Let [tex]e[/tex] and [tex]r[/tex] be the number of elves and reindeers, respectively.
We know that:
[tex]r+e=14[/tex] (so far 14 of them have arrived)
[tex]4r+2e = 38[/tex](each reindeer has 4 legs and each elf has two)
If we multiply the first equation by 2 we have [tex]2r+2e=28[/tex], and if we subtract this equation from the second we have [tex]2r=10[/tex] which implies [tex]r=5[/tex].
So, there are 5 reindeers and 9 elves (remember that they have to sum up to 14).
The number of reindeers is 5 and the number of elves is 9.
Two equations can be derived from the equation:
e + r = 14 equation 1
2e + 4r = 38 equation 2
Where:
e = number of elves at the meeting
r = number of reindeers at the meeting
In order to determine the value of r, multiply equation 1 by 2.
2e + 2r = 28 equation 3
Subtract equation 3 from 2
2r = 10
Divide both sides of the equation by 2
r = 5
To solve for e substitute for r in equation 1
5 + e = 14
e = 14 - 5
e = 9
A similar question was answered here: brainly.com/question/23589883?referrer=
Prove that log(3) 7 is an irrational number
Answer:
Proof below
Step-by-step explanation:
Irrational and Rational Numbers
We need to use the basic property of logarithms:
[tex]log_b\ a=x\ \ \Rightarrow b^x=a[/tex]
We are given:
[tex]log_3\ 7[/tex]
And we will prove it's an irrational number, i.e., it's not a rational number.
Recall a rational number can always be expressed as a fraction a/b, where a and b are integer numbers. Thus, if the expression was a rational number, then:
[tex]\displaystyle log_3\ 7=\frac{a}{b}[/tex]
Applying the property:
[tex]\displaystyle 3^{\frac{a}{b}}=7[/tex]
Raising to the power of b:
[tex]3^a=7^b[/tex]
It's not possible to find two integers a and b that satisfy the condition above. That contradiction comes from the assumption that [tex]log_3\ 7[/tex] is rational, thus, it's proven [tex]log_3\ 7[/tex] is irrational.
Rewrite the following equation into slope-intercept form (y = mx + b).
3x - y = 7
Answer:
y=3x-7
Step-by-step explanation
Subtracted 3x, then divided by -1, made the 7 negative and the 3x positive
Please help with these 3
Answer:
3) 146 degrees
4) 471 degrees
5) x = 100 and 3x = 300
Step-by-step explanation:
all three are polygons whose sum of all interior angles can be found by using the formula (n - 2)*180 where 'n' refers to the number of sides
In #3 and 5 there are 5 sides, so (5 - 2)*180 = 3(180) giving a total of 540 degrees. Add all known angles and deduct from 540.
#4 has 7 sides, so (7 - 2)*180 = 1260 degrees. Add all known angles and deduct sum from 1260.
#5 Add all integers plus 'x' + '2x' to get 240 + 3x = 540
Who can help me with this problem
Answer:
y=94x
Step-by-step:
If you have any trouble understanding how i got this please let me know and i will do another explanation.
Please help and click on this. I've been trying to get this question on brainy for about 3 whole days and nobody bothers to answer. How many ounces of pure vinegar must be added to 80 ounces of a 10% solution to make a 25% solution? please and thank you
Answer:
32 ounces
Step-by-step explanation:
[tex]M_{1} v_1=M_2v_2\\(0.10)80=(0.25)x\\(1/0.25) (0.10)80=(0.25)x(1 /0.25)\\\frac{(0.10)80}{0.25} =32 ounces[/tex]
jimmy wants to buy socks that cost $20 how much change does he receive if he gives the cashier $100?
5
Jody has 3 red marbles, 5 blue marbles, and 8 yellow marbles. What is the ratio of red marbles to blue marbles?
Answer:
3:5
Step-by-step explanation:
There are 3 red marbles
5 blue marbles
SO
3:5
Answer: 3:5
Step-by-step explanation:
There are 3 red marbles and 5 blues marbles so the ratio of red marbles to blue marbles will be 3:5 or 3 to 5, or 3/5
Automobiles arrive at the drive-through window at a post office at the rate of 7 every 10 minutes. The average service time is 7 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. (Note: the given equations are NOT necessarily in the correct order.) What is the average time a car is in the system?Formulas for 13.17 What is the average number of cars in the system? What is the average time cars spend waiting to receive service? What is the average number of cars in line behind the customer receiving service? What is the probability that there are no cars at the window? What percentage of the time is the postal clerk busy? What is the probability that there are exactly two cars in the system?
