The difference in height between Mt. Everest and Mt. Rushmore is 45,792 feet expressed in standard notation and 4.5792x10^4 feet in scientific notation.
Explanation:
The student is asked to calculate the difference in height between Mt. Everest and Mt. Rushmore and express that difference in scientific notation. The height of Mt. Everest is 54,768 feet and the height of Mt. Rushmore is 8,976 feet. To calculate the difference in height, subtract the height of Mt. Rushmore from the height of Mt. Everest: 54,768 feet - 8,976 feet = 45,792 feet.
To express this difference in scientific notation, move the decimal point to just after the first digit (4), resulting in 4.5792. Then count how many places you moved the decimal. In this case, it moved 4 places, so the exponent is 4. Therefore, the difference in height between Mt. Everest and Mt. Rushmore is approximately 4.5792x10^4 feet in scientific notation.
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A family of four goes to a movie theater and spends $30.50.They buy 2 tickets for children at $3.50 per ticket,2tickets for adults,and 3 boxes of popcorn at $2.50 per box.What is the cost of one adult movie ticket?
On the first day of school, the school bookstore sold 348 notebooks, some at 25¢ each and the rest at 38¢ each. The total amount of money paid for the notebooks was $100.91. How many of each kind were sold?
Final answer:
The bookstore sold 107 notebooks at 38¢ each and 241 notebooks at 25¢ each. A system of equations was used to determine the number of each notebook sold.
Explanation:
Let's denote the number of notebooks sold at 25¢ each as [tex]x[/tex] and the number of notebooks sold at 38¢ each as [tex]y[/tex] .
We are given two pieces of information:
The total number of notebooks sold is [tex]348: x + y = 348[/tex]The total amount of money collected is [tex]$100.91: 0.25x + 0.38y = 100.91[/tex]We can set up a system of two equations to represent this information:
[tex]x+ y = 348[/tex] (Equation 1)
[tex]0.25x + 0.38y = 100.91[/tex] (Equation 2)
Now, we can solve this system of equations to find the values of x and y.
Multiply Equation 1 by 0.25 to make the coefficients of x in both equations the same:
[tex]0.25x + 0.25y = 87[/tex] (Equation 3)
Now, subtract Equation 3 from Equation 2 to eliminate [tex]x[/tex] :
[tex]( 0.25x + 0.38y ) - ( 0.25x +0.25 y) = 100.91 - 87[/tex]
[tex]0.13 y = 13.91[/tex]
[tex]y = 107[/tex]
Now that we have the value for y, substitute it back into Equation 1 to find x:
[tex]x + 107 = 348[/tex]
[tex]x = 241[/tex]
Hence , the solution is x = 241 and y = 107, meaning 241 notebooks were sold at 25¢ each and 107 notebooks were sold at 38¢ each.
Without actually calculating, how much greater is the product of 98x50 than the product of 97x50
Monique had $20. She spent $5 on lunch and $10 at the bookstore.
The budget for a film production includes the following employee pay scales: $15,000 for each technical crew member (e.g. camera, lighting, sound), and $10,000 for each support staff (e.g., drivers, craft services, production assistants). A minimum of 20 employees is needed, but the locations can accommodate a maximum of 50 people. There must be at least 12 technical crew members to shoot the film, and there must be at least half as many crew members as support staff. Which combination of employees will minimize the cost, and what is the minimum feasible cost?
Final answer:
The minimum cost combination of film production employees is 12 technical crew members and 24 support staff members, with a minimum feasible cost of $420,000.
Explanation:
To determine the combination of employees that will minimize the cost, let's set up variables for technical crew members (T) and support staff members (S).
The pay scales are $15,000 for each technical crew member (T) and $10,000 for each support staff member (S).
The objective is to minimize the cost C, where C = 15,000T + 10,000S.
From the constraints provided:
There must be a minimum of 20 employees: T + S ≥ 20.The maximum number of people that can be employed is 50: T + S ≤ 50.There must be at least 12 technical crew members: T ≥ 12.There must be at least half as many crew members as support staff: T ≥ 0.5S.To minimize the cost while satisfying all constraints, we should aim to hire as few technical crew members as possible, given they are more expensive.
If T = 12 (the minimum), we can solve for S using T ≥ 0.5S, which gives us S ≥ 24.
However, S must be even due to the constraint T ≥ 0.5S and hence we can set S = 24 as a candidate solution, resulting in the minimum number of employees (12 + 24 = 36).
