83
EDFN 1090/1092
Assignment 4
1. From statistics grades, John has a mean of 70 and Sx(standard deviation) of 15, Jane
has a mean of 70 and Sx(standard deviation) of 5. Hint: create a 68% Range)
Describe the two students in terms of consistency of their grades and give reason.

Answer:

The correct answer will be "-1.66".

Step-by-step explanation:

Let z₀ be,

[tex]P(z<z_0)=4.8 \ percent[/tex]

                [tex]=0.048[/tex]

⇒ [tex]\Phi (z_0)=0.048[/tex]

Now,

⇒ [tex]\Phi (-1.6646)=0.048[/tex]

   [tex]z_0=-1.6646[/tex]

       [tex]\simeq -1.66[/tex]

Thus the above is the right answer.

Answer:

its 1900 Bc. Because BC stand for before chirst

Step-by-step explanation:

Step-by-step explanation:

here is the ans

the perimeter= 130m

hope so this might help you

Step-by-step explanation:

[tex] \frac{ \frac{6}{7} }{ \frac{9}{14} } [/tex]

[tex] = \frac{6}{7} \times \frac{14}{9} [/tex]

[tex] = \frac{2}{1} \times \frac{2}{3} [/tex]

[tex] = \frac{4}{3} = 1 \frac{1}{3} (Ans) [/tex]

[tex] \frac{18}{x} = \frac{6}{10} [/tex]

[By cross multiplication]

=> 18 × 10 = 6 × x

[tex] = > \frac{18 \times 10}{6} = x[/tex]

=> 3 × 10 = x

=> x = 30 (Ans)

Answer:

1 3 5 7 9 11

Step-by-step explanation:

same like this do the question the answer will come

Given that,

The angles in a triangle are represented by x, x+10, and x+50.

We had to,

find the measure of the largest angle.

Let's start to solve,

→ x + (x+10) + (x+50) = 180°

→ x + x + x = 180° (-50 -10)

→ 3x = 180° -60

→ 3x = 120

→ x = 120/3

→ x = 40°

Then the value of x + 10,

→ x + 10

→ 40 + 10

→ 50°

Then the value of x + 50,

→ x + 50

→ 40 + 50

→ 90°

The measure of the largest angle is,

→ D. 90 degrees

Hence, option (D) is correct answer.

Step-by-step explanation:

good of you and good workings

Answer:

Variance = 3.6 voteres

Step-by-step explanation:

Probability of favour voters, P = 0.22

Total number of voters, n = 21

The probability of voters who are in not favour of new hospital construction = 1  - P

The probability of voters who are in not favour of new hospital construction = 1  - 0.22

The probability of voters who are in not favour of new hospital construction, P* = 0.78

Variance = n x p* x (1 - p*)

Variance = 21 x 0.78 x 0.22

Variance = 3.6 voters

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[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]

In this question:

7 + 18 = 25 employees, which means that [tex]N = 25[/tex]

7 over 50, which means that [tex]k = 7[/tex]

10 dismissed, which means that [tex]n = 10[/tex]

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]

0.055 = 5.5% probability that exactly 5 employees were over 50.

Answer:

a) 0.0808 = 8.08% probability that the sample mean rent is greater than $2700.

b) 0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.

c) The 25th percentile of the sample mean is of $2596.

d) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.

e) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

If |Z|>2, the measure X is considered unusual.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2630. Assume the standard deviation is $500.

This means that [tex]\mu = 2630, \sigma = 500[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{500}{\sqrt{100}} = 50[/tex]

a) What is the probability that the sample mean rent is greater than $2700?

This is the 1 subtracted by the p-value of Z when X = 2700. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2700 - 2630}{50}[/tex]

[tex]Z = 1.4[/tex]

[tex]Z = 1.4[/tex] has a p-value 0.9192

1 - 0.9192 = 0.0808

0.0808 = 8.08% probability that the sample mean rent is greater than $2700.

b) What is the probability that the sample mean rent is between $2450 and $2550?

This is the p-value of Z when X = 2550 subtracted by the p-value of Z when X = 2450.

X = 2550

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2550 - 2630}{50}[/tex]

[tex]Z = -1.6[/tex]

[tex]Z = -1.6[/tex] has a p-value 0.0548

X = 2450

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2450 - 2630}{50}[/tex]

[tex]Z = -3.6[/tex]

[tex]Z = -3.6[/tex] has a p-value 0.0002

0.0548 - 0.0002 = 0.0546.

