Lilliana is training for a marathon. She runs the same distance every day for a week on Monday,
Wednesday, and Friday, she runs 2 laps on a running trail and then runs 6 more miles. On Tuesday and
Sunday, she runs 4 laps on the trail and then runs 2 more miles. On Saturday, she just runs laps. How
many laps does Lilliana run on Saturday?

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Number of families __________Expenditure

______midpoint (x) ____Town A __Town B

21-30 __25.5____________3 _______2

31-40 __35.5____________61 ______14

41-50 __45.5___________132 _____ 20

51-60 __55.5__________ 153 ______27

61-70 __65.5__________ 140 ______ 28

71-80 __75.5___________ 51 _______ 7

81-90 __85.5___________ 2 _______ 2

The variability is the variance and standard deviation :

The variance (s):

√Σ(x - m)²/Σf(x)

Town A:

m = Σ(X * f(x)) / Σf ; Σf = 542

Σ x * f(x) = (25.5*3) + (35.5*61) + (45.5*132) + (55.5*153) + (65.5*140) + (75.5*51) + (85.5*2)

= 29931 / 542

= 55. 22

Σf(x - m)² / Σf - 1 = [3(25.5-55.22)^2 + 61(35.5-55.22)^2 + 132(45.5-55.22)^2 + 153(55.5-55.22)^2 + 140(65.5-55.22)^2 + 51(75.5-55.22)^2 + 2(85.5-55.22)^2] / 541

= 76458. 4928 / 541

Variance = 141.32808

Standard deviation = √variance

Standard deviation = √141.32808

Standard deviation = 11.89

TOWN B:

m = Σ(X * f(x)) / Σf ; Σf = 100

Σ x * f(x) = (25.5*2) + (35.5*14) + (45.5*20) + (55.5*27) + (65.5*28) + (75.5*7) + (85.5*2)

= 5490 / 100

= 54.90

Variance :

Σf(x - m)² / Σf - 1 = [2(25.5-54.90)^2 + 14(35.5-54.90)^2 + 20(45.5-54.90)^2 + 27(55.5-54.90)^2 + 28(65.5-54.90)^2 + 7(75.5-54.90)^2 + 2(85.5-54.90)^2] / 99

= 16764 / 99

= 169.33

Standard deviation = √variance

Standard deviation = √169.3333

Standard deviation = 13.013

From the result above, Town A has lesser variability than Town B due to the slightly lower variance and standard deviation values.

Answer:

The ball's speed will be 10 m/s at t=1.22 seconds

Step-by-step explanation:

The vertical motion of an object is controlled by the force of gravity. This means that there is a non-zero net force acting on the object that makes it accelerate downwards.

If the object is thrown upwards at speed vo, its speed at time t is:

[tex]v_f=v_o-g.t[/tex]

Where g is the acceleration of gravity [tex]g=9.8 m/s^2.[/tex]

Our ball is thrown upwards with v0=22 m/s. We need to calculate the time when its speed is vf=10 m/s.

Solving the above equation for t:

[tex]\displaystyle t=\frac{v_o-v_f}{g}[/tex]

Substituting:

[tex]\displaystyle t=\frac{22-10}{9.8}=\frac{12}{9.8}[/tex]

t=1.22 seconds

The ball's speed will be 10 m/s at t=1.22 seconds

Answer:

1.23

Step-by-step explanation:

103.32/(7*12)

103.32/84

1.23

Answer:

7/2

Step-by-step explanation:

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

3.5

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

Answer:

[tex]\%seniors = 16\%[/tex]

Step-by-step explanation:

Given

[tex]Students = 250[/tex]

[tex]Seniors = 40[/tex]

Required

Determine the percentage of seniors

This is calculated as thus;

[tex]\%seniors = \frac{Seniors}{Students} * 100\%[/tex]

[tex]\%seniors = \frac{40}{250} * 100\%[/tex]

[tex]\%seniors = \frac{4000\%}{250}[/tex]

[tex]\%seniors = 16\%[/tex]

Answer: -63E2

Step-by-step explanation: i think

Answer:

25%

Step-by-step explanation:

Macy’s error is that the store employees get a 25% markdown off the current price. In the first markdown (i.e 50%) should have been reduced to 25% in the second markdown, instead of being totally free.

Answer:

fdsfskdfdsjg,dgkdfjkgjkdfgjkfjkdghdkj

Step-by-step explanation:

Answer:

This statement is true because if F statistics is significant, then the entire multiple regression model is useful for the prediction of y.

Step-by-step explanation:

Solution:

In a multiple linear regression analysis, the statistical model utility is determined by the value of R2 and ∂2, while the Global F test p-value determines the practical model.

This statement is true because if F statistics is significant, then the entire multiple regression model is useful for the prediction of y.

The F test is a statistical test that is very flexible. F test can evaluate multiple model terms.

The F test indicates whether a linear regression model provides a better fit to data than a model that contains no independent variable.

The F test for overall significance has two hypotheses:

1- Null hypothesis:

                              The fit of the intercept only model and your model are equal.

2- Alternative hypothesis:

                               The fit of the intercept-only model is significantly reduced compared to your model.

Compare p-value for the F test,

If the p-value is less than the significance level, the sample data provide sufficient evidence  that the regression model fits the data better with no independent variable.

Answer:

7 and 5

Step-by-step explanation:

3 divided by 2/25 will be 15/2 in fraction form, and will be 7.5 in decimal form.

Answer:

The quotient is 7 1/2.

