Answer:
7776 m^3
Step-by-step explanation:
The ratio of volumes is the cube of the scale factor. Here, the actual tower has dimensions 60 times those of the model, so the actual volume is ...
(36,000 cm^3)(60^3) = 7.776·10^9 cm^3
= 7.776·10^9(10^-2 m)^3
= 7776 m^3
The actual tower block has a volume of 7776 m^3.
Answer:
Therefore, volume of actual tower = 2.16 m³
Step-by-step explanation:
Scale of model to actual tower = 1:60
This means that the actual tower is larger than the model tower by a scale of 60 times
To calculate the volume of the actual tower, the following steps are used:
1 cm³ of model tower = 60 cm³ of actual tower
∴ 36,000 cm³ of model tower = 60 × 36,000 = 2,160,000 cm³
converting to m³
100 cm = 1 m
(100 cm)³ = (1 m)³
1,000,000 cm³ = 1 m³
∴ 1 cm³ = [tex]\frac{1}{1,000,000} m^{3}[/tex]
∴ 2,160,000 cm³ = [tex]\frac{2,160,000}{1,000,000} m^{3}[/tex] = 2.16 m³
Therefore, volume of actual tower = 2.16 m³
y=(x+9)÷(x-3)
Find the value of y when x=5
solution,
X=5
[tex]y = \frac{x + 9}{x - 3} \\ = \frac{5 + 9}{5 - 3} \\ = \frac{14}{2} \\ = 7[/tex]
hope this helps...
Good luck on your assignment..
Answer:
When x=5
Y=(5+9)÷(5-3)
= 14 ÷2
= 7
In a local ice sculpture contest, one group sculpted a block into a rectangular based pyramid. The dimensions of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this sculpture.
Answer:
87.6m²
Step-by-step explanation:
From the above question, we are given the following information
The dimensions of the base were 3 m by 5 m:
Length = 3m
Width = 5m
The pyramid was 3.6 m high
Height = 3.6m
To calculate the amount of ice needed for this sculpture, we would have to find the Surface Area of the Rectangular Prism
This is calculated as:
Surface Area =2(wl+hl+hw)
= 2(3 × 5 + 3.6 × 3 + 3.6 × 5)
= 2(15 + 10.8 + 18)
= 2(43.8)
= 87.6m²
The amount of ice needed for this sculpture is 87.6m²
John’s parents put $40 on his school account for lunch. Each day is a three dollars for lunch. Y represent the amount of money John has after x days in a school account.
Answer:
y = $40 - ($3/day)x
Step-by-step explanation:
y = $40 - ($3/day)x represents the amount of money John has left after x days.
Two students use different methods to solve this multiplication problem: 2/5x- 15 5/8 Read each of their methods below and then enter numbers to correctily complete their work.
Answer: so the answer would be 120 because 15 times 8 would be 120 thank you i might be wrong but i tried
Step-by-step explanation:
What is π/6? I don’t know. No calculators!
Answer:
You could approximate pi to be 3.14, and divide that by 6.
Step-by-step explanation:
Answer:
30 degrees
Step-by-step explanation:
If π/6 is an angle in radians
So, Converting it into degrees will make :
=> π/6 * 180 => 30 degrees
PLEASE HELP!!!
For the data set 7, 5, 10, 11, 12, the mean, x, is 9. What is the standard
deviation?
==================================================
Explanation:
The weird or fancy looking E symbol is the greek uppercase letter sigma. It is effectively the english version of S to represent summation. So we add up all the [tex](x-\overline{x})^2[/tex] terms to get this. Luckily this has already been done for us in the table where they wrote "sum = 34", so [tex]\sum(x-\overline{x})^2 = 34[/tex]
From here, we substitute this into the formula, along with n = 5 since there are 5 items in the original list
So,
[tex]s = \sqrt{\frac{1}{n-1}\sum(x-\overline{x})^2} \\\\s = \sqrt{\frac{1}{5-1}*34} \\\\s = \sqrt{\frac{1}{4}*34} \\\\s = \sqrt{0.25*34} \\\\s = \sqrt{8.5} \\\\s \approx 2.91547594742266 \\\\s \approx 2.9 \\\\[/tex]
This computes the sample standard deviation. To get the population standard deviation, you'd basically change the "n-1" to simply "n", and the rest of the formula is identical.
