Answer:
x+ 3
Step-by-step explanation:
you can only simplify but not getting the value of "x" cuz it isn't an equation
Greg can eat an entire large (18-inch) pizza by himself and believes that if his partner can eat the same amount, they should be able to eat a 36-inch pizza. Explain why you agree or disagree.
Answer:
Yes if Greg and his partner can both eat 18 inch pizza then together they can eat a 36 inch pizza
Step-by-step explanation:
18+18=36
x(36) is greater then or equal to 36 making this equation true
Give me three sides to a right triangle. Explain how you can use the Pythagorean theorem to know that your three sides will create a right triangle.
Ms. Lincoln has a bucket full of pencils that she would like to divide up equally to her 28 students. If each student got 3 pencils, how many did she start with
Answer:
84
Step-by-step explanation:
28*3= 84
a data set has its first and third quartiles as 9 and 17 respectively. Which of the following data points would be considered an outlier for the data set
A. 27
B. 17
C. 3
D. 41
In which of these cases should the mean be used?
A. When the data is left-skewed
B. When the data is symmetric
C. When the data is right-skewed
D. When the data has extreme values
To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).
We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:
IQR = Q3 - Q1 = 17 - 9 = 8
To identify outliers, we can use the following rule:
- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.
Using this rule, we can evaluate each data point:
A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.
B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).
C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.
D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.
Therefore, the outliers in the data set are A (27) and D (41).
As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.
Therefore, the correct option would be B. When the data is symmetric.
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What property of adaptive immunity allows a person to have the chicken pox when he or she is six years old and still be immune to chicken pox at age 45?
The property of adaptive immunity enables a person to have the chicken pox when he or she is six years old and still be immune to chicken pox at age 45 exists Memory.
What is adaptive immunity?Specificity and memory are two crucial properties that determine adaptive immunity. Both specificity and memory pertain to the adaptive immune system's capacity to recognize and attack certain diseases, as well as to promptly react to pathogens to which it has already been exposed.
Adaptive immunity can offer an enduring defense, perhaps for the duration of a person's lifespan. In certain circumstances, such as with chickenpox, it does not confer permanent protection; for instance, a person who recovers from measles is now protected against measles for the rest of their life.
Specificity, diversity, specialization, memory, and self/non-self identification are the immunologic characteristics that define adaptive immunity, and these cells both create and show antigen-binding cell surface receptors.
The property of adaptive immunity enables a person to have the chicken pox when he or she is six years old and still be immune to chicken pox at age 45 exists Memory.
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Mr. Walker gave his class the function f(x) = (x + 3)(x + 5). Four students made a claim about the function. Each student’s claim is below.
Jeremiah: The y-intercept is at (15, 0).
Lindsay: The x-intercepts are at (–3, 0) and (5, 0).
Stephen: The vertex is at (–4, –1).
Alexis: The midpoint between the x-intercepts is at (4, 0).
the only student that is correct is Stepheh. "The vertex is at (–4, –1)."
Which claims are true?
Here we have the quadratic equation:
f(x) = (x + 3)*(x + 5)
The first claim is: "The y-intercept is at (15, 0)."
This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.
The second claim is:
"The x-intercepts are at (–3, 0) and (5, 0)"
This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.
Third claim:
"The vertex is at (-4, -1)"
The middle value between the zeros is:
(-3 + (-5))/2 = -4
Evaluating the function in x = -4 we get the y-value of the vertex:
f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1
So the vertex is at (-4, -1), this claim is true.
The fourth claim is:
"The midpoint between the x-intercepts is at (4, 0)."
Which is false, we already saw that the midpoint between the x-intercepts is at x = -4
Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."
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A family of four visits the zoo café for lunch. They ordered 2 bacon cheeseburgers, 1
hamburger, 1 chicken fajita taco, 2 large orders of french fries, an order of onion rings, and 4
juices. What was the family’s total bill? Show your work.
Answer:
29.65
Step-by-step explanation:
What is the solution to the inequality 4x + 10 > 28 - 2x?
