For items 21 - 23 determine whether each sequence is arithmetic. if the sequence is arithmetic, then

Answer:

degrees of freedom = 15

tc= 1.746

Step-by-step explanation:

The degrees of freedom is given by n-1 where n is the sample size .

so the degrees of freedom for a t distribution is 16-1= 15

Now we have to find tc for 95%  confidence interval. For this we look at the t- table under the 1-0.95= 0.05  for alpha for 15 degrees of freedom and the value is 1.746

This area is to  the right side under the t distribution with the given degrees of freedom for the given alpha.

It can also be found out by other calculators such as graphing calculator.

Using the degree of freedom formula and the Tcritical distribution, the degree of freedom and Tcritical value are 15 and 2.131 respectively

Given that :

Hence, the degree of freedom, df = 16 - 1 = 15

The t critical value :

Tcritical = [tex]t_{\frac{0.05}{2}}, 15 = 2.131 [/tex]

Hence, the Tcritical value is 2.131.

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Answer:

Here  x=2−3–√ ................…………………………………….....(1)

Hence  12−3√=12−3√⋅2+3√2+3√=2+3–√ .....................(2)

From (1) and (2) we get  x+1x=4 .......……………………………....(3)

and  x−1x=−23–√ ...............…………………….………....(4)

From (3) and (4) we get  x2−1x2=(x+1x).(x−1x)=−83–√.

Hoped I helped

Answer:

The value is  [tex]y'(t) = \frac{k}{\sqrt{y(t)} }[/tex]

Step-by-step explanation:

From the question we told that are

      The rate of growth of mice is inversely proportional to the square of the population

   This above statement can be mathematically represented as

        [tex]\frac{d y }{dt} \ \ \ \alpha \ \ \frac{1}{\sqrt{y(t)} }[/tex]

Here  [tex]y(t)[/tex] is the population

=>     [tex]\frac{d y }{dt} = \frac{k}{\sqrt{y(t)} }[/tex]

=>     [tex]y'(t) = \frac{k}{\sqrt{y(t)} }[/tex]

Step-by-step explanation:

sorry jesica I don't know the answer

Answer:

  x = 3

Step-by-step explanation:

Maybe you want the equation of the line.

__

A vertical line has undefined slope. Its equation is of the form ...

  x = constant

In order for the line to go through a point with an x-coordinate of 3, the constant must be 3.

  x = 3 . . . . equation of the line

Explanation:

Remember: we have to isolate the variable x, so that means we have to get x by itself.

Step 1:

Let’s look at our equation:

[tex]6x+57=2x+315[/tex]

Let’s subtract 2x from both sides of the equation, since our goal is to isolate the variable. You could also subtract 6x from both sides, but you would end up with a negative number, and I find it easier to deal with positive numbers.

[tex]6x(-2x)+57=2x(-2x)+315\\4x+57=315[/tex]

Step 2:

Now, let’s subtract 57 from both sides of our equation.

[tex]4x+57(-57)=315(-57)\\4x=258[/tex]

Step 3:

Since we have to isolate x, let’s divide both sides of the equation by 4.

[tex]4x/4=x\\258/4=64.5[/tex]

Our final answer: x = 64.5

None of your options is the correct answer. Notify your teacher, tutor, etc. since there none of the options are correct.

Answer:

The  value is  [tex]k = 3 \ inches[/tex]

Step-by-step explanation:

From the question we are told that

   The  length is   [tex]l = 25 \ ft[/tex]

   The  width is  [tex]w = 12 \ inches = \frac{12}{12} = 1\ ft[/tex]

Generally let assume that (k ft)  was turned up on each side hence the remaining width is  

             [tex](1 - 2 k ) \ ft[/tex]

Now  the capacity is also the volume it can hold which is mathematically represented as

         [tex]C = 25 (1- 2k) k[/tex]

          [tex]C = 25 (k- 2k^2)[/tex]

          [tex]C = 25k - 50k^2[/tex]

At maximum  or minimum  

     [tex]\frac{dC}{dk} = 0[/tex]

=>    [tex]\frac{dC}{dk} = 25 - 100k = 0[/tex]

=>    [tex]k = 0.25\ ft[/tex]

