Answers
============================================================
Explanations:
Problem 10
The order of the toppings doesn't matter. All that matter is the group itself. We'll use the combination formula nCr = (n!)/(r!*(n-r)!) where n = 12 and r = 3 in this case.
So,
nCr = (n!)/(r!*(n-r)!)
12C3 = (12!)/(3!*(12-3)!)
12C3 = (12!)/(3!*9!)
12C3 = (12*11*10*9!)/(3!*9!)
12C3 = (12*11*10)/(3*2*1)
12C3 = 1320/6
12C3 = 220
-------------------------
Problem 11
Like with problem 10, the order doesn't matter. This is assuming that each member on any given team has the same rank as any other member.
If you used the nCr combination formula, with n = 9 and r = 5, you should get the answer 126
Here's another way to get that answer.
There are 9*8*7*6*5 = 15120 different permutations. If order mattered, then we'd go for this value instead of 126
Within any group of five people, there are 5! = 120 different ways to arrange them. So we must divide that 15120 figure by 120 to get the correct value of 126 combinations
15120/120 = 126
Note the connection between nCr and nPr, namely,
nCr = (nPr)/(r!)
-------------------------
Problem 12
Now this is where order matters, because the positions in basketball are different (eg: a point guard differs from a center).
We have 13 choices for the first position, 12 for the second, and so on until we reach 13-r+1 = 13-5+1 = 9 as the number of choices for that last slot.
So we'll have 13*12*11*10*9 = 154,440 different permutations
Now if the condition that "each player can play any position" isn't the case, then the answer would very likely be different. This is because for the center position, for instance, we wouldn't have 13 choices but rather however many choices we have at center. To make the problem simpler however, your teacher is stating that any player can play at any slot. Realistically, the answer would be far less than 154,440
-------------------------
Problem 13
We have 6 applications for the 2 math positions. Order doesn't matter. That means we'll have 6C2 = 15 different ways to pick the math people. Use the nCr formula mentioned in problem 10. Since we'll use this value later, let's make x = 15.
There are 2 people applying for the chemistry teaching position, meaning there are 2 ways to fill this slot. We could compute 2C1 = 2, but that's a bit overkill in my opinion. Let y = 2 so we can use it later.
Similarly, there are 10 applicants for the Spanish teacher position, leading to 10 ways to get this position filled. You could compute 10C1 = 10 if you wanted to. Let z = 10 so we can use it later.
Once we figured out those x,y,z values, we multiply them together to get our final answer: x*y*z = 15*2*10 = 30*10 = 300
There are 300 different ways to select 2 math teachers, a chemistry teacher, and a Spanish teacher from a pool of 6 math applicants, 2 chemistry applicants, and 10 Spanish teacher applicants.
Related Questions
Evaluate 9.3p + 8.7r when p=6 and r=7 .
Answers
Answer:
116.7
Step-by-step explanation:
Given: p = 6, r = 7
Plug in 6 for p, and 7 for r in the given expression:
9.3p + 8.7
9.3(6) + 8.7(7)
Remember to follow PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction.
First, multiply:
9.3 * 6 = 55.8
8.7 * 7 = 60.9
Next, add:
55.8 + 60.9 = 116.7
116.7 is your answer.
~
Answer:
9.3p + 8.7r when p=6 and r=7 .
substituting value
9.3*6+8.7*7
55.8+60.9
116.70is a required answer.
What is the median of the data?
3
8
5
5.5
Answers
Answer:
Median= middle number
(Example) 1, 4 ,6, 7 ,12
6 Would be the median here
so, 3, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8,
5 Is the middle number and the median
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
3, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8
Hope this helped! Please leave any questions or concerns in the comments byeee <3
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The number of Internet users in Latin America grew from 40.8 million in 2009 to 85.6 million in 2016. Use the geometric mean to find
the annual growth rate. (Round your answer to 2 decimal places.)
2
points
Mean annual growth rate
S 02 21:50
References
Answers
CMON DAWG
What is the equation for this word problem?:
Salma has 18 cars available to rent.
Last C be the number of cars she would have left after renting R of them.
Help!!!
Answers
Answer:
equation: C = 15 - R
C = 15 - 7
C = 8
Step-by-step explanation:
Okay first of all stan the karl pfp
Choose A B C or D
State if the triangles in each pair are similar. If so, state how you
know they are similar
A) similar; SAS similarity
C) not similar
B) similar; SSS similarity
D) similar, AA similarity
Answers
Answer:
Option D
Step-by-step explanation:
From the picture attached,
m∠K ≅ m∠C [Given]
m∠L = m∠D [Given]
By AA property of similarity,
Both the triangles ΔDEC and ΔLMK are the similar triangles.
