A study about commuting time for workers in a certain city. The distribution is clustered on the left with most of the values less than about 40 minutes commute. There are a fairly large number of values that are much higher, even stretching out to 150 minutes. There is a 15% chance that a random worker has a commute time of greater than 45 minutes. If you were to sketch this distribution, what would it look like, how would you describe it, and how do you represent the 15% probability?

The first 3 terms of the sequence are 21, 24 and 29

From the question, we have the following parameters that can be used in our computation:

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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The function f(x) = -2|x - 3| + 2 involves a horizontal shift of 3 units to the right, a vertical reflection, and a downward stretch. Its domain is all real numbers, and its range is all real numbers less than or equal to 2.

The function f(x) = -2|x - 3| + 2 is a transformation of the basic absolute value function f(x) = |x|. Let's analyze the transformations and then graph both functions.Transformations:

1. Shifting: The function f(x) = -2|x - 3| + 2 involves a horizontal shift of the absolute value function f(x) = |x|. The term (x - 3) inside the absolute value causes a shift of 3 units to the right.

2. Reflecting: The negative sign in front of the absolute value function reflects the graph across the x-axis. It causes the function to be reflected vertically.

3. Compressing or stretching: There is no compression or stretching factor present in this particular function.

Graph of the basic function f(x) = |x|:

The graph of the basic function f(x) = |x| is a V-shaped graph that passes through the origin (0, 0). It has symmetry with respect to the y-axis.Graph of the given function f(x) = -2|x - 3| + 2:

To graph the given function, we start with the basic absolute value function f(x) = |x| and apply the transformations: a horizontal shift of 3 units to the right and a vertical reflection. The negative coefficient (-2) affects the amplitude, making the graph steeper.

Domain of f(x) = -2|x - 3| + 2:

The domain of the given function is all real numbers since there are no restrictions on the input values of x.

Range of f(x) = -2|x - 3| + 2:

The range of the given function is the set of all real numbers less than or equal to 2, as the vertical reflection and the coefficient (-2) cause the graph to be reflected and stretched downward.

Note: Without specific constraints on the values of x, the domain and range of the given function follow the typical domain and range of absolute value functions.

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Answer:

69

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

\(\frac{5x}{6} = 20\\5x = 120\\x = 24\)

Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

Answer:

Based on the given information, it is not possible to definitively determine whether the number generator is fair or not. However, we can make some observations and inferences:

We know that 70% of the socks in the drawer are black, which means that in a random selection of 10 socks, we would expect to see around 7 black socks on average.

The dot plot shows the number of black socks in 10 trials of the number generator. We can see that the number of black socks varies from 0 to 10, with some frequencies being higher than others.

Without knowing the exact frequencies or probabilities, we can see that the dot plot does not appear to be centered around 7 black socks, which is what we would expect from a fair number generator. However, it is difficult to determine whether the deviations from 7 are statistically significant or not, without more information.

Therefore, based on the given information, the most accurate statement is:

The number generator's fairness cannot be determined with certainty from the given data, but there are indications that it may not be perfectly fair.

Step-by-step explanation:

The table which represents a linear relationship that is also proportional is table 1.

There is a linear relationship between y and x when the rate of change of y with respect to x will be equal.

Table 1:

xy

00

42

84

When x = 4

y = kx

2 = k×4

2 = 4k

k = 2/4

k = 0.5

y = kx

y = 0.5x

when x = 8

y = 0.5(8)

y = 4

Table 2:

xy

01

23

45

y = kx

when x = 2

3 = k × 2

3 = 2k

k = 3/2

k = 1.5

when x = 4

y = 1.5x

y = 1.5(4)

y = 6

Therefore, table 1 is proportional and represents a linear relationship with the equation y = 0.5x.

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Answer:

1st one

Step-by-step explanation:

Answer:

a = 24

a = 150

a = 66

Step-by-step explanation:

your welcome

Answer:

125 pounds = 2500 five pence

Answer:

Step-by-step explanation

£1.00=100p

The exponential regression equation that best fits the data (2,7), (3,10), (5,50), and (8,415) is; C. y = 1.47(2.02)ˣ

An exponential regression is the process of finding the equation of the exponential function that fits best for a set of data.

In the case of function A, we will consider that the base of the power is to be 1. Thus, no matter by which value we replace the “x” and “y”, the answer will always be 2.89.

Let us try the first point.

x = 2 and y = 7

Replace x by 2 in the three options to get;

B. y = 8.3521

C. y = 5.998188

D. y = 4.365018

The closest answer to y = 7 is y = 5.998188 which is option C.

Let us confirm by doing the same thing to x for other points.

For the point (3, 10), we have;

x = 3 and y = 10

Replace x by 3 in the three cases to get;

B. y = 24.137569

C. y = 12.11633976

D. y = 6.41657646

The closest answer to y = 10 is y = 12.11633976 which is option C.

