Answers
Answer:
Step-by-step explanation:
Triangle DEF is a right angle triangle.
From the given right angle triangle
DF represents the hypotenuse of the right angle triangle.
With m∠D as the reference angle,
DE represents the adjacent side of the right angle triangle.
EF represents the opposite side of the right angle triangle.
To determine EF, we would apply the Sine trigonometric ratio
Sin θ = opposite side/hypotenuse. Therefore,
Sin 26 = EF/4.5
0.44 = EF/4.5
EF = 4.5 × 0.44 = 1.98 yo 2 decimal places
Related Questions
Select all expressions that represent a correct solution to the equation 6(x+4)=20. copied for free from openupresources.Org Select all that apply: A. (20−4)÷6 B. 16(20−4) C. 20−6−4 D. 20÷6−4 E. 1/6(20−24) F. (20−24)÷6
Answers
Option D: [tex]20 \div 6-4[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]
Option E: [tex]\frac{1}{6} (20-24)[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]
Option F: [tex](20-24) \div 6[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]
Explanation:
The expression is [tex]6(x+4)=20[/tex]
Let us find the value of x.
[tex]\begin{aligned}6(x+4) &=20 \\6 x+24 &=20 \\6 x &=-4 \\x &=-\frac{2}{3}\end{aligned}[/tex]
Now, we shall find the expression that is equivalent to the value [tex]x=-\frac{2}{3}[/tex]
Option A: [tex](20-4) \div 6[/tex]
Simplifying the expression, we have,
[tex]\frac{16}{6}=\frac{8}{3}[/tex]
Since, [tex]\frac{8}{3}[/tex] is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex](20-4) \div 6[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option A is not the correct answer.
Option B: [tex]16(20-4)[/tex]
Simplifying the expression, we have,
[tex]16(16)=256[/tex]
Since, 256 is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]16(20-4)[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option B is not the correct answer.
Option C: [tex]20-6-4[/tex]
Simplifying the expression, we have,
[tex]20-10=10[/tex]
Since, 10 is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]20-6-4[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option C is not the correct answer.
Option D: [tex]20 \div 6-4[/tex]
Using PEMDAS and simplifying the expression, we have,
[tex]$\begin{aligned}(20 \div 6)-4 &=\frac{10}{3}-4 \\ &=\frac{10-12}{3} \\ &=-\frac{2}{3} \end{aligned}$[/tex]
Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]20 \div 6-4[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option D is the correct answer.
Option E: [tex]\frac{1}{6} (20-24)[/tex]
Simplifying the expression, we have,
[tex]$\begin{aligned} \frac{1}{6}(20-24) &=\frac{1}{6}(-4) \\ &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$[/tex]
Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]\frac{1}{6} (20-24)[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option E is the correct answer.
Option F: [tex](20-24) \div 6[/tex]
Simplifying the expression, we have,
[tex]$\begin{aligned}(20-24) \div 6 &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$[/tex]
Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex](20-24) \div 6[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]
Hence, Option F is the correct answer.
To solve 6(x + 4) = 20, we isolate x to get x = -2/3. The correct expressions representing the solution are E. 1/6(20 - 24) and F. (20 - 24) / 6.
To solve the equation 6(x + 4) = 20, we need to isolate x.
First, distribute the 6 on the left-hand side:
6x + 24 = 20
Next, subtract 24 from both sides:
6x = -4
Finally, divide by 6:
x = -4/6 = -2/3
Now, let's analyze the given choices:
A. (20 - 4) ÷ 6: This simplifies to 16 / 6, which does not match x = -2/3.B. 16(20 - 4): This simplifies to 16 × 16, which is incorrect.C. 20 - 6 - 4: This simplifies to 10, which is incorrect.D. 20 ÷ 6 - 4: This simplifies to 10/3 - 4, which is incorrect.E. 1/6(20 - 24): This simplifies to 1/6(-4) = -2/3, which matches the solution.F. (20 - 24) / 6: This simplifies to -4/6 = -2/3, which matches the solution.Therefore, the correct choices are E and F.
