a sample of 60 information system managers had an average hourly income of $45.80 with a standard deviation of $7.00. what is the lower limit for the 95% confidence interval estimate for the average hourly wage of all information system managers? round your answer to two decimal places.

ab⁶ is not a variable term found in the binomial expansion of [tex](a + b)^{8}[/tex]as this is because, the powers must sum up to 8

A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.

The Binomial Expansion of [tex](a+b)^8[/tex] is -

[tex](a + b)^8 = a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a3^b^5 + 28a^2b^6 + 8ab^7 + b^8.[/tex]

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Answer:

9

C

D

Step-by-step explanation:

By using exponent properties we will find the equivalent expression:

(-2)⁴/(-2)² = (-2)² = 4

Here we need to use the exponent property:

xⁿ/xᵇ = xⁿ⁻ᵇ

Here the expression we have is:

(-2)⁴/(-2)²

Using the above property we can rewrite the expression as:

(-2)⁴/(-2)² = (-2)⁴⁻² = (-2)²

Now we can solve this:

(-2)² = (-2)*(-2) = 4

Then the equivalent expression is 4.

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The constant of proportionality from a graph of any proportional relationship is find as below.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The constant of proportionality from a graph of any proportional relationship.

Now,

Let the solution of the graph = (2, 10)

Then, The constant of proportionality from a graph of any proportional relationship is find as;

⇒ Constant of proportionality = 10 / 2

                                             = 5

Thus, The constant of proportionality from a graph of any proportional relationship is find as above.

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The triangles in the image given are classified as:

11. isosceles 12. scalene 13. equilateral

Therefore:

11. The triangle has two congruent sides, therefore, it is classified as isosceles.

12. The triangle has different side lengths, therefore it is scalene.

13. All the three sides of the triangle are congruent, therefore, it is an equilateral triangle.

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Answer:

1.8x101

Step-by-step explanation:

Answer:

Step-by-step explanation:

A B

Answer:

2

Step-by-step explanation:

you take 1 and add 1 to it... and bam... 2

Answer:

2

Step-by-step explanation:

1+1=2 because 2-1=1 :0

Answer:

after 4 months dan and sydney will have paid the same amount

Step-by-step explanation:

Answer:

Step-by-step explanation:

dan and sydney are getting high speed internet access at the same time.dans provider charges $60 for installation and $42.95 each month. sydney's provider has free installation and charges 57.95 per month. after how many months will dan and sydney have paid the same amount?

let 'm' represent the number of months they have subscribed

dan's total:

42.95m + 60

sydney's total:

57.95m

we want to calculate 'm' when the two totals are equal:

42.95m + 60 = 57.95m

60 =15m

m = 60/15 = 4

after 4 months dan and sydney will have paid the same amount

1/2 gallons of water rush down the slide each seconds.

For the given question-

Rate of running water = 1 half gallon every 3 seconds.

Rate of running water = 1 1/2 = 3/2 gallon every 3 seconds.

It means-

In every 3 seconds ----> 3/2 gallons water flows.

Thus for 1 sec, divide both side by 3.

1 seconds ----> 1/2 gallons water flows.

Therefore, 1/2 gallons of water rush down the slide each seconds.

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The cost of each white led lights and colored led lights is $12 and $15 respectively.

Let

w + c = 27

3w + 2c = 66

From (1)

w = 27 - c

Substitute w = 27 - c into (2)

3w + 2c = 66

3(27 - c) + 2c = 66

81 - 3c + 2c = 66

- 3c + 2c = 66 - 81

- c = - 15

c = 15

Substitute c = 15

w + c = 27

w + 15 = 27

w = 27 - 15

w = 12

In conclusion, the task content can be solved using the concept of simultaneous equation.

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We will see that the odd functions were f(x) = x5 - 3*x3 + 2*x and f(x) = 1/x since only those were true under the specified circumstances.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. The most basic definition is that a function is a collection of ordered pairs of items, which in our instance will be numbers, but they may also be anything else, and which have the feature that their initial members are all distinct from one another. The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.

Here,

A function is odd,

f(-x) = -f(x) for every value of x in its domain.

1) f(x) = x^3 - x^2

f(-x) = (-x)^3 - (-x)^2

= -x^3 - x^2

f(-x) ≠ -f(x)

This function is not odd.

2) f(x) = x^5 - 3*x^3 + 2*x

f(-x) = (-x)^5 - 3*(-x)^3 + 2*(-x)

= -x^5 + 3*x^3 - 2*x = -f(x)

This function is odd.

3) f(x) = 4x + 9

f(-x) = 4*(-x) + 9

= -4*x + 9

-f(x) = -( 4*x + 9)

= -4*x - 9

f(-x) ≠ -f(x)

This function is not odd.

Because only these were true under the specified circumstances, we will find that the odd functions are f(x) = x^5 - 3*x^3 + 2*x and f(x) = 1/x.

