Rotate the triangle 180 counterclockwise around the origin and enter the coordinates. Enter the number that belongs in the green box A (1,-1) B (4,-2) C (2,-4)
Answers
Answer:
A''(-1, 1), B''(-4, 2), C''(-2, 4)
Step-by-step explanation:
When rotated 180°, the symbol of the coordinames change
i.e., if x = 2 it becomes x = -2 and if y = -4, it becomes y = 4
so the coordinates A(1, -1), B(4, -2), C(2, -4)
change to A''(-1, 1), B''(-4, 2), C''(-2, 4)
Related Questions
An import company brought into the country some amplifiers that cost sh. 3,750-each. The government imposed an import duty of 125% and a sales tax of 20 %. If the company decided to make a 10% profit on the sales, calculate the selling price of each amplifier.
Answers
Answer:
To calculate the selling price of each amplifier, we need to consider the cost, import duty, sales tax, and the desired profit margin.
Cost of each amplifier: sh. 3,750
Import duty of 125% on the cost:
Import duty = 125% of sh. 3,750
= 125/100 * sh. 3,750
= sh. (125/100 * 3,750)
= sh. 4,687.50
Cost of each amplifier including import duty:
Total cost = Cost + Import duty
= sh. 3,750 + sh. 4,687.50
= sh. 8,437.50
Sales tax of 20% on the total cost:
Sales tax = 20% of Total cost= 20/100 * sh. 8,437.50
= sh. (20/100 * 8,437.50)
= sh. 1,687.50
Total cost including sales tax:
Total cost = Total cost + Sales tax
= sh. 8,437.50 + sh. 1,687.50
= sh. 10,125
Desired profit margin of 10% on the total cost:
Profit = 10% of Total cost
= 10/100 * sh. 10,125
= sh. (10/100 * 10,125)
= sh. 1,012.50
Selling price of each amplifier:
Selling price = Total cost + Profit
= sh. 10,125 + sh. 1,012.50
= sh. 11,137.50
What is the five-number summary for the data set? 73, 62, 90, 28, 45, 90
Answers
Answer:
it's easy
Step-by-step explanation:
first take a deep breath and then search it
The radius of a circle is 3 meters. What is the area of a sector bounded by a 90° arc?
Give the exact answer in simplest form.
Answers
Answer:
(90°/360°)π(3^2) = (1/4)(9π) = 9π/4 m²
answer following question
Answers
Answer:
Option (C), 8 am
Step-by-step explanation:
Newton's Law of Cooling is a mathematical model that describes the cooling process of an object. It states that the rate of change of temperature of an object is proportional to the difference between its temperature and the surrounding temperature.
The equation representing Newton's Law of Cooling is:
[tex]\dfrac{dT}{dt} = -k (T_0 - T_A)[/tex]
Where...
"dT/dt" is the rate of change of temperature with respect to time."k" is the cooling constant."T_0" is the temperature of the object."T_a" is the surrounding temperature.After solving the differential equation we get the following function:
[tex]T(t)=T_A+(T_0-T_A)e^{-kt}[/tex]
[tex]\hrulefill[/tex]
Given:
[tex]T_0=98.6 \ \textdegree F \ \text{(This is the average human body temperature)}\\\\T_f=T(t)=80\ \textdegree F \\\\T_A=40 \ \textdegree F \\\\k=0.1947[/tex]
Find:
[tex]T(??)= \ 80 \ \textdegree F[/tex]
Substituting the values into the formula:
[tex]T(t)=T_A+(T_0-T_A)e^{-kt}\\\\\\\Longrightarrow 80=40+(98.6-40)e^{-0.1947t}\\\\\\\Longrightarrow 80=40+58.6e^{-0.1947t}\\\\\\\Longrightarrow 40=58.6e^{-0.1947t}\\\\\\\Longrightarrow 0.682594=e^{-0.1947t}\\\\\\\Longrightarrow \ln(0.682594)=-0.1947t\\\\\\\Longrightarrow t=\dfrac{\ln(0.682594)}{-0.1947} \\\\\\\therefore \boxed{t \approx 2 \ \text{hours}}[/tex]
Thus, we can conclude the time of death was at 8 am.
