Marc mixes blue and yellow paint to make his favorite shade of green, which he'll use to paint his house. He has 14 cans of blue paint and 20 cans of yellow paint when he starts.
He wants the same green color every time he mixes, so the amounts of blue and yellow must always be proportional to the original mixture.
On day 1, he mixes 4 cans of blue and 6 cans of yellow.
On day 2, he mixes 6 cans of blue and 9 cans of yellow.
Fill in the blanks to find the highest number of cans of each color Marc can mix to make the same shade of green on day 3.
Answers
In the simplest form, the ratio of blue paint to yellow paint is 2 : 3.
The number of blue paint he used on the first and second day is 10.
The number of yellow paint he used on the first and second day is 15.
On the third day, the highest number of can of blue paint he can use is 2
On the third day, the highest number of can of yellow paint he can use is 3.
What is the highest number of blue and yellow paint he can use?The ratio of blue paint to yellow paint can be determined by determining the simplest form of the paints used: 4 : 6 = 2: 3
Total blue paint used on the first and second day = 4 + 6 = 10
Blue cans remaining = 14 - 10 = 4
Total yellow paint used on the first and second day = 6 + 9 = 15 cans
Yellow cans remaining = 20 - 15 = 5 cans
Maximum ratio of blue and yellow cans that can be used is 2 : 3.
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Related Questions
Write an equation of the line passing through the point (7,3) that is parallel to the line y=2x-4.
Answers
Answer:
y=2x-11
Step-by-step explanation:
arralel lines have same gradient
since gradient of the known line is 2( the coefficient of x), it therefore follows that the gradient of the second line we want to find is also 2
So we know the gradient of the second line is 2, and we have one known point (7,3). We can therefore apply the formula for finding gradient to come up with the line
[tex]2=\frac{y-3}{x-7} \\\\y-3=2(x-7)\\\\y-3=2x-14\\\\y=2x-14+3\\\\y=2x-11[/tex]
84. A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. As a result of the contingent’s survey, would you agree with the Newsweek poll? In complete sentences, also give three reasons why the two polls might give different results.
Answers
Critical value z_{0.05}=-1.645
Decision Rule, Reject H if z< -1.645
We do not reject the null hypothesis.
What is the Decision?Generally, the equation for the hypothesis is mathematically given as
H P=0.3
H2:P<0.13
Therefore
[tex]z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n}}}\\\\\\z=\frac{0.11-0.13 }{\sqrt{\frac{0.13(1-0.13)}{76}}}[/tex]
z=-0.52
In conclusion, from the table
Critical value z_{0.05}=-1.645
Decision Rule, Reject H if z< -1.645
In conclusion, we do not reject the null hypothesis.
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Compare the graph of m(x) = 0.7x² + 4 with the graph of n(x) = x².
The graph of m(x) is narrower.
Both graphs open upward.
Both have the axis of symmetry x = 1.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
The graph of m(x) is wider.
Both graphs open upward.
Both have the axis of symmetry x = 0.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
The graph of m(x) is wider.
Both graphs open downward.
Both have the axis of symmetry x = 0.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
The graph of m(x) is narrower.
Both graphs open upward.
Both have the axis of symmetry x = 1.
The vertex of m(x) is (0, 4), the vertex of n(x) is (0, 2).
Answers
Answer:
B.) The graph of m(x) is wider.
Both graphs open upward.
Both have the axis of symmetry x = 0.
The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
Step-by-step explanation:
When the coefficient before x² is greater than 1, the curve of the graph is narrower. When the coefficient is less than 1, the curve of the graph is wider.
When the coefficient in front of x² is positive, the graph opens upwards. When the coefficient is negative, the graph opens downwards.
The axis of symmetry is the "x" value which divides the curve into two equal sections. Their axis of symmetry are both x = 0 because their vertexes (the lowest point of the curve) are both at x = 0.
