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4 years ago

ABCD is a rectangle.Work out the angle 'a' in each diagram.Help please!!

Mathematics

1 answer:

Liono4ka [1.6K]4 years ago

6 0

Top one: Since corners of rectangles are 90 degrees, angle ABD would be 28 degrees, and angle CBE would be 41 degrees. Subtract 90 by both numbers, and the answer is 21.

Bottom one: With the same logic, angle ADE would be 38 degrees, and angle CDB would be 35. Because of that, angle a is 55 degrees (90-35=55)

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What is the percent of change to 125 centimeteres 87.5 centimeters?

MrRa [10]

I hope this helps you

125-87,5=37,5

125 37,5

100 ?

?.125=100.37,5

?=3750/125

?=30

30%

5 0

3 years ago

Eight times the reciprocal of a number equals 4 times the reciprocal of 2. find the number

uysha [10]

Answer:

The number is 4

Step-by-step explanation:

Let the number = 'x'

Reciprocal of 'x' = 1/x

Reciprocal of 2 = 1/2

8 times the reciprocal of 'x' = $8*\frac{1}{x}\\$

$8*\frac{1}{x}= 4* \frac{1}{2}\\\\8*\frac{1}{x}= 2\\$

Now multiply both sides by x

$8*\frac{1}{x}*x = 2*x\\\\8 = 2x$

Now divide both sides by 2

$\frac{8}{2}=\frac{2x}{2}\\\\4 = x$

x = 4

4 0

3 years ago

A coin is tossed 71 times and 34 heads are observed. Is the coin fair? Use a 98% level confidence interval to base your inferenc

Fofino [41]

Answer:

a) $\hat p=\frac{34}{71}=0.48$ estimated proportion of heads observed.

b) $Se= \sqrt{\frac{0.479(1-0.479)}{71}}=0.0593$

c) $z_{\alpha/2}=2.33$

d) $0.479 - 2.33 \sqrt{\frac{0.479(1-0.479)}{71}}=0.341$

e) $0.479 + 2.33 \sqrt{\frac{0.479(1-0.479)}{71}}=0.617$

f) In order to be fair the coin needs to have included the 0.5 on the interval, and for this case it's included, so we can say that at 2% of significance we can say that the coin is fair.

Step-by-step explanation:

Notation and definitions

$X=34$ number of heads observed.

$n=71$ random sample taken

$\hat p=\frac{34}{71}=0.479$ estimated proportion of heads observed.

$p$ true population proportion of heads observed.

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

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

The point estimator for the population proportion of heads is: Answer with two decimal precision.

$\hat p=\frac{34}{71}=0.48$ estimated proportion of heads observed.

The standard error in this estimate is: Answer with four decimal precision.

The confidence interval would be given by this formula

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

And the standard error is given by:

$Se= \sqrt{\frac{\hat p(1-\hat p)}{n}}$

$Se= \sqrt{\frac{0.479(1-0.479)}{71}}=0.0593$

The correct table value for the 98% level confidence interval is: Answer with two decimal precision

For the 98% confidence interval the value of $\alpha=1-0.98=0.02$ and $\alpha/2=0.01$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.33$

The lower end point of the CI is: Answer with three decimal precision.

And replacing into the confidence interval formula we got:

$0.479 - 2.33 \sqrt{\frac{0.479(1-0.479)}{71}}=0.341$

The upper end point of the CI is: Answer with three decimal precision.

$0.479 + 2.33 \sqrt{\frac{0.479(1-0.479)}{71}}=0.617$

And the 90% confidence interval would be given (0.341;0.617).

Based on the confidence interval, it is plausible that the coin is fair.

In order to be fair the coin needs to have included the 0.5 on the interval, and for this case it's included, so we can say that at 2% of significance we can say that the coin is fair.

4 0

4 years ago

Eleven computer science students stand in line at the student service. The three students are called Nikola. How many ways can t

Angelina_Jolie [31]

Answer:

3 ways

Step-by-step explanation:

8 0

3 years ago

Write the standard form of the line with the given information. Include your work in your final answer. Type your answer in the

earnstyle [38]

I am going to show you the procedure with any slope (given that you did not write the value of the slope)

general slope value: m
generic point (x1,y1)

Formula: y - y1 = m (x -x1)

y - y1 = mx - mx1

y - mx - y1 + mx1 = 0

x1 = -2 , y1 = -3 =>

y - mx - (-3) + m(- 2) = 0

y - mx + (3 -2m) = 0

Now suppose a value for m. Lets say it is m = 5.

y - 5x + (3 - 2*5) = 0

y - 5x + (3 - 10) = 0

y - 5x + (-7) = 0 and that is the standard form if the slope is 5. Now you can do the same with any slope.

4 0

3 years ago

Read 2 more answers