If hose A takes x hours to fill the pool, hose B will take x+3 hours to fill the pool. So, each hour, A will fill [tex]\bf{\dfrac{1}{x}}[/tex] parts of the pool and B will fill [tex]\bf{\dfrac{1}{x+3}}[/tex] parts. Since using both hoses fills the pool completely, you have to:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ 1= \frac{1}{x}+\frac{1}{x}+\frac{1}{x+3}+\frac{1}{x+3} } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ =\frac{2}{x}+\frac{2}{x+3} } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ =\frac{2x+2x+6}{x(x+3)} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+3x=4x+6\ \Longrightarrow\ \ 0=x^2-x-6=(x-3)(x+2) } \end{gathered}$}[/tex]
Hose A takes 3 hours to fill the pool and Hose B takes 6 hours.
y=4(3)^x complete a table showing y values for values of x from 0 to 5
To solve this problem, we just have to substitute the values into the exponential equations and solve.
Exponential EquationIn the given exponential equation, we simply need to plug in the values of x from 0 to 5
[tex]y = 4(3)^x[/tex]
when x = 0
[tex]y = 4(3)^x\\y = 4(3)^0\\y = 4[/tex]
when x = 1
[tex]y = 4(3)^x\\y = 4(3)^1\\y = 12\\[/tex]
when x = 2
[tex]y = 4(3)^2\\y = 36[/tex]
when x = 3
[tex]y = 4(3)^3\\y = 108[/tex]
when x = 4
[tex]y = 4(3)^4\\y = 324[/tex]
when x = 5
[tex]y = 4(3)^5\\y = 972[/tex]
From the calculations above, the value of y when x is from 0 to 5 are
x(0) = 4x(1) = 12x(2) = 36x(3) = 108x(4) = 324x(5) = 972Learn more on exponential equations here;
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Chelsea wants to rearrange her room. She makes a scale drawing of the room and cuts out pieces of paper to represent her furniture. The paper representing her desk is 1 1/4 inches by 2 1/4 inches. What are the actual dimensions of her desk?
A: 1 3/4 feet by 3 feet
B: 2 1/2 feet by 5 feet
C: 2 1/4 feet by 4 1/4 feet
D: 2 1/2 feet by 4 1/2 feet
Since the paper representing her desk is 1 1/4 inches by 2 1/4 inches, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft
To answer the question, we need to know what scale is
What is a scale?A scale is the ratio of two dimension and it is given on a scale drawing.
Given that Chelsea makes a scale drawing of the room and cuts out pieces of paper to represent her furniture, and the paper representing her desk is 1 1/4 inches by 2 1/4 inches.
Since on the scale, we have 1/2 in = 1 foot ⇒ 1 in = 2 ft
Actual dimensions of deskSo, the actual dimensions of her desk are
1 ¹/₄ in by 2 ¹/₄ in = 5/4 in by 9/4 in
= 5/4 × 1 in by 9/4 × 1 in
= 5/4 × 2 ft by 9/4 × 2 ft
= 5/2 ft by 9/2 ft
= 2 ¹/₂ ft by 4 ¹/₂ ft
So, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft
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Write an equation of the parabola in vertex form that passes through ( 3 , -2 ) and has a vertex of ( 5,8 )
Answer:
Parabola in vertex form: y = a(x - h)2 + k
Vertex: (h, k) = (3, 2) and (x, y) = (13, 8)
y = a(x - h)2 + k
y = a(x - 3)2 + 2 <== with substitution (h, k) = (3, 2)
8 = a(13 - 3)2 + 2 <== with substitution (x, y) = (13, 8)
8 = a(10)2 + 2
100a = 8 - 2 ==> 100a = 6 ==> a = 6/100 ==> a = 3/50
Parabola in vertex form: y = a(x - h)2 + k
y = (3/50)(x - 3)2 + 2 (Final Answer - Parabola in vertex form)
Step-by-step explanation:
Answer:
Hi,
Step-by-step explanation:
Parabola has the equation:
y=k*(x-5)²+8
if x=3, y=-2: -2=k*(-2)²+8 ==> 4k=-10==> k=-5/2
So y=-5/2(x-5)²+8
A rental car company charges $63.41 per day to rent a car and $0.05 for every mile driven. Ella wants to rent a car, knowing that: She plans to drive 275 miles. She has at most $200 to spend. What is the maximum number of days that Ella can rent the car while staying within her budget?