The vertex can be found by plugging x = 0 into both of the equations and then solving. The resulting value is the "y" position of the vertex.
m(0) = 0.7(0)² + 4 n(0) = (0)²
m(0) = 0 + 4 n(0) = 0
m(0) = 4
Therefore, the vertexes are m(x) = (0,4) and n(x) = (0,0).
Answer:
Step-by-step explanation:
m(x) =.7x^2 + 4
n(x) = x^2
In the graph below
green = m(x)
blue = n(x)
Answer:
Just look at the graph belowBoth graphs open upward.The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).The graph of m(x) is wider.Which is the distance betweeen parallel lines with the equations y=-1/3x+3 and y=-1/3x-7
Answers
Answer:
the distance is 10
Step-by-step explanation:
since the slope is the same you know they're parallel, but just find the difference from the two y intercepts (the +3/-7) the difference is 10, so 10.
At a party there is one bottle of coke for every 3 guests, one bottle of sprite for every 6 guests, and one bottle of lift for every 4 guests. There are 54 bottles of drink at the party. How many guests are there? At a party there is one bottle of coke for every 3 guests , one bottle of sprite for every 6 guests , and one bottle of lift for every 4 guests . There are 54 bottles of drink at the party . How many guests are there ?
Answers
Answer:
72 guests
Step-by-step explanation:
We can add up the numbers of bottles per guest, then use that total to find the number of guests from the number of bottles.
SetupLet g represent the number of guests at the party. Then there are ...
g/3 bottles of cokeg/6 bottles of spriteg/4 bottles of liftThe total number of bottles is ...
g(1/3 +1/6 +1/4) = 54
SolutionMultiplying by the inverse of the coefficient of g, we find its value to be ...
g(4/12 +2/12 +3/12) = g(9/12) = 54
g = 54(12/9) = 72
There are 72 guests at the party.
Use the demoivres theorem
Answers
By de Moivre's theorem,
[tex]\left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)^{18} = \cos\left(\dfrac{18\pi}6\right) + i \sin\left(\dfrac{18\pi}6\right) \\\\ ~~~~~~~~ = \cos(3\pi) + i \sin(3\pi) = \boxed{-1}[/tex]
The value of the given complex number is -1
De'moivres theorem
Given the polar form of a complex number expressed as:
[tex](cos\theta + isin\theta)^n\\[/tex]
This can also be expressed according to the de moivre's theorem as;
[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]
Given the expression below;
[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]
Hence the value of the given complex number is -1
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using ruler and set square draw AB 8cm long. construct line PQ parallel to line AB such that distance apart is 2.5cm
Answers
Step-by-step explanation:
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[tex]\red{ \rule{500pt}{900000pt}}[/tex]
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write as an algebraic expression and then simplify the number that is x more than 2x+1
Answers
The algebraic expression is x > 2x + 1 and simplification form of the algebric expression is x < -1
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
The number that is x more than 2x+1
x is the number.
x > 2x + 1
After simplification:
2x - x < -1
x < -1
x ∈ (-∞, -1)
Thus, the algebraic expression is x > 2x + 1 and simplification form of the algebric expression is x < -1
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1/2 divided 8 as a whole number
Answers
Answer:
16
Step-by-step explanation:
A fraction that is divided by a number is just multiplication with the denominator. So with that 8(2)=16
Hayley and Tyler are on the cross-country team. Tyler can run 1 mile (at a
constant speed) in 8 minutes and 20 seconds. Hayley's distances and times
a training run are given by the equation y = 8x, where x represents distance
miles and y represents time in minutes. Who ran farther in 10 minutes? How
much farther?
Answers
The person who ran farther is Hayley.
Who ran farther?
Average speed is the total distance travelled per time.
