Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 4 feet and a height of 10 feet. Container B has a radius of 2 feet and a height of 20 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full. After the pumping is complete, what is the volume of water remaining in Container A, to the nearest tenth of a cubic foot?
Answers
The volume of water remaining in Container A is approximately 251.2 cubic feet.
The volume of water in Container A can be calculated as follows:
V(A) = πr²h
= π(4)²(10)
= 160π ft³
The volume of water that will be transferred from Container A to Container B is equal to the volume of Container B:
V(B) = πr²h
= π(2)²(20)
= 80π ft³
So, the remaining volume of water in Container A is:
V(A) - V(B) = 160π - 80π
V(A) - V(B) = 80π ft³
V(A) - V(B) ≈ 80(3.14) = 251.2 ft³
Therefore, the volume of water remaining in Container A is approximately 251.2 cubic feet.
Learn more about the volume of containers here:
https://brainly.com/question/15318909
#SPJ1
Related Questions
Find the smallest whole number by which 16087 should be multiplied or divided to get a perfect square
Answers
There is no whole number by which you can multiply or divide 16087 to make it a perfect square.
To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.
In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.
To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.
A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.
Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.
For more questions on whole number
https://brainly.com/question/9879870
#SPJ8
Two-thirds of the students at the local community college live in the county. If there are 2028 students enrolled, how many do not live in the county?
Answers
SOLUTION:
Step 1:
In this question, we are told that the two-thirds of the students at the local community college live in the county.
If there are 2028 students enrolled, we are meant to find how many do not live in the county.
Step 2:
If two-thirds of the students live in the county.
Then, we have that:
\((\text{ 1 - }\frac{2}{3})\text{ = }\frac{1}{3}\text{ do not live in the county.}\)Step 3:
Then, to calculate the number of students that do not live in the county. we have that:
\(\frac{1}{3}\text{ x 2028 = }\frac{2028}{3}=\text{ 676 students}\)CONCLUSION:
There are 676 students that do not live in the county.
How can you use the double number line diagram to find what percent 120 is of 150?
Answers
Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.
To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.
On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.
This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.
To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.
To learn more about : percentage
https://brainly.com/question/24877689
#SPJ8
You spin each spinner and find the sum. How many different sums are possible?
these are the spinners:
Answers
The different sums are possible are 18.
As, the number of different sums possible is given by the equation:
Number of different sums = n x m
In other words, we multiply the number of outcomes for the first spinner by the number of outcomes for the second spinner to get the total number of unique sums.
So, the different sums are possible
= 2 x 3 x 3
= 18
Learn more about outcome here:
https://brainly.com/question/32037007
#SPJ1
6(-3) - | -5 | + | 3 | =
16
-10
-20
Answers
Answer:
its negative 20
Step-by-step explanation:
-20
6(-3)-|-5|+|3|
-18-5+3
-23+3
-20
please help me with this one
here is the picture
Answers
The value of the composition of functions are
a) f o g ( 5 ) = 1315
b) g o f ( 5 ) = 59
What is Composition of functions?Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the value of the the function be f ( x ) = x² + 6x
Let the value of the function g ( x ) = x + 4
Now , the composition of functions is given by
f o g ( 5 ) is given by
g ( 5 ) = 5 + 4 = 9
So , the value of f ( 9 ) = ( 9 )² + 6 ( 9 ) = 81 + 54 = 135
Therefore , the value of f o g ( 5 ) = 135
Now , the composition of functions is given by
g o f ( 5 ) is given by
f ( 5 ) = ( 5 )² + 6 ( 5 ) = 25 + 30 = 55
Now , the value of g ( 55 ) = 55 + 4 = 59
Therefore , the value of g o f ( 5 ) = 59
Hence , the composition of functions are solved
To learn more about composition of functions click :
https://brainly.com/question/17673639
#SPJ1
What color printer prints 11 pages in 6 minutes how many minutes does it take per page
Answers
Answer:
11/7 = 1.6
Step-by-step explanation:
11 pages divide 7 1.57 pages
____ = __________
7 minutes divide 7 1 minute
Describe the transformation.y = - [xl-5reflect over x-axis, vertical compress by factor of 3, and shift down 5reflect over x-axis, vertical compress by factor of 3, and shift up 5reflect over x-axis, vertical stretch by factor of 2, and shift down5reflect over x-axis, vertical stretch by factor of 2, and shift up 5
Answers
we have the equation
\(y=-\frac{1}{3}\mleft|x\mright|-5\)the parent function is
\(y=\mleft|x\mright|\)so
the transformations of the parent function to the given equation are
1) Reflection over x-axis
the rule is
(x,y) -------> (x,-y)
so
\(\mleft|x\mright|---\longrightarrow\text{ -}\mleft|x\mright|\)2) vertical compress by factor of 3
\(-|x|---\longrightarrow\text{ -}\frac{1}{3}|x|\)3) shift down 5
\(\text{-}\frac{1}{3}|x|---\longrightarrow\text{ -}\frac{1}{3}|x|-5\)therefore
the answer is
reflect over x-axis, vertical compress by factor of 3, and shift down 5In the diagram below of circle O, chords AD and BC intersect at E, and chords AB and CD are drawn.
