Here is a cube of side length 2.5 cm.
2.5 cm
Work out the surface area of this cube.

Answer:

90

Step-by-step explanation:

the colums add up to angle 1, which make angle 2 adjacent.

9-9=0

Answer:

Step-by-step explanation:

A relation may or may not represent a function.

Table (a), (c) and (d) represent a function

The tables represent a relation

For a relation to be a function, then:

The y values must have unique (or distinct) x-values.

From the list of tables, we have the following observations

Hence, all the tables represent a valid function, except table (b)

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Step-by-step explanation:

ex : Cow Produce Milk 2.5 Litters/day

1 Month = 30 days(Assume in 30 days )

for second Months

2.5 litters/day x 30 days

= 75 Litters/Month

Answer:

its the 4 one

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total number of outcome are  

1320

.

Explanation:

It is apparent that there are  

12

ways in which the post of President can be filled. Once President's post is filled, there are  

11

ways to fill the post of Vice President and then  

10

ways to fill the post of Secretary,

Hence a total of  

12

⋅

11

⋅

10

or  

1320

ways or outcomes.

Answer:

1320

Step-by-step explanation:

Answer: 0.555

Step-by-step explanation:

Answer:

0.9842 = 98.42% probability that at least six of them find employment in their chosen field within three months.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they found employment, or they did not. The probability of a student finding employment is independent of any other student, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

88% of students who graduate from the university successfully find employment in their chosen field within three months of graduation.

This means that [tex]p = 0.88[/tex]

Nine randomly selected students

This means that [tex]n = 9[/tex]

What is the probability that of nine randomly selected students who have graduated from this university, at least six of them find employment in their chosen field within three months?

This is:

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{9,6}.(0.88)^{6}.(0.12)^{3} = 0.0674[/tex]

[tex]P(X = 7) = C_{9,7}.(0.88)^{7}.(0.12)^{2} = 0.2119[/tex]

[tex]P(X = 8) = C_{9,8}.(0.88)^{8}.(0.12)^{1} = 0.3884[/tex]

[tex]P(X = 9) = C_{9,9}.(0.88)^{9}.(0.12)^{0} = 0.3165[/tex]

Then

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0.0674 + 0.2119 + 0.3884 + 0.3165 = 0.9842[/tex]

0.9842 = 98.42% probability that at least six of them find employment in their chosen field within three months.

Answer:

C. tan K=31/24

Step-by-step explanation:

Relations in right triangles:

The sine of an angle is the length of the opposite side to the angle divided by the length of the hypotenuse.

The cosine of an angle is the length of the adjacent side of the angle divided by the length of the hypotenuse.

The tangent of an angle is the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this question:

Sides 24 and 31.

Side opposite to K: 31

Side adjacent to K: 24

Then

tan K=31/24

And the correct answer is given by option D.

Answer:

(in attachment)

Step-by-step explanation:

you can find the points by inputting the x-values into the equation to solve for the y-values, then connecting the plotted points to create the line.

When x=-4

y=1/2(-4)

y=-2

(-4,-2)

Repeat for all values.

Answer:

◦•●◉these are related functions

Answer: the answer is b

Answer:

The ratio between two values A and B is just the quotient between these two values:

ratio = A/B

a) $280 in 7m

Here the ratio is:

$280/7m = $40/m

This also can be read as:

$40 per meter.

b) 105 miles in 2 hours

Here the ratio is:

105mi/2h = 52.5 mi/h

This also can be read as:

52.5 miles per hour

c) $33 for 5lb

The ratio is:

$33/5lb = $6.6/lb

This can be read as:

$6.6 per pound.

d) 50 pages in 2 hours

the ratio is:

(50 pages)/2h = 25 pages/h

this can be read as:

25 pages per hour.

Answer:

  B.  x ≤ 1 or x > 6

Step-by-step explanation:

Subtract 8 and divide by 2. (Same steps for both inequalities.)

  2x +8 ≤ 10

  2x ≤ 2

  x ≤ 1

__

  2x +8 > 20

  2x > 12

  x > 6

The solution is x ≤ 1 or x > 6.

Answer:

The warranty period should be of 30 months.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Eco-Cook rice cooker has a mean time before failure of 38 months with a standard deviation of 6 months.

This means that [tex]\mu = 38, \sigma = 6[/tex]

What should be the warranty period, in months, so that the manufacturer will not have more than 8% of the rice cookers returned?

The warranty period should be the 8th percentile, which is X when Z has a p-value of 0.08, so X when Z = -1.405.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.405 = \frac{X - 38}{6}[/tex]

[tex]X - 38 = -1.405*6[/tex]

[tex]X = 30[/tex]

The warranty period should be of 30 months.

Answer:

The p-value of the test statistic is 0.2019.

Step-by-step explanation:

Test if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds.

At the null hypothesis, we test if it relieves pain in at most 384 seconds, that is:

[tex]H_0: \mu \leq 384[/tex]

At the alternative hypothesis, we test if it relieves pain in more than 384 seconds, that is:

[tex]H_1: \mu > 384[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

384 is tested at the null hypothesis:

This means that [tex]\mu = 384[/tex]

For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23.

This means that [tex]n = 41, X = 387, \sigma = 23[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{387 - 384}{\frac{23}{\sqrt{41}}}[/tex]

[tex]z = 0.835[/tex]

P-value of the test:

The p-value of the test is the probability of finding a sample mean above 387, which is 1 subtracted by the p-value of z = 0.835.

Looking at the z-table, z = 0.835 has a p-value of 0.7981.

