Answer:
Option B and Option D is correct.
The inequalities are among the constraints for the given situation is,
[tex]12x+8y\geq 1000[/tex] and [tex]x+y\leq 200[/tex]
Explanation:
Let x represents the number of regular ticket sold.
and y represents the number of student ticket sold.
then, 12x represents the regular tickets at $12 each,
and 8y represents the student tickets at $8 each.
As the manager wants to collect at least $ 1000 from the ticket sale or we can say that the manager wants $ 1000 or more from the ticket sale.
then, we have the inequalities for this;
[tex]12x+8y\geq 1000[/tex]
As, the theater can seat at most 200 people or we can also say that the theater can seat 200 or less people .
therefore, the inequalities for this we have;
[tex]x+y\leq 200[/tex]
Therefore, the inequalities are among the constraints for the given situation is,
[tex]12x+8y\geq 1000[/tex] and [tex]x+y\leq 200[/tex]
15x - 10 = -9x + 2
please help me !!!!!
The French helped the Patriot war effort by
A. attacking the main island of Britain to distract British forces.
B. keeping Spain out of the war.
C. going to war against hostile Native American groups. End of exam
D. providing a navy and military support.
Triangle FGH is an isosceles right triangle with a hypotenuse that measures 16 units. An altitude, GJ, is drawn from the right angle to the hypotenuse.
What is the length of GJ?
A. 2 units
B. 4 units
C. 6 units
D. 8 units
The value of the length GJ for the given triangle will be 8 units thus option (D) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
As per the given isosceles triangle which has two equal sides so suppose the length of those sides is x unit.
By Pythagoras' theorem,
⇒ x² + x² = 16²
⇒ 2x² = 256
⇒ x² = 128
The area of a triangle is given as,
⇒ (1/2) × x × x
⇒ (1/2) x²
⇒(1/2) × 128
⇒ 64 units²
The area of the triangle will also be given as,
A = (1/2) × 16 × (GJ)
Compare both areas as
64 = (1/2) × 16 × GJ
GJ = 8 units
Hence"For the provided triangle, the length GJ value will be 8 units".
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PLEASE HELP ASAP
Rich bought two baseballs for $ 4 each and two basketballs for $ 22 each. Use the distributive property to find the total cost.
Rich spent $8 on baseballs and $44 on basketballs for a total expense of $52. This application of buying multiple items at a given cost and then summing across categories demonstrates the distributive property in mathematics.
Explanation:Rich bought two baseballs at a cost of $4 each. This cost could be represented as 2 * $4 = $8. He also bought two basketballs for $22 each. This cost could be represented as 2 * $22 = $44. By using the distributive law, we multiply the cost of each basketball or baseball with the quantity purchased and then adding the total costs together which is adding $8 and $44. Hence, the total is $8 + $44 = $52 which represents the total cost of the baseballs and basketballs that Rich bought. This is a clear demonstration of the distributive property where operations inside parentheses can be distributed over other operations.
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A rectangle is 3 times as long as it is wide. the perimeter is 60 cm. find the dimensions of the rectangle. round to the nearest tenth if necessary. (1 point) 7.5 cm by 22.5 cm 7.5 cm by 52.5 cm 20 cm by 60 cm 15 cm by 22.5 cm
Jenny is 65 years old, retired, and good health, and likes to travel to wor Jenny is 65 years old, retired, and good health, and likes to travel to world. Which lifestage best describes her?
Jenny is at the life stage of Mature Adulthood, this is the stage of where an adult has established their goals in life such as that involve in work, or anything that they have contributed in their life. They were able to raise a family and has learned things that happened in his or her life.
In a public opinion poll 624, people from a sample of 1100 indicate they would vote for a specific candidate. How many votes can the candidate expect to revive from a Population of 40,000
To solve this problem the best way is
624/1100 = x/40000
x = 624*40000/1100
x = 24960000/1100
x = 22690 votes
Around 22690 votes can be expected to revive from a Population of 40,000 by taking the same ratio.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Let's say x votes can be expected to revive from a Population of 40,000.
Now,
By taking the same ratio;
x/40000 = 624/1100
x = 22690.9090 which can be counted as 22690.
Hence " Around 22690 votes can be expected to revive from a Population of 40,000 by taking the same ratio".
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A commuter plane provides transportation from an international airport to the surrounding cities. one commuter plane averaged 280 mph flying to a city and 120 mph returning to the international airport. the total flying time was 3 h. find the distance between the two airports.
