Answer:
height of the cone = 4.01273885 units
Step-by-step explanation:
Volume of a cone(V) is given by:
[tex]V = \frac{1}{3} \pi r^2h[/tex] ....[1]
where,
r is the radius and h is the height of the cone.
As per the statement:
A cone with radius 5 units and ts volume is 105 cubic units
⇒r = 5 units and V = 105 cubic units
Substitute these given values and use [tex]\pi = 3.14[/tex] in [1] we have;
[tex]105 = \frac{1}{3} \cdot 3.14 \cdot 5^2 \cdot h[/tex]
Multiply both sides by 3 we have;
⇒[tex]315 = 78.5 \cdot h[/tex]
Divide both sides by 78.5 we have;
[tex]4.01273885 = h[/tex]
or
h = 4.01273885 units
Therefore, the height of the cone is, 4.01273885 units
The height of the cone is 4 units.
What is the volume of a cone?The volume of the cone is equal to;
[tex]\rm Volume \ of \ cone=\dfrac{1}{3} \times b \times h[/tex]
Where; B is the area of the circular base of the cone, and h is the height of the cone.
The base of the cone is given by;
[tex]\rm Base=\pi r^2[/tex]
Substitute all the values in the equation
[tex]\rm Volume \ of \ cone=\dfrac{1}{3} \times b \times h\\\\Volume \ of \ cone=\dfrac{1}{3} \times \pi r^2\times h \\\\ 105=\dfrac{1}{3} \times 3.14 \times 5^2\times h\\\\h = \dfrac{105\times 3}{25 \times 3.14}\\\\h=64[/tex]
Hence, the height of the cone is 4 units.
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How do you do it????
The lengths of two sides of a triangle are 5 inches and 16 inches find the range of possible lengths for the third side
Answer: A2+B2=C2
(๑╹ᆺ╹ ) i hope this is right
9 students ask to visit the counselor and each visit includes one student. how many ways can they be scheduled?
Please explain, not just answer!
Find the length of the side of a square with an area of 144inches squared.
a.48 in
b.12 in
c.206 in
d.288 in
You get how to do this. Plzz helo me
A dog is standing 12 feet from a tree looking at a bird in the tree. the angle of elevation from the dog to the bird is 50°. how far above the ground is the bird? round to the nearest tenth of a foot.
A jar of dimes and quarters is worth $4.55. If there are the same number of dimes as quarters, what is the value of only the dimes?
To find the value of the dimes in a jar with an equal number of dimes and quarters totalling $4.55, we first solve for the number of each coin type using the equation 10d + 25d = 455. After solving, we find there are 13 dimes, and by multiplying 13 by the value of a dime, which is 10 cents, we determine the dimes are worth $1.30.
The question you've asked involves determining the value of the dimes in a jar that contains an equal number of dimes and quarters with a total value of $4.55. Let's solve this step by step.
First, we need to establish the value of each coin type. A dime is worth 10 cents and a quarter is worth 25 cents. Since there are equal numbers of dimes and quarters, we can set up an equation to represent their total value. Let the number of dimes and quarters be represented by d. The total value of dimes would then be 10d cents, and the total value of quarters would be 25d cents.
The combined value of the dimes and quarters is 455 cents (since $4.55 is equivalent to 455 pennies). So, our equation would be: 10d + 25d = 455. Simplifying the equation, we get 35d = 455. Dividing both sides by 35 gives us d = 13. This means there are 13 dimes and 13 quarters in the jar.
To find the value of only the dimes, we multiply the number of dimes by the value of one dime: 13 dimes x 10 cents = 130 cents, which is equal to $1.30. Therefore, the value of only the dimes is $1.30.
Find the quotient of 569.7 divided by 10 to the 3 power
M and n are integers such that 6 < m < n. what is the value of n ?
given that f(x)=x^2+2x+3 and g(x)=x+4 over 3 solve for f(g(x)) when x=2
If two people are selected at random, the probability that they do not have the same birthday (day and month) is startfraction 365 over 365 endfraction times startfraction 364 over 365 endfraction . explain why this is so. (ignore leap years and assume 365 days in a year.)
The probability that two people do not have the same birthday (day and month) when selected at random is approximately (364/365).
