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3 years ago

14

There are 12 red marbles in a bag. The ratio of the total number of marbles in the bag to the number of red marbles in the bag i

s 5:2. How many marbles are in the bag?

1 answer:

harina [27]3 years ago

5 0

Answer:

30 marbles

Step-by-step explanation:

x = total # marbles

5/2 = x/12

2x = 60

x = 30

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how many cubic sugar of edge 20cm can be fitted into cuboid container of dimension 40cm by 60cm by100cm

Sloan [31]

Answer:

n =30

Step-by-step explanation:

Given that,

Size of a sugar cube = 20 cm

The dimension of the container is 40cm by 60cm by100cm.

Let n be the number of sugar cube that are contained in the container.

So,

$n=\dfrac{\text{volume of container}}{\text{volume of sugar cube}}\\\\n=\dfrac{40\times 60\times 100}{20^3}\\\\n=30$

So, there are 30 sugar cube that are fitted in the container.

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3 years ago

What is a random variable

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Answer:

Check Below.

Step-by-step explanation:

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2 years ago

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

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3 years ago

I need help with numbers 1 and 2

Snowcat [4.5K]

Answer:

1.No, 143 is not a prime number. The list of all positive divisors the list of all integers that divide 143 is as follows: 1, 11, 13, 143. To be 143 a prime number, it would have been required that 143 has only two divisors, itself and 1.

2.Since the polynomial can be factored, it is not prime.

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3 years ago

The point (-5, 3) is reflected across the x axis. What are the coordinates of this reflection? Group of answer choices

harina [27]

Answer:

( -5, -3)

Step-by-step explanation:

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