There are 6720 ways by 8 distinguishable books be placed in 5 shelves.
According to statement
The number of books (n) is 8
The number of shelves (r) is 5
Now, we find the ways by which the 8 books be placed in 5 distinguishable shelves
From Permutation formula
P(n,r) = n! / (n-r)!
Substitute the values then
P(n,r) = 8! / (8-5)!
P(n,r) = (8*7*6*5*4*3*2*1) / (3*2*1)
P(n,r) = 8*7*6*5*4
P(n,r) = 6720
So, there are 6720 ways by 8 distinguishable books be placed in 5 shelves.
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what is the answer to 12y+d=−19y+t for y
Answer:
12y + d = -19y + t
31y + d = t
31y= - d + t
y = (- d + t ) / 3 ;)
Answer:
y = (t-d) / 31
Step-by-step explanation:
12y + d = -19y + t
12y + 19y = t - d
31y = t - d
y = (t-d) / 31
2 Add the given fractions. Write the answers in the simplest form
A. 18/16 and 22/24 =
B. 23/13 and 42/15 =
C. 27/16 + 15/12 =
Answer:
A. 18/16 + 22/24 = 49/24
B. 23/13 + 42/15 = 297/65
C. 27/16 + 15/12 = 47/16
Step-by-step explanation:
18/16 + 22/24
= 54/48 + 44/48
= 98/48
= 49/24
…………………
23/13 + 42/15
=(23×15)/(13×15) + (42×13)/(13×15)
= 345/195 + 546/195
= 891/195 (divide both sides by 3)
= 297/65
……………………………………
27/16 + 15/12
= 81/48 + 60/48
= 141/48 (divide both sides by 3)
= 47/16
Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams, with the following results: Mean Grade Standard Deviation Professor 1 79.3 22.4 Professor 2 82.1 12.0 What are the degrees of freedom for the numerator of the F ratio
The degrees of freedom for the numerator of the F ratio can be calculated to be 9.
How many degrees of freedom is the numerator of the F ratio?The degrees of freedom for the numerator can be found to be:
= number of exams graded - 1
Solving gives:
= 10 - 1
= 9
In conclusion, the degrees of freedom for the numerator of the F ratio is 9.
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can you please answer the question?
The trigonometric expression [tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex] is equivalent to the trigonometric expression [tex]\sec \alpha \cdot \csc \alpha + 1[/tex].
How to prove a trigonometric equivalence
In this problem we must prove that one side of the equality is equal to the expression of the other side, requiring the use of algebraic and trigonometric properties. Now we proceed to present the corresponding procedure:
[tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex]
[tex]\frac{\tan^{2}\alpha}{\tan \alpha - 1} + \frac{\frac{1}{\tan^{2}\alpha} }{\frac{1}{\tan \alpha} - 1 }[/tex]
[tex]\frac{\tan^{2}\alpha}{\tan \alpha - 1} - \frac{\frac{1 }{\tan \alpha} }{\tan \alpha - 1}[/tex]
[tex]\frac{\frac{\tan^{3}\alpha - 1}{\tan \alpha} }{\tan \alpha - 1}[/tex]
[tex]\frac{\tan^{3}\alpha - 1}{\tan \alpha \cdot (\tan \alpha - 1)}[/tex]
[tex]\frac{(\tan \alpha - 1)\cdot (\tan^{2} \alpha + \tan \alpha + 1)}{\tan \alpha\cdot (\tan \alpha - 1)}[/tex]
[tex]\frac{\tan^{2}\alpha + \tan \alpha + 1}{\tan \alpha}[/tex]
[tex]\tan \alpha + 1 + \cot \alpha[/tex]
[tex]\frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\sin \alpha} + 1[/tex]
[tex]\frac{\sin^{2}\alpha + \cos^{2}\alpha}{\cos \alpha \cdot \sin \alpha} + 1[/tex]
[tex]\frac{1}{\cos \alpha \cdot \sin \alpha} + 1[/tex]
[tex]\sec \alpha \cdot \csc \alpha + 1[/tex]
The trigonometric expression [tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex] is equivalent to the trigonometric expression [tex]\sec \alpha \cdot \csc \alpha + 1[/tex].