Answer:

The algebraic expression is​ 0.90p

Step-by-step explanation:

The presentation of the algebraic expression is​ shown below:

Let us assume that the original price is p.

So,

The Orginal price is P

and the item would be less a 10% discount

So it could be written as 0.10p

Now the required expression could be written as

p - 0.10 p = 0.90p

Hence the algebraic expression is​ 0.90p

The same is to be considered

Answer:

///////////////////

Step-by-step explanation:

Answer:

Step-by-step explanation:   2x+y=1

                                               4x+y=9        

we substract equals. 2x=8 so x=4 , y=-7

Answer:

Step-by-step explanation:

the answer in point-slope form is y = 1/4x-2 so your y-intercept is -2 and from there, move up one and right four. your points would be (0, -2) and (4, -1)

hope this helped! :)

Answer:

j

Step-by-step explanation:

Answer:

Taylor will pay $10.75

Step-by-step explanation:

If 1.25 PER/for each/for one pound that means you would multiply. So the equation is 8.6 x 1.25 = 10.75

Hope that helps and have a great day!

Answer:

10.75

Step-by-step explanation: 1.25 times 8.6 is 10.75 so that is the answer.

Answer:

5 ≤ y

Step-by-step explanation:

Answer:

12.54

Step-by-step explanation:

Answer:

How to Calculate a Rate. "Rate" simply means the number of things per some other number, usually 100 or 1,000 or some other multiple of 10. A percentage is a rate per 100. Infant mortality rates are calculated per 1,000.

Step-by-step explanation:

Answer:

0.17

Step-by-step explanation:

hope i helped

Answer:

85

Step-by-step explanation:

Answer:

30$*3=90$ - its the answer

Step-by-step explanation:

To get the answer we can first divide 60 by 2 to see how much cost 5 burgers. Then we have to multiply that result times 3 to get the answer.

60:2=30$ ----- 5 burgers.

30$*3=90$ - its the answer

We're given two pairs of congruent sides, and a pair of congruent angles. The angles are not between the two congruent sides. So we don't have enough information to know if the triangles are congruent or not. SSA is not a valid congruence theorem. This is because there are some cases where two triangles are possible leading to ambiguity.

If the marked angles were between the tickmarked sides, then we could use SAS.

Answer:

The probability that the proportion of books checked out in a sample of 774 books would be less than 10% is 0.0066

Step-by-step explanation:

We are given that The director of the library believes that 13% of the library's collection is checked out.

[tex]\mu = p = 0.13[/tex]

Total no. of books = 774

Standard deviation =[tex]\sqrt{\frac{p(1-p)}{n}}[/tex]

Standard deviation = [tex]\sqrt{\frac{0.13(1-0.13)}{774}}=0.012[/tex]

We are supposed to find  the probability that the proportion of books checked out in a sample of 774 books would be less than 10%

[tex]P(\hat{p}<0.1)\\Z=\frac{x-\mu}{\sigma}\\Z=\frac{0.1-0.13}{0.012}\\Z=-2.48\\P(Z<-2.48)=0.0066[/tex]

So,[tex]P(\hat{p}<0.1)=0.0066[/tex]

Hence  the probability that the proportion of books checked out in a sample of 774 books would be less than 10% is 0.0066

Answer:

The dimensions of the aquarium that minimize the cost of the materials:

[tex]x=y = \sqrt[3]{\frac{2V}{9}} , z = \sqrt[3]{\frac{81V}{4}}[/tex]

Step-by-step explanation:

Let x, y and z be the dimensions of aquarium .

Surface area of an aquarium = xy+2yz+2xz

Volume of aquarium V= [tex]Length \times Breadth \times Height =xyz----A[/tex]

We are given that slate costs five times as much (per unit area) as glass

So, Cost function : C=9xy+2yz+2xz

Now we will use langrage multiplier to find the dimensions of the aquarium that minimize the cost of the materials.

[tex]\nabla C = \lamda \nabla V\\(\frac{\partial C}{\patial x},\frac{\partial C}{\partial y}, \frac{\partial C}{\partial z})=\lambda(\frac{\partial V}{\patial x},\frac{\partial V}{\partial y}, \frac{\partial V}{\partial z})\\(9y+2z,9x+2z,2y+2x)=\lambda(yz+zx+xy)[/tex]

So,[tex]9y+2z=\lambda yz -----1\\9x+2z=\lambda zx -------2\\2y+2x=\lambda xy --------3[/tex]

Multiply 1 ,2 and 3 by x,y and z respectively.

[tex]9xy+2xz=\lambda xyz ------4\\9xy+2zy=\lambda zxy -------5\\2yz+2xz=\lambda xyz --------6[/tex]

Now equate 4 and 5

9xy+2xz=9xy+2yz

x=y

Substitute y=x in 5 and 6 and equate them

[tex]9x^2+2xz=2xz+2xz\\9x=2z\\\frac{9x}{2}=z[/tex]

Substitute the values in A

[tex]Volume = xyz=(x)(x)(\frac{9x}{2})\\Volume V = \frac{9x}{2}x^3\\\sqrt[3]{\frac{2V}{9}}=x\\x=y=\sqrt[3]{\frac{2V}{9}}\\z=\frac{9(\sqrt[3]{\frac{2V}{9}})}{2}\\z=\sqrt[3]{\frac{81V}{4}}[/tex]

Hence,

The dimensions of the aquarium that minimize the cost of the materials:

[tex]x=y = \sqrt[3]{\frac{2V}{9}} , z = \sqrt[3]{\frac{81V}{4}}[/tex]