A study of tipping behaviors examined the relationship between the color of the shirt worm by the server and whether or not the customer left a tip. There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip.


a.find the large-sample 95% confidence interval for the difference in proportions and use the scenario to explain the meaning of the confidence interval.

b.perform the large-sample significance test and use the scenario to explain the meaning of the significance test.

(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when [tex]t=0[/tex] and [tex]t=3[/tex], and because the velocity function is continuous, you need only check the sign of [tex]v(t)[/tex] for values on the intervals (0, 3) and (3, 6).

We have, for instance [tex]v(1)\approx-0.91<0[/tex] and [tex]v(4)\approx0.91>0[/tex], which means the particle is moving the positive direction for [tex]3<t<6[/tex], or the interval (3, 6).

(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:

[tex]\displaystyle\int_0^6|v(t)|\,\mathrm dt=\int_0^3-v(t)\,\mathrm dt+\int_3^6v(t)\,\mathrm dt[/tex]

which follows from the definition of absolute value. In particular, if [tex]x[/tex] is negative, then [tex]|x|=-x[/tex].

The total distance traveled is then 4 ft.

(g) Acceleration is the rate of change of velocity, so [tex]a(t)[/tex] is the derivative of [tex]v(t)[/tex]:

[tex]a(t)=v'(t)=-\dfrac{\pi^2}9\cos\left(\dfrac{\pi t}3\right)[/tex]

Compute the acceleration at [tex]t=4[/tex] seconds:

[tex]a(t)=\dfrac{\pi^2}{18}\dfrac{\rm ft}{\mathrm s^2}[/tex]

(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)

Answer:

The factors that cause Earth to experience seasons are:

1. the tilt of Earth’s axis

2. the directness of the Sun’s rays

The factors that cause Earth to experience seasons are:

1. the tilt of Earth’s axis

2. the directness of the Sun’s rays

The reason why the Earth contains various seasons because it deals with the variation of the sun's rays angles and the earth titles to the 23.5 degrees on its axis. Also along with the earth rotation, the earth orbits should be around to the sun because of which various parts should be exposed to the different amount of lights

Therefore, the above two points should be considered.

Learn more about earth here: https://brainly.com/question/442818

The situation can illustrate the distributive property in math (6*(2+3)=6*2 + 6*3), representing 'a' as six cars, and 'b' and 'c' as the people in each car.

The situation described can be used to illustrate the distributive property in mathematics. The distributive property states a(b + c) = ab + ac. In this scenario, the six cars can be represented as 'a', while the 'b' and 'c' can represent the two people in front and the three in the back. Therefore, the total number of people in all cars is 6*(2+3) which according to the distributive property equals 6*2 + 6*3. That is, 12 people in the front seats and 18 in the back seats, summed up to be 30 people in total.

https://brainly.com/question/37341329

#SPJ2

Final answer:

The distributive property states that the product of a number and a sum is equal to the sum of the individual products. In this situation with the cars, we can use the distributive property to calculate the total number of people in all the cars.

Explanation:

The distributive property in mathematics states that the product of a number and a sum is equal to the sum of the individual products. In this situation with the cars, we can use the distributive property to calculate the total number of people in all the cars. Each car has 2 people in front and 3 people in back, so we can write the expression as (2 + 3) * 6. Using the distributive property, we can simplify this expression to 2 * 6 + 3 * 6, which equals 12 + 18, or 30 people in all the cars.

Answer:

7/25

Step-by-step explanation:

Just did on delta math

Answer:

a) 54 mph to 144 mph

Step-by-step explanation:

We don't know the shape of the distribution, so we use Chebyshev's Theorem to solve this question. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

At least eight-ninths of the player's serves.

8/9 is approximately 89%

So

Mean: 99, standard deviation: 15

99 - 3*15 = 54

99 + 3*15 = 144

So the correct answer is:

a) 54 mph to 144 mph

Answer:5000

Step-by-step explanation:

A kilometer is equal to 1000 meters.

5*1000=5000.

Answer:

5000 meters

Step-by-step explanation:

It is given that Monique ran in a 5 kilometer race.

