Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:
1.) 3.075 gallons.
How to find the remaining amount of water in the barrel?
To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.
We have that:
The initial amount was of 15 gallons.The amount used was of: 6.8 + 5 + 1/8(relative to the one-eight) = 11.925 gallons.Hence the remaining amount is:
15 - 11.925 = 3.075 gallons.
Which means that option 1 is correct.
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Answer: 3.075 gallons
Step-by-step explanation:
order of operations MC
Joshua purchased a game card for the arcade for a total of $15. He played two basketball hoop games for $2.75 each and three rounds of air hockey for $1.25 each. How much did he have left on the game card?
Answer: $5.75
Step-by-step explanation: 2.75 x 2 = 5.5 1.25 x 3 = 2.75 2.75 + 5.5 = 9.25 $15 - $9.25 = $5.75
Pls help it’s due soon
Answer:
Movie duration:1.5hrs
Solve the nonlinear inequality. Expr
x³-9x>0
(-3,0) U (3,00)
Graph the solution set.
How would I graph this on a number line ?
Answer:
x∈(-3;0)∪(3;+∞).
Step-by-step explanation:
1) if to solve the inequality x³-9x>0, then
x(x-3)(x+3)>0, and solution is
x∈(-3;0)∪(3;+∝).
2) the graph is provided in the attachment (it is marked with red colour).
when a pipe constricts as shown in the figure below, the velocity v of fluid flowing through the pipe is inversely proportional to the pipes cross sectional area a. suppose water flows through a section of pipe of area 10 cm^2 at a velocity of 4 m/s. if the pipe constricts to an area of 2.5 cm^2, what will its velocity be in this section of pipe
Answer:
A because of the way the pipe is designed
Order the numbers from least to greatest -3 , -8, |-6|, 2
Answer: -8, -3, 2, |-6|
Step-by-step explanation:
-3 , -8, |-6|, 2
|-6|=6
6>2
-3>-8 since a negative number closer to 0 is the greater number.
Order: -8, -3, 2, 6 ==> -8, -3, 2, |-6|
What is the solution to this inequality?
X-8>-3
OA. x < -11
OB. x>-11
OC. x<5
OD. x>5
Answer:
OD
Step-by-step explanation:
move the -8 to the right, and change its sign
x > 5
How do I factor 7.2x2y - 0.9xy2
Answer:
[tex]xy\left(7.2x-0.9y\right)[/tex]
Step-by-step explanation:
[tex]Rule: a^{b+c}=a^ba^c\\(x^2y=xxy,\:xy^2=xyy)\\=7.2x(xy)-0.9xyy\\=xy\left(7.2x-0.9y\right)[/tex]
Translate the sentence into an equation.
Four less than the product of 9 and a number equals 5.
Use the variable c for the unknown number.
Answer:
(9c) - 4=5
Step-by-step explanation:
Product means 'The answer when you multiply' So we are working in multiplication. ( x )
9c is the multiplication.
It says 'less' which means subtracting to our answer. So we subtract 4. So far our equation is: (9c) - 4 (Brackets are needed as we are multiplying 9 by c and not multiplying 9 by c - 4)
Lastly, it says the answer must be 5 so we add that at the end. So the answer is:
(9c) - 4=5
Alexandra is creating a video game. Every time the main character jumps in the game, the image follows a translation using the coordinate rule
(
x
,
y
)
→
(
x
+
4
,
y
+
9
)
. If the main character is located at
(
−
5
,
0
)
, what will the new location be after a jump? (
,
)
Using translation concepts, the new location after the jump will be at (9,9).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The translation rule for this problem is:
(x,y) -> (x + 4, y + 9).
Which means that the coordinates move 4 units right and 9 units up.
The initial position is:
(5,0).
Hence the final position is:
(5,0) -> (5 + 4, 0 + 9) = (9,9).
The new location after the jump will be at (9,9).
