(a) Volume of any Pyramid = [tex]\frac{1}{3} * (Base-Area)*height = \frac{1}{3} *220.22*9 = 660.66[/tex] cubic units
(b) Sarah doesn't have to go through all the hard work as the smaller pyramid has a ratio of 2:3 to the bigger pyramid, so we get the equation, to help us solve it.
[tex]660.66 = \frac{2}{3} *(Area-of-larger-pyramid)[/tex]
Hope that helps!
Step-by-step explanation:
(a) To calculate the volume of a pyramid, you can use the formula: V = (1/3) * B * h, where V is the volume, B is the area of the base, and h is the height of the pyramid.
In this case, Sarah has the area of the base (B) as 220.22 square units and the height (h) as 9 units. Let's substitute these values into the formula:
V = (1/3) * 220.22 * 9
V ≈ 660.66 square units
Therefore, the volume of the smaller pyramid is approximately 660.66 cubic units.
(b) No, Sarah doesn't need to go through the hard work again to find the volume of the larger pyramid. Since the two pyramids are similar, the ratio of their volumes will be equal to the cube of the ratio of their corresponding sides.
The scale factor of the smaller pyramid compared to the larger pyramid is 2:3. Since the scale factor is determined by the corresponding sides, it applies to both the base length and the height of the pyramid. Therefore, the volume of the smaller pyramid compared to the larger pyramid is (2/3)^3 = 8/27.
In other words, the volume of the smaller pyramid is 8/27 times the volume of the larger pyramid. So if Sarah already knows the volume of the smaller pyramid, she can simply multiply it by 27/8 to find the volume of the larger pyramid.
(c) To calculate the volume of the larger pyramid, we can use the ratio mentioned above:
Volume of the larger pyramid = (Volume of the smaller pyramid) * (27/8)
Volume of the larger pyramid ≈ 660.66 * (27/8)
Volume of the larger pyramid ≈ 2239.99 square units
Therefore, the volume of the larger pyramid for Sarah is approximately 2239.99 cubic units.
Please mark as y
By look at the graph, which interval is negative
Answer:
The answer is A because the line is in -2 negative and positive 5
the midpoint of the segment as an ordered pair (5,8) (1,2)
Answer:
Midpoint :(3,5)Step-by-step explanation:
Mid point :
[tex] \frac{x_1 + x_2}{2} \: \frac{y_1 +y _2}{2} [/tex]
x1 = 5
y1 = 8
x2 = 1
y2 = 2
Midpoint :
[tex]( \frac{5 + 1}{2} \: \frac{8 + 2}{2} ) \\ ( \frac{6}{2} \: \frac{10}{2} )[/tex]
Simplify
[tex](3 \: 5)[/tex]
Blake collects coins. He collected a total of 225 coins. If 68% of the coins he collected were foreign, how many other coins did he collect?
Answer: 72
Step-by-step explanation:
convert 68% to decimal:
0.68
Multiply by 225
0.68*225
= 153
Subtract:
225-153=
72
What is the simplified expression for the expression below? One-half (8 x 4) one-third (9 minus 3 x) 5x 5 7x 1 x 7 3x 5.
Answer:
3x+5
Step-by-step explanation:
That is your answer
find the circumference of a circle with a radius of 12ft
Answer
74.40
Step-by-step explanation:
circumference= 2πr
so, 12×2×pi= 24π
24π= 75.39822369
=75.40
What is 2x+y<20 in slope intercept form?
Answer:
[tex]y < -2x+20[/tex]
Step-by-step explanation:
[tex]2x+y < 20[/tex]
[tex]\mathrm{Subtract\:}y\mathrm{\:from\:both\:sides}[/tex]
[tex]2x+y-y < 20-y[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]2x < 20-y[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}2[/tex]
[tex]\frac{2x}{2} < \frac{20}{2}-\frac{y}{2}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x < \frac{20-y}{2}[/tex]
[tex]Also[/tex] [tex]written[/tex] [tex]as[/tex] [tex]y < -2x+20[/tex]
Answer:
y= mx + b
y< -2x +20
Step-by-step explanation:
2x+y<20
Subtract 2x
from both sides of the inequality. y<20
−2x
Rearrange terms. y<−2x+20
Multiply the polynomials.
(2x2 + 6x + 6)(3x-2)
You're answer would be 6x3 + 14x2 + 6x - 12
What is the correct answer NEED IT ASAP PLEASE
It is the last choice
Amount she makes at McDonald's: 9xAmount she makes at babysitting: 12xWants to save at least $1000[tex]9x+12y\geq 1000[/tex]
Hope that helps!
The 10 little piggies $600 per month on groceries. This is 15% of their
monthly budget. What is their monthly budget? *
Answer the questions below. Be sure to mark all answers that apply.
