Answers
Answer:
You have 120 bottles of Cola and 120 bottles of Sprite.
You can exchange 3 empty Cola bottles for a new bottle of Sprite.
You can exchange 4 empty Sprite bottles for a new bottle of Cola.
You can borrow empty bottles, but must return them in the end.
What is the maximal number of bottles of drink that you can drink? Prove the optimality of your result.
As this is a puzzle, please give short and clever answers rather than tedious bruteforce calculations.
Related Questions
The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?
(–∞, –7)
(–∞, –1)
(–∞, 1)
(–∞, 7)
Answers
Answer:
(−∞,−1) interval is is the function decreasing..Step-by-step explanation:
Given : The graph of f(x) = |x|f(x)=∣x∣ is transformed to g(x) = |x+1|-7g(x)=∣x+1∣−7To find : On which interval is the function decreasing?Solution :First we plot the graph of both the functions, The graph of f(x) = |x|f(x)=∣x∣ is shown with black line.The graph of g(x) = |x+1|-7g(x)=∣x+1∣−7 is shown with violet line. The graph shows the interval over which it is increasing or decreasing.As we notice it is increasing on the interval (-1,\infty)(−1,∞)Decreasing on (-\infty,-1)(−∞,−1)Therefore, (-\infty,-1)(−∞,−1) interval is the function decreasing. please markse as brainliests please for my effort...The function [tex]g(x) =|x + 1| - 7[/tex] decreases at interval [tex](-\infty, -1)[/tex]
The parent function is given as:
[tex]f(x) =|x|[/tex]
The transformed function is given as:
[tex]g(x) =|x + 1| - 7[/tex]
Both functions are absolute value functions, and an absolute value function is represented as:
[tex]y=a| x-h |+k[/tex]
Where, the vertex of the function is:
[tex]Vertex = (h,k)[/tex]
By comparing [tex]y=a| x-h |+k[/tex] and [tex]g(x) =|x + 1| - 7[/tex], we have:
[tex](h,k) = (-1,-7)[/tex]
[tex]a= 1[/tex]
Because (a) has a positive value (i.e. 1) and (h) is negative, then the vertex represents a minimum.
This also means that, the function will decrease from infinity, till it gets to the x-coordinate of the vertex.
Hence, the function [tex]g(x) =|x + 1| - 7[/tex] decreases at interval [tex](-\infty, -1)[/tex]
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Who can do 20 assignments in math for me rn needs to b finish in 5 hours?
Answers
u need to finish 4 assignments in 1 hour
What is the height h of the garage roof?
Answers
Explanation:
Use Pythagorean theorem which is a^2 + b^2=c^2
30/2=15
15^2+b^2=17^2
225 +b^2= 289
289-225=64; b^2=64
8^2=64
b=missing side=8
h=8
Carson has a smart phone data plan that costs $35 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Carson have to pay in a month where he used 3 GB over the limit? How much would Carson have to pay in a month where he used went over by x GB?
Answers
Answer:
3 GB over: $80 x GB over: $35+$15x
Step-by-step explanation:
First, 3 GB over is 3 times 15 plus 35, which equals 80. x GB over is x times 15 plus 35, hence the answer. Hope this helps!
For using 3GB of data more, she'll be charged $80.
a. Amount charged per month = $35
Amount charged for over-usage = $15 per gb.
Therefore, when she uses 3gb more, the amount charged will be:
= $35 + ($15 × 3)
= $35 + $45.
= $80
When she uses x gb more, the amount that she'll be charged will be:
= $35 + ($15 × x)
= $35 + 15x
= 35 + 15x
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A phone company charges each customer a monthly fee of $11.25. In addition, it charges $0.03 per minute for in-state calls and $0.11 per minute for out-of-state calls. What is the total monthly charge for a customer who made 340 minutes of in-state calls and 84 minutes of out-of-state calls?
