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3 years ago

Draw a frequency polygon for the following data:

Mathematics

1 answer:

const2013 [10]3 years ago

8 0

Answer:

See attachment

Step-by-step explanation:

Given

$\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}$

Required

The frequency polygon

We have:

$\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}$

First, we calculate the midpoint of each class

$\begin{array}{ccccccc}{Midpoint} & {(0+10)/2} & {(10+20)/2} & {(20+30)/2} & {(30+40)/2} & {(40+50)/2} & {(50+60)/2}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}$

$\begin{array}{ccccccc}{Midpoint} & {5} & {15} & {25} & {35} & {45} & {55}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}$

Lastly, we plot the midpoint against the frequency of students (see attachment)

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You wish to compute the 99% confidence interval for the population proportion. How large a sample should you draw to ensure that

Nataly_w [17]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.13}{2.58})^2}=98.47$

And rounded up we have that n=99

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.13$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We assume the value for $\hat p =0.5$ since we don't have previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.13}{2.58})^2}=98.47$

And rounded up we have that n=99

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A baseball player hits a ball at an angle of 52 degrees and at a height of 4.5 ft. if the ball's initial velocity after being hi

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Answer:

$t\approx 5.865\,s$

Step-by-step explanation:

The motion equations that describe the ball are, respectively:

$x = \left[\left(152\,\frac{ft}{s} \right)\cdot \cos 52^{\circ} \right] \cdot t$

$y = 4.5\,ft + \left[\left(152\,\frac{ft}{s} \right)\cdot \sin 52^{\circ} \right] \cdot t - \frac{1}{2}\cdot \left(32.174\,\frac{ft}{s^{2}} \right) \cdot t^{2}$

The time required for the ball to hit the ground is computed from the second equation. That is to say:

$4.5\,ft + \left[\left(152\,\frac{ft}{s} \right)\cdot \sin 52^{\circ} \right] \cdot t - \frac{1}{2}\cdot \left(32.174\,\frac{m}{s^{2}} \right) \cdot t^{2} = 0$

Given that formula is a second-order polynomial, the roots of the equation are described below:

$t_{1}\approx 5.865\,s$ and $t_{2} \approx -0.048\,s$

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Prakash bought a new car at the dealership for $27,000. it is estimated that the value of the car will decrease 7% each year. wh

Dennis_Churaev [7]

The exponential function models the value v of the car after t years is V = 27000 * (0.93)^t

<h3>How to determine the exponential model?</h3>

The given parameters are:

Initial value, a = $27,000

Depreciation rate, r = 7%

The value of the car is then calculated as:

V = a * (1 -r)^t

Substitute known values

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Evaluate the difference

V = 27000 * (0.93)^t

Hence, the exponential function models the value v of the car after t years is V = 27000 * (0.93)^t

Read more about exponential function at:

brainly.com/question/11464095

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jocelyn bought 2 sweaters for the same price. she paid 23.56,including sales tax of 1.36 and a 5.00 discount coupon. what was th

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Number of sweaters bought by Jocelyn = 2
Price of the 2 sweaters including tax and discount coupon = 23.56
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Amount of discount coupon = 5.00
Then
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Then
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So
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Answer:

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Step-by-step explanation:

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