The solution to the equations are
The number of adults for 12 students is 3 adults
The number of adults for 24 students is 6 adults
The number of adults for 40 students is 10 adults
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the number of students for 1 adult be 4 students
So , the proportion of students to adults is 1 : 4
Now , the equation will be
The number of adults for 12 students = 12 / 4
The number of adults for 12 students = 3 adults
The number of adults for 24 students = 24 / 4
The number of adults for 24 students = 6 adults
The number of adults for 40 students = 40 / 4
The number of adults for 40 students = 10 adults
Now , when the number of students is 33 students
The number of adults = 33 / 4 = 8.25 adults ≈ 8 adults
Hence , the proportion is 1 : 4
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Mary is looking to lease a car. Gerald's Auto has a car available with a money factor of 0.00355. Hillspring's Auto has the exact same car available with a money factor of 0.00324. Which of the following statements is true
Answer:
B
Step-by-step explanation:
Mrs. Newman's famous peanut butter cookies call for 1 cup of peanut butter for every
1
2
of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?
In a case whereby Mrs. Carter's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil the amount of peanut butter she should use can be expressed as 2 cups of peanut butter.
How can the amount of peanut butter be calculated?The concept that will be used is simplification. Base on the provided information from the question,
(1/2 cup of oil )= (1 cup of peanut butter)
we can represent (1 cup of oil) as (x)
The if we perfor a Cross Multipliplication we have:
(1/2x) =( 1 × 1)
x = (1 × 2/1)
x = 2 cups of peanut butter.
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consider the following mixture problem and the table used to translate the problem Drink A is 20% fruit juice and drink B is 5% fruit juice. how much should be used in order to make 30 gal of a drink that is 10% fruit juice? complete the following table letting x=gallons of drink A and y=gallons of drink B.
Substance Gallons % Fruit Juice
Drink A x 20%
Drink B y 5%
Total x + y = 30 10%
To find the number of gallons of Drink A and Drink B that should be used, we can write two equations based on the percentage of fruit juice.
20% * x = 10% * (x + y)
5% * y = 10% * (x + y)
Simplifying and solving for x and y:
x = 1.5 * y
10% * (x + y) = 10% * 30
y = 15
x = 1.5 * 15 = 22.5
So, we would use 22.5 gallons of Drink A and 15 gallons of Drink B to make a 30 gallon mixture that is 10% fruit juice.
The perimeter of a rectangle is 34 units. Its width is 6.5 units.
Write an equation to determine the length (t) of the rectangle.
Find the length of the rectangle.
On solving the provided question, we can say that the equation foe the rectangle will be = 34 = 12 + 2W
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
Perimeter of rectangle is = 2(L+W)
the equation foe the rectangle will be =
34 = 2(6.5 + W)
34 = 12 + 2W
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9k^2+8=-48
5a^2+10=-70
Topics:
Direct Solving
Factoring
Upon solving using direct factoring, the value of k = 56i / 3, a = 4i.
What is the straightforward approach to the quadratic equation?The algebraic square and simplify method is used to finish the square in a quadratic equation in order to obtain the required equation roots. The answer to the quadratic equation ax2 + bx + c = 0 is a 0. To obtain the roots, we simplify this equation to read as ax2 + bx + c = 0.
What strategy is direct?It is referred to as the direct technique since it allows us to solve the given system of linear equations in a finite number of specified steps.
Given the equation are -
9k² + 8 = - 48
9k² = -48 - 8
9k² = - 56
k = -√56 / √9
k = -√56 / 3
5a² + 10 = - 70
5a² = -80
a² = -16
a = 4i
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the points o(0,0,0), p(,,), and q(,,) lie at three vertices of a parallelogram. find all possible locations of the fourth vertex.
The two possible locations for the fourth vertex of the parallelogram are p and q.
The fourth vertex of a parallelogram can be obtained by adding the vector difference between two of its vertices to the third vertex. In this case, the vector difference between two vertices can be found by subtracting one vertex from the other, i.e. p-o and q-o. So, the fourth vertex can be found by adding either of these vectors to vertex o, i.e. r = p - o + o = p or r = q - o + o = q.
Therefore, the two possible locations for the fourth vertex of the parallelogram are p and q.
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What is the dollar amount of the Gentrys' annual transportation and taxes budgets combined? $2,676. 82 $11,004. 70 $8,327. 88 $18,737. 72 NEXT QUESTION
Option (b) $11004.70 is correct answer. The amount of the Gentrys' annual transportation and taxes budgets combined is approx $11004.70 .