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help asap, please and thank you
By understanding the proportions of each section with respect to the entire hexagon we have:
{1, 1/2, 1/3, 1/6} {6, 3, 2, 1}{3, 3/2, 1, 1/2}{2, 1, 2/3, 1/3}How to construct a diagram related to possible sections of a hexagonThe first row represents the proportion of each section with respect to the entire hexagon, which is shown below:
{1, 1/2, 1/3, 1/6}
The elements of the second row are obtained by mutiplying all the elements of the first row by 6:
{6, 3, 2, 1}
The elements of the third row are calculated by multiplying all the elements of the first row by 3:
{3, 3/2, 1, 1/2}
And the elements of the fourth row are determined by multiplying all the elements of the first row by 2:
{2, 1, 2/3, 1/3}
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A worker at a farm supply company in Franklin County is mixing up a 420-kilogram batch of its special grain blend for horses, which costs $5.80 per kilogram to make. If the mixture includes oats that cost $9.40 per kilogram and feed corn that costs $3.40 per kilogram, how many kilograms of each should the worker include in the mixture?
_?__ Kilograms of oats
_?__ Kilograms of feed corn
Answer:
168 kg oats and 252 kg corn
Step-by-step explanation:
2 equations and 2 unknowns
eq 1: x + y = 420
x is the amount of oats
y is amount of corn
eq 2: 9.4x + 3.4y = 5.8*420
solve equation 1 for x
x = 420 - y
substitute the value of x in eq 2
9.4(420-y) + 3.4y = 2436
y = 252
substitute y in eq 1
x + 252 = 420
x = 168
Nora and her children went into a grocery store and see by $5 worth of apples and bananas each Apple cost $1 each banana costs $0.50. She bought 3 times as many bananas as apples. By following the stars below determine the number of apples, x, and the number of banana, y, that Nora bought.
Solving a system of equations, we will see that Nora bought 2 apples and 6 bananas.
How many apples and bananas Nora did bought?Let's define the variables:
x = number of apples.y = number of bananas.We know that She buys 3 times as many bananas as apples.
y = 3*x
The total cost is $5.
x*$1 + y*$0.50 = $5
Then we have a system of equations:
y = 3*x
x*$1 + y*$0.50 = $5
Replacing the first equation into the second one we get:
x*$1 + (3x)*$0.50 = $5
Now we can solve this for x.
x*$1 + x*$1.50 = $5
x*$2.50 = $5
x = $5/$2.50 = 2
So She bought 2 apples, and:
y = 3*x = 3*2 = 6
And 6 bananas.
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A six sided die is rolled three times. Find the probability that the result is an even number for every roll.
A. 1/9
B. 3/8
C. 1/3
D. 1/8
[tex]|\Omega|=6^3\\|A|=3^3\\\\P(A)=\dfrac{3^3}{6^3}=\left(\dfrac{3}{6}\right)^3=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}=12.5\%[/tex]
Evaluate the expression
a. tan(arctan 25) =
Step-by-step explanation:
Newton's second law of motion describes the relationship between force and acceleration. They are directly proportional. If you increase the force applied to an object, the acceleration of that object increases by the same factor. In short, force equals mass times acceleration.
You have a bag of marbles that has 12 red, 5 green, 6 yellow, and 4 blue. If you draw one at random, what is P(red or green)? (What is the percentage)
[tex]|\Omega|=12+5+6+4=27\\|A|=12+5=17\\\\P(A)=\dfrac{17}{27}\approx63\%[/tex]
Triangle A B C is shown. The length of side A is 12 inches, the length of side B is 6 StartRoot 3 EndRoot, and the length of side C is 6 inches.
What are the angle measures in triangle ABC?
m∠A = 90°, m∠B = 30°, m∠C = 60°
m∠A = 60°, m∠B = 90°, m∠C = 30°
m∠A = 90°, m∠B = 60°, m∠C = 30°
m∠A = 60°, m∠B = 30°, m∠C = 90°
The angle measures in triangle ABC are (d) m∠A = 60°, m∠B = 30°, m∠C = 90°
How to determine the angle measures?The side lengths are given as:
AB = 12 inches
BC = 6√3 inches
CA = 6 inches
From the list of options, the angles are 30°, 60° and 90°, respectively.
In a triangle, the angle opposite the largest side is the largest angle and vice versa.
This means that:
∠C = 90° --- opposite AB
∠A = 60° --- opposite BC
∠B = 30° --- opposite CA
Hence, the angle measures in triangle ABC are (d) m∠A = 60°, m∠B = 30°, m∠C = 90°
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Complete question
The length of side AB is 12 inches, the length of side BC is 6√3, and the length of side CA is 6 inches.
