When you mix two colors of paint in equivalent ratios, the resulting color is always the same. Complete the table as you answer the questions.
How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green? Explain or show your reasoning.
Make up a new pair of numbers that would make the same shade of green. Explain how you know they would make the same shade of green.
row 1
cups of blue paint
cups of yellow paint
row 2
2
10
row 3
1
5
row 4
3
15
What is the proportional relationship represented by this table?
What is the constant of proportionality? What does it represent?
Answers
By Calculating the Constant of Proportionality, we get,
1. 5 cups of yellow paint is required for 1 cup of blue paint.
2. For 4 cups of blue paint, 20 cups of yellow paint is required.
For 5 cups of blue paint, 25 cups of yellow paint are required.
3. Cups of Yellow Paints = 5* Cups of Blue Paints
4. The constant of Proportionality is 5.
Let the cups of blue paint = x
and cups of yellow paint = y
From the table, we can infer that to make the same shade of green, we need to mix 5 cups of yellow color with 1 cup of blue.
We have, To make the same shade of green,
we need to mix 5 cups of yellow color with 1 cup of blue.
we need to mix 10 cups of yellow color with 2 cups of blue.
we need to mix 15 cups of yellow color with 3 cups of blue.
So, here we can see a relationship between the two colors, blue (x) and green(y)
Let k be the constant of proportionality, then, we have :
10 = k *2
k =[tex]\frac{10}{2} = 5[/tex]
Hence, For one cup of blue paint, we need 5 cups of yellow paint to make the same shade of green.
And the equation of the same is y =kx, that is y =5x....equation(1)
To make new pair of numbers that would make the same shade of green.
We can use the equation 1,
for x = 4, we need y = 20
foe x =5, we need y = 25
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Related Questions
In 1991 the average family income was about 39000, and in 2011 it was about 66820.
Let
x
=
0
represent 1991,
x
=
1
represent 1992, and so on. Find values for
a
and
b
(rounded to one decimal place if necessary) so that
f
(
x
)
=
a
x
+
b
models the data
a
=
b
=
What was the average family income in 2006?
$
Answers
The average family income in 2006 is $59865.
What is the income?Based on the information illustrated, the required model is given as:
y = ax + b
y = average family income
x = years since 1991
The slope based on the information given is b = 39000.
Therefore, the family income in 2006 will be:
= (1391 × 15) + 39000
= 59865
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A physics class has 40 students. Of these, 18 students are physics majors and 17 students are female. Of the physics majors, seven are female. Find the probability that a randomly selected student is female or a physics major.
Answers
Answer:
Probability (Physics Major or Female) = 28/40 = 0.7
Step-by-step explanation:
The probability of being a female is 17/40
The probability of being a physics major is 18/40
The number of students counted twice is 7/40
Probability (Physics Major or Female) = 17/40 + 18/40 - 7/40
Probability (Physics Major or Female) = 28/40 = 0.7
Add.
−2.35+(−1.602)
Enter your answer in the box.
Answers
Answer:
i think its
-3.952
There are 21 cats and 17 dogs in an animal shelter. What fraction of the animals are cats?
A)21/38
B)21/17
C)17/21
D)17/38
Answers
Answer: B) 21/17
Step-by-step explanation:
Answer:
21/38
Step-by-step explanation:
Demonoator= 21+17=38
Numerator= number of cats
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At the toy store you could get 4 board games for $22.96. Online the price for6board games is $34.74. Which place has the Highest price for a board game?
Answers
To determine the price for each board game on the stores, we need to divide the total price by the number of board games bought.
[tex]\begin{gathered} \text{board 1}=\frac{22.96}{4}=5.74 \\ \text{board 2}=\frac{33.74}{6}=5.79 \end{gathered}[/tex]The price online is higher, because it is $5.79 per board game.
