See attached pic for problem. Answer has to include cancelling of units and proper number of significant figures.
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We have:
1 cubic meter = 35.3147 cubic feet
60 seconds = 1 minute
Therefore given 0.618 cubic meters per second:
[tex]0.618\frac{m^3}{s}\times\frac{35.3147ft^3}{1m^3}\times\frac{60s}{1\min }[/tex]Then solve:
[tex]1309.47\frac{ft^3}{\min }[/tex]Answer: 1309.5 cubic feet per minute
Related Questions
can you please give me some more information about this
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We can see that the segment is defined by the points (-5, 5) & (-3, -4).
Now, we calculate the mid-point by using the following expression:
[tex]mp=(\frac{x_2-x_1}{2},\frac{y_2-y_2}{2})[/tex]So, now we replace:
[tex]mp=(\frac{-5-(-3)}{2},\frac{-4-5}{2})\Rightarrow mp=(-1,\frac{1}{2})[/tex]So, the mid point is (-1, 1/2).
How do I write an equation of a line passing through
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The equation is:
[tex]y=\frac{1}{2}x+2[/tex]Explanation:Given the point (2, 3), and the equation:
y - 4 = -2(x + 3) .............................................(1)
[tex]\begin{gathered} y=-2x-6+4 \\ =-2x-2 \end{gathered}[/tex]Comparing with the equation of a line:
[tex]y_{}=mx+b[/tex]where m is the slope, and b is the y-intercept
The slope in (1) is -2
Note that perpendicular lines have their slopes as negative reciprocals of each other.
The negative reciprocal of -2 is 1/2
The equation of a line perpendicular to (1) is:
[tex]y=\frac{1}{2}x+b[/tex]Applying the given point (2, 3), we have x = 2, y = 3
[tex]\begin{gathered} 3=\frac{1}{2}(2)+b \\ \\ b=3-1=2 \end{gathered}[/tex]The equation is therefore;
[tex]y=\frac{1}{2}x+2[/tex]move the numbers to the blanket to order them from least to greatest value.
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The given numbers from least to greatest are
• 1 - 21 = -20
,• -0.89
,• 0.4
,• 0.5
,• 9/8 = 1.125
To order the number from least to greatest, we just have to know the value of each one. For example, 1 - 21 equals -20, this will be the least number because it has the greatest absolute value as a negative number. Then, we have -0.89, which is greater than -20. And so on.
Rachel practiced 1/2 of an hour on Monday, 1/3 of an hour on Tuesday, 1/4 of an hour on both Wednesday and Thursday, and 1/2 of an hour on Friday. Find how many minutes she practiced each day and then find how many minutes she practiced in all during the week.
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ANSWER and EXPLANATION
We want to find the number of minutes she practiced each day and in total.
An hour is equal to 60 minutes.
On Monday, she practiced 1/2 of an hour. To convert this to minutes, multiply 1/2 by 60 minutes. That is:
[tex]\begin{gathered} \frac{1}{2}\cdot60 \\ \Rightarrow30\min \end{gathered}[/tex]On Tuesday, she practiced for 1/3 of an hour. That is:
[tex]\begin{gathered} \frac{1}{3}\cdot60 \\ \Rightarrow20\min \end{gathered}[/tex]On Wednesday, she practiced for 1/4 of an hour. That is:
[tex]\begin{gathered} \frac{1}{4}\cdot60 \\ \Rightarrow15\min \end{gathered}[/tex]On Thursday, she practiced for 1/4 of an hour. That is also equal to:
[tex]\Rightarrow15\min [/tex]On Friday, she practiced for 1/2 of an hour. That is equal to:
[tex]=>30\min [/tex]To find the total number of minutes that she practiced in all during the week, find the sum of the number of hours for all the days given.
[tex]\begin{gathered} 30+20+15+15+30 \\ \Rightarrow110\min \end{gathered}[/tex]She practiced for 110 minutes during the week.