Helppp i need answer asap
Answers
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle
BC represents the hypotenuse of the right angle triangle.
With m∠B as the reference angle,
AB represents the adjacent side of the right angle triangle.
AC represents the opposite side of the right angle triangle.
To determine BC , we would apply the Sine trigonometric ratio which is expressed as
Tan θ = opposite side/hypotenuse. Therefore,
Sin 44 = 10/BC
0.695 = 10/BC
BC = 10/0.695
BC = 14.4 to 1 decimal place.
Question 5 options: What is the approximate area of a circle with a radius of 11 cm? Use 3.14 for π. ______ cm2
Answers
The area of circle is 379.94 cm².
Step-by-step explanation:
Given,
Radius of circle = 11 centimeters
We have to calculate the area of circle.
We know that;
Area of circle = [tex]\pi r^2[/tex]
Here;
π = 3.14 , r = 11
Area of circle = [tex]3.14*(11)^2[/tex]
Area of circle = 3.14*121
Area of circle = 379.94 squared centimeters
The area of circle is 379.94 squared centimeters.
Keywords: area, circle
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In a certain corporation, 2/3 of the employees are men and 1/3 are women. Of the men, 5/8 are college-educated and 3/8 are not. Of the women, 2/5 are college-educated and 3/5 are not. What percentage of the employees are college-educated? What percentage of the college-educated employees are women?
Answers
Answer:
55% and 24%
Step-by-step explanation:
Firstly, we need an arbitrary number to serve as the number of students.
Let the total number of students be 120.
Firstly we need college-educated percentage.
Men are two-thirds, women are one-third
Men = 2/3 * 120 = 80
Women = 1/3 * 120 = 40
5/8 of men are college educated = 5/8 * 80 = 50
2/5 of women are college educated = 2/5 * 40 = 16
Total college educated = 50+ 16 = 66
% college educated = 66/120 * 100 = 55%
Percentage of college educated that are women.
Total college educated = 66
The % is 16/66 * 100 = 24%
Airplane at 19,200 feet descending at a rate of 40 feet per second. Another airplane takes off and ascends at a rate of 60 feet per second. After how many seconds will the airplanes be at the same height? What is the height
Answers
Answer:
Step-by-step explanation:
Let t = flying time in seconds for each plane
Descending rate = 40 ft/s
Ascending rate = 60 ft/s
Descending height, hd= 19200 - 40t
Ascending height, ha = 60t
Equating hd = ha, therefore:
60t = 19200-40t
60t + 40t = 19200
100t = 19200
t = 19200/100
t = 192 seconds
h = 19200 - 192(40)
h = 19200 - 7680
= 11,520 ft.
After 192 seconds, the two airplanes will be at the same height, which is 11,520 feet.
Explanation:To find the time it takes for the two airplanes to be at the same height, we need to set up an equation based on their rates of ascent and descent. Let's assume the height of the descending airplane is given by h1 and the height of the ascending airplane is given by h2. The descending airplane is descending at a rate of 40 feet per second, so its height after t seconds can be represented by the equation h1 = 19,200 - 40t. The ascending airplane is ascending at a rate of 60 feet per second, so its height after t seconds can be represented by the equation h2 = 60t. To find the time at which the two airplanes are at the same height, we can set h1 equal to h2 and solve for t: 19,200 - 40t = 60t. Simplifying this equation, we get 100t = 19,200, so t = 192 seconds. Therefore, after 192 seconds, the two airplanes will be at the same height.
To find the height at which the two airplanes are at, we can substitute the value of t into either the equation for h1 or h2. Let's use the equation for h1: h1 = 19,200 - 40(192) = 19,200 - 7,680 = 11,520 feet. Therefore, after 192 seconds, the two airplanes will be at a height of 11,520 feet.
