Ask question

Ask question

All categories

3 years ago

14

Tanya has a garden with a trench around it. The garden is a rectangle with width 2 1/2 m and length 2 m. The trench and garden t

ogether make a rectangle with width 3 1/2 m and length 3 m. What is the area of the trench?

2 answers:

vichka [17]3 years ago

5 0

Answer:

The area of a trench is 5.5 m² .

Step-by-step explanation:

Formula

Area of a rectangle = Length × Breadth

As given

Tanya has a garden with a trench around it.

$The\ garden\ is\ a\ rectangle\ with\ width\ 2\frac{1}{2}\ m\ and\ length\ 2\ m.$

i.e

$The\ garden\ is\ a\ rectangle\ with\ width\ \frac{5}{2}\ m\ and\ length\ 2\ m.$

Put in the above formula

$Area\ of\ garden = \frac{5\times 2}{2}$

= 5 m²

As given

$The\ trench\ and\ garden\ together\ make\ a\ rectangle\ with\ width\ 3 \frac{1}{2}\ m\ and\ length\ 3 m.$

i.e

$The\ trench\ and\ garden\ together\ make\ a\ rectangle\ with\ width\ \frac{7}{2}\ m\ and\ length\ 3 m.$

$Area\ of\ garden\ with\ trench = \frac{7\times 3}{2}$

$Area\ of\ garden\ with\ trench = \frac{21}{2}$

= 10.5 m²

Area of the trench = Area of garden with trench - Area of garden

Put the value in the above

Area of the trench = 10.5 m² - 5 m²

= 5.5 m ²

Therefore the area of a trench is 5.5 m² .

Goshia [24]3 years ago

5 0

10 1/2 for area, you take length times width so for this you take 3 1/2 x 3 = 10 1/2

You might be interested in

ANYONE PLEASE HELP!!

lapo4ka [179]

Answer:

A

Step-by-step explanation:

Corresponding angles are angles that you can follow down the transversal and they will land in the same spot on the other parallel line. Look at angle 8. It is the bottom left angle in the group of 4 angles around it. If you slide it to the left it would land right on top of angle 4 which is also in the bottom left of its group of 4 angles.

You can do the same thing taking angle 8 down to angle 12.

4 0

1 year ago

Read 2 more answers

A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 86m long and 62m wide.

-Dominant- [34]

The area of the rectangle is 5,332.

6 0

3 years ago

Simplify the expression the root of negative sixteen all over the quantity of three minus three i plus the quantity of one minus

aliya0001 [1]

The first step is to multiply the fraction by (3 +3i) / (3 +3i) to delete the i terms from the denominator:

$\frac{ \sqrt{-16} }{3-3i} . \frac{3+31}{3+3i} +1-2i= \frac{4i(3+3i)}{9+9} +1-2i= \frac{12i-12}{18} +1-2i=$

$\frac{12i-12+18-36i}{18} = \frac{6-24i}{18} = \frac{1}{3} - \frac{4}{3} i$

7 0

3 years ago

At the beginning of 1990, 21.7 million people lived in the metropolitan area of a particular city, and the population was grow

Gennadij [26K]

Answer:

approximately 27.5 million

Step-by-step explanation:

If 1990 is the initial year, we will rename it as 0. This is the x coordinate in a pair we will need to write the equation that models this particular situation. The y coordinate that goes along with it is 21.7 (x is time in years, y is number of people). The next coordinate pair we have is (6, 25). If 1990 is year 0, 1996 is year 6.

The standard form for an exponential equation is

$y=a(b)^x$

where y is the number of people, x is the number of years gone by, a is the initial value, and b is the growth rate. We fill in equation 1 with the x and y coordinates from coordinate pair (0, 21.7):

$21.7=a(b)^0$

andything rised to the power of 0 = 1, so b raised to 0 = 1:

21.7 = a(1) so

a = 21.7

Now we use coordinate pair (6, 25) in equation 2, subbing in our value for a also:

$25=21.7(b)^6$

Divide both sides by 21.7 to get

$1.152073733=b^6$

We "undo" that power of 6 by taking the 6th root of both sides:

$(1.152073733)^{\frac{1}{6}} =(b^6)^{\frac{1}{6}}$

That gives you that

b = 1.0238 (rounded).

Now that we have a and b, we can write the model for this situation:

$y=21.7(1.0238)^x$

Now that we have the model, we can find y when x = 10 (2010):

$y=21.7(1.0238)^{10}$

First raise 1.0238 to the 10th power to get

y = 21.7(1.266097) and

y = 27.47

5 0

2 years ago

Direct mail advertisers send solicitations ("junk mail") to thousands of potential customers in the hope that some will buy the

Arte-miy333 [17]

Answer:

The 90% confidence interval for the percentage of people the company contacts who may buy something is between 10.82% and 14%

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 1160, \pi = \frac{144}{1160} = 0.1241$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1241 - 1.645\sqrt{\frac{0.1241*0.8759}{1160}} = 0.1082$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1241 + 1.645\sqrt{\frac{0.1241*0.8759}{1160}} = 0.14$

The 90% confidence interval for the percentage of people the company contacts who may buy something is between 10.82% and 14%

3 0

3 years ago