A tank in the shape of a hemisphere has a radius of 3 feet. If the liquid that fills the tank has a density of 88.2 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answer:
4988 pounds
Step-by-step explanation:
Volume of Hemisphere
4/3 x π x r^3 = 4/3 x 3^3 x π = 4/3 x 27π = 36π = Volume of Sphere
To calculate volume of Hemisphere = 36π / 2 = 18π foot^3
Weight of the liquid
88.2 pounds / foot^3 means that every cubic foot weighs 88.2 pounds so
88.2 pounds x 18π = 4987.5925 which to the nearest pound = 4988 pounds.
Item
Small pizza (plain) $8.99
Large pizza (plain) $13.99
Each topping $0.75
Anna ordered a large pizza
with 2 toppings. What was the total cost of her pizza Show your equation and the total cost
Part B
Anna gave the clerk two 10- dollar bill. She received $4.51 in change. Anna said the clerk was incorrect and should have given her 14.51. Who is correct Explain your answer and include an equation or example using money to support your answer.
Answer:
$15.49
Step-by-step explanation:
0.75 x 2 = 1.5
1.50 + 13.99 = 15.49
The clerk is correct; Anna only gave 20 dollars (10x2). 20 - 15.49 = 4.51, which then would be the correct change.
Q6. The first three terms of an arithmetic series are 60, 4p and 2p-6 respectively (a) Show that p= 9 (b) Find the value of the 20th term of this series. (c) Prove that the sum of the first n terms of this series is given by the expression 12n (6 - n)
Answer:
p=9
t20=516
Step-by-step explanation:
a
4p-60=2p-6-2p
6p=54
p=9
b
a=60.. d=24
t20=a+19d
=60+19×24
=516
c
Sn=12.5+12.3+12.1
=12n(6-n)
What is the surface area of the triangular prism shown?
A triangular prism. The triangle faces have base 14 meters and height 24 meters. The rectangular bottom has dimensions 10 meters by 14 meters. The height of the prism is 25 meters.
558 m2
976 m2
1,680 m2
1,750 m2
Answer: 726 meters²
Step-by-step explanation:
We will need to find the area of five shapes. The base, the top/bottom, and the two triangle sides.
The area of a triangle is B * H / 2. Since we have two congruent triangles, I will not be dividing by two.
14 * 24 = 336 meters²
-> This value is for both of the triangle faces
The rectangular bottom is L * W
14 * 10 = 140 meters²
The two rectangles for the top and bottom will also be L * W. Since these are congruent, I will find the area of one and multiply it by two.
10 * 25 = 250 meters²
Now I will add them all together for the total surface area:
336 + 140 + 250 = 726 meters²
-> I don't see this as an option choice listed. I will review my work, but I am currently confused on the options they provide.
There's a picture with all the info
Answer:
3 un wer
8 lnter
12 jin
Step-by-step explanation:
of the corret anwer
Help PLEASE
(explanation included please.)
Answer:
x = 12.714
Step-by-step explanation:
Vertical angles sum to 180 degrees
8x-12 + 6x + 14 = 180
solve for x = 12.714
!!!!????????!!!!!??????
Answer:
h = 19 mm
Step-by-step explanation:
the volume (V) of the prism is calculated as
V = Ah ( A is the area of the base and h the height )
the base is a regular pentagon whose area (A) is calculated as
A = [tex]\frac{1}{2}[/tex] pa ( p is the perimeter and a the apothem )
p = 5 × 12 = 60 mm and a = 5 mm , then
A = [tex]\frac{1}{2}[/tex] × 60 × 5 = 30 × 5 = 150 mm²
given V = 2850 , then
150h = 2850 ( divide both sides by 150 )
h = 19 mm
EZ QUESTION, FREE BRAINLIEST
The maximum possible area is 36 square units.
Answer:
36sq Units at max? i think
Step-by-step explanation:
Have a good day!
#ViolentJax~
Resuelva los siguientes sistemas de ecuaciones 3x+2y₌75x–2y₌1
1)
[tex]x = 25 - \frac{2}{3} y[/tex]
[tex]y = 37.5 - 1 \frac{1}{2} x[/tex]
2)
[tex]x = 1 + 2y[/tex]
[tex] y = \frac{1}{2} - \frac{1}{2} x[/tex]
Which statement describes the value of the expression 7 times (24,672 - 589)?
