We can form 15 different 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Out of these, 30 are even numbers. We used the concept of combination to find these numbers.
Combination is a mathematical technique used to calculate the number of ways in which a group of objects can be selected from a larger set, without considering their order.
We can use the combination formula to find the total number of possible combinations:
C(4, 3) = 4! / (3! * 1!) = 4
This means that we can form four different 3-digit numbers using the digits 1, 2, 3, and 4, without repetition.
Now, coming back to our original problem, we need to form 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Using the same combination formula, we can find the total number of possible combinations:
C(6, 4) = 6! / (4! * 2!) = 15
This means that we can form a total of 15 different 4-digit numbers using the given digits.
Next, we need to find out how many of these numbers are even. An even number is a number that is divisible by 2, and in our case, this means that the last digit of the number must be either 2, 8, or a combination of 1 and 7.
To find the number of even 4-digit numbers, we can use the same combination formula, but this time we have to consider only 3 digits (2, 8, and a combination of 1 and 7) for the last digit:
C(3, 1) * C(5, 3) = 3 * 10 = 30
This means that we can form a total of 30 different 4-digit even numbers using the given digits.
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A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 19 mg every six hours. Complete parts (a) and (b) below. a. Following this dosage, how many 13.2 mg chewable tablets would be taken in a week? b. This antihistamine also comes in a liquid form with a concentration of 13.2 mg/ 10mL. Following the prescribed dosage, how much liquid antihistamine should a 100-pound person take in a week?
A 100-pound person could take mL in a week? this is the question i need answered the most...thank you
Answer: First, let's find out how many times a 100-pound person would take the antihistamine in a week:
Every 6 hours * 24 hours/day = 4 times a day
4 times a day * 7 days/week = 28 times a week
Next, let's find the number of 13.2 mg chewable tablets taken in a week:
A typical dose of 19 mg * 28 doses/week = 532 mg
532 mg / 13.2 mg/tablet = 40 tablets
So, a 100-pound person would take 40 chewable tablets in a week following the prescribed dosage.
Now, let's find the amount of liquid antihistamine to be taken in a week:
A typical dose of 19 mg * 28 doses/week = 532 mg
532 mg / 13.2 mg/10 mL = 40.15 mL
So, a 100-pound person would take 40.15 mL of liquid antihistamine in a week following the prescribed dosage.
Step-by-step explanation:
Simplify this radical.
O 13√x
O 6x√x
O x√√x¹2
O x√x
Describe the long run behavior of f(p)=(p+1)^3(p+4)^3(p-1)
Answer:
Step-by-step explanation:
The long-run behavior of a function can be determined by examining its asymptotes and the behavior of the function near these asymptotes.
For the function f(p)=(p+1)^3(p+4)^3(p-1), there are three points to consider as possible asymptotes: p = -1, p = -4, and p = 1.
At p = -1, the factor (p-1) is equal to zero, so the function has a vertical asymptote there. This means that as p approaches -1 from either side, the function will approach infinity.
At p = -4, the factor (p+4)^3 is equal to zero, so the function also has a vertical asymptote there. Similarly, as p approaches -4 from either side, the function will approach infinity.
At p = 1, the factor (p+1)^3 is equal to zero, so the function has another vertical asymptote there. In this case, as p approaches 1 from either side, the function will approach negative infinity.
So, the long-run behavior of the function can be described as follows:
The function approaches infinity as p approaches -1 or -4 from either side.
The function approaches negative infinity as p approaches 1 from either side.
Therefore, the long-run behavior of f(p)=(p+1)^3(p+4)^3(p-1) is characterized by three vertical asymptotes at p = -1, p = -4, and p = 1.
Answer:
[tex]\text{As } p \to -\infty, f(p) \to -\infty\\\\\text{As } p \to \infty, f(p) \to \infty[/tex]
====================================================
Explanation:
Each factor is a cubic of degree 3.
The degree of the entire polynomial is 3+3+3 = 9.
Since the degree is odd and the leading coefficient is positive, this means the graph falls to the left and rises to the right.
"falls to the left" means [tex]\text{As } p \to -\infty, f(p) \to -\infty[/tex]
"rises to the right" means [tex]\text{As } p \to \infty, f(p) \to \infty[/tex]
This is verified using a graphing tool like Desmos as shown in the screenshot below. I'm using x in place of p.
