The national park has a new kiosk which visitors pass through as they enter the park. The kiosk is in the shape of a cylinder with a diameter of 5 meters and a height of 3 meters and a conical roof that measures 2 meters in height. What is the volume of the kiosk? Round your answer to the nearest cubic meter.
Given:
Kiosk is the combination of a cylinder and a cone.
Diameter of cylinder and cone = 5 m
Height of the cylinder = 3 m
Height of the cone = 2 m
To find:
The volume of the kiosk.
Solution:
We know that the radius is half of the diameter. So,
Radius of cylinder and cone = [tex]\dfrac{5}{2}[/tex] m
= [tex]2.5[/tex] m
Volume of the cylinder is:
[tex]V_1=\pi r^2h[/tex]
Where, r is the radius and h is the height of the cylinder.
Putting [tex]\pi =3.14, r=2.5, h=3[/tex] in the above formula, we get
[tex]V_1=(3.14)(2.5)^2(3)[/tex]
[tex]V_1=(3.14)(6.25)(3)[/tex]
[tex]V_1=58.875[/tex]
Volume of a cone is:
[tex]V_2=\dfrac{1}{3}\pi r^2h[/tex]
Where, r is the radius and h is the height of the cone.
Putting [tex]\pi =3.14, r=2.5, h=2[/tex] in the above formula, we get
[tex]V_2=\dfrac{1}{3}(3.14)(2.5)^2(2)[/tex]
[tex]V_2=\dfrac{1}{3}(3.14)(6.25)(2)[/tex]
[tex]V_2\approx 13.083[/tex]
The volume of the kiosk is the sum of volume of cylinder and the volume of cone.
[tex]V=V_1+V_2[/tex]
[tex]V=58.875+13.083[/tex]
[tex]V=71.958[/tex]
[tex]V\approx 72[/tex]
Therefore, the volume of the kiosk is 72 cubic meter.
Solve for x.
9 <17 - 4.0
Enter your answer, as an inequality, in the box.
9 <= 17 -4x
Subtract t 17 from both sides:
-8 <= -4x
Divide both sides by-4,
2 <= x
Rewrite the inequality with the x on the left side.
Answer: x <=2
how many zeroes are there
Answer:
infinity zeros are there
Step-by-step explanation:
please make me brainlsit answer
Covert 11 pints to fluid ounces plz
Answer:
176
Step-by-step explanation:
11 pints is 176 US fluid ounces
Find the diameter, given the circumference of a circle is 40.035 cm.
Answer:
12.75
Step-by-step explanation:
c = π x d
40.035= 3.14 x d
40.035/3.14 = 12.75
pls help me wit this asap
Answer:
not sure but I think the answers c
HELP, I don’t understand as this is due today!!!!
Answer:
in orange you cost 5.52
in apple you cost 3.9
Step-by-step explanation:
1 1/2=2×1+1=3
so multiplied the 3 in the price per pound
so in orange you got this solution
3×1.84=5.52
and in apple you got this solution
3×1.30=3.9
#CARRY ON LEARNING
#MARK ME AS BRAINLIEST
#100% SURE
factorize, completely each of the following expression
1-4h^2
Answer:
(1 + 2h)(1 - 2h)
Step-by-step explanation:
[tex]1 - 4h^2 = 1 ^2 - (2h)^2[/tex]
[tex]=(1 - 2h)(1 + 2h)[/tex] [tex][ \ a^2 - b^2 = (a - b)(a+b) \ ][/tex]
Solve for X. Answer as a decimal.
Answer:
2
Step-by-step explanation:
Evaluate the function f(x) = 3x2− 2x for x= 4.
The value of the function f(x) = 3x2− 2x for x= 4 is _ .
Answer:
40
Step-by-step explanation:
f(4) = 3(4²) - 2(4)
= 3(16) - 8
= 48 - 8
= 40
when x=4, f(x) = 40
Mr. Theorem writes the expression 6^2 Divided bye 23 on the board. What is the value
Answer:
[tex]1\frac{13}{23}[/tex]
Step-by-step explanation:
6² ÷ 23
36 ÷ 23
[tex]1\frac{13}{23}[/tex]
22 dividido en 3 es?
Answer:
Step-by-step explanation:
7.3
Answer:
7.3
Step-by-step explanation:
22/3 = 22/3
(Decimal: 7.333333)
please help me with this i really need it, thank you!
Each gridline represents one mile. If Ryan drove from home to the soccer field and then from the soccer field to the library, traveling in a straight line to each destination, he would have traveled ___ miles by the time he reached the library.
Answer:
13 miles
Step-by-step explanation:
the distance from the soccer field to the library is 8 miles
the distance between home and soccer field is a hypotenuse, use Pythagorean theorem to find the distance.
[tex]a^2+b^2=c^2\\\\4^2+3^2=c^2\\\\16+9=c^2\\\\c^2=25\\\\c=5[/tex]
the distance is 5 miles
5 + 8 = 13 miles total
PLS HELP THIS IS DUE TODAY
Answer:
Draw a C plane and plot the dots if the coordinates
Answer:
it's a triangle draw the chart
How do you solve this?