168,581
________________________________________________________
SolveFollow PEMDAS
parenthesesexponentsmultiplicationdivisionadditionsubtractionAlways start with the top of the list, parentheses. Prioritize anything in parentheses.
[tex](24,672 - 589)[/tex]
start in hundreds place, then subtract from there.
[tex](24,672 - 589) = 24,083[/tex]
Next, multiply by 7.
[tex]24,083 * 7 = 168,581[/tex]
________________________________________________________
Questions?Ask in the comments box.
Please help! I dont know how to do these :(
Answer:
t = 4 s
Step-by-step explanation:
Given function:
[tex]h(t)=-16t^2+48t+64[/tex]
where:
h = height of the ball (in feet)t = time (in seconds)When the ball hits the ground, its height will be 0 ft.
Therefore, set the function to zero and solve for t:
[tex]\begin{aligned}h(t) &=0\\ \implies -16t^2+48t+64 & =0\\ -16(t^2-3t-4)& =0\\ t^2-3t-4 &=0\\ t^2+t-4t-4&=0\\ t(t+1)-4(t+1)&=0\\(t-4)(t+1)&=0\\ \implies t&=4, -1\end{aligned}[/tex]
As time is positive, t = 4 s (only).
Given
[tex]h = - 16 {t}^{2} + 48t + 64[/tex]
Where:- h= Height of ball (given in feet[ft]) and,
t= time (in seconds [s])
To find:-Time = (t)
SolutionWe know,
[tex] \text{When the ball hits the ground its height will be 0}[/tex]
[tex] \therefore h(t) = 0[/tex]
[tex] \implies - 16 t^{2} + 48t + 64 = 0 \\ \\ \fbox{taking - 16 as common multiple} \\ \\ \implies - 16(t {}^{2} - 3t - 4) = 0 \\ \\ \implies t {}^{2} - 3t - 4 = 0 \\ \\ \fbox {factorising the \: equation} \\ \\ \implies t {}^{2} - t - 4t - 4 = 0 \\ \\ \implies t(t + 1) - 4(t + 1) = 0 \\ \\ \implies(t - 4)(t + 1) = 0[/tex]
[tex] \tt{Either} \\ t - 4 = 0 \\ t = \red{ 4 } \\ \\ \tt{Or} \\ t + 1 = 0 \\ t = \red{ - 1}[/tex]
We know, Time cannot be negative.
So, Time (t) = 4 seconds
What is the surface area of the figure below
Answer: Its 120 cm
Step-by-step-explenation:
All you have to do is multiply
3x2=6
6x5=30
30x4=120
What does AC=?
Round your answer to the nearest hundredth.
Please help
Answer: About 3.06
Step-by-step explanation:
We can use trigonometry functions to solve for AC. Let the ?, representing AC, be "x" in our mathematical work.
Since we have the hypotenuse and x is adjacent to the angle given, I am going to use cosine.
cos(θ) = [tex]\frac{adjacent}{hypotenuse }[/tex]
cos(40) = [tex]\frac{x}{4}[/tex]
0.766 ≈ [tex]\frac{x}{4}[/tex]
3.06 ≈ x
x ≈ 3.06
Prove algebraically that the difference between the squares of any two consecutive
odd numbers is always a multiple of 8
Answer:
See below ↓
Step-by-step explanation:
Let the odd integers be :
2x + 12x + 3Solving
(2x + 3)² - (2x + 1)²4x² + 12x + 9 - 4x² - 4x - 18x + 8 = 8(x + 1)On substituting any value for 'x', the value will be a multiple of x.Examples
8(1) + 8 = 16 = 8 x 28(2) + 8 = 24 = 8 x 38(3) + 8 = 32 = 8 x 4Answer:
Let one odd number be (2n + 1)
Therefore, its consecutive odd number is (2n + 3)
Difference between the two squares of these numbers:
[tex]\begin{aligned}\sf (2n+3)^2-(2n+1)^2 & = \sf (4n^2+12n+9)-(4n^2+4n+1)\\ & = \sf4n^2+12n+9-4n^2-4n-1\\ & = \sf 8n+8\\ & = \sf8(n+1)\end{aligned}[/tex]
Thus proving that the difference between the squares of any two consecutive odd numbers is always a multiple of 8.
200
g of fertiliser is required for a plot of land
that has an area of 8 m?. Find
(i) the amount of fertiliser needed for a plot of
land that has an area of 14 m²,
(ii) the area of land that can be fertilised by
450 g of fertiliser
Answer:
(i) 350 g; (ii) 18 m². This is done by using proportion
Step-by-step explanation:
Find all values of k for which the equation 3x^2−4x+k=0 has no solutions.
Answer:
k>1 1/3
Step-by-step explanation:
i have rsm too bro
The given equation has no solution when K is any real number and k>12
We have given that
3x^2−4x+k=0
△=b^2−4ac=k^2−4(3)(12)=k^2−144.
What is the condition for a solution?If Δ=0, it has 1 real solution,
Δ<0 it has no real solution,
Δ>0 it has 2 real solutions.
We get,
Δ=k^2−144 here Δ is not zero.
It is either >0 or <0
Δ<0 it has no real solution,
Therefore the given equation has no solution when K is any real number.
To learn more about the solution visit:
https://brainly.com/question/1397278
Noah and his sister are making gift bags for a birthday party. Noah puts 3 pencil erasers in each bag. His sister puts x stickers in each bag. After filling 4 bags, they have used a total of 44 items.:Draw a diagram for the story and find the unknown amount.
Answer:
x=8
Step-by-step explanation:
Answer:
44 items in 4 bags means there are 11 items in each bag (44/4).
each bag has 3 erasers + x stickers. So, 3 + x = 11
subtract three from each side of the equation to isolate the variable (x):
3+x-3=11-3
x=8
I need help I really don't get this ?
Answer:
466,207,795.2 cm^3
Step-by-step explanation:
The equation to find both, the volume of the sphere and cube, are given.
The sphere:
V = [tex]\frac{4}{3}[/tex]πr^3
the radius is 7 ft therefore
V = [tex]\frac{4}{3}[/tex]π7^3
The problem says to use 3 for pie therefore
V = [tex]\frac{4}{3}[/tex](3)7^3
7 to the power of three is
V = [tex]\frac{4}{3}[/tex](3)343
[tex]\frac{4}{3}[/tex] and 3 cancel each other out to equal 4
V = 4 × 343
V = 1,372 ------> volume of sphere
______________________________________________
The cube:
V = Legth × width × height
V = 12 × 12 × 12
V = 1,728 ------> volume of cube
_______________________________________________
Total volume:
1,372 + 1,728 = 3,100 ft^3
But the question asks for the mesurement in centimeters so convert feet to centimeters using a calculator :)
3,100 ft^3 = 87,782,080 cm^3
please help i am not smart
Answer:
Step-by-step explanation:
Number of shells she had in the begining = 40
Number of shells collected in the morning and at noon = 6 + 3 = 9
Now the number of shell at the end = 40 + 9 = 49
Icreased shells = 49 - 40 = 90
[tex]\text{Percentage increase = $\dfrac{49- 40}{40}*100$}[/tex]
[tex]=\dfrac{9}{40}*100\\\\\\= 22.5 \ \%[/tex]
and right triangle sin (40 - x)° equals cos(3x)° degrees what is the value of x.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: \sin(40 - x) = \cos(3x) [/tex]
[tex]\qquad \sf \dashrightarrow \: \cos\{90 - (40 - x ) \} = \cos(3x) [/tex]
[tex]\qquad \sf \dashrightarrow \:90 - (40 - x) = 3x[/tex]
[tex]\qquad \sf \dashrightarrow \:90 - 40 + x = 3x[/tex]
[tex]\qquad \sf \dashrightarrow \:3x - x = 50[/tex]
[tex]\qquad \sf \dashrightarrow \:2x = 50[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 25 \degree[/tex]
Factor.
x^2 4x +4
(x + 2)^2
(x+4)^2
(2 – 2)^2
(2 – 4)^2
Answer: The answer is [tex](x+2)^2[/tex]
Step-by-step explanation:
Because [tex](x+2)^2[/tex] means [tex](x+2)(x+2)[/tex]
So we use the foil method to factor
First: [tex]x*x=x^2[/tex]
Outside: [tex]x*2=2x[/tex]
Inside: [tex]2*x=2x[/tex]
Last: [tex]2*2=4[/tex]
So we now write the following equation [tex]x^2+2x+2x+4[/tex]
Simplfied [tex]x^2+4x+4[/tex]
If f(x) = x-3/x and g(x) = 5x-4, what is the domain of (f•g)(x)?
Answer: x cannot equal 4/5 (3rd choice)
Step-by-step explanation:
f(g(x)) = f(5x-4)
plug 5x-4 into all values of x in the f(x) equation
f(5x-4)= ((5x-4) - 3))/ (5x-4)
f(5x-4) = (5x-7)/(5x-4)
set denom = 0 and solve for x to find domain
5x-4 = 0
5x = 4
x = (4/5)
x cannot equal (4/5)
How do you quarter pi
Answer:
I think its this answer I believe 0.7853982 if this is correct can u mark me brainliest
Suppose a triangle has two sides of length 42 and 35, and that the angle
between these two sides is 120°. Which equation should you solve to find the
length of the third side of the triangle?
A. c²=422+352-2(42)(35)sin120°
sin 35
B.
sin42
120
=
b
OC.
2²=42²+35²-2(42)(35)cos120°
D. c=42+352(42)(35)cos120°
Answer:
The correct option is C because it shows the accurate cosine rule
Equation to get the third side : [tex]c = \sqrt{(42^2 +35^2 -2\times 42\times35\times cos(120\degrees ))}[/tex]
The correct option is C.
Given, that sides of triangle are 42 cm and 35 cm .
The third side can be found using the Law of Cosines,
[tex]c^2 = a^2 +b^2 - 2ab\times cos(C)[/tex]
where C is the angle opposite the third side (c) .
For the given side lengths, then the third side can be found .
Here,
a = 42
b = 35
∠C = 120°
Substitute the values,
[tex]c = \sqrt{(42^2 +35^2 -2\times 42\times35\times cos(120\degrees ))}[/tex]
[tex]c = \sqrt{1764 + 1225 + 1470} \\c = \sqrt{4456}\\c = 66.75[/tex]
Hence the third side is of 66.75 units.
The correct option is C .
Know more about cosine law,
https://brainly.com/question/30766161
#SPJ5
A full-length mirror cost $144.99 when the cpi was 163. what will a full-length mirror cost when the cpi is 211, to the nearest cent? a. $305.93 b. $214.59 c. $187.68 d. $88.95
The cost of a full-length mirror when the cpi is 211 is $187.68. Then the correct option is C.
What are ratio and proportion?A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.
A full-length mirror cost $144.99 when the cpi was 163.
The cost of a full-length mirror when the cpi is 211, to the nearest cent will be
[tex]\dfrac{x }{211} = \dfrac{144.99}{163}\\\\x \ \ \ = \$187.68[/tex]
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
8x + 8 + -3
I need help finding this question
Answer:
8x+5
Step-by-step explanation:
8x + 8 + (-3) = 8x+8 - 3 = 8x + 5.
Hope this helps!
Also, please mark as brainliest!
Answer:
The answer is 8x+5
Step-by-step explanation:
1. Combine like terms so it will be 8 and -3
2. this will leave you with 8x+5 which you cannot do anything further.
Which measure of spread is least affected by the long tail in the
graph?
Vehicle A
>
0
1
2
2
3
5
6
0)
7
CO
9
4
Repairs per Vehicle
MAD
IQR
Range
Answer:
IQR
Step-by-step explanation:
I got it right :)
Isaiah earned a score of 61 on Exam A that had a mean of 78 and a standard deviation
of 10. He is about to take Exam B that has a mean of 200 and a standard deviation of
50. How well must Isaiah score on Exam B in order to do equivalently well as he did
on Exam A? Assume that scores on each exam are normally distributed.
Answer:
isaiah must get a score of 115
Yo I need to bring up my math grade bad so
4x-5y>20
(please show it graphed already :D
Here is how it is graphed:
A. Find the perimeter of each figure
(Math) [please answer this correctly] thank you