) + g(x) = 3x
Step-by-step explanation:
if axis deviation is present, which leads that normally have positive qrs complexes will have negative qrs complexes?
Answers
If there is an axis deviation, it can result in a reversal of the QRS complex polarity in certain leads. Leads that normally have positive QRS complexes may have negative QRS complexes, and vice versa.
For example, if there is a left axis deviation, leads I and aVL, which normally have positive QRS complexes, may have negative QRS complexes.
Axis deviation refers to the direction in which the electrical activity is traveling through the heart. If the electrical activity is deviated from its normal pathway, it can cause a change in the orientation of the QRS complex, which is a graphical representation of the electrical activity generated by the ventricles during the cardiac cycle.
The change in polarity occurs because the direction of the electrical activity is now opposite to what it would be in a normal heart. This change in polarity can be used to help diagnose the location and type of axis deviation. Understanding the significance of the polarity changes can help healthcare providers determine appropriate treatment plans for patients.
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If each unit on the coordinate plane represents one mile, what is the total distance the truck travels on its route?
Answers
Answer:
36.16 miles
Step-by-step explanation:
A recycling truck begins its weekly route at the recycling plant at point A, as pictured on the coordinate plane below. It travels from point A to point B, then points C, D, and E, respectively, before returning to the recycling plant at point A at the end of the day. The truck’s route is illustrated on the coordinate plane below. If each unit on the coordinate plane represents one mile, what is the total distance the truck travels on its route?
Answer:
The distance between two points X(\(x_1,y_1\)) and Y\((x_2,y_2)\) is given as:
\(|XY|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
From the image attached, the coordinates of the plane are:
A(-1, -1), B(1, -1), C(5, 2), D(0, 13), E(-5, 2).
The lengths are:
\(|AB|=\sqrt{(1-(-1))^2+(-1-(-1))^2}=2\ units\\ \\|BC|=\sqrt{(5-1)^2+(2-(-1))^2}=5\ units\\\\|CD|=\sqrt{(0-5)^2+(13-2)^2}=12.08\ units\\\\|DE|=\sqrt{(-5-0)^2+(2-13)^2}=12.08\ units\\\\|AE|=\sqrt{(-5-(-1))^2+(2-(-1))^2}=5\ units\)
But 1 mile = 1 unit
Total distance = |AB| + |BC| + |CD| + |DE| + |AE| = 2 + 5 + 12.08 + 12.08 + 5 = 36.16 miles
The measure of an angle is 39.4°. What is the measure of its complementary angle?
This is IXL
Answers
Answer:
50.6°
Step-by-step explanation:
complementary angles sum to 90° , that is
complementary angle + 39.4° = 90° ( subtract 39.4° from both sides )
complementary angle = 90° - 39.4° = 50.6°
Do anyone know this
Make sure is the correct answer please
Answers
9514 1404 393
Answer:
(a) P = 44 cm + 18 cm + 18 cm = 80 cm
(b) 396 cm²
(c) (i) see attached: radius = 7 cm; height ≈ 16.58 cm; slant height = 18 cm
(c) (ii) 7 cm
Step-by-step explanation:
(a) The length of arc PQR is given by the formula ...
s = rθ . . . . . where r is the radius and θ is the angle in radians
The angle θ in radians is (140°)(π/180°) = (140)(22/7)/(180) = 22/9
So, the arc length is ...
PQR = (18 cm)(22/9) = 44 cm
Then the perimeter of the figure is ...
P = PQR +RO +OP = 44 cm + 18 cm + 18 cm
P = 80 cm
__
(b) The area of a sector is given by ...
A = 1/2r²θ = 1/2(rs)
A = (1/2)(18 cm)(44 cm) = 396 cm² . . . area of the sector
__
(c) (i) A drawing of the cone is attached. The "slant height" is 18 cm. The radius is found in part (ii) as 7 cm. The height is given by the Pythagorean theorem:
height = √((slant height)² - radius²) = √(18² -7²) = √275
height ≈ 16.58 . . . cm
(ii) The length of arc PQR is the circumference of the base of the cone, given by ...
C = 2πr . . . . where r is the radius of the base of the cone
Filling in the known values, we find ...
44 cm = 2(22/7)r
(44 cm)(7/44) = r = 7 cm . . . . . multiply by 7/44 to find r
The radius of the base of the cone is 7 cm.
I just need to know if it’s a b c or d please and thx u
Answers
Answer:
i think its B
Step-by-step explanation:
sorry if its wrong have a good day/night ;)
what is the unit rate for snowfall?