=================================================
Explanation:
If we plugged (x,y) = (0,8) into the first inequality, then we get
y < x^2+6
8 < 0^2+6
8 < 0+6
8 < 6
which is false. So we can rule out choice A.
----------------
Trying choice B leads us to
y < x^2+6
2 < 4^2+6
2 < 16+6
2 < 22
That last statement is true, so the first inequality is true for (x,y) = (4,2)
Let's try the other inequality
y > x^2-4
2 > 4^2-4
2 > 16-4
2 > 12
That's false. Since one of the inequalities is false (it doesn't matter which one), this means the entire system is false. We cross choice B off the list.
----------------
Now onto choice C
You should find that y < x^2+6 becomes -4 < 10 after plugging in (x,y) = (-2,-4). Since -4 < 10 is true, we move onto the next inequality.
The inequality y > x^2-4 becomes -4 > 0 after plugging in those mentioned x,y values. The inequality -4 > 0 is false.
We cross choice C off the list.
----------------
The only thing left is choice D. It has to be the answer.
Let's find out if we get true inequalities when plugging in (x,y) = (2,6)
y < x^2+6
6 < 2^2+6
6 < 10 ... true
and
y > x^2-4
6 > 2^2-4
6 > 4-4
6 > 0 .... also true
Both inequalities are true, so the entire system is true. Therefore, (x,y) = (2,6) is one of the infinitely many solutions to this system.
Choice D is confirmed as the answer
----------------
Refer to the diagram below. I've graphed the two dashed boundary curves and the shaded region between. This region is above the y = x^2-4 curve, and below the y = x^2+6 curve. So we're ignoring the stuff above the y = x^2+6 curve.
Points A through D represent the four answer choices in the order given. We see that point D is the only point in the shaded region, so that visually confirms we have the correct answer.
Note: points on the dashed boundaries do not count as solutions.
WILL GIVE BRAINLIST
MATH
WRITE THE SEQUENCE AS AN EQUATION USE X TO REPRESENT “ a number “
Six times the difference of 11 and a number is -72.
6×11-x= -72
Step-by-step explanation:6×11-x= -7266-x= -72-x= -72-66-x=-138x=138checking:6×11-138= -7266-138= -72-72= -72hope you understood it please mark me as brainliest
Which is an equation of a direct proportion?
A: y=16x+6
B: y=6x
C: y=6x−6
D: y=6x
Answer:
B) y=6x
Step-by-step explanation:
what is the lcm of 8 27 72
Answer:
216
Step-by-step explanation:
Answer:
In common notation: lcm (27,72) = 216
Pls need help in test
A fruit stand has to decide what to charge for their produce. They charge $8 for 4 apples and 4 oranges. They also charge $10 for 6 apples and 4 oranges. If we put this information into a system of linear equations, can we find a unique price for an apple and an orange?
A. Yes; they should charge $1.00 for an apple and $1.50 for an orange.
B. Yes; they should charge $1.00 for an apple and $1.00 for an orange.
C. No; the system has many solutions.
D. No; the system has no solution.
i think its C.No;the system has many solución
Answer:
thanks the quark is w wl1pp39iejbs sthe akwyve s akw9u27 2babe
According to a 2016 survey, 6 percent of workers arrive to work between 6:45 A.M. and 7:00 A.M. Suppose 300 workers will be selected at random from all workers in 2016. Let the random variable W represent the number of workers in the sample who arrive to work between 6:45 A.M. and 7:00 A.M. Assuming the arrival times of workers are independent, which of the following is closest to the standard deviation of W?
A. 0.24
B. 4.11
C. 4.24
D. 16.79
E. 16.92
Answer: B. 4.11
Step-by-step explanation:
Using Binomial distribution ( as the arrival times of workers are independent).
Formula for standard deviation: [tex]\sqrt{{p(1-p)}{n}}[/tex], where p= population proportion, n= sample size.
As per given ,
p= 0.06, n=300
Required standard deviation= [tex]\sqrt{0.06\left(1-0.06\right)300}[/tex]
[tex]=\sqrt{(0.06)(0.94)(300)}\\\\=\sqrt{16.92}\approx4.11[/tex]
Hence, the correct option is B.
A rectangular dog pen is constructed using a barn wall as one side and 63 m of fencing for the other three sides what is the maximum area of the dog pen
Can someone help me?
B. [tex] \sqrt{x} + \sqrt{x - 1} [/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \frac{1}{ \sqrt{x} - \sqrt{x - 1} } \\ \\= \frac{1}{ \sqrt{x} - \sqrt{x - 1} } \times \frac{ \sqrt{x} + \sqrt{x - 1} }{ \sqrt{x} + \sqrt{x - 1} } \\ \\ = \frac{ \sqrt{x} + \sqrt{x - 1} }{ ({ \sqrt{x} })^{2} - { (\sqrt{x - 1} })^{2} } \\\\ [∵(a + b)(a - b) = {a}^{2} - {b}^{2} ] \\ \\= \frac{ \sqrt{x} + \sqrt{x - 1} }{x - (x - 1)} \\ \\= \frac{ \sqrt{x} + \sqrt{x - 1} }{ x - x + 1} \\ \\= \sqrt{x} + \sqrt{x - 1} [/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
A dolphin is 9 feet below the surface of the ocean. If its position can be recorded as −9 feet, what would the position of 0 represent?