Given,
Total yearly income of the family = $29,742.42
% Expenses for Transportation = 9%
% Expenses for Taxes = 28%
We know that ,
Percentage is from total income of the family,
Expenses for transportation in $ = 9% of $29742.42
= 0.09 * 29742.42
= $2676.8178
Expenses for taxes in $ = 28% of $29742.42
= 0.28 * 29742.42
= $8327.8776
Total expense Transportation + Taxes = $2676.8178 + $8327.8776
= $11004.694
≈ $11004.70
Hence, amount of the Gentrys' annual transportation and taxes budgets combined is approximately $11004.70 .
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The complete question is :
What is the dollar amount of the Gentrys' annual transportation and taxes budgets combined?
(a)$2,676. 82
(b) $11,004. 70
(c) $8,327. 88
(d) $18,737.
Gentry Family
Three Children Yearly Budget; Yearly Income - $29,742.42
Item Percentage
Tithe 10%
Taxes 28%
Food 20%
Housing 30%
Clothing 6%
Transportation 9%
Doctor, Medicine, etc. 8%
Which fraction have a leat common denominator of 36?
A ) 3/4 and 5 18 B ) 5/6 and 7/9 C ) 7/8 and 1/12
3/4 and 5 18 is fraction have a leat common denominator of 36.
How do you determine a fraction's least common denominator?There are several possible pairs of two whole numbers whose Least Common Denominator is 36: 36 and 36 comes first, followed by 1 and 36, 2 and 36, 3 and 36, 4 and 18 and 9, 6 and 36, 9 and 12, 12 and 36, 18 and 36, and finally 4 and 9 and 36.I would choose 4/5 and 9/13 if you want fractions in their simplest form, with several denominators, and an LCD of 36.These, in my opinion, work because 5, 13, and 36 are all pairwise relatively prime (meaning that the product of any two of them is the LCD of the other), and because the LCD of 4 and 9 is pairwise relatively prime.3/4 and 5 18 is fraction have a leat common denominator of 36.
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Is this statement true or false? Explain.
4x(3+5)-10=4x3+5-10
Answer:
False. The two sides evaluate to different numbers.
Step-by-step explanation:
Let's evaluate each side:
4 × (3 + 5) - 10 = 4 × 8 - 10 = 32 - 10 = 22
4 × 3 + 5 - 10 = 12 + 5 - 10 = 17 - 10 = 7
evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim x → 8 12−x − 2 24−x − 4
The limit does not exist as x approaches 8 for (√(12−x) − 2)/ (√(24−x) − 4).
Therefore the answer is dne.
The square root of 12 - x approaches 2 as x approaches 8 and the square root of 24 - x approaches 4 as x approaches 8.
The limit fails to exist because both the numerator and the denominator approach 0 as x approaches 8, but the ratio of the two approaches positive infinity. This shows that the limit is undefined or "dne".
As both the numerator and denominator approach 0, the fraction they form can approach any real number or it can oscillate between two values, leading to an undefined limit. In such cases, the limit fails to exist.
--The question is not readable, answering to the question below--
"evaluate the limit, if it exists. (if an answer does not exist, enter dne.)
lim x → 8 (√(12−x) − 2)/ (√(24−x) − 4)"
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determine the indices for the directions shown in the following cubic unit cell
The direction of A for the given indices of the cubic unit cell is:
A = [3 3 -1].
What do cubic lattice system Miller indices mean?A notation used to pinpoint crystal planes is called a Miller index.
The three integers define plane-obstruction directions, forming reciprocal basis vectors. The standard notation for negative integers is an overbar.These indices [-u, -v, -w] simply indicate the opposite side of the exact direction as [uvw]. These direction indices all are integer that whenever a primitive unit cell is used, but they could be rational whenever a centred unit cell is used.For the direction of A:
Head point: [1 1 1/3]Tail point: [0 0 2/3]Direction of A = [(1 - 0) , (1 - 0), (1/3 - 2/3)]
= [ 1 1 -1/3]
Multiply each by 3.
= [3 3 -1]
Thus, the direction of A for the given indices of the cubic unit cell is:
A = [3 3 -1].
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The complete question is-
Determine the indices for A, the directions shown in the following cubic unit cell.
The diagram is attached:
Answer:
Step-by-step explanation:
PLS HELP ITS URGENT ILL GIVE YOU POINTS
The life of a Goldline auto battery is normally distributed with a mean of 42. 5 months and a
standard deviation of 6. 5. The battery warranty is 36 months. What is the probability that a
battery will last for 52 months?
