Answer:
The depth of the swimming pool is 2.52 meters
Step-by-step explanation:
To solve this problem properly, the first thing we are to do is to ensure that we are working in the same units at all points in time during the solution.
First of all, we will convert the length and breadth of the pool from feet to yards.
1 foot = 0.3333 yards
30 feet = 10 yards
20 feet = 6.67 yards.
The next step is to find the depth of the swimming pool using the volume and the available dimensions.
From the dimensions given, we can tell that the swimming pool will have a cuboidal shape. This means that the volume will be = length X breadth X depth.
hence we have
184 = 10 X 6.67 X depth
depth = 2.76 yards.
The final step will be to convert the answer we obtained in yards to meters.
1 yard = 0.9144metres
2.76 yards = 2.52 meters
The depth of the swimming pool is 2.52 meters
Please help........................
Answer:
a. (0,0), (2,0), (4,0)
b. (0,0)
Step-by-step explanation:
To find the x-intercept points, you set the equation equal to 0.
0=x³-6x²+8x [factor out an x]
0=x(x²-6x+8) [factor (x²-6x+8)]
0=x(x-2)(x-4) [set each factor equal to 0]
x=0
x-2=0 [add both sides by 2]
x=2
x-4=0 [add both sides by 4]
x=4
Now, we know our x-intercept points: (0,0), (2,0), (4,0).
To find the y-intercept points, we know that it is located on the y-axis, meaning x=0. We plug in 0 for x, and we will know our y-intercept point.
y=(0)³-6(0)²+8(0) [multiply]
y=0
The y-intercept point is (0,0).
A second number is 9 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 760, find the numbers. The three numbers are (Use a comma to separate answers as needed.)
I WILL MARK BRAINIEST PLEASE HELP ME ON THIS QUESTION
Lulu Ruby and Emma went shopping went a total of £261. Each of them had different amount of money. Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money. Each of them spent the same amount of money.how much did money did they begin with?
Answer:
Lulu's money = £81
Ruby's money= £108
Emma's money= £72
Step-by-step explanation:
Let
Lulu's money = x
Ruby's money= y
Emma's money= z
x+y+z= 261
Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.
2/3x = 1/2y= 3/4z
2/3x= 1/2y
4/3x= y
2/3x= 3/4z
8/9x= z
x+y+z= 261
x+4/3x+8/9x= 261
9x+12x+8x= 2349
29x= 2349
X= 81
4/3x= y
4/3(81) =y
108= y
8/9x= z
8/9(81)= z
72= z
Answer:
Step-by-step explanation:
Each of them had different amount of money. Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.
1 answer
·
Top answer:
Answer:Lulu= £81Ruby=£108Emma=£ 72
Find the midpoint of the segment with the following endpoints.
(6,4) and (9,1)
Answer:
[tex]=\left(\frac{15}{2},\:\frac{5}{2}\right)[/tex]
Step-by-step explanation:
[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(6,\:4\right),\:\left(x_2,\:y_2\right)=\left(9,\:1\right)\\\\=\left(\frac{9+6}{2},\:\frac{1+4}{2}\right)\\\\=(\frac{15}{2} , \frac{5}{2} )\\\\[/tex]
How does the value of the 8 in 20,831 compare to the value of the 8 in 20,381?
Answer:
The eight in the first number is ten times larger than the eight in the second number.
A drama club has 22 members. Each member pays monthly dues of $18. On the first day of the month, 6 members paid their dues. The remaining members paid their dues on the second day of the month. How much money was collected in dues on the second day of the month?
Answer:
$288
Step-by-step explanation:
Use back substitution to solve this problem
Answer:
z = -5
y = 1
x = 4
Step-by-step explanation:
2z = -10 ➡ z = -5
4y -(-5) = 9 ➡ 4y = 4 and y = 1
2x + 3 + (-5) = 6 ➡ 2x = 8 and x = 4
Express 0.2 degrees without decimals
If a student is selected at random, what is the
probability that the student is a graduate
(rounded to the nearest percent)? [? ]%
Answer: 24%
Step-by-step explanation:
There are a total of 2610 graduates and if that is the divided by the total which is 10730 you will get 0.2432 which is about 24%
Answer:
24%
Step-by-step explanation:
I checked it on the test to make sure, I have acellus too.
