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2 years ago

Look at image………………………

Mathematics

2 answers:

PolarNik [594]2 years ago

6 0

Answer:

If I directly give you the answers they won't help you...so I've shown you how to do the questions instead

Step-by-step explanation:

8/9 + 5/6 (make them have the same denominator)

= 48/54 + 45/54

= 93/54 (make it a mixed fraction)

1 and 39/54

(The second and third one are done the same way... make them have the same denominator by using their equivalent fractions (e.g 1/2 = 2/4), add the numerators ONLY... simplify the result)

1 and 6/9 divided by 5/6

(make the first number an improper fraction)

1 x 9 + 6 = 15 (this is the numerator...the denominator remains the same)

15/9 divided by 5/6 (reciprocate the number after the division sign and then change the division sign to a multiplication sign)

15/9 x 6/5

(Then simplify. e.g the 5 in 6/5 can be divided by the 15 in 15/9)

3/9 x 6/1

(The 6 in 6/1 and the 9 in 3/9 have a common factor... 3)

3/3 x 2/1

(3/3 = 1)

1 x 2

(The other questions are done in the same way... Make the mixed fraction an improper fraction(This means the denominator is larger than the numerator)... reciprocate the number after the division sign (This means flipping it (e.g 2/3 becomes 3/2) then change the division sign to a multiplication sign and either directly multiply the result or simplify it first by dividing numerators with denominators (e.g instead of 9/3 x 12/4 = 108/12 = 9, you could say 1 divided 3 = 4 thus 9/1 x 4/4 (which is = 1) thus 9 x 1 = 9). Either way you should get the same answer whichever way you choose.

PS: YOU COULD ALSO USE A CALCULATOR TO CONFIRM YOUR ANSWER

olya-2409 [2.1K]2 years ago

6 0

8/9÷5/6=8/9×6/5=16/15

7/10÷12/25=7/10×25/12=35/25

2/3÷1/5=2/3×5=10/3

1-6/9÷5/6=15/9×6/5=2

2-3/4÷3/8=11/4×8/3=22/3

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Read 2 more answers

3. Using the sample size of 800 and the proportion 0.47, calculate the margin of error associated with the estimate of the propo

salantis [7]

Answer:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

We assume for this case a confidence level of 95%. 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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

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

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 if we replace the values obtained we got this:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

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3 years ago

5. Suppose that a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organ

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Answer:

Probability that the sample proportion will be greater than 0.5 is 0.8133.

Step-by-step explanation:

We are given that the a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p.

Suppose that the polling organization takes a simple random sample of 500 voters.

Let $\hat p$ = sample proportion

The z-score probability distribution for sample proportion is given by;

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

where, $\hat p$ = sample proportion

p = population proportion = 48%

n = sample of voters = 500

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the sample proportion will be greater than 0.5 is given by = P( $\hat p$ > 0.50)

P( $\hat p$ > 0.50) = P( $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < $\frac{0.50-0.48}{\sqrt{\frac{0.50(1-0.50)}{500} } }$ ) = P(Z < 0.89) = 0.8133

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.89 in the z table which has an area of 0.8133.

Therefore, probability that the sample proportion will be greater than 0.50 is 0.8133.

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