Answer: 1) 1/3,654 2) 3/406 3) 72,684,900,288,000 4) 120
Step-by-step explanation:
1) First and Second and Third
[tex]\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}\times \dfrac{1\ remaining\ prize}{27\ remaining\ people}=\dfrac{6}{21,924}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad =\large\boxed{\dfrac{1}{3,654}}[/tex]
2) First and Second
[tex]\dfrac{3\ total\ prizes}{29\ total\ people}\times \dfrac{2\ remaining\ prizes}{28\ remaining\ people}=\dfrac{6}{812}=\large\boxed{\dfrac{13}{406}}[/tex]
[tex]3)\quad \dfrac{29!}{(29-10)!}=\large\boxed{72,684,900,288,000}[/tex]
[tex]4)\quad _{10}C_3=\dfrac{10!}{3!(10-3)!}=\large\boxed{120}[/tex]
Which of the following sets are subspaces of R3 ?
A. {(x,y,z)|3x+8y-5z=2}
B. {(x,y,z)|-4x-9y+7z=0}
C. {(x,y,z)|x
D. {(-4,y,z)|y,z arbitrary numbers}
E. {(x,0,0)|x arbitrary number}
F. {(-2x,-3x,-8x)|x arbitrary number}
Answer:
The following are the solution to the given points:
Step-by-step explanation:
for point A:
[tex]\to A={(x,y,z)|3x+8y-5z=2} \\\\\to for(x_1, y_1, z_1),(x_2, y_2, z_2) \varepsilon A\\\\ a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)[/tex]
[tex]=3(aX_l +bX_2) + 8(ay_1 + by_2) — 5(az_1+bz_2)\\\\=a(3X_l+8y_1- 5z_1)+b (3X_2+8y_2—5z_2)\\\\=2(a+b)[/tex]
The set A is not part of the subspace [tex]R^3[/tex]
for point B:
[tex]\to B={(x,y,z)|-4x-9y+7z=0}\\\\\to for(x_1,y_1,z_1),(x_2, y_2, z_2) \varepsilon B \\\\\to a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)[/tex]
[tex]=-4(aX_l +bX_2) -9(ay_1 + by_2) +7(az_1+bz_2)\\\\=a(-4X_l-9y_1+7z_1)+b (-4X_2-9y_2+7z_2)\\\\=0[/tex]
[tex]\to a(x_1,y_1,z_1)+b(x_2, y_2, z_2) \varepsilon B[/tex]
The set B is part of the subspace [tex]R^3[/tex]
for point C: [tex]\to C={(x,y,z)|x<y<z}[/tex]
In this, the scalar multiplication can't behold
[tex]\to for (-2,-1,2) \varepsilon C[/tex]
[tex]\to -1(-2,-1,2)= (2,1,-1)[/tex] ∉ C
this inequality is not hold
The set C is not a part of the subspace [tex]R^3[/tex]
for point D:
[tex]\to D={(-4,y,z)|\ y,\ z \ arbitrary \ numbers)[/tex]
The scalar multiplication s is not to hold
[tex]\to for (-4, 1,2)\varepsilon D\\\\\to -1(-4,1,2) = (4,-1,-2)[/tex] ∉ D
this is an inequality, which is not hold
The set D is not part of the subspace [tex]R^3[/tex]
For point E:
[tex]\to E= {(x,0,0)}|x \ is \ arbitrary) \\\\\to for (x_1,0 ,0) ,(x_{2},0 ,0) \varepsilon E \\\\\to a(x_1,0,0) +b(x_{2},0,0)= (ax_1+bx_2,0,0)\\[/tex]
The [tex]x_1, x_2[/tex] is the arbitrary, in which [tex]ax_1+bx_2[/tex]is arbitrary
[tex]\to a(x_1,0,0)+b(x_2,0,0) \varepsilon E[/tex]
The set E is the part of the subspace [tex]R^3[/tex]
For point F:
[tex]\to F= {(-2x,-3x,-8x)}|x \ is \ arbitrary) \\\\\to for (-2x_1,-3x_1,-8x_1),(-2x_2,-3x_2,-8x_2)\varepsilon F \\\\\to a(-2x_1,-3x_1,-8x_1) +b(-2x_1,-3x_1,-8x_1)= (-2(ax_1+bx_2),-3(ax_1+bx_2),-8(ax_1+bx_2))[/tex]
The [tex]x_1, x_2[/tex] arbitrary so, they have [tex]ax_1+bx_2[/tex] as the arbitrary [tex]\to a(-2x_1,-3x_1,-8x_1)+b(-2x_2,-3x_2,-8x_2) \varepsilon F[/tex]
The set F is the subspace of [tex]R^3[/tex]
Forty seven hundredths in standard form
Answer is .47
Fourty seven hundredths in standard form is .47,
Stacy put 2/5 of her monthly earnings into a savings jar. Then she decided to take 1/4 of the money in the jar to put aside for vacation. If Stacey earned $550 this month,how much money did she set aside for vacation?
