ian invested an amount of money at 3% per annum compound interest. At the end of 2 years the value of the investment was £2652.25 Work out the amount of money Ian invested.

Answer:

answer 1 /9x^3

Step-by-step explanation:

9ײ/81×⁵​

change the expression to indices form

3^2 x^2 /3^4 x^5

1 /3^2 x^3

1 /9x^3

Answer: 1. [tex]-\dfrac{5}{6}[/tex]  2. [tex]-\dfrac{1}{3}[/tex] . 3. [tex]-3[/tex]

Step-by-step explanation:

Formula: Slope[tex]=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

1. (-2,2) (3,-3)

Slope [tex]=\dfrac{-3-2}{3-(-2)}[/tex]

[tex]=\dfrac{-5}{3+2}\\\\=\dfrac{-5}{6}[/tex]

Hence, slope of line passing through  (-2,2) (3,-3) is [tex]-\dfrac{5}{6}[/tex] .

2. (-5,1) (4,-2)

Slope [tex]=\dfrac{-2-1}{4-(-5)}[/tex]

[tex]=\dfrac{-3}{4+5}\\\\=\dfrac{-3}{9}\\\\=-\dfrac{1}{3}[/tex]

Hence, slope of line passing through  (-2,2) and (3,-3) is [tex]-\dfrac{1}{3}[/tex] .

3. (-1,5) (2,-4)

Slope [tex]=\dfrac{-4-5}{2-(-1)}[/tex]

[tex]=\dfrac{-9}{2+1}\\\\=\dfrac{-9}{3}\\\\=-3[/tex]

Hence, slope of line passing through (-1,5) and (2,-4) is -3.

Answer:

The lower bound = 35.443

The upper bound = 71.697

The error bound = 18.127

Step-by-step explanation:

We are given that a survey of the average amount of cents off that coupons gives was done by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News.

The following data were collected (X): 20cents; 70cents; 50cents; 65cents; 30cents; 55cents; 40cents; 40cents; 30cents; 55cents; 150 cents; 40cents; 65cents; 40cents.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                              P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean worth of coupons = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{750}{14}[/tex] = 53.57 cents

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 31.40 cents

            n = sample size = 14

            [tex]\mu[/tex] = population mean worth of coupons

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.16 < [tex]t_1_3[/tex] < 2.16) = 0.95  {As the critical value of t at 13 degrees of

                                             freedom are -2.16 & 2.16 with P = 2.5%}  

P(-2.16 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.16) = 0.95

P( [tex]-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}{[/tex] < [tex]2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ]

 = [ [tex]53.57-2.16 \times {\frac{31.40}{\sqrt{14} } }[/tex] , [tex]53.57+2.16 \times {\frac{31.40}{\sqrt{14} } }[/tex] ]

 = [35.443, 71.697]

Therefore, a 95% confidence interval for the population mean worth of coupons is [35.443, 71.697].

Answer:

37

Step-by-step explanation:

To find the fifth term , we have to take the value of n as 5

So, F(5)= 6.5 (5) +4.5

= 32.5 + 4.5

= 37

Answer:

y=1/5x+11/5

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula  y-y^1=m(x-x^1) to find line parallel to -x+5y=1

Hope this helps

Answer: y = 1/5x+ 2.2

Step-by-step explanation:

First, change the expression into y-intercept form

-x+5y=1

5y=x+1

y=1/5x+1/5

For a line to be parallel to another line, it must have the same slope.  Thus, the slope must be 1/5x.  Then, to find the y-intercept simply do:

y = 1/5x+b, where x = -1 and y = 2

2=1/5(-1)+b

2 = -1/5+b

b = 2 1/5.

Thus, the equation y = 1/5x+ 2.2

Hope it helps <3

Answer:

Step-by-step explanation:

If  x and y be real numbers satisfying 2/x=y/3=x/y, then any two of the equation are equated as shown;

2/x = y/3 ... 1 and;

y/3 = x/y... 2

From equation 1, 2y = 3x ... 3

and from equation 2; y² = 3x ... 4

Equating the left hand side of equation 3 and 4 since their right hand sides are equal, we will have;

2y = y²

2 = y

y = 2

Substituting y = 2 into equation 3 to get the value of x;

2y = 3x

2(2) = 3x

4 = 3x

x = 4/3

The value of x³ will be expressed as (4/3)³ = 4*4*4/3*3*3 = 64/27

Answer:

a

  [tex]z_t = -1.645[/tex]

b

 We should reject the Upper  [tex]H_o[/tex]

Step-by-step explanation:

From the question we are told that

   The test statistics is     [tex]t_s = -3.43[/tex]

     The probability is   [tex]p < 0.39[/tex]

      The level of significance is [tex]\alpha = 0.05[/tex]

Now looking at the probability we can deduce that this is a left tailed test

The  second step to take is to obtain the critical value of [tex]\alpha[/tex] from the critical value table  

    The value  is  

               [tex]t_ {\alpha } = 1.645[/tex]

Now  since this  test is  a  left tailed test  the critical value will be

               [tex]z_t = -1.645[/tex]

This because we are considering the left tail of the normal distribution curve

 Now  since the test statistics falls within the  critical values the Null hypothesis is been rejected

Answer:

Step-by-step explanation:

cool

Step-by-step explanation:

a = 14.56231 cm

b(width) = 9 cm

a+b = 23.56231 cm

A(area) = 343.1215 cm

Sorry if this doesnt help

Answer:

length = [9/2 + (9/2)sqrt(5)] cm

length = 14.56 cm

Step-by-step explanation:

In a golden rectangle, the width is a and the length is a + b.

The proportion of the lengths of the sides is:

(a + b)/a = a/b

Here, the width is 9 cm, so we have a = 9 cm.

(9 + b)/9 = 9/b

(9 + b)b = 81

b^2 + 9b - 81 = 0

b = (-9 +/- sqrt(9^2 - 4(1)(-81))/(2*1)

b = (-9 +/- sqrt(81 + 324)/2

b = (-9 +/- sqrt(405)/2

b = -9/2 +/- 9sqrt(5)/2

Length = a + b = 9 - 9/2 +/- 9sqrt(5)/2

Length = a + b = 9/2 +/- 9sqrt(5)/2

Since the length of a side of a rectangle cannot be negative, we discard the negative answer.

length = [9/2 + (9/2)sqrt(5)] cm

length = 14.56 cm

Answer:

11% of the Total the entire voting population

Step-by-step explanation:

Let's bear in mind that the total number of sample candidates is equal to 600.

But out of 600 only 66 preffered candidate A.

The proportion of sampled people to that prefer candidate A to the total number of people is 66/600

= 11/100

In percentage

=11/100 *100/1 =1100/100

=11% of the entire voting population

Answer:

Savita will have more bags

Step-by-step explanation:

Savita: 250 cherries, 8 cherries per bag

Gail: 350 cherries, 12 cherries per bag

Savita: 250/8 = 31.25 bags

Gail: 350/12 = 29.17 bags

Savita will have more bags since 31.25 > 29.17

Answer:

Savita will have more bags

Step-by-step explanation:

Savita has 250 cherries and 8 cherries per bag

Gail has 350 cherries and 12 cherries per bag

Savita

=250/8 = 31.25 bags

Gail

=350/12 = 29.17 bags

therefore Savita will have more bags since 31.25 is more than Gail with 29.17 bags

Answer:

Step-by-step explanation:

The derivative of your function is ...

  y' = dy/dx = 2e^(2x) +6

At x=0, the value is ...

  y'(0) = 2e^0 +6 = 8

  dy = 8·dx

__

  Δy = y'(0)·Δx

  Δy = 8(.03)

  Δy = 0.24

Answer:

Surface area of the reflective glass is 543234.4 square feet.

Step-by-step explanation:

Given that: height = 311 feet, sides of square base = 619 feet.

To determine the slant height, we have;

[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]

   = 96721 + 95790.25

   = 192511.25

⇒ l = [tex]\sqrt{192511.25}[/tex]

      = 438.761

The slant height, l is 438.8 feet.

Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height

  area =  [tex]\frac{1}{2}[/tex] × 619 × 438.8

          = 135808.6

          = 135808.6 square feet

Since the pyramid has four reflective surfaces,

surface area of the reflective glass = 4 × 135808.6

                                                          = 543234.4 square feet

Answer:

[tex]\boxed{15 \ dime \ and \ 10 \ nickel \ coins}[/tex]

Step-by-step explanation:

1 dime = 10 cents

1 nickel = 5 cents

So,

If there are 15 dimes

=> 15 dimes = 15*10 cents

=> 15 dimes = 150 cents

=> 15 dimes = $1.5

Rest is $0.5

So, for $0.5 we have 10 nickels coins

=> 10 nickels = 10*5

=> 10 nickels = 50 cents

=> 10 nickel coins = $0.5

Together it makes $2.00

Answer:

The percent of households with rates from $100 to $115. is      [tex]P(100 < x < 115) =[/tex]94.1%

Step-by-step explanation:

From  the question we are told that  

   The  mean rate is [tex]\mu =[/tex]$ 106.50  per month

    The standard deviation is  [tex]\sigma =[/tex]$3.85

Let the lower rate be  [tex]a =[/tex]$100

Let the higher rate  be  [tex]b =[/tex]$ 115

Assumed from the question  that the data set is normally

The  estimate of the percent of households with rates from $100 to $115. is mathematically represented as

         [tex]P(a < x < b) = P[ \frac{a -\mu}{\sigma } } < \frac{x- \mu}{\sigma} < \frac{b - \mu }{\sigma } ][/tex]

here x is a random value rate  which lies between the higher rate and the lower rate so

     [tex]P(100 < x < 115) = P[ \frac{100 -106.50}{3.85} } < \frac{x- \mu}{\sigma} < \frac{115 - 106.50 }{3.85 } ][/tex]

      [tex]P(100 < x < 115) = P[ -1.688< \frac{x- \mu}{\sigma} < 2.208 ][/tex]

Where  

      [tex]z = \frac{x- \mu}{\sigma}[/tex]

Where z is the standardized value of  x

So

     [tex]P(100 < x < 115) = P[ -1.688< z < 2.208 ][/tex]

     [tex]P(100 < x < 115) = P(z< 2.208 ) - P(z< -1.69 )[/tex]

Now  from the z table we obtain that

      [tex]P(100 < x < 115) = 0.9864 - 0.0455[/tex]

     [tex]P(100 < x < 115) = 0.941[/tex]

    [tex]P(100 < x < 115) =[/tex]94.1%

Hey there! I'm happy to help!

If we add Machine 1's 459 satisfactory pistons and 51 unsatisfactory pistons, we get 510 total pistons.

If we add Machine 2's 360 satisfactory pistons and 40 unsatisfactory pistons, we get 400 total pistons.

First, we want to find the probability of choosing an unsatisfactory piston from Machine 1.

We see that 51/510 (unsatisfactory pistons out of total pistons) simplifies to equal 1/10, so there is a 1/10 chance of getting an unsatisfactory piston from Machine 1.

For Machine 2, there are 360 satisfactory and 400 total. This gives us 360/400, which simplifies to 9/10.

Now, we multiply our two probabilities together to find the probability that they both happen.

1/10×9/10=9/100

Therefore, the probability that a piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory is 9/100 or 9%.

Have a wonderful day! :D

Answer:

The height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].      

Step-by-step explanation:

It is given that,

Distance between a person and an elephant is 15 ft

The angle of elevation of the elephant is 30 degrees.

We need to find the height of the elephant. For this let us consider that height is h. So,

[tex]\tan\theta=\dfrac{P}{B}\\\\\tan(30)=\dfrac{h}{15}\\\\h=15\times \tan(30)\\\\h=\dfrac{15}{\sqrt3}\ ft[/tex]

So, the height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].      

Answer:

k = [tex]\frac{980a}{b}[/tex]

Step-by-step explanation:

Fisherman noticed a stretch in the spring = 'b' centimetres

Weight of the fish = a kilograms

If force applied on a spring scale makes a stretch in the spring then Hook's law for the force applied is,

F = kΔx

Where k = spring constant

Δx = stretch in the spring

F = weight applied

F = mg

Here 'm' = mass of the fish

g = gravitational constant

F = a(9.8)

  = 9.8a

Δx = b centimetres = 0.01b meters

Therefore, 9.8a = k(0.01b)

k = [tex]\frac{9.8a}{0.01b}[/tex]

k = [tex]\frac{980a}{b}[/tex]

Therefore, spring constant of the spring will be determined by the expression, k = [tex]\frac{980a}{b}[/tex]

Answer:

Aquarium dimensions:

x = 3,106 m

h = 6,22 m

C(min) = 1277,62 $

Step-by-step explanation: (INCOMPLETE QUESTION)

We have to assume:

The shape of the aquarium  (square base)

Let´s call "x" the side of the base, then h ( the heigh)

V(a) = x²*h          h = V(a)/x²      

Cost of Aquarium   C(a) = cost of the base (in stones) + 4* cost of one side (in glass)

C(a) = Area of the base *120 + 4*Area of one side*30

Area of the base is x²

Area of one side  is   x*h   or  x*V(a)/x²  

Area of one side is V(a)/x

C(x) = 120*x² + 4*30*60/x

C(x) = 120*x² +  7200/x

Taking derivatives on both sides of the equation we get

C´(x) = 2*120*x  - 7200/x²

C´(x) = 0 means    240 *x  - 7200/x² = 0

240*x³ - 7200 = 0

x³ = 7200/240

x = 3,106 m   and  h = 60 /x²     h =   6,22 m

and C (min) = 120*(3,106)³ - 7200 / 3,106

C(min) =  3595,72 - 2318,1

C(min) = 1277,62

Answer:

calls first evening = 26

calls second evening  = 80

calls third evening = 20

Step-by-step explanation:

Let x = calls third evening

x+6 = calls first evening

4x = calls second evening

x+6 + 4x + x = total calls = 126

Combine like terms

6x+6 = 126

Subtract 6 from each side

6x =120

Divide by 6

6x/6 =120/6

x = 20

x+6 = calls first evening = 20+6 = 26

4x = calls second evening = 4*20 = 80

Let x = calls third evening = 20

Answer:

Answer y=7

Step-by-step explanation:

Hi there! :)

Answer:

w = 7 cm.

Step-by-step explanation:

Given:

P = 56

Use the formula P = 2l + 2w to solve for the perimeter of the rectangle.

Let w = width, and

3w = length

Plug these into the equation:

56 = 2(3w) + 2(w)

56 = 6w + 2w

Combine like terms:

56 = 8w

Divide both sides by 8:

w = 7 cm.

The width of rectangle is 7 cm.

Answer:

196 ft

6 seconds

Step-by-step explanation:

Solution:-

We have a quadratic time dependent model of the ball trajectory which is thrown from the top of a 96-foot building as follows:

                     [tex]y(t) = -16t^2 + 80t + 96[/tex]

The height of the ball is modeled by the distance y ( t ) which changes with time ( t ) following a parabolic trajectory. To determine the maximum height of the ball we will utilize the concepts from " parabolas ".

The vertex of a parabola of the form ( given below ) is defined as:

                     [tex]f ( t ) = at^2 + bt + c[/tex]

                    Vertex: [tex]t = \frac{-b}{2a}[/tex]

- The modelling constants are: a = -16 , b = 80.

                   [tex]t = \frac{-80}{-32} = 2.5 s[/tex]

- Now evaluate the given function " y ( t ) " for the vertex coordinate t = 2.5 s. As follows:

                    [tex]y ( 2.5 ) = -16 ( 2.5 )^2 + 80*(2.5) + 96\\\\y ( 2.5 ) = 196 ft\\[/tex]

Answer: The maximum height of the ball is 196 ft at t = 2.5 seconds.

- The amount of time taken by the ball to hit the ground can be determined by solving the given quadratic function of ball's height ( y ( t ) ) for the reference ground value "0". We can express the quadratic equation as follows:

                    [tex]y ( t ) = -16t^2 + 80t + 96 = 0\\\\-16t^2 + 80t + 96 = 0[/tex]

Use the quadratic formula and solve for time ( t ) as follows:

                    [tex]t = \frac{-b +/- \sqrt{b^2 - 4 ac} }{2a} \\\\t = \frac{-80 +/- \sqrt{80^2 - 4 (-16)(96)} }{-32} \\\\t = \frac{-80 +/- 112 }{-32} = 2.5 +/- (-3.5 )\\\\t = -1, 6[/tex]

Answer: The value of t = -1 is ignored because it lies outside the domain. The ball hits the ground at time t = 6 seconds.

Answer:

Number : 41

Step-by-step explanation:

Say that this number is x. The sum of this number ( x ) and 9 subtracted from 60 will be 10. Therefore we can create the following equation to solve for x,

60 - (x + 9) = 10,

60 - x - 9 = 10,

51 - x = 10,

- x = 10 - 51 = - 41,

x = 41

This number will be 41

Step-by-step explanation:

Hello there!

Its simple,

Given that, Ade had 23 hand bags.

selling price of each bag=$409

total sold bags= 22.

now, total amount he got was = no.of sold bag×sp of each bag.

so, total amount = 22×$409

=$8998.

Therefore, he has $ 8998 now.

Hope it helps...

Answer:

[tex]B(a)=\frac{a}{5} -7[/tex]

Step-by-step explanation:

The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.

y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),

y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )

Now switch the positions of y and b -

b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,

[tex]y+7=\frac{a}{5}[/tex],

[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]

Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7

Answer:

A) Fail to Reject the Null Hypothesis

Step-by-step explanation:

Given that:

A local Internet provider wants to test the claim that the average time a family spends online on a Saturday is at least 7 hours.

sample size = 30

sample mean [tex]\bar x[/tex] = 6

standard deviation [tex]\sigma[/tex] = 1.5

level of significance ∝ = 0.05

The null hypothesis and the alternative hypothesis can be computed as:

[tex]\mathbf{ H_o: \mu \leq 7}[/tex]

[tex]\mathbf{ H_i: \mu \geq 7}[/tex]

The test statistic  can be computed as:

[tex]z = \dfrac{\bar x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{6 -7} {\dfrac{1.5}{\sqrt {30}}}[/tex]

[tex]z = \dfrac{-1} {\dfrac{1.5}{5.477}}}[/tex]

[tex]z = \dfrac{-5.477} {1.5}[/tex]

z = -3.65

Given that ;

level of significance of 0.05;

z = -3.65

degree of freedom = 30 -  1 = 29

The p-value = P([tex]t_{29}[/tex] > - 3.65)

= 0.9998

Decision Rule: Reject [tex]H_o[/tex] if p-value is less than the level of significance

But since the p -value is greater than the level of significance, we conclude that There is no enough evidence to support the  Internet provider  claim, Therefore;

Fail to Reject the Null Hypothesis

Answer: 0.476

Step-by-step explanation:

Let A = Event of choosing an even number ball.

B = Event of choosing an 8 .

Given, A lottery game has balls numbered 1 through 21.

Sample space: S= {1,2,3,4,5,6,7,8,...., 21}

n(S) = 21

Then, A= {2,4,6,8, 10,...(20)}

i.e. n(A)= 10

B= {8}

n(B) = 1

A∪B = {2,4,6,8, 10,...(20)} = A

n(A∪B)=10

Now, the probability of selecting an even numbered ball or an 8 is

[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]=\dfrac{10}{21}\approx0.476[/tex]

Hence, the required probability =0.476

Answer:

184, 185, 186

Step-by-step explanation:

If the first number is x, the other numbers are x + 1 and x + 2, therefore we can write:

x + x + 1 + x + 2 = 555

3x + 3 = 555

3x = 552

x = 184 so the other numbers are 185 and 186.

Answer:

-8 i + 19 j , 105.07°

Step-by-step explanation:

Solution:

- Define two unit vectors ( i and j ) along x-axis and y-axis respectively.

- To draw vectors ( v and w ). We will move along x and y axes corresponding to the magnitudes of unit vectors ( i and j ) relative to the origin.

  Vector: v = 2i + 5j

Vector: w = 4i - 3j

- The algebraic manipulation of complex numbers is done by performing operations on the like unit vectors.

                      [tex]2*v - 3*w = 2* ( 2i + 5j ) - 3*(4i - 3j )\\\\2*v - 3*w = ( 4i + 10j ) + ( -12i + 9j )\\\\2*v - 3*w = ( 4 - 12 ) i + ( 10 + 9 ) j\\\\2*v - 3*w = ( -8 ) i + ( 19 ) j\\[/tex]

- To determine the angle ( θ ) between two vectors ( v and w ). We will use the " dot product" formulation as follows:

                     v . w = | v | * | w | * cos ( θ )

                     v . w = < 2 , 5 > . < 4 , -3 > = 8 - 15 = -7

                     [tex]| v | = \sqrt{2^2 + 5^2} = \sqrt{29} \\\\| w | = \sqrt{4^2 + 3^2} = 5\\\\[/tex]

- Plug the respective values into the dot-product formulation:

                     cos ( θ ) = [tex]\frac{-7}{5\sqrt{29} }[/tex]

                      θ = 105.07°