Kyle filled 6 10-oz cup(s), 11 14-oz cup(s), and 4 20-oz cup(s).
Let's define the variables:
x = number of 10-oz cups of coffee sold.
y = number of 14-oz cups of coffee sold.
z = number of 20-oz cups of coffee sold.
We know that:
Kyle served 21 cups of coffee, then:
x + y + z = 21
He used 294 ounces of coffee, then:
x*10 oz + y*14 oz + z*20 oz = 294 oz
He collected a total of $24.35, then:
x*($0.95) + y*($1.15) + z*($1.50) = $24.35
Then we have a system of 3 equations:
x + y + z = 21
x*10 oz + y*14 oz + z*20 oz = 294 oz
x*($0.95) + y*($1.15) + z*($1.50) = $24.35
To solve this, the first thing we need to do is isolate one of the variables in one of the equations, let's isolate x in the first one.
x = 21 - y - z
Now we can replace this in the other two equations to get:
(21 - y - z)*10 oz + y*14 oz + z*20 oz = 294 oz
(21 - y - z)*($0.95) + y*($1.15) + z*($1.50) = $24.35
Now we can simplify these two equations:
y*4 oz + z*10 oz = 294 oz - 210oz = 84 oz
y*($0.20) + z*($0.55) = $24.35 - $19.94 = $4.40
Now we need to do the same thing, we need to isolate one of the variables in one of the equations, we can isolate z in the first one:
z*10 oz = 84oz - y*4 oz
z = (84oz - y*4 oz)/10oz
z = 8.4 - y*0.4
Now we can replace this in the other equation:
y*($0.20) + ( 8.4 - y*0.4)*($0.55) = $4.40
Now we can solve this for y.
y*($0.20) + $4.62 - y*$0.22 = $4.40
y*$0.02 = $4.40 - $4.62 = $0.22
y = $0.22/$0.02 = 11
Now that we know the value of y, we can use:
z = 8.4 - y*0.4
z = 8.4 - 11*0.4 = 4
Now that we know the value of z and y we can use:
x = 21 - y - z
x = 21 - 11 - 4 = 6
Then we found:
x = 6
y = 11
z = 4
this means that:
Kyle filled 6 10-oz cup(s), 11 14-oz cup(s), and 4 20-oz cup(s).
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/20067450
Which expression is equivalent to -6(-⅔+2x)?
O-4-12x
O-4+ 2x
O 4-12x
O 4+ 12x
Answer:
4-12x
Step-by-step explanation:
opening the brackets;
(-6×-2/3)- 12x
-2×-2 -12x
4-12x
Answer:
4 - 12x
Step-by-step explanation:
We can find an equivalent expression by distributing
-6(-⅔+2x)
Distribute by multiplying -6 times what's inside of the parenthesis ( -2/3 and 2x )
-6 * -⅔ = 4
-6 * 2x = -12x
We would be left with 4 - 12x
2. How to find the variance and standard deviation of a discrete
random variable?
Answer:
To find the variance just take the second moment and subtract that from the first moment squared
To find the standard deviation just take the square root of the variance
Step-by-step explanation:
the probability that a customer of a network operator has a problem about you needing technical staff's help in a month is 0.01. This operator installs internet for 500 households in a residential area a, Calculate the average number of households in this residential area having internet problems in a certain month
b, Calculate the probability that in 6 consecutive months there is only one month that no customer in this area has a network problem that needs the help of technical staff
Answer:
(a) average calls = 5
(b) probability that there is exactly one call in 6 consecutive monts = 0.038
Step-by-step explanation:
Let event of a customer requiring help in a particular month = H
and event of a customer not requiring help in a particular month = ~H
Given
p= 0.01, therefore
Number of households, n = 500.
Binomial distribution:
x = number of households requiring help in a particular month
P(x,n,p) = C(x,n)*p^x*(1-p)^(n-x)
where
C(x,n) = n!/(x!(n-x)!) is the the number of combinations of x objects out of n
(a) Average number of households requiring help = np = 500*0.01 = 5
(b)
Probability that there are no calls requiring help in a particular month
P(0), q= C(0,n)*p^0(1-p)^(n-0)
= 1*1*0.99^500
= 0.006570483
Applying binomial probability over six months,
q = 0.006570483
n = 6
x = 1
P(x,n,q)
= C(x,n)*q^x*(1-q)^(n-x)
= 6!/(1!*5!) * 0.006570483^1 * (1-0.006570483)^5
= 0.038145
Therefore the probability that in 6 consecutive months there is exactly one month that no customer has called for help = 0.038
can someone give me the anwser please?