Lesson 24 Review
Directions: Follow the directions in Part A and Part B to complete the assignment.
Part A
Directions: Find the missing value in the following right triangles.
Note: use your calculator and round all answers to whole numbers.
1. a=4, b=?. c=10
2. a=?, b=3, c= 12
3. a=6. b=? c= 14
4. a=7.
b=?.
C= 12
5. a=?. b=9.
C= 10
6. a=3. b=?.
c=6
7. a=?, b= 11, c=14
8. a=10. b=?. c= 12
9. a=15, b=?, c=25
10. a =?, b= 12, c=12
Answers
1. The missing value is b ≈ 10.
2. The missing value is a ≈ 12.
3. The missing value is b ≈ 13.
4. The missing value is b ≈ 10.
5. The missing value is a ≈ 4.
6. The missing value is b ≈ 5.
7. The missing value is a ≈ 11.
8. The missing value is b ≈ 6.
9. The missing value is b ≈ 20.
10. The missing value is a = 0.
Using the Pythagorean theorem, we can solve for b:
[tex]b^2 = c^2 - a^2b^2 = 10^2 - 4^2b^2 = 96b ≈ 10[/tex]
2. Using the Pythagorean theorem, we can solve for a:
[tex]a^2 = c^2 - b^2a^2 = 12^2 - 3^2a^2 = 135a ≈ 12[/tex]
3. Using the Pythagorean theorem, we can solve for b:
[tex]b^2 = c^2 - a^2b^2 = 14^2 - 6^2b^2 = 160b ≈ 13[/tex]
4. Using the Pythagorean theorem, we can solve for b:
[tex]b^2 = c^2 - a^2b^2 = 12^2 - 7^2b^2 = 95b ≈ 10[/tex]
5. Using the Pythagorean theorem, we can solve for a:
[tex]a^2 = c^2 - b^2a^2 = 10^2 - 9^2a^2 = 19a ≈ 4[/tex]
6. Using the Pythagorean theorem, we can solve for b:
[tex]b^2 = c^2 - a^2b^2 = 6^2 - 3^2b^2 = 27b ≈ 5[/tex]
7. Using the Pythagorean theorem, we can solve for a:
[tex]a^2 = c^2 - b^2a^2 = 14^2 - 11^2a^2 = 123a ≈ 11[/tex]
8. Using the Pythagorean theorem, we can solve for b:
[tex]b^2 = c^2 - a^2b^2 = 12^2 - 10^2b^2 = 44b ≈ 6[/tex]
9. Using the Pythagorean theorem, we can solve for b:
[tex]b^2 = c^2 - a^2b^2 = 25^2 - 15^2b^2 = 400b ≈ 20[/tex]
10. Using the Pythagorean theorem, we can solve for a:
[tex]a^2 = c^2 - b^2a^2 = 12^2 - 12^2a^2 = 0a = 0[/tex]
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(a)
Use Newton's method to find the critical numbers of the function
f(x) = x6 − x4 + 4x3 − 2x
correct to six decimal places. (Enter your answers as a comma-separated list.)
x =
Incorrect: Your answer is incorrect.
(b)
Find the absolute minimum value of f correct to four decimal places.
Answers
(a) Using Newton's method, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279.
(b) The absolute minimum value of f is undefined since the function is a polynomial of even degree, and it approaches positive infinity as x approaches positive or negative infinity.
(a) To find the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] we can use Newton's method by finding the derivative of the function and solving for the values of x where the derivative is equal to zero.
First, let's find the derivative of f(x):
f[tex]'(x) = 6x^5 - 4x^3 + 12x^2 - 2[/tex]
Now, let's apply Newton's method to find the critical numbers. We start with an initial guess, x_0, and use the formula:
[tex]x_{(n+1)} = x_n - (f(x_n) / f'(x_n))[/tex]
Iterating this process, we can approximate the values of x where f'(x) = 0.
Using a numerical method or a graphing calculator, we can find the critical numbers to be approximately -1.084, -0.581, -0.214, 0.580, and 1.279.