Answer:
x>3
Step-by-step explanation:
Step-by-step explanation:
1 - subtract 10 from both sides so (4x+10-10>28-2x-10)
2 - Simplify (4x>-2x+18)
3 - Add 2x to both sides (4x+2x>-2x+18+2x)
4 - Simplify (6x>18)
5 - Divide both side by 6 (6x/6>18/6)
6 Simplify which gives you (x>3)
Answer: x>3
Step-by-step explanation:
1- subtract 10 from both sides so (4x+10-10>28-2x-10)
2 - Simplify (4x>-2x+18)
3 - Add 2x to both sides (4x+2x>-2x+18+2x)
4 - Simplify (6x>18)
5 - Divide both side by 6 (6x/6>18/6)
6 Simplify which gives you (x>3)
If you run for a seat in the House against the incumbent, the odds are very much against you. true or false
The given statement "If you run for a seat in the House against the incumbent, the odds are very much against you." is True because The odds of winning a seat in the House against an incumbent are very much against you.
Incumbents have a significant advantage in elections due to name recognition, established political networks, and fundraising capabilities. Incumbents have built relationships with their constituents and have a track record to campaign on. They have also likely secured endorsements from influential groups, such as political parties, labor unions, and interest groups.
Incumbents also have the benefit of having staff members manage their campaigns and legislative work, which frees them up to spend more time on fundraising and campaigning. Moreover, incumbents can use their position to obtain media coverage, especially during times of crisis. This increases their visibility and enables them to shape the narrative around their work. They may also use their access to government resources, such as staff and offices, to communicate with their constituents, giving them an edge over challengers.
All of these advantages make it difficult for challengers to win against incumbents. Challenging an incumbent requires significant resources, both financial and organizational, and a compelling campaign strategy. Even then, it is rare for challengers to overcome the incumbent advantage, making the odds very much against them.
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good morning, day, or night wherever you may be !! ,, i hope your having a great morning , night , or day . but i really need help with this math !!
Answer: 0,5 i think srry its wrong
Step-by-step explanation:
Given a∥b and m∠5=77° .
What is m∠2 ?
Enter your answer in the box.
Answer:
Step-by-step explanation:
m<5 and m<4 are supplementary angles => m<5 + m< 4 = 180
m<4 = 180 -77 = 103
m<4 and m<2 are corresponding angles => m<4 = m<2 = 103
The measure of the angle m∠2 is 103.
What are supplementary angles?The supplementary angles are defined as the angles having a sum of 180 degrees. The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
In the given image the given angle is m∠5=77°. The measure of the angle m∠2 will be calculated by using some of the angle properties.
m∠5 and m∠4 are supplementary angles:-
m∠5 + m∠4 = 180
m∠4 = 180 -77 = 103
m∠4 and m∠2 are corresponding angles => m∠4 = m∠2 = 103
Therefore, the measure of the angle m∠2 is 103.
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A pizzeria makes pizzas in different sizes and with different toppings. The pizzeria wants its customers to have 12 options when they create a pizza. Which combination of size and toppings will give customers 12 options? Select three options. 4 sizes and 3 toppings 2 sizes and 10 toppings 3 sizes and 9 toppings 2 sizes and 6 toppings 3 sizes and 4 toppings.
Answer:
Step-by-step explanation:
Any 2 numbers that multiply to 12 will work.
4 sizes and 3 toppings
2 sizes and 6 toppings
3 sizes and 4 toppings
Answer:
4 sizes and 3 toppings
2 sizes and 6 toppings
3 sizes and 4 toppings
Step-by-step explanation:
Hope dis helps :/
a study of treatments for angina (pain due to low blood supply to the heart) compared bypass surgery, angioplasty, and use of drugs. the study looked at the medical records of thousands of angina patients whose doctors had chosen one of these treatments. it found that the average survival time of patients given drugs was the highest. what do you conclude?
We can conclude that due to the help of nurses, the survival time of patients given drugs was the highest.
The nurse takes the patient's cardiac output and makes a decision on how the patient will react to the medication.
What types of tasks does a nurse perform?
Registered nurses (RNs) administer and supervise patient care, educate the public about various ailments, and provide psychological support and counseling to patients' relatives. Most nurses collaborate to doctors in a variety of contexts.
How many years do such people live?
