The number of sports drinks in a cooler during practice is modeled by the equation y=648-24x where y is the number of ounces in the cooler after practice and x is the number of players at the practice who take drinks from the cooler.
Part A
Based on the information in the equation, press the hotspots of three statements that are true.
Hint: 648 is the starting point.
-24 is the slope (rate of change).
Answers
The answers are:
B. Before practice, there are 648 ounces of sports drink in the cooler.
C. Each plater drinks approximately 24 ounces of sports drink at practice.
E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice.
Why?We are given the equation:
[tex]y=f(x)=648-24x[/tex]
Let's discard each of the given options in order to find the three correct options.
A. The cooler is meant to be used only by 24 players: False.
If we want to calculate how many players can use the cooler, we need to isolate "x" (rate of change) from the given equation, so, isolating we have:
[tex]f(x)=648-24x[/tex]
[tex]0=648-24x[/tex]
[tex]648=24x\\\\24x=648\\\\x=\frac{648}{24}=27[/tex]
We have that the cooler can be used by 27 players, so, the first option that states that "The cooler is meant to be used only by 24 players" is false.
B. Before practice, there are 648 ounces of sports drink in the cooler: True.
We have that before the practice when the cooler is not being used by any player (or there is no any player) has 648 ounces (full), we can calculate it making the variable "x" equal to 0, so, calculating we have:
[tex]f(x)=648-24x[/tex]
[tex]f(0)=648-24*(0)=648[/tex]
Therefore, we have that the statement "Before practice, there are 648 ounces of sports drink in the cooler." is true.
C. Each plater drinks approximately 24 ounces of sports drink at practice: True.
From the statement, we know that the rate of change is equal to (-24), and it's equal to the number of ounces that each player drinks.
Hence, we have that the statement "Each plater drinks approximately 24 ounces of sports drink at practice." is true.
D. If 24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink: False.
If we want to calculate the number of ounces that 24 players will drink, we need to use the slope value. If we know that each player drinks 24 ounces, so, to calculate how many ounces of sports drink will 24 players drink, we need to use the following equation:
[tex]DrankOunces=24oz*Players\\\\DrankOunces=24oz*24=576oz[/tex]
We have that 24 players will drink a total of 576 ounces, so, the statement "If 24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink." is false.
E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice: True.
From the statement and the equation, we know that the slope (rate of change) is negative, meaning that for each player (x) it will be 24 fewer ounces of sports drink after practice, for example, calculating for 1 and 2 players, we have:
[tex]f(1)=648-24*1=624[/tex]
[tex]f(x)=648-24*2=600[/tex]
We can see that for each player, it will be 24 fewer ounces of sports drink after practice.
Hence, we have that the statement "For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice." is true.
Therefore, the correct options are:
B. Before practice, there are 648 ounces of sports drink in the cooler.
C. Each plater drinks approximately 24 ounces of sports drink at practice.
E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice.
Have a nice day!
Related Questions
what is the solution to this equation?
x/5=-20
Answers
Answer:
-100
Step-by-step explanation:
Answer:
-100
Step-by-step explanation:
You need to multiply
-20 x 5= -100
Hope this helped please mark me the brainliest answer? Have a good day :)
A lifeguard at a swimming pool gives one-hour swim lessons to children in the morning before the pool is open to the public. She earns four dollars per class and fifty cents per swimmer. The minimum wage in her state is $7.25. She hopes to earn more than that amount of money during each class. Write an inequality that models the situation and find the minimum number of students she must teach in each class so that her earnings for that hour exceeds the minimum wage in her state.
Answers
Answer:
brainliest ps :)
Step-by-step explanation:
her wage is $4.00 + s*0.5 so 7.25-4> s*.5== 3.25 > s*.5 == 6.5 > s
The inequality for the given information can be written as 6.5 > s.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
A lifeguard at a swimming pool gives one-hour swim lessons to children in the morning before the pool is open to the public. She earns four dollars per class and fifty cents per swimmer. The minimum wage in her state is $7.25.
