Answer:
a. $0.47 per ounce
b. $0.36 per ounce
c. the gallon size costs less per ounce
Step-by-step explanation:
A unit rate is a rate that is expressed with one unit in the denominator. That is, it is <some amount> per unit. The <some amount> value will generally depend on what unit is chosen. This problem suggests the desired unit is 1 oz of paint.
__
a.Unit cost for a quart:
ratio = cost/ounces = $14.99/(32 oz) ≈ $0.468/oz ≈ $0.47/oz
__
b.Unit cost for a gallon:
ratio = cost/ounces = $45.99/(120 oz) ≈ $0.359/oz ≈ $0.36/oz
__
c.The cost per ounce is less for the gallon size. If at least 3 quarts of paint is needed, then buying it in the gallon size will cost less.
If less than 3 quarts are needed, then a gallon container will cost more than is necessary for the paint required. The "better deal" depends on the amount of paint required.
PLS HELP QUICKLY
Which pair of functions are inverses of each other?
5
O A. f(x) = -2 and g(x) = +2
B. f(x) = 7x-2 and g(x) = 2
C. f(x) =x/5+ 6 and g(x) = 5x - y
D. f(x) = 3+ 6 and g(x) = 6x³
Answer: B
[tex]f(x) = 7x-2[/tex] and [tex]g(x) = \frac{x+2}{7}[/tex]
How to solve:
check if the composite functions of f(x) and g(x) are equal to x (this means they are inverses)
f[g(x)] = x
g[f(x)] = x
Step-by-step explanation:
Checking A.
[tex]f(x) = \frac{5}{x} -2[/tex]
[tex]g(x) = \frac{x+2}{5}[/tex]
[tex]f(g(x)) = f(\frac{x+2}{5} ) = \frac{5}{\frac{x+2}{5} } -2[/tex]
This does not equal x, so we know these are not inverses
Checking B.
[tex]f(x) = 7x-2[/tex]
[tex]g(x) = \frac{x+2}{7}[/tex]
[tex]f(g(x)) = f(\frac{x+2}{7} ) = 7(\frac{x+2}{7}) - 2 = x+2-2 = x[/tex]
[tex]g(f(x)) = g(7x-2) = \frac{7x-2 + 2}{7} = \frac{7x}{7} = x[/tex]
since both f(g(x)) = x and g(f(x)) = x, we can determine that they are inverses of each other.
Help to solve give brainliest
Answer:
(B) 32Step-by-step explanation:
equation of The line L : y = -(1/2)x + 6
A(8 , b) ∈ L then b = -(1/2)(8) +6 then b = -4 + 6 = 2
Therefore ,
A(8 , 2)
AB = 2
CD = 6
BC = 8
…………………………………………
Area of the trapezoid ABCD
= (CB÷2)×(AB + CD)
= (8÷2)×(6+2)
= 32
The length of each side of a square is 8.5 cm rounded to 1 decimal place.
Write the error interval for the perimeter, p, in the form a _< p
Answer:
make it more clear its not clear enough to understand the question
Point Q is on line segment PR . Given PQ=16 and PR=19, determine the length of QR
Answer:
QR = 3
Step-by-step explanation:
given that Q is on the segment PR , then
PQ + QR = PR ( substitute values )
16 + QR = 19 ( subtract 16 from both sides )
QR = 3
The calculated length of the segment QR is 3 units
How to determine the length of the segment QRFrom the question, we have the following parameters that can be used in our computation:
Point Q is on line segment PR
PQ = 16 and PR = 19
using the above as a guide, we have the following:
PQ + QR = PR
substitute the known values in the above equation, so, we have the following representation
16 + QR = 19
So, we have
QR = 19 - 16
Evaluate
QR = 3
Hence. the length of the segment QR is 3
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PLS HELP ASAP find the measure of side b. round to the nearest whole number
Answer:
b=204
Step-by-step explanation:
The law of sine states that: [tex]\frac{SinA}{a} =\frac{SinB}{b} =\frac{SinC}{c}[/tex]
We know that a triangle has 180° total, so we can subtract the two angle measures we know to find the third angle: [tex]180-90-41=49[/tex]°.
Using these two things, we can come up with the equality [tex]\frac{Sin90^{o} }{270} =\frac{Sin49^o}{b}[/tex], which we can use to solve for side b.