Write an equation of the line that passes through the points (1,-4) and (2,-1).
An equation of the line is y=
]
PLEASE HELP!!
Answer:
y = 3x -7
Step-by-step explanation:
The 2-point form of the equation of a line is useful for this.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (-1 -(-4))/(2 -1)(x -1) -4
y = 3(x -1) -4
y = 3x -7
A pack of paper costs $3.75, including tax. Mr. Cooper wants to purchase packs of paper for his class and has a $20 budget. Write an inequality to solve for the number of packs of paper Mr. Cooper can purchase.
Answer:
($3.75)n ≤ $20
Step-by-step explanation:
Represent this number by n. Then the total purchase price can be represented by ($3.75)n ≤ $20, which is appropriate because Cooper can't spend more than $20.
The desired inequality is ($3.75)n ≤ $20. If a solution is desired, divide both sides by $3/75):
$20
n ≤ ______ = 5 1/3.
$3.75
Cooper can purchase up to 5 whole packs of paper and have a bit of money left over.
6. b. In the figure, suppose CD = 11.5 cm, DE = 5.3 cm, and the
perimeter of the figure is 73.8 cm.
What is GE?
Answer:
GE = 11 cm.
Step-by-step explanation:
The figure provided is attached below.
The information given is:
CD = 11.5
DE = 5.3
BC = 8
AH = 11
Perimeter = 73.8
BC = FG = EF
HA = GH
AB = GE
The perimeter of any figure is the sum of all its sides.
The perimeter of the figure provided is:
Perimeter = AB + BC + CD + DE + EF + FG + GH + HA
Perimeter = AB + BC + CD + DE + BC + BC + HA + HA
[tex]73.8=AB+8+11.5+5.3+8+8+11+11[/tex]
[tex]73.8=AB+62.8[/tex]
[tex]AB=11[/tex]
The value of side AB is 11 cm.
Then the value of GE is also 11 cm.
Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator.
log4(2x2 - 20x + 12y)
Answer:
[tex]f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})[/tex]
Step-by-step explanation:
Let be [tex]f(x,y) = \log_{4}(2\cdot x^{2}-20\cdot x +12\cdot y)[/tex], this expression is simplified by algebraic and trascendental means. As first step, the second order polynomial is simplified. Its roots are determined by the Quadratic Formula, that is to say:
[tex]r_{1,2} = \frac{20\pm \sqrt{(-20)^{2}-4\cdot (2)\cdot (12\cdot y)}}{2\cdot (2)}[/tex]
[tex]r_{1,2} = 5\pm \sqrt{25-6\cdot y}[/tex]
The polynomial in factorized form is:
[tex](x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})[/tex]
The function can be rewritten and simplified as follows:
[tex]f(x,y) = \log_{4} [(x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})][/tex]
[tex]f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})[/tex]
Evaluate if m = 16 and p = 2. 1/2m + 3p A) 10 B) 14 C) 18 D) 48
Answer:
B) 14
Step-by-step explanation:
We can plug in the values of m and p into the equation:
1/2 m + 3p = 1/2 (16) + 3 (2) = 8 + 6 = 14.
What is the solution set to the inequality 1 + 7x + 5x< 13?
Answer:
[tex]x<1[/tex]
Step-by-step explanation:
So we have the inequality:
[tex]1+7x+5x<13[/tex]
First, combine like terms:
[tex]1+12x<13[/tex]
Subtract 1 from both sides:
[tex]12x<12[/tex]
Divide both sides by 12:
[tex]x<1[/tex]
And that's our answer :)
Answer:
Step-by-step explanation:
12x + 1 < 13
12x < 12
x < 1
There are five members on a student council. Two of these members will serve on a spring formal committee. How many possible spring formal committees are there
Answer:
10
Step-by-step explanation:
Given that:
There are a total of 5 members on a student council.
2 of these members will serve in Spring Formal Committee.
To find:
How many possible spring formal committees can be there ?
Solution:
If the observe this problem closely, we are actually asked nothing but the number of ways to select 2 members out of 5.
This is a simple selection problem in which we have to find the number of ways to select [tex]r[/tex] objects out of [tex]n[/tex].
