Answer:
The answer is "840".
Step-by-step explanation:
Following are the number of ways in which selecting a team A by 9 children:
[tex]= ^{9_{C_{3}}\\\\\\[/tex]
[tex]=\frac{9!}{3! \times 6!} \\\\=\frac{9\times 8\times 7\times 6!}{3 \times 2\times 1\times 6!}\\\\=\frac{9\times 8\times 7}{3 \times 2\times 1}\\\\=\frac{3\times 4\times 7}{1}\\\\=\frac{84}{1}\\\\=84[/tex]
Following are the number of ways in which selecting a team B by remaining 6 children:
[tex]= ^{6}_{C_{3}}[/tex]
[tex]= \frac{6!}{(3! \times 3!)}\\\\= \frac{6!}{(3\times 2\times 1 \times 3!)}\\\\= \frac{6\times 5 \times 4 \times 3!}{(3\times 2\times 1 \times 3!)}\\\\= \frac{ 5 \times 4 \times 3!}{3!}\\\\= 5 \times 4 \\\\=20[/tex]
Following are the number of ways in which selecting a team C by remaining 3 children:
[tex]= ^{3}_{C_{3}}\\\\=\frac{3!}{3!}\\\\= 1[/tex]
Following are the number of ways in which making 3 teams by 9 children:
[tex]= \frac{(84 \times 20 \times 1)}{3!}\\\\= \frac{(84 \times 20 )}{6}\\\\= 14 \times 20\\\\= 280\\\\[/tex]
(Note: we've split by 3! Because it also is necessary to implement three teams between themselves)
Now 3 leagues have to be played. One is going to be run by each team.
That is the way it is
Different possible divisions
[tex]= 280 \times 3!\\\\= 280 \times (3 \times 2 \times 1)\\\\= 840[/tex]
A tax form asks people to identify their age, annual income, number of dependents, and social security number. For each of these four variables, identify the scale of measurement that probably is used and identify whether the variable is continuous or discrete.
Variable Nominal Ordinal Interval Ratio
Social security number
Annual income
Number of dependents
Variable Discrete Continuous
Social security number
Annual income
Number of dependents
Answer:
Types of variables:
Continuous variable include: income
Discrete variable include: number of dependents
Scale of measurement:
Nominal data include: Social security number
There is no ordinal data included
There is no interval data included
Ratio data include: Annual income,
Number of dependents.
Explanation:
Continuous variables are variables that are obtained by just counting, example: counting the number of times someone eats in a day.
Discrete variables are simply variables that are measured and are usually more precise than continuous variables, example: time, weight, length etc.
Nominal data are data types that are in the form of labels or names and do not have any particular order, example :social security number basically identifies a person and is not ranked or ordered in any way.
Ordinal data are data types that also in the form of names but with ranking and order.
Interval data are data types that rank and order data but with continuous measurement that may take on negative values, example measure of temperature.
Ratio data is same as interval data but does not take negative values, example we can not say that someone is -6 years old.
Which choice is equivalent to(√6)( √8). How do you solve
A. 4√6
B. 4√3
C. 16√3
D. 3√16
Answer:
B
Step-by-step explanation:
(6)^1/2 × (8)^1/2
6^1/2 × 2 (2)^1/2
4 (3)^1/2
the volume of a rectangular pyramid with a length of 7 feet, a width of 6 feet, and a height of 4.5 feet.
Answer:
Volume = 63 feet
Step-by-step explanation:
To find the volume of a cube or a rectangular prism, the formula is
(L x W x H)/3. In other words, it is the length of the prism, times the width of the prism, times the height of the prism, whole divided by three, since it has a "triangular shape."
Let's substitute in values for these letters, L, W, and H. You said the length was 7, the width was 6, and the height was 4.5. Therefore, it will result in
(7 x 6 x 4.5)/3. That results in 189/3, which is 63.
Hope this helped!!!
..................................................................
Answer:
Hello?
Step-by-step explanation:
x - 3y +3=0
a) The length of the perpendicular drawn from the point (a, 3) on the line
3x + 4y + 5 = 0 is 4. Find the value of a.
Answer:
We know that for a line:
y = a*x + b
where a is the slope and b is the y-intercept.
Any line with a slope equal to -(1/a) will be perpendicular to the one above.
So here we start with the line:
3x + 4y + 5 = 0
let's rewrite this as:
4y = -3x - 5
y = -(3/4)*x - (5/4)
So a line perpendicular to this one, has a slope equal to:
- (-4/3) = (4/3)
So the perpendicular line will be something like:
y = (4/3)*x + c
We know that this line passes through the point (a, 3)
this means that, when x = a, y must be equal to 3.
