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OverLord2011 [107]

3 years ago

11

The area of a rectangle is 27ft squared, and the length of the rectangle is 3ft less than twice the width. Find the dimensions o

f the rectangle.

1 answer:

oksano4ka [1.4K]3 years ago

6 0

Answer:

width =4.5ft

length=6ft

Step-by-step explanation:

w = x

L = 2x-3

area = L*w

27 = x(2x-3)

$27=2x^{2} -3x$

$2x^{2} -3x-27=0$

$2x^{2} +6x-9x-27=0$

2x(x+3)-9(x+3)=0

(2x-9)(x+3)=0

2x-9=0

2x=9

x=9/2

x=4.5

L=2x-3=2*4.5-3 =9-3=6

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What is the period of the function y=-4sin (2/3x-pi?3)?

ad-work [718]

2/3 x = 2 pi
x = 2pi × 3/2 = 3pi

period = 3pi

7 0

3 years ago

Radio tower had a special on rechargeable batteries. It sold AA for $1 and AAA for $0.75. It sold 42 batteries on a single day a

PIT_PIT [208]

AA = $1
AAA= $0.75

AA + AAA = 42

$1AA + $0.75AAA= $37

AA + AAA = 42
AA + AAA-AAA= 42- AAA
AA = 42- AAA

$1(42- AAA) + $0.75AAA= $37
$42 - AAA +0.75AAA = $37
$42 -0.25AAA= $37
$42-$42 -0.25AAA= $37 -$42
-0.25AAA= -5
-0.25AAA/-0.25 = -5/-0.25
AAA= 20

AA + AAA= 42
AA + 20 = 42
AA +20 -20 = 42-20
AA= 22

Check
$1AA + $0.75AAA= $37
$1(22)+ $0.75(20)= $37
$22 + $15 =$37
$37 = $37

5 0

3 years ago

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

rusak2 [61]

Answer:

$x=30\\y=68\\z=82$

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

$y+z=5x$

The third angle is 14 more than the second

$z=y+14$

And remember that the sum of these three angles must be equal to 180.

$x+y+z=180$

Let's take these equations

$y+z=5x\\z=y+14\\x+y+z=180$

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

$x+5x=180$

Combine like terms;

$6x=180$

Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

$2y=180-44\\2y=136$

Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

$x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82$

5 0

3 years ago

Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-

soldi70 [24.7K]

Answer:

Jaime's. Interval not centered around the point estimate.

Step-by-step explanation:

When constructing a confidence interval based on a point estimate, the obtained point estimate must be the central value of the interval.

For Jaime's interval

Lower bound = 0.078

Upper Bound = 0.193

$Central = \frac{0.078+0.193}{2} =0.1355$

For Mariya's interval

Lower bound = 0.051

Upper Bound = 0.189

$Central = \frac{0.051+0.189}{2} =0.12$

For a point estimate of 0.12, only Mariya's interval is adequate since Jaime's is not centered around the point estimate.

4 0

2 years ago

A meteorologist keeps hourly temperature records over the course of several years in order to look for long-term variations. Thi

Aleks04 [339]

Answer:

Observational study

Step-by-step explanation:

There are 3 types of statistical study:

1) Experimental: Under this, any experiment is done on a certain group of population.

2) Observational: Under this study, the events are observed regularly and the record is made.

3) Survey : Under this study, a survey is conducted with a a group of population and the record is made.

According to question, A meteorologist keeps hourly temperature records over the course of several years in order to look for long-term variations, this is an example of <u>observational study</u>.

4 0

3 years ago