The radius of the sphere 1.5 units
The volume of the cone is pi (3)^2 *4 / 3 units^3 = 12pi units^3
The volume of the sphere is (4/3)pi (1.5)^3 units^3 = 4.5 units^3
So ratio of the volume of the sphere to the cone is :
4.5 pi / 12 pi = 4.5 / 12 = (9/2) / (24/2) = 9 / 24 = 3 / 8
What is radius?In geometry, the radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary. It is an important part of circles and spheres which is generally abbreviated as 'r'. The plural of radius is "radii" which is used when we talk about more than one radius at a time. The largest line segment in a circle or sphere joining any points lying on the opposite side of the center is the diameter, and the length of the radius is half of the length of the diameter. It can be expressed as d/2, where 'd' is the diameter of the circle or sphere. Look at the image of a circle given below showing the relationship between radius and diameter.To learn more about diameter refer to:
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I SWEAR I NEED HELP PLEASEEEEEEEEEEE NO LINKS
50 POINTS! Calculate the expression in the most efficient way possible. Show steps.
5^1125 * 0.2^1123
Answer:
25
Step-by-step explanation:
Given expression:
[tex]5^{1125} \times 0.2^{1123}[/tex]
Rewrite 0.2 as a fraction:
[tex]\implies 5^{1125} \times \left(\dfrac{1}{5}\right)^{1123}[/tex]
[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]
[tex]\implies 5^{1125} \times \dfrac{1^{1123}}{5^{1123}}[/tex]
Simplify the numerator by applying the exponent rule a¹ = a:
[tex]\implies 5^{1125} \times \dfrac{1}{5^{1123}}[/tex]
[tex]\textsf{Apply the fraction rule} \quad a \times \dfrac{b}{c}=\dfrac{ab}{c}:[/tex]
[tex]\implies \dfrac{5^{1125} \times1}{5^{1123}}[/tex]
[tex]\implies \dfrac{5^{1125}}{5^{1123}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 5^{1125-1123}[/tex]
Simplify the exponent:
[tex]\implies 5^{2}[/tex]
Simplify:
[tex]\implies 5 \cdot 5[/tex]
[tex]\implies 25[/tex]
x-3y less than or equal to 18
We're given too less information with this problem. we would need to know what the variables X and Y represent. The value of the equation is unknown.
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The local pizza placed has placed a new circular sign above the restaurant. The circumference of the sign is 37.68 feet, and the diameter is 12 feet. Which expression best represents the value of it? * The local pizza place has placed a new circular sign above the restaurant. The circumference of the sign is 37.68 feet, and the diameter is 12 feet. Which expression best represents the value of pi?
A.37.68/6
B.37.68/12
C.12/37.68
D.6/37.68
Answer:
B
Step-by-step explanation:
The circumference of a circle can be described as the linear distance round the circle
The circumference of a circle = 2πr or πD
π = 3.14
r = radius
d = diameter
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
π = circumference / 2r or circumference / D
37.68 / 12
how many even numbers of 3 digits can be formed of the digits 1,2,3,4,5,6 when repitition of digits is allowed
Answer:
To find the number of three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with repetition allowed, we can use the formula for permutations:
Step-by-step explanation:
Number of permutations = (number of choices for the first digit) x (number of choices for the second digit) x (number of choices for the third digit)
In this case, we have 6 choices for each digit, since we are allowed to repeat the digits. Using the formula, we get:
Number of permutations = 6 x 6 x 6 = 216
Therefore, there are a total of 216 three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with repetition allowed.
However, not all of these will be even. For a number to be even, the last digit must be even, so the last digit can only be 2, 4, or 6. This means that there are 3 choices for the last digit.
Therefore, the total number of even 3-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 is 366=108.
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PLEASE
[tex](4x-3)=(6x+13)[/tex]
Answer:
x = -8
Step-by-step explanation:
4x - 3 = 6x + 13
+ 3 + 3
4x = 6x + 16
-6x -6x
-2x = 16
-2 / -2x = 16 / -2
x = -8
Ask if you wanted a different answer
1. If triangle ABC has the following measurements, find the measure of angle A. a = 17 b = 21 C = 25 42.3° 137.7° 56.2° 81.5°
Answer: Triangle ABC is a right triangle, because it satisfies the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
c^2 = a^2 + b^2
25^2 = 17^2 + 21^2
625 = 289 + 441
625 = 730
Since it is a right triangle, angle A is the angle opposite side a, which is the side that is the length of 17.
