Multiple Transformations

What is the value of n?

n/3−5=12

Enter your answer in the box.

n = ?

Answer:approximatly -1.63092975357148

Step-by-step explanation:To solve the equation (1/2)^7x+1 = -9, we first need to get all the terms on one side of the equation by subtracting 1 from both sides. This gives us (1/2)^7x = -10.

Next, we need to get x by itself, so we take the log base 2 of both sides.

This gives us log base 2 of (1/2)^7x = log base 2 of -10.

The log base 2 of (1/2)^7 is -7, so we have -7x = log base 2 of -10

Finally, we divide both sides by -7 and get x = log base 2 of -10/-7

Using a calculator we can calculate this value which is approximatly -1.63092975357148

x = log base 2 of -10/-7 = -1.63092975357148

Answer:

see explanation

Step-by-step explanation:

x² + 12x + 22 = 0 ( subtract 22 from both sides )

x² + 12x = - 22

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(6)x + 36 = - 22 + 36

(x + 6)² = 14 ( take square root of both sides )

x + 6 = ± \(\sqrt{14}\) ( subtract 6 from both sides )

x = - 6 ± \(\sqrt{14}\)

Then

x = - 6 + \(\sqrt{14}\) ≈ - 2.26 ( to the nearest hundredth )

x = - 6 - \(\sqrt{14}\) ≈ - 9.74 ( to the nearest hundredth )

The range or the given data is calculated as 10.2 . Range is the difference between minimum value and maximum value.

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we can make use of the formula for range in statistics which is given as follows:[\large Range = Maximum\ Value - Minimum\ Value\]

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we need to arrange the data in either ascending or descending order, but since we only need to find the range, it is not necessary to arrange the data.

From the data given above, we can easily identify the minimum value and maximum value and then find the difference to get the range.

So, Minimum Value = 1.0

Maximum Value = 11.2

Range = Maximum Value - Minimum Value

                  = 11.2 - 1.0

                     = 10.2

Therefore, the range of the given data is 10.2.

Learn more about Range:

brainly.com/question/30339388

#SPJ11

The three girls baked 88 cupcakes altogether.

Cupcakes Baked by Each

Number of cupcakes baked by Tina, T = 40

It is given that Daisy baked 4/5 as many cupcakes as Tina.

Therefore, number of cupcakes baked by Daisy, D = (4T/5) (Applying fractions)

⇒ D = (4/5)×40

⇒ D = 4 × 8

⇒ D = 32

Also, it is given that Miko baked 1/2 as many cupcakes as Daisy.

Thus, number of cupcakes baked by Miko, M = D/2 (Applying fractions)

⇒  M = 32/2

⇒ M = 16

Calculating Total Number of Cupcakes Baked

Cupcakes baked by the three girls altogether = T + D + M

= 40 + 32 + 16

= 88

Hence, the girls together baked 88 cupcakes.

Learn more on fractions here:

https://brainly.com/question/10354322

#SPJ4

Answer

5/36 (\(\frac{5}{36}\))

Answer:

22/35

Step-by-step explanation:

27/9 = 3

3 × 11/5 ×2/21

=22/35

The calculation of (6 X 5) X 1 can be simplified as 30

The calculation of (6 X 5) X 1 can be simplified as follows:

(6 X 5) X 1 = 30 X 1 = 30

When you multiply 6 and 5, you get 30. And when you multiply 30 by 1, you get the same number, 30. So, (6 X 5) X 1 equals 30.

However, none of the options given in the question match the result of the calculation.

Option A suggests that (7 X 5) X 1 equals 35, but that's not correct.

Option B suggests that (6 X 6) X 1 equals 36, which is also not correct.

Option C suggests that (7 X 5) X 1 equals 35, which, as we know, is incorrect.

Therefore, the correct answer to the given calculation is 30, but it's not listed among the choices.