Answer:
2 days
Step-by-step explanation:
275 miles times 0.05 = $13.75 for mileage
200-13.75=186.25 left
186.25/63.41(daily fee)= 2.93
She can rent it for 2 days
What is the area of an isosceles right triangle whose hypotenuse is 5 √2 m long?
Answer:
Sides other than hypotenuse of an isosceles triangle are equal.
Let the other two sides be x each.
Using pythagoras theorem
x
2
+x
2
=(5
2
)
2
2x
2
=50
⇒x
2
=25
⇒x=5cm
So the other two sides are 5cm each.
Pippa has a box containing n pens.
there are only black pens and red pens in the box.
the number of black pens in the box is 3 more than the number of red pens.
pippa is going to take at random 2 pens from the box.
the probability that she will take a black pen followed by a red pen is
9
35
find the possible values of n.
show clear algebraic working.
The possible values of N from the given probability parameters is; N equals 15 or 21
How to Solve Algebra Problems?We are told that;
Number of pens in the box = N
Let the number of red pens be x
Thus; number of black pens = x + 3
Thus;
x + x + 3 = N
x = (N - 3)/2
The probability that she will take a black pen followed by a red pen is;
P(she will take a black pen followed by a red pen) = (x + 3)/N * x/(N - 1)
Plugging in he relevant values and solving for N gives ;
Solving for N gives N equals 15 or 21
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For the function f(x) and g(x) given in the graph. Find f(g(2))
Answer:
f(g(2)) = 4
Step-by-step explanation:
find g(2) then substitute the value obtained into f(x)
locate x = 2 on the x- axis, go vertically up to meet g(x) at (2, 5 )
locate x = 5 on the x- axis, go vertically up to meet f(x) at (5, 4 )
then f(g(2)) = 4
My age this year is a multiple of 7. Next year it will be a multiple of 5. I am more than 20 years of age but less than 80. How old will I be 6 years from now?
Answer:
You will be 55
Step-by-step explanation:
What is the value of the expression when n = 3?
6 (n² + 2)
n
O 16
O22
O 30
O 66
Answer:
66
Step-by-step explanation:
6(n² + 2)
6(3² + 2)
6(9 + 2)
6(11)
66
I NEED HELP LIKE ASAP
50 points!!
5. The table shows the number of stories in eight
buildings. Which statement is true?
Table:
15 15 18 20 22 24 26 40
a. The mode is greater than the mean.
b. There are no outiers.
c. The mode best describes the data.
d. The meon is greater than the median
A baseball field is a square with sides of length 90 feet. What is the
shortest distance between first base and third base?
A.90
B.180 squared
C.90
D.16200 squared
a is a common factor of 72 and 108
b is common multiple of 4 and 10
work out the highest possible value of a/b
Answer:
the value is 14
Step-by-step explanation:
because im just trying to get points
A giant pie is created in an attempt to break a world record for baking. The pie is shown below: What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
78.13 ft
82.43 ft
86.31 ft
91.98 ft
if the "d"iameter of the pie is 30, then its radius must be half that, or 15.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=15\\ \theta =42 \end{cases}\implies \begin{array}{llll} A=\cfrac{(42)\pi (15)^2}{360}\implies A=\cfrac{105\pi }{4} \\\\\\ \stackrel{using~\pi =3.14}{A\approx 82.43} \end{array}[/tex]
Find the 50th term of the sequence: 65536,49152,36846,27648
Step-by-step explanation:
first you should check whether the sequence is arithmetic and geometric .as you see the sequence is arithmetic with the common difference of -16384.
