Data was collected for 221 randomly selected 10 minute intervals. For each ten-minute interval, the number of people entering the atrium of a large mall were recorded. The data is summarized in the table below. Number of Guests Frequency 100 – 119 45 120 – 139 76 140 – 159 56 160 – 179 17 180 – 199 27 What is the class width for this GFDT?

Answer:

The answer to the problem is 5.

Answer:

Step-by-step explanation:

[tex]-3-\left(-8\right)\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=-3+8\\\\\mathrm{Add/Subtract\:the\:numbers:}\:\\-3+8\\=5[/tex]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the  the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = [tex]\dfrac{1}{2}[/tex]

[tex]\theta = -\dfrac{\pi}{3}, \ \ \dfrac{\pi}{3}[/tex]

Now, the area of the  region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

[tex]A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \ \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ 5^2 d \theta[/tex]

[tex]A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \ \theta d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ d \theta[/tex]

[tex]A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} \dfrac{cos \ 2 \theta +1}{2} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}[/tex]

[tex]A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} {cos \ 2 \theta +1} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}[/tex]

[tex]A =25 \begin {bmatrix} \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}} \ \ - \dfrac{25}{2} \begin {bmatrix} \dfrac{2 \pi}{3} \end {bmatrix}[/tex]

[tex]A =25 \begin {bmatrix} \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3}) \end {bmatrix} - \dfrac{25 \pi}{3}[/tex]

[tex]A = 25 \begin{bmatrix} \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} + \dfrac{\pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}[/tex]

[tex]A = 25 \begin{bmatrix} \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}[/tex]

[tex]A = \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}[/tex]

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Answer:

2.0

Step-by-step explanation:

Answer:

B. 2.0 miles

Step-by-step explanation:

Tony ran 1/2 of a mile for 1/4 of an hour.

First, to make it easier, change each fraction into decimals:

1/2 = 0.5

1/4 = 0.25

It takes Tony 0.25 hours to run 0.5 miles.

You are solving for 1 hours worth. Multiply 4 to both terms:

0.25 hr x 4 = 1 hr

0.5 miles x 4 = 2.0 miles

B. 2.0 miles is your answer.

~

Answer:

A) A = 200w - w²

B) w = 100 yards

C) Max Area = 10000 sq.yards

Step-by-step explanation:

We are told that Robert has available 400 yards of fencing.

A) we want to find the expression of the area in terms of the width "w".

Since width is "w", and perimeter is 400,if we assume that length is l, then we have;

2(l + w) = 400

Divide both sides by 2 gives;

l + w = 200

l = 200 - w

Thus, Area of rectangle can be written as;

A = w(200 - w)

A = 200w - w²

B) To find the value of w for which the area is largest, we will differentiate the expression for the area and equate to zero.

Thus;

dA/dw = 200 - 2w

Equating to zero;

200 - 2w = 0

2w = 200

w = 200/2

w = 100 yards

C) Maximum area will occur at w = 100.

Thus;

A_max = 200(100) - 100(100)

A_max = 10000 sq.yards

Answer:

4 months

Step-by-step explanation:

Club A

registration fee: $0

monthly fee: $105

After every month, the total cost increases by $105.

month 0: $0

month 1: $105

month 2: $210

month 3: $315

month 4: $420

month 5: $525

month 6: $630

Club B

registration fee: $375

monthly fee: $80

Notice how Club B's total reaches Club A's total after 2 months.

month 0: $375

month 1: $455

month 2: $535

month 3: $615

month 4: $695

Answers:

Distance = 14 km

Displacement = 4 km east

==============================================

Explanation:

The total distance is simply the sum of the values given. So he traveled a total of 5+4+5 = 9+5 = 14 km overall.

----------------------

The displacement is where a drawing may come in handy. Draw an xy axis. Place point A at the origin (0,0). This is where Michael starts his trip. Then move up to (0,5) to indicate he goes 5 km north. Call this point B.

Afterward, mark point C at (4,5) to show he has gone 4 km east. Finally, point D is at (4,0) because he went 5 km south

The displacement is only concerned with two points: The start and end point. Nothing else matters. We started at A(0,0) and ended at D(4,0). So we've gone 4 km east overall. The direction is important when it comes to displacement. Simply saying "4 km" isn't enough. So in a sense, we could take a shortcut from A directly to D, bypassing the other points B and C.