Learn more about simplification here: https://brainly.com/question/28008382

#SPJ1

Answer:

x = number of children

y = number of students

x/2 = number of adults

225

x + y + x/2 = 225

x*5 + y*7 + x/2 (12) = 1628

two equations in two unknowns.  solve for x and y and use to get the number of each

Step-by-step explanation:

Answer:

The bus drives 84 miles

Step-by-step explanation:

The question relates to relationship between average speed and time

The given parameters are;

The time duration in which the bus drives = 3/2 hours = 1.5 hours

The average speed of the bus = 56 mph

The formula average speed is given as follows;

\(Average \ speed = \dfrac{The \ total \ distance \ driven}{The \ time \ duration \ of \ travel}\)

Therefore, we have;

The total distance driven = Average speed × The time duration of travel

The total distance driven = The distance the bus drives

Substituting the given values, gives;

The distance the bus drives = 56 miles/hour × 1.5 hours = 84 miles

The distance the bus drives = 84 miles.

Answer:

196 miles

Step-by-step explanation:

To find the distance that the bus drives, we can use the formula:

distance = rate x time

where rate is the average speed and time is the duration of the trip.

In this case, the average speed of the bus is 56 mph and the duration of the trip is 3 1/2 hours. However, it is easier to work with time in terms of a single unit, so let's convert 3 1/2 hours to 7/2 hours:

3 1/2 hours = (2 x 3) + 1/2 hours = 7/2 hours

Now we can plug in the values into the formula:

distance = rate x time

distance = 56 mph x 7/2 hours

We can simplify by multiplying 56 by 7 and then dividing by 2:

distance = (56 x 7) / 2 = 196 miles

Therefore, the bus drives 196 miles.

The quotient is -16.4

\(\frac{-0.0328}{0.002}\)

Apply the fraction rule: \($\frac{-a}{b}=-\frac{a}{b}$\) \($=-\frac{0.0328}{0.002}$\)

Divide the numbers: \($\frac{0.0328}{0.002}=16.4$\)\($=-16.4$\)

The quotient rule is a calculus technique for determining the derivative or differentiation of a function that is represented as a division or ratio of two differentiable functions.

Therefore, we can apply the quotient method to get the derivative of a function of the form f(x)/g(x), where f(x) and g(x) are both differentiable functions and g(x) ≠ 0. The quotient rule immediately follows the product rule and the notion of limits of derivation in differentiation.

Learn more about quotient rule https://brainly.com/question/15568137

#SPJ9

Answer:

d = 105

Step-by-step explanation:

 9d - 25 = 920

Bring -25 to the other side of the equation, which will become +25

 9d = 920 + 25

 9d = 945

Divide both sides by nine, so that we can cancel out the 9 with d, and find the value of d.

 \(\frac{9d}{9} \) = \(\frac{945}{9} \)

 d =    \(\frac{945}{9} \)

 d = 105

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.

Know more about scrum here:

https://brainly.com/question/27960967

#SPJ4

We need to find the inverse of the function gof (x). First we need to find the composite function gof (x) which is given by:

\(g(f(x)) = g(3x - 6)\)

= \((1/3)(3x - 6) + 1\)

= x - 1 + 1

= x

Thus,

gof (x) = x.

Now we need to find the inverse of the function gof (x) to obtain

\((gof)^-1 (x).\)

We have gof (x) = x

which implies\((gof)^-1 (x)\)

= gof (x)^-1

= x^-1

= 1/x,

x ≠ 0

Therefore,

\((gof)^-1 (x) = 1/x\)

which is option (3) (x+1) since 1/x can be written as 1/(x+1-1), where (x+1-1) is the denominator of 1/x.

Hence, the correct option is (3).

To know more about two functions visit:

https://brainly.com/question/19517220

#SPJ11

To find (g(f))^-1 (x), substitute the expression for f(x) into g(x) and simplify. The composition of g(f) is x and its inverse is also x. Therefore, (g(f))^-1 (x) equals x.

To find (g(f))^-1 (x), we need to first find the composition of g(f) and then find its inverse. Start by substituting the expression for f(x) into g(x): g(f(x)) = g(3x-6) = \frac{1}{3}(3x-6) + 1 = x - 1 + 1 = x. So, g(f(x)) = x. Now, to find the inverse of g(f), we switch the x and y variables and solve for y: y = x. Therefore, (g(f))^-1 (x) = x.

https://brainly.com/question/33783470

#SPJ12

The histogram of the 200 sample means would be an approximate display of the sampling distribution of means.

