We shοuld mix 9 οunces οf yellοw paint with 24 οunces οf blue paint tο make the same cοlοr as the sample.
What are Ratiοs?Ratiοs are a way οf cοmparing twο οr mοre quantities by expressing their relative sizes οr amοunts. They can be written in the fοrm a:b οr a/b, where a and b are the quantities being cοmpared. Ratiοs are οften used in mathematics and everyday life tο express prοpοrtiοns, rates, and οther relatiοnships between quantities.
Tο make the same cοlοr as the sample, we need tο maintain the same ratiο οf blue tο yellοw paint.
The ratiο οf blue tο yellοw paint in the sample is 3:8, which simplifies tο 3/8.
If we have 24 οunces οf blue paint, we can use this ratiο tο find the amοunt οf yellοw paint needed:
(3/8) * 24 = 9 οunces
Therefοre, we shοuld mix 9 οunces οf yellοw paint with 24 οunces οf blue paint tο make the same cοlοr as the sample.
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If a firm has a production quota of 400=5x1^2+8x1x2+15x2^2, what combination of good x1 and x2 should the firm produce to minimize cost of C=x1^2+x2^2
The firm should produce good x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .
What is Lagrange multipliers ?
Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.
To minimize the cost C = x₁² + x₂²
We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:
L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)
Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:
∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0
∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0
∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0
Solving these equations simultaneously, we get:
x₁ = 4
x₂ = 8
λ = 1/20
Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.
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3. The trick with ratios is to always multiply or divide the numbers by the same value. If a recipe uses 3 cups of flour and 2 cups of milk and 2 quantities of the recipe is needed, what would be the ratio for 2 quantities of flour and milk?
Answer: ____
a) 1 : 3 b) 12 : 8 c) 4 : 8 d) 6 : 4
The ratio for 2 quantities of flour and milk is given as follows:
d. 6:4.
How to obtain the ratio?The ratio 2 quantities of flour and milk is obtained applying the proportions in the context of the problem.
A proportion is applied as to obtain the ratio between two amounts, you simply divide one amount by the other. The ratio is expressed as a fraction, and can also be expressed as a decimal or a percentage.
The amounts for a single recipe are given as follows:
3 cups of flour.2 cups of milk.Hence for two quantities, the amounts are multiplied by two as follows:
6 cups of flour.4 cups of milk.Meaning that the ratio is given as follows:
6:4.
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just now
Mathematics
College
Look at the relative-frequency table below of the probability distribution of the discrete random variable X, with X = "the number of pets in a household."
x P(X = x)
0 .09
1 .29
2 .42
3 .15
4 .05
What is the expected value of pets in a randomly selected household?
Answer: To find the expected value of X, we need to multiply each possible value of X by its probability and then add up the results:
E(X) = Σ(x * P(X = x))
where Σ denotes the sum over all possible values of X.
Using the table given, we have:
E(X) = 0 * 0.09 + 1 * 0.29 + 2 * 0.42 + 3 * 0.15 + 4 * 0.05
E(X) = 0 + 0.29 + 0.84 + 0.45 + 0.2
E(X) = 1.78
Therefore, the expected value of pets in a randomly selected household is 1.78.
Step-by-step explanation:
calculati 14,7+21,8+0,9
Answer:
18.4
Step-by-step explanation:
ur welcome
Douglas bought a $20 game card at a game center. The go-karts cost $3.50 each time you race. He wants to have at least $7.75 left on his card to play arcade games. Write and solve an inequality to determine how many times Douglas can race the go-karts. Then interpret the solution.
Answer:
3 races
Step-by-step explanation:
(Let t = total number of races)
Each race costs $3.50, so the total cost of racing t times is 3.50 × t or 350t. Douglas wants to have at least $7.75 left on his card, so an inequality to represent this would look like this:
20 - 3.50x >= 7.75Solving this inequality, we get:
-3.50x >= -12.25x <= 3.5Or we can do this.
20 - 3.50 = 16.50 (1st race)16.50 - 3.50 = 13.00 (2nd race)13.00 - 3.50 = 9.50 (3rd race)9.50 > 7.75Therefore, Douglas can race the go-karts 3 times and still have at least $7.75 left on his card to play arcade games.