Answer:
5/6 + 11/6 = 16/ 6
Step-by-step explanation:
Distance between any Teo labeled tick marks =
(1 - 2/3) / 2 = 1/3 ÷ 2 = 1/3 * 1/2 = 1/6
From the left :
2/3 + 1/6 = 5/6
5/3 + 1/6 = 11/6
5/6 + 11/6 = (5 + 11) / 6 = 16/6
5/6 + 11/6 = 16/ 6
Write the following equation in the general form Ax + By + C = 0.
y - x - 1 = 0
2x - 3y + 6 = 0
2x - 3y - 6 = 0
-2x + 3y - 6 = 0
Answer:
C. -2x +3y-6=0
this is the answer
PLEASE help! I really appreciate it thanks!
Answer:
h=A-πr²÷2πr
Step-by-step explanation:
Making h subject
A=2πrh+πr²
A-πr²=2πrh
A-πr²÷2πr=h
h=A-πr²÷2πr
Answer:
The answer is [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].
Step-by-step explanation:
To solve for (h), start by subtracting ([tex]\pi r^{2}[/tex]) from both sides, and the equation will look like [tex]A-\pi r^{2}= 2\pi rh+\pi r^2-\pi r^2[/tex]. The next step is to simplify the equation, which will look like [tex]A-\pi r^{2} =2\pi rh[/tex].
Next, divide both sides of the equation by [tex]2\pi r[/tex], and it will look like [tex]\frac{A-\pi r^{2} }{2\pi r} =\frac{2\pi rh}{2\pi r}[/tex]. Finally, simplify the equation, and the answer will be [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].
\lim _{x\to 0}\left(\frac{\sqrt{1+3x+x^2}-1}{\arcsin \left(2x\right)}\right)
Step-by-step explanation:
[tex]\displaystyle \lim_{x \to 0} \left(\dfrac{\sqrt{x^2 + 3x + 1} - 1}{\arcsin 2x} \right)[/tex]
Note that as [tex]x \rightarrow 0[/tex], the ratio becomes undefined. Using L'Hopital's Rule, where
[tex]\displaystyle \lim_{x \to c} \dfrac{f(x)}{g(x)} = \lim_{x \to c} \dfrac{f'(x)}{g'(x)} [/tex]
where f'(x) and g'(x) are the derivatives of the functions f(x) and g(x), respectively. Note that
[tex]f(x) = \sqrt{x^2 + 3x + 1} \:\:\text{and}\:\: g(x) = \arcsin 2x[/tex]
[tex]f'(x) = \dfrac{2x + 3}{2(\sqrt{x^2 + 3x + 1})}[/tex]
[tex]g'(x) = \dfrac{2}{\sqrt{1 - 4x^2}}[/tex]
Therefore,
[tex]\displaystyle \lim_{x \to 0} \dfrac{f'(x)}{g'(x)} = \lim_{x \to 0} \dfrac{2x + 3}{2(\sqrt{x^2 + 3x + 1})} \times \left(\dfrac{\sqrt{1 - 4x^2}}{2} \right)[/tex]
or
[tex]\displaystyle \lim_{x \to 0} \left(\dfrac{\sqrt{x^2 + 3x + 1} - 1}{\arcsin 2x} \right) = \dfrac{3}{4}[/tex]
find the coordinates of 6x² + 6x = 12
Answer:
1 , -2
Step-by-step explanation:
6x^2 + 6x = 12
6x^2 + 6x - 12 = 0
using middle term break method
6x^2 + (12 - 6)x - 12 = 0
6x^2 + 12x - 6x - 12 = 0
6x(x + 2) - 6(x + 2) = 0
(x + 2)(6x - 6) = 0
either (x + 2) = 0 OR (6x - 6) = 0
x + 2 = 0
x = 0 -2
x = -2
6x - 6 = 0
6x = 6
x = 6/6
x = 1
therefore , x = 1 , -2
Pls I don’t know what to do
Answer:
[tex]{ \bf{area = \pi {r}^{2} }} \\ { \tt{ = 3.14 \times {( {8.1}) }^{2} }} \\ = { \tt{206.1 \: {cm}^{2} }}[/tex]
please help me please help me please help me
Answer:
B.50
Step-by-step explanation:
The two angles form a right angle ( indicated by the little square )
Right angles have a measure of 90 degrees
Hence, x + 10 + 30 = 90
( Note that we just created an equation that we can use to solve for x )
We now solve for x using the equation we created
x + 10 + 30 = 90
Combine like terms
x + 40 = 90
Subtract 40 from both sides
x = 50
In which of the following drawings is DE parallel to AC?
