Number of balls ≈ \(1.03 * 10^9\)
To calculate how many table tennis balls can fit into the coin building, we need to first figure out the volume of the building and the volume of the table tennis ball.
Then, we can divide the volume of the building by the volume of the ball to get an estimate of the number of balls that can fit inside.
The volume of a table tennis ball can be calculated using the formula for the volume of a sphere, which is:
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14), and r is the radius of the ball. In this case, the radius is given as 0.04m, so we can plug that in and get:
V = (4/3) x 3.14 x 0.04³
\(V =2.14 * 10^{-5} m^3\)
Next, we need to find the volume of the coin building. The building has a width of 20m and a height of 110m, but we don't know its depth.
Let's assume that the building is a rectangular prism with a depth of 10m. Then, we can calculate its volume using the formula:
V = l x w x h
where l is the length, w is the width, and h is the height. Plugging in the given values, we get:
V = 20 x 10 x 110
V = 22000 m³
Now, we can divide the volume of the building by the volume of the ball to get an estimate of how many balls can fit inside:
Number of balls ≈ \(V_building / V_ball\)
Number of balls ≈ 22000 / 2.14 x \(10^-5\)
Number of balls ≈ \(1.03 * 10^9\)
So we can estimate that approximately 1.03 billion table tennis balls can fit into the coin building.
As for the accuracy of this prediction, it's important to keep in mind that we made some assumptions and estimations in our calculations.
For example, we assumed that the building is a rectangular prism with a depth of 10m, which may not be completely accurate.
Additionally, we rounded some of our values and used approximations for pi.
Therefore, our estimate should be considered as a rough approximation rather than an exact calculation. Nonetheless, it gives us an idea of the scale of the building and how many objects it can hold.
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The equation of the conic with focus at (1,−1) directrix along x−y+1=0 and with eccentricity 2 is.O x2−y2=1O xy=1O 2xy−4x+4y+1=0O 2xy+4x−4y−1=0
The equation of the conic with Points at (1,−1) directrix along x−y+1=0 and with eccentricity 2 is 2xy - 4x -4y +1 = 0 .
Equation:
An equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. Solving an equation involving variables involves determining which values of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that satisfy the equation are called solutions of the equation. There are two types of comparisons: identity comparisons and conditional comparisons. The identity is true for all values of the variable. Conditional comparisons are only true for certain values of variables
According to the Question:
Let P(x, y) be any point on conic. Then,
\(\sqrt{(x-1)^2+(y+1)^2}\) = \(\sqrt{2} (\frac{x-y+1}{\sqrt{2} } )\)
⇒ (x-1)²+(y+1)² = (x- y+ 1)²
⇒ 2xy - 4x -4y +1 = 0
The above equation is the required equation of conic.
Complete Question:
The equation of the conic with focus at (1,−1) directrix along x−y+1=0 and with eccentricity 2 is.
1) x²− y²=1O
2) xy =1O
3) 2xy−4x+4y+1 =0
4) 2xy+4x−4y−1 =0
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PPLEASE HELP FOR 10 POINTS!!!!!
Write an equation to represent the verbal description.
In a computer game, Nikolai started with x points. After losing 50 points, Nikolai then tripled his score for a total of y points.
Answer:
\(y=3(x-50)\)
Hope This Helps! :)Please Give Brainliest if this is correct!
(Which I am pretty confident in...)
If f(x) = 3x + 1 and f^-1 = x-1/3 , then the ordered pair of f(3) =
Answer:
10
Step-by-step explanation:
f(x) = 3x + 1
f^-1 = x-1/3 , it is known as inverse function.
f(3)= 3*3 +1
=9+1
=10
To find inverse,
x=3x + 1
y=3x+1
Exchanging the position or x and y
x=3y+1
x-1=3y
.•. y=x-1/3
I need help plz can you please help
Answer:
The answer should be -156-61i
Spin a spinner numbered 1-8 and you land on 8 twice in a row what is the probability?
The probability that you land on 8 twice is 1/64
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
We spin a spinner numbered 1-8 twice
The total sample space can be given by considering all the possible values
Hence the total number of spins are 8*8= 64 spins
The possibility that getting 8 twice is only once possible. As it will be only one pair in all the possible values.
Hence, The total probability is 1/64
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Aisha has $100 saved from her job. She wants to buy as many charms for her bracelet, at $4 each on earrings at $5 per set as she can without spending all of her money. The inequality represents her spending where x is the number of charm,s and y is the number of sets of earrings.
The inequality representing Aisha's spending is 4x + 5y ≤ 100, where x is the number of charms and y is the number of sets of earrings.