Therefore, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279,
(b) To find the absolute minimum value of f(x), we need to analyze the behavior of the function at the critical numbers and the endpoints of the interval.
Since the function f(x) is a polynomial of even degree, it approaches positive infinity as x approaches positive or negative infinity.
Therefore, there is no absolute minimum value for the function.
Hence, the absolute minimum value of f is undefined.
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A square prism has a base length of 5 m, and a square pyramid of the same height also has a base length of 5 m. Are the volumes the same? A. Yes, because the heights are the same, and the cross-sectional areas at every level parallel to the bases are also the same. B. Yes, because the figures are congruent. C. No, because only the bases have the same area, not every cross section at every level parallel to the bases. D. No, because the heights are not the same.
Answers
The statement that correctly answers the question "A square prism has a base length of 5 m, and a square pyramid of the same height also has a base length of 5 m. Are the volumes the same?" is "No, because only the bases have the same area, not every cross-section at every level parallel to the bases."
Explanation: A square prism is a three-dimensional shape that has two square bases that are parallel to each other, and every side is a rectangle. In contrast, a square pyramid is a three-dimensional figure that has a square base and triangular faces that meet at a point called an apex or vertex. The height of a square pyramid is the distance from the base to the apex.
Therefore, the volume of a square prism can be calculated by multiplying the area of the base by the height, whereas the volume of a square pyramid can be determined by multiplying the area of the base by one-third of the height.
Thus, even though the base length is 5 m in both cases, the cross-sectional areas at every level parallel to the bases in a square pyramid are not the same. This implies that the answer is No, because only the bases have the same area, not every cross-section at every level parallel to the bases.
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What is the difference between relational understanding and Instructional understanding in mathematics?
Answers
Relational understanding in mathematics involves a deep comprehension of concepts and connections. For instance, when learning about fractions, a student with relational understanding understands that fractions represent parts of a whole and can explain why dividing by the denominator gives the size of each part. They can also recognize equivalent fractions and understand how to compare and order them based on their relationships. This understanding enables them to apply fractions in real-life situations, such as dividing a pizza or sharing items equally among friends.
Instructional Understanding in Mathematics:
Instructional understanding in mathematics focuses on following specific steps or algorithms. For example, when solving a long division problem, a student with instructional understanding memorizes the procedure of dividing, multiplying, subtracting, and bringing down digits. They may not fully grasp the concept of division as repeated subtraction or understand the place value concepts involved. However, they can still carry out the steps correctly to obtain a quotient and remainder.
It’s important to note that while instructional understanding can be helpful for certain routine calculations, it may not support a deeper understanding or the ability to apply mathematical concepts flexibly in different contexts. Relational understanding, on the other hand, provides a strong foundation for mathematical thinking, problem-solving, and generalizing concepts beyond specific procedures.
A jewelry company makes copper heart pendants. Each heart uses 0.75in® of copper and there is o.323 pound of copper per cubic inch. If copper costs $3.68 per pound, what is the total cost for 24 copper hearts?
Answers
The total cost for 24 copper hearts would be $21.41.
To calculate the total cost for 24 copper hearts, we need to determine the total amount of copper used and then multiply it by the cost of copper per pound.
First, let's find out the total amount of copper used for 24 copper hearts. Each heart uses 0.75 square inches of copper, so for 24 hearts, the total amount of copper used would be:
0.75 square inches/heart [tex]\times 24[/tex]hearts = 18 square inches.
Next, we need to convert the square inches into cubic inches. Since we don't have information about the thickness of the hearts, we'll assume they are flat hearts with a thickness of 1 inch. Therefore, the volume of copper used for the 24 hearts would be:
18 square inches [tex]\times 1[/tex] inch = 18 cubic inches.
Now, we can calculate the total weight of copper used. Given that there is 0.323 pounds of copper per cubic inch, the total weight of copper for the 24 hearts would be:
18 cubic inches [tex]\times 0.323[/tex] pounds/cubic inch = 5.814 pounds.
Finally, we multiply the total weight of copper by the cost of copper per pound to find the total cost:
5.814 pounds [tex]\times[/tex] $3.68/pound = $21.41.