People who have access for informal health information as having a nurse or doctor in the parents 10% more likely to remain past the age of 80, according study released in a journal article by that of the Directorate of Economic Research.
Therefore, we can conclude that due to the help of nurses, the survival time of patients given drugs was the highest.
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Margo spends a quarter of her paycheck on a new dress, one-eighthof her paycheck on shoes, and $24 on a birthday present. if she spent $60 altogether, how much was margo’s paycheck? $96 $160 $216 $504
Answer:
$96
Step-by-step explanation:
Find an equation of the line containing the point (2,-5) and parallel to y = – 4x – 2.
Write your answer in slope-intercept form.
Answer:
the desired equation is y = – 4x + 3
Step-by-step explanation:
Parallel lines have the same slope and thus similar equations. Thus, the equation of a line parallel to the given line has the form y = – 4x + C. We need only find C.
The new line goes through (2, -5), and so we substitute 2 for x and -5 for y to obtain
-5 = – 4(2) + C. Then -5 + 8 = C, or C = 3.
Then the desired equation is y = – 4x + 3
PLEASR HELP TODAY WHIEVER GIVES ANSWER GWTS BRAINLEST
The angle measures are given as follows:
m < 5 = 75º.m < 11 = 75º.m < 16 = 65º.How to obtain the angle measures?Angles 5 and 8 form a linear pair, hence they are supplementary, meaning that the mesure of angle 5 is given as follows:
m < 5 + m < 8 = 180º
m < 5 + 105º = 180º
m < 5 = 75º.
Angles 5 and 11 are alternate exterior angles, hence they are congruent and the measure of angle 11 is given as follows:
m < 11 = 75º.
Angles 1 and 13 are corresponding angles, meaning that they are congruent, hence the measure of angle 13 is given as follows:
m < 13 = 115º.
Angles 13 and 16 form a linear pair, hence they are supplementary, meaning that the mesure of angle 16 is given as follows:
m < 13 + m < 16 = 180º
m < 16 = 180º - 115º
m < 16 = 65º.
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-) The Student Council is organizing a field trip to a skating rink for 50 students. They
pay the rink $475 to cover the rental fees for one pair of skates and one locker for
each student. The rental fee for one pair of skates is $6.
4) Which quantity is unknown?
) the rental fee for a locker
) Letr equal the rental fee for one locker. Write an equation that
represents the situation.
The quantity that is unknown in this situation is the rental fee for one locker, or "r" and the equation is as follows: 50 * ($6 + r) = $475
To write an equation that represents the situation, you can use the information given in the problem. The total cost of the field trip, $475, covers the rental fees for 50 students, and the rental fee for one pair of skates is $6. Since the cost of the field trip is the sum of the rental fees for one pair of skates and one locker for each student, you can write an equation as follows:
50 * ($6 + r) = $475
This equation represents the situation in which the Student Council is organizing a field trip for 50 students, and the total cost of the field trip is the sum of the rental fees for one pair of skates and one locker for each student. The unknown quantity, "r", represents the rental fee for one locker.
Therefore, The quantity that is unknown in this situation is the rental fee for one locker, or "r" and the equation is as follows: 50 * ($6 + r) = $475
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Can u help me with this as will pls
Stay safe everyone
Answer:
Option B, 116.6 m = Shortcut
Step-by-step explanation:
A² + B² = C²
100² + 60² = Shortcut²
10,000 + 3600 = Shortcut²
13600 = Shortcut²
\(\sqrt{13600}\) = Shortcut
116.6 = Shortcut
Hope this helps!
Hello! I need a little bit of help with this question please. (As of now this is not from an active test, this is a question from a book I am studying in order to take my Army ASVAB later.)
Solution:
Given a triangle;
Where
\(\begin{gathered} RS=RT \\ m\operatorname{\angle}RTS=m\operatorname{\angle}RST\operatorname{\lparen}\text{base angle of an }\imaginaryI\text{sosceles tr}\imaginaryI\text{angle}\operatorname{\rparen} \end{gathered}\)To find the measure of angle S, i.e.
