Using the combination formula, it is found that there are 3300 ways to choose the songs.
The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For the rock songs, we have three from a set of eleven, hence:
[tex]C_{11,3} = \frac{11!}{3!8!} = 165[/tex]
For the alternative songs, we have four from a set of five, hence:
[tex]C_{5,4} = \frac{5!}{4!1!} = 5[/tex]
For the rap songs, we have three from a set of four, hence:
[tex]C_{4,3} = \frac{4!}{3!1!} = 4[/tex]
Since the songs are independent, the total number of ways is given by:
[tex]T = 165 \times 5 \times 4 = 3300[/tex]
More can be learned about the combination formula at https://brainly.com/question/25821700
An object is thrown upward from the top of 96-foot building with an initial velocity of 80 feet per second. The height h of the object after t seconds is given by the quadratic equation h=16t^2+80t+96. When will the object hit the ground?
The function of the object height is an illustration of a projectile motion
The object will never hit the ground
How to determine when the object hits the ground?
The function is given as:
h=16t^2+80t+96.
When the object hits the ground, h = 0
So, we have:
16t^2+80t+96 = 0
Divide through by 16
t^2+5t+6 = 0
Expand
t^2 + 3t + 2t + 6 = 0
Factorize
t(t + 3) + 2(t + 3) = 0
Factor out t + 3
(t + 2)(t + 3) = 0
Solve for t
t = -2 or t = -3
The time (t) cannot be negative.
Hence, the object will never hit the ground
Read more about projectile motion at:
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Answer:
6
Step-by-step explanation:
did this question in savvas
What is the area of the figure below ?
A. 12
B. 15
C. 18
D. None of these
Step 1: Find the area of the larger rectangle
Area of a rectangle = base x height
Area = 4 x 3 = 12
Step 2: Find the area of the other rectangle
The tricky part about this one is that we aren't given the length of this rectangle. We do know, however, that the whole base of the figure is 6 and 3 units are taken up by the first rectangle. Therefore, the length of this rectangle is 3.
Area = 2 x 3 = 6
Step 3: Find the area of the figure
Now that we know the area of both rectangles by themselves, all that's left to do is add them up.
6 + 12 = 18
Answer: 18
Hope this helps!
Answer:
18
Step-by-step explanation:
A=bh
A=3x4 A=3x2
12+6=18.
What is g(-2) for g(x) =1/2x^2+2x?
Does anyone know this
Step-by-step explanation:
please mark me as brainlest
the legnth of a rectangle is three times its width. if the length of the perimeter is 64 in, find the length and width
Answer:
Length and width of rectangle is 24 and 8 inchesStep-by-step explanation:
Given:
Length of rectangle is three times the widthPerimeter of rectangle is 64 InchesTo Find:
Length and WidthSolution:
Let's assume Width of rectangle x inches and length be 3x inches. To calculate the dimensions of The rectangle we will use the formula of Perimeter of rectangle:
Perimeter of rectangle = 2(L + B)
→ 64 = 2(3x + x)
→ 64 = 2(4x)
→ 64/2 = 4x
→ 32 = 4x
→ 32/4 = x
→ 8 = x
Hence,
Length of the rectangle = 3x = 3(8) = 24 inchesWidth of the rectangle = x = 8 inchesAnswer:
Length = 24 inchesWidth = 8 inches⠀
Step-by-step explanation :
⠀
As it is given that, the legnth of a rectangle is three times its width and the perimeter is 64 in and we are to find the length and width of the rectangle. So,
⠀
Let us assume the width of the rectangle as w inches and therefore, the length will be 3w inches .
⠀
Now, According to the Question :
⠀
[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (3 x + x )= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (4x )= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{8x= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{ x = \dfrac{64}{8} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 8}} }}} }\: \: \bigstar[/tex]
⠀
Therefore,
The width of the rectangle is 8 inches .⠀
Now, We are to find the length of the rectangle:
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3x }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3 \times 8 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \underline{ \boxed{ \frak{\pmb{Length = 24}}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The length of the rectangle is 24 inches .⠀
The side of the clip on a clip board appears to be a right triangle. The
leg lengths are 2 millimeters and 2.1 millimeters and the hypotenuse
is 2.9 millimeters. Is the side of the clip a right triangle?