0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.

c) Find the 25th percentile of the sample mean.

This is X when Z has a p-value of 0.25, so X when Z = -0.675.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-0.675 = \frac{X - 2630}{50}[/tex]

[tex]X - 2630 = -0.675*50[/tex]

[tex]X = 2596[/tex]

The 25th percentile of the sample mean is of $2596.

Question d and e)

We have to find the z-score when X = 2645.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2645 - 2630}{50}[/tex]

[tex]Z = 0.3[/tex]

|Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.

9514 1404 393

Answer:

  below

Step-by-step explanation:

When signed numbers are used to represent elevation with respect to sea level, positive signs are used for values above sea level, and negative signs are used for values below sea level. The given elevation of Death Valley indicates it is 282 feet below sea level.

Answer:

x^2+y^2=1

Step-by-step explanation:

Since cos^2(x)+sin^2(x)=1, x^2+y^2=1

Answer:

17/15

Step-by-step explanation:

6/5 * 17/18

1/5 * 17/3

17/15

Answer:

i think its 2 1

Step-by-step explanation:

Answer:

y =2/3x-1

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

   = ( 3-1)/ (6-3)

   = 2/3

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 2/3x +b

Using a point

3 = 2/3(6)+b

3 = 4+b

3-4 =b

-1=b

y =2/3x-1

Answer:

x≤9/2

Step-by-step explanation:

8x+15≤51

Subtract 15

8x+15-15≤51-15

8x+≤36

Divide by 8

8x/8≤36/8

x≤9/2

Answer:

yes it represents the graph accurately

Answer:

Pertaining to the mathematical expression conveyed, the answer to such proposed interrogate is acknowledged as the following:

Degree: 2nd degree term.

Classification: Quadratic trionomial.

Step-by-step explanation:

Evaluating the Degree:

The degree is acknowledged as the predominating term adjacent to a base of a peculiar value that denotes the particular allocation within a polynomial.

4x^2 has the highest degree of 2.

32x has the degree of one, being that x individually is x^1.

Since polynomials are defined by the term in which obtains the greatest degree, ^2 is referred to as quadratic, whereas ^3 is cubic, ^4…

Classification Evaluation:

Such could be determined by evaluating for the quantity of terms present within the mathematical expression or statement.

4x^2 is the first term.

32x is the second term.

63 is the third term (considered a constant).

Thus, the correct answer is a quadratic trinomial.

*I hope this helps.

Answer:

A the answer is A if you look at it .

Answer:

The first one is B) point D

The second one is D) (0,0)

Hope this helps!

btw, coordinates are in (x,y) form, so the other answer above me is wrong.

Answer:

[tex]5 \frac{1}{8}[/tex]

Step-by-step explanation:

Remember that [tex]\frac{1}{2} = \frac{4}{8}[/tex], so we want to find [tex]\frac{4}{8} + 4 + \frac{5}{8} = 4 + \frac{9}{8}[/tex]. However, this is not in it's simplest form because [tex]\frac{9}{8}[/tex] should be [tex]1 \frac{1}{8}[/tex]. Therefore, the final answer is [tex]4+1+\frac{1}{8} = 5 \frac{1}{8}[/tex].

Answer:

5 1/8 correct answer to question

Answer:

[tex]y-3=\frac{3}{4} (x-5)\\\\y-3=\frac{3}{4}x-\frac{3}{4}(5)\\\\y=\frac{3}{4} x+3-\frac{15}{4} \\\\y=\frac{3}{4} x+\frac{12}{4} -\frac{15}{4} \\\\y=\frac{3}{4} x-\frac{3}{4}[/tex]

Is this standard form? :\

Answer:

3x-4y=3

Step-by-step explanation:

Hi there!

