what is 2(x-1) + 5 = x + 7

a) SS = {HHH, THH, HTH, HHT, THT, TTH, HTT,  TTT} i) P(1 head) = 0.375 ii) P(at least 2 heads) = 0.5 iii) P(no heads) = 0.125.

Suppose that a coin is tossed three times and the side showing face up on each toss is noted. Suppose also that on each toss heads and tails are equally likely. Let HHT indicate the outcome heads on the first two tosses and tails on the third, THT the outcome tails on the first and third tosses and heads on the second, and so forth.

Given that

a) A coin is tossed three times and the side showing face up on each toss is noted.

The total number of possible outcome are 2³ = 8

The sample space is given by

SS = {HHH, THH, HTH, HHT, THT, TTH, HTT,  TTT}

b) Write each of the following events as a set, in set-roster notation, and find its probability.

(i)The event that exactly one toss results in a head.

In this case we need to include only those outcomes where we have exactly on head,

E(1 head) = {THT, TTH, HTT}

So there are 3 such outcomes, the probability is

P(1 head) = no. of desired outcomes/total number of outcomes

P(1 head) = 3/8

P(1 head) = 0.375

(ii) The event that at least two tosses result in a head

In this case we need to include only those outcomes where we have at least two heads which means two or greater than two,

E(at least 2 heads) = {HHH, THH, HTH, HHT}

So there are 4 such outcomes, the probability is

P(at least 2 heads) = 4/8

P(at least 2 heads) = 0.5

(iii) The event that no head is obtained.

In this case we need to include only those outcomes where we have no heads at all.

E(no heads) = {TTT}

So there is only 1 such outcome, the probability is

P(no heads) = 1/8

P(no heads) = 0.125

Hence the answer is a) SS = {HHH, THH, HTH, HHT, THT, TTH, HTT,  TTT} i) P(1 head) = 0.375 ii) P(at least 2 heads) = 0.5 iii) P(no heads) = 0.125.

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Answer:

x = 2

Step-by-step explanation:

3x + 12 = -5x + 28

3x + 12+ 5x = -5x + 28 + 5x

8x + 12 = 28

8x + 12 - 12 = 28 - 12

8x = 16

8x/8 = 16/8

x = 2

Answer:

1).  The constant of variation is 7

2).  w = 6 for the given values of x and y

Step-by-step explanation:

"Varies jointly" tells us that y is a direct result of a mathematic operation involving x and w.  We will assume y is directly prorportional to x and w, in the sense that we can find a multiplicative relationship of the form y=Kxw, where K is the constant of variation.

We are given one data point:  y=-42 where x is 2 and w is -3.  Let's put those values into our trrial expression:

y=Kxw

-42=K(2)(-3)

-42 = -6K

K = 7

The constant of variation is 7.

The value of w for y=3 and x=(1/14) would be:

  y=7xw

  3 = 7*(1/14)*w

3 = (1/2)*w

Answer:

1)  k = 7

2)  w = 6

Step-by-step explanation:

Joint variation equation

If y varies jointly with x and w:

[tex]\boxed{y \propto xw \implies y=kxw}[/tex]

for some constant k.

Given:

Substitute the given values into the joint variation equation and solve for k:

[tex]\begin{aligned}y&=kxw\\\implies -42&=k \cdot 2 \cdot -3\\-42&=-6k\\k&=\dfrac{-42}{-6}\\k&=7\end{aligned}[/tex]

Therefore, the equation is:

[tex]\boxed{y=7xw}[/tex]

To find w when y = 3 and x = 1/14, substitute these values into the found equation and solve for w:

[tex]\begin{aligned}y&=7xw\\\implies 3&=7 \cdot \dfrac{1}{14} \cdot w\\3&=\dfrac{7}{14} \cdot w\\42&=7w\\w&=6\end{aligned}[/tex]

Answer:

-6

Step-by-step explanation:

-(-3)²+3

-9 + 3

-6

Professor Very Busy needs to allocate time next week to include time for office hours then TAF(Week 7) = S(Week 6) + T(Week 6) = 57.5 + (-5.5) = 52.0

Smooth the pattern as well as the arrangement to get the outlook this year.

