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3 years ago

13

gave each student a pair of standard dice. The students rolled the dice once and reported their results to the teacher. How many

of his 126 students should the teacher have expected to roll a 3 or a multiple of 3 on both dice?

1 answer:

Salsk061 [2.6K]3 years ago

8 0

42 times is the answer

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What is -29/30 + 7/12 / 1/2

inn [45]

-29/30 +7/12÷1/2
7/12÷1/2=7/6
-29/30 + 7/6=1/5
1/5

7 0

3 years ago

Read 2 more answers

\int (x+1)\sqrt(2x-1)dx

Nezavi [6.7K]

Answer:

$\int (x+ 1) \sqrt{2x-1} dx = \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C$

Step-by-step explanation:

$\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v = \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}$

$\int (x+1)\sqrt(2x-1)dx\\\\ = uv - \int v du$

$= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ u = x + 1 => du = dx \ ]$

$= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\$

6 0

3 years ago

if the area of the rectangle shown is 150 square feet, we can use the equation 2x squared - 5x = 150 to find its dimensions. if

Juliette [100K]

Factoring the left side of the equation

x(2x-5) = 150

x = 10 so the dimension are 10 and (2(10) - 5 = 15

length = 15 feet , width = 10 feet.

5 0

3 years ago

Seth and Eva are biking on a trail.

musickatia [10]

Answer:

<u>It will take Eva 4 hours to catch up with Seth on the trail.</u>

<u></u>

Step-by-step explanation:

1. Seth: 4/hour Eva: 6/hour

2. Hour 1: S:12 E:6

Hour 2: S:16 E:12

Hour 3: S:20 E:18

Hour 4: S:24 E:24

___

Hope this helps you! :)

5 0

3 years ago

Read 2 more answers

Which two numbers have a sum of 15 and a product of 36

Aliun [14]

Answer:

3 and 12

Step-by-step explanation:

let the 2 numbers be x and y then

x + y = 15 → (1)

xy = 36 → (2)

From (1) : y = 15 - x → (3)

substitute y = 15 - x into (2)

x(15 - x) = 36

15x - x² = 36 ( subtract 36 from both sides )

15x - x² - 36 = 0 ( multiply through by - 1 and arrange in standard form )

x² - 15x + 36 = 0 ← in standard form

(x - 3)(x - 12) = 0 ← in factored form

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 12 = 0 ⇒ x = 12

substitute these values into (3) for corresponding value of y

x = 3 → y = 15 - 3 = 12

x = 12 → y = 15 - 12 = 3

Hence the 2 numbers are 3 and 12

6 0

3 years ago