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]
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A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 17. A randomly selected group of 35 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 116.8. If the organization's claim is correct, what is the probability of having a sample mean of 116.8 or less for a random sample of this size
Answer:
0.3372 = 33.72% probability of having a sample mean of 116.8 or less for a random sample of this size
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean IQ score of its members is 118, with a standard deviation of 17.
This means that [tex]\mu = 118, \sigma = 17[/tex]
Sample of 35:
This means that [tex]n = 35, s = \frac{17}{\sqrt{35}}[/tex]
What is the probability of having a sample mean of 116.8 or less for a random sample of this size?
This is the pvalue of Z when X = 116.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{116.8 - 118}{\frac{17}{\sqrt{35}}}[/tex]
[tex]Z = -0.42[/tex]
[tex]Z = -0.42[/tex] has a pvalue of 0.3372
0.3372 = 33.72% probability of having a sample mean of 116.8 or less for a random sample of this size
How would I solve this?
If you help me with my last question I will help you with this one
Charles paid $398.57 for a new computer. He knew that the total included about 28$ in tax. What is the approximate percentage of the total that was tax?
Answer:
7 percent.
Step-by-step explanation:
Hope this helps!
Which describes the cross section of a cube that passes through the vertices A, B, C, and D shown below?
a rectangle that is not a square
a square
a paralelogram that is not a rectangle or a square
a trapezoid
Answer:
B. A square
Step-by-step explanation:
the area of a circle is 0.2826 square miles. what's is the circle's radius? use 3.14 for pi
Choose the item that has measurable volume.
newspaper page
a water bottle
a dollar bill
a postage stamp
Answer:
A water bottle
Step-by-step explanation:
It's a water bottle because you cannot measure volume with a dollr bill or postage stamp.
The chart shows the results of 20 spins that Kristie made with a spinner.
Based on these results, what is the probability that Kristie's spinner will land on Mexico the next time?
Answer:
3 / 10
Step-by-step explanation:
The required outcome = mexico ; number of spins = 6 spins
Total possible outcomes = sum. Of all spins = (6 + 4 + 5 + 5) = 20
P(Mexico on next spin) = required outcome / Total possible outcomes
P(Mexico on next spin) = 6 / 20 = 3 / 10
Find the surface area of each figure. Round answers to two decimal places. Use 3.14 for pi
Answer:
the top wpuld be 73.14 and i cant see the numbers at the bottom
Step-by-step explanation:
The total surface area of the given figure which has cone and hemisphere is 944.08 square inches
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Let us find the height of the cone by using pythagoras theorem
7²+h²=15²
49+h²=225
Subtract 49 from both sides
h²=225-49
h²=176
h=13.2
Now let us find surface area of cone
A=πr(r+√(h²+r²))
A = 482.5
The surface area of hemisphere is 3πr²
A=3×3.14×(7)²
=3×3.14×49
=461.58
The total surface area = 482.5+461.58
=944.08 square inches
Hence, the total surface area of the given figure which has cone and hemisphere is 944.08 square inches
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
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ABCD m angle ACD=2x+4 and m angle ACB=5x-5 . For what value of ABCD rhombus?
Please help quick ! This is a timed test
Answer:
I don't have a picture but since it is a rhombus, I'll give it my best shot.
IF those two angles are across from each other, they are equal, then:
2x+4 = 5x-5
add 5 to each side of the equation:
2x+9 = 5x
subtract 2x from each side:
3x = 9
divide both sides by 3:
x = 3
IF those two angles are adjacent, their sum is 180°, then:
2x+4 + 5x-5 = 180°
combine like terms:
7x - 1 = 180
add 1 to each side of the equation:
7x = 181
divide both sides by 7:
x = 25.86
Rosalind made 969 donuts and put 8 donuts into each box. How many boxes of donuts were made
Answer:
121 donuts in each box
Step-by-step explanation:
969 divided by 8 = 121.125
(Ignore the remainder)
Step by step solution:
We know that there are 969 doughnuts, and there are 8 doughnuts per box. What we need to find out is how many boxes of doughnuts were made.