Let us try the third point (5, 50)

x = 5 and y = 50

Replace x by 3 in the three cases to get;

B. y = 201.59939

C. y = 49.439512

D. y = 13.86558

The closest answer to y = 50 is y = 49.439512 which is option C.

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Answer:

the answer is 41

Step-by-step explanation:

Maddy's class has 10 less so X-10=31

31+10=41 so 41 is your answer :)

Answer:

41

Step-by-step explanation:

we are given the number of students in Maddy's class, 31, the problem also says that Maddy's class is 10 less than Doris's class. So, to solve we make an equation with the information provided:

31+10= 41

Answer: 3 inches tall

Step-by-step explanation:

Answer:

∠C = 62°

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

PROCEDURE :-

As ABCD is a cyclic quadrilateral ,

∠B + ∠D = 180°

\(=> 3x + x + 20 = 180\)

\(=> 4x = 180 - 20\)

\(=> x = \frac{160}{4} = 40\)

Putting the values of x gives :-

∠A = (2×40 + 38)° = 118°

∠B = (3×40)° = 120°

∠D = (40 + 20)° = 60°

Also,

∠A + ∠C = 180°

⇒ ∠C = 180° - 118° = 62°

To know the inverse function, we have to change variables of the original function as follows:

Isolating for y:

Thus, the inverse function is:

Based on the latter, we can see that the intersection with y -axis = 1, coordinate (0, 1). While the intersection with x - axis = 3, coordinate (3, 0)

Answer: C. Y

Answer:

1. Angle A + Angle C = 180 degrees, hence Angle B cannot have a value is ABC is a triangle

2. If Angle A = 90 and Angle C = 90, line AB is parallel to AC and therefore these two lines cannot touch and form a triangle

Step-by-step explanation:

Answer:A triangle can’t have two right angles.

Step-by-step explanation: Three angles inside of a triangle have to sum to 180°. In this triangle the sum of angels will be greater than 180° which is not possible.

The population in this scenario consists of all employees in the firm, which totals 4,500 individuals. The sample is a subset of the population, specifically 60 randomly selected employees who are part of a committee evaluating the implementation of sensitivity training.

the population refers to the entire group of employees in the firm, which consists of 4,500 individuals. The sample, on the other hand, is a smaller group of 60 employees who have been randomly selected to form a committee. This committee's purpose is to evaluate the proposal of implementing sensitivity training online instead of the current in-person format.

The sample of 60 employees is chosen in a random manner to ensure representativeness and minimize potential bias. By selecting a subset of the population, the committee can provide insights and perspectives that are representative of the larger employee base. Each committee member will have the opportunity to vote "yes" or "no" on the proposal, and their votes will be used to determine the overall sentiment of the committee regarding the implementation of online sensitivity training.

It's important to note that the sample of 60 employees is being used as a representative group to make inferences about the entire population.

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Answer:

20x-3/15=8

We move all terms to the left:

20x-3/15-(8)=0

determiningTheFunctionDomain

20x-8-3/15=0

We multiply all the terms by the denominator

20x*15-3-8*15=0

We add all the numbers together, and all the variables

20x*15-123=0

Wy multiply elements

300x-123=0

We move all terms containing x to the left, all other terms to the right

300x=123

x=123/300

x=41/100

Answer:

x = 0.41

Step-by-step explanation:

20x-3/15=8

20x - 1/5 = 8

20x - 1/5 = 40/5

20x = 41/5

20x = 8.2

x = 0.41

The interval of convergence is (6-1/6, 6+1/6) = (35/6, 37/6).

To find the Taylor series of f(x) = ln(x) centered at c = 6, we first need to find the derivatives of f(x). We have:
f(x) = ln(x)
f'(x) = 1/x
f''(x) = -1/x^2
f'''(x) = 2/x^3
f''''(x) = -6/x^4
The Taylor series formula for a function centered at c is:
f(x) = f(c) + f'(c)(x-c)/1! + f''(c)(x-c)^2/2! + f'''(c)(x-c)^3/3! + ...
Plugging in the derivatives of f(x) and c = 6, we get:
f(x) = ln(6) + (1/6)(x-6) - (1/72)(x-6)^2 + (1/216)(x-6)^3 - (1/864)(x-6)^4 + ...
The first five nonzero terms are:
ln(6) + (1/6)(x-6) - (1/72)(x-6)^2 + (1/216)(x-6)^3 - (1/864)(x-6)^4
To find the interval of convergence of the series, we need to check the radius of convergence. The formula for the radius of convergence of a Taylor series centered at c is:
R = lim n->inf |(f^(n)(c))/n!|
Using the derivatives we calculated earlier, we have:
R = lim n->inf |(-1)^(n+1)/(n*6^(n-1))|
Using the ratio test, we can show that this limit is equal to 1/6, so the radius of convergence is R = 1/6. Therefore, the interval of convergence is (6-1/6, 6+1/6) = (35/6, 37/6).