the function h is defined by the following rule. =hx+−x1
Answers
The complete table of values for the x values in function h(x) is
x | -2 -1 0 1 2
h(x) | 3 2 1 0 -1
How to complete the table of the function h(x)?From the question, the definition of the function is given as
h(x) = 1 - x
Also, from the table of the values;
We have the following x values
x = -2, -1, 0, 1 and 2
The next step is that
We substitute each value of x in the equation h(x) = 1 - x
So, we have
When x = -2
h(-2) = 1 + 2
Evaluate
h(-2) = 3
When x = -1
h(-1) = 1 + 1
Evaluate
h(-1) = 2
When x = 0
h(0) = 1 + 0
Evaluate
h(0) = 1
When x = 1
h(1) = 1 - 1
Evaluate
h(1) = 0
When x = 2
h(2) = 1 - 2
Evaluate
h(2) = -1
When represented on a table of values, we have
x | -2 -1 0 1 2
h(x) | 3 2 1 0 -1
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Possible question
The function h is defined by the following rule h(x) = 1 - x
Find H(x) For Each x-Value In The Table
x = -2, -1, 0, 1 and 2
Determine the cost of a taxi trip of 9 miles if the fare is $1.10 forthe first 1/6 mile and $.20 for each additional 1/6 mile (or fraction).a. $1.80b. $10.50c. $9.30d. $11.70
Answers
We are given :
-Cab fare for the first 1/6 mile = $1.10
-subsequent miles = $20
- total miles = 9
Calculations :
• 9 -1/6 = 54/6
= 54/6 - 1/6
= 53/6
• y = 1.10 + 53* 0.20 =$11.70
So correct option is number D
Ahmad will rent a car for the weekend. he can choose one choose one of two plans. the first plan has an initial fee of $55 and cost an additional $0.13 per mile driven the second plan has an initial fee of $48 and cost am additional $0.17 per mile driven
Answers
SOLUTION
(a) The first plan cost $55 and an additional $0.13 per mile driven,
while the second plan cost $48 and an additional $0.17 per mile driven
Let the amount of driving be x
Then, this means that for the first plan we have
[tex]\begin{gathered} 55+(0.13\times x) \\ =55+0.13x \end{gathered}[/tex]And the second plan becomes
[tex]\begin{gathered} 48+(0.17\times x) \\ =48+0.17x \end{gathered}[/tex]So, for the plans to cost the same for a particular amount of driving x, it means that
[tex]55+0.13x=48+0.17x[/tex]Collecting like terms we have
[tex]\begin{gathered} 55-48=0.17x-0.13x \\ 7=0.04x \\ x=\frac{7}{0.04} \\ x=175 \end{gathered}[/tex]Hence the two plans cost the same at 175 miles
(b) The cost when the two plans cost the same is
[tex]\begin{gathered} 55+0.13x \\ 55+0.13(175) \\ =55+22.75=77.75 \\ Or\text{ } \\ 48+0.17x \\ =48+0.17(175) \\ =48+29.75=77.75 \end{gathered}[/tex]Hence the answer is $77.75
What is the probability that a card drawn randomly from a standard deck of 52 cards is a red four? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
We have a deck of 52 cards.
We have to calculate the probability that when a card is randomly drawn from the deck, this cart is a red four.
There is only one red four in the deck. Then, if we calculate the probability of an event as the quotient between the number success events (getting a red four, in this case) and the total possible events (getting any card), we will get:
[tex]p=\frac{S}{N}=\frac{1}{52}[/tex]As there is only one card in the deck that gives a success event within the 52 cards, the probability is 1 in 52.
Answer: the probability is 1/52.
Define a variable, used let statements, set up an equation, then solve. Morgan is making two cookie recipes. Recipe A calls for one-third third less than twice the number of cups of sugar that Recipe B calls for. If she needs four and one-sixths cups of sugar in all, how many cups will she need for Recipe A?
Answers
EXPLANATION
Let's see the facts:
-Morgan is making ----------------> 2 cookie recipes.
Recipe A ---> A = 2RecipeB -(1/3) 2RecipeB
-She needs-----------> Recipe A + Recipe B = 4 1/6 cups of sugar
Now, we have a system of equations:
(1) A = 2B -(1/3)2B
(2) A + B = 4 1/6
Multiplying both sides of (1) by 3:
3A = 6B - B
Simplifying:
3A = 5B
Isolating B:
B = 3/5 A
Substituting B-value in (2)
[tex]A\text{ + }\frac{3}{5}A\text{ = 4}\frac{1}{6}[/tex]Reordering:
[tex]A+\frac{3}{5}A=\text{ }\frac{25}{6}[/tex]Multiplying both sides by 30:
[tex]30A\text{ + 18A = 25}\cdot5[/tex][tex]48A\text{ = 125}[/tex]Dividing both sides by 48:
[tex]A\text{ = }\frac{125}{48}[/tex]Representing as mix fraction and rounding:
[tex]A=\text{ 2}\frac{2}{3}[/tex]ANSWER: She will need two and two-thirds cups of Recipe A.
which of the following is the equation of the line that passes through the point (-3,7) and is parallel to the y-axis.