The histogram below gives the length of service of members of the Department of Mathematics and Statistics at a particular university. The
classes, in years of service, are 0-4.9, 5-9.9, etc., and the vertical axis represents the number of faculty.
What percent of the department faculty have 20 or more years of service?
Answer:
%
14
13-
12-
V
11
OF
18
9
8
7
6
5
10
4
3
24
1
8
Mathematics and Statistics Faculty
10
15
20
25
38
35
4
Answer:
approx 20% of the department faculty have 20 or more years of service
Step-by-step explanation:
To find the percentage of the department faculty with 20 or more years of service, we need to add up the number of faculty members in the "20-24.9" and "25 or more" year categories, since anyone with 20 or more years of service would fall into one of these categories.
Looking at the histogram, we see that there are 24 faculty members in the "20-24.9" year category, and an additional 4 in the "25 or more" year category. Therefore, the total number of faculty members with 20 or more years of service is 24 + 4 = 28.
To calculate the percentage of faculty members with 20 or more years of service, we need to divide this number by the total number of faculty members in the department, which we can find by adding up the heights of all the bars in the histogram. Based on the heights of the bars in the histogram, we can estimate that the total number of faculty members is approximately 140.
Therefore, the percentage of faculty members with 20 or more years of service is:
(28/140) x 100% = 20%
So, approximately 20% of the department faculty have 20 or more years of service.
What is the rate of change in miles ran from September 18th to September 21st?
I will mark you brainiest!
Which set of coordinates, when paired with (-3, -2) and (-5, -2), result in a square?
A) (-5, -2) and (-3, -2)
B) (-3, 0) and (0, -2)
C) (-3, 0) and (-5, 0)
D) (0, -2) and (0, -3)
The high temperatures for several days are shown in the table. Which answer describes the average rate of change from day 3 to day 5?
Responses
The high temperature changed by an average of −6 degrees per day from day 3 to day 5.
The high temperature changed by an average of −2 degrees per day from day 3 to day 5.
The high temperature changed by an average of −4 degrees per day from day 3 to day 5.
The high temperature changed by an average of −3 degrees per day from day 3 to day 5.
"From days 3 to 5, the high temperature changed by an average of almost 4 degrees per day," is the appropriate answer.
How to determine the average rate of change?We can determine the average rate of change from day 3 to day 5 by splitting the difference in high temperature between those two days by the distance between them (which is 2), or 2.
The highest temps on Day 3 was 85°F.
The highest temperature on Day 5 was 77°F.
Extreme temperature variation: 77°F to 85°F equals -8°F
Between day three and day five, there are two days.
(Change in maximum temperature) / (number of days) yields an average rate of change of -8°F / 2°F per day.
This leads to the conclusion that the right response is "The high temperature changed by an average of 4 degrees per day from day 3 to day 5".
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I need help with this please
Answer:
2500ml
Step-by-step explanation:
1litre=1000millilitres
2.5=?
=2.5×1000
=2500millilitres
please answer quickly. I am begging you
Answer:
ok, what do you want me to answer?
factoring polynomial x(6x-1)-3(6x-1)
The factored version of the provided polynomial is (6x-1) according to the given assertion.(x-3).
What in mathematics is a polynomial?An expression that consists of variables, factors, and exponents and is mixed using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial. (No division operation by a variable).
To factor the polynomial x(6x-1)-3(6x-1), we can first simplify the expression by factoring out the common factor of (6x-1):
x(6x-1)-3(6x-1) = (6x-1)(x-3)
Therefore, the factored form of the given polynomial is (6x-1)(x-3).
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i’m confused can someone pls help me
In the given diagram, using the tangent theorem, the value of x to the nearest tenth is 16.6
Tangent theorem: Calculating the value of xFrom the question we are to determine the value of x.
From one of the tangent theorems, we have that
The tangent to the circle is perpendicular to the radius of the circle at the point of contact.
Thus, the triangle is a right triangle
From the Pythagorean theorem which states that, in a right triangle, the square of the hypotenuse equals sum of squares of the other two sides.
Then, we can write that
x² = 9² + 14²
x² = 81 + 196
x² = 277
x = √277
x = 16.6433
x ≈ 16.6 (to the nearest tenth)
Hence, the value of x is 16.6
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Company XYZ closed at $53.21 per share with a P/E ratio of 13.26 . Answer the following questions. a. How much were earnings per share? b. Does the stock seem overpriced, How much were earnings per share? b. Does the stock seem overpriced, underpriced, or about right given that the historical P/E ratio is 12-14?ced, or about right given that the historical P/E ratio is 12-14?
