A bus arrives at a bus stop at a randomly selected time within a 1-hour period. A passenger arrives at the bus stop at a randomly selected time with the same hour. The passenger is willing to wait for the bus for up to 1/4 of an hour. What is the probability that the passenger will catch the bus?

Answer:

28 or 29%

Step-by-step explanation:

There are 7 days total, 2 of which start with “S”, divide the 2 by 7 to get your percentage of 28-29%

The probability of picking a day that begins with the letter s is 2/7.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

There are seven days in a week, and two of them start with the letter s: Sunday and Saturday.

Now,

The probability of picking a day that begins with the letter s.

= 2/7

Or,

= 0.2857

Or,

= 0.2857 x 100%

= 28.57%.

Thus,

The probability of picking a day that begins with the letter s is 2/7.

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Answer: For every 12 blue pens, she has 6 red pens 12:6

Simplifying this would be: 2:1

Answer:

3 : 1

Step-by-step explanation:

18 : 6

simplified ratio is

3 : 1

Answer:

.54444 = .54444/1 = 5.4444/10 = 54.444/100 = 544.44/1000 = 5444.4/10000 = 54444/100000, any one of those works

Answer:

54/99

Step-by-step explanation:

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $9

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $9

Step-by-step explanation:

We are given that a report on a certain fast food restaurant states that μ, the mean order total, is $9. The manager of the restaurant believes the mean is higher.

A random sample of orders will be selected. The sample mean x¯ will be calculated and used in a hypothesis test to investigate the belief.

Let [tex]\mu[/tex] = the mean order total

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $9

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $9

Here, null hypothesis states that  the mean order total is equal to $9 and the manager claim's is not correct.

On the other hand, alternate hypothesis states that  the mean order total is higher than $9 and the manager claim's is correct.

So, this would be the correct set of hypotheses for testing.

Based on the null hypothesis, the mean order to total is $9, and the manager's belief is wrong. Based on alternate hypothesis, the mean order total is more than $9, and the manager is right.

Given information:

A report on a certain fast food restaurant states that μ, the mean order total, is $9.

The manager of the restaurant believes the mean is higher.

So, according to the null hypothesis, [tex]H_0[/tex]

[tex]\mu=9[/tex]

And, according to alternate hypothesis, [tex]H_a[/tex]

[tex]\mu>9[/tex]

Therefore, based on the null hypothesis, the mean order to total is $9, and the manager's belief is wrong. Based on alternate hypothesis, the mean order total is more than $9, and the manager is right.

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Answer:

2 seconds and 38 seconds

Step-by-step explanation:

h=-16t²-vot

1,200=-16t²-640t

turn this into standard form

16t²-640t+1200=0

now plug thes numbers into the quadratice formula

a 16 b -640 c 1200

solve with quadratic formula to get ≅2 and ≅38 seconds

Answer:

t≈2 seconds,t≈38 seconds

Step-by-step explanation:

h=−16t2+ v0t

Step 1. Solve the equation.

1,200= −16t^2+ 640t

We know the velocity, v0, is 640 feet per second.

The height is 1,200 feet. Substitute the values.

This is a quadratic equation. Rewrite it in standard form. Solve the equation using the quadratic formula.

ax^2 +   bx  +      c .   = 0

16t^2 −640t +  1,200 = 0

Identify the values of a, b, and c.

a=16,  b=−640, c=1,200

Write the quadratic formula.

t=−b± √b2−4ac‾‾‾‾‾‾‾‾

               2a

640+ √332,800‾‾‾‾‾‾‾‾   t= √640− √332,800‾‾‾‾‾‾‾

             32                                           32

Rewrite to show two solutions.

t=640+332,800‾‾‾‾‾‾‾‾√32,t=640−332,800‾‾‾‾‾‾‾‾√32

Approximate the answer with a calculator.

t≈2 seconds,t≈38 seconds

Step 2. Check the answer. The check is left to you.

Step 3. Answer the question.

