All categories

3 years ago

find the perimeter and diagonal of a square whose area is equal to the area of a rectangle whose length is 9m and breadth is 4m

1 answer:

4 0

$Area\ of\ a\ rectangle:A_{\fbox{ }}=9m\times4m=36m^2\\\\a-side\ of\ a\ square\\\\Area\ of\ a\ square:A_{\fbox{}}=a^2\\\\A_{\fbox{ }}=A_{\fbox{}}\Rightarrow a^2=36m^2\Rightarrow a=\sqrt{36m^2}\Rightarrow a=6m\\\\Perimeter\ of\ the\ square:P=4a\Rightarrow P=4\times6m=\boxed{24m}\\\\Diagonal\ of\ the\ square:d=a\sqrt2\Rightarrow d=\boxed{6\sqrt2\ m}$

You might be interested in

The vertex of this parabola is at (-5, -2). When the x-value is -4, the y-value is 2. What is the coefficient of the squared exp

Montano1993 [528]

Answer:

The coefficient of the squared expression in the parabola equation is $a=4$

Step-by-step explanation:

The equation of a parabola in its vertex form is:

$y = a(x-h) ^ 2 + k$

Where the vertex of the parabola is the point (h, k)

a is the ceoficiente of the term to the square.

We need to find the equation of a parabola that has its vertex in the point:

(-5, -2)

So:

$h = -5\\\\k = -2$

Therefore the equation is:

$y = a(x - (-5)) ^ 2 -2\\\\y = a(x + 5) ^ 2 -2$

We know that the point (-4, 2) belongs to this parable. Then we can find the value of a by replacing the point in the equation of the parabola

$(2) = a((-4) + 5) ^ 2 -2\\\\2 = a(1) ^ 2 -2\\\\2 = a -2\\\\a = 4$

Finally the coefficient is a = 4

7 0

3 years ago

A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data

Rasek [7]

Answer: a. 1.981 < μ < 2.18

b. Yes.

Step-by-step explanation:

A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.

First, we calculate mean of the sample:

$\overline{x}=\frac{\Sigma x}{n}$

$\overline{x}=\frac{2.31=2.09+...+1.97+2.02}{12}$

$\overline{x}=$ 2.08

Now, we estimate standard deviation:

$s=\sqrt{\frac{\Sigma (x-\overline{x})^{2}}{n-1} }$

$s=\sqrt{\frac{(2.31-2.08)^{2}+...+(2.02-2.08)^{2}}{11} }$

s = 0.1564

For t-score, we need to determine degree of freedom and $\frac{\alpha}{2}$ :

df = 12 - 1

df = 11

$\alpha$ = 1 - 0.95

α = 0.05

$\frac{\alpha}{2}=$ 0.025

Then, t-score is

$t_{11,0.025}$ = 2.201

The interval will be

$\overline{x}$ ± $t.\frac{s}{\sqrt{n} }$

2.08 ± $2.201\frac{0.1564}{\sqrt{12} }$

2.08 ± 0.099

The 95% two-sided CI on the mean is 1.981 < μ < 2.18.

B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.

8 0

3 years ago

A toy store’s percent of markup is 30%. A model train costs the store $50. Find the markup.

Ede4ka [16]

$104 because 30% of $80 is $24 and $80+$24 is $124 so...... that's what I got

8 0

3 years ago

Lettuce is packed four to a box . If there are 3.5 boxes of Lettuce in the cooler , how many bags of Lettuce would there be

Tanya [424]

3.5 x 4 = 14 lettuces

8 0

3 years ago

What is the value of t?<br> 40°<br> 39°

kramer

Answer:41

Step-by-step explanation:

because the 49 degrees and t equal a right angle which is 90 degrees you subtract 49 from 90 which makes the remaining degree aka t 41

5 0

2 years ago