[tex]\displaystyle\\|\Omega|=\binom{72}{4}=\dfrac{72!}{4!68!}=\dfrac{69\cdot70\cdot71\cdot72}{2\cdot3\cdot4}=1028790\\|A|=\binom{46}{4}=\dfrac{46!}{4!42!}=\dfrac{43\cdot44\cdot45\cdot46}{2\cdot3\cdot4}=163185\\\\P(A)=\dfrac{163185}{1028790}=\dfrac{473}{2982}\approx0.1586[/tex]
3) Find an estimated product.
59 x 42 = ?
Oa.) 50 x 40 = 2500
Ob.) 60 x 50 = 3500
Oc.) 60 x 40 = 2400
Answer:
c.
Step-by-step explanation:
we estimate by rounding the factors to "easy numbers". that means numbers we can easily calculate even in our heads, and we get at just a ballpark number as result for orientation.
59 is much closer to 60 than to 50.
42 is much closer to 40 than to 50.
of course, we round to the closest "round numbers", so that the loss of precision through the rounding is as little as possible, so that the estimation still gives a much value as possible.
and the sum of the differences of the factors should be as close to 0 as possible.
so, 60×40 is the closest and therefore best estimation.
the sum of the factor differences is (+1 - 2) = -1.
compare to the real result :
59×42 = 2,478
answer a and b are by the way not correct :
50×40 = 2000 (and not 2500)
60×50 = 3000 (and not 3500)
FYI - in this case 50×50 = 2500 would be the closest estimation.
and the sum of the factor differences would be (-9 + 8) = -1.
normally, this wide "jumping" (-9 to +8) would make it only second choice.
John has four times as much money as his sister Debbie who has half as much as their friend David. Together the three children have $105. a) How much money does Debbie have? Answer b) How much money does John have? Answer.. c) How much money does David have? Answer.. (1)
Let's say that the money that each person has is equal to a letter:
A=Debbie, B=John, C=David.
Now we can write some equations.
"John has four times as much money as his sister Debbie who has half as much as their friend David."
B = 4A
A = 0.5C
"Together the three children have $105"
A+B+C=105
This is now a system of equations problem. Substitute to solve.
A + (4A) + C = 105
(0.5C) + 4(0.5C) + C = 105
3.5C = 105, so C = 30.
Plug this into the previous equations to get A=15 and B=60
So Debbie has $15, John has $60, and David has $30
Caroline is looking for a tool to measure the mass of a dictionary. Which tool should she use?
A.
ruler
B.
pan balance
C.
stopwatch
D.
1‐liter container
[tex]\bold{Q:}[/tex]
Caroline is looking for a tool to measure the mass of a dictionary. Which tool should she use?[tex]\bold{Ans:}[/tex]
B. pan balanceA balance or scale is an instrument used to measure mass.
Hope it helps.
[tex]\bold{Feel \: free \: to \: correct \: me}[/tex]~
I paid $8000 to burrow $50000 for 2 years. What was the rate of simple interest charged?
[make brainliest if got correct and 20pts]
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$8000\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &2 \end{cases} \\\\\\ 8000=5000[1+(\frac{r}{100})(2)]\implies \cfrac{8000}{5000}=1+\cfrac{r}{50}\implies \cfrac{8}{5}=1+\cfrac{r}{50} \\\\\\ \cfrac{8}{5}-1=\cfrac{r}{50}\implies \cfrac{3}{5}=\cfrac{r}{50}\implies \cfrac{3(50)}{5}=r\implies 30=r[/tex]
Find the surface area of the prism. 8 4 14
Answer:
4 8 1 4 0,683 the (783)-213=509
To determine how American college students feel about commuting, 100 students at a private
the university was chosen by selecting 50 men and 50 women to participate. They were asked
how far they commute each day (in minutes) to campus.
a. Is this an observational study or experiment?
b. What is the sample?
c. What is the target population?
d. What is the sampling method? (Simple random, stratified, convenient, …)
e. Is the data collected qualitative or quantitative?
f. Why is it unlikely that the results of this study will be valid?
The nature of the research is called Observational Study while the target Population is American Students.
How to find the sampling method?
1) In study, we survey members of a sample without trying to affect them while in experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive treatment. Thus, this is an observational study.