ADEF~ AJHI; Find EF.
D
G
9
E
x+8
F
H
3x-2
+
K
14
H
Answer:
EF = 18
Step-by-step explanation:
Given similar triangles DEF and JHI, midpoints G and K of sides DE and HI, with sides marked GF=9, EF=x+8, KI=14, HI=3x-2, you want to know the length of EF.
ProportionCorresponding sides in similar triangles are proportional. This means ...
EF/GF = HI/KI
(x+8)/9 = (3x-2)/14 . . . . substitute given values
14(x +8) = 9(3x -2) . . . . multiply by 14·9
14x +112 = 27x -18 . . . . eliminate parentheses
130 = 13x . . . . . . . . . . . add 18-14x
10 = x . . . . . . . . . . . . . divide by 13
Now, we can find EF:
EF = x+8 = 10 +8
EF = 18
What is the measure of each angle in a regular polygon with 14 sides? If necessary, round your answer to the nearest tenth.
Answer:
154.3° (to the nearest tenth)
Step-by-step explanation:
1 exterior angle=360/number of sides
360/14=25.714285
To get the one angle within the 14 sided polygon, take 1 exterior angle away from 180, as they are on a straight line
180-25.714285=154.285714
To the nearest tenth:
154.3°
If the r-value, or correlation coefficient, of a data set is 0.934, what is the
coefficient of determination to three decimal places?
О A. 0.872
• B. 0.834
• C. 0.966
• D. 0.942
If the r-value, or correlation coefficient, of a data set is 0.934, the
coefficient of determination to three decimal places is: A. 0.872.
How to find the coefficient of determination?The coefficient of determination (R-squared) is the square of the correlation coefficient (r) and represents the proportion of the variance in the dependent variable (y) that can be explained by the independent variable (x).
So, to find the coefficient of determination, we need to square the correlation coefficient:
R-squared = r^2
= 0.934^2
= 0.872 (Rounded to three decimal places)
Therefore, the answer is (A) 0.872.
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Identify the percent of change as an increase or a decrease.
9 points to 4 points
o increase
decrease
Find the percent of change. Round to the nearest tenth of a percent if necessary.
The percent of change is
%.
The percent of change from 9 points to 4 points is approximate -55.6%, indicating a decrease of 55.6%.
What is the Percent of change?
The percent of change is a measure that compares the difference between two values to the original, or initial, value. It is usually expressed as a percentage and indicates how much a value has increased or decreased from its initial value.
To find the percent of change from 9 points to 4 points, we need to first calculate the amount of change, which is the difference between the final value (4 points) and the initial value (9 points):
Amount of change = Final value - Initial value = 4 - 9 = -5
The negative sign indicates a decrease in value.
Next, we can calculate the percent of change using the formula:
Percent change = (Amount of change / Initial value) x 100%
Substituting the values we get:
Percent change = (-5 / 9) x 100% ≈ -55.6%
Hence, the percent of change from 9 points to 4 points is approximate -55.6%, indicating a decrease of 55.6%.
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Alba Isabel bought a Bluray disc player on sale for $219.99. What is the sales tax if Alba lives in Kingston, New York, where the state tax is 4% and the county tax is 4%?
The sales tax on the Bluray disc player is $17.60.
What is percentage ?
Percentage can be defined as product of ratio of given value, total value and hundred.
To calculate the sales tax on the Bluray disc player, we need to add the state tax and county tax to the sale price of the player.
First, we can calculate the amount of the state tax. The state tax rate is 4%, which can be expressed as a decimal by dividing by 100:
State tax rate = 4% = 0.04
To find the amount of state tax, we can multiply the sale price by the state tax rate:
State tax = 0.04 x $219.99 = $8.80
Next, we can calculate the amount of the county tax. The county tax rate is also 4%, so we can use the same method as above to find the county tax:
County tax rate = 4% = 0.04
County tax = 0.04 x $219.99 = $8.80
Now, we can find the total sales tax by adding the state tax and county tax:
Total sales tax = State tax + County tax
= $8.80 + $8.80
= $17.60
Therefore, the sales tax on the Bluray disc player is $17.60.
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Carlos had $400. He decided to spent 40% of it on clothes, and 50% of the remaining money on video games. How much money did Carlos spend? How much does Carlos have left?
