You randomly select 500 students and observe that 85 of them smoke. Estimate the probability that a randomly selected student smokes.
a.) .27
b.) .50, since there are two possible outcomes for every student surveyed (smoke, don't smoke)
c.) 0.17
d.) 1.2

Answer:

Wyatt walks 3 miles per day for 6 days, so he walks a total of:

3 x 6 = 18 miles

Aaliyah walks 4 1/2 miles each day for 6 days, so she walks a total of:

4 1/2 x 6 = 27 miles

To find how many more miles Aaliyah walks than Wyatt, we can subtract Wyatt's total distance from Aaliyah's total distance:

27 - 18 = 9 miles

Therefore, Aaliyah will walk 9 more miles than Wyatt in 6 days.

Step-by-step explanation:

The fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit. Option ( A )

Multiplication is a mathematical operation that involves finding the product of two or more numbers or quantities. It is a way of adding a number to itself multiple times. The symbol used to represent multiplication is an "x" or a dot "·". For example, in the expression 5 x 6 = 30, 5 and 6 are multiplied together to give the product of 30. Multiplication can also be represented using parentheses, such as (5)(6) = 30. In addition, multiplication can be done with decimals, fractions, variables, and matrices.

To find the fixed cost per unit based on the cost of the machine per part manufactured, we need to calculate the total number of units produced by the machine over its estimated useful life, and then divide the cost of the machine by that number.

The machine runs at its capacity of 1,000 units per month for 10 years, so the total number of units produced by the machine is:

10 years x 12 months/year x 1,000 units/month = 120,000 units

The cost of the machine is $50,000, so the fixed cost per unit based on the cost of the machine per part manufactured is:

$50,000 ÷ 120,000 units = $0.4167 per unit

Rounding this to the nearest penny gives us the final answer of:

$0.42 per unit (option a)

Therefore, the fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.

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The measure of CFE is 28^o.

When the measures of two or more angles add up to the sum of angle on a straight line i.e. 180^o, then the set of angles are said to be supplementary.

Given point F on line CD in the question, we have;

<CFE + <DFE = 180^o  (definition of supplementary angles)

So that;

<CFE + 152 = 180

<CFE = 180 - 152

         = 28

<CFE = 28^o

Therefore, the measure of <CFE is 28^o.

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The area of the shaded part is 100.48cm²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area of the shaded part can be expressed as;

area of shaded part = 4 × area of semi circle

Area of semi circle = 1/2 πr²

radius = diameter/2

radius = 8/2 = 4

= 1/2 × 3.14 ×4²

= 3.14 ×16×1/2

= 3.14 × 8

= 25.12 cm²

Since the shaded parts are semi circles

then the area of the shaded part = 4× 25.12

= 100.48cm²

therefore the area of shaded part is 100.48cm²

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Mike works 39 hours per week at Job A and 20 hours per week at Job B.

We need to formulate some expressions here.

Let:

Hours Mike works at Job A = x

Hours Mike works at Job B = y

We know that:

x + y = 59 ---------- equation 1

We also know that he makes $6 per hour at Job A, and $7 per hour at Job B, and his total pay is $374. So we can set up another equation based on his total pay:

6x + 7y = 374 --------- equation 2

Now we have two equations with two unknowns, which we can solve simultaneously.

Using substitution method:

solve for x in terms of y:

x = 59 - y

We can substitute this expression for x into equation 2:

6(59 - y) + 7y = 374

Simplifying and solving for y:

354 - 6y + 7y = 374

y = 20

So Mike works 20 hours per week at Job B. We can substitute this value for y into equation 1 to find x:

x + 20 = 59

x = 39

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Based on the information, there is not sufficient evidence to conclude that tablets contain the right amount of active ingredients.

H0: µ = 320 versus Ha: µ ≠ 320

This is a two tailed test.

The test statistic formula is given as below:

t = (x - µ)/[S/✓(n)]

n = Sample size = 36 n = Population mean = 320 x = Sample mean = 319 S = Sample Standard deviation = 3

We have = Level of significance = 0.09 from the given data.

df = n - 1 = 35

1.7436 is the critical value.

[Using a t-table, we can determine this value.]

The P-value is 0.0533.

P-value = 0.09.

So, we reject the null hypothesis. There is not sufficient evidence to conclude that tablets contain the right amount of active ingredients.