To determine the maximum number of charms and sets of earrings Aisha can buy without spending all of her $100, we need to solve the inequality. The left-hand side of the inequality, 4x + 5y, represents the total cost of her purchases. The inequality states that the total cost must be less than or equal to $100.
By substituting different values for x and y, we can find combinations that satisfy the inequality. We can also use trial and error or graphing methods to find the valid combinations within the given constraint. The maximum number of charms and sets of earrings Aisha can buy will depend on the specific values of x and y that satisfy the inequality, ensuring she doesn't spend more than $100.
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2x(5-x)+3x^2
shown work please
\(\\ \rm\Rrightarrow 2x(5-x)+3x^2\)
\(\\ \rm\Rrightarrow 10x-2x^2+3x^2\)
\(\\ \rm\Rrightarrow 10x+(-2+3)x^2\)
\(\\ \rm\Rrightarrow 10x+x^2\)
\(\\ \rm\Rrightarrow x^2+10\)
How much sales tax will be charged at Store B?
Answer: $94.50 is how much sales tax will be charged at store B asumming you are talking about the image attached to this answer, if not could you attach an image?
HURRY ASAP
(-x + 5)(-x - 4)
Answer:
x^2-x-20
Step-by-step explanation:
Expand the polynomial using the FOIL method
The coach for a basketball team wants to try I buy new shoes for her 12 players.
The same shoes are available on double dribble’s web site for $57.75. A 9% processing fee will be applied to the cost of the shoes, plus a shipping fee of $5.99 for each pair.
What is the difference in the total costs of the 12 pairs of shoes between the two sites?
The difference in the total costs of the 12 pairs of shoes between the two sites is $46.77,
How to find the cost difference and total cost?Total cost is the sum up cost for all the individual process. we can find it by adding the cost for each steps.
In the given ques,
Super Sports is offering a 20% discount.
and shoes were originally priced at $72.50 and that a 6.5% sales tax will be applied.
On Double Dribbles, the same shoes were on for $54.75, and a 9% is added and has an extra $5.99 for shipping.
i.e. we have to find the difference in the total costs..
Now we have to multiply 12 by 72.50. The answer to that is 870. Next, we need to multiply 8 by 870 and divide it by 10. The answer to that is 696. Then, we need to add the price and the tax. The price will be 100%, and the tax will be 6.5%. 100 + 6.5 = 106.5. After that, we need to 106.5 by 100. The answer it that is 1.065. Now do times 1.065 by 696. And the answer to that is $741.24.
Do the same for other store. The answer to it is 788.01.
Thus, making Super Sports a better deal.
As, we need to find the difference. So, 788.01 - 741.24 = $46.77.
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The complete question is :
The coach for a basketball team wants to buy new shoes for her 12 players.
Super Sports is offering a 20% discount on each pair of shoes, which were originally priced $72.50. A 6.5% sales tax will be applied to the discounted price.
The same shoes are also available on Double Dribble's website for $54.75. A 9% processing fee will be applied to the cost of the shoes, plus a shipping fee of $5.99 for each pair.
What is the difference in the total costs of the 12 pairs of shoes between the two stores?
Describe how to compare the two ratios 5:8 to 7:9. Tell each step to set up the ratios, then explain what to do to be able to compare the ratios. Finally make sure to answer how the ratios compare. ~ 100 POINTS AND ILL GIVE YOU BRAINLIEST IF YOU ANSWER CORRECTLY AND 5 SENTENCES NEEDED
Step-by-step explanation:
The ratio's can be expressed as fractions and you may compare those.
5 : 8 = 5/87 : 9 = 7/9In order to compare fractions you need to bring them into equal denominator.
8 and 9 have LCM of 8*9 = 72 since they have no common factors.
The equivalent fractions with common denominator are:
5/8 = 9*5/(9*8) = 45/727/9 = 8*7/(8*9) = 56/72Now we can compare the fractions:
45/72 < 56/72, since 45 < 56Kaye will compute for the area of a circle using the formula A=π×r2.If given is the diameter of a circle , what should be computed first?
Answer:
Find the radius.
Step-by-step explanation:
The task is to solve for area of a circle, and you are given the diameter.
The formula for area is :
Area of a circle = π × (radius)²
In this formula, there is only one input value, and that is the radius.
To find the radius, you must know the relation :
Radius x 2 = Diameter
Hence, the radius must be computed first and foremost.
Image transcription textDenzel needs a new car. At the dealership, he finds the car that he likes. The dealership gives him two payment options:
1. Pay $30,000 today for the car.
2. Pay $3,000 at the end of each quarter for three years.
Required:
1-a. Assuming Denzel uses a discount rate of 12% (or 3% quarterly), calculate the present value.