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Approximately 34% of American adults have a mobile phone but not a landline, based on the given proportions from the study conducted by the Centers for Disease Control.

The proportion of American adults who have a mobile phone but not a landline, we need to subtract the proportion of those who have both a mobile phone and a landline from the proportion of those who have a mobile phone.

Let's denote the proportion of American adults who have a mobile phone as P(M), the proportion who have a landline as P(L), and the proportion who have neither as P(N).

Given information:

P(M) = 89% (proportion with a mobile phone)

P(L) = 57% (proportion with a landline)

P(N) = 2% (proportion with neither)

We can now calculate the proportion of adults who have a mobile phone but not a landline using the following equation:

P(M and not L) = P(M) - P(M and L)

To find P(M and L), we can subtract P(N) from P(L) since those who have neither are not included in the group with a landline:

P(M and L) = P(L) - P(N)

P(M and L) = 57% - 2%

P(M and L) = 55%

Now we can substitute the values back into the equation to find P(M and not L):

P(M and not L) = P(M) - P(M and L)

P(M and not L) = 89% - 55%

P(M and not L) = 34%

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The value of y' by implicit differentiation is y' = 2x / y  and the value of y is y = √2x² + 2C

Given

The function is .

2x² – y² = 5

x and y are variables.

a)

Differentiation implicitly to get y'

So,

Function =   2x² – y² = 5

Differentiate,

4x - 2y y' = 0

-2 y y' = -4x

y' = 2x / y

b)

To solve the equation explicitly for y and differentiate to get y' in terms of x.

y' = 2x / y

Apply seperation of variables,

yy' = 2x

Integrate both sides,

y²/2 = x² + C

y² = 2x² + 2C

Take square root on both sides,

y = √2x² + 2C

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Answer:

B

Step-by-step explanation:

locate f(x) = - 1 on the y- axis

Move across horizontally until meeting the graph at (1, - 1 ) with x- coordinate x = 1

Thus x = 1 when f(x) = - 1

To summarize, the equivalent expression to the cube root of 343 multiplied by 9 to the power of y and 12 to the power of z and 6 is 7 x 9y x 12z x 2 x 3.

To find the equivalent expression to the cube root of 343 multiplied by 9 to the power of y and 12 to the power of z and 6, we can simplify the expression as follows:

1. The cube root of 343 can be simplified to 7 because 7 x 7 x 7 equals 343.

2. We can rewrite 9 to the power of y as 9y.

3. We can rewrite 12 to the power of z as 12z.

4. We can rewrite 6 as 2 x 3.

Putting it all together, the equivalent expression is 7 x 9y x 12z x 2 x 3.

To summarize, the equivalent expression to the cube root of 343 multiplied by 9 to the power of y and 12 to the power of z and 6 is 7 x 9y x 12z x 2 x 3.

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5 square root - 2 square root is 0.821854415 and it is rational.

Given,

5 square root - 2 square root

That is,

√5 - √2

We have to find this is rational or not.

First we have to solve the equation:

√5 - √2 = 0.821854415

Irrational numbers cannot be stated as a fraction, although rational numbers can be expressed as ratios (such as P/Q and Q0). However, both of the numbers are genuine and can be shown on a number line.

So, here 0.821854415 is a rational number.

That is, 5 square root - 2 square root is  rational.

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Answer:

2.9184

Step-by-step explanation:

i hope this is correct i think it is..

c:

Answer:

12 for 6.97 is better

Step-by-step explanation:

for 12 pack

$6.97/12 markers = .58 per marker

for 4 pack

$2.77/4 markers = .69 per marker

thus 12 pack is better, a lower cost per marker

Answer:

12 for $6.97

Step-by-step explanation:

If u get 12 pack for $6.97 its .58 for each marker

If u get 4 pack for $2.77 its .69

And I would prefer to get a 12 pack cuz its cheaper and more markers.

I hope this helped:)

Yes, the equation y - 250x = 500 represents the same relationship between the distance from the start of the trail and the elevation.

The given equation is y - 250x = 500.
The above equation is of the form y = mx + c, where m = slope of the line and c = y-intercept of the line.
Let us convert the given equation into the form y = mx + c, y - 250x = 500, y = 250x + 500. Now, we can see that this equation is of the form y = mx + c, where m = 250, which means that the slope of the line is 250 and the value of y-intercept is 500.

Thus, the equation y - 250x = 500 represents the relationship between the distance from the start of the trail and the elevation.

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The allowance time, if the standard time is 234.15 minutes and the basic time is 233.4 minutes is 0.75 minute

To calculate the allowance time, we can use the following formula:

Allowance time = Standard time - Basic time

Thus, Allowance time = 234.15 minutes - 233.4 minute = 0.75 minutes

Therefore, the allowance time is 0.75 minutes.

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