We are given the equation y-3=[tex]\frac{3}{4}(x-5)[/tex], and we want to write it in standard form

Standard form is given as ax+by=c, where a, b, and c are integer coefficients, a CANNOT be 0 and CANNOT be negative, and b also CANNOT be 0

So let's expand the parentheses in the equation

Do the distributive property

y-3=[tex]\frac{3}{4}x-\frac{15}{4}[/tex]

Add 3 to both sides

y=[tex]\frac{3}{4}x-\frac{3}{4}[/tex]

We expanded the parentheses, but the equation is now in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

Remember that we want it in standard form, which is ax+by=c

Subtract [tex]\frac{3}{4}x[/tex] from both sides

[tex]\frac{-3}{4}x+y=\frac{-3}{4}[/tex]

Remember that the coefficients of a, b, and c need to be integers, and also that a (the coefficient in front of x) CANNOT be negative

So multiply both sides by -4

[tex]-4(\frac{-3}{4}x+y)=-4(\frac{-3}{4})[/tex]

Distribute -4 to every number

[tex]-4(\frac{-3}{4}x)+-4(y)=-4(\frac{-3}{4})[/tex]

Multiply

[tex]\frac{12}{4}x-4y=\frac{12}{4}[/tex]

Simplify

3x-4y=3

There's the equation in standard form

Hope this helps!

Answer:

[tex]5\sqrt{2} \\45[/tex]

Step-by-step explanation:

just multiply

Answer:

a) 5√2

b) 135

Step-by-step explanation:

√5·√10 is equivalent to √50, which in turn is equivalent to √25·√2, or 5√2.

√27·√75 can be simplified by factoring:

√3·√9·√3√25, or (because √3·√3 = 3):

(3)(9)(5) = 135

9514 1404 393

Answer:

  Graph C: Daily High Temperatures and Bottled Water Sales

  On a graph, points are grouped together and form a line with positive slope.

Step-by-step explanation:

Apparently, Graph C shows data with the greatest degree of correlation. This suggests that any model of the data is likely to have less error than if the data were less well correlated.

Answer:

Graph C: Daily High Temperatures and Bottled Water Sales

On a graph, points are grouped together and form a line with positive slope.

Step-by-step explanation:

Answer:

y= -3x +40

Step-by-step explanation:

Properties of perpendicular bisector:

• perpendicular to the given line

• cuts through the center of the given line

The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y -intercept.

Let's find the gradient of the given line first.

[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]

Gradient of given line

[tex] = \frac{6 - 2}{18 - 6} [/tex]

[tex] = \frac{4}{12} [/tex]

[tex] = \frac{1}{3} [/tex]

The product of the gradients of perpendicular lines is -1.

m(⅓)= -1

m= -1(3)

m= -3

Substitute m= -3 into the equation:

y= -3x +c

To find the value of c, substitute a pair of coordinates in which the perpendicular bisector passes through into the equation. Since perpendicular bisectors passes through the center of the segment, we can find the point in which the perpendicular bisector passes through using the mid- point formula.

[tex]\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}[/tex]

Midpoint

[tex] = ( \frac{6 + 18}{2} , \frac{6 + 2}{2} )[/tex]

[tex] = ( \frac{24}{2} , \frac{8}{2} )[/tex]

[tex] = (12,4)[/tex]

y= -3x +c

when x= 12, y= 4,

4= -3(12) +c

4= -36 +c

c= 4 +36

c= 40

Thus, the equation of the perpendicular bisector is y= -3x +40.

Answer:

7, 8, 9, 10, 11

Step-by-step explanation:

7+8+9+10+11

7 + 8 = 15

15 + 9 = 24

24 + 10 = 34

34 + 11 = 45

Answer:

v nnv vb n

Step-by-step explanation:

b ng chfxhc.jx.gc,fhxfgfdkhgvn gghcjfuoctykfd mmyegfiuegfypgerukf khergfuoegrfyurgfirge jgreuyofrgiregvoifgr riygfepiygfreu;k frugfyrfbhrevf rrgfbreuobghfre rgeuherhbgerui freurehuregh ruogysfhurgiugwhlerghre rgiuyrge97grukbgr ker ruipuhrgeugregariyarga ;rskfglfsglgsfuifgryrgljs kjger;ugiergs hope this was helpful good luck!

Answer:

see below

Step-by-step explanation:

a) (– 3, –2) and (–3, 4)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(4 - (-2) / (-3 - (-3))

Simplify the parentheses.

= (4 + 2) / (-3 + 3)

Simplify the fraction.

(6) / (0)

= undefined

If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.

In this case, the x-coordinate for both points is -3.

Therefore, your equation is x = -3.

b) (3, 2) and (–4, –5)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-5 - 2) / (-4 - 3)

Simplify the parentheses.

