The volume of the cylindrical water tank that has a length of 20 feet and a radius of 12 feet is about 9,048 cubic feet.
The correct option is option d;
d. 9,048
What is the volume of a solid?The volume of a solid indicates the amount of space the solid takes at a location.
The formula for finding the volume of the cylindrical tank is presented as follows;
V = π·r²·L
Where;
r = The radius of the tank
L = The length of the tank
From a similar question on the website, we have;
The length of the tank, L = 20 feet
Therefore;
The volume of the tank, V = π × 12² × 20 ≈ 9048
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Multi-Step Problem You are choosing between two electricity providers. The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. a. Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service. Write the two equations representing the cost of each company's service for one month.
The equation that represents the total cost of electric service using Zap Electric company is y = $0.06r + $6.55
The equation that represents the total cost of electric service using Bolt Electric Company is y = $0.12r + $2.83
What are the equations?The equation that can be used to determine the total cost of electric service is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one. When drawn on a graph, a linear equation is usually a straight line.
The total cost is the sum of the monthly service fee and the total cost of the kilowatt used.
Total cost = service fee + (charge per kilowatt x number of kilowatts used)
Zap Electric company : $0.06r + $6.55
Bolt Electric Company : y = $0.12r + $2.83
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Use a calculator to estimate the values of the limits correctly to two decimal places.
*h is approaching 0 in both of these limits
[tex]\lim_{h \to \0} \frac{2.7^h-1}{h} \\\\ \lim_{h \to \0} \frac{2.8^h-1}{h}[/tex]
Try this option ↓
Step-by-step explanation:
1) if to evaluate the given limits using math methods, then:
[tex]\lim_{h \to 0} \frac{2.7^h-1}{h}=[\frac{0}{0}]= \lim_{h \to 0} \frac{(2.7^h-1)'}{(h)'}= \lim_{h \to 0} \frac{2.7^h*ln2.7}{1} =ln2.7;[/tex]
and
[tex]\lim_{h \to 0} \frac{2.8^h-1}{h}=[\frac{0}{0}]= \lim_{h \to 0} \frac{(2.8^h-1)'}{(h)'}= \lim_{h \to 0} \frac{2.8^h*ln2.8}{1} =ln2.8;[/tex]
2) for more info see the attached graphs; note, ln2.7≈0.993252, ln2.8≈1.029619 and the function is undefined in the points where x=0.
Diana has 240 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answer:
80y by 40y
Step-by-step explanation:
The area of the rectangle that maximizes the enclosed area is
80 by 40
80+80=160
40+40=80
160+80=240 yards.
- Mark has scored 8,14,10,20, and 5 points in the past 5 basketball games. Write and solve the inequality that can be used to solve for the number of points he will need to score in the next game in order for Mark to average at least 15 points per game.
The number of points at least 23 he will need to score in the next game in order for Mark to average at least 15 points per game.
Mark has scored 8,14,10,20, and 5 points in the past 5 basketball games.
Let the required number of points would be x
n = 6
∑x = 8 + 14 + 10 + 20 + 5 + x = 57 + x
As per the given question, we can write the inequality as:
∑x/n ≥ average per game
(57 + x)/6 ≥ 15
57 + x ≥ 15 × 6
57 + x ≥ 80
x ≥ 80 - 57
x ≥ 23
Thus, the number of points at least 23 he will need to score in the next game in order for Mark to average at least 15 points per game.
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Explain how the graph of the function f(x) = 4x^2 compares to its parent function f(x)=x^2 in terms of whether it faces up or down, has a maximum or minimum, and if it’s stretched or compressed.
Answer:
f(x)=4x^2 is facing up, it has a minimum, and it's horizontally compressed
Step-by-step explanation:
It's facing up because there's no negative sign in front of the coefficient of x.
It has a minimum because any quadratic function that faces up will have a minimum, and any quadratic function that faces down will have a maximum.
It's horizontally compressed because as can be seen in the picture below, f(x)=4x^2 (red) has more "slope," so it's condensed toward the y-axis. Hence, if the coefficient is bigger than 1, then the function will be horizontally compressed, and if the coefficient is smaller than 1, then the function will be horizontally stretched.
the frequency of the letter e in written English is about 13%. On a page of a novel that has bout 2000 letters per page, about how many occurrences of the letter e can we expect to find?