The number of ways = [tex]_nC_r =\frac {n!}{r!(n-r)!}[/tex]
Here,
[tex]n = 5\\r=2[/tex]
Hence, the required number of ways are:
[tex]_5C_2 =\frac {5!}{2!(5-2)!}\\\Rightarrow \dfrac {5!}{2!3!} = \dfrac {5\times 4\times 3!}{2!3!}\\\Rightarrow \dfrac {5\times 4}{2} = \dfrac{20}{2}\\\Rightarrow \bold{10}[/tex]
So, the number of possible spring formal committees are 10.
1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m². 2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm. 3. Find the area of the equilateral triangle whose each side is 8 cm. 4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².
a = 51 m, b = 37 m, c = 20 m
semiperimeter: p = (51+37+20):2 = 54 m
Area of triangle:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}\\\\A=\sqrt{54(54-51)(54-37)(54-20)}\\\\A=\sqrt{54\cdot3\cdot17\cdot34}\\\\A=\sqrt{9\cdot2\cdot3\cdot3\cdot17\cdot17\cdot2}\\\\A=3\cdot2\cdot3\cdot17\\\\A=306\,m^2[/tex]
Rate: ₹ 3 per m².
Cost: ₹ 3•306 = ₹ 918
2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.
a = 5 cm
a+2b = 11 cm ⇒ 2b = 6 cm ⇒ b = 3 cm
p = 11:2 = 5.5
[tex]A=\sqrt{5.5(5.5-3)^2(5.5-5)}\\\\ A=\sqrt{5.5\cdot(2.5)^2\cdot0.5}\\\\ A=\sqrt{11\cdot0.5\cdot(2.5)^2\cdot0.5}\\\\A=0.5\cdot2.5\cdot\sqrt{11}\\\\A=1.25\sqrt{11}\,cm^2\approx4.146\,cm^2[/tex]
3. Find the area of the equilateral triangle whose each side is 8 cm.
a = b = c = 8 cm
p = (8•3):2 = 12 cm
[tex]A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2[/tex]
4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
a = 2x
b = 3x
2x + 2•3x = 32 cm ⇒ 8x = 32 cm ⇒ x = 4 cm ⇒ a = 8 cm, b = 12 cm
p = 32:2 = 16 cm
[tex]A=\sqrt{16(16-8)(16-12)^2}\\\\ A=\sqrt{16\cdot8\cdot4^2}\\\\ A=\sqrt{2\cdot8\cdot8\cdot4^2}\\\\ A=8\cdot4\cdot\sqrt2\\\\ A=32\sqrt2\ cm^2\approx45.2548\ cm^2[/tex]
What are the possible values of x and y for two distinct points, (5, –2) and (x, y), to represent a function? The value of x can be .
Answer:
x ≠ 5
Step-by-step explanation:
For the two points to represent a function, the value of x cannot be repeated. The only restriction on the values of x and y is that x is not 5. (x can be anything but 5.)
Answer:
The value of x can be
✔ any real number except 5
.
The value of y can be
✔ any real number
Step-by-step explanation:
i got it correct on edguinty
Find the approximate side length of a square game board with an area of 131 in2.
Answer:
11.4
Step-by-step explanation:
You find the square root
Write 100 as a product of prime factors
Prime factorization of 100 is 2 * 2 * 5 * 5
100 as a product of prime factors will be 2 ×2×5×5 .
Given,
Number = 100
Now,
To write 100 as prime factor product ,
Take LCM of 100
LCM 100 = 2 ×2×5×5
Thus the factors obtained in the LCM is prime factors only .
So we can write 100 as the product of prime factors:
100 = 2 ×2×5×5
Know more about prime factors,
https://brainly.com/question/29763746
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The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,750 per day. FSF supplies hot dogs to local restaurants at a steady rate of 270 per day. The cost to prepare the equipment for producing hot dogs is $67. Annual holding costs are 47 cents per hot dog. The factory operates 297 days a year. Find
A) The optimal run size.
B) The number of runs per year.
C) The length (in days) of a run.
