Answer:
(a) 3628800 ways
(b) 17280 ways
(c) 120960 ways
Step-by-step explanation:
Given
[tex]Novels = 5[/tex]
[tex]Maths = 4[/tex]
[tex]Biology = 1[/tex]
[tex]Total = 10[/tex]
Solving (a): Arrangement with no restriction.
We simply count each book with no restriction. i.e. 10 books
So, the number of arrangement is:
[tex]Arrangement =10![/tex]
[tex]Arrangement =10*9*8*7*6*5*4*3*2*1[/tex]
[tex]Arrangement =3628800[/tex]
Solving (b): Maths book together and Novels together
First, arrange the 4 maths books as:
[tex]Maths = 4![/tex]
Next, arrange the 5 novels as:
[tex]Novels = 5![/tex]
Lastly, take the 4 maths book as [1], the 5 novels as [1] and the remaining [1] biology book.
So, we have: 3 books
Arrange 3 books, we have:
[tex]Books = 3![/tex]
Total arrangement is:
[tex]Total = 4! * 5! * 3![/tex]
[tex]Total = 4*3*2*1 * 5*4*3*2*1 * 3*2*1[/tex]
[tex]Total = 17280[/tex]
Solving (c): Maths book together
First, arrange the 4 maths books as:
[tex]Maths = 4![/tex]
Next, take the 4 maths book as [1], then the remaining 6 books (i.e. 5 novels and 1 biology)
So, we have: 7 books
Arrange 7 books, we have:
[tex]Books = 7![/tex]
Total arrangement is:
[tex]Total = 4! * 7![/tex]
[tex]Total = 4*3*2*1 * 7*6*5*4*3*2*1[/tex]
[tex]Total = 120960[/tex]
What is the inverse statement,"If I listen to this song, then it will get stuck in my head"?
Answer:
D. If I do not listen to this song, then it will not get stuck in my head.
Step-by-step explanation:
Answer:
"If I don't listen to this song, then it won't get stuck in my head."
A data set includes data from student evaluations of courses. The summary statistics are n, , s. Use a significance level to test the claim that the population of student course evaluations has a mean equal to . Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
Complete question :
A data set includes data from student evaluations of courses. The summary statistics are nequals92, x overbarequals4.09, sequals0.55. Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
Answer:
H0 : μ = 4.25
H1 : μ < 4.25
T = - 2.79
Pvalue =0.0026354
we conclude that there is enough evidence to conclude that population mean is different from 4.25 at 10%
Step-by-step explanation:
Given :
n = 92, xbar = 4.09, s = 0.55 ; μ = 4.25
H0 : μ = 4.25
H1 : μ < 4.25
The test statistic :
T = (xbar - μ) ÷ s / √n
T = (4.09 - 4.25) ÷ 0.55/√92
T = - 0.16 / 0.0573414
T = - 2.79
The Pvalue can be obtained from the test statistic, using the Pvalue calculator
Pvalue : (Z < - 2.79) = 0.0026354
Pvalue < α ; Hence, we reject the Null
Thus, we conclude that there is enough evidence to conclude that population mean is different from 4.25 at 10%
Answer:
Step-by-step explanation:
The null and alternative hypotheses are:
Null hypothesis: The population mean of student course evaluations is equal to 4.25.
Alternative hypothesis: The population mean of student course evaluations is not equal to 4.25.
The significance level is 0.01, so the test will be a two-tailed test.
The test statistic is calculated as:
t = (x - μ) / (s / √n) = (4.18 - 4.25) / (0.54 / √97) = -2.63
The degrees of freedom for the t-distribution is n-1 = 96. Using a t-table or a calculator, the P-value for a two-tailed test with 96 degrees of freedom and a t-value of -2.63 is approximately 0.010.
Since the P-value (0.010) is less than the significance level (0.01), we reject the null hypothesis. We have sufficient evidence to conclude that the population mean of student course evaluations is not equal to 4.25.
In other words, the data provides strong evidence to suggest that the average student course evaluation rating is significantly lower than 4.25.
If right I’ll mark brainiest need ASAP
Answer
Step-by-step explanation: Anybody who help me I will mark brainliest in give you 180 points you have to go on my page in answer all my questions
Determine the amplitude or period as requested . Amplitude of y = - 1/5 * sin x a - 1/5 1/5 b 5 d. pi/5
Answer:
The amplitude is 1/5
Step-by-step explanation:
Given
[tex]y = -\frac{1}{5}\sin(x)[/tex]
Required
Determine the amplitude
The general cosine function is:
[tex]y = A\sin(k(x + c)) +d[/tex]
Where
[tex]Amplitude = |A|[/tex]
Compare [tex]y = A\sin(k(x + c)) +d[/tex] and [tex]y = -\frac{1}{5}\sin(x)[/tex]
[tex]A = -\frac{1}{5}[/tex]
So:
[tex]Amplitude = |-\frac{1}{5}|[/tex]
[tex]Amplitude = \frac{1}{5}[/tex]
Which angle is an acute angle?