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Answer:

Step-by-step explanation:

Answer: I believe it is 18/5

 or Decimal Form:

3.6

or Mixed Number Form:

3 3/5

Step-by-step explanation

4/5 x 4 1/2

Step-by-step explanation:

where is the diagram?

please

Answer:

a) 53+(8p+10)+(2p+17)=180

  p= 10

b) 53 degrees

   8p+10 = 90 degrees

  2p+17= 37 degrees

Step-by-step explanation:

sum of all angles of a triangle equal 180 degrees

so we can add all these angles together and set it equal to 180

53+(8p+10)+(2p+17)=180

53+10p+27=180

10p+80=180

    -80.    -80

10p=100

/10. /10

p=10

now we can fill in p to find the angles

we already know 53 degrees

8p+10

8(10)+10

80+10

90 degrees

2p+17

2(10)+17

20+17

37 degrees

hopes this helps please mark brainliest

Answer:

a)   53° + (8p + 10)° + (2p + 17)° = 180°

      p = 10

b)   53°, 90° and 37°

Step-by-step explanation:

Interior angles of a triangle sum to 180°.

Therefore, to find the value of p, equal the sum of the given angles to 180°, then solve for p.

⇒ 53° + (8p + 10)° + (2p + 17)° = 180°

⇒ 53 + 8p + 10 + 2p + 17 = 180

⇒ 8p + 2p + 53 + 10 + 17 = 180

⇒ 10p + 80 = 180

⇒ 10p + 80 - 80 = 180 - 80

⇒ 10p = 100

⇒ 10p ÷ 10 = 100 ÷ 10

⇒ p = 10

To find the measure of the angles, substitute the found value of p into the expression for each angle:

⇒ (8p + 10)° = (8(10) + 10)° = (80 + 10)° = 90°

⇒ (2p + 17)° = (2(10) + 17)° =  (20 + 17)° = 37°

Therefore, the measures of the three angles are:

x =2173

Step-by-step explanation:

The correct option d. 90 - 95%, is the percentage of diabetes patients having type 2.

A disorder in the body's ability to control and utilize sugar (glucose) as fuel is type 2 diabetes.

The recipe for diabetes management is a healthy diet.

Thus, one in ten Americans, or more than 37 million people, have diabetes, and 90–95% of them suffer from type 2 diabetes.

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Answer:

D

Step-by-step explanation:

90-95

The number of months required to complete the payments are 63 months.

We will make a equation, which represent total purchase amount in terms of number of months.

Let we consider number of months be t.

Total purchase amount = $17500, one time deposit = $1750

and monthly payment = $250

Then,

17500 = 1750 + 250t

250t = 17500-1750

250t = 15750

t = 15750/250

t = 63 months

Thus number of months required are 63.

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Answer:

A. No

B. No

C. Yes

D. Yes

Step-by-step explanation:

The perimeter of ABCD, given the vertices of the trapezoid, can be found to be 28.13 units

To find the perimeter of this trapezoid, you need to find the distances between AB, BC, CD, and AD. To find these, you can use the formula for finding the distance between vertices.

That formula is:

= √( ( X₂ - X₁ ) + ( Y₂ - Y ₁))

Using this formula, the distance of AB is 4.47 units.

The distance between BC is 6 units.

The distance between CD is 5.66

The distance between AD is 12 units

The perimeter is the distance around the shape:

= 4.47 + 6 + 5.66 + 12

= 28.13 units

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Answer:

56

Step-by-step explanation:

Take two points as far apart on the line (for maximum accuracy), preferably on grid points, and then calculate the vertical difference divided by the horizontal difference.

So (4, 224) and (0,0) are on the line, and (224-0)/(4-0) = 56

Time required to diffuse the F2 gas under the same conditions pressure and temperature with same volume is equal to 14 mins( approximately).

As given in the question,

Time taken by 1.5L sample of He gas to diffuse = 4.55 min.

Molar mass of He gas = 4g

Volume of He gas = 1.5L

Volume of F2 gas = 1.5L

Molar mass of F2 = 38gm

Formula of Rate of diffusion is given by :

Rate of diffusion of He / Rate of diffusion of F2

= √Molar mass of F2 / √Molar mass of He

Now,

Rate of He = Volume of He / time taken

                  = 1.5 / 4.55  

Rate of F2 = [ ( Rate of He ) ×√ Molar mass of He ] / √ Molar mass of F2

                 = ( 1.5 / 4.55 ) × ( √4 / √38)

                 = 3 / 28.028

                 = 0.107 L / min

Time of F2 = Volume of F2 / Rate of F2

                  = 1.5 / 0.107

                  = 14.02 minutes

                  ≈ 14 minutes.

Therefore, the time taken by F2 to diffuse under the same condition of He is equal to 14 minutes.

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Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

A field estimates 40 by 80 yards. Larysa makes a scale drawing with a size of 1 in. to 5 yd., and Prakash makes his own scale drawing with a size of 1 in. to 8 yd.

The dimension of the Larysa drawing is given as,

⇒ 40 x 1/5

⇒ 8 in

⇒ 80 x 1/5

⇒ 16 in

The dimension of the Prakash drawing is given as,

⇒ 40 x 1/8

⇒ 5 in

⇒ 80 x 1/8

⇒ 10 in

The dimension of the Prakash's drawing is less than the dimension of the Larysa's drawing. The Larysa's drawing has the larger area.