Answers
Identify each of the following as an observation, a hypothesis, an experiment, or a conclusion:
a. One hour after drinking a glass of regular milk, Jim experi- enced stomach cramps.
b. Jim thinks he may be lactose intolerant.
c. Jim drinks a glass of lactose-free milk and does not have any stomach cramps.
d. Jim drinks a glass of regular milk to which he has added lactase, an enzyme that breaks down lactose, and has no stomach cramps.
Answers
a. One hour after drinking a glass of regular milk, Jim experi- enced stomach cramps.=> It is an observation.
b. Jim thinks he may be lactose intolerant. => It is a hypothesis.
c. Jim drinks a glass of lactose-free milk and does not have any stomach cramps. => It is an experiment.
d. Jim drinks a glass of regular milk to which he has added lactase, an enzyme that breaks down lactose, and has no stomach cramps. => It is an experiment.
Here, we have,
Given Information that,
We need to determine observation, experiment, hypothesis, and conclusion for the given events.
The scientific method is a process that scientists use to make observations to explain natural phenomena. It includes:
Observation
Experiment
Hypothesis
We know,
Observations: It is considered as the first step of the scientific method about what you observe.
Hypothesis: It gives an explanation for an observation.
Experiments: To determine if a hypothesis is true or false, experiments are done to find a relationship between the hypothesis and the observations.
Conclusion/Theory: A conclusion is made after the experiments are analyzed.
Analysis of each event
a. It is an observation.
b. It is a hypothesis.
c. It is an experiment.
d. It is an experiment.
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Use the function below (whose parameters qualify it as a STC function) to answer the questions.
"STC "=" 6 "+"9 Q - 3" "Q" ^2 +" (1/3)" "Q" ^3
a) Total fixed cost is $_________
b) Obtain the AFC function from (a) and write it here __________________
c) Obtain the AVC function contained in the STC function and write the AVC function here _________________________
d) Write here the MC function __________________________
e) Find the value which AFC approaches as Q gets very large. Also write a sentence or two explaining what this implies for fixed costs per unit (AFC) as production quantities get ever larger.
f) Find the value of Q at which AVC is a minimum.
g) Is productive efficiency at the value in (f) greatest or least?
h) Demonstrate that the value of SMC equals the value of AVC at the value of Q where AVC is a minimum. Hint: The level of Q you found in (f) is where AVC is a minimum. If you plug this level of Q into AVC (see c) and also into MC (see d) the two outcomes should be the same if SMC crosses AVC at this level of Q.
i) Why does the derivative of Short Run Total Cost (STC) equal the derivative of Total Variable Cost (TVC)? Stated another way, why does dSTC/dQ = dTVC/dQ? Explain in a couple of sentences.
j. Find the value of Q where increasing returns ceases and diminishing returns begins. Hint: Diminishing returns begins at the level of Q where MC is a minimum
Answers
Total fixed cost is $6. The value of AFC is $6 / Q. Productive efficiency is greatest at Q = 4.5. Diminishing returns begin when Q = 3. The total fixed cost (TFC) does not change because it is fixed.
a) Total fixed cost is $6
b) We can obtain the average fixed cost function (AFC) from the total fixed cost (TFC) by dividing it by output (Q) as follows: AFC = TFC / Q. So, the value of AFC is $6 / Q.
c) The AVC function is calculated by dividing total variable cost (TVC) by output (Q).
STC = TFC + TVC6 + 9Q - 3Q2 + (1/3)Q3TVC = 9Q - 3Q2 + (1/3)Q3AVC = TVC / QAVC = (9Q - 3Q2 + (1/3)Q3) / QAVC = 9 - 3Q + (1/3)Q2
d) The MC function is derived by taking the first derivative of the STC function with respect to output (Q). The derivative of the STC function is: MC = dSTC / dQMC = 9 - 6Q + Q2
e) As Q approaches infinity, the denominator of AFC becomes larger and larger. So, AFC approaches zero as Q gets very large. This implies that fixed costs per unit decrease as production quantities get larger.
f) We can find the value of Q at which AVC is a minimum by taking the first derivative of the AVC function and setting it equal to zero. The first derivative of AVC is: AVC = 9 - 3Q + (1/3)Q2
dAVC / dQ = -3 + (2/3)Q= 0
Q = 4.5
g) Productive efficiency is greatest when AVC is at its minimum. Therefore, productive efficiency is greatest at Q = 4.5.