Average speed = total distance / total time
Tyler's average speed = 1 / 8.30 seconds = 0.12 miles per minute
The distance covered by Tyler in 10 minutes = 0.12 x 10 = 1.2 miles
Distance covered by Hayley in 10 minutes : 10 = 8x
x = 10 / 8 = 1.25 miles
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What is the value of log(x exponent 2 y exponent 3 divided by z) when given the following:
log(x) = 3
log(y) = 2
log(z) = -1
A. 12
B. 13
C. 16
D. 18
Urgently need answer
Answers
Answer:
B. 13
Explanation:
[tex]\sf\:Given\:expression: log(\dfrac{x^2 y^3}{z} )[/tex]
Logarithm rules:
[tex]\sf (i) \ \sf log(ab) = log(a) + log(b)\\ \\ (ii) \ log(a/b) = log(a) - log(b)\\\\ (iii) \ log(a^n) = n log(a)[/tex]
Breakdown of the expression:
[tex]\rightarrow \sf log\left(\dfrac{x^2y^3}{z}\right)[/tex]
[tex]\rightarrow \sf log\left(x^2\right) + log\left(y^3\right) - log(z)[/tex]
[tex]\rightarrow \sf 2\log\left(x\right)+3\log \left(y\right)-\log \left(z\right)[/tex]
insert given values
[tex]\rightarrow \sf 2(3)+3(2)-(-1)[/tex]
[tex]\rightarrow \sf 13[/tex]
Miss Brandy is preparing her unit on architecture. She set up the construction area with a variety of objects and tools for measuring. She also included paper and pencils for children to record their results. An assortment of books on architecture were set up for the children to explore. Which mathematical thinking standard is being addressed in this learning center?
A. Children are extending a simple AB repeating pattern.
B. Children are identifying measurable attributes such as length and weight and solve problems by making direct comparisons of objects.
C. Children are constructing and count sets of objects.
Answers
In this scenario, children are identifying measurable attributes such as length and weight and solve problems by making direct comparisons of objects.
What is measurement?Measurement refers to a process through which the dimensions, size (weight), or other physical quantities of magnitude that are associated with an object is taken, especially for use in a scientific research and experiment such as direct comparison.
In this scenario, we can infer and logically deduce that the children are identifying measurable attributes such as length and weight and solve problems by making direct comparisons of objects.
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Pls help! 20 points very ugrent
Answers
Answer: -2, 1, all real numbers, all real numbers
Step-by-step explanation:
g o f(n) is basically g(f(n))
Using the question as an example we can get that f(0) = 1 so
g(f(0)) = g(1) = -2
f(1) = 0 so g(f(1)) = g(0) = 1
The domain of f(x) is all real numbers and the range of g(x) is all real numbers
Someone help me with this please, solve it in process please ;-;
Answers
Step-by-step explanation:
2A and 2B are scalar multiplications : every item in the matrix has to be multiplied by that factor.
the subtraction then of 2A - 2B is simply to subtract every positive in B from the corresponding same position in A.
that is all.
2A =
4 0
-6 2
2B =
0 2
-4 6
2A - 2B =
4-0 0-2
-6--4 2-6
=
4 -2
-2 -4
LMNP is rotated 180 degrees clockwise around the origin. What are the coordinates of L?
Answers
[tex]\huge\boxed{L^\prime(0, -1)}[/tex]
To rotate a point around the origin by 180 degrees, multiply both parts of the coordinate point by [tex]-1[/tex]. (This means you go from [tex](x, y)[/tex] to [tex](-x, -y)[/tex].)
[tex]L(0, 1)[/tex]
[tex]L^\prime(0*(-1), 1*(-1))\\\boxed{L^\prime(0, -1)}[/tex]
Given the right triangle shown, solve for X, Y and Z. The triangle may not be drawn to scale
Answers
Answer:
X ≈ 8.58 ftY ≈ 9.46 ftZ = 65°Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to help you remember the relationships between sides of a right triangle and trig functions of the acute angles. It tells you ...
Sin = Opposite/HypotenuseCos = Adjacent/HypotenuseTan = Opposite/AdjacentSidesThe given triangle shows values of an acute angle and its opposite side. You are to find the other two sides in the triangle, as well as the other acute angle.