The inequality can be written as:-
$4.00 + ( s x 0.5 )
7.25-4 > ( s x 0.5 )
3.25 > ( s x 0.5 )
6.5 > s
To know more about inequality follow
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Which is the solution of the quadratic equation (4y – 3)2 = 72?
Answers
Answer:
y = 9.75
Step-by-step explanation:
(4y - 3)2 = 72
Opening the brackets;
8y - 6 = 72
8y = 72 + 6 = 78
y = 78 ÷ 8 = 9.75
Answer:
[tex]y = \frac{3+6\sqrt{2}}{4}\text{ and } y = \frac{3-6\sqrt{2}}{4}[/tex]
Step-by-step explanation:
Given quadratic equation,
[tex](4y-3)^2=72[/tex]
[tex]\implies 4y - 3 = \pm \sqrt{72}[/tex] ( Taking root on both sides )
[tex]4y=3 \pm 6\sqrt{2}[/tex] ( Additive property of equality ),
[tex]y = \frac{3 \pm 6\sqrt{2}}{4}[/tex] ( Division property of equality )
[tex]\implies y = \frac{3+6\sqrt{2}}{4}\text{ or }y =\frac{3-6\sqrt{2}}{4}[/tex]
Hence, the solution of the given equation is,
[tex]\implies y = \frac{3+6\sqrt{2}}{4}\text{ and }y =\frac{3-6\sqrt{2}}{4}[/tex]
could anyone help me? I will mark you as brain liest who ever helps me!
Answers
Answer:
1)163.28 (3.14*52)
2)13ft 6in (163.28/12)
3)129 times
4) 31 times
Step-by-step explanation:
1) multiply 52 times pie(3.14)
2)divide 163.28(your total) by 12
3) 1760 divided by 52
4) 1760 divided by 56.52
this is for the other 2 ones
Find the value of X
Answers
Answer:
C. 66
Step-by-step explanation:
32 + x =98
The sum of interior angles of a triangle add up to the exterior opposite angle;
solving for x yields;
x = 98 - 32
x = 66 degrees
Answer:
x = 66°
Step-by-step explanation:
Since DAC is a straight line, the angles must add up to 180° and 98° is given so the missing angles is 180° - 98° = 82°
Angles in a triangle add up 180° and 32° and 82° are given →
x + 32° + 82° = 180°
x + 114° = 180°
x = 66°
The scatter plot shows the study times and test scores for a number of students. How long did the person who scored 81 study?
Answers
Answer: Option A
50 minutes
Step-by-step explanation:
Observe in the diagram that the vertical axis represents the score obtained and the horizontal axis represents the study time.
To find out how many hours the person with a score of 81 studied, locate the point that is at a vertical distance of 81.
Now draw a vertical line from this point to the horizontal axis. Note that the vertical line traced intercepts the vertical axis at x= 50
Then the person who got a score of 81 studied 50 minutes
The answer is the option A
Andy and Jacob work as technicians in a laboratory where gemstones are tested and certified. Andy has already tested 30 gemstones and continues testing at a rate of 30 gemstones per hour. Jacob has already tested 40 gemstones and continues testing at a rate of 25 gemstones per hour. Which function can Andy and Jacob use to determine the total number of gemstones they have tested after x hours? How many gemstones will they have tested after 5 hours? A. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 10. Thus, they will have tested 285 gemstones in 5 hours. B. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 70x + 55. Thus, they will have tested 405 gemstones in 5 hours. C. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 70. Thus, they will have tested 345 gemstones in 5 hours. D. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 60x + 65. Thus, they will have tested 365 gemstones in 5 hours.
Answers
Answer:
Option C is correct.
