Patrick’s luck had changed over night – but not his skill at mathematical reasoning. The day after graduating from college he used the $20 that his grandmother had given him as a graduation gift to buy a lottery ticket. He knew his chances of winning the lottery were extremely low and it probably was not a good way to spend this money. But he also remembered from the class he took in business analytics that bad decisions some-times result in good outcomes. So he said to himself, "What the heck? Maybe this bad decision will be the one with a good outcome." And with that thought, he bought his lottery ticket.The next day Patrick pulled the crumpled lottery ticket out of the back pocket of his bluejeans and tried to compare his numbers to the winning numbers printed in the paper. When his eyes finally came into focus on the numbers they also just about popped out of his head. He had a winning ticket! In the ensuing days he learned that his share of the jackpot would give him a lump sum payout of about $500,000 after taxes. He knew what he was going to do with part of the money, buy a new car, pay off his college loans, and send his grandmother on an all expenses paid trip to Hawaii. But he also knew that he couldn’t continue to hope for good outcomes to arise from more bad decisions. So he decided to take half of his winnings and invest it for his retirement. So what do you think? Who is right, Josh or Peyton? And more important, why?

Answer:   Mixed Number to Fraction

Mixed Numbers to Improper Fraction

Mixed Numbers Improper Fraction

3 3/4                      15/4

3 3/8                      27/8

3 8/9                      35/9

Hope this helps!!

Answer:

a.vertical translation

Answer:

the base is 5 meters long.

Step-by-step explanation:

To find the a missing side when given the area you have to multiply the area by 2 which in this case would be 50 so 50/10 would be 5m which is your answer.

So the right answer is 5m

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Before Andrei adds the marbles to the glass tank, the glass tank was empty. This means that the volume of the empty tank is when n = 0 and the volume is 32 liters.

Given that:

[tex]W = 32 - 0.05n[/tex]

A linear function is represented as:

[tex]y = b + mx[/tex]

Where

[tex]b \to[/tex] y intercept

Literally, the y intercept is the initial value of the function.

In this function, the y intercept means the initial volume of the glass tank before filling it with marbles.

Compare [tex]y = b + mx[/tex] and [tex]W = 32 - 0.05n[/tex]

[tex]b = 32[/tex]

This means that the volume of the glass tank is 32 liters.

Read more about linear functions at:

https://brainly.com/question/21107621

Answer:

0.05

Step-by-step explanation:

Answer: y= -15 - 3x/5 is the answer.

Step-by-step explanation:

Answer:

The second graph

Step-by-step explanation:

Answer is 5 calories/min

75 divided by 15 is 5

Answer:five cal per min.15 in five groups equals ''75''

Answer

About 219-220

Step-by-step explanation:

Answer: $219.047619

Step-by-step explanation: 1150.00 ÷ 5.25 = 219.047619

Answer: 0.149

Step-by-step explanation:

As Scientists wondered how the snails could travel such long distances. A recent study provides the answer. Biologist Shinichiro Wada fed 174 live snails to birds and found that 26 of the snails were excreted live out the other end.

The best estimate for the proportion of all snails of this type to live after being eaten by a bird can be achieved by calculating the ratio of survival/number of eaten snails

Where the number of eaten snails = 174

The number of survivors = 26

Estimated proportion = 26/174 = 0.1494

Therefore, the best estimate for the proportion of all snails of this type to live after being eaten by a bird will be 0.149 approximately.

Completed Question

1. OSHA is an agency responsible for workplace safety, read its rule and sketch a  diagram that shows the proper relationship between the ladder, wall and ground .

Rule: Non-self-supporting ladders, which must lean against a wall or other support, are to be positioned at such an angle  that the horizontal distance from the top support to the foot of the ladder is about the 1/4 working length of the ladder.

