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3 years ago

Can a common denominator of mixed numbers be 20?

Mathematics

2 answers:

Dominik [7]3 years ago

4 0

Yes you are correct have a good night and day

gladu [14]3 years ago

3 0

Yes, a common denominator is just the smallest multiple of all numbers in a group.

So the common denominator of 4, 8 and 12 would be 4, because 4 goes into all those numbers.

You might be interested in

Use a half-angle identity to find the exact value of tan 22.5°.

dusya [7]

Answer:

$\sqrt{2} -1$

Step-by-step explanation:

22.5 degrees is half of 45 degrees (special angle for which we know exactly the value of all three basic trigonometric functions (sine, cosine, and tangent).

So we start recalling the formula for tangent of a half angle: $tan(\frac{\alpha }{2} )= \frac{1-cos(\alpha) }{sin(\alpha) }$

We need just the values of:

$sin(\alpha )=sin(45^o)=\frac{\sqrt{2} }{2}$

and of

$cos(\alpha )=cos(45^o)=\frac{\sqrt{2} }{2}$

to answer the question. Then, we use those values in the original formula for tangent of a half angle:

$tan(\frac{\alpha }{2} )= \frac{1-cos(\alpha) }{sin(\alpha) }\\tan(22.5^o)=\frac{1-\frac{\sqrt{2} }{2} }{\frac{\sqrt{2} }{2}} =\frac{2-\sqrt{2} }{\sqrt{2} } =\frac{2\sqrt{2}-2 }{2} =\sqrt{2} -1$

3 0

3 years ago

Read 2 more answers

2. A marketing firm is trying to estimate the proportion of potential car buyers that would consider

Maurinko [17]

Answer:

a. The number of people that should be in the pilot study are 600 people

b. The point estimate is 0.62 $\overline 6$

c. At 95% confidence level the true population proportion of potential car buyers of hybrid vehicle is between the confidence interval (0.588, 0.6654)

d. Two ways to reduce the margin of error are;

1) Reduce the confidence interval

2) Use a larger sample size

Step-by-step explanation:

a. The given parameters for the estimation of sample size is given as follows;

The margin of error for the confidence interval, E = 4% = 0.04

The confidence level = 95%

The sample size formula for a proportion as obtained from an online source is given as follows;

$n = \dfrac{Z^2 \times P \times (1 - P)}{E^2}$

Where, P is the estimated proportions of the desired statistic, therefore, we have for a new study, P = 0.5;

Z = The level of confidence at 95% = 1.96

n + The sample size

Therefore, we have;

$n = \dfrac{1.96^2 \times 0.5 \times (1 - 0.5)}{0.04^2} = 600.25$

Therefore, the number of people that should be in the pilot study in order to meet this goal at 95% confidence level is n = 600 people

b. The point estimate for the population proportion is the sample proportion given as follows;

$\hat p = \dfrac{x}{n}$

Where;

x = The number of the statistic in the sample

n = The sample size

From the question, we have;

The number of potential car buyers, n = 600

The number of respondent in the sample that indicated that they would consider purchasing a hybrid, x = 376

Therefore, the point estimate, for the proportion of potential car buyers that would consider buying a hybrid vehicle, $\hat p$ = 376/600 = 0.62 $\overline 6$

c. The confidence interval for a proportion is given as follows

$CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

Therefore, we get;

$CI=0.62 \overline 6\pm 1.96\times \sqrt{\dfrac{\hat{0.62 \overline 6}\cdot (1-\hat{0.62 \overline 6})}{600}}$

C.I. ≈ 0.6267 ± 0.0387

The 95% confidence interval for the true population proportion of potential buyers of hybrid vehicle, C.I. = (0.588, 0.6654)

d. The margin of error is given by the following formula;

$MOE_\gamma = z_\gamma \times \sqrt{\dfrac{\sigma ^2}{n} }$

Where;

$MOE_\gamma$ = Margin of error at a given level of confidence

$z_\gamma$ = z-score

σ = The standard deviation

n = The sample size

Therefore, the margin error can be reduced by the following two ways;

1) Reducing the confidence interval and therefore, the z-score

2) Increasing the sample size

6 0

2 years ago

Simplify [2*(10+5)]-5

Tcecarenko [31]

[2*(10 + 5)] - 5
[2*(15)] - 5
[2(15)] - 5
[30] - 5
25

5 0

2 years ago

Read 2 more answers

Pls what’s the answer

zimovet [89]

Answer:

I think the answer is D. I hope it helps.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the critical value.

Korvikt [17]

Answer:

The degrees of freedom are given by $df = n-1 = 28$

And since we are conducting a right tailed test we need to find in the right tail of the t distribution with 28 degrees of freedom a value who accumulates $\alpha=0.005$ and we got:

$t_{cric}= 2.763$

Step-by-step explanation:

For this case we are assuming a right tailed test for a parameter, let's say $\mu$

The system of hypothesis for this case are:

Null hypothesis: $\mu \leq \mu_o$

Alternative hypothesis: $\mu > \mu_o$

Where $\mu_o$ is the value to check

The degrees of freedom are given by $df = n-1 = 28$

And since we are conducting a right tailed test we need to find in the right tail of the t distribution with 28 degrees of freedom a value who accumulates $\alpha=0.005$ and we got:

$t_{cric}= 2.763$

3 0

3 years ago