See attachment
(C.) m∠A = 90°, m∠B = 60°, m∠C = 30°
Got it wrong, the correct answer was revealed to be C.
Solve the inequality
x² + 2x + 1 < 0.
Hello
x² + 2x + 1 < 0 ⇔ (x + 1)² < 0
S = {∅} because a² ≥ 0
A grocery store is offering a sale on bread and soup. Khalil buys four cans of soup and loaves of bread for $11.67. Ronda buys eight cans of soup and one loaf of bread for $12.89.
a) rite equations for both Khalil's and Ronda's purchases.
b)solve the system to find the price of one can of soup and the price of one loaf of bread.
please help :((
Answer:
a. The equation should be
4x + 3y = $11.67
8x + y = $12.89
b. The price of one can of soup and the price of one loaf of bread is $1.355 and $2.09
The calculation is as follows:
here we assume the soup be x and bread be y
So, the equations are
4x + 3y = $11.67 .........(1)
8x + y = $12.89.........(2)
Here we need to multiply by 2 in equation 1
8x + 6x = $23.34
8x + y = $12.89
5y = $10.45
y = $2.09
Now x should be
8($2.09) + y = $12.89
x = $1.355
Hope this helps :)
Answer:
A)
Khalil: 4s + 1b = 11.67
Ronda: 8s + 1b = 12.89
B)
Can of soup = $0.305
Loaf of Bread = $10.45
(Please mark brainliest)
Step-by-step explanation:
Make s a can of soup
Make b a loaf of bread
A)
Khalil: 4s + 1b = 11.67
Ronda: 8s + 1b = 12.89
B)
12.89 - 11.67 = 1.22
1.22 / 4 = 0.305
11.67 - 1.22 = 10.45
Can of soup = $0.305
Loaf of Bread = $10.45
Bob can chop down 10 trees in 30 minutes, while Frank can chop down 15 trees in 30 minutes. Working together, how long will it take them to chop down 100 trees
It will take 120 minutes to chop down 100 trees.
Bob chops 10 trees in 30 minutes, so he can chop 100 trees in 300 minutes.
Frank chops 15 trees in 30 minutes, so he can chop 100 trees in 200 minutes.
Solve this using the following equation:
15 / 30 = 100 / x
Solving for x gives 120 minutes.
The unitary approach is a way of solving a hassle via first locating the price of a single unit, after which locating the necessary cost with the aid of multiplying the single unit fee.
The formula of the unitary approach is to find the cost of a single unit after which multiply the cost of an unmarried unit via the quantity of units to get the important price.
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Rashad is considering two designs for a garden. In Design 1 he would use fencing to surround a square plot of land that has an area of 1,296 square feet. In Design 2 he would divide a plot of land into two rectangular sections, each 15 feet by 36 feet, and surround the plot with fencing, as well as place fencing along the dividing line of the two sections.
Two designs for a garden are shown. Design 1 is a square with an area of 1,296 square feet. Design 2 is 2 rectangles with lengths of 15 feet and 36 feet that are connected at one side.
Which plan would cost less in fencing? Explain.
Design 1, because it requires 12 fewer feet of fencing than Design 2
Design 1, because it requires 24 fewer feet of fencing than Design 2
Design 2, because it requires 12 fewer feet of fencing than Design 1
Design 2, because it requires 24 fewer feet of fencing than Design 1
The plan that would cost less in fencing is B. Design 1, because it requires 24 fewer feet of fencing than Design 2.
How to depict the information?From the information given, Design 1 would use fencing to surround a square plot of land that has an area of 1,296 square feet and Design 2 would divide a plot of land into two rectangular sections, each 15 feet by 36 feet.
Therefore, the plan that would cost less in fencing is Design 1, because it requires 24 fewer feet of fencing than Design 2.
In conclusion, the correct option is B.
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Answer:
B
Step-by-step explanation:
In the diagram below, if AB = 24, AC = 8, and BD = 6, then find the length of DC.
A) 8
B) 2
C) 12
D) 3
thank you :)
Answer: 2
Step-by-step explanation:
By the angle bisector theorem,
[tex]\frac{8}{24}=\frac{DC}{6}\\\\DC=2[/tex]
The length of DC is 2
What is angle bisector theorem?Angle bisector theorem states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Given:
AB = 24, AC = 8, and BD = 6
Now, using angle bisector theorem
AB/ AC = BD / DC
24 / 8 = 6 / DC
3 DC= 6
DC = 2
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HELP HELP HELP
Quick algebra 1 questions
Hello:
Okay, this problem should be taken in a series of steps:
What is the slope's formula?