In this scenario, random samples of size 30 are taken from the population of duathlon participants. Each sample mean is calculated from the finishing times of the participants in that specific sample. The process is repeated 200 times, resulting in 200 sample means.

The sampling distribution of means refers to the distribution of these sample means. It shows the variation in the sample means that would be expected when repeatedly sampling from the same population.

The Central Limit Theorem states that under certain conditions (such as when the sample size is sufficiently large and the population distribution is not heavily skewed), the sampling distribution of means tends to follow a normal distribution, regardless of the shape of the population distribution. The mean and standard deviation of the sampling distribution of means can be calculated based on the population mean and standard deviation, as well as the sample size.

Therefore, the histogram of the 200 sample means would provide an approximation of the sampling distribution of means, which gives insights into the likely range and variability of the sample means that could be obtained from repeated sampling.

To learn more about histogram

https://brainly.com/question/28170074

#SPJ11

The value of the quantity d is 0.0462 m^2/s.

Here,

The quantities a=3.7m, b=3.7s, c=80m/s.

We have to find the value of d = a^3/cb^2

What is quantity?

A quantity is an amount, number, or measurement that answers the question 'how much?' Quantities can be expressed in numbers or non-standard units.

Now,

The quantities a=3.7m, b=3.7s, c=80m/s.

The value of d;

\(d = \frac{a^{3} }{cb^{2} }\)

\(d = \frac{3.7*3.7*3.7 }{80 * 3.7^{2} }\)

\(d = \frac{3.7}{80}\)

\(d = 0.0462\)

Hence, The value of the quantity d is 0.0462 m^2/s.

Learn more about the quantities visit:

https://brainly.com/question/809966

#SPJ4

Answer:

A(x) = 35x² + 54x + 17

Step-by-step explanation:

Relation in the polynomials has been defined as,

A(x) = L(x).W(x) - M(x).N(x)

L(x) = (6x + 5)

W(x) = (6x + 5)

M(x) = (x + 4)

N(x) = (x + 2)

By substituting the polynomials in the expression,

A(x) = (6x + 5)(6x + 5) - (x + 4)(x + 2)

      = (6x + 5)² - (x + 4)(x + 2)

      = (36x² + 60x + 25) - (x + 4)(x + 2) [Since, (a + b)² = a² + 2ab + b²]

      = (36x² + 60x + 25) - [x(x + 2) + 4(x + 2)]

      = (36x² + 60x + 25) - [x² + 2x + 4x + 8]

      = (36x² + 60x + 25) - [x² + 6x + 8]

      = (36x² - x²) + (60x - 6x) + (25 - 8)

      = 35x² + 54x + 17

A(x) = 35x² + 54x + 17

Answer:

35° and 55°

Step-by-step explanation:

(x - 20) and x form a right angle (90° ) and are complementary

complementary angles sum to 90° , then

x - 20 + x = 90

2x - 20 = 90 ( add 20 to both sides )

2x = 110 ( divide both sides by 2 )

x = 55

then the 2 angles are

x = 55°

x - 20 = 55 - 20 = 35°

Emma's luggage may be lost with probability p = 0.1. The luggage and its content are estimated to be worth 316.05. Emma's utility insures against the loss of the luggage. What is the maximum insurance premium I that Emma would be willing to pay?

Solution:To calculate Emma's maximum insurance premium, let's start by calculating her expected utility if she doesn't insure her luggage.U (no insurance) = 0.9 x U (316.05) + 0.1 x U (0)where U (316.05) is Emma's utility function for 316.05 value, and U (0) is Emma's utility function for a loss of the luggage. Emma has not insured her luggage, hence, if it gets lost, she will get 0 value for it.A sum of 316.05 is worth more than 0, Emma will still get a certain amount of utility, which will be larger than 0.