See the diagram below for a visual.

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

From the question

y = - 4x + 3

Comparing with the general equation above

Slope / m = - 4

Since the lines are parallel their slope are also the same

Slope of parallel line = (-3 , 2) and slope

- 4 is

We have the final answer as

Hope this helps you

Answer:

y=-4x-14

Step-by-step explanation:

Answer:

The slope would be 7/3

The y-intercept would be -11

Step-by-step explanation:

To find the answer rearrange your equation.

First subtract 14x from both sides, getting -6y= -14x + 66.

Then divide both sides by -6, getting y= 7/3x -11

This is now written in y=mx+b form. Your m is your slope and b is the y intercept!

Answer:

Well, there is a lot of answers to that. Check explanation, please!

Step-by-step explanation:

For example, some basic fractions that are less than 1/7 are:

You can also set up a number line, and compare the fractions.

Hopefully, this answer helps! :D

Answer:

It´s rational

Step-by-step explanation:

27,14159 = 2714159/100000

Rational

Answer and Step-by-step explanation: The Trapezoidal and Simpson's Rules are method to approximate a definite integral.

Trapezoidal Rule evaluates the area under the curve (definition of integral) by dividing the total area into trapezoids.

The formula to calculate is given by:

[tex]\int\limits^a_b {f(x)} \, dx = \frac{b-a}{2n}[f(x_{0})+2f(x_{1})+2f(x_{2})+...+2f(x_{n-1})+f(x_{n})][/tex]

The definite integral will be:

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{9-4}{2.8}[2+2.\sqrt{5} +2.\sqrt{6} +2.\sqrt{7}+2.\sqrt{8}+3][/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{5}{16}[25.3193][/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = 7.9122[/tex]

Simpson's Rule divides the area under the curve into an even interval number of subintervals, each with equal width.

The formula to calculate is:

[tex]\int\limits^a_b {f(x)} \, dx = \frac{b-a}{3n}[f(x_{0})+4f(x_{1})+2f(x_{2})+...+2f(x_{n-2})+4f(x_{n-1})+f(x_{n})][/tex]

The definite integral will be:

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{9-4}{3.8}[2+4.\sqrt{5} +2.\sqrt{6} +4.\sqrt{7} +4\sqrt{8} +3][/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{5}{24}[40.7398][/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = 8.4875[/tex]

Calculating the definite integral by using the Fundamental Theorem of Calculus:

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \int\limits^9_4 {x^{\frac{1}{2} }} \, dx[/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{2.\sqrt[]{x^{3}} }{3}[/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{2.\sqrt[]{9^{3}} }{3}-\frac{2.\sqrt[]{4^{3}} }{3}[/tex]

[tex]\int\limits^9_4 {\sqrt{x} } \, dx = 12.6667[/tex]

Comparing results, note that Simpson's Rule is closer to the exact value, i.e., gives better approximation to the exactly value calculated by the fundamental theorem.

Answer:

{-3, 2}U{2, 5}

Step-by-step explanation:

For an equation to be negative, it would need to be in a negative range (below the x-axis or the coordinates are negative y-values). Therefore, we can examine this question and see that the graph is negative when the function crosses the x-axis at -3 and it remains negative until you reach 2 on the x-axis.

Therefore, the first set of negative values is (-3, 2).

Secondly, applying the same logic as before, the function decreases at 2 and then touches the x-axis again at 5. Therefore, the second negative value would be (2, 5).

The negative values are {-3, 2}U{2, 5}.

Answer:

{-3, 2}U{2, 5}

Step-by-step explanation:

Answer:

P ([tex]\hat p[/tex] ≤ 0.10)

Step-by-step explanation:

The probability in terms of statistics for this given problem can be written as follows.

