Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 21 cups of coffee, using 294 ounces of coffee, while collecting a total of $24.35. How many cups of each size did Kyle fill?
Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ 20-oz cup(s).
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 symmetry does y= -x^2-2x have? x-axis symmetry, y-axis symmetry, origin symmetry, or no symmetry?
Answer:
Step-by-step explanation:
The curve is symmetric about x = 1
so does not qualify for y-axis symmetry, nor the others.
NO LINKS!! Stat whether A and B are independent or dependent. Part 2
Answer:
Step-by-step explanation:
A). "If you do not study and fail the next test"
Two statements are combined in the given statement.
"If you don't study" and "fail the next test"
Second statement is the consequence of the first statement.
Therefore, events are dependent.
B). If you select a card from a deck and without replacing it, you select another card.
Here, selection of a card from a deck without replacing it doesn't affects the selection of another card.
Therefore, both the events are independent.
d. Pic
d. Z-a
PART II. ACTIVITIES
. Encircle the letter of the correct answer.
1. It contains two related data. It has horizontal axis and vertical axis.
a. Pie Graph
b. Bar Graph c. Line Graph
2. What do you call the horizontal axis of the line graph?
a. w-axis
b. x-axis
c. y-axis
3. What do you call the vertical axis of the line graph?
a. w-axis
b. x-axis
c. y-axis
4. Which of the following is not a step in making line graph?
a. Put a title on the line graph.
b. Connect the points with a line.
Draw the line for the x-axis and the z-axis.
d. Plot the points that correspond to each variable in the table,
5. It is shown just above the table or a line graph.
b. body
d. z-a
a, title
c. table
d. n
3. Directions: Study the line graph below. Encircle the letter of the corr
slope of (0,45) (6,33) (15,15)
Answer:
The slope is -2
Step-by-step explanation:
Given
[tex](x_1,y_1) = (0,45)[/tex]
[tex](x_2,y_2) = (6,33)[/tex]
[tex](x_2,y_3) = (15,15)[/tex]
Required
The slope (m)
Slope is calculated as:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{33 -45}{6 - 0}[/tex]
[tex]m = \frac{-12}{6}[/tex]
[tex]m =-2[/tex]
Sam is collecting pennies. On the first day of the month, Sam is given 11 pennies. Each day after that he gets 7 more pennies. Which of the following equations defines how many pennies he has after the nth day?
Answer:
he would have 74 pennies i think
Step-by-step explanation:
he already has 11 pennies on the first day and each day after he gets 7 more. so putting that into a equation,specifically y=mx+b, the equation would be y=7x+11. since there are 9 days after that,9 would replace the x value. so you would plug 9 in making the new equation y=7×9+11. all u do now is solve, 7×9 is 63,then plus 11 is 74
HELP ON NUMBER 2 PLEASE
c
step by step explanation
hope this helps
Answer:
its C
Step-by-step explanation:
if u need some explanation just ask
Factor completely, then place the factors in the proper location on the grid. a8 - 12a4 + 36
Answer:
[tex]{ \tt{ {a}^{8} - {12a}^{4} + 36}} \\ = { \tt{ {a}^{4} ( {a}^{2} - 12) + 36 }} \\ = ( {a}^{2} - 12)( {a}^{4} + 36) \\ [/tex]
A box with a square base and open top must have a volume of 256000 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base.
Answer:
Follows are the response to the given question:
Step-by-step explanation:
The volume of the box:
[tex]V = x\times x \times h = 256000 \ cm^3\\\\\to x^2 \times h = 256000\\\\\to h = \frac{256000}{x^2}[/tex]
The surface area of the open box is:
[tex]A(x) = x \times x + 2 \times (x \times h +x \times h)\\\\A(x) = x^2 + 4 \times x \times h\\\\A(x) = x^2 + \frac{1024000}{x}\\\\\frac{d(x^n)}{dx} = n \times x^{(n - 1)}\\\\[/tex]
Use above formula
[tex]A'(x) = 2 \times x - \frac{1024000}{x^2}\\\\[/tex]
[tex]A'(x) = 0\\\\2\times x - \frac{1024000}{x^2} = 0\\\\2x = \frac{1024000}{x^2}\\\\x^3 = 512000\\\\x = (512000)^{(\frac{1}{3})} = 80\ cm\\\\[/tex]
Now
[tex]A''(x) = 2\times 1 + 2\times \frac{1024000}{x^3}\\\\A''(x) = 2 + \frac{2048000}{x^3}\\\\x = 80 \ cm\\\\A''(80) = 2 + \frac{2048000}{80^3} = 6\\\\[/tex]
therefore [tex]A"(x) > 0,[/tex] x amount of material used in minimum.
