A room has an area of 456 square feet. One dimension is 5 feet more than the other. Find the dimensions of the room.
Dimensions of the room with area of 456 square feet is 19 feet by 24 feet.
To solve for the dimensions of a room where the area is 456 square feet and one dimension is 5 feet more than the other, we can set up the following equations:
Let the width be x feet.
Then the length will be (x + 5) feet.
The area of a rectangle is given by the multiplication of its length and width, so the equation to represent the area is x(x + 5) = 456.
Expanding this, we get x2 + 5x - 456 = 0.
This is a quadratic equation which can be factored or solved using the quadratic formula. Factoring gives us (x - 19)(x + 24) = 0.
Since a room cannot have a negative dimension, we take the positive value of x, which is 19 feet.
Therefore, the width of the room is 19 feet, and the length is 19 + 5 = 24 feet.
A store received 300 containers of milk to be sold by February 1. Each container cost the store $0.79 and sold for $1.55. The store signed a contract with the distributor in which the distributor agreed to a $0.50 refund for every container not sold by February 1. If 270 containers were sold by February 1, how much profit did the store make?
The total profit did the store make is $196.5 and this can be determined by using the formula of profit and using the given data.
Given :
A store received 300 containers of milk to be sold by February 1. Each container cost the store $0.79 and sold for $1.55. The store signed a contract with the distributor in which the distributor agreed to a $0.50 refund for every container not sold by February 1.The formula of profit is given below:
Profit = Revenue - Expenses --- (1)
So, first determine the total cost of the 300 containers.
Total Cost = 300 [tex]\times[/tex] 0.79
= $237
Now, determine the revenue for the 270 sold containers.
Revenue = 270 [tex]\times[/tex] 1.55
= $418.5
Now, the determine the revenue for the 30 unsold containers.
Revenue = 30 [tex]\times[/tex] 0.50
= $15
So, the total revenue is given by:
Total Revenue = 418.5 + 15
= $433.5
Now, substitute the known terms in the equation (1).
Profit = 433.5 - 237
= $196.5
So, the total profit did the store make is $196.5.
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For Frank"s Funky Sounds, units of production depreciation on the trucks is a
a. variable cost. c. mixed cost.
b. fixed cost. d. high-low cost.
The employees from maintenance go for coffee together every day at 9 a.m. On Monday, Hector paid $5.35 for three cartons of milk, six cups of coffee, a seven doughnuts. On Tuesday, Guillermo paid 4.80 for four milks, two coffees, and eight doughnuts. On Wednesday, Anna paid $4.40 for two milks, five coffees, and six doughnuts. On Thursday, Alphonse had to pay for two milks, five coffees, and seven doughnuts. How much change did he get back from his $10bill?
Prehistoric cave paintings were discovered in a cave in France. The paint contained
23% of the original carbon-14. The half-life of carbon-14 is 5730 years. Estimate the age of the paintings
Janelle bought a pair of sneakers for $75.65. There was a 15% discount. What was the original price of the sneakers?
To determine the original price of Janelle's sneakers, we calculate the inverse of the 15% discount that left her with a final price of $75.65, revealing the original price to be $89.00.
To find the original price of the sneakers that Janelle bought with a 15% discount, we need to understand that the final price after the discount represents 85% of the original price. This is because a 15% discount reduces the original price by 15%, leaving us with 100% - 15% = 85% of the original price. Janelle's sneakers cost her $75.65 after the discount.
Let's denote the original price by x. Therefore, 85% of x is equal to $75.65. We can set up an equation to represent this relationship:
0.85x = $75.65
To find x, we divide both sides of the equation by 0.85:
X = $75.65 / 0.85
x = $89.00
Thus, the original price of the sneakers was $89.00 before the 15% discount.
Christina has two pieces of lace trim with lengths as shown in the table.Complete the table give each length in inches,feet,and yards.
Answer:
Step-by-step explanation:
bs
Find the x-intercepts of the parabola with vertex (-3,-18) and y-intercept at (0,0)
To find the x-intercepts of the parabola given its vertex and y-intercept, we can first determine the equation of the parabola. Then, we set y equal to zero and solve for x. In this case, the x-intercepts are 0 and -6.
Explanation:The x-intercepts of a parabola can be found by setting the y-coordinate to zero and solving for x. The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex. In this case, the vertex is (-3, -18), so the equation of the parabola is y = a(x + 3)^2 - 18. Since the y-intercept is at (0, 0), we can substitute these values into the equation to solve for a. Plugging in the values gives: 0 = a(0 + 3)^2 - 18. Solving for a, we get a = 2. Therefore, the equation of the parabola is y = 2(x + 3)^2 - 18. To find the x-intercepts, we set y equal to zero and solve for x: 0 = 2(x + 3)^2 - 18. Simplifying, we have 2(x + 3)^2 = 18. Dividing both sides by 2 gives (x + 3)^2 = 9. Taking the square root of both sides, we get x + 3 = ±3. Solving for x gives the x-intercepts as x = 0 and x = -6.