Interpret the average rate of change of -14/7 that you found previously. What does this mean in terms if the waterslide, from x=0 to x=15
Answers
Answer:
1. The vertical components decrease by 14 units while the horizontal component increase by 3 units
2.it therefore means that the vertical component decreases by 70units
Step-by-step explanation:
Slope of a graph is change in the vertical axis over the the change in the horizontal axis
in the above question, if the average rate of change is -14/7 it therefore means that the vertical components decrease by 14 units while the horizontal component inc rfease by 3 units
what does that mean if the waterslide from x=0, and x=15
it means that the vertical components decrease why there is an increment distance in the horizontal axis
mathematically, we say
-14/3=-y/[tex]s= \frac{dy}{dx} , slope=s\\-14/3=\frac{-y}{15-0}[/tex]
14/3=y/15
y=70
it therefore means that the vertical component decreases by 70units
Answer:
On average, the slide drops 14 feet for every 3 feet of horizontal distance.
On average, the slide drops about 4.7 feet for every 1 foot of horizontal distance.
Step-by-step explanation:
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A line perpendicular to another line or to a tangent line is called a normal line. Find an equation of the line perpendicular to the line that is tangent to the following curve at the given point P.
Y=x^2-3x
P (7, 28)
The equation of the normal line at P(7, 28) is:
Answers
Answer:
The equation of the normal line to the curve y = x² - 3x at the point (7, 28) is 11y + x - 315 = 0
Step-by-step explanation:
First, we need to find the slope of the line tangent to the curve at the point (7, 28).
To do this, we need to differentiate y with respect to x and evaluate at the point x0 = 7.
Given y = x² - 3x
dy/dx = 2x - 3
So, the slope, m of the tangent line is dy/dx at x = 7:
m = 2(7) - 3 = 11
Slope, m = 11
The slope, m2 of the line perpendicular to the tangent is given as m2 = -1/m
m2 = −1/11
Finally, given the slope m of a line, and a point (x0, y0) on the line, we can use the point-slope form of the equation of a line:
y - y0=m(x - x0)
The perpendicular line has slope m2 = -1/11, and (7, 28) is a point on that line, the desired equation is:
y - 28 = (-1/11)(x - 7)
Or multiplying by 11, we have
11y - 308 = -x + 7
11y + x - 315 = 0
The slope of the curve at point (7,28) is 11, found by differentiating the given function. The slope of the normal line is the negative reciprocal of that, -1/11. Inserting these into the line equation, we get y - 28 = -1/11 * (x - 7).
Explanation:To find the equation of the line perpendicular to the tangent line, we first find the slope of the tangent line. The derivative of the given function y = x^2 - 3x tells us the slope of the curve at any point, so let's find the derivative:
y' = 2x - 3
Now, let's find the slope of the tangent line at the point (7,28) by plugging 7 into the derivative:
y'(7) = 2*7 - 3 = 11
The slope of the line perpendicular to this (the normal line) is the negative reciprocal of the tangent line's slope, so it's -1/11.
The equation of the line with slope m that goes through the point (x1, y1) is:
y - y1 = m*(x - x1)
Substitute the slope of -1/11 and the point (7,28) into this equation to get the equation of the normal line:
y - 28 = -1/11 * (x - 7)
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A square park has a diagonal walkway from one corner to another. If the walkway is 120 meters long, what is the approximate length of each side of the park?
Answers
Answer:
85 m
Step-by-step explanation:
The diagonal of a square is √2 times the length of the side. The park will have a side length of 120/√2 m ≈ 84.85 m, about 85 meters.
_____
The relations are ...
diagonal = (√2)×(side length)
side length = diagonal/√2 . . . . . . . . . divide the above equation by √2
The celluloid cinema sold150 tickets to a movie. Some of these were child tickets and the rest were adult tickets.A child ticket cost $7.75 and an adult ticket cost $10.25. If the cinema sold $1470 worth of tickets, which system of equations could be used to determine how many adult tickets,a,and how many child tickets,c, were sold
Answers
Answer: the system of equations are
a + c = 150
7.75a + 10.25b = 1470
Step-by-step explanation:
Let a represent the number of adult tickets that were sold.
Let c represent the number of child tickets that were sold.