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what is the angle of depression zipline
Answer and Explanation:
The problem provides the following information:
Hypotenuse
=
h
y
p
=
5129
ft
Vertical drop
=
o
p
p
=
1275
ft
To find the angle of depression, the best trigonometric ratio to use is the sine ratio. After equating it with the ratio of the opposite side over the hypotenuse, get the inverse of the sine ratio as shown:
sin
θ
=
o
p
p
h
y
p
θ
=
sin
−
1
(
o
p
p
h
y
p
)
θ
=
sin
−
1
(
1275
ft
5129
ft
)
θ
=
sin
−
1
(
0.2485864691
)
θ
=
14.3938824691
≈
14.4
∘
The angle of depression is
14.4
The U.S. Census Bureau defines a household as all of the people who occupy a housing unit as their usual
place of residence. The number of households is not equal to the population because multiple people may
live in the same housing unit.
82.1% of Cincinnati households have a computer. If 111.804 households in Cincinnati have a computer, how
many households are there altogether in Cincinnati? Show your work. Round to the nearest whole number.
Answer: total household present are 136
Step-by-step explanation:
Given:
82.1% of Cincinnati households have a computer.
111.804 households in Cincinnati have a computer.
According to ratio and proportions we have:
let total number of houses be x;
then
(111.804/x)*100=percentage of Cincinnati households having a computer. [[tex]gain/total*100 =gain %[/tex]]
then
(111.804/x)*100=82.1
cross multiplying we have
x=(111.804*100)/82.1
x=136 households (Round to the nearest whole number.)
so total household present are 136
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The value of the 7 in 57,264 is ten times greater than the value of the 7 in which of these numbers?
A. 17,810
C. 78,893
B. 61,715
D. 95,371
C.78893
Step-by-step explanation:
-_-_+_(*;#-✓✓
Solve 4(0.5n-6)=n-0.25(12+8n)
Please give an accurate answer!
Define the set X = {(x,y)|x > 0,y ≤ √x}.
(a) Sketch the set X in a graph.
(b) Is the set X convex? Explain why or why not.
(c) Is it closed? Explain why or why not. (d) Is it bounded? Explain why or why not. (e) Is it compact? Explain why or why not.
The set X is convex.
In geometry, a subset of an affine space over the real numbers, or more broadly a subset of a Euclidean space, is said to be convex if it contains the entire line segment connecting any two points in the subset. A solid cube is an example of a convex set, whereas anything hollow or with an indent, such as a crescent shape, is not. Alternatively, a convex region is a subset that crosses every line into a single line segment.
b)The set X is convex as any two points on the set X is included in the whole set as x>0. So a line joining any two points on the set X is completely inside the set x.
c)set X is not a closed set as the compliment of the set is not an open set.
d)Set X is not bounded. If a set S contains both upper and lower bounds, it is said to be bounded. A set of real numbers is therefore said to be bounded if it fits inside a defined range. hence set x is not bounded.
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i need help asap. plsss give me the right answer
Answer:
x < 3
Step-by-step explain: I used quizlet
An octopus dives 10 meters per second for 12 seconds then rises 15 meters which expression represents this situation
Answer: -10s +15
-10 = 10 meters down
s = seconds
+ 15 = 15 meters risen
A group of friends wants to go to the
amusement park. They have no more than
$125 to spend on parking and admission.
Parking is $9, and tickets cost $20 per
person, including tax. Write and solve an
inequality which can be used to determine
p, the number of people who can go to the
amusement park.
The required inequality solution is x ≤ 8.
What is inequality?
A connection that contrasts two numbers and perhaps other mathematical expressions inequitably is known as inequality in mathematics. On the number line, size comparisons involving two numbers are typically conducted.The interaction between two values that aren't equal is described by inequalities.An unequal comparison between two numbers and perhaps other mathematical expressions is called an inequality.x represents the number(no.) of people who can go to the amusement park.
They have no more than $125(one hundred twenty-five) to spend
Parking 15.00(fifteen), Tickets 12.50(12.five zero) per person
$15 + $12.50x ≤ $125
x = 110/12.5 ≤ 8.8
x ≤ 8
Therefore, the required inequality solution is x ≤ 8.
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Answer:
Inequality: 20p+9 ≤ 125
Answer: p ≤ 5.8
Step-by-step explanation:
Solve:
20p+9≤125
subtract -9 from both sides
20p≤116
20p/20 ≤ 116/20 Divide both sides by 20
p ≤ 5.8
A certain hybrid car can travel 1 9/11 times as far as a similar no hybrid car will on one gallon of gasoline . If the non hybrid car can travel 33 miles per gallon of gasoline, how far can the hybrid travel on 4/5 gallon of gasoline ?
