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3 years ago

Malcolm is filling bags with rice. He starts with a 5 1/4 pound container of rice and fills each

Mathematics

1 answer:

Sliva [168]3 years ago

6 0

Basically we want to know how many times 5/8 goes into 5 1/4.

5 1/4 ÷ 5/8 = 21/4 ÷ 5/8 = 21/4 × 8/5 = 42/5 = 8.4 bags

Since we cannot have a fraction of a bag, he can fill 8 bags completely.

answer: 8 bags

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What is the measure of B (2n + 15) and D (3n - 5)? If ABCD is a parrallelogram

katovenus [111]

Answer : The value of angle B and angle D is 25⁰ and 35⁰ respectively.

Step-by-step explanation :

As we know that the opposite angles are equal in parallelogram.

According to the given figure,

∠A = ∠C

and

∠B = ∠D

Given:

∠B = (3n - 5)⁰

∠D = (2n + 15)⁰

From this we conclude that:

∠B = ∠D

(3n - 5)⁰ = (2n + 15)⁰

3n - 5⁰ = 2n + 15⁰

3n - 2n = 15⁰ - 5⁰

1n = 10⁰

n = 10⁰

∠B = (3n - 5)⁰ = (3×10 - 5)⁰ = 25⁰

∠D = (2n + 15)⁰ = (2×10 + 15)⁰ = 35⁰

Therefore, the value of angle B and angle D is 25⁰ and 35⁰ respectively.

5 0

3 years ago

A bag contains 5 white, 3 black, and 2 green balls. Balls are picked at random.

Soloha48 [4]

Answer:

look down there

Step-by-step explanation:

First ball:

Probability of drawing a white ball is 5/8

Probability of drawing a black ball is 3/8

Second ball:

This depends on the first ball drawn, lets say you drew a white ball initially, 4 white balls are left out of 7 balls in total. The probability of a white ball in the second pick is 4/7.

Total probability of drawing two white balls is 5/8*4/7 (since they are independent events).

If you picked a black ball initially, picking another black ball would have a probability of 2/7, on similar grounds , total prob for 2 blacks would be 3/8*2/7.

The probability that you pick 2 balls of same color is (5/14 + 3/28) = 13/28. (Since they are mutually exclusive events)

6 0

4 years ago

PLEASE HELP ME 2x+45=90

arsen [322]

Answer:

x = 45/2 = 22.5 cm

Step-by-step explanation:

2x + 45 = 90

2x = 90- 45= 45

2x = 45

x = 45/2 = 22.5 cm

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you .

if you find it useful.

8 0

3 years ago

99 POINT QUESTION, PLUS BRAINLIEST!!!

VladimirAG [237]

First, we have to convert our function (of x) into a function of y (we revolve the curve around the y-axis). So:

$y=100-x^2\\\\x^2=100-y\qquad\bold{(1)}\\\\\boxed{x=\sqrt{100-y}}\qquad\bold{(2)} \\\\\\0\leq x\leq10\\\\y=100-0^2=100\qquad\wedge\qquad y=100-10^2=100-100=0\\\\\boxed{0\leq y\leq100}$

And the derivative of x:

$x'=\left(\sqrt{100-y}\right)'=\Big((100-y)^\frac{1}{2}\Big)'=\dfrac{1}{2}(100-y)^{-\frac{1}{2}}\cdot(100-y)'=\\\\\\=\dfrac{1}{2\sqrt{100-y}}\cdot(-1)=\boxed{-\dfrac{1}{2\sqrt{100-y}}}\qquad\bold{(3)}$

Now, we can calculate the area of the surface:

$A=2\pi\int\limits_0^{100}\sqrt{100-y}\sqrt{1+\left(-\dfrac{1}{2\sqrt{100-y}}\right)^2}\,\,dy=\\\\\\= 2\pi\int\limits_0^{100}\sqrt{100-y}\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=(\star)$

We could calculate this integral (not very hard, but long), or use (1), (2) and (3) to get:

$(\star)=2\pi\int\limits_0^{100}1\cdot\sqrt{100-y}\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=\left|\begin{array}{c}1=\dfrac{-2\sqrt{100-y}}{-2\sqrt{100-y}}\end{array}\right|= \\\\\\= 2\pi\int\limits_0^{100}\dfrac{-2\sqrt{100-y}}{-2\sqrt{100-y}}\cdot\sqrt{100-y}\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=\\\\\\ 2\pi\int\limits_0^{100}-2\sqrt{100-y}\cdot\sqrt{100-y}\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\cdot\dfrac{dy}{-2\sqrt{100-y}}=\\\\\\$

$=2\pi\int\limits_0^{100}-2\big(100-y\big)\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\cdot\left(-\dfrac{1}{2\sqrt{100-y}}\, dy\right)\stackrel{\bold{(1)}\bold{(2)}\bold{(3)}}{=}\\\\\\= \left|\begin{array}{c}x=\sqrt{100-y}\\\\x^2=100-y\\\\dx=-\dfrac{1}{2\sqrt{100-y}}\, \,dy\\\\a=0\implies a'=\sqrt{100-0}=10\\\\b=100\implies b'=\sqrt{100-100}=0\end{array}\right|=\\\\\\= 2\pi\int\limits_{10}^0-2x^2\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx=(\text{swap limits})=\\\\\\$

$=2\pi\int\limits_0^{10}2x^2\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx= 4\pi\int\limits_0^{10}\sqrt{x^4}\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx=\\\\\\= 4\pi\int\limits_0^{10}\sqrt{x^4+\dfrac{x^4}{4x^2}}\,\,dx= 4\pi\int\limits_0^{10}\sqrt{x^4+\dfrac{x^2}{4}}\,\,dx=\\\\\\= 4\pi\int\limits_0^{10}\sqrt{\dfrac{x^2}{4}\left(4x^2+1\right)}\,\,dx= 4\pi\int\limits_0^{10}\dfrac{x}{2}\sqrt{4x^2+1}\,\,dx=\\\\\\=\boxed{2\pi\int\limits_0^{10}x\sqrt{4x^2+1}\,dx}$

Calculate indefinite integral:

$\int x\sqrt{4x^2+1}\,dx=\int\sqrt{4x^2+1}\cdot x\,dx=\left|\begin{array}{c}t=4x^2+1\\\\dt=8x\,dx\\\\\dfrac{dt}{8}=x\,dx\end{array}\right|=\int\sqrt{t}\cdot\dfrac{dt}{8}=\\\\\\=\dfrac{1}{8}\int t^\frac{1}{2}\,dt=\dfrac{1}{8}\cdot\dfrac{t^{\frac{1}{2}+1}}{\frac{1}{2}+1}=\dfrac{1}{8}\cdot\dfrac{t^\frac{3}{2}}{\frac{3}{2}}=\dfrac{2}{8\cdot3}\cdot t^\frac{3}{2}=\boxed{\dfrac{1}{12}\left(4x^2+1\right)^\frac{3}{2}}$

And the area:

$A=2\pi\int\limits_0^{10}x\sqrt{4x^2+1}\,dx=2\pi\cdot\dfrac{1}{12}\bigg[\left(4x^2+1\right)^\frac{3}{2}\bigg]_0^{10}=\\\\\\= \dfrac{\pi}{6}\left[\big(4\cdot10^2+1\big)^\frac{3}{2}-\big(4\cdot0^2+1\big)^\frac{3}{2}\right]=\dfrac{\pi}{6}\Big(\big401^\frac{3}{2}-1^\frac{3}{2}\Big)=\boxed{\dfrac{401^\frac{3}{2}-1}{6}\pi}$

Answer D.

6 0

4 years ago

Read 2 more answers

2. Suppose there are 50 cats in a neighborhood. The ratio of cats to dogs is 2/1 . many dogs are in the neighborhood? (4 points)

Rus_ich [418]

Answer: 25 Dogs

Reason: If the ratio of cats to dogs is 2/1, there are 2 cats for every 1 dog. That would mean that the number of cats is double the number of dogs. 25 x 2 = 50

3 0

3 years ago