The celluloid cinema sold 150 tickets to a movie. Some of these were child tickets and the rest were adult tickets. This means that
a + c = 150 - - - - - - - - - - - - - -1
A child ticket cost $7.75 and an adult ticket cost $10.25. If the cinema sold $1470 worth of tickets, it means that
7.75a + 10.25b = 1470 - - - - - - - - -2
The question can be answered by creating two linear equations, one representing the total number of tickets (a + c = 150) and the other representing the total earnings from the ticket sales (10.25a + 7.75c = 1470). Solving this system of equations will yield the number of adult and child tickets sold.
Explanation:This problem can be solved using a system of linear equations, where one equation represents the total number of tickets sold and the other equation represents the total dollar value of the tickets sold.
The first equation is formed from the total number of tickets, which is the sum of adult tickets and child tickets: a + c = 150
The second equation is formed from the total cost of the tickets, where $10.25, the cost of an adult ticket, is multiplied by the number of adult tickets, and $7.75, the cost of a child ticket, is multiplied by the number of child tickets. This sum should be the total earnings from the ticket sales: 10.25a + 7.75c = 1470
Therefore, the system of equations to solve this problem is a + c = 150 and 10.25a + 7.75c = 1470.
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Find the volume of a cube with side length of 7 in.
A: 147 in³ B: 49 in³
C:215 in³ D: 343 in³
Answers
Answer: 343 in³
Explanation: In this problem, we're asked to find the volume of a cube.
It's important to understand that a cube is a type of rectangular prism and the formula for the volume of a rectangular prism is shown below.
Volume = length × width × height
In a cube however, the length, width, and height are all the same. So we can use the formula side × side × side instead.
So the formula for the volume of a cube is side × side × side or s³.
So to find the volume of the given cube, since each side has a length of 7 inches, we can plug this information into the formula to get (7 in.)³ or (7 in.)(7 in.)(7 in).
7 x 7 is 49 and 49 x 7 is 343.
So we have 343 in³.
So the volume of the given cube is 343 in³.
Answer:
343 in³
Step-by-step explanation:
The range for a list of measurements equals the greatest measurement minus the least measurement. The two lists of measurements, X and Y, combined consist of 30 measurements with a range of 25. What is the range for the measurements in list X?
Answers
Answer:
Insufficient information
Step-by-step explanation:
The information provided us isn't sufficient to determine the range for the measurements in list X. Because we need to be given the range for the measurements in Y at least. We also need the number of measurements in both X and Y.
When you add their numbers together you get 207 . Jen's number is 9 more than Carrie's, and Fran's number is 3 less than Jen's number. What is Fran's number?
Answers
Final answer:
By defining equations based on the relationships between Jen's, Carrie's, and Fran's numbers and solving them, we find that Carrie's number is 64, Jen's number is 73, and Fran's number is 70.
Explanation:
To solve for Fran's number, we need to use the information given: Jen's number is 9 more than Carrie's, and Fran's number is 3 less than Jen's number. Their total sum is 207. We can set up equations to solve this. Let Carrie's number be c, Jen's number be c + 9 (since it is 9 more than Carrie's), and Fran's number be c + 9 - 3 (since it is 3 less than Jen's).
The equation to express the sum of their numbers will be: c + (c + 9) + (c + 9 - 3) = 207.
Now let's solve the equation:
Combine like terms: 3c + 15 = 207Subtract 15 from both sides: 3c = 192Divide both sides by 3: c = 64Now that we have Carrie's number, we can find Fran's number:
Carrie's number, c, is 64.Jen's number is c + 9, which is 64 + 9 = 73Fran's number is c + 9 - 3, which is 73 - 3 = 70Therefore, Fran's number is 70.
Solve each equation below for x show all work and check your answer by substituting it back into the equation and verifying that it makes the equation true
Answers
The solutions to the equations:
(a) x/3 = 6 => x = 18 (Verified)
(b) (5x + 9)/2 = 12 => x = 3 (Verified)
(c) x/4 = 9/6 => x = 6 (Verified)
(d) 5/x = 20/8 => x = 2 (Verified)
To solve the equation, follow these steps: identify the equation with one unknown, isolate x, substitute known values and solve, and check the solution.