A. An angle measuring 325°
B. An angle measuring 265°
C. An angle measuring 125°
D. An angle measuring 85°
Answer:
The answer is Option D
Step-by-step explanation:
Option D is the right answer since 85° is a acute angle. Acute angles are angles below 90°
Hope this helps!
Have a good day
im sooooooooo bord sooooo you get 100 points for ansering 1+1¥¥¥¥¥¥¥¥
Answer:
1+1=2
Step-by-step explanation:
THANKS YOU YAY HOPE IT HEOPS
Answer:
2 thanks
Step-by-step explanation:
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius ?
Step-by-step explanation:
Cone Volume = 1/3 ×( π r² h) h = 2 × diameter = 2 × 2 × r
Cone Volume = 1/3 ×( π r² h) h = 2 × diameter diameter = 2r
= 2 × (2 × r)
= 4r
Cone Volume = 1/3 ×( π r² 4r)
= (4 π r³ / 3)
Gino wants to leave at least 20% tip on his restaurant bill of $197.40. Approximately how much tip should he add to the bill?
PLEASE HELP THIS IS DUE TODAY
rearrange the parallelogram as a rectangle. Then find the area.
find the cost of fencing a rectangular field 250m long and 130m wide at rupees 30 per meter
Answer:
length of rectangular =250m
breath =130m
perimeter of rectangular field =(130*250)
=32500m
cost of fencing a rectangular field at the rate of 30 per meter
cost of the rectangular field =32500*30
=rupees 975000
hope it helps
{7x+4y=-8
{-8x-5y=13
Solve system of equation
Answer:
(x,y)=(4,-9)
Step-by-step explanation:
The solution of the equation 7x + 4y = – 8 and 8x + 5y = –13 will be (4, –9).
What is the solution of the equation?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The solution of the equation means the value of the unknown or variable.
The system of the equation is given below.
7x + 4y = – 8 …1
8x + 5y = –13 …2
Multiply equation 1 by 5 and equation 2 by 4. Then subtract the equation 1 from 2, then we have
32x – 35x = –52 – (–40)
–3x = –12
x = 4
Substitute the value of x in equation 1, then the value of y will be
7(4) + 4y = – 8
28 + 4y = –8
4y = –36
y = –9
The solution of the equation 7x + 4y = – 8 and 8x + 5y = –13 will be (4, –9).
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ5
A company bought 7 machines. Each machine weighs 642.4 pounds. How many pounds do the 7 machines weigh altogether?
Answer:
4496.8 pounds
multiply 642.4by7
Please solve this: the area of a rectangular piece of card is 56cm square.
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Answer:
7 cm
Step-by-step explanation:
The formula for the area of a rectangle tells you the area is the product of length and width:
A = LW
56 = 8W
From your knowledge of multiplication tables, you know that ...
56 = 8·7
That is, W = 7 . . . cm.
The width of the card is 7 cm.
Answer:
7 cm is the answer.Step-by-step explanation:
#CarryOnLearningAdd.write the answer as a mixed number in the simplest form.
Answer:
5[tex]\frac{11}{12}[/tex]
Step-by-step explanation:
GCF of 4 and 6 is 12
1/6 = 2/12
3/4 = 9/12
4 + 1 = 5
2/12 + 9/12 = 11/12
5 11/12
Answer:
71/12Step-by-step explanation:
First you want to make the denominators in the fractions the same number. To do so, we need to multiply both the numerators and the denominators. Do this until the denominators are the same.
[tex]\frac{1}{6} *\frac{4}{4} = \frac{4}{24}[/tex]
[tex]\frac{3}{4} *\frac{6}{6} = \frac{18}{24}[/tex]
Now add
[tex]4\frac{4}{24} + 1\frac{18}{24} = 5\frac{22}{24}[/tex]
After adding, you need to multiply the whole numbers by the denominator and add that number to the numerator.
[tex]5*24=120[/tex]
[tex]\frac{120}{24} +\frac{22}{24} = \frac{142}{24}[/tex]
Finally simplify
[tex]\frac{142}{24} / \frac{2}{2} = \frac{71}{12}[/tex]
Two women share 60 eggs
it the ratio 1 to 2. How many eggs does each recieves?
Answer:
One woman receive 20 eggs
And the other receive 40 Egss
Explanation:
So the ratio is 1:2 so we gonna add them to get the total so 1+2=3
To find each amount divide each by the total so 1/3 and 2/3
To find the first amount
1/3×60=20
To find the other amount you can either subtract
60-20=40
or
2/3×60=40
One woman receive 20 eggs and the other receive 40 eggs.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
So the ratio is 1:2 so we have to add them to get the total.