We also need to ensure that S ≤ 2T to satisfy the condition T ≥ 0.5S; with T = 12, the maximum S can be is 24.
The minimum feasible cost is determined by plugging T = 12 and S = 24 into the cost equation:
C = 15,000(12) + 10,000(24) = 180,000 + 240,000 = $420,000.
how would you solve this equation?
x/6-x/7=ab
To solve x/6 - x/7 = ab, find the common denominator, simplify, and then isolate x by multiplying both sides of the equation by the common denominator. The solution is x = 42ab. Always check your answer to ensure it satisfies the original equation.
Explanation:To solve the equation x/6 - x/7 = ab, one must find a common denominator for the fractions. In this case, the common denominator is 42 because 6 and 7 are both factors of 42. By converting both fractions to have the denominator of 42, we have:(7x/42) - (6x/42) = ab
This simplifies to x/42 = ab, since 7x - 6x is x. Now, multiply both sides by 42 to get x = 42ab.
If we want to solve the equation for a variable other than x, such as y, we might need to return b to denominator status, which implies that we need to divide both sides by b if b represents a multiplication factor for y.
It's also important to confirm that our manipulations haven't altered the value of the equation, which can be done by checking the answer at the end to ensure it is reasonable and satisfies the original equation.
HELP ASAP!!!!!!
A figure skater needs a total score of at least 90 to move on to the next round. Her total score is the average of four judges’ scores. The first three judges’ scores were 83, 88, and 92. The figure skater found out she made it to the next round.
What is the minimum score the fourth judge could have given her?
a pineapple drink contains 15% pineapple juice. how much pure pineapple juice should be added to 8 quarts of the pineapple drink to obtain a mixture containing 50% pineapple juice
To solve the problem, set up an equation based on the given information to find the amount of pure pineapple juice needed to obtain a 50% mixture.
To solve this problem, we need to set up an equation based on the given information.
Let x be the amount of pure pineapple juice to be added.
The initial amount of pineapple juice in the drink is 15% of 8 quarts, which is 0.15 * 8 = 1.2 quarts.
After adding x quarts of pure pineapple juice, the total volume of the mixture becomes 8 + x quarts.
Setting up the equation: 1.2 + x = 0.5 * (8 + x).
Solving for x gives the amount of pure pineapple juice needed to obtain a 50% mixture.
m<9=2x-4 and m<10=2x+4
m<6.5 & m<3 I just solved it so I hope I helped answering that question
I really need help....
Clint prepares and sells trails mixes at his store. This week, he used 3/8 of his supply of raisins to make regular trail mix and 1/4 of his supply to make spicy trail mix. If Clint uses 20 pounds of raisins this week, how many pounds of raisins did he have at the beginning of the week? Show your work.
The amount of raisins at the beginning is 43/8 pounds.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
3/8 of his supply of raisins to make regular trail mix and 1/4 of his supply to make spicy trail mix.
Clint uses 20 pounds of raisins
amount of raisin at the begining
= 1/4 x 20 + 3/8
= 5 + 3/8
= 40/8 + 3/8
= 43/8 pounds
Hence, the amount of raisins at the beginning is 43/8 pounds.
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Brandon rode his bike 90% of the distance that Carlee did this week. He rode 58.5 miles. How many miles did Carlee ride?
To find out how many miles Carlee rode, you need to divide the distance Brandon rode (58.5 miles) by 0.9 (representing 90%). The result is that Carlee rode 65 miles.
Explanation:The problem requires you to determine the distance that Carlee biked based on the information provided. Given that Brandon rode his bike 90% of the distance Carlee did, and he rode 58.5 miles, to calculate the distance Carlee traveled, you would divide the distance Brandon rode by 0.9 (which represents 90%).
So, the calculation would be: 58.5 ÷ 0.9 = 65.
Therefore, Carlee must have biked 65 miles in total given the information provided.
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Which represents all the values of x that make the rational expression -6x + 42/3x + 9 undefined?
Answer: -3
A. On E 2020
Step-by-step explanation:
−8x+5−2x−4+5x− when x=2
What is the average speed of a runner if he ran 2 1/3 of a mile in 20 minutes?
Answer:
The average speed of the runner is 7 miles per hour.
Step-by-step explanation:
Given:
Distance ran by [tex]2\frac{ 1}{3} miles[/tex]
Time taken by the runner = 20 minutes.
To find:
The average speed of a runner=?