Which statement must always be true?
PLEASE HELP!
Answers
The correct answer is (C) \(\angle B \cong \angle C.\) when In the diagram below of circle O, chords AD and BC intersect at E.
What is a circle ?
A circle is a two-dimensional geometric shape that consists of all the points in a plane that are at a fixed distance from a given point, called the center.
In the given diagram, we have a circle O with chords AB, CD, AD, and BC. The chords AD and BC intersect at point E.
Based on the diagram, we can see that the opposite angles in the quadrilateral AEDC are supplementary (i.e., they add up to 180 degrees). Therefore, we have:
\(\angle A + \angle C = 180^\circ\)
Similarly, the opposite angles in the quadrilateral BEFC are supplementary. Thus,
\(\angle B + \angle C = 180^\circ\)
We can rewrite the second equation as:
\(\angle C = 180^\circ - \angle B\)
Substituting this value of \angle C into the first equation, we get:
\(\angle A + 180^\circ - \angle B = 180^\circ\)
Simplifying, we get:
\(\angle A = \angle B\)
Therefore, the correct answer is (C) \(\angle B \cong \angle C.\)
To learn more about chords visit the link :
https://brainly.com/question/1654080
#SPJ1
1. Find the equation of a parabola with a focus of (0, -6) and directrix y = 6.
Max points
Answers
9514 1404 393
Answer:
(d) y = -1/24x² (b) y = 1/36x²Step-by-step explanation:
1. The point halfway between the focus and directrix is the origin. That is, the vertex of the parabola is the origin. Then its equation can be written ...
y = 1/(4p)x²
where p is the distance from the vertex (origin) to the focus. Here, that distance is -6, so 4p = -24 and the parabola's equation is ...
y = -1/24x²
__
2. Same deal. The vertex is the origin, but this time the focus is above the origin by 9 units. Then the equation is ...
y = 1/36x²
Hazel plans to mow her neighbors' yards to earn money. She charges a base fee of $25 and $7 for every hour she mows. The amount she earns per yard can be represented by the linear function M(t) = 7t + 25. What is the value of M(2), and what is its interpretation?
a. M(2) = 39; If Hazel mows 2 yards, she will earn $39.
b. M(2) = 14; If Hazel mows 2 yards, she will earn $14.
c. M(2) = 39; If Hazel mows a yard for 2 hours, she will earn $39.
d. M(2) = 14; If Hazel mows a yard for 2 hours, she will earn $14.
Answers
The correct option is M(2) = 39; If Hazel mows a yard for 2 hours, she will earn $39 . Option C
What is a function?A function can be defined as an expression that shows the relationship between an independent variable and a dependent variable.
Given the function;
M(t) = 7t + 25
Where;
M is the amount she earns per yardt is the time in hoursFor M(2), we substitute the value of t as 2 in the function
M(2) = 7(2) + 25
M(2) = 14 + 25
M(2) = $39
This explains that the she mows the yard for t = 2 hours, she would earn $39
Thus, the correct option is M(2) = 39; If Hazel mows a yard for 2 hours, she will earn $39. Option C
Learn more about functions here:
https://brainly.com/question/25638609
#SPJ1
Solve and graph.
2a − 10 < 2
Answers
The calculated solution to the inequality is a < 6
How to determine the solution to the inequalityfrom the question, we have the following parameters that can be used in our computation:
2a - 10 < 2
Divide through the equation by 2
So, we have
a - 5 < 1
Add 5 to both sides
a < 6
Hence, the solution to the inequality is a < 6 and the graph is attached
Read more about inequality at
https://brainly.com/question/32124899
#SPJ1
Is (1, -7) a solution of y=x-8?
Νο
Yes
Answers
hi die cry why guy shy fiy
Answer:
Yes
Step-by-step explanation:
You just plug in the values. \(-7 = 1-8\). You plug in 1 for x, and -7 for y
A bath tub drained at a constant rate. The table shows the number of gallons of water left in the tub after being drained for two amounts of time
Answers
The rate at which the water was drained from the tank is 6 gallons of water per minute (option A)
To know the speed at which the tank was drained, we must carry out the following operations:
Taking into account the information provided by the table we establish how much water has been drained from the tank in 20 minutes.