260 occurrences of the letter e we can expect to find.
Frequency = 13%
Total letters = 2000
E letters = 13% of 2000
= (13/100)*2000
= 13*20
= 260
Hence, there are 260 e letters in 2000 of total letters.
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. Which segment is a dilation of BC using A as the center of dilation and a scale
factor of ?
2. Which segment is a dilation of BC using A as the center of dilation and a scale
factor of ?
3. Which segment is not a dilation of BC, and how do you know
Using A as the center of dilation and a scale factor, BC is dilated by 12 units.
What is scale factor?In the ratio indicated by the scale factor, a line segment dilates by becoming longer or shorter. The segments (sides) of the image will be longer than the corresponding sides of its pre-image if the scaling factor is more than 1 (k > 1). (an enlargement).If both the new and original dimensions are known, the scaling factor may be determined. A figure's scale factor can be calculated using the following simple formula: Dimension of the original shape minus the dimension of the new shape is the scale factor.To learn more about scale factor refer to:
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Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 3 ≤ x ≤ 4.
If the function over the interval 3 ≤ x ≤ 4 then, the average rate of change, in simplest form, is 9.
What is average rate of change?
It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.The rate of change of the function is its gradient or slope.
The formula for calculating the gradient of a function is expressed as:
m = dy/dx
m =y₂ - y₁ / x₂-x₁
The function over the interval 3 ≤ x ≤ 4.
Using the coordinate points from the table (3, 31) and (4, 22)
Here, y₂ = 22, y₁ = 31 , x₂= 4, x₁ = 3.
Substitute the coordinate into the expression:
= 22 - 31 / 4 - 3
= 9 / 1
m = 9
Hence, the function over the interval 3 ≤ x ≤ 4 ; the average rate of change is 9.
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A
(2x + 7)°
в
(4x-10)
(7x-25)°
C
m/
Answer:
ima need a complete question
Step-by-step explanation:
Given: O is the midpoint of PT and RS
Prove: APOR = ATOS
Given O is the midpoint of PT and RS
Therefore, In triangles POR and TOS, we have
PO = TO (O, the midpoint of PT);
∠POR=∠TOS, (vertically opposite angles);
RO=OS, (O, the midpoint of RS)
So by SAS postulate, we have
△POR = △TOS Hence proved
What is the midpoint?
The midpoint is a line segment's center point in geometry. The midpoint is also the centroid of the segment and the endpoints are equally spaced from both endpoints. The midpoint can also be described as a point that divides a segment in half or as one that is equally spaced from both ends of a line.
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Jerry and his cousin are playing a game where they pick up colored sticks. Jerry currently has 20 points and likes to pick up the pink sticks, earning 4 points every turn. His cousin just lost all her points on the previous turn, and has a strategy to catch up by getting all the red ones, earning 6 points per turn. In a certain number of turns, the score will be tied. How many points will they each have?
If Jerry currently has 20 points and likes to pick up the pink sticks, earning 4 points every turn, and his cousin has a strategy to catch up to jerry from 0, by getting all the red ones, earning 6 points per turn, then their scores will be tied after 10 turns from now on, and their points then will be 60.
As per the question statement, Jerry and his cousin are playing a game where they pick up colored sticks and Jerry currently has 20 points picking up the pink sticks which earn him 4 points every turn. His cousin just lost all her points on the previous turn, and has a strategy to catch up by picking all the red ones, which can earn 6 points per turn.
Then we are required to calculate the number of turns from now on, after which, their scores will be tied, and the magnitude of their points at that instant.
Let us assume that, their scores will be tied after "x" turns from now on.
Then, [{20 + (4 * x) = (6 * x)]
Or, [(20 + 4x) = 6x]
Or, [20 = (6x - 4x)]
Or, (2x = 20)
Or, [x = (20/2)]
Or, (x = 10)
That is, their scores will be tied after 10 turns from now on, and their points then will be [(20 + 4x) = (20 + 40) = 60].
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Answer: 4
Step-by-step explanation:
Wanda has a watering
schedule for her plants. Her
cacti gets watered every 10 days and her ferns get watered every 3days. If she waters both the plants today after.how many
days will they be watered together again?