Answer:
Step-by-step explanation:
We can start by finding how much money Carlos spent on clothes. To do this, we simply multiply the original amount of $400 by 40%:
Clothes = $400 * 40% = $400 * 0.40 = $160
Next, we find how much money Carlos has left after spending on clothes. To do this, we subtract the amount spent on clothes from the original amount:
Remaining Money = $400 - $160 = $240
Finally, we find how much money Carlos spent on video games. To do this, we multiply the remaining money by 50%:
Video Games = $240 * 50% = $240 * 0.50 = $120
So, in total, Carlos spent $160 on clothes and $120 on video games, for a total of $160 + $120 = $280.
And Carlos has $400 - $280 = $120 left.
After spending 40% of the $400 on clothes, Carlos has $400 x (100 - 40) / 100 = $240 left.
Next, he spent 50% of the remaining $240 on video games, which is $240 x 50 / 100 = $120.
Therefore, Carlos spent a total of $400 - $240 = $160.
Finally, Carlos has $240 - $120 = $120 left.
gracecollege.sparxmaths.uk/student 2: Item A < Back to task Start Bookwork code: F50 A savings account gathers compound interest at a rate of 5% per annum. The amount of money in the account over the first two years is shown below. After 1 year Copy and complete the expression below for the amount of money in the account after n years. After 2 years £600.00 £630.00 £661.50 E Watch video Calculator allowed £ 9,203 XP n Answer
a) The expression showing the amount of money in the savings accounts compounded at 5% per annum after one year is 600 (1 + 0.05), which equals £630.
b) The expression showing the amount of money in the savings accounts compounded at 5% per annum after one year is 600 (1 + 0.05)^2, which equals £661.50.
What is a mathematical expression?A mathematical expression combines constants, numbers, variables, and values with mathematical operations without adding the equation symbol (=).
When the equation symbol is added to mathematical expressions, they become an equation.
In this situation, the compound interest final amount is depicted like an exponential growth function as follows:
f(x) = a(1+r)ˣ
f(x) = exponential growth function
a = initial amount
r = growth rate
x = number of time intervals
Initial amount = £600
Growth rate = 5% or 0.05
x = 1 or 2 years.
f(x) = 600 (1.05)^x
Thus, if $600 is compounded at 5% yearly for 1 or 2 years, the mathematical expressions showing the value of the account are 600 (1 + 0.05) and 600 (1 + 0.05)^2, respectively.
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Find the x - and y -components of the vector d⃗ = (5.0 km , 29 ∘ left of +y -axis).
Express your answer in kilometers. Enter the x and y components of the vector separated by a comma.
The x- and y-components of the vector [tex]\mathbf{\hat d }[/tex] are approximately -2.25 km and 4.30 km, respectively.
What is vector?In physics and mathematics, a vector is a mathematical object that has both magnitude and direction. Vectors are often represented by arrows, with the length of the arrow indicating the magnitude of the vector, and the direction of the arrow indicating the direction of the vector.
For example, the velocity of a moving object is a vector quantity, because it has both a magnitude (the speed of the object) and a direction (the direction in which the object is moving).
To find the x-components and y-components of the vector [tex]\mathbf{\hat d }[/tex] = (5.0 km, 29° left of +y-axis), we can use trigonometry.
The magnitude (or length) of the vector is given by the first component, which is 5.0 km.
The angle between the vector and the positive y-axis is 29° left of +y-axis, which means it forms a 61∘ angle with the negative y-axis (since 29∘ + 61° = 90°).
The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:
x-component = magnitude x cos(angle) = 5.0 km x cos(61°) ≈ -2.25 km
The negative sign indicates that the x-component is in the opposite direction of the positive x-axis.
The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:
y-component = magnitude x sin(angle) = 5.0 km x sin(61°) ≈ 4.30 km
Therefore, the x- and y-components of the vector [tex]\mathbf{\hat d }[/tex] are approximately -2.25 km and 4.30 km, respectively.
Expressed as an ordered pair, the components are (-2.25 km, 4.30 km).
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In a fair out of 5 people 2 are men and 2 are women and the remaining are children there are 2500 people at the fair. what percentage of people are adult?
Answer:
Step-by-step explanation:
4 out of the 5 people are adults (since 2 women and 2 men) therefore 80% of people are adults.