Answer:
its option D because the lines are not even close to crossing.
Step-by-step explanation:
hope this helps :)
A veterinary assistant is working at a shelter that houses 53 animals. The shelter uses 1,484 pounds of food each month. How much on average does each animal consume per day in a 28-day month
Answer:
Each = 1 lb per animal
Step-by-step explanation:
Given
[tex]Animals = 53[/tex]
[tex]Food = 1484lb[/tex]
Required
Daily consumption of each animal in a 28-day month
First, we calculate the daily consumption of all animals
[tex]All = \frac{Food}{28}[/tex]
[tex]All = \frac{1484lb}{28}[/tex]
[tex]All = 53 lb[/tex]
The consumption of each animal is then calculated as:
[tex]Each = \frac{All}{Animals}[/tex]
[tex]Each = \frac{53lb}{53}[/tex]
Each = 1 lb per animal
what are the adjectives in this sentence: the class cheered when Sonia had finished reading her funny poem.
GUIDE QUESTIONS:
1. What is the idea or theme of the play?
2. How do you feel after watching the performance?
3. Does the integration of musical sound, songs, dialogue, and dance affect the
overall mood of the play?
Answer:
1.sowwy I dunno
2.its so good and it's perfect
3.i dunno ulet hehe
Step-by-step explanation:
Sorry walang matino na sagot.
Find the volume of this rectangular pyramid.
Be sure to include the correct unit in your answer.
6 m
3 m
9 m
Answer:
54 m^3
Step-by-step explanation:
this is the answer = 54 m^3
Volume of the rectangular pyramid will be 54[tex]m^{3}[/tex].
What is Rectangular Pyramid?Rectangular pyramid has 5 faces where one face is rectangular which is at bases and other 4 faces are triangular which is connected at the one point .
How to calculate the volume of the rectangular pyramid?If we assume that l is the length of the base and b is the width of the base and h is height of the rectangular pyramid then we can calculate the volume of the rectangular pyramid using the formula stated below
Volume of the rectangular pyramid = V= (1/3)×l×b×h
According to the asked question
l = 6m
b = 3m
h = 9m
then we can calculate the volume of the rectangular pyramid by using the above formula
= V= (1/3)×l×b×h
= (1/3)×6m×3m×9m
= 54[tex]m^{3}[/tex]
Learn more about volume of the rectangular pyramid
Here:https://brainly.com/question/924442
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Whoever helps gets Brainliest!!! PLEASE HELP!!!
Question 5(Multiple Choice Worth 1 points)
(02.04 LC)
What is the equation of a line that contains the points (2,-2) and (0, -2)?
O y = 0
Ox= -2
O y = -2
Ox=0
rational numbers.
Example 6: Write any 3 rational numbers between –2 and 0.
-20
0
ondas
-
Answer:
my firnd coli
Step-by-step explanation:
In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.
One evening Papa John’s sold a total of 33 pizzas topped with pepperoni, sausage, or pepperoni and sausage. There were 29 pizzas that had pepperoni. Of these, 15 also had sausage. How many more pizzas had pepperoni only than had sausage only?
Answer:
10
Step-by-step explanation:
Total pizza topped with pepperoni, sausage or pepperoni and sausage = 33
Number of pizzas with pepperoni = 29
Number of pizzas with pepperoni and sausage = 15
Pizza with pepperoni only = 29 - 15 = 14
Pizza with sausage only = 33 - 29 = 4
Pepperoni only than sausage only :
14 - 4 = 10
3. What is the distance between -49 and 167?
a) -216 units
b) -118 units
c) 118 units
d) 216 units
Answer:
c) IS THE ANSWER
Step-by-step explanation:
What is the slope of the line that passes through the points (-6, -2) and (2, -2)?
Answer:
0
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( -2 - -2)/(2 - -6)
= (-2+2)/(2 +6)
= 0/8
= 0
Answer:
Slope is 0
Step-by-step explanation:
Slope formula is (y2-y1)/(x2-x1)
-2 - (-2)/2 - (-6)
0/8
0
pls help pls help pls help
Answer:
Step-by-step explanation:
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 14 people took the trip. She was able to purchase coach tickets for $370 and first class tickets for $1140. She used her total budget for airfare for the trip, which was $10,570. How many first class tickets did she buy? How many coach tickets did she buy?