Answers
340 x 0.03 = 10.2 (in state)
84 x 0.11 = 9.24 (out of state)
10.2 + 9.24 + 11.25
= $30.69 monthly charge
hope it helps :)
The total monthly charge for a customer is given as $30.69.
What is simplification?Simplifying allows us to test each process and strategy to determine which is the most efficient and best suited for its specific goal.
here,
A phone provider costs each customer $11.25 per month. Furthermore, it charges $0.03 per minute for in-state calls and $0.11 for out-of-state calls.
Charge within the boundary of state for 340 minutes = 340 x 0.03 = 10.2
Charge beyond the boundary of state for 84 minutes = 84 x 0.11 = 9.24
Total monthly charge = 10.2 + 9.24 + 11.25
= $30.69 monthly charge
Thus, A customer's total monthly price is shown as $30.69.
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Find the missing side
Answers
Answer:
x = 14
[tex]h^2 = p^2 + b^2\\h^2 = 7^2 + 12^2\\x^2 = 49 + 144\\x^2 = 193\\so, x = 13.89\\so, x = 14[/tex]
4 of 204 of 20 Questions
Question 4
What is the equation of the line that is parallel to y−5=−13(x+2) and passes through the point (6,−1)?
Answers
Answer:
y= -13x+77
Step-by-step explanation:
Parallel lines do not share any points but have the same slope.
First, put the equation y-5=-13(x+2) into slope-intercept form.
y= -13x-21
Slope= -13x
Y-Intercept= (0,-21)
Now that we know the slope...
y-(-1)=-13(x-6)
becomes
y+1=-13x+78
y-1=-13x+78-1
y=-13x+77
Emma earns a $39,000 salary in the first year of her career. Each year, she gets a 5% raise. How much does Emma earn in total in the first 11 years of her career?
Answers
Answer:
554,000
Step-by-step explanation:
that is the answer
Emma earns $554,064.80 in total in the first 11 years of her career
We are to determine the future value of $39,000 each year for 11 years given the growth rate of 5%
The formula for calculating future value:
FV = P (1 + r)^n
Where :
FV = Future value
P = Present value
R = interest rate
N = number of years
First year = $39,000
Second year = 39,000 x (1.05) = $40,950
Third year = 39,000 x (1.05)^2 = $42,997.50
Fourth year = 39,000 x (1.05)^3 = $45,147.38
Fifth year = 39,000 x (1.05)^4 = $47,404.75
Sixth year = 39,000 x (1.05)^5 = $49,774.99
seventh year = 39,000 x (1.05)^6 = $52,263.74
eighth year = 39,000 x (1.05)^7 = $54,876.93
ninth year = 39,000 x (1.05)^8 = $57,620.78
tenth year = 39,000 x (1.05)^9 = $60,501.82
eleventh year = 39,000 x (1.05)^10 = $63,526.91
Sum of the earnings for the first eleven years = $554,064.80
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Simplify the complex number √-16+8.
Answers
Answer:
[tex]\sqrt{-16} +8[/tex]
[tex]=4i+8[/tex]
OAmalOHopeO
Use the function below to find F(-4).
F(x) = 2^x
Answers
Answer:
Step-by-step explanation:
F(x)=2^x
[tex]F(-2)=2^{-2} =\frac{1}{2^2} =\frac{1}{4}[/tex]
Can someone explain
Answers
Answer:
You need to use sohcahtoa to find your answer.
first you gotta identify what sides of the triangle you have.
You're missing the hypotenuse, and you have the value of the adjacent.
since you have the adjacent and need the hypotenuse, you're going to use cosine to find x
cos(65) = 16/x
x = 37.859
Answer:
x = 37.85
this is a standard "trig" question
it requires two pieces of insight.
