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3 years ago

Are the ratios 3:9 6:18 9:27 12:36 and 15:45 all proportional?

Mathematics

1 answer:

KatRina [158]3 years ago

5 0

Yes they are all proportional

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A child's tent can be modeled as a pyramid with a square base whose sides measure 60 inches and whose height measures 84 inches.

IgorC [24]

Answer:

The volume of the tent is $100,800\ in^{3}$

Step-by-step explanation:

we know that

The volume of the square pyramid (child's tent) is equal to

$V=\frac{1}{3}b^{2}h$

we have

$b=60\ in$

$h=84\ in$

substitute

$V=\frac{1}{3}(60^{2})(84)=100,800\ in^{3}$

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3 years ago

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A 20-pound bag of dog food costs $16. What is the unit price per pound?

ch4aika [34]

Answer:

0.8

Step-by-step explanation:

To calculate the cost of any item per pound, divide the cost of the item by its weight in pounds: cost ÷ pounds = cost per pound.

Hope This Helped!!

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3 years ago

Find the sum of the series Summation from n equals 1 to infinity (StartFraction 3 Over StartRoot n plus 2 EndRoot EndFraction mi

Marizza181 [45]

Looks like the series is supposed to be

$\displaystyle\sum_{n=1}^\infty\frac3{\sqrt{n+2}}-\frac3{\sqrt{n+3}}$

The series telescopes; consider the $k$ th partial sum of the series,

$S_k=\displaystyle\sum_{n=1}^k\frac3{\sqrt{n+2}}-\frac3{\sqrt{n+3}}$

$S_k=\displaystyle\left(\frac3{\sqrt3}-\frac32\right)+\left(\frac32-\frac3{\sqrt5}\right)+\cdots+\left(\frac3{\sqrt{k+1}}-\frac3{\sqrt{k+2}}\right)+\left(\frac3{\sqrt{k+2}}-\frac3{\sqrt{k+3}}\right)$

$\implies S_k=\dfrac3{\sqrt3}-\dfrac3{\sqrt{k+3}}$

As $k\to\infty$ , the second term converges to 0, leaving us with

$\displaystyle\sum_{n=1}^\infty\frac3{\sqrt{n+2}}-\frac3{\sqrt{n+3}}=\frac3{\sqrt3}=\boxed{\sqrt3}}$

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3 years ago

Tori examined the pattern of exponents in the table.

gregori [183]

Answer:

The value of b = 1/36

As exponent decreases, each previous value is divided by 6

If the table was extended, the value of 6^-3 would be 1/216

Step-by-step explanation:

Given in the question a table containing power of 6

We will use negative rule of exponent to write the equivalent of negative power of 6

b^{-n}= 1 / b^{n}

we know that

$6^{1}=6$

$6^{-1} =\frac{1}{6^{1} }$

= 1/6

and

$6^{2} = 36$

So,

$6^{-2} = \frac{1}{6^{2} }$

$\frac{1}{36}$

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3 years ago

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Find the equation in slope-intercept form of a line with slope -2 and y-intercept 4.

Sergio039 [100]

Answer:

D. y=-2x+4

Step-by-step explanation:

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3 years ago