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1 year ago

The length and breath of a rectangular field is in the ratio 3:4. It’s area is 6912 sq.cm find its dimensions.

Mathematics

1 answer:

anastassius [24]1 year ago

5 0

Answer:

The ratio of length to breadth is 3:4

let the length be 3x

breadth be 4x

area = 4x x 3x

6912 = 12x^2

x^2 = 576

x=24

length= 72

breadth =96

actually length will be greater than breadth

so the ratio must be 4:3 then alter the above length and breadth values

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A sample of 900 college freshmen were randomly selected for a national survey. Among the survey participants, 372 students were

Rufina [12.5K]

Answer:

a) $ME=2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.0423$

b) $0.413 - 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.371$

Step-by-step explanation:

1) Data given and notation

n=900 represent the random sample taken

X=372 represent the students were pursuing liberal arts degrees

$\hat p=\frac{372}{900}=0.413$ estimated proportion of students were pursuing liberal arts degrees

$\alpha=0.01$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

p= population proportion of students were pursuing liberal arts degrees

2) Solution to the problem

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

If we replace we have:

$ME=2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.0423$

And replacing into the confidence interval formula we got:

$0.413 - 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.371$

$0.413 + 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.455$

And the 99% confidence interval would be given (0.371;0.455).

We are confident (99%) that about 37.1% to 45.5% of students were pursuing liberal arts degrees.

7 0

2 years ago

Which two statements are missing in steps 3 and 4?

Snezhnost [94]

Answer:

∠B ≅ ∠Y △ABC ~ △ZYX by the SAS similarity theorem.

Step-by-step explanation:

1. $AB=6$ units

$YZ=3$ units

$BC=8$ units

$XY=4$ units, then

$\dfrac{AB}{ZY}=\dfrac{BC}{YX}=2$

2. $\angle B$ and $\angle Y$ are right angles - given

3. $\angle B\cong \angle Y$ two right angles are always congruent.

4. $\triangle ABC\sim \triangle ZYX$ by SAS similarity theorem.

SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

4 0

1 year ago

Read 2 more answers

Type the correct answer in each box. A music company is introducing a new line of acoustic guitars next quarter. These are the c

andre [41]

Answer:

The company has to produce more than 92 guitars and sell them for making a profit.

Step-by-step explanation:

These are the cost and revenue functions, where x represents the number of guitars to be manufactured and sold: R(x) = 120x, and C(x) = 100x + 1840.

Therefore, the condition for no loss-no gain for manufacturing x number of guitars is

R(x) = C(x)

⇒ 120x = 100x + 1840

⇒ 20x = 1840

⇒ x = 92

Therefore, the company has to produce more than 92 guitars and sell them for making a profit. (Answer)

7 0

2 years ago

Answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Sergeu [11.5K]

Answer:

Step-by-step explanation:

1 is d 2 is b 3 is a 4 is b 5 is c and 6 is b

6 0

2 years ago

Read 2 more answers

? A survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits

Anastasy [175]

Percent means per one-hundred

300(10/100)=30

So 30 of the 300 workers were satisfied with their benefits.

5 0

2 years ago