S(Week 5) = TAF(Week 5) + alpha*(Actual(Week 5) - TAF(Week 5))

                = 75 + 0.5(65 - 75) = 70

S(Week 6) = TAF(Week 6) + alpha*(Actual(Week 6) - TAF(Week 6))

                = 65 + 0.5(50 - 65) = 57.5

T(Week 6) = T(Week 5) + beta*(TAF(Week 6) - TAF(Week 5) - T(Week5))

               = -5 + 0.1(65 - 75 - (-5)) = -5 + (-0.5) = -5.5

Therefore, TAF(Week 7) = S(Week 6) + T(Week 6) = 57.5 + (-5.5) = 52.0

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On the assumption that each curve has only real roots, the quartic function is the graph C.

In this question we have four choices of graphs of polynomials, that is algebraic expressions of the form:

p(x) = Σ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., m - 1, m}

Where m is the grade of the polynomial.

The factor form of the polynomial is described below:

p(x) = a · Π (x - rₙ), for n = {0, 1, 2, 3, ..., m - 1, m}

If we consider that each choice has real roots, then the grade of the polynomial coincides with the number of times that the curve pass through the x-axis. Then, the graph C represent a quartic function, that is, a polynomial with grade 4 with the special feature that is a function of the form f(x) = a · x² · (x - r₁) · (x - r₂).

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Ship travels 33miles in 3 hours.

What is distance?

Distance is the actual distance that a body travels. Additionally known as path length. For instance, the path length for an item going from point O to point P will be distance OP = 360 m. It is a scalar quantity, the distance. It lacks direction and just possesses magnitude.

Ship travels in one hour = 11miles

Therefore, Ship travels in 3 hours = 11×3

                                                         = 33miles

Hence, Ship travels 33 miles in 3 hours.

*SHIP OFF COURSE IS NOT GIVEN IN THE QUESTION.

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Answer:

 122°

The measure of the central angle is twice the measure of the inscribed angle that subtends the same arc.

 ∠ABC = 2×∠ADC = 2×61°

 ∠ABC = 122°

Step-by-step explanation:

Since the scooter is rented for $1 and the firm charges $0.15 per minute, the necessary expression is 1+0.15m.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Here,

rent of scooter=$1

rent of scooter per minute=$0.15

The expression,

=1+0.15m

The required expression is 1+0.15m as rent of scooter is $1 and per minute rent charged by company is $0.15.

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There are 4 different 12-bit strings possible that begin with 0101, end with 1100 or have 0110 as the four middle bits.

We have to find the number of 12-bit strings that are starting with 0101, end with 1100 or have 0110 in the middle bits.

So, the first four position are reserved for 0101 and we have two options for the middle four bits and the end four positions.

So, we can write here,

Total possible different positions for 1100 and 0110 is,

= 2 x 2

= 4

Because, the two combination can appear simultaneously or they can appear one by one.

So, the total different 12-bit strings possible that have 0101 in the start, 1100 in the end or 0101 in the middle are 4.

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The length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.

Using cos law:

W = √(41² + 17² - 2×41×17 cos 134)

After solving:

W = 54.20 cm

Thus, the length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.

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The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5) = 0.0603.

P(M 169.3 cm 168.3 cm) = 0.7724

Given that,

Steel rods are produced by a firm. The lengths of the steel rods have a mean of 125.2 cm and a standard deviation of 2.3 cm, and they are regularly distributed. 25 steel rods are packaged together for shipping.

We have to determine the probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5-cm) =

We know that,

Mean =μ= 125.2

Standard deviation=σ=2.3

n=25

P(M<124.5)= P[(M-μ)/σ< 124.5-125.2/0.46]

=P(z<-1.522)

Using the z-table,

=0.0603

Therefore, The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5) = 0.0603.

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Answer:

Step-by-step explanation:

greater than

Answer: Greater than

0.27 = 0.0027% probability that this bulb was produced by factory B.

Given,

In the question:

Three factories produce light bulbs to supply the market. Factory a produces 20%, 50% of the tools are produced in factory B and 30% in factory C. 2% of the bulbs produced in factory A, 1% of the bulbs produced in factory b and 3% of the bulbs produced in factory C are defective.

We use the conditional probability formula to solve this question. It is

P(A|B) = P(A∩B) / P(A)

In which,

P(B|A) is the probability of event B happening, given that A happened.

P(A∩B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Bulb is defective.

Event B: Produced by factory A.

Probability of a bulb being defective.