Now  to see if the value  obtained is positive or negative we differentiate a second time

    So

        [tex]\frac{d^2C}{dk^2} = - 100k[/tex]

at  k  =  0,25 ft

       [tex]\frac{d^2C}{dk^2} = - 100(0.25)[/tex]

       [tex]\frac{d^2C}{dk^2} = -25[/tex]

since a negative  value is obtained then k is  the maximum value  

converting to inches

     [tex]k = 0.25 * 12[/tex]

     [tex]k = 3 \ inches[/tex]

Answer:

A. 224 messages per hour

B. 256 messages per hour

C. 544 messages per hour

D. 1296 messages per hour

Step-by-step explanation:

First you need to figure out how many messages Nick wrote in 1 hour

36 messages ÷ 2.25

2.25 hours ÷ 2.25

=

16 messages

1 hour

=

16 messages

hour

Then you multiply how ever many hours by 16 because Nick can write 16 messages in 1 hour.

Answer:

1).

Difference = $6

Interest rate= 4.03%

2).diffrence = $97

Interest rate = 14.37%

3). Difference = $7

Interest rate= 4.67%

4). difference= 191

Interest rate= 9.6%

5). Difference= 2.25

Interest rate= 3%

6). Difference=$ 302

Interest rate=9.12%

Step-by-step explanation:

1).$10 per months for 15 months

= 10*15=$150

PLus a down payment of $5= $155

Interest = 155-149= $6

Interest rate = 6/149*100= 4.03%

2.)$120.00 per month for 6 months

= 120*6=$ 720

Plus a down payment of $52=$772

Interest= 772-675= $97

Interest rate = 97/675 *100= 14.37%

3). $12.00 per month for 11 months

= 12*11= 132 plus down payment of $25

= $157

Interest= 157-150= $7

Interest rate=7/150 *100= 4.67%

4).$74.00 per month for 24 months

= 74*24=$1776

Plus a down payment of $400=$ 2176

Interest= 2176-1985= 191

Interest rate= 191/1985*100= 9.6%

5).$4.75 per week for 11 weeks

= 4.75*11=$52.25

Plus a down payment if $25

= 25+52.25=$ 77.25

Interest= 77.25-75= 2.25

Interest rate= 2.25/75 *100= 3%

6).$300 a month for 10 months

= 300*10= $3000

Plus a down payment of $600

= $3600

Interest=3600-3298= 302

Interest rate= 302/3298 *100=9.12%

Answer:

Rylee spent $25 for fuel at the gas station. This money is leaving her bank account, so represent the amount with a negative sign: -$25.

Step-by-step explanation:

None. the expression explains it.

Answer:3/8

Step-by-step explanation:

The simplest form of  

15 /40  is  3 /8 .

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 15 and 40 is 5

Divide both the numerator and denominator by the GCD

15 ÷ 5

40 ÷ 5

Reduced fraction:  

3 /8

Therefore, 15/40 simplified to lowest terms is 3/8.

Answer:

Step-by-step explanation:

Given the vectors ⟨−39,b,3⟩ and ⟨b,b²,b⟩, for the vectors to be orthogonal, the dot product of both vectors must be equal to zero.

Taking the dot product of both vectors and equating it t zero we will have;

⟨−39,b,3⟩*⟨b,b²,b⟩ = -39(b)+ b(b²)+3(b)

(Note that when multiplying, we multiply component wise and take the sum of the product if each component)

Since the vectors are orthogonal, then -39(b)+ b(b²)+3(b) = 0

open the parenthesis

-39b+b³+3b = 0

on rearranging

b³+3b-39b= 0

b³-36b= 0

factor out b from the equation

b(b²-36) = 0

b = 0 and b²-36 = 0

from b²-36 = 0

add 36 to both sides of the equation

b²-36+36= 0+36

b² = 36

take the square root of both sides

√b² = ±√36

b = ±6

Hence the values of b for the vectors to be orthogonal are 0, -6 and 6.

