Given two similar cylinders with a height ratio of 2:3 what is the ratio of their volumes?

Answer:

q = 55

Step-by-step explanation:

      [tex]p\ \alpha\ \frac{1}q} \\\\p = k \times \frac{1}{q}\\\\22 = k \times \frac{1}{5}\\\\22 \times 5 = k\\\\k = 110\\\\[/tex]

Find q when p = 2

   [tex]p = k \times \frac{1}{q}\\\\2 = 110 \times \frac{1}{q}\\\\2 \times q = 110\\\\q = \frac{110}{2}\\\\q = 55[/tex]

Answer:

[tex]y=1[/tex]

Step-by-step explanation:

Given:

[tex]6=2(y+2)[/tex]

Distribute the parenthesis

[tex]6=2y+4[/tex]

Subtract both sides by 4

[tex]2=2y[/tex]

Divide both sides by 2 to get [tex]y[/tex] alone

[tex]1=y[/tex]

Hope this is helpful

Answer:

C. 64, 32, 16

Step-by-step explanation:

This geometric sequence is made by dividing the numbers by 2:

512 ÷ 2 = 256

256 ÷ 2 = 128

Hence, the next term will be

128 ÷ 2 = 64

64 ÷ 2 = 32

32 ÷ 2 = 16

Therefore, the correct answer is C.

The next 3 terms in the given geometric sequence are 64, 32, and 16, respectively. The correct option is C.

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.

The given series is a geometric sequence, therefore, the common ratio between any two terms will be the same. Therefore, we can write, the ratio as,

Common ratio, r = a₂ / a₁ = 256 / 512 = 1/2

Now, the nth term of the given sequence can be defined as,

aₙ = a₁ × r⁽ⁿ⁻¹⁾

   = 512 × (1/2)⁽ⁿ⁻¹⁾

Therefore, the next term of the given geometric progression will be,

a₄ = 512 × (1/2)³ = 64

a₅ = 512 × (1/2)⁴ = 32

a⁶ = 512 × (1/2)⁵ = 16

Hence, the next 3 terms in the given geometric sequence are 64, 32, and 16, respectively.

Learn more about Geometrical Series here:

https://brainly.com/question/4617980

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Answer:

2.208 kg

Step-by-step explanation:

Total mass of glass marble

= 18.5×48

= 888 g

Total mass of steel marble

= 66×20

= 1320 g

Total mass of 68 marble including steel 20 and glass 48

= 888 + 1320

= 2208 g

In kilograms 2208

= 2.208 kg

Please mark as brainliest answer

Answer:

D: (x^2 + 3x + 9) (x^2 - 3x + 9)

-

G: (x^2 + 3x + 5) (x^2 - 3x + 5)

Answer:

[tex]d) \: \: ( {x}^{2} + 3x + 9)( {x}^{2} - 3x + 9)[/tex]

[tex]g) \: \: ( {x}^{2} + 2x + 5)( {x}^{2} - 2x + 5)[/tex]

Step-by-step explanation:

Hope it is helpful....

√9 is rational and √3 irrational number

Answer:

Step-by-step explanation:

Line segment          Point         Point         Distance    Proof

AB                           A(-3 , 4)      B(2,4)          5                2 - (-3) = 2 +3 = 5

BC                          B(2,4)          C(5,4)          3                 5 - 2 = 3

CD                          C(5,4)          D(5,-1)          5              4 -(-1) = 4 +1 = 5

DE                           D(5 , -1)       E(5,-3)          2             -1 -(-3) = -1 +3 = 2

EF                           E(5, -3)        F(-5,-3)         10            5 - (-5) = 5+5 = 10

Answer:

42 in binary number is 101010.

Answer:

k =0.156

Step-by-step explanation:

According to the Question,

We Have To apply Just some Basic Properties of log here.

[tex]log_{3}4 = log_{1/27}k\\\frac{log_{}4 }{log_{}3 } = \frac{log_{}k }{log_{}1/27 }\\\\\frac{log_{}4 }{log_{}3 } = \frac{log_{}k }{log_{}1-log_{27} }\\\\frac{log_{}4 }{log_{}3 } = \frac{log_{}k }{0-3*0.4771} }\\\[/tex]

0.620/0.4771 = ㏒k / -1.4313

㏒k = -1.86

k = anti㏒(-1.86)

k =0.156

I have attached some answers in the photos below hope you find them useful

Answer:

0 and 1

Step-by-step explanation:

Given :

[tex]y= 2x-3\\y=2x^{2} -3[/tex]