After 30 Days will they be watered together again.
The smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple.
What is LCM ?Finding the smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple.
List the initial range of each number's multiples.Search for multiples that appear on both lists. Write out additional multiples for each number if there aren't any common multiples in the lists.Find the least quantity that appears on both lists.The LCM is this number.cacti gets watered every 10 days.
ferns get watered every 3days
LCM of 3 and 10 is 30.
After 30 Days will they be watered together again.
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The graph of g(x) is the result of translating the graph of f(x) = 3* six units to the right. What is the equation of g(x)?
O g(x)= 3x-6
Og(x)=3x+6
Og(x)=3*-6
Og(x)=3* +6
The equation of the graph g(x) is [tex]3^{x-6}[/tex]
What is a graph ?
A diagram that shows how a variable's variation compares to that of one or more other variables, such as a collection of points, lines, line segments, curves, or areas. all points whose coordinates satisfy a specific relation;
In mathematics, the word "graph" has (at least) two distinct meanings. A function graph or "graph of a function," also known as a plot, is referred to as a "graph" in elementary mathematics. A graph is a set of points and the connections between some subset of those points and their lines, which may or may not be empty.
The translation of the graph of the function y = f(x) a units to the right gives the function y = f(x-a)
If the graph of the function f(x) = 3^x is translated 6 units to the right , then the function becomes
g(x) = f(x - 6)
= [tex]3^{x-6}[/tex]
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Which sets of ordered pairs represent functions?
The ordered pair in roaster form {(2,8), (3, 12), (4, 16), (5, 20)} is a function.
What is the domain and range of a function?Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x is defined.
We know a function can be many one which means different inputs leads to same output but one to many is not a function as same input can not lead to different outputs.
{(2,8), (3, 12), (4, 16), (5, 20)} is a function as each different input leads to a different output.
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$11,900 is invested, part at 8% and the rest at 5%. If the interest earned from the amount invested at 8% exceeds the interest earned from the amount invested at 5% by $441.00, how much is invested at each rate? (Round to two decimal places if necessary.) Define variables x and y and set up a system of two linear equations that represents the information given in the problem.
$7969.24 invested at 8% and $3930.76 invested at 5%
From given information,
Amount invested = $11,900
Rate of interest for first part = 8%
Rate of interest for second part = 5%
Let the amount invested for 8% be 'x'.
Let the amount invested for 5% be 'y'
According to question, we get an equation,
0.08x - 0.05y = 441
x + y = 11,900
x = 11,900 - y
0.08(11,900 - y) - 0.05y = 441
952 - 0.08y - 0.05y = 441
-0.13y = -511
y = (-511)/(-0.13)
y = 3930.76
so, x = 11,900 - 3930.77
x = 7969.23
Therefore, $7969.24 invested at 8% and $3930.76 invested at 5%
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use the given triangle to solve for x.
Answer:
X=5
Angle c is 42 degrees
Step-by-step explanation:
sum of all angles in a triangle equal 180 degrees so we set all these angles equal to that
(9x-3)+(22x+1)+(42-3x)=180
31x-2+42-3x=180
28x+40=180
-40. -40
28x=140
/28. /28
x=5
So now to find angle c we just fill in X
9(5)-3
45-3
42
Hopes this helps please mark beainliest
A spherical granite boulder weighs 560 tons. Specific gravity of granite is 2.6 - 2.7. What is the diameter of the boulder assuming a sphere.
The diameter of the boulder assuming a sphere. is 38m
Specific gravity is defined as density of a substance to the density of water
SG = density of boulder/ density of water
Since (at standard temperature and pressure) water has a density of 1
SG = mass of boulder / volume of boulder
2.6 = 560 x 1000/ x
x = 56000/2.7
x = 20740.74
The volume of a sphere = 4/3 πr³ =
20740.74 = 4/3 (3.14) r³
r³ = 4953
r = 17.04
Diameter = 2r = 2x17.04 = 38.08
Therefore, the diameter of the boulder assuming a sphere. is 38m
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A famous painting was sold in 1945 for $21,210. In 1987 the painting was sold for $33.3 million. What rate of interest compounded continuously did this this investment earn?