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The equation of line g is y = (3/10)x + 1.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of line f is y - 7 = (3/10)(x - 4).

Since line g is parallel to line f, it will have the same slope as line f, which is 3/10.

Hence, the equation of line g can be written in the form:

y - y1 = m(x - x1)

Where (x1, y1) is the given point (10, 4) and m is the slope of line f, which is 3/10.

Substituting the values, we get:

y - y1 = m(x - x1)

y - 4 = (3/10)(x - 10)

y - 4 = (3/10)x - 3

y = (3/10)x + 1

Therefore, y = (3/10)x + 1 is the equation of line g.

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Answer:

Number of $ 8 priced tickets = 210

Number of $10 priced tickets = 140

Number of $ 12 priced tickets = 70

Step-by-step explanation:

Framing and solving equations with three variables:

Let the number of $ 8 priced tickets = x

Let the number of $10 priced tickets = y

Let the number of $ 12 priced tickets = z

  Total number of tickets = 420

                 x +  y + z = 420           --------------(i)

         Total income = $ 3920

        8x + 10y + 12z = 3920      ----------------(ii)

Combined number of $8 and $10 priced tickets= 5 * the number of $12 priced tickets

                      x + y  = 5z

                x + y - 5z = 0         -------------------(iii)

(i)        x + y + z = 420

(iii)      x + y - 5z = 0

       -     -     +      +   {Subtract (iii) from (i)}

                    6z = 420

                      z = 420÷ 6

                     [tex]\sf \boxed{\bf z = 70}[/tex]

(ii)            8x + 10y + 12z = 3920

(iii)*8       8x + 8y - 40z   = 0  

             -       -     +            -           {Now subtract}

                     2y  + 52z = 3920   -----------------(iv)

Substitute z = 70 in the above equation and we will get the value of 'y',

                 2y + 52*70 = 3920

                2y + 3640   = 3920

                               2y = 3920 - 3640

                               2y = 280

                                 y = 280 ÷ 2

                                 [tex]\sf \boxed{\bf y = 140}[/tex]

substitute z = 70 & y = 140 in equation (i) and we can get the value of 'x',

         x +  140 + 70 = 420

                  x + 210 = 420

                          x  = 420 - 210

                          [tex]\sf \boxed{x = 210}[/tex]

Number of $ 8 priced tickets = 210

Number of $10 priced tickets = 140

Number of $ 12 priced tickets = 70

Answer:

There is enough sufficient evidence to support the claim.

Step-by-step explanation:

There is sufficient evidence to support the claim that the new CAI training method performs differently than the traditional method. The conclusion is that utilizing the new CAI training approach, it takes much less time on average to obtain a basic driving license than it does using the conventional method.

To determine if the new license training method using computer aided instruction (CAI) performs differently than the traditional method, we need to conduct a hypothesis test. Let's define the null and alternative hypotheses as follows:

Null hypothesis (H0): The mean time to receive a basic driving license using the new CAI training method is equal to the mean time using the traditional method, i.e., μ = 99.

Alternative hypothesis (Ha): The mean time to receive a basic driving license using the new CAI training method is different from the mean time using the traditional method, i.e., μ ≠ 99.

We are given that the sample size is 260, the sample mean is 98, and the population standard deviation is 7. We can use a z-test to test the hypothesis since the sample size is large (n > 30).

The test statistic can be calculated as:

z = (x - μ) / (σ / √n) = (98 - 99) / (7 / √260) = -2.475

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

The corresponding p-value for a two-tailed test is 0.013, which is less than the level of significance of 0.1. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the new CAI training method performs differently than the traditional method.

In other words, the mean time to receive a basic driving license using the new CAI training method is significantly different from the mean time using the traditional method.

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The percentage of his budget allotted to the variable expenses is 46%.

Winston has $2,003 to budget each month. He budgets $1,081 for fixed expenses and the remainder of his budget is set aside for variable expenses.

Therefore, the percentage allotted for variable expenses can be calculated as follows:

Hence,

percent for allotted for variable expenses = 2003 - 1081 / 2003 × 100

percent for allotted for variable expenses = 922 / 2003 × 100

percent for allotted for variable expenses = 92200 / 2003

percent for allotted for variable expenses = 46.0309535696

percent for allotted for variable expenses = 46%

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The mean replacement time for the quartz timepieces produced by Company XYZ is 15.7 years with a standard deviation of 1.2 years. The company wants to provide a warranty so that only 1.5% of the quartz timepieces will be replaced before the warranty expires.