Answer:
She bought 7 coach tickets and 7 first class tickets.
Step-by-step explanation:
1. Set the equations up using y to represent first class and x to represent coach:
x + y = 14
370x + 1140y = 10,570
2. Use a graphing calculator to graph the equations and find the point where they intersect. The intersection point will tell you the number bought:
Answer:
Sarah bought y = 8 first class tickets.
Step-by-step explanation:
You can set up a system of equations for this problem. Let x = number of coach tickets and y = number of first class tickets. Then:
330x + 1220y = 12730 (cost of coach tickets plus cost of first class tickets is total budget)
x + y = 17 (number of coach tickets plus number of first class tickets is total number of people)
Solve the second equation for y to get y = 17 - x, then plug that into the first equation and solve for x:
330x + 1220(17 - x) = 12730
330x + 20740 - 1220x = 12730
-890x + 20740 = 12730
-890x = -8010
x = 9
Sarah bought x = 9 coach tickets. Plug that into the second equation and solve for y:
9 + y = 17
y = 8
Sarah bought y = 8 first class tickets.
Hope this answer helps you :)
Have a great day
Mark brainliest
hello, i need help with this question
Answer:
a
Step-by-step explanation:
what is the x and y intercepts for y=3x-1 on a graph
Answer:
x = [tex]\frac{1}{3}[/tex] y = -1
Step-by-step explanation:
x = 0 to solve for y
[tex]y=3x-1[/tex]
[tex]y=3(0)-1[/tex]
[tex]y=-1[/tex]
y = 0 to solve for x
[tex]y=3x-1[/tex]
[tex]0=3x-1[/tex]
Add 1 to both sides
[tex]1=3x[/tex]
Divide by 3 to isolate x
[tex]\frac{1}{3} =x[/tex]
determin 16x - 4y + 2 = 0
Answer:
16inches is your answer
The slope f '(x) at each point (x, y) on a curve. y = f (x) is given along with a particular point (a, b) on the curve. Use this information to find f (x).
[CLO-3] f '(x) = 9 x 2 + 4 x - 4; (0, -7)
By the fundamental theorem of calculus,
f(x) = f (0) + ∫₀ˣ f '(t) dt
We're given that the plot of f(x) passes through the point (0, -7), so f (0) = -7, and
f(x) = -7 + ∫₀ˣ (9t ² + 4t - 4) dt
f(x) = -7 + (3t ³ + 2t ² - 4t )|₀ˣ
f(x) = -7 + (3x ³ + 2x ² - 4x)
f(x) = 3x ³ + 2x ² - 4x - 7
A random sample of 21 desktop PCs is selected. The mean life span is 6.8 years with a standard deviation of 2.4 years. Construct a 95% confidence interval for the mean life span of all desktop PCs. Assume that the life spans of all desktop PCs are approximately normally distributed (a) (5.85, 7.75) (b) (1.68, 3.12) (c) (5.60, 8.00) (d) (5.71, 7.89) (e) (5.77, 7.83)
Answer:
(d) (5.71, 7.89)
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 21 - 1 = 20
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 20 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.086
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.086\frac{2.4}{\sqrt{21}} = 1.09[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 6.8 - 1.09 = 5.71 years
The upper end of the interval is the sample mean added to M. So it is 6.8 + 1.09 = 7.89 years
So the confidence interval is (5.71, 7.89), and the correct answer is given by option b.
help i got to pee!!!!!!!!!!!!1
Answer:
23s - 7
Step-by-step explanation:
17s - 10 + 6s + 3
=23s - 7
Answer:
[tex]23s-7[/tex]
Step-by-step explanation:
Given:
[tex]17s-10+3(2s+1)[/tex]
Distribute the parenthesis
[tex]17s-10+6s+3[/tex]
Combine like terms
[tex]23s-7[/tex]
Hope this helps
+
= 1
Which ellipse has a major axis that is vertical?
A (x + 1)2 (y + 12)2
20
6
8 3x2 + 7y2 - 21 = 0
© An ellipse with foci (0, 15) and (0, -15) and co-vertices (4,0).and (-4, 0)
An ellipse with vertices (0, 4) and (30, 4) and co-vertices (15, 3) and (15,5)
Answer:
Step-by-step explanation:Bó tay
