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3 years ago

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A student makes a sign out of a rectangular piece of cardboard for an upcoming event at school. The piece of cardboard has a len

gth of 50 inches (in.) and a width of 25 inches. The sign is in the shape of an arrow, as shown. how much cardboard, in square inches, is not used for the sign?

1 answer:

seraphim [82]3 years ago

3 0

Answer:

915 in²

Step-by-step explanation:

The area of the rectangle :

Length = 32 inches

Width = 25 - (10+10) = 25 - 20 = 5 inches

Area of rectangle = Length * width

Area = 32 * 5 = 160 in²

Area of triangle :

Base = 25 inches

Height = (46 - 32) inches = 14 inches

Area of triangle = 1/2 * base * height

Area of triangle = 1/2 * 25 * 14 = 175 in²

Total area = (160 + 175)in² = 335 in²

Total area of cardboard :

50 inches * 25 inches = 1250 in²

Amount of cardboard not used :

(1250 - 335) in² = 915 in²

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Answer:

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Step-by-step explanation:

The problem states that low-strength children’s/adult chewable aspirin tablets contains 81 mg of aspirin per tablet. And asks how many tablets may be prepared from 1 kg of aspirin.

Since the problem measures the weight of a tablet in kg, the first step is the conversion of 81mg to kg.

Each kg has 1,000,000mg. So

1kg - 1,000,000mg

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3 years ago

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Step-by-step explanation:

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2 years ago

Lim n→∞[(n + n² + n³ + .... nⁿ)/(1ⁿ + 2ⁿ + 3ⁿ +....nⁿ)]

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Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

Given expression is

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To, evaluate this limit, let we simplify numerator and denominator individually.

So, Consider Numerator

$\rm :\longmapsto\:n + {n}^{2} + {n}^{3} + - - - + {n}^{n}$

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So, using Sum of n terms of GP, we get

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Now, Consider Denominator, we have

$\rm :\longmapsto\: {1}^{n} + {2}^{n} + {3}^{n} + - - - + {n}^{n}$

can be rewritten as

$\rm :\longmapsto\: {1}^{n} + {2}^{n} + {3}^{n} + - - - + {(n - 1)}^{n} + {n}^{n}$

$\rm \: = \: {n}^{n}\bigg[1 +\bigg[{\dfrac{n - 1}{n}\bigg]}^{n} + \bigg[{\dfrac{n - 2}{n}\bigg]}^{n} + - - - + \bigg[{\dfrac{1}{n}\bigg]}^{n} \bigg]$

$\rm \: = \: {n}^{n}\bigg[1 +\bigg[1 - {\dfrac{1}{n}\bigg]}^{n} + \bigg[1 - {\dfrac{2}{n}\bigg]}^{n} + - - - + \bigg[{\dfrac{1}{n}\bigg]}^{n} \bigg]$

Now, Consider

$\rm :\longmapsto\:\displaystyle\lim_{n \to \infty} \frac{n + {n}^{2} + {n}^{3} + - - + {n}^{n} }{ {1}^{n} + {2}^{n} + {3}^{n} + - - + {n}^{n} }$

So, on substituting the values evaluated above, we get

$\rm \: = \: \displaystyle\lim_{n \to \infty} \frac{\dfrac{ {n}^{n} - 1}{1 - \dfrac{1}{n} }}{{n}^{n}\bigg[1 +\bigg[1 - {\dfrac{1}{n}\bigg]}^{n} + \bigg[1 - {\dfrac{2}{n}\bigg]}^{n} + - - - + \bigg[{\dfrac{1}{n}\bigg]}^{n} \bigg]}$

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Now, we know that,

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So, using this, we get

$\rm \: = \: \dfrac{1}{1 + {e}^{ - 1} + {e}^{ - 2} + - - - - \infty }$

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$\rm \: = \: \dfrac{1}{\dfrac{1}{1 - \dfrac{1}{e} } }$

$\rm \: = \: \dfrac{1}{\dfrac{1}{ \dfrac{e - 1}{e} } }$

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Hence,

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2 years ago

What is the slope of the line?

riadik2000 [5.3K]

Answer:

The slope of the line must be 3

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

step 1

we know that

The volume of a rectangular prism is equal to

$V_r_p=Bh$ ----> equation A

where

B is the area of the base of the prism

h is the height of the rectangular prism

step 2

The volume of a square pyramid is equal to

$V_s_p=\frac{1}{3}Bh$ -----> equation B

where

B is the area of the square base of pyramid

h is the height of the pyramid

step 3

substitute equation A in equation B

$V_s_p=\frac{1}{3}V_r_p$

Find the relationship between the volume of a rectangular prism and the volume of a square pyramid

$\frac{V_r_p}{V_s_p}=3$

therefore

The slope of the line must be 3

let's check it

To solve for the slope of the line, you must choose two coordinates first and use the formula

$m=\frac{y2-y1}{x2-x1}$

Choosing the points (2,6) and (3,9)

substitute

$m=\frac{9-6}{3-2}=3$ ----> is correct

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likoan [24]

It 42 units hopes this helps

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3 years ago

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