To find the time length of the warranty, we can use the formula for z-score:

z = (x - μ) / σ

where x is the value, we want to find, μ is the mean, σ is the standard deviation and z is the corresponding z-score.

We can use a z-score table or calculator to find that the z-score corresponding to 1.5% is approximately -2.33.

-2.33 = (x - 15.7) / 1.2

Solving for x gives:

x = 13.9 years (rounded to one decimal place)

Therefore, Company XYZ should provide a warranty of 13.9 years so that only 1.5% of the quartz timepieces will be replaced before the warranty expires.

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To determine which of the following systems of equations have nonzero solutions, we need to solve each system and see if there are any non-trivial solutions (i.e., solutions where not all variables are zero). If there are non-trivial solutions, then the system has nonzero solutions. Otherwise, the system has only the trivial solution of all variables being zero.

Let's take each system one at a time:

1) x + y = 0, 2x + 2y = 0
This system can be simplified to x + y = 0. Solving for y, we get y = -x. This system has infinitely many solutions, all of which are of the form (x, -x) for any real value of x except zero. Therefore, this system has nonzero solutions.

2) x + y = 0, 2x + 2y = 1
This system can be simplified to x + y = 0. Solving for y, we get y = -x. Substituting this into the second equation, we get 2x + 2(-x) = 1, which simplifies to 0 = 1, which is impossible. Therefore, this system has no solutions.

3) x + y = 1, 2x + 2y = 2
This system can be simplified to x + y = 1. Solving for y, we get y = 1 - x. Substituting this into the second equation, we get 2x + 2(1 - x) = 2, which simplifies to 0 = 0. This is always true, regardless of the value of x. Therefore, this system has infinitely many solutions, all of which are of the form (x, 1 - x) for any real value of x. Therefore, this system has nonzero solutions.

In summary, the first and third systems have nonzero solutions, while the second system has no solutions. The first system has infinitely many solutions, while the third system also has infinitely many solutions.

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Yes, repeating two simple arithmetic operations will eventually transform every positive integer into 1.

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

f(n) = n/2 if n%2 = 0

f(n) = 3n + 1 if n%2 = 1

The above definition means that

f(n) = n/2 if n is even

f(n) = 3n + 1 if n is odd

To check if repeating operations would transform to 1, we can set n = 10

and then evaluate the function values

So, we have

f(10) = 10/2 = 5

f(5) = 3(5) + 1 = 16

f(16) = 16/2 = 8

f(8) = 8/2 = 4

f(4) = 4/2 = 2

f(2) = 2/2 = 1

See that the end result of the operations is 1

Hence, repeating two operations will transform every positive integer into 1

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there are 1365 possible committees that can be formed from this group of 15 people, regardless of gender.

To form a committee of 4 people from a group of 9 women and 6 men, we need to consider all possible combinations of 4 people, regardless of gender.

The number of ways to choose 4 people from a group of 15 (9 women and 6 men) is given by the combination formula:

C(15,4) = 15! / (4! * (15-4)!) = 15! / (4! * 11!) = (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1) = 1365

Therefore, there are 1365 possible committees that can be formed from this group of 15 people, regardless of gender.

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The X bar chart, two values were out-of-control points and had assignable causes is 6.68 and Revised central lines / Revised control limits on X bar chart and R chart is 6.7364.

The X-bar chart, a form of Shewhart control chart, is used in industrial statistics to track the arithmetic means of subsequent samples of fixed size, n. For variables that may be monitored on a continuous scale, such as weight, temperature, thickness, etc., this sort of control chart is employed. For instance, one might sample five shafts from the production process once per hour, measure each shaft's diameter, and then display the mean of the five diameter values for each sample on a chart.

a) Here we are given that,

k=24

n=5

The sum of the subgroup averages is 160.25.

ΣΧ =160.25

The sum of the subgroup ranges is 2.19.

ΣR = 2.19

(1) Determine Trial central lines / Trial control limits on X bar chart and R chart.