[tex]\rm\hookrightarrow \frac{y_2-y_1}{x_2-x_1}[/tex]
(x₁,y₁) -- first point(x₂,y₂) -- second pointOkay, now let's use this knowledge
10. (5,-19) and (-5,21)
[tex]Slope = \frac{21--19}{-5-5} =\frac{40}{-10}=-4[/tex]
11. (12,1) and (12, -1)
[tex]Slope = \frac{-1-1}{12-12} =\frac{-2}{0}[/tex]
12. (8,7) and (4,7)
[tex]Slope = \frac{7-7}{4-7} =0[/tex]
Answer:
Question 10: -4Question 11: undefinedQuestion 12: 0Hopefully that helps!
find the volume of a cone with a base diameter of 6ft and a height of 12ft
Answer:
452.389 cubic feet
Step-by-step explanation:
Answer:
Step-by-step explanation:
The formula for finding the volume of the cone: [tex]\pi r^2h/3[/tex]
Height= 12ft
Diameter= 6, radius= [tex]\frac{6}{2}[/tex]= 3
[tex]\frac{22}{7} *3^2*\frac{12}{3} \\\\\frac{22}{7} *3^2*2\\\frac{22}{7} *9*2\\\\\frac{22}{7} *18\\\\56.57[/tex]
A survey conducted by a reputed Business School in Texas among 400 students showed that students spend on an average $500 for textbooks in a year. The sample standard deviation was $80. What is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%
[489.68, 510.32] is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%.
n=400
sample mean (x)=500
sample standard deviation (s)=80
99% confidence interval for mean
α=0.01
critical value [tex]Z_{\frac{a}{z} }[/tex] =2.58
Standard error of sample mean Sx = [tex]\frac{s}{\sqrt[]{n} }[/tex] = [tex]\frac{80}{\sqrt[]{400} }[/tex] = [tex]\frac{80}{20}[/tex] = [tex]4[/tex]
∴ Sx = 4
Confidence interval (μ)
μ= [tex]x[/tex] ± [tex]Z_{\frac{a}{z} }[/tex] [tex]\frac{s}{\sqrt[]{n} }\\[/tex]
μ= [tex]x[/tex] ± [tex]Z_{\frac{a}{z} }[/tex] (Sx)
=500 ± 2.58(4)
=500 ± 10.32
lower limit = 500 - 10.32 = 489.68
upper limit= 500 + 10.32= 510.32
Hence, [489.68, 510.32] is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%.
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What is the additive identity for 2 x 4 matrices?
Answer:
The additive identity matrix would be a zero matrix (all its entries are zeros .) The sum between two matrices can be done if and only if the two matrices are similar, that means that they have the same numbers of rows and columns.
Step-by-step explanation:
if the ratio of red to blue circles is 1:3 how many more red circles need to be added to make it a ratio of 3:1
Answer:
8Step-by-step explanation:
if the ratio of red to blue circles is 1:3 how many more red circles need to be added to make it a ratio of 3:1
add 8 red =
9/3 = 3/1
Tayli wishes to advertise her business, so she gives packs of 13 red flyers to each restaurant owner and sets of 20 blue flyers to each clothing store owner. At the end of the day, Tayli realizes that she gave out the same number of red and blue flyers. What is the minimum number of flyers of each color she distributed?
The minimum number of flyers of each color distributed is 1.
What is the minimum flyer distributed?
In order to determine the minimum number of flyers of each color distributed, the common factor of 13 and 20 has to be determined. The factor of a number is a number that divides another number perfectly without any remainder.
Factors of 13 = 1, 13
Factors of 20 = 1, 2, 4, 5, 10, 20
Common factor = 1
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What is the circumference of a circle (to the nearest
whole number) whose diameter is 12?
Answer:
A
Step-by-step explanation:
The formula for circumference is π×diameter.
π×12= 37.6991, which can be rounded up to 38.
Place valu of 4 in 65400 is
Answer:
hundreds place in what the place value of the number 4 in 65400 the 6 is the hundred thousand place the 5 is the thounds place the four is the hundred place. The first zero is the 10th place. in the seconds, zero is the one place value
Answer:
The value 4 is in the hundreds place.
