Suppose you write the set {1000, 1001, 1002,..., 2000} in base 10. Then you record this set in base 5 and find the number in the new set whose digits have the least sum. What is this number, written in decimal notation? This number is

Answers

Answer 1

Decimal notation is a way of expressing a number in base ten but with a decimal part. Therefore, from the given question;

The number required is 1500The number in decimal notation is 1500.0

Number bases is a method of expressing numbers in different notations with respect to the required base. When given numbers in base ten, it is required to divide it by the number base for conversion using long division method so as to convert it to any required base. So converting each element in the given set to base 5, we have:

{1000, 1001, 1002, 1003, 1004,......, 2000}

So that:

i. 1000 converted to base 5, we have:

5 1000

5 200 r 0

5 40 r 0

5 08 r 0

5 01 r 3

00 r 1

⇒ [tex]13000_{5}[/tex]

ii. 1001 converted to base 5, we have:

5 1001

5 200 r 1

5 40 r 0

5 08 r 0

5 01 r 3

00 r 1

⇒ [tex]13001_{5}[/tex]

iii. 1002 converted to base 5, we have:

5 1002

5 200 r 2

5 40 r 0

5 08 r 0

5 01 r 3

00 r 1

⇒ [tex]13002_{5}[/tex]

So then, the set in base 5 is:

{13000, 13001, 13002, 13003, 13004,......, 31000}

To determine the number whose digits have the least sum;

a. 13000 = 1 + 3 + 0 + 0 + 0 = 4

b. 13001 = 1 + 3 + 0 + 0 + 1 = 5

c. 13002 = 1 + 3 + 0 + 0 + 2 = 6

d. 13003 = 1 + 3 + 0 + 0 + 3 = 7

e. 13004 = 1 + 3 + 0 + 0 + 4 = 8

. . . . . . .

z. 31000 = 3 + 1 + 0 + 0 + 0 = 4

Thus it would be observed that in base five, 1000, 1500 and 2000 digits gave the least sum of 4, so then:

[tex]\frac{1000+1500+2000}{3}[/tex] = 1500

The number is 1500The number in decimal notation is 1500.0

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Answer 2

Answer:

I think its 1500

Step-by-step explanation:

1500

Related Questions

7. Your class wants to raise more than $350 for the Freshman party and you choose to sell candy and cookies to accomplish this task. You earn $6 on
each basket of candy, b, and $3 on each box of cookies, c, that you sell.
a Write a linear inequality that represents this situation
3b + 6c > 350
b. If the number of box of cookies sold is 78, at least how many baskets of candy will you need to sell to reach your goal?

Answers

Answer:

Step-by-step explanation:

first, find out how much money you already made:

78 x 3 = 234

then, find out how much more you need to make:

350-234=116

divide the price of candy baskets by the amount of money left y out need to make:

116/6=19.3

round becauee you can’t sell .3 of a basket

19.3 rounds to 20

Question in on picture attached

Answers

Answer: 12

Step-by-step explanation:

180 = 76 + (3x+3) + (6x-7) = 12

A group of friends were working on a student film that had a budget of $1200. They use 63% of their budget on equipment. How much money did they spend on equipment?

Answers

Answer:

convert 6 7/8 to an improper fraction: 55/8, which equals 110/16

P = 2(163/16) · 2(110/16)

P = 326/16 + 220/16

P = 546/16

P = 34 1/8 inches

8x^2x WHATS THE STANDARD FORM WHATS THE COEFFICIENT QUICKLY PLSS

Answers

8x3 answer correct good.

5. Write the following numbers in order from least to greatest. 1.23; 1.2; 2.31; 3.2

Answers

1.2, 1.23 , 2.31, 3.2

Answer the following problem using the SOLVE Method Math Club members are selling Math club members are selling Pi Day T-shirts for $7.50 each. The goal is to raise $500 by Friday. The figure below shows how much they have raised by Wednesday. What is the minimum number of T-shirts they must still sell in order to reach their goal? Explain your reasoning.

Answers

The minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts

Let x represent the number of Pi Day T-shirts sold.

They are selling Pi Day T-shirts for $7.50 each, So to raise $500:

7.5x > 500

Dividing through by 7.5:

7.5x / 7.5 > 500 / 7.5

x > 66.7

Hence, the minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts

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The DEGREE of algebraic expression 2xy + 7 is

A) 2
B) 3
C) 7
D) xy

TY!!

Answers

I think the answer is A)2

Each diagram shows △ABC and △DEF on the coordinate plane, with ∠A ≅ ∠E,
and ∠C ≅ ∠F. Identify whether the two triangles are congruent. If they are not
congruent, explain how you know. If they are congruent, find the length of each
side of each triangle.

Please help a brother out, I need this for a test.