I need help with this math problem I have a picture that I can show you of what it is
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The 18 % off of the listed price x can be denoted as,
[tex]\frac{100-18}{100}x=0.82x[/tex]18% more than the amount x can be denoted as,
[tex]\frac{100+18}{100}x=1.18x[/tex]3/10 of the origianl voulme x drained out is denoted as,
[tex]x-\frac{3}{10}x=\frac{10x-3x}{10}=\frac{7x}{10}[/tex]3/10 stock is added,
[tex]x+\frac{3}{10}x=\frac{10x+3x}{10}=\frac{13x}{10}[/tex]The shore, a rope, and a dock that is 8 meters long enclose a rectangular swimming area along thelakeshore. The length of swimming area is 6 meters more than its width and the swimming area must bemore than 180 square meters. If the rope is 34 meters long, then what are the dimensions of theswimming area?
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So we have two conditions, the first one is that the length (L) of the swimming area is 6 meters more than the width (W) so:
[tex]L=6W[/tex]and the other condition is that the area is 180 square meters so we can writte it like:
[tex]180=L\cdot W[/tex]Now we have 2 equations and 2 ingognitas so we can replace the first equation into the second equation like this:
[tex]180=(6W)\cdot W[/tex]and we solve for W so
[tex]\begin{gathered} 180=6W^2^{} \\ W^2=\frac{180}{6}=30 \\ W=\sqrt[]{30}=5.5 \end{gathered}[/tex]Now with the value of W we can replace it in the first equation so:
[tex]L=6(5.5)[/tex]so:
[tex]L=33[/tex]The dimensions are:
[tex]\begin{gathered} \text{length}=33m \\ \text{width}=5.5m \end{gathered}[/tex]plot the solution of the equation on the number line
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Answer:
Explanation:
Given the equation:
[tex]7x+7=-14[/tex]First, subtract 7 from both sides:
[tex]\begin{gathered} 7x+7-7=-14-7 \\ 7x=-21 \end{gathered}[/tex]Next, divide both sides by 7:
[tex]\begin{gathered} \frac{7x}{7}=-\frac{21}{7} \\ x=-3 \end{gathered}[/tex]The solution of the equation on the number line is shown below:
I need help with my math
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Step 1: write out the formula for slope
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Step2: Identify the point in the diagram
[tex]\begin{gathered} (-2,-4)\text{ and (2,2)} \\ x_1=-1,x_2=2,y_1=-4,y_2=2 \end{gathered}[/tex]Step3: Substitute the value into the given formula above
[tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ =\text{ }\frac{2-(-4)}{2-(-2)} \\ =\frac{2+4}{2+2} \\ =\frac{6}{4} \end{gathered}[/tex][tex]\text{slope}=\frac{3}{2}[/tex]Hence the slope of the line is 3/2
Ernesto already has 6 flowers in his garden and his garden he will grow 4 more flowers per seed packet he plants.let s represent the number of seed packets he plants and f represent the total number of flowers he will have. Complete the equation that represent the relationship between s and f
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Suppose you roll a pair of six-sided dice and add their totals.(a) What is the probability that the sum of the numbers on your dice is 9 or 11? (b) What is the probability that the sum of the numbers on your dice is an even number or a number less than 6? (c) What is the probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
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Rolling a pair of six-sided dice, we have the following sample space:
(a) The probability that the sum of the numbers on your dice is 9 or 11 is
P(X = 9) + P(X = 11)
= 4/36 + 2/36
= 6/36
= 1/6
(b) The probability that the sum of the numbers on your dice is an even number or a number less than 6 is:
P(X = even) + P(X < 6)
= 21/36 + 10/36
= 31/36
(c) The probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
P(X = prime) + P(X > 5)
= 14/36 +