Step-by-step explanation:
Andy tested gemstones already = 30
Jacob tested gemstones already = 40
Total gemstones tested by Andy and Jacob already = 30+40 = 70
Andy continue to test gemstones per hour = 30
Jacob continue to test gemstones per hour = 25
Total gemstones tested by Andy and Jacob per hour = 30 +25 = 55
The total number of gemstones tested by Andy and Jacob after x hours will be: 55x
So, the equation will be: f(x) = 55x + 70
After 5 hours i.e. x =5
f(5) = 55(5) + 70
f(5) = 275 + 70
f(5) = 345
Andy and Jacob will have tested 345 gemstones in 5 hours.
So, Option C is correct.
A picture that measures 8 cm by 6 cm is to be surrounded by a mat. The mat is to
be surrounded by a mat. The mat is to be the same widt
all sides of the picture. The combined area of the mat and the picture is double the arca
What is the width of the mat to the nearest tenth? Include a diagram. (5)
Answers
Answer:
1.4 inches
Step-by-step explanation:
The picture is a rectangle 8 cm by 6 cm. The area of a rectangle is length * width. The area of the picture is 8 cm * 6 cm = 48 cm^2
After the mat is applied, the area doubles, so the new area will be 2 * 48 cm^2 = 96 cm^2.
Let the width of the mat be x. The mat has the same width all around the rectangular picture, so it adds x on each side of the length and x on each side of the width.
old length: 8
new length: 2x + 8
old width: 6
new width: 2x + 6
Area of the new rectangle with mat = new length * new width
area = (2x + 8)(2x + 6)
The new area is 96, so that give us an equation.
(2x + 8)(2x + 6) = 96
Use FOIL on the left side:
4x^2 + 12x + 16x + 48 = 96
Combine like terms, and subtract 96 from both sides:
4x^2 + 28x - 48 = 0
Divide both sides by 4:
x^2 + 7x - 12 = 0
To factor the trinomial, we need two numbers that add to 7 and multiply to -12. There are no such numbers, so we need to use the quadratic formula.
x = [-b +/- sqrt(b^2 - 4ac)]/(2a)
x = [-7 +/- sqrt(7^2 - 4(1)(-12)]/[2(1)]
x = [-7 +/- sqrt(49 + 48)]/2
x = [-7 +/- sqrt(97)]/2
x = 1.4 or x = -8.4
Since the mat cannot have a negative width, the negative solution is discarded.
Answer: The width of the mat is 1.4 inches.
The graphs below have the same shape. f(x) = x^2 what is the equation of the graph of g(x)?
Answers
Answer:
A. [tex]g(x)=(x-4)^2[/tex]
Step-by-step explanation:
The graph of [tex]f(x)=x^2[/tex] is transformed to obtain the graph of g(x).
We can see from the diagram that, f(x) is shifted 4 units to the right to obtain the graph of g(x).
Therefore [tex]g(x)=f(x-4)[/tex].
Hence the equation of g(x) is
[tex]g(x)=(x-4)^2[/tex]
The correct answer is A.
The equation of the graph of g(x) is g(x) = (x - 4)²
How to determine the equationFrom the graph shown, we can see that the f(x) = x² as shown is shifted 4 units to the right to obtain the graph of g(x).
Then, we have that this shift can be achieved by replacing x in the equation of f(x) with x - 4 to represent the horizontal shift.
We have the equation of the graph of g(x), to be;
g(x) = (x - 4)²
This equation represents a horizontal shift of the graph of f(x) by by 4 units to the right, as g(x) remains the same shape f(x) but is shifted horizontally to the right by 4 units.
Learn about graphs at: https://brainly.com/question/19040584
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What is the standard deviation of the following data set rounded to the nearest tenth?
30, 26, 28, 32, 28, 30
Answers
Answer:
Standard Deviation is: 2.09762 or rounded to nearest tenth is 2.1
Step-by-step explanation:
If ABC and GEF are congruent, the value of x is and the value of y is
Answers
Answer:
The value of x is 10, and the value of y is 6
Step-by-step explanation:
ABC and GEF are congruent
so
x - 8 = 2
x = 10
x - y = 4
10 - y = 4
y = 10 - 4
y = 6
Answer
x = 10, y = 6
Answer:
x = 10 and y = 6
Step-by-step explanation:
In the given figure ΔABC and ΔGEF are congruent which means all the corresponding sides of the given triangles should be congruent.