A right triangle also has one angle which is always 90 degree, that is the angle opposite the hypotenuse, so the remaining angle is A, which is 90- angle C, which is
90 - 42.3 = 47.7 degree.
Therefore the measure of angle A is 47.7°
So the correct answer is C. 42.3°
Step-by-step explanation:
solve for x: 5x - 18 = -8
Answer:
x = 2
Step-by-step explanation:
5x - 18 = -8
+18 +18
5x = 10
5x/5 = 10/5
x = 2
The vertices of triangle ABC have coordinates A(-2,-1) B(10,-1) and C(4,4). Determine and state the area of triangle ABC
A report states that of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 6 percentage points with confidence
To estimate the true proportion of home owners who have vegetable gardens to within 6 percentage points with confidence, a sample size of 384 would be needed.
How big of a sample is required to confidently estimate the true percentage of homeowners having vegetable gardens to within 6 percentage points?This can be calculated using a sample size calculator and the given margin of error and desired confidence level.The size of the sample needed can be calculated using the formula n = (z2 * p * (1-p)) / e2, where n is the size of the sample, z is the z-score associated with the desired confidence level (1.96 for 95% confidence), p is the estimated proportion of home owners having a vegetable garden, and e is the margin of error (6 percentage points).Assuming a conservative estimate of p = 0.50, the sample size needed to estimate the true proportion of home owners having a vegetable garden to within 6 percentage points with 95% confidence is:n = (1.962 * 0.50 * 0.50) / (0.06)2 = 384.9 ≈ 385Therefore, a sample size of 385 home owners is needed to estimate the true proportion of home owners having a vegetable garden to within 6 percentage points with 95% confidence.The equation is: n = (z_alpha/2)^2 * (p*(1-p)) / e^2 Where n is the sample size, z_alpha/2 is the z-score for the desired confidence level (e.g., z = 1.96 for a 95% confidence level), p is the estimated population proportion, and e is the margin of error. For this example, we can assume a 95% confidence level (z = 1.96), a population size of N = 100,000, and a margin of error of 6 percentage points (e = 0.06). Plugging these values into the sample size equation, the required sample size is n = (1.96/2)^2 * (0.5*(1-0.5)) / 0.06^2 This gives us a sample size of n = 384.To learn more about the Theory of Confidence Intervals refer to:
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1. Which describes the parametric equations x=t-1 and y=-t+2?
A. y=-x+3 The orientation is up to the right
B. y=-x+3 The orientation is down to the right
C. y=-x+1 The orientation is up to the right
D. y=-x+1 The orientation is down to the right
2. Which describes the conic section with parametric equations x=2 cos t and y=4 sin t?
A. 1=x^2/4+y^2/16; an ellipse with vertical major axis
B. 1=x^2/4-y^2/16; a hyperbola with horizontal transverse axis
C. 1=x^2/16+y^2/4; an ellipse with horizontal major axis
D. 1=x^2/16-y^2/4; a hyperbola with vertical transverse axis
3. A skateboarder goes off of a ramp at a speed of 52ft./s. The ramp is 5ft. above the ground with a 30° angle of elevation. Which set of parametric equations represents the skater's jump? The acceleration due to gravity is 32ft./s^2.
A. x=26√3t+5 and y=-16t^2+26t+5
B. x=36√3t and y=-16t^2+26t+5
C. 26t+5 and y=-16t^2+26√3t+5
D. 26√3t and y=-16t^2+26t
Answer:
Just did the Connexus Parametric functions Review Practice:
1. D
2. A
3. B
4. A C and D
5. C
6. C
7. D
8. B
9. A C and E
10. D
11. D
12. C
13. A
14. D
For part 1 the equation y = -x +1 and orientation is down to the right and for part 2 the equation 1=x^2/4+y^2/16; an ellipse with vertical major axis
What are parametric equations?A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
1) We have parametric equations x = t - 1 and y = -t + 2
After converting from parametric to Cartesian form, we will get:
y = -x +1 and orientation is down to the right
2) For parametric equations, x = 2cost and y = 4sint
In the Cartesian form:
[tex]\rm 1=\dfrac{x^2}{4}+\dfrac{y^2}{16}[/tex]
With vertical major axis
Similarly, we can get parametric equations represents the skater's jump.