You have 3 6 sided dice. One is red one is blue one is green What is the probability that you roll a one on the red die a 2 on the blue die and a 3 on the green
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Solution
Step 1
[tex]Probability\text{ of any event = }\frac{number\text{ of required outcomes}}{number\text{ of sample space}}[/tex]Step 2:
For each die, the number of sample space is (1 ,2,3,4,,6)
Note: AND represent multiplication
Step 3:
The probability that you roll a 1 on the red die a 2 on the blue die and a 3 on the green
[tex]\begin{gathered} =\text{ }\frac{1}{6}\text{ }\times\text{ }\frac{1}{6}\text{ }\times\text{ }\frac{1}{6} \\ \text{= }\frac{1}{216} \end{gathered}[/tex]Final answer
[tex]\frac{1}{216}[/tex][tex]6 \sqrt{72} [/tex]Simplify in simplest form:
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we have:
[tex]\frac{6}{\sqrt[]{72}}[/tex]first, we can multiply and divide by sqrt{72} (to get the sqrt of the denominator)
[tex]\frac{6}{\sqrt[]{72}}\cdot\frac{\sqrt[]{72}}{\sqrt[]{72}}=\frac{6\sqrt[]{72}}{(\sqrt[]{72)^2^{}}}=\frac{6\cdot\sqrt[]{72}}{72}[/tex]now we can simplify sqrt{72} writing 72 as 2*36
[tex]\frac{6\cdot\sqrt[]{36\cdot2}}{72}=\frac{6\cdot\sqrt[]{36}\cdot\sqrt[]{2}}{72}=\frac{6\cdot6\cdot\sqrt[]{2}}{72}=\frac{\sqrt[]{2}}{2}[/tex]So the answer is:
[tex]\frac{\sqrt[]{2}}{2}[/tex]what is the equation of the line that passes through the point[tex]( - 3 - 11)[/tex]y=2x-4
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Answer
To check if a line passes through a point replace x in the equation
For example:
y= 2x-4
replacing
y = 2*( -3) -4
y= -6-4
y = -10
So then y= 2x-4 passes through the point (-3, -10)
3 5 6 Graphs and Tables: To determine matching graphs and tables you would use your answer choices to plug in x values and solve to see if you get the correct y value for each pair. 10. 9. Which linear equation matches the table shown? The equation y = 3x - 4 represents the relationship in which of the following tables? 3 10 5 7 6 9 2 11 2 10 y у 6 18 11 17 23 29 35 3 y - 2 3 A. y = x + 8 X - - O B. y = 4x - 1 y-10 -> - C. y = 3x + 2 14 17 20 D. y = 5x - 4
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Determine the linear equation for the table.
[tex]\begin{gathered} y-17=\frac{23-17}{7-5}(x-5) \\ y-17=\frac{6}{2}(x-5) \\ y=3x-15+17 \\ y=3x+2 \end{gathered}[/tex]So equation for the table is y = 3x + 2.
What is the product?6 2/5, 5/6, 1 1/4
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Given
[tex]6\frac{2}{5},\frac{5}{6},1\frac{1}{4}[/tex]Product means multplication
[tex]6\frac{2}{5}\times\frac{5}{6}\times1\frac{1}{4}[/tex]Change the mixed fraction to improper fraction
[tex]\begin{gathered} \frac{32}{5}\times\frac{5}{6}\times\frac{5}{4}=\frac{4}{1}\times\frac{1}{3}\times\frac{5}{1} \\ \frac{4}{1}\times\frac{1}{3}\times\frac{5}{1}=\frac{20}{3}=6\text{ }\frac{2}{3} \end{gathered}[/tex]The final answer
[tex]6\text{ }\frac{2}{3}\text{ or }6.6667[/tex]Two sides of a triangle have the followingmeasures. Find the range of possiblemeasures for the third side.
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The sum of the lengths of any two sides of a triangle must be greater than the third side.
So:
A+B>C
B+C > A
C+A > B
Given the 2 sides: 31 and 44, suppose they are sides A and B:
44-31 < c < 44+31
Range
13 < C < 75
Divide 180 into two parts such that the first part is 12 less thantwice the second part.a 100, 80b 90,90c 116, 64d 99. 81
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You can find a math expression dividing the statment as follow:
Divide 180 into two parts such that: x and y
the first part: X
is 12 less than: X= -12
twice the 2(
second part: Y
the first (X) part is 12 less than twice the second part (Y):
X=2Y-12
Examples: Find the area of the following figures.1.6cm10cm7cm4cm
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The figure below is a Trapezium.