h) We can demonstrate that the value of SMC equals the value of AVC at the value of Q where AVC is a minimum by plugging Q = 4.5 into both the AVC and MC functions. AVC = 9 - 3(4.5) + (1/3)(4.5)2AVC = 7.125MC = 9 - 6(4.5) + 4.52MC = 7.125
Since SMC = MC, we can conclude that SMC equals AVC at the value of Q where AVC is a minimum.
i) In the short run, the total fixed cost (TFC) does not change because it is fixed. Therefore, the derivative of the STC function with respect to output (Q) is equal to the derivative of the TVC function with respect to output (Q). This means that dSTC / dQ = dTVC / dQ.
j) Increasing returns to scale cease when the marginal cost (MC) is equal to average total cost (ATC). Diminishing returns to scale begins when MC exceeds ATC. ATC is calculated by dividing the total cost (TC) by output (Q). TC is calculated by adding total fixed cost (TFC) and total variable cost (TVC).
ATC = TC / QATC = (6 + 9Q - 3Q2 + (1/3)Q3) / Q
Now, we can find the level of Q where increasing returns to scale cease by calculating the first derivative of ATC and setting it equal to zero.
ATC = (6 + 9Q - 3Q2 + (1/3)Q3) / QdATC / dQ = (6 - 6Q + Q2) / Q2= 0
Q = 3
Now, we can calculate the marginal cost function and find the level of Q where diminishing returns begins. We know that diminishing returns begin where the marginal cost is at its minimum.
MC = 9 - 6Q + Q2MC = 9 - 6(3) + 32MC = 3
So, diminishing returns begin when Q = 3.
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are computers better than a straight edge and compass
Answers
Answer:
Yes
Step-by-step explanation:
They are exact and you can't mess up or accidentally slide the compass or straightedge around. This is just my opinion though.
Answer
it depends
Step-by-step explanation:
through: (-2, -1), slope = -1
Answers
y= -1x -3
that's equation of the line
Triangle ABC is a right triangle. ∠A measures 48°. What is the measure of ∠C?
Answers
Answer:
42°
Step-by-step explanation:
angles in a triangle add up to 180°
angle B 90°. 90 ° because this is a right-angled triangle. how do we know that B is the 90° degree? because we are told ABC. the letter in the middle is the angle.
so for angle A (48°), we could be told that angle CAB = 48°. A is in the middle of CAB.
as for our missing angle C, this can be found by subtracting the sum of the other two angles from 180.
angle C = (180 - 90 - 48)°
= 42°
An automatic filling machine is used to fill 2-litre bottles of cola. The machine’s output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of 0.01 litres. Output is monitored using means of samples of 5 observations.
Determine the upper and lower control limits that will include roughly 95.5 percent of the sample means.
If the means for 6 samples are 2.005, 2.001, 1.998, 2.002, 1.995 and 1.999, is the process in control?
Answers
The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.
Now let's check if the process is in control using the given sample means:
To determine the upper and lower control limits for the sample means, we can use the formula:
Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))
Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))
In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.
For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.
Given:
Mean = 2.0 litres
Standard Deviation = 0.01 litres
Sample size (n) = 5
Using the formula, we can calculate the upper and lower control limits:
UCL = 2.0 + (1.96 * 0.01 / sqrt(5))
LCL = 2.0 - (1.96 * 0.01 / sqrt(5))
Calculating the values:
UCL ≈ 2.0018 litres
LCL ≈ 1.9982 litres
Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.
Now let's check if the process is in control using the given sample means:
Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997
Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.
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Suppose that a polling company surveyed 600 people about how much time they spend exercising each week. the results of this survey were compiled and used to create this relative frequency histogram.
Answers
A survay of 600 people related to time(in hours) which they spent on excercise each week,
a) The percentage of respondents said that they exercise less than three hours per week is 46.
b) The number of respondents who exercise between two and four hours per week are 32% i.e 32×600/100 = 192 respondents.
What is histogram?A histogram is a chart which display the statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size.
What is Relative Frequency?Relative frequency is defined as how often something happens divided by all the possible outcomes. The relative frequency formula is:
Relative frequency = Number of sucessful trials/total number of trials. A relative frequency histogram is a type of graph that display how often something happens, in percentages.
We have provide a relative frequency histogram (above figure)for results of this survey of polling companie' people about how much time they spend exercising each week.
Total survayed people = 600
a) We have to determine the percentage of respondents said that they exercise less than three hours per week ,
from the histogram, the required percentage = one hour + two hour = 20% + 26% = 46%.
b)Respondents said that they exercise between two and four hours per week = two hours + four hours = 19% + 13% = 32%
Hence,required percentage is 32%i.e 192.