The distance between the two airports is 252 miles
What is Speed?
Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the distance between the two airports be = D
Now ,
Let the first airport be = A
Let the second airport be = B
And , the speed from Airport A to Airport B averaged = 280 mph
The speed from Airport B to Airport A averaged = 120 mph
The total time taken for the journey = 3 hours
So , the value of Time T = 3 hours
So , the equation will be
Time = Distance / Speed
Since , the distance between the airports remains the same on the journey,
Time = D/280 + D / 120
Substituting the values in the equation, we get
D/280 + D / 120 = 3
The LCM of 280 and 120 is 840 , so
( 3D + 7D ) / 840 = 3
On simplifying the equation , we get
Multiply by 840 on both sides of the equation , we get
10D = 2520
Divide by 10 on both sides of the equation , we get
D = 252 miles
Therefore , the value of distance D from the equation is 252 miles
Hence , The distance between the two airports is 252 miles
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Final answer:
By solving the equation 280t = 120(3 - t), we find that the time taken to fly to the city is 0.9 hours. Multiplying this by the speed of 280 mph, the distance between the two airports is determined to be 252 miles.
Explanation:
To find the distance between the two airports, we can use the formula distance = speed × time, but first, we need to find the time taken for each leg of the journey. Let t be the time (in hours) it takes for the plane to fly to the city at 280 mph. Hence, the time taken to return to the international airport at 120 mph will be 3 - t hours. We can establish the following equations based on this information:
To the city: 280t (since distance = 280 mph × t)
Returning: 120(3 - t) (since distance = 120 mph × (3 - t))
Since the distances are equal for both trips, we can set the equations equal to each other:
280t = 120(3 - t)
Solving for t, we get:
280t = 360 - 120t
400t = 360
t = 0.9
The time taken to fly to the city at 280 mph is 0.9 hours. Now we can find the distance:
Distance to the city = 280 mph × 0.9 h = 252 miles.
Therefore, the distance between the two airports is 252 miles.
Dan is using tiles to add –8 + 6. He begins with the tiles shown below.
mc006-1.jpg
What is the sum of –8 + 6?
–14
–2
2
14
Answer:
Step-by-step explanation:
Alright, lets get started.
The given expression is : [tex]-8+6[/tex]
-8 can be written as [tex]-6-2[/tex]
So, the expression will be = [tex]-6-2+6[/tex]
The plus six and minus six will be cancelled. so,
-2 will be remaining.
So the answer is -2 : Answer
Hope it will help :)
Answer:
-2
Step-by-step explanation:
Which of the following best describes the algebraic expression 15x + 8? A. the sum of fifteen times a number and eight B. the product of fifteen plus a number and eight C. fifteen times the sum of a number and eight D. fifteen times the quantity of a number plus 8
Answer: A. [tex]\text{the sum of fifteen times a number and eight }[/tex]
Step-by-step explanation:
The given algebraic expression : [tex]15x + 8[/tex]
We can see that the constant term here is [tex]8[/tex].
The variable term is [tex]15x[/tex].
The operation used here = Addition
To convert any algebraic expression into a statement we represent the variable i.e. x by word "number".
Then the variable term is represented as : Fifteen times a number
Therefore, the best describes the given algebraic expression will be :-
"[tex]\text{the sum of fifteen times a number and eight }[/tex]"
Travis runs an average of 25 miles per week give or take six miles. let m be the number of miles travis runs each week
A contestant on a game show is given $100 and is asked five questions. The contestant loses $20 for every wrong answer. Is the graph discrete or continuous? Determine the domain and range.
A function can either be discrete or continuous, depending on the input values of the function
The graph is discreteThe domain is [0,5]The range is [0,100]From the question, we understand that:
The contestant would be asked 5 questionsThe contestant would lose $20, for each wrong answerNotice that:
It is impossible to ask the contestant 1.5 questions
And base on the possible earnings, the contestant cannot earn $50.5 or number with decimal
When the data we are dealing with are non-decimal numbers, then the distribution is discrete
The domain and range
There are 5 possible questions to ask;
So, the domain is [0,5]
The contestant starts with $100.
So, the range is [0,100]
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Jamarcus's employer pays 80 percent of his medical insurance. If the insurance costs Jamarcus $20 a week, how much is his employer paying?
Answer:
$80
Step-by-step explanation:
The total amount of his medical insurance is 100%. As such if Jamarcus's employer pays 80 percent , then the amount he pays would be equivalent to 20%.