Answer:
1) the average time a car is in the system is 0.1587 min
2) the average number of cars in the system 0.1111
3) the average time cars spend waiting to receive service is 0.01587 min
4) the average number of cars in line behind the customer receiving service is 0.01111
5) the probability that there are no cars at the window is 0.9
6) the percentage of time that the postal clerk is busy is 10%
7) the probability that there are exactly two cars in the system is 0.1217
Step-by-step explanation:
Given that;
Arrival rate λ = the rate of 7 every 10 minutes = 7/10 = 0.7
Average service time μ = 7 minutes
The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.
1) What is the average time a car is in the system?
Average in the system W = 1 / (μ - λ)
= 1 / (7 - 0.7) = 1 / 6.3 = 0.1587 min
therefore the average time a car is in the system is 0.1587 min
2) What is the average number of cars in the system?
Average number of cars L = λ / (μ - λ)
= 0.7 / (7 - 0.7) = 0.7/6.3 = 0.1111
Therefore the average number of cars in the system 0.1111
3) What is the average time cars spend waiting to receive service?
Average time spend waiting for services Wq = λ / μ(μ - λ)
= 0.7 / 7(7 - 0.7) = 0.7/44.1 = 0.01587 min
Therefore the average time cars spend waiting to receive service is 0.01587 min
4) What is the average number of cars in line behind the customer receiving service?
average number of cars in line behind the customer receiving service
Lq = λ² / μ(μ - λ) = (0.7)² / 7(7 - 0.7) = 0.49 / 44.1 = 0.01111
Therefore the average number of cars in line behind the customer receiving service is 0.01111
5) What is the probability that there are no cars at the window?
probability that there are no cars at the window = 1 - (λ / μ)
= 1 - (0.7 / 7) = 1 - 0.1 = 0.9
Therefore the probability that there are no cars at the window is 0.9
6) What percentage of the time is the postal clerk busy?
percentage of the time is the postal clerk busy = (λ / μ)
= (0.7 / 7) = 0.1 ≈ 10%
Therefore the percentage of time that the postal clerk is busy is 10%
7) What is the probability that there are exactly two cars in the system?
the probability that there are exactly two cars in the system = (λ²e^-λ) / 2!
= (0.7²e^-0.7) / 2! = 0.2433 / 2 = 0.1217
Therefore the probability that there are exactly two cars in the system is 0.1217
Daniel bought 3 comic books at the bookstore. He spent $8.33 on the first book and $7.33 on the
second book. He spent a total of $24.69 on all three books.
How much did Diego spend on the
,
third book?
Answer:
The third book cost $9.03
Step-by-step explanation:
Answer:
the 3rd book is 9.03
Step-by-step explanation:
all you have to do is add 8.33 + 7.33 and thate 15.66 so 24.69 - 15.66 is 9.03
Rob did 15 push-ups on Monday, but on Tuesday he did 3 more than on Monday. What was the percent change?
Answer:
20%
Step-by-step explanation:
where do i graph?
please send picture of your own for me to copy
Answer:
Step-by-step explanation:
Compound inequality has been given as,
12(2x - 10) + 24 ≥ 48 Or 6x + 15 - 9x ≥ 6
By simplifying it further,
12(2x - 10) + 24 ≥ 48
[tex]\frac{12(2x - 10)}{12}+\frac{24}{12}\geq \frac{48}{12}[/tex]
(2x - 10) + 2 ≥ 4
(2x - 10) + 2 - 2 ≥ 4 - 2
2x - 10 ≥ 2
2x - 10 + 10 ≥ 2 + 10
2x ≥ 12
[tex]\frac{2x}{2}\geq \frac{12}{2}[/tex]
x ≥ 6
6x + 15 - 9x ≥ 6
(6x - 9x) + 15 ≥ 6
(-3x) + 15 ≥ 6
-3x + 15 - 15 ≥ 6 - 15
-3x ≥ -9
3x ≤ 9
x ≤ 3
We have to plot the inequality on a number line
x ≥ 6 Or x ≤ 3
Question Help X 3.8.IP-5 Draw a bar diagram to model the situation. Then write and solve an equation. A grocery store ordered 10 crates of tomatoes from a supplier. Each crate contains 195 tomatoes. How many tomatoes did the store order? ? tomatoes ? D. 195 195 195 195 195 195 195 195 195 195 10 crates 195 tomatoes in each crate Let x be the number of tomatoes the store ordered. The equation represents this situation. (Use the operation symbols in the math palette as needed. Do not perform the calculation.) More.
brian lest and points if you get it right and if you do i will mark you as a brian lest
Answer:
i think its d. well thats the only answer on there
put the steps, for changing the formula for sector area of a circle in degrees to the formula for the sector area of a circle in radians, in the correct order
Answer:
see explanation
Step-by-step explanation:
The area (A) of a sector is calculated as
A = area of circe × fraction of circle
= πr² × [tex]\frac{0}{360}[/tex] ← where θ is in degrees
[ note that 360° = 2π radians ], then
A = πr² × [tex]\frac{0}{2\pi }[/tex] ← where θ is in radians
( Cancel π on numerator/ denominator )
A = [tex]\frac{1}{2}[/tex]θr²
9514 1404 393
Answer:
top down: 2, 4, 1, 7, 6, 5, 3, 8
Step-by-step explanation:
It appears the expected order may be ...