2. Calculate the angle that the ladder makes with the ground using a trigonometric ratio.

3. If a ladder is x feet long, how high up a wall can it safely reach?

4. Would a 51-foot ladder be long enough to climb a 50-foot wall?

Answer:

(a)See attachment

(b)75.52 degrees

(c)[tex]Height ,h=\dfrac{x\sqrt{15}}{4} $ feet[/tex]

(d) NO

Step-by-step explanation:

Part 1

Let the length of the ladder =x

Since by the given rule, Horizontal Distance =[tex]\dfrac14$ of the length of the ladder[/tex]

Horizontal Distance = [tex]\dfrac14x[/tex]

In the sketch of the problem attached below,

Part 2

From Triangle ABC

[tex]\cos C=\dfrac{BC}{AC} \\\cos C=\dfrac{x/4}{x} \\\cos C=\dfrac{1}{4}\\ C=\arccos \dfrac{1}{4}\\C \approx 75.52^\circ[/tex]

The angle that the ladder makes with the ground is 75.52 degrees.

Part 3

If the ladder is x feet long

Using Pythagoras theorem in Triangle ABC below

[tex]x^2=(x/4)^2+h^2\\h^2=x^2-\dfrac{x^2}{16}\\ h^2=\dfrac{15x^2}{16}\\h=\sqrt{\dfrac{15x^2}{16}} \\h=\dfrac{x\sqrt{15}}{4}$ feet[/tex]

Part 4

If x=51 feet

[tex]Height ,h=\dfrac{51\sqrt{15}}{4}$ = 49.38 feet[/tex]

Therefore, a 51 feet ladder would not be enough to climb a 50 feet wall as it would violate the safety rule.

Answer:

  3.84 units

Step-by-step explanation:

By the properties of angle bisectors, ...

  WZ/ZX = WY/YX

Solving for WY, we have ...

  WY = (YX)(WZ)/(ZX) = (6.5/6)(WZ)

The length YZ is ...

  YZ = 8 = WY +WZ

  8 = (6.5/6)(WZ) +WZ = 12.5/6(WZ) . . . . substitute for WY

  WZ = 8(6/12.5) . . . . multiply by 6/12.5

  WZ = 3.84

Answer:

The correct answer is indeed 3.84 units

Step-by-step explanation:

I just took the test and got it correct hope this helps ☺

Answer:

y = 8 - 5x

Step-by-step explanation:

both equations shares the same gradient as they are parallel

from y= 9-5x, the gradient is -5

subst x = 0, y=8, and m= -5 into the y = mx + c to find the value of c

8 = (-5)(0) + c

c= 8

therefore the eqn is y = 8 - 5x

Answer:

Once both the House and Senate have approved the bill in identical form, it becomes "Enrolled" and sent to the President of the United States. The President may sign the bill into law. The President can also take no action on the bill for ten days while Congress is in session and the bill will automatically become law.

Answer:

0.62% probability that the mean of our sample is greater than $70.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question, we have that:

[tex]\mu = 65, \sigma = 20, n = 100, s = \frac{20}{\sqrt{100}} = 2[/tex]

What is the probability mean of our sample is greater than $70.

This is 1 subtracted by the pvalue of Z when X = 70. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{70 - 65}{2}[/tex]

[tex]Z = 2.5[/tex]

[tex]Z = 2.5[/tex] has a pvalue of 0.9938

1 - 0.9938 = 0.0062

0.62% probability that the mean of our sample is greater than $70.

A becuase i worked it out and i got that so im really confident

Answer: –55x + 570

Step-by-step explanation:

The person above me completely missed the question so this is the right one

Answer:

Option B is correct.

It is reasonable to believe that the mean magnesium ion concentration may be greater than 199.5 as the confidence interval obtained contains values that are greater than 199.5

Step-by-step explanation:

Complete Question

Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal.

170 201 199 202 173 153

Based on a 95% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 199.5? (Hint: you should first calculate the 95% confidence interval for the mean magnesium ion concentration.)

A) The likelihood cannot be determined.

B) Yes

C) No

Solution

For this question, obtaining the confidence interval will give a clear solution to the problem.

Since the Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence, if the range obtained contains values greater than the standard we are comparing against (199.5), then the confidence interval proves that the mean magnesium ion may be greater than 199.5.

But to obtain the confidence interval, we need the mean and standard deviation for the sample.

170, 201, 199, 202, 173, 153

Mean = (sum of variables)/(total number of variables)

Sum of variables = 170+201+199+202+173+153 = 1098

Total number of variables = 6

Mean = (1098/6) = 183

Standard deviation = σ = √[Σ(x - xbar)²/N]

x = each variable

xbar = mean = 183

N = number of variables = 6

Σ(x - xbar)² = (170-183)² + (201-183)² + (199-183)² + (202-183)² + (173-183)² + (153-183)²

= 169 + 324 + 256 + 361 + 100 + 900

= 2110

σ = √(2110/6) = 18.75

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = 183

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 6 - 1 = 5.