Answers
ANSWER
[tex]x=-3[/tex]EXPLANATION
We want to write the equation of the line that passes through the point (-3, 7) and is parallel to the y-axis.
The general equation of a line is given as:
[tex]y=mx+c_{}[/tex]where m =slope
c = y intercept
A line parallel to the y-axis is a vertical line. The slope of a vertical line is undefined and so the equation of a vertical line is given as:
[tex]x=a[/tex]where a is the x coordinate of any point that it passes through.
Therefore, since the line passes through (-3, 7), the equation of the line is:
[tex]x=-3[/tex]Finding Slope
HELP ME PLS
Answers
Answer:
-3 because (-1,-7) and (1,-13) takes -6 to get from -7 to -13 and 2 to get from -1 to 1. -6/2 is -3, so the slope/answer is -3.
Step-by-step explanation:
Answer:
Formula for finding slope is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.
Slope = -13-(-7) ÷ 1-(-1)
= (-13+7) ÷ (1+1)
= -6 ÷ 2
= -3
A phone company offers two monthly plans. Plan A costs $19 plus an additional $0.07 Tor each minute of calls. Plan B costs $12 plus an additional $0.11 for each minute of calls. For what amount of calling do the two plans cost the same? minutes What is the cost when the two plans cost the same? Х Submit AS
Answers
Explanation
Step 1
let x represents the number of minutes.
hence:
Plan A costs $19 plus an additional $0.07 for each minute of calls
[tex]A=19+0.07x[/tex]Plan B costs $12 plus an additional $0.11 for each minute of calls
[tex]B=12+0.11x[/tex]Step 2
there is a number of minutes x, such both plnas cost the same,so
[tex]undefined[/tex]Brand A granola is 25% nuts and dried fruit and brand B granola is 20% nuts and dried fruit. How much of sweet item A and sweet item B should be mixed to form a 10-lb batch of sweetsthat is 22% nuts and dried fruit?The batch of sweets should contain of Brand A granola and of Brand B granola.
Answers
The batch of sweet should contain 4 lb of Brand A granola
The batch of sweet should contain 6 lb of Brand B granola
Explanations:Total amount of sweet items = 10 lb
Let the amount of brand A granola be x
Amount of brand B granola = 10 - x
Amount of nuts and dried fruits in the total sweet items = 22% of 10
Amount of nuts and dried fruits in the total sweet items = 0.22 x 10
Amount of nuts and dried fruits in the total sweet items = 2.2lb
Amount of nuts and dried fruits in brand A granola = 25% of x
Amount of nuts and dried fruits in brand A granola = 0.25x
Amount of nuts and dried fruits in brand B granola = 20% of (10-x)
Amount of nuts and dried fruits in brand B granola = 0.2(10 - x)
Amount of nuts and dried fruits in brand A granola + Amount of nuts and dried fruits in brand B granola = Amount of nuts and dried fruits in the total sweet items
0.25x + 0.2(10 - x) = 2.2
0.25x + 2 - 0.2x = 2.2
Collect like terms
0.25x - 0.2x = 2.2 - 2
0.05x = 0.2
x = 0.2 / 0.05
x = 4 lb
The batch of sweet should contain 4 lb of Brand A granola
Amount of brand B granola = 10 - x
Amount of brand B granola = 10 - 4
Amount of brand B granola = 6 lb
The batch of sweet should contain 6 lb of Brand B granola
(｀・ω・´) thx for answering
Answers
Answer:
3nd one
Step-by-step explanation:
Hope I helped!
If I got it incorrect, please tell me, so I can at least try and see what I did wrong.
What are three fractions equivalent to 5/4
Answers
The Three Fractions are :-
10/8, 15/12, 20/16
Find the missing value.Hint: Use the number line to find the missing value.-(-5) = -7A-15-10-5051015
Answers
Given:
The expression is ___-(-5) = -7.
