Ten years ago, college students spent an average of 120 hours per semester on extra-curricular activities. A researcher believes that now college students spend less time on extra-curricular activities than they did ten years ago. A simple random sample of 100 college students found that in the past year the average number of hours spent per semester in extracurricular activities was 107 hours with a standard deviation of 45 hours. If we are testing at a significance level of 0.05, based on the p-value, what is your conclusion?

Answer:

Answer: 600

Step-by-step explanation:

5x5=25

3x8=24

25x24=600

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.

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.

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Answer:

c. a proper fraction

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

c. 80/3

Step-by-step explanation:

...

Answer: 1 = 57.2

2 = angle S

3 = the triangles are similar (the second choice)

Step-by-step explanation: i got the question right on my work on e d g e n u i t y

Consider the triangles.

Triangle C D E. Angle C is blank, angle D is 87.3 degrees, angle E is 35.5 degrees. Triangle R S T. Angle R is blank, angle S is 57.2 degrees, angle T is 87.3 degrees.

Answer the questions about these triangles.

What is the measure of angle C?

✔ 57.2

Which angle corresponds to angle C?

✔ angle S

What can be concluded about the triangles?

✔ The triangles are similar.

The measure of angle C in triangle CDE is 57.2 degrees, Angle C corresponds to angle R in triangle RST,  and the two triangles are  similar or congruent.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Since the sum of angles in a triangle is always 180 degrees, we can find the measure of angle C in triangle CDE by subtracting the measures of angles D and E from 180 degrees:

Angle C = 180 degrees - Angle D - Angle E

Angle C = 180 degrees - 87.3 degrees - 35.5 degrees

Angle C = 57.2 degrees

Therefore, the measure of angle C in triangle CDE is 57.2 degrees.

Angle C corresponds to angle R in triangle RST, since they are both unknown angles in their respective triangles.

We can conclude that the two triangles are  similar or congruent.

Hence, the measure of angle C in triangle CDE is 57.2 degrees, Angle C corresponds to angle R in triangle RST,  and the two triangles are  similar or congruent.

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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.

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Answer:

2,5, and 6

Step-by-step explanation:

hope this helps

The solid will be a triangular prism .The solid will have some faces that are rectangles and some faces that are triangles.

The solid will have five faces.

(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:

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.

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:

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:

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:

$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:

55%

Step-by-step explanation:

Answer:

a A=$47,887.81

b.A=$46,430.80

Step-by-step explanation:

a. Given the initial amount is $40,000 with a 3-year term and a 6% rate compounded daily.

-Take 1 year=365 days

#First we calculate the effective interest rate corresponding to the daily compounding;

[tex]i_m=(1+i/m)^m-1\\\\=(1+0.06/365)^{365}-1\\\\=0.06183[/tex]

#We use the calculated effective rate, 0.06183, to solve for the future value as:

[tex]A=P(1+i_m)^n\\\\=40000(1.06183)^3\\\\=47887.81[/tex]

Hence, the total future value for a daily compounding is $47,887.81

b. For a sinking fund with a 5% compounded quarterly:

#We calculate the annual effective rate:

[tex]i_m=(1+i/m)^m-1\\\\=(1+0.05/4)^4-1\\\\=0.05095[/tex]

#We use the calculated effective rate, 0.05095, to solve for the future value as:

[tex]A=P(1+i_m)^n\\\\=40000(1.05095)^3\\\\=46430.80[/tex]

Hence, the future value of the sinking fund is $46,430.80

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.

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]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:

$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

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.

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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:

The answer is Steps 1 and 2.                                Step 1: -3(x+2) = 5(x-7)

                                                                               Step 2: -3x-6 = 5x-35

Step-by-step explanation:

Answer:

[a]. sample is 25 randomly selected students

    also population is all students

[b]. (20.0, 23.0)

[c]. (8.8, 24.2)

Step-by-step explanation:

here is a step by step process to solving this, i hope you find this helpful.

1). The population is all students who graduated from his school  while the

sample is 25 randomly selected students from the email list

2). given alpha = 1-0.86=0.14

critical z value(two tailed) for 86% confidence level is:

z=normsinv(0.07) or normsinv(0.93)=1.476

Margin of error=1.476*(4.6/SQRT(20))=1.5

86% confidence interval for population mean

=21.5+/-1.5

=(20.0, 23.0)

3). if population standard deviation is not known,we will use t distribution.

df=20-1=19

t*=tinv(0.05,19)=2.093

Margin of error=2.093*(5.7/sqrt(20))=2.7

95% confidence interval for population mean

=21.5+/-2.7

=(18.8, 24.2)

cheers i 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:

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:

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:

[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:

Adb , cbd, 1

Step-by-step explanation:

Answer:

ADB CBD 1

Step-by-step explanation:

Answer:

the answer is A.Use the numbers in the table to create ordered pairs. and D.Draw a straight line that starts at the origin and connects all the points.

Step-by-step explanation:

I just did it on edgnuity and got it right.

Answer:

The correct answer is A C and D

Step-by-step explanation:

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.

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