Find the sum of the first six terms in the sequence (1,5,9,13....)​

Answer:

Rs. 32,000

Step-by-step explanation:

height = 4m

let length = x m

breadth = x/3 m

Area of the 4 walls = 2(length × height) + 2(breadth × height)

Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3

Area = (32x)/3 m²

1 m² = Rs. 5

The cost for an area that is (32x)/3 m²=  (32x)/3  × 5 Rs.

The cost of plastering 4 walls at Rs.5 per m² = 640

(32x)/3  × 5  = 640

(160x)/3 = 640

x = length = 12

Area =  (32x)/3 m² = (32×12)/3 = 128m²

The cost of carpeting its floor at the rate of Rs. 250/m²:

= 128m² × Rs. 250/m² = 32,000

The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000

Answer:

3x/8 - 41/5

Step-by-step explanation:

Simplify each term.

3x/8 − 9+4/5

To write −9 as a fraction with a common denominator, multiply by 5/5

3x/8−9 x 5/5 + 4/5

Combine −9 and 5/5

Combine the numerators over the common denominator.

3x/8 + −41/5

Move the negative in front of the fraction

3x/8 - 41/5

Hope this helps you

Answer:

x = {-3, -2, -1, 0}

Step-by-step explanation:

x ≤ 0

x > -4

then

x {-3, -2, -1, 0}

Answer: C. 3.68

Step-by-step explanation:

Given that;

Sample size n = 18

degree of freedom for numerator k = 2

degree of freedom for denominator = n - k - 1 = (18-2-1) = 15

level of significance = 5% = 5/100 = 0.05

From the table values,

the critical value of F at 0.05 significance level with (2, 18) degrees of freedom is 3.68

Therefore option C. 3.68 is the correct answer

Answer:

work shown and pictured

Answer:

x= -1  y = 1

Step-by-step explanation:

Answer:

9.06×10 to the power of 8(8 is superscript above 10)

Answer:

9.06 x 10^8

Step-by-step explanation:

906000000 = 9.06 x 10^8

8 decimal places in

Answer:

(2x^2+1)(4x+3)

Step-by-step explanation:

8x^3 + 6x^2 + 4x+3

Split into two groups

8x^3 + 6x^2       + 4x+3

Factor out 2x^2 from the first group and 1 from the second group

2x^2( 4x+3)  +1( 4x+3)

Factor out (4x+3) from each group

(4x+3) (2x^2+1)

Rearranging the order

(2x^2+1)(4x+3)

Answer:

(2x²+1)(4x+3)

Step-by-step explanation:

Correct choice is the second one

Answer:

2/5

Step-by-step explanation:

(7-5)/(6-1)

The correct answers are Part 1: 7x + 12y  50, x,y 0; Part 2: 7; Part 3: 0: Part 4: 2 old and 3 new video games.

Step-by-step explanation:

Penny's parents gave her $50 to buy new video games.

Price of used games are $7 and new games are $12.

Let Penny buy x number of old video games and y number of new video games.

Part 1:

Total price she spent on buying the video games are 7x + 12y.

This amount should be less than or equal to the amount of money she possess. therefore 7x + 12y  50, x, y  0.

Part 2:

Maximum number of used game she can buy can be given when she spends all her money just on used games. Therefore y = 0. This implies x .

Thus the maximum number of used game she can buy is 7 where she does not buy any new game and has $1 left with her after the purchase.

Part 3:

Minimum number of new games that Penny can buy is zero. She can not buy any new games and spent all her money purchasing old games.

Part 4:

The possible combination in which she can purchase both the video games is 2 old games and 3 new games.

hope this helps

Answer:

Hello There!!

Step-by-step explanation:

Your answer will be 83/99. Because, We have to expressed the 0.83¯ as a fraction in simplest form. Let x = 0.83¯ = 0.8383. Then, We have to multiply by 100 to both sides we have: 100x = 83.8383. After, Subtract (One) to (Two) we will have: 99x = 83. Then, We will divide both sides by 99 we have: x = 83/99. Therefore, the 0.83¯ as a fraction in simplest form is, 83/99. Hope This Helps!!~ Sorry, If the example confusing...

