A rectangular tank 50 centimetres by 30 centimetres by 25 centimetres is 40 percent full of water. How many litres of water are needed to fill the tank completely?Volume of water needed = Volume of empty spaceHeight of empty space = ________ cm x 0.6 = ________ cmVolume of water needed= ________ cm x ________ cm x ____________ cm= ________ cm^3 = _______ mL = ____________ L_________ litres of water are needed to fill the tank completely.
Answers
ANSWER
22.5 liters
EXPLANATION
We know that the tank is 40% full of water. This means that 60% of the tank is empty, so the height of the empty space of the rectangular tank is,
\(h_{empty}=h_{tank}\cdot\frac{60}{100}=h_{tank}\cdot0.6cm\)The volume of the empty space, since the tank is a rectangular prism, is the product of the empty space dimensions,
\(V_{empty}=h_{empty}\cdot l_{empty}\cdot w_{empty}=0.6h_{tank}\cdot l_{tank}\cdot w_{tank}\)As we can see, the volume of the empty space is equal to 60% of the tank's volume,
\(V_{empty}=0.6V_{tank}=0.6(50cm\cdot30cm\cdot25cm)=0.6\cdot37,500cm^3=22,500cm^3\)1 cubic centimeter is equivalent to 1 milliliter,
\(V_{empty}=22,500cm^2=22,500mL\)Now, to transform from milliliters to liters, we have to divide this volume by 1000 or, in other words, move the decimal point 3 units to the left,
\(V_{empty}=22,500mL=22.5L\)Hence, 22.5 liters of water are needed to fill the tank completely.
Related Questions
Certain advertisers would like to estimate the proportion of viewers who spend the majority of their television time
watching alone. The consensus is that this percentage has been increasing over the years due to the increased
number of television sets in households.
a. Determine the sample size needed to construct a 90% confidence interval with a margin of error of no more than
6% to estimate the true proportion of viewers who watch television alone.
b. What impact would a pilot sample that showed that 44% of viewers spend the majority of their television time
watching alone have on your on results.
a. The sample size needed is
(Round up to the nearest integer.)
b. The new sample size needed would be 0
(Round up to the nearest integer.)
Answers
Answer:
Step-by-step explanation:
I swear. I’m just lazy. LOL XD
Answers
Med range = 65+15 /2 = 40
Range = 65-15=50
Simplify: 3√50+ √24 - 2√72
A. 3√6 +2√2
B. 3√9+2√5
C. 3√2+2√6
D. 10√2+2√6
Answers
Answer:
Step-by-step explanation:
13+(-3)^2+4(-3)+1- {-10-(-6)}
_________________________
[4+5}/ [4^2-3^2(4-3)-8]+12
15/3=5
On a recent holiday evening, a sample of 500 drivers was stopped by the police. Three hundred seventy-five were under 30 years of age. A total of 275 were under the influence of alcohol. Of the drivers under 30 years of age, 225 were under the influence of alcohol.
Let A be the event that a driver is under the influence of alcohol.
Let Y be the event that a driver is less than 30 years old.
1. Show the joint probability table.
2. Are A and Y mutually exclusive events? Explain.
3. Are A and Y independent events? Explain.
Answers
Answer:
Joint probability table :
_____ A _____ A'
_ Y_ 0.45 ___ 0.30
_ Y'_ 0.05___ 0.20
No
No
Step-by-step explanation:
Given :
Sample, size n = 500
A = driver is under the influence of alcohol :
Y = driver is less than 30 years old
P(A) = 275 / 500 = 0.55
P(Y) = 375 / 500 = 0.75
P(AnY) = 225 / 500 = 0.45
P(YnA') = (1 - 225/375)*0.75 = 0.4 * 0.75 = 0.30
Joint probability table :
_____ A _____ A'
_ Y_ 0.45 ___ 0.30
_ Y'_ 0.05___ 0.20
To determine if it is mutually exclusive : P(AnY) = 0
P(AnY) = 0.45 ; hence, it is not mutually exclusive
For A and Y to be independent ; P(A|Y) = P(A) ;
P(A|Y) = P(AnY) / P(Y)
P(A|Y) = 0.45 / 0.75 = 0.6
Hence, A and Y are not independent.
The cost of the lunches for the field trip can be represented by the expression:
4(29) + 4(6)
Identify the values to make these expressions true.