\(\begin{gathered} m\angle RST \\ m\operatorname{\angle}RTS+m\operatorname{\angle}RST+m\angle SRT \end{gathered}\)Where
\(\begin{gathered} m\operatorname{\angle}RTS=m\operatorname{\angle}RST\text{ be represented by x} \\ m\angle SRT=70\degree \end{gathered}\)Then,
\(\begin{gathered} m\operatorname{\angle}RTS+m\operatorname{\angle}RST+m\angle SRT=180\degree\text{ \lparen Sum of angles in a triangle\rparen} \\ x+x+70\degree=180\degree \\ Collect\text{ like terms} \\ 2x=180\degree-70\degree \\ 2x=110\degree \\ x=\frac{110\degree}{2} \\ x=55\degree \end{gathered}\)Recall that;
\(\begin{gathered} m\operatorname{\angle}RTS=m\operatorname{\angle}RST=x=55\degree \\ And; \\ Measure\text{ of angle S}=m\angle RST=55\degree \end{gathered}\)Hence, the measure of angle S is 55°
The last term of an arithmetic sequence is 14 and the ninth term is -1. Find the first four
terms of the sequence.
Answer:
13
Step-by-step explanation:
where n is the number of terms, a1 is the first term and an is the last term. The sum of the first n terms of an arithmetic sequence is called an arithmetic series . Example 1: Find the sum of the first 20 terms of the arithmetic series if a1=5 and a20=62 .An arithmetic sequence is a sequence where the difference between any two consecutive terms is a constant. ... As with any recursive formula, the initial term of the sequence must be given. An explicit formula for an arithmetic sequence with common difference d is given by an=a1+d(n−1) a n = a 1 + d ( n − 1 ) .
the number of times a variable appears in a data set is called _____
Answer:
The number of times a variable appears in a date set is called a constant.
A minimum element is deleted from a (min) binary heap with N elements. The running time worst case of this operation is
a. O(N)
b. O(N2)
c. O(logN)
d. O(NlogN)
(c) The worst-case running time of deleting the minimum element from a (min) binary heap with N elements is O(logN).
Determine the binary heap?In a binary heap, the minimum element is always located at the root, which is the topmost element of the heap. When the minimum element is deleted, it needs to be replaced with a new element from the heap in order to maintain the heap property.
The process of replacing the root element and restoring the heap property is known as "heapify" or "heap-down." In the worst case, the replacement element may need to be compared and swapped multiple times with its children until it reaches its correct position in the heap.
Since the height of a binary heap is logarithmic with respect to the number of elements (N), the worst-case number of comparisons and swaps required during the heap-down process is proportional to the height of the heap, which is O(logN).
Therefore, (c) the worst-case running time of deleting the minimum element from a binary heap is O(logN).
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A fruit stand has to decide what to charge for their produce. They need $5.30 for 1 apple and 1 orange. They also need $7.30 for 1 apple and 2 oranges. We put this information into a system of linear equations.
Can we find a unique price for an apple and an orange?
- Yes; they should charge $3.30 for an apple and $2.00 for an orange.
- Yes; they should charge $2.00 for an apple and $3.30 for an orange.
- No; the system has many solutions.
- No; the system has no solution.
Answer:
Yes; they should charge $3.30 for an apple and $2.00 for an orange.
Step-by-step explanation:
We can answer this question by creating some simultaneous equations.
Let \(x\) = an apple and let \(y\) = an orange.
With the information given, we can say that the price for an apple and an orange is equal to $5.30 while the price for an apple and 2 oranges is equal to $7.30.
Therefore:
\(x+y = 5.30\) (1st equation)
\(x + 2y = 7.30\) (2nd equation)
There are a couple of ways to solve these equations but I'll show you the substitution method. This is when we substitute the value of one of the equation into the other one.
So let's re-arrange one of them.
\(x+y=5.30\) can be re-arranged into \(x= 5.30-y\)
Now we know the value of \(x\), we can replace the \(x\) in the second equation.
Therefore \(5.30-y + 2y=7.30\). We can simplify this to give us \(5.30 + y = 7.30\) and re-arrange to solve for y: \(y = 2\).
Now we know the value of y, let's put it into the first equation:
\(x+2 =5.30\)
and solving for \(x\) we get: \(x = 3.30\).