So 1+2=3
In order to find each amount divide each by the total.
So 1/3 and 2/3
The first amount,
1/3 × 60 = 20
The other amount,
60-20=40
or
2/3 × 60 = 40
Thus, One woman receive 20 eggs and the other receive 40 eggs.
Learn more about the unitary method;
https://brainly.com/question/23423168
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[tex]\boxed {\boxed {prove : \: 3 \: is \: greater \: than \: 5 }} [/tex]
3 has more letters than 5. Hence 3 is greater than 5
Which of the following is equivalent to 19 L?
A. 1,900 mL
B. 0.019 mL
C. 19,000 mL
D. 0.0019
the answer is A which is 1900 ml
Yesterday, a movie theater sold 269 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all the movie theater made $494 from
popcom sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.
The movie theater sold large bags of popcorn and small bags of popcorn.
Answer:
S=194, L=75 L+S=269, 4L+1S=$494
Step-by-step explanation:
what is the surface area of this design
Answer:
the correct answer is 197 in^2
The height meters of a mass projected vertically upwards at a time seconds s=ut-0.5gt².
Determine how long the mass will take after being projected to reach a height of 16m on the ascent.
b. on the descent when u=30m/s and g=9.8m/s
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Answer:
t ≈ 0.590 s (ascent); 5.532 s (descent)
Step-by-step explanation:
We are interested in the values of t when s=16.
s = 30t -4.9t²
4.9t^2 -30t +16 = 0 . . . . . substitute 16 for s; put in standard form
The quadratic formula can be used to find the solutions:
t = (-(-30) ±√((-30)² -4(4.9)(16)))/(2(4.9))
t = (30 ±√586.4)/9.8 ≈ 0.59023, 5.53221 . . . . seconds after launch
a) It will take 0.590 seconds to reach 16 m height initially.
b) It will take 5.532 seconds to return to 16 m height on descent.
Santino fires a paintball 3 meters from the ground such that the initial trajectory is perfectly horizontal. Assume the paintball does not hit anything and the ground is level. When will the paintball hit the ground?
Help me somebody pleaseeee
1. find the greatest mass
that can be taken on exact
number of times from 360g
504g, and 672 g
Answer:
72g
Step-by-step explanation:
I hope it's right I figured it out by common factor
A car wash attendant counted the number of cars washed and the total amount of money earned. The company charged the same price for each car washed and earned $165 for 15 cars, $231 for 21 cars, and $275 for 25 cars. Write an equation for the relationship between the number of cars washed, n, and the number of dollars earned, m.
HELP!
Which expression is equivalent to -6(-2/3+2x) ?
Answer:
-6(-2/3+2x)
=12/3+12x
=4+12x
4(1+3x)
Joe wants his overall test average to be 85%. What score would he need on his next test if the test scores he has so far are: 70%, 105%, 75%, 90%, 90%?
Answer:
He would need a score of 0.8 = 80%.
Step-by-step explanation:
Average score:
The average score is the sum of all scores divided by the number of tests.
What score would he need on his next test if the test scores he has so far are: 70%, 105%, 75%, 90%, 90%?
Combining with the next text, there will be 6, and the sum will be: 0.7 + 1.05 + 0.75 + 0.9 + 0.9 + x = 4.3 + x.
Joe wants his overall test average to be 85%.
So
[tex]\frac{4.3 + x}{6} = 0.85[/tex]
[tex]4.3 + x = 5.1[/tex]
[tex]x = 5.1 - 4.3 = 0.8[/tex]
He would need a score of 0.8 = 80%.
A bag contains 2 red, 4 blue, and 4 yellow marbles. What is the probability of pulling a red marble, putting the marble back, and then pulling a blue marble?\
Answer:
Di ko po alam sorry
Step-by-step explanation:
Di ko alam putaenamo
PLEASE ANSWER ASAP TIMED! A candle shop owner collected data on customers favorite scents as shown in the table. A customer is randomly selected. If the probabilities of a customer choosing floral and coconut as their favorite scents are the same what is the value of the missing probabilities? Inside the chart lavender 0.31 vanilla 0.18 cinnamon 0.23 floral? Coconut? The answer choices are 0.10 0.14 0.20 0.28
Answer: .14
Step-by-step explanation: 2020 edg
Answer:
.14
Step-by-step explanation:
I just took the test
Can someone please help
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Answer:
C. 39°
Step-by-step explanation:
The measure of the angle where the chords cross is the average of the measures of the subtended arcs.
x = (AB +CD)/2 = (28° +50°)/2 = 78°/2
x = 39°
I need the answer real fast PLZ
Answer:
54%
Step-by-step explanation:
I did the test.