Expand 29 to create an equivalent expression with friendly numbers.
40 ) + 4(6)
Distribute the 4
Evaluate the multiplication
80 + 36 + 24 =
Answers
Answer: 4(20+9)+4(6) thats the first one
4(20)+4(9)+4( 6) thats the second one
80+36+24=140 that is the third
Step-by-step explanation:
Answer:
4(20+9)+4(6)
4(20)+4(9)+4( 6)
Step-by-step explanation:
In ΔLMN, the measure of ∠N=90°, MN = 6 feet, and NL = 3.5 feet. Find the measure of ∠L to the nearest degree.
Answers
please help me Asap
Answers
Answer:
its b or c
Step-by-step explanation:
i really think its c
fresh milk costs 12.50 per liter what is the cost of y liters of fresh milk?
Answers
Answer:
12.50y
Step-by-step explanation:
If 1 ltr=12.50 what about y ltrsTherefore, 1 ltr= 12.50
y ltrs=?
you do cross multiplication
hence, 12.50 × y= 12.50y
total cost= sh.(12.50y)
What is double fifteen point 5
Answers
Answer: 31
Step-by-step explanation:
A satellite orbits the Earth with an elliptical orbit modeled by x squared over 47 million four hundred seventy two thousand one hundred plus y squared over forty four million two hundred twenty two thousand five hundred equals 1 comma where the distances are measured in km. The Earth shares the same center as the orbit. If the radius of the Earth is 6,370 km, what is the maximum distance between the satellite and the Earth?
Answers
The maximum distance between the earth and the satellite orbit with an elliptical orbit is 520 km.
In the question, we are given that a satellite orbits the Earth with an elliptical orbit modeled by x squared over 47 million four hundred seventy two thousand one hundred plus y squared over forty four million two hundred twenty two thousand five hundred equals 1, where the distances are measured in km. The Earth shares the same center as the orbit.
We are asked to find the maximum distance between the satellite and the Earth if the radius of the Earth is 6,370 km.
Given elliptical form is:
x²/47,472,100 + y²/44,222,500 = 1,
or, x²/6,890² + y²/6,650² = 1.
The radius of the Earth, R = 6,370 km.
We know that the standard elliptical form is:
(x - h)²/a² + (y - k)²/b² = 1, Where, in a horizontal ellipse;
a = The major axis (the longer axis), which gives the maximum distance between the satellite and Earth.
b = The minor axis (the shorter axis).
On comparing the given elliptical form to the standard elliptical form, we get a = 6,890.
The distance between the satellite and the surface of the Earth, d, is given as follows:
d = a - R
Which gives;
d = 6,890 km - 6,370 km = 520 km.
Thus, the maximum distance between the earth and the satellite orbit with an elliptical orbit is 520 km.
Learn more about elliptical forms at
https://brainly.com/question/25498775
#SPJ9
What’s the answer to number 10 you may have to zoom in
Answers
Answer:
1.
Step-by-step explanation:
.What is the capital of canada.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer:
C
Step-by-step explanation:
Step-by-step explanation:
Hi tag brainliest ❣️
Thanks
Since the shaded area equal 4
our answer is A
that is the number of shaded area ÷ the total number of points
-
I need questions 16, 17, and 18
The number of guests staying at the Toasty Inn from January to
December 2019 can be approximated by
N(x) = - 10%2 + 120x + 120
where x represents the number of months after
January 2019 (* = 0 represents January, x = 1
represents February, etc.), and N(x) represents the number of guests who stayed at the inn. During which month did the inn have the greatest number of guests?
How many people stayed at the inn during that month?
Answers
the inn had the greatest number of guests in December 2023, with 1428 guests staying at the inn during that month.
What is the quadratic function?To find the month with the greatest number of guests, we need to find the maximum value of N(x) over the range of x from 0 to 11 (representing January to December).
We can find the maximum value of N(x) by taking the derivative of N(x) with respect to x, setting it equal to zero, and solving for x. However, since N(x) is a quadratic function, we can also use the vertex formula to find the x-value of the vertex of the parabola.
The vertex formula states that the x-value of the vertex of the parabola \(y = ax^2 + bx + c\) is given by \(x = -b/2a\) .
In this case, N(x) is a quadratic function with a = -10%, b = 120, and c = 120. Plugging these values into the vertex formula, we get:
\(x = -b/2a = -120/(2\times -10%) = 60\)
Since x represents the number of months after January 2019, the month with the greatest number of guests is the 60th month after January 2019, which is December 2023.
