Step-by-step explanation:
The given objective function is [tex]C = 60x + 85y[/tex]
To check that which ordered pair is minimizing the objective function-we will substitute all the ordered pair one by one in the given function and we will calculate the value of C. The ordered pair which will give the minimum value will be the answer.
For (0, 160)
[tex]C=60\times 0+85\times 160=13600[/tex]
For (55, 70)
[tex]C=60\times 55+85\times 70=9250[/tex]
For (80, 50)
[tex]C=60\times 80+85\times 50=9050[/tex]
For (80, 50)
[tex]C=60\times 170+85\times 0=10200[/tex]
Hence the ordered pair which minimizes the objective function is (80, 50)
Jeremiah is saving money for a tutoring job after the first 3 weeks he saved 135$ assume the situation is proportional use the unit rate to write an equation relating the amount saved s to the number of weeks w worked at this rate how much will Jeremiah save after eight weeks? Plz help
Answer:
s = 45w
Step-by-step explanation:
Jeremiah is saving money for a tutoring job.
He saved $135 after 3 weeks.
Therefore, his saving per week = [tex]\frac{\text{Total amount}}{\text{Number of weeks}}[/tex]
= [tex]\frac{135}{3}[/tex]
= $45
If he works for w weeks then at the same rate total amount saved by him will be
= $45w
If this amount is equal to $s then equation that represents the total saving after w weeks will be
s = 45w
21 people are going to the show. They have 3 vans and 1 car. If 6 people fit in each van, how many will have to ride in a car?
Question 8 options:
3
4
5
6
Last week, there were 225 student absences at Johnson High. The circle graph below summarizes them by the day of the week on which they occurred. The central angle for the Tuesday slice is 86.4° . What percentage of the absences occurred on Tuesday?
The percentage of student absences that occurred on Tuesday is approximately 24%.
The circle graph represents the distribution of student absences by day of the week. The central angle for the Tuesday slice is given as 86.4°. To find the percentage of absences on Tuesday, we use the formula: (Central Angle / Total Central Angle) * 100%. In this case, (86.4° / 360°) * 100% ≈ 24%. Therefore, approximately 24% of the student absences occurred on Tuesday.
The central angle represents the proportion of the total absences attributed to each day. A circle has a total central angle of 360°, and the central angle for each day is a fraction of this total. Tuesday's central angle of 86.4° indicates that Tuesday's absences make up 24% of the total absences.
This method applies because the circle graph represents a whole, and each sector's central angle corresponds to its share of the total. Consequently, the calculation accurately reflects the percentage of absences on Tuesday in relation to the entire week.
what percent of 92 is 69
The number 69 is 75 % or 75 percentage of the number 92
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the percentage be represented as A
Let the first number be n₁ = 92
Let the second number be n₂ = 69
And , the percentage value of 69 of the number 92 is given by
n₂ = ( A / 100 ) x 92
On simplifying , we get
69 = ( A / 100 ) x 92
Multiply by 100 on both sides , we get
6900 = 92A
Divide by 92 on both sides , we get
A = 6900 / 92
A = 75 %
Therefore , the value of A is 75 %
Hence , the percentage value of 69 of the number 92 is 75 %
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To the nearest hundred, what is the greatest whole number that rounds to 2,500
The greatest whole number that rounds to 2,500 to the nearest hundred is 2549.
Explanation:To answer this question, we need to understand how rounding works. When we round to the nearest hundred, any number that falls exactly in the middle or above will round up to the next hundred. Any number that falls below the middle will round down to the previous hundred. The middle point between 2400 and 2500 is 2549. Therefore, 2549 would be the greatest whole number that rounds down to 2500 when rounded to the nearest hundred.
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A. Multiplication comes before division because in PEMDAS the M comes before D.
Students who use PEMDAS often think that multiplication must come before division but that's not necessarily the case. If division appears before multiplication when your reading the problem from left to right, do your division first and then move on to your multiplication.