Answer:

Answer: 600

Step-by-step explanation:

5x5=25

3x8=24

25x24=600

Answer:

Adb , cbd, 1

Step-by-step explanation:

Answer:

ADB CBD 1

Step-by-step explanation:

Lower Quartile: 2

Upper Quartile: 5.25

Median: 3

Final answer:

In the given data set 2, 2, 2, 4, 5, 6, the lower quartile is 2, the median is 3, and the upper quartile is 5.

Explanation:

To find the lower quartile, median, and upper quartile of the given data set 2, 2, 2, 4, 5, 6, we first need to organize it in ascending order, which is already done. Next, we compute the median, which is the middle value when the data set is listed in order. Since there are six numbers, the median will be the average of the third and fourth numbers, (2+4)/2, which is 3.

To find the first quartile (Q1) or lower quartile, we take the median of the lower half of the data set, not including the median. This would be the median of the first three numbers: 2, 2, and 2, which is simply 2. To find the third quartile (Q3) or upper quartile, we look at the upper half of the data set, again not including the median. The median of the last three numbers 4, 5, and 6 is 5.

Therefore, the lower quartile is 2, the median is 3, and the upper quartile is 5.

Answer:

Half way in between negative 1 and negative 2.

Step-by-step explanation:

Answer:

Steve should use:

Step-by-step explanation:

Let Steve cut the wire so that the first piece has length x.

Therefore, the second piece will have a length of (52 - x).

The wire of length x is used to make a circle

Circumference of a Circle,

[tex]c = 2\pi r\\Therefore\\2\pi r=x\\r=\dfrac{x}{2\pi}[/tex]

[tex]\text{Area of a circle, A}=\pi r^2= \pi (\dfrac{x}{2\pi})^2=\pi (\dfrac{x^2}{4\pi^2})\\A=\dfrac{x^2}{4\pi}[/tex]

The wire of length (52-x) is used to make a square.

[tex]\text{Side length of the Square,}[/tex] [tex]s= \dfrac{52-x}{4}[/tex]

[tex]\text{Area of the Square},s^2= \left(\dfrac{52-x}{4}\right)^2=\dfrac{(52-x)^2}{16}=\dfrac{x^2-104x+2704}{16}[/tex]

Total Area = Area of Circle + Area of Square

[tex]Area=\dfrac{x^2}{4\pi}+\dfrac{x^2-104x+2704}{16}[/tex]

Let us simplify the expression

[tex]Area=\dfrac{16x^2+\pi(x^2-104x+2704)}{16\pi}\\=\dfrac{16x^2+\pi x^2-104\pix+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)-104\pi x+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)}{16\pi}-\dfrac{104\pi x}{16\pi}+\dfrac{2704\pi}{16\pi}\\A=\dfrac{x^2(16+\pi)}{16\pi}-6.5x+169[/tex]

This is the function of a parabola which opens up.

To find where A is minimum, find the axis of symmetry.

[tex]$Using \: x=-\frac{b}{2a}[/tex]

[tex]a=\dfrac{16+\pi}{16\pi}, b=-6.5\\ x=-\dfrac{-6.5}{2(\dfrac{16+\pi}{16\pi})}=8.53\:Inches[/tex]

Steve should cut the wire so that the length of wire used to make a circle is 8.53 Inches.

Length of wire used to make the square =52-8.53=43.47 Inches

Answer:

These questions focus on how the proportion of females will vary in random samples if we assume that 0.60 of the population of part-time college students is female.

1. Before we use a simulation to simulate the selection of random samples from this population, let’s make sure we are clear about who is in the population. For this situation which statement best describes the population?  part-time college students

2. What are we assuming to be true about the population? The proportion of the population that is female is 0.60

3. Which of the following sequences of sample proportions is the most likely to occur in random samples of 25 students from this population? 0.56, 0.60, 0.44, 0.68, 0.76

Answer:

Orange juice bottle has greater percent of water.

Percent of water in apple juice bottle=40%

Step-by-step explanation:

We are given that

Total mass of apple juice bottle=80 ounce

Apple juice contains water=32 ounces

Total mass of orange juice bottle=64 ounce

Orange juice bottle contain water=48 ounces

We have to find that which juice has greater percent of water and find the percent of water in  the bottle of apple juice .