First that a triangle has 180° interior angles.
from that you can determine that the third angle is 25° because
90 + 65 + β = 180
the red symbol lets you know that it is 90°
the second think that will help is SOHCAHTOA
that is if you have a "right triangle" (one with a 90° angle)
in this problem (in your mind rotate the triangle so the 65° is at the bottom left and the two long sides are pointing up
in this case you have the 16 on the bottom (adjacent to the angle) and
the x is on the hypotenuse...
you have the A& H that is COS
thus you have cos(65) = [tex]\frac{16}{x}[/tex]
x = 37.85
Step-by-step explanation:
4[30-(10-2)x3] what is the answer?
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{4[30-(10-2)\times3]}}[/tex]
[tex]\huge\boxed{\rightarrow\mathsf{4[30 - (\bold{8}}) \times3]}[/tex]
[tex]\huge\boxed{\rightarrow \mathsf{4[30 - \bf 24]}}[/tex]
[tex]\huge\boxed{\rightarrow \mathsf{4(30) + 4(-24)}}[/tex]
[tex]\huge\boxed{\rightarrow \mathsf{\bf 120 - 96}}}[/tex]
[tex]\huge\boxed{\rightarrow\mathsf{\bf 24}}[/tex]
[tex]\huge\boxed{\rm{Answer: \mathsf{24}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
24Step-by-step explanation:
4[30 - (10 - 2)*3] = 4[30 - 8*3] =4[30 - 24] = 4*6 = 24(a) Write
[tex] {2}^{5} \div {2}^{5} [/tex]
as a single power if 2.
Answers
Answer:
2^0
Step-by-step explanation:
When you are dividing 2 exponents with the same base (in this case, 2) you subtract them. 2^5 ➗ 2^5 => 2^(5-5) = 2^0 => which is equal to 1, but the answer here would be 2^0.
There are two ways to go about this problem.
The first way, the generic way, is to know that,
[tex]\frac{a^n}{a^m}=a^{n-m},a\neq0[/tex].
So,
[tex]\frac{2^5}{2^5}=2^{5-5}=\boxed{2^0}[/tex].
The second way is to realise that both numerator and denominator are equal and when diving two equal numbers you obtain 1. (except when diving zeros) aka,
[tex]\frac{a}{a}=1, a\neq0[/tex]
And 1 equals to any number raised to the power of zero,
[tex]a^0=1,a\neq0[/tex]
So we just have to say that the 1 we got is rewritten as some base to the power of zero.
Since our base needs to be 2, we just simply say,
[tex]2^0[/tex].
Et Viola.
Hope this helps.
answer please it's urgent
Answers
Answer:
HOPE IT HELP YOU . Plz tell me if it is write or wrong .
If is added to a number and the sum is 8 multiplied by 2, the answer is What is the number? 3
Answers
Answer:
Let the number be x
Given that
⇒(x+
3
2
)×2=
3
16
⇒x+
3
2
=
3
8
⇒x=
3
8
−
3
2
⇒x=
3
6
⇒x=2
Thus the number is 2
Let f(x)=1/2|x−2|. Write a function g whose graph is a translation 7 units to the left of the graph of f.
Answers
Answer:
g(x) = -2(x - 6) - 7
Step-by-step explanation:
Sorry if I'm wrong
Please help I don’t understand math
Answers
Answer:
x = 12
Step-by-step explanation:
The sum of the two smaller angles is 140
80+5x = 140
Subtract 80 from each side
80+5x-80 =140-80
5x = 60
Divide each side by 5
5x/5 = 60/5
x = 12
Question
If a 45°-45°-90° triangle has a hypotenuse length of 72, what is the length of each leg of the triangle?
Select the correct answer.
O 7V2
O 7
O V2
O 2
Answers
Answer: B
Step-by-step explanation:
We are given that a 45-45-90 triangle has a hypotenuse of [tex]7\sqrt{2}[/tex].
In a 45-45-90 triangle, the legs are congruent. Therefore we can use the Pythagorean Theorem to solve.
[tex]a^2+a^2=(7\sqrt{2})^{2}[/tex] [combine like terms]
[tex]2a^2=(7\sqrt{2})^2[/tex] [square root both sides]
[tex]a\sqrt{2} =7\sqrt{2}[/tex] [divide both sides by root 2]
[tex]a=7[/tex]
Now, we know that a leg is length 7, which is B.