Thus, for part 1 the equation y = -x +1 and orientation is down to the right and for part 2 the equation 1=x^2/4+y^2/16; an ellipse with vertical major axis.
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0.5 (ug)^2 (Mm)^-3 is equivalent to
...... kg^2 cm^-3
gong rented a truck for one day. There was a base fee of $19.95, and there was an additional charge of 71 cents for each mile driven. Hong had to pay $125.74 when he returned the truck. For how many miles did he drive the truck?
Answer:
19.95 + .71 × x = 125.74
x = 141.053
x is the answer
Sovle for b ;3b-8=-5
Answer:
b=1
Step-by-step explanation:
First we need to isolate the variable (kind of like social distancing) well lets move -8 to the other side and make it positive since we moved it to the other side.
3b = -5+8
3b = 3
b = 1
What is the perimeter of a 30 60 90 triangle whose shorter leg is 5 inches long?
The perimeter of the triangle is 23.66 inches
According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].
Now in the question
As shown in the diagram, if the shorter leg of the triangle at 30°, 60°, and 90° is extended in the direction of the right angle by an amount equal to itself and connected to the third point, we obtain a triangle that is congruent with the original triangle. It is clear that the combined triangle is an equilateral triangle with equal sides and angles.
The greatest leg, AB, in the picture is therefore twice as long as the shortest leg of the original triangle and equal to base BC.
Therefore according to the question
given that the shorter leg is 5 inches,
hypotenuse = 5*2 = 10 inches.
the longest leg = 5[tex]\sqrt{3}[/tex], and
The perimeter is thus 5 + 10 + 5[tex]\sqrt{3}[/tex] = 15 + 5[tex]\sqrt{3}[/tex] = 23.66 inches
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homework i need to do pls help
Answer:
1.
(a) 4y
(b) 5w
(c) 6a
(d) 3s
(e) 2n
(f) 3g
(g) 2y
(h) 0
2.
(a) -2u
(b) -w
(c) -3a
(d) -7y
3.
(a) 7a+3b
(b) 12y+4h
(c) 2g+10a
(d) 15m+10p
(e) 10e+4
(f) 12+5a
Step-by-step explanation:
Don't be intimidated by the "letter" variables. It is really just simple addition and subtraction. Examples:
For Q1=
y + y + y + y = 4y because there are 4 y's, and since we don't know the values of the y, this is the farthest we can simplify it.
For Q2=
4u - 6u = -2u. Since these two numbers have the same variable, this is just a simple subtraction problem. 4 - 6 = -2.
For Q3=
3a + 2b + 4a + b = 7a + 3b.
Look for the numbers with the same variable. 3a and 4a both have a's, so we add the two and get 7a. 2b and b (b is the same thing as 1b) both have b's, so we add them and would get 3b.
Therefore, the answer is 7a + 3b.
I hope this helped! Good luck with future endeavors!!
Step-by-step explanation:
attached the answers below, hope that helps...
in a trivia game, you lose point for wrong answers. You answer the first 5 questions incorrectly. Your score after the 5 questions is -90. How many points is each incorrect answer worth?
How do I solve these problems?
Answer:
- 32, - 7, 18 and 127, 106, 85
Step-by-step explanation:
Add the common difference d to the previous term
(1)
a₁ = - 32
a₂ = a₁ + 25 = - 32 + 25 = - 7
a₃ = a₂ + 25 = - 7 + 25 = 18
The first 3 terms are - 32, - 7, 18
(2)
a₁ = 127
a₂ = a₁ + d = 127 - 21 = 106
a₃ = a₂ + d = 106 - 21 = 85
The first 3 terms are 127, 106, 85
Answer:
-32, -7, 18 and
127, 106, 85
Step-by-step explanation:
You can use the following formula to solve this:
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
a is the nth term in the sequence. So at the 3rd term, n = 3
a₁ is the first term in the sequence. In your first question, a₁ is -32. In your second, a₁ is 127.
(n - 1) represents the term before a, or the term before the current term. So at the 3rd term, (n - 1) = 3-1, which is 2.
d represents the common difference between terms. Aka what you add or subtract to a term to get the next one.