Option D will be the correct option.
HELP ASAP! I will GIVE BRAINLY !! Need the whole answer please :(
Answers
Answer:
y = -1/2x + 1
Step-by-step explanation:
use 2 points to find slope, i used: (0,1) (4,-1)
m = 1-(-1) / 0-4
m = 2/-4
m = -1/2
as seen in graph, y-intercept is 1
∴ y = -1/2x + 1
Answer:
y=-2/4x+1
Step-by-step explanation:
the slope would be rise/run and y-intercept is wherever the line crosses the y-axis
their sum is -11 and the difference is 41
Answers
Answer:
x+41=-11 I guess
Step-by-step explanation:
Rochelle received a $15 gift card to an online music store. She downloaded 12 songs that each cost the same price. After the gift card was applied, her total was $8.88. Which equation can be used to find , the price of each song?
A.) 12p - 15 = 8.88
B.) 8.88 - 12p = 15
C.) 12p + 8.88 = 15
D.) 15p + 12 = 8.88
Answers
Answer:
D
Step-by-step explanation:
please solve and show steps I don't know how to solve this
Answers
Answer:
plug 3 into the equation:
y = 1/3(3) + 1
= 1 + 1
= 2
Y= 1/3(3/1)+1
Y=1+1
Y=2
FIND EACH ANGLE MEASURE.
FIGURES ARE NOT DRAWN TO SCALE.
Answers
Answer: See explanation
Step-by-step explanation:
M1 49
M2 22
M3 27
M4 63
M5 68
M6 22
4) Associate with each of the following sampling methods the most appropriate example from the list, given below.
1. Simple random sample ______ 4. Systematic sample ______
2. Stratified random sample _______ 5. Quota sample ______
3. Cluster sample ______ 6. Convenience sample _____
Examples:
a) Standing at a mall or a grocery store and asking people to answer questions.
b) Names picked from a hat.
c) Every 10th person is chosen randomly from each ward in a hospital.
d) Four secondary schools in a town is selected at random, then every pupil in
that school is surveyed.
e) One person in ten is chosen from an alphabetical list of employees.
f) People are stopped in the street according to instructions such as ‘stop equal
numbers of men and women.
Answers
Answer:
Step-by-step explanation:
Fd
PLZ HELP ILL GIVE BRAINLIEST FOR RIGHT ANSWER!!!
This line plot shows the number of hours students studied for a final exam.
How many students studied at least four hours for the final exam?
Enter your answer in the box.
___students
Answers
Answer:
4
Step-by-step explanation:
the answer is 4 because 2 people studied 4 hours, 1 person studied 4.5 hours and one person studied 8.5 (they are insane) which would total to 4 people studying for at least 4 hours.
Plz mark brainliest
Wavelength and Frequency
Which component in a musical note is referred to as the pitch of a sound?
a. wavelength
b. frequency
c. time
d. distance
Please select the best answer from the choices provided
Answers
Answer:
B. Frequency
Step-by-step explanation:
I calculated it logically
2. Medication B is available in a liquid capsule of 150 mg per capsule. 600 mg/kg per
day is ordered for a child weighing 44 lbs. How many mgs should be given to this child
per day? How many capsules will the nurse administer to the child per day?
Answers
Answer:
12000 mg/day or 80 capsules
Step-by-step explanation:
First let's convert 44 lbs to kg. You could divide by 2.205 to get more precise answer but since 44 divides perfectly by 2.2 I don't think it's a coincidence it's meant to be rounded.
44/2.2=20 kg
600*20=12000 mg per day
12000/150=80 capsules
Seems a bit excessive but looking over my process I don't see any mistakes.
Solve for x.
17
6
15
Answers
Answer:
x = 11
Step-by-step explanation:
Use the Secant-Secant Product Theorem. This theorem states that if two secants intersect in the exterior of a circle, then the products of the lengths of one secant segment and its external segment equal the products of the lengths of the other secant segment and its external segment. \
Use formula : (whole*outside = whole*outside)
1. Formula
WO = WO
2. Substitute variables and setup equation
7(x+7) = 6(6+15)
3. Simplify and remove parentheses
7x+49 = 126
4. Isolate and solve for (x)
7x = 77
x = 11
Answer: 11
Given:
The figure of circle and two secants from an external point.
To find:
The value of x.
Solution:
According to intersecting secant theorem: If two secants (I and II) intersect each other outside the circle then
(I secant) × (external segment of I) = (II secant) × (external segment of II)
Using the intersecting secant theorem, we get
[tex]7(7+x)=6(6+15)[/tex]
[tex]49+7x=36+90[/tex]
[tex]7x=126-49[/tex]
[tex]7x=77[/tex]
Divide both sides by 7.