What is 612 times 87 with work shown multiply by multi digit number
solve each equation. 8.5 - 3z = - 8z
4 yd. 8 in + 6 yd. 6 in
The sum of the expression 4 yards 8 inches and 6 yards 6 inches will be 10 yards and 14 inches.
What is addition?The sum of the numbers is known as an addition.
The expressions are given below.
4 yd. 8 in and 6 yd. 6 in
The sum of the expression 4 yards 8 inches and 6 yards 6 inches will be
⇒ (4 + 6) yd and (8 + 6) in
⇒ 10 yards and 14 inches
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Final answer:
To solve the addition of 4 yards 8 inches and 6 yards 6 inches, we add yards to yards and inches to inches, resulting in 10 yards 14 inches, which simplifies to 10 yards and 2 inches because 12 inches make a foot, and 3 feet make a yard.
Explanation:
The student's question involves adding two measurements together: 4 yards 8 inches and 6 yards 6 inches. In mathematics, especially in the measurement units topic, it is common to work with both the same and different units when performing calculations. To add these two measurements, we must add the yards together and the inches together separately. Since 1 yard equals 3 feet, this information can be used to convert yards to feet if necessary.
\n\n
First, add the yards: 4 yards + 6 yards = 10 yards. Next, add the inches: 8 inches + 6 inches = 14 inches. Because there are 12 inches in a foot, 14 inches is equivalent to 1 foot 2 inches. Thus, we need to convert this extra foot into yards, knowing that there are 3 feet in 1 yard, so 1 foot = 1/3 yard.
\n\n
We have 10 yards from the initial addition and an additional 1/3 yard from converting the extra foot to yards. Adding these together, we get 10 yards + 1/3 yard = 10 1/3 yards. Since there are no more than 12 inches in the remaining inches part, our final answer in yards and inches is 10 yards 2 inches.
Find the product to the nearest ten. (100.8) (24.5)
Death will most likely occur following exposure to: 100 R's 200 R's 500 R's
Tara read 1/3 of a book on Monday, 2/7 of the book on Tuesday, and 2/9 of the book on Wednesday. How much of the book did she read?
david counts the quarters in his change jar. He has 24 more quarters than his brother Rob. if r is the number of quarters Rob has, which expression represent the number of quarters and david and Rob have it all
How can we tell the difference between a common multiple problem and a common factor problem?
You need to arrange four of your favorite books along a small shelf. How many different ways can you arrange the books assuming the order of the books make a difference
Final answer:
To determine the number of different arrangements of four books, we calculate the permutation 4!, which equals 24. Hence, there are 24 different ways to arrange the four books.
Explanation:
The question asks about the number of different ways to arrange four books on a shelf, assuming the order of the books makes a difference. This problem is an example of a permutation, where the arrangement of a set of items is important.
To calculate this, we use the formula for permutations, which is n!, where 'n' is the number of items to arrange. In this case, we have four books, so we calculate 4! (which is shorthand for 4 × 3 × 2 × 1).
Therefore, 4! = 24. There are 24 different ways to arrange the four books on the shelf.
Simplify the expression in detail plz
Patrick subtracted 4,832-2,322 and got 2,510.is hus difference reasonable?explain
What property is 6 (m×n)=(6×m)n
Six friends each 3/4 of a mile in a relay. What is the total distance they ran
the are 90 girls and 60 boys in the sixth grade at a middle school. Of these students, 9 girls and 3 boys write left-handed. What percentage of the sixth graders at this middle school write left-handed.
how do you graph 8a-10=38 but a=6?