Step-by-step explanation:
We have the number 65400. The last digit in the number is 0, the 0 is in the ones place. The next number, which is also 0, is in the tens place. The next number after that is a 4, which is in the hundreds place. This shows that the 4 is in the hundreds place.
ten-thousands thousands hundreds tens ones
6 5 4 0 0
Hope this helps!
If not, I am sorry.
isha wants to paint the four walls of her living room.
Each wall is 2.6 m high and 3.5 m long.
One wall has a door of 2.2 m by 0.8 m.
Tins of paint cost £11 per 2 litre tin.
Each litre of paint can cover 8 m2 of wall.
There is an offer of: Buy 2 tins get the 3rd at half price.
How much will Aisha pay to paint her living room?
The amount Aisha would pay to paint her living room is £38.50.
What is the cost of painting the living room?The first step is to determine the area of the walls that do not have doors.
Area of a wall = length x width
3 x (2.6 x 3.5) = 27.30 m²
Dimensions of the wall with the door : (2.6m - 2.2m) x (3.5 - 0.8) = 0.4m x 2.7m
Area of the wall with the door : 0.4m x 2.7m = 1.08 m²
Total area of the walls: 27.30 m² + 1.08 m² = 28.38 m²
Number of paint tins needed for the walls : 28.38 / 8 = 3.55 = 4 tins
Cost of the paint tins : (11 x 3) + (0.5 x 11) = £38.50
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Select the correct answer from each drop-down menu.
How can you summarize the ruler placement postulate?
The summary of the ruler placement postulate is given as:
there is a one-to-one correspondence between the set of points on the line and the set of real numbers, and.the distance between two points equals the absolute value of the difference between the corresponding numbers.What is the ruler placement postulate?This states that the points of a line can be matched and correspond to a set of points on the line and the set of real numbers,
Therefore, based on the fact that your question is incomplete, a general overview of the ruler placement postulate is given to give you a better understanding of the concept.
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Answer: You can measure the positive distance between points A and B by using either point as zero
Step-by-step explanation:
2 c) factorize : x² - 2xy + y²
Answer:
(x-y)²
Since, it's formula of (x+y)² ...
Hello!
This is an identity :
[tex]\boxed {(x - y)^2 = x^2 - 2xy + y^2}[/tex]
∴ The factors are (x - y) and (x - y).
Please answer the question below
The value of x in the given sector is determined as 7.1.
Area of the sectorTotal area of the sector = area of the shaded + area of the unshaded
Since shaded and unshaded areas are equal, the value of x is calculated as follows;
πr²θ/360 = πx²60/360 + πx²60/360
πr²θ/360 = 2(πx²θ/360)
πr² = 2(πx²)
r² = 2x²
x² = r²/2
x² = (10²)/2
x² = 50
x = √50
x = 7.1
Thus, the value of x in the given sector is determined as 7.1.
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Audrey is driving to a concert and needs to pay for parking. There is an automatic fee of $6 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. How much total money would Audrey have to pay for parking if she left her car in the lot for 5 hours? How much would Audrey have to pay if she left her car in the lot for tt hours?
Answer:
a. $16
b. $26
Step-by-step explanation:
a. 6+2(5)= 16
b. im assuming tt means ten 6+2(10)=26
If Audrey leaves her car in the lot for "t" hours, she would have to pay a total of $6 + $2t for parking.
If Audrey leaves her car in the parking lot for 5 hours, she will have to pay the initial fee of $6 plus $2 for each hour she parked. For 5 hours, she will pay:
Initial fee: $6
Additional fee for 5 hours: $2 * 5 = $10
Total parking cost: $6 + $10 = $16
If Audrey leaves her car in the parking lot for "t" hours, the total parking cost can be calculated as:
Total parking cost = Initial fee + Additional fee for "t" hours
Total parking cost = $6 + $2t
So, if Audrey leaves her car in the lot for "t" hours, she would have to pay a total of $6 + $2t for parking.
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Given a line segment containing the points A,B, & C, in order, if AB is 11 and BC is 12, then the length of AC would be ____.
Answer:
23 or 1
Step-by-step explanation:
for answer 23: we considered the segment ABC which means A is the leftest point and C is the rightest point. then AC = AB+BC
for answer 1: we considered the segment CAB which means C is the leftest point, and B is the rightest point. Then AC = CA = BC-AB = 12-11=1