"The diameter of Pluto is 6/17 the diameter of Mars. Mars has 17/300 the diameter of Saturn. What fraction of the diameter of Saturn is the diameter of Pluto?"

Final answer:

The rule for the function with the given points is f(x) = x^2 + 2/19, as derived from observing the relationship between x-values and their corresponding y-values where the y-values increase by the square of the x-value with a constant fractional part of 2/19.

Explanation:

To find the rule for the function represented by the set of points given, we need to look for a pattern in the y-values relating to the x-values. The provided points are (0,2/19), (1,1 2/19), (2,4 2/19), (3, 9 2/19), (4, 16 2/19), and (5, 25 2/19). Observing the differences between the y-values, it appears that the fractional part remains constant at 2/19, whereas the whole number part increases by the square of the x-value. Therefore, we can express the function rule as f(x) = x2 + 2/19.

Let's verify this by substituting the x-values from the points into our proposed rule:

As we can see, the values match perfectly, confirming that the rule of the function is indeed f(x) = x2 + 2/19.

The number square root of 220 is greater than that of 14 3/4.

Given are two numbers.

The square root of 220 and 14 3/4.

We have to find which number is greater.

We know that :

14 3/4 = 14 + 3/4 = 14.75

Now,

14² = 196

15² = 225

So the number 220 lies between 196 and 225.

So √220 lies between 14 and 15.

Since 220 is closest to 225 which is the square of 15, the square root os 220 is more close to 15.

√220 ≈ 14.8

Hence √220 is greater.

Learn more about Square Roots here :

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we have

[tex]y\leq 2x+1[/tex] ------> inequality A

The solution of the inequality A is the shaded area below the solid red line

see the attached figure N [tex]1[/tex]    

[tex]y>-2x-3[/tex] ------> inequality B

The solution of the inequality B is the shaded area above the dotted blue line

see the attached figure N [tex]2[/tex]

therefore

The solution of the system of inequalities is the shaded area between the solid red line and the dotted blue line

see the attached figure N [tex]3[/tex]

therefore

the answer in the attached figure N [tex]3[/tex]

Answer:

2300

Step-by-step explanation:

Suppose that you have a stack of pennies. If you want to know without counting whether there is an odd or even number of pennies, then you have to split them into two parts, for example,  placing one coin left and one coin  right.

If the number of pennies is even, then no coins will left, if the number is odd, then one coin will be extra.

Solve for b, i.e separate b in one side and the other terms in the other side

A = ah + bh

A - ah = bh

(A - ah) / h = b

[tex]b= \frac{A-ah}{h} [/tex]

I hope that helps!

area of a square - S^2, where S is the length of a side

 to find S when you know the area, take the square root

 so S = sqrt(8)

S = 2.828

rounded to nearest hundredth = 2.83 inches

List A. –5, –2.1, 0.3, 3.1, is ordered from least to greatest.

To determine which list is ordered from least to greatest, we need to compare the numerical values in each list and arrange them in ascending order. Here's a step-by-step explanation:

List A is properly ordered from least to greatest:

Therefore, the correct answer is: A

-1/4 x 2/7

 multiply the 2 top numbers and then multiply the 2 bottom numbers

1*2 = 2+4*7 =28

 so answer is -2/28 which can reduce to - 1/14

Answer:

B.204 square inches

C.2016 cents

Step-by-step explanation:

We are given that Jared sells square frames of various sizes made of wood .To find the area of a frame ,Jared uses the formula

[tex]A=s^2-(s-2w)^2[/tex]

Where s=Length of a side of the frame

w=Width of the frame

B.We are given that length of each side=s=20 inches

Width of frame=w=3 inches

Substitute the values in the above given   formula

Then, we get

A=[tex](20)^2-(20-2\times 3)^2[/tex]

[tex]A=400-(20-6)^2[/tex]

[tex]A=400-196=204 [/tex]square inches

Hence, area of frame=204 square inches

C.We are given that

Cost of 1 square inch=18 cents

Length of each side of frame=s=16 inches

Width of frame=w=2 inches

Substitute the values in the given above formula

Then ,we get [tex]A=(16)^2-(16-2\times 2)^2[/tex]

[tex]A=256-(12)^2[/tex]

[tex]A=256-144=112[/tex] square inches

Cost of 112 square inches=[tex]112\times18[/tex]=2016 cents

Hence, he will charge for a frame =2016 cents

Answer: Each dimension would be 21.1875 inches and 2.375 inches respectively.

Step-by-step explanation:

Since we have given that

Width of a surfboard = [tex]21\dfrac{3}{16}\ inches[/tex]

Thickness of a surfboard = [tex]2\dfrac{3}{8}\ inches[/tex]

We need to rewrite each dimension as a decimal.

We first write it in improper fraction:

Width becomes

[tex]21\dfrac{3}{16}\\\\=\dfrac{339}{16}\ inches[/tex]

Thickness becomes

[tex]2\dfrac{3}{8}\\\\=\dfrac{19}{8}\ inches[/tex]

Now, we change it into decimal form:

[tex]\dfrac{339}{16}=21.1875\ inches\\\\and\\\\\dfrac{19}{8}=2.375\ inches[/tex]

Hence, each dimension would be 21.1875 inches and 2.375 inches respectively.

It will take 36 minutes for an object to travel 5 1/5 miles at a steady speed of 8 2/3 mph.

To find out how long it will take an object traveling at a steady speed of 8 2/3 mph to travel 5 1/5 miles, you can use the formula

time = distance / speed.

First, convert the mixed numbers to improper fractions:

Speed: 8 2/3 mph = (8 × 3 + 2) / 3 = 26/3 mph

Distance: 5 1/5 miles = (5 × 5 + 1) / 5 = 26/5 miles

Next, calculate the time:

Time = Distance / Speed

= (26/5) miles / (26/3) mph

= (26/5) × (3/26) hours

= 3/5 hours

To convert hours into minutes, multiply by 60:

= 3/5 hours × 60 minutes/hour

= 36 minutes