As such, if the insurance costs Jamarcus $20 a week and the total amount is Y
then,
20% of Y = $20
0.2Y = $20
Y = $100
His employer will be paying
= 80% of $100
= $80
Please help me with the problem below! :)
I need help with starring the answer in mixed fraction
When adding two numbers, such as 123 and 423, care is taken to first line them up and then add like digits. How does expanding this expression to [(1 × 10^2 ) + (2 × 10^1 ) + (3 × 10^0 )] + [(4 × 10^2 ) + (2 × 10^1 ) + (3 × 10^0 )] make the operation more like a polynomial addition problem?
So difficult!!! Someone help
If two ants are walking in straight lines but in different directions their paths cannot cross more than once. Write the postulate that justifies this statement.
45 1/2% percent as a fraction in simplest form
45 1/2 per cent as a fraction in simplest form is 91/200.
We need to write 45 1/2% as a fraction in the simplest form.
How to write a fraction in the simplest form?A fraction is in its simplest form when the top and bottom cannot be any smaller, while still being whole numbers.
To simplify a fraction: Divide the top and bottom by the greatest number that will divide both numbers exactly (they must stay whole numbers).
Now, 45 1/2% can be written as 45.5/100
Multiply both numerator and denominator by 10.
That is 455/1000
Now, 455/1000 = 91/200
Therefore, 45 1/2 per cent as a fraction in simplest form is 91/200.
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Simplify -8 - 7(y+2)
After a researcher adds 5 points to every score in a sample, the standard deviation is found to be s = 10. the original sample had a standard deviation of s = 5.
a. True
b. False
A computer system password requires five characters, all lowercase letters (remember there are 26 letters), and all the letters must be different. how many different passwords are possible?
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The number of ways in which the password can be formed is 7,893,600.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given that a computer system password requires five characters, all lowercase letters (remember there are 26 letters), and all the letters must be different. Therefore, if a letter is used once it can not be used again.
For the first place available options = 26 letter
Now, one letter is only used therefore, there are only 25 options available for the next place.
For the Second place available options = 25 letter
Now, two letters are only used therefore, there are only 24options available for the next place.
For the third place available options = 24 letter
Now, three letters are only used therefore, there are only 23 options available for the next place.
For the fourth place available options = 23 letter
Now, the four letter are only used therefore, there are only 22 options available for the next place.
For the fifth place available options = 22 letter
Further, the number of ways in which the password can be formed is,
Number of ways = 26 × 25 × 24 × 23 × 22 = 7,893,600
Hence, the number of ways in which the password can be formed is 7,893,600.
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Final answer:
There are 789,360 different passwords that are possible.
Explanation:
To find the number of different passwords that are possible, we can consider the problem in a step-by-step manner.
For the first character, there are 26 choices since we can choose any lowercase letter.For the second character, there are 25 choices remaining since one letter has already been used.Similarly, for the third character, there are 24 choices remaining.For the fourth character, there are 23 choices remaining.And finally, for the fifth character, there are 22 choices remaining.To find the total number of possible passwords, we can multiply these choices together: 26 × 25 × 24 × 23 × 22 = 789,360.
2(-3 x + 1) = 9 x - 8
which equation represents the table below? sal's and carries ages
Answer:
c = s + 4
Step-by-step explanation:
We have given the Sal's and Carrie's ages. We need to represents the table below using equation.
Sal = 3 5 8 13 15
Carrie = 7 9 12 17 19
Out of given options, equation (3) should be followed. We can proof it as :
c = s + 4
Putting one by one the ages of Sal in the above equation to get Carrie's age.
1. c = 3 + 4 = 7
2. c = 5 + 4 = 9
3. c = 8 + 4 = 12
4. c = 13 + 4 = 17
5. c = 15 + 4 = 19
Hence, the correct option is (c).
What is the measure of an angle whose sine is√3/2 ? 60 45 30
How many elements does each of these sets have where a and b are distinct elements?
a.p({a,b,{a,b}})
b.p({∅,a,{a},{{a}}})?
What is a mathematical phrase that contains numbers, variables, or operators, but no equal sign?
I need help!
Step 1 ?
Step 2 ?
Step 3 ?
Step 4 ?
what two numbers multiply to make 6 and also add to make 8
Pamela bought an electric drill at 85% of the regular price. she paid $32.89 for the drill. What was the regular price ( Round to the nearest cent)