If the total cost before tax was $11.5, then the cost of each bottle of juice j= $1.6 which can be found by the equation 5j + $3.50 = $11.50.
The cost of each bottle can be determined by using an algebraic expression.
An algebraic expression can be defined as the use of both numerals and letters in a mathematical equation.
To find the cost of each bottle, an algebraic expression can be given as,
Cost of a 5-pack of juice bottles + Cost of popcorn = Total cost before tax
5j + $3.50 = $11.50
Solving for j,
5j = 11.50 - 3.50
5j = 8
j = 8/5
j = $1.6
Hence, the cost of each bottle from a 5-pack of juice bottles is calculated to be $1.6
To learn more about algebraic expressions, click here:
https://brainly.com/question/4344214
#SPJ4
Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute. How many liters of water are in Tank A after the following amounts of time have passed?
4 minutes
80 seconds
minutes
How many minutes have passed, , when Tank A contains the following amounts of water?
151 liters
191.5 liters
270.25 liters
liters
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. How many liters of water remain in the tank after the following amounts of time?
30 seconds
7 minutes
minutes
For how many minutes, , has the water been draining when Tank B contains the following amounts of water?
75 liters
32.5 liters
18 liters
liters
1)
In this question, we have been given Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.
1 minute = 9 liters
⇒ 60 seconds = 9 liters
⇒ 20 seconds = 3 liters
We need to find the amount of water in the tank A
a) when 4 minutes
Given that, 1 minute = 9 liters
Let y1 liters of water in the tank A after 4 minutes
So, we get an equation,
y1 = 9 × 4
y1 = 36 liters
36 + 124 (initial water level) = 160 liters
Hence, 160 liters of water in the tank A after 4 minutes been passed.
b) when 80 seconds
From given information, 20 seconds = 3 liters
Let y2 liters of water in the tank A after 80 seconds
So, we get an equation,
20 (y2) = 3 × 80
y2 = 12 liters
12 + 124 (initial water level) = 136 liters
Hence, 136 liters of water in the tank A after 80 seconds been passed.
Now we need to find the amount of time passed when Tank A contains the following amounts of water.
i) 151 liters
151 - 124 = 27 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t1 be the required time.
so, we get an equation,
9 × t1 = 1 × 27
t1 = 27 / 9
t1 = 3 minutes
This means, 3 minutes have passed when Tank A contains 151 liters of water.
ii) 191.5 liters
191.5 - 124 = 67.5 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t2 be the required time.
so, we get an equation,
9 × t2 = 1 × 67.5
t2 = 67.5 / 9
t2 = 7.5 minutes
t2 = 7 minutes 30 seconds
This means, 7 minutes 30 seconds have passed when Tank A contains 191.5 liters of water.
iii) 270.25 liters
270.25 - 124 = 146.25 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t1 be the required time.
so, we get an equation,
9 × t1 = 1 × 146.25
t3 = 146.25 / 9
t3 = 16.25 minutes
t3 = 16 minutes 15 seconds
This means, 16 minutes 15 seconds have passed when Tank A contains 270.25 liters of water.
----------------------------------------------------------------------------------------------------
2)
In this question, Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute.
⇒ 1 minute = 2.5 liters of water drained
⇒ 60 seconds = 2.5 liters
⇒ 10 seconds = 0.42 liters
We need to find the amount of water drained from tank B
a) after 30 seconds
Let x1 be the amount of water drained after 30 seconds
Given that, 1 minute = 2.5 liters
So, we get an equation.
10 (x1) = 30 × 0.42
x1 = 3 × 0.42
x1 = 1.26 liters
b) after 7 minutes
Let x2 be the amount of water drained after 30 seconds
Given that, 1 minute = 2.5 liters
So, we get an equation.
x2 = 7 × 2.5
x2 = 17.5 liters
Now, we need to find the time in which the water is draining when Tank B contains
i) 75 liters
80 - 75 = 5 liters of more water drained.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t1 be the required time.
so, we get an equation,
2.5 × t2 = 5
t1 = 5 / 2.5
t1 = 2 minutes
This means, after 2 minutes Tank B contains 5 liters of water.
ii) 32.5 liters
80 - 32.5 = 47.5 liters of more water drained.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t2 be the required time.
so, we get an equation,
2.5 × t2 = 47.5
t2 = 47.5 / 2.5
t2 = 19 minutes
This means, after 19 minutes Tank B contains 32.5 liters of water.
iii) 18 liters
80 - 18 = 62 liters of more water filled.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t3 be the required time.
so, we get an equation,
2.5 × t3 = 62
t3 = 5 / 2.5
t3 = 24.8 minutes
t3 = 24 minutes 48 seconds
This means, after 24 minutes 48 seconds Tank B contains 18 liters of water.