Replacing these in the above line equation, we get:
3 = (4/3)*a + c
c = 3 - (4/3)*a
Then the equation for our line is:
y = (4/3)*x + 3 - (4/3)*a
We can rewrite this as:
y = (4/3)*(x -a) + 3
now we need to find the point where this line ( y = -(3/4)*x - (5/4)) and the original line intersect.
We can find this by solving:
(4/3)*(x -a) + 3 = y = -(3/4)*x - (5/4)
(4/3)*(x -a) + 3 = -(3/4)*x - (5/4)
(4/3)*x - (3/4)*x = -(4/3)*a - 3 - (5/4)
(16/12)*x - (9/12)*x = -(4/3)*a - 12/4 - 5/4
(7/12)*x = -(4/13)*a - 17/4
x = (-(4/13)*a - 17/4)*(12/7) = - (48/91)*a - 51/7
And the y-value is given by inputin this in any of the two lines, for example with the first one we get:
y = -(3/4)*(- (48/91)*a - 51/7) - (5/4)
= (36/91)*a + (153/28) - 5/4
Then the intersection point is:
( - (48/91)*a - 51/7, (36/91)*a + (153/28) - 5/4)
And we want that the distance between this point, and our original point (3, a) to be equal to 4.
Remember that the distance between two points (a, b) and (c, d) is:
distance = √( (a - c)^2 + (b - d)^2)
So here, the distance between (a, 3) and ( - (48/91)*a - 51/7, (36/91)*a + (153/28) - 5/4) is 4
4 = √( (a + (48/91)*a + 51/7)^2 + (3 - (36/91)*a + (153/28) - 5/4 )^2)
If we square both sides, we get:
4^2 = 16 = (a + (48/91)*a + 51/7)^2 + (3 - (36/91)*a - (153/28) + 5/4 )^2)
Now we need to solve this for a.
16 = (a*(1 + 48/91) + 51/7)^2 + ( -(36/91)*a + 3 - 5/4 + (153/28) )^2
16 = ( a*(139/91) + 51/7)^2 + ( -(36/91)*a - (43/28) )^2
16 = a^2*(139/91)^2 + 2*a*(139/91)*51/7 + (51/7)^2 + a^2*(36/91)^2 + 2*(36/91)*a*(43/28) + (43/28)^2
16 = a^2*( (139/91)^2 + (36/91)^2) + a*( 2*(139/91)*51/7 + 2*(36/91)*(43/28)) + (51/7)^2 + (43/28)^2
At this point we can see that this is really messy, so let's start solving these fractions.
16 = (2.49)*a^2 + a*(23.47) + 55.44
0 = (2.49)*a^2 + a*(23.47) + 55.44 - 16
0 = (2.49)*a^2 + a*(23.47) + 39.44
Now we can use the Bhaskara's formula for quadratic equations, the two solutions will be:
[tex]a = \frac{-23.47 \pm \sqrt{23.47^2 - 4*2.49*39.4} }{2*2.49} \\\\a = \frac{-23.47 \pm 12.57 }{4.98}[/tex]
Then the two possible values of a are:
a = (-23.47 + 12.57)/4.98 = -2.19
a = (-23.47 - 12.57)/4.98 = -7.23
Graph: y = (x + 3)2 – 4
Which values are solutions of the quadratic equation
0 = (x + 3)2 – 4? Check all that apply.
y
X
-4
WIEC
6
0 -5
-4
.
0 -3
-1
-6
-4
-2
2
4
6
02
3
-2 -4
0,5
-6
Answer:
0.534375
45328
36763
-6
-78
The values of x and y that satisfy the graphs are:
(-1, 0), and (-5, 0).
What is a quadratic equation?A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
We can start by simplifying the quadratic equation:
y = (x + 3)² – 4
y = x² + 6x + 9 - 4
y = x² + 6x + 5
Now, we can use various methods to find values of x and y that satisfy this equation. Here are five possible values:
If we substitute x = -1, we get:
y = (-1)² + 6(-1) + 5
y = 0
So, one solution is (-1, 0).
If we substitute x = 0, we get:
y = 0² + 6(0) + 5
y = 5
So, another solution is (0, 5).
If we substitute x = -5, we get:
y = (-5)² + 6(-5) + 5
y = 0
So, another solution is (-5, 0).