Answer:
Part A: Only 460 is divisible by 2
Part B: 385, and 460 are divisible by 5
Part C: Only 460 works for this one
obtain the area and perimeter of the shaded region
Answer:
area = 132 m²
perimeter = 62 m
Step-by-step explanation:
The easiest way to calculate the area of the shape is to work out the area of the entire rectangle, then subtract the area of the 2 small (white) square:
Area of a rectangle = width x length
⇒ area = 10 x 15 = 150 m²
Area of one square = 3 x 3 = 9
Total area = 150 - 9 - 9 = 132 m²
Perimeter = (2 x 10) + 15 + (9 x 3) = 62 m
Kiran's mother gets a restaurant bill for $25. She has a coupon for 15% off. After the discount is applied, she adds 20%
as a tip
What is the total after the discount and tip?
Answer:
the answer is 25.50
Step-by-step explanation:
so you multiply 25×.15 which gives 3.75.
you subtrct that from 25. 25-3.75=21.25.
then multiply 21.25 by .20. 21.25×.20=4.25
add that to 21.25 and you get 25.50
Answer:
25.50
Hope it helps
Solve five and three sixths minus two and one third.
Two and three eighteenths
two and two ninths
three and two ninths
three and three eighteenths
Answer:
I believe the answer is D.) three and three eighteenths
Explanation:
5 3/6 = 33/6
2 1/3 = 7/3 = 14/6
33/6 - 14/6 = 19/6 = 3 1/6 or 3 3/18
I hope I helped! ^-^
What are three ways in which stereotypical views of gender could negatively affect progressive growth of society
Tell whether the table of values represents a linear function, an exponential function, or a quadratic funtion
Answer:
Step-by-step explanation:
if it is linear then it will be a straight line(gradient is the same)
if quadratic then curve(gradeint isnt the same)
y=mx+c
m=[y(2)-y(1)]/[x(2)-x(1)]
you can choose any 2 points from the table
m=2-0.4/0-1
m=-1.6
repeat but 2 different coordinates
m=0.4-0.08/-1--2==>-2.24
m=-2.24
different coordinate therefore quadratic
cant be exponential, because nothing is being raised to some power
Crazy Coffee wants to change how they sell their take home coffee. Currently it is
sold in cylindrical canisters. They want to change to rectangular prisms to better fit
on their shelves. The current cylindrical canister has a radius of 4 inches and a height
of 8 inches. The new rectangular prisms have to have a length of 4 inches and a
width of 3 inches to fit on the shelves. What does the height need to be of the
rectangular prism box to have the same volume as the original canister?
33.5 inches
2025 inches
09.17
33.5
Step-by-step explanation:
Please help me with this with steps
Answer:
(x - y) = 9
Step-by-step explanation:
**Note: we cannot use similar triangle proportionality, as ΔABC is NOT a right triangle**
Using Pythagoras' Theorem a² + b² = c²
(where a and b are the legs and c is the hypotenuse of a right triangle)
Create equations for both smaller interior right triangles using Pythagoras' Theorem:
Larger right triangle
CD² + x² = 17²
⇒ CD² = 17² - x²
Smaller right triangle
CD² + y² = 10²
⇒ CD² = 10² - y²
Equate equations:
CD² = CD²
⇒ 17² - x² = 10² - y²
Given:
AB = 21 and AB = x + y
⇒ x + y = 21
⇒ y = 21 - x
Substitute y = 21 - x into 17² - x² = 10² - y² and solve for x:
⇒ 17² - x² = 10² - (21 - x)²
⇒ 17² - x² = 10² - (441 - 42x + x²)
⇒ 17² - x² = 10² - 441 + 42x - x²
⇒ 289 = 100 - 441 + 42x
⇒ 630 = 42x
⇒ x = 630 ÷ 42
⇒ x = 15
Substitute found value for x into y = 21 - x and solve for y:
⇒ y = 21 - 15 = 6
Finally, substitute found values for x and y into (x - y):
⇒ x - y = 15 - 6 = 9
Convert polar equation to the standard form of each rectangular equation: r=2cosθ-3sinθ
[tex]\\ \rm\Rrightarrow r=2cos\theta-3sin\theta[/tex]
a(rcosTheta) +b(r sintheta)=ax+by[tex]\\ \rm\Rrightarrow \dfrac{2}{r}cos\theta-\dfrac{3}{r} sin\theta=1[/tex]
[tex]\\ \rm\Rrightarrow 2x-3y=1[/tex]
[tex]\\ \rm\Rrightarrow 2x-3y-1=0[/tex]
Answer:
[tex](x-1)^2+(y+1.5y)^2=3.25[/tex]
Step-by-step explanation:
[tex]x=r \cos(\theta)[/tex]
[tex]y=r \sin(\theta)[/tex]
Given polar equation:
[tex]r=2\cos(\theta)-3 \sin(\theta)[/tex]
Multiply both sides by r:
[tex]r^2=2r\cos(\theta)-3r \sin(\theta)[/tex]
Know that [tex]x^2+y^2=r^2[/tex]:
[tex]x^2+y^2=2r\cos(\theta)-3r \sin(\theta)[/tex]
Substitute [tex]x=r \cos(\theta)[/tex] and [tex]y=r \sin(\theta)[/tex] :
[tex]x^2+y^2=2x-3y[/tex]
Therefore,
[tex]x^2-2x+y^2+3y=0[/tex]
Complete the square:
[tex](x-1)^2-1+(y+1.5y)^2-2.25=0[/tex]
[tex](x-1)^2+(y+1.5y)^2=3.25[/tex]
Choose the equation that correctly shows the Commutative Property of Multiplication.
