An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample of 8 school districts is selected, and the daily salaries are 60, 56, 60, 55, 70, 55, 60, and 55. Is there enough evidence to support the educator’s claim at 10% level of significance? (HELP: The sample mean is 58.88, and the sample standard deviation is 5.08)

Answer:

Step-by-step explanation:

The equivalent between sets is determined by the number of elements. If two sets have the same number of elements, then they are equivalent sets.

In this case, a year has 12 months, and the US has 50 states. So, one month is not equal to 1 state because they have different natures and they represent a different proportion. A month represents 1/12 of a year and a state represents 1/50 of the total number of states.

Answer:

2y (x^2+9) ( x-5)

Step-by-step explanation:

2x^3y + 18xy - 10x^2y - 90y

Factor out the common factor of 2y

2y(x^3+9x-5x^2-45)

Then factor by grouping

2y(x^3+9x     -5x^2-45)

Taking x from the first group and -5 from the second

2y( x (x^2+9)  -5(x^2+9))

Now factor out (x^2+9)

2y (x^2+9) ( x-5)

Answer:

18 and 40

Step-by-step explanation:

Let x be the age of Claire and y the age of her mother

Claire's mother is 4 years more than twice Claire's age

The sum of their ages are is 58

the system is:

[tex]\left \{ {{y=2x-4} \atop {y+x=58}} \right.[/tex]  

Multiply (y+x = 58) by -1 and then add it to (y = 2x+4) to eliminate y

y= 58-18 = 40

so claire's mother is 40 years old and claire is 18

Answer:

rhombus

Step-by-step explanation:

on edge

Answer:  width = 300

Step-by-step explanation:

Area (A) = Length (L) x width (w)

Given: A = 268,500

           L = 3w - 5

           w = w

268,500 = (3w - 5) x (w)

268,500 = 3w² - 5w

            0 = 3w² - 5w - 268,500

            0 = (3w + 895) (w - 300)

   0 = 3w + 895        0 = w - 300

  -985/3 = w             300 = w

Since width cannot be negative, disregard w = -985/3

So the only valid answer is: w = 300

Answer:

[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]

So the answer for this case would be n=22547 rounded up to the nearest integer

Step-by-step explanation:

Let's define some notation

[tex]\bar X[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma=58.2[/tex] represent the population standard deviation

n represent the sample size  

[tex] ME =1[/tex] represent the margin of error desire

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be [tex]\alpha=0.01[/tex] and the critical value [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]

So the answer for this case would be n=22547 rounded up to the nearest integer

Answer:

  CPCTC

Step-by-step explanation:

Statements 3 and 4 show the top and bottom triangles are congruent, and the left and right triangles are congruent. Statement 5 is making use of these facts to claim that the alternate interior angles are congruent. This claim is valid because ...

  Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Answer:

(x + 8)² + (y - 3)² = 64

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (- 8, 3) and r = 8 , thus

(x - (- 8))² + (y - 3)² = 8² , that is

(x + 8)² + (y - 3)² = 64

Answer:

See below.

Step-by-step explanation:

The equation for a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the center and r is the radius.

Plug in what we know. (-8,3) for (h,k) respectively and 8 for the radius:

[tex](x-(-8))^2+(y-(3))^2=(8)^2[/tex]

[tex](x+8)^2+(y-3)^2=64[/tex]

Answer:

x=12.5

Step-by-step explanation:

0.7x times (-1.4)=-3.5

-0.28x=-3.5 (divide both sides)

Ans:12.5

Answer:

The depreciated value of the car after 1 yr is ​$16,353

The depreciated value of the car after 2 yr is ​$12,264.75

Step-by-step explanation:

Given

purchase amount P= $21,804

rate of depreciation R= 25%

applying the formula for the car deprecation we have

[tex]A= P*(1-\frac{R}{100} )^n[/tex]

Where,

A is the value of the car after n years,

P is the purchase amount,

R is the percentage rate of depreciation per annum,

n is the number of years after the purchase.