Learn more about an equation here:
https://brainly.com/question/649785
#SPJ1
What transformations of the graph of (x)=|x| are applied to graph the function g?
The function g(x) = - |x| + 2 is the result of applying a reflection about the x-axis and a translation 2 units up.
What transformation must be applied to modify the absolute value function?
In this problem we find a resulting expression, that is, the function g(x) = - |x| + 2. This is the result of a sequence of rigid transformations done on the parent absolute value function, that is, the function f(x) = |x|. Rigid transformations are transformations applied on functions such that Euclidean distance is conserved in the entire function.
After a quick inspection, we find that two rigid transformations were used in the following order:
Reflection around the x-axis.Translation 2 units up.Now we proceed prove this procedure:
f(x) = |x|
Step 1
f'(x) = - |x|
Step 2
g(x) = - |x| + 2
To learn more on rigid transformations: https://brainly.com/question/28004150
#SPJ1
Sal is selling two types of printed socks.he sells type a at r45 a pair.he sells type b at r30 if he sold 16 pairs in total,and had a total income of r585,how many pairs of sock did sal sell
Sal sold 7 pairs of type a socks and 9 pairs of type b socks
Let the number of type a socks sold by Sal be x
Let the number of type b socks sold by Sal be y
The selling price of type a socks = 45
The selling price of type b socks = 30
Total pairs sold = 16
Total income = 585
Therefore, the equations will be
x + y = 16-------(1)
45x + 30y = 585--------(2)
Multiplying equation (1) by 30 we get
30x + 30y = 480 ------(3)
Equating equations (2) and (3) we get,
15x = 105
x = 7
Putting x = 7 in (1) we get
y = 9
Sal sold 7 pairs of type a socks and 9 pairs of type b socks
Learn more about linear equations:
https://brainly.com/question/19549098
#SPJ4
Three consecutive even integers such that the sum of the smallest integer and twice the middle integer is 20 more than the largest integer. What is the largest integer?
14 is the largest integer.
Let x, x+2 & x+4 be the 3 integers.
x + 2 (x+2)= (x+4)+20
x + 2x + 4 = x + 4 + 20
3x + 4 = x + 24
3x - x = 24 - 4
2x = 20
x = 20/2
x=10 for the smallest integer.
10 + 2 = 12 for the middle integer.
10 + 4 = 14 for the largest integer.
To learn more about this; visit: https://brainly.com/question/4986038
#SPJ9
Given that 12q x + 16p + 10p = 192x + 312. Find the values of p and q
Answer:
p = 12, q = 16,
Step-by-step explanation:
On a coordinate plane, a parabola with equation f (x) = squared minus 4 x + 2 opens up. It goes through (0, 2), has a vertex at (2, negative 2), and goes through (4, 2).
Consider the function shown. How can you restrict the domain so that f(x) has an inverse? What is the equation of the inverse function?
x > –2; f Superscript negative 1 Baseline (x) = 2 minus StartRoot x + 4 EndRoot
x > –2; f Superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot
x > 2; f Superscript negative 1 Baseline (x) = 2 minus StartRoot x + 4 EndRoot
x > 2; f Superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot
The domain at which the function f(x) = x² - 4•x + 2, and the inverse of the function, f(x), is given by the option;
x > 2; [tex] f^{-1}(x) = 2 + \sqrt{x + 2} [/tex]How can the inverse function and the domain of the inverse function be found?The given function is f(x) = x² - 4•x + 2.
The points through which the parabola passes are;
(0, 2)(2, -2), which is the vertex(4, 2)The inverse of the function is found as follows;
f(x) = x² - 4•x + 2
The standard form of a quadratic equation is f(x) = a•(x - h)² + k
Where;
(h, k) = The coordinates of the vertex
a = The coefficient of x²
Comparing, we have;
(h, k) = (2, -2)
a = 1
Which gives;
f(x) = x² - 4•x + 2 = (x - 2)² - 2
f(x) = (x - 2)² - 2
Let f(x) = y
y = (x - 2)² - 2
y + 2 = (x - 2)²
x - 2 = √(y + 2)
x = √(y + 2) + 2 = 2 + √(y + 2)
x = 2 + √(y + 2)
Therefore, f(x) has an inverse when y > -2, which gives;
The domain where f(x) has an inverse is x > 2, given that the expression, 2 + √(y + 2), is always positive.
