Using the following data on the Observations 10, 13, 4, and 20 confirm that the complete linkage distance between the cluster containing 《10, 13) and the cluster containing (4, 20) s 2.577 units as displayed in the dendrogram
Observation
13 20 0.032 0.195 -0510 0.466 0.741 0.8750.207 0.474 0.700 0.748 -0.004 -0.490 -0.892 0.735 0.219 0.655 -0.1731.013 0.943 0.083 -0.693 -0.489-0.702 -0.458 1.620 2.275 1328 1.733 -0.863 1.035 0.724 0.721 10 Income/Debt Return Cost Load Peak Sales TotalFuelCosts
If required, round your answers to three decimal places.Do not round intermediate calculations
1. Distance from Observation 10 and Observation 4:
2. Distance from Observation 10 and Observation 20:
3. Distance from Observation 13 and Observation 4:
4. Distance from Observation 13 and Observation 20:

Answer:

f(4) =2

Step-by-step explanation:

f(x) = 2х^2 - 30,

Let x=4

f(4) = 2 (4)^2 -30

     = 2*16 -30

       =32-30

      = 2

Answer:

1. (y - x)²  = 256

2. 128g needed to be added

Step-by-step explanation:

1.

9 + 5 + 2 + y + x = 2(8 + 4 + 1 + 3 + x)

16 + y + x = 32 + 2x

y - x = 16

∴ (y - x)²  = 256

2.

x = mass of alcohol to add

480 × 0.24 = 115.2 ← current mass of alcohol

0.4(480 + x) = 115.2 + x      (×5)

2(480 + x) = 576 + 5x

960 + 2x = 576 + 5x

3x = 384

x = 128g

Answer:

1 + 4x

Step-by-step explanation:

Let's break this down.

"The sum of one" means that something is being added to the number one:

1 +

"and" whatever comes after the word 'and' will be added to the number one

"the product of 4 and a number x" this means that the number four and the variable x are being multiplied:

4x

Put it together:

1 + 4x

Therefore, the expression is 1 + 4x.

Answer: 3ab + 3ac

Step-by-step explanation: Although the terms in this problem look like one another, there are no like terms.

Therefore, this problem cannot be simplified.

So the answer is the same as the question.

Answer:

4 pizza's

Step-by-step explanation:

hope this helps :)

Answer:

the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.

Step-by-step explanation:

Suppose, the weight of the alloy with 50% silver content is x  kilograms.

As, the weight of the mixed alloy should be 10 kilograms, so the weight of the alloy with 25% silver content will be:  kilograms

The percentage of silver content in the mixed alloy is 40%. So the equation will be calculated as

[tex]0.5x+0.25(10-x)=0.4\times10\\0.5x+2.5-0.25x=4\\0.25x=1.5\\\Rightarrow x=\frac{1.5}{0.25} = 6[/tex]

So, the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.

Answer:

B

Step-by-step explanation:

Let's arrange it into slope-intercept form.

2x - y = 4

y = 2x - 4

We are looking for a line with slope of 2 and y-intercept -4. This line is Line B.

Answer:

d) −8

Step-by-step explanation:

x − 2+2 < −8+2

x < -6

The only number less than -6 is -8

Answer:

4

Step-by-step explanation:

2(6x+4)-6+2x=3(4x+3)+1

=14x+2=12x+10

=14x+2-2=12x+10-2

=14x=12x+8

=14x-12x=12x+8-12x

=2x=8

=2x/2=8/2

x=4

Answer:

The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.

Step-by-step explanation:

Two planes:

The first one's speed is x

The second is y.

One plane is flying at twice the speed of the other.

I will say that y = 2x.

Two airplanes leave an airport at the same time, flying in the same direction

Same direction, so their relative speed is the subtraction of their speeds. 2x - x = x.

Means that after 1 hour, they will be x miles apart.

If after 4 hours they are 1800 km apart, find the speed of each plane

After 1 hour, x km apart. After 4, 1800. So

1 hour - x km apart

4 hours - 1800 km apart

4x = 1800

x = 1800/4

x = 450

2x = 2*450 = 900

The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.

Answer:

  698 cm²

Step-by-step explanation:

The volume is given by ...

  V = LWH

Filling in the given values, we have ...

  1020 = (17)(5)y . . . . . . . using L=17, W=5, H=y

  y = 1020/(17·5) = 12

The surface area is given by ...

  A = 2(LW +H(L+W))

  A = 2(17·5 +12(17+5)) = 2(85 +264) . . . . . . . using L=17, W=5, H=y=12

  A = 698 . . . . square centimeters

Answer:

25

Step-by-step explanation:

use a Poisson process to model the arrival.

the mean rate of arrivals  is λ=4.5

The standard deviation is calculated as:

σ==√λ =2.1213

The z-value for a 98% CI is z=2.3262.

If the 98% CI has to be within a error of 0.5 then:

Ul-Ll=2z*σ/√n=2*0.5=1

√n=z*σ=2.3262*2.1213=4.9346

√n=4.9346  and n = 4.9346^2=24.35 rounded to 25

The sample size needed is n=25.

Answer:

[tex]z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17[/tex]  

The p value for this case would be given by:

[tex]p_v =P(z>3.17)=0.00076[/tex]  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Step-by-step explanation:

Information provided

n=400 represent the random sample taken

X=59 represent number of defectives from the company B

[tex]\hat p=\frac{59}{400}=0.1475[/tex] estimated proportion of defectives from the company B  

[tex]p_o=0.1[/tex] is the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to verify if the true proportion of defectives is higher than 0.1 then the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.1[/tex]  

Alternative hypothesis:[tex]p > 0.1[/tex]  

The statistic would be given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17[/tex]  

The p value for this case would be given by:

[tex]p_v =P(z>3.17)=0.00076[/tex]  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Answer:

4, 8, 16,64 and 4096.

Step-by-step explanation:

We are already given: [tex]4096=2^{12}[/tex]

To determine other whole numbers that can be raised to a power to obtain 4096, we apply the product rule of indices.

Product Rule of Indices: [tex]a^{xy}=(a^x)^y[/tex]

Now 12 can be factored in the following ways where one of the terms must be a perfect square:

[tex]2^{12}=(2^2)^6=4^6\\\\2^{12}=(2^6)^2=64^2\\\\2^{12}=(2^4)^3=16^3\\\\2^{12}=(2^3)^4=(8^2)^2=8^{2*2}=8^4\\\\2^{12}=(2^{12})^1=4096^1 $(This is the trivial case)[/tex]

Therefore, the other whole numbers that can be raised tp a power to obtain 4096 are: 4, 8, 16, 64 and 4096.

Answer: 7.2 frames per bit.

Step-by-step explanation:

Our teempo is 200 bpm.

in one minute we have 60 seconds, so here we have:

200b/60s = 3.33 bits per second.

For movies, the standar is 24 frames per second

now, we can take the quotient between the frames per second and the bits per second and get the frames per bit.

24fps/3.33bps = 7.2 frames per bit.

Answer:

19.51% probability that none of them voted in the last election

Step-by-step explanation:

For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

42% of Americans voted in the previous national election.

This means that [tex]p = 0.42[/tex]

Three Americans are randomly selected

This means that [tex]n = 3[/tex]

What is the probability that none of them voted in the last election

This is P(X = 0).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951[/tex]

19.51% probability that none of them voted in the last election

Answer: About 6.2%

Step-by-step explanation:

He starts with 5500 and gains 893.75 in 2.5 years.

The equation is then 5500*(x)^2.5 = 5500+893.75, or

5500*x^2.5 = 6393.75.

x is about 1.0621, or about 6.2% because it's interest.

Hope that helped,

-sirswagger21

Answer: 137.5%

Step-by-step explanation

Answer:

5,586.17

Step-by-step explanation:

A = $ 5,586.17

A = P + I where

P (principal) = $ 4,000.00

I (interest) = $ 1,586.17

Compound Interest Equation

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Answer:

5 units

Step-by-step explanation:

make h the subject

Answer:53/6

Step-by-step explanation:

Let X be the other rational number

-5/6+X=8

Add 5/6 to both sides

-5/6+5/6+X=8+5/6

0+X= 53/6 (inverse property)

X=53/6. (Identity property)

Answer:

the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

Step-by-step explanation:

Let assume that n should represent the number of the students

SO, [tex]\bar x[/tex] can now be the sample mean of number of students  in GPA's

To obtain n such that [tex]P( \bar x \leq 2.3 ) \leq .04[/tex]

⇒ [tex]P( \bar x \geq 2.3 ) \geq .96[/tex]

However ;

[tex]E(x) = \int\limits^4_2 Dx (2+e^{-x} ) 4x = D \\ \\ = D(e^{-x} (e^xx^2 - x-1 ) ) ^D_2 = 12.314 D[/tex]

[tex]E(x^2) = D\int\limits^4_2 (2+e^{-x})dx \\ \\ = \dfrac{D}{3}[e^{-4} (2e^x x^3 -3x^2 -6x -6)]^4__2}}= 38.21 \ D[/tex]

Similarly;

[tex]D\int\limits^4_2(2+ e^{-x}) dx = 1[/tex]

⇒ [tex]D*(2x-e^{-x} ) |^4_2 = 1[/tex]

⇒ [tex]D*4.117 = 1[/tex]

⇒ [tex]D= \dfrac{1}{4.117}[/tex]

[tex]\mu = E(x) = 2.991013 ; \\ \\ E(x^2) = 9.28103[/tex]

∴  [tex]Var (x) = E(x^2) - E^2(x) \\ \\ = .3348711[/tex]

Now; [tex]P(\bar \geq 2.3) = P( \bar x - 2.991013 \geq 2.3 - 2.991013) \\ \\ = P( \omega \geq .691013) \ \ \ \ \ \ \ \ \ \ (x = E(\bar x ) - \mu)[/tex]

Using Chebysher one sided inequality ; we have:

[tex]P(\omega \geq -.691013) \geq \dfrac{(.691013)^2}{Var ( \omega) +(.691013)^2}[/tex]

So; [tex](\omega = \bar x - \mu)[/tex]

⇒ [tex]E(\omega ) = 0 \\ \\ Var (\omega ) = \dfrac{Var (x_i)}{n}[/tex]

∴ [tex]P(\omega \geq .691013) \geq \dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2}[/tex]

To determine n; such that ;

[tex]\dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2} \geq 0.96 \\ \\ \\ (.691013)^2(1-.96) \geq \dfrac{-3348711*.96}{n}[/tex]

⇒ [tex]n \geq \dfrac{.3348711*.96}{.04*(.691013)^2}[/tex]

[tex]n \geq 16.83125[/tex]

Thus; we can conclude that; the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

Answer:

c) 5√2 cm

Step-by-step explanation:

A square with side length l has a perimeter given by the following equation:

P = 4l.

In this question:

P = 20

So the side length is:

4l = 20

l = 20/4

l = 5

Diagonal

The diagonal forms a right triangle with two sides, in which the diagonal is the hypothenuse. Applying the pytagoras theorem.

[tex]d^{2} = l^{2} + l^{2}[/tex]

[tex]d^{2} = 5^{2} + 5^{2}[/tex]

[tex]d^{2} = 50[/tex]

[tex]d = \pm \sqrt{50}[/tex]

Lenght is a positive meausre, so

[tex]d = \sqrt{50}[/tex]

[tex]d = \sqrt{2 \times 25}[/tex]

[tex]d = \sqrt{2} \times \sqrt{25}[/tex]

[tex]d = 5\sqrt{2}[/tex]

So the correct answer is:

c) 5√2 cm

Answer:

Answer:-

a) The circumference of the circle  C = 21.98 m

b) The circumference of the circle  C = 37.68 ft

c)  The circumference of the circle  C = 40.82 km

d) The radius of the circle = r = 11 c.m

    The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m

e) The circumference of the circle = 21.98 inches

  Step-by-step explanation:

a)  In First diagram

Given radius of the circle 'r' = 7.1 m

  The circumference of the circle  C = 2πr

                                                            C = 2 (3.14) (7.1)

                                                            C = 21.98 m

The circumference of the circle  C = 21.98 m

b) In second diagram

Given diameter of the circle 'd' = 12 ft

   The circumference of the circle  C = 2πr

                                                            C = π(2 r)

                                       Diameter = 2 X radius

                                               d = 2 r

 The circumference of the circle  C = πd

                                                          C = 3.14 ×12

The circumference of the circle  C = 37.68 ft

c)

Given diameter of the circle 'd' = 13 km

   The circumference of the circle  C = 2πr

                                                            C = π(2 r)

                                       Diameter = 2 X radius

                                               d = 2 r

 The circumference of the circle  C = πd

                                                          C = 3.14 ×13

 The circumference of the circle  C = 40.82 km

7) The circumference of the circle  C = 2πr

    Given The circumference of a circle is 34.54 cm

          Now       2πr = 34.54

                   2(3.14) r = 34.54

                           [tex]r = \frac{34.54}{3.14} = 11[/tex]

   The radius of the circle = r = 11 c.m

    The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m

8) Given radius of the circle 'r' = 3.5 inches

   The circumference of the circle  C = 2πr

                                                            C = 2 (3.14) (3.5)

                                                            C = 21.98

  The circumference of the circle = 21.98 inches

Answer:

AOB = 73

BOC = 107

Step-by-step explanation:

So make an equation.

9x + 27 = 180

9x = 153

x = 17

AOB = 73

BOC = 107

Answer:

The average of the extracted scores  = 133.33

Step-by-step explanation:

Given data the average mark of candidates in an aptitude test was 138.5 with a standard deviation of 10.6

mean of the aptitude test = 138.5

Standard deviation of the  aptitude test = 10.6

Given three scores extracted from the test are 178,122,100

The average of the extracted scores = ∑x / n

The average of the extracted scores

                                        = [tex]\frac{178 +122 +100}{3}[/tex]

                                        = 133.33

Final answer:-

The average of the extracted scores  = 133.33

Answer:

Yes

Step-by-step explanation:

the function that gives the alcohol level is:

[tex]A ( x ) = - 0.015 x^3 + 1.05 x[/tex]

where x is the number of hours.

we need to know if after 4 hours an average person is legally drunk, thus:

[tex]x=4[/tex]

and we substitute this in the function:

[tex]A ( 4 ) = - 0.015 (4)^ 3 + 1.05(4)[/tex]

solving these operations we obtain:

[tex]A(4)=-0.015(64)+4.2\\A(4)=-0.96+4.2[/tex]

[tex]A(4)=3.24[/tex]

the alcohol level after 4 hours is 3.24.

Since a person is considered to be legally drunk if the level exceeds 1.5, and we obtained 3.24 which is greater than 1.5, a person who has been drinking for 4 hours under the conditions indicated by the problem would be considered legally drunk.

Answer:

The table that illustrates this equation is table A:

1   -6   0   up   (0,0)

Step-by-step explanation:

The values of the parameters a, b, and c have to agree with the values for the general quadratic equation in standard form:

[tex]y = a\,x^2+b\,x+c[/tex]

compared to:

[tex]y=x^2-6\,x[/tex]

So the coefficient "a" of the quadratic term in our case is: "1"

the coefficient "b" of the linear term is : "-6"

the coefficient "c" for the constant term s : "0" (zero)

since the coefficient "a" is a positive number, we know that the parabola's branches must be opening "UP".

The y intercept can be found by evaluating the expression for x = 0:

[tex]y=x^2-6x\\y=(0)^2-6\,(0)\\y=0[/tex]

Therefore the y-intercept is at (0, 0)

These results agree with those of Table "A"

Answer:

Table A.)

Step-by-step explanation:

a 1, b -6, c 0, up, (0, 0), Table A.

Answer:

Step-by-step explanation:

7. 1, for r = 0 - 1, for r = 1 Hence, determine alo. Using characteristic root ... find the solution of the recurrence relation y, + 9 y, 2 = 6y, 1, subjected to the ... Solve a, -5a, 1 + 6a, 2 = 0 , given initial conditions ao = 2 and a1 = 5. ... Solve the recurrence relation a, – 7a, 1 + 16a, 2 – 12a, 3 = 0 for n > 3 with ... 2"; 3. a = (2)” – n.

Answer:

2

Step-by-step explanation:

I solved in the picture

Hope this helps ^-^

Answer:

Option (2). x = 20°

Step-by-step explanation:

In the figure attached,

ΔABC is an equilateral triangle.

By the property of equilateral triangle, all sides of the triangle are equal and measure of all angles of the triangle is 60°.

By this property,

m∠B = 60°

and y = 46 - 16 = 30

By applying Sine rule in ΔBCD,

[tex]\frac{\text{sin}60}{BD}=\frac{\text{sin}80}{46}=\frac{\text{sin}(\angle CBD)}{DC}[/tex]

[tex]\frac{\text{sin}80}{46}=\frac{\text{sin}(\angle CBD)}{y}[/tex]

sin(∠CBD) = [tex]\frac{30\times \text{sin}80}{46}[/tex]

                 = 0.6423

m∠CBD = 39.96

              ≈ 40°

m∠ABD = 60° - 40°

             = 20°

Therefore, Option (2). 20° will be the answer.