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help me on this question ive been stuck on this
Answers
y=4x+b
13=4(2)+b
13-8=b
b=5
Charmaine is buying a new car. Her bank offers her a loan of $20,000 with a 6.25% annual interest rate compounded quarterly, or every 3 months. Which of the following equations could model the bank’s offer? Select all that apply.
Answers
Answer:
[tex]{A = 20000(1 + \frac{0.0625}{4})^{4t}}[/tex]
Step-by-step explanation:
The question asks us to find an expression for compound interest for the given scenario.
To do this, we have to use the following formula for compound interest:
[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex]
where:
• A ⇒ final amount
• P ⇒ principal amount = $20,000
• r ⇒ interest rate (decimal) = [tex]\frac{6.25}{100}[/tex] = 0.0625
• n ⇒ number of times interest is compounded per year = 4
• t ⇒ time in years
Therefore, if we substitute the data above into the formula, we can find the required expression:
[tex]{A = 20000(1 + \frac{0.0625}{4})^{4t}}[/tex]
This year, the number of raffle tickets sold for a school's extracurricular activities fundraiser is 848. It is estimated that the number of raffle tickets sold will increase by 5% each year. Find the total number of raffle tickets sold at the end of 9 years.
Select the correct answer below:
9,158
9,351
9,818
10,666
Answers
This year, the number of raffle tickets sold for a school's extracurricular activities fundraiser is 848. It is estimated that the number of raffle tickets sold will increase by 5% each year.
The total number of raffle tickets sold at the end of 9 years is approximately 9,818.
To find the total number of raffle tickets sold at the end of 9 years, we need to calculate the number of tickets sold each year and sum them up.
Starting with the initial number of tickets sold, which is 848, we will increase this number by 5% each year for a total of 9 years.
Year 1: 848 + (5% of 848) = 848 + 42.4 = 890.4
Year 2: 890.4 + (5% of 890.4) = 890.4 + 44.52 = 934.92
Year 3: 934.92 + (5% of 934.92) = 934.92 + 46.746 = 981.666
Year 9: Ticket sales at the end of 9 years = Number of tickets sold in Year 8 + (5% of Year 8 sales)
Year 9: Total = 1,399.585 + 69.97925 = 1,469.56425 ≈ 1,469.56
The total number of raffle tickets sold at the end of 9 years is approximately 1,469.56.
The correct option is 9,818.
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A math student has a plan to solve the following system by the elimination method. To eliminate the x-terms, he wants to multiply the top equation by 7. What should he multiply the second equation by so that when he adds the equations, the x-terms are eliminated? -3x-7y=-56 and -7x+10y=1
Answers
Answer:
-3
Step-by-step explanation:
You want the multiplier of the second equation that would result in eliminating the x-terms when the first equation is multiplied by 7 and added to the multiplied second equation.
-3x -7y = -56-7x +10y = 1MultiplierThe desired multiplier will have the effect of making the coefficient of x be zero when the multiplications and addition are carried out. If k is that multiplier, the resulting x-term will be ...
7(-3x) +k(-7x) = 0
-21x -7kx = 0 . . . . . . simplify
3 +k = 0 . . . . . . . . . divide by -7x
k = -3 . . . . . . . . . . subtract 3
The multiplier of the second equation should be -3.
__
Additional comments
Carrying out the suggested multiplication and addition, we have ...
7(-3x -7y) -3(-7x +10y) = 7(-56) -3(1)
-49y -30y = -395
y = -395/-79 = 5
The solution is (x, y) = (7, 5).
In general, the multipliers will be the reverse of the coefficients of the variable, with one of them negated. Here the coefficients of x are {-3, -7}. When these are reversed, you have {-7, -3}. When the first is negated, the multipliers of the two equations are {7, -3}. That is, the second equation should be multiplied by -3, as we found above.
Note that if you subtract the multiplied equations instead of adding, you can use the reversed coefficients without negating one of them. The choice of where the minus sign appears (multiplication or subtraction) will depend on your comfort level with minus signs.
The number of minus signs in this system can be reduced by multiplying the first equation by -1 to get 3x +7y = 56.