__
Write the formula for a sector area of a circle with central angle, θ, in degrees.
[tex]\textit{Area of a Sector}=\dfrac{\theta}{360^{\circ}}\cdot\pi r^2[/tex]
Replace 360° with 2π radians.
[tex]\dfrac{\theta}{360^{\circ}}=\dfrac{\theta}{2\pi}[/tex]
Replace the angle ratio in degrees with the angle ratio in radians.
[tex]\textit{Area of a Sector}=\dfrac{\theta}{2\pi}\cdot\pi r^2[/tex]
Simplify by cancelling
[tex]\textit{Area of a Sector}=\dfrac{1}{2}\theta r^2[/tex]
The letters in the word SANTA CLAUS are printed on identical index cards with one letter per card. The ten cards are then placed in a hat, and one card is randomly chosen (without looking) from the hat. The chance process we are interested in is what letter is on the selected card.
The missing part:
Make a model of probability showing the set of outcome and the probability value of each outcome.
Answer:
Step-by-step explanation:
From the given information:
a) From the word SANTA CLAUS, outcomes are all distinct letters.
This implies that the outcomes are S, A, N, T, C, L, U, S
For S, N, T, C, L, U, S letters, each of them is repeated once.
Thus, their respective probability = [tex]\dfrac{1}{10}[/tex]
A is repeated thrice, so probability for A = [tex]\dfrac{3}{10 }[/tex]
Using the probability distribution table; we have the following.
outcome S A N T C L U S
probability [tex]\dfrac{1}{10}[/tex] [tex]\dfrac{3}{10 }[/tex] [tex]\dfrac{1}{10}[/tex] [tex]\dfrac{1}{10}[/tex] [tex]\dfrac{1}{10}[/tex] [tex]\dfrac{1}{10}[/tex] [tex]\dfrac{1}{10}[/tex] [tex]\dfrac{1}{10}[/tex]
On weekdays , a movie theater charges different rates for adults and children. If 3 adults and 2 children go for a movie on a weekday, the total cost of the tickets is $31. If 2 adults and 3 children go on a weekday the total cost of the tickets is 29$ . If a group of adults and 6 children go to the movie theatre on a weekday and pay $58 for tickets , how many adults are in this group ?
Dec 4,
PM
Find an equation for the perpendicular bisector of the line segment whose endpoints
are (-1, 4) and (-9, --6).
Answer:
y = -0.8x - 5
Step-by-step explanation:
x1 = (XA + XB) / 2 = -5
y1 = (YA + YB) / 2 = -1
m = (XA - XB) / (YA - YB) = -0
__________________________________________
(y - -1) = -0.8(x - -5)
y - -1 = -0.8x - 4
y = -0.8x - 4 + -1
y = -0.8x - 5
question in the image
Answer:
thats not a question
Step-by-step explanation:
for the function g (x) shown graphed below, over which of the following intervals is g (x) > 0
Answer:
g(-1) is lesser than 0 while h(-1) is -3(-1) + 8 = 11 so g(-1) is lesser than h(-1)
g(1) is 5 while h(1) is -3(1) + 8 = 5 so g(1) is equal to h(1)
Step-by-step explanation:
The function g(x) is greater than zero when the value of x lies in between -3 and 5 and this can be determined by using the given graph.
Given :
The graph of the function g(x) is given.
The following steps can be used in order to determine the interval for g(x):
Step 1 - The value of g(x) means the value of y.
Step 2 - The value of g(x) is positive when the graph of g(x) is in the first or in the second quadrant.
Step 3 - So, according to the graph function g(x) is positive when the value of x is in between -3 and 5.
Therefore, the correct option is 3).
For more information, refer to the link given below:
https://brainly.com/question/5245372
PLEASE HELP ASAP, WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Answer:
D. y = -6x + 38
Step-by-step explanation:
Equation of a sequence
We are given the following sequence of numbers corresponding to the positions x={1,2,3,4,5,...}
y={32,26,20,14,8....}
To find the equation of the sequence, we must recall the general term of a sequence is:
[tex]a_x=a_1+(x-1).r[/tex]
Where r is the common difference between two consecutive terms, an and a1 are the x-th and the first terms respectively.