Step 1:
Set up an equation for Number of doughnuts (969) / Number of doughnuts per box (8) = Number of boxes made (x), which would look like this:
969/8 = x
Step 2:
Doing this, we can get 121.125, which leaves us with
121.125 = x
121.125 = 121.125
Which gives us the answer of 121.125, which we can shorten to 121, as the decimal is not necessary.
Checking our answer:
We can check our answer simply be rewording our 1st equation to solve for the number of doughnuts made. This would give us the equation Number of doughnuts per box (8) * Number of boxes made (121.125) = x. Solving this equation would look like
8 * 121.125 = x
969 = x
969 = 969
Answer: By completing the steps above we get 121, and we can check our work by rewording the problem to solve for the number of Doughnuts. Good Luck!
HEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPP
Answer:
The volume of the tissue is 42 cubic inches
Step-by-step explanation:
Given
[tex]Base\ Area = 8.4in^2[/tex]
[tex]Height = 5in[/tex]
Required
The volume of the tissue
This is calculated as:
[tex]Volume = Base\ Area * Height[/tex]
So, we have:
[tex]Volume = 8.4in^2 * 5in[/tex]
[tex]Volume = 42in^3[/tex]
The measure of
the arc is for all and each no rush!
Answer:
Step-by-step explanation:
1)
The given angle is 57° at least I think it is . so we need to look at the triangle being formed inside the circle. the legs from the center to the edge are both the radius. so they are the same lengths. so that triangle is an isosceles. and the two angle at the circles perimeter are going to be both the same, b/c that's a rule of an isosceles triangle. so now we not both angles on the perimeter of the circle of that inner triangle are both 57° :) that's great, b/c now we can find the angle of the inner point of that triangle. it's going to be 180 = 57 + 57 + inner angle x
180 - 57 -57 = inner angle x
66 = x , so that inside angle on the isosceles is 66°
that's great to know, that angle is also part of the bigger triangle that goes outside the circle and I'm pretty sure the angle that is at the top of the triangle , at least in the picture, is a right angle or 90° sooo we now know two angle of the triangle and can figure our the "?" one. :)
180 = 66 + 90 + ?
180-66-90 = ?
24 = ?
so that angle at the point with the "?" is 24 ° :)
2)
The given angle is 24° :0 look above.. that last we we solved was also 24°
everything is the same in drawing 2, as in drawing 1. We can simply use all the things we know about drawing 1.. The inside angle at the center of the circle will be 66 ° and the two angle out by the perimeter of the circle will be 57° just like in drawing 1. They made that a little too easy :D Le'ts hope we get a few more like that :)
3)
I'm just sure why the drew the circle in this drawing. we don't need it to solve this triangle. Maybe you're not supposed to use this very common way to solve the triangle yet? but maybe it's good to introduce it anyway? since we are given the hypotenuse (long side) and the adjacent side (next to) the angle we can just use SOH CAH TOA to find any angle or side of this triangle. I'll put the useful remind of how trig functions ( sin, cos, ect.) fit on triangles and then we'll use them to find the parts we want. :)
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
copy the above down. and put in in a handy place on your computer , for quick reference any time you have to solve a triangle. it's really super helpful :)
okay now look at the triangle in question 3) what do we know, and what do we want to find? we know the Hyp and Adj and one angle and want to find the Opposite (Opp) side from the known angle. sooo we have a choice of SOH or TOA.. let's use SOH,
SOH ⇒ Sin(Ф) = Opp / Hyp
Sin(53) = Opp/ 10
algebra skill engage :P
10* Sin(53) = Opp
7.9863551 = Opp
so that side with the question mark is 8.0 long. ( rounded to nearest 10th)
4)
On this triangle we are given the Opp and the Adj sides and an angle and are asked to find the Hyp
which trig function would you like to use?