Let's write out the formula for the area of a trapezium,
[tex]\text{Area of a trapezium=}\frac{1}{2}(a+b)h[/tex]1) Let us write out the data given in the first figure,
[tex]\begin{gathered} a=7\operatorname{cm} \\ b=10\operatorname{cm} \\ h=4\operatorname{cm} \end{gathered}[/tex]Let us solve for the area of the figure,
[tex]\begin{gathered} \text{Area of the trapezium=}\frac{\text{1}}{2}(7+10)\times4 \\ =\frac{1}{2}(17)\times4 \\ =34cm^2 \end{gathered}[/tex]The area of the trapezium is 34cm².
can u help me with the boxplot of Area 1?
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In order to create a boxplot of the Area 1 dataset, first let's put the dataset in crescent order:
[tex]12,24,30,32,35,44,45,56,57,59,61,65,68,92,100.[/tex]Since the set has 15 elements, the median is the 8th element, so the median is 56.
The median will divide the set into two smaller sets with 7 elements each. The first interquartile (IQ1) is the median of the first subset (so it will be the 4th element), and the third interquartile (IQ3) is the median of the second subset (so it will be the 12th element).
So the first interquartile is 32 and the third interquartile is 65.
Now we need the lower and upper limit of the set.
The lower limit is 12 and the upper limit is 100.
Now, creating the boxplot, we have:
2. Determine the equation of the asymptote for the following exponential functions: *y=2x-3 b. y = (3)* + 2 c. ** y = 2(3)* d. 2 + 3x I *** a.
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a) y = -3
b) y = 2
c) y = 0
d) y = 2
Explanation:The asymptote is the constant added to the expression of the variable
a) y = 2^x - 3
Theexpression of the variable = 2^x
The number after it is is - 3
So the asymptote is y = -3
b) y = (1/3)^x + 2
The number added to the expression of the variable is 2
Asymptote is y = 2
c) y = 2(3)^x
y = 2(3)^x + 0
The expression of the variable = 2(3)^x
There is no number added to the expression of the variable
Hence, Asymptote is y = 0
d) 2 + 3^x
[tex]\begin{gathered} The\text{ function is not equated to y} \\ Since\text{ we are told they are all exponntial function,} \\ \text{let 2 + 3}^x\text{ = y} \end{gathered}[/tex]The expression of the variable = 3^x
The number added to this expression is 2
Asymptote is y = 2
Prior to making deposits of $75 and $50 Marian had a balance of $102in her checking account. How much must she deposit so that her balance winbe at least $300 and she can avoid a service fee
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Marian had a balance of $102
Then she made two deposits, one of $75 and the other for $50
We can calculate the balance of her checking account after the deposits were done
New balance = $102 + $75 + $50 = $227
The account needs to have at least $300 to avoid a service fee, so we calculate how much is needed to complete that amount
New deposit = $300 - $227 = $73
So, if Marian deposits at least $73, the account balance will be $300 or more
Answer: She must deposit at least $73
1. Identify the population and the sample of the following scenarios,Part A: A survey of 1353 American Households found that 18% of the households own acomputer,Part B: A recent survey of 2625 elementary school children found that 28% of thechildren could be classified obese,Part C: The average weight of every dh person entering the mall within three hourperiod was 146 lb.
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Let's begin by listing out the information given to us:
The population refers to the entire group from which you want to make a conclusion
The sample refers to the specific subject from whom data is obtained
Part A
Population = 1353
Sample = 18% of the population = 18% * 1353 = 243.54 ≈ 244
Part B
Population = 2625
Sample = 28% of the population = 28% * 2625 = 735
Part C
Population = every person that came into the mall
Sample = every person that came into the mall within the 3 hour period
Part EWhat is a possible explanation for why the y-intercept is negative for all three functions?