A)92. 8%
B)73. 8%
C)87. 3%
D)37. 4%
The probability that the battery will last for 52 months is approximately 0.928, or 92.8%.
To calculate the probability that a battery will last for 52 months, we need to find the z-score of 52 months, using the formula:
z = (x - μ) / σ
Plugging in the values, we get:
z = (52 - 42.5) / 6.5 = 1.384615
Next, we can use a z-table to find the probability that a battery will last more than 52 months.
In this case, the z-score is positive, so we look up the area to the right of 1.384615 in the z-table. The area to the right of 1.384615 is approximately 0.928.
Therefore, the probability that a battery will last for 52 months or more is approximately 0.928, or 92.8%.
So the answer to the question is: A) 92.8%
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The first term of an A.Pis -1 and the common difference is 0.5. Find the 6th term.
Answer:
Step-by-step explanation:
-4
Work Shown:
[tex]a_1 = -1 = \text{ first term} \\\\d = 0.5 = \text{ common difference} \\\\a_n = a_1 + d(n-1)\\\\a_n = -1 + 0.5(n-1)\\\\a_6 = -1 + 0.5(6-1)\\\\a_6 = -1 + 0.5(5)\\\\a_6 = -1 + 2.5\\\\a_6 = 1.5\\\\[/tex]
when using a graduated pipet, at which point do you measure the volume?
The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.
1. Place the graduated pipet on a flat surface and make sure it is level
2. Draw the liquid up until the meniscus is level with the etched line that corresponds to the desired volume
3. Make sure the liquid is not touching the etched line above it
4. Observe the bottom of the meniscus and take the reading at the point where the liquid level is between the two etched lines
The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.
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using separation of variables, solve the differential equation, use c to represent the arbitrary constant. 10 x^8
Since C is any arbitrary constant, [tex]y^{2} = \frac{1}{5} ln (3 + x^{10}) + 2C[/tex] is the final solution of the differential equation.
The equation given to us is:
[tex](3 + x^{10})\frac{dy}{dx} = \frac{x^{9}}{y}[/tex]
We can re-write the above equation:
[tex]y dy = \frac{x^9}{3 + x^{10}} dx[/tex]
This is separation of variables.
A separable differential equation is any equation that can be written in the form y′=f(x)g(y). The method of separation of variables is used to find the general solution to a separable differential equation.
Now, if we differentiate the denominator,
[tex]\frac{d}{dx} (3 + x^{10} ) = 10x^9[/tex]
Integrating both sides,
[tex]\frac{y^2}{2} = \frac{1}{10} ln (3 + x^{10})[/tex] + C
⇒ [tex]y^{2} = \frac{1}{5} ln (3 + x^{10})[/tex] + 2C
Since C is any arbitrary constant, [tex]y^{2} = \frac{1}{5} ln (3 + x^{10}) + 2C[/tex] is the final solution of the differential equation.
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Move 1 1/4 units in the negative direction from 3/4, and then plot a point at this location.
Answer:
The point you would plot would be at -1/2
Explanation:
3/4 - 1 1/4 = -1/2
Two points determine a line. Find an equation of the line passing through the points.
(-5,16) and (- 2,7)
(Also u don’t need to write the explanation. Js the answer :p)
Answer: 3
Step-by-step explanation:
what is the probability that the digit 7 doesn’t appear among 100 digits where each digit is one of (0-9) and all sequences are equally likely?
The probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.
The probability that the digit 7 doesn't appear among 100 digits where each digit is one of (0-9) and all sequences are equally likely is given by the probability that all 100 digits are chosen from the set {0, 1, 2, 3, 4, 5, 6, 8, 9}. There are 10 choices for each digit, so there are 10^100 possible sequences of 100 digits. The number of sequences that don't contain the digit 7 is 9^100. Therefore, the probability that the digit 7 doesn't appear among 100 digits is: P(7 doesn't appear) = (9^100) / (10^100) = 9 / 10
Therefore, the probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.
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Which given value, if any, is a solution of the equation a + 16 = −30 for a: {–46, –14, 14, 36}?
The value of a is -46 which is the solution of equation a + 16 = −30.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is a+16=-30
a plus sixteen equal to minus thirty
In the equation the variable is a
a+16=-30
Subtract 16 from both sides
a=-30-16
a=-46
Hence, the value of a is -46 which is the solution of equation a + 16 = −30.
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Bill reflects the point (-3, 5) over the x-axis. What is the coordinate of the new point after the reflection?.
Answer:
(-3, -5)
Step-by-step explanation:
When reflected over the x-axis, the x remains the same, and the y change to their opposite sign.