X is the side adjacent to the given angle, so the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(25°) = (4 ft)/X
Solving for X gives ...
X = (4 ft)/tan(25°) . . . . . . . . multiply by X/tan(25°)
X ≈ 8.58 ft
Y is the hypotenuse, so the relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(25°) = (4 ft)/Y
Y = (4 ft)/sin(25°) . . . . . . multiply by Y/sin(25°)
Y ≈ 9.46 ft
AngleThe sum of angles in a triangle is 180°, so if one of them is 90°, the sum of the other two is 90°.
Z = 90° -25°
Z = 65°
The store has p packages of batteries. Each package contains 12 batteries. Write an expression that shows the number of batteries.
Answers
an expression that shows the number of batteries is '12p'
hope this helps.
The value of the equation is A = 12p , where p is the number of packages of batteries
What is an Equation?Equations are mathematical statements with two algebraic expressions on either side of the equals (=) sign.
It depicts how the expressions on the left and right sides are linked together.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are all parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of packages be represented as p
Let the number of batteries in one package = 12 batteries
So , the total number of batteries in p packages A = number of packages x number of batteries in one package
The total number of batteries in p packages A = 12p
Hence , the equation is A = 12p
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If one number is three less than five times m, what is the number?
Answers
Answer:
Step-by-step explanation:
n = the number
n = 5m - 3
find domain and range
Answers
Domain: [-4, ∞)
Range: (-∞, 0]
*Domain are all x-values listed. Here you can see the graph going the right (positive) of -4 (Doesn't go to the left)
*Range are all y-values listed. Here you can see the graph starts from zero and goes down (negative)
Hope it helps!
Consider the quadratic function y equals 4 x squared minus 4 x minus 1.
What is the graph of this function?
First accurate answer gets brainliest
Answers
Answer:
Graph D (look in the attached picture)
The way you do this is use the quadratic formula to solve for the x intercepts which are [tex](\frac{1+\sqrt{2} }{2} )[/tex] and [tex](\frac{1-\sqrt{2} }{2})[/tex]
In the video Mouse Count, Miss Ashley read a book about a snake that captured mice and placed them one-by- one in a jar for his dinner. Which Number and Operations standard would this part of the story represent?
A. Combining sets
B. Removing sets
C. Dividing into equal parts
Answers
Based on the fact that the snake was placing the mice one - by - one into a jar, this is A. Combining sets.
What does combining sets entail?When sets are combined, it means that numbers from a certain set of variables are combined with those from another set.
The snake had captured the mice separately which means they were in different sets. Putting them into one jar means they are being combined so this is combining sets.
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When half of 3,926 is added to a quarter of 1,924
Answers
Answer:
Again, this would be 2444.
Step-by-step explanation:
Because of the previous answers 1963 and 481, we can add them together to make 2444.
3926/2=1963
1924/4=481
Add them together is 2444
1963+481=2444
Drag each graph to the correct location on the table. The points on the graphs represent relations. Classify these relations according to whether or not they are functio 1-3 -2 -1 3. -40 2 1 -2 -3 1 2 Function -3 -2 -1 -1 -2 3 D 2 3 -3 2 101 -1 3 1240 1 24 2 10 3 Not a Function Drag each graph to the correct location on the table . The points on the graphs represent relations . Classify these relations according to whether or not they are functio 1-3 -2 -1 3. -40 2 1 -2 -3 1 2 Function -3 -2 -1 -1 -2 3 D 2 3 -3 2 101 -1 3 1240 1 24 2 10 3 Not a Function
Answers
Answer:
Function: BNot a function: A, CStep-by-step explanation:
A relation is a function if there is only one y-value for each x-value. If you can draw a vertical line on the graph that intersect more than one point, the relation is not a function. (This is the "vertical line test.")
ApplicationGraph A: there are 3 y-values associated with x=2. Not a function.
Graph B: passes the vertical line test: A function.