Answer:
80%
Step-by-step explanation:
Its either too easy or too hard. 2+2=4 obviously, and 4/5=8/10. 8/10, 0.80, or 80% is the answer. If I got this right I don't know how lol.
The opportunity cost of treating HIV/AIDS cases increases as more HIV/AIDS cases are treated.
Draw a curve that shows the production possibilities for the world economy that produces HIV/AIDS treatments and other goods and services. Label the curve PPF0.
Then draw the PPF that shows the effect of an advance in technology on HIV/AIDS treatments. Label the curve PPF1.
On solving the provided question, we can say that from the graphs The curve preceding technological advancement is called PPF0. PPF1 is the curve following technological advancement.
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
The curve preceding technological advancement is called PPF0. PPF1 is the curve following technological advancement.
Prior to technological advancement, the opportunity cost of treating HIV/AIDS rises as the world deviates from its PPF. The potential cost of treating more HIV/AIDS cases falls as a result of technological advancements since less other commodities and services must be sacrificed in order to treat more HIV/AIDS patients. Alternatively, the world might treat more HIV/AIDS patients right now by forgoing the same number of other commodities and services.
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The correct question is -
More than 50 years after it jumped the species barrier and became one of the most devastating viruses to affect mankind, HIV remains a stubborn adversary. Treatment has improved dramatically over the past 20 years and now, a cure could be in sight.
Source: The Guardian, November 30, 2018
Make a graph of the production possibilities frontier with HIV/AIDS cases treated on the x-axis and other goods and services on the y-axis before and after the advance in technology.
Question content area bottom left
Part 1
The opportunity cost of treating HIV/AIDS cases increases as more HIV/AIDS cases are treated.
Draw a curve that shows the production possibilities for the world economy that produces HIV/AIDS treatments and other goods and services. Label the curve PPF0.
Then draw the PPF that shows the effect of an advance in technology on HIV/AIDS treatments. Label the curve PPF1.
Multiply. (Simplify your answer
(-5y4z)(-7y6z³)
Answer:
35y^(10)z^(4)
Step-by-step explanation:
Solution Given:
(-5y^(4)z)(-7y^(6)z³)
Here while opening bracket
If their is like terms they can be multiplied ,divided,subtracted as well as added.
So
Here
opening bracket and keeping in serially
-5*-7*y^(4)*y^(6)*z*z^(3)
here if their is like terms their power is added.
And solving remaining one.
35y^(4+6)z^(1+3)
Here -5*-7=35
Again
Solving it.
35y^(10)z^(4)
Answer:
[tex]35y^{10}z^4[/tex]
Step-by-step explanation:
Given expression:
[tex](-5y^4z)(-7y^6z^3)[/tex]
Apply the rule: (-a) · (-b) = ab
[tex]\implies 5y^4z \cdot 7y^6z^3[/tex]
Multiply the numbers: 5 · 7 = 35
[tex]\implies 35y^4zy^6z^3[/tex]
Collect like terms:
[tex]\implies 35y^4y^6z^3z[/tex]
[tex]\textsf{Apply exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 35y^{(4+6)}z^{(3+1)}[/tex]
Simplify the exponents:
[tex]\implies 35y^{10}z^4[/tex]
For a certain company, the cost function for producing x
items is C(x)=30x+200
and the revenue function for selling x
items is R(x)=−0.5(x−80)2+3,200
. The maximum capacity of the company is 130
items.
The profit function P(x)
is the revenue function R(x)
(how much it takes in) minus the cost function C(x)
(how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!
Answers to some of the questions are given below so that you can check your work.
Assuming that the company sells all that it produces, what is the profit function?
P(x)=
Preview Change entry mode .
Hint: Profit = Revenue - Cost as we examined in Discussion 3.
What is the domain of P(x)
?
Hint: Does calculating P(x)
make sense when x=−10
or x=1,000
?
The company can choose to produce either 50
or 60
items. What is their profit for each case, and which level of production should they choose?
Profit when producing 50
items =
Number
Profit when producing 60
items =
Number
Can you explain, from our model, why the company makes less profit when producing 10 more units?
Answer: The profit function P(x) can be found by subtracting the cost function C(x) from the revenue function R(x), so:
P(x) = R(x) - C(x) = (-0.5(x-80)^2 + 3,200) - (30x + 200)
The domain of P(x) is the set of all possible values of x for which the profit calculation makes sense. In this case, the company has a maximum capacity of 130 items, so the domain of P(x) is 0 <= x <= 130.