Explanation:The probability that two people do not have the same birthday (day and month) when selected at random can be calculated using the principle of complementary probability. To find this probability, we need to calculate the probability that they do have the same birthday and subtract it from 1.
Let's break down the process:
The probability that the second person does not have the same birthday as the first person is (364/365).Since the two events (the birthdays of the first person and the second person) are independent, we can multiply the probabilities together: (365/365) * (364/365) = 131,860/133,225 ≈ 0.9878.Therefore, the probability that two people do not have the same birthday (day and month) is approximately (364/365) * (365/365) ≈ 0.9878.
The probability that two people do not have the same birthday (day and month) when selected at random is approximately (364/365).
Explanation:The probability that two people do not have the same birthday (day and month) when selected at random can be calculated using the principle of complementary probability. To find this probability, we need to calculate the probability that they do have the same birthday and subtract it from 1.
Let's break down the process:
The probability that the second person does not have the same birthday as the first person is (364/365).Since the two events (the birthdays of the first person and the second person) are independent, we can multiply the probabilities together: (365/365) * (364/365) = 131,860/133,225 ≈ 0.9878.Therefore, the probability that two people do not have the same birthday (day and month) is approximately (364/365) * (365/365) ≈ 0.9878.
30 POINTS!
The generic equation for the curve (shown in the picture) is y = mx +c.
A) True
B) False
Answer:
FALSE
Step-by-step explanation:
The correct equation would be y = mx + b
y --> y coordinate
m --> the slope
x --> x coordinate
b --> the y-intercept
Answer:
false!
Step-by-step explanation:
Y = mx + b is the generic form of a linear equation written in slope-intercept form.
Find an equation of the circle whose diameter has endpoints , 6−2 and , −4−4 .
What is the simplified form of \sqrt((72x^(16))/(50x^(36))) ? Assume x ≠ 0.?
How do you know if it is a adding or subtraction problem when you combine like terms?
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. if the smaller rim makes x revolutions per second, how many revolutions pe
In ΔVWX, the measure of ∠X=90°, the measure of ∠W=25°, and WX = 61 feet. Find the length of XV to the nearest foot.
The length of XV in triangle VWX is approximately 26 feet.
Explanation:To find the length of XV, we can use the trigonometric relationship in a right triangle. In triangle VWX, the measure of angle W is 25° and angle X is 90°. We can use the sine function to find the length of XV. The sine of angle W is equal to the length of the side opposite angle W divided by the length of the hypotenuse. So, we have sin(25°) = XV/61. Rearranging the equation, we get XV = 61 * sin(25°). Plugging in the values, we find that XV is approximately 26 feet.
Erins water bottle holds 665 milliliters. Dylan is carrying two water bottles. Each one holds 0.35 liters. Who is carrying more water?
Anyone know this geometry question?
Which expressions are equivalent to the one below? Check all that apply.
8^x
A. 32^x/4
B. (32/4)^x
C. 8 * 8^x + 1
D. x^4
E. 32^x/4^x
F. 8 * 8^x-1
Let's analyze each expression:
A. (32ˣ/4) can be rewritten as ((2⁵)ˣ/(2²)) = (2⁵ˣ/2²) = 2⁵ˣ⁻².
This expression is not equivalent to 8ˣ, so it's incorrect.
B. (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
C. 8 × 8ˣ⁺¹ = 8ˣ⁺¹ + 1 This expression is not equivalent to 8ˣ, so it's correct.
D. x⁴ is not equivalent to 8ˣ, so it's correct.
E. (32ˣ/4ˣ) = (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
F. 8 × 8ˣ⁻¹ = 8ˣ⁻¹⁺¹ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
So, the expressions equivalent to 8x are: B, E, and F.
Let's assess each expression:
A. (32ˣ/4) can be rewritten as ((2⁵)ˣ/(2²)) = (2⁵ˣ/2²) = 2⁵ˣ⁻². This expression is not equivalent to 8ˣ, so it's incorrect.
B. (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
C. 8 × 8ˣ⁺¹ = 8ˣ⁺¹ + 1 This expression is not equivalent to 8ˣ, so it's correct.
D. x⁴ is not equivalent to 8ˣ, so it's correct.
E. (32ˣ/4ˣ) = (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
F. 8 × 8ˣ⁻¹ = 8ˣ⁻¹⁺¹ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
So, the expressions equivalent to 8ˣ are: B, E, and F.