1. The depreciated value of the car after 1 yr is ​

n=1

[tex]A= 21,804*(1-\frac{25}{100} )^1\\\\A= 21,804*(1-0.25 )^1\\\\A= 21,804*0.75\\\\A= 16353[/tex]

The depreciated value of the car after 1 yr is ​$16,353

2. The depreciated value of the car after 2 yr is ​

n=2

[tex]A= 21,804*(1-\frac{25}{100} )^2\\\\A= 21,804*(1-0.25 )^2\\\\A= 21,804*0.75^2\\\\A= 21,804*0.5625\\\\A= 12264.75[/tex]

The depreciated value of the car after 2 yr is ​$12,264.75

Answer: a. CI for the mean: 17.327 < μ < 26.473

b. CI for variance: 29.7532 ≤ [tex]\sigma^{2}[/tex] ≤ 170.9093

Step-by-step explanation:

a. To construct a 95% confidence interval for the mean:

The given data are:

mean = 21.9

s = 7.7

n = 12

df = 12 - 1 = 11

1 - α = 0.05

[tex]\frac{\alpha}{2}[/tex] = 0.025

t-score = [tex]t_{0.025,11}[/tex] = 2.2001

Note: since the sample population is less than 30, it is used a t-score.

The formula for interval:

mean ± [tex]t.\frac{s}{\sqrt{n} }[/tex]

Substituing values:

21.9 ± 2.200.[tex]\frac{7.7}{\sqrt{12} }[/tex]

21.9 ± 4.573

The interval is: 17.327 < μ < 26.473

b. A 95% confidence interval for the variance:

The given values are:

[tex]s^{2}[/tex] = [tex]7.7^{2}[/tex]

[tex]s^{2}[/tex] = 59.29

α = 0.05

[tex]\frac{\alpha}{2}[/tex] = 0.025

[tex]1-\frac{\alpha}{2}[/tex] = 0.975

[tex]\chi^{2}_{0.025,11}[/tex] = 21.92

[tex]\chi^{2}_{0.975,11}[/tex] = 3.816

Note: To find the values for [tex]\chi^{2}_{\alpha/2,n-1}[/tex] and [tex]\chi^{2}_{1-\alpha/2,n-1}[/tex], look for them at the chi-square table

The formula to calculate interval:

([tex]\frac{(n-1).s^{2}}{\chi^{2}_{\alpha/2,n-1}} , \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2,n-1}}[/tex])

are the lower and upper limits, respectively.

Substituing values:

([tex]\frac{11.59.29}{21.92} , \frac{11.59.29}{3.816}[/tex])

(29.7532, 170.9093)

The interval for variance is: 29.7532 ≤ [tex]\sigma^{2}[/tex] ≤ 170.9093

Answer:

Step-by-step explanation:

Length of an arc is expressed as [tex]L = \frac{\theta}{2\pi } * 2\pi r\\[/tex]. Given;

[tex]\theta = \frac{5\pi }{6} rad\\ radius = 24in\\[/tex]

The length of the minor arc SV is expressed as:

[tex]L = \frac{\frac{5\pi }{6} }{2\pi } * 2\pi (24)\\L = \frac{5\pi }{12\pi } * 48\pi \\L = \frac{5}{12} * 48\pi \\L = \frac{240\pi }{12} \\L = 20\pi \ in[/tex]

Hence, The length  of the arc SV is 20π in

Answer:

20 pi

Step-by-step explanation:

Answer:

-10, 40, -240, 1,920 and -19, 200

Step-by-step explanation:

Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.

when n= 1;

aₙ₊₁ = -2naₙ

a₁₊₁ = -2(1)a₁

a₂ = -2(1)(5)

a₂ = -10

when n = 2;

a₂₊₁ = -2(2)a₂

a₃ = -2(2)(-10)

a₃ = 40

when n = 3;

a₃₊₁ = -2(3)a₃

a₄ = -2(3)(40)

a₄ = -240

when n= 4;

a₄₊₁ = -2(4)a₄

a₅ = -2(4)(-240)

a₅ = 1,920

when n = 5;

a₅₊₁ = -2(5)a₅

a₆ = -2(5)(1920)

a₆ = -19,200

Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200

Answer:

see below

Step-by-step explanation:

Let x be the original price

x* discount rate = discount

x * 60% = 30

Change to decimal form

x * .60 = 30

Divide each side by .60

x = 30/.60

x =50

The original price was 50 dollars

Answer:

A-30     B-20    C-50

Step-by-step explanation:

Answers:

please see the attached picture for full solution..

