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3 years ago

What is the arc length if the radius is 12 cm?*

Mathematics

1 answer:

ladessa [460]3 years ago

4 0

Answer:

4π cm

Step-by-step explanation:

The length of an arc of a circle with radius r and central angle θ is given by ...

s = rθ

where θ is in radians.

Here, your arc measures 60° = π/3 radians, so the arc length is ...

s = (12 cm)(π/3) = 4π cm

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Samantha has a rectangular shaped fish tank in her room. The tank has a height of 2.6 ft, a width of 2.1 ft, and a length of 3.9

andrezito [222]

Answer: the BEST approximation of the amount of water her fish tank can hold is 21ft^3

Step-by-step explanation:

The shape of Samantha's fish tank is rectangular. The volume of the rectangular fish tank would be expressed as LWH

Where

L represents length of the tank

W represents the width of the tank.

H represents the height of the tank.

The tank has a height of 2.6 ft, a width of 2.1 ft, and a length of 3.9 ft.

This means that the volume of the fish tank would be

Volume = 2.6 × 2.1 × 3.9

= 21.294 ft^3

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4 years ago

If sin(y degrees) = cos(x degrees), which of the following statements is true?

grin007 [14]

Answer:

Angle y and Angle x are complementary angles

Step-by-step explanation:

we know that

sin(y°)=cos(x°)

then

Angle y and Angle x are complementary angles

∠y+∠x=90°

∠x=90°-∠y

sin(y°)=cos(90°-y°)

therefore

The sine of an angle is equal to the cosine of its complementary angle

6 0

3 years ago

4. The constant of proportionality between the height of the water in a sink (h) in centimeters and the number of minutes it has

RUDIKE [14]

Answer:

i got 38

Step-by-step explanation:

6 0

3 years ago

Say you're playing three-card poker; that is, you're dealt three cards in a row at random from a standard deck of 52 cards. What

Brums [2.3K]

Answer:

Step-by-step explanation:

Given

There are 52 cards in total

there are total of 13 pairs of same cards with each pair containing 4 cards

Probability of getting a pair or three of kind card=1-Probability of all three cards being different

Probability of selecting all three different cards can be find out by selecting a card from first 13 pairs and remaining 2 cards from remaining 12 pairs i.e.

$=\frac{52\times 48\times 44}{52\times 51\times 50}$

for first card there are 52 options after choosing first card one pair is destroyed as we have to select different card .

For second card we have to select from remaining 12 pairs i.e. 48 cards and so on for third card.

Required Probability is $=1-\frac{52\times 48\times 44}{52\times 51\times 50}$

$=\frac{22776}{132600}$

7 0

3 years ago

The values of 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-gr

postnew [5]

Answer:

Only 60 is an identified outlier

Step-by-step explanation:

Given

Age group: 40 to 50

$Min = 60$ $Q_1 = 70$ $Median= 73$

$Q_3 = 76$ $Max = 85$

Conditions for outlier

$Value > Q_3 + 1.5 * IQR$

$Value < Q_1 - 1.5 * IQR$

See attachment for complete question

Required

Which of 60, 62 and 84 is an outlier of age grout 40 to 50 years

First, calculate the IQR of group 40 to 50.

This is calculated as:

$IQR = Q_3 - Q_1$

Where:

$Q_3 = 76$ and $Q_1 = 70$

So:

$IQR = 76 - 70$

$IQR = 6$

Next, is to test the outlier conditions on each value (i.e. 60, 62 and 84)

Testing 60

Condition 1

$Value > Q_3 + 1.5 * IQR$

$60 > 76 + 1.5 * 6$

$60 > 76 + 9$

$60 > 85$ --- False

Condition 2

$Value < Q_1 - 1.5 * IQR$

$60 < 70 - 1.5 * 6$

$60 < 70 - 9$

$60 < 61$ --- True

Because one of the conditions is true, then 60 is an outlier of group 40 - 50 years

Testing 62

Condition 1

$Value > Q_3 + 1.5 * IQR$

$62> 76 + 1.5 * 6$

$62 > 76 + 9$

$62 > 85$ --- False

Condition 2

$Value < Q_1 - 1.5 * IQR$

$62 < 70 - 1.5 * 6$

$62 < 70 - 9$

$62 < 61$ --- False

Because both conditions are false, then 62 is not an outlier of group 40 - 50 years

Testing 84

Condition 1

$Value > Q_3 + 1.5 * IQR$

$84> 76 + 1.5 * 6$

$84 > 76 + 9$

$84 > 85$ --- False

Condition 2

$Value < Q_1 - 1.5 * IQR$

$84 < 70 - 1.5 * 6$

$84 < 70 - 9$

$84 < 61$ --- False

Because both conditions are false, then 84 is not an outlier of group 40 - 50 years

5 0

3 years ago