Answer: The surface of the ocean
Answer: It represents being at the surface
Negative values are below the surface, while positive values are above the surface.
In other words, -9 means 9 feet below sea level. The value 0 is at sea level. Something like 12 means you're 12 feet above sea level.
Find the perimeter of the figure. SOMEONE PLS HELP ME IVE ASKED THIS QUESTION 3 TIMES NOW
Answer:
Step-by-step explanation:
The lengths of the tangents drawn from an external point tot he circle are equal.
RA = RB = 12.2
QA = QC = 5.9
PC = PQ - QC = 27.4 - 5.9 = 21.5
PC = PB = 21.5
QR = QA + RA = 5.9 + 12.2 = 18.1
PR = PB + RB = 21.5 + 12.2 = 33.7
Perimeter = PQ + QR + PR
= 27.4 + 18.1 + 33.7
= 79.2
Two angles of a triangle are 120° and 6° What is the measure of the third angle?
Answer: 54
The angles of a triangle add up to equal 180.
Since we already know two angles, we can just use simple math to find the third.
120 + 6 = 126
180 - 126 = 54
Answer:
54°
Step-by-step explanation:
A triangle ALWAYS measure a 180° Angle in total so if the first and second angle is 120° and 6°, just add it together and will form a 126° Angle so subtract it to 180° Angle and it will result in a 54° Angle
Thank you and please mark me as brainliest ^^
Suppose y varies directly with x, and y = 65 when x = 13. What direct variation equation relates x and y?
Answer:
y = 5x
Step-by-step explanation:
y = kx
65 = k (13)
65/13 = k
k = 5
~~~~~~~~~~~~
y = 5x
Translate; a)A man's age 2 years ago b) the product of y and z
Step-by-step explanation:
a. represent the man's current age by n. Two years ago his age was n - 2.
b. Multiplication of n by the product of y and z would be (y×z)×n.
Hank has to drain his pool so repairs can be done on a crack on the bottom. The company coming to fix the pool is scheduled to arrive at 2:00 PM. They asked Hank to be sure to have his pool drained before they arrive. It is currently 8:00 AM Will Hank have the pool drained in time? The dimensions of the pool are 2m deep, 10m long, and 8m wide. Water can be drained at a rate of 130 gallons per minute.
Answer:
The answer to the question: "Will Hank have the pool drained in time?" is:
Yes, Hank will have the pool drained in time.Step-by-step explanation:
To identify the time Hank needs to drain the pool, we can begin with the time Hank has from 8:00 AM to 2:00 PM in minutes:
Available time = 6 hours * 60 minutes / 1 hour (we cancel the unit "hour")Available time = 360 minutesNow we know Hank has 360 minutes to drain the pool, we're gonna calculate the volume of the pool with the given measurements and the next equation:
Volume of the pool = Deep * Long * WideVolume of the pool = 2 m * 10 m * 8 mVolume of the pool = 160 m^3Since the drain rate is in gallons, we must convert the obtained volume to gallons too, we must know that:
1 m^3 = 264.172 galNow, we use a rule of three:
If:
1 m^3 ⇒ 264.172 gal160 m^3 ⇒ xAnd we calculate:
[tex]x = \frac{160 m^{3}*264.172 gal }{1m^{3} }[/tex] (We cancel the unit "m^3)x = 42267.52 galAt last, we must identify how much time take to drain the pool with a volume of 42267.52 gallons if the drain rate is 130 gal/min:
Time to drain the pool =[tex]\frac{42267.52gal}{130\frac{gal}{min} }[/tex](We cancel the unit "gallon")Time to drain the pool = 325.1347692 minutesTime to drain the pool ≅ 326 minutes (I approximate to the next number because I want to assure the pool is drained in that time)As we know, Hank has 360 minutes to drain the pool and how it would be drained in 326 minutes approximately, we know Hank will have the pool drained in time and will have and additional 34 minutes.
Express sin T as a fraction in simplest terms.
Answer:
sinT = [tex]\frac{15}{17}[/tex]
Step-by-step explanation:
We require to calculate RT before obtaining sinT
Using Pythagoras' identity in the right triangle
RT² = 30² + 16² = 900 + 256 = 1156 ( take the square root of both sides )
RT = [tex]\sqrt{1156}[/tex] = 34 , then
sinT = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{RS}{RT}[/tex] = [tex]\frac{30}{34}[/tex] = [tex]\frac{15}{17}[/tex]
Rewrite in simplest rational exponent form √x • 4√x
Answer:
4x
Step-by-step explanation:
[tex]\sqrt{x} \cdot \sqrt{x} = \sqrt{x^2} = x^{ 2 \times \frac{1}{2}} = x[/tex]
[tex]given :\\\\ \sqrt{x} \cdot 4\sqrt{x} = 4 \cdot\sqrt{x} \sqrt{x} = 4 \sqrt{x^2} = 4x[/tex]