1 - 0.7981 = 0.2019

The p-value of the test statistic is 0.2019.

Answer:

[tex]x=216 salads[/tex]

Step-by-step explanation:

One Hour:

Salad=40

Sandwich=19

Total work time[tex]T=7[/tex]

Generally

Time to make 30 sandwiches is

[tex]T_s=\frac{30}{19}[/tex]

[tex]T-s=1.6hours[/tex]

Therefore

Bill has 7-1.6 hours to make salads and can make x about of salads in

[tex]x=(7-1.6)*40[/tex]

[tex]x=5.4*40[/tex]

[tex]x=216 salads[/tex]

Answer:

r=-4+2[tex]\sqrt{5}[/tex], r=-4-2[tex]\sqrt{5}[/tex]

Answer:

r=-4+2[tex]\sqrt{5}[/tex], r=-4-2[tex]\sqrt{5}[/tex]

Step-by-step explanation:

It was right for me

Answer:

[tex] \displaystyle 4[/tex]

Step-by-step explanation:

we are given that A vegetable garden and a surrounding as a shaped like a square that together a 11 ft wide. The path is 2 feet wide.since together the width of Vegetable garden and path is 11 ft, the width of the vegetables garden will be the difference between the total width and the width of path Thus,

[tex] \displaystyle \rm W _{ garden} = 11 - 2[/tex]

simplify substraction:

[tex] \displaystyle \rm W _{ garden} = 9[/tex]

recall that, every single side of a square is equal to each other therefore the the area of the garden will be

[tex] \displaystyle {9}^{2} [/tex]

simplify square:

[tex] \displaystyle 81[/tex]

together the garden and path makes a square of every side length 11 ft saying that the area will be:

[tex] \displaystyle {11}^{2} [/tex]

simplify square:

[tex] \displaystyle 121[/tex]

the area of path will be the difference between the total area and the garden area therefore,

[tex] \displaystyle 121 - 81[/tex]

simplify addition:

[tex] \displaystyle 40[/tex]

to figure out how many bags are needed to cover the path. we just need to divide the area of the path by the area of a bag of gravel and that yields:

[tex] \displaystyle \frac{40}{10} [/tex]

simplify division:

[tex] \displaystyle \boxed{\rm4}[/tex]

hence,

4 bags are needed to cover the path.

Answer:

Following are the solution to the given points:

Step-by-step explanation:

For question a:

The chart is called a cumulative frequency polygon.

For question b:

The total number of sold homes in last month= 250

For question c:

The class intervels are:

[tex]\to 100-50 = 50[/tex]

For question d:

[tex]\to[/tex] 240000 (75% of houses)

For question e:

[tex]\to[/tex] 230000

Answer:

Ungrouped data refers to the data that is first gathered from a study, it is a raw data that is, i.e it has not sorted into categories or grouped. To calculate the mean of ungrouped data we use the formula

Step-by-step explanation:

Answer:

e. All of the above statements are correct.

Option e is correct. All of the above statements are correct.

Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data

Data Scientist makes value out of data, he is expert in various tools and technologies like machine learning, deep learning, artificial intelligence and he solve business problems by presenting a model to predict business future.

During data preparation, data scientists and DBAs aggregate the data and merge them from different sources. During data preparation, data scientists and DBAs define the variables to be used in the model.

Hence, All of the above statements are correct, Option e is correct.

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Answer:

1. >

2. <

3. =

4. <

Step-by-step explanation:

23.197 > 23.179

3 2/10 which is the same as,

3.2 < 3.243

30.423 = 30 423/1000

18.546 < 18 56/100

Answer:

Answer

Step-by-step explanation:

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Answer:

The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

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

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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

California:

Sample of 296 voters, 146 voted. This means that:

[tex]p_{Ca} = \frac{146}{296} = 0.4932[/tex]

[tex]s_{Ca} = \sqrt{\frac{0.4932*0.5068}{296}} = 0.0291[/tex]

Colorado:

Sample of 215 voters, 127 voted. This means that:

[tex]p_{Co} = \frac{127}{215} = 0.5907[/tex]

[tex]s_{Co} = \sqrt{\frac{0.5907*0.4093}{215}} = 0.0335[/tex]

Test if the population proportion of voter turnout in Colorado is higher than that in California:

At the null hypothesis, we test if it is not higher, that is, the subtraction of the proportions is at most 0. So

[tex]H_0: p_{Co} - p_{Ca} \leq 0[/tex]

At the alternative hypothesis, we test if it is higher, that is, the subtraction of the proportions is greater than 0. So

[tex]H_1: p_{Co} - p_{Ca} > 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]X = p_{Co} - p_{Ca} = 0.5907 - 0.4932 =  0.0975[/tex]

[tex]s = \sqrt{s_{Co}^2+s_{Ca}^2} = \sqrt{0.0291^2+0.0335^2} = 0.0444[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.0975 - 0}{0.0444}[/tex]

[tex]z = 2.2[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference above 0.0975, which is 1 subtracted by the p-value of z = 2.2.

Looking at the z-table, z = 2.2 has a p-value of 0.9861.

1 - 0.9861 = 0.0139.

The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.

Answer:

There are 75 ways to form the committee.

Step-by-step explanation:

The order in which the people are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Considering the eldest has to be there, 2 men from a set of 6 and 4 boys from a set of 5(excluding the youngest), so:

[tex]T = C_{6,2}C_{5,4} = \frac{6!}{2!4!} \times \frac{5!}{1!4!} = 3*5*5 = 75[/tex]

There are 75 ways to form the committee.