Answer:

1/8x + 1/2 y

Step-by-step explanation:

Charlotte gets 1/4x from dayna

Charlotte now has

1/4x+y

She lends 1/2 of this

1/2  ( 1/4x +y)

1/8x + 1/2 y

Answer:

[tex]A(-1,-8)[/tex]

Step-by-step explanation:

Given

Point: A(2,6)

Translation: 1 left and 3 up

Rotation: 180 degrees

Required

Image of Point A

Taking the exercise one after the other

Represent the function as: (x,y)

Such that

[tex]A(x,y) = A(2,6)[/tex]

1 unit left translation means the function becomes (x - 1, y)

2 unit up translation means the function becomes (x - 1, y + 2)

Applying the above transformation

[tex]A(2,6) -> A(2-1,6+2)[/tex]

[tex]A(2,6) -> A(1,8)[/tex]

At this stage, the coordinate becomes

[tex]A(1,8)[/tex]

When a function (x,y) is rotated by 180, the new function becomes (-x,-y)

So;

The further transformation of A is

[tex]A(1,8) -> A(-1,-8)[/tex]

Hence, the new image of A is

[tex]A(-1,-8)[/tex]

Answer:

its -1,-9

Step-by-step explanation:

Answer:

3 ; 4.5 ; 7.25

Step-by-step explanation:

Given the sample :

8 2 9 5 3 7 4 2 7 4 10 4 3 5

Calculate, the first, second, and third quartiles

Arranging the data in ascending order :

2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 7, 8, 9, 10

First quartile :

Q1 = [(n + 1) /4]th value

n = 14

Q1 = [(14 + 1) /4]th = (15/4)th = 3.75 value

Taking the average of the 3rs and 4th observation:

(3 +3) / 2 = 3

Second quartile :

Q2 = [2(n + 1) /4]th value

Q2 = 2(15)/4 = (30/4)th value

Q2 = 7.5 ; taking the 7th and 8th value

Q2 = (4 +5) /2 = 9/2 = 4.5

Q3 = [3(n + 1) /4]th value

Q2 = 3(15)/4 = (45/4)th value

Q2 = 11.25 ; taking the 11th

Q2 = 7 + 0.25 = 7.25

It does not deal with numeric values, but rather we're talking about names or labels when we are talking about nations of origin. This variable is categorical and nominal. It is not ordinal as we cannot order the nations in any way. You could argue about alphabetical ordering of course, but that won't apply here because you could do that about any set of labels (eg: colors red,green,blue can be ordered alphabetically but intrinsically it doesn't make sense to sort colors).

Since "nation of origin" involves categories or labels representing different countries, it is considered a qualitative variable.

We have,

Qualitative variables, also known as categorical variables, represent characteristics or qualities that cannot be measured numerically.

These variables typically involve categories or labels that describe different groups or attributes.

In the case of "nation of origin," it refers to the country from which someone originates.

This variable is qualitative because it involves different categories or labels representing different nations or countries.

Examples of possible categories for nation of origin include "United States," "Canada," "France," "China," and so on.

Therefore,

Since "nation of origin" involves categories or labels representing different countries, it is considered a qualitative variable.

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Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-74,-76) and (-35,4)

The distance between the points is

We have the final answer as

Hope this helps you

Answer:

The linear speed of the bike is 19.242 miles per hour.

Step-by-step explanation:

If sliding between the bottom of the wheel and ground can be neglected, the motion of the wheel can be well described by rolling, which is a superposition of coplanar pure rotation and translation, The speed of the bike occurs at the center of the wheel, where resulting instantaneous motion is pure translation parallel to ground orientation. The magnitude of the speed of bike ([tex]v_{B}[/tex]), measured in inches per second, is:

[tex]v_{B} = R\cdot \omega[/tex]

Where:

[tex]R[/tex] - Radius, measured in inches.

[tex]\omega[/tex] - Angular speed, measured in radians per second.