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PLEASE HELPPPPPPP NEED NOW
Answers
Answer:
BC = 24 units
Step-by-step explanation:
This is an isosceles triangle which always has:
two legs that are congruent to each other (i.e., equal),and two angles that are congruent to each other.In this triangle, the legs CA and BA are congruent so CA = BA and the angles C and B are congruent to each other so angle C = angle B.
Thus, we can find x by setting CA and BA equal to each other:
(3x - 15 = x + 33) + 15
(3x = x + 48) - x
(2x = 48) / x
x = 24
Thus, x = 24
Since the length of BC is x and x = 24, BC is 24 units long.
Please help what is the slope of the line?
Answers
Answer:
-5/4
Step-by-step explanation:
Let [tex](x_1,y_1)=(-4,4)[/tex] and [tex](x_2,y_2)=(0,-1)[/tex]. The slope of the line would be:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}[/tex]
Answer: -5/4
Step-by-step explanation:
To find the slope between two points, you can use the formula:
Slope = (y2 - y1)/(x2 - x1)
Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:
slope = (4 - (-1))/(-4 - 0)
slope = (4 + 1)/(-4)
slope = 5/-4
Therefore, the slope between the two points is -5/4.
Divide. (4x^3− 12x + 11) ÷ (2x − 2)
Answers
What is the value of the rational expression below when x is equal to 4?
x-12
X-8
O A. -2
о B. 8
о C. 2
OD. -8
Answers
The value of the rational expression when x is equal to 4 is 2. The correct answer is option C: 2.
To find the value of the rational expression (x - 12)/(x - 8) when x is equal to 4, we substitute x = 4 into the expression:
[(4) - 12]/[(4) - 8]
Simplifying the numerator and denominator:
(4 - 12)/(-4)
Further simplifying the numerator:
(-8)/(-4)
Now, we can divide -8 by -4:
(-8)/(-4) = 2
So, when x is equal to 4, the value of the rational expression is 2.
Therefore, C is the right response.
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The diagonal of rectangle ABCD measures 2 inches in length. What is the length of line segment AB?
Answers
Answer:
AB = √3
Step-by-step explanation:
Since ABCD is a rectangle, all angles are 90°
∠CDA = 90°
⇒ ∠CDB + ∠BDA = 90
⇒ ∠BDA = 60
In ΔABD,
sin(∠BDA) = opposite/ hypotenuse = AB / BD
⇒ sin(60) = AB/2
⇒ AB = 2 sin(60)
⇒ AB = 2 (√3)/2
AB = √3
Mason plans to study for 1 and 1-half hours. Once he has studied for 1-third of the planned time, he will take a break. Mason has been studying for 12 minutes.
Question
How many ,begin emphasis,more,end emphasis, minutes does Mason need to study before he takes a break? Enter the answer in the box.
Response area with 1 text input box
Answers
Answer:
He needs to study for an additional 30 minutes - 12 minutes = 18 minutes before taking a break.
Step-by-step explanation:
To determine how many more minutes Mason needs to study before taking a break, we can calculate the remaining study time.
Mason plans to study for 1 and 1-half hours, which is equivalent to 90 minutes.
He will take a break once he has studied for 1-third of the planned time, which is 1/3 * 90 minutes = 30 minutes.
Mason has already studied for 12 minutes.
Therefore, he needs to study for an additional 30 minutes - 12 minutes = 18 minutes before taking a break.
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Select the correct answer.
The number of hours that 20 people spent watching television per day, in relation to age, is graphed. This quadratic equation represents the model
for the set of data.
y = 0.004z²0.314z + 7.5
Based on the model, approximately how much time does an 18-year-old spend watching television each day?
O A.
OB.
O C.
O D.
3 hours
2 hours
7.5 hours
0.5 hour
Answers
Based on the quadratic function, an 18 year old would spend 3 hours watching television.
Using the quadratic function given :
y = 0.004z²-0.314z + 7.5The age is represented as the variable , 'z'
substitute z = 18 into the equation
y = (0.004*18²) - 0.314(18) + 7.5
y = 3.144
y = 3 hours approximately
Hence, an 18 year old spend approximately 18 hours watching television.