To calculate the profit when producing 50 items and 60 items, we simply plug in these values for x in the profit function:
Profit when producing 50 items = P(50) = (-0.5(50-80)^2 + 3,200) - (30 * 50 + 200) = $2350
Profit when producing 60 items = P(60) = (-0.5(60-80)^2 + 3,200) - (30 * 60 + 200) = $2280
Since the profit is higher for producing 50 items, the company should choose to produce 50 items.
From our model, we can see that as the production increases, the cost also increases linearly with a slope of 30, while the revenue increases parabolically but with a negative slope, meaning that after reaching a certain point, the increase in revenue becomes slower compared to the increase in cost. This is why the profit decreases as the production increases, and therefore the company makes less profit when producing 10 more units.
Step-by-step explanation:
Looking for answer key to Gina Wilson All Things Algebra Unit 3 Parallel and Perpendicular Lines Homework 5 Slopes of lines; Parallel and Perpendicular Lines
It's important to work through the problems yourself to improve your understanding and problem-solving skills.
For the unit 3 homework on parallel and perpendicular lines, you should have learned about the slope of lines, how to find the slope of a line given two points, and the relationship between parallel and perpendicular lines.
To find the slope of a line given two points, you can use the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
To determine if two lines are parallel, you can compare their slopes. Parallel lines have the same slope.
To determine if two lines are perpendicular, you can use the fact that the product of their slopes is -1. That is, if m1 and m2 are the slopes of two lines, and m1 * m2 = -1, then the lines are perpendicular.
It's important to practice working through problems using these concepts and formulas to develop your skills and understanding. Additionally, you can seek assistance from your teacher or tutor if you have specific questions or concerns.
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There are 12 consecutive parking slots available in a hotel parking lot in how many ways can four distinct cars be packed so that at least one parking slot remains vacant between into cars
Answer:
4 different spots
Step-by-step explanation:
12 - 4 spaces in between = 8 spaces
8 spaces / 4 cars = 4 spots
4 spots and 4 cars = 4 different spots for each car
16
Solve the quadratic equation by the square root method and write the solution in radical form. simplify the solution. 4y^2=80
Answer:
[tex]y=\pm2\sqrt{5}[/tex]
Step-by-step explanation:
[tex]4y^2=80\\y^2=20\\y=\pm\sqrt{20}\\y=\pm2\sqrt{5}[/tex]
The square root method for solving a quadratic equation involves isolating the squared term, and then taking the square root of both sides of the equation.
Starting with the equation 4y^2 = 80, we can isolate the squared term by dividing both sides of the equation by 4:
y^2 = 20
Next, we take the square root of both sides of the equation:
y = ±√20
The solution in radical form is y = ±√20. To simplify the radical, we can factor 20 into 2 * 10. Then, we can simplify the square root as follows:
y = ±√2 * √10 = ±2√10
So, the simplified solution is y = ±2√10.
A family buys a studio apartment for 150000 . They pay a down payment of 45000 . a. Their down payment is what percent of the purchase price? b. What percent of the purchase price would a $7500 down payment be?
Answer:
Step-by-step explanation:
This question I can not figure out Someone please help.
Answer:
x y
0 -2
4 -1
graph: should look like the picture attached
explanation:
Which of the following is equivalent to the expression below?
√-98
A. -2i√7
B. 2i√7
c. 7i√2
D. -7i√2
Answer: Choice C) [tex]7i\sqrt{2}[/tex]
Work Shown:
[tex]\sqrt{-98} = \sqrt{-1*49*2}\\\\\sqrt{-98} = \sqrt{-1}*\sqrt{49}*\sqrt{2}\\\\\sqrt{-98} = i*7*\sqrt{2}\\\\\sqrt{-98} = 7i\sqrt{2}\\\\[/tex]
Each worker at a store gets paid $15.90 for that first 40 hours worked. After 40 hours, they earn time and a half wages. Every employee has a 28% of his/her gross pay deducted for taxes, insurance etc. how much of a net pay does each worker take home?
Each worker would take home a net pay of $586.71.
What is the net pay?
The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.
To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.
To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.