On 4/5 gallon of gasoline, hybrid car will travel a distance of 48 miles.
How to solve Algebra Word Problems?Suppose, non hybrid car travel "x" distance in 1 gallon of gasoline
Then, hybrid will travel " 1 ⁹/₁₁ * x" distance in 1 gallon of gasoline
Given that, non hybrid car travel distance per gallon is; x = 33 miles per gallon
Then, hybrid car travel, 1 ⁹/₁₁ * x = 1 ⁹/₁₁ * x * 33 = 60 miles per gallon
On 1 gallon of gasoline hybrid car travel 60 miles
On 4/5 gallon of gasoline hybrid car will travel = 4/5 * 60 = 48 miles
On 4/5 gallon of gasoline, hybrid car will travel 48 miles of distance.
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If anyone can help me to solve this!!
Answer:
[tex]\textsf{1.} \quad x=-6, \quad x=6[/tex]
[tex]\textsf{2.} \quad x=-5, \quad x=2[/tex]
[tex]\textsf{3.} \quad x=-3, \quad x=7[/tex]
[tex]\textsf{4.} \quad x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]
[tex]\textsf{5.} \quad x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]
Step-by-step explanation:
Question 1Method: Extracting the Square Root
[tex]\begin{aligned}& \textsf{Given}: & x^2 & = 36\\& \textsf{Square root both sides}: & \sqrt{x^2} & = \sqrt{36}\\& \textsf{Simplify}: & x & = \pm 6\\&\textsf{Solution}:&x& = -6, 6\end{aligned}[/tex]
Question 2Method: Factoring
[tex]\begin{aligned}& \textsf{Given}: & x^2+3x-10 & = 0\\& \textsf{Split the middle term}: & x^2+5x-2x-10 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x+5)-2(x+5)&=0\\& \textsf{Factor out the common term $(x+5)$}: & (x-2)(x+5)&=0\\& \textsf{Apply the zero-product property}: & (x-2)=0 \implies x&=2\\ &&(x+5)=0 \implies x&=-5\\ & \textsf{Solution}: & x&=-5,2\end{aligned}[/tex]
Question 3Method: Factoring
[tex]\begin{aligned}& \textsf{Given}: & x^2-4x-21 & = 0\\& \textsf{Split the middle term}: & x^2-7x+3x-21 & = 0\\& \textsf{Factor the first two and the last two terms}: & x(x-7)+3(x-7)&=0\\& \textsf{Factor out the common term $(x-7)$}: & (x+3)(x-7)&=0\\& \textsf{Apply the zero-product property}: & (x+3)=0 \implies x&=-3\\&&(x-7)=0 \implies x&=7\\& \textsf{Solution}: & x & = -3, 7\end{aligned}[/tex]
Question 4Method: Quadratic Formula
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]
Given:
[tex]5x-4=-2x^2[/tex]
Rearrange into standard form by adding 2x² to both sides:
[tex]\implies 2x^2+5x-4=0[/tex]
Therefore:
[tex]a=2, \quad b=5, \quad c=-4[/tex]
Substitute the values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2)(-4)} }{2(2)}[/tex]
[tex]\implies x=\dfrac{-5 \pm \sqrt{25+32} }{4}[/tex]
[tex]\implies x=\dfrac{-5 \pm \sqrt{57} }{4}[/tex]
Therefore, the solutions are:
[tex]x=\dfrac{-5 +\sqrt{57} }{4}, \quad x=\dfrac{-5 -\sqrt{57} }{4}[/tex]
Question 5Method: Quadratic Formula
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Quadratic Formula}\end{center}\\\\\begin{center}$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\end{center}\\\\\\\begin{center}when $ax^2+bx+c=0$\end{center}\end{minipage}}[/tex]
Given:
[tex]5x^2-7x-13=0[/tex]
Therefore:
[tex]a=5, \quad b=-7, \quad c=-13[/tex]
Substitute the values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(5)(-13)} }{2(5)}[/tex]
[tex]\implies x=\dfrac{7 \pm \sqrt{49+260} }{10}[/tex]
[tex]\implies x=\dfrac{7 \pm \sqrt{309} }{10}[/tex]
Therefore, the solutions are:
[tex]x=\dfrac{7+ \sqrt{309} }{10}, \quad x=\dfrac{7-\sqrt{309} }{10}[/tex]
What is 4 gal 6 qt 112 oz in standard notation?