2) The sample is the 100 students made up of 50 boys and 50 girls.
3) The target Population are American College Students
4) The sampling method is; Simple random Sampling
5) The data is qualitative because it deals with description of feelings rather than dealing with numbers and figures.
6) It is unlikely that the results would be invalid because of sampling bias as it was only done in a private university.
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In the diagram, points D and E are marked by drawing arcs of equal size centered at B such that the arcs intersect and . Then, intersecting arcs of equal size are drawn centered at points D and E. Point P is located at the intersection of these arcs.
Based on this construction, m∠ABP is
°, and m∠ABC is
Based on this construction, the value of m∠ABC is 64°.
How to find the angle?From the point, E and D, two arcs are made which are intersecting each other at point P.
It means, that line BP is the bisector of angle ABC. ABC will be:
= 2 * 32=64
Therefore, based on this construction, the value of m∠ABC is 64°.
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What part of the circle below is highlighted in red?
A. Radius
OB. Chord
O C. Diameter
OD. Center
Hi Student!
Let's go through each of the options that were provided to the question stating what part of the circle was highlighted in red and talk about what they mean.
First off, radius is the distance from the outer line to the middle which perfectly incapsulates what the red line is. Therefore, the correct answer would be option A, Radius.
However, if you want to understand the rest of the definitions you can follow with the bullets provided.
Chord - This isn't a math termDiameter - This term is actually quite similar to that of radius but instead this is the length from one side of the outer line to the other side of the outer line. This would cause the diameter to be twice the length of the radius and so if we want to determine the radius using the diameter we can just divide it by 2Center - This just description the dot in the middle of the circleA. Saving money at the grocery store by using unit pricing.
a. Toilet paper A is 6 mega rolls for $4.59.
b. Toilet paper B is 12 mega rolls for $9.02.
In order to save money, the person should buy Toilet paper B.
Which option is cheaper?In order to determine the unit price of each option, divide the total cost by the number of rolls. The option that would save money is the cheaper option.
Unit cost = total cost / number of rolls
$4.59 / 6 = $0.77
$9.02 / 12 = $0.75
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x − y = 12
x + 2y = 21
Answer: x=15, y=3
Step-by-step explanation:
Subtracting the two equations, we get -3y=-9, meaning y=3.
Substituting this into the first equation, we get that x-3=12, and thus, x=15.
Help please…………………..
hi everyone today is world environment day please give me 100 to 200 word eassy on environment to save nature can anyone help this ~
The conditions or surroundings in which we all live is called the environment. The main elements of the environment are air, water, temperature, weather conditions and more.
The environment is the base of the life cycle. It is the most precious gift of nature. But now our environment is in danger. Saving the environment is very important for living a comfortable life. It is the biggest challenge for humans to revert the environment to its real state. But nothing is impossible.
We need to take some steps immediately in order to save the environment and revert it back to its original form. Using natural resources efficiently is a powerful way to save our environment.
♥happy environment day♥☆...hope this helps...☆
_♡_mashi_♡_
Angles in circles
How many degrees are in a half of a full turn?
Answer:
180 degrees
Step-by-step explanation:
Because 360 is i full turn around and you can divide 360 by 2 and you will get 180
Hope This Helped
There are 9 squares and 6 circles. What is the simplest ratio of circles to squares?
Answer:
2:3, 2 to 3
Step-by-step explanation:
9 and 6 are both factors of three, so you have to reduce. 3 goes into 9 tree times, and 3 goes into 6 twice. Since it is circles to squares, the 2 comes first then 3.
Hope this helps!
If y = 9 inches, z = 14 inches, h = 5 inches, and w = 4 inches, what is the area of the object?
Answer:
126
Step-by-step explanation:
Suppose there is this little town with a finite number of people: (1) No two inhabitants have exactly the same number of hairs. (2) No inhabitant has exactly 743 hairs or no hairs at all. (3) There are more inhabitants than there are hairs on the head of any inhabitant. So, what is the highest possible number of inhabitants in that little town?
The highest possible number of inhabitants in that little town are 743.
What are inhabitant?A person or animal that lives in a place is called as the inhabitant.
Suppose there is this little town with a finite number of people: (1) No two inhabitants have exactly the same number of hairs. (2) No inhabitant has exactly 743 hairs or no hairs at all. (3) There are more inhabitants than there are hairs on the head of any inhabitant.