The rectangle below has an area of 15k^4 + 35k^3 + 20k^2. The width of the rectangle is equal to the greatest common monomial factor of 15k^4, 35k^3, and 20k^2. What is the length and width of the rectangle?
The greatest common factor is the biggest number that divides evenly into each one of the numbers without a remainder...the only thing that's different about our situation is that we have variables in addition to regular number (but the same logic applies...we need to find the biggest variable that goes into k^4 , k^3 , and k^2 ).
The biggest number that goes into 15, 35 and 20 is the number 5. The biggest variable that goes into k^4 , k^3 , and k^2 is k^2
Combining the number and the variable, we get that the greatest common monomial factor is 5k^2
Since area is length x width, and we just figured out that width is 5k2 , all we have to do to find length is divide 15k4+35k3+20k2 by 5k2 , and we get that the length is 3k^2+7k+4
So the width is 5k^2 and the length is 3k2+7k+4
:))
-Eli
a plane flies 90 kilometres on a bearing 030 and then flies 150 kilometres due east how far east of the of the starting point is the plane
Answer: 45√3 + 150 ≈ 227.94
Step-by-step explanation:
A bearing of 30° means we can create a 30-60-90 triangle. We are looking for the x-value = 45√3 ≈ 77.94
Add to that value, the additional 150 due east.
77.94 + 150 ≈ 227.94
Through any 2 points there is exaclty_____line.
Answer:
One
Step-by-step explanation:
Through any 2 points, there is exactly one line.
Answer:
ONE
Step-by-step explanation:
Through any 2 points there is exaclty ONE line.
Find the gradient of the line segment between the points (-2,3) and (-5,6).
Answer:
-1Solution,
Let the points be A and B.
A(-2,3)---->(X1,y1)
B(-5,6)---->(x2,y2)
Now,
[tex] \frac{y2 - y1}{x2 - x1} \\ = \frac{6 - 3}{ - 5 - ( - 2)} \\ = \frac{3}{ - 5 + 2} \\ = \frac{3}{ - 3} \\ = - 1[/tex]
Hope this helps..
Good luck on your assignment..
Find the missing side length
What is the range? Explain
Answer:
Range = [5, ∞)
Step-by-step explanation:
The initial number of snakes is 5 and it is increasing at a high rate so the maximum number is infinite. The population is increasing exponentially according to the equation P = 5(2)^t where t = the number of years.
The play director spent 190190190190 hours preparing for a play. That time included attending 35353535 rehearsals that took varying amounts of time and spending 933493 \dfrac{3}{4}934393, start fraction, 3, divided by, 4, end fraction hours on other responsibilities related to the play. What question does the equation 35x+9334=19035x+93\dfrac{3}{4}=19035x+9343=19035, x, plus, 93, start fraction, 3, divided by, 4, end fraction, equals, 190 help answer?
Answer:
The equation above represents the total time the play director spent preparing for a play.
Step-by-step explanation:
The time spent by the play director for preparing for a play is, 190 hours.
Of these 190 hours, the director spent varying amounts of time attending 35 rehearsals for the play.
Let the varying amounts of time be denoted by, x.
The director also spent 3/4th of an hour, i.e. 45 minutes, on other responsibilities related to the play.
The equation provided is:
[tex]35x+\frac{3}{4}=190[/tex]
The equation above represents the total time the play director spent preparing for a play.
sector of a circle is given with radius 7cm and angle subtended by the sector of a circle is 500
,
Calculate,
(i) area of sector,
Answer:
The area of the sector is 21.39 cm^2
Step-by-step explanation:
Mathematically, to calculate the area of a sector, the formula to use is;
A = Theta/360 * pi * r^2
where Theta is the angle subtended at the center of the circle = 50 degrees
r is the radius of the circle = 7cm
pi = 22/7
Substituting these values into the area of sector equation, we have;
A = 50/360 * 22/7 * 7 * 7 = (5 * 22*7 )/36 = 21.39 cm^2
Jane is using a ladder to paint under a window of her house. The straight line distance from the bottom of the window to the ground is 6ft. (leg a). The bottom of the ladder is 5 ft. From the house (leg b). How tall must the ladder be to reach the window. You are finding "c".