The firework will go up and then fall back down. As the firework goes up, it will reach 1,200 feet after approximately 2 seconds. It will also pass that height on the way down at 38 seconds.

Answer:

1/12

Step-by-step explanation:

1/6 * 3/6 (First roll has a one in 6 chance, second 3 in 6)

1*3 / 36 =

3 / 36 =

1/12

Answer:

30

Step-by-step explanation:

Everything has to add up to 90.

Add EVERYTHING together.

3x + 33

3x + 33 = 90

90 - 33 = 57

57 / 3 = 19

19 = x

19 x 2 = 38

38 - 8 = 30

Answer:

The answer for ∠CDF is 30°.

Step-by-step explanation:

It ia given that complemetary angle is 90° so we can make an expression in terms of x :

It ia given that complemetary angle is 90° so we can make an expression in terms of x :∠AFB + ∠BFC + ∠CFD = 90°

32° + (x+9)° + (2x-8)° = 90°

In order to find ∠CFD, we have to find the value of x first so we have to move all the like-terms to one side :

32° + x + 9° + 2x - 8° = 90°

2x + x = 90° - 32° - 9° + 8°

3x = 57°

Then divide both sides by 3 :

3x ÷ 3 = 57° ÷ 3

x = 19°

We have already found the value of x. Now, the question ask us to find ∠CDF, (2x-8)°. We just have to substitute x value into the expression :

Let x = 19,

∠CDF = 2x - 8

= 2(19) - 8

= 30°

Answer: The copy machine makes 171 copies in 4 minutes and 45 seconds.

Step-by-step explanation:

Let's dissect the question. The copy machine makes 36 copies per minute.

36 per min.

To see how many copies it makes in 4 minutes and 45 seconds, we multiply 36 * 4.75. 45 seconds is 3/4ths of a minute, or 0.75 of a minute.

[tex]36 * 4.75=171[/tex]

It makes 171 copies in 4 minutes and 45 seconds.

Answer:

0.233

Step-by-step explanation:

There are a total of 16 marbles.

The probability the first marble is blue is 8/16.

Assuming the marble isn't replaced, the probability the second marble is blue is 7/15.

So the probability of both marbles being blue is 8/16 × 7/15 = 7/30 ≈ 0.233.

The probability of drawing two blue marbles without replacement is 0.233 to the nearest thousandth, calculated by multiplying the individual probabilities of the first and second draws.

The probability of drawing two blue marbles from a bag without replacement involves a two-step calculation because the outcome of the first draw affects the second. Since there are 3 red, 8 blue, and 5 green marbles, the total number of marbles is 16. The probability of drawing a blue marble first is 8/16 or 1/2.

After drawing one blue marble, there would be 7 blue marbles left in a bag of 15 total marbles. The probability of drawing a blue marble on the second draw is then 7/15. To find the combined probability of both events occurring, we multiply the two probabilities: (1/2) × (7/15) = 7/30, which is approximately 0.233 to the nearest thousandth.

Thus, the probability of drawing two blue marbles in a row without replacement is 0.233 to the nearest thousandth.

Answer:

You dont multiply anything, you just round

Step-by-step explanation:

basically, you round the 2.3 to the nearest whole number which is most likely 2 because 3 is under five so it doesnt round up

Answer:

x = 5/3

y = 14/3

Step-by-step explanation:

y=4x−2

y=x+3

​Since they are both equal to y, we can set them equal to each other

4x-2 = x+3

Subtract x from each side

4x-2-x = x+3-x

3x-2 =3

Add 2 to each side

3x-2+2 = 3+2

3x =5

Divide each side by 3

3x/3 =5/3

x = 5/3

Now we need to find y

y = x+3

y =5/3+3

y = 5/3+9/3

y = 14/3

Answer:

x=5/3; y=14/3

Step-by-step explanation:

Subtract the following:

-4x+y=-2

-x+y=3

= -3x=-5

x=5/3

substitute x into one of the given equations.

y=5/3+3

y= 14/3

Answer:

80

Step-by-step explanation:

So if 50 tablets are made and 2 are defective then it’s 50:2. That means for every 50 tablets are made 2 are defective. And since 50 goes into 2000 40 times, you would multiply 40 x 2 to get 80, the number defective tablets

Answer:

3.8

Step-by-step explanation:

Answer:

8 1/3

Step-by-step explanation:

2 1/2 * 3 1/3

Change each to an improper fraction

2 1/2  = (2*2 +1)/2 = 5/2

3 1/3 = (3*3+1)/3 = 10/3

5/2 *10/3 = 50/6

Divide the top and bottom by 2

25/3

Change to a mixed number

3 goes into 25    8 times with 1 left over

8 1/3

Answer:

Yes, there are only 676 different possibilities, which is less than the number of people in the group.

Step-by-step explanation:

Assuming that the English alphabet has 26 different letters, the number of possible combinations of first and last name initials is:

[tex]n = 26*26\\n=676[/tex]

If we try to assign a different combination to each person in the group, it would only be possible to do it for the first 676 people, while the remaining 24 would have a repeated first and last initial. Therefore, the answer is yes, there must be 2 people who have matching first and last initials.

The Pigeonhole Principle in mathematics implies in a group of 700 people, there must be at least two people who have matching first and last initials.

The concept of this problem involves understanding the Pigeonhole Principle in mathematics. Considering the English alphabet has 26 letters, we can have 26 possible first initials and 26 possible last initials. Therefore, there are 26x26=676 unique combinations of first and last initials. However, we have a group of 700 people which is more than 676. The Pigeonhole Principle states that if you try to distribute more items than there are containers, then at least one container must hold more than one item. Therefore, applying this principle, there must be at least two people among the group of 700 who have matching first and last initials because the number of people (700) is greater than the possible unique combinations of first and last initials (676).

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Answer:

Expected number of matches that occur = 4 matches

Step-by-step explanation:

First of all, let X_i be the event that when we turn over card i if it matches the required cards face.

Thus, for example X_1 is the event that turning over one card results in an ace while X_2 is the event that turning over second card reveals a deuce.

The number of matched cards "N" is given by the sum of this indicator random variable as shown in the attached file;

The expected number of matches when cards are drawn from a standard 52-card deck is 4.

We define a match for each card position as X_i = 1 if a match occurs, and X_i = 0 otherwise. The expectation E(X_i) for each card is 1/13 because the probability of the ith card being an i-matched card (Ace in the 1st position, Two in the 2nd position, and so on up to King in the 13th, then repeat with Ace) is 1/13.

Given there are 52 cards, each having the same pattern of matching, the expected number of matches is computed as:

E(X) = E(X_1 + X_2 + ... + X_52) = E(X_1) + E(X_2) + ... + E(X_52)

Since E(X_i) = 1/13 for all i:

E(X) = 52 * (1/13) = 4

Therefore, the expected number of matches is 4.

Answer:

a) MSE = 61.33

Forecast for 8th month = 15

b) MSE = 34.51

Forecast for 8th month = 18

c) The average method provides a better forecast because of its low MSE

Explanation:

Check the attached file for the solvings.

To answer this two-part question, you'll need to calculate the mean square errors (MSE) using two different forecasting methods: using the most recent value as a forecast and using the average of all data for a forecast. The one with lower MSE is the correct prediction. The forecast for the next month is always based on the previous value or average value depending on the method.

To answer this question, you need to understand how mean square error (MSE) and forecasting work. For (a), we use the last value as the forecast for the next value and compute MSE. For (b), we use the average of all data as the forecast for the next value and calculate the MSE. Finally, we compare which method gives a lower MSE, therefore better forecasting.

For (a), the forecast values would be the previous month's data, i.e., forecast for month 2 is 23, month 3 is 14 and so on. To calculate MSE, you subtract each monthly value from its forecast, square the result and find the average of these squares. The forecast for month 8 would be the value of month 7 which is 15.

