Since one of the seven performers insists on being the first act, the remaining six performers can be arranged in '6!' (factorial of 6) ways. Therefore, there are 720 different ways to schedule the appearances of the variety show.
Explanation:This problem is a permutation problem. Since one performer insists on being the first act of the evening, this leaves 6 other acts that can be arranged in any order. In permutation, if you have 'n' different items, they can be arranged in 'n!' (n factorial) ways. The factorial of a number n, denoted as 'n!', is the product of all positive integers less than or equal to n.
In this case, 6 performers can be arranged in '6!' ways. The factorial of 6 (6!) is 6 * 5 * 4 * 3 * 2 * 1 = 720. Therefore, there are 720 different ways to schedule the appearances of the remaining 6 acts after the first performer has gone on.
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Change -40° to radians.
A). 2π/9
B). -2π/9
C). 4π/9
D). -4π/9
Find the length of the third side of a right triangle with a hypotenuse of 17 and a leg of 10.
Find f(-7) if f(x) = 2x + 8.
what percentage does the third quartile represent?
a newspaper carrier earns a fixed amount for each newspaper he delivers, and yesterday his average hourly wage was 7.50 an hour. If he worked 4 hours yesterday and delivered 120 newspapers, how much does he earn for each newspaper delivered?
NEED HELP ASAP!!!
find the equation that goes through points (18,3) and (21,1) find slope and y-intercept
Select the objects that hold the same amount of liquid as a 98 fluid ounce jug
which undefined geometric term is described as a two dimensional set of points that has no beginning or end
Express the fraction in simplest form.
9/12
a.2/3
b.3/4
c.12/16
d.10/13
algebra mid-unit review quiz Unit 3 lesson 5
1. simplify the rational expression; 2m^2 - 72/ m - 6.
A. 2 ( m+6)
B. 2
C. 2 ( m-6)
D. m + 12
2. simplify the rational expression; -8z^2/ z^4 - z^2.
A. -8z
B. -8
C. -8/ z^2
D. -8/ z^2 - 1
3. simplify the rational expression; 6x-54/ 7x-63.
A. - 6/7
B. 6/7
C. 6(x-9)/ 7
D. 6/ 7 (x-9)
The solutions to the problems in the mid-unit review quiz for Algebra Unit 3 Lesson 5 are A(2(m+6)), D(-8/(z^2-1)), and B(6/7). These are found by factoring out common factors and simplifying the expressions.
Explanation:Let's solve the algebra mid-unit review quiz Unit 3 lesson 5 one by one.
To simplify the rational expression 2m^2 - 72/ m - 6, first factor out a 2 from the numerator to obtain 2(m^2 - 36). This can be further broken down as 2(m - 6)(m + 6). Given the denominator is (m - 6), we cancel out (m - 6) from both the numerator and denominator to get the answer as 2(m+6) hence option A is correct.To simplify the rational expression -8z^2/ z^4 - z^2, first take out -8z^2 from the numerator to get -8*z^2/z^2*(z^2 - 1). On simplifying, we are left with -8/(z^2-1), i.e. option D is correct. To simplify the rational expression 6x-54/ 7x-63, we factor out a 6 from the numerator and a 7 from the denominator. This gives us 6(x - 9)/7(x - 9). By cancelling out the common factor, (x - 9), we get 6/7, i.e., option B is correct.Learn more about Algebra simplification here:
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What values of x makes the inequality true? 2(x−4)−9x≤-4x+13
Answer : x >= -7
On simplifying,
2x - 8 - 9x <= -4x + 13
-7x - 8 <= -4x + 13
-3x - 8 < = 13
-3x <= 21
x >= -7
what is the solution to the following system of equations (3x-4y=-25)( 3x+ 4y=5)? PLEASE HURRY!!!!!!!!!!!
A park in a subdivision has a triangular shape. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53 degrees. Find the area of the park to the nearest square foot.
Answer:
The area of the park is 1,11,739 square feet.
Step-by-step explanation:
Since, the area of a triangle is,
[tex]A=\frac{1}{2}\times s_1\times s_2\times sin\theta[/tex]
Where, [tex]s_1[/tex] and [tex]s_2[/tex] are the adjacent sides and [tex]\theta[/tex] is the included angle of these sides,
Here, the two adjacent sides of the park are 533 feet and 525 feet, while, the angle included by these sides is 53°.
That is, [tex]s_1[/tex] = 533 ft, [tex]s_2[/tex] = 525 ft and [tex]\theta[/tex] = 53°,
Hence, the area of the park is,
[tex]A=\frac{1}{2}\times 533\times 525\times sin 53^{\circ}[/tex]
[tex]=\frac{279825\times 0.79863551004}{2}[/tex]
[tex]=\frac{223478.181599}{2}=111739.090799\approx 111739\text{ square ft}[/tex]
HELPPPPPPPPP and explain why
A recipe calls for 5 8 pound of cheese per batch. Assuming you have enough of the other ingredients, how many batches of the recipe can you make with 5 pounds of cheese?
if a crate contains 25,500 oz of rice , about how many kg does it contains ? 1 pound equals 16 oz & 1 pound equals 0.454 kg
351 kg
724 kg
25500 kg
185000 kg
To find the mass of 25,500 ounces of rice in kilograms, one needs to convert ounces to pounds, then pounds to kilograms. After the conversions, the crate contains approximately 724 kg of rice.