Therefore the price of an apple (\(x\)) is $3.30 and the price of an orange (\(y\)) is $2.
From the list of answers, there is only one correct option which is:
- Yes; they should charge $3.30 for an apple and $2.00 for an orange.
suppose that a soup recipe calls for two teaspoons of salt. how many milligrams of sodium is that? ?
Two teaspoons of salt contains 7.16 grams of Na or 7160 milligrams of Na.
Given that a soup recipe calls for two teaspoons of salt. We need to find out how many milligrams of sodium is that?
1 teaspoon = 5.69 grams 1 gram = 1000 milligrams
2 teaspoons of salt = 2 * 5.69 grams = 11.38 grams of salt
11.38 grams of salt = 11.38 * 1000 milligrams = 11380 milligrams of salt
Now, we have to find out how much sodium (Na) is there in 11380 milligrams of salt. Sodium chloride is the chemical name for table salt (NaCl). So, the atomic mass of NaCl can be calculated as follows:
Na = 1Cl = 35.45
Atomic mass of NaCl = Na + Cl= 1 + 35.45= 36.45
So, 1 mole of NaCl = 36.45 grams 11380 milligrams of NaCl = 11380/1000 grams= 11.38/36.45 moles
Therefore, Moles of Na = 11.38/36.45 = 0.3121
mol Atomic mass of Na is 22.99 g/mol.
So, 1 mole of Na weighs = 0.3121 * 22.99= 7.16 grams
Therefore, 11380 milligrams of NaCl = 7.16 grams of Na. Hence, two teaspoons of salt contains 7.16 grams of Na or 7160 milligrams of Na.
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Payton runs a gas station on Route 66. On Thursday, exactly half of his bags of chips got sold to customers. On Friday when he restocked the shelves, he put out 68 more bags of chips. If there are now 200 bags of chips, how many did the gas station start with on Thursday morning?
Answer:
264
Step-by-step explanation:
If there are 200 bags of chips after the addition of 68 more bags of chips, subtract the two to get the amount before he added the bags of chips.
200 - 68 = 132
This is exactly half of what he originally had. Multiply this value by 2.
132 × 2 = 264
Payton originally had 264 bags of chips on Thursday morning.
How do I find the fraction that 480 is divided by to get 300
Answer: Final answer: :: written in four ways :: As an improper fraction (numerator larger than denominator): 480/300 = 8/5As a mixed number (mixed fraction) (a whole number and a proper fraction, of the same sign): 480/300 = 1 3/5As a decimal number: 480/300 = 1.6As a percentage: 480/300 = 160%
Step-by-step explanation:
A fraction consists of two numbers and a fraction bar: 480/300The number above the bar is the numerator: 480 The number below the bar is the denominator: 300 The fraction bar means that the two numbers are dividing themselves: 480/300 = 480 ÷ 300 Divide the numerator by the denominator to get fraction's value: Value = 480 ÷ 300 'Percent (%)' means 'out of one hundred': p% = p 'out of one hundred', p% = p/100 = p ÷ 100 The fraction 100/100 = 100 ÷ 100 = 100% = 1 Multiply a number by the fraction 100/100, ... and its value doesn't change.To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF. To calculate the greatest common factor, we build the prime factorization of the two numbers. Prime Factorization of a number: finding the prime numbers that multiply together to make that number. 480 = 25 × 3 × 5; 480 is not a prime, is a composite number; 300 = 22 × 3 × 52; 300 is not a prime, is a composite number; * Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself. * A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.A proper fraction: numerator smaller than denominator. 8 ÷ 5 = 1 and remainder = 3 => 8 = 1 × 5 + 3 => 8/5 = (1 × 5 + 3) / 5 = (1 × 5) / 5 + 3 / 5 = 1 + 3/5 = 1 3/5 As a decimal number: 1 3/5 = 1 + 3/5 = 1 + 3 ÷ 5 = 1.6As a percentage: 1.6 = 1.6 × 100/100 = 160/100 = 160%4. 40% percent of 295 students say they do not like homework. How many students like homework?
Answer:
118 Students hate homework but 177 students like homework.
Step-by-step explanation:
The answer is 177 because 40% of 295 is 118 and 295 minus 118 is 177.
