(b) If 124n= 232 five, find n.

Answer:

0.05547

Step-by-step explanation:

Given :

_____Peter __ Alan __ Sui__total

Before 1838 __ 418 ___1475 _3731

After _ 1420 __ 329 ___1140_2889

Total _3258 __ 747 __ 2615 _6620

The expected frequency = (Row total * column total) / N

N = grand total = 6620

Using calculator :

Expected values are :

1836.19 __ 421.006 __ 1473.8

1421.81 ___325.994__ 1141.2

χ² = Σ(Observed - Expected)² / Expected

χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)

χ² = 0.05547

Base case (n = 1):

• left side = 1×2² = 4

• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4

Induction hypothesis: Assume equality holds for n = k, so that

1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12

Induction step (n = k + 1):

1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²

= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²

= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)

= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

On the right side, we want to end up with

(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12

which suggests that k + 2 should be factor of the cubic. Indeed, we have

3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)

and we can rewrite the remaining quadratic as

3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10

so we would arrive at the desired conclusion.

To see how the above rewriting is possible, we want to find coefficients a, b, and c such that

3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c

Expand the right side and collect like powers of k :

3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c

==>   a = 3   and   2a + b = 17   and   a + b + c = 24

==>   a = 3, b = 11, c = 10

Answer:

6 hours.

Step-by-step explanation:

x = supervisor's hours alone

Since there are two people working together, you need to incorporate some kind of 2 in this problem.

If the postal worker was cloned, it would take 4 hours.

3 x 2 = 6.

Answer:

There is not enough evidence to support the claim that the bags are under filled.

Step-by-step explanation:

Given :

Population mean, μ = 433

Sample size, n = 26

xbar = 427

Variance, s² = 324 ; Standard deviation, s = √324 = 18

The hypothesis :

H0 : μ = 433

H0 : μ < 433

The test statistic :

(xbar - μ) ÷ (s/√(n))

(427 - 433) / (18 / √26)

-6 / 3.5300904

T = -1.70

The Pvalue :

df = 26-1 = 25 ; α = 0.05

Pvalue = 0.0508

Since Pvalue > α ; WE fail to reject the Null and conclude that there is not enough evidence to support the claim that the bags are underfilled

Answer:

65% of 27.69 is 18.

Step-by-step explanation:

Formula = Number x 100

Percent = 18 x 100

65 = 27.69

Following shows the steps on how to derive this formula

Step 1: If 65% of a number is 18, then what is 100% of that number? Setup the equation.

18

65% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

65Y = 18 x 100

65Y = 1800

Y = 1800

100 = 27.69

Answer:

side AC is 5

Step-by-step explanation:

by using th pythagorean theorm you would square both sides add them together and the square root the sum to get you answer.

AB =3 BC=4

9+16=25

25 square root is 5

makeing AC=5

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

Explanation:

Add up the values to get

1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54

Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.

So the mean is approximately 1.8876923

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

Now make a spreadsheet as shown below

We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.

After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.

That sum is approximately 0.04403076924

Next, we divide that over n-1 = 13-1 = 12

0.04403076924 /12 = 0.00366923077

That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.

sqrt(0.00366923077) = 0.06057417576822

This rounds to 0.061 which is the final answer.

Answer:

84°

Step-by-step explanation:

the total angle in a straight line sum up to 180°

Answer:

a. mg/c b. 4. It is the speed the object approaches as time goes on.

Step-by-step explanation:

a. Calculate lim v  as t→[infinity]

Since v = mg/c(1 - e^ -ct/m)

[tex]\lim_{t \to \infty} v = \lim_{t \to \infty} (\frac{mg}{c}[1 - e^{-\frac{ct}{m} } ] )[/tex]

[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - e^(-c(∞)/m))

[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - e^(-∞/m))

[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - e^(-∞))

[tex]\lim_{t \to \infty} v =[/tex] mg/c(1 - 0)

[tex]\lim_{t \to \infty} v =[/tex] mg/c(1)

[tex]\lim_{t \to \infty} v =[/tex] mg/c

b. What is the meaning of this limit?

