A sphere is inscribed in a cone with height 4 and base radius 3. What is the ratio of the volume of the sphere to the volume of the cone

Viewing the given triangle, the information given helped to determine side UY to be 90

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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Answer:

-2/5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(2-0)/(-4-1)

m=2/-5

m=-2/5

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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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.

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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

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...

Answer:

19.95 + .71 × x = 125.74

x = 141.053

x is the answer

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.

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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Answer:

Step-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.

To 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.

The 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.

Answer:

The answer is 5

Step-by-step explanation:

add all numbers up then divide by  how many numbers there are.

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

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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Answer:

x = 2

Step-by-step explanation:

5x - 18 = -8

    +18   +18

5x  =  10

5x/5  =  10/5

x = 2

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

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

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

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]

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

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:

Answer:

1/27

Step-by-step explanation:

do good!

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.