Answer: a. To find the earnings per share (EPS), we can use the formula:
P/E ratio = Price per share / Earnings per share
Rearranging this formula to solve for EPS, we get:
Earnings per share = Price per share / P/E ratio
Substituting the given values, we have:
Earnings per share = $53.21/13.26 ≈ $4.01
Therefore, the earnings per share were approximately $4.01.
b. To determine if the stock is overpriced, underpriced, or about right given the historical P/E ratio of 12-14, we can compare the current P/E ratio to this range. Since the current P/E ratio is 13.26, which falls within the historical range, the stock seems to be about right in terms of valuation. However, it's important to note that other factors should also be considered before making any investment decisions.
Step-by-step explanation:
simplify the following algebric expression X^2-x-12/x^2-4
Step-by-step explanation:
So first of all u going to make sure all the base is the same so it 's easier for u to simplify
and then after that in order to make all the base the same so u need to multiple (x²-4) ...
5.A committee of 6 members is to be selected from 8 men and 7 women. In how many ways can this be done so as to include
a. 3 women
b. at least 4 men
c. at most 3 women
There are 252 different ways to assemble the committee.
What is permutation and combination?Permutation:
A simple definition of permutation is the various ways to arrange some or all of the members in a particular order.
It is the process of orderly disorganisation.
A permutation is what is meant by this.
Combination: Combination is the process of choosing one or more objects from a group of objects so that, unlike permutations, the order in which the objects are chosen is irrelevant.
It describes the combination of N items drawn randomly from a collection of K items at a time.
Hence, There are 252 different ways to assemble the committee.
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PLEASE HURRY WILL GIVE 100 POINTS!!!!!!!
Using the Distributive Property as a good first step to solving the equation, you could simplify to get which of these choices?
5(4x + 3) = -4(5 - 2x)
Answer:
e
Step-by-step explanation:
5(4x +3)=-4(5-2x)
5×4x +5×3=-4 ×5 -4 × -2x
20x +15=-20+8x
An individual stock is selected at random from the portfolio represented by the boxand-whisker plot shown. Find the probability that:
a. The stock price is less than $51
b. The stock price is between $22 and $51
c. The stock price is $30 or more
The portfolio depicted as a box-and-whisker plot has a random selection of one stock, with probabilities of 0.51, 0.50, and 0.50.
The probability formula is what?The probability is frequently described as the ratio of favourable results to all favourable results in the sample. The likelihood of an occurrence P(E) = (The number of favorable events) is how it is stated (Sample space).
What are the basics of probability?Probability is just the possibility that something will happen. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Biostatistics seems to be the analysis of occurrences with a probability distribution.
Given the box plot,
(a)
[tex]P(X < 51) = 0.51[/tex]
(b)
[tex]P(22 < X < 51) = 0.50[/tex]
(c)
[tex]P(X \geq 30) = 0.50[/tex]
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please help with this i beg you
Answer:
To make the piano player's practice seem consistent, adjust the Y-axis scale, use a line graph, and add a trend line or moving average.
Step-by-step explanation:
To adjust the graph to make it seem like the piano player is pretty consistent in practicing, we can make the following changes:
Adjust the scale of the Y-axis to make the differences in the average practice times appear smaller. For example, we can change the range of the Y-axis from 0-15 to 8-14, since all the data points fall within this range. This would compress the data vertically and make the differences in the average practice times appear smaller.
Use a line graph instead of a bar graph to better show the trend of the data over time. This would allow us to see any patterns or trends in the average practice times over the course of the year.
Add a trend line or moving average to the graph to show the overall trend in the data and smooth out any fluctuations. This would further emphasize the consistency in the piano player's practice habits.
By making these adjustments, the graph would show that the piano player is consistently practicing for around 10-11 hours per week throughout the year, with some slight variations. This would convey the message that the piano player is dedicated and consistent in their practice habits.
Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]
In the figure below, there are three right trangles. Complete the following.
(a) Write a similiarity statement relating the three right triangles.