Answer:
Yes, it is a right triangle.
Step-by-step explanation:
Answer:
Yes, this is a right triangle.
Step-by-step explanation:
For this, you would use the Pythagorean theorem a^2 + b^2=c^2
Here we have 2^2+2.1^2=2.9^2
So we must check to see if that checks out. What we find is that both sides are equal to 8.41 which means we have a right triangle.
I had to only use a pic because no one would be able to understand, worth 100 points IF you get it correct.
Total left
2-1/4+2/4+1-3/49/4+2/4+7/49+2+7/418/44-2/4Answer:
[tex]4\:\dfrac{2}{4}[/tex]
Step-by-step explanation:
Add the amounts of each pie left :
[tex]2 \frac{1}{4}+\dfrac{2}{4}+1 \frac{3}{4}[/tex]
Separate the whole numbers and the fractions:
[tex]\implies 2+ \dfrac{1}{4}+\dfrac{2}{4}+1+\dfrac{3}{4}[/tex]
Add the whole numbers and fractions separately:
[tex]\implies 2+1+\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}[/tex]
[tex]\implies 3+\dfrac{6}{4}[/tex]
Convert 6/4 into a mixed number:
[tex]\implies 3+1\frac{2}{4}[/tex]
Add the whole numbers:
[tex]\implies 4\frac{2}{4}[/tex]
Kim is 15 years old. Her father is 4 times as old as her now. In how many years time their total age be 115 years.
Answer:
100 later kim will be 115
For the function f(x)=−7x2+8x−8, find f(4).
Answer:
- 88
Step-by-step explanation:
[tex]f(x ) = - 7 {x}^{2} + 8x - 8 \\ plug \: x = 4 \\ \\ \implies \: f(4 ) = - 7 {(4)}^{2} + 8(4) - 8 \\\\ \implies \: f(4 ) = - 7 \times 16 + 32 - 8 \\\\ \implies \: f(4 ) = - 112+ 32 - 8 \\ \\ \implies \: f(4 ) = - 120+ 32 \\\\ \implies \: f(4 ) = - 88 \\[/tex]
Question
The sum of four times a number and two is 14. Find the number.
Answer:3
Step-by-step explanation:let the number be x
4x+2=14
4x=14-2
4x=12
divide both sides by 4
4x/4=12/4
x=3
Modern Electronics offers a one-year monthly installment plan for a big screen TV. The payment for the first month is 882, and then it increases by 4% each month for the rest of the year. Which expression can be used to find the total amount paid in the first 12 months?
✿————✦————✿
Answer: A
[tex]62=\frac{12(1.04^{12}-1) }{1.04-1}[/tex]
✿————✦————✿
Help help help help
Step-by-step explanation:
can you tell me what you don't understand about this ?
because it is really simple, once you understand the transformations of equations.
remember, whatever we do to one side. we have to do also to the other side, so that the information in general stays the same.
(7 - 3x)/2 = 8 multiply both sides by 2
7 - 3x = 16 subtract 7 from both sides
-3x = 9 divide both sides by 3
-x = 3 multiply both sides by -1
x = -3
and that's the whole "secret" about solving an equation.
Answer:
x = -3Step-by-step explanation:
In the question we are given with an equation that is ( 7 - 3x ) / 2 = 8 . And we have asked to find the value of x .