Let consider X to the random variable that represents the number of 6's in 7 throws of a dice, then:

X [tex]\sim[/tex]Bin ( n = 72, p = 0.167)

E(X) = np

E(X) = 72× 0.167

E(X) = 12.024

E(X) [tex]\simeq[/tex]  12

p+q =1

q = 1 - p

q = 1 - 0.167

q = 0.833

V(X) = npq

V(X) = 72 × 0.167 × 0.833

V(X) = 10.02

V(X) [tex]\simeq[/tex] 10

∴ X [tex]\sim[/tex] N ([tex]\mu = 12, \sigma^2 =10[/tex])

⇒ [tex]\hat p = \dfrac{X}{n} \sim N ( p, \dfrac{pq}{n})[/tex]

where p = 0.167 and [tex]\dfrac{pq}{n}[/tex] = [tex]\dfrac{0.167 \times 0.833}{72}[/tex] = 0.00193

∴ P(at most 10% of rolls are 6's)

i.e

P ([tex]\hat p[/tex] ≤ 0.10)

Answer: y=4/5x+12

Step-by-step explanation:

Slope-intercept form: y=ax+b, where a is the slope and b is the y-intercept

When a line is parallel to another line, they will have the same slope. So the slope of the new line is also 4/5.

y=4/5x+b

To find the y-intercept, we simply plug in the point it passes through.

y=4/5x+b

8=4/5(-5)+b

8=-4+b

b=12

y=4/5x+12

Hope this helps!! :)

Please let me know if you have any question

Answer:

Option 1, 3 and 5 are correct

Step-by-step explanation:

Given

Eggplants = $1.79 each

Apples = $0.59 each,

Bags of spinach = $2.55 each

Cartons of orange juice = $3.89 each

Required

Select three true statements

To do this, we'll check the options one after the other

1. 4 eggplants cost about $0.50 less than 3 bags  of spinach

First, we need to calculate the cost of 4 eggplants

4 Eggplants = 4 * 1 Eggplants

4 Eggplants = 4 * $1.79

4 Eggplants = $7.16

Next, we calculate the cost of 3 bags of Spinach

3 bags of Spinach = 3 * 1 bag of Spinach

3 bags of Spinach = 3 * $2.55

3 bags of Spinach = $7.65

Determine the difference

Difference = |Eggplants - Bags of Spinach|

Difference = |$7.16 - $7.65|

Difference = |-$0.49|

Difference = $0.49

This statement is true because $0.49 approximates to $0.50

2. Total cost of 4 apples and 2 eggplants $0.50 is more than $6.00

First, we need to calculate the cost of 4 apples

4 Apples = 4 * 1 Apples

4 Apples = 4 * $0.59

4 Apples = $2.36

Next, we calculate the cost of 2 Eggplants

2 Eggplants = 2 * 1 Eggplant

2 Eggplants = 2 * $1.79

2 Eggplants = $3.58

Add this two results together

Total = 4 Apples + 2 Eggplants

Total = $2.36 + $3.58

Total = $5.94

This statement is false because the sum is less than $6.00

3. Total cost of 4 eggplants, 4 apples and 1 carton of orange juice is $13.41

In (1) & (2) above

4 Eggplants = $7.16

4 Apples = $2.36

1 carton of orange juice = $3.89

Add the above together

Total = $7.16 + $2.36 + $3.89

Total = $13.41

This statement is true because the sum is $13.41

4. Total cost of 5 eggplants is greater than cost of 4 bags of spinach

First, we need to calculate the cost of 5 eggplants

5 Eggplants = 5 * 1 Eggplants

5 Eggplants = 5 * $1.79

5 Eggplants = $8.95

Next, we calculate the cost of 4 bags of Spinach

4 bags of Spinach = 4 * 1 bag of Spinach

4 bags of Spinach = 4 * $2.55

4 bags of Spinach = $10.20

This statement is false because 4 Eggplants costs less than $ bags of spinach

5. Total cost of 2 eggplants, 2 apples and 2 cartons of orange juice is $9.99 more than cost of 1 bag of spinach

From (2) above

2 Eggplants = $3.58

Next, we need to calculate the cost of 2 apples

2 Apples = 2 * 1 Apples

2 Apples = 2 * $0.59

2 Apples = $1.18

Next, we need to calculate the cost of 2 cartons of orange juice

2 Cartons = 2 * 1 Carton

2 Apples = 2 * $3.89

2 Apples = $7.78

Sum these up

Total = $3.58 + $1.18 + $7.78

Total = $12.54

1 Bag of spinach = $2.55 each

Subtract 1 Bag of spinach from the $12.54

Difference = $12.54 - $2.55

Difference = $9.99

This statement is true because the difference is $9.99

Answer:

this is wind turbine angular speed

Step-by-step explanation:

given data

angular speed ω = 64 rpm

time = 1 min = 60 seconds

solution

we know that angular speed ω is expess as

ω = [tex]\frac{2\pi }{T}[/tex]    .........................1

ω = 64 × [tex]\frac{2\pi }{T}[/tex]

ω  = 6.70 rad/s

so this is wind turbine angular speed

Answer:

Step-by-step explanation:

Since the square canvas was completely covered using 77.8 in.² of fabric without any overlap, to get the side length of the canvas, we will use the formula for calculating the area of a square.