1-b. Which option gives him the lower cost?
Complete this question by entering your answers in the tabs below.
Req 1A
Req 1B
Which option gives him the lower cost?
Which option gives him the lower cost?
< Reg 1A... Show more
1-a. The present value of option 1 is $30,000 and the present value of option 2 is approximately $31,745.15. 1-b. Option 1 gives Denzel the lower cost.
The present value of an investment is the current value of future cash flows, taking into account the time value of money. To calculate the present value in this scenario, we need to determine the value of each payment option.
For option 1, Denzel pays $30,000 today. Since there are no future cash flows, the present value is simply $30,000.
For option 2, Denzel pays $3,000 at the end of each quarter for three years. To calculate the present value, we need to discount each future cash flow using the discount rate of 3% per quarter.
We can use the formula for calculating the present value of an annuity:
PV = C * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value
C = Cash flow per period
r = Discount rate per period
n = Number of periods
In this case, C = $3,000, r = 3% per quarter, and n = 12 quarters (3 years * 4 quarters per year). Plugging these values into the formula, we get:
PV = $3,000 * [(1 - (1 + 0.03)^(-12)) / 0.03]
Calculating this, we find that the present value of option 2 is approximately $31,745.15.
Therefore, the present value of option 1 is $30,000 and the present value of option 2 is $31,745.15.
To determine which option gives Denzel the lower cost, we compare the present values. Option 1 has a lower present value of $30,000 compared to option 2's present value of $31,745.15. Therefore, option 1 gives Denzel the lower cost.
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Is -4 greater than-8
Answer:
the answer is yes
Answer:
Yes, it is greater because the higher a negative number is the less the value. If that makes sense.
Step-by-step explanation:
What is the value of the expression below.
Answer:
138
Step-by-step explanation:
Answer:
C. 138
Step-by-step explanation:
Substitute the values for their given variables:
6(5)² - 5(4) + 8 ⇒ 150 - 20 + 8 ⇒ 138
Which of the following expressions is larger? 3.67 x 10^2 or 1.9 x 10^2
Answer:
3.67 x 10^2 is larger
Step-by-step explanation:
Answer:
3.67 x 10^2 is larger than 1.9 x 10^2
Step-by-step explanation: Multiply
You continue shopping for your holiday feast. The price for a 5 lb. bag at H-E-B is $2.98. The price for a 10 Ib. bag at Kroger is $5.99. Which store has the best unit price for potatoes?
Answer:
$8.97 and no decimal include in itwhoever can solve all these is the best.
y = 5x + 9 m = _____
y = -3x + 4 m = _____
y = 6 – 7x m = _____
y = 15 – 12x m = _____
Answer:
hope these helps
Step-by-step explanation:
y = 5x + 9 m = 5
y = -3x + 4 m = -3
y = 6 – 7x m = -7
y = 15 – 12x m = -12
Someone help it’s due in some time
Answer:
A
Step-by-step explanation:
Answer:
3/2
Step-by-step explanation:
Divide second triangle measurements by first to see what was used to multiply
6/4 = 3/2
7.5/5 = 3/2
12/8 = 3/2
You have 63.50. You earn additional money by raking leaves. Then you buy a sweatshirt for 44.99 and have 53.51 left. How much money do you earn by raking leaves?
Answer:
you earned 35 dollars raking leaves.
start with 63.50 and subtract the 44.99.
63.50-44.99=18.51.
then subtract the 53.41 dollars from 18.51 and get 35.
51.41-18.51=35
Answer: $35
Step-by-step explanation:
lets create an equation
x is going to be the amount of money gained by raking leaves
(63.50 + x) - 44.99 = 53.51
now remember, whatever you do to one side, you do to the other side.. oppositely.
so lets add 44.99 to both sides, either side of the equal sign, because the opposite of -44.99 is +44.99
63.50 + x = 98.50
now subtract 63.50 from both sides
x = 35
1) Pedro decidiu construir um cercado de formato retangular cuja área será 36 m².Quantos metros de tela terá que comprar para fazer o cercado considerando que um dos lados terá 3 metros a mais que o outro?
a) 25 m
b)27 m
c)26 m
d)28
alguem me explica por que da 26
Answer:
Option (a).
Step-by-step explanation:
1) Pedro decided to build a rectangular enclosure with an area of 36 m². How many meters of canvas will he have to buy to make the enclosure considering that one side will be 3 meters more than the other?
Let the length of the rectangle be x then the width will be (3+x) m
The area of a rectangular enclosure is 36 m².
To find how may meter of canvas will he have to buy to make the enclosure, we can find its perimeter. Firstly finding length and breadth using formula of area of rectangle.