[tex]\frac{Sin90^o}{270} =\frac{1}{270}[/tex], so we know that [tex]\frac{1}{270} =\frac{Sin49^o}{b}[/tex].
Next, we would multiply both sides by b to get [tex]\frac{1}{270}b=Sin49^o[/tex].
Sin49°≈0.75471, so to find b we would multiply 0.75471×270=203.77
Since the problem asks us to round to the nearest whole number, b=204
Hope this helps! :)
A bag contains 8 red m&m's, 3 brown m&m’s, and 7 green m&m’s. Draw one m&m what’s the probability of drawing a brown m&m?
Answer:
8+3+7=18
probability of brown m&m is
[tex] \frac{3 }{18 } [/tex]
PLEASE ANSWER ASAP!!!!!!!!!!!! MUCH APPRECIATED!!
Based on the amount being deposited into the account each month, and the interest, the account will triple in value on 25 months..
When will the value of the account triple?First find the value of the account when tripled:
= 1,000 x 3
= $3,000
We can then use a spreadsheet to find the number of periods it will take to triple.
Convert the interest to a monthly figure as:
= 3.15% / 12
= 0.2625%
When you put the figures into the spreadsheet as shown, the number of months would be 25 months.
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At a sale this week,a table is being sold for $476.This is a 15% discount from the original price.
Answer:
547.40
Step-by-step explanation:
476*15%
15 percent *476
= (15/100)*476
= (15*476)/100
= 7140/100 = 71.40
71.40 + 476 = 547.40 as original price
What is the length of the line?
Answer:
5 units
Step-by-step explanation:
Use Pythagorean Theorem
x = 4 units y = 3 units
4^2 + 3^2 = L^2
16 + 9 = L^2
L = 5
Answer:
5 units
Step-by-step explanation:
By the Pythagorean theorem:
c² = a² + b²
c = length of the line
a = 4
b = 3
Then:
c² = 4² + 3²
c² = 16 + 9
c² = 25
√c² = √25
c = 5
pls help me dis is due at 3:00 pm 2day ASAP attachment above ^
|
Answer:
s=0.20p
Step-by-step explanation:
20% off an product means to subtract 20% of the original price from the original price.
What is the value of the expression below?
2[3(16+)]-8
Answer:
94Step-by-step explanation
2 * [3 * (16 + 1)] - 8 =
2 * [3 * 17] - 8 =
2 * 51 - 8
102 - 8 =
94
Solve (4x+1) - (3x-4)
Answer:
= x + 5
Step-by-step explanation:
(4x+1) - (3x-4)
= (4x+1) -3x + 4
= 4x - 3x + 1 + 4
= x + 5
hannah and andrea were selling tickets to the homecoming dance. they were set up in different
locations, and while andrea sold h number of homecoming tickets, hannah sold 3h. what
information can we gather about the relationship between how many tickets andrea sold and how
many hannah sold?
The relationship between the number of tickets is that Hannah sold three times as many tickets as Andrea.
How to determine the relationship?From the question, we have:
Andrea = h
Hannah = 3h
This means that:
Hannah = 3 * Andrea
So, the relationship is that Hannah sold three times as many tickets as Andrea.
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what is the area of the base?
EASY QUESTION Miguel plots points A, B, and C in the coordinate plane.
A. Distance between A and B is: 5 units.
B. Triangle ABC is not an equilateral triangle because only two of its sides are equal.
What is an Equilateral Triangle?An equilateral triangle has three sides that have the same length.
Given the vertices with their coordinate points as:
A (-3, 2)
B (-6, -2)
C (0, -2)
Use the distance formula, [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB, BC, and AC:
AB = √[(−6−(−3))² + (−2−2)²]
AB = √25
AB = 5 units
BC = √[(−6−0)² + (−2−(−2))²]
BC = √36
BC = 6 units
AC = √[(−3−0)² + (2−(−2))²]
AC = 25
AC = 5 units
Only two of the sides of the triangle, AB and AC, are equal. Therefore, it is not an equilateral triangle.
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Write this percentage as a fraction in its simplest form. 96 %
(pls)
Answer:
24/25
Step-by-step explanation:
96%=0.96. 96/100=48/50=24/25
help help help help help help
Answer: 95 cm³
Step-by-step explanation: To find the volume of any prism, you have to multiply the base × width × height.