Answer:
A) 22812 hotdogs per run
B) 75 runs/yr
C) 4 days in a run
Step-by-step explanation:
We are given;
Production rate;p = 5750 per day
Steady Usage rate;u = 270 per day
Setup cost of hotdog;S = $67
Annual carrying cost (H) = 47 cents = $0.47 per hot dog
No. of Production days; d = 297 days
A) Let's first find the annual demand given by the formula;
Annual demand;D = pd
D = 5750 × 297
D = 1707750 hot dogs/yr
Now, formula for optimal run size is given by;
Q_o = √[(2DS/H) × (p/(p - u))]
Plugging in the relevant values gives;
Q_o = √[(2 × 1707750 × 67/0.47) × (5750/(5650 - 270))]
Q_o =√520375454.7971209
Q_o = 22812 hotdogs per run
B) formula for Number of runs per year is given as;
No. of Runs = D/Q₀
Thus;
no. of runs = 1707750/22812
no. of runs ≈ 75 runs/yr
C) Length of a run is given by the formula;
Length = Q₀/p
Length = 22812/5750
Length ≈ 4 days in a run
Two lines intersect in a plane in form for angles what are the angles formed fathers intersect is a 53° angle what are the measures of the other three angles explain your answer
Answer:
53°, 127°, 127°
Step-by-step explanation:
Two intersecting lines form two pairs of angles:
Pair of vertical angles. They are opposite to each other and are equalPair of adjacent angles which are supplementary angles and their sum is 180°So if one of the angles is measured 53°, then the other angles are:
53°- vertical angle with the first one180° - 53° = 127°180° - 53° = 127°A bulb after certain testing had a life of 25 months. The standard deviation based on this sample of size one is
Answer:
25 monthsStep-by-step explanation:
Using the formula for calculating the standard error of the mean to get the standard deviation. The standard error of the mean is expressed as;
SE = S/√n where;
S is the standard deviation
n is the sample size
Given SE = 25 months and n = 1, on substituting this parameters into the formula, we will have;
25 = S/√1
25 = S/1
cross multiply
S = 25*1
S = 25 months
Hence the standard deviation based on the sample is 25 months
What is the value of x & y?
Answer:
x=23, y=14
Step-by-step explanation:
The triangles are indeed simular
4x=x+18 solve for x
Answer:
X = 6
Step-by-step explanation:
Subtract 1 x from both sides so the equation will be 3x = 18. Then divide 3x by 3 and 18 by 3 to get 6
Answer: [tex]x=6[/tex]
Subtract x from both sides
[tex]4x-x=x+18-x\\3x=18[/tex]
Divide both sides by 3
[tex]3x=3=18/3\\x=6[/tex]
F(x)=x^2+7x-30
Find the intercepts, domain and range
Answer:
domain (-inf, +inf)
range [-30, +inf)
y-int = -30
x-int = -10, 3
Step-by-step explanation:
Which is equivalent to3/4
Answer:
75%
Step-by-step explanation:
Answer:
6/8
Step-by-step explanation:
An easy way to do this is to draw a giant rectangle. when you do you simply want to stay a line going straight across in the middle. draw 3/4 ontop and 6/8 on the bottom. or another fraction that's close to it. then shade in 3/4 and the same with 6/8. if the shading is the same length, that's how you know it's equivalent
Sammy's pizza shop charges $12 for a large pizza in $2.50 per topping. If a pizza cost $19.50 how many toppings are on the pizza?
Answer: 3 toppings
Step-by-step explanation:
Let x=the number of toppings
12+2.5x=19.5
2.5x=7.5
x=3
Hope this helps!! :)
Please let me know if you have any question
When is the product of the square root of a prime number and a nonzero rational number a rational number?
Answer:
The square root of a prime number is always an irrational number, then the product of the square root of a prime number and a nonzero rational number is equivalent to:
"the product of an irrational number and a rational number different than zero...."
We know that the product of an irrational number and a rational number (different than zero) is ALWAYS an irrational number.
Then "When is the product of the square root of a prime number and a nonzero rational number a rational number?"
Never, the product will always be irrational.
What is the area of a table with a diameter of 28 inches? How did you figure it out? pls help i need the answer asap
Answer:
The answer is 615 inches
Step-by-step explanation:
The formula for solving the area of a circle is :
A= 1/4 π d^2
So since we only know the diameter the formula would be:
A= 1/4 of 3.14 x 28^2
The first thing you need to do is square 28 which is 784Them times 784 by 3.14 which is 2461.76After all that, your equation should look like this: A = 1/4 of 2461.76So then you would times 2461.76 by 1/4 which is 615.75216 or 615.75Hope this helped :)