Area of a square = Length * Length

A = L*L

A = L²

Given the Area of the area of the square canvas as 77.8 in², on substituting this values into the formula to get L we have;

77.8 = L²

Take the square root of both sides

√77.8 = √L²

L = √77.8

L = 8.82 in

L ≈ 9inches

The length 8.82in gotten was approximated to 9in because the first value after the decimal point is greater that 4 and once we have such case 1 will be added to the value before the decimal point i.e 8 to make it 9.

Hence measurement that is closest to the side length of this canvas in inches is 9inches.

Answer:

A. 2880 acres

Step-by-step explanation:

Formula: a = 640 s

Given information: s = 4.5

--> a = 640 x 4.5 = 2880 (acres)

Answer:

term=14x+19

cofficient=14+19

constant=19

Answer:

Terms :

14x , 19

Coefficients:

14

Constants:

19

Hope it helps.

Answer:

First recipe needs = 3/8

Second recipe needs = 5/8

Step-by-step explanation:

Given:

Two recipes needs butter = 1 pound

One recipe needs 1/4 pound more

Find:

Each recipe needs butter

Computation:

Assume;

First recipe needs = x

Second recipe needs = x + (1/4)

Two recipes needs butter = First recipe needs + Second recipe needs

x + x + (1/4) = 1

2 x = 1 - (1/4)

2 x = 3/4

x = 3/8 pound

First recipe needs = 3/8

Second recipe needs = x + (1/4) = (3/8) + (1/4) = 5/8

Second recipe needs = 5/8

Answer:

[tex] \frac{7}{3} [/tex]

Step-by-step explanation:

Given that,

p = -6,

q = 6

r = -19

Plug in the above values to evaluate the expression, [tex] \frac{\frac{q}{2} - \frac{r}{3}}{\frac{3p}{6} + \frac{q}{6}} [/tex]

[tex] \frac{\frac{6}{2} - \frac{(-19)}{3}}{\frac{3(-6)}{6} + \frac{6}{6}} [/tex]

[tex] \frac{\frac{3}{1} - \frac{(-19)}{3}}{\frac{-3}{1} + \frac{1}{1}} [/tex]

[tex] \frac{\frac{9 -(-19)}{3}}{3 + 1} [/tex]

[tex] \frac{\frac{28}{3}}{4} [/tex]

[tex] \frac{28}{3}*\frac{1}{4} [/tex]

[tex] \frac{28*1}{3*4} [/tex]

[tex] \frac{7*1}{3*1} [/tex]

[tex] \frac{7}{3} [/tex]

Answer:

the answer is 4.115 x 10^5

Step-by-step explanation:

hope that helps

Complete question :

A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:

City - - - - - - - Price ($) -- - Sales

River City - - 1.30 - - - - - - 100

Hudson - - - 1.60 - - - - - 90

Ellsworth - - - 1.80 - - - - - 90

Prescott - - - - 2.00 - - - - 40

Rock Elm - - 2.40 - - 38

Stillwater - - 2.90 - - 32

Answer:

78.39%

Step-by-step explanation:

Given the data :

Price (X) :

1.30

1.60

1.80

2.00

2.40

2.90

Sales (y) :

100

90

90

40

38

32

The percentage of the total variation in candy bar sales explained by the regression model can be obtained from the value of the Coefficient of determination(R^2) of the regression model. The Coefficient of determination is a value which ranges between 0 - 1 and gives the proportion of variation in the dependent variable which can be explained by the dependent variable.

R^2 value is obtained by getting the squared value of R(correlation Coefficient).

The R value obtained using the online R value calculator on the data is : - 0.8854

Hence, R^2 = (-0.8854)^2 = 0.7839

Expressing 0.7839 as a percentage ;

0.7839 × 100 = 78.39%

Answer:

A. 5 < AC < 10

Step-by-step explanation:

If ∆ABC is a right angled triangle, we use the Pythagoras formula:

c² = a² + b²

Where c = longest side

When given sides AB, AC and BC, the formula becomes:

AB² = AC² + BC²

Where AB = Longest side

In the question,

AB = 10 and BC = 5.