Now equate the both equation :

[tex]2x-3=2x^{2} -3[/tex]

2x=2[tex]x^{2}[/tex]

x-[tex]x^{2}[/tex]=0

x(1-x)=0

x=0

1-x=0

x=1

Therefore, x=0,1

Answer:

11

Step-by-step explanation:

mode is the number that is most frequent

11

Answer:

11

Step-by-step explanation:

Mode means the highest repeated observation in the data set,

Therefore Mode = 11, as 11 has repeated 3 times, the most in the data set

Answer:

[tex]V=36.63cm^3[/tex]

Step-by-step explanation:

Volume formula for rectangular prism is [tex]V=lwh[/tex]

Volume = length * width * height

[tex]V=4.5*2.2*3.7[/tex]

[tex]V=36.63[/tex]

Hope this helps

Answer:

1/4

Step-by-step explanation:

because there 25% change

Answer:

for the blue its 1/4 or 2/8 and not likely.

For the yellow one it is 7/8 and likely.

Answer: 20 nickels to make $2.00

Step-by-step explanation:

Answer:

5x = 200

x=40

Step-by-step explanation:

Answer:

1. Terminating

2. 60

3. I don't know

Step-by-step explanation:

Answer:

option D

Step-by-step explanation:

take 39 degree as reference angle

using cos rule

cos 39 = adjacent / hypotenuse

0.77 = x / 7

x = 7*0.77

x = 5.39

x = 5.4

Answer:

D. 5.4

Step-by-step explanation:

Using trigonometric ratio

cos 39 = x/7

cross multiple

x = cos39(7)

x=5.4

Step-by-step explanation:

-6y + y=-30

-5y = -30

y=6

x=-6 ×6= -36

Answer:

multiplying a fraction by a repeating decimal

Step-by-step explanation:

any fraction is rational

any repeating decimal is rational

therefore, product of the two would be rational

Answer:

option A

Step-by-step explanation:

22 : 15 + 10hours = 8 : 15

                              8 : 15 + 35 minutes = 8 : 50

Therefore the difference = 10 hours 35 minutes

Answer:

a. P(x = 5) = 0.24

b. P(x ≥ 6) = 0.43

c. P(x < 4)= 0.14

Step-by-step explanation:

According to the Question,

⇒We use Binomial Probability Formula

[tex]P(X = x ) = \frac{n!}{x!((n-x)! } * p^{x} * (1-p)^{n-x}[/tex]

Where, p=0.52 & n=10

a. The probability that the number of U.S. adults who have very little confidence in newspapers is ​exactly​ five . So, (x=5)

Thus, [tex]P(X = 5 ) = \frac{10!}{5!((10-5)! } * 0.52^{5} * (1-0.52)^{10-5}[/tex]

On Solving Above Equation we get,

P(5)=0.2441 ≈ 0.24

b. The probability that the number of U.S. adults who have very little confidence in newspapers is at least 6 . So, (x≥6)

Then,

P(x≥6) = P(6)+P(7)+P(8)+P(9)+P(10)

P(x≥6) = [tex]\frac{10!}{6!((10-6)! } * 0.52^{6} * (1-0.52)^{10-6}[/tex] + [tex]\frac{10!}{7!((10-7)! } * 0.52^{7} * (1-0.52)^{10-7}[/tex] +[tex]\frac{10!}{8!((10-8)! } * 0.52^{8} * (1-0.52)^{10-8}[/tex] + [tex]\frac{10!}{9!((10-9)! } * 0.52^{9} * (1-0.52)^{10-9}[/tex]+[tex]\frac{10!}{10!((10-10)! } * 0.52^{10} * (1-0.52)^{10-10}[/tex]

On solving above equation we get,

P(x≥6) =  0.4270 ≈ 0.43

c. The probability that the number of U.S. adults who have very little confidence in newspapers is less than 4 . So, (x<4)

Then,

P(x < 4)=P(3) + P(2)+P(1)+P(0)

P(x<4) = [tex]\frac{10!}{3!((10-3)! } * 0.52^{3} * (1-0.52)^{10-3}[/tex] + [tex]\frac{10!}{2!((10-2)! } * 0.52^{2} * (1-0.52)^{10-2}[/tex]+ [tex]\frac{10!}{1!((10-1)! } * 0.52^{1} * (1-0.52)^{10-1}[/tex] + [tex]\frac{10!}{0!((10-0)! } * 0.52^{0} * (1-0.52)^{10-0}[/tex]