450 gallons - 330 gallons = 120 gallons.
Subsequently, we must divide the amount of water (120 gallons) that was drained by the time it was drained (20 minutes).
120 gallons ÷ 20 minutes = 6 gallons / minute.
According to the above, we can establish that the bath drain rate is 6 gallons / minute (option A).
Note: This question is incomplete because there is some missing information. Here is the complete information:
What is the rate at which the water was drained from the tank?
6 gallons of water per minute. 11 gallons of water per minute. 45 gallons of water per minute. 120 gallons of water per minute.
Learn more about linear equation in: https://brainly.com/question/11897796
PLEASE HELP FAST simplify: sqrt 8 + 2 sqrt 15
Answers
Answer:
2\(\sqrt{2}\) + 2\(\sqrt{15}\)
Step-by-step explanation:
\(\sqrt{8}\) = \(\sqrt{4}\)\(\sqrt{2}\) = 2\(\sqrt{2}\)
Given f(x) = 2x - 1 h(x) = x^2 + 1Find f[h(7)]
Answers
Answer:
\(f\lbrack h(7)\rbrack\text{ = 99}\)Explanation:
Given the functions:
\(\begin{gathered} f(x)=2x-1 \\ h(x)=x^2+1 \end{gathered}\)We want to find:
\(f\lbrack h(7)\rbrack\)First of all, we need to find:
\(f\lbrack h(x)\rbrack\)This is done by inserting the value of h(x) into f(x)
So, we have:
\(\begin{gathered} f\lbrack h(x)\rbrack=2(x^2+1)-1 \\ =2x^2+2-1 \\ =2x^2+1 \end{gathered}\)Substituting 7 for x in f[h(x)], we have f[h(7)]
\(\begin{gathered} f\lbrack h(7)\rbrack=2(7^2)+1 \\ =2(49)+1 \\ =98+1 \\ =99 \end{gathered}\)Which is what we are looking for.
Please someone help me! I need someone to be quick ASAP!
Answers
Answer:
Whats? explication?? khe??
Answer:
Step-by-step explanation:
A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answers
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
Read more about tangent lines at
https://brainly.com/question/21595470
#SPJ1
if x represents the number since 1988 what does x=32 represents
Answers
Explanation:
x is the number of years since 1988
x = 0 represents the year 1988
x = 1 is the year 1988+1 = 1989
x = 2 is the year 1988+2 = 1990
etc
x = 32 is the year 1988+32 = 2020
The table below shows a company's Manufacturing Cost, Overhead, Total
Sales, Profit, and Dividend per Shareholder over 4 years. Assume the
relationships among Manufacturing Cost, Overhead, Total Sales, Profit,
and Dividend per Shareholder remain the same over the years.
What should have been the Dividend per Shareholder in 2017,
assuming the number of Shareholders has remained unchanged
during the period 2017-2020?
SELECT ONE ANSWER
$17.45
$19.50
$20.00
$25.00
Answers
The Dividend per Shareholder in 2017 is $20.
As, Dividend per Shareholder = Profit / Number of Shareholders
Since the number of shareholders is assumed to have remained unchanged during the period 2017-2020, we can calculate the dividend per shareholder in 2017 using the profit value for that year.
Based on the given table, the profit for 2017 is $7,000.
Dividend per Shareholder in 2017
7000/x = 15500 / 44.29
7000/x = 349.966
x = 7000/349.966
x= 20.01
Learn more about Shares problem here:
https://brainly.com/question/30475800
#SPJ1
solve for x what is the answer?
Answers
Answer:
x=12
Step-by-step explanation:
The side lengths on the big polygon are just the side lengths of the small one by 4.
Herman is drawing a rectangle with a base that is
four times the length of its height. The perimeter of
his rectangle is 60 feet. How long are the base and
height of Herman's Rectangle?
Answers
heightAnswer:
12
Step-by-step explanation:
(x representing the smallest size)
x + 4x = 60
5x = 60
x = 12
the height is 12
to confirm:
12 x 4 = 48
48 + 12 = 60
I need explanation for example 8.
Thankyou
Answers
There is a probability of 94/315 that the problem will be solved.
We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.
The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.
The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.
The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.
The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.
To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:
2/7 + 4/7 + 4/9 = 94/315
To know more about probability here
https://brainly.com/question/11234923
#SPJ1
A study was conducted on the educational level of patients with AIDS, it was asume that
with ten years of education will be in group A, between 10 and 20 group B and between 20
group C. After the analysis it was realized that group A had 100 persons while group B and C had 30 persons
(a) If you decide to select based on proportion of 10% from each group how many patien
selected from each group. Show your calculation.