So, the answer is (-3, -5)
there are two ducks in front of a duck, two ducks behind a duck and a duck in the middle. how many ducks are there?
Answer:
3 Ducks
Step-by-step explanation:
Two ducks are in front of the last duck; the first duck has two
ducks behind; one duck is between the other two
Hence , there are 3 ducks
Hope it is correct
Answer: I think 7
Step-by-step explanation: Sorry if its wrong.
Fells had 9 boxes. Scarlett had 18 boxes but fewer than Dylan. Dylan had 2 times minus 1 boxes than Fells. How many boxes do they have in all?
You'll get 40 points.
The number of boxes with three of them are 44.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Fells had 9 boxes.
Dylan had 2 times minus 1 boxes than Fells.
2(9)-1 which is 18-1= 17 boxes.
Scarlett had 18 boxes but fewer than Dylan
The total number of boxes are 9+17+18
44 boxes
Hence, the number of boxes with three of them are 44.
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consider the following data: −11,−5,−5,−11,13,−11,−5 step 1 of 3 : calculate the value of the sample variance. round your answer to one decimal place.
The value of the sample variance rounded to one decimal place is 76.0.
What is the Mean?
The mean is a measure of the central tendency of a set of data, calculated as the sum of the values divided by the number of values in the set.
The sample variance of a set of data is a measure of the spread or dispersion of the data around the mean. To calculate the sample variance, you can follow these steps:
Calculate the mean of the data: First, find the sum of all the data points and divide by the number of data points (n).
For the given data, the mean is: (-11 + -5 + -5 + -11 + 13 + -11 + -5) / 7 = -7
Subtract the mean from each data point: Next, subtract the mean from each data point to get the deviations from the mean.
For the given data, the deviations are: (-11 - -7) = -4, (-5 - -7) = 2, (-5 - -7) = 2, (-11 - -7) = -4, (13 - -7) = 20, (-11 - -7) = -4, (-5 - -7) = 2
Square the deviations: Square each deviation to get rid of negative values.
For the given data, the squared deviations are: (-4)^2 = 16, (2)^2 = 4, (2)^2 = 4, (-4)^2 = 16, (20)^2 = 400, (-4)^2 = 16, (2)^2 = 4
Sum the squared deviations: Sum all the squared deviations.
For the given data, the sum of the squared deviations is: 16 + 4 + 4 + 16 + 400 + 16 + 4 = 456
Divide the sum by n - 1: Finally, divide the sum of the squared deviations by the number of data points minus 1 (n - 1). This gives us the sample variance.
For the given data, the sample variance is: 456 / (7 - 1) = 456 / 6 = 76
Hence, the value of the sample variance rounded to one decimal place is 76.0.
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What are the domain and range of the function represented by the set of
ordered pairs?
{(-13, 9), (-7, -5), (5, 14). (11, -10))
The domain and range of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) is as follows:
domain = [-13, -7, 5, and 11]
range = {9, -5, 14 and -10}
How to find the domain and range of a function?The domain of a function is independent variable of a function. The domain is the input value of the function. The domain lies on the x axis of the function.
Therefore, the domain of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) is [-13, -7, 5, and 11]
The range is the dependent value of the function. The range is also called the output value of the function. The range lies on the y-axis of the function.
Therefore, the range of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) are {9, -5, 14 and -10}
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Answer all theses for a surprise ⬇️
Definitely not at school rn
The proportionate equation for each problems are:
constant of proportionality: 4.75; price per unitconstant of proportionality: 8.5; times per ditance or minutes per milesy = 1.5x y = 18x 10.5 cups of water15 3/4 yards of fabricLet's discuss each problem we have:
1. Liv earns $9.50 for every 2 bracelets she sells.
y = 4.75x
because y = kx, then:
y = $9.50
x = 2
4.75 --> constant of proportionality
--> price per unit of bracelet sold
2. John ran 3 miles in 25.5 minutes
y = 8.5x
y = 25.5 minutes
x = 3 miles
8.5 --> constant of proportionality
--> minuntes per miles
--> times per distance
3. Lincoln bought 3 bottles of energy drink for $4.50
y = kx
y = $4.50
x = 3
$4.50 = k (3)
k = $1.50 --> price of a bottle of energy drink
4. Total cost of 4 hours renting a cotton candy machine is $72.
y = kx
y = $72
x = 4 hours
$72 = k(4)
k = $18 --> price of renting per hour
5. 7 cups of water are used to make 4 loaves of French bread.