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In this problem
x -----> number of meals sold
y ----> profit
Remember that
the y-intercept is the value of y, when the value of x is zero
In this context
the y-intercept is the value of the profit when the restaurant begin or start to sell meals
In this case, the y-intercept is negative, which means when the restaurant started, there have a negative profit (loss) {the cost is greater than the revenue) because the number of meals sold is zero.
Answer:
The restaurants incur costs to prepare meals, such as labor and supplies, before any meals are sold. So, the restaurants will lose money until they sell a number of meals equal to the first x-intercept.
Step-by-step explanation:
Edmentum
4x+3y=14-yx-5y=23. IF (x, y) is a solution to the system of equationsabove, what is x - y?A) 1B)C) 3D) 18
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C. 3
The profit y in dollars) for a business from selling x gloves is represented by y = 21x. Graph the equation.
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The equation is:
[tex]y=21x[/tex]To graph that equation, as it is a equation for a line, you need to find the coordinates (x,y) for two points on the line.
To find a point on the line you give for one of the variables a value and calculate the value of the other variable with the equation.
If x= 5
[tex]\begin{gathered} y=21(5) \\ y=105 \end{gathered}[/tex]Then, when x=5 y=105. The first point have coordinates (5, 105)
If y= 0
[tex]\begin{gathered} 0=21x \\ \frac{0}{21}=x \\ x=0 \end{gathered}[/tex]Then, when y=0 x=0. The second point have coordinates (0, 0)
You put that points in the plane:
Draw a line that passes through taht points:
is 1/8 greater than 18%
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Consider than 18% in decimal is 0.18.
Next, take into that 1/8 = 0.125
0.18 is great
find the excluded value(s) of x in the rational expression f(x)= x^2+7x/ x^+14x+49so how am I supposed to combine like terms and get to the answer
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Given
[tex]f(x)=\frac{x^2+7x}{x^2+14x+49}[/tex]
Procedure
Factoring
[tex]\begin{gathered} f(x)=\frac{x(x+7)}{(x+7)(x+7)} \\ f(x)=\frac{x}{x+7} \end{gathered}[/tex]Answer:
x ≠ – 7
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Answer:1.7 * 10^5 m
Step-by-step explanation:
A drone that costs $129.50 is discounted 40%. the next month,the sale price is discounted and additional 60%. is the drone now free .if the drone is free please explain.if the drone is not free what is the sales price?
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We have an original price of $129.50.
Then, the price is discounted 40%. After that, the price is discounted 60%.
We can think of this discount in steps:
1) the first discount of 40% means that the new price is 100%-40% = 60% of the original price:
[tex]P^{\prime}=(\frac{100-40}{100})\cdot P=0.6\cdot P[/tex]2) The second discount of 60% means that the new price is 100%-60% = 40% of the already discounted price:
[tex]P^{\prime\prime}=(\frac{100-60}{100})P^{\prime}=0.4\cdot P^{\prime}=0.4\cdot(0.6P)=0.24\cdot P[/tex]Then, the final price after the two discounts is 24% of the original price:
[tex]P^{\prime\prime}=0.24\cdot P=0.24\cdot129.50=31.08[/tex]Answer: The drone is not free. The final price of the drone is $31.08.
what are all the possible causes of x that satisfy x/4+8>24?
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Answer : x > 64
Given that
x / 4 + 8 > 24
[tex]\begin{gathered} \frac{x}{4}\text{ + 8 > 24} \\ \text{Firstly, we n}eed\text{ to find the common denominator} \\ \frac{x\text{ + 32}}{4}\text{ > 24} \\ \text{Cross multiply} \\ \text{x + 32 > 24 }\cdot\text{ 4} \\ \text{x + 32 > 96} \\ \text{Isolate x} \\ x\text{ > 96 - 32} \\ x\text{ > 64} \end{gathered}[/tex]