Then,

[tex]\bar{\bar{X}}= \sum k=160.25/24=6.68[/tex]

Therefore,[tex]\bar{\bar{X}}=6.68[/tex]

b) Determine Revised central lines / Revised control limits on X bar chart and R chart.

From the statistical quality control chart

we get,

For, n=5

We have,

A₂=0.58

D₃=0

D₄=2.11

Revised Control limits for X -chart is,

[tex]UCLX =\bar{\bar{X}}+A2*\bar{R}=6.69+(0.58*0.08)=6.69+0.0464=6.6436[/tex]

[tex]CLX =\bar{\bar{X}}=6.69[/tex]

[tex]LCLX =\bar{\bar{X}}-A2*\bar{R}=6.69-(0.58*0.08)=6.69-0.0464=6.7364[/tex]

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Answer:

Step-by-step explanation:

Option D is the correct option.

What is Mean Absolute Deviation?

'The mean absolute deviation (MAD) is the mean (average) distance between each data value and the mean of the data set.'

According to the given problem,

The mean height Variety A = 19 [ from the table ]

The mean height of variety B = 13 [ from the table ]

The spread is given by the mean absolute deviation, which 1.2 for Variety A and 2.4 for Variety B. So we can see that, the spread in Variety A is lesser than the spread in Variety B, which shows that the average height of Variety A varies less than the average height of Variety B.

We can see from the table that the average height of a variety A is indeed greater than that of Variety B. Also we can see that the Mean Absolute deviation of Variety A is 1.2 which is lesser than the Mean Absolute deviation of Variety B.

Hence, option D is correct since the average height of Variety A is greater than Variety B, and also the mean varies lesser in Variety A than in Variety B.

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Answer:

D

Step-by-step explanation:

hope this helps

The slope of the line is 3 which represents that the time is rising as the distance increases.

The slope of the line that passes through the pair of points (3, 6) and (1, 3) is calculated as follows:

slope = (6 - 3) / (3 - 2)

slope = (3) / (1)

slope = 3

In this case, the slope of 3 means that the time is rising as the distance increases.

Therefore, the slope of the line that passes through the pair of points  (3, 6) and (1, 3) is 3.

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Based on the given options, the diagram that best represents the activity of a sales clerk manually preparing a sale receipt during a power outage would be option D.

A trapezoid could represent the shape of a receipt, a curved side rectangle could represent the shape of the clerk's desk or the paper she is using, and a circle could represent the shape of a calculator or cash register. Therefore, a trapezoid to a curved side rectangle to a circle could represent the process of the clerk manually calculating and recording the sale amount and inputting it into a calculator or cash register to produce a receipt.

It is important to note that during a power outage, technology-dependent activities such as electronic sales and transactions may be disrupted, and manual methods may have to be used as a backup. This highlights the power of technology in our daily lives and the impact that power outages can have on businesses and individuals.
The question is about selecting the correct diagram that represents the sales clerk manually preparing a sale receipt due to a power outage. Given the options:

a. trapezoid to curvy side rectangle to curved rectangle
b. curved side rectangle to circle to curved rectangle
c. circle to curved side rectangle to curved rectangle
d. trapezoid to curved side rectangle to circle

The appropriate answer for this question cannot be determined based on the provided information. Diagrams typically require visual representation, and the description of the shapes alone is insufficient to convey the activity of preparing a receipt manually. Moreover, the terms "power," "outage," "clerk," "receipt," "trapezoid," "curved," and "curved" don't necessarily correspond to the shapes given in the options.

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Answer:Domain is all real numbers

Step-by-step explanation:

f(x)=x^2

it is a parabola and all parabola’s domains are all real numbers

The given set of ordered pairs represents a function because each output has exactly one corresponding input. So, the correct answer is A) Yes, because for each output there is exactly one input.

A relation between two variables is a set of ordered pairs, where the first element in each pair corresponds to the input or independent variable (usually denoted by x), and the second element corresponds to the output or dependent variable (usually denoted by y).

In the given set of ordered pairs, each output has exactly one corresponding input, and therefore the relation satisfies the definition of a function. For example, the input of 3/4 is associated with only one output of -2, and the output of -7 is associated with only one input of -2. Hence, the relation represents a function.

So, the correct answer is A).

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The estimate of the given fraction, 15 9/10 + 5 3/7, is 21

From the question, we are to estimate the answer of the given expression

From the given information, we have a fraction expression.

