Keywords:
Tank, capacity, water, gallons, rule of three, variable, days
For this case we have a tank with a capacity of 18,000 gallons, we want to know how many days 12000 gallons of the tank are emptied, with the use of water following an average rate of 450 gallons per day. So we make a rule of three according to the use of water per day:
450 gallons -----------> 1 day
12000 gallons -------> x
Where the variable "x" represents the number of days when water takes to reach 6000 gallons.
[tex]x = \frac {12000 * 1} {450}\\x = 26.67[/tex]
Rounding the nearest whole we have:
[tex]x = 27[/tex]
Answer:
For the tank to go from 18,000 gallons of water to 6000 gallons of water, it should take approximately 27 days, using the water at an average rate of 450 gallons per day.
[tex]x = 27\ days[/tex]
350 yards to 420 yards
The range from 350 yards to 420 yards is of 70 yards.
To understand the range from 350 yards to 420 yards, it is important to recognize that this involves simple subtraction and addition within a specific interval. The interval is calculated as follows:
The lower limit: 350 yardsThe upper limit: 420 yardsThe range between these two distances is:
Lower Limit: 350 yardsUpper Limit: 420 yardsTo find the difference, which represents the span or range between these two points, simply subtract the smaller number from the larger number:
420 yards - 350 yards = 70 yards
Thus, the range between 350 yards and 420 yards is a total of 70 yards.
Mr.Mason's height is at most 4 inches mire than twice his daughters height Mr.Mason's height is 70 inches.
Can someone help me out here . Thanks!
Jamal is planting seeds for garden nursery.he plants 9 seeds In each container.if Jamal has 296 seeds to plant ,about how many containers will use?
which parachute has a slower descent a red parachute that was 10 feet in 4 seconds or a blue parachute that falls 1
2 feet in 6 seconds
which is a solution of the inequality y < x - 8
A solution to the inequality 'y < x - 8' is any point where the y-value is less than the x-value minus 8. An example solution is the point (10, 1). To find all solutions, one would graph the boundary line y = x - 8 and shade the region below it, without including the line itself.
Explanation:The question 'which is a solution of the inequality y < x - 8' falls within the subject of Mathematics, specifically under the topic of inequalities in algebra. A solution to this inequality is any ordered pair (x, y) where the y-value is less than the x-value minus 8. For example, if x is 10, then y must be less than 2 to satisfy the inequality, such as the point (10, 1).
To visualize this, you would graph the line y = x - 8 and then shade the region below this line on a coordinate plane. The shaded region represents all the points where the y-coordinate is less than the x-coordinate minus 8, thus showing all the potential solutions to the inequality. Points on the boundary line are not included since the inequality is strictly less than, not less than or equal to.
A bathtub holds about 2 hectoliters of water. If 25 liters of water are let down the drain, how many liters of water are still in the bathtub?
Chris wants to leave a 15% tip on the price of the food, calculated before sales tax. What is the maximum cost of food the group can order and not go over $63? Help Please
What is another way to write 300+20+5
Lilah completed the division problem below.
7.84 divided by 2
Select True or False for each statement.
A. The first step of the division is to multiply 7.84 and 2 by 10
B. The quotient will be a whole number.
C. The quotient multiplied by 2 will equal 7.84
D. The first digit of the quotient will be in the ones place.
E. The quotient will have two decimal places.
A certain TV can be purchased from the manufacturer for $160. A certain online retailer has a standard markup of 30%, and a certain superstore has a standard markup of 40%.
(a) What is the price of the TV when purchased online? What is the price of the TV when purchased at the superstore?
(b) What is the difference between the prices in Part (a)? How does this relate to the difference in the markup?
Answer:
The price of the TV purchased online is $208
The price of the TV purchased at the superstore is $224
Explanation
To solve this, we are going to use the markup formula solved for price:
[tex]Price=markup*cost+cost[/tex]
where
[tex]markup[/tex] is expressed in decimal form
- For the online retailer:
We know that the the TV can be purchased from the manufacturer for $160, so [tex]cost=160[/tex]. We also know that its markup is 30%; to express the markup as a decimal, we just need to divide it by 100%, so [tex]markup=\frac{30}{100} =0.3[/tex]. Now we can replace the values in our formula to find the price of the TV at the online retailer:
[tex]Price=markup*cost+cost[/tex]
[tex]Price=0.3*160+160[/tex]
[tex]Price=48+160[/tex]
[tex]Price=208[/tex]
The price of the TV purchased online is $208
- For the superstore:
The cost is the same, so [tex]cost=160[/tex]. The markup this time is 40%, so [tex]markup=\frac{40}{100}=0.4[/tex]. Let's replace the values to find the price:
[tex]Price=0.4*160+160[/tex]
[tex]Price=64+160[/tex]
[tex]Price=224[/tex]
The price of the TV purchased at the superstore is $224
(b)Answer
The difference between the prices is $16
The difference relates to the markup in two ways:
- When the markup increases 10% (from 30% to 40%), the price of the TV increases by $16.