4. It is the speed the object approaches as time goes on.

This is because, since t → ∞ implies a long time after t = 0, the limit of v as t → ∞ implies the speed of the object after a long time. So, the limit of v as t → ∞ is the speed the object approaches as time goes on.

Answer:

[tex]15y^9 - 7y^3 + y[/tex]

Nonic polynomial

Step-by-step explanation:

Given

[tex]y - 7y^3 + 15y^9[/tex]

Required

Write in standard form

The standard form of a polynomial is:

[tex]ay^n + by^{n-1} + ......... + k[/tex]

So, we have:

[tex]y - 7y^3 + 15y^9[/tex]

The standard form is:

[tex]15y^9 - 7y^3 + y[/tex]

And the name is: Nonic polynomial (because it has a degree of 9)

Answer:

-7.5

Alternatively,

-0.5(units^-1) + (-4(units^0)) + (-3(units))

Step-by-step explanation:

On graph, only clearly defined points:

1. x = -3 , y = 0

2. x = -3 , y = -8

3. x = 5 , y = -4

So for:

1. -3 = c ( + a×(0^2) + b×0)

And

2. -3 = a×((-8)^2) + b×(-8) + c = 64×a + (-8)×b + c

Since c = -3 ==> 64×a - 8×b = 0

Simplified ==> 8×a - b = 0 ==> b = 8×a

3. 5 = a×((-4)^2) + b×(-4) + c = 16×a + (-4)×b + c

Since c = -3 ==> 16×a - 4×b = 5 - (-3) = 8

Simplified ==> 4×a - b = 2

Since b = 8×a ==> 4×a - (8×a) = 2

Simplified ==> 2×a - 4×a = 1

==> -2×a = 1

==> a = -0.5

Since b = 8×a ==> b = 8×(-0.5) = -4

So...

c = -3

b = -4

a = -0.5

Then...

a + b + c = -0.5 - 4 - 3 = -7.5

Answer:

CI ≈ (173.8 < μ < 196.2)

Step-by-step explanation:

We are told that laboratory tested twelve chicken eggs. Thus;

n = 12

Mean; x¯ = 185 mg

S.D; s = 17.6 mg

DF = n - 1 = 12 - 1 = 11

We have a 95% confidence level. Thus; α = 0.05

Since n < 30, we will use t-sample test.

Thus, from t-table attached at 95% Confidence level and DF = 11, we have;

t = 2.201

Thus,formula for Confidence interval is;

CI = (x¯ - t(s/√n)) < μ < (x¯ + t(s/√n))

CI = (185 - 2.201(17.6/√12)) < μ < (185 + 2.201(17.6/√12))

CI = (185 - 11.1825) < μ < (185 + 11.1825)

CI = (173.8175 < μ < 196.1825)

CI ≈ (173.8 < μ < 196.2)

Answer:-10

-3+-4+-3

-3-4=-7

-7+-3=-7-3

=-10

Answer: [tex]y=\frac{1}{3}x+\frac{13}{3}[/tex]

Step-by-step explanation:

(slope = m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-6}{-1-5}=\frac{-2}{-6}=\frac{1}{3}[/tex]

[tex]y=mx+b, (5,6), (-1,4), m=\frac{1}{3}[/tex]

[tex]y=mx+b\\6=\frac{1}{3}(5)+b\\b=6-\frac{5}{3} \\b=\frac{13}{3}\\y=\frac{1}{3}x+\frac{13}{3}[/tex]

Answer:

y = 2x - 5

Step-by-step explanation:

[tex]y+3=2(x-1)\\y+3=2x-2\\y+3-3=2x-2-3\\y=2x-5[/tex]

Answer:

A. 1 + 3x = -89

B. x = -30

Step-by-step explanation:

Let the unknown variable be x.