6 x 7/8 = 7/8 ÷ 6
6 x 7/8 = 6 x 7/8
6 + 7/8 = 7/8 x 6
6 x 7/8 = 7/8 x 6
The equation which correctly shows the Commutative Property of Multiplication is 6 x 7/8 = 7/8 x 6
What is cummutative property?This is the property which holds when a set of operations are changed but still remain the same value.
Check all that applies:
6 x 7/8 = 7/8 ÷ 6
7/8 ÷ 6
= 8/7 × 6
No
6 x 7/8 = 6 x 7/8
Yes
6 + 7/8 = 7/8 x 6
No
6 x 7/8 = 7/8 x 6
Yes
Therefore, 6 x 7/8 = 7/8 x 6 is the answer because the values were interchanged but still remain the same.
Learn more about cummutative property:
https://brainly.com/question/2542910
HELP ME PLS!!!!!!!!!!!
Answer: READ MY EXPLANATION.
Yes, both of them have 90 degrees And sided triangles.
Step-by-step explanation: Hi m4rra! I'm sorry to say but your account has been reported quite a few times and you may want to start a new account, it has been reported by the following people: maylie186, ionfieldbest, gtchappymuch, and many more. I'm going to repeat what I mean but in less formal words. your account has been reported quite a bit, we are going to need you to delete this account. you may make a new one if you wish. . . sincerely, . The Brainly Team
A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow rainwater to drain. A cross-section of the road can be represented on a graph using the function f(x) = (x – 16)(x 16), where x represents the distance from the center of the road, in feet. Rounded to the nearest tenth, what is the maximum height of the road, in feet? 0. 1 0. 8 1. 3 1. 6.
The maximum height of the road which is made in such a way that the center of the road is higher off the ground than the sides of the road is 16 feet.
What is the maxima of parabola?The maxima of a parabola is where, it opens down its vertex at the maximum point in a coordinate graph. By equating the derivative of equation of parabola equal to zero, it can be found out.
A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow rainwater to drain.
A cross-section of the road can be represented on a graph using the function,
[tex]f(x) = (x - 16)(x+ 16),[/tex]
Here, x represents the distance from the center of the road, in feet.
This equation can be written as,
[tex]f(x) = (x - 16)^2[/tex]
Now to find the maximum height, find the derivative of the above function as,
[tex]f(x) = (x - 16)^2\\f'(x) = (x - 16)^2\\f'(x)=2(x-16)(1)\\f'(x)=2(x-16)[/tex]
Equate the above equation to zero as,
[tex]0=2(x-16)\\0=x-16\\x=16[/tex]
Thus, the maximum height of the road which is made in such a way that the center of the road is higher off the ground than the sides of the road is 16 feet.
Learn more about the maxima of parabola here;
https://brainly.com/question/5399857
Y=-x^2 +78x-512 I need help with this problem
Answer:
Step-by-step explanation:
subtract-5 from the additive inverse of 4
Answer:
-9
Step-by-step explanation:
The additive inverse of 4 is -4. Why? 4 + -4 = 0
-4 - 5 = -9
Answer:
i think -9
Step-by-step explanation:
How can you use formulas you already know to find the area and perimeter of a composite figure? The six lane track shown in the made up of a rectangle. Terminology and helpful formulas: A straightway is the non curved section of the track. In this specific track each straightaway is 85.0 meters long. Area of rectangle: A=l w. Area of circle A=r2 Circumference C=2r. In the straightaways, each lane is rectangle. What is the area and perimeter of each lane in the straightaways?
The area of the composite figure = 10,874.1 sq. m.
The perimeter of the composite figure = 406.9 m
What is the Area and Perimeter of a Rectangle and Circle?Perimeter of a rectangle = 2(length + width)
Area of a rectangle = length × width
Perimeter of a circle = 2πr
Area of a circle = πr²
What is Area of the composite figure?The figure is made up of two semicircles (1 full circle) and a rectangle.