To find the number of guests who stayed at the inn during that month, we can plug x = 11 (representing December) into the formula for N(x):
\(N(11) = -10%(11^2) + 120(11) + 120\)
\(= -0.1(121) + 1320 + 120\)
\(= -12.1 + 1440\)
\(= 1427.9\)
Since the number of guests must be a whole number, we round 1427.9 to the nearest integer, which is 1428.
Therefore, the inn had the greatest number of guests in December 2023, with \(1428\) guests staying at the inn during that month.
Learn more about quadratic here:
https://brainly.com/question/18958913
#SPJ1
16) The number of guests during that month was 720.
17) In the year 2003, there were 4,600 triplet and higher order births.
18) The greatest average viewership occurred in the year 2015, with 17.95 million viewers per game.
16) How to find the month during which the inn had the greatest number of guests?
To find the month during which the inn had the greatest number of guests, we need to find the maximum value of the quadratic function N(x) = -10x² + 120x + 120.
We can begin by finding the x-coordinate of the vertex of this quadratic function, which is given by x = -b/2a, where a = -10 and b = 120.
x = -b/2a = -120/(2×(-10)) = 6
So the vertex of the quadratic function is at x = 6.
To find the maximum value of the function, we can evaluate N(6):
N(6) = -10(6)² + 120(6) + 120 = 720
So the inn had the greatest number of guests during the 6th month, which represents June 2019. The number of guests during that month was 720.
17) How to find the year when the number of triplet and higher order births was greatest?
To find the year when the number of triplet and higher order births was greatest, we need to find the maximum value of the function N(t). The formula for the maximum value of a quadratic function is -b/2a, where a is the coefficient of the squared term, b is the coefficient of the linear term, and c is the constant term.
In this case, a = -0.266 and b = 6.974. So, the t-value for the maximum number of triplet and higher order births is t = -b/(2a) = -6.974/(2×(-0.266)) = 13.12
Rounding this value to the nearest whole number, we get t = 13.
Therefore, the year when the number of triplet and higher order births was greatest is 1990 + 13 = 2003
To find the maximum number of triplet and higher order births, we substitute t = 13 into the function N(t):
N(13) = -0.266(13)² + 6.974(13) + 27.056 = 45.7 (in hundreds)
Rounding this value to the nearest whole number, we get 46.
Therefore, in the year 2003, there were approximately 4,600 triplet and higher order births
18) How to find the vertex of the quadratic function A(x)?
We can start by finding the vertex of the quadratic function A(x) to determine the year in which the greatest average viewership occurred:
The x-coordinate of the vertex of the quadratic function A(x) is given by x = -b/2a, where a = -0.59 and b = 3.5. Substituting these values,
x = -3.5/(2*(-0.59)) = 2.966
This means that the vertex occurs approximately 2.966 years after 2012, which corresponds to the year 2015.
To find the maximum average viewership, we can simply plug in x = 2.966 into the function A(x):
A(2.966) = -0.59(2.966)² + 3.5(2.966) + 12.71 ≈ 17.95 million viewers per game
Therefore, the greatest average viewership occurred in the year 2015, with approximately 17.95 million viewers per game.
Learn more about average here,
https://brainly.com/question/130657
#SPJ1
John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?
Answers
Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:
10x + 5y ≥ 500 (minimum 500 units of vitamins)
5x + 10y ≥ 600 (minimum 600 units of minerals)
15x + 15y ≥ 1200 (minimum 1200 calories)
We want to minimize the cost, which is given by:
0.5x + 0.4y
This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:
10x + 5y = 500
5x + 10y = 600
15x + 15y = 1200
Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.
Next, we can calculate the value of the cost function at each corner point of the feasible region:
Corner point A: (20, 40) -> Cost = 20
Corner point B: (40, 25) -> Cost = 25
Corner point C: (60, 0) -> Cost = 30
Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.
linda buys 2 sweaters
Answers
Answer:
now she has 2 sweaters to wear
Alex learned 80 new vocabulary words for his English exam. The following function gives the number of words he remembers after t days: W(t) = 80(1 - 0.1t)^3 What is the instantaneous rate of change of the number of words Alex remembers after 5 days? Choose 1 answer: A. 10 days B. 10 words per day C. -6 days D. -6 words per day
Answers
The instantaneous rate of change is -6 words per day,
the number of words Alex remembers after 5 days, option (D).