The equations are
(a) x/3 = 6
(b) (5x + 9)/2 = 12
(c) x/4 = 9/6
(d) 5/x = 20/8
The answers to the question are
(a) x = 18
(b) x = 3
(c) x = 6
(d) x = 2
Step-by-step explanation:
(a) x/3 = 6
Therefore x = 3×6 = 18
x =18
Substituting the value of x in the above equation, we have
18/6 = 3 verified
(b) (5x + 9)/2 = 12
Multiplying both sides by 2 gives
(5x + 9)/2 × 2 = 12×2 = 24
5x + 9 = 24 or x = (24-9)/5 = 3
Substituting the value of x in the above equation, we have
(5×3 + 9)/2 = 24/2 = 12 verified
x = 3
(c) x/4 = 9/6
Multiplying both sides by 4, we have
x/4×4 = 9/6×4 = 6
x = 6
Substituting the value of x in the above equation, we have
(6/4 = 9/6 = 3/2 verified
(d) 5/x = 20/8
Inverting both equations, we have
x/5 = 8/20
Multiplying both sides by 20 we have x/5 × 20 = 8/20 × 20 or 4x = 8 and x = 2
Substituting the value of x in the original equation, we have
2/5 = 2/5 = 8/20 verified
x = 2
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Verify that parallelogram ABCD with vertices A(-5, -1), B(-9, 6), C(-1, 5) and D(3, -2) is a rhombus by showing that it id a prallelogram sith perpendicular
Answers
Answer:
Step-by-step explanation:
The diagonals of the parallelogram are A(-5, -1), C(-1, 5) and B(-9, 6), D(3, -2).
Slope of diagonal AC = (5 - (-1)) / (-1 - (-5)) = (5 + 1) / (-1 + 5) = 6 / 4 = 3/2
Slope of diagonal BD = (-2 - 6) / (3 - (-9)) = -8 / (3 + 9) = -8 / 12 = -2/3
For the parallelogram to be a rhombus, the intersection of the diagonals are perpendicular.
i.e. the product of the two slopes equals to -1.
Slope AC x slope BD = 3/2 x -2/3 = -1.
Therefore, the parallelogram is a rhombus.
Sally and Adam work at different jobs. Sally earns $5 per hour and Adam earns $4 per hour. They each earn the same amount per week but Adam works 2 more hours. How many hours a week does Adam work?
Answers
Answer:
10 hrs
Step-by-step explanation:
sally earns $5/hr while Adam earns $4/hr
let the number of Hour sally works be 'x'
From question Adam work 2 hrs more than sally,
therefore Adam works (x + 2)hrs also the both earn same amount per week
therefore;
4 x [tex](x + 2)[/tex] = 5 x [tex]x[/tex]
4x + 8 = 5x
5x - 4x = 8
x = 8hrs
Adam works for (8+2)hrs = 10hrs
The drawing plan for an art studio shows a rectangle that is 19.2 inches by 6 inches. The scale in the plan is 3 in.: 5 ft. Find the length and width of the actual studio. Then find the area of the actual studio.
Answers
Answer:
321.24 ft²
Step-by-step explanation:
If 3in = 5ft
1in = x
5/3 = 1.6
So 1in = 1.67 ft
Actual dimensions will be;
L = 19.2*1.67 = 32.06ft
W = 6*1.67 = 10.02ft
Area = 32.06 * 10.02 = 321.24 ft²
To find the length and width of the actual studio, set up a proportion to convert the given dimensions from the scale to the actual dimensions. Then, find the area of the actual studio by multiplying the length and width.
Explanation:To find the length and width of the actual studio, we need to convert the given dimensions from the scale to the actual dimensions. Since the scale is 3 in.: 5 ft, we can set up the proportion:
3 in / 5 ft = 19.2 in / x ft
Cross multiplying and solving for x, we get:
x = 32 ft
The length of the actual studio is 32 ft. Similarly, we can find the width:
3 in / 5 ft = 6 in / y ft
Solving for y, we get:
y = 10 ft
The width of the actual studio is 10 ft.