[tex]h = \frac{256000}{80^2} = 40\ cm[/tex]
A group of campers is going to occupy 6 campsites at a campground. There are 16 campsites from which to choose. In how many ways can the campsites be chosen?
Answer:
The campsites can be chosen in 5,765,760 different ways.
Step-by-step explanation:
Given that a group of campers is going to occupy 6 campsites at a campground, and there are 16 campsites from which to choose, to determine in how many ways the campsites can be chosen, the following calculation must be performed:
16 x 15 x 14 x 13 x 12 x 11 = X
240 x 182 x 132 = X
240 x 24,024 = X
5,765,760 = X
Therefore, the campsites can be chosen in 5,765,760 different ways.
Pls answer will mark as brainliest
Answer:
[tex]\theta = 64.8^o[/tex]
Step-by-step explanation:
Given
[tex]h = 500m[/tex] --- altitude
[tex]x = 235m[/tex] --- horizontal distance
Required
The angle of elevation [tex]\theta[/tex]
The question is illustrated with the attached image.
From the attachment,
[tex]\tan(\theta) = \frac{h}{x}[/tex]
This gives:
[tex]\tan(\theta) = \frac{500m}{235m}[/tex]
[tex]\tan(\theta) = 2.128[/tex]
Take arctan of both sides
[tex]\theta = \tan^{-1}(2.128)[/tex]
[tex]\theta = 64.8^o[/tex]
Which function of x has a y-intercept of -3?
Answer:
C. y = 2x - 3
Step-by-step explanation:
you look at the number without the x. and the minus three means it's negative. But if it's a plus three then it's positive
Fill in the y values of the t–table for the function y = RootIndex 3 StartRoot x EndRoot
x y
−8
−1
0
1
8
Answer:
the answer will - 16
Step-by-step explanation:
because 8 minus 1 is 7 and plus 0 is also 7 then you have add 1 means you have to plus 1 and then their will be 8 and then plus another 8 and the answer will be minus 16
The y values of the table for the function will be -2, -1, 0, 1, and 2.
How to depict the values?The given function is y = 3✓x. Therefore, for x = -8, y = 3✓-8 = -2. For x = -2, y will be = 3✓-1 = -1.
For x = 0, y = 3✓0 = 0. When x = 1, y = 3✓1 = 1 and lastly when x = 8, y = 3✓8 = 2.
In conclusion, the y values of the table for the function will be -2, -1, 0, 1, and 2.
Learn more about t tables on:
https://brainly.com/question/12488423
Select the correct answer. What is the value of this expression when g= -3.5? 8-[2g-5]
Answer:
20
Step-by-step explanation:
2g = -3.5x2 = -7
-7 - 5= -12
8 - -12=20
(8+2)-5=???????????????????
Find an equation for a line with slope of 3/4 passing through (2, -3)
Answer:
y=3/4x-9/2
Step-by-step explanation:
en un bolillero hay 10 bolitas iguales numeradas del 0 al 9 ¿cual es el espacio muestral?
WILL GIVE BRAINLIEST IF CORRECT
Answer:
The second answer.
Step-by-step explanation:
Tim is correct. Absolute value is just the distance away from 0. In this case, both P and Q are 3/8 away from zero, even though they have opposite signs. In fact, opposites signs of the same number will always have the same absolute value because they are the same distance from 0.
So, it is the second one.
Hope this helps!
Answer:
2nd answer choice:
Tim, because each point is 3/8 unit away from 0
Step-by-step explanation:
The absolute value of a number is how far it is from 0 in the number line, not including direction.
On this number line, point P is -3/8 and point Q is 3/8.
In the number line, count how many units each point is away from 0. You will find that they each have a distance of 3/8 from the number line. Therefore they have the same absolute values.
PS: absolute values are NEVER negative.
Hope this helps!
When we expand (2x + 1/2)^6, what is the coefficient on the x^4 term?