In this case, this 3D shape is split into 2 parts.
The first part's dimensions are 8×5×2. So the volume is 80 cm³.
The second part's dimensions are 1×3×5. So the volume is 15 cm³.
Finally, you add both volumes together, and the final answer is 95 cm³.
In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:
(2, 1990) (5, 4225) (9, 7205)
Find the slope and y-intercept. Explain what each represents.
The slope of the line is 745, the y-intercept of the line is 500 and the equation of the line is y = 745x + 500
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]
We have points on the graph:
(2, 1990) (5, 4225) (9, 7205)
The slope can be found using two points:
[tex]\rm m =\dfrac{4225-1990}{5-2}\\[/tex]
m = 745
The line can be written as:
y = mx + c
y = 745x + c
Plug point (2, 1990)
1990 = 745x + c
1990 = 745(2) + c
c = 500
y = 745x + 500
The pace of increase in money per month is represented by the slope.
Every month, the sum increases by $745.
The initial quantity of money when the business opened is represented by the y-intercept.
The company began with a $500 investment.
Thus, the slope of the line is 745, the y-intercept of the line is 500 and the equation of the line is y = 745x + 500
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What are the correct trigonometric ratios that could be used to determine the length of ln? check all that apply. sin(20°) = startfraction l n over 8 endfraction cos(70°) = startfraction 8 over l n endfraction tan(70°) = startfraction l n over m n endfraction sin(20°) = startfraction 8 over l n endfraction cos(70°) = startfraction l n over 8 endfraction
The correct answer is option E which is Cos ( 70 ) = [tex]\dfrac{LN}{8}[/tex].
The complete question is attached with the answer below:-
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
As we can see from the figure that ∠L = 70 and ∠M = 20 We can see that the length LN will be calculated as:-
Cos 70 = Base / Hypotenuse
So for an angle of 70, the base is LN and the hypotenuse is equal to 8 units.
Cos 70 = LN = 8
Therefore the correct answer is option E which is Cos ( 70 ) = [tex]\dfrac{LN}{8}[/tex].
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Answer:
A & E
Step-by-step explanation:
Jus took it on edge
Factorise completely 12 x³y - 18 xy²
..:
[tex]12 {x}^{3} y - 18x {y}^{2} \\ [/tex]
Factor out 6xy:
[tex]\boxed{(6xy)(2 {x}^{2} - 3y)} [/tex]
(which is the maximum you could get(atleast in this problem))
find the equation of a line that is parallel to y=3x+6 and passes through A
) (0,-2) B. (2,5) C.(4,1)
Answer:
Step-by-step explanation:
We'll look for an equation with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0.
A line parallel to y=3x+6 will have the same slope, 3.
We can write y=3x+b. Any value of b can be used to generate a parallel line.
If we want that line to go through a specific point, such as (0,-2), we need to find a value of b that shifts the line so that it includes (0,-2). This can be done by using that point in the equation y=3x+b:
y=3x+b
-2=3*(0)+b for point (0,-2)
b = -2
The equation becomes y=3x-2
See the attached plot.
===========================
Do that same thing for the remaining two points.
For B: (2,5) The equation is y=3x-1
For C: (4,1) The equation is y=3x-11
Two urns contain blue and green balls. urn 1 contains 3 blue balls and 4 green balls. urn 2 contains 7 blue balls and 16 green balls.
1. if a blue ball is drawn, what is the probability that it came from urn 2?
2. if a green ball is drawn, what is the probability that it came from urn 1?
Answer: 3/20
Step-by-step explanation:
Probability of drawing a blueball from Urn I is
PI=66+4=610
Probability of drawing a blue ball from Urn II is
PII=22+6=28
Probability that both balls are blue
P=PI⋅PII=610⋅28=320
In a scale drawing, 3 inches
represents 10 miles. How many
inches represent 45 miles?
Answer:
13.5 inches
Step-by-step explanation:
3inches:10 miles
x inches: 45 miles
do cross multiply:
3*45=135
10*x=10x
so 135=10x
x=13.5 inches
What is the exact value of x
x = 6(√2)
Step 1:
Say, 6 is perpendicular and x is the hypotenuse.
Step 2:
As we know sine is the ratio of perpendicular and hypotenuse.