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Complete question:
Suppose that a polling company surveyed 600 people about how much time they spend exercising each week. The results of this survey were compiled and used to create this relative frequency histogram. 30- 20 10 Weekly hours of exercise Assume that all percentages shown in the histogram are whole numbers. Each of the bars in this histogram includes only the left endpoint of the class except for the last bar, which also includes the right endpoint. What percentage of respondents said that they exercise less than three hours per week? How many respondents said that they exercise between two and four hours per week? respondents.
Kevin has money in two savings accounts. One rate is 6% and the other is 12%. If he has $600 more in the 12% account and the total interest is $279, how much is invested in each savings account?
Answers
Answer:
• The amount invested at 6% is $1,150.
,• The amount invested at 12% is $1,750.
Explanation:
Let the amount invested at 6% = x
\(\text{Interest earned at 6\%}=0.06x\)Kelvin has $600 more in the 12% account, therefore:
The amount invested at 12% = $(x+600).
\(\text{Interest earned at 12\%}=0.12(x+600)\)The total interest is $279.
\(0.06x+0.12(x+600)=279\)We solve the equation for x.
\(\begin{gathered} 0.06x+0.12x+72=279 \\ 0.18x+72=279 \\ \text{Subtract 72 from both sides} \\ 0.18x+72-72=279-72 \\ 0.18x=207 \\ \text{Divide both sides by 0.18} \\ \frac{0.18x}{0.18}=\frac{207}{0.18} \\ x=1150 \end{gathered}\)The amount invested at 6% is $1,150.
The amount invested at 12% is:
\(1150+600=\$1750\)The amount invested at 12% is $1,750.
A quadratic equation of the form 0=ax2+bx+c has a discriminant value of -16. How many real number solutions does the equation have? -1012.
Answers
The given quadratic equation will have zero real-number solutions.
Since the given equation is: ax²+bx+c =0, and the discriminant value is -16, since the discriminant is a portion of the quadratic equation, the formula for calculating is b²-4ac, where a, b and c are the coefficients now if the discriminant is more than 0, then the respective equation has two real solutions, whereas if it is less than 0, it has zero real solutions and last, if the discriminant is equal to zero then the equation has only one real solution.We know the :-b±√b²-4ac /2a, here the square root of -16 can't give us a real number instead it will give us an imaginary number
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Find the areas of the sectors formed by NMP. Round your answer to the hundredth of a square centimeter.
Answers
Consider that the area of a sector of a circle is given by:
\(A=\frac{\theta}{360}\pi r^2\)where θ is the angle of the sector and r is the radius.
For θ=40 and r = 8cm, you obtain:
\(A=\frac{40}{360}\pi(8cm)^2=22.34cm^2\)The area of the small sector is about 22.34 cm^2.
Now, for θ=320 and r = 8cm, you obtain:
\(A^{\prime}=\frac{320}{360}\pi(8cm)^2=178.72cm^2\)The area of the small sector is about 178.72 cm^2.
The price of a computer is marked down from $550 to $484 for a sale. The
following week, the computer is marked down again by the same percent as
during the week before. How much lower than the original price is the price after
the second markdown?
A $425.92
C
$124.08
B $132.00
D
$58.08
Answers
Answer:
A) $425.92
Step-by-step explanation:
The new price percentage with relation to the previous can be determined by dividing \(p = \frac{484}{550}\). Once we calculate p, we can multiply it by 484, which is equivalent to applying the same discount, thus \(\frac{484}{550}484=425.92\)
work out the volume of the cone,giving your answer to 3 significant figures
Answers
The volume of the cone is 1, 139. 49 cm³
How to determine the volumeHeight of cone = 17cm
Base of cone = 16cm
Diameter = 16cm
Radius = diameter/2 = 16/2 = 8cm
Formula for volume of a cone = \(\pi r^{2} \frac{h}{3}\)
Substitute the values
Volume = \(3. 142\) × \(8\) × \(8\) × \(\frac{17}{3}\)
Volume = \(201. 088\) × \(5. 67\)
Volume = 1, 139. 49 cm³
Thus, the volume of the cone is 1, 139. 49 cm³
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Cycle City charges an initial price of $15 plus $0.75 per hour for bike rentals, which is
represented by the expression 15 +0.75h.
Complete each statement to describe the terms.
The variable h represents ?