y = kx
y = 7
x = 4
7 = k(4)
k = 7/4
Proportionate equation: y = 7/4 x
(x = 6)
y = 7/4 (6)
y = 21/2 = 10.5 cups of water
6. 6 3/4 yards of fabrics are used to make 3 elf costumes
y = kx
y = 6 3/4
x = 3
6 3/4 = k (3)
27/4 = 3k
--------------- x 4
27 = 12k
k = 9/4
Proportionate equation: y = 9/4 x
(x = 7)
y = 9/4 (7)
y = 63/4
y = 15 3/4 yards of fabric
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the value of a certain two digit number is 9 times the sum of its digits. it the digits are reversed, the resulting number is 63 less than the original number. find the original number
Answer:
Step-by-step explanation:
10x+y=9(x+y)
10y+x=10x+y-63
now put x alone and solve for x then y and add the values of x and y and you will get your answer
John make two clay pot. Each pot i fired independently. The probability that a pot crack while being fired i 0. 03 Calculate the probability that only one of John’ pot crack while being fired
The Probability that only one of John's pot crack while being fired is 0.06.
The probability that only one of John's pots cracks while being fired can be calculated using the formula for the binomial distribution:
P(X = 1) = C(2, 1) * (0.03)^1 * (1 - 0.03)^(2 - 1)
= 2 * 0.03 * 0.97
= 0.0582
Where C(2, 1) is the number of combinations of 2 items taken 1 at a time, and (0.03)^1 and (1 - 0.03)^(2 - 1) are the probabilities of the first pot cracking and the second pot not cracking, respectively.
So, the probability that only one of John's pots cracks while being fired is approximately 0.06.
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Fabian harvests 10 pounds of tomatoes from his garden. He needs
2 2/5
pounds to make a batch of soup. If he sets aside 2.8 pounds of tomatoes to make spaghetti sauce, how many batches of soup can Fabian make? Drag numbers to write and solve an equation. Numbers may be used once, more than once, or not at all.
2.8 returned to choices list.
2.2 2.4 2.5 2.6 2.8 3 5 6 8 10
x + =
x =
PLEASE HELP ME
The number of batches of soup that Fabian can make is given as follows:
3 batches.
How to obtain the number of batches of soup?The number of batches of soup is obtained applying the proportions in the context of the problem.
He has 10 pounds, and sets aside 2.8 pounds of tomatoes to make spaghetti sauce, hence the amount remaining for soup is given as follows:
10 - 2.8 = 7.2 pounds.
He needs 2 and 2/5 = 2 + 0.4 = 2.4 pounds for each batch, hence the number of batches is obtained as follows:
7.2/2.4 = 3.
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I need help with ‘classifying polynomials; adding & subtracting polynomials’
Classifying polynomials refers to categorizing polynomials based on the degree of the polynomial and the number of terms in the polynomial.
The degree of a polynomial is the highest exponent in the polynomial. Polynomials can be classified into several types, including constant polynomials (degree 0), linear polynomials (degree 1), quadratic polynomials (degree 2), and so on. Adding and subtracting polynomials is the process of combining two or more polynomials by combining like terms. Like terms are terms with the same variable and exponent. To add or subtract polynomials, simply line up the terms with the same variable and exponent and add or subtract the coefficients. The result will be a new polynomial with the combined terms.
For example, to add the polynomials [tex]2x^2 + 3x + 4[/tex] and [tex]-x^2 + 5x - 6[/tex], we line up the terms with the same variable and exponent and add the coefficients:
[tex](2x^2 + 3x + 4) + (-x^2 + 5x - 6) = (2x^2 - x^2) + (3x + 5x) + (4 - 6) \\[/tex]
[tex]= x^2 + 8x - 2.[/tex]
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SALARY The average salary for an entry-level mechanical engineer position in Texas ranges from $63,000 to $73,500
a year.
Write a compound inequality to represent the possible monthly salary m of an entry-level mechanical engineer in Texas.
Answer:
$5,250 ≤ m ≤ $6,125
Step-by-step explanation:
A compound inequality is a mathematical statement that combines two inequality statements using "and" or "or". In this case, the compound inequality represents the range of possible monthly salary for an entry-level mechanical engineer in Texas.
The average salary for this position ranges from $63,000 to $73,500 per year. To find the monthly salary, we need to divide these amounts by 12 months, which gives us the minimum and maximum monthly salary:
$63,000/12 = $5,250
$73,500/12 = $6,125
Therefore, the compound inequality is:
$5,250 ≤ m ≤ $6,125
This means that the monthly salary of an entry-level mechanical engineer in Texas could be anywhere between $5,250 and $6,125.