2% of 20%(factory A)

1% of 50%(factory B)

3% of 30%(factory C). So

P(A) = 0.02 x 0.2 + 0.01 x 0.5 + 0.03 x 0.3

P(A) = 0.018

Defective and from factory B:

1% of 50%. So

P(A∩B) = 0.01 x 0.5 = 0.005

What is the probability that this bulb was produced by factory B?

P(A|B) = P(A∩B) / P(A)

P(A|B) = 0.005/ 0.018

P(A|B) = 0.27

Hence, 0.27 = 0.0027% probability that this bulb was produced by factory B.

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Answer:

Step-by-step explanation:

Given equation,

→ y = 3x + 5

The value of y when x is 10,

→ y = 3x + 5

→ y = 3(10) + 5

→ y = 30 + 5

→ [ y = 35 ]

The value of y when x is -10,

→ y = 3x + 5

→ y = 3(-10) + 5

→ y = (-30) + 5

→ [ y = -25 ]

So, these are the values of y.

The required closest approximation of city A's population is 1.185 million.

Percentages  are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, on the off chance that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.

We have, city A is 23.5% of city B

A/B = 235/1000 = 47/200 = (B)47/200-----------(1)

and, city B is 51% of city C.

B/C = 51/100

B = (51/100)×9.89 = 5.0439 million

As C = 9.89 million

Put the value of c in equation (1)

A =  (5.0439)47/200 = 1.185 million

Thus, required population of city A is 1.185 million.

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Bradon is 24 years old and Micheal is 72 years old.

Michael is 3 times as old as brandon. 18 years ago, michael was 9 times as old as brandon

Let m represent Michael

Let b represent Brandon

Then,

m = 3b                    <-----------"Michael is 3 times as old as Brandon."

m - 18 = 9(b - 18)    <-----------"18 years ago, Michael was 9 times as old as Brandon."

3b - 18 = 9b - 162

-18 = 6b - 162

144 = 6b

b = 24     <-------This is Brandon's age.

3b = m

3(24) = 72 <------This is Michael's age.

Therefore, Michael is 3 times as old as Brandon. Also, 18 years ago, Brandon would have been 6 and Michael would have been 54

Now, Bradon is 24 years old and Micheal is 72 years old.

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Answer:

radius = 6.5

Step-by-step explanation:

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 42.25 ← is the equation of a circle centred at the origin

with r² = 42.25 ( take square root of both sides )

r = [tex]\sqrt{42.25}[/tex] = 6.5

The number of those who have insomnia has a standard deviation of 22.23.

Given,

People suffer from insomnia = 5%

Total number of people in the community = 10,400

We have to find the standard deviation of the number of people who suffer from insomnia;

Here,

p = 0.05

q = 0.95

n = 10,400

Then,

np = 10400 x 0.05 = 202

Now,

npq = 202 x 0.95 = 494

Standard deviation = √npq = √494 = 22.23

That is,

The standard deviation of the number of people who suffer from insomnia is 22.23

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The correct conclusion for "it was expected that the hourly wage in October 2019 would increase, and the p-value associated with the hypothesis test is .001" is "the average wage is not increased."

A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. A strong hypothesis outlines the predicted link between the dependent and independent variables and is succinct and straightforward. It is best to be as specific and testable as possible when describing this relationship.

The answer to the statement "it was predicted that the hourly wage in October 2019 would grow, and the p-value associated with the hypothesis test is.001" should be "the average wage is not raised."

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Three problems would arise if the frequency of scrum was lowered to every two or three days.

(A) There may be missed opportunities to examine and amend the sprint backlog.

(B) The Sprint strategy deteriorates; barriers are raised and taken down more slowly.

(C) Too much time is spent updating the scrum board prior to meetings.

Scrum is a project management framework that was initially focused on software development, while it has now been applied to other areas such as research, sales, marketing, and cutting-edge technology.

It is intended for groups with ten or fewer members who divide their work into tasks that can be finished in sprints, which are time-boxed iterations that can be done in as little as one month and most frequently two weeks.

If the frequency was reduced to every two or three days, there would be three issues.

(A) The chances to review and modify the Sprint Backlog may be missed.

(B) The Sprint plan becomes imprecise; obstacles are raised and removed more slowly.

(C) Too much time is spent before meetings updating the scrum board.

Therefore, three problems would arise if the frequency was lowered to every two or three days.

(A) There may be missed opportunities to examine and amend the sprint backlog.