Let's use CAH this time. We could also use SOH , but we just used that one. let's try out the "tools" of the trade :)
CAH ⇒ Cos(Ф) = Adj / Hyp
Cos(37) = 8/Hyp
use algebra skillz
Hyp = 8 / Cos(37)
use calculator to find Cos(37) :/
Hyp = 10.01708
? = 10.0 ( rounded to nearest 10th )
5)
oh for this one we do need the circle, and I don't know why they want people to know this , nobody uses this math :? Anyway,
there is a confusing formula for this type of problem
∠ = (bigger arc - smaller arc ) / 2
since we're given the 65° , we know that 2*65= 130 which is the angle of the bigger arc - smaller arc = 130 °
now we have to use our really keen algebra skillz to see that
if the total all the way around a circle is 360 and we have 130 of those left so
eq. 1) 360 = big arc + small arc
then
360-smal arc = big arc
and
eq. 2) 130 = big arc - small arc
plug in for "big arc" what we know from above :P
130 = 360-small arc - small arc
130 = 360 - 2small arc
130 + 2 small arc = 360
2 small arc = 230
small arc = 115
:0 wow.. we solved it.. that was a lot of fancy algebra huh :P
? = 115° ( the small arc)
6)
same as 5
given 72°
72*2=144°
eq. 1) 360 = big arc + small arc
eq. 2 ) 144 = big arc - small arc
solve for big arc this time
360-bigl arc = small arc
now plug into eq. 2
144 = big arc - (360-big arc)
144 = big arc - 360 + big arc
144 = 2big arc - 360
144+ 360 = 2 big arc
504 = 2 big arc
252° = big arc
yay solved !! phew.. that was a lot of algebra.. :P
5 and 6 are tough, ask the teacher how many others got it :)
50 points) please help! no links, brainliest, extra points.
I understand if you need points, you can go to my old questions and answer them for points, please only answer if your 100% sure you're correct. I've redone this over 20 times, asked over 50, and failed all those times. thank uu.
The dot plot below shows the number of vacations taken by the sixth-grade students at Walker Junior High one year.
What is the interquartile range of the data set shown?
A. 4
B. 3
C. 1
D. 2
I'm positive its B.3
Step-by-step explanation:
Answer:
B. 3
Step-by-step explanation:
[tex]interquatile \: range = (Q _{3} - Q _{1}) \\ = ( ( \frac{3}{4} \times 6) - ( \frac{1}{4} \times 6)) \\ = (4.5 - 1.5) \\ = 3[/tex]
Which table matches with the linear equation y = - 2x - 3?
X-
20
-1-3
35
0-8
X-2-1
y 1-1-5
4
-11
2
X-4-1
y 1-2 3
-5
X
-503 6
2 -3 -6-9
y
Answer:
b
Step-by-step explanation:
Find the product. Simplify.
(8 – 6b)(5 – 36) =
Someone help me pls!!
Answer:
-62
Step-by-step explanation:
(8 – 6b)(5 – 36)
(8 – 6b)(-31)
-248 + 186
-62
8. A box is filled with candies in different colors. We have 40 white candies, 24 green ones, 12
red ones, 24 yellow ones and 20 blue ones. If we have selected one candy from the box
without peeking into it, find the probability of getting a green or red candy.
Answer:
[tex]P(Green\ or\ Red) = 0.30[/tex]
Step-by-step explanation:
Given
[tex]White = 40[/tex]
[tex]Green = 24[/tex]
[tex]Red = 12[/tex]
[tex]Yellow = 24[/tex]
[tex]Blue = 20[/tex]
Required
[tex]P(Green\ or\ Red)[/tex]
The total numbe of candy is:
[tex]Total = 40 + 24 + 12 + 24 + 20[/tex]
[tex]Total = 120[/tex]
This probability is calculated as:
[tex]P(Green\ or\ Red) = P(Green) + P(Red)[/tex]
For each, we have:
[tex]P(Green\ or\ Red) = \frac{Green}{Total} + \frac{Red}{Total}[/tex]
Take LCM
[tex]P(Green\ or\ Red) = \frac{Green+Red}{Total}[/tex]
[tex]P(Green\ or\ Red) = \frac{24+12}{120}[/tex]
[tex]P(Green\ or\ Red) = \frac{36}{120}[/tex]
[tex]P(Green\ or\ Red) = 0.30[/tex]
Which if the shaded regions below represents 3/5 of the whole circle
Answer:B
Step-by-step explanation: i have the same test
Michael made a scale model of the Empire State Building. The building has an actual height of 381m. Michael's models used a scale in which 1 cm = 50 m. what is the height of of the model in cm
Answer:
7.62 cm
Step-by-step explanation:
set up a proportion then cross-multiply:
1 / 50 = x / 381
50x = 381
x = 381/50
saniyah collected a total of 9 seashells she gave 1/3 to her sis how many seashells did Saniyah have left?
