The height of the silo is 56 feet.
Here, we are given that a large grain silo is to be constructed in the shape of a circular cylinder.
The diameter of the silo = 30 feet
⇒ The radius of the cylinder = 15 feet
and also the radius of the hemisphere = 15 feet
The volume of a hemisphere = 2πr^3/3
Volume = 2 × π × 15 × 15 × 15 × 1/3
Volume of cube = 2250π
Thus, the volume of cylinder = volume of the silo - volume of the hemisphere
= 11,475(3.14) - 2250π
π = 3.14
⇒ 11,475(3.14) - 2250(3.14)
3.14 (11,475 - 2250)
= 3.14 (9225)
= 9225π
Now, the volume of cylinder = πr^2h
Thus, 9225π = π(15) (15) h
9225π/ 225π = h
h = 9225/225
h = 41
Thus, the height of the cylinder = 41
The height of the silo will be the height of hemisphere + height of the cylinder = 15 + 41 = 56 feet.
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1) alice decides to take a trip from the east coast of the united states to the west coast. while planning, she chooses to drive, fly, and ride a train. her first leg of the trip is traveling by car, from sacramento, california to denver, colorado. along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. after driving for many hours, alice finally makes it to denver, colorado spending $874.80 in gas. a) let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. create an equation that models the situation.
The equation will be: 4.65r + 4.95p = 874.80
The total cost of gas will be sum of the individual costs of both the types of gas. Firstly, calculating cost of regular and premium gas followed by forming the equation.
The total cost of regular gas = Amount of regular gas × Cost of regular gas per gallon
The total cost of regular gas = 4.65 × r
The total cost of premium gas = Amount of premium gas × Cost of premium gas per gallon
The total cost of regular gas = 4.95 × p
We are given overall spending = 874.80
Forming the equation -
Total cost of regular gas + total cost of premium gas = overall spending on gas
4.65r + 4.95p = 874.80
Hence, the equation that models the situation is 4.65r + 4.95p = 874.80.
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M∠1=19 , m∠2 what is the answer?
Answer:
161 degrees since 180 - 19 would be 161 since they are supplementary if they are
Step-by-step explanation:
A foreign exchange student from Denmark would like to buy gifts for her family. She finds a special deal, 7 t-shirts for $90.93, that she would like to purchase for her family. However, her family only consists of 5 people. If she wants to purchase 5 t-shirts for her family members at that special rate, what would be the cost of these t-shirts in her currency of Krona? (Currency conversion rate is 1 U.S. Dollar = 8.6964 Krona)
Using proportions, it is found that the cost of the 5 t-shirts would be of 564.83 Kronas.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for currency conversion problems, as multiplication or division operations are applied according to the rates of each coin.
For this problem, we have that 7 t-shirts cost $90.93, hence the cost of a t-shirt in U.S. dollars is given applying the proportion to find the unit rate as follows:
$90.93/7 = $12.99.
The cost of 5 t-shirts will be given by:
5 x 12.99 = $64.95.
Applying the proportion 1 U.S. Dollar = 8.6964 Krona, the cost in Kronas is:
64.95 x 8.6964 = 564.83 Kronas.
The cost of the 5 t-shirts would be of 564.83 Kronas.
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How many simple random samples of size 4 can be selected from a population of size 8?
a. 70
b. 32
c. 1680
d. 4
70 simple random samples of size 4 can be selected from a population of size 8
According to the question, samples of size 4 have to be selected from a population of size 8. The selection can be made in
8C4 ways.
Selection=8C4=8!(8−4)!4!
Selection=8!(8−4)!4!
Selection=8×7×6×5×4!4!×4×3×2
Selection=2×7×5
Selection=70
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How do I get the answer
Answer:11
Step-by-step explanation:
Answer:
11 units
Step-by-step explanation:
use the absolute value function to find the difference between A and E
A = - 6 , E = 5 , then
AE = | - 6 - 5 | = | - 11 | = | 11 | = 11
or
AE = | 5 - (- 6) | = | 5 + 6 | = | 11 | = 11
Select the correct product of the exponential expression.
3^5
OA. 3.5
OB. 3.3.3.3.3
OC. 5.5.5
OD. 15
The correct product of the exponential expression 3⁵ is equal to 3.3.3.3.3.
As given in the question,
Given exponential expression is equal to 3⁵
General form of exponential expression is given by aˣ
a is the base and x is the exponent
This means 'x' times ' a ' is multiplied to ' a '
Compare 3⁵ with general form
3 is base
5 is exponent
This means '5' times ' 3 ' is multiplied to '3'
3⁵ = 3.3.3.3.3
Therefore, the correct product of the exponential expression 3⁵ is equal to 3.3.3.3.3.