Significance level for 95% confidence interval

(100% - 95%)/2 = 2.5% = 0.025

t (0.025, 5) = 2.57 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 18.75

n = sample size = 6

σₓ = (18.75/√6) = 7.656

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 183 ± (2.57 × 7.656)

CI = 183 ± 19.675

95% CI = (163.325, 202.675)

95% Confidence interval = (163.3, 202.7)

It is reasonable to believe that the mean magnesium ion concentration may be greater than 199.5 as the confidence interval obtained contains values that are greater than 199.5

Hope this Helps!!!

Expectation is linear, meaning

E(a X + b Y) = E(a X) + E(b Y)

= a E(X) + b E(Y)

If X = 1 and Y = 0, we see that the expectation of a constant, E(a), is equal to the constant, a.

Use this property to compute the expectations:

E(X + 10) = E(X) + E(10) = $110

E(5Y) = 5 E(Y) = $450

E(X + Y) = E(X) + E(Y) = $190

Variance has a similar property:

V(a X + b Y) = V(a X) + V(b Y) + Cov(X, Y)

= a^2 V(X) + b^2 V(Y) + Cov(X, Y)

where "Cov" denotes covariance, defined by

E[(X - E(X))(Y - E(Y))] = E(X Y) - E(X) E(Y)

Without knowing the expectation of X Y, we can't determine the covariance and thus variance of the expression a X + b Y.

However, if X and Y are independent, then E(X Y) = E(X) E(Y), which makes the covariance vanish, so that

V(a X + b Y) = a^2 V(X) + b^2 V(Y)

and this is the assumption we have to make to find the standard deviations (which is the square root of the variance).

Also, variance is defined as

V(X) = E[(X - E(X))^2] = E(X^2) - E(X)^2

and it follows from this that, if X is a constant, say a, then

V(a) = E(a^2) - E(a)^2 = a^2 - a^2 = 0

Use this property, and the assumption of independence, to compute the variances, and hence the standard deviations:

V(X + 10) = V(X)  ==>  SD(X + 10) = SD(X) = $90

V(5Y) = 5^2 V(Y) = 25 V(Y)  ==>  SD(5Y) = 5 SD(Y) = $40

V(X + Y) = V(X) + V(Y)  ==>  SD(X + Y) = √[SD(X)^2 + SD(Y)^2] = √8164 ≈ $90.35

Answer:

The critical value is T = 2.2622.

The 95% confidence interval for the mean waste recycled per person per day for the population of Florida is between 1.352 pounds and 4.248 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622, which is the critical value.

The margin of error is:

M = T*s = 2.2622*0.64 = 1.448

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 1.448 = 1.352 pounds

The upper end of the interval is the sample mean added to M. So it is 2.8 + 1.448 = 4.248 pounds

The 95% confidence interval for the mean waste recycled per person per day for the population of Florida is between 1.352 pounds and 4.248 pounds.

Answer:

The width or range of the confidence interval with sample size 200 will be about half of that of the confidence interval with sample 50.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)

- For the two random samples, of sizes 50 and 200, the Central limit theorem allows us to say that the sample mean is approximately equal to the population mean as this random sample satisfies the condition of being a simple random sample and a distribution obtained from a normal distribution.

- Making the right assumption that population standard deviation is known and z-distribution is used to find the critical value

Critical value for 95% = 1.96

The critical value for both samples are the same then.

- Standard Error of the mean = σₓ = (σ/√n)

where σ = population standard deviation

n = sample size

For the two distributions

Confidence Interval = (Sample mean) ± [(Critical value) × (Standard Error of the mean)

(Sample mean)₅₀ = (Sample mean)₂₀₀

(Critical value)₅₀ = (Critical value)₂₀₀

(Standard Error of the mean)₅₀ = (σ/√50) = 0.1414σ

(Standard Error of the mean)₂₀₀ = (σ/√200) = 0.0707σ

0.1414σ = 2 × 0.0707σ

(Standard Error of the mean)₅₀ = 2 × (Standard Error of the mean)₂₀₀

(Standard Error of the mean)₅₀ > (Standard Error of the mean)₂₀₀

Hence,

(Margin of Error)₅₀ > (Margin of Error)₂₀₀

(Margin of Error)₅₀ = 2 × (Margin of Error)₂₀₀

Confidence Interval = (Sample mean) ± (Margin of error)

Hence, the width or range of the confidence interval with sample size 50 will be about two times larger than the confidence interval with sample 200.