To find the area of the actual studio, we multiply the length and width:
Area = length x width = 32 ft x 10 ft = 320 ft²
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The least number of customers in a shop at any time during the day was 15. Fran represented this situation with the inequality c > 15, where c is the number of customers in the shop. Is Fran correct? Explain.
Answers
Answer:
Fran was incorrect.
Correct representation: [tex]c \geq 15[/tex], where c is the number of customer during any time of day.
Step-by-step explanation:
We are given the following in the question:
Fran used the given inequality to represent the number of customers in a shop at any time.
[tex]c > 15[/tex]
where c is the number of customer during any time of day.
The least number of customers in a shop at any time during the day was 15.
Thus there could be 15 or greater than 15 customers in shop during any ime of day.
Thus, Fran was incorrect.
The correct representation is given by the inequality
[tex]c \geq 15[/tex]
where c is the number of customer during any time of day.
Answer:
Fran is incorrect.
The inequality is c ≥ 15
Step-by-step explanation:
How do you do this question?
Answers
Answer:
E) 13
Step-by-step explanation:
∫₀⁴ f'(t) dt = f(4) − f(0)
8 = f(4) − 5
f(4) = 13
Find the area of the circle
Answers
A= (pie)1.5^2
A= 7.07(pie)
Buck rented a truck for $39.95 plus $0.32 per mile. Before returning the truck, he Filled the tank with gasoline, which cost $9.85. If the total cost was $70.23. How far was the truck driven?
Answers
Answer:
Step-by-step explanation:
Let x represent the distance that the truck was driven.
Buck rented a truck for $39.95 plus $0.32 per mile. This means that the total cost of driving x miles with the truck would be
39.95 + 0.32x
Before returning the truck, he Filled the tank with gasoline, which cost $9.85. This means that the total amount that he spent is
39.95 + 0.32x + 9.85
If the total cost was $70.23, it means that
39.95 + 0.32x + 9.85 = 70.23
49.8 + 0.32x = 70.23
0.32x = 70.23 - 49.8 = 20.43
x = 20.43/0.32 = 63.8
Approximately 64 miles
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A pitcher throws a baseball straight into the air with a velocity of 72 feet/sec. If acceleration due to gravity is -32 ft/sec^2, how many seconds after it leaves the pitcher's hand will it take the ball to reach its highest point? Assume the position at time t = 0 is 0 feet.
Answers
t= 2.25 secs
Step-by-step explanation:
Step 1 :
Equation for motion with uniform acceleration is v = u+ at
where v is the final velocity
u is the initial velocity
a is the acceleration due to gravity
and t is the time
Step 2 :
Here , v = 0 because at the highest point final velocity is 0.
u = 72 feet/sec
a = -32 ft/sec^2
We need to find the time t.
Substituting in the equation we have,
0 = 72 -32 * t
=> 32 t = 72
=> t = 72/32 = 2.25 secs
Delegates from 10 countries, including Russia,
France, England, and the United States, are to
be seated in a row. How many different seating arrangements are possible if the French and
English delegates are to be seated next to each
other and the Russian and U.S. delegates are not
to be next to each other
Answers
Answer:
564,480
Step-by-step explanation:
The appliocation of factorial n! = n(n-1)(n-2)(n-3).....
Arrangement when french and English delegates are to seat together ;
since we have 10 delegates, Freench and english will be treated as 1 delegates as such we have 9groups. The number of ways of arranging 9groups = 9! and if the french and English are to be treated as a group = 2!
Hence, number of ways of arrangement = 9! x 2! = 725,760
In this case, English and french are to be seated next to each other while russia and US delegates are not to seat nect to each other ; both groups will be treated as 2 as such we have 8groups, the number of ways of arranging 8groups = 8!
french and english together = 2!
Russia and US together = 2!
The number of ways of arrangement = 8! x 2! x 2! = 161,280
hence the number of ways of arranging 10 delegates if french and english are to be seated next to each other and Russia and US are not to be seated next to each other;
N = 725,760 - 161,280 = 564,480
There are 282,240 different seating arrangements possible if the French and English delegates are to be seated next to each other and the Russian and U.S. delegates are not to be next to each other.