Let say there are 519 people in the town. and make them stand in a line with increasing number of hairs on their heads. This way, there will be a person on the last, who has no hair.
There are more number of people than the hairs. From bald to 742 hairs, 743 is the limit.
Thus, the highest possible number of inhabitants in that little town are 743.
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Find the sum of the first n terms
using the formula:
a(1-rn)
1-r
85 +85(.9) +85(.9)² + ...
. (5 terms)
The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.
What is the sum of terms of a geometric sequence?Let's suppose its initial term is a , multiplication factor is r and let it has total n terms,
then, its sum is given as:
[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
Given geometric sequence;
85 +85(.9) +85(.9)² + ...
a = 85
r = 0.9
its sum is given as:
[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]
[tex]S_n = \dfrac{85(0.9^5-1)}{0.9-1}\\\\S_n = \dfrac{85(0.5904-1)}{-0.1}\\\\\\S_n = \dfrac{85(-0.4095)}{-0.1}\\\\S_n = 348.08[/tex]
Thus,
The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.
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What is the area of the parallelogram?
Answer:
Area = 120 in²Step-by-step explanation:
follow the formula in the picture
Area = b * h
Area = 15 * 8
Area = 120 in²
Which equation can be used to solve for c?
Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 35 degrees. The length of C B is 5 inches, the length of A C is b, and the length of B A is c.
The equation which is used to find the value of c will be c = 5/Cos 35
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
We are given the following
m<ACB = 90degrees
m<ABC = 35degrees
The side opposite to m<ABC is AC
BA = hypotenuse
CB = adjacent = 5inches
Required
The equation to solve BA which is c
Using the Pythagoras theorem;
Cos Ф = Adjacent/Hypotenuse
Cos m<ABC = CB/BA
Cos m<ABC = 5/c
c = 5/cosm<ABC
c = 5/Cos 35
Hence the equation that can be used to solve for c is c = 5/Cos 35
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A triangle has side lengths 9 cm, 12 cm, and 16 cm.
Answer:
https://www.calculator.net/triangle-calculator.html?vc=&vx=16&vy=9&va=&vz=12&vb=&angleunits=d&x=54&y=24
Step-by-step explanation:
I went to this website
https://www.calculator.net/triangle-calculator.html
put in what I knew of the triangle and got all the information you may need.
Please help me with this question!
Step-by-step explanation:
Yes it is .
7x+9 _> 7•3
7x+9_> 21
7x_> 21 - 9
7x _> 12 divide both side with 7 to find x
then x _> 1.4
which mean x can be any number that is greater than or equal to 1.4 so 2 is correct .
Hi Student!
Looking at the problem statement, we can see that they are asking for us to determine whether x = 2 is a solution of the expression provided or not. The first step that we take is plugging in all the values which means that we take 2 and plug it into all of the x's that we have in the expression that we provided. Then we simplify that expression down on both sides. If the expression in the end results to true then x = 2 is a solution of the expression but if it defaults to false than x = 2 isn't a solution.
Plug in the values
[tex]7x + 9 \ge 7 * 3[/tex][tex]7(2) + 9 \ge 7 * 3[/tex]Simplify both sides
[tex]14 + 9 \ge 7 * 3[/tex][tex]23 \ge 21[/tex]The final expression states that 23 is greater than or equal to 21 which is true. Therefore, x = 2 is a solution of the expression that was provided in the problem statement.
Maria has 14 fewer apps on her phone than Orlando. If the total number of apps on both phones is 34, how many apps are on each phone?
Setting up and equation from the word problem, Orlando has 24 apps on his phone, and Maria has 10 apps on her phone.
How many apps are on each phone?Let's assume that Orlando has x number of apps on his phone. According to the given information, Maria has 14 fewer apps, so the number of apps on Maria's phone would be (x - 14).
The total number of apps on both phones is 34, so we can set up the equation:
x + (x - 14) = 34
Simplifying the equation:
2x - 14 = 34
Adding 14 to both sides:
2x = 48
Dividing both sides by 2:
x = 24
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3/x=2
How do you solve this without get a loop
Answer:
x= 3/2
Step-by-step explanation:
3/x=2
Multiply x both sides so,
3 =2x
Divide 2 to get the value of x so,
x= 3/2
pls help me with this problem :)
The areas of two similar triangles are 9 cm² and 49 cm². One of the sides of the first
triangle is 2 cm. What is the length of the corresponding side of the other triangle?