Answer:
55
Step-by-step explanation:
First you need to know how much is 2/5 of 550 since that is how much she put in the jar. 2/5 * 550 = 220 and then you need to find a 1/4 of that since that is how much she takes from th jar for vecation. 1/4 * 220 = 55 which is the awnser
Solve this linear system 28x + 44y = 964.40 21x + 33y = 723.30
28x + 44y = 964.40
21x + 33y = 723.30
Let's multiply the first equation by 4 and the second by -4
84x + 176y = 3857.6
-84x - 132y = -2893.2
Add the equations together.
0 + 44y = 964.4
Simplify
44y = 964.4
Divide both sides by 44
y = 964.4/44
Since we have the value of y, let's plug 964.4/44 into y for the first equation.
28x + 44(964.4/44) = 964.40
Simplify the left side
28x + 964.4 = 964.4
Subtract 964.4 from both sides
28x = 0
Divide both sides by 0
x = 0
In conclusion,
y = 964.4/44
x = 0
(True or False) The set of ordered pairs {(6,4),(2,-5),(-2,4),(6,-4)} is a function
Answer:
False
Step-by-step explanation:
The same function input (the first number in the pair) cannot have two different outputs (the second number in the pair).
(6, 4) 4 is one output.
(6, -4) -4 is another output.
Solve all these to be marked the brainlest
302 + 299 + 296 + 293 ... + 2 = _____ what is the sequence using Gauss’s Law
By Gauss's Law the approach of solving sum of a sequence of n terms in arithmetic progression is :
[tex]S_n=\dfrac{n}{2}(a_1+a_n)[/tex] ......1 )
Here, [tex]a_n = 302[/tex] , [tex]a_1=2[/tex] .
We know :
[tex]a_n=a_1+(n-1)d\\\\302=2+3(n-1)\\\\n = 101[/tex]
Putting, all values in equation 1) we get :
[tex]S_n=\dfrac{101}{2}\times (2+302)\\\\S_n=101\times 152\\\\S_n=15352[/tex]
Therefore, the sum of sequence using Gauss's Law is 15352.
Hence, this is the required solution.
A student rolls a fair die 10 times and obtained an even number 10 times. The student believes that the next roll will
be an odd number because "odds are due."
Is this correct?
Yes, if the die is fair, then an odd number is due because the probability will approach 50%.
No, an even number is due based on past experience.
Yes, it is certain that an odd number will be rolled next because it is impossible to roll an even number 11 times in
a row.
No, an even or odd outcome is equally likely for each roll, regardless of what has happened in the past.
Answer:
N0, an even or odd outcome is equally likely for each roll regardless of what happened in the past
Step-by-step explanation:
Answer:
D. No, an even or odd outcome is equally likely for each roll, regardless of what has happened in the past.
A government agency has 6000 employees. As an alternative to the traditional five day work week, employees were asked whether they preferred a four day work week (10 hours per day) or flexible hours. The employee data provides the results by age category. What is the probability that a randomly selected employee at this government agency prefers a four day work week or is under 30
The table showing the data is missing, so i have attached it.
Answer:
0.8
Step-by-step explanation:
We want to find the probability that a randomly selected employee at this government agency prefers a four day work week or is under 30.
