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2 years ago

The perimeter of a rectangle is 202. The length is 26 more than 4 times the width. Find the dimensions

Mathematics

1 answer:

jek_recluse [69]2 years ago

6 0

Answer:

$P = 2*(26+4y) + 4y$

And if we solve for y we got:

$202= 52 +8y +4y$

$202= 52 +12 y$

And replacing we got:

$150 = 12y$

And we got:

$y = \frac{150}{12}= 12.5$

And for x we got:

$x = 26 +4*12.5 = 76$

So then the length would be 76 and the width we got 12.5

Step-by-step explanation:

For this case we have a rectangle. The perimeter is given by:

$P= 2x+2y$

Where x represent the length and y the the width. We can set the following conditions:

$x = 26 +4y$

And if we replace the conditions we got:

$P = 2*(26+4y) + 4y$

And if we solve for y we got:

$202= 52 +8y +4y$

$202= 52 +12 y$

And replacing we got:

$150 = 12y$

And we got:

$y = \frac{150}{12}= 12.5$

And for x we got:

$x = 26 +4*12.5 = 76$

So then the length would be 76 and the width we got 12.5

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Calculate a23 for the product of the following matrices

s344n2d4d5 [400]

If $A$ is the matrix product

$A=\underbrace{\begin{pmatrix}1&2\\4&3\end{pmatrix}}_{M_1}\underbrace{\begin{pmatrix}6&1&5\\7&3&4\end{pmatrix}}_{M_2}$

and $a_{2,3}$ is the entry of $A$ in the second row and third column, then

$a_{2,3}=\begin{pmatrix}4&3\end{pmatrix}\begin{pmatrix}5\\4\end{pmatrix}=4\times5+3\times4=\boxed{32}$

That is, the 2nd row, 3rd column entry of $A$ is the product of the 2nd row of $M_1$ and the 3rd column of $M_2$ .

6 0

1 year ago

The owner of a manufacturing plant employs eighty people. As part of their personnel file, she asked each one to record to the n

wariber [46]

Answer:

Mean of the sample = 27.83

The variance of the the sample = 106.96

Standard deviation of the sample = 10.34

Step-by-step explanation:

Step(i):-

Given random sample of six employees

x 26 32 29 16 45 19

mean of the sample

$x^{-} = \frac{26+32+29+16+45+19}{6} = 27.83$

Mean of the given data = 27.83

Step(ii):-

Given data

x : 26 32 29 16 45 19

x - x⁻ : -1.83 4.17 1.17 -11.83 17.17 -8.83

(x - x⁻)² : 3.3489 17.3889 1.3689 139.9489 294.80 77.9689

∑ (x-x⁻)² = 534.8245

Given sample size 'n' =6

The variance of given data

S² = ∑(x-x⁻)² / n-1

$S^{2} = \frac{534.8245}{6-1} = 106.9649$

The variance of the given sample = 106.9649

Step(iii):-

Standard deviation of the given data

$S = \sqrt{variance} = \sqrt{106.9649} =10.3423$

Standard deviation of the sample = 10.3423

8 0

2 years ago

The point (1, 4) lies on a circle that is centered at (1, 1). Which statements are correct? Check all that apply.

Semenov [28]

the circle's radius is 3 units

the point (- 2, 1 ) lies on the circle

the equation of a circle in standard form is

(x - a)² + (y - b)² = r²

where (a, b) are the coordinates of the centre and r is the radius

the radius is the distance from the centre to the point (1, 4 ) on the circle

using (1, 4) and (1,1) in the distance formula, then

r = √(1 - 1 )² + (1 - 4)² = √(0 + 9) =√9 = 3 ⇒ r² = 9

(x - 1 )² + (y - 1 )² = 9 ← equation of circle

substitute the given points into the equation and if equation is true then they lie on the circle

(- 2, 1 ) : (- 2 - 1 )² + (1 - 1 )² = 9 + 0 = 9 ← true

Hence (- 2, 1 ) lies on the circle

(3, 3 ) : (3 - 1 )² + (3 - 1 )² = 4 + 4 = 8 ≠ 9

(3, 3 ) does not lie on the circle

6 0

2 years ago

Read 2 more answers

A bar graph titled Album Type Sold per Year has year on the x-axis and number of albums sold on the y-axis. For C D s, in 2008 t

stira [4]

Answer:

True, True, False, True, False, True

Step-by-step explanation:

CDs have a higher mean than digital

Let's check. CD mean is (1000 + 800 + 800 + 600 + 400 + 200)/6 = 633.33

Digital mean: (100 + 300 + 300 + 500 + 700 + 900)/6 = 466.67

CD's mean is higher. Since you are dividing byt he same number you also could have just added the amount and found which was a larger number. But yes, this is true.

The range of digital is 800

The range is the highest number inus the lowest number. For digital the highest is 900 and lowest is 100 so the ange is 900-100 = 800. So this is true.

The median of CDs is 400.

The median is the middle value for odd numbers of values, or the average of the two middle values. 6 total values means you have to take the third and fourth and average them. in CDs the middle values are 800 and 600, the average is 700, so that is what the median is. this is false.

Both have the same interquartile range.

Interquartile range is to find the middle number or numbers like in median, then take the two parts it is split into and find the "median" of those. Then subtract the larger one fromt he smaller one.

IQR of CD the first half is 200, 400, 600 so the middle here is 400, second half has a middle number of 800 so IQR here is 800-400=400

IQR of digital is 700-300 = 400 so yes both are the same.

Both have the same median

We know the medan of CDs is 700 then findign the median of digital is (300+500)/2 = 400. So no, the medians are not the same.

Digital’s mean is around 467.

We founf the mean for digital to be 466.67 which rounds up to 467, So I would say it is true.

8 0

2 years ago

Read 2 more answers

Oni was timing her 100 meter sprints. Her first five sprints were 12.568 seconds, 11.426 seconds, 12.324 seconds, 11.981 seconds

oksian1 [2.3K]

Answer:

Rounding to the nearest tenth and rounding to the nearest one hundredth.

Step-by-step explanation:

round all up or down then line up and add

12.568= 13

11.426= 11

12.324= 12

11.981= 12

12.601= 13

add the totals then you see

60.83 sames as 61

4 0

1 year ago

Read 2 more answers