To find rational solutions, we can factor in the quadratic expression:
y = x² + 6x + 5
y = (x + 1)(x + 5)
So, the solutions are x = -1 and x = -5. Substituting these values into the equation, we get:
For x = -1, y = (-1)² + 6(-1) + 5 = 0
For x = -5, y = (-5)² + 6(-5) + 5 = 0
So, the solutions are (-1, 0) and (-5, 0).
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Simplify the expression
Answer: …
Step-by-step explanation: you need an image
Answer:
what expression?
Step-by-step explanation:
Round 620 to the nearest ten! Hurry please and please don't answer if you know you wrong !
Answer:
620 to the nearest ten is already rounded correctly.
Step-by-step explanation:
620 to the nearest ten is 620.
The graph below has the same shape as the graph of G(x) = x, but it is
shifted three units to the right. Complete its equation. Enter exponents using
the caret (-); for example, enter x4 as x^4. Do not include "G(x) =" in your
answer.
G(x) =
Step-by-step explanation:
The graph of Fx), shown below in pink, has the same shape as the graph of G(x)-x, but it is shifted to the right two units. Complete its equation below Enter exponents using the caret (a), for example, enter x as x 4. Do not include Fx)-in your answer. .5 5 F(x) = Answer: 0
The equation of the graph is,
⇒ G (x) = (x - 3)⁴
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The graph of function G (x) is shown in image.
Here, The graph is 3 units left to function F (x) = x⁴.
Hence, The equation of the graph is,
⇒ G (x) = (x - 3)⁴
Thus, The equation of the graph is,
⇒ G (x) = (x - 3)⁴
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Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Answer:
her salary will increase by $ 145 for every week
Step-by-step explanation:
x=1st paycheck (integer).
weekly raise = $ 145.
After completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get
$ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
A charter school did a local beach cleanup. They collected a total of 55 pounds of plastic bottles and aluminum cans. The California refund value for plastic is $1.60 per pound and $1.28 per pound for aluminum. The school recycled a total of $77.60 worth of plastic and aluminum. How many pounds of each, plastic and aluminum, did the class collect?
Answer:
Plastic is 22.5 pounds and aluminum is 32.5 pounds.
Step-by-step explanation:
total junk = 55 pounds
Value of plastic = $ 1.60 per pound
Value of aluminum = $ 1.28 per pound
Total value= $ 77.60
Let the plastic is p and the aluminum is 55 - p.
Total cost
77.60 = 1.6 p + (55 - p) x 1.28
77.60 = 1.6 p + 70.4 - 1.28 p
7.2 = 0.32 p
p = 22.5 pounds
So, plastic is 22.5 pounds and aluminum is 32.5 pounds.
Convert the following to a simplified fraction. Show all your work.
Answer:
11/6
Step-by-step explanation:
Is 237405 divisible by 11 Correct Answer = Brainliest
Answer:
Yes.
Step-by-step explanation:
.
The time for a professor to grade a student’s homework in statistics is normally distributed with a mean of 13.3 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 17 minutes to grade?
Answer:
0.96784
Step-by-step explanation:
17-13.3/2
=1.85
p(x<1.85)
=0.96784
The probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.
Mean [tex]\mu[/tex]=13.3 minutes
Standard deviation[tex]\sigma[/tex]=2 minutes
What is a z-score?The value of the z-score tells you how many standard deviations you are away from the mean.
So, the z-score of the above data
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{17-13.3}{2}[/tex]
[tex]z=1.85[/tex]
From the standard normal table, the p-value corresponding to z=1.85
Or, p(x<1.85)=0.9678 or 96.78%
Hence, the probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.
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When you compute with decimals you should always check your answer is reasonable why
Answer:
Ang pangit mo
Kamuka mo Yong clown
Question 4*
4. Sam's goal is to exercise for 400 minutes each
week. This week, he reached 128% of his goal.
How many minutes did he exercise?
Answer: Get at least 150 minutes of moderate aerobic activity or 75 minutes of vigorous aerobic activity a week, or a combination of moderate and vigorous activity. The guidelines suggest that you spread out this exercise during the course of a week. Greater amounts of exercise will provide even greater health benefit.
Step-by-step explanation:
If Sam reached 128% of his goal to exercise each week, he would have exercised for 512 minutes.
How many minutes did Sam exercise this week?Given the parameters:
Sam's goal is to exercise for 400 minutes each week.
This week, he reached 128% of his goal.
The number of minutes =?
To determine how many minutes Sam exercised this week, we simply calculate 128% of his goal.
Number of minutes = 128% × Sam's goal of exercise
Number of minutes = 128% × 400 minutes
Note that: 128% = 128/100
Number of minutes = 128/100 × 400 minutes
Number of minutes = 128 × 4 minutes
Number of minutes = 512 minutes
Therefore, Sam exercised for 512 minutes this week.
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would someone mind looking over my answers to geometry!!
Answer:
Question 1: x = 6
Question 2: Correct!
Question 3: x = 11
Question 4: Correct!
Step-by-step explanation:
Question 1:
Angle 22x - 2 DOESN'T equal 50 degrees. Only Alternate Interior Angles will equal each other. These two angles are Same Side Interior Angles, meaning if you added them together, they would equal 180 degrees.
Knowing that adding 22x - 2 and 50 will equals 180 degrees, here's how we solve for x:
First, subtract 50 from 180 to find what angle 22x - 2 will equal:
180 - 50 = 130
130 = 22x - 2
Now use basic algebra to solve for x:
130 = 22x - 2
(add 2 to both sides)
132 = 22x
(divide both sides by 22)
x = 6
Question 3:
Angle 5x + 15 DOESN'T equal 9x + 11. They make up a line, which is 180 degrees, so they are supplementary angles.
With that in mind, to solve for x, add the two equations and set it equal to 180:
5x + 15 + (9x + 11) = 180
Now use basic algebra to solve for x:
5x + 15 + 9x + 11 = 180
(add like terms)
14x + 26 = 180
(subtract 26 from both sides)
14x = 154
(divide 14 from both sides)
x = 11
Hope it helps (●'◡'●)
help me plz----------------------------
9514 1404 393
Answer:
A. 5 should have been subtracted in step 4
Step-by-step explanation:
No question is stated, so there is no "answer."
__
If we assume the question is, "What error did Keith make?" then choice A properly describes it.
Step 4 should look like ...
x -5 = 7y . . . . . . . 5 should be subtracted from both sides
and the final result should be ...
g(x) = (x -5)/7
Which of the following situations WOULD NOT represent a binomial application? A. Choosing a card randomly from a standard deck and noting its color (remember color has only two outcomes black or red) B. Choosing a card randomly from a standard deck and noting whether its a face card C. Choosing a card randomly from a standard deck and noting its suit D. Choosing a card randomly from a standard deck and noting whether or not it's an ace
Answer:
Choosing a card randomly and noting its suit
Step-by-step explanation:
Choosing a card randomly and noting its suit
This is because binomial distributions only work for bernoulli trials (a trail in which there are only two outcomes)
What is the value of x?
2
3
6
7
Geometry B - 5.0 - Extended – 2
Answer:
I think 6.............,..........
if f(x)=-5^x-4 and g(x)=-3x-2,find (f+g) (x)
Answer: (f-g)(x) = - 5^x + 3x - 2
Step-by-step explanation:
if f(x) = -5^x - 4 and g(x)= - 3x - 2,find (f-g)(x)
(f-g)(x) = -5^x - 4 - (-3x - 2)
(f-g)(x) = -5^x - 4 + 3x + 2
(f-g)(x) = - 5^x + 3x - 2
A large container holds 4 gallons of chocolate milk that has to be poured into bottles. Each bottle holds 2 pints.
If the ratio of gallons to pints is 1: 8,
bottles are required to hold the 4 gallons of milk.
Answer:
64 Bottles
Step-by-step explanation:
that is the procedure above
Approximate 5.7255 to the nearest thousand
round 5.7255 to thousands place
place after thousands place (5) rounds up the 5 before it
therefore 5.726 ur ans
MARK above ANS as branliest
Which pair of points have equal x-coordinates?
Answer:
A. Q and R
Step-by-step explanation:
The x-axis is the horizontal line. The y-axis is the vertical line.
On the x-axis, go to the left, all the way to -5.
Look at the line that goes through -5 vertically. You will see that that line intersects with both Q and R.
This means that Q and R have equal x-coordinates, -5.
They're x and y coordinates would be
Q- (-5, 6)
R- (-5, -7)
I hope this helps!
Answer: Q and R
Step-by-step explanation:
See since in the photo the Q coordinate(Q) is directly above the R coordinate(R), that can only mean that they have the same X coordinate(X) or else it wouldn't be possible for Q to be right above R. The reason Q is right above R is because their Y coordinates(Y) are different, not because of X.
I hope this helps!
1,620 to the nearest ten ? Please don't answer if you know your wrong !