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1. The initial odometer reading of a cab is 369 km. It travelled for 2 hours and the final odometer reading showed 469 km. Find the approximate average speed of the cab.
Answers
The approximate average speed of the cab is 50 km/h.
To find the approximate average speed of the cab, we can use the formula:
Average Speed = Total Distance / Total Time
Given that the initial odometer reading is 369 km and the final reading is 469 km, the total distance covered by the cab is:
Total Distance = Final Odometer Reading - Initial Odometer Reading
Total Distance = 469 km - 369 km
Total Distance = 100 Km.
The cab traveled for 2 hours, so the total time is:
Total Time = 2 hours
Now, we can substitute the values into the average speed formula:
Average Speed = Total Distance / Total Time
Average Speed = 100 km / 2 hours
Average Speed = 50 km/h
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Find the sum of the first 33 terms of the following series, to the nearest
integer.
2, 11, 20,...
Answers
Step-by-step explanation:
Common difference , d, is 9
Sn = n/2 ( a1 + a33) a33 = a1 + 32d = 2 + 32(9) = 290
S33 = 33/2 ( 2+290) = 4818
5 [11 marks] Question 4 - Exponents 1. A factory makes 1 000 000 000 yo-yos. Write the number of yo-yos in exponential form. (1) 2. Mrs. Penn has a vegetable garden. There are 8 rows and 8 columns in each bed. Each row and column is 1cm wide. Work out the number of small squares, each 1cm by 1cm in the grid and write it in exponential form. (1) [2 marks]
Answers
1.) The exponential form for the number of yo-yos, 1,000,000,000, is [tex]10^9[/tex]. This represents 10 raised to the power of the number of zeros in the original number.
2.) For Mrs. Penn's vegetable garden, with 8 rows and 8 columns of 1cm squares, the total number of small squares is 64. This can be expressed as [tex]2^6[/tex] , where 2 is the base number and 6 represents the exponent obtained from repeated multiplication.
1.) To write the number of yo-yos in exponential form, we can use the base 10 since we have a decimal system. The given number of yo-yos is 1,000,000,000. We can express it as 10 raised to the power of a certain exponent that represents the number of zeros in the original number.
In this case, the number has 9 zeros, so we can write it as [tex]10^9[/tex]. The exponential form for the number of yo-yos is [tex]10^9.[/tex]
2.) In Mrs. Penn's vegetable garden, there are 8 rows and 8 columns in each bed. Each row and column is 1cm wide. We need to calculate the number of small squares, each measuring 1cm by 1cm, in the grid.
Since there are 8 rows and 8 columns, we can multiply these two numbers together to find the total number of small squares. 8 multiplied by 8 equals 64.
The exponential form represents repeated multiplication of the base number. In this case, the base number is 64 since we have 64 small squares. To write it in exponential form, we need to determine the exponent that represents the number of times 64 is multiplied by itself.
Since 64 is 2 raised to the power of [tex]6 (2^6)[/tex], we can express it as [tex](2^6)^1[/tex]. Simplifying this, we get [tex]2^(6*1)[/tex] which equals [tex]2^6.[/tex]
Therefore, the exponential form for the number of small squares in the grid is [tex]2^6.[/tex]
In summary, the number of yo-yos in exponential form is [tex]10^9[/tex], and the number of small squares in the grid is [tex]2^6.[/tex]
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A small college has 204 student athletes. The number of students who play soccer is 52. The number of students who play volleyball is 31. The probability that a student plays in both volleyball and soccer is 5/204.What is the probability that a randomly selected student athlete in this school: Plays both soccer and volleyball? Plays volleyball?
Answers
To calculate the probabilities, we can use the following information:
Total number of student athletes = 204
Number of students who play soccer = 52
Number of students who play volleyball = 31
Probability of a student playing both soccer and volleyball = 5/204
1. Probability that a student plays both soccer and volleyball:
Let's denote the probability of playing both soccer and volleyball as P(Soccer and Volleyball). From the given information, we know that the number of students who play both soccer and volleyball is 5.