(b)Complete each proportion.
a. ΔEGF~ΔGHF~ΔEHG are the similarities between the three right triangles.
b. HF/HG = GH/EH; EF/EG = EG/EH
Information about Similar Triangles?According to the similar right triangle theorem, if a right triangle's altitude is drawn from its right angle, two similar right triangles are created, and both similar right triangles are identical to the original right triangle. All three right triangles are essentially the same.
Similar triangles contain three pairs of comparable side lengths that are proportionate to one another, or whose ratios are identical.
The corresponding side lengths are taken into account when constructing similarity statements.
A similarity assertion linking the three right triangles is thus: ΔEGF~ΔGHF~ΔEHG.
b. They will have the following side ratios: EF/EG = EG/EH HF/HG = GH/EH
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Find a formula for the linear function depicted in the following graph.
f(x)=
Step-by-step explanation:
f(X)=ax+q
domain: X element of real numbers
Graph the linear equation by finding and plotting its intercepts.
x-y=1
Answer: To graph the linear equation x - y = 1, we can find its intercepts by setting one of the variables to zero and solving for the other.
Step-by-step explanation:
Setting x = 0, we get:
0 - y = 1
Solving for y, we get:
y = -1
So the y-intercept is (0, -1).
Setting y = 0, we get:
x - 0 = 1
Solving for x, we get:
x = 1
So the x-intercept is (1, 0).
Now we can plot the intercepts on a coordinate plane and draw a straight line passing through them:
|
| .
| .
| .
| .
| .
| .
------------------------------------------
| | | | |
-2 -1 0 1 2
Therefore, the graph of the linear equation x - y = 1 is a straight line passing through the points (0, -1) and (1, 0).
Find all solutions of the following polynomial equation.
-7x + 4x²-28 + x³ = 0
Therefore , the solution of the given problem of quadratic equation comes out to be x = 2, -3 + √(5)i, -3 - √(5)i.
What is quadratic equation ?Regression modelling uses the polynomial answer x = ax2 + b + c=0 for one-variable equations. The First Proposition of Algebra claims that since this proposition has a second order, there can only be one solution. There are simple and complicated solutions available variable . Even as the name suggests, a "non-linear formula" has four factors. According to this, there might be just one squared term. In the formula ax2 + bx + c = 0
Here,
The provided polynomial equation can be rewritten as follows:
=> x³ + 4x² - 7x - 28 = 0
The constant term in this situation is -28, with components of 1, 2, 4, 7, 14, and 28, and a leading coefficient of 1. Therefore, 1, 2, 4, 7, 14, and 28 are among the polynomial's potential rational solutions.
It is possible to factor the polynomial by discovering that x = 2 is one of its roots.
=> (x - 2)(x² + 6x + 14) = 0
The quadratic formula can be used to calculate the quadratic factor:
=> x = (-6 ± √(6² - 4114)) / (2*1)
=> (-6 ± √(-20)) / 2
=> -3 ± √(5)i
Thus, the following are the answers to the algebraic equation:
=> x = 2, -3 + √(5)i, -3 - √(5)i.
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In a race, 24 out of the 25 bicyclists finished in less than 56 minutes. What percent of bicyclists finished the race in less than 56 minutes? Write an equivalent fraction to find the percent.
The percentage of bicyclists that finished the race in less than 56 minutes is 96 %
What is percentage?Percentage is a ratio out of hundred
If in a race, 24 out of the 25 bicyclists finished in less than 56 minutes. To find what percent of bicyclists finished the race in less than 56 minutes, we first write it in a fraction as number/total
Since
number = 24 and total = 25We have that
fraction = number/total
= 24/25
Now to write it as a percentage, we multiply by 100.
So, we have that percentage = fraction × 100 %
So, we have that in percentage = 24/25 × 100 %
= 24 × 4 %
= 96 %
So, the percentage is 96 %
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Pleaseeeeeeeeeeeee help
Answer:
Step-by-step explanation:
i cant see good
Answer:
I think it would be commutative property
Step-by-step explanation:
the commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The commutative property only works with addition and multiplication.
4. Find the area of the following figure.
10 cm
16 cm
10 cm
12 cm
The correct option is 312 cm² as the area of the composite figure calculated to be equal to 312 square centimeters.