For (b), you calculate the average of all the data available and use it as a forecast for all the next periods. The MSE and forecast for month 8 can be calculated in a similar manner as in (a).

In step (c), compare the MSE calculated in step (a) and step (b). A lower MSE indicates a better forecast and consequently represents an accurate choice for a predictive model.

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Answer:

[tex]t=\frac{255.8-270.74}{\sqrt{\frac{(8.215)^2}{6}+\frac{(11.903)^2}{8}}}}=-2.788[/tex]  

[tex]p_v =2*P(t_{(12)}<-2.788)=0.0164[/tex]

So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that we have significant difference in the means of the two groups

Step-by-step explanation:

Data given and notation

Disk:[269.0 249.3 255.2 252.7 247.0 261.6]

Oval:[ 268.8 260.0 273.5 253.9 278.5 289.4 261.6 280.2]

[tex]\bar X_{D}=255.8[/tex] represent the mean for the sample Disk

[tex]\bar X_{O}=270.74[/tex] represent the mean for the sample Oval

[tex]s_{D}=8.215[/tex] represent the sample standard deviation for the sample Disk

[tex]s_{O}=11.903[/tex] represent the sample standard deviation for the sample Oval

[tex]n_{D}=6[/tex] sample size for the group Disk

[tex]n_{O}=8[/tex] sample size for the group Oval

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means are different, the system of hypothesis would be:

Null hypothesis:[tex]\mu_{D} = \mu_{O}[/tex]

Alternative hypothesis:[tex]\mu_{D} \neq \mu_{O}[/tex]

If we analyze the size for the samples both are less than 30 and the population deviations are not given, so for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{D}-\bar X_{O}}{\sqrt{\frac{s^2_{D}}{n_{D}}+\frac{s^2_{O}}{n_{O}}}}[/tex] (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

We can replace in formula (1) the results obtained like this:

[tex]t=\frac{255.8-270.74}{\sqrt{\frac{(8.215)^2}{6}+\frac{(11.903)^2}{8}}}}=-2.788[/tex]  

Statistical decision

For this case we don't have a significance level provided [tex]\alpha[/tex], but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:

[tex]df=n_{D}+n_{O}-2=6+8-2=12[/tex]

Since is a bilateral test the p value would be:

[tex]p_v =2*P(t_{(12)}<-2.788)=0.0164[/tex]

So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that we have significant difference in the means of the two groups

Answer:

Whats on the list?????

Step-by-step explanation:

Answer:

bcd

Step-by-step explanation:

Answer:

B C D

Step-by-step explanation:

Answer:

32¾

Step-by-step explanation:

1 pound (lb) = 16 ounces

12 oz = 12/16 = 3/4 lb

32 pounds 12 oz

32 ¾ lb

Answer:

x ≤-9/4

Step-by-step explanation:

x/3-x-1/2≥1

Multiply each side by 6 to get rid of the fractions

6(x/3-x-1/2)≥1*6

2x -6x -3≥6

Combine like terms

-4x-3≥6

Add 3 to each side

-4x-3+3≥6+3

-4x ≥9

Divide each side by -4, remembering to flip the inequality

-4x/-4 ≤9/-4

x ≤-9/4

On solving the inequality x/3 - x - 1/2 ≥ 1, we get x ≤ -3. Hence the correct option is A.

Solve the inequality: x/3 - x - 1/2 ≥ 1

Combine like terms: x/3 - (2x + 1)/2 ≥ 1

Get a common denominator: 2x/6 - 3(2x + 1)/6 ≥ 6/6

Simplify the equation: -4x - 3 ≥ 0

Solve for x: x ≤ -3

Answer:

The maximum price that the dealer will sell is $7471 and the minimum is $5513.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

In this problem, we have that:

[tex]\mu = 6492, \sigma = 1025[/tex]

Middle 66%

50 - (66/2)  = 17th percentile

50 + (66/2) = 83rd percentile

17th percentile

X when Z has a pvalue of 0.17. So X when Z = -0.955.

