if the breadth of a rectangle is one third of its length and perimeter is 80 cm find the length and breadth of rectangle

Serhud [2]

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8 0

2 years ago

A high school principal wishes to estimate how well his students are doing in math. Using 40 randomly chosen tests, he finds tha

ollegr [7]

Answer:

99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Step-by-step explanation:

We are given that a high school principal wishes to estimate how well his students are doing in math.

Using 40 randomly chosen tests, he finds that 77% of them received a passing grade.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of students received a passing grade = 77%

n = sample of tests = 40

p = population proportion

<em>Here for constructing 99% confidence interval we have used One-sample z proportion test statistics.</em>

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5%

level of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

P( $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

<u>99% confidence interval for p</u> = [ $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.77-2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }$ , $0.77+2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }$ ]

= [0.5986 , 0.9414]

Therefore, 99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Lower bound of interval = 0.5986

Upper bound of interval = 0.9414

6 0

2 years ago

(PLEASE HELP) (NO SPAM) Complete the special right tringale:

marusya05 [52]

Answer:

Step-by-step explanation:

BD is opposite the 30° angle. The sine of 30° is 0.5. The sin of an angle in a right triangle is opposite/hypotenuse so BD = sin 30°x8.

Now you have two known lengths The third can be found by applying the Pythagorean theorem: BC²+BD²=CD², from which you can establish a numerical value for BC.

6 0

3 years ago

Explain how you use estimation to check the reasonableness of a solution to a practical problem.

Oxana [17]

Answer:

Well, one way to use reasonableness is to estimate the answer to see if your answer is an outrageous answer or not. So, looking at your problem, you see that you are multiplying a two hundred something number by 4 and then subtracting 10 from it.

Step-by-step explanation:

3 0

3 years ago

Y+3 1/2=6 help pleaseee

Verdich [7]

3 1/2 = 7/2
so y+7/2 = 6
y=6-7/2 = 12-7 / 2 = 5/2 = 2 1/2

8 0

2 years ago

if the breadth of a rectangle is one third of its length and perimeter is 80 cm find the length and breadth of rectangle ​

if the breadth of a rectangle is one third of its length and perimeter is 80 cm find the length and breadth of rectangle