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assuming 69.6 heartbeats/minutes, estimate the total number of times the heart of a human beats in an average lifetime of 89.3 y. assume 365.25 days per year. answer in units of heartbeats. your answer must be within ± 5.0%
The total number of times a human heart beats in an average lifetime of 89.3 years is estimated to be 3,268,988,688.8 heartbeats.
To calculate time:
We are to estimate the total number of times a human heart beats in an average lifetime based on the question.Based on the information provided,We will assume 69.6 heartbeats per minute.To calculate the total number of times the heart of human beats in an average lifetime of 89.3 years,
In 89.3 years, we will calculate the number of minutes.
89.3 years = 89.3 × 365.25 × 24 × 60 minutes89.3 years = 46968228 minutesBecause there are 69.6 heartbeats per minute
Then,
There are 46968228 heartbeats in 46968228 minutes.
46968228 × 69.6 = 3,268,988,688.8 heartbeatsTherefore, the total number of times a human heart beats in an average lifetime of 89.3 years is estimated to be 3,268,988,688.8 heartbeats.
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Brainliest for correct answer
The correct symbols that complete the statements are
h(0) = g(0)
h(1) > g(1)
Graph of functionsFrom the question, we are to determine the correct symbols that complete the given statements
The given statements are
h(0) ___ g(0)
and
h(1) ___ g(1)
To complete the statements, we will find the values of the given functions from the graph
From the graph of h(x), we can observe that
h(0) = 4
and
From the graph of g(x), we can observe that
g(0) = 4
Thus,
The two functions are equal
h(0) = g(0)
Also,
From the graph of h(x),
h(1) = 3
and
From the graph of g(x),
g(1) = 2
That is, h(1) is greater than g(1)
Thus,
h(1) > g(1)
Hence, the correct symbols that complete the statements are
h(0) = g(0)
h(1) > g(1)
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(2-y)(3y+8)=0 solve
Answer:
Step-by-step explanation:
(2 - y)(3y + 8) = 0
2 - y = 0
y = -2
3y + 8 = 0
y = -8/3
pls help! marking brainliest
Answer:
296
Step-by-step explanation:
Use long division.
296
21 |6216
-42
201
-189
126
-126
0
Hope this helps!
Solve the following equation
3(1-3x)=2(-4+7)
Answer:
x=-1/3
Step-by-step explanation:
3(1-3x)=2(-4+7)
Use distributive property.
3-9x=-8+14
Combine like terms.
3-9x=6
Subtract 3 from both sides.
-9x=3
Divide -9 from both sides.
x=-1/3
Hope this helps!
Please mark as brainliest if correct!
Answer:
The value of x is -1/3.
Step-by-step explanation:
Given equation,
→ 3(1 - 3x) = 2(-4 + 7)
Now the value of x will be,
→ 3(1 - 3x) = 2(-4 + 7)
→ 3 - 9x = 2 × 3
→ -9x = 6 - 3
→ x = 3/(-9)
→ [ x = -1/3 ]
Hence, the value of x is -1/3.
Mr. Hazel is a professional plumber. To fix a drain that is clogged, he charges a customer
$50 per hour, plus a fixed fee of $25 for the service call, as represented by the function
f(x)= 50x + 25. In the equation, what is represented by the variable "x"?
Answer:
The x is how much hours the job takes,
You can see that 25 is a fixed fee which is why there is no x attached to it, and 50 is the variable that can change, hope that made sense!
Step-by-step explanation:
^^^
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
Eli, Freda and Geoff were given 800 pounds to share in the ratio of there age. Eli is 9 years old Freda is 13 years old and Geoff is 18 years old. How much should they each have?
An angel measures 109 what is the measure of it it’s supplement
Answer:
71°
Step-by-step explanation:
A supplementary angle is the sum of two angles whom are less than 180 degrees, yet the sum will only be 180 degrees. Because we are finding the supplement angle, we must subtract.
[tex]\sf Long\:Subtraction\\9\:doesnt\:go\:into\:10,borrow\:1\\= 10\\= 10 - 9\\= 1\\8\:cant\:go\:into\:0,take\:1\:since\:you\:just\:borrowed\\= 7\\= 7 - 0\\= 7\\1 - 1\\= 0\\\\= \boxed{71}[/tex]
➲ Hope this helps.
Please help me please help me
Answer: T (4,4)
Step-by-step explanation:
Melina receives a chain e-mail that she forwards to 7 of her friends. Each of her friends
forwards it to 7 of their friends.
Chain E-Mail
Melina
How many people will receive the e-mail after 6 forwards?
Answer:
823543 Or 7^7
Step-by-step explanation:
Directions: Translate equation DO NOT SOLVE!