∴ [tex]sin 45 = \frac{perpendicular}{hypotenuse}=\frac{6}{x}[/tex] ......................................(1)
Step 3:
As we know, sin45 = 1/√2
∴ put the value in equation 1
⇒ [tex]\frac{1}{\sqrt{2}} = \frac{6}{x}[/tex]
By solving the above equation, we get,
x = 6(√2)
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Which of the following are good ideas to use when gathering your resources?
Check all that apply.
A. Write down the facts.
B. Organize into a table.
C. Guess at the solution and see if you are close.
D. List potential formulas.
E. Form an equation.
F.Draw a diagram.
Answer:
a, b, d, e
maybe c
Step-by-step explanation:
Does the table represent a function? Why or why not?
X
y
4
5
OA. Yes, because there is the same number of x-values as y-values.
B. Yes, because every x-value corresponds to exactly one y-value.
C. No, because two of the y-values are the same.
O
D. No, because one x-value corresponds to two different y-values.
579
03232
The correct answer is option D which is No because one x-value corresponds to two different y-values.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
We can see from the table that the value of x at 5 is giving two different values of y that is 2 and 3. For a function, it is not possible to have two different outputs for the same input.
Therefore the correct answer is option D which is No because one x-value corresponds to two different y-values.
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A pendulum is raised to a certain height and released from point A, as shown in the image below. At its release, the pendulum is also given an initial velocity of 14 m/s. Assuming that the effects of friction and air resistance can be ignored, what will be the maximum height that the pendulum can reach - that is , what is the height at point B? (Recall that g = 9.8 m/s2.)
Answer:
D. 20 m
Step-by-step explanation:
The potential energy at Point B will be the sum of the potential and kinetic energies at point A.
__
energy formulasFor mass M, the potential energy at h meters above a rest height is ...
PE = Mgh
The kinetic energy of mass M with velocity v is ...
KE = 1/2Mv²
point A energyA pendulum with mass M launched downward at v = 14 m/s will have a total energy of ...
PE +KE = M(9.8 m/s²)(10 m) +1/2(M)(14 m/s)² = M(98 +98) = 196M J/kg
point B energyWhen the pendulum comes to rest at point B, its energy will all have been converted to potential energy. Then the height at point B is given by ...
PE = Mgh
196M J/kg = M(9.8 m/s²)h
h = (196M)/(9.8M) m = 20 m
The height of the mass at point B will be 20 meters.
Based on the graph how many distinct real numbers solutions does the equation X^3 + 6x^2 + 12x + 8 = 0 have?
Answer:
no real roots
Step-by-step explanation:
Find discriminant of quadratic equation:
A
= 62 - 4aC
2 Identify a,b,c
Identify a,b,c through coefficient:
a
b
C
6
= 12
8
Substitute and calculate
Substitute the value of a,b,c and calculate
discriminant (b2 - 4ac) :
-48
Determine number of solution Determine number of solution with
discriminant:
no real roots
what is the term to term rule of 3,6,17,48,87
Answer:
term to term rule. • a rule that defines the value of each term in a sequence. if the previous terms are known, e.g. the Fibonacci sequence. xn = xn-1 + xn-1.
Step-by-step explanation:
To work out the term to term rule, give the first term and then the pattern. The first term is 17, and the pattern is to subtract 3 each time, so the term to term rule is 'start at 17 and subtract 3'. The next two terms of the sequence are 5 and 2, giving the sequence as: Question.
(2x³+4x²-x+8) / (x² + 3x + 2)
[tex]\dfrac{2x^3+4x^2 -x+8}{x^2 +3x+2}\\\\\\=\dfrac{2x^3+6x^2+4x-2x^2-6x-4+x+12}{}\\\\=\dfrac{2x(x^2 +3x+2)-2(x^2 +3x+2)+x+12}{x^2 +3x+2}\\\\\\=\dfrac{2x(x^2+3x+2)}{x^2 +3x +2 }- \dfrac{2(x^2 +3x +2)}{x^2 +3x +2 } + \dfrac{x+12}{x^2 +3x+2}\\\\\\=2x-2 + \dfrac{x+2}{x^2 +3x +2}\\\\\\=2x-2 + \dfrac{x+12}{x^2 +2x +x +2}\\\\\\=2x-2 + \dfrac{x+12}{x(x+2) + x+2}\\\\\\=2x-2 + \dfrac{x+12}{(x+1)(x+2)}\\[/tex]