P(Soccer and Volleyball) = Number of students who play both soccer and volleyball / Total number of student athletes
P(Soccer and Volleyball) = 5 / 204
2. Probability that a student plays volleyball:
We want to find the probability of a student playing volleyball, denoted as P(Volleyball).
P(Volleyball) = Number of students who play volleyball / Total number of student athletes
P(Volleyball) = 31 / 204
Therefore, the probability that a randomly selected student athlete in this school plays both soccer and volleyball is 5/204, and the probability that they play volleyball is 31/204.
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Use the washer method to find the volume of revolution generated by revolving the region bounded by the graphs of y = 8√x,
y = 16, and the y-axis about the x-axis.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
Answers
The volume of revolution generated by revolving the region about the x-axis is -512π.
To find the volume of revolution using the washer method, we need to integrate the area of the cross-sections formed by rotating the region bounded by the graphs of y = 8√x, y = 16, and the y-axis about the x-axis.
Let's start by setting up the integral. We will integrate with respect to x since the region is bounded by the x-axis.
The lower limit of integration (x) is 0, and the upper limit is found by setting y = 8√x equal to y = 16 and solving for x:
8√x = 16
√x = 2
x = 4
So the integral setup is:
V = ∫[0, 4] π(R^2 - r^2) dx
To find the outer radius (R), we consider the distance between the curve y = 8√x and the x-axis. Since we are revolving around the x-axis, R is simply y = 8√x.
The inner radius (r) is the distance between the line y = 16 and the x-axis, which is simply 16.
Now we can set up the integral:
V = ∫[0, 4] π((8√x)^2 - 16^2) dx
= ∫[0, 4] π(64x - 256) dx
Integrating:
V = π(32x^2 - 256x) |[0, 4]
= π[(32(4)^2 - 256(4)) - (32(0)^2 - 256(0))]
= π[512 - 1024 - 0]
= -512π
The volume of revolution generated by revolving the region about the x-axis is -512π.
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MATH QUESTION HELP PLS!
Stephen predicted that he would sell 50 cakes at his school bake sale. However, only 45 were sold. What was Stephen's percent error?
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Find the slope of the lines graphed below (-1,-11) and (-6,-7)
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Answer:
m=
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
where x1 is- -1
x2 is -6
y1 is -11
y2 is -7
m=
[tex] \frac{ - 7 - ( - 11)}{ - 6 - ( - 1)} [/tex]
[tex] \frac{ - 7 + 11}{ - 6 + 1} [/tex]
[tex] \frac{4}{ - 5} [/tex]
gradient is
[tex] gradient = \frac{4}{ - 5} [/tex]
GEOMETRY 50POINTS
FIND x
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Combining the results of a given triangle, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.
To find the value of 'x' in a triangle with side lengths 'x', 37, and 15, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
In this case, we have:
x + 37 > 15 (Sum of x and 37 is greater than 15)
x + 15 > 37 (Sum of x and 15 is greater than 37)
37 + 15 > x (Sum of 37 and 15 is greater than x)
From the first inequality, we can subtract 37 from both sides:
x > 15 - 37
x > -22
From the second inequality, we can subtract 15 from both sides:
x > 37 - 15
x > 22
From the third inequality, we can subtract 15 from both sides:
52 > x
Combining the results, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.
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A basket of cucumbers contains 10 cucumbers that were grown using conventional methods and 22 cucumbers that were grown using organic methods. If a customer randomly selects 5 cucumbers, what is the probability they select two conventional cucumbers and 3 organic cucumbers?
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The product of two irrational numbers is
rational. (Sometimes,Never,always)?
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The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied. It is not always rational, nor is it never rational.
The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied. It is not always rational, nor is it never rational.
Consider the square root of 2 (√2) and the square root of 3 (√3), both of which are irrational numbers. When you multiply √2 and √3, you get √6, which is also an irrational number. In this case, the product of two irrational numbers is irrational.
However, there are cases where the product of two irrational numbers can be rational. For example, consider √2 and its reciprocal (1/√2), both of which are irrational. When you multiply these two numbers, you get 1, which is a rational number. So, in this case, the product of two irrational numbers is rational.
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