The rate of interest compounded continuously is 16.7%
What does the math term "rate of interest" mean?
The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.
Formula: [tex]A=Pe^{rt}[/tex]
Where A = final amount
P = initial amount
e =mathematical constant approximated as 2.7183
r = rate of interest
t = time
Initially (t=0) in 1945 a famous painting was sold for $21,210
[tex]21210 = Pe^{0} \\P = 21210[/tex]
In 1987 (t=42) the painting was sold for $33.3 million
[tex]33.3 * 10^{6} = 21210 e^{42r} \\e^{42r} = \frac{33.3 * 10^{6}}{21210 } \\\\e^{42r} = 1570.014\\42r = ln( 1570.014)\\r = \frac{1}{42} ln( 1570.014)\\r = \frac{1}{42} 7.36\\r = 0.167\\r = 16.7%[/tex]
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Evaluate the expression with the given replacement values. x^5; x=−3
Answer:
-243
Step-by-step explanation:
x^5 = x * x * x * x * x
( - 3 )^5 = (-3) * (-3) * (-3) * (-3) * (-3) = -243
Ali and Kris are driving to a city that is 120 miles from their house. They have already traveled 20 miles, and they are driving at a constant rate of 50 mi/h. Write a function that models their distance from home as a function of time. What is a reasonable domain for this situation?
Function notation in slope-intercept form: f(x) = ___+___x
A reasonable domain is ___≤ x ≤___.
The function that models the distance in miles is f(x) = 20 + 50x
The domain of the function is 0 ≤ x ≤ 2
How to determine the function that models the distanceInformation given in the question include
Ali and Kris are driving to a city that is 120 miles from their house
They have already traveled 20 miles
they are driving at a constant rate of 50 mi/h
The function can be modeled as a linear function
What is linear function ?A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = c + mx
Definition of variables to suit the problem to be solved
y = total mileage covered = f(x)
m = mileage covered per hour = 50 mph
x = number of hours
c = miles already covered = 20 miles
The function is substituted to the equation as below
y = c + mx
f(x) = 20 + 50x
The domain refers to the reasonable time spent during the journey
this is time at minimum distance = 0 to time at maximum distance = 120
f(x) = 20 + 50x
0 = 20 + 50x
-20 = 50x
x = -2/5
since there is no negative time, it is more reasonable to start with zero
120 = 20 + 50x
120 - 20 = 50x
50x = 100
x = 100 / 50
x = 2 hours
A reasonable domain is 0 ≤ x ≤ 2
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jade has an unopened package of beads. she also has 8 beads in a package that is already open. jade puts all the beads together and divides then into 4 equal groups to share with her friends. how many beads are in each group?
The number of beads that are in each group when Jade divides the beads is 30.
How to calculate the number of beads?From the information, Jade has 72 unopened package of beads and she also has 8 beads in a package that is already open. Jade puts all the beads together.
The addition will be:
= 72 + 8
= 80
She then divides then into 4 groups, the number in each group will be:
= Total beads / Number of group
= 80 / 4
= 20 beads
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Complete question
Jade has 72 unopened package of beads. she also has 8 beads in a package that is already open. Jade puts all the beads together and divides then into 4 equal groups to share with her friends. how many beads are in each group?
inequality symbol.
Solving Equations: S
17+2.6b=30
2.6b-30-17=
2.6b 13
b=13/2.6
2.6b/2.6=13/2.6 X
2.6b/2.6=5
b=5
Check:
b=5
5+2.6+5=17-30 is the check correct?
Answer:
it's correct
Step-by-step explanation:
17+2.6b=30
2.6b=30-17
2.6b=13
b=13÷2.6
b=5
{Question 8} Please help! Need this by tonight! {Click on picture}
The cost per message is $0.025 and the graph that represents the Jerry's text message plan is graph 2
The cost of every 30 messages = $0.75
To find the cost of one message we have to use the unitary method
The cost of 1 message = The cost of every 30 messages / 30
Substitute the values in the equation
The cost per message = 0.75 / 30
Divide the terms
= $0.025
Next find the cost 40 messages = The cost per message × 40
Substitute the values in the equation
The cost of 40 messages = 0.025 × 40
= 1
Using these details the graph that represents the Jerry's text message plan is graph 2
Hence, the cost per message is $0.025 and the graph that represents the Jerry's text message plan is graph 2
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Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k
f(x)=?