Explanation:To determine the number of different seating arrangements, we can treat the French and English delegates as a single entity. Therefore, we have 9 entities overall (Russia, (France and England), United States, and the 6 remaining countries).
The number of arrangements of these 9 entities is 9! (9 factorial) which is equal to 362,880. However, since the Russian and U.S. delegates cannot be seated next to each other, we need to subtract the number of arrangements where they are together.
Let's consider the Russian and U.S. delegates as a single entity as well. Now we have 8 entities to arrange (Russian and U.S., (France and England), and the 6 remaining countries). The number of arrangements of these 8 entities is 8! which is equal to 40,320.
Finally, we need to consider the arrangements of the Russian and U.S. delegates within their entity. The Russian and U.S. delegates can be arranged in 2! (2 factorial) ways, which is equal to 2.
Therefore, the total number of different seating arrangements is 362,880 - (40,320 * 2) = 362,880 - 80,640 = 282,240.
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What is the common difference between the terms in the following sequence?
{17,11,5,−1,−7...}
Answers
Answer:
-6
Step-by-step explanation:
Take a couple of differences and see:
11 -17 = -6
5 -11 = -6
The common difference is -6.
The radius of a cylindrical gift box is (4x + 1) inches. The height of the gift box is three times the radius. What is the surface area of the cylinder? Write your answer as a polynomial in standard form.
Answers
Answer:
S = 128πx² + 64πx + 8π
Step-by-step explanation:
Suraface area of a cylinder is given by:
S = 2πrh + 2πr²
We know that the height is 3 times as big as the radius, hence:
h = 3r
so we can plug in the new h value and rewrite the S equation as:
S = 2πrh + 2πr²
S = 2πr(3r) + 2πr²
S = 6πr² + 2πr²
S = 8πr²
We're given in the question that the radius is (4x + 1) inches, so plug that into r.
Given: r = 4x + 1
Therefore,
S = 8πr²
S = 8π(4x + 1)²
S = 8π(16x²+8x+1)
S = 128πx² + 64πx + 8π
Answer:
The answer to your question is 128πx² + 64πx + 8π
Step-by-step explanation:
Data
radius = (4x + 1)
height = 3(4x + 1)
Formula
Area = 2πrh + 2πr²
Substitution
Area = 2π(4x + 1)(3)(4x + 1) + 2π(4x + 1)
Simplification
Area = 6π(4x + 1)² + 2π(4x + 1)²
Area = 6π(16x² + 8x + 1) + 2π(16x² + 8x + 1)²
Area = 96πx² + 48πx + 6π + 32πx² + 16πx + 2π
Area = 128πx² + 64πx + 8π
Speed cell wireless offers a plan of $40 for the first 400 minutes, and an additional $0.50 for every minute over 400. Let t represent the total talk time in minutes. Write a piecewise-defined function to represent the cost C(t)
Answers
The function that represent cost is c(t) = 40 + 0.5(t -400).
For the first 400 minutes [tex](\(0 \leq t \leq 400\))[/tex], the cost is a flat rate of $40.
T represents the overall conversation time in minutes in the provided question.
Speed cell wireless offers a $40 package for the first 400 minutes.
Additional $0.50 per minute for remaining time
Time remaining = (t - 400) minutes
So, the cost for more beyond 400 minutes is 0.5(t -400). $
Thus, the entire cost, c(t), is 40 + 0.5(t -400).
Use the function f(x) = x2 + 6x + 6 and the graph of g(x) to determine the difference between the maximum value of g(x) and the minimum value of f(x). a parabola that opens down and passes through 0 comma 3, 3 comma 12, and 5 comma 8 15 12 9 3
Answers
The answer is 15,
because F(X)'s minimum value is (-3, -3)
and G(X)'s maximum value is (12, 3)
So when you subtract -3 from 12, you get a number that is greater then both. (because of the negative 3)
12 - (-3) = 15
Answer:
A. 15
Step-by-step explanation:
I got it rigth on the test :)
Have a great day fam!