OP=
04
06
08
Helppppppppppppp
Answer:
the answer is 6 just add the radius of both circle
Answer:
OP is 6
Step-by-step explanation:
Because we av being given d parameters
4 is d radius of the first circle and 2 is d radius of the second circle so automatically d answer is 6
Can anyone please help me with this I been working on this for hours
The functions f and g are defined as follows.
f(x)=2x²-3x
g(x) = -4x-1
Find f(-2) and g (7).
Simplify your answers as much as possible.
f(-2) =
믐
X
9 (7) =
Ś ?
Answer:
f(-2) = -14g(7) = -29Step-by-step explanation:
~1
Given Polynomial:
f(x)=2x²-3xTo Find:
f(-2)Solution:
f(x)=2x²-3xSubstitute x = -2 onto the given polynomial,as we need to find f(-2),so x = -2.
f(6) = 2(-2)² -3(-2)Simplify using PEMDAS,then.
f(6) = -8 - 6f(6) = -14Hence, f(6) = -14
[tex] \rule{225pt}{2pt}[/tex]
~2
Given polynomial:
g(x) = -4x-1To Find:
g(7)Solution:
g(x) = -4x-1
Substitute x = 7 onto the given polynomial,as we need to find g(7),so x = 7.
g(7)= -4(7) - 1Simplify using PEMDAS.
g(7) = -28 - 1g(7) = -29Hence, g(7) = -29.
[tex] \rule{225pt}{2pt}[/tex]
(3+13-10)+14÷2+4 how do you solve this ?
Answer: 17
Step-by-step explanation:
Don't forget about PEMDAS. (parentheses, exponents, multiplication, division, addition, subtraction)
Start with parentheses
(3+13-10)... 13+3= 16, 16-10=6 ...
so (3+13-10)=6
Now we have...
6 + 14 / 2 + 4
No exponents so we go on.
no multiplication so we go on
Now division...
14 / 2 = 7 because 7 x 2 = 14
Now we have...
6 + 7 + 4
now we do addition, addition is commutative so you can add it in any order you want
6 + 7 = 13, 13 + 4 = 17
therefore, the answer is 17
Calculate the Theoretical probability of the following experiments.
Use a tree diagram to visualize your calculations. *** Note that these are independent experiments. Once she has removed a fruit, she will put it back in before removing a second fruit.***
Jane has a bag with 5 oranges, 4 grapefruits, and 3 apples.
What is the probability that she will NOT randomly take out two oranges in a row?
What is the probability that she will NOT randomly take out two grapefruits in a row?
What is the probability that she will NOT randomly take out two apples in a row?
What is the probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order?
The probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order is 0.2917.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
A.) The probability that she will NOT randomly take out two oranges in a row,
Probability = 1 - (5/12)² = 0.8264
B.) The probability that she will NOT randomly take out two grapefruits in a row,
Probability = 1 - (4/12)² = 0.8264 = 0.8889
C.) The probability that she will NOT randomly take out two apples in a row,
Probability = 1 - (3/12)² = 0.8264 = 0.9375
D.) The probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order,
Probability = (7/12) × (9/12) × (8/12) = 0.2917
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Latoya bought 8 pounds of potatoes at a local wholesaler for $18. Her friend Herman bought 6 pounds of potatoes at the supermarket for $15. Herman thinks he got the better deal because $15 is less than $18.
Answer:
Herman is wrong. Latoya got the better deal.
Step-by-step explanation:
Latoya bought 8 pounds of potatoes for $18.
► 18 / 8 = $2.25 per pound
Herman bought 6 pounds of potatoes for $15.
► 15 / 6 = $2.50 per pound
Cheaper per pound is better!
Emily is trying to rewrite 45 - 27 as the product of the GCF of the two numbers and
a difference. Will this work? Explain.
55 POINTS!!!!!! WILL GIVE BRAINLIEST!!!!!!! PLS HELP ASAP!!!!!
Danielle is trying to solve the equation [tex]8^x=\frac{1}{64}[/tex]. Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Answer:
x=-2
Step-by-step explanation:
Given equation:
8^x= 1/64
Ensure both sides of the equation are in power format by changing 1/64
1/64 = 64^-1
8^x = 64^-1
2^3(x) = 2^6(-1)
The bases will cancel out each other
3(x) = 6(-1)
3x = -6
x = -6/3
x = -2
Check
8^x = 1/64
x = -2
8^-2
= 1/8²
= 1/8*8
= 1/64
A student looked at the diagram below and concluded x=y.