How to calculate for the area of the figureThe composite figure can be observed to be made up of two identical triangle and a rectangle, so we shall calculate for the area of one triangle, multiply the result by 2, and add the area to the area of the rectangle to get the total area of the composite figure as follows:
area of one of the triangle = 1/2 × 12 cm × 10 cm
area of one of the triangle = 6 cm × 10 cm
area of one of the triangle = 60 cm²
area of one of the two triangle = 2 × 60 cm²
area of one of the two triangle = 120 cm²
area of the rectangle = 16 cm × 12 cm
area of the rectangle = 192 cm²
total area of the composite figure = 120 cm² + 192 cm²
total area of the composite figure = 312 cm²
Therefore, the area of the composite figure is equal to 312 square centimeters.
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A jet airplane begins a steady climb of 15° and flies for two miles (measured horizontally). What is the change in altitude in feet? Round your answer to the nearest hundredth of a foot.
Answer:
Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.
Step-by-step explanation:
To solve this problem, we can use trigonometry. The angle of climb is 15 degrees, which means that the ratio of the change in altitude to the horizontal distance traveled is the tangent of 15 degrees:
tan(15°) = change in altitude / horizontal distance
We can rearrange this equation to solve for the change in altitude:
change in altitude = horizontal distance x tan(15°)
Substituting the given values, we get:
change in altitude = 2 miles x tan(15°)
We can convert the distance to feet by multiplying by 5280:
change in altitude = 2 miles x 5280 feet/mile x tan(15°)
Using a calculator, we get:
change in altitude ≈ 514.77 feet
Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.
Please help! For each function, state whether it is linear, quadratic, or exponential.
The types of functions are as follows:
1) Quadratic function
2) None of the above
3) Exponential function.
What is a function?
A relation between a set of inputs and a set of allowable outputs is called a function. It has the property that every input is associated with exactly one output. A function from one set X to another allocates precisely one element of the other set Y to each element of X. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.
The ways to determine the different functions are as follows:
a) If for a constant change in x-values, the y-values also change constantly, the function is linear.
b) If as the x values change constantly, the y- values also change, but the difference in differences of y-values remains constant, then the function is quadratic.
c) If the ratio between two consecutive y- values is the same, when x-values change constantly, then the function is exponential.
Let us look into each function.
1) x-values are increasing constantly by one.
The difference in y-values are:
13-7 = 6
21-13 = 8
31-21 = 10
43-31 = 12
Now the difference of difference in y-values.
8-6 = 2
10-8 = 2
12-10 = 2
This is constant. So the function is a quadratic function.
2) The difference in y-values are:
-6+21 = 15
-21+30 = 9
-33+30= -3
-30 + 33 = 3
This function can be categorised as none of the above.
3) The ratio of the consecutive y-values are:
-12/-3 = 4
-48/-12 = 4
-192/-48 = 4
-768/-192 = 4
Since the ratio is constant, the function is an exponential function.
Therefore the types of functions are as follows:
1) Quadratic function
2) None of the above
3) Exponential function.
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Write in descending order in terms of y
In descending order in terms of y, the expression is -x³y⁵ - 2x²y³ + 4xy + x⁴.
What is descending order?When a pattern of numbers in mathematics has a decreasing value, the numbers are said to be in descending order. It indicates that the numbers are sorted from highest to lowest. Information is considered to be in descending order if it is arranged from highest to lowest. For example 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 are ordered in descending order. In other terms, it is considered to be in descending order if the numbers are listed from greatest to smallest.
The given expression is:
x⁴- x³y⁵+ 4xy - 2x²y³
To arrange in descending order, place the highest value first followed by the smaller value.
Therefore, in decreasing order in terms of y, the expression is -x³y⁵ - 2x²y³ + 4xy + x⁴.
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nate went on a trip, and he used a table of values to repeatedly record the time he had been traveling and the distance from his starting point. The function represented by the table of values is linear, and the rate of change is 50 miles per hour. What is one way for Nate to determine the initial value?
After addressing the issue at hand, we can state that We know that when function x = 0, y = b because the function has the form y = mx + b.
what is function?Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.
We know that the function represented by the table of values has the form y = mx + b because it is linear, where y represents the distance from Nate's starting point and x represents the time he has been travelling.
The rate of change is known to be 50 miles per hour. This means that Nate's distance from his starting point increases by 50 miles for every hour he travels. In other words, m equals 50.
We know that when x = 0, y = b because the function has the form y = mx + b.
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