What is the instantaneous rate of change ?
An instantaneous rate is the rate at some instant in time. An instantaneous rate is a differential rate: -d[reactant]/dt or d[product]/dt. We determine an instantaneous rate at time t: by calculating the negative of the slope of the curve of concentration of a reactant versus time at time t.
Have given,
Alex learned 80 new vocabulary words
and after t days he learned,
W(t) = \(80 (1-0.1t)^{3}\)
differentiate respect of t
W'(t) = \(80 \frac{d}{dt} (1-0.1t)^{3}\)
W'(t) = \(80 * 3(1-0.1t)^{2} \frac{d}{dt}(1-0.1t)\)
W'(t) = \(240(1-0.1*5)^{2} (0.1)\)
W'(t) = 6
That's mean , the instantaneous rate of change is -6 words per day.
To learn more about instantaneous rate visit : brainly.com/question/28837697
#SPJ4
find the sale price then find the total cost
Answers
Answer:
$2.40 sales tax
Total $ 62.40
Step-by-step explanation:
60 * .04 =$2.40 sales tax
Total cost is 60 + 2.40 or $ 62.40
Solve the following compound inequality
Answers
The solution of the compound inequality 5x + 7 ≤ - 3 or 3x - 4 ≥ 11 is x ≤ -2 or x ≥ 5. Therefore, the answer is C.
How to solve compound inequalities?An inequality is an expression containing <, >, ≤ and ≥.
A compound inequality is an inequality that combines two simple inequalities.
Therefore, let's solve the compound inequality as follows:
5x + 7 ≤ - 3 or 3x - 4 ≥ 11
5x + 7 ≤ - 3
5x ≤ -3 - 7
5x ≤ - 10
divide both sides by 5
x ≤ - 10 / 5
x ≤ -2
3x - 4 ≥ 11
3x ≥ 11 + 4
3x ≥ 15
x ≥ 15 / 3
x ≥ 5
Therefore,
x ≤ -2 or x ≥ 5
learn more on inequality here: https://brainly.com/question/28600203
#SPJ1
Use the equation and type the ordered-pairs. y=3^x
Answers
The ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)
How to type the ordered pairs?The equation is given as:
y = 3^x
Let x = 0, 1 and 2
y = 3^0 = 1
y = 3^1 = 3
y = 3^2 = 9
So, we have the following ordered pairs (0,1), (1,3) and (2,9)
Hence, the ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)
Read more about exponential functions at:
https://brainly.com/question/2456547
#SPJ1
On Monday, one share of a certain stock costs $41.45. On Tuesday, the cost goes up by $0.58. It goes down by $0.26 on both Wednesday and Thursday. On Friday, it goes down by $0.06. Write an expression to represent the cost of one share of the stock on Friday. Then evaluate the expression to find the cost on Friday.
Answers
$41.45 + $0.58 - $0.26 - $0.26 - $0.06
Simplifying this expression gives:
$41.45 + $0.58 - $0.26 - $0.26 - $0.06 = $41.45 + $0.58 - $0.58
The two negative terms cancel out, leaving:
$41.45 + $0.00 = $41.45
Therefore, the cost of one share of the stock on Friday is $41.45.
Answer:
The cost of one share of the stock on Friday is $41.45
Step-by-step explanation:
The initial cost of one share of the stock on Monday is $41.45.
On Tuesday, the cost goes up by $0.58, so the cost becomes:
$41.45 + $0.58 = $42.03
On Wednesday, the cost goes down by $0.26, so the cost becomes:
$42.03 - $0.26 = $41.77
On Thursday, the cost also goes down by $0.26, so the cost becomes:
$41.77 - $0.26 = $41.51
Finally, on Friday, the cost goes down by $0.06.
So the expression to represent the cost of one share of the stock on Friday is:
$41.51 - $0.06
To evaluate this expression, we simply subtract $0.06 from $41.51:
$41.51 - $0.06 = $41.45
Therefore, the cost of one share of the stock on Friday is $41.45
Determine the slope given the following information:
The line passes through points (2, 4) and (0, -4)
Answers
Answer
4/1
Explanation step by step
4-(-4)/2-0
8/2
4/1
I will mark you brainiest!
