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A field is 53 1/3 yards wide. What is the width of the field in feet?

Umnica [9.8K]

Answer: The width of the field = 160 feet

Step-by-step explanation:

We are given that , A field is $53\dfrac{1}{3}$ yards wide.

That means , The width of the field = $53\dfrac{1}{3}$ yards

Since , the fraction is in mixed for , so first we convert this into improper fraction.

$53\dfrac{1}{3}=\dfrac{3(53)+1}{3}=\dfrac{160}{3}$

Therefore , the width of the field = $\dfrac{160}{3}$ yards

Since 1 yard = 3 feet.

⇒ the width of the field = $\dfrac{160}{3}\times3$ feet

Therefore , the width of the field = 160 feet

5 0

3 years ago

Find an ordered pair to represent a in the equation<br> a=2b+c if b=(6,3) and c=(-4,8)

zaharov [31]

Answer:

The ordered pair to represent a in the equation a=2b+c if b=(6,3) and c=(-4,8) is: a=(8,14)

Step-by-step explanation:

b=(6,3)

c=(-4,8)

a=2b+c

Replacing b and c in the equation above:

a=2(6,3)+(-4,8)

Multiplying:

a=(2*6,2*3)+(-4,8)

a=(12,6)+(-4,8)

Adding:

a=(12+(-4),6+8)

a=(12-4,14)

a=(8,14)

8 0

4 years ago

Which of the following is an example of a statistic? a.) A value used to represent a population b.) Standard deviation of all fi

natita [175]

Answer:

d

Step-by-step explanation:

statistic is a number that represents as numerical data

. An example of statistics is a report of numbers saying how many followers of each religion there are in a particular country.

6 0

3 years ago

According to a bridal magazine, the average cost of a wedding reception for an American wedding is $8213. Assume that this avera

Thepotemich [5.8K]

Answer:

a. The point estimate of the corresponding population mean is of $8213.

b. The margin of error is of $103.

c. The 98% confidence interval for the corresponding population mean is between $7973.5 and $8452.5, which means that for all weedings, we are 98% sure that the true population mean is in this interval.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. What is the point estimate of the corresponding population mean?

The sample mean is of $8213. So, by the Central Limit Theorem, the point estimate of the corresponding population mean is of $8213.

b. What is the margin of error for this estimate (use2 standard deviations (divided by Vn) to either side of the mean is used when no specific confidence level is stated).

Sample of 450, standard deviation of $2185. So

$M = \frac{2185}{\sqrt{450}} = 103$

The margin of error is of $103.

c. Create and interpret a 98% confidence interval for the corresponding population mean.

The confidence interval is given by:

$\mu \pm M*z$

In which $\mu$ is the sample mean and z is the value related to the confidence level.

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a pvalue of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.325$ .

Then

$\mu - M*z = 8213 - 2.325*103 = 7973.5$

$\mu + M*z = 8213 + 2.325*103 = 8452.5$

The 98% confidence interval for the corresponding population mean is between $7973.5 and $8452.5, which means that for all weedings, we are 98% sure that the true population mean is in this interval.

4 0

3 years ago

Which of these triangle pairs can be mapped to each other using two reflections? Triangles X Y Z and P Y T are connected at poin

Irina18 [472]

Answer:

The correct option is the first option;

Triangle XYZ and PYT are connected at point Y. Triangle XYZ is reflected across XY and then is reflected another time across YZ to form triangle PYT

Step-by-step explanation:

To answer the question we look at each option as follows;

1) The parameters given are triangle XYZ and PYT are connected at point Y

Triangle XY is reflected about XY will shift the marked angle from left to right while the right angle will remain at the same location and the triangle will remain upright to give triangle X'Y'Z'

Reflection about the YZ will give; the marked angle and the right angle in the same location and the vertex X will then be changed to P

Therefore, triangle XYZ can be mapped to triangle PYT with two reflections

2) In the second option, we have triangle XYZ is reflected 3 times which is more than 2 times as in the question, therefore, option two is less suited as an answer to the question

3) Triangle XYZ is reflected across side XY and then is shifted down to form triangle AYT

Therefore, since we have only one reflection, option 3 is also not appropriate as an answer

4) In option 4 triangle XYZ is reflected and then rotated therefore option 4 is also not a correct option.

6 0

4 years ago

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