For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:
Gross Pay for 40 hours = $15.90/hour x 40 hours = $636
For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:
Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88
Therefore, their total gross pay would be:
Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88
Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:
Total Deductions = 28% x $814.88 = $228.17
Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:
Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71
Therefore, each worker would take home a net pay of $586.71.
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Please help me with this question
<1 + <4 = 180 supplementary angles
180 - 95 = 85 degrees
what must be added to each term of the ratio 49:64 , so that it becomes 3:4 ?
Answer:
Hence x= 8 should be added to the terms of 49:68 to get the ratio 3:4.
Step-by-step explanation:
have a nice day.
10x² 18x -4
Factor number And find answer
Answer: 4(45x^(3)-1)
Step-by-step explanation:
Use de Morgan’s laws to rewrite a statement that is equivalent to the following statement.
It is not true that April and August are both spring months
Using de Morgan’s laws to rewrite a statement : It is true that April is not a spring month OR August is not a spring month
What is de Morgan’s laws?This refers to a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan. He was a 19th-century British mathematician. De Morgan's laws can also be called De Morgan's theorem.
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HelpThe ratio of the perimeters of two similar quadrilaterals is 2:4. What is the ratio of their areas? PLLLLLLLLLLSSSSSSss WILL GIVE 20 POINTS EASY
a.1:2
b. 4.8
c. 2:4
d. 4:16
e. 5:3
In a class of 50 students, 20 play hockey and 35 play football . 10 students play both hockey and football.
The number of students who either play hockey or football is given by the equation n ( A ∪ B ) = 45 students
What is Set Theory Formula?The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
Given data ,
Let the total number of students in the class be n ( U ) = 50 students
Let the number of students who play hockey be n ( A ) = 20 students
Let the number of students who play football be n ( B ) = 35 students
Let the number of students who play hockey and football n ( A ∩ B ) = 10
So , from the set theory n(A∪B) = n(A) + n(B) - n(A⋂B)
Substituting the values in the equation , we get
The number of students who play hockey or football = 20 + 35 - 10
On simplifying the equation , we get
The number of students who play hockey or football = n( A ∪ B ) = 45 students
And , the number of students who do not play hockey or football is given by the equation = n ( U ) - n ( A ∪ B )
On simplifying the equation , we get
The number of students who do not play hockey or football = 50 - 45 = 5 students
Hence , the number of students who play hockey or football is 45 students
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The terminal side of θ in standard position contains the point (–14, 0). Find the exact values of the six trigonometric functions of θ.
sin(θ) =
cos(θ) =
tan(θ) =
csc(θ) =
sec(θ) =
cot(θ) =
The exact values of the six trigonometric functions of θ are:
sin(θ) = 0
cos(θ) = -√2/2
tan(θ) = 0
csc(θ) = undefined
sec(θ) = -√2
cot(θ) = undefined
The given point (-14,0) lies on the x-axis in the negative x-axis direction. Drawing a line from the origin to this point creates a right triangle with the hypotenuse being the line from the origin to (-14,0), the opposite side being the y-coordinate of (-14,0), and the adjacent side being the x-coordinate of (-14,0). The length of the hypotenuse can be found using the Pythagorean theorem:
h^2 = (-14)^2 + 0^2
h^2 = 196
h = 14√2
Using the definitions of the six trigonometric functions in terms of the opposite, adjacent, and hypotenuse sides of a right triangle, we can find the exact values of these functions for θ:
sin(θ) = opposite/hypotenuse = 0/14√2 = 0
cos(θ) = adjacent/hypotenuse = -14/14√2 = -√2/2
tan(θ) = opposite/adjacent = 0/-14 = 0
csc(θ) = 1/sin(θ) = undefined (since sin(θ) = 0)
sec(θ) = 1/cos(θ) = -√2
cot(θ) = 1/tan(θ) = undefined (since tan(θ) = 0)
Therefore, the exact values of the six trigonometric functions of θ are:
sin(θ) = 0
cos(θ) = -√2/2
tan(θ) = 0
csc(θ) = undefined
sec(θ) = -√2
cot(θ) = undefined
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Need help I’m stuck on this question
Answer:
range = 33
Step-by-step explanation:
the range of a data set is the difference between the largest and smallest values in the set.
largest value = 163 and smallest value = 130 ( from diagram ), then
range = 163 - 130 = 33
