Find an integer that leaves a remainder of 2 when divided by either 3 or 5, but that is divisible by 4.

Answers

Answer 1

Answer: We want an integer $x$ such that

$x\equiv\begin{cases}2&\pmod3\n0&\pmod4\n2&\pmod5\end{cases}$

Note that the moduli are all relatively prime, so we can use the Chinese remainder theorem right away. As a first step, let's suppose

$x=4\cdot5\cdot2+3\cdot5\cdot0+3\cdot4\cdot2$

Taken modulo 3, the last two terms immediately vanish, and $4\cdot5\cdot2=40\equiv1\pmod3$ . We want a remainder of 2, so we just multiply this term by 2.

$x=4\cdot5\cdot2^2+3\cdot5\cdot0+3\cdot4\cdot2$

Next, taken modulo 4, all terms vanish, so we're good here.
Then, taken modulo 5, the first two terms vanish and we're left with $3\cdot4\cdot2\equiv24\equiv4\pmod5$ . We want a remainder of 2. To rectify this, we can first multiply this term by the inverse of 4 modulo 5, then multiply again by 2. This guarantees that

$3\cdot(4\cdot4^(-1))\cdot2^2\equiv2\pmod5$

The inverse of 4 modulo 5 is 4, since $4^2\equiv16\equiv1\pmod5$ , so we end up with

$x=4\cdot5\cdot2^2+3\cdot5\cdot0+3\cdot4^2\cdot2^2=272$

You can confirm for yourself that 272 satisfies the desired conditions. The CRT says that any integer of the form

$272\pmod{3\cdot4\cdot5}\equiv32\pmod60$

will work, i.e. $32+60n$ where $n\in\mathbb Z$ , and in particular 32 is the smallest positive solution.

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Forty-five CEO’s from the electronics industry were randomly sampled and a 99 % % confidence interval for the average salary of all electronics CEO’s was constructed. The interval was $101,866<μ<$115,016 $101,866<μ<$115,016 To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. What will result in a reduced interval width? Select one: a. Any of these methods will result in a reduced interval width. b. Keep the sample size the same and decrease the confidence level. c. Keep the sample size the same and increase the confidence level. d. Decrease the sample size and keep the same confidence level.
6. Find the value of the expression.40 = 8 x 9

Renee has a triangular garden with an area of 24 square feet. Which drawing shows Renee's garden?3 ft.
6 ft.
6
ft.

Answers

the third option is the answer

Answer:

3 ft

Step-by-step explanation:

A small hard drive measured 0.7553 centimeters across round to the nearest tenth

Answers

Answer:

0.8

Step-by-step explanation:

7 is in the tenth place since there is a 5 in the hundreds we round up to 8.

hope this helped =3

If I have 5 plates and give 2 how many do I have

Answers

Answer:

Step-by-step explanation:

if you have 5 plates and you subtract 2 then you have 3 plates left

5-2=3

Answer:

Step-by-step explanation:

Use the formula for compound interest to find A.A = P (1+r)^n
P = $20000,r = 0.13, and n = 2 years
At the end of 2 years A is ____

Answers

easy peasy
A=20,000(1+0.13)^2
A=20,000(1.13)^2
A=20,000(1.2769)
A=25538

A is $25,538

Please help me with my math!!!!!!!!!

Answers

12.8 km per hour

51.2 km in 4 hours

PLEASE ANSWER ILL GIVE YOU BRAINLIEST

Answers

Answer:

V=3052.1 square units.

Step-by-step explanation:

Using the formulas

V=4

3πr^3

d=2r

Solving for V

V=1

1/6πd^3=1

1/6·3.14·18^3=3052.08

round to the nearest tenth place so your volume would be 3052.1 :)

Answer:

3052.1

Step-by-step explanation:

The formula for volume of a sphere: 4/3 x pi x r^3 (4/3 x pi x radius x radius x radius).

Here, only the diameter is shown. To find the radius, we must divide the diameter (18) by 2.

18 / 2 = 9

9 is the radius.

Now, we have our final equation:

4/3 x pi x radius x radius x radius

4/3 x 3.14 x 9 x 9 x 9 = 3052.08

(3.14 is commonly used for pi)

3052.08 rounded to the nearest tenth is 3052.1

Therefore, 3052.1 is the volume of the sphere.

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