Therefore, Emma's utility function is likely to be positive, so let us assume that U (0) = 0.If we plug this information into the above equation, we will have:U (no insurance) = 0.9U (316.05) + 0.1 × 0 = 0.9U (316.05)Hence, Emma's expected utility, if she doesn't insure her luggage, will be 0.9U (316.05).However, if Emma chooses to insure her luggage, she will pay the insurance premium I. If the luggage gets lost, she will get reimbursed by the insurance company for 316.05. Her expected utility function, if she insures her luggage, will be:

U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05)Where U (316.05 – I) is Emma's utility function for 316.05 – I value. Emma will get this amount if the luggage is not lost, but she has to pay the premium I.If we compare Emma's expected utility when she insures her luggage and when she doesn't insure her luggage, we will have the following inequality:

U (insurance) ≥ U (no insurance)0.9U (316.05 – I) + 0.1U (316.05) ≥ 0.9U (316.05)Let us solve this inequality:0.9U (316.05 – I) + 0.1U (316.05) ≥ 0.9U (316.05)0.9U (316.05 – I) ≥ 0.8U (316.05)U (316.05 – I) ≥ 0.89U (316.05)Since U (316.05 – I) is a decreasing function, it will get smaller as I gets larger.

Hence, to maximize Emma's expected utility, we need to minimize the insurance premium I that she pays to the insurance company.If Emma doesn't insure her luggage, her expected utility will be 0.9U (316.05)Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage.U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05)0.9U (316.05 – I) ≥ 0.8U (316.05)U (316.05 – I) ≥ 0.89U (316.05)Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage. Hence,Emma's maximum insurance premium I that Emma would be willing to pay is $31.35.

If Emma chooses to insure her luggage, she will pay the insurance premium I. Her expected utility function, if she insures her luggage, will be U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05). Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage. Therefore, Emma's maximum insurance premium I that Emma would be willing to pay is $31.35. The utility function is considered decreasing as Emma has to pay more premium.

To know more about utility function :

brainly.com/question/30652436

#SPJ11

Answer:

Step-by-step explanation:

\(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boxed{ \boxed{\boldsymbol{Rule : a^{-1}=\frac{1}{a} }}} \\\\\\\\ (2+3)^{-1} \times (2^{-1}+2^{-1}) = \\\\1)\ (2+3)^{-1}=5^{-1}=\frac{1}{5} \\\\2)\ 2^{-1}+2^{-1}=\frac{1}{2} +\frac{1}{2} } =1 \\\\3)\ \frac{1}{5} \cdot 1=\boxed{\frac{1}{5} }\)

The curve for the relationship between balloon rides and price when the temperature is constant at 50 degrees is illustrated below.

The term constant in math is defined as  a value or number that never changes in expression it's constantly the same.

When the temperature is constant, it means that one of the variables that can affect the demand for balloon rides is eliminated. This allows us to focus on the relationship between balloon rides and price. The relationship between these two variables can be represented by a curve. The curve can show us how the price of a balloon ride changes as the number of rides changes.

Then table for the relationship between balloon rides and price when the temperature is constant at 50 degrees is attached below.

when the temperature is constant, the relationship between balloon rides and price can be shown by a curve. The shape of the curve will depend on the relationship between the two variables, which can be upward-sloping, downward-sloping, or remain constant. The constant temperature allows us to focus on the relationship between balloon rides and price without the interference of other factors that can affect the demand for rides.

To know more about constant here.

https://brainly.com/question/30042865

#SPJ4

Answer:

B. 6

Step-by-step explanation:

Step 1: Subtract 3 from both sides.

6=n

Answer B. 6 equals n

Step-by-step explanation:

9 = 6 + 3

Answer:

0

Step-by-step explanation:

2(3x – 5) = -12 + 6x

6x - 10 = 6x - 12

Subtract 6x from both sides.

-10 = -12

Since -10 = -12 is a false statement, there is no solution.

Answer: 0

Step-by-step explanation:

Answer:

what do you need help with

Step-by-step explanation:

Answer:

AB=PQ (given)
ABO=POQ (alternate angles)

Step-by-step explanation:

AB=PQ (given)
ABO=POQ (alternate angles)
but i lose to find AO=OQ and BO=OP

Since AB and PQ are parallel and AQ is transversal:

Since AB and PQ are parallel and BP is transversal:

This gives us:

Since the triangles are congruent, their corresponding sides are congruent too:

Answer:The solution is in the attached file

Step-by-step explanation: