One thousand families were surveyed to
determine the distribution of families by size. The
results follow.
Family Size 2
3
4
5 6 7 8
Frequency
350
200 245 125
66
10
To the nearest percent, the probability that a given
family has 3 people is [? ]%.

Answer:

It is a geometric sequence and the common scale factor is [tex]\frac{2}{3}[/tex].

Step-by-step explanation:

In an arithmetic sequence, the difference between consecutive terms is always the same.

[tex]a_n=a_1+(n-1)d[/tex]

where aₙ is the nth term, a₁ is the first term, n is the index, and d is the common difference.

In a geometric sequence, each consecutive term was multiplied by some factor over the last.

[tex]a_n=ax^n^-^1[/tex]

where aₙ is the nth term, n is the index, and x is the scale factor.

In the given sequence, there is no common difference so it is not an arithmetic sequence. There is, however, a common scale factor applied to each consecutive term. Each term is multiplied by [tex]\frac{2}{3}[/tex] over the last.

The formula for this sequence would be:

[tex]a_n=a\frac{2}{3} ^{n-1}[/tex]

Answer:

r = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

If the sequence is geometric then there will be a common ratio r between consecutive terms , that is

r = a₂ ÷ a₁ = a₃ ÷ a₂ = a₄ ÷ a₃

Then

a₂ ÷ a₁ = [tex]\frac{2}{9}[/tex] ÷ [tex]\frac{1}{3}[/tex] = [tex]\frac{2}{9}[/tex] × 3 = [tex]\frac{2}{3}[/tex]

a₃ ÷ a₂ = [tex]\frac{4}{27}[/tex] ÷ [tex]\frac{2}{9}[/tex] = [tex]\frac{4}{27}[/tex] × [tex]\frac{9}{2}[/tex] = [tex]\frac{2}{3}[/tex]

a₄ ÷ a₃ = [tex]\frac{8}{81}[/tex] ÷ [tex]\frac{4}{27}[/tex] = [tex]\frac{8}{81}[/tex] × [tex]\frac{27}{4}[/tex] = [tex]\frac{2}{3}[/tex]

Then sequence is geometric with common ratio r = [tex]\frac{2}{3}[/tex]

Answer:

4-5 ounces or 113-142 grams

Step-by-step explanation:

Answer:

C:6

Step-by-step explanation:

Answer:

10x+5.................

Answer:

Step-by-step explanation:

For scale factor k and center of dilation (p, q), the transformation is ...

  (x, y) ⇒ (kx +(1-k)p, ky +(1-k)q)

For k=1/4 and (p, q) = (-3, 3), the coordinates are transformed to ...

  (x, y) ⇒ (1/4x -9/4, 1/4y +9/4)

Then the preimage points are dilated to ...

  A(1, -1) ⇒ A'(1/4 -9/4, -1/4 +9/4) = A'(-2, 2)

  B(1, -5) ⇒ B'(1/4 -9/4, -5/4 +9/4) = B'(-2, 1)

  C(5, -5) ⇒ C'(5/4 -9/4, -5/4 +9/4) = C'(-1, 1)

Refer to the attachments.

Answer:

b(3b−10)(b−1)

Step-by-step explanation:

b(3b−10)(b−1)

Answer:

Divide 3 on both sides to get x < 1

Step-by-step explanation:

Hope this helps :)

Answer:

D. 3x^2-10x+8

Step-by-step explanation:

[tex] \: \: \: \: \: [/tex]

hope it helps

refer to the attachment

[tex] \: \: \: \: \: [/tex]

Answer:

If there are 2 quarters for every 3 nickels,

then there are [tex]45*\frac{2}{3} =30[/tex] quarters.

If there are 2 dimes for every quarter,

then there are [tex]30*2=60[/tex] dimes.

If the number of pennies and nickels together are equal to the number of dimes, then there are [tex]60-45=15[/tex] pennies.

Answer:

In chemistry, a dehydration reaction, also known as Zimmer's Hydrogenesis, is a chemical reaction that involves the loss of water from the reacting molecule or ion. It is the most common type of condensation reaction. Dehydration reactions are common processes, the reverse of a hydration reaction.

Answer:

In chemistry, a dehydration reaction, also known as Zimmer's Hydrogenesis, is a chemical reaction that involves the loss of water from the reacting molecule or ion. It is the most common type of condensation reaction. Dehydration reactions are common processes, the reverse of a hydration reaction.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Thx for the points:) have a nice day

Answer:

x=1

Step-by-step explanation:

Answer:

40, 60, 80

Step-by-step explanation:

angles are 40, 3x, 4x

40+ 3x + 4x = 180

40 + 7x = 180

7x = 180 - 40

7x = 140

x = 20

so the angles are 40, 60, 80

Answer:

23.6 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

I’m doing this too right now and can’t figure it out

The answer is A. Sentence 1

Answer:

For the first row, it's 6, 12, 18, 24, 30

Second row: 4, 8, 12, 16, 20

Step-by-step explanation:

You're just counting by multiples of 6 for the first row and 4 for the second row. Denominator means the number underneath the fraction line

Answer:

y = x + 8

Step-by-step explanation:

Let's build the equation:

There are 8 entries to start

y = 8

Adding 1 entry every day

y = x + 8

Answer:

B.) 30 miles in 5 hours

Step-by-step explanation:

If you were to simplify all the ratios:

A) 12:3 divided by 3/3 is 4:1

B) 30:5 divided by 5/5 is 6:1

C) 35:5 divided by 5/5 is 7:1

D) 45:9 divided by 9/9 is 5:1

B is 6:1.

Answer:

the angle 3x is 42 degrees, the angle 12x-30=138 degrees

Step-by-step explanation:

first, write an equation to represent the problem.

3x+(12x-30)=180

3x+12x=210

15x=210

x=14

Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day.

We can solve this problem in 2 steps, one being Theory and the second being Solving. I'll start off with Theory.

Theory

There are many theorems in Geometry, from the very simple to the very complex, you also have got the standard information that is usually known by many people.

In this case, we can see that it is a Supplementary Angle. We know that Supplementary Angles add up to 180 degrees and Complementary Angles add up to 90 degrees.

Now that we know that we can solve the problem.

Solving

So, we know that both angles have to add up to 180 degrees because the line is a straight line and that means that the angles on it must be 180 degrees.

Since we know this, we can state the following equation:

[tex]3x+12x-30=180[/tex]

We can say this due to the rule of Supplementary angles adding up to 180 degrees.

We can now use Algebra to simplify the equation:

[tex]3x+12x-30=180\\3x+12x=210\\15x=210\\x=14[/tex]

After doing algebra we can see that x s equal to 14 degrees, we can check our answers by putting that back into the equation.

[tex]3(14)+12(14)-30=180?\\42+168-30=180?\\210-30=180?\\180=180[/tex]

We have proven that our answer is correct, therefore the answer is [tex]x=14[/tex] degrees.

Cheers!

Answer:  81ײ=27×     x = 6

Answer:

161 Remainder 4

Step-by-step explanation:

trust me on this

Answer:

_

161.2 BUT if with remainder it is 161 with a remainder of 4

Step-by-step explanation:

By the way the 2 is a repeating number so make sure to add that line at the top.

Answer:

its got 6

Step-by-step explanation:

I REALLY DONT KNOW

Answer:

Step-by-step explanation:

Let t be the unit cost of the tomatoes:  e. g., t = $1.25/lb.

If Keith spent $8 on tomatoes, the number he bought would then be

   $8

------------- = 6.4 lb of tomatoes

$1.25/lb

Of course he couldn't buy 0.4 tomato, but this method of calculating how many tomatoes he could buy theoreticallyl is correct.

The general formula would be

   $8

------------   and the end result would be the number of pounds Keith could

  $t / lb                               buy for $8.

Step-by-step explanation:

two equations if you want an inequality

y = -3x + 60

3x <= 60

graph it and you get x = 20 which is your answer

Answer:

Below.

Step-by-step explanation:

1/3 is equivalent to 4 oranges so number of oranges = 3 * 4 = 12.

In the same way there are 7 * 4 = 28 grapefruit.

Total pieces of fruit = 12 + 28

= 40.

[tex]\\ \sf\longmapsto x-5/3=1[/tex]

[tex]\\ \sf\longmapsto x=1+5/3[/tex]

[tex]\\ \sf\longmapsto x=3+5/3[/tex]

[tex]\\ \sf\longmapsto x=8/3[/tex]

Done

[tex]\sf \longmapsto \: x- \dfrac{5}{3} =1[/tex]

[tex]\sf \longmapsto \: x + \dfrac{ - 5}{ 3} = 1[/tex]

[tex]\sf \longmapsto x + \dfrac{ - 5}{3} + \dfrac{5}{3} = 1 + \dfrac{5}{3} [/tex]

[tex]\sf \longmapsto \: x = \dfrac{8}{3} [/tex]

[tex] \boxed{\sf { \red{ x = \dfrac{8}{3}}} }[/tex]

Answer:

the slope is

2/3x+2

Hope This Helps!!!