Answer:
Step-by-step explanation:
The ladder forms a right angle triangle with the wall. The straight line distance from the bottom of the window to the ground forms the opposite side. The distance from the bottom of the ladder to the house represents the adjacent side. To determine the required length of the wire, c, we would Pythagorean theorem which us expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
c² = 6² + 5² = 36 + 25 = 61
c = √61 = 7.81 ft
what is the volume of the cylinder below?
Answer:
A
Step-by-step explanation:
vol of a cylinder = pie* r^2×h
r= 5
h= 9
......vol= 9×5^2 pie= 225pie units ^3
HELP PLZ It is your turn to wash the dishes. When you are finished, you begin to drain the water from the sink. The water's draining can be defined by the function V = -.75t + 10 where V is the volume of water in gallons and t is the time in minutes. What is the rate of change and would you interpret that?
Answer:
The rate of change is -0.75
Step-by-step explanation:
For each unit of t the volume of water is decreasing by 0.75.
At t=13.333 the volume of water is 0. at t=0 the volume of water is 10
Hope this helps
Which of the following is the equation of a line that passes through the point
(3.2) and is parallel to the yaxis?
Answer:
y=2 is the correct ans.
here, tge equn of st line passing through the point (3,2) and is also parallel to y axis.
we have, equn of st line parallel to y xaus is y= b
so , the equn of st line passing through the point (3,2) is y= 2 (where 2 is likely to b).
Avery wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 3.2% and the other bank is offering a rate of 3% compounded annually. If Avery decides to deposit $7,000 for 5 years, which bank would be the better deal? 1. a simple interest rate of 3.2% 2. a compound interest rate of 3%
Answer: a simple interest rate of 3.2% will be the better deal.
Step-by-step explanation:
Hi, to answer this question we have to apply the compounded interest formula:
A = P (1 + r/n) nt
Where:
A = Future value of investment (principal + interest)
P = Principal Amount
r = Nominal Interest Rate (decimal form, 3/100= 0.03)
n= number of compounding periods in each year (1)
Replacing with the values given
A = 7000 (1+0.03/1)^(1x5)
A = 7000( 1.03)^5 = $8,114.92
For simple interest:
I = p x r x t
Where:
I = interest
Replacing with the values given:
I = 7000 x (3.2/100) x 5 = $1,120
Adding the principal amount: 7000+1120 = $8,120
Since 8,120 (simple) >8,114.92(compound)
a simple interest rate of 3.2% will be the better deal.
Write the expression as a square of a binomial if possible: 19x^2+2/15xy+1/25y^2 Anyone who answers my question I will name brainliest. Thank You
Answer:
Formula: a² + 2ab + b² = (a + b)²
The square root of 1/9x² = 1/3x so a = 1/3x and b = 1/5y.
The answer is (1/3x + 1/5y)².
a line segment may have more than one midpoint true or false
Answer: false
Step-by-step explanation: A line segment may not have more than one midpoint.
(Plz hurry) Given that cosθ=817 and sinθ=−1517 . What is the value of tanθ? 815 −815 158 −158
Answer:
D. -15/8Step-by-step explanation:
Given the following;
cosθ=8/17 and sinθ=−15/17
In trigonometry identity, tanθ = sinθ/cosθ
Substituting the given values in the equation;
tan θ = (−15/17)/(8/17)
tanθ = −15 /17 * 17/8
tanθ = -15/8
Answer:
D. -15/8
Step-by-step Explanation
Which of the following can be represented by the inequality below? 69h + 126 > 540 A. Yvonne is driving more than 540 miles on a trip. She has already driven 126 miles and drives 69 miles each hour. B. Yvonne is driving less than 540 miles on a trip. She has already driven 126 miles and drives 69 miles each hour. C. Yvonne is driving less than 126 miles on a trip. She has already driven 69 miles and drives 540 miles each hour. D. Yvonne is driving more than 540 miles on a trip. She has already driven 69 miles and drives 126 miles each hour.