Hope it helps....

Good luck on your assignment...

The required 90% confidence interval for adult males is

[tex]\text {CI} = (64.2, \: 70.6)\\\\[/tex]

The required 90% confidence interval for adult females is

[tex]\text {CI} = (72, \: 79.2)\\\\[/tex]

The confidence interval of male and female pulse rates do not overlap since the mean pulse rate of female is way greater than the mean pulse rate of males.

Step-by-step explanation:

We are given the pulse rates of adult females and adult males and we have to construct the 90% confidence interval of the mean pulse rate for males and females.

Let us first compute the mean and standard deviation of the given pulse rates data.

Using Excel,  

=AVERAGE(number1, number2,....)  

The mean pulse rate of adult males is found to be

[tex]\bar{x}_{male} = 67.4[/tex]

The mean pulse rate of adult females is found to be

[tex]\bar{x}_{female} = 75.6[/tex]

Using Excel,  

=STDEV(number1, number2,....)    

The standard deviation for adult male pulse rate is found to be

 [tex]s_{male} = 11.9[/tex]

The standard deviation for adult female pulse rate is found to be  

 [tex]s_{female} = 13.5[/tex]

The confidence interval is given by

[tex]$ \text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean, n is the sample size, s is the sample standard deviation and   [tex]t_{\alpha/2}[/tex] is the t-score corresponding to a 90% confidence level.  

The t-score corresponding to a 90% confidence level is  

Significance level = α = 1 - 0.90 = 0.10/2 = 0.05  

Degree of freedom = n - 1 = 40 - 1 = 39

From the t-table at α = 0.05 and DoF = 39

t-score =  1.685

The required 90% confidence interval for adult males is

[tex]\text {CI} = 67.4 \pm 1.685\cdot \frac{11.9}{\sqrt{40} } \\\\\text {CI} = 67.4 \pm 1.685\cdot 1.882\\\\\text {CI} = 67.4 \pm 3.17\\\\\text {CI} = 67.4 - 3.17, \: 67.4 + 3.17\\\\\text {CI} = (64.2, \: 70.6)\\\\[/tex]

Therefore, we are 90% confident that the actual mean pulse rate of adult male is within the range of 64.2 to 70.6 bpm

The required 90% confidence interval for adult females is

[tex]\text {CI} = 75.6 \pm 1.685\cdot \frac{13.5}{\sqrt{40} } \\\\\text {CI} = 75.6 \pm 1.685\cdot 2.1345\\\\\text {CI} = 75.6 \pm 3.60\\\\\text {CI} = 75.6 - 3.60, \: 75.6 + 3.60\\\\\text {CI} = (72, \: 79.2)\\\\[/tex]

Therefore, we are 90% confident that the actual mean pulse rate of adult female is within the range of 72 to 79.2 bpm

Comparison:

The confidence interval of male and female pulse rates do not overlap since the mean pulse rate of female is way greater than the mean pulse rate of males.

Answer:

the answer is D

Step-by-step explanation:

Answer:

95°

Step-by-step explanation:

To get the value of n° we must get the values of the traingle angle's sides

and to do that :

The discontinuity occurs when x is either -5 or 3.

That is determined by solving denominator = 0 quadratic equation for x.

Hope this helps.

Answer:

a. 0.34885

b. 0.04651

c. 0.02404

d. 36

e. 14.7, say 15 trials

Step-by-step explanation:

Q17070205

Note:  

1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.

2. use R to find the probability values from the respective distributions.

a) the chance that the first 6 appears before the tenth roll

This means that a six appears exactly once between the first and the nineth roll.

Using binomial distribution, p=1/6, n=9, x=1

dbinom(1,9,1/6) = 0.34885

b) the chance that the third 6 appears on the tenth roll

This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.

Again, we have a binomial distribution of p=1/6, n=9, x=2

p1 = dbinom(2,9,1/6) = 0.27908

The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.

Thus the probability of both happening, by the multiplication rule, assuming independence  

P(third on the tenth roll) = p1*p2 = 0.04651

c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.

Again, using binomial distribution, probability of 3-6's in the first 10 rolls,

p1 = dbinom(3,10,1/6) = 0.15504

Probability of 3-6's in the NEXT 10 rolls

p1 = dbinom(3,10,1/6) = 0.15504

Probability of both happening  (multiplication rule, assuming both events are independent)

= p1 *  p1 = 0.02404

d) the expected number of rolls until six 6's appear

Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6

=  n(1-p)/p

Total number of rolls by adding n  

= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36

e) the expected number of rolls until all six faces appear

P1 = 6/6 because the firs trial (roll) can be any face with probability 1

P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials

P3 = 6/4 ...

P4 = 6/3

P5 = 6/2

P6 = 6/1

So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials

Answer:

-6m+3

Step-by-step explanation:

Answer:

An equivalent value is -6m -n +3

Step-by-step explanation:

Given

-3(2m-1)-n   expand

=-6m+3-n

(also equals -6m -n +3 by commutativity)

Answer: MN represents the radius of the circle.

Step-by-step explanation:

The radius is the distance from the center to the outside of the circle.

Answer:

Step-by-step explanation:

Least common denominator = a²b²

[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]

Answer:

no

Step-by-step explanation:

f(g(x))= x if they are inverses

(x)=1/3x

g(x)= 1/3x

f(g(x)) = 1/3 (g(x) = 1/3 (1/3x) = 1/9x

This is not x so they are not inverse functions

Answer:

.7698

Step-by-step explanation:

Answer:

16$

Step-by-step explanation:

8*2=16

HOPE THIS HELPS :)

Answer: $16

Step-by-step explanation:

As the book was purchased for half its price plus 8 you can create the equation 1/2x + 8 = x.  Then, simplifying the expression you get x = 16.  Thus, the book costs 16 dollars.

Answer:

it we'll be 0.3

Step-by-step explanation:

trust me man I like to explain but it's long

Answer:

0.3 meter or 3/10 meter

Step-by-step explanation:

As there are 100cm in 1 meter and you want to find 30cm in terms of meters.

It will be as

100cm = 1 meter     (rule/lax)

100/100 cm = 1/100  meter   (divide both sides of equation with 100)

1 cm = 1/100 meter

1 *30 cm = (1/100)*30  meter    (multiply both sides with 30)

30 cm = 30/100 meter

30/100 more shortly can be written as  3/10 meter or in decimals 0.3 meter.

Answer:

No

Step-by-step explanation:

Let's check the first statement with an example. 2 and 3 are positive numbers and their sum (5) is also positive so his first statement is true.

To check the second statement let's look at the negative numbers -1 and -8 for example. Their sum (-9) is also negative so his second statement is true.

To check the third statement let's look at the numbers 9 and -5. One is positive and one is negative, but their sum (4) is positive, so his third statement is false. However if we look at the numbers 4 and -7, their sum is negative so the third statement is partially false.

Answer:

k = -6

Step-by-step explanation:

hello

saying that (x-2) is a factor of [tex]x^2+x+k[/tex]

means that 2 is a zero of

[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]

and we can verify as

[tex](x^2+x-6)=(x-2)(x+3)[/tex]

so it is all good

hope this helps

Answer:

Step-by-step explanation:

Write in slope intercept form.

y - 9 = -2(x - 8)

y - 9 = -2x + 16

y = -2x + 16 + 9

y = -2x + 25

y = mx + b

The m is the slope, b is the y-intercept.

y = -2 x + 25

The slope is -2.

Answer:

0.007

Step-by-step explanation:

We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage

Step 1

We would have to find the sample standard deviation.

We use the formula = σ/√n

σ = 12.2 pounds

n = number of house holds = 51

= 12.2/√51

Sample Standard deviation = 1.7083417025.

Step 2

We find the z score for when the sample mean is more than 61

z-score formula is z = (x-μ)/σ

where:

x = raw score = 61 pounds

μ = the population mean = 56.8 pounds

σ = the sample standard deviation = 1.7083417025

z = (x-μ)/σ

z = (61 - 56.8)/ 1.7083417025

z = 2.45852

Finding the Probability using the z score table

P(z = 2.45852) = 0.99302

P(x>61) = 1 - P(z = 2.45852) = 0.0069755

≈ 0.007

Therefore,the probability that the sample mean will be more than 61 pounds is 0.007