Answer:
I will say 2,000 yes so that is what I am putting
A senior class of 420 students will rent buses and vans for a class trip. Each bus can transport 50 students and 3 chaperones and costs $1200 to rent. Each van can transport 10 students and 1 chaperone and costs $100 to rent. There are 36 chaperones available (so they can't all go in vans). How many vehicles of each type should be rented in order to minimize the cost
Answer:
37 buses and 1 van.
Step-by-step explanation:
The cost to rent a van is $1200 for 50 students and 3 chaperones, while a bus for 10 students and a chaperone is $100 .
The cost of renting buses for 50 students is $500
What we do is rent 37 buses and 1 van
37 buses will take in 370 students with empty 2 spaces in 2 buses for chaperones since the chaperones are 36.
Then rent 1 van to take in 50 students and 1 chaperone.
The total cost here will be
$3700 + $1200 = $ 4900
This will help to safe cost.
Which of the following proportions is true?
10/40 = 8/36
8/18 = 6/16
9/15 = 44/50
12/18 = 16/24
Answer:
D. 12/18 = 16/24
Step-by-step explanation:
The method we must go about to solve this is finding the constant. For A, we can solve it by doing 10 divided by 8 (which is 1.25) and then 40 divided by 1.25 to see if it is 36. Alternatively, we can do 10 divided by 8 and then 40 divided by 36 to see if the constant is the same. It's up to you!
My answers:
A. No (constant varies)
B. No (constant varies)
C. No (constant varies)
D. Yes! Constant is 0.75
How to solve for D:
12/16 = 0.75
18/0.75 = 24 OR 18/24 = 0.75
I hope this helps! Please don't hesitate to reach out with more questions!
Hello!
10/40 = 8/36 ?
10 × 36 = 40 × 8
360 = 40 × 8
360 ≠ 320 => 10/40 ≠ 8/36
8/18 = 6/16 ?
8 × 16 = 18 × 6
128 = 18 × 6
128 ≠ 108 => 8/18 ≠ 6/16
9/15 = 44/50 ?
9 × 50 = 15 × 44
450 = 15 × 44
450 ≠ 660 => 9/15 ≠ 44/50
12/18 = 16/24 ?
12 × 24 = 18 × 16
288 = 18 × 16
288 = 288 => 12/18 = 16/24
Good luck! :)
evaluate the expression when b=3
y = -7
4b-y
Answer:
5
Step-by-step explanation:
Given :
b = 3 y = -7To Find :
Value of 4b - y .Solution:
Put on the respective values ,
⇒ 4b - y = 4 × 3 - 7
⇒ 4b - y = 12 - 7
⇒ 4b - y = 5
Hence the required answer is 5 .
Answer: 5
Step-by-step explanation:
We can plug in the numbers for variables. So, our new equation would becomes 4x3-7. We first evaluate 4x3=12. Then, 12-7=5. Hence, your answer is 5.
You have some money to invest in one of two accounts. The first account pays
5% simple interest, and the second pays 4% compound interest. How would
you decide which account to use? Discuss your answer.
Answer:
compound interest
Step-by-step explanation:
compound interest yields higher profit than simple interest
Answer:
the simple interest function will be greater in the beginning, but the
compound interest equation will overtake the simple after a while.
it appears that the 4% compound equation will overtake the simple at about 10 years
Step-by-step explanation:
[tex]1 + .05t = 1(1.04)^t[/tex]
-moves "The string of a kite is perfectly taut" and always makes an angle of 35 degrees above horizontal. (a) If the kite flyer has let out 500 feet of string, how high is the kite? (b) If the string is let out at a rate of 10 feet per second, how fast is the kite's height increasing?
Answer:
a) [tex]h=286.8ft[/tex]
b) [tex]\frac{dh}{dt}=5.7ft/s[/tex]
Step-by-step explanation:
From the question we are told that:
Angle [tex]\theta=35[/tex]
a)
Slant height [tex]h_s=500ft[/tex]
Generally the trigonometric equation for Height is mathematically given by
[tex]h=h_ssin\theta[/tex]
[tex]h=500sin35[/tex]
[tex]h=286.8ft[/tex]
b)
Rate of release
[tex]\frac{dl}{dt}=10ft/sec[/tex]
Generally the trigonometric equation for Height is mathematically given by
[tex]h=lsin35[/tex]
Differentiate
[tex]\frac{dh}{dt}=\frac{dl}{dt}sin35[/tex]
[tex]\frac{dh}{dt}=10sin35[/tex]
[tex]\frac{dh}{dt}=5.7ft/s[/tex]