Answer:
The answer is A.
Step-by-step explanation:
The inequality states that the amount that Yvonne drives is more than 540 miles. Since h represents the number of hours, we know that 69 probably means the number of miles Yvonne can drive per hour. Finally, 126 shows the amount of miles that Yvonne has already driven.
Which situation is best modeled by the inequality g ≤ 13? A. You cannot play a game at age 13. B. You must be at least 13 to play a game. C. You must be no older than 13 to play a game. D. You must be younger than 13 to play a game.
Answer:
C)you must be no older than 13 to play the game.
Step-by-step explanation:
≤this means equal to or less than which in this case is 13
The situation represented by the inequality g ≤ 13 will be option C. You must be no older than 13 to play the game.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the inequality is g ≤ 13.
The inequality can be represented by the situation you must be no older than 13 to play a game.
To know more about inequality follow
https://brainly.com/question/24372553
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Triangle ABC is rotated 45° about point X, resulting in triangle EFD. Triangle A B C is rotated 45 degrees about point X to form triangle E F D. The lengths of sides A C and D E are congruent, the lengths of sides A B and E F are congruent, and the lengths of sides D F and C B are congruent. If EF = 4.2 cm, DF = 3.6 cm, and DE = 4.5 cm, what is CB? 3.3 cm 3.6 cm 4.2 cm 4.5 cm
Answer:
CB = 3.6 cm
Step-by-step explanation:
Here, triangle ABC is rotated about point X which results in triangle EFD. Since triangle ABC is rotated it retains its shape and dimensions. This means that triangle ABC is parallel to triangle EFD ie, ABC≈EFD, also both dimensions will be congruent.
Thus
AB = EF
BC = FD
AC = ED
CB = DF
BA = FE
CA = DE
Since length of side DF = length of side CB, and DF = 3.6 cm. Therefore, CB = DF = 3.6 cm
Length of CB = 3.6 cm
Answer: B it's B
Step-by-step explanation: I got it right
The graphs below have the same shape. What is the equation of the blue
graph?
Answer:
Option (A)
Step-by-step explanation:
Parent function (in red) graph is represented by,
f(x) = x²
If this function is translated by 'a' units to the right, rule to be followed,
f(x) → f(x - a)
If the parent function is shifted by 4 units to the right (blue graph), the new function will be,
g(x) = f(x - 4)
g(x) = (x - 4)²
Therefore, Option (A) will be the correct option.
Can you help me cause I’ve been struggling
Answer:
-8
Step-by-step explanation:
Hope it helps you.
Can you mark my answer as a Brainliest Please
24. A quantity represented by 3x - 4 is
subtracted from the quantity 5x – 7. What is
the result?
A 2x - 3
© 2x – 11
B 2x + 3
D 2x + 11
Answer:
The answer is option A. 2x - 3
The expression 3x - 4 is subtracted from
5x - 7 is written as
5x - 7 - (3x - 4)
= 5x - 7 - 3x + 4
= 2x - 7 + 4
= 2x - 3
Hope this helps
find a18 of the arithmetic sequence 2, -5, -12, -19
Answer:
The 18th term of the sequence is -117.
Step-by-step explanation:
The given sequence is 2,-5,-12,-19
From this AP,
First term, a = 2
Common difference, d = -5-2 = -7
It is required to find the 18th term of the sequence. The nth term of an AP is given by :
[tex]a_n=a+(n-a)d\\\\a_{18}=a+17d\\\\a_{18}=2+17\times (-7)\\\\a_{18}=-117[/tex]
So, the 18th term of the sequence is -117.
Please answer this in two minutes
Answer:
TUV=52
Step-by-step explanation:
2z+65+59+26z=180
28z+124=180
28z=56
z=2
26*2=52
Answer:
TV
Step-by-step explanation:
The sum of the angles of a triangle are 180
z+59 + z+65 + 26z = 180
Combine like terms
28z + 124 = 180
Subtract 124
28z = 180-125
28z =56
Divide by 28
28z/28 = 56/28
z=2
The smallest side is opposite the smallest angle
26*2 = 52
<u is the smallest angle so TV is the smallest side