Answer:

-1/2

Step-by-step explanation:

At this point you can guess and try. And it seems that x = -1/2, lets check:

So, this is correct: x= -1/2

Answer:

[tex]6-8cos2x+2cos4x[/tex]

Step-by-step explanation:

We are given that

[tex]16sin^4 x[/tex]

We can write the given expression as

[tex]16(sin^2x \times sin^2 x)[/tex]

[tex]16(\frac{1-cos2x}{2})(\frac{1-cos2x}{2})[/tex]

By using the formula

[tex]sin^2\theta=\frac{1-cos2\theta}{2}[/tex]

[tex]4(1-cos2x)^2[/tex]

[tex]4(1-2cos2x+cos^2(2x)[/tex]

Using the identity

[tex](a-b)^2=a^2+b^2-2ab[/tex]

[tex]4(1-2cos2x+\frac{1+cos4x}{2})[/tex]

[tex]4-8cos2x+2+2cos4x[/tex]

[tex]6-8cos2x+2cos4x[/tex]

This is required expression.

Answer:

CI = ( μ  -  1,64 * σ /√n ;  μ  +  1,64 * σ /√n )

Step-by-step explanation:

We assume Normal Distribution

For Confidence Interval, CI = 90 %     and  α = 10 %

α = 0,1  and  α/2  =  0,05

So  we will look for z score reciprocate to these values, at the two tails of the bell

z(α/2) = 1,64 at th right tail  and -1,64 at the left

CI = ( μ  ±  1,64 * σ /√n  )

CI = ( μ  -  1,64 * σ /√n ;  μ  +  1,64 * σ /√n )

Answer:

Hence the approximate 98% confidence interval for the voters in favor of the approval of the bill is  ( 0.541 , 0.683)

Step-by-step explanation:

The sample proportion is = p = 112/181 = 0.61878= 0.612

q = 1-p = 1- 0.612= 0.388

The degree of confidence is 98 % so z₀.₀₂₅= 1.96  taking α = 5 at 95 %

The interval X~± 0.98  is a random variable because X does not have a particular value but takes different values in different samples.

In repeated samples of size 16 from a normal distribution with standard deviation 2 the interval X~± 0.98 will contain true unknown value of mean about 95 percent of the time .

p ± z ( base alpha by 2) √pq/n

Substituting the values

0.612 ± 1.96√0.612*0.388/181

Multiplying p and q

= 0.612 ± 1.96 √0.237456/181

Solving the square root

=0.612 ± 1.96( 0.03622)

Multiplying  value of z with the value of square root

=0.612 ±  0.07099

Adding or subtracting will give   0.683, 0.541

Hence the approximate 98% confidence interval for the voters in favor of the approval of the bill is  ( 0.541 , 0.683)

Answer:

75%.

Step-by-step explanation:

In total, there are 3 gnarly boards in the first shop and 1 gnarly board in the second. We know that he has selected one gnarly board out of the 3 + 1 = 4 existing boards.

The probability the board came from the first shop is 3 / 4 = 0.75 = 75%.

Hope this helps!

Answer:

Step-by-step explanation:

We will develop a test to compare the mean of two population

Population 1.

population mean μ₀₁  = 25  ; Sample variance 27 ; and sample size n = 45

Population 2.

population mean μ₀₂  = 23 ; Sample variance 7,56; and sample size n = 36

As our major interest is to investigate if the new machine uses less time for the same production, the test will be a one tail test ( left test)

Test Hypothesis        

Null Hypothesis                   H₀     ⇒         μ₀₂ -  μ₀₁  = 0    

Alternative Hypothesis       Hₐ     ⇒         μ₀₂ -  μ₀₁ < 0

We will use  confidence of 90 %, therefore α = 10 %   α = 0,1

α  = 0,1    

We get    z score of z = 1,28   or   z = - 1,28   ( left tail)

And  compute z(s)  = ( μ₀₂ -  μ₀₁ ) /√ (s₁)²/n₁   + (s₂)²/n₂

z(s) = -  2 / √(729/45) + (57,15/36)

z(s) = - 2 / √16,2  + 1,59

z(s) =  - 2 / 4,2178

z(s) =  - 0,4742

As |z(s)|  < |z(c)|

We are in the acceptance region. If we lok at 90 % as Confidencial Interval α = 0,1 and  α/2 =  0,05 in this case

₀,₉CI (  μ₀₂ -  μ₀₁)  =  [  -2  ± z(0,05)√  (s₁)²/n₁   + (s₂)²/n₂ )

From z Table  z ( 0,05 )   ⇒ z score   z = 1,64

And √  (s₁)²/n₁   + (s₂)²/n₂ ) =  √(729/45) + (57,15/36)  =  4,2178

₀,₉CI (  μ₀₂ -  μ₀₁)  = [ -2  ± 1,64 *4,2178]

₀,₉CI (  μ₀₂ -  μ₀₁)  = (  - 8,917 ;  4,917 )

We can see that 0 is a possible value in the ₀,₉CI (  μ₀₂ -  μ₀₁) so again we cannot reject H₀. Then as we are not quite sure about the strengths of the new machine over the old one  we should not recomend to purchase the new machine

Answer:

Step-by-step explanation:

In ACB and ECD

AC =~ CE [ Given ]

BC =~ CD [ Given ]

<ACD =~ <ECD [ Vertical angles ]

Hence, ∆ ACB =~ ECD by SAS congruency of triangles.

Then, <B = <D

In ∆ABC , sum of all three angles must be 180°

<A + <B + <C = 180°

plug the values

[tex] 30 + < d \: + 70 = 180[/tex]

Add the numbers

[tex]100 + < d = 180[/tex]

Move constant to R.H.S and change it's sign

[tex] < d = 180 - 110[/tex]

Subtract the numbers

[tex] < d = 80[/tex] °

Hope this helps..

Best regards!!

Answer:

Choice C. [tex]84\, x + C[/tex].

Step-by-step explanation:

Consider the power rule for integration. Let [tex]n[/tex] be a real number that is not equal to [tex](-1)[/tex]. The power rule for integration states that:

[tex]\displaystyle \int x^{n}\, d x = \frac{1}{n + 1}\, x^{n+ 1} + C[/tex],

How could this rule apply to this question, since there's apparently no [tex]x[/tex] (or its powers) in the integrand? Keep in mind that [tex]x^{0} = 1[/tex] for all real (and particularly non-zero) values of [tex]x[/tex]. In other words, the integrand [tex]84[/tex] is equal to [tex]84\, x^0[/tex]. The integral becomes:

[tex]\displaystyle \int 84\, x^{0}\, dx[/tex].

The constant can be moved outside the integral sign. Therefore:

[tex]\displaystyle \int 84\, x^{0}\, dx= 84 \int x^{0}\, dx[/tex].

Now that resembles the power rule. In particular, [tex]n = 0[/tex], such that [tex]n + 1 = 1[/tex]. By the power rule:

[tex]\begin{aligned}84 \int x^{0}\, dx = 84\, \left(\frac{1}{1}\, x^{1} + C\right) = 84\, x + 84\, C\end{aligned}[/tex].

The non-zero constant in front of [tex]C[/tex] can be ignored (where [tex]C[/tex] represents the constant of integration.) Therefore:

[tex]\displaystyle \int 84\, dx = 84\, x + C[/tex].

If a is a constant then it's inetgration is

[tex]\boxed{\sf \displaystyel\int adx=ax+C}[/tex]

[tex]\\ \rm\Rrightarrow \displaystyle\int 84dx[/tex]

[tex]\\ \rm\Rrightarrow 84x+C[/tex]

Option C

Answer:

78

Step-by-step explanation:

The measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles.

x = 31 + 47

x = 78

Problem 1

Focus: (5, 0)

Directrix:  y = -18

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

Explanation:

The given equation can be written as 4*9(y-(-9)) = (x-5)^2

Then compare this to the form 4p(y-k) = (x-h)^2

We see that p = 9. This is the focal distance. It is the distance from the vertex to the focus along the axis of symmetry. The vertex here is (h,k) = (5,-9)

We'll start at the vertex (5,-9) and move upward 9 units to get to (5,0) which is where the focus is situated. Why did we move up? Because the original equation can be written into the form y = a(x-h)^2 + k, and it turns out that a = 1/36 in this case, which is a positive value. When 'a' is positive, the focus is above the vertex (to allow the parabola to open upward)

The directrix is the horizontal line perpendicular to the axis of symmetry. We will start at (5,-9) and move 9 units down (opposite direction as before) to arrive at y = -18 as the directrix. Note how the point (5,-18) is on this horizontal line.

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

Problem 2

Focus:  (13,-3)

Directrix:  x = 3

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

Explanation:

We'll use a similar idea as in problem 1. However, this time the parabola opens to the right (rather than up) because we are squaring the y term this time.

20(x-8) = (y+3)^2 is the same as 4*5(x-8) = (y-(-3))^2

It is in the form 4p(x-h) = (y-k)^2

vertex = (h,k) = (8,-3)

focal length = p = 5

Start at the vertex and move 5 units to the right to arrive at (13,-3). This is the location of the focus.

Go back to the focus and move 5 units to the left to arrive at (3,-3). Then draw a vertical line through this point to generate the directrix line x = 3

Answer:

32

Step-by-step explanation:

8(3 + 4) = 24 + ?

8(3)+8(4)= 24 + ?

24+32= 24 + ?

24-24+32=?

32=?

Answer:

? = 32

Step-by-step explanation:

Let's assume a = 8 , b = 3 , c = 4

[tex] \sf \: So :- \: \: a(b + c) = 8(3 + 4)[/tex]

[tex]8 \times 3 + 8 \times 4[/tex]

[tex]24 + 32[/tex]

Hence, The required value of ? = 32 .

Step-by-step explanation:

Hi, there!!..

The format of report writing are given in points;

and start your body,

and write conclusion,

You may add comments on it.

Hope it helps....

Answer:

  5/18

Step-by-step explanation:

There are a couple of ways to look at this.

1) If you make a matrix of all possibilities, you find there are 36 possible outcomes from the roll of a die twice. (That is the same number as for rolling two dice once.) Of those 36 outcomes, 10 are outcomes in which a 5 shows exactly once: (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (1, 5), (2, 5), (3, 5), (4, 5), (6, 5).

The probability of obtaining exactly one 5 is 10/36 = 5/18.

__

2) As listed above, there are two ways to get exactly one 5 in two rolls:

  (5 on the first, non-5 on the second) or (non-5 on the first, 5 on the second)

When the rolls are independent, as we assume here, the probability of a certain sequence is the product of the probabilities of the events in that sequence.

  P(5, non-5) = (1/6)(5/6) = 5/36

  P(non-5, 5) = (5/6)(1/6) = 5/36

The probability of obtaining either event is the sum of their individual probabilities:

  P({5, 5'} or {5', 5}) = 5/36 +5/36 = 10/36 = 5/18

__

The probability of obtaining exactly one 5 in two rolls of a die is 5/18.

Answer:

S= (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

    (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

    (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

    (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

    (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

    (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

For this case the size of the sample space is 36 now we count the number of pairs with exactly one 5 and we have:

(1,5), (2,5), (3,5), (4,5), (6,5), (5,6), (5,4), (5,3), (5,2), (5,1)

And then the probability would be:

[tex] p=\frac{10}{36}= \frac{5}{18}[/tex]

Step-by-step explanation:

For this case w ehave the following sample space:

S= (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

    (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

    (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

    (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

    (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

    (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

For this case the size of the sample space is 36 now we count the number of pairs with exactly one 5 and we have:

(1,5), (2,5), (3,5), (4,5), (6,5), (5,6), (5,4), (5,3), (5,2), (5,1)

And then the probability would be:

[tex] p=\frac{10}{36}= \frac{5}{18}[/tex]

Answer:

A) 64 observations

B) analytic study

Step-by-step explanation:

Given:  

There are 3 number of factors i.e. armature length, spring load, and bobbin depth.

There are 4 levels i.e. low, fair, moderate, and high

There is a single i.e. 1 observation on flow made for each combination of levels.

A)

To find:

Number of observations.

There are 4 levels so these 4 levels are to be considered for each factor.

Number of observations = 4.4.4 = 64

For example if we represent low fair moderate and high as L,F,M,H

and factors armature length, spring load, and bobbin depth as a,s,b

Then one of the observations can be [tex]L_{a} F_{s} H_{b}[/tex]

So resulting data set has 64 observations.  

B)

This is analytic study.

The study basically "analyses" the amount of flow through a solenoid valve in an automobiles pollution control system. This study is conducted in order to obtain information from this existing process/experiment and this study focuses on improvement of the process, which created the results being analysed. So the goal is to improve amount of flow through a solenoid valve practice in the future. Also you can see that there is no sampling frame here so if the study was enumerative that it should focus on collecting data specific items in the frame so it shows that its not enumerative but it is analytic study.

Answer:

[tex]\boxed{x = 7}[/tex]

Step-by-step explanation:

75 = 11x-2 (Corresponding angles are equal)

11x -2 = 75

Adding 2 to both sides

11x = 75+2

11x = 77

Dividing both sides by 11

x = 7

Answer:

[tex]\left[\begin{array}{ccc}\\x = 7\\\end{array}\right][/tex]

Step-by-step explanation:

Well to find x we can set up the following equation,

11x - 2 = 75

So we have to single out x.

+2 to both sides

11x = 77

Divide 11 by both sides

x = 7

Thus,

x = 7.

Hope this helps :)

Answer:

Dang shes rich, but what is the question?

Step-by-step explanation:

Answer:

a

   $10,151   [tex]< \mu <[/tex]  $11448.12

b

  [tex]n = 158[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample size is  n  =  19

    The  sample mean is  [tex]\= x =[/tex]$10,800

     The  standard deviation is  [tex]\sigma =[/tex]$1095  

    The  population mean is  [tex]\mu =[/tex]$225

Given that the confidence level is 99%  the level of significance is mathematically represented as

       [tex]\alpha = 100 -99[/tex]

      [tex]\alpha = 1[/tex]%

=>    [tex]\alpha = 0.01[/tex]

Now the critical values of [tex]\alpha = Z_{\frac{\alpha }{2} }[/tex] is obtained from the normal distribution table as

        [tex]Z_{\frac{0.01}{2} } = 2.58[/tex]

The reason we are obtaining values for [tex]\frac{\alpha }{2}[/tex] is because [tex]\alpha[/tex] is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while [tex]\frac{\alpha }{2}[/tex]  is the area under the normal distribution curve for just one tail and we need the  value for one tail in order to calculate the confidence interval

Now the margin of error is obtained as

     [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

    [tex]MOE = 2.58* \frac{1095 }{\sqrt{19} }[/tex]

     [tex]MOE = 648.12[/tex]

The  99% confidence interval for the population mean yearly premium is mathematically represented as

    [tex]\= x -MOE < \mu < \= x +MOE[/tex]

substituting values

   [tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]

    [tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]

   $10,151   [tex]< \mu <[/tex]  $11448.12

The  largest sample needed is mathematically evaluated as

      [tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{\mu} ][/tex]

substituting values

       [tex]n = [ \frac{ 2.58 * 1095}{225} ]^2[/tex]

      [tex]n = 158[/tex]

Answer:

Spinner: 50%

Die: 50%

Step-by-step explanation:

Well for the spinner it depends on the amount of numbers it has,

in this case we’ll use 6.

So The probability of landing on the even numbers in a 6 numbered spinner.

2, 4, 6

3/6

50%

Your average die has 6 sides so the odd numbers are,

1, 3, 5

3/6

50%

Answer:

41.1 miles

Step-by-step explanation:

84 - 42.9 = 41.1

Answer:

h = 7.1 cm

Step-by-step explanation:

To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:

[tex]S = \sqrt{p(p-a)(p-b)(p-c)}[/tex]

Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:

[tex]p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm[/tex]

So the area of the triangle is:

[tex]S = \sqrt{20(20-15)(20-8)(20-17)}[/tex]

[tex]S = 60\ cm^2[/tex]

Now, to find the height, we can use the following equation for the area of the triangle:

[tex]S = base * height/2[/tex]

The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:

[tex]60 = 17 * h/2[/tex]

[tex]h = 120/17[/tex]

[tex]h = 7.06\ cm[/tex]

Rounding to the nearest tenth, we have h = 7.1 cm

Answer:

7.1 cm

Step-by-step explanation:

:D