So measure of AC = mfg
x - 8 = 2
x = 2 + 8
x = 10
Similarly mBC = mEF
x - y = 4
10 - y = 4
y = 10 - 4 = 6
Therefore, answer are x = 10 and y = 6
Write the expression as a single logarithm 4 log x-6 log (x+2)
Answers
Final answer:
To combine the expression 4 log x - 6 log (x+2) into a single logarithm, we use the exponentiation and division rules for logarithms to obtain log((x^4)/(x+2)^6).
Explanation:
To write the expression 4 log x - 6 log (x+2) as a single logarithm, we can apply log rules.
The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: log(x^n) = n log x.
The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log xy = log x + log y.
The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: log(x/y) = log x - log y.
Using these rules, we can
rewrite the given expression:
4 log x - 6 log (x+2) can be rewritten as log(x^4) - log((x+2)^6), which simplifies to log((x^4)/(x+2)^6) according to the division rule for logarithms.
The expression [tex]4 log x - 6 log (x+2)[/tex] can be simplified as a single logarithm by using the logarithm properties of exponents and division, resulting in [tex]log(x^4 / (x+2)^6).[/tex]
Explanation:The student is asking to write the expression [tex]4 log x - 6 log (x+2)[/tex] as a single logarithm. To do this, we recall two important properties of logarithms:
The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: [tex]log(a^n) = n log a.[/tex]The logarithm of the division of two numbers is the difference between the logarithms of the two numbers: [tex]log(a/b) = log a - log b.[/tex]Using these properties, we can rewrite the expression:
First, apply the exponent property: 4 log x becomes log(x^4), and 6 log (x+2) becomes log((x+2)^6).Next, apply the division property:[tex]log(x^4) - log((x+2)^6)[/tex] becomes [tex]log(x^4 / (x+2)^6).[/tex]
Therefore, the expression [tex]4 log x - 6 log (x+2)[/tex] written as a single logarithm is[tex]log(x^4 / (x+2)^6).[/tex]
Two video games, Star Chasers and Song Hero, had the same average price over a 10-month period. During that time, the price of Song Hero showed greater variability. If Song Hero was priced between $35 and $49 during the 10-month period, which statement is most likely true about price of Star Chasers during that time?
The highest price and the lowest price of the game differ by more than $14.
The highest price and the lowest price of the game differ by less than $14.
The mean price was more than $42.
The mean price was less than $42.
Answers
Answer:
The answer would be B. The highest price and the lowest price of the game differ by less than $14. Hope this helps!
B. The highest price and the lowest price of the game differ by less than $14.
Step-by-step explanation:Given is that the the price of Song Hero showed greater variability. This means their prices are more varied in range.
If Song Hero was priced between $35 and $49 during the 10-month period, This means the variability of Star chasers is less than [tex]49-35=$14[/tex]
Since, $14 is Song Hero’s range, the range for Star chasers should be less.
Therefore, option B is correct.
What linear equation represents the graph of the line that coincides with the y-axis?
a. x =0
b. y = 0
c. x =3
Answers
Answer:
Option b. y = 0
Step-by-step explanation:
we know that
The slope of the line that coincides with the y-axis is equal to zero (horizontal line) and the equation is equal to
y=0
The graph of the function f(x)=6/x-3 is shown below. What is the vertical asymptote of the function
Answers
Answer:
The vertical asymptote is [tex]x=3[/tex]
Step-by-step explanation:
we know that
The vertical asymptote is the value of x that makes the denominator equal to zero:
In this problem we have
[tex]f(x)=\frac{6}{x-3}[/tex]
[tex]x-3=0[/tex]
Solve for x:
[tex]x-3+3=0+3[/tex]
[tex]x=3[/tex]
The vertical asymptote is [tex]x=3[/tex]
see the attached figure to better understand the problem
Write a function describing the relationship of the given variables.