On solving we get,

P(x < 4)= 0.1410 ≈ 0.14  

Answer:

the triangle was 2x scale (*2)

it was reflected across y=0

and translated x +2

Step-by-step explanation:

Answer:

x+8

Step-by-step explanation:

Simplify the numerator

list the factors of 16

16: 1, 2, 4, 8, 16

look for two factors that add up to the b value

in this case it is 18

by looking at the factors 2 and 8 add up 10

so you can rewrite the numerator as [tex]x^{2}+2x+8x+16[/tex]

Split the trinomial into two separate binomials each having one of the factors that add up to 10

So it should be [tex]x^{2} +2x and 8x+16[/tex]

Factor both binomials

you can factor an x from the first one

Then it is x(x+2)

Factor an 8 from the second one

8(x+2)

So it should be [tex]x(x+2) 8(x+2)[/tex]

This can rewritten as (x+8)(x+2)

So now you have [tex]\frac{(x+2)(x+8)}{x+2)}[/tex]

simplify it by canceling out the two (x+2)'s

this is because (x+2)/(x+2) is 1

Finally you get x+8

Answer:

9

Step-by-step explanation:

Question:

Minimum number of balls to ensure there is at least one ball of each colour marked with each number.

The quantity of distinct numbers are:

red: 4

Yellow 3

Blue 2

So the minimum number of balls to satisfy the given requirements is

4+3+2= 9

Time = distance / speed

Time = 450 miles / 65 miles per hour

Time = 6.9 hours

Answer:

[tex]a_{n}[/tex] = 6n + 1

Step-by-step explanation:

This is an arithmetic sequence with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 13 - 6 = 7 and d = 6 , then

[tex]a_{n}[/tex] = 7 + 6(n - 1) = 7 + 6n - 6 = 6n + 1

Answer:

the first few terms would be

7, 13, 19, 25, 31

nth term = 7 + 6(n+1)

nth term = 7+ 6n + 6

nth term = 6n + 13

Answer:

[tex]P(none) = 0.0859[/tex]

Step-by-step explanation:

Given

[tex]p =20\%[/tex] --- proportion of household that tuned to September

[tex]n =11[/tex] --- selected households

Required

[tex]P(none)[/tex]

Using the complement rule, the proportion that did not tune (q) is:

[tex]q= 1 - p[/tex]

[tex]q= 1 - 20\%[/tex]

[tex]q= 1 - 0.20[/tex]

[tex]q= 0.80[/tex]

So, the probability that none of the 11 tuned in is:

[tex]P(none) = q^{11}[/tex]

[tex]P(none) = 0.80^{11}[/tex]

[tex]P(none) = 0.0859[/tex]

Answer:

x = 9

Step-by-step explanation:

24x - 18 - 8x - 30 = 96

add or subtract like terms

16x - 48 = 96

shift - 48 to right hand side . when it goes to other side minus changes to plus

16x = 96 + 48

16x = 144

x = 144/16

x = 9

to prove that the value of x satisfy the given equation or not.

to prove that the value of x is 9 substitute 9 inplace of x and if it gives 96 then it satisfy

24x - 18 - 8x - 30 = 96

24*9 - 18 - 8*9 - 30 = 96

216 - 18 - 72 - 30 = 96

216 - 120 = 96

96 = 96

since both sides is equal to 96 it can be concluded that the value of x is 9.

Which value of “x” would satisfy the following equation 24x - 18 - 8x - 30 = 96?

24x - 18 - 8x - 30 = 96

First let's just add/subract the following terms.

16x - 48 = 96

Second.. shift the 48 to the right side. after that change the minus sign into plus sign.

16x = 48 + 96

16x = 44

x = 144/16

x = 9

Explanation:

So we begin to solve it!

24x - 18 - 8x - 30 = 96

24*9 - 18 - 8*9 - 30 = 96

216 - 18 - 72 - 30 = 96

216 - 120 = 96

Since that all both sides are equal to 96 it can be concluded that the value of x is 9.

#LearnwithBrainly

Answer:

about 3 years

Step-by-step explanation:

Using the compound interest formula;

A = P(1+r)^t

Given

Amount A == $2400

Principal P = $1200

rate = 24.77% = 0.2477

Substitute the given values

2400 = 1200(1+0.2477)^t

2400/1200 = (1+0.2477)^t

2 = (1+0.2477)^t

ln 2 = tln1.2477

t = ln2/ln1.2477

t = 3.13

Hence it will take about 3 years  until Brad owes the  credit card company $2,400