[tex]x=\dfrac{77}{7}[/tex]
[tex]x=11[/tex]
Therefore, the value of x is 11.
a sqaure pieace of platic has sides that are 3 centimeter long. what is the platic pieace of teh area? answers
Answers
3 x 3 = 9
9 is the answer.
find any domain restrictions on f(g(x))
f(x)= square root x-3 and g(x)=x+5
Answers
Answer:
[tex]x \ge -2[/tex]
Step-by-step explanation:
The "argument" of a square root (the quantity you're finding the square root of) must be greater than or equal to 0.
[tex]f(x)=\sqrt{x-3}[/tex] requires [tex]x-3 \ge 0 \Rightarrow x \ge 3[/tex].
But in the function f(g(x)), the input to f is g(x) = x + 5, so x + 5 must be greater than or equal to 3.
[tex]x+5 \ge 3 \Rightarrow x\ge -2[/tex]
Composite functions can be confusing; one reason is the use of the same symbol, x to represent numbers from the domain of EACH function. See if it helps to call the domain of g by the name x, and the domain of f by some other name.
[tex]f(z)=\sqrt{z-3}\\g(x)=x+5\\f(g(x))=f(x+5)=\sqrt{(x+5)-3}=\sqrt{x+2}[/tex]
The square root will require [tex]x+2 \ge 0 \Rightarrow x \ge -2[/tex]
Write an equivalent expression for -24 + 54n.
Answers
Answer:
30n
Step-by-step explanation:
-24+54=30×n=30n
I needed 20 more letters so ya lol
Answer:
-6 (4-9n)
Step-by-step explanation:
HELP PLZZZ I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!
A survey found that 40% of shoppers at Max-a-mart like chocolate ice cream. If 20 shoppers like chocolate ice cream, how many people were surveyed?
a) 20
b) 30
c) 50
d) 100
Answers
Solving
Tamika and Bryan hiked 7 miles a day.they hiked for 5days
Kurt and Sade hiked 5 miles a day. How many days did it take Kurt and sade
to hike the same distance as Tamika and bryan
sentence to solve.
Answers
Answer:
7 days
Step-by-step explanation:
Tamika and Bryan :
Distance per day = 7 miles
Number of days = 5
Tottal distance hiked = 7*5 = 35 miles
Kurt and Sade :
Distance per day = 5 miles
Number of days = x
Total distance hiked = 5x
35 = 5x
x = 35 /5
x = 7
A 50% coupon was used on a $365 online order. How
much was the order?
Answers
Answer:
$182.5
Step-by-step explanation:
365/2= 182.5
Answer:
$182.50
Step-by-step explanation:
365/2 = 182.5
7. Of 101 randomly selected adults
over 30 who frequent a very large
mall, 35 admitted to having lost their
car at the mall. Construct a 95%
confidence interval for the true
percentage of all adults over 30 who
shop at that mall who admit to having
lost their car at the mall.
Answers
Answer:
The 95% confidence interval for the true percentage of all adults over 30 who shop at that mall who admit to having lost their car at the mall is (25.37%, 43.93%).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Of 101 randomly selected adults over 30 who frequent a very large mall, 35 admitted to having lost their car at the mall.
This means that [tex]n = 101, \pi = \frac{35}{101} = 0.3465[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3465 - 1.96\sqrt{\frac{0.3465*0.6535}{101}} = 0.2537[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3465 + 1.96\sqrt{\frac{0.3465*0.6535}{101}} = 0.4393[/tex]
As percentages:
0.2537*100% = 25.37%
0.4393*100% = 43.93%
The 95% confidence interval for the true percentage of all adults over 30 who shop at that mall who admit to having lost their car at the mall is (25.37%, 43.93%).
Solve for x Round to the nearest tenth, if necessary.
Answers
Answer:
Step-by-step explanation:
take 20 degree as reference angle
using sin rule
sin 20=opposite/hypotenuse
0.34=3/x
x=3/0.34
x=8.82
x=8.8
A brochure from the department of public safety in a northern state recommends that motorists should carry 12 items (flashlights, blankets, and so forth) in their vehicles for emergency use while driving in winter. The following data give the number of items out of these 12 that were carried in their vehicles by 15 randomly selected motorists.
5.3 78 0 105 12 10 7 6 7 119
Find the mean, median, and mode for these data. Round your answers to two decimal places, where appropriate.