\(A=l\times b\\\\36=x(x+3)\\\\x^2+3x-36=0\)
\(x=\dfrac{-3+\sqrt{3^{2}-4(1)(-36)}}{2\times(1)},\dfrac{-3-\sqrt{3^{2}-4(1)(-36)}}{2\times(1)}\\\\x=4.68\ m\ \text{and}\ -7.68\ m\)
Neglecting negative value, we get the length is 4.64 m
Width, b = (3+x) = (3+4.64) = 7.64 m
The perimeter of rectangle is :
P = 2(l+b)
P = 2(4.64 m+7.64 m)
P = 24.56 m
or
P = 25 m
Hence, 25 m of canvas will he have to buy to make the enclosure.
42.4 divide by 7.28 pls help me T-T
Answer: The answer is 5.82417582
I dont know what your answer's are but if you can let me know i can tell you which one is best
Answer:5.824175824175824
Step-by-step explanation:
find the average rate of change for the following equation over the interval -4≤x≤1
y=x^2 + 4x -1
To find the average rate of change of a function over an interval, we need to calculate the slope of the secant line connecting the points on the function at the two endpoints of the interval.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. In the case of a secant line, we can calculate the slope by using the formula:
m = (y2 - y1) / (x2 - x1)
For the function y = x^2 + 4x - 1, we can plug in the values of x and y at the two endpoints of the interval, (-4 and 1), to find the slope of the secant line:
m = [(1)^2 + 4(1) - 1] - [(-4)^2 + 4(-4) - 1] / (1 - (-4))
Simplifying this expression, we get:
m = (1 + 4 - 1) - (16 + 16 - 1) / (-3)
This simplifies to:
m = -20 / -3
Therefore, the average rate of change of the function y = x^2 + 4x - 1 over the interval -4 ≤ x ≤ 1 is 6.5.
The ratios in an equivalent ratio and 3:12 , 4:16 and 5:20 if frost number is 10 what is the second number ?
Which expression is equivalent to is m<4
Answer:
(g*h)=x.
Step-by-step explanation:
the expression is equivalent
Use the following diagram to find the length of the arc indicated.
The value of the length of the arc indicated is,
⇒ 28π/3 feet
We have to given that;
Radius of circle = 14 feet
And, Central angle = 120 degree
Hence, We can formulate;
⇒ Arc length = 14 x 120 x π /180
⇒ Arc length = 28π/3
Thus, The value of the length of the arc indicated is,
⇒ 28π/3 feet
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Pls help struggling w maths homework
Answer:
Step-by-step explanation:
Pythagorean Theorem
(AB)² = 5.6² + 3.9² = 46.57
radius r = (√46.57)/2 cm
area = πr² = π46.57/4 ≈ 36.5759925 cm l²
Homework: Section 11.1 Question 7. Complete the square to find the x-intercepts of the function given by the equation listed. f(x)=x² +34x+104 What are the x-intercepts? **** (Simplify your answer. T
Answer:
x² + 34x + 104 = 0
x² + 34x = -104
x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²
x² + 34x + 17² = -104 + 17²
x² + 34x + 289 = 185
(x + 17)² = 185
x + 17 = +√185
x = -17 + √185
Help me solve the question in the picture (pls show working)
Answer:
92.75 cm²
Step-by-step explanation:
area of polygon = area of ∆EDA + area of ∆ADC +area of ∆ACB.
area of triangles is ½×base×height.
area of ∆EDA=½×EF×AD
=½×4.5×12
=27 cm². -------->(1)
area of ∆ADC=½×AD×DC
=½×12×5
=30 cm². --------->(2)
area of ∆ACB=½×AC×BG
=½×AC×5.5
from pythagorean theorem
(AC)²=(AD)²+(CD)²
= 25+144
= 169 cm then. AC= 13 cm
then area of ∆ACB=½×5.5×13
=35.75 cm² ---------->(3)
from equation (1), (2) and (3):
then the area of polygon = 27 + 30 + 35.75
=92.75 cm²
Any has 10 pieces of fruit. 7 are apples and the rest are oranges.
She chooses a piece of fruit at random eats it then chooses a second piece of fruit at random
Please draw this
The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.
What fraction should go into the boxes?Total number of fruits Amy has = 10
Number of Apples = 7
Number of Oranges = 3
First random pieces of fruits chosen:
Probability of choosing Apples = 6/9
Probability of choosing Oranges = 3/9
Second random pieces of fruits chosen:
Probability of choosing Apples = 6/8
= 3/4
Probability of choosing Oranges = 2/8
= 1/4
Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.
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