"four times the difference of a number and 7
is 32"
Number 11:
“ten increased by the quotient of a number and 2 is -15”
Sorry for taking so long :/
Step-by-step explanation:
*Four times the difference of a number and 7 is 32*
Answer-
4(x-7)=32
ten increased by the quotient of a number and 2 is 15-
Answer-
10+(x/2= -15
or
10+x/2=-15
anyone of them
find the equations that describe the circle of radius 3 centered at (8, 5, 6) that is parallel to the xy-plane.
The equation of the circle can be given by: (x - 8)² + (y - 5)² = 9.
What is a circle's equation?The equation for a circle in standard form is (x - x1)² + (y - y1)² = r², where (x, y) denotes arbitrary coordinates on the circle's perimeter, r denotes the circle's radius, and (x1, y1) denotes the coordinates of the circle's center.
Now,
Every point on a circle fulfills the equation describing it. A circle with radius r and a point (h, k, l) parallel to the xy plane have the following equation: (x - h)² + (y - k)² = r²We are given the values of h as 8, k as 5 and r as 3. On substituting them in the given equation, we get:=> (x - 8)² + (y - 5)² = 9
Hence, the equation that describe the circle of radius 3 centered at (8, 5, 6) that is parallel to the xy-plane is given by: (x - 8)² + (y - 5)² = 9
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a car averages 35 miles per gallon of gasoline. how many liters of gasoline will be needed for a trip of 450 km? some conversion factors which may be helpful are the following:
For 450 km, the car need 9.32 liters of gasoline to cover the distance of 450km.
Given,
Car averages 35 miles per gallon of gasoline.
Here we need to find how many liters of gasoline will be needed for a trip of 450 km.
First we have to convert the km into miles in order to solve it.
1 mile = 0.621371 miles
So, 450 km is equal to,
=> 450 x 0.621371 miles
=> 279.617 miles.
Now, we already know that,
1 gallon of gasoline will cover 35 miles.
So, for 279.617 miles, it will need,
Let x be the liters of gasoline will be needed to cover the distance.
So,
=> x = 279.617 / 30
=> x = 9.32
Therefore, we need 9.32 liters of f gasoline will be needed for a trip of 450 km.
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how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
"Extend the domain of the trigo functions using the unit circle" Cluster A.
What is unit circle?The following steps can be used to calculate the sine and cosine of any angle thetatheta and allow us to extend the domain of sine and cosine to any real numbers:
Move counterclockwise around the unit circle starting at (1, 0), (1, 0), (1, comma, 0, right parenthesis, until the angle created by your position, the origin, and the positive xxx-axis equals thetatheta.
The yyy-coordinate of your point is equal to sin(theta)sin(theta)sine, and the xxx-coordinate is equal to cos(theta)cos(theta)cos(theta)cosine, left parenthesis, theta, right parenthesis.
There are several references to and issues with in the worlds of calculus, pre-calculus, and trigonometry.
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regina has five brothers who are 4, 6, 6, 9, and 15 years of age. the mean age of regina's brothers is .
The calculated mean age of Regina's brothers is 7. This is being attained by using the concept of measure of central tendency i.e. mean.
What is a mean?
Mean is interpreted as the total of all values divided by the total number of values. It is also called a mathematical average. There are three types of mean namely, arithmetic, geometric and harmonic mean.
Calculation of the mean age of Regina's brothers
Total number of Regina's brothers = 5
Sum of their ages = 4 + 6 + 6 + 9 + 10
= 35
Mean age = sum of their ages / total number
= 35 / 5
= 7
Hence, the calculated mean ages of Regina's brothers is 7
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I NEED HELP WITH THIS ANSWER ASAP!!!!!!
A sequence is defined by the formula U(subscript 1)=4/27, u(subscript n+1)=3 x u(subscript n), n>1.
A) Show the sequence is geometric and find the common ratio
From the recursive definition, the next term of a sequence is the previous term multiplied by 3, hence it is a geometric sequence with a common ratio of 3.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The recursive definition of a geometric sequence is:
[tex]a_{n+1} = qa_n[/tex]
In this problem, the sequence is given by:
[tex]u_{n+1} = 3u_n[/tex]
With first term [tex]u_1 = \frac{4}{27}[/tex].
Hence it is a geometric sequence with a common ratio of 3.
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what is 343250394065834698350968549846÷57547547
Answer: 5.9646399e+21
2 tickets cost 11.00 they bought 2 drinks and used a 5.00 off coupon. the total cost was 29.18 how much was 1 drink
After buying tickets and drinks the total cost is 29.18 and using 5.00 off coupon, the cost of one drink is 11.59
As per the question statement, 2 tickets cost 11.00 and they bought 2 drinks and used a 5.00 off coupon. The total cost was 29.18. We are supposed to find out the cost of one drink.