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Someone came into my shop and stole $100.00 from the register without my knowledge. The person came back in with the same $100.00 five minutes later and he bought $70.00 worth of items and gave him back $30.00 in change. How much money did I lose?
a patient weighs 65 kilograms how much does the patient weigh in pounds
Please help ASAP
Kevin and randy muise have a jar containing 39 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $ 7.15 . How many of each type of coin do they have?
The jar contains how many quarters and nickels ?
Question Help
The bank statement included bank charges. On the bank reconciliation, this item is:
A.
a deduction from the balance per company books.
B.
a deduction from the balance per bank statement.
C.
an addition to the balance per bank statement.
D.
an addition to the balance per company books.
Since bank charges are deductions from the bank statement balance, the correct answer is:
B. a deduction from the balance per bank statement.
When reconciling a bank statement with the company's books, bank charges are typically deducted from the balance per bank statement.
Let's break down the process:
1. Balance per bank statement: This is the ending balance reported by the bank on the statement.
2. Additions to the bank statement balance: These are items such as deposits in transit (deposits made but not yet recorded by the bank), interest earned, or other credits.
3. Deductions from the bank statement balance: These are items such as outstanding checks (checks issued by the company but not yet cleared by the bank), bank fees or charges, and NSF (non-sufficient funds) fees.
Identify a pattern in the given list of numbers.Then use this pattern to find the next number.
1,4,1,20,1,100,1
The number sequence alternates between 1 and multiples of 5. The pattern of the multiples of 5 increases by a factor of 5 each time, next number in the sequence being 500.
The sequence shown is 1, 4, 1, 20, 1, 100, 1.
To find the next number in this sequence, we can observe that the sequence of numbers (not including the 1's) is increasing by a factor of 5 each time =(4, 20, 100, ...).
Since 100 =5*20, to find the next number after the last 1, we need to multiply 100 * 5.
So, the next number after the last 1 would be 100* 5 = 500.
Use a linear approximation (or differentials) to estimate the given number.
e^−0.01
The approximate value of e^-0.01 is 0.99
Given :
we use linear approximation to estimate the given number
[tex]e^{-0.01}[/tex]
For linear approximation we use equation
[tex]L(x)=f(a)+f'(a)(x-a)[/tex]
Lets assume some value for 'a' that is close to -0.01
Lets assume a=0
[tex]f(x)=e^x\\f(0)=e^0\\f'(x)=e^x\\f'(0)=e^0[/tex]
Lets plug in all the values
[tex]L(x)=f(a)+f'(a)(x-a)\\L(x)=e^0+e^0(x-0)\\L(x)=1+1(x-0)\\L(x)=1+1x[/tex]
Now we estimate e^-0.01
the value of x is -0.01
[tex]L(x)=1+x\\L(-0.01)=1-0.01\\L(-0.01)=0.99[/tex]
The approximate value is 0.99
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To estimate the value of e^−0.01 using linear approximation or differentials, we can use the fact that the derivative of e^x is e^x. Specifically, we can linearize the function at a point close to x = -0.01 and use the linear equation to estimate the value of e^−0.01.
Explanation:To estimate the value of e^−0.01 using linear approximation or differentials, we can use the fact that the derivative of e^x is e^x.
Specifically, we can linearize the function at a point close to x = -0.01 and use the linear equation to estimate the value of e^−0.01.
Let's use the point x = 0 as our approximation point.
The linear equation is given by y = f'(a)(x - a) + f(a), where y represents the value of e^x, f'(a) represents the derivative of e^a at x = a, and f(a) represents the value of e^a at x = a.
Since the derivative of e^x is simply e^x, we have f'(0) = e^0 = 1.
Plugging in the values, we get y = 1(x - 0) + e^0 = x + 1. Therefore, substituting x = -0.01 into the equation, we estimate that e^−0.01 ≈ -0.01 + 1 = 0.99.
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four accounting majors two economic majors and three marketing majors have interviewed for five different positions with a large company. find the number of different ways that five of these people could be hired if the first position is to be filled by an accounting major, the second by an economics.major, and the third by a marketing major, and the last two positions can be filled by any major
There are 1,152 different ways that five people can be hired for different positions in the company.
Explanation:In this question, we need to determine the number of different ways that five people can be hired for different positions in a company.
Given that the first position must be filled by an accounting major, the second position by an economics major, and the third position by a marketing major, we have 4 choices for the first position, 2 choices for the second position, and 3 choices for the third position.
For the last two positions, any major can be hired, so we have 9 choices for the fourth position and 8 choices for the fifth position.
To find the total number of ways, we multiply all the choices together: 4 * 2 * 3 * 9 * 8 = 1,152.
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Solve in terms of x and Y
Write a multiplication problem in which the product is between 0.05 and 0.75
If Cade shoots 275 free throw baskets in 2 hours, about how many can he shoot in 5 hours.
The Harper family is traveling to visit friends. The distance to the friend’s house is 276.45 miles. It takes the family 5.82 hours to complete the trip.