Answer: The answer is 3.
Step-by-step explanation: You would multiply 9x1/3 which would give you 3. If you want to understand even better here's how to do so: Put 3(the answer that you got from multiplying 9x1/3) into the fraction 1/3 as 1. In other words, it would look something like this 3/3. Then, just multiply the two numbers 3x3 and that equals 9, the number you started with.
Hope that this helped!!:)
Considering the provided information in the given question, we have :
Total seashells Saniyah have = 9Number of seashells Saniyah gave to her sister = [tex]\sf \dfrac{1}{3} [/tex] of total.We need to find how many seashells did Saniyah have left.
⇒ Number of seashells Saniyah have left = Total seashells – Number of seashells she gave to her sister
⇒ [tex] \sf {Left \: seashells = 9 - \Bigg \lgroup \dfrac{1}{3} \times 9 \Bigg \rgroup } [/tex]
⇒ [tex] \sf {Left \: seashells = 9 - \Bigg \lgroup 1 \times 3 \Bigg \rgroup } [/tex]
⇒ Left seashells = 9 – 3
⇒ Left seashells = 6
Therefore, Saniyah have left [tex] \bf {6 \: seashells } [/tex].
I need more help this is so bad
Answer:
perimeter of square=4×side
perimeter of square =4×13cm
perimeter of square = 52cm
area of square = side²
area of square = (13cm)²
area of square = 169cm²
Answer:
52 cm / 169 cm²
Step-by-step explanation:
To find the perimeter, we can add together the lengths of all the sides. Since the height and width of the square are the same length, we can tell all four sides are equal.
13 + 13 + 13 + 13 = 52
The perimeter is 52 cm.
The area is the length times the width of the shape, so we have to multiply 13 by 13.
13 · 13 = 169
The area is 169 cm².
The answer is the third option, 52 cm / 169 cm².
Good luck :)
How many ways can three people be selected from a group of seven people if order DOES matter?
Answer:
no it doesnt matter unless you do this The fundemetal principle of counting.
7 ways 3 people = 21 ways
Step-by-step explanation:
Need help fast plz. Math
The number 9.636363 is rational
What is 12% of 36 plz help
Answer:
12% of 36 is 4.32
What is the measurement of angle ACD?
Answer:
136
Step-by-step explanation:
theory: sum of opposite interior angles is equal to exterior angle
do oh understand?
Step-by-step explanation:
x=75+61{ sum of of interior angle of triangle is is equal to its opposite exterior angle }
x=136°
ACD=x=136°
hope it helps.
Plz help I have a time limit
Answer:
Area 108cm2
Step-by-step explanation:
triangle =1/2 ×base× height
rectangle =length × width
then add the area of each shape
Factorise :
3x² -5x + 6
Answer:
The expression is not factorable with rational numbers.
Step-by-step explanation:
Solve the system of inequalities bu graphing and shading: y<2x-3 and 2x+y>2
Answer:
Step-by-step explanation:
In the screenshot
Please help \^.^/
What is the solution to the inequality below?
x² =< 49
the answer would be B. I used m a th way to find out what the answer was, you could use that app if you ever come across a similar question!
-100-95-90-85-...;11th Term
Answer:
50
Explanation:
The difference is always 5