We can find the value of r by subtracting any pair of consecutive terms:
r = 26-32 = 20-26 = 14-20 = -6
Now we apply the formula:
y=32+(x-1).(-6)
Operating:
y=32-6x+6
y = -6x + 38
Answer:
D. y = -6x + 38
I did not do as good as I hoped on my math model :(
Answer:
you're going to get an A
Step-by-step explanation:
.............
An athlete's target heart rate, in beats per minute, is $80\%$ of the theoretical maximum heart rate. The maximum heart rate is found by subtracting the athlete's age, in years, from 220. To the nearest whole number, what is the target heart rate of an athlete who is 26 years old
Answer:
155
Step-by-step explanation:
Since the question states that;
Maximum heart rate= 220 - athletes age
If athletes age = 26 years
Maximum heart rate= 220 - 26 = 194
Again;
athlete's target heart rate= 80% × Maximum heart rate
Athlete's target heart rate= 0.8 × 194= 155
Madea hires a caterer to provide food for her birthday. The caterer charges
her $225 for food and supplies and $25 per hour to serve during the party.
Madea ends up paying $350 total. How many hours did the caterer serve?
Use the equation 25x+225=350 to solve.
Answer:
The caterer served 5 hours. x = 5
Step-by-step explanation:
25x + 225 = 350
We must use inverse operations to get x
25x + 225 - 225 = 350 - 225
25x = 125
25x ÷ 25 = 125 ÷ 25
x = 5
the caterer served 5 hours.
I hope this helped and if it did I would appreciate it if you marked me Brainliest. thank you and have a nice day!
Supervisor: "I see that 1000 calls were sent to your extension this month. 15% of those calls were not answered, which means that you did not answer __________ calls this month."
Step-by-step explanation:
850 calls
1000:100=10
1%=10
10×85=850
Discount is the reduction in value. The total number of calls not answered this is 150 calls
Discount and percentagesGiven the following
Total number of calls = 1000 calls
If 15% of those calls were not answered, the total calls that were not answered is given as:
Total call not answered . = 0.15 * 1000
Total call not answered = 150 calls
Hence the total number of calls not answered this is 150 calls
Learn more on percentages here: https://brainly.com/question/24304697
#SPJ2
I WILL GIVE YOU BRAINLIEST IF YOU ANSWER CORRECT!!
The school library received a donation of 42 boxes of books. Each box contains 15-18 books. The library has 10 empty bookshelves. Each bookshelf can hold up to 60 books. Does the library have enough shelf space for all the new books? Explain how you solved the problem.
Answer:
No the school libary doesn not have enough pace for all the books. If the least amount of books came which is 15 books in all of 42 boxes (15*42), it would be 630 books and the school libary shelf can only hold 600 books becuase 10 shelves * 60 books on each shelf is 10*60 which is 600. If the least amount of books can’t even fit then the others wold defietnly not fit.
Identify the pattern for the following sequence. Find the next three terms in the sequence. . a. -15, -11, -7, -3, ____, _____, _____,...
A: Subtract 4; -7, -11, -15
B. Add 4; 2, 6, 10
C. Subtract 4; 1, 5, 9
D. Add 4; 1, 5, 9
Please select the best answer from the choices provided.
Answer: c
Step-by-step explanation:
Answer:
B you add 4. a negative plus a positive is a negative. -15 +4 is -11
What is 3/8 divided by 4/1
You don't have to give reasons please help soon
Answer:
heyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answer:
52
Step-by-step explanation:
angle R is a right angle which is 90°
if you add angle S and angle R you get angle PQS because sum of two opposite interior angle is equal to it's exterior angle
34°+90°=x+72°
124°=x+72°
x=124°-72°
x=52°
which comparisons can be made using these fraction bars?
Find those ^^^^^^^^^^^^^^
Answer:
m<G=60 degrees.
equilateral or equiangularTriangle
Step-by-step explanation:
triangle is 180 degrees
all these angles are congruent
means they all equal the same
180/3=60
I need help please asap
Answer:
0, 1/13, 49/100, 1/2, 11/20, 8/9, 1
Step-by-step explanation:
You know the smallest is 0, largest is 1
the middle is 1/2
49/100 is slightly smaller than 1/2 or 50/100
11/20 is slightly larger than 1/2 or 10/20
1/13 is slightly larger than 0
8/9 is slightly smaller than 1
please give thanks :)
and brainliest :)