V
varies directly with the square of
t
and when
t
=
6
,
V
=
108
V
=
Answers
Answer:
The function describing the relationship of V and t is V = 3t²
Step-by-step explanation:
* Lets explain the meaning of direct variation
- The direct variation is a mathematical relationship between two
variables that can be expressed by an equation in which one
variable is equal to a constant times the other
- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the
constant of variation
* Now lets solve the problem
# V is varies directly with the square of t
- Change the statement above to a mathematical relation
∴ V ∝ t²
- Chang the relation to a function by using a constant k
∴ V = kt²
- To find the value of the constant of variation k substitute V and t
by the given values
∵ t = 6 when V = 108
∵ V = kt²
∴ 108 = k(6)² ⇒ simplify the power 2
∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k
∴ 3 = k
- The value of the constant of variation is 3
∴ The function describing the relationship of V and t is V = 3t²
What is the area of the kite
Answers
Answer:
The area of the kite is 60 square feet
Step-by-step explanation:
The area of a kite is given as half multiplied by the product of the diagonals.
The longer diagonal measures 30 feet.
The shorter diagonal measures 4 feet.
The area of the kite is; [tex]\frac{1}{2}*30*4=60[/tex]
ANSWER
The area of the kite is 60 square feet
EXPLANATION
The area of a kite is half times the product of the diagonals.
The longer diagonal is 10+20=30 feet.
The shorter diagonal is 2+2 =4 feet.
The area of this kite
[tex] = \frac{1}{2} \times 30 \times 4[/tex]
This simplifies to,
[tex] = 60 {ft}^{2} [/tex]
Therefore the area of the kite is 60 square feet
Question 3 answer please
Answers
Answer:
34.48
Step-by-step explanation:
Use PEMDAS
12.98-(7.6÷19)+22
12.98-0.4+22
12.48+22
34.48
Answer:
34.480000000000000000000000
Step-by-step explanation:
find the conplex conjugate of z1 of z1=i+4
Answers
Answer:
- i + 4
Step-by-step explanation:
Given a complex number a + bi then the complex conjugate is a - bi
Note the real part remains unchanged while the sign of the imaginary part is negated.
Hence conjugate of i + 4 = - i + 4
How do I solve this?
A football punted upward has a trajectory given by the equation y = 48x − 16x2, where y represents the football's height x seconds after it has been kicked. What is the maximum height, in feet, attained by the ball?
Giving brainliest + 30 points
Answers
The maximum happens at x = -b/2a
x = -48/2(-16) = 3/2
Now replace x in the equation and solve for y:
y = 48(3/2) - 16(3/2)^2
y = -72 - 36
y = 36
The maximum height is 36 feet.
Kate is painting a ceramic paperweight shaped like a rectangular prism, as shown here. (dimensions of .8 ft , 1.2 ft, 1.2 ft)She wants to find the surface area of the paperweight so she can determine how much paint she needs.
The area of one of the bases is _____
The area of each lateral rectangular face is _____
The surface area of the paperweight is _____
Answers
Answer:
The area of one of the bases is 0.96 ft²
The area of each lateral rectangular face is 4.8 ft²
The surface area of the paperweight is 6.72 ft²
Step-by-step explanation:
we know that
The surface area of the rectangular prism is equal to
SA=2B+LA
where
B is the area of one of the bases
LA is the lateral area of the prism
Find the area of one of the bases B
B=(0.8)(1.2)=0.96 ft²
Find the lateral area LA
The lateral area is the area of each lateral rectangular face
LA=2[(0.8)(1.2)]+2[(1.2)(1.2)]=4.8 ft²
Find the surface area
SA=2(0.96)+4.8=6.72 ft²
Answer: 1.44, 0.96, and then 6.72.
Step-by-step explanation:
the person who answered first is wrong.
3. Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches.