(B) The Sprint strategy deteriorates; barriers are raised and taken down more slowly.

(C) Too much time is spent updating the scrum board prior to meetings.

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30% was the discount recived

The probability that the average fracture strength of 100 randomly selected pieces will be equal to 33.19%.

In order to find the probability first we find the Z score. The Z score related the standard deviation and the mean of any data as

Z = X - μ/σ where Z is the Z score, X is the random variable, μ is the mean and σ is the standard deviation.

The standard deviation of the randomly selected 100 variables will be given as

s = σ/√n where n = 100 and σ = 2

s = 2/√100

s = 0.2

Now, the Z score for this data will be

Z = X - μ/s where X = 13.8, and μ = 13.5 and the value of s = 0.2

Z = 13.8 - 13.5/0.2

Z = 1.5

Now, for Z = 1.5 the p value will be 0.66807

The probability will be P = 1 - 0.66807 = 0.33193 that is 33.19%

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After 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.

Given,

Cost of auto =$40,000

Residual value =$4000

Estimated lifetime =5 years

Straight-line Method:-

Depreciation cost can be calculated by formula,

[tex]Depreciation=\frac{cost\ of\ assest-residual}{estimated\ lifetime}[/tex]

It is constant for every year.

Accumulated depreciation can be calculated by formula,

[tex]Accumulation\ Depreciation=\frac{cost\ of\ assets-residual}{estimated\ lifetime}*Number\ of\ years[/tex]

Book value at start of year is nothing the cost of asset at that year and Book value at end of year is difference between  cost of asset at that year and depreciation cost.

Using the above formulas all the values for each year is caculated and formed into a table.

Year      BookValue     DepreciationCost     Accumulation    Book Value

                  Start                                                                              End

1         $40,000               $7,200.00                $7,200           $32,800

2         $32,800                $7,200.00                $14,400           $25,600

3         $25,600               $7,200.00              $21,600           $18,400

4         $18,400               $7,200.00              $28,800           $11,200

5          $11,200           $7,200.00                       $36,000           $4,000

Thus, after 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.

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The sample mean versus desired mean is not a type of comparison one would anticipate for a two-sample test to be performed. Therefore, the option C holds true.

A sample test can be referred to or considered as the test that includes the conducting of an activity to determine the nearest possible outcome of a much larger set of observations. The purpose of conducting such a test is testing that two population means are the same in a set of observations. If the means are same, it means that the test is successful.

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The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

A normal distribution has symmetrically distributed data that is skew-free. As one proceeds away from the center, values tend to decrease and tend to cluster more frequently in that area. The mean, mode, and median of a normal distribution are all equal measures of central tendency.

Given data:

X: height of seaweed.

X~N (μ;σ²)

 μ= 10 cm    

 σ= 2 cm

We will calculate the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

                P(X ≤ x) = 0.30

                P(X ≥ x) = 0.70

Now by using the standard normal distribution,

we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula

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

translates the Z value to the corresponding X value.

                    P(Z ≤ z) = 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

                    z= -0.52

Now you have to clear the value of X:

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

                  X= (Z * σ) + μ

                 X = (-0.52 * 2)

                     = 8.96

hence, the value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

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The longest possible length is 3

The smallest square achieving this length : 38² = 1444.

Square:

A quadrilateral with four equal sides is called a square. There are numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. The complete length of a square's boundary is its perimeter. As a result, the length of each side can be added to determine the square's perimeter. Since a square has four sides, its perimeter may be calculated by adding all four of its sides. The space a square takes up is its area.

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The 3360 possible four-digit numbers are greater than 2999.

What is the combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

We know it has to be a four-digit number,

The first digit has to be between 3 and 9 (inclusive) so there are 7 options.

The unit digit can be any number so there are 10 options.

The answer will be 7 * (# of possible middle digit combos) * 10.

There are 7*48*10 = 3360 possible four-digit numbers.

Hence, the 3360 possible four-digit numbers are greater than 2999.

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Step-by-step explanation:

of course there is an explanation. and a correct answer (not just a wild guess).

f(x) = 2x

g(x) = 2x² - 1

f(g(x)) means that x is first processed by g, and then the result of that is processed by f.

in other words, the whole functional expression of g becomes the input argument for f.

therefore,

f(g(x) = 2(2x² - 1) = 4x² - 2

so, the correct answer is light blue.