Percent of water in apple juice=[tex]\frac{water}{total\;mass}\times 100=\frac{32}{80}\times 100=[/tex]40%

Percent of water in orange juice bottle=[tex]\frac{48}{64}\times 100=[/tex]75%

Orange juice bottle has greater percent of water.

Answer:

The number of ways she can select her lunches N ;

N = 10×10×10×10×3 = 30000 ways

Step-by-step explanation:

Number of week days = 5

Total number of dishes = 10

Number of vegetarian dishes = 3

Note; on other week days apart from Friday she can select any lunch she want vegetarian or not...

Therefore, on Monday to Thursday she has ten choices per day, and on Friday she has 3 choices

The number of ways she can select her lunches N ;

N = 10×10×10×10×3 = 30000 ways

Answer:

It takes 3 seconds for the diver to reach the water.

Step-by-step explanation:

The height, in feet, is given by the following equation:

[tex]h(t) = -16t^{2} + 144[/tex]

How many seconds will it take for the diver to reach the water?

He reaches the water when his height is 0, that is, when h(t) = 0. So

[tex]h(t) = -16t^{2} + 144[/tex]

[tex]0 = -16t^{2} + 144[/tex]

[tex]16t^{2} = 144[/tex]

[tex]t^{2} = \frac{144}{16}[/tex]

[tex]t^{2} = 9[/tex]

[tex]t = \pm \sqrt{9}[/tex]

[tex]t = \pm 3[/tex]

There are no negative instant of time, so just t = 3.

It takes 3 seconds for the diver to reach the water.

Given Information:

Occupancy rate of Ginger’s hotel = 85%

Competitive set available rooms = 150,000

Competitive set sold rooms = 115,000

Required Information:

Occupancy rate INDEX = ?

Answer:

Occupancy rate INDEX = 111%

Step-by-step explanation:

The occupancy rate INDEX is given by

Occupancy rate INDEX = Occupancy rate of Ginger’s hotel/Occupancy  rate of competitive set

We are given the occupancy rate of Ginger’s hotel so we need to first find out occupancy  rate of competitive set which is given by

Occupancy rate of competitive set = Competitive set sold rooms/Competitive set available rooms

Occupancy rate of competitive set = 115,000/150,000

Occupancy rate of competitive set = 0.7667

Occupancy rate of competitive set ≈ 76.67%

Finally, we can now find the occupancy rate INDEX

Occupancy rate INDEX = Occupancy rate of Ginger’s hotel/Occupancy rate of competitive set

Occupancy rate INDEX = 85/76.67

Occupancy rate INDEX = 1.108

Occupancy rate INDEX = 110.8%

Occupancy rate INDEX ≈ 111%

Therefore, the approximate occupancy rate INDEX last month for Ginger's hotel is 111%

Answer:

[tex]z=\frac{7.4-7.6}{\frac{0.9}{\sqrt{130}}}=-2.534[/tex]    

[tex]z_{\alpha}=-2.054[/tex]

If the calculated value is less than the critical value we reject the null hypothesis.

P value

The p value for this test would be:  

[tex]p_v =P(Z<-2.534)=0.0056[/tex]  

Since the p value is lower than the significance level given we have enough evidence to reject the null hypothesis at the 25 of significance level given.

Step-by-step explanation:

Information given

[tex]\bar X=7.6[/tex] represent the sample mean

[tex]\sigma=0.9[/tex] represent the population deviation

[tex]n=130[/tex] sample size  

[tex]\mu_o =7.4[/tex] represent the value that we want to check

[tex]\alpha=0.02[/tex] represent the significance level for the hypothesis test.  

z would represent the statistic

[tex]p_v[/tex] represent the p value for the test

System of hypothesis  

We want to check if the mean pressure is less then 7.6 pounds/square inch, the system of hypothesis are:  

Null hypothesis:[tex]\mu \geq 7.6[/tex]  

Alternative hypothesis:[tex]\mu < 7.6[/tex]  

The statistic would be:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex]  (1)  

Replacing the values we got:

[tex]z=\frac{7.4-7.6}{\frac{0.9}{\sqrt{130}}}=-2.534[/tex]    

Critical value

we need to find a critical value who accumulates 0.02 of the area in the left of the normal standard distribution and we got:

[tex]z_{\alpha}=-2.054[/tex]

If the calculated value is less than the critical value we reject the null hypothesis.