= (-7) / (-7)

Simplify the fraction.

-7/-7

= 1

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.

2 = 1(3) + b

To find b, multiply the slope and the input of x(3)

2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-1 = b

Plug this into your standard equation.

y = x - 1

This is your equation.

Check this by plugging in the other point you have not checked yet (-4, -5).

y = 1x - 1

-5 = 1(-4) - 1

-5 = -4 - 1

-5 = -5

Your equation is correct.

Hope this helps!

Answer:

a.5005

b.[tex]\frac{1960}{5005}[/tex]

c.1/715

d.714/715

Step-by-step explanation:

We are given that

Total men=8

Total women=7

Total people, n=8+7=15

r=6

a.

Combination formula:

Selection of r out of n people by total number of ways

[tex]nC_r[/tex]

Using the formula

We have n=15

r=6

Total number of ways=[tex]15C_6[/tex]

Total number of ways=[tex]\frac{15!}{6!9!}[/tex]

Using the formula

[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]

Total number of ways=[tex]\frac{15\times 14\times 13\times 12\times 11\times 10\times 9!}{6\times 5\times 4\times 3\times 2\times 1\times 9!}[/tex]

Total number of ways=5005

b. The probability of having exactly 3 men in the group

=[tex]\frac{8C_3\times 7C_3}{15C_6}[/tex]

Using the formula

Probability,[tex]P(E)=\frac{favorable\;cases}{Total\;number\;of\;cases}[/tex]

The probability of having exactly 3 men in the group=[tex]\frac{\frac{8!}{3!5!}\times \frac{7!}{3!4!}}{5005}[/tex]

=[tex]\frac{\frac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\times \frac{ 7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}}{5005}[/tex]

=[tex]\frac{56\times 35}{5005}[/tex]

The probability of having exactly 3 men in the group

=[tex]\frac{1960}{5005}[/tex]

c. The probability of all the selected people in the group are women

=[tex]\frac{8C_0\times 7C_6}{5005}[/tex]

The probability of all the selected people in the group are women

[tex]=\frac{\frac{8!}{0!8!}\times \frac{7\times 6!}{6!1!}}{5005}[/tex]

The probability of all the selected people in the group are women

[tex]=\frac{7}{5005}=\frac{1}{715}[/tex]

d. The probability of having at least one man in the group

=1- probability of all the selected people in group are women

The probability of having at least one man in the group

[tex]=1-\frac{1}{715}[/tex]

[tex]=\frac{715-1}{715}[/tex]

[tex]=\frac{714}{715}[/tex]

The probability of having at least one man in the group [tex]=\frac{714}{715}[/tex]

Answer:

0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.

Step-by-step explanation:

We have the mean during a time interval, which means that the Poisson distribution is used to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5.

This means that [tex]\mu = 5[/tex]

Calculate the probability of getting at least 4 calls between eight and nine in the morning.

This is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-5}*5^{0}}{(0)!} = 0.0067[/tex]

[tex]P(X = 1) = \frac{e^{-5}*5^{1}}{(1)!} = 0.0337[/tex]

[tex]P(X = 2) = \frac{e^{-5}*5^{2}}{(2)!} = 0.0842[/tex]

[tex]P(X = 3) = \frac{e^{-5}*5^{3}}{(3)!} = 0.1404[/tex]

Then

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0067 + 0.0337 + 0.0842 + 0.1404 = 0.265[/tex]

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.265 = 0.735[/tex]

0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.

Answer:

rectangle- 2 lines of reflection

trapezoid- 0 lines of reflection

regular pentagon- 5 lines of reflection

square- 4 lines of reflection

Step-by-step explanation:

Answer:

33 years

Step-by-step explanation:

Given the quadratic model :

P=0.006A2−0.02A+120

P = blood pressure ; A = Age

Given a blood pressure value of 126 mmHg ; the age, A will be ;

The equation becomes :

126 = 0.006A2−0.02A+120

0.006A² - 0.02A + 120 - 126 = 0

0.006A² - 0.02A - 6 = 0

Using the quadratic formula :

-b ± (√b²-4ac) / 2a

a = 0.006 ; b = - 0.02 ; c = - 6

Using calculator :

The roots are :

a = 33.333 or a = - 30

Age cannot be negative, hence, the age, A will be 33.333

Total the nearest year ; Age = 33 years