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2 years ago

If 12 pens cost 3.48 how much do 20 cost

Mathematics

1 answer:

VARVARA [1.3K]2 years ago

7 0

Step-by-step explanation:

12/3.48= cost of 1 book

cost of 20 books = 12/3.48×20 =68.95

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Sandra knows the Pythagorean identity sin 2 ⁡ θ + cos 2 ⁡ θ = 1 . If she is told that 0 ≤ θ ≤ π 2 and cos ⁡ θ = 5 12, what will

slavikrds [6]

Answer:

$\text{tan}(\theta)=\frac{\sqrt{119}}{5}$

Step-by-step explanation:

We have been given that Sandra knows the Pythagorean identity $\text{sin}^2(\theta)+\text{cos}^2(\theta)=1$ . She is told that $0\leq \theta\leq \frac{\pi}{2}$ and $\text{cos}(\theta)=\frac{5}{12}$ .

First of all, we will find value of sine theta using the given identity.

$\text{sin}^2(\theta)+\text{cos}^2(\theta)=1$

$\text{sin}^2(\theta)+(\frac{5}{12})^2=1$

$\text{sin}^2(\theta)+\frac{25}{144}=1$

$\text{sin}^2(\theta)+\frac{25}{144}-\frac{25}{144}=1-\frac{25}{144}$

$\text{sin}^2(\theta)=\frac{144-25}{144}$

$\text{sin}^2(\theta)=\frac{119}{144}$

$\text{sin}(\theta)=\sqrt{\frac{119}{144}}$

$\text{sin}(\theta)=\frac{\sqrt{119}}{12}$

$\text{tan}(\theta)=\frac{\text{sin}(\theta)}{\text{cos}(\theta)}$

$\text{tan}(\theta)=\frac{\frac{\sqrt{119}}{12}}{\frac{5}{12}}$

$\text{tan}(\theta)=\frac{\sqrt{119}*12}{5*12}=\frac{\sqrt{119}}{5}$

Therefore, $\text{tan}(\theta)=\frac{\sqrt{119}}{5}$ .

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3 years ago

Find the area of a circle with the radius of 73 feet

White raven [17]

Answer:

Step-by-step explanation:

area of a circle=πr^2

=3.14*(73)^2

=3.14*5329

=16733.06 ft^2

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2 years ago

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What is the midpoint?

coldgirl [10]

The midpoint is (-0.5, 0.5).

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2 years ago

traveling at 45 mph, how many minutes, rounded to the nearest whole number, does it take to drive 240 miles from Orlando to Miam

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$v=\frac{d}{t}\\\\v-velocity;\ d-distance;\ t-time\\-------------------------\\v=\frac{d}{t}\ \ \ \ |multiply\ both\ sides\ by\ t\\vt=d\ \ \ \ |divide\ both\ sides\ by\ v\\\\t=\frac{d}{v}\\------------------------$

$v=45\ mph;\ d=240\ mi\\\\t=\frac{240}{45}=\frac{240:15}{45:15}=\frac{16}{3}\ (h)\\\\1h=60min\\\\therefore\\\\t=\frac{16}{3}\cdot60min=16\cdot20min=\boxed{320min}$

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3 years ago

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What is the ordered pair of X′ after point X (3, 4) is rotated 180°?

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2 years ago

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