Solution:
Now, we know that ,
distance = speed x time
Then, [tex]2\frac{ 1}{3} miles[/tex] = average speed x 20 minutes
=> average speed = [tex]\frac{(2 \frac{1}{3} miles)}{(20 minutes)}[/tex]
=> average speed = [tex](\frac{(2 x 3 + 1)}{3} miles)}{(20\times\frac{1}{60} hours)[/tex]
=> average speed=[tex]\frac{(\frac{(6+1)}{3})}{(\frac{20}{60})}[/tex]
=> average speed = [tex]\frac{ (\frac{7}{3})}{(\frac{1}{3})}[/tex]
=>average speed = [tex]\frac{7}{3}\times\frac{3}{1}[/tex]
=>average speed = 7
what are perfect trios as a whole number?
The term 'perfect trios' as a whole number is not a standard mathematical term, but it may refer to something like Pythagorean triples, which are sets of three positive integers that satisfy the equation a² + b² = c². Without additional context, the term remains unclear.
Explanation:The term "perfect trios" is not a standard mathematical term, so it is a bit unclear what it refers to. It may be a term used in a specific textbook or class to refer to a certain type of number trio or to phenomena in physics or another field. However, in mathematics, we can talk about perfect numbers, which are positive integers that are equal to the sum of their proper divisors (excluding the number itself). Additionally, we may consider Pythagorean triples, which are sets of three positive integers a, b, and c, such that a² + b² = c². These are special cases of perfect squares and can be considered when discussing whole number trios in a mathematical sense.
Without more context, we can assume that 'perfect trios' might be an informal term for sets of three numbers that have some special property, such as those that make up a Pythagorean triple.
For example, the Pythagorean triple (3, 4, 5) is well-known because 3² + 4² = 5². Similarly, (5, 12, 13) is another Pythagorean triple as 5² + 12² = 13².
solve the equation for y:
x=2y-3
A recipe calls for31/4 cups of sugar.amy has already put in 31/9 cups . How many more cups does she need
The Boston Marathon is 26.2 miles. Use the times shown in the table to calculate the miles per hour for each division winner. Round to the nearest thousandth.
Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal.
Answer:
Yes, she is correct.
Step-by-step explanation:
A real number that can be expressed as [tex]\frac{p}{q}[/tex],
Where,
p and q are integers,
Such that, q ≠ 0,
is called a rational number.
A terminating decimal is always a rational number,
Thus, 2.11 is a rational number,
Verification :
2.11 = [tex]\frac{211}{100}[/tex]
Where,
Both 211 and 100 are integers,
Such that 100 ≠ 0.
The value 2.11 is a rational number and not a repeating decimal.
Given the number 2.11 ;
Rational numbers Can be expressed in the form p/q ; where q ≠ 0. However, irrational numbers cannot be be expressed in the form p/q. 2.11 is written into two decimal places ; therefore it can be expressed thus ;(2.11 × 100) ÷ 100 [tex] \frac{211}{100} [/tex][tex]since \: 2.11 = \frac{211}{100} [/tex]
Then, we can conclude that 2.11 is a rational number
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what time will lunch end if it starts at 11:15 and they only have 35 minutes to eat what time does lunch end
write an equation you could use to find the length of the missing side of each triangle. Then find the missing length. Round to the nearest tenth if necessary.
If f(x) = 2x−5, then what is the value of f(2) + f(5)
a veterinary student estimated the weight of a snapping turtle to be 147 pounds. the actual weight was 175 pounds. what is the percent error between the actual weight of the turtle and the estimated weight
write the slope - intercept equation that describes the line that passes through (-3,1) amd is parallel to the line described by y=4x+1
are all terminating and repeating decimals ration numbers?
your computer supply store sells two types of laser printers. the first type, a, costs $137 and you make a $50 profit on each one. the second type, b, costs $110 and you make a $40 profit on each one. you expect to sell at least 100 laser printers this month and you need you make at least $4400 profit on them. if you must order at least one of each type if printer, how many of each type of printer should you order if you want to minimize your cost?
How can I solve this awencer
Harriet made a list of all her monthly expenses. What is Harriet’s total cost for housing in a month?
eating out = $40
cell phone bill = $55
rent = $370
car insurance = $48
groceries = $160
renter’s insurance = $27
gas = $60
Total Housing=$______
What is the measure of angle AXB
Answer:
70
Step-by-step explanation:
10*7=70
Find the area of the model!!! ASAP PLEASE
area of a square is S^2
2.6^2 = 6.76 square cm