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

[tex]-0.955 = \frac{X - 6492}{1025}[/tex]

[tex]X - 6492 = -0.955*1025[/tex]

[tex]X = 5513[/tex]

83rd percentile

X when Z has a pvalue of 0.83. So X when Z = 0.955.

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

[tex]0.955 = \frac{X - 6492}{1025}[/tex]

[tex]X - 6492 = 0.955*1025[/tex]

[tex]X = 7471[/tex]

The maximum price that the dealer will sell is $7471 and the minimum is $5513.

Answer:

3x√x²y, –12x√x²y, x√yx², 2√x²y. or on Edge is A,B,D,F

Step-by-step explanation:

Got 100% on edge...

Answer:

b) False

Calculated value Z  =  1.635 < 1.96 at 0.05 level of significance.

The null hypothesis is accepted.

Step-by-step explanation:

Explanation:-

Step:- (1)

Given data the opinion poll recently sampled 1500 voting age citizens.

Given sample size 'n' = 1500

Given data the opinion poll recently sampled 1500 voting age citizens in selected 1020 of the sampled citizens were in favor of an increase in cigarette taxes.

The sample proportion[tex]'p' = \frac{1020}{1500} = 0.68[/tex]

Given data the state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66

Population proportion 'P' =0.66

                                      Q  = 1-P

                                      Q = 1-0.66 = 0.34

Null hypothesis :H₀: 'P' >0.66

Alternative hypothesis: H₀: 'P' <0.66

Level of significance ∝=0.05

Step:-(2)

The test statistic

                             [tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]

                            [tex]Z = \frac{0.68-0.66}{\sqrt{\frac{0.66 X 0.34}{1500} } }[/tex]

                            Z  =  1.635

The calculated value   Z  =  1.635

The tabulated value Z = 1.96 at ∝=0.05 level of significance.

Therefore  Z  =  1.635 < 1.96 at 0.05 level of significance.

The null hypothesis is accepted.

The alternative hypothesis is rejected.

Conclusion:-

The null hypothesis is accepted at 0.05 level of significance.

The proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66

Answer:

Step-by-step explanation:

Hello!

You need to construct a 95% CI for the population variance of the forces the safety helmets transmit to wearers.

The variable of interest is X: Force a helmet transmits its wearer when an external force is applied (pounds)

Assuming this variable has a normal distribution, the manufacturer expects it to have a mean of μ= 800 pounds and a standard deviation of σ= 40 pounds

A test sample of n=40 was taken and the resulting mean and variance are:

X[bar]= 825 pounds

S²= 2350 pounds²

To estimate the population variance per confidence interval you have to use the following statistic:

[tex]X^2= \frac{(n-1)S^2}{Sigma^2} ~~X^2_{n-1}[/tex]

And the CI is calculated as:

[[tex]\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}}[/tex];[tex]\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}}[/tex]]

[tex]X^2_{n-1;1-\alpha /2}= X^2_{39;0.975}= 58.1[/tex]

[tex]X^2_{n-1;\alpha /2}= X^2_{39;0.025}= 23.7[/tex]

[[tex]\frac{39*2350}{58.1}[/tex];[tex]\frac{39*2350}{23.7}[/tex]]

[1577.45; 3867.09] pounds²

Using a confidence level of 95% you'd expect that the interval [1577.45; 3867.09] pounds² contains the value of the population variance of the force the safety helmets transmit to their wearers when an external force is applied.

I hope this helps!

Answer:

Binomial probability distribution.

Step-by-step explanation:

For each watch, there are only two possible outcomes. Either it fails within 1 year of purchase, or it does not. The probability of a watch falling within 1 year of purchase is independent of other watches. So the type of of distribution will best model the number of watches out of the 15 sampled that fail within 1 year is the binomial probability distribution.

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.

Answer:

A = 81 pi ft^2

Step-by-step explanation:

The area of a circle is found by

A = pi r^2

The radius is 9

A = pi 9^2

A = 81 pi ft^2