Area of the composite figure = area of circle + area of rectangle
= πr² + length × width
r = 36.5 + 1.2 = 37.7 m
length = 85.0 m
width = 2(36.5) + 2(1.2) = 75.4 m
Substitute
Area of the composite figure = π(37.7)² + 85.0 × 75.4 = 10,874.1 sq. m.
What is Perimeter of the Composite Figure?Perimeter of the composite figure = perimeter of circle + 2(length of the rectangle)
= 2πr + 2(L)
Plug in the values
= 2π(37.7) + 2(85.0)
Perimeter of the composite figure = 406.9 m
Learn more about composite figures on:
https://brainly.com/question/391747
Find the area and perimeter of the compound figure below. (6 points)
Answer:
area: 27.8 square unitsperimeter: 21.2 unitsStep-by-step explanation:
The area of a compound figure is the sum of the areas of its parts. The perimeter is the sum of the lengths of all of the edges.
AreaThis compound figure is conveniently divided into a semicircle of radius 2.5 and a trapezoid with bases 5 and 7, and height 3.
Semicircle
The area of the semicircle is half the area of a circle with the same radius. It will be ...
A = 1/2πr²
A = 1/2π(2.5²) = 3.125π . . . . square units
Trapezoid
The area of the trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
A = (1/2)(5 +7)(3) = 18 . . . . square units
Then the total area of the figure is ...
3.125π +18 ≈ 27.8 . . . . square units
__
Perimeter
The perimeter will be the sum of the lengths of the straight line segments and the length of the semicircular arc.
Arc
The arc length is half the circumference of the circle, so is ...
arc = 1/2(2πr) = πr = 2.5π . . . . units
Diagonal segments
The figure is bounded by two congruent line segments that are each the hypotenuse of a triangle 1 unit wide and 3 units high. The Pythagorean theorem tells us that length is ...
diagonal length = √(1² +3²) = √10 . . . . units
The two diagonal sides have a total length of 2√10 units.
Horizontal segments
The figure is bounded by two congruent horizontal segments of length 1 unit each, and one horizontal segment of length 5 units. Their total length is ...
horizontal length = 1 + 1 + 5 = 7 . . . . units
The total perimeter is ...
perimeter = horizontal length + diagonal length + arc length
7 +2√10 +2.5π ≈ 21.2 . . . . units
The radius of a sphere is 7 cm. What is the sphere's volume? Round to the nearest tenth, and use 3.14
Answer:
1436.8 cm3
Step-by-step explanation:
4/3 π r^3 ; r = 7 (substitute)
4/3 π (7)^3 (cube)
4/3 π 21 (reorder)
4/3 (21) π (muptiply)
28 π (multiply)
87.96..... (round)
88cm^3
What is the value of z?
Sum of interior angles of a triangle is 180 degrees
Add the angles up
2z-1+z+14+95 = 180
3z+108 = 180
3z = 72
z = 24
Z = 24
Use a calculator to find the measure of ∠B to the nearest tenth.
9. 11. 13.
are the ones i need done!
Answer:
Step-by-step explanation:
9 is 16.12
11 is 38.36
13 is 9
What is the percent change from 147 to 298? Round your answer to the nearest tenth.
Answer:
(147 - 298)/298 x 100
-151/298 × 100
Change ≈ -50.6711%
Step-by-step explanation:
Answer:
102.7
Step-by-step explanation:
your starting number is 147,
your earned number is 298,
to get the percentage, it will be in decimal form
the answer is-
102.72108843537416 %
Now you round to the nearest tenth-
102.7
I hope this helps you-
Step 1: Calculate the change (subtract old value from the new value) ...
Step 2: Divide that change by the old value (you will get a decimal number)
Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)
can you help me, please ……..
Answer: The correct answer is 44.60
Step-by-step explanation:
Let's find the area of the rectangle first, and then add it with the area of the Circle to find the total area of the whole shape.
We know that the area of a Rectangle is L(Length) x W(Width)
So using the given information, 8 x 4 = 32
So the Area of the Rectangle = 32
Now let's find the area of the given circle,
Area of a Circle: πr2 Remember ^ = stands for power
The radius is half of the diameter
The diameter of the circle is 4
4/2 = 2 which is our radius, and now let's replace it in the equation.
= 3.14(r)^2
= 3.14(2)^2
= 3.14(4)
= 12.56 or some may have got 12.57
So now we add all areas together to get the total area,
32+12.57 = 44.57
Now rounding off to the nearest tenths, would give us 44.60
So the area of the figure rounded to the nearest tenth is 44.60
Answer:
[tex]44.56[/tex]
Step-by-step explanation:
Rectangle area:
[tex]4 \times 8 = 32[/tex]
2 circles area (full circle, since they are both a half of circle):
[tex] { (\frac{4}{2}) }^{2} \times π = 12.56[/tex]
Total area:
[tex]32 + 12.56 = 44.56[/tex]