Which function can be used to find r, the total amount the teacher pays in dollars when
z scissors are ordered?
A teacher is ordering scissors for her classroom.
• the teacher pays a one-time fee of $8.
• the teacher also pays $2 for each pair of scissors ordered.
Answers
To find the total, 2 times the number of scissors plus 8 for delivery
All of the following statements are true, except for which?
A. LIZM
B. FG = JK
C. ZJE ZF
D. LMHG
Answers
except for letter a. LIZM
What is the area of polygon ABCDEFGHI in the coordinate plane from the figure below?
Answers
Which linear inequality is represented by the graph?
Answers
Answer:
D
Step-by-step explanation:
The correct answer is D
Answer:
D
Step-by-step explanation:
y<2/3 x-1 is the answer
EVALUATE: 10x – 2y3 (if x = 5 and y = 2)
Answers
Answer:
10*(5) - 2*(2)^3
= 50 - 2*8
= 50 - 16
=34
Answer:
Step-by-step explanation:
với x=5 và y=2
phương trinh trở th a
10* 5 - 2 * 2^ 3
=50 - 2*8
=50 - 16
=34
Geometry homework I need help pls pls pls
Answers
Answer:
vertex of 4 is 2
Step-by-step explanation:
cuh cuh uchuch uch uch uch
If a = 4 -√15, find a^4 + 1/a^4
Please answer this question with correct steps. I will mark brainliest
Answers
Answer:
Hello,
3842
Step-by-step explanation:
[tex]a=4-\sqrt{15} \\\\\dfrac{1}{a} =\dfrac{1}{4-\sqrt{15}} \\\\=\dfrac{4+\sqrt{15}}{(4-\sqrt{15})*(4+\sqrt{15})}\\\\=\dfrac{4+\sqrt{15}}{16-15} \\\\=4+\sqrt{15}\\\\[/tex]
[tex]a+\dfrac{1}{a} =4-\sqrt{15}+4+\sqrt{15}=8\\\\[/tex]
[tex](a+\dfrac{1}{a} )^2=a^2+\dfrac{1}{a^2} +2\\\\a^2+\dfrac{1}{a^2} =8^2-2=62\\[/tex]
[tex](a+\dfrac{1}{a} )^3=a^3+\dfrac{1}{a^3} +3*\dfrac{a^2}{a} +3*\dfrac{a}{a^2} \\\\8^3=a^3+\dfrac{1}{a^3} +3(a+\dfrac{1}{a} )\\\\a^3+\dfrac{1}{a^3} =8^3-3*8=488\\[/tex]
[tex](a+\dfrac{1}{a} )^4=a^4+\dfrac{1}{a^4} +4*\dfrac{a^3}{a} +6*\dfrac{a^2}{a^2} +4*\dfrac{a}{a^3}\\\\a^4+\dfrac{1}{a^4}=(a+\dfrac{1}{a} )^4-4*a^2-4*\dfrac{1}{a^2} -6\\a^4+\dfrac{1}{a^4} =8^4-4*62-6\\\\=4096-248-6\\\\=3842\\\boxed{a^4+\dfrac{1}{a^4} =3842}\\[/tex]
Using a calculator:
[tex]a=4-\sqrt{15}=0,1270166537925831148207346002176....\\\\a^4= 2,6028112122495108436170792979303e-4\\\\\dfrac{1}{a} =4+\sqrt{15} =7,8729833462074168851792653997824...\\\\\dfrac{1}{a^4}=3841,9997397188787750489156382921....\\\\a^4+\dfrac{1}{a^4} \\\\= 2,6028112122495108436170792979303e-4+3841,9997397188787750489156382921....\\\\=3842\\[/tex]
How to solve this plsssss
Answers
Answer:
Hope this helps you
Answered by G a u t h m a t h
Which will result in a difference of squares?