Solution : -
[tex] \longrightarrow \qquad \: \dfrac{7 - 3x}{2} = 8[/tex]
Step 1 : Multiplying both sides by 2 :
[tex] \longrightarrow \qquad \: \dfrac{7 - 3x}{ \cancel{2} }\times \cancel{2 }= 8 \times 2 [/tex]
On further calculations, We get :
[tex] \longrightarrow \qquad \: 7 - 3x = 16[/tex]
Step 2 : Subtracting with 7 on both sides :
[tex] \longrightarrow \qquad \: \cancel{ 7 }- 3x - \cancel{ 7 }= 16 - 7[/tex]
On calculating further, We get :
[tex] \longrightarrow \qquad \: - 3x = 9[/tex]
Step 3 : Dividing with -3 on both sides :
[tex] \longrightarrow \qquad \: \dfrac{ \cancel{ - 3}x}{ \cancel{-3}} = \cancel{\dfrac{9}{ - 3} }[/tex]
On calculating further, We get :
[tex] \longrightarrow \qquad \: \red{\underline{\boxed{\frak{x = - 3}}}}[/tex]
Therefore, value of x is -3 .Verifying : -
Now , we are verifying our answer by substituting value of x in given equation . So ,
( 7 - 3x ) / 2 = 8[ 7 - 3 ( -3 ) ] / 2 = 8( 7 + 9 ) / 2 = 816 / 2 = 88 = 8L.H.S = R.H.SHence, Verified .Therefore , our answer is valid .
#Keep Learningconsider the equation 2 x +9 y = -18 A line parallel to the above line would have a slope of_________
A line perpendicular to the above line would have a slope of ________________
Tony saw 6 birds in a tree. 1/6 of them flew away. How many were left?
Answer:
5 birds flew away
Step-by-step explanation:
1/6x6=1
( 1 bird flew away)
so, 6-1=5
Answer:
[tex]\huge\boxed{\bf\:5\:\:birds}[/tex]
Step-by-step explanation:
Number of birds Tony saw = 6Fraction that flew away = ⅙Number of birds that flew away = ?
Number of birds that flew away = Number of birds × Fraction that leftNumber of birds that flew away = 6 × ⅙Number of birds that flew away = 1Number of birds remaining = ?
Number of birds remaining = Total number of birds - Number of birds that flew awayNumber of birds remaining = 6 - 1Number of birds remaining = 5[tex]\rule{150pt}{2pt}[/tex]
Chicago is home to 2.706 million people and the city sees approximately 55 million visitors each year. China has a population of 1.393 billion. If their visitors were proportional to Chicago, how many visitors could China expect? Write your answer in scientific notation rounded to two decimal places. Provide your answer below: x 10^ visitors
China could expect a quantity of visitors of 8.512 × 10⁶ in Chicago.
How to apply direct proportions
A direct proportion is a direct relationship between two variables, which in this case is represented between the quantity of tourists in the city of Chicago and the population of the country of origin.
Let suppose the existence of direct proportionality and world has a population of 9000 million people, the quantity of Chinese visitors in the city of Chicago is determined by the following formula:
x = (1.393 × 10⁹ / 9 × 10⁹) × 55 × 10⁶
x = 8.512 × 10⁶
China could expect a quantity of visitors of 8.512 × 10⁶ in Chicago. [tex]\blacksquare[/tex]
To learn more on direct proportions, we kindly invite to check this verified question: https://brainly.com/question/14389660
90 is the product of five and Diego’s age use a variable D to represent Diego’s age
Answer:
Deigo is 18years of age
explaination
[tex]5 \times d = 90 \\ 5 d = 90 \\ 5d \div 5 = 90 \div 5 \\ d = 18[/tex]
this is how to solve it.
......................................
Answer:
D. f(x) = x - 4
Step-by-step explanation:
If you plug in the x values for the expression x - 4:
3 - 4 = -1
4 - 4 = 0
5 - 4 = 1
6 - 4 = 2
This means that the function rule is f(x) = x - 4
Hope this helps :)
pls help...
What is the mode for the set of data?
Answer:
9
[tex]\rule{70mm}{2pt}[/tex]
Step-by-step explanation:
In statistics, the mode is the value that is repeatedly occurring or you can say that has higher frequency in a given set of numbers or values. For instance in (1, 2, 5, 6, 2, 3) mode is 2 because it has appeared in the given set twice.
As in the given problem, the cross represents the number of a particular number, indicating whether the given number is repeated or not. And if repeated, how many times?