The inverse of the function is obtained by changing x to [tex] f^{-1}(x) [/tex] and y to x in the equation, x = 2 + √(y + 2), to give;
[tex] f^{-1}(x) = \mathbf{2 + \sqrt{x + 2}} [/tex]The correct option is therefore;
x > 2, f superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot
Learn more about writing quadratic equations in standard form here:
https://brainly.com/question/24628957
#SPJ1
Answer:
Its D.x > 2; f Superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot
Step-by-step explanation:
Mr. drew wants to build a square sandbox with an area of 64 square feet. what is the total length of wood mr. drew needs to make the sides of the​ sandbox?
Mr. Drew needs woods of a total length of 32 feet to make the sides of the sandbox.
What do we mean by square shape?A square is a regular quadrilateral in Euclidean geometry, which means it has four equal sides and 4 equal angles (90-degree angles, /2-radian angles, or right angles). It can also be described as a rectangle with two adjacent sides of equal length. It is the only frequent polygon with internal, central, and external angles that are all equal (90°) and diagonals that are all identical in length. ▢ABCD denotes a square with vertices ABCD.So,
A square with an area of 64ft² has sides that are √64 = 8 ft long.Because there are four of them, the perimeter is 8 × 4 feet = 32 feet.Therefore, Mr. Drew needs woods of a total length of 32 feet to make the sides of the sandbox.
Know more about squares here:
https://brainly.com/question/25092270
#SPJ4
whats 4x5x6x32x4x4x4x4
Answer:
983,040
Step-by-step explanation:
4×5=20
6×32=192
4×4=16
4×4=16
20×192×16×16
=983,040
A 6 inch personal pizza has 610 calories, with 240 of those from fat. A 16 inch pizza is cut into 8 slices. Estimate the number of calories in one slice of a 16 inch pizza.
Answer:
203 1/3 calories
Step-by-step explanation:
I make a proportion for inches of pizza to calories
[tex]\frac{6}{610}[/tex] = [tex]\frac{16}{x}[/tex] I know that a 6 inch pizza has 610 calories, so I am trying to figure out how many calories are in a 16 inch pizza.
I can cross multiply to get
6x = (16)(610)
6x = 9760 Divide both sides by 6
x = 1626 [tex]\frac{2}{3}[/tex] This is how many calories are in a whole pizza. Now I want to know how many calories are in 1 slice. I would take this number and divide by 8.
1626 2/3 as an improper fraction would be
[tex]\frac{4880}{3}[/tex] ÷ 8 Which is the same as
[tex]\frac{4880}{3}[/tex] x [tex]\frac{1}{8}[/tex] =[tex]\frac{4880}{24}[/tex]=203 [tex]\frac{1}{3}[/tex]
Rewrite (4^7)^3 using a single exponent
Answer:
[tex]4^{21}[/tex]
Step-by-step explanation:
7 * 3 = 21
Add it as the exponent.
Which is the order from least to greatest of the following: four thirds, 0.8, one fifth, thirty percent?
four thirds, 0.8, one fifth, thirty percent
thirty percent, four thirds, 0.8, one fifth
one fifth, four thirds, thirty percent, 0.8
one fifth, thirty percent, 0.8, four thirds
The order from least to greatest of the numbers will be D. one fifth, thirty percent, 0.8, four thirds.
How to calculate the value?It should be noted that 1/5 = 0.2
It should be noted that 30% = 0.3
It should be noted that 4/3 = 1.33
Therefore the order from least to greatest of the numbers will be one fifth, thirty percent, 0.8, four thirds
In conclusion, the correct option is D.
Learn more about percentages on:
brainly.com/question/24877689
#SPJ1
the function f(x) is shown. the function g(x)= 2x - 6 compare slopes
Answer: The slope of f(x) is less than the slope of g(x) because the slope of f(x) is -3
Step-by-step explanation:
Define slope?
The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
We can write:
m=(y2-y1) / (x2-x1)
If,
g(x) = 2x - 6
The slope of g(x), m = 2
Let, x1=0
y1=2
x2=-1
Y2=1
So, we take (x1, y1) and (x2, y2) Then consider (0, 2) and (-1, 1)
Solve it:
Replace with x1, y1 and x2, y2
m = [1-(-2)/(-1)]
m=[(1+2) /(-1) ]
m=3/(-1)
m=-3
Thus, the slope of f(x) is less than the slope of g(x) because the slope of f(x) is -3.
Learn more about area here https://brainly.com/question/12353670
#SPJ9
Better taxi service charges $3.00 for the first mile plus $0.20 for each additional mile. Best
taxi service charges $6.00 for the first two miles plus $0.10 for each additional mile. How
many miles will a person travel in order to spend an equal amount of money using either
service?