Explanation:To calculate the mass of 25,500 ounces of rice in kilograms, we first convert ounces to pounds and then pounds to kilograms using the conversion rates provided.
First, we need to find out how many pounds are equivalent to 25,500 ounces. We use the proportion 1 pound = 16 ounces.Divide the total number of ounces by 16 to find the number of pounds:Now, we'll convert pounds to kilograms: 1 pound = 0.454 kg.Multiply the number of pounds by the kilogram equivalent:When we round this number to the nearest whole number, we get 724 kg, which is the approximate mass of the rice in the crate.
The frequency of A4 is 440.00 Hz. What is the frequency of A6, which is two octaves above A4?
A) 110.00 Hz
B) 220.00 Hz
C) 880.00 Hz
D) 1760.00 Hz
what is the image of point (3,4) for mapping (x.y) , (x+4, y+6)
What are the zeros of f(x) = x(x – 8)?
A. x = 0 and x = 8
B. x = 0 and x = –8
C. x = 0 only
D. x = 8 only
The zeros of the function f(x) = x(x – 8) are x = 0 and x = 8, which correspond to each factor of the equation being set equal to zero. Therefore, the correct answer is option A.
To identify the zeros of the function f(x) = x(x – 8), we should solve for x when f(x) is set to zero. Setting the function equal to zero gives us the equation 0 = x(x – 8).
We can find the zeros by looking for the values of x that make each factor in the equation equal to zero. The first factor is x, and it is equal to zero when x = 0. The second factor is (x – 8), which is equal to zero when x = 8.
Therefore, the zeros of the function f(x) are x = 0 and x = 8.
Selection A is the correct answer: The zeros of the function x(x – 8) are x = 0 and x = 8.
Dylan opened a credit card account with $675.00 of available credit. Now that he has made some purchases, Dylan's account only has $384.75 of available credit. What is the percentage decrease of the amount of available credit in Dylan's account?
Which expression is equal to sin 75°? sin 135° cos 60° – cos 135° sin 60° cos 135° cos 60° + sin 135° sin 60° sin 135° cos 60° + cos 135° sin 60° cos 135° cos 60° – cos 135° cos 60°?
Answer:
The answer is A
A radio station wants to determine whether its audience would like to listen to more rap music. It asks its listeners to call in and participate in a survey. Each listener is asked: “Do you want us to play more rap music or less rap music?” One hundred fifty listeners call in, and their responses are recorded.
What is the focus of the study?
The type of music listeners want to hear.
The playing of rap music.
The number of listeners who respond.
The response of the listeners.
A radio station made a survey of their listeners to determine whether the audience would like to listen to more rap music. They asked the question “Do you want us to play more rap music or less rap music?” The station recorded one hundred fifty listeners who call in.
The focus of the study is about the playing of the rap music because it is what the question is about. Not the type of music listeners want to hear, nor the number of listeners who respond nor the response of listeners.the response of listeners to give opinion on to play more or less rap music
HELP WHOEVER ANSWERS CORRECTLY WILL BE BRAINLIEST!!!!
2. The robot was initially placed at position (6,9), and at = 2 seconds, its position is (10,15).
a. How far did the robot travel in 2 seconds?
b. What is the speed of the robot?
Could you work it out
if a train travels 25 miles in 2 hours and 15 minutes, what is it's average speed in miles per hour?
• 10 mph
• 11.1 mph
• 12.5 mph
• 9.1 mph
Ed and Marge were candidates for the city council. Marge won with 93 more votes than Ed. The total number of votes cast in the election was 587. Find the number of votes received by each candidate.
Gary number has 6 in thousands and a7 in hundred and a 5 in ones. when rounded to the nearest ten, the number is 6760. what is gary's number
Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given XY = WZ and XW = YZ
a.
No; you cannot determine that the quadrilateral is a parallelogram.
b.
Yes; two opposite sides are both parallel and congruent.
c.
Yes; opposite sides are congruent.
d.
Yes; diagonals of a parallelogram bisect each other.
From the information provided a. No; you cannot determine that the quadrilateral is a parallelogram.
A parallelogram is a quadrilateral (has four sides and four angles) in which opposite sides are parallel and congruent to each other. The diagonals of a parallelogram bisect each other.
Given XY = WZ and XW = YZ, this means that the opposite sides are congruent.
Just from the information provides, we cannot determine that the quadrilateral is a parallelogram.
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Which regular polygon would have each of its interior angles measure 120°? hexagon heptagon octagon nonagon?
I keep getting 70 but that's not an answer??
Betty's bite size candies are packaged in bags the number of candies per bag is normally distributed with a mean of 50 candies and a standard deviation of 3. At a quality control checkpoint a sample of bags is checked and 12 bags contain fewer than 47 candies how many bags were probably taken as samples?
a) 15
b) 75
c) 36
d) 24