Graph C: there are 2 y-values at each of x=1 and x=2. Not a function.
write an inequality to represent the graph
Answers
Find slope using (difference in y/ difference in x) of the two points (5/2)
y-intercept given (-3)
y is greater than because the shaded region is above the dotted line
Answer:
y ≤ 2.5x-3
Step-by-step explanation:
we know two points: (2 , 2 ) and ( 0 , -3)
[tex]Grad = \frac{2--3}{2-0} =\frac{5}{2} =2.5\\[/tex]
we also know the y intercept is -3
therefore equation in question is : [tex]y = 2.5x-3[/tex]
we take any point either above the line or below the line and substitute in the equation above. Let us try point (0,0) which is above the line and in the unwanted(shaded region):
y = 2.5x-3
0=2.5(0)-3
0=-3
Normally 0 can never be equal to -3 but is ≥ -3.
Since the point taken was not in the wanted region we reverse ≥ to ≤ to show the wanted region. The inequality in question becomes :
y ≤ 2.5x-3
Pls Help! Geometry
How much will the molding cost?
Answers
Answer: $412.50
Step-by-step explanation:
The area of the square formed by combining the painting and the molding is [tex](25)(28)=700[/tex] square inches.
The area of the painting itself is [tex](22)(25)=550[/tex] square inches.
Therefore, the area of the molding is [tex]700-550=150[/tex] square inches, and thus costs [tex](150)(2.75)=\$412.50[/tex]
Given the data set in the image, which of the following equations best represents a line of best fit?
Answers
Answer:
C.
Step-by-step explanation:
6(1+5x)=5(1+6x) solve x
Answers
Answer:
No solutions
Step-by-step explanation:
Hello!
To solve for x, we should expand the parenthesis and isolate the variable x.
Solve for x6(1 + 5x) = 5(1 + 6x)6 + 30x = 5 + 30x6 ≠ 5The are no solutions for x, as 6 does not equal to 5.
The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut weighs 196 pounds on the surface of the Earth, what will this astronaut weigh 300 miles above the Earth? Assume that the radius of the Earth is 4000 miles. (Round off your answer to the nearest pound.)
Answers
the astronaut would weigh 1 pound above the Earth.
How to calculate the weightGiven that;
Gravitational force = Gm/r^2
M1 = 196 pounds
M2 = unknown
R1 = 4000 miles
R2 = 300 miles
We can deduce that;
[tex]\frac{m1}{r^21} = \frac{m2}{r^22}[/tex]
Let's substitute the values
[tex]\frac{196}{4000^2} = \frac{x}{300^2}[/tex]
[tex]\frac{196}{1.6 *10^7} = \frac{x}{9 *10^4}[/tex]
Cross multiply
196 × 9 ×10^4 = x × 1.6 ×10^7
1.76 × 10^7 = x × 1.6 ×10^7
Make 'x' the subject of formula
x = [tex]\frac{1.76* 10^7}{1.6*10^7}[/tex]
x = 1.1
x = 1 pound
Thus, the astronaut would weigh 1 pound above the Earth.
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equation
3/8 + 5/12 =
Answers
Answer:
19/24
Step-by-step explanation:
3/8=36/96
5/12=40/96
36/96+40/96=76/96
76/96=19/24
SEVEN TIMES THE SUM OF THREE CONSECUTIVE EVEN INTEGERS IS 140 MORE THAN ELEVEN TIMES THE
MIDDLE INTEGER. FIND THE INTEGERS
Answers
The integers are 12,14 and 16
How to determine the integers?Consecutive even integers are represented as:
x, x + 2 and x + 4
So, the statement is represented as:
7 * (x + x + 2 + x +4) = 140 + 11 * (x + 2)
Evaluate the like terms
7 * (3x + 6) = 140 + 11 * (x + 2)
Open the brackets
21x + 42 = 140 + 11x + 22
Collect the like terms
21x -11x =
Evaluate
10x = 120
Divide by 10
x = 12
So, we have
x + 2 = 14
x + 4 = 16
Hence, the integers are 12,14 and 16
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