- When the markup increases 10% (from 30% to 40%), the price of the TV increases 7.7%.
Explanation
To find the difference of our prices, we just need to subtract the price of the TV purchased at the superstore from the price of the TV purchased online:
$224 - $208 = $16
Now, to find how much the cost increased when the markup increases from 30% to 40%, we are going to divide the result of the difference of the two prices by the price of the TV at the online retailer, and then multiply by 100%:
[tex]\frac{16}{208} *100=7.69[/tex]
Which rounds to 7.7%
We can conclude that when the markup increases 10% (from 30% to 40%), the price of the TV increases 7.7%.
We can also conclude that when the markup increases 10% (from 30% to 40%), the price of the TV increases by $16.
Answer:
a) The price online of the TV is 208$
And in the superstore, it is 224$
b) The difference between the prices is $16.
208 - 224 = 16
The market difference is related as follows:
When the markup increases by 10% (from 30% to 40%), the price of the TV increases by $16.
Gina hiked down a canyon and stopped each time she descended ½ mile to rest. She hiked a total of 4 sections. What is her overall change in elevation?
A family is tracking its spending habits. Over the past year, the grocery bill has ranged from $110 to $170.
Suppose you were going to plot these points on a coordinate grid.
(a) What is a good scale to use for the y-axis? Explain your reasoning.
(b) What is a good interval to use for the y-axis? Explain your reasoning.
Answer:
A. $10
B. 12 points
Step-by-step explanation:
Let, the x-axis represents the number of months and y-axis represents the money for the grocery.
Now, as we have the range of the grocery bills from $110 to $170.
Thus, taking the scale of $10 on y-axis will give us 7 intervals in which the changes in the grocery bills can be viewed.
Hence, a scale of $10 is a good scale.
Further, as y-axis represents the number of months. Thus, taking 12 months will be sufficient to plot the graph and show the changes in the grocery bills.
Hence, 12 points representing months are sufficient.
Dominic, Ralf and Peter have just eaten a HUGE Christmas meal. Dominic now weighs half as much as Ralf, and Peter weighs three times as much as Dominic. Together they weigh 720 pounds. How much does Dominic weigh?
What does x equal? 3(14x-15)=-72
deshawn deposited $6500 into a bank account that earned 11.5percent simple interest each year . he earned $4485 in interest befour closing the account. if no money was deposited into or withdrawn from the account, for how many years was the money in the account round the answer to the nearest whole year
The money was in the account for 6 years.
Explanation:To find the number of years the money was in the account, we can use the formula for simple interest: I = P * r * t, where I is the interest earned, P is the principal (initial amount), r is the interest rate, and t is the time in years. We are given that Deshawn earned $4485 in interest and the interest rate is 11.5%. Let's plug in these values and solve for t:
4485 = 6500 * 0.115 * t
Simplifying the equation gives us:
t = 4485 / (6500 * 0.115) ≈ 6.1337
Rounding to the nearest whole year, we can conclude that the money was in the account for 6 years.
The ordered pairs (1, 16), (2, 25), (3, 36), (4, 49), and (5, 64) represent a function. What is a rule that represents this function?
Also, how do I know how to find the rules of functions?
Answer:
The rule representing the function is [tex]f(x)=(x+3)^2[/tex].
Step-by-step explanation:
We are given,
The ordered pairs for the function are (1, 16), (2, 25), (3, 36), (4, 49), and (5, 64).
It is required to find the rule representing the function.
Now, we see that,
[tex]16=(1+3)^2[/tex]
[tex]25=(2+3)^2[/tex]
[tex]36=(3+3)^2[/tex]
[tex]49=(4+3)^2[/tex]
[tex]64=(5+3)^2[/tex]
From the pattern,we get the function is [tex]f(x)=(x+3)^2[/tex].
Hence, the rule representing the function is [tex]f(x)=(x+3)^2[/tex].
A bakery used 475 pounds of apples to make 1000 apple tarts. each jar contains the same amount of apples. how many pounds of apples are used in each tart.
Jordan has 4/5 as many DVDs as Joseph. If Jordan has 56 DVDs, then how many does joseph have?
Lee,Shawn, and Jade share a box of 754 beads. The ratio of Lee's share of beads to Shawn's share of beads is 4:3. The ratio of Shawn's share of beads to Jade's share of beads is 9:5. How many beads does Lee have?