The equation of the parabola as described in the task content is; f (x) = -3 (x - 5)² + 9.
What is the equation of the parabola as described in the task content?It follows from the task content that the equation of the parabola which has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f (x) = a (x-h)² + k be determined.
Recall that the vertex of a quadratic equations of the given form is defined by the coordinates (h, k).
On this note, the required equation of the parabola by substitution of h and k is;
f (x) = -3 (x - 5)² + 9.
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You are given the expressions x(3.25y - 4.86) and x(-1.75y + 5y - 3.86) + x. A. Expand each expression. B. Are these expressions equivalent? Explan?
Expansion of x(3.25y - 4.86) is 3.25xy - 4.86x and expansion of
x(-1.75y + 5y - 3.86) + x is 3.25xy - 2.86x. The expressions are not equivalent as the coefficient of x is different in the expanded form.
What are equivalent expressions?
In expanded form, the expression combines all its like terms.
Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other.
According to the given question:
The given expressions are
1. x (3.25y - 4.86)
2. x (-1.75y + 5y - 3.86) + x
Expanding each expression
1. x (3.25y - 4.86)
= 3.25*x*y - 4.86*x
= 3.25xy - 4.86x
2. x (-1.75y + 5y - 3.86) + x
= -1.75*x*y + 5*x*y - 3.86*x + x
= 3.25xy - 2.86x
Clearly coefficient of x variable is different after expansion of expressions. Therefore, the expressions are not equivalent.
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It takes Sam 4 hours to rake the front lawn, while his brother, Dave, can rake the lawn in 2 hours. How long will it take them to rake the lawn working together?
The number of hours it will take them to lawn is 4 / 3 hours.
How to find the number of hours it will take them to lawn?It take Sam 4 hours to rake the front lawn, while his brother, Dave, can rake the lawn in 2 hours.
The number of hours it will take both of them to rake the lawn together is as follows:
Hence, recall they a doing the same work
1 / t = 1 / 4 + 1 / 2
where
t = time(hours) both of them will work together
1 / t = 1 + 2 / 4
1 / t = 3 / 4
cross multiply
4 = 3t
divide both sides by 3
t = 4 / 3
Therefore,
t = 4 / 3 hours
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Why is 3^7 equal to 7 1/3
The required answer is [tex](7^{\frac{1}{3}})^{3} = (7^{\frac{1}{3}*3}) = 7^1=7[/tex].
what is a power rule for exponents ?
[tex](a^m)^n=a^{mn}[/tex] is known as the power rule for exponents. Exponent times power is how you raise a number with an exponent to a power.
A number's exponent demonstrates how many times we are multiplying a given number by itself. 3^4, for instance, indicates that we are multiplying 3 by four. 3*3*3*3 is its expanded form. The power of a number is another name for an exponent. It could be an integer, a fraction, a negative integer, or a decimal.
[tex](7^{\frac{1}{3}})^{3} = (7^{\frac{1}{3}*3}) = 7^1=7[/tex]
Here, we have used the rule [tex](a^m)^n=a^{mn}[/tex]
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Find the measure of angle b
Answer:
b = 65°
Step-by-step explanation:
Now we have to,
→ find the required value of b.
Forming the equation,
→ 115° + b = 180°
Then the value of angle b is,
→ 115° + b = 180°
→ b = 180° - 115°
→ [ b = 65° ]
Hence, the value of b is 65°.
Which expression is equivalent to 2(3x^2-6x+4)+2(-2x+25x+100)?
The expression that is equivalent to 2(3x^2-6x+4)+2(-2x+25x+100) is 2(3x² + 1x + 104)
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
This will be illustrated as:
2(3x^2-6x+4)+2(-2x+25x+100)
= 6x² - 12x + 8 - 4x + 50x + 200
= 6x² +34x + 208
= 2(3x² + 1x + 104)
The equivalent expression is 2(3x² + 1x + 104).
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At what rate will a sum of money triple itself in 10 years?
Answer:
20%.
Step-by-step explanation:
A sum of money will triple itself in ten years at an annual interest rate of 20%.