The objective is to find the missing value using number line.
Consider the missing value as x.
Now, the expression can be rearranged as,
[tex]\begin{gathered} x-(-5)=-7 \\ x+5=-7 \\ x=-7-5 \end{gathered}[/tex]So, we have to solve -7-5 on number line, which means starting from -7 subtract 5 in the number line.
Hence, the missing value is -12.
Which equation represents a line that has a slope of 1/3 and passes through point (-2, 1)? O y=1/3x-1 Oy=1/3x+5/3 O y=1/3 x-5/3 O y=3x+1
Answers
Explanation:
The equation of a line in the slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We have that the line has a slope of 1/3:
[tex]y=\frac{1}{3}x+b[/tex]To find the y-intercept b we have to use the point. Replace x = -2 and y=1 and solve for b:
[tex]\begin{gathered} 1=\frac{1}{3}(-2)+b \\ 1=-\frac{2}{3}+b \\ b=1+\frac{2}{3}=\frac{5}{3} \end{gathered}[/tex]Answer:
The equation is:
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]evaluate the following expression using exponential rules write the result in standard notation
Answers
this is
[tex]undefined[/tex]I need help with my pre-calculus homework, please show me how to solve them step by step if possible. I need help with how to apply the problem on the calculator. The image of the problem is attached.Instructions: Make sure your calculator is in degree mode.
Answers
To convert 81 degrees to radian, we will apply the conversion:
1 π rad = 180°
let the 81° in rad = y
1 π rad = 180°
y = 81°
cross multiply:
1π rad (81) = 180 y
To get y, we divide both sides by 180:
[tex]\begin{gathered} \text{y = }\frac{1\pi rad\text{ }\times\text{ 81}}{180} \\ y\text{ = }\frac{81\text{ }\pi}{180}\text{ = }\frac{9\times9\text{ }\pi}{9\times0}\text{ } \\ 9\text{ is co}mmon\text{ to numerator and denominator. }It\text{ cancels out} \\ y\text{ = }\frac{9\pi}{20} \\ \\ 81\degree\text{ = }\frac{9\pi}{20}\text{ radians (option A)} \end{gathered}[/tex]Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
Answers
The three equations that have the same value of x as 3/5(30 x minus 15) = 72 are:
C) 18x - 9 = 72D) x = 4.5E) 18x = 81.What are equations?Equations are mathematical statements that show the equality of mathematical expressions.
These statements claim that two or more expressions are equal or equivalent.
To show this equality, the expressions are joined with the equal sign (=).
3/5(30x - 15) = 72
= 18x - 9 = 72
18x = 81
x = 4.5 (81/18)
Thus, the three correct equations, sharing the same value of x as 3/5(30 x minus 15) = 72 are Options C, D, and E.
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Question Completion with Options:A) 18x - 5 = 72
B) 50x - 25 = 72
C) 18x - 9 = 72
D) x = 4.5
E) 18x = 81
State one rational number between -0.45 and -0.46 (answer must be in decimal form.)
Answers
A rational number between the two given ones is -0.455, such that:
-0.45 > -0.455 > -0.46
How to find a rational number between the two given ones?A rational number is any number that can be written as a quotient between two integer numbers.
Particularly, any number with a finite number of digits after the decimal point is also a rational number.
So to find a rational number between -0.45 and -0.46 we could se:
-0.455, such that:
-0.45 > -0.455 > -0.46
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6) Write an equation of the line parallel to: y = -1/4x + 8 with a y-intercept of -10.
Answers
The given equation is
[tex]y=-\frac{1}{4}x+8[/tex]The y-intercept of the new line is -10.
We have to find a new parallel line to the given equation, which means they must have the same slope.
Remember that the coefficient of x is the slope, so the slope of the given line is -1/4. This means the new line has a slope fo -1/4 because it's parallel.
So, we know that the new line has a slope of -1/4 and its y-intercept is -10. We use the slope-intercept form to write the equation.
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{4}x-10 \end{gathered}[/tex]Therefore, the equation is[tex]y=-\frac{1}{4}x-10[/tex]Write a formula for the function of tamed when the graph is shifted as described below
Answers
Given the function
[tex]f(x)=|x|[/tex]Then, the function is shifted down 3 units means you subtract 3 to f(x).
