Prove or give a counterexample: Every positive integer can be expressed as the sum of three or fewer perfect squares. (A perfect square is an integer n for which there is an integer k with the property: n

Answer:

100 digits

Step-by-step explanation:

One trillion is 10¹², so it adds 12 zeros.

8000 adds 4 digits.

8 trillions add 8·12 = 96 zeros.

So in total you have 96+4 = 100 digits

This number would also be called 8 googol, since 1 googol is 10¹⁰⁰

9514 1404 393

Answer:

Step-by-step explanation:

The amount of cheese Mrs Mack needs is an odd number of eighths of a pound. So, she must buy an odd number of the 7/8 pound packages.

If she were to buy any 1/5 pound packages, she would have to buy a multiple of 5 of them so as to have an integral number of eighths. The only suitable multiple is 0.

If Mrs Mack buys 1 of the 7/8 pound packages, she cannot make up the difference with half-pound packages. She must buy 3 of the 7/8 pound packages, for a total of 2 5/8 pounds of American cheese. The remaining pound can be bought as 2 of the 1/2 pound packages.

To buy 3 5/8 pounds, Mrs Mack must purchase ...

  3 packages of American cheese (7/8 lb each)

  2 packages of Cheddar cheese (1/2 lb each)

Given:

An annual pass to a park costs $120.

To find:

The 200% of the full price using percent model.

Solution:

In the percent model,

100% = 1 box

It means 1 box represents park costs $120.

200% = 2 box

[tex]120+120=240[/tex]

It means 2 box represents park costs $240.

Therefore, 200% of the full price is $240.

Answer:

It is 1/4

Step-by-step explanation:

If you go from dot to dot on the line, starting with the first dot:

you go to the right 4 times and then up 1 to get to the next dot.

If you put that into a fraction it is [tex]\frac{rise}{run}[/tex] so going up (1) is ontop of going to the right (4), which is 1/4.

Answer:

[tex]\frac{256}{81q^{4} }[/tex]

Step-by-step explanation:

Answer:

518125161348

Step-by-step explanation:

                316

518125161032

-------------------------

518125161348

Answer:

b c and a

Step-by-step explanation:

Answer:

A, B, C

Step-by-step explanation:

Answer:

w = 9

x = 12

y = 5

z = 3

Step-by-step explanation:

The corresponding sides of similar polygons are proportional.

Therefore:

[tex] \frac{w}{3} = \frac{x}{4} = \frac{15}{y} = \frac{9}{z} = \frac{6}{2} [/tex]

Solve for each variable as follows:

✔️[tex] \frac{w}{3} = \frac{6}{2} [/tex]

Multiply both sides by 3

[tex] w = \frac{6}{2} \times 3 [/tex]

[tex] w = 3 \times 3 [/tex]

[tex] w = 9 [/tex]

✔️[tex] \frac{x}{4} = \frac{6}{2} [/tex]

Multiply both sides by 4

[tex] x = \frac{6}{2} \times 4 [/tex]

[tex] x = 3 \times 4 [/tex]

[tex] x = 12 [/tex]

✔️[tex] \frac{15}{y} = \frac{6}{2} [/tex]

Cross multiply

[tex] y \times 6 = 2 \times 15 [/tex]

[tex] 6y = 30 [/tex]

Divide both sides by 6

[tex] y = 5 [/tex]

✔️[tex] \frac{9}{z} = \frac{6}{2} [/tex]

Cross multiply

[tex] z \times 6 = 2 \times 9 [/tex]

[tex] 6z = 18 [/tex]

Divide both sides by 6

[tex] z = 3 [/tex]

Answer: t - 5d

Step-by-step explanation: Since you are buying 5 and they cost d dollars you would multiply 5 by d. Then since you have t dollars as a total you subtract 5d from t so you get t -5d.

Answer:21

Step-by-step explanation:

x=length

x(x-6)=315

x^2-6x=315

x^2-6x-315=0

(x-21)(x+15)

x=21, x=-15

x cannot be negative so the only answer is 21

Answer:

$180

Step-by-step explanation:

10+30+30+100+10=180

Answer:

13.5 feet

Step-by-step explanation:

Square root of 182 = 13.49

Answer:

he will make 170.80 that day

Step-by-step explanation:

12.20*1.75*8

Answer:

good question................

Answer:

The distance from Earth to Mars is 8×10¹¹ m.

Step-by-step explanation:

Given that,

The speed of light is 3×10⁸ m/s. The sun is approximately 230,000,000,000 m from Mars. If the sun is approximately 1.5 x 10¹¹ meters from Earth, what is the approximate distance from Earth to Mars.

The sun is approximately 2.3 × 10¹¹ m from Mars.

The sun is approximately 1.5 x 10¹¹ m from Earth.

The distance between from Earth to Mars is :

d = 2.3 × 10¹¹ m - 1.5 x 10¹¹ m

= 8×10¹¹ m

Hence, the distance from Earth to Mars is 8×10¹¹ m.

Answer:

The new price of the couch is $960

Step-by-step explanation:

Answer:

6 were late taht is a step to help you

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

Given that:

Irina measured the weight of her dog to be 13 pounds.

The greatest possible error that could have to occur will be the maximum error.

Let assume that the 13th value obtained was rounded between the range of 12.5 → 13.49 to 13 pounds

Then;

The greatest possible error that could have to occur = 13.0 - 12.5 pounds

The greatest possible error that could have to occur = 0.5 pounds

Answer:

0.5

Step-by-step explanation:

EDGE 2020 Unit Test

Answer:

The answer is 27

Step-by-step explanation:

You count how many lines it takes up and add them together

Answer:

9 cm explained to

Step-by-step explanation:

explained that

Answer: 7 units

Step-by-step explanation:

Just plot the numbers, then count the distance between them

Answer:

c) 4

Step-by-step explanation:

Area of a square is its length times its length, or length²

Square root of 16 is 4

Answer:

if you mean 206 divided by 6 than the answer will 34.3 (rounded)

Step-by-step explanation:

I used a calculator

Answer:

6x - 18

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define expression

(2x - 6) + 4(x - 3)

Step 2: Simplify

Answer:

right option

Step-by-step explanation:

Answer:

D. [tex] 4\frac{2}{5} [/tex]

Step-by-step explanation:

Area of fabrics = 2¾ square yards

Width of fabrics = ⅝ yard

Length of fabrics = x

Area = length * width

Therefore:

2¾ = ⅝*x

Change the mixed fraction to improper fraction

[tex] \frac{11}{4} = \frac{5x}{8} [/tex]

Cross multiply

[tex] 4*5x = 11*8 [/tex]

[tex] 20x = 88 [/tex]

Divide both sides by 20

[tex] \frac{20x}{20} = \frac{88}{20} [/tex]

[tex] x = \frac{22}{5} [/tex]

[tex] x = 4\frac{2}{5} [/tex]

[tex] length = 4\frac{2}{5} [/tex]