Hope this Helps!!!

Answer:

The number of the class containing the  largest score can be found in frequency  24 and the class is  98 - 103

For the third class 78 - 83 ; the upper limit = 83

The class width for this histogram 5

The number of students that took the exam simply refers to the frequency is  84

The percentage of students that scored higher than 95.5 is 53%

Step-by-step explanation:

The objective of this question is to use the following histogram that shows the exam scores for a Pre-algebra class to answer the question given:

NOW;

The table given in the question can be illustrated as follows:

S/N           Class                Score          Frequency

1                 68  - 73            70.5           0

2                73 - 78             75.5           4

3                78 - 83             80.5           8

4                83 - 88             85.5           12

5                88 - 93            90.5           16

6                93 - 98            95.5           20

7                98 - 103           100.5          24                            

TOTAL:                                                 84

a) The number of the class containing the  largest score can be found in frequency  24 and the class is  98 - 103

b) For the third class 78 - 83 ; the upper limit = 83  ( since the upper limit is derived by addition of  5 to the last number showing  in the highest value specified by the number in the class interval which is 78 ( i.e 78 + 5 = 83))

c)   The class width for this histogram 5 ; since it  is the difference  between the upper and lower boundaries  limit of the given class.

So , from above the difference in any of the class will definitely result into 5

d) The number of students that took the exam simply refers to the frequency ; which is (0+4+8+12+16+20+24) = 84

e) Lastly; the percentage of students that scored higher than 95.5 is ;

⇒[tex]\dfrac{20+24}{84} *100[/tex]

= 0.5238095 × 100

= 52.83

To the nearest percentage ;the percentage of students that scored higher than 95.5 is 53%

Answer:

1. 98-103 (6th class)

2. 88

3. 5

4. 84

5. 52%

Step-by-step explanation:

Find attached the frequency table.

The class of exam scores falls between (1, 2, 3, 4, 5, or 6).

The exam score ranged from 68-103

1) The largest number of exam scores = 24

The largest number of exam scores is in the 6th class = 98 -103

Step 2 of 5:

The upper class limit is the higher number in an interval. Third class interval is 83-88

The upper class limit of the third class 88.

Step 3 of 5:

Class width = upper class limit - lower class limit

We can use any of the class interval to find this as the answer will be the same. Using the interval between 73-78

Class width = 78 - 73

Class width for the histogram = 5

Step 4 of 5:

The total of students that took the test = sum of all the frequency

= 0+4+8+12+16+20+24 = 84

The total of students that took the test = 84

Step 5 of 5:Find the percentage of students that scored higher than 95.5

Number of student that scored higher than 95.5 = 20 + 24 = 44

Percentage of students that scored higher than 95.5 = [(Number of student that scored higher than 95.5)/(total number of students that took the test)] × 100

= (44/84) × 100 = 0.5238 × 100 = 52.38%

Percentage of students that scored higher than 95.5 = 52% (nearest percent)

Answer:

ED = 3.2 cm

Step-by-step explanation:

According to chord-chord power theorem,

(AE)(EB) = (CE)(ED)

2*4 = 2.5 *ED

8/2.5 = ED

ED = 3.2 cm

Answer:

As  [tex]{x \to \infty}, \,\,{f(x) \to -\infty[/tex]  and as  [tex]{x \to -\infty}, \,\,{f(x) \to \infty[/tex]

Step-by-step explanation:

Please look at the plotted points in the attached image. There we see that as x grows toward infinity (to the right), the values for f(x) seem to become more negative (so f(x) seems to go towards  minus infinity).

As we move towards the left with values of x (x going towards negative infinity, f(x) seems to become more and more positive (grow toward infinity)

Answer:

3. 72.9%

Step-by-step explanation:

Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.