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The following data sets represents the required properties:

a. . Same mean but different standard deviation :

3   3   3  3   3                

1    2   3   4  5              

2    2  3   4  4    

b.  Same mean but different medians

1    2   3   4  5            

1    1   4   4   5            

1    2   2   5  5  

c. Same median but different median:

1      2    3    5   5        

1      2   3    4    5          

2     2   3    5    5  

As given in the question,

Three data sets with 5 numbers representing :

a. Same mean but different standard deviation :

                                       Mean                  Standard deviation

3   3   3  3   3                  15/5 = 3                 0

1    2   3   4  5                 15/5 = 3                  2.5      

2    2  3   4  4                 15/5 = 3                  1    

Mean of the data set = 3

Standard deviation = [tex]\frac{\sum (x - \bar{x} )^{2} }{n -1}[/tex]

b. Same mean but different medians :

                                   Mean                     Median

1    2   3   4  5             3                                3

1    1   4   4   5             3                                4

1    2   2   5  5            3                                 2

c. Same median but different median:

                                    Mean          Median

1      2    3    5   5          3.2                3

1      2   3    4    5            3                 3

2     2   3    5    5          3.4                3

Therefore, above are the following data set to represent same mean different standard deviation, same mean different median and same median different mean.

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The largest value less than 500 that the arithmetic progressions have in common = 479

In this question, we have been the arithmetic progressions {2,5,8,11, . . .} and {3,10,17,24, . . .}

We need to find the largest value less than 500 that they have in common.

We know that the formula for the n-th term of arithmetic progression is: an = a + (n – 1)d

For arithmetic progression {2,5,8,11, . . .}

a_m = 2 + (m - 1)3

For arithmetic progression {3,10,17,24, . . .}

a_n = 3 + (n - 1)7

if we solve for m, n then m =160 and n =69

2 + (160 -1)*3 = 479  which is the 160th term in the arithmetic progression {2,5,8,11, . . .}

3 + (69 - 1)*7  =479 which is the 69th term in the arithmetic progression {3,10,17,24, . . .}

Therefore, the value which less than 500 that both the progressions have in common = 479

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Given that the test's p-value is 0.0562>0.05, there is enough data to conclude that the machines' manufacturer should perform a new calibration.

A statistic employed in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.

Here,

x=4.88 cm

μ=5 cm

σ=0.44 cm

n=49

The test statistic,

=(4.88-5)/(0.44/7)

z=-1.909

The p-value of the test is the probability that the sample mean is different by at least 4.88 - 5 = 0.12 from the target value, which is P(|z| > -1.909), which is 2 multiplied by the p-value of z = -1.909

At z=-1.909, p-value=0.0281

2*0.0281=0.0562

The test's p-value is 0.0562>0.05, indicating that there is enough data to conclude that the machines' manufacturer should perform a recalibration.

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The length of the guy wire will be equal to 27.78 feet.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that Janelys places a 5-foot tall pole to support the guy wire. After placing the pole, Janelys measures the distance from the stake to the pole to be 14 ft. She then measures the distance from the pole to the tower to be 24 ft.

The length of the wire will be calculated as,

L² = 24² + 14²

L² = 576 + 196

L² = 772

L = √772

L = 27.78 ft

Therefore, the length of the guy wire will be equal to 27.78 feet.

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Answer:

40ft

Step-by-step explanation:

The solutions for the given conditions are;

1. True

2. True

3. False

4. False

5. False

6. True

7. True

1) For estimating a population parameter, a confidence interval is used.

TRUE → CI is used for estimating a population parameter. But, it can also be used to estimate the sample statistic.

2) The sample statistic is always captured by a confidence interval.

TRUE → CI is calculated using the sample statistic.

3) The population parameter is always captured by a confidence interval.

FALSE → There is a type 1 error possibility.

4) Z-critical values should always be used when creating confidence intervals.

FALSE → Z stat is used only in a normal distribution with sizes>30. Else, it is recommended to use a t distribution.

5) The center of the confidence interval is determined by the margin of error.

FALSE → ME determines the maximum deviation from the center at a given confidence level

6) In general, we would like to have a high level of confidence and a precise confidence interval.

TRUE → This is attainable when we increase the sample size.

7) A large sample size is required to create a proportion's confidence interval.

TRUE → Along with the large sample, we also need to have np and nq at least 10.

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Since these two lines overlap, the variable's value is 25, and the angle's value is 38 degrees.

The empty set, a point, or another line can cross another line in Euclidean geometry. Examples of applications for identifying these circumstances and locating the intersection include computer graphics, motion planning, and collision detection. In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the crossing lines share a common point.

Here,

Both the angles are equal as they are intersecting lines and opposite angles are equal in this.

x+13=3x-37

3x-x=37+13

2x=50

x=25

x+13=25+13

angle=38

3x-37=3*25-37

angle=38

The value of variable is 25 and the value of angle in 38 degree as they are the intersecting lines.

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