Now, we are told that the government agency has 6000 employees. Also, from the attached table, we see that the number of people who prefer a 4 day work week are a total of:
600 + 1200 + 2100 = 3900
Thus, probability of people who prefer a 4 day work week = 3900/6000 = 39/60
Also, we see that total number of people aged under 30 = 600 + 300 = 900
Thus, probability of people aged under 30 is;
900/6000 = 3/20
Thus;
probability that a randomly selected employee at this government agency prefers a four day work week or is under 30 = 39/60 + 3/20 = 48/60 = 4/5 = 0.8
Joyce saved $130 on an item that was 35 % off. What was the original price?
Answer:
x=$200
Step-by-step explanation:
cross-multiply
130=0.65x
Help me and show me how to do it
.....................
The product of 79 and -0.22 is a positive number. True Or False
Answer:
False
Step-by-step explanation:
We know that this statement is false because a positive number times a negative number will produce a negative answer.
Answer:
False
Step-by-step explanation:
You will get a positive number only by multiplying two positive numbers or two negative numbers.
100 POINTS HELP / Which is correct about the graph’s slope?
Its slope is positive.
Its slope is negative.
Its slope is zero.
It has no slope.
Answer:
slope is zero
Step-by-step explanation:
it is a horizontal line which means the slope all points that lie on the line have a -coordinate
[tex]\huge\boxed{No\;slope}[/tex]
There is no rise over run therefore, there is no slope.
You have to have rise over run to be able to have a slope.
in order to be invited to tutoring or extension activities a student's performance must be at least 20 points higher or lower than an average score is 105 which inequality represents P the scores for students who are eligible for tutoring or extension activities
Answer:
i think its p ≤ 85 or p ≥ 125
Step-by-step explanation:
p can be 85 and higher but can be passed 125 but it can be 125 which makes the equality signs have the line under them meaning less than or equal to, and could also mean greater than or equal to.
The inequality that represents P the scores for students who are eligible for tutoring or extension activities is p ≤ 85 or p ≥ 125.
What is an Average?Average is the mean of the data set obtained by summing all the values of the data set and then dividing it by the number of data in the set.
The average score is 105
The score required for tutoring is at least 20 points higher than average
The score required for extension activities is at least 20 points lower than average
P is the scores for students who are eligible for tutoring or extension activities
Then p ≤ 105 -20 = p ≤ 85
p ≥ 105+20 = p ≥125
p ≤ 85 or p ≥ 125
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How many days equal 7344 minutes?
The answer is 5.1 days
60*24= 1440 minutes in one day
7344/1440= 5.093 or 5.1 rounded to the nearest tenth
Elizabeth is a manager at a nursery and is in charge of displaying potted trees in a row Elizabeth has 150 citrus trees and 180 Palm trees she wants to make rows of trees so that each row has the same number of trees and each tree is in the same row. if the citrus trees and the palm trees must not be mixed in the rows what is the largest number of trees she can have in a row
Answer: the greatest number of trees that ElizaBeth can have in a row is 30
Step-by-step explanation:
given data:
citrus trees = 150
palm trees = 180
As we have to find the greatest number of trees that Elizabeth can have in a row, we will find the GCF or greatest common factor.
150 = 2 x 3 x 5 x 5
180 = 2 x 2 x 3 x 3 x 5
Greatest common factor is = 2 x 3 x 5 = 30
Therefore, the largest number of trees that ElizaBeth can have in a row is 30.
someone please help me with #63! WILL MARK BRAINLIEST
Answer:
cos60=b/h
1/2= b/3
b= 3/2=1.5
again
sin60=p/h
[tex]\sqrt3[/tex]/2= p/3
p =3[tex]\sqrt3[/tex]/2
Step-by-step explanation:
Answer:
1.5 in. and [tex]\frac{3\sqrt{3} }{2}[/tex]in.
Step-by-step explanation:
easier method:
angle opp. to 30 degrees is 1/2 of hypotonuse:
3/2=1.5 inches
angle opp. to 60 degrees is [tex]\sqrt{3}[/tex] of 30 degree angle:
3/2*[tex]\sqrt{3}[/tex]=3[tex]\sqrt{3}[/tex]/2
HELP ME PLEASE IM CRYING SO BAD
Answer:
V'= ( 5,2 )
U'= ( 8,2 )
T'= ( 7,12 )
S'= ( 3,12 )
Answers:
S ' (3, 7)T ' (7, 7)U ' (8,2)V ' (5,2)Check out the diagram below
===================================================
Explanation:
When reflecting over horizontal lines like this, the x coordinate stays the same as the original point. Only the y coordinate changes.