P value

The p value for this test would be:  

[tex]p_v =P(Z<-2.534)=0.0056[/tex]  

Since the p value is lower than the significance level given we have enough evidence to reject the null hypothesis at the 25 of significance level given.

Answer:

55%

Step-by-step explanation:

Answer:

[tex]p_v =P(z>1.82)=0.034[/tex]  

Assuming a standard significance level of [tex]\alpha=0.05[/tex] the best conclusion for this case would be:

4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).

Because [tex] p_v <\alpha[/tex]

If we select a significance level lower than 0.034 then the conclusion would change.

Step-by-step explanation:

Data given

n=300 represent the random sample taken

X=120 represent the people who have a smart phone

[tex]\hat p=\frac{120}{300}=0.4[/tex] estimated proportion of people who have a smart phone

[tex]p_o=0.35[/tex] is the value that we want to test

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to test the claim that the true proportion of people who have a smart phone is higher than 0.35, the system of hypothesis are.:  

Null hypothesis:[tex]p\leq 0.35[/tex]  

Alternative hypothesis:[tex]p > 0.35[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.4 -0.35}{\sqrt{\frac{0.35(1-0.35)}{300}}}=1.82[/tex]  

Statistical decision  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>1.82)=0.034[/tex]  

Assuming a standard significance level of [tex]\alpha=0.05[/tex] the best conclusion for this case would be:

4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).

Because [tex] p_v <\alpha[/tex]

If we select a significance level lower than 0.034 then the conclusion would change.

Answer:

Total no  of different ways can the 4 computers be chosen  = 70

Step-by-step explanation:

Given -

A computer retail store has 8 personal computers in stock.A buyer wants to purchase 4 of them.

(Using the combination formula)

The combination of n events taking r at a time = [tex]\mathbf{\binom{n}{r}}[/tex]

where n = 8 and r = 4

Total no  of different ways can the 4 computers be chosen = [tex]\mathbf{\binom{8}{4}}[/tex]

    =  [tex]\boldsymbol{\frac{8!}{(4!)(4!)}}[/tex]

=   70

The number of different ways that 4 computers can be chosen from a stock of 8 is 70.

The number of different ways that 4 computers can be chosen from a stock of 8 is determined by the concept of combinations. In this case, we want to find the number of combinations of 8 items taken 4 at a time. The formula for combinations is given by:

C(n, r) = n! / r!(n-r)!

where n is the total number of items and r is the number of items to be chosen. Applying the formula to this problem, we have:

C(8, 4) = 8! / 4!(8-4)!

Simplifying the expression, we get:

C(8, 4) = 8! / 4!4!

Using the factorial function, we can compute:

C(8, 4) = 8 × 7 × 6 × 5 / (4 × 3 × 2 × 1)

C(8, 4) = 70

Therefore, there are 70 different ways that the 4 computers can be chosen from the stock of 8.

https://brainly.com/question/24703398

#SPJ11

An infinite geometric series would only converge if the common ratio is a proper fraction.

An infinite geometric series can be defined as the sum of a geometric sequence that typically has a constant common ratio between successive terms but no last term.

In Mathematics, it is a fact that if the common ratio of an infinite geometric series is a proper fraction, this would make it to converge because each successive term gets smaller and smaller.

In conclusion, an infinite geometric series would only converge if the common ratio is a proper fraction such as 3/6.

Read more on geometric series here: brainly.com/question/12630565

#SPJ2

Answer:

c. a proper fraction

b and d. -2/3 and 3/4

c. 80/3

Step-by-step explanation:

...

Answer:

147.58 cm

Step-by-step explanation:

Circumference is represented by 2πr.

R is 23.5, and I'll approximate π to 3.14, as is common.