So, the probability P(M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:

P(M∪C) = P(M) + P(C) - P(M∩C)

Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:

P(M) = 145/317 = 0.4574

There are 167 customers that prefer chocolate chips Scones ( 317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:

P(C) = 167/317 = 0.5268

Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate  chip scones is:

P(M∩C) = 81/317 = 0.2555

Therefore,  P(M∪C) is equal to:

P(M∪C) = 0.4574 + 0.5268 - 0.2555

P(M∪C) = 0.7287

P(M∪C) = 72.9%

Answer:

3. 72.9%

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.

There are 172 female customers and 317-172 = 145 male customers.

150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.

81 of those are male, so 167 - 81 = 86 are female.

So the total of desired outcomes is 86 + 145 = 231

Total outcomes:

317 total customers.

Probability:

231/317 = 0.729

So the correct answer is:

3. 72.9%

Answer:

x=-21

Step-by-step explanation:

x+12=-9

minus twelve on both sides

-9-12 equals -21

x=-21

Answer:

CI = (70.861 , 94.418)

Step-by-step explanation:

In order to determine the 90% confidence interval you use the following formula (for a population approximately normal):

[tex]CI=(\overline{x}-Z_{\alpha/2}\frac{\sigma}{\sqrt{n}},\overline{x}+Z_{\alpha/2}\frac{\sigma}{\sqrt{n}})[/tex]    (1)

[tex]\overline{x}[/tex]: mean = 82.64

σ: standard deviation = 14.32

n: sample = 4

α: tail area = 1 - 0.9 = 0.1

Z_α/2 = Z_0.05: Z factor =  1.645

You replace these values and you obtain:

[tex]Z_{0.05}(\frac{14.32}{\sqrt{4}})=(1.645)(\frac{14.32}{\sqrt{4}})=11.778[/tex]

The confidence interval will be:

[tex]CI=(82.64-11.778,82.64+11.778)=(70.861,94.418)[/tex]

The 90% confidence interval is (70.861 , 94.418)

Answer:

Step-by-step explanation:

Answer:

height = 5

Step-by-step explanation:

The volume of a prism is V = l*w*h

You are not given any information about the exact values of l and w.

You do know however that L and w when multiplied together = 20, so you can put that in for l*w. Then the formula becomes

V = 20*h

You are told that the volume is 100. Now the problem is simplified. You get

100 = 20 * h               Divide both sides by 20

100/20 = 20*h/20     Combine like terms.

5 = h

Answer:

A

Step-by-step explanation:

They are congruent because of the SSS theorem.  The chords are congruent because the angles are congruent (angles are congruent because they are vertical angles).  Congruent central angles have congruent chords.  The other two sides are congruent because they are all radii of the circle and radius are always congruent.

Answer:

A

Step-by-step explanation:

The triangles are isosceles and congruent  too. ( both have 2  sides congruent  as  radius and the angles between them are congruent- SAS)

Answer:

(0, -4)

Step-by-step explanation:

The graph that represents the function is (c) on a coordinate plane, an absolute value graph has a vertex at (0, -4)

The equation of the function is given as:

[tex]f(x) = |x| - 4[/tex]

The above function is an absolute value function shifted down by 4 units

Hence, the graph that represents the function is a graph that has its vertex at (0,-4)

Read more about absolute value graphs at:

https://brainly.com/question/2166748

Answer:

The z score when x =72 is:

[tex] z = \frac{72-58}{11}= 1.273[/tex]

The mean is 58

This z-score tells you that x= 72 is 1.273 standard deviations to the right of the mearn.

Step-by-step explanation:

Assuming the following info for the question: Suppose John's words per minute on a typing test are normally distributed. Let X -the number of words per minute on a typing test. Then X N(58, 11) If necessary, round to three decimal places.

Provide your answer below rds per minute in a typing test on Sunday. The z score when x =72 is

For this case we know that the variable of interest is modelled with the normal distribution:

[tex]X \sim N (\mu= 58, \sigma=11)[/tex]

And the z score is given by:

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

And replacing we got:

[tex] z = \frac{72-58}{11}= 1.273[/tex]

The mean is 58

This z-score tells you that x= 72 is 1.273 standard deviations to the right of the mearn.

Answer: 1/20

Step-by-step explanation:

Decimal Fraction Percentage

0.05 1/20          5%