The value of 4 gal 6 qt 112 oz expressed in standard notation is; 6.375
How to express in Standard Notation?
Standard notation of a number is defined as when a number is written with only number digits. This is the typical way to write numbers since words are not used in standard number notation.
Now, from conversions, we know that;
1 oz = 0.0078125 gallons
1 qt = 0.25 gallons
Thus, 4 gal 6 qt 112 oz expressed in gallons is;
4 + (6 * 0.25) + (112 * 0.0078125)
= 4 + 1.5 + 0.875
= 6.375
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the points on the table are in a line what is the slope
Answer:
the slope of the table is -0.857
In a study conducted by a human resource management organization, human resource professionals were surveyed. Of those surveyed, % said that their companies conduct criminal background checks on all job applicants. Complete parts (a) through (d).
What is the exact value that is 41% of 379 survey subjects?
(Type an integer or a decimal. Do not round.)
The exact value is ____
Using proportions, it is found that the exact value of 41% of 379 is of 155.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The proportion of 41% of 379 is given as follows:
0.41 x 379 = 155.39.
Since 0.39 < 0.5, the exact value is rounded to 155.
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Suppose you invest in an annuity that pays 5% annual interest, compounded quarterly. If you contribute $400 every quarter for 20 years, how much interest would you earn during the 20 years? Enter your answer, rounded to the nearest cent, without the dollar sign or comma ($23,678.1235 should be entered as 23678.12.)
If you contribute $400 every quarter for 20 years, the amount of interest you would earn during the 20 years is $22,447.52
What future value formula is applicable in this case?
The applicable future value formula is that of an ordinary annuity which determines the future worth of $400 quarterly savings for 20 years bearing in mind that the quarterly interest rate is the annual interest rate divided by 4
FV=PMT*(1+r)^N-1/r
FV=worth of the annuity after 20 years=unknown
PMT=quarterly deposit=$400
r=quarterly interest rate=5%/4=1.25%
N=number of quarterly savings in 20 years=20*4=80
FV=$400*(1+0.0125)^80-1/0.0125
FV=$54,447.52
interest=$54,447.52-($400*80)
interest=$ 22,447.52
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Wilson has a number in mind. If he takes away one-third of the number from it the
result is 10. Find the number.
hi
if he takes 1/3 , then remains 2/3
then 2/3 X = 10
X = 10 / 2/3
X = 10 * 3/2
X = 30/2
X = 15
let's check :
1/3 of 15 = 15/3 = 5
15 -5 = 10
all macth, so answer is correct
d + 9 = 35 6th grade
Answer:
D = 26
Step-by-step explanation:
All you have to do is subtract 35 by 9, which is 26.
So,
26 + 9 = 35
n=.1515
You need to multiply n by a power of 10 to help you find the fraction. Decide on the power of 10 to multiply by, and tell how you identified that number.
Answer:
the answer is two because ur multiplying hope this helps
6 less the quantity 9 times a number
Answer:
6-9x
Step-by-step explanation:
Converted from word to standard form.
Hope it helps!
Please help! thanks!
Identify the segment bisector of
__
XY
The segment bisector of line segment XY is line n.
The length of the line segment XY is 6 units.
How do you define the line segment?A line segment is a section of a line with two endpoints. A line segment, unlike a line, has a fixed length.
A line segment's length can be measured in metric units including such millimeters and centimeters, or in customary units such as feet or inches.A bisector is a line that separates a straight line or perhaps an angle into two equal parts. A segment's bisector always contains the segment's midpoint.As per the given diagram in the question.
It is clear that the line segment XY is being divided by another line named n.
Thus,
The two segment of the line segment XY must be equal.
XM = MY
Substitute the values from the diagram;
5x + 8 = 9x + 12
Simplifying;
4x = -4
x = -1
Put the values in each segment;
XM = 5x + 8
XM = 5(-1) + 8
XM = 3 units.
Put the value in MY
MY = 9x + 12
MY = 9(-1) + 12
MY = 3 units.
As, it is clear from above values that the both segment are equal of 3 units each.
XY = XM + MY
XY = 3 + 3 = 6
Therefore, the value of XY is 6 units.
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Simplify the expression √48