Rate is found by dividing distance by time.
What is the rate for the family’s trip in miles per hour?
need now plz
Answer: 47.5 miles per hour
Step-by-step explanation:
We know that ,
[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
Given : The distance to the friend’s house is 276.45 miles. It takes the family 5.82 hours to complete the trip.
i.e. Distance = 276.45 miles
Time = 5.82 hours
Then, the rate(speed) for the family’s trip in miles per hour will be :-
[tex]\text{Speed}=\dfrac{276.45}{5.82}=47.5\text{ miles per hour}[/tex]
Hence, the rate for the family’s trip = 47.5 miles per hour
1.enter a quadratic polynomial which has zeros at 11 and 3
2.enter a quadratic polynomial which has zeros at -2 and 6
3.enter a quadratic polynomial which has a double root at -6
An equation with zeroes at r1 and r2 factors to (x-r1)(x-r2).
double root at r1 just means (x-r1)^2
We have given that,
enter a quadratic polynomial which has zeros at 11 and 3
What is the quadratic polynomial?A quadratic polynomial is a second-degree polynomial where the value of the highest degree term is equal to 2. The general form of a quadratic equation is given ax^2+bx+C=0
1. f(x)=(x-11)(x-3)
2. f(x)=(x-(-2))(x-6) or f(x)=(x+2)(x-6)
3. f(x)=(x-(-6))^2 or f(x)=(x+6)^2
if you wanted an expanded form
1. f(x)=x²-14x+33
2. f(x)=x²-4x-12
3. f(x)=x²+12x+36
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does -x plus -x result in -x?
In a survey, 480 people, or 75%, said they attended a movie at least once a month. How many people were surveyed?
what is the nearest tenth of 47.5?
36% of a number is 9. What is the number
Answer:
25
Step-by-step explanation:
0.36 × (a number) = 9
9/0.36 = (a number) = 25 . . . . . divide by the coefficient of the variable
The number is 25.
The price of a DVD is $19 . The price is 12% lower than last week.
What was the price of the DVD last week?
Round your answer to the nearest cent.
Need answer in less than 10 mins. plz
The fox population in a certain region has an annual growth rate of 8% per year. In the year 2012, there were 24,900 foxes counted in the area. What is the fox population predicted to be in the year 2020? (Round your answer to the nearest whole number.)
The fox population predicted to be in the year 2020 is 46090.
We have,
The population growth can be represented using the equation:
= [tex]I (1 +R)^n[/tex]
Where I is the initial population, R is the growth rate and n is the number of years.
Now,
I = 24,900
R = 8% = 8/100 = 0.08
n = 2020 - 2012 = 8
Substituting the values.
The population growth
= [tex]I (1 +R)^n[/tex]
= [tex]24900 \times (1 + 0.08)^8[/tex]
= 24900 x [tex]1.08^8[/tex]
= 24900 x 1.8509302102819
= 46089.9
= 46090
Thus,
The fox population predicted to be in the year 2020 is 46090.
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How to find the are and perimeter
liberty middle school is holding a fundraiser the sixth graders have raised 52% of thier goal amount the seventh and eighth graders have raised 0.57 and 2/5 of thier goal amounts respectively list the classes in order from least to greatest of thier goal amounts
The correct answer would be, from least to greatest:
8th graders = 2/5 x 100 = 40%
6th graders = 52%
7th graders = 0.57x100 = 57%
Step-by-step explanation:
Liberty middle school holds a fundraising. Many classes participated in the fundraising event. The data for sixth, seventh and eighth grades are given in the question. According to question:
6th Grade raised 52% of their goal.
7th Grade raised 0.57 of their goal, which will be 0.57 * 100 = 57%
8th Grade raised 2/5 of their goal, which will be 0.4 = 0.4 * 100 = 40%
So in the order from least to greatest, The classes are classified as below:
8th Graders: 40%
6th Graders: 52%
7th Graders: 57%
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list the following units in order of increasing length: meter, inch, centimeter, kilometer, yard, foot, mile, hectometer
The units listed in order of increasing length are: inch, centimeter, foot, yard, meter, hectometer, kilometer, mile.
To list the given units in order of increasing length, we need to understand both the metric and customary systems of measurement commonly used. The metric system is primarily used in the world and includes units like the meter, centimeter, and kilometer. The U.S. customary units include the inch, foot, yard, and mile. Here's the list from smallest to largest:
Inch (1 inch is approximately 2.54 centimeters)
Centimeter (1 centimeter is 1/100 meter)
Foot (1 foot is 12 inches)
Yard (1 yard is 3 feet)
Meter (1 meter is slightly more than 3 feet; 100 centimeters)
Hectometer (1 hectometer is 100 meters)
Kilometer (1 kilometer is 1000 meters)
Mile (1 mile is 5280 feet or approximately 1.609 kilometers
If the actual length of the bridge is 4200 feet, then what is the scale of the diagram of the bridge?