This creates 2 • 3.14 • 23.5

Simplify to: 147.58, which is your circumference

Answer:

148

Step-by-step explanation:

To find the circumference, use 2r*3.14 for a approximate answer. in this case, 23.5*2=47.

47*3.14=147.58.

Rounded to the nearest whole number, the answer is 148.

Answer:

We accept H₀ we don´t have enough evidence to conclude that a consumer group position is correct

Step-by-step explanation:

We have a case of test of proportion, as a consumer group is suspicious of the claim and think the proportion is lower we must develop a one tail test (left tail) Then

1.- Test hypothesis:

Null hypothesis  H₀                   P = P₀

Alternative hypothesis  Hₐ       P < P₀

2.- At significance level of α  = 0,05   Critical value

z(c)  =  -1,64

3.-We compute z(s) value as:

z(s)  =  ( P - P₀ )/ √P*Q/n      where   P = 44/80     P = 0,55   and Q = 0,45

P₀ = 0,6   and  n = 80

Plugging all these values in the equation we get:

z(s)  = ( 0,55 - 0,6 ) / √(0,2475/80)

z(s)  =  - 0,05/ √0,0031

z(s)  =  - 0,05/0,056

z(s)  =  - 0,8928

4.-We compare  z(s)  and  z(c)

z(s) > z(c)      -0,8928 on the left side it means that z(s) is in the acceptance region so we accept H₀

Answer:

It will take 10 years for her money to double.

Step-by-step explanation:

The compound interest formula is given by:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the number of years the money is invested or borrowed for.

In this exercise:

We want to find t for which the money doubles, that is, t when A = 2P.

Compounded monthly, an year has 12 months, so n = 12

Interest rate of 7%, so r = 0.07.

The following logarithm property is used:

[tex]\log{a^{t}} = t\log{a}[/tex]

So

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]2P = P(1 + \frac{0.07}{12})^{12t}[/tex]

[tex](1.0058)^{12t} = 2[/tex]

[tex]\log{(1.0058)^{12t}} = \log{2}[/tex]

[tex]12t\log{1.0058} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{12\log{1.0058}}[/tex]

[tex]t = 10[/tex]

It will take 10 years for her money to double.

Answer:

$34.20

Step-by-step explanation:

First, find the cost with tax

You are paying 7.2% tax, but you are also paying for 100% of the bill

100%+7.2%=107.2%

So, you are really paying for 107.2% of the bill

Convert 107.2% to a decimal by dividing by 100 or moving the decimal 2 spaces to the right

107.2/100=1.072

Multiply the decimal by the cost of the bill

1.072*45.90=49.2048

But, we also have a coupon for $15 off

Subtract 15 from the cost with tax

49.2048-15=34.2048

Round to the nearest cent/hundreth

$34.20

Hope this helps! :)

Answer:

The volume is 2144.66

Step-by-step explanation:

The equation i used when solving this question.

V=4/3πr3

The volume of sphere when rounded to nearest 100th will be 2143.574 cubic units

Given: a sphere of radius 8 units

To find: Volume of sphere

The volume of a sphere can be calculated using the formula [tex]V = \frac{4}{3}\pi r^3[/tex], where r is the radius of the sphere. To find the volume, plug in the value of the radius into the formula and calculate the result.

[tex]V = \frac{4}{3}\pi r^3\\[/tex]

[tex]V = \frac{4}{3}\pi (8)^3\\[/tex]

[tex]V = \frac{4}{3}\pi (8)^3 = 682.667 \pi[/tex]

If we insert the value of [tex]\pi = 3.14[/tex] we get:

[tex]V = 682.667 \times 3.14 = 2143.57438[/tex]

When rounded to nearest 100th we will get volume equal to 2143.574 cubic units.

Answer:

$2,977.54

Step-by-step explanation:

You are going to use the compound interest formula:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate

n = number of times compounded annually

t = time

First, change 6% into the decimal form:

6% -> [tex]\frac{6}{100}[/tex] -> 0.06

Next, lets plug in the values:

[tex]A=2,500(1+\frac{0.06}{1} )^{3(1)}[/tex]

[tex]A=2,977.54[/tex]

Your answer will be $2,977.54