→ 5, 6, 10 = 1 (number of repetition; each)
→ 7, 8 = 2 (number of repetition; each)
→ 9 = 3 (number of repetition)
Therefore, the mode for the given set of data is 9.
[tex] \rm \sum_{n = 1}^{ \infty } \frac{( - {1)}^{n + 1} }{n \binom{2n}{n} } \\ [/tex]
Recall the well-known series
[tex]\displaystyle 2 \arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}[/tex]
Replace x with √x :
[tex]\displaystyle 2 \arcsin^2(\sqrt x) = \sum_{n=1}^\infty \frac{(4x)^n}{n^2 \binom{2n}n}[/tex]
Differentiate both sides:
[tex]\displaystyle -\frac{\arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^n}{n \binom{2n}n}[/tex]
Multiply by 4x :
[tex]\displaystyle -\frac{4x \arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^{n+1}}{n \binom{2n}n}[/tex]
All the series I've mentioned converge for |x| < 1, so we can take x = -1/4 to find the value of the sum we want.
[tex]\displaystyle \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n \binom{2n}n} = -\frac{4 \times \left(-\frac14\right) \arcsin\left(\sqrt{-\frac14}\right)}{2\sqrt{-\frac14-\left(-\frac14\right)^2}} = -\frac{\arcsin\left(\frac i2\right)}{\frac{\sqrt5\,i}2}} = \boxed{\frac2{\sqrt5} \mathrm{arsinh}\left(\frac12\right)}[/tex]
where
[tex]\arcsin\left(\frac i2\right) = z \iff 2\sin(z) = -2i\sinh(iz) = i \implies z = i \, \mathrm{arsinh}\left(\frac12\right)[/tex]
Help help help help help
Answer:
(-9, -6)
Step-by-step explanation:
What is the value of x in the equation –2.4x = 8.4?
Answer:
x= 3.5
Step-by-step explanation:
2.4 x= 8.4
x= 8.4 /2.4
x= 3.5
Answer:
X= -3.5
Step-by-step explanation:
You are trying to find what x is, and x is being multiplied with -2.4. The easiest way to find the answer is to divide 8.4 by -2.4. This way, you will get your answer of -3.5. Because two negatives make a positive when you multiply, 8.4 is not negative.
How I solved this.
-2.4x = 8.4
8.4=total
-2.4= Needs to be multiplied with x
x=?
8.4/-2.4=-3.5
Check your work:
-2.4(-3.5)=8.4
Final answer:
x= -3.5
I hope this helps!
-No one
Help picture below problem 6
Answer:
g is 37
Step-by-step explanation:
supplementary means two angles that add up to 180°
180-143=37
In the game of roulette, a player can place a $7 bet on the number 5 and have a 1/38 probability of winning. If the metal ball lands on , the player gets to keep the $7 paid to play the game and the player is awarded an additional $245. Otherwise, the player is awarded nothing and the casino takes the player's $7. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose? Question content area bottom Part 1 The expected value is $ -0.37. the player would expect to lose about $
Answer:
973.68 times
Step-by-step explanation:
Since you would expect to win 1 in 38, the amount of times you will win in 1000 times is 1000 / 38 which is 26.32. therefore you would expect to lose 1000 - 26.32 times which is 973.68
The equation is:
Answer: the number of labor was :
Answer:
equation: 1368 = 380 +52xlabor hours: 19Step-by-step explanation:
The desired equation will relate labor cost, parts cost, and total cost.
A.The total cost is the sum of the parts cost and the product of labor hours and labor rate. We're told to use x to represent labor hours.
total cost = part cost + (labor rate)(labor hours)
1368 = 380 + 52x
__
B.This equation can be solved in 2 steps:
988 = 52x . . . . . . . step 1, subtract 380 from both sides
19 = x . . . . . . . . . . step 2, divide both sides by the coefficient of x
The number of labor hours was 19.
A gym has 12 exercise stations, including 4 weightlifting benches.