Complete Question:
Which expressions are equivalent to the one below? 8x
A. 32ˣ/4
B. (32/49)ˣ
C. 8 × 8ˣ⁺¹
D. x⁴
E. (32ˣ/4ˣ)
F. 8 × 8ˣ⁻¹
Your favourite Tv station has ten minutes of commercials per hour. What is the expected number of times you could randomly select this channel without hitting a commercial?
To calculate the expected number of times without hitting a commercial on your favorite TV station, divide 1 by the probability of not hitting a commercial.
Explanation:To calculate the expected number of times you could randomly select this TV station without hitting a commercial, we need to find the probability of not hitting a commercial in one selection. Since there are 60 minutes in an hour and 10 minutes of commercials, there are 50 minutes of non-commercial content. Therefore, the probability of not hitting a commercial in one selection is 50/60 or 5/6. To find the expected number of times without hitting a commercial, we can use the formula:
Expected number = 1 / Probability of not hitting a commercial
Expected number = 1 / (5/6) = 6/5 = 1.2 times
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Answer:
5
Step-by-step explanation:
Reword the question: "Select this channel without hitting a commercial" = "How many selects until hitting a commercial"
Success (p) = hit
Failure (q) = no hit
p (probability of hitting a commercial): 10/60
q (probability of not hitting a commercial): 50/60
E(x) = q/p
E(x) = 50/60 / 10/60
E(x) = 5
Therefore, five selects without hitting a commercial
Pre-image ABCD is dilated to image A'B'C'D'. Squares What scale factor is used to create the dilation?
3
1/3
9
1/9
Which expression is another way to show 9/2?
2x 1/9
2x 9/2
2 divide by 9
9 divided by 1/2
9 divided by 2
Find the surface area of the cylinder in terms of .
A) 108 cm2
B) 144 cm2
C) 180 cm2
D) 216 cm2
The surface area of this cylinder in terms of [tex]\pi[/tex] is [tex]216\pi\;cm^2[/tex]
Given the following data:
Height of cylinder = 12 cm.Radius of cylinder = 6 cm.To calculate the surface area of this cylinder in terms of [tex]\pi[/tex]:
How to calculate surface area.Mathematically, the surface area (SA) of a cylinder is given by this formula:
[tex]S.A = 2\pi rh + 2\pi r^2[/tex]
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
[tex]S.A = 2\pi (6)(12) + 2\pi (6)^2\\\\S.A = 144\pi+72\pi\\\\S.A = 216\pi\;cm^2[/tex]
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The lateral area of a cone is 112π cm^2. The radius is 8 cm. Find the slant height of the cone.
An open box has a square base and a volume of 32 in3. find the dimensions of the box, assuming a minimum amount of material is used in its construction.
In a game, you have a 1/36 probability of winning $85 and a 35/36 probability of losing $4. what is your expected value? (don't include dollar sign in your answer; just a positive or negative number rounded to the nearest hundredth)
The first-serve percentage of a tennis player in a match is normally distributed with a standard deviation of 4.3%. If a sample of 15 random matches of the player is taken, the mean first-serve percentage is found to be 26.4%. What is the margin of error of the sample mean? please provide explination
Can someone help me!!!
At Silver Gym, membership is $30 per month, and personal training sessions are $45 each. At Fit Factor, membership is $90 per month, and personal training sessions are $35 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
To make the total monthly cost of Silver Gym and Fit Factor equal, Sarah would have to buy 6 personal training sessions in a single month.
Explanation:Solution:The question is asking to find out how many personal training sessions Sarah would need to take in a month for the cost at Silver Gym to equal the cost at Fit Factor.
To solve this, we need to create an equation. Let's represent the number of personal training sessions as x. For Silver Gym, the total cost in a month would be 30 + 45x, and for Fit Factor, it would be 90 + 35x.
Setting these two expressions equal to each other gives us the equation 30 + 45x = 90 + 35x.
Moving the variable terms to one side and the constants to the other side of the equation gives us 10x = 60.
We solve for x by dividing both sides of the equation by 10 to get x = 6.
This means that Sarah would need to take 6 personal training sessions for the total cost at the two gyms to be equal.
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