The student justified that conclusion by saying that both angles are subtended by arc AB.
What is the students error?
What are the values of X and y?
Answer:
[tex]y = 85[/tex]
[tex]x = 95[/tex]
scientist wants to estimate the puffin population on puffin island
Answer:
The cliffs are home to many seabirds. Despite its name, there are few puffins (around 50 pairs during the April-July breeding season).
Step-by-step explanation:
James defines a circle as the set of all the points equidistant from a given point. His statement is not precise enough because he should specify that.
A circle has a center, radius, diameter and points in a plane. Depending on the context, the definition of a circle must contain at least one of the following terms:
Center
Radius
Diameter
Points in a plane
The complete question is as follows:-
James defines a circle as "the set of all the points equidistant from a given point." His statement is not precise enough
because he should specify that
A circle includes its diameter
The set of points is in a plane
A circle includes its radius
The set of points is collinear
What is a circle?A circle is a two-dimensional geometry on the plane having a center point and the circular line is drawn equidistant from the center point.
Based on James' definition of a circle, he needed to specify that the points are in a plane (option c).
As presented in his definition "the set of all the points" can be interpreted in several ways. Some of which are:
the set of points on a line
the set of points in a plane
the set of points in a region
Etc
Of these numerous possible interpretations, James should have specified that the set of points is in a plane
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1 pound is equivalent to ____ grams.
Answer: 453.592 grams
Step-by-step explanation:
I searched it up online. But if you're going to use this to calculate. Use 454 grams.
Answer:
453.592 rounded would be 454* grams witch is equal to 1 pound
Step-by-step explanation:
1 pound is equivalent to __453.592 or just say 454*__ grams.
Had to fix that hehehe
Hope This Helped
Rhombus RSTU is congruent to rhombus
WXYZ. Could rhombus RSTU be a
translation image of rhombus WXYZ?
Why or why not? Can you be sure that
rhombus RSTU is a translation image of
rhombus WXYZ? Why or why not?
Rhombus RSTU is congruent to WXYZ, and are translational images of each other because all their sides and angles are equal
What are the properties of a rhombus?Some of the properties of a rhombus are;
The sides are congruent.All the opposite sides are parallel to each other.Diagonals bisect each other perpendicularly.The angles are supplementary, that is, they add up to 180°If Rhombus RSTU is congruent to WXYZ, then they are both translation images of each other because all their sides and angles are equal.
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A cylinder has a diameter of 10 inches in the height four times the radius what is the volume
Answer:
500π in^3
Step-by-step explanation:
The radius is half the diameter, so the radius is 5 in. Since the height is four times that, the height is 20 in.
The equation for the volume of a cylinder is:
[tex]V = \pi r^{2}h[/tex]
We can plug in the radius and height:
[tex]V = \pi \times (5)^{2} \times 20\\V = \pi \times 25 \times 20\\V = 500\pi in^{3}[/tex]
Evaluate the surface integral ∫sf⋅ ds where f=⟨2x,−3z,3y⟩ and s is the part of the sphere x2 y2 z2=16 in the first octant, with outward normal orientation away from the origin
Parameterize S by the vector function
[tex]\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle[/tex]
with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.
Compute the outward-pointing normal vector to S :
[tex]\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle[/tex]
The integral of the field over S is then
[tex]\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv[/tex]
[tex]\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv[/tex]
[tex]\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}[/tex]
Distribute and simplify these radicals.
√12-(-1+√5)
O-4√3
0-2√3+2√15
O 4√3
06√3
K
[tex] \sqrt{12} + 1 - \sqrt{5} \\ = \sqrt{4} \times \sqrt{3} + 1 - \sqrt{5} \\ = 2 \sqrt{3} + 1 - \sqrt{5} [/tex]