Answer:
I believe it should be rounded to 11, if not decimal would be 10.88
Step-by-step explanation:
49 divided by 9 equals 5.44 which is the amount times the 49cm^2 triangle is compared to the 9cm^2. So then the side is 2cm, multiply by the amount times bigger the other triangle is which would be 10.88. Hopefully I'm not wrong:)
Answer:
The answer is 4 and 2/3 cm²
Step-by-step explanation:
Take the square root of 49 and 9 and you'll get 7 and 3 since the scale factor is the large area over the small area.
The large area would be √49 cm²
The small area would be √9 cm²
7 x cm
------ = ----------, cross multiply
3 2 cm
7 × 2 = 3 × x
14 = 3x
x = 14/3, x = 4 and 2/3
1) Which is the first INCORRECT step in the
solution of the inequality shown below?
2(x+1)-(3-x) ≤ -4:
Step 1: 2x + 2-3+x≤-4;
Step 2: 3x - 1≤-4;
Step 3: 3x
-3;
Step 4: x>-1
(a) Step 1
(b) Step 2
(c) Step 3
(d) Step 4
Step-by-step explanation:
we are missing the inequality sign in step 3.
step 1 and step 2 are correct.
step 4 is wrong.
the correct step 3 looks like
3x <= -3
if your original step 3 says the same, then the first wrong step is step 4.
if your original step 3 does not say the same, then the first wrong step is step 3.
Simplify the following expression:
(3i + 4) - i + 4(6 + 2i)
A. 27 + 11i
B. 28 + 10i
C. 14 + 8i
D. 14 + 4i
The simplified form of this expression is 28 + 10i
This question is an expression of imaginary numbersImaginary numbers are numbers that are composed of a real number and an imaginary part.
< To resolve this issue, let's remove the first parenthesis:
(3i + 4) - i + 4(6 + 2i)
3i + 4 - i + 4(6 + 2i)
< In the second parentheses, let's apply the distributive property:
3i + 4 - i + 4(6 + 2i)
3i + 4 - i + 4 . 6 + 4 . 2i
3i + 4 - i + 24 + 8i
< Finally, let's just sum the like terms, along with the real terms:
3i + 4 - i + 24 + 8i
10i + 4 + 24
10i + 28
28 + 10i
Therefore, the correct value will be 28 + 10i
X=
08
09
0 10
4
10 X
Answer:
8
Step-by-step explanation:
Intersecting Chords Formula:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
5*x = 4*10
5x = 40
Divide by 5
5x/5 = 40/5
x = 8
Consider the halfpipe with a diameter of 7 cm and a height of 20 cm.
Find its volume, rounding to 2 decimal places.
Answer: 384.85
Step-by-step explanation
Can anyone please help me solve this and show how you did it? Thank you so much!
-3(-2w-6)<=10-2(-2w-4.5)
(WILL GIVE OUT 50 POINTS!!)
Blake has a points card for a movie theater. He receives 35 rewards points just for signing up. He earns 11.5 points for each visit to the movie theater. He needs 196 points for a free movie ticket. How many visits must Blake make to earn a free movie ticket?
Answer:
14 visits
Step-by-step explanation:
The total number of points on Blake's card will be the sum of the initial number and the number earned for visits. The number earned for visits is the product of the number of visits and the the points earned per visit.
__
setupThe number of points on Blake's card will be ...
p = 35 +11.5x . . . . . when Blake makes x visits to the theater
We want to find x when p=196, so we have ...
196 = 35 +11.5x
solutionThis 2-step equation is solved in the usual way.
161 = 11.5x . . . . step 1, isolate the variable term by subtracting the constant
14 = x . . . . . . . . step 2, divide by the variable coefficient
Blake must make 14 visits to earn a free movie ticket.
Answer:
A
tyler has a points card for a movie theater.
he receives 75 rewards points just for signing up.
• he earns 10.5 points for each visit to the movie theater.
he needs 180 points for a free movie ticket.
.
a
how many visits must tyler make to earn a free movie ticket?
Step-by-step explanation: