Answer:
Minimum 7 buckets of water is needed to completely fill spherical storage tank.
Step-by-step explanation:
We are given the following in the question:
Cylindrical bucket:
Radius, r = 6 inches
Height = 18 inches
Volume of bucket = Volume of cylinder
[tex]V = \pir^2 h \\V = 3.14\times (6)^2\times 18\\V =2034.72\text{ cubic inches}[/tex]
Spherical storage tank:
Radius, r = 15 inches
Volume of tank = Volume of sphere =
[tex]V =\dfrac{4}{3}\pi r^3\\\\\V = \dfrac{4}{3}\times 3.14\times (15)^3\\\\V = 14130\text{ cubic inches}[/tex]
Number of baskets required =
[tex]n = \dfrac{\text{Volume of tank}}{\text{Volume of bucket}}\\\\n =\dfrac{14130}{2034.72} = 6.94 \approx 7[/tex]
Thus, minimum 7 buckets of water is needed to completely fill spherical storage tank.
The area of a rectangular fountain is x2 + 9x + 20 square feet. A 3-foot walkway is built around the fountain. Find the dimensions of the outside border of the walkway. The dimensions of the outside border of the walkway are
Answer:
(x+11) by (x+10)
Step-by-step explanation:
We know that Area = Length x width
Given: Area = x²+9x+20
Lets sort this out first
Area = x²+5x + 4x + 20
Area = x(x+5) + 4(x+5)
Area = (x+5) (x+4)
Therefore, it is concluded that:
Length 'l' = (x+5) feet
Width 'w' = (x+4) feet
if a 3-foot walkway is built around the fountain, we'll add 3 feet on both sides
Therefore,
Outer Length = (x+5+3+3) = (x+11) feet
Outer Width = (x+4+3+3) = (x+10) feet
Answer:
The fountain is (x+5) by (x+4).
dimensions of the outside border of the walkway are (x+11) by (x+10)
The volume of a cylinder is 180 cubic meters. The height of the cylinder is 11.25 meters. What is the radius of the cylinder?
Answer:
2.26 meters
Step-by-step explanation:
so the volume for a cylinder is
v= π r² x h
now just substitute in the numbers you know:
180= π r² x 11.25
now rearrange the formula:
180= r² x 11.25π
(rearranging allows you to do this next bit with ease)
now divide by 11.25π on both sides to get
[tex]\frac{180}{11.25\pi }[/tex]= r²
to maintain accuracy, don't divide yet
now you know what r² is but you want r, so square root it:
[tex]\sqrt{\frac{180}{11.25\pi } }[/tex]=r
type that into a calculator and i think the answer is ...
2.25675833419
write the long answer in case you make a mistake when rounding
round appropriately : 2.26 meters ( I've done it to 2 decimal places)
and hopefully that's the correct answer.
Evaluate the piecewise function for ƒ(4).
A) −7
B) 9
C) 16
D) 24
f(4)= 16.
The answer is **C) 16**.
Here's how to evaluate the piecewise function f(4):
1. **Identify the appropriate rule:**
- Since 4 is greater than 2 (4 > 2), we'll use the second rule of the function: f(x) = 5x - 4.
2. **Substitute x = 4:**
- f(4) = 5(4) - 4
3. **Simplify:**
- f(4) = 20 - 4 = 16
Therefore, f(4) = 16.
The other options are incorrect because they either use the wrong rule (A and D) or miscalculate the result (B).
Will mark brainlist
Given. QR I PT and
Prove: APQR – ATSR
Angles
Segments
Triangles Statements Reasons
ZQPR
ZQRP
The mathematics question involves proving two triangles congruent in geometry, likely using congruence criteria such as SSS, SAS, or ASA, with the given information that line QR is parallel to PT.
Explanation:The subject of this question is Mathematics, specifically it involves geometry and the proof of congruent triangles. The statement 'QR I PT' suggests that line QR is parallel to line PT. To prove triangles APQR and ATSR are congruent, one would need to demonstrate that they satisfy the criteria for congruence such as side-side-side (SSS), side-angle-side (SAS), or angle-side-angle (ASA). The angles mentioned, such as ∠QPR and ∠QRP, are likely parts of the required congruence criteria. However, additional information and a specific criteria of congruence need to be applied in a step-by-step explanation.
Solve the system of equations by substitution.
x+y=18
y=8x
Answer:
x=2, y=16
Step-by-step explanation:
x+y=18
y=8x
x+8x=18
x=2
y=16
Answer:
2
Step-by-step explanation:
x + y = 18
y = 8x
x + 8x = 18
9x = 18
x = 18÷9
x = 2
Find the common difference Ce:-34,-29,-24,-19,...
Answer:
d = 5
Step-by-step explanation:
The common difference d is the difference between consecutive terms in the sequence
- 29 - (- 34) = - 29 + 34 = 5
- 24 - (- 29) = - 24 + 29 = 5
- 19 - (- 24) = - 19 + 24 = 4
Thus the common difference is d = 5
The common difference between consecutive terms in the given sequence is 5.
Explanation:The given sequence is {-34, -29, -24, -19, ...}
To find the common difference, we need to look for a pattern between consecutive terms. So, let's observe the differences between consecutive terms:
-29 - (-34) = 5
-24 - (-29) = 5
-19 - (-24) = 5
As we can see, the common difference between consecutive terms is 5.
Solve for p
p/8=7/9
P=?
Answer:
56/9
Step-by-step explanation:
mathhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
21
Step-by-step explanation:
2³ = 8
8/2
= 4
3.4(5)
= 17
4 + 17
= 21
Answer:
Your answer is going to be: 21.
Step-by-step explanation:
In this problem, we're going to be using PEMDAS.
[tex]\frac{1}{2} x^{3} +3.4y[/tex]
Now, we have to fill the blanks:
[tex]\frac{1}{2} 2^{3} +3.45[/tex] [tex](5)\\[/tex]
There's no parenthesis (3.45(5) is just another way of multiplying so that doesn't count). So, we move to the exponent part.
[tex]\frac{1}{2} 8+3.4(5)[/tex]
Everything else is just multiplication.
[tex]\frac{8}{2} + 17[/tex] = 4+ 17
Add it all together and your answer is going to be:
21.
P.S. Good luck with the rest of your assignment!!
Four lines are drawn on a coordinate plane to form trapezoid WXYZ.
Which statements are true about the lines? Select three options.
Line WZ has the same slope as line XY.
Line YX has a greater slope than line ZY.
Line XW has a lesser slope than line YZ.
Line ZW has the same y-intercept as line YZ.
Line XY has a lesser y-intercept than line XW.
Answers: Line WZ has the same slope as line XY. Line XW has a lesser slope than line YZ. Line ZW has the same y-intercept as line WZ.
Oil prices are projected to increase by 100% by next june. A quart of oil currently costs $2.45. What is the projected cost of a gallon of oil next june?
Answer:
The projected cost of a gallon of oil by next june is $19.60.
Step-by-step explanation:
Given:
Oil prices are projected to increase by 100% by next june.
A quart of oil currently costs $2.45.
Now, to find the cost of a gallon of oil next june.
So, to get the projected cost of a quart of oil by next june:
Cost of one quart of oil currently = $2.45.
Rate of oil prices projected to increase by = 100%.
[tex]100\%\ of\ \$2.45+\$2.45\\\\=\frac{100}{100}\times 2.45+2.45\\\\=2.45+2.45\\\\=\$4.90.[/tex]
Now, to get the projected cost of a gallon of oil by next june we use conversion factor:
4 quart = 1 gallon.
If, 1 quart oil price = $4.90.
Then, 4 quarts oil price = [tex]\$4.90\times 4[/tex] = [tex]\$19.60.[/tex]
Thus, 1 gallon oil price = $19.60.
Therefore, the projected cost of a gallon of oil by next june is $19.60.
Answer:
19.60
Step-by-step explanation:
use the pythagorean theorem to prove whether or not each set of numbers represent the side length of a right triangle in your final answer, include your proof A. 6,12,15 B. 5,,12, and 13
Answer:
a. no, it is not a right triangle
b. yes, it is a right triangle
Step-by-step explanation:
) Yoona gives guitar lessons for $70 per session. She gives a 10% discount to students who
come to her studio for the lesson.
The question is about calculating the price of guitar lessons after a 10% discount and the answer explains the steps to calculate the discounted price.
Explanation:The subject of this question is Mathematics and the grade level is High School.
To calculate the amount after the discount, subtract 10% of $70 from $70. 10% of $70 is $7, so the discounted price is $70 - $7 = $63.
Therefore, Yoona gives a 10% discount to students which means the price per session is $63.
Learn more about calculating prices after discount here:https://brainly.com/question/30814332
#SPJ11
Akikta bought 25 trees for $15.40 each. Chloe bought 35 trees for $14.30 each. What was the difference between the total amounts that the girls paid for the trees?
Answer: $115.50
Step-by-step explanation:
500.5-385 = x
Answer:
$115.50
Step-by-step explanation:
Janine walks on a circular track whose radius is 60 meters. If she walks a total of 100 meters, which of the following represents the radian angle she rotates about the center of the track?
(1) 5/3
(2) 3/5
(3) 5π/3
(4) 3π/5
Answer: OPTION 1
Step-by-step explanation:
For this exercise you need to remember that, by definition, the Arc length can be calculated with the following formula:
[tex]arc\ length=rC[/tex]
where "C" is the central angle of the arc in radians and "r" is the radius.
Since you need to find the Central angle, you have to solve for "C" from that formula, as following:
[tex]C=\frac{arc\ length}{r}[/tex]
According to the information given in the exercise, you can identify that:
[tex]arc\ length=100\ m\\\\r=60\ m[/tex]
Therefore, the final step is to substitute these values into the formula and evaluate, in order to find the value of "C":
[tex]C=\frac{100\ m}{60\ m} \\\\C=\frac{5}{3}\ rad[/tex]
The measure of central angle RST is pi radians. What is the area of the shaded sector? 4pi units^2 8pi units^2 16pi units^2 20pi units^2
Answer:
8π units²
Step-by-step explanation:
Area of the circle can be defined as pi 'π' times the radius squared 'r²'
A= πr²
radius given is 4 (see attachment for the figure)
r=4
A = π4²
A= 16π
Now, if you look at the figure, you can see that the shaded area of the circle is 'half' of the whole circle.
We will half the Area which we have found it above in order to determine the area of shaded sector
Therefore,
area of the shaded sector = 16π/2 => 8π units²
Answer:
8[tex]\pi[/tex] [tex]units^{2}[/tex]
Step-by-step explanation:
did it on edge
What method can we use to rewrite Quadratic Equation in standard form to a Quadratic Formula? Go ahead and rewrite ax^2 + bx+c = 0 to quadratic formula. (please help. this is urgent.)
Answer:
SOLUTION: Rewrite the quadratic equation in standard form by completing the square. f(x)=x^2+8x+14 Answer (f(x)= (x, plus or minus ___)^2 plus or minus ____ I have worked this to x, 4 a Algebra -> Quadratic Equations and Parabolas -> SOLUTION: Rewrite the quadratic equation in standard form by completing the square.
Step-by-step explanation:
A jar contains 2 caramels, 7 mints and 16
dark chocolates. What is the probability of
choosing a dark chocolate, eating it, then
choosing a caramel?
Answer:
Answer A: 16/25
Answer B: 2/24
Step-by-step explanation:
There are 16 dark chocolates, so the probability of choosing one is 16/25. the total number of candies is 25, so when one is eaten, the number changes to 24. There are 2 caramels, so the number is 2/24.
The ages of the members of four teams are summarized below. Answer the questions about them.
Team A: The mean age is 52 and the range of ages is 27.
Team B: The mean age is 49 and the range of ages is 28.
Team C: The mean age is 48 and the range of ages is 31.
Team D: The mean age is 54 and the range of ages is 33.
(a) Based on the information above, which team has the youngest members on average?
Team A
Team B
Team C
Team D
(b) Based on the information above, which team's ages have the least variability?
Team A
Team B
Team C
Team D
The answer the statement a and statement b is
a) the answer is team C
b)we can conclude that the answer is team A.
We have given that,
The ages of the members of the four teams are summarized below. Answer the questions about them.
Team A: The mean age is 52 and the range of ages is 27.
Team B: The mean age is 49 and the range of ages is 28.
Team C: The mean age is 48 and the range of ages is 31.
Team D: The mean age is 54 and the range of ages is 33.
We have to determine the a and b
a) The information above, which team has the youngest members on average
from the above observations we can conclude that the answer is team C.
What is the least variability?
A related measure of variability is called the semi-interquartile range. The semi-interquartile range is defined simply as the interquartile range divided by 2.
b) The information above, which team's ages have the least variability
from the above observations, we can conclude that the answer is team A.
Learn more about the data visit:
https://brainly.com/question/19243813
#SPJ2
Using the rule of 72, how long will it take for the principal to double with an annual compound interest rate of 6%?
A. 6
B. 9
C. 12
D. 15
Answer:
C. 12
Step-by-step explanation:
With the rule of 72, you would divide 72 by the periodic interest rate to get the number of years for the principal to double
72 ÷ 6 = 12
the midpoint of AB is M (6,3). If the coordinates of A are (7,4) what are the coordinates of B
Answer:
B(5,2)
Step-by-step explanation:
The ratio of dogs to cats at the local pet store is 5:3
If there is 12 cats at the pet store, how many dogs
are at the pet store?
Answer:
20 dogs
Step-by-step explanation:
Answer:
20 Dogs.
Step-by-step explanation:
5:3=x:12
12/3=4
5x4=20
Question 2
If it takes 8 meters of fabric to make 5 pairs of curtains, how many meters are required to make 22 pairs?
Answer:
35.2m
Step-by-step explanation:
8 meters of fabric make 5 pairs of curtains so divide 8 by 5 to find that it takes 1.6 meters of fabric to make 1 pairs of curtains
multiply 1.6 by 22 to get 35.2 meters of fabric
What are the length and width of a rectangular
traffic sign if the length exceeds the width by 6
inches and the perimeter is 112inches?
Answer:
width is 25 inches
length is 31 inches
Step-by-step explanation:
We will need the formula for perimeter of a rectangle:
P = 2(l + w)
"l" is length, "w" is width
If the length exceeds the width by 6, then:
l = w + 6 <= Substitute this into the equation
P = 2(l + w)
P = 2(w + 6 + w)
Remember we also know the perimeter is 112:
112 = 2(w + 6 + w)
Collect like terms:
112 = 2(2w + 6)
Start isolating "w" to find width.
56 = 2w + 6 Divided both sides by 2
50 = 2w Subtracted 6 from both sides
25 = w Divided both sides by 2
w = 25 Variable on left for standard formatting
The width is 25 inches.
Find the length using "length exceeds width by 6".
l = w + 6
l = 25 + 6 Substitute the width
l = 31
The length is 31 inches.
∴ The length is 31 inches and the width is 25 inches.
Check your answer with the perimeter formula.
P = 2(l + w)
112 = 2(31 + 25) Substitute all the variables.
112 = 2(56)
112 = 112 Same answer
LS = RS Left side equals right side
The answer is correct.
What is the average rate of change for f(x) = -3* + 1 over the interval -2 < x <-1?
A. -1/9. B. -2/9. c. 1/9. d. 2/9
Answer:
B
Step-by-step explanation:
You can check it before choosing the answer.
I think 85% correct.
Which two-dimensional figure results from slicing the sphere with the blue plane?
A square
A circle
A line
A cone
A parabola
Nicole sells T-shirts, t, for $8, and sells sweatshirts, s, for $18. She earns $475
in revenue. Which equation below represents this relationship?
Answer:
Step-by-step explanation:
Cost of t, T-shirts = t*8 = 8t
Cost of s, sweatshirts = s*18 = 18s
Equation:
8t + 18s = 475
Please help, I’m not too smart
Answer:
x = - 4
Step-by-step explanation:
Given
r(x) = - 5x - 1 and r(x) = 19, then equating the right sides gives
- 5x - 1 = 19 ( add 1 to both sides )
- 5x = 20 ( divide both sides by - 5 )
x = - 4
(x + 3)2 + (x + 3) - 2 = 0
Answer:
x=-7/3
Step-by-step explanation:
2(x+3)+(x+3)-2=0
2x+6+x+3-2=0
3x+7=0
3x=-7
x=-7/3
Answer:
Step-by-step explanation:
Find the value of x in the triangle
Answer:
x = 28
Step-by-step explanation:
The sum of the angles of a triangle add to 180
85+67+x = 180
Combine like terms
152 +x =180
Subtract 152 from each side
152-152+x = 180-152
x = 28
Answer:
x=28 degrees
Step-by-step explanation:
180-85=95
95-67=28
simplify 12^3 over 12^7
Answer:
12^3/12^7= 1/12^(7-3)= 1/12^4
Step-by-step explanation:
The solution to the problem '12 to the power of 3 over 12 to the power of 7' is 12 to the power of negative 4 or written as a fraction, it is 1 over 12 to the power of 4 or 1 over 20736.
Explanation:The expression 123 over 127 refers to the mathematical concept of 'division of exponentials with the same base'. The rule in this case is to subtract the exponents. Therefore, 123 over 127 simplifies to 12-4. This can be understood as 1 over 124, or further simplified, 1 over 20736 if you multiply out the exponent.
Learn more about Division of exponentials here:https://brainly.com/question/31953341
#SPJ2