A) 3
B) 6
C) 9
D) 12
Answers
The value of x, considering the similar triangles, is given as follows:
B) 6.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.Considering that the triangles for this problem are similar, the proportional relationship for the side lengths is given as follows:
9/3 = 12/4 = x/2.
Since the constant is of 3, the value of x is obtained with cross multiplication as follows:
x/2 = 3
x = 6.
More can be learned about similar triangles at brainly.com/question/14285697
#SPJ1
Help me plss. ASAP, ty
Answers
Answer:
A) 16 / 9 B) 7/9
Step-by-step explanation:
find the y intercept and x intercept of the line 2x+3y=-5
Answers
Lets write the equation in slope-intercept form
\(y=mx+b,\)where m is the slope and b is the y-intercept.
Then, we have
\(\begin{gathered} 3y=-5-2x \\ y=-\frac{2}{3}x-\frac{5}{3} \end{gathered}\)By comparing equations, we can note that the y-intercept is
\(\begin{gathered} \\ b=-\frac{5}{3} \end{gathered}\)Now, the x-intercept occurs at y=0. By substituting this value into our line equation, we get
\(0=-\frac{2}{3}x-\frac{5}{3}\)then, the x-intercept is given by
\(\begin{gathered} -\frac{2}{3}x=\frac{5}{3} \\ x=-\frac{\frac{5}{3}}{\frac{2}{3}} \\ x=-\frac{5\cdot3}{2\cdot3} \\ x=-\frac{5}{2} \end{gathered}\)Therefore, the answer is
- x intercept is -5/2
- y-intercept is -5/3
Will give brainliest if your answer is correct, please help me with this question it is past due (I have more questions like this that are also pat due, check my profile and go to questions to see them once I post the questions)
Answers
Answer:
Equal angles; Vertical angles ( which means equal ) ; Angles do not share special relationship; and right angles.... Hope this helps!
Step-by-step explanation:
what is c cubed = -64
Answers
The value of the expression is -4
What is cube root?
The cube root of a number can be defined as the factor multiplied by three times by itself to get that number.
Cube root is represented using the formula, '∛'
From the information given,
c³ = -64
Take the cube root of both sides
∛c³ = ∛ - 64
c = - 4
Thus, the value of the expression is -4
Learn more about cube root here:
https://brainly.com/question/28256285
#SPJ1
If I had 60 units needed and units per case was 14 how many full cases and additional items are needed to fufill the order
Answers
60 units / 14 units per case ≈ 4.29 cases
Since you can't have a fractional number of cases, you would need to round up to the nearest whole number of cases. Therefore, you would need 5 full cases.
To determine the number of additional items needed to fulfill the order, you can subtract the number of units in the full cases from the total number of units:
60 units - (5 cases * 14 units per case) = 10 additional items
So, in total, you would need 5 full cases and 10 additional items to fulfill the order of 60 units.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The three statements that are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² .......equation 1.
Where:
h and k represents the coordinates at the center of a circle.
r represents the radius of a circle.
Based on the information provided, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
By comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius (r) = 3
Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).
(x - 0)² + (y - 0)² = 3²
x² + y² = 9.
Read more on equation of a circle here: brainly.com/question/17028215
#SPJ1
How many different ways are there to arrange the letters in the word MISSISSIPPI?
Answers
Answer: 34,650 permutations
PLEASE HELP I DO NOT UNDERSTAND!
Solve these equations for x.
1. 4+2x=-2
2. -1(3x-12)=9x-4
3. x-4=13(6x-54)
Answers
Answer:
1. x = -3
2. x = 4/3
3. x = 698/77
Step-by-step explanation:
4+2x=-2
-4 -4
2x= -6
/2 /2
x=-3
You have to get x alone on one side. Search up on yt "How to solve for x on two sides."
Answer:
1.) x = -3 2.) x = 4/3 3.) x = 698/77 or 9.1
Step-by-step explanation:
1.) 4 + 2x = -2
2x = -2 - 4
2x = -6
x = -3
2.) -1 (3x - 12) = 9x - 4
-(3x - 12) = 9x - 4
-3x + 12 = 9x - 4
-3x - 9x = -4 - 12
-12x = -16
x = 4/3
3.) x - 4 = 13 (6x - 54)
x - 4 = 78x - 702
x - 78x = -702 + 4
-77x = -698
x = 698/77 or 9.1