The constant 15 represents ?
The variable term 0.75h represents ?
Answers
The constant 15 represents the initial price charged by Cycle City for bike rental.
The variable term 0.75h represents the additional price charged by Cycle City for each hour of bike rental.
I NEED HELP!! WILL GIVE BRAINLEST!!!
Solve the system below by GRAPHING:
Y=5x-8
Y=1/3x+6
Answers
Answer:
I promise you the app Math. way will save you it will do it for u and show you where to put it on the graph just download it
The number of hours of sunshine in Barbados for successive days during a and 11.8. Find the daily certain week were 11.1, 11.9, 11.2, 12.0, 11.7, 12.9 average. The following week the daily average was 11 hours. How many more hours of sunshine were there the first week than the second?
Answers
Answer:
5.6
Step-by-step explanation:
11*7=77
11.8*7= 82.6
82.6-77=5.6
Which of the following numbers are solutions of the sentence x - 3 < 2?
I -3
II 0
III 2
IV 5
A. II only
B. III only
C. I and III only
D. I, II, and III only
E. I, II, and IV
Answers
Answer:
The answer is D.I,II and III only.
guys can you help me with the like terms plz plz dont answer if you dont know it
Answers
Answer:
like terms are numbers or letters that are a like.
y² is the only letter with a square in this problem. Whilst xy and 2xy are the same.
y²+ xy + 2xy
y² there is no letter with square again.
xy+2xy is the same as one orange + two orange.
1 is never written against a letter.
y²+ xy + 2xy
y²+3xy
PLS Help me! This graph shows the outside temperature (in degrees Celsius) over the course of 12 hours, starting at midnight (x = 0). What is the domain? What does the domain mean in terms of the problem? What is the range? What does the range mean in terms of the problem? When is the function decreasing? What does this decreasing interval mean in terms of the problem?
Answers
Answer:
The domain is the set of all possible x-values
Domain is the time hereThe range is the resulting y-values
The range is the outside temperature is hereFunction is decreasing between x= 0 to 3It means the temperature is decreasing between midnight and 3 AM
*Remember solutions are found in the shaded area or on a solid line (points on a dashed line are not a solution)
Answers
The solutions for the inequality are -
(2, 2)(4, 4)(6, 6)What is the general equation of a Straight line? What is linear inequality?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
A inequality is used to compare two or more expressions. The straight line inequalities are of the form -
y > mx + c
y < mx + c
y ≥ mx + c
y ≤ mx + c
We have the following inequality -
y ≥ - x - 1
Refer to the graph of the inequality attached. The plotted points in the shaded region represent the solutions for the inequality. We can write -
(2, 2)(4, 4)(6, 6)Therefore, the solutions for the inequality are -
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pleaseee help
BRAINLIESt!!!!
Answers
Answer:
C y cause it was already there plus ik super late but hey sum points
Step-by-step explanation:
What is the value of the expression 5x2-8x+4 when x = -3
Answers
Answer:
5 x 2 - 8x + 4
5 x 2 - 24 + 4
10 - 24 + 4
-10
Answer: -10
Write an exponential function in the form y=ab^x that goes through points (0,6) and (7, 768)
Answers
Answer:y=6(2)*x
Step-by-step explanation:
A rectangle and triangle are shown below.
The area of the rectangle is equal to the perimeter of the triangle.
Solve for x.
If your answer is a decimal, convert it to 1 d.p.
Answers
Answer:
5
Step-by-step explanation:
We know that the area of the rectangle is equal to the perimeter of the triangle
S (rectangle) = (x + 8) × (2x - 1)
P (triangle) = (5x - 1) + (6x + 8) + (8x + 15)
Now we can form an equation:
(x + 8) × (2x - 1) = (5x - 1) + (6x + 8) + (8x + 15)
\( {2x}^{2} - x + 16x - 8 = 5x - 1 + 6x + 8 + 8x + 15\)
\(2 {x}^{2} - 4x - 30 = 0\)
\(d = {b}^{2} - 4 \times a \times c = ({ - 4})^{2} - 4 \times 2 \times ( - 30) = 16 + 240 = 256 > 0\)
\(x1 = \frac{ - b - \sqrt{d} }{2 \times a} = \frac{4 - 16}{4} = \frac{ - 12}{4} = - 3\)
-3 is a negative number and we cannot use it, since x must be a natural number
\(x2 = \frac{ - b + \sqrt{d} }{2 \times a} = \frac{4 + 16}{4} = \frac{20}{4} = 5\)