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3 years ago

6

Nina can ride her bike 63,000 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour. What is Nina’s rate in mil

es per hour if there are 5,2080 feet in a mile?

1 answer:

miss Akunina [59]3 years ago

4 0

Answer:

Step-by-step explanation:

u need to multiply.

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The skating rink rented 218 pairs of skates during the month of April and 3 times that many in May. How many pairs of skates did

Marrrta [24]

Answer: Total number of pairs =872

Step-by-step explanation:

Since we have given that

Number of pairs of skates during the month of April =218

Number of pairs of skates during the month of May =3 × 218=654

As we know that total means altogether in which we perform the additive operation.

Total pairs of skates the skating rent during April and May = 218+654=872

∴ Total number of pairs =872

7 0

3 years ago

Read 2 more answers

Evaluate g(3) if g(x)=2x+2

klemol [59]

Plug in 3 for x so
2(3)+2
6+2=
8
The evaluation is 8

4 0

3 years ago

9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

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

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

so

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

Find the smallest value of n such that the LCM of n and 15 is 45

krek1111 [17]

Answer:45

Step-by-step explanation:

9 and 15 both go into 45, and 45 is the LCM of those numbers.

6 0

3 years ago

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Autumn measures the angle of elevation from the ground to the top of an 18-foottall tree as 27°. To the nearest tenth of a foot,

cricket20 [7]

Answer:

35.3 ft (nearest tenth)

Step-by-step explanation:

Please see the attached picture for the full solution.

3 0

3 years ago