30 miles will a person travel in order to spend an equal amount of money using either service.
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given:
Better taxi service charges $3.00 for the first mile plus $0.20 for each additional mile.
Best taxi service charges $6.00 for the first two miles plus $0.10 for each additional mile.
So, if equal amount of money spends on both services
3+0.2x = 3(2)+0.1x
3 +0.2x = 6 +0.1x
0.2x - 0.1x = 6-3
0.1x = 3
x = 30 miles
Hence, 30 miles will a person travel in order to spend an equal amount of money using either service.
Learn more about algebra here:
https://brainly.com/question/13715639
#SPJ1
Natalie is paid for writing numbers on pages of a book. She is paid for writing each digit of the number. If she wrote 702 digits, how many pages is the book?
Answer:
I think 1,000??
25 points plus brainliest
Answer:
-(4/3) is ans by using slope formula
. The expression 3x+1 is equal to 9 for a certain value of x. Which of the following is the value of the
expression 12x+4 for the same value of x?
(1) 18
(3) 36
(2) 28
(4) 112
Answer:
(3) 36
Step-by-step explanation:
3x + 1 = 9
Minus 1 from both sides.
3x = 8
Divide both sides by 3.
x = 2 2/3
Plug it in.
12 (2 2/3) + 4
32 + 4
36
Solve 3.78 + (−13.2). anyone know the answer :,)
Answer:
-9.42
Step-by-step explanation:
Are the compositions of f(x) = 1 and g(x) = 2 commutative? Why or why not?
They are commutative, because f(x) and g(x) are constant functions.
They are commutative, because f(g(x)) and g(f(x) are constant functions.
They are not commutative, because f(x) and g(x) are not equal.
They are not commutative, because f(g(x)) and g(f(x) are not equal.
Answer:
first option
Step-by-step explanation:
They are cumulative because they are constant functions.
Is the following relation a function? Justify your answer.
Yes, because each output value has only one input value
Yes because each input value has only one output value
No, because there is an input value with more than one output value
No, because there is an output value with more than one input value
Answer:
No, because there is an output value with more than one input value.
Step-by-step explanation:
If you are using the same function equation, than you should not get the same output if you use two different inputs.
The sum of 5 times a number m and 12 is equal to 27
The value of m is 3
How to calculate the value of m ?The expression can be written as follows
The sum of 5 times a number m and 12 is equal to 27
5m + 12 = 27
collect the like terms
5m= 27-12
5m= 15
Divide both sides by the coefficient of m which is 5
5m/5 = 15/5
m= 3
Hence the value of m is 3
Read more on expression here
https://brainly.com/question/11960892?referrer=searchResults
#SPJ1
Information from the records of conundrum company for september was as follows: sales $307,500 selling and administrative expenses 52,500 direct materials used 66,000 direct labor 75,000 variable factory overhead 50,000 factory overhead 51,250 inventories sept. 1 sept 30 direct materials $ 8,000 $10,500 work in process 18,750 21,000 finished goods 17,250 14,250 conundrum company produced 20,000 units. the prime costs per unit (rounded to the nearest cent) for september were
The prime costs per unit (rounded to the nearest cent) for September were $7.05 per unit.
What is the total cost?In economics, total cost is the sum of all costs a company incurs in generating a certain output level.
It is typically expressed as the sum of all fixed costs (for example, the costs of a building lease and heavy machinery) that do not vary with the amount of output produced and all variable costs (the costs of labour & of raw materials).The concept of total cost is used to describe average cost (the total cost divided by the amount of units produced) and marginal cost (the marginal cost of a provided unit of output is the increase in total cost required to produce that unit).Now, as per the question;
Prime cost = (cost of direct material + cost of direct labour)/number of units.
Cost of direct materials used = $66,000
Cost of direct labour = $75,000
Number of units = 20,000
Substituting the values;
= ($66,000 + $75,000) / 20,000 units
= $141,000 / 20,000 units
= $7.05 per unit
Thus, the prime cost per unit in September is found to be $7.05 per unit.
To know more about the total cost, here
https://brainly.com/question/24314569
#SPJ4
The cost per unit of an item is called what?
Answer:
The cost per unit of an item is called unit cost
help because i paay 30 a month 4 thisssd
Answer:
2c+2
The number that will go in the green box is 2.
Step-by-step explanation:
3c-1-c+3
Combine the like terms.
3c-1-c+3=2c+2
Hope this helps!
Please mark as brainliest if correct!
Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin(x) at the point 6 , 1 .
[1/2, sqrt(3)/2] and [-1/2, -sqrt(3)/2] are the unit vectors that are parallel to the tangent line to the curve.