Chelsea earns $30 per day plus $5 for every sale that she makes at her job. On thursday ,she wants to earn at least $60
At Southside Middle School, 30% of the students play an instrument. There are 310 students. How many students play an instrument? 93 students 130 students 217 students 290 studentsAt Southside Middle School, 30% of the students play an instrument. There are 310 students. How many students play an instrument?
Answer:
93 students
Step-by-step explanation:
We need to calculate the 30% of 310 students.
We can calculate with a direct rule of 3. If the 100% is 310 students, how many students are the 30%?
[tex]100 -\!\!\!-\!\!\!- \text{310 students}\\ 30 -\!\!\!-\!\!\!- \text{x students}[/tex]
We use the formula of the direct rule of 3:
[tex]x = \frac {30 * 310}{100} \\ \\ x = \frac {9,300}{100}\\[/tex]
x = 93
93 students play an instrument at Southside Middle School.
On a scale drawing with a scale of 1 cm: 3 m , the height of a tree is 5 cm. How tall is the actual tree?
-5 1/3 divided by 2 3/4 in fraction form
1. Explain how you would model 5 x 2/3
2. When you multiply 2/3 by a fraction less than one, how does the product compare to the factors? Explain.
3. There is 5/6 of an apple pie left from dinner. Tomorrow, Victor plans to eat 1/6 of the pie that was left. How much of the whole pie will he eat tomorrow?
A. 1/36
B. 5/36
C. 1/3
D. 2/3
4. Matt made the model below to help him solve his math problem. Which of the expressions could he have been working out? (Yes, I made the model which emojis.)
Blue Heart: Green Square
Yellow Heart: Yellow Square
Broken Heart: Blank Square
A. 3/12 x 3/4
B. 3/4 x 3
C. 3/12 x 3/12
D. 1/3 x 3/4
5. If an angle measures 100 degrees, through what fraction of a circle does the angle turn?
A. 1/100
B. 1/4
C. 100/360
D. 1/2
Final answer:
To model 5 x 2/3, think of having 5 groups of 2/3 each. Multiplying 2/3 by a fraction less than one yields a smaller product. Victor will eat 5/36 of the whole apple pie, and an angle of 100 degrees represents 100/360 of a full circle.
Explanation:
To model 5 x 2/3, you can visualize having 5 groups of something, with each group containing 2/3 of that item. For example, if you have 5 pies, and you take 2/3 out of each pie, you would have a total of (5 x 2/3 = 10/3) pies.
When you multiply 2/3 by a fraction less than one, the product is smaller than the original fraction of 2/3 because you're effectively taking a portion of a portion, which reduces the overall size.
For the apple pie scenario, Victor plans to eat 1/6 of the 5/6 of a pie that is left, so the amount he will eat is (5/6 x 1/6 = 5/36) of the whole pie, which means the correct answer is Option B, 5/36.
Without the visual model provided, it is challenging to determine exactly which expressions Matt could have been working out. However, if you can provide the model, the answer would depend on the relationship between the hearts, squares, and the blank squares in Matt's model.
An angle of 100 degrees represents 100/360 or roughly 5/18 of a full circle since a full circle has 360 degrees. Therefore, the answer is Option C, 100/360.
estimate then find the product 48x38
Nadia charges $6.50 an hour for babysitting. She babysits 16.50 hours the first week of the month and 22 hours the second week of the month.Suppose Nadia raises her rate by $0.65 an hour. How many hours would she need to work to earn the same amount of money she made in the first two weeks of the month?
Need help with this problem thx!!!!!!
f(x)=x^2-x-1 , average rate of change of f over interval -1 greater than or equal to x less than or equal to 1
The average rate of change of the function f(x)=x^2-x-1 over the interval from -1 to 1 is calculated as the change in the function's values over the change in x, which results in -1.
Explanation:The average rate of change of a function f(x) over a given interval [a, b] is defined as the change in f(x) divided by the change in x. It is equal to the value of the function at point b minus the value of the function at point a, divided by (b-a).
For the function f(x)=x^2-x-1, we are given the interval from -1 to 1. In this case, a=-1 and b=1.
So first calculate f(a) and f(b), i.e., f(-1) = (-1)^2 -(-1)-1 = 1, and f(1) = (1)^2 -(1)-1 = -1.
Then, plug these values into the average rate of change formula, which gives us (-1-1) / (1 - (-1)) = -2 / 2 = -1. So the average rate of change of the function f over the interval from -1 to 1 is -1.
Learn more about Average Rate of Change here:https://brainly.com/question/34745120
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list all of the factors of 72