A. Translating the word problem into an algebraic expression, we have;

1 + 3x = -89

B. To solve for the unknown variable;

1 + 3x = -89

3x = -89 -1

3x = -90

x = -90/3

x = -30

Check:

1 + 3x = -89

Substituting the value of x;

1 + 3(-30) = -89

1 + (-90) = -89

1 - 90 = -89

-89 = -89

Answer:

f(x) can not be equal to g(x)

Step-by-step explanation:

If the result is possible:

f(x) = g(x)

x + 8 = x + 2

x + 8 - (x + 2) = x + 2 - (x + 2)

6 = 0

Because 6 can't be equal to 0, so do f(x) can't be equal to g(x)

Answer:

Political stability is a variable of great importance in a country's evolution since, across time, it was identified as causing law level of economic growth, but also it was presented as a consequence of poor economic development.

9514 1404 393

Answer:

  the red angle has no specific value

Step-by-step explanation:

There is sufficient information here to specify all of the angles except the two unknown angles in the 70° (dark blue) triangle. Those two angles must total 110°, but that measure cannot be allocated between them based on the information in the diagram.

The attachments show that all of the given angle constraints can be met while the red angle may vary considerably. It can range through the interval (0°, 110°), but cannot be either of those end values.

Answer:

The milk cost $2.10 each the snacks cost $1.535 each the water cost $3.07 each

Step-by-step explanation:

I think Im right

Answer:

$3.55

Step-by-step explanation:

1st number after 0 is tenths, 2nd is hundredths.

since the number after is 5, we round up

Answer:

The answer is Line Segment SR.

This value is approximate.

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

Explanation:

We have a normal distribution with these parameters

The goal is to find the area under the curve from x = 68 to x = 158, where x is the number of text messages sent per day. So effectively, we want to find P(68 < x < 158).

Let's convert the score x = 68 to its corresponding z score

z = (x-mu)/sigma

z = (68-128)/30

z = -60/30

z = -2

This tells us that the score x = 68 is exactly two standard deviations below the mean mu = 128.

Repeat for x = 158

z = (x-mu)/sigma

z = (158-128)/30

z = 30/30

z = 1

This value is exactly one standard deviation above the mean

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

The problem of finding P(68 < x < 158) can be rephrased into P(-2 < z < 1)

We do this because we can then use the Empirical rule as shown in the diagram below.

We'll focus on the regions between z = -2 and z = 1. This consists of the blue 13.5% on the left, and the two pink 34% portions. So we will say 13.5% + 34% + 34% = 81.5%

Approximately 81.5% of the the population sends between 68 and 158 text messages per day. This value is approximate because the percentages listed in the Empirical rule below are approximate.

Answer:

C. 81.5%

Step-by-step explanation:

Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.

g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]

Option C

Hope this helps!

Answer:

y=0.5

Step-by-step explanation:

14y-6(y-3)=22

14y-6y+18=22

8y+18=22

8y=4

y=0.5

Then we check our work...

14(0.5)-6((0.5)-3)=22

7-6(-2.5)=22

7+15=22

7+15 does equal 22, so this solution is correct.

Answer:

False

Step-by-step explanation:

The ratio of customers  from Zone 1 to  from Zone 3 is 1 : 2

This question appears to be incomplete.

Please find attached the graph required to answer this question

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

The graph is in the image is a bar graph

A bar graph is a pictorial representation of data. The rectangles measure the length of the data

Looking at the graph, the interval is 100

Looking at the rectangle that represents zone 1, it appears to be halfway between 400 and 500. It is concluded that the number of customers in zone 1 is 450

Looking at the rectangle that represents zone 3, it appears to lie on 900.

It can be concluded that there are 900 customers in zone 3

the ratio of zone 1 to 3

450 : 900

to convert to its simplest form, divide both side of the ratio by 450

1 : 2

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