(b) What name can be given to the classified groups?
(c) What method of sampling was employed in the selection process?
1. State and explain the three major data collection techniques.
What is a variable?
What is a Parameter?
Answers
A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.
Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.
(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.
(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.
(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.
The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.
The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.
A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.
Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.
A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.
Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.
For more such questions on Parameters
https://brainly.com/question/29673432
#SPJ8
I am lost please help thank you all
Answers
Answer:
Step-by-step explanation:
At least 9 means more than 9 and includes 9
x ≥ 9 and [9, +∞)
At most 9 means numbers less than 9
x≤9 and (-∞, 9]
more than 9 means bigger than 9 but not including 9
x > 9 and (9, +∞)
fewer than 9 means less than 9 but not including 9
x<9 and (-∞, 9)
strictly between 7 and 9 means between 7 and 9 but not including
7<x<9 and (7,9) (This is the only one I'm unsure of. Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)
between 7 and 7 inclusive. means it's just =7 There's no boundaries
x=7
no more than 7 means less than 7 and includes 7
x ≤ 7 and (-∞, 7]
Help please!!! What was the number of small, medium, and large pizzas delivered to the college?
Answers
In the word problem above, 0 small pizzas, 1 medium pizza, and 5 large pizzas were delivered to the college.
How is this so?Let S = number of small pizzas delivered
Let M = number of medium pizzas delivered
Let L = number of large pizzas delivered
We'll start by solving equation 1 for one variable and substituting it into the other equations.
S + M + L = 12
We can rewrite this equation as -
S = 12 - M - L
Now, substitute this value of S in equations 2 and 3 -
4S + 10M + 15L = 109
4(12 - M - L) + 10M + 15L = 109
48 - 4M - 4L + 10M + 15L = 109
6M + 11L = 61
2S + 4M + 13L = 81
2(12 - M - L) + 4M + 13L = 81
24 - 2M - 2L + 4M + 13L = 81
2M + 11L = 57
Now we have a system of two equations with two variables -
6M + 11L = 61 ...(4)
2M + 11L = 57 ...(5)
Subtract equation (5)from equation (4) -
(6M + 11L) - (2M +11L) = 61 - 57
4M = 4
M = 1
Substitute the value of M into equation (5) -
2(1) + 11L = 57
2 + 11L = 57
11L = 55
L = 5
Now substitute the values of M and L into equation (1) -
S + 1 + 5 = 12
S + 6 = 12
S = 6 - 6
S = 0
Therefore, the solution is -
S = 0 (no small pizzas)
M = 1 (1 medium pizza)
L = 5 (5 large pizzas)
Learn more about word problem at:
https://brainly.com/question/21405634
#SPJ1
Full Question:
Although part of your question is missing, you might be referring to this full question:
a pizza shop delivered 12 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $109. a small pizza costs $4 and contains 2 ounces of pepperoni. a medium pizza costs $10 and contains 4 ounces of pepperoni. a large pizza cost $15 and contains 13 ounces of pepperoni. the owner of the pizza shop used 5 pounds 1 ounces of pepperoni in making the 12 pizzas. how many pizzas of each size were delivered to the college?
1/3x+ 1/3y=–9/5
in standard form
helpp
Answers
There is the answer to this equation problem
Find the angles a, b, c and d.
Answers
Answer:a b and c are 6
Step-by-step explanation:
Figure ABCDE has an area of 26 cm/. ABD and CBE are straight lines.
Find the area of the shaded triangle BDE,
Answers
The area of the shaded triangle BDE is 4 cm²
What is Area?The area is the amount of space within the perimeter of a 2D shape.
area of ΔADE= / *b *h
=1/2 * 8 *5
= 20 cm²
area of ΔBCD
= 26-20
= 6 cm²
area of CDE
= 1/2* 5 * 4
= 10 cm²
Area of shaded triangle,
=10-6
=4 cm²
Learn more about area of triangle here:
https://brainly.com/question/27683633
#SPJ1
A cookie factory uses 1 1/3 bags of flour in each batch of cookies. The factory used 6 2/3 bags of flour yesterday. How many batches of cookies did the factory make
Answers
Answer: you can get the full fraction by multiplying 6x3 which is 18 so then you add 18 and 2 and you get 20 so now the fraction is 20/3
and you need 11/3 for a batch so now you have 1 whole batch and 9/3 so you just make the 11 a percentage which is 81%
so the answer is 1 whole batch and 81% of another
or 1 9/3