show how to move the parentheses in the expression 2+(3+4)9 so that the value of the expression is 9
5 1/2
-
3 3/4
______
5 1/2 - 3 3 /4 =
11/2 - 15/4 =
22/4 - 15/4 = 7/4 = 1 3/4
What are the side lengths of the rectangle. Area=40 square inches. Perimeter=28 inches
what is the algebraic expression for:
1. 4 times a number cubed decreased by 7
2. 3 more than 5 times the number
3. 15 less than a number squared
4. The product of 5 and y added to 3
a = a is an example of which algebraic property (A) Symmetric property (B) transitive property (C) reflexive property (D) commutative property of multiplication
Answer:
(C) reflexive property
Step-by-step explanation:
In algebra there are several rules and properties that help us work and discover new things, the reflexive property of algebra states that every single thing is equal to itslef, this means that you can use any term, let´s say "w", and "w" will always be equal to itself. W=W, just as a=a.
A turkey costs $18.75 plus a 4% sales tax. How much will the turkey cost with the tax?
how do i solve this equation
What is the area of the following parallelogram in square centimeters?
A) 396 cm2
B) 360 cm2
C) 3.6 cm2
D) 3.96 cm2
Which of the following sets of numbers is a Pythagorean triple?
A) 42, 40, 82
B) 42, 40, 58
C) 41, 41, 58
D) 40, 41, 57
Answer with explanation:
1.⇒Area of Parallelogram = Corresponding height × Base
= 2 cm × 18 mm
→1 cm = 10 mm
So, Area of Parallelogram
= 2 cm × 1.8 cm
= 3.6 cm²
Option C: →3.6 cm²
→→→2. A triplet ,that is set of three numbers is called Pythagorean triplet, if it is of the form of : {m²-1, 2 m , m²+1}
That is if you write the Pythagorean rule for Right triangle, having sides , m²-1, 2 m , m²+1
then ,→ Square of Largest side = Sum of squares of two smallest side
Square of Largest Side = (m²+1)²
Sum of squares of two smallest side= (2 m)² + (m²-1)²
= 4 m² + (m²)² -2 m²+1
= (m²)² +2 m²+1
=(m²+1)²
So, we will check out , out of four options which of them are Pythagorean Triplet.
Option 1.
Square of Largest Number = 82²=6724
Sum of squares of two smaller number= 42² + 40²
= 1764 +1600
= 3364
→Square of Largest Number ≠Sum of squares of two smaller number
6724 ≠ 3364
Not a Pythagorean Triple.
Option 2.
Square of Largest Number = 58²=3364
Sum of squares of two smaller number= 42² + 40²
= 1764 +1600
= 3364
→Square of Largest Number =Sum of squares of two smaller number
3364= 3364
A Pythagorean Triple.
Option 3.
Square of Largest Number = 58²=3364
Sum of squares of two smaller number= 41² + 41²
= 1681 +1681
= 3362
→Square of Largest Number ≠Sum of squares of two smaller number
3364 ≠ 3362
Not a Pythagorean Triple.
Option 4.
Square of Largest Number = 57²=3249
Sum of squares of two smaller number= 41² + 40²
= 1681 +1600
= 3281
→Square of Largest Number ≠Sum of squares of two smaller number
3249 ≠ 3281
Not a Pythagorean Triple.
Option B: (42, 40,58) is a Pythagorean triple.
Answer:
C
Step-by-step explanation:
write 7 1/5 as a decimal
The solution of the expression [tex]7\dfrac{1}{5}[/tex] which is in the mixed fraction as a decimal form is 7.2.
The combination of a whole number and a proper fraction is called as mixed fraction.
The solution of the expression [tex]7\dfrac{1}{5}[/tex] as a decimal is calculated as:
First, convert the given mixed fraction into the improper fraction.
[tex]7\dfrac{1}{5} =\dfrac{(7 \times 5)+1}{5}[/tex]
On further solving,
[tex]\dfrac{(7 \times 5)+1}{5} = \dfrac{36}{5}[/tex]
The improper fraction is converted into the decimal by dividing 36 by 5,
which results to 7.2.
The solution of the expression [tex]7\dfrac{1}{5}[/tex] as a decimal, is 7.2.
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