Mean items
Median items
Mode - items
Answers
Answer:
[tex]Mean = 6.07[/tex]
[tex]Median = 7[/tex]
[tex]Mode = 7[/tex]
Step-by-step explanation:
Given
[tex]Data: 5\ 3\ 7\ 8\ 0\ 1\ 0\ 5\ 12\ 10\ 7\ 6\ 7\ 11\ 9[/tex]
[tex]n = 15[/tex]
Solving (a): The mean
Mean is calculated as:
[tex]Mean = \frac{\sum x}{n}[/tex]
This gives:
[tex]Mean = \frac{5+ 3+ 7+ 8+ 0+ 1+ 0+ 5+ 12+ 10+ 7+ 6+ 7+ 11+ 9}{15}[/tex]
[tex]Mean = \frac{91}{15}[/tex]
[tex]Mean = 6.07[/tex]
Solving (b): The median
Sort the data in ascending order:
[tex]Data: 5\ 3\ 7\ 8\ 0\ 1\ 0\ 5\ 12\ 10\ 7\ 6\ 7\ 11\ 9[/tex]
[tex]Sorted: 0\ 0\ 1\ 3\ 5\ 5\ 6\ 7\ 7\ 7\ 8\ 9\ 10\ 11\ 12[/tex]
The median is:
[tex]Median = \frac{n + 1}{2}th[/tex]
[tex]Median = \frac{15 + 1}{2}th[/tex]
[tex]Median = \frac{16}{2}th[/tex]
[tex]Median = 8th[/tex]
The 8th item on the sorted dataset is 7; So:
[tex]Median = 7[/tex]
Solving (c): The mode
[tex]Mode = 7[/tex]
Because it has a frequency of 3 (more than any other element of the dataset).
Adila sells T-shirts at a rock concert. She earns $8.00/h, plus $0.50 for each T-shirt she sells.
How many T-shirts must Adila sell to earn $80 in a 6-h shift?
Answers
Answer:
64 Shirts
Step-by-step explanation:
For 8 hrs she already earns $48 because 8*6=48. She needs $32 more from shirts to make $80. If its $0.50 per shirt it takes 64 to make $32
Find the slope of a line going through the two points (10, -6) and (3, 9).
Answers
Answer:
-15/7
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(9-(-6))/(3-10)
m=(9+6)/-7
m=15/-7
I’ve been stuck on this can I get help.
Answers
Answer:
12 days
Step-by-step explanation:
720-240=480
480÷8= 60
1 day= 60 chairs
? days= 70 chairs
12 days = 720 chairs
hope this helps
Find the distance between the two points rounding to the nearest tenth (if necessary).
(8,
-4) and (3,8)
Find the distance between the two points rounding to the nearest tenth (if necessary).
(8,
-4) and (3,8)
Answers
Answer:
13 units
Step-by-step explanation:
(8, -4) and (3,8)
To find the distance of two points, we use the distance formula:
[tex]d = \sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2 }[/tex]
Let's plug in what we know.
[tex]d = \sqrt{(3 -8)^2 + (8 - (-4))^2 }[/tex]
Evaluate the double negative.
[tex]d = \sqrt{(3 -8)^2 + (8 + 4)^2 }[/tex]
Evaluate the parentheses.
[tex]d = \sqrt{(-5)^2 + (12)^2 }[/tex]
Evaluate the exponents.
[tex]d = \sqrt{(25) + (144) }[/tex]
Add.
[tex]d = \sqrt{(169)}[/tex]
Evaluate the square root.
[tex]d = 13[/tex]
13 units
Hope this helps!
Answer:
12
Step-by-step explanation:
a⋅(a+b)= c⋅(c + d) formula
9⋅(9+x)= 3⋅(3+60)
81+9x=3(63)
81+9x=189
-81 -81
9x=108
x=12
what is the answer to this?
Answers
Answer:
This is the answer:
330550=
A lab assistant needs to create a 600 mL mixture that is 3% hydrochloric acid. The
assistant has solutions of 1.5% and 4% in supply at the lab. Using the variables x and
y to represent the number of milliliters of the 1.5% solution and the number of
milliliters of the 4% solution respectively, determine a system of equation that
describes the situation.
Enter the equations below separated by a comma.
How many milliliters of the 1.5% solution should be used?
How many milliliters of the 4% solution should be used?
Answers
Answer:
240 ml of 1.5% solution and 360 ml of 4% solution should be used.
Step-by-step explanation:
Since a lab assistant needs to create a 600 mL mixture that is 3% hydrochloric acid, and the assistant has solutions of 1.5% and 4% in supply at the lab, to determine the number of milliliters of the 1.5% solution and the number of milliliters of the 4% solution that must be used, the following calculations must be performed:
50 x 0.015 + 50 x 0.04 = 0.75 + 2 = 2.75
40 x 0.015 + 60 x 0.04 = 0.6 + 2.4 = 3
600 x 0.4 = 240
Therefore, 240 ml of 1.5% solution and 360 ml of 4% solution should be used.