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1 year ago

What's the area of the above figure which has sides of length 6 and 8

Mathematics

2 answers:

Sunny_sXe [5.5K]1 year ago

6 0

Area of a rectangle is length times width. In the figure above, the length is 8 and the width is 6. So you just multiply 8 by 6 to get 48.

A = l x w
A = 8 x 6
A = 48

san4es73 [151]1 year ago

3 0

Area means times so wouldn’t it just be 6 times 8 which is 48?!

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Two boats leave port at noon. Boat 1 sails due east at 12 knots. Boat 2 sails due south at 8 knots. At 2 pm the wind diminishes

Ivan

Answer:

14.86 knots.

Step-by-step explanation:

<em>Given that:</em>

The boats leave the port at noon.

Speed of boat 1 = 12 knots due east

Speed of boat 2 = 8 knots due south

At 2 pm:

Distance traveled by boat 1 = 24 units due east

Distance traveled by boat 2 = 16 units due south

Now, speed of boat 1 changes to 9 knots:

At 3 pm:

Distance traveled by boat 1 = 24 + 9= 33 units due east

Distance traveled by boat 2 = 16+8 = 24 units due south

Now, speed of boat 1 changes to 8+7 = 15 knots

At 5 pm:

Distance traveled by boat 1 = 33 + 2 $\times$ 9= 51 units due east

Distance traveled by boat 2 = 24 + 2 $\times$ 15 = 54 units due south

Now, the situation of distance traveled can be seen by the attached right angled $\triangle AOB$ .

O is the port and A is the location of boat 1

B is the location of boat 2.

Using pythagorean theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^{2} = 51^{2} + 54^{2}\\\Rightarrow AB^{2} = 2601+ 2916 = 5517\\\Rightarrow AB = 74.28\ units$

so, the total distance between the two boats is 74.28 units.

Change in distance per hour = $\dfrac{Total\ distance}{Total\ time}$

$\Rightarrow \dfrac{74.28}{5} = 14.86\ knots$

6 0

1 year ago

Round 1627187 to the nearest ten?

Eduardwww [97]

Answer:

1627190

Step-by-step explanation:

(see attached for reference)

Given the number 1627187, we can see that the number in the tens place is the number 8.

How we round this depends on the number immediately to the right of this number. (i.e the digit in the ones place)

Case 1: If the digit in the ones place is less less than 5, then the number in the tens place remains the same and replace all the digits to its right with zeros

Case 2: If the digit in the ones places is 5 or greater, then we increase the digit in the tens place and replace all the digits to its right with zeros.

In our case, the digit in the ones places is 7, this greater than 5, hence according to Case 2 above, we increase the digit in the tens place by one (from 8 to 9) and replace all the digits to its right by zeros giving us:

1627190

7 0

1 year ago

Read 2 more answers

According to a survey, 10% of Americans are afraid to fly. Suppose 1100 Americans are sampled. a) What is the probability that 1

JulijaS [17]

Answer:

a) 14.46%

b) 0.00%

c) 1.54%

Step-by-step explanation:

According to the survey, 10% of Americans are afraid to fly.

This means $p=0.10$ and $q=1-0.10=0.90$ .

If 1100 Americans are sampled, then the sample size is $n=1100$ .

The mean of the distribution is $\mu=np$ .

This means $\mu=1100\times 0.10=110$

The standard deviation is $\sigma=\sqrt{npq}$

We substitute the values to get:

$\sigma=\sqrt{1100\times 0.1\times 0.9}=9.95$

a) We want to find the probability that 121 or more Americans in the survey are afraid to fly.

We first apply the continuity correction factor to get: $P(X\ge121)=P(X\:>\:121-0.5)\\P(X\ge121)=P(X\:>\:120.5)$

We now convert to Z-scores to get:

$P(X\:>\:120.5)=P(z\:>\:\frac{120.5-110}{9.95})=1.06\\$

From the standard normal distribution table P(z>1.06)=0.1446

As a percentage, the probability is 14.46%

b) We want to find the probability that 165 or more Americans in the survey are afraid to fly.

We apply the CCF to get:

$P(X\ge165)=P(X\:>\:165-0.5)\\P(X\ge165)=P(X\:>\:164.5)$

We convert to z-scores:

$P(X\:>\:164.5)=P(z\:>\:\frac{164.5-110}{9.95})=5.48$

From the normal distribution, P(z>164.5)=0

c) First, 8% of 1100 is 88.

We want to find the probability that 88 or less Americans in the survey are afraid to fly.

We apply the CCF to get:

$P(X\le88)=P(X\:$

We convert to z-scores:

$P(X\:$

From the normal distribution, P(z>\:-2.16)=0.0154

As a percentage, we get 1.54%

3 0

2 years ago

Pat's income is 20 % more than Adam. How much percent is Adam's income less than Pat's?

pantera1 [17]

Answer: 20%

Step-by-step explanation: The same number applies here. Think about it this way, let's say you have a friend named Sofia and she has 3 dollars more than you, how many dollars do you have less than Sofia? 3 dollars. That's the easiest way I can explain it.

4 0

1 year ago

Oliver and Paula both read the same book. Paula started reading after Oliver had already read 30 pages.

ahrayia [7]

Their lines intersect at this point, which mean that they did the same thing, so it can't be A or D, and we dont know the total number of pages so we can't for sure say it's B.

So it's C, because we can see that the point is on 10 for the x-axis, which represents # of nights, and 150 for the y-axis, which represents # of pages read.

3 0

2 years ago

Read 2 more answers