Now, the angular speed must be converted from revolutions per minute into radians per second:

[tex]\omega = \left(154\,\frac{rev}{min} \right)\cdot \left(2\pi\,\frac{rad}{rev} \right)\cdot \left(\frac{1}{60}\,\frac{min}{s} \right)[/tex]

[tex]\omega \approx 16.127\,\frac{rad}{s}[/tex]

The speed of the bike is: ([tex]R = 21\,in[/tex] and [tex]\omega \approx 16.127\,\frac{rad}{s}[/tex])

[tex]v_{B} = (21\,in)\cdot \left(16.127\,\frac{rad}{s} \right)[/tex]

[tex]v_{B} = 338.667\,\frac{in}{s}[/tex]

Lastly, the outcome is converted into miles per hour:

[tex]v_{B} = (338.667\,\frac{in}{s} )\cdot \left(3600\,\frac{s}{h} \right)\cdot \left(\frac{1}{63360}\,\frac{mi}{in} \right)[/tex]

[tex]v_{B} = 19.242\,\frac{mi}{h}[/tex]

The linear speed of the bike is 19.242 miles per hour.

Answer:

Differences=

[tex] {120cm}^{3} [/tex]

Step-by-step explanation:

Volume of first box=15cm×4cm×8cm

[tex]480 {cm}^{3} [/tex]

Volume of second box=10cm×9cm×4cm

[tex] {360cm}^{3} [/tex]

a. −4

b. 2

c. −125

d. −1,348

e.  27

f. 398

[tex]PV=nRT\implies P=V^{-1}nRT[/tex].

Hope this helps.

its hard to explain and show work but so you know the answer is no and its because they converted yards to miles and did the formula for ft to miles instead of yd to miles they did 5280 ft per mile and not 1760 yd per miles

Answer:

13.63 miles per hour

Step-by-step explanation:

100 yards / 15 sec  converted to miles per hour

100 yards  x  60 sec  x   60 min   x  1 mile       =  13.63 miles/hr

   15 sec           1 min            1 hr         1760 yards

the mistake on Mrs Dukes is the conversion from miles to yards.

1 mile = 1760 yards NOT 5280 yards

Answer:

Computed mean = 51.6

Actual mean > computed mean

Step-by-step explanation:

Low temp. - - Freq(f) - - midpoint(x) - - fx

40−44 - - - - - 2 - - - - - - - 42 - - - - - - 84

45−49 - - - - - 7 - - - - - - - 47 - - - - - - 329

50−54 - - - - - 9 - - - - - - - 52 - - - - - - 468

55−59 - - - - - 5 - - - - - - - 57 - - - - - - 285

60−64 - - - - - 2 - - - - - - - 62 - - - - - - 124

Mean (m) = Σ(fx) / Σ(f)

Σ(fx) = 84 + 329 + 468 + 285 + 124 = 1290

Σ(f) = 2 + 7 + 9 + 5 + 2 = 25

Mean (m) = 1290 / 25

Computed mean (m) = 51.6

Actual mean = 56.6

Actual mean > computed mean

56.6 > 51.6

Answer:

$306.40

Step-by-step explanation:

Multiply 15.32 by 20

Answer:

  4.32%; no

Step-by-step explanation:

The value of 0.24 differs from the mean by 0.84 -0.24 = 0.60. 2 standard deviations from the mean would be a difference of 2×0.35 = 0.70.

A statistical calculator says the probability of a depth less than 0.24 mm for the given distribution is about 4.32%.

The value differs from the mean by less than 2 standard deviations, so is not considered unusual.

Answer:

64 dollars

Step-by-step explanation:

8 children and 8 adults

2 dollars for a child and 6 dollars for an adult

cost for children

8 children * 2 dollars each = 16

cost for adults

8 adults * 6 dollars each = 48

Add the two costs together

16+48 =64

Answer:

8×2=16

8×6=48

48+16=64

Answer:

(64)^-4= 1/64^4= 1/16777216

Step-by-step explanation:

435 handshakes

hope this would be the right answer....

The total hands shake will be 435 hands shakes.

The combination will apply when order dose not matter and when order matter permutation will apply.

the permutation and combination rule.

nCr=n!/r!(n−r)!

here. we have,

To find the total number of hands shakes we have to apply the permutation and combination rule.

nCr=n!/r!(n−r)!

Given:

There are 30 people in meeting.

In the given question order not does not matter so combination will applicable.

Calculate the number of hands shakes

C(30,2) = 30!/ 2! (30-2)!

            =435

Thus, the total hands shake will be 435 hands shakes.

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