Explain what a unit vector is?
A quantity with both magnitude and direction is referred to as a vector. A unit vector is one with a magnitude of 1. It also goes by the name Direction Vector.y=2sin(x)
dy/dx equals 2 cos x at pi/6 for x.
pi/6 = 2 cos pi/6 = 2 sqrt(3)/2 = sqrt = dy/dx(pi/6) (3)
the line sqrt(3) (x-pi/6) is the tangent to y at pi/6.
Atan Theta = sqrt is the angle with the x axis (3)
θ = pi/3 radians at 60 degrees
the vectors of units at (pi/6,1) [cos(60), sin(60)] and [-cos(60), -sin(60)] are parallel to this line.
[1/2, sqrt(3)/2] as well as [-1/2, -sqrt(3)/2]
Learn more about unit vector
brainly.com/question/14291312
#SPJ4
If the price of an apple is $0.50, the marginal utility per dollar spent on the fifth apple is: ________
a) 20
b) 30
c) 40
The marginal utility per dollar spent on the fifth apple is 60. The correct option is D.
What is marginal utility?The marginal utility simply refers to the change or extra satisfaction derived from the change in consumption.
Hence, the marginal utility of the fifth apple equals :
Difference /change or extra satisfaction derived by consuming one more than 4 apples = (total utility of 5th apple - total utility of 4th apple)
= (250 - 220) = 30
Hence, marginal utility per dollar: Marginal utility/price per apple
Price per apple = $0.5
Marginal utility of 5th apple = 30
Marginal utility of 5th apple = 30 / 0.5
Marginal utility of 5th apple = 60
Therefore, the marginal utility per dollar spent on the fifth apple is 60. The correct option is D.
Complete question :
If the price of an apple is $0.50, the marginal utility per dollar spent for the fifth apple is:
a) 20
b) 30
c) 40
d) 60
Number of apples ____total utility
2__________________130
3__________________180
4__________________220
5__________________250
6__________________270
7__________________280
To know more about marginal utility follow
https://brainly.com/question/15050855
#SPJ4
4 (c) The high mountains of the world
Find a vector function r(t), that represents the curve of intersection of the two surfaces. the cylinder x2 y2=36 and the surface z=4xy
Given:
[tex]\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}[/tex]
Express 16 as [tex]4^{2}[/tex]: [tex]x^2+y^2=16[/tex]
[tex]x^2+y^2=4^2\\x^2+y^2=4^2 \times 1[/tex]
Trignometry,
[tex]\cos ^2(t)+\sin ^2(t)=1[/tex]
Now, substitute [tex]\cos ^2(t)+\sin ^2(t)[/tex] for 1:
[tex]\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)[/tex]
Law of indicates:
[tex]\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2[/tex]
Taking positive square roots as follows:
[tex]x=4 \cos (t), y=4 \sin (t)[/tex]
Recall that, z = xy.
Now, we have:
[tex]\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}[/tex]
Now, substitute the values:
[tex]r(t)=x_t i+y_t j+z_t k[/tex]
So, the vector r(t) is: [tex]r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i[/tex]
Therefore, the vector function r(t) is written as: [tex]r(t)=x_t i+y_t j+z_t k[/tex]
Know more about vector functions here:
https://brainly.com/question/14895420
#SPJ4
Without random selection, we cannot appropriately apply the laws of probability to perform inference. True or false?.
Answer:
true
Step-by-step explanation:
needed to eliminate bias
What is 424.4 ÷ 8? show your work
Answer: 53.05
Step-by-step explanation: Simply divide both using the division method. Show your work as the method. (would recommend drawing out the problem)
Answer:
60.5
Step-by-step explanation:
60.5
8 424
-42
0
4.0
4.0
0
Find EFgiven E(-7, -2) and F(11, 3)
According to the given statement;
EF=18.682.
What is Distance Formula?
The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.
Distance formula used to find the distance measure between two lines, the sum of the lengths of all the sides of a polygon, perimeter of polygons on a coordinate plane, the area of polygons and many more.
According to the given value;
(-7, - 2) ; x1 = - 7 ; y1 = - 2
F = (11, 3) ; x2 = 11 ; y2 = 3
EF = √((x2 - x1)² + (y2 - y1)²)
EF = √((11 - -7)² + (3 - -2)²)
EF = √((11 + 7)² + (3 + 2)²)
EF = √(18² + 5²)
EF = √324 + 25
EF = √349
EF = 18.6815
EF = 18.682 units (3 decimal places )
To know more about Distance Formula, visit;
https://brainly.com/question/8283882
#SPJ9
