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2 years ago

14

A team played 42 games and won 5/14 of them. how many games were lost?

1 answer:

sergejj [24]2 years ago

3 0

27 games were lost

fraction of games lost = 1 - $\frac{5}{14}$ = $\frac{14}{14}$ - $\frac{5}{14}$ = $\frac{9}{14}$

number of games lost = $\frac{9}{14}$ of 42

= $\frac{9}{14}$ × 42 = 27

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The average diameter of sand dollars on a certain island is 5.00 centimeters with a standard deviation of 0.90 centimeters. If 1

Montano1993 [528]

Answer:

the probability that the average diameter of those sand dollars is more than 4.73 centimeters is 0.5910

Step-by-step explanation:

Given information:

mean, x = 5

standard deviation, σ = 0.9

number of sample, n = 16

now we calculate the probability that the average diameter of those sand dollars is more than 4.73 centimeters.

P(x>4.73) = P (z > (4.73 - x) / (σ $\sqrt{n}$ )

= P (z > (4.73 - 4) / (0.9 $\sqrt{16}$ )

= P (z > 0.203)

= 0.5910

4 0

2 years ago

A factory bottles 360 bottles of juice in 5 minutes. Find the factory's unit rate of bottles per minute.

castortr0y [4]

Find the unit rate by dividing 360 bottles by 5 minutes:

360 bottles

-------------------- = 72 bottles/minute

5 minutes

3 0

2 years ago

Prove that (sec 12A-1)/(sec 6A-1)=tan 12A/tan 3A

adelina 88 [10]

Let $x=3A$ . Recall the following identities,

$\cos^2\theta=\dfrac{1+\cos2\theta}2$

$\sin^2\theta=\dfrac{1-\cos2\theta}2$

$\sin2\theta=2\sin\theta\cos\theta$

Now,

$\dfrac{\sec12A-1}{\sec6A-1}=\dfrac{\sec4x-1}{\sec2x-1}$

$=\dfrac{\cos2x(1-\cos4x)}{\cos4x(1-\cos2x)}$

$=\dfrac{2\cos2x\sin^22x}{\cos4x(1-\cos2x)}$

$=\dfrac{2\cos2x\sin^22x(1+\cos2x)}{\cos4x(1-\cos^22x)}=\dfrac{2\cos2x\sin^22x(1+\cos2x)}{\cos4x\sin^22x}=\dfrac{2\cos2x(1+\cos2x)}{\cos4x}$

$=\dfrac{4\cos2x\cos^2x}{\cos4x}$

$=\dfrac{4\cos2x\cos^2x\sin4x}{\cos4x\sin4x}=\dfrac{4\cos2x\cos^2x\tan4x}{\sin4x}$

$=\dfrac{4\cos2x\cos^2x\tan4x}{2\sin2x\cos2x}=\dfrac{2\cos^2x\tan4x}{\sin2x}$

$=\dfrac{2\cos^2x\tan4x}{2\sin x\cos x}=\dfrac{\cos x\tan4x}{\sin x}$

$=\dfrac{\tan4x}{\frac{\sin x}{\cos x}}=\dfrac{\tan4x}{\tan x}=\dfrac{\tan12A}{\tan3A}$

QED

5 0

2 years ago

A teacher reviews 4-1/2 papers per hour, how many papers will that teacher review in 6-1/3 hours

MrRa [10]

Answer:

$28\frac{1}{2}\ papers$

Step-by-step explanation:

step 1

Convert mixed numbers to an improper fractions

$4\frac{1}{2}=\frac{4*2+1}{2}=\frac{9}{2}$

$6\frac{1}{3}=\frac{6*3+1}{3}=\frac{19}{3}$

step 2

we know that

A teacher reviews 9/2 papers per hour

using proportion

Find how many papers will the teacher review in 19/3 hours

Let

x-----> the number of papers

$(9/2)/1=x/(19/3)$

$x=(19/3)(9/2)$

$x=28.5\ papers$

Convert to mixed numbers

$28.5=28\frac{1}{2}\ papers$

5 0

2 years ago

A semicircular flower bed has a diameter of 3 metres. What is the area of the flower bed?

Yuri [45]

The area of circle is

$A_{\text{circle}}=\pi r^2.$

Then the area of semicircular region is

$A_{\text{semicircular region}}=\dfrac{1}{2} \pi r^2.$

If r=3 m, you have

$A_{\text{semicircular region}}=\dfrac{1}{2} \pi \cdot 3^2=\dfrac{9\pi}{2}=4.5\pi \approx 14.13$ sq. m.

Answer: $A_{\text{semicircular region}}=4.5\pi \approx 14.13$ sq. m.

3 0

2 years ago

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