To find what the y coordinate changes to, we need to measure the vertical distance from the point to the line. Point S has a y coordinate of y = -5 and the vertical distance to the line of reflection (y = 1) is |-5-1| = |-6| = 6 units. So we move 6 units up to go from point S to the line of reflection. We must move another 6 units to get to the location for S' where its reflected point would end up, which has y coordinate y = 7.
The same applies for the other points as well. Point T also goes up 6 units to get to y = 1, then it moves another 6 units to get to y = 7
Points V and U only move up 1 unit to get to the green dotted line of reflection. So they'll move only one additional unit to have their reflected points have y coordinates of y = 2.
The diagram hopefully visually summarizes everything discussed so far. The mirroring line cuts the distance from S to S' in half, same for T to T', and so on.
What is the value of n?
Answer: 3 cm
Step-by-step explanation:
Set up a proportion to find the value of n. 4/8 = n/6Cross multiply. 8x = 24Divide 8 on both sides. x = 3please help! BRAINLIEST to best answer!
Answer:
I'm not sure if I'm right but you should try X = the x value of the vertex.
put in order smallest to largest
cups court pint gallons ounces quarts
Answer:
ounces, cups, pints, quarts, and gallons
Step-by-step explanation:
Solve for t.
-3t + 3 – 7t = -90 – 7
Answer:
t = 10Step-by-step explanation:
-3t + 3 - 7t = -90 - 7
Simplify both sides of the equation
That's
- 10t + 3 = - 97
Using the subtraction property subtract 3 from both sides of the equation
We have
- 10t + 3 - 3 = -97 - 3
- 10t = - 100
Divide both sides by - 10
[tex] \frac{ - 10t}{ - 10} = \frac{ - 100}{ - 10} [/tex]
We have the final answer as
t = 10Hope this helps you
Answer:
Step-by-step explanation:
-3t + 3 - 7t = -90 - 7
-10t + 3 = -97
-10t = -100
t = 10
Use the graph to estimate the x- and y-intercepts.
Answer:
x- intercept is 6 y- intercept is -18
Step-by-step explanation:
Just use the graph, this graph is hard to get the answer but you just have to estimate.
Find the difference. (3 • 1,000) - (2• 100)
The value of ( 3 x 1,000 ) - ( 2 x 100 ) is 2,800.
Here,
Given that, ( 3 x 1,000 ) - ( 2 x 100 )
What is subtraction of two number?
Subtraction is the operation of taking the difference of two numbers.
Now,
Firstly the value of 3 x 1000 = 3000
And, 2 x 100 = 200
⇒ 3000 - 200 = 2800
Hence, The value of ( 3 x 1,000 ) - ( 2 x 100 ) is 2,800.
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You have 2.5 pounds of egg whites
You need 37 ounces to make one serving of consommé
How many servings can you make?
round 355,668 to the nearest hundred thousands
Answer:
400,000
Step-by-step explanation:
Describe what is means for slope to be a ratio
Answer:The slope of a line is the ratio of the 'change' in y to the 'change' in x (ratio of vertical change to horizontal change) often referred to as rise compared to run. .
Step-by-step explanation: heart it up
A basketball player shoots free throws and makes them with probability 1/7. What is the probability of the event the player will miss three in a row?
Answer:
216/343 or 0.6297 (4dp)
Step-by-step explanation:
Anytime the probability of an event occurs more than once in a particular order (one time after another in the same instance), then the probability is multiplied together. If the probability of him making the shot is 1/7, then the probability of him missing it is 6/7. This is because this is the only other possible outcomes and all outcome probabilities must add to 1 (1-1/7 - 6/7).
So, if he misses it three times in a row then the probability is:
6/7 (probability miss this first time) x 6/7 (probability miss second time) x 6/7 (probability miss 3rd time).
6/7 x 6/7 x 6/7 = 216/343
or 0.6297 (4dp)
Hope this helped!
find the solution to K+1=3k-1
Answer: k=1
Step-by-step explanation: Isolate the variable by dividing each side by factors that do not contain the variable.
I hope this helps you out! :)
Step-by-step explanation:
the answer would be k=1