Let the cost of one drink be "x"
Cost of 2 tickets = 11
Off coupon is of 5.00
Cost of two drinks = [tex]2x[/tex]
Total money paid = 29.18
Hence, [tex]11+2x-5=29.18\\2x=29.18+5-11=23.18\\x=\frac{23.18}{2} \\x=11.59[/tex]
Therefore the cost of one drink is [tex]x=11.59[/tex]
This question was a classic example of how to form equations when all the given conditions are in statements.
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Bashir is the youngest of four siblings whose ages are consecutive integers. If the sum of their ages is 66, find Bashir's age.
Answer:
15
Step-by-step explanation:
x+x+1+x+2+x+3=66
simplify into 4x+6=66
subtract 6 from both sides to get 4x=60
divide both sides by 4 to get x=15
The age of Bashir is 15 years.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the consecutive age be x, x+1, x+2 and x+3.
Now, sum of their ages is 66
So, x+ x+1 + x+2 + x+3 = 66
Simplifying for x, we get
4x+6=66
subtract 6 from both sides
4x=60
divide both sides by 4
4x /4 = 60/4
x= 15
Hence, Bashir age is 15 years.
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What is the product of −2 1/4 and −4 1/2?
select the correct answer. which measurement is equivalent to 350 milliliters? a. 3.5 × 102 liters b. 3.5 × 101 liters c. 3.5 × 10–2 liters d. 3.5 × 10–1 liters
According to the given information the measurement is equivalent to 350 milliliters = 3.5 x 10⁻¹.
The correct option is D.
What is conversion factor?A conversion factor is a quantity that is used to multiply as well as divides one set of units by another. When converting to an equivalent value, the appropriate conversion factor must be utilized. To convert inches to feet, for example, the suitable conversion value is 12 inches equal 1 foot.
What is the significance of conversions?Conversion KPIs are critical for determining the efficacy of marketing campaigns. Only by measuring how many users convert as a result of that spend can you calculate your ROAS.
According to the given data:We are given an amount of 350 milliliters and asked to convert it to liters.
We know that :
1 liter = 1000 milliliters
We are given an amount of 350 milliliters and asked to convert it to liters.
1 liter/x liter = 1000/350
x = 350/1000
x = 3.5 x 10⁻¹
The given information the measurement is equivalent to 350 milliliters = 3.5 x 10⁻¹.
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I understand that the question you are looking for is:
Which measurement is equivalent to 350 milliliters?
A. 3.5 × 102 liters
B. 3.5 × 101 liters
C. 3.5 × 10–2 liters
D. 3.5 × 10–1 liters
So you see...
The question in my math workbook is,
45 ÷ 3 = (30 + ___) ÷ 3
= 30 ÷ 3 + ___ ÷ 3
= 10 + 5
= 15
sorry my brain is broken right now- I have a feeling this problem is really easy to solve, but as I said my brain is broken lol
The blank will be filled with 15.
The Bodmas rule is arranged according to the letters in the acronym BODMAS, which stand for brackets, position of power or roots, division, and multiplication. A stands for addition and S for subtraction. According to the BODMAS rule, multi-operator mathematical equations must be resolved in the BODMAS order from left to right.
The explanation goes like:
45 ÷ 3 = ( 30 + 15 ) ÷ 3
= 30 ÷ 3 + 15 ÷ 3
= 10 + 5
= 15
Hence the answer is 15.
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evaluate 3(x-4)+2x-x2 for x=5
Answer:-12
Step-by-step explanation:
Im going to assume that x2 means x squared. You can just substitute "x" for 5. 3(5-4)+2(5)-5^2. First parenthesis equals 3(1)+10-5^2. Then it equals 3+10-5^2. So then it would be 13-5^2. 5^2 equals 25. so it would be 13-25. Which equals -12.
help with explanation!
In a heptagon, the sum of all seven angles is 900 degrees. If you add up the four given angles you will get 600 degrees. In the question it says, "the remaining interior angles are EQUAL" so therefore, the only way to get from 600 to 900 from the remaining three angles is 100. Each remaining angle is 100 degrees
Answer:
Heptagons are known to have seven interior angles that add up to 900°, so we must find the last 3. First, add the first four they gave us.
[tex]160\circ + 130\circ = 290\circ\\= 290\circ + 170\circ + 140\circ\\170\circ + 140\circ = 310\circ\\= 290\circ + 310\circ\\= 600\circ[/tex]
We now know that the remaining angles are all 100°, because the question mentions the rest of the interior angles being equal. The only reasonable 3 equal numbers to add up to 900° would be three 100s in this case.