The given expression is

15 9/10 + 5 3/7

To estimate the answer, we will add the fractions

First,

Convert the fractions from mixed to improper fractions

159/10 + 38/7

Find the LCM of 10 and 7

LCM of 10 and 7 = 70

Using the LCM, add the fractions

[7(159) + 10(38)]/70

(1113 + 380)/70

1493/70

= 21 23/70

≈ 21

Hence,

The estimate is 21

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The  sum of the vectors u and v is (-1,1).

To find the sum of the vectors u and v, we need to add their corresponding components.

The vector u has initial point (2,0) and terminal point (3,2), which means its components are (3-2, 2-0) = (1,2).

The vector v has initial point (2,2) and terminal point (0,1), which means its components are (0-2, 1-2) = (-2,-1).

To find the sum of these vectors, we simply add their corresponding components:

u + v = (1,2) + (-2,-1) = (1-2, 2-1) = (-1,1).

Therefore, the sum of the vectors u and v is (-1,1).

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Answer:

(−∞,∞)

Step-by-step explanation:

y = x² - 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

So, the domain of this quadratic function is: (−∞,∞)

Answer:

Step-by-step explanation:

300

in sequare

Answer: 3060 in³

Step-by-step explanation:

Volume is how much a shape can hold.  It's a 3 dimensional measurement so you need to multiply 3 dimensions

V= length x width x height

Sometimes students get confused with which is which side but it really doesn't matter because multiplication is commutative meaning you can switch it and it doesn't matter.  Like  5x2 is the same thing as 2x5  both will still be 10

length=15

width=12

height= 17

If Volume = length x width x height

=15 x 12 x 17 =  =3060

Because it's 3 dimensional, units are are cubed as well. but questions says no units

The transformations that move the pentagon FGHIJ onto the pentagon F'G'H'I'J' includes a rotation and a reflection. The correct option therefore is the option C.

C. Rotation, reflection

A rotation transformation is one in which a geometric figure is rotated about a fixed point or location, known as the center of rotation.

The coordinates of the image are; I(-5, 4), H(-2, 4), G(-1. 3), F(-2, 0), and J(-4, 1)

The coordinates of a point, (x, y), following a 90 degrees clockwise rotation are; (y, -x)

Therefore, the coordinates of the image of the after a 90 degrees rotation are; I'(4, 5), H'(4, 2), G'(3, 1), F'(0, 2), J'(1, 4)

The coordinates of the point on the preimage, (x, y), following a reflection over the y-axis is the point (x, -y), therefore;

The coordinates of the image of the figure F'G'H'I'J' after a reflection over the x-axis are;
I''(4, -5), H''(4, -2), G''(3, -1), F''(0, -2), and J''(1, -4)

The above points corresponds to the coordinates of the figure, F'G'H'I'J' in the diagram, therefore;

The series of transformations that maps the pentagon FGHIJ onto the pentagon F'G'H'I'J' is a 90 degrees clockwise rotation and a reflection over the y-axis. Option C is the correct option

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Answer: m∠CBD = 98°

Step-by-step explanation:

The equation for the relationship would be y = 0.25x - 2 and the unknown value would be 2. 5.

To find the equation, you first need to find the slope of the line by picking two points and applying the slope formula. The two points are (4, -1) and (12, 1).

The slope is:

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

= ( 1 - ( - 1 ) ) / ( 12 - 4)

= 2 / 8

= 0. 25

We can then find the full equation :

y - ( - 1 ) = 0.25 (x - 4)

y = 0.25x - 2

The unknown y value when x is 18 is:

y = 0.25 ( 18 ) - 2

y = 2. 5

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There are indeed 48 triangles that can be chosen from the rectangular array shown .

To find the 48 triangles, you should use the Combination formula which will show you the number of ways to pick 3 points when given 8 points.

C ( n, k ) = n! / ( k ! x ( n - k ) ! )

C ( 8 , 3 ) = 8 ! / (3 ! x ( 8 - 3 ) ! )

C ( 8, 3 ) = 336 / 6

C ( 8, 3) = 56

Now, there are technically 56 ways to pick the points but some of these ways are collinear and these cannot form triangles. Each row will have 4 such points so the number of ways to pick triangles is:

= 56 - ( 4 x 2 )

= 48 triangles

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