What is the probability that a randomly selected exercise station will be a weightlifting bench?
probability : 1/3
Explanation:
total people : 12weightlifting benches : 4probability = selected/total
Here,
probability = 4/12 = 1/3 = 0.33E=Weightlifting bench
So
P(E)=4/12P(E)=1/3A construction company is building the house shown below. They need to use a scale
of 1 in: 8f (1 inch = 8 feet). They measured the drawing to find that that the height of
the building is 2.5 in.
1.) Explain to the construction workers how they would use this information to
calculate the height of the final building.
2.) What is the height of the final building?
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Using proportions, we have that:
The height of the building is found using a rule of three.The height is of 20 feet.What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The scale is of 1 inch = 8 feet. What is the height for 2.5 inches? The rule of three is given by:
1 inch - 8 feet.
2.5 inches - x feet
Applying cross multiplication, the height in feet of the final building is given by:
x = 8 x 2.5 = 20 feet.
More can be learned about proportions at https://brainly.com/question/24372153
The height of the building is calculated by representing 1 inch as 8 feet. The final building has a height of 20 feet.
What is scaling?Scaling is the increase or decrease in the height of an object by a scale factor k.
Given that the scale used is:
1 inch = 8 feet. Hence:
Since the height of the building is 2.5 in, hence:
Height of the final building = 2.5 in * 8 ft per 1 in = 20 feet
The height of the final building is 20 feet.
Find out more on scaling at: https://brainly.com/question/25722260
Event A has a 90% chance of occurring. Event B has a 20% chance of occurring. The correlation (i.e. whether they tend to occur together, or separately, or are unrelated) between the events is unknown.
What is the maximum probability that both event A and event B will occur?
What is the minimum probability that both event A and event B will occur?
The maximum probability that both event A and event B will occur is 18%.
How to compute the probability?From the information, Event A has a 90% chance of occurring. Event B has a 20% chance of occurring. Therefore, the maximum probability will be:
= 90% × 20%
= 18%
The minimum probability that both event A and event B will occur will be:
= (90% + 20%) - 1
= 1.10 - 1
= 10%
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A production process produces 2.5% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?
Using the binomial distribution, it is found that there is a 0.0058 = 0.58% probability that the sample contains exactly two defective parts.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, we want P(X = 2) with p = 0.025, n = 5, hence:
[tex]P(X = 2) = C_{5,2}.(0.025)^{2}.(0.975)^{3} = 0.0058[/tex]
There is a 0.0058 = 0.58% probability that the sample contains exactly two defective parts.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
PLSSS HEELPPP A line passes through (3, -2) and (6, 2).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
a. y+2= 4/3(x+3); -4x+ 3y= -18
b. y+2= 4/3(x-3); -4x+3y= -18
c. y-2= 4/3(x-3); -4x+3y= 18
d. y-3= 4/3(x+2); -4x+3y= 17
Answer:
b)
Step-by-step explanation:
Question (a)
[tex]\sf let \ (x_1,y_1)=(3,-2)\\\\\sf let \ (x_2,y_2)=(6,2)[/tex]
[tex]\sf slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-(-2)}{6-3}=\dfrac43[/tex]
Point-slope formula: [tex]\sf y-y_1=m(x-x_1)[/tex]
Substituting m and point (3, -2) into the formula:
[tex]\sf y-(-2)=\dfrac43(x-3)[/tex]
[tex]\sf y+2=\dfrac43(x-3)[/tex]
Question (b)
Rewrite in standard form:
[tex]\sf y+2=\dfrac43x-4[/tex]
[tex]\sf \implies y=\dfrac43x-6[/tex]
[tex]\sf \implies 3y=4x-18[/tex]
[tex]\sf \implies -4x+3y=-18[/tex]
A Cinema has 240 seats. 144 seats were sold
for the current movie. What percent of seats
are empty?
Need help please :)
Answer:
the answer is 40%
Step-by-step explanation:
240 – 144 = 96
96÷240=0.4=40%
Hope this helps:)....if not then sorry for wasting your time and may God bless you:)
I’m not sure the steps to figure out the problem. X = 2 to x =4
Answer:
you have to put the Y in the formula or make a comparison