Lisa has a home-based business making and selling scented soaps. She intially spent $72 to purchase soap-making equipment, and the materials for each pound of soap cost $7. Lisa sells the soap for $10 per pound. Eventually, she will sell enough soap to cover the cost of the equipment. What will be Lisa's total sales and costs be? How much soap will that be?
Answers
Answer:
Step-by-step explanation:
Let x represent the number of pounds of soap that she makes and eventually sells.
She intially spent $72 to purchase soap-making equipment, and the materials for each pound of soap cost $7. This means that the total cost of making x pounds of soap would be
7x + 72
Lisa sells the soap for $10 per pound. This means that her revenue for x pounds of soap would be
10 × x = 10x
If she eventually sells enough soap to cover the cost of the equipment, then
7x + 72 = 10x
10x - 7x = 72
3x = 72
x = 72/3 = 24
She would need to sell make and sell 24 soaps.
The cost would be
72 + 7 × 24 = $240
The total sales would be
10 × 24 = $240
HELP ASAP FOR BRAINLIEST:
Find the sixth term of a geometric sequence with t5 = 24 and t8 = 3
Thank you sooo much! Show work!
Answers
Answer:
The answer is 12
Step-by-step explanation:
t5 = 24 = a × r⁴
t8 = 3 = a × r⁷
We divide one by the other
r³= 1 / 8
r = 1 / 2
t6 = a × r⁵ = t5 × r = 24 × (1/2) = 12.
Therefore the sixth term of the geometric sequence is 12
The residents of a downtown neighborhood designed a triangular-shaped park as part of a city beautification program. The park is bound by streets on all sides. The second angle of the triangle is 7° more than the first. The third angle is 7° less than seven times the first. Find the measures of the angles.
Answers
So one angle is 20 degrees
The second angle is 27 degrees
And the third angle is 133 degrees.
The measure of the first, second and third angles are 20°, 27° and 133°.
What is an exterior angle of a triangle ?An exterior angle of a triangle is the sum of two opposite interior angles.
According to given question
The residents of a downtown neighbourhood designed a triangular-shaped park as part of a city beautification program.
Let us assume the first angle to be x°.
Therefore from the given data second angle is (x + 7)° and the third angle is (7x - 7)°.
We know that the sum of all the interior angles of a given triangle is 180°.
∴ x + (x + 7) + (7x - 7) = 180°
9x = 180°
x = 180°/9
x = 20°.
So, The first angle of the triangular park is 20°, The second angle is 27° and the third angle is 133°.
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One container is filled with a mixture that is 30%acid a second container is filled with a mixture that is 50%acid the second containet is 50%larger than the first and that twocontainers are are emptied into a third what percent of acid is the third container
Answers
Answer:
The amount of acid in third container is =42%
Step-by-step explanation:
Given , one container is filled with a mixture that is 30% acid a second container filled with a mixture that is 50% acid and the second container 50% larger than the first .
Let, the volume of first container is = x
Then , the volume of second container = (x+ x of 50%)
= x + 0.5 x
= 1.5 x
Therefore the amount of acid in first container [tex]=x \times \frac{30}{100}[/tex] = 0.3 x
The amount of acid in second container [tex]=1.5x \times \frac{50}{100}[/tex] = 0.75x
Total amount of acid= 0.3x + 0.75x = 1.05 x
Total amount of solution = x+1.5x = 2.5x
The amount of acid in third container is = [tex]\frac{1.05x}{2.5x} \times 100%[/tex] %
= 42%
Final answer:
By calculating the total acid content and total volume when two containers with different acid concentrations are mixed, we find that the third container has an acid concentration of 42%.
Explanation:
The question involves mixing two solutions of different acid concentrations and calculating the final concentration of acid. Let's assume the first container has 1 unit of volume. Since the second container is 50% larger, it has 1.5 units of volume. The first container has 30% acid, so it contains 0.3 units of acid. The second container has 50% acid, resulting in 0.75 units of acid. Together, the total volume of the solution is 2.5 units, and the total amount of acid is 1.05 units.
Therefore, the percentage of acid in the third container is calculated by dividing the total acid by the total volume: (1.05 units of acid / 2.5 units of volume) x 100% = 42%.