a
(negative 7 x + 4)(negative 7 x + 4)
b
(negative 7 x + 4)(7 x minus 4)
c
(negative 7 x + 4)(negative 7 x minus 4)
d
(negative 7 x + 4)(4 minus 7 x)
Answers
Answer:
C
Step-by-step explanation:
The correct answer is C, love from Gauthmath
Answer:
the correct answer is option C
Step-by-step explanation:
(negative 7 x + 4)(negative 7 x minus 4)
Find the lateral surface area of the
following prism:
5 cm
5 cm
-apothem = 3.44 cm
5 cm
5 cm
10 cm
5 cm
Answers
Answer:
250 cm²
Step-by-step explanation:
Lateral area of the prism is,
5×10×5
= 250 cm²
Lateral surface area of the given prism is equals to [tex]250cm^{2}[/tex].
What is lateral surface area?" Lateral surface area is defined as the sum of area of the all the surfaces except top and bottom of the given geometrical shape."
Formula used
Lateral surface area of pentagonal prism [tex]=5ah[/tex]
[tex]a=[/tex] edge length of the base
[tex]h=[/tex] height of the prism
According to the question,
For the given pentagonal prism,
Edge length of the base [tex]'a' = 5cm[/tex]
Height of the prism [tex]'h' = 10cm[/tex]
Substitute the value in the formula of lateral surface area we get,
Lateral surface area of pentagonal prism [tex]= 5 \times 5\times 10[/tex]
[tex]= 250cm^{2}[/tex]
Hence, lateral surface area of the given prism is equals to [tex]250cm^{2}[/tex].
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What is the quadratic regression equation that fits these data?
Number of seconds Helght (In feet)
0
12
1
14
2
15
3
14
4
10
5
6
O A. y=-1.94x2 + 0.62x+ 9.62
B. y = -3.69x2 + 2.08x+8.07
O C. y = 15.68(0.88)
O D. y=-0.89x2 + 3.24x+11.93
SUBMIT
Answers
Answer:
Step-by-step explanation:
The answer is D. Use the Stat and then Edit button on your TI calculator to edit the values in L1 and L2 tables. In L1 enter 0, 1, 2, 3, 4, 5 and then arrow over and enter the y values into L2 the same way. Enter the number 12, then hit enter; enter the number 14, hit enter; enter the number 15 and then hit enter, etc. Do the same for the values that are going into L1.
When that is done, hit the Stat button again and arrow down to QuadReg and hit enter. Depending upon your calculator, you may have to arrow down to "calculate" or the calculator may display the equation immediately after hitting QuadReg. Again, it all depends upon your calculator.
The required correct quadratic regression equation that fits the given data is y = -0.89x² + 3.24x+11.93. Option D is correct.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
To find the quadratic regression equation, we need to use a calculator or software that can perform a quadratic regression analysis. Using such a tool, we obtain the following equation:
y = -0.89x² + 3.24x+11.93
This equation fits the data points (0, 12), (1, 14), (2, 15), (3, 14), (4, 10), and (5, 6) with a high degree of accuracy.
The equation is in the form of a quadratic function, which has a parabolic shape when graphed. The coefficient of the x² term (-0.89) indicates that the parabola is downward-facing, while the other coefficients determine the exact shape and position of the parabola.
Option A is incorrect because its equation does not fit the data points accurately. Option B is also incorrect because it is not a quadratic equation, and option C is incorrect because its equation also does not fit the data points accurately.
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May anyone help me with this
Answers
Answer:
Step-by-step explanation:
y=3(x−3)^2+75
Answer:
(x - 3)² = - 25
Step-by-step explanation:
Given
- 3x² = - 18x + 102 ( add 18x to both sides )
- 3x² + 18x = 102 ( divide through by - 3 )
x² - 6x = - 34
To complete the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(- 3)x + 9 = - 34 + 9
(x - 3)² = - 25