For the first question, you know a₁ and d, so you can substitute them into the equation to find the second and third terms:
a = -32 + (n - 1)25
You also know (n-1), because a is 2 when you're looking for the second term. So (n-1) = 2-1, which is 1. So put that in the formula and simplify:
a = -32 + (1)25
a = -32 + 25
a = -7
The second term is -7. To find the 3rd term, do the same thing.
a = -32 + (n - 1)25
(n-1) is 2, since you're on the third term and n is 3.
a = -32 + (2)25
a = -32 + 50
a = 18
So the first 3 terms are -32, -7, and 18.
For the second one, the formula looks like this:
a = 127 + (n - 1)-21
The first term is 127. Find the 2nd (n is 2):
a = 127 + (1)-21
a = 127 -21
a = 106
Then find the 3rd term (n is 3)
a = 127 + (2)-21
a = 127 -42
a = 85
So the first 3 terms are 127, 106, and 85.
Please help me i was having trouble!!
Answer:
The answer is 5
Step-by-step explanation:
add all numbers up then divide by how many numbers there are.
find the slope of the line passing through the points (1,0) and (-4,2)
Answer:
-2/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-0)/(-4-1)
m=2/-5
m=-2/5
PLEASE HELP!!!! YOU DON"T MULTIPLY THEM TOGETHER I ALREADY TRIED THATIf you help me and get it right I will mark brainliest and more!!!
Answer:
The surface area of this prism is 800 ft^2
Step-by-step explanation:
To get this answer you need to add all the base edges, which will equal to 40. Then you times 40 with 20 which will equal to 800 ft^2. Hope this helps!
Answer:
520ft^2
Step-by-step explanation:
triangles
A=1/2bh
A=60
since both those half triangles make one trianlge there is no need to multipply 60 by 2
back rectangular
A= l x w
A= 8x20
A= 160
face rectangle
A= l x w
A=20 x 17
bottom rectangle
A=lxw
A = 300
add it all up
60+160+300=520ft^2
LET ME KNOW IF I MADE A MISTAKE
I need help with my starr review again im littarly sorry.. its math!
please help quickly
If UY=13p-1 and VX=20p-95 than what is UY
Viewing the given triangle, the information given helped to determine side UY to be 90
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
WX and WY, XV and YU
The solution is worked out using sides WX and XV, WY and YU
WX / WY = XV / YU
WX / WY = 1/2 since it is a mid segment
1 / 2 = (20p - 95) / (13p - 1)
13p - 1 = 2 * (20p - 95)
13p - 1 = 40p - 190
190 - 1 = 40p - 13p
189 = 27p
p = 7
solving for UY
= 13p - 1
= 13 * 7 - 1
= 90
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a marble bag contains three red marbles and four gray marbles six white marbles and five black marbles what is the probability of randomly drawing a red marble and then a gray marble if the first marbel is replaced
Answer:
1/27
Step-by-step explanation:
do good!
(m² - 7m - 11) ÷ (m-8)
By diving polynomials
Angie puts 1/3 of a gallon of gas in her lawn mower. She can mow the lawn 4 times before
she needs to refill it How many gallons of gas does it take to mow the lawn once? How
many times can she mow the lawn with one gallon of gas?
( please explain how u got your answer )
Answer:
1/12 gallon per mowing12 mowings per gallonStep-by-step explanation:
Given that Angie can mow her lawn 4 times using 1/3 gallon of gas, you want to know how much gas is required for each mowing, and how many times Angie can mow on one gallon of gas.
Gallons per mowingTo find the number of gallons required for each mowing of the lawn, divide the number of gallons by the number of mowings:
(1/3 gal)/(4 mowings) = 1/(3·4) gal/mowing = 1/12 gal/mowing
It takes 1/12 gallon to mow the lawn once.
Mowings per gallonThe reciprocal of this value has the reciprocal units.
1/(1/12 gal/mowing) = 12 mowings/gal
Angie can mow the lawn 12 times with one gallon of gas.
__
Additional comment
It often proves useful to keep the units with the numbers when working rate problems. This can eliminate a lot of mistakes. The units are treated as you would treat a variable.
The diagram shows a circle inside a square.
16 cm
Work out the area of the circle.
Answer:
200.96cm^2
Step-by-step explanation:
the circle's diameter is 16cm --> the radius is 8cm
the area of the circle is 8^2 x 3.14 = 200.96 cm^2