Answers

Answer:

1. -9 because -9x6= -54, -10 because 5 x -10= -50, and x=1 because -2 x 1= -2

Step-by-step explanation:

Answer:

1. = −9

2. = −10

3. = 1

Step-by-step explanation:

Combine the like terms to create an equivalent expression:
-12-6p-(-2)

Answers

Answer:-2(5+3p)

Step-by-step explanation:

-2(5+3p) trust me this is really simple if you just think about it

For the equation y = -x +5, find y when x = -2

Answers

Answer:

y = 7

Step-by-step explanation:

y = -x + 5

when x = -2

y = - (-2) + 5

Double negative is positive

y = 2 + 5

y = 7

Answer:

y=7

Step-by-step explanation:

When x=-2,

y=-x+5

=-(-2)+5

=2+5

Your Fourthknight team is holding a fundraiser. The list shows all expenses for the fundraiser.

- A tablet that costs $250

- Soccer tickets that cost $150

- Gift cards totaling $425

- The cost of catering is $875

The members of the team will sell tickets at the fundraiser. The ticket cost is set so that 68 tickets will pay for the cost of prizes and food.
How much does each ticket cost?

Model the profit for the fundraiser using an equation:

Answers

Answer:

Step-by-step explanation:

Because when you add all the cost and divide by the amount of tickets you get 25

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Factor completely given the following factors: (x+5) and (x+3)

There should be 6 factors (2 given, 2 binomials, and 2 trinomials.)
show steps

Answers

Answer:

(x+3)(x+5)(x-2)(x-1)(x^2+2x+4)(x^2+x+1) where the given one is bolded the 2 binomials is italicized and the 2 trinomials is underlined

Step-by-step explanation:

How to find left and right inverse of a 3x2 matrix.

Answers

Let A be a 3×2 matrix, L its left inverse, and R its right inverse. L and R are then matrices such that LA = I₂ (the 2×2 identity matrix) and AR = I₃ (the 3×3 identity matrix). Clearly L must be 2×3 and R must be 3×2 in order for the matrix products to be defined.

To find L and R, we start by introducing a square matrix on the the left sides of either equation above. In particular, we uniformly multiply both sides by the transpose of A, then solve for the inverse.

For the left inverse, we have

[tex]LA=I[/tex]

[tex](LA)A^\top = IA^\top[/tex]

[tex]L\left(AA^\top\right) = A^\top[/tex]

[tex]\left(L\left(AA^\top\right)\right)\left(AA^\top\right)^{-1} = A^\top \left(AA^\top\right)^{-1}[/tex]

[tex]L\left(\left(AA^\top\right)\left(AA^\top\right)^{-1}\right) = A^\top \left(AA^\top\right)^{-1}[/tex]

[tex]LI = A^\top \left(AA^\top\right)^{-1}[/tex]

[tex]L = A^\top \left(AA^\top\right)^{-1}[/tex]

We do the same thing for the right inverse, but take care with how we multiply both sides of AR = I₃.

[tex]AR=I[/tex]

[tex]A^\top(AR)=A^\top I[/tex]

[tex]\left(A^\top A\right)R = A^\top[/tex]

[tex]\left(A^\top A\right)^{-1} \left(\left(A^\top A\right)R\right) = \left(A^\top A\right)^{-1} A^\top[/tex]

[tex]\left(\left(A^\top A\right)^{-1} \left(A^\top A\right)\right) R = \left(A^\top A\right)^{-1} A^\top[/tex]

[tex]IR = \left(A^\top A\right)^{-1} A^\top[/tex]

[tex]R = \left(A^\top A\right)^{-1} A^\top[/tex]

Which equation gives the line shown on the graph?

Answers

Answer:

[tex]y=\frac{1}{2} x+4[/tex]

Step-by-step explanation:

so the last option

hope this helps!

Zane calculated the missing side length of one of these triangles using the pythagorean theorem. Which triangle is it? a b c d.

Answers

Answer:

Step-by-step explanation:

Please solve correctly :)

Part C only!!!

Answers

Answer:

So, the average rate of change is 0.475.

Step-by-step explanation:

If n = 2, then f(n) = 8.82. If n = 6, then f(n) ≈ 10.72. Now, 10.72 – 8.82/ 6 – 2 = 1.9/ 4 = 0.475.

Is this a function?

Answers

Answer:

No, because if you do the vertical line test, the line will hit that two times, Therefore it is not a function.

Step-by-step explanation:

Can someone please help me? Thank you!

Answers

Answer:

Step-by-step explanation:

1) [tex]5^{\frac{2}{3} }[/tex] is in exponential form.

Now, radical form is [tex]\sqrt[3]{5^{2} }[/tex]

2) [tex]5^{\frac{1}{2} }[/tex] is in exponential form.

Radical form is [tex]\sqrt{5}[/tex]

3) [tex]3^{\frac{2}{5} }[/tex] is in exponential form.

Radical form is [tex]\sqrt[5]{3^{2} }[/tex]

4) [tex]3^{\frac{5}{2} }[/tex] is in exponential form.

Radical form is [tex]\sqrt{3^{5} }[/tex]

If you need to ask any question, please let me know.

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