10² = AC² + 5²

AC² = 10² - 5²

AC² = 100 - 25

AC² = 75

AC = √75

AC = 8.6602540378

Therefore, the expression that is always true = A. 5 < AC < 10

Answer:

see below

Step-by-step explanation:

a  R=k(L/A)

Substitute what we know into the equation

.08 = k (100/.05)

.08 = k 2000

Divide each side by 2000

.08/2000 = k

.00004 = k

R=.00004 (L/A)

b R=.00004 (L/A)

We know L = 4000 and A = .02

R=.00004 (4000/.02)

R = 8

Answer:

The answer is below

Step-by-step explanation:

Velocity is the rate of change of displacement. Velocity is the ratio of distance to time.

The velocity v(t) = [tex]\frac{d}{dt}r(t)[/tex]

Where r(t) is the position function

Given that:

r(t)=⟨−8tsint,−8tcost,2t²⟩

[tex]v(t)=\frac{d}{dt}r(t)= <-8tcost-8sint,8tsint-8cost,4t>[/tex]

Acceleration is the rate of change of velocity, it is the ratio of velocity to time. Acceleration a(t) is given as:

[tex]a(t)=\frac{d}{dt}v(t)= \frac{d}{dt} <-8tcost-8sint,8tsint-8cost,4t>\\=<8tsint-16cost,8tcost+16cost,4>\\\\a(t)=<8tsint-16cost,8tcost+16cost,4>[/tex]

Speed = |v(t)| = [tex]\sqrt{(-8tcost-8sint)^2+(8tsint-8cost)^2+(4t)^2}\\\\ =\sqrt{64t^2cos^2t+128tcostsint+64sin^2t+64t^2sin^2t-128tsintcost+64cos^2t+16t^2}\\ \\=\sqrt{64t^2cos^2t+64t^2sin^2t+64sin^2t+64cos^2t+16t^2}\\\\=\sqrt{64t^2(cos^2t+sin^2t)+64(sin^2t+cos^2t)+16t^2}\\\\=\sqrt{64t^2+64+16t^2}=\sqrt{80t^2+64}[/tex]

Answer:

add the expressions 832

Answer:

Pay for the day = $ 123.25

Step-by-step explanation:

From the question given:

Monday morning:

Time in: 8:15

Time out: 12:15 pm

Monday afternoon:

Time in: 13:00

Time out: 17:30

Pay = $ 14.5 /hr

Next, we shall determine the number of hours of work in the morning. This is illustrated below:

Time in: 8:15

Time out: 12:15 pm

Difference in time = 12:15 – 8:15 = 4 hrs

Next, we shall determine the pay for the work done in the morning. This can be obtained as follow:

Pay = $ 14.5 /hr

Pay for work done in the morning

= 4 × 14.5 = $ 58

Next, we shall determine the number of hours of work in the afternoon. This is illustrated below:

Time in: 13:00

Time out: 17:30 pm

Difference in time = 17:30 – 13:00 = 4 hrs 30 minutes

Next, we shall convert 4 hrs 30 minutes to hours. This is illustrated below:

60 minutes = 1 hr

30 minutes = 30/60 = 0.5 hrs.

Therefore,

4 hrs 30 minutes = 4 + 0.5 = 4.5 hrs

Next, we shall determine the pay for the work done in the afternoon. This can be obtained as follow:

Pay = $ 14.5 /hr

Pay for work done in the afternoon

= 4.5 × 14.5 = $ 65.25

Finally, we shall determine the pay for the day as follow:

Pay for work done in the morning

= $ 58

Pay for work done in the afternoon

= $ 65.25

Pay for the day = pay for morning + pay for afternoon

Pay for the day = $ 58 + $ 65.25

Pay for the day = $ 123.25

Therefore, the pay for the day is

$ 123.25

Answer: D. This variable is a discrete numerical variable that is ratio-scaled.

Step-by-step explanation:

A Discrete variables are variables which are countable in a finite amount of time. For example, you can count the amount of money in your bank wallet, but same can’t be said for the money you have deposited in eveyones bank account as this is infinite.

So the number of times an individual changes job in a five years period is a perfect example of  a discrete numerical variable that is ratio scaled because it can be counted.