[tex]f(x)=|x|-3[/tex]And the function is shifted to the right 1 unit means you subtract 1 from the argument of f(x), this is "x". Therefore, the new function is:
[tex]f(x)=|x-1|-3[/tex]Answer:
[tex]f(x)=|x-1|-3[/tex]1. Suppose a designer has a palette of 6 colors to work with, and wants to design a flag
with 5 vertical stripes, all of different colors.
How many possible flags can be created?
2. Evaluate the expression P(9,3), equivalently 9P3
Answers
Part a: The total possible flags can be created using 6 colours is 720.
Part b: ⁹P₃ = 60480.
What is defined as the permutation?When the order of the arrangements matters, a permutation is a mathematical method that calculates the number of possible arrangements in a set. A common mathematical problem involves selecting only a few items from the a set of items in a specific order.For the given question;
Part a: A designer has total 6 palette of colors.
A flag has to made with 5 vertical stripes, all of different colors.
The, this could be done by using permutation.
= 6!
= 6×5×4×3×2×1
= 720
Thus, the total possible flags can be created is 720.
Part b: The value of the expression P(9,3), equivalently ⁹P₃.
⁹P₃ = 9!/3!
⁹P₃ = (9×8×7×6×5×4×3!)3!
⁹P₃ = 9×8×7×6×5×4
⁹P₃ = 60480.
Thus, the equivalent value of the expression is ⁹P₃ = 60480.
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Measure the angle in degrees.0806100-110120130140150160170-1800The measure of this angle is
Answers
The measure of this angle is 65°
The measure of this angle is 60°
Explanation:
1) From the diagram the angle is between 10° and 75°
One of the arrows is on 10°
the other arrow is on 75°
the measure of the angle is between the two angles, so we subtract the smaller one from the bigger one
The angle in degrees is the difference between the 75° and 10°
= 75 - 10
= 65°
The measure of this angle is 65°
2) The second diagram is from 0° to 60°
Difference between them = 60° - 0°= 60°
The measure of this angle is 60°
Nina has 19.50 to ride the subway around New York it will cost her 0.75 every time she rides identify the dependent variable and independent variable in this scenario
Answers
The independent variable is the cost of riding the subway.
The dependent variable is the number of times she can ride the subway.
What is independent variable and independent variable?The independent variable is the variable whose value is given. It is the value of the independent variable that determines the dependent variable. The dependent variable is the variable whose value is determined by changes in the independent variable.
In this question, the cost of each ride is given. There is little or nothing Nina can do to change the price of the subway ride. Thus, it is the independent variable. The total amount of rides Nina can go on is dependent on the cost per ride and the total amount she has. Thus, it is the dependent variable.
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A bag contains 1 gold marbles, 7 silver marbles, and 25 black marbles. Someone offers to play this game: You randomlyselect one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.What is your expected value if you play this game?
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate the expected value for the game, so we obtain the following:
We will substitute in the following formula:
Expected Value=(Black Gain)*Black Chance (Gold Gain)*Gold Chance+(Silver Gain)*Silver Chance
Expected Value=(-1)*(25/33)+(3)*(1/33)+(2)*(7/33)
Expected Value≈-0.24
Finally we obtain that the expected value is approximately $-0.24.
Please help me I’ll mark u brainly
Answers
Answer:
yes
Step-by-step explanation:
for each point, both the x and y coordinates are inverted
Cameron is playing 9 holes of golf. He needs to score a total of at most 11 over par on the last four holes tobeat his best golf score. On the last four holes, he scores 5 over par, 3 under par, 6 over par, and 3 underpar.Part 1 out of 3Enter and find the value of an expression that gives Cameron's score for 4 holes of golf.The expression is? Cameron's score is?Can someone please help?
Answers
Let the numbers over par is (+) and the numbers under par is (-)
he scores 5 over par, 3 under par, 6 over par, and 3 under
par.
so, the expression is : (5) + (-3) + (6) + (-3)
So, the result will be:
over par = 5 + 6 = 11
under par = 3 + 3 = 6
subtract under par from over par
so, 11 - 6 = 5
So, the Cameron's score = 5