P.S Can I have brainliest?
The optimal amount of x1, x2, P1, P2 and income are given by the
following:
x1= 21/ 7p1 x2= 51 / 7p2
The original prices are: P1=10 P2=5 The original income is: I
=4189 The new price of P1 is the foll
The total change in the consumed quantity of x₁ as per given price and income is equal to 213.
x₁ = (21/7)P₁
x₂ = (51/7)P₂
P₁ = 10
P₂ = 5
P₁' = 81
To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',
The difference between the quantities consumed at the original price and the new price.
Let's calculate the quantity consumed at the original price,
x₁ orig
= (21/7)P₁
= (21/7) × 10
= 30
x₂ orig
= (51/7)P₂
= (51/7) × 5
= 36.4286 (approximated to 4 decimal places)
Now, let's calculate the quantity consumed at the new price,
x₁ new
= (21/7)P1'
= (21/7) × 81
= 243
x₂ new
= (51/7)P2
= (51/7) × 5
= 36.4286
The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,
Change in x₁
= x₁ new - x₁ original
= 243 - 30
= 213
Therefore, the total change in the quantity consumed of x₁ is 213.
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The above question is incomplete, the complete question is:
The optimal amount of x1, x2, P1, P2 and income are given by the following:
x1= 21/ 7p1 x2= 51 / 7p2
The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?
Please answer step by step
a rectangular plot of land measures 40.0 m by 120.0 m, with a parcel 10.0 m by 12.0 m out of one corner for an electrical transformer. what is the area, in meters squared, of the remaining plot?
The area of the remaining rectangular plot of land is 4680m²
Area of rectangle:
Area of rectangle means the area covered by the rectangle.
The formula for area of rectangle is
A = l x b
where,
l is the length of the rectangle
b is the breadth or width of the rectangle
Given,
A rectangular plot of land measures 40.0 m by 120.0 m, with a parcel 10.0 m by 12.0 m out of one corner for an electrical transformer.
Here we need to find the remaining area of the rectangular plot land.
For that first, we have to find the area of each separately,
Like,
The area of the rectangular plot is,
A₁ = 40.0 x 120.0 m²
A₁ = 4800m²
Similarly, the area of the electric transformer is,
A₂ = 10.0 x 12.0 m²
A₂ = 120m²
Now the remining area is,
A = A₁ - A₂
A = 4800 - 120 m²
A = 4680m²
Therefore, the area of the remaining rectangular plot is 4680m².
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Sarah will mix yellow paint and red paint in the ratio 2 parts yellow to 3 parts red to create a certain shade of orange paint.
She needs 10 quarts of the orange paint. How much will Sarah spend for the paint she needs if the price of the yellow paint
is $5. 50 per quart and the price of the red paint is $6. 25 per quart?
A. $29. 75
B. $58. 00
C. $58. 75
D. $59. 50
E. $117. 50
$59.50 will Sarah spend for the paint she needs if the price of the yellow paint is $5. 50 per quart and the price of the red paint is $6. 25 per quart
To find the cost of the orange paint, we need to determine how much yellow and red paint Sarah will need to mix in order to make 10 quarts of the desired shade of orange.
Since Sarah is mixing the yellow and red paint in a ratio of 2:3, this means that for every 2 quarts of yellow paint, she will need 3 quarts of red paint. We can use this ratio to set up a proportion:
2 parts yellow : 3 parts red = x quarts yellow : (10 - x) quarts red
where x represents the amount of yellow paint needed.
Cross-multiplying, we get:
2(10 - x) = 3x
Expanding and simplifying:
20 - 2x = 3x
20 = 5x
x = 4
So Sarah will need 4 quarts of yellow paint and 6 quarts of red paint to make 10 quarts of the desired shade of orange.
To calculate the cost, we can simply multiply the amount of each paint by its respective price and add them up:
Cost of yellow paint = 4 quarts * $5.50 per quart = $22.00
Cost of red paint = 6 quarts * $6.25 per quart = $37.50
Total cost = $22.00 + $37.50 = $59.50
Therefore, the answer is D. $59.50.
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