Answer: The coefficient before x^4 is 60
Step-by-step explanation:
Hey! So I am not an expert at this, but you have to use the binomial theorem
I have attached of the Pascals Triangle (one shows the row numbering as well)
Basically in a pascal triangle, you add the two numbers above it to get the next number below
As you can see, the rows start from 0 instead of 1
The 6th row contains the numbers 1, 6, 15, 20, 15, 6, 1 which would be the coefficient terms
NOTE: the exponents always add to 6, the first term starts at 6 and decrease it's exponent by 1 each time (6, 5, 4, 3, 2, 1, 0) and the second term increases it's exponent by 1 each time (0, 1, 2, 3, 4, 5, 6)
Using this information the third term from the sixth row (15) would be where it is x^4 (I have circled it on the second image)
It would be 15 × 2^4 × (1/2)^2 = 60
The reason why it is 2^4 and (1/2)^2 is because the third term has the exponents 4 and 2 (bolded on the NOTE) which means that the first term must be put to the power of 4 and the second term must be put to the 2nd power
Sorry for the lousy explanation. I really hope this makes sense! Let me know if this helped :)
xác định m để 3 vector sau đây phụ thuộc tuyến tính
u=(m+1,1,m+1),v=(1,1,1),u(2,0,m+2
0
Answer:
i dont know hahaha
Step-by-step explanation:
soryy
The absolute value of -7
Answer:
7
Step-by-step explanation:
|-7| means find the distance from 0
We take the non negative value
|-7| = 7
10) y=p+ar
Find y when p=-5,q=3 and r=-7.
y
Write p in terms of q, r and y.
So for this problem what I did was I divided 210 (the total number of calories) / 10 (calories from the fat). The total came out to be 21 but the answer is incorrect. How would I go about solving this problem?
For percentages, we divide the part by the whole. In this case, the part is the number of calories from fat and the whole is the total number of calories.
10 / 210 = 0.0476 = 4.76%
Then, we need to round to the nearest tenth.
The answer is 4.8%
Hope this helps!
solve for surface area
formula for cube:
SA = 2 (s times s) + (4s) ( H)
system of equations amanda bought 9 shirts for a total of 69$ Tee shirts cost 7$ and long sleeve shirts cost 8$ how many of each type did she buy
9514 1404 393
Answer:
6 shirts at $83 shirts at $7Step-by-step explanation:
Let x and y represent the numbers of $8 and $7 shirts, respectively. Your system of equations can be written ...
x + y = 9
8x +7y = 69
Subtracting 7 times the first equation from the second gives ...
(8x +7y) -7(x +y) = (69) -7(9)
x = 6
Then y is ...
y = 9 -x = 9 -6 = 3
Amanda bought 6 tees costing $8 and 3 tees costing $7.
0=5x+3 solve equation
5x+3=0
5x=–3
x=–3/5
x=– 0.6
Answer:
x = -3/5
Step-by-step explanation:
0 = 5x + 3
shift 3 to left hand side . when u are shifting 3 to other side it becomes negative
0 - 3 = 5x
-3 = 5x (5x means 5*x)
now shift 5 to left hand side . multiplication changes to division when u shift.
-3/5 = x
The length of a rectangle is eight more than double the width. If the perimeter is 130 inches, find the
dimensions.
Answer:
The length is 46 inches and the width is 19 inches
Step-by-step explanation:
Let w represent the width.
The length of the rectangle can be represented by 2w + 8, since it is eight more than double the width.
Use the perimeter formula, p = 2l + 2w. Plug in 130 as the perimeter and 2w + 8 as l, then solve for w:
p = 2l + 2w
130 = 2(2w + 8) + 2w
130 = 4w + 16 + 2w
130 = 6w + 16
114 = 6w
19 = w
So, the width is 19 inches. Plug in 19 as w into 2w + 8 to find the length:
2w + 8
2(19) + 8
38 + 8
= 46
The length is 46 inches and the width is 19 inches
find the value of x to the nearest tenth
Answer:
cosine 44 = 6 / x
x = 6 / cosine 44
x = 6 / 0.71934
x = 8.34097
Step-by-step explanation:
Right angle Trigonometry, please help me solve (find the angle ) and explain!
Answer:
<A = 41.41
Step-by-step explanation:
You want angle A. Call it theta.
AC is the adjacent side. It is the side that is NOT the Hypotenuse.
The Hypotenuses is the longest side in a right triangle.
Cos-1 (Adjacent Side / Hypotenuse ) = theta
Adjacent side = 6
Hypotenuse = 8
Cos-1(6 / 8) = theta
theta = Cos-1(0.75)
theta = 41.41 rounded.
Pls I’m confusedddddddddddd
Answer:
[tex]{ \bf{area = \pi {r}^{2} }} \\ { \tt{ = 3.14 \times {( {3.82}) }^{2} }} \\ { \tt{ = 45.8 \: {m}^{2} }}[/tex]