(a) Without using your calculator, approximate the decimal equivalent of each number to the nearest
tenth
(b) Order the ribbon sizes from least to greatest.
tromont
Answers
Answer:
a. 2,2,3,3
b. 1.7 2.2 pi= 3.14 3.4= 2,2,3,3
Step-by-step explanation:
Maggie spent $46.20 to by pencil sharpeners for her gift shop. If each pencil sharpener cost 60 cents how many pencil sharpeners did she buy
Answers
Answer:
Maggie bought 77 pencil sharpeners
$46.20 divided by .60 = 77
Step-by-step explanation:
46.20÷0.60= 77
Maggie can buy 77 pencil sharpeners is she would like
Please, please, pppllleeeeaassssee
Mark Brainlyest
Michael earned 50.43 in 6.15 hours. how much did he earn in an hour?
Answers
Answer: $8.2
Step-by-step explanation:
Answer:
8.2 dollars an hour is the answer
Step-by-step explanation:
50.43 divided by 6.15 is 8.2
1. Complementary Angeles
2. Angel1-37
What is angel 4
3
Angel 1-40
What is angel 5
Answers
Answer:
1. D ∠4 and ∠5
2. C 37°
3. A 50°
Step-by-step explanation:
1. Complementary angles are those that add up to 90°.
From the diagram you can see that angles 4 and 5 together form right angle, so angles 4 and 5 are complementary.
2. Angles 1 and 4 are vertical angles. Vertical angles have the same measure, so
∠4=∠1=37°
3. From 1,
∠4+∠5=90°
From 2
∠1=∠4
Since ∠1=40°, then ∠4=40°
So,
∠5=90°-40°=50°
Help ASAP WILL MARK BRAINLIEST THANK YOU!
Answers
Answer:
D
Step-by-step explanation:
half of the miles he drove yesterday is (42/2) and +5 because he said five more than half.
hope this helps and is correct!
Answer:
○ D. (42 ÷ 2) + 5
Step-by-step explanation:
Five more than half tells it all. He 42 miles on Monday, then drove 5 more than half:
(42 ÷ 2) + 5
Half means you either multiply by ½, or divide by 2.
I am joyous to assist you anytime.
Find the specific solution of the differential equation dy/dx= 4y/x^2 with condition y(-4)=1
A. y=-1-4/x
B. y=-e^1/x
C.y=e^(-4/x)
D. None of these
Answers
This ODE is separable:
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4y}{x^2}\implies\dfrac{\mathrm dy}y=\dfrac4{x^2}\,\mathrm dx[/tex]
Integrating both sides gives
[tex]\ln|y|=-\dfrac4x+C[/tex]
Given the initial condition [tex]y(-4)=1[/tex] we find
[tex]\ln|1|=-\dfrac4{-4}+C\implies C=-1[/tex]
so that the particular solution is
[tex]\ln|y|=-\dfrac4x-1[/tex]
[tex]\implies y=e^{-(1+4/x)})[/tex]
so the answer is D.
What type of number is [tex]\sqrt{13}[/tex]
Choose all answers that apply:
(Choice A)
A
Whole number
(Choice B)
B
Integer
(Choice C)
C
Rational
(Choice D)
D
Irrational
Answers
The number √{13} is an irrational number because it cannot be expressed as a ratio of two integers and is not a whole number or integer either.
The number √{13} is not a whole number, an integer, or a rational number because it cannot be expressed as a ratio of two integers. The square root of a positive number that is not a perfect square is always irrational. Therefore, the only correct choice for the type of number that represents √{13} is (Choice D) Irrational.
The distance between the two points pictured is d = Use the distance formula to find n. d = n =
Answers
Answer:
the answer is 61units
n=61
Step-by-step explanation:
I NEED HELP PLEASE!!!!!
Answers
Answer is 1)
3V= pi•h•r^2 divide both sides by (pi•h) ; 3V/pi•h = r^2; sqrt (3V/pi•h) =r