What is the horizontal shift for the absolute value function f(x)=3 |x+6| +9

The simplified cube roots expressions are:

Rational numbers: Rational numbers include terminating decimals, non-terminated with repeating decimals, perfect squares, integers, whole numbers, perfect squares, and fractions.

Example: 2.434343; 5.2; 1/2, -8; √4; etc.

Irrational numbers: Irrational numbers include non-terminated decimals, non-repeated decimals, non-perfect squares, and infinite decimals, and do not form ratios of two numbers.

Example: π = 3.141.....; √2; e/√2; etc.

The given cube root expressions are:

1. [tex]\sqrt[3]{81}[/tex]

2. [tex]\sqrt[3]{-64}[/tex]

Simplifying the first expression, we get

[tex]\sqrt[3]{81}=\sqrt[3]{3\times3\times3}[/tex]

⇒ [tex]\sqrt[3]{81}[/tex] = 3∛3 = 4.3267....

Thus, the cube root of 81 gives an irrational number since it is a non-terminating decimal and has no repeated decimals in it.

Now, simplifying the second expression, we get

[tex]\sqrt[3]{-64}=\sqrt[3]{-4\times-4\times-4}[/tex]

⇒ [tex]\sqrt[3]{-64}[/tex] = -4

Since the result is an integer, the cube root of -64 is a rational number.

Therefore, the given cube root expressions give irrational and rational numbers respectively. They are:

[tex]\sqrt[3]{81} =4.32674...[/tex]  and [tex]\sqrt[3]{-64} = -4[/tex]

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So for a gallon of punch, you would need around two thirds of a cup of cranberry juice.

Equations go into one of two categories: identities or conditional equations. An identity holds true for each value of the variables. A conditional equation is valid only for certain values of the variables. An equation is represented by the equals sign ("="), which separates two expressions.

Here,

In essence, this can be set up in a proportion.

Two cups of cranberry juice are required per gallon of punch. The quantity of cranberry juice required for one gallon is what you need to determine. So, in order to set up your percentage, do as follows:

Following cross-multiplication, you should have the following:

=> 3x = 2

then division should result in this:

=> x = 2/3

So for a gallon of punch, you would need around two thirds of a cup of cranberry juice.

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The probability of getting a tails and a number less than 3 is equal to 1/6.

As given in the question,

Probability of getting heads or tail is:

P (H) = P(T) = 1/2

The probability of getting any number on the die is:

P (1) = P (2) = P(3) = P (4) = P (5) = P (6) = 1/6

The probability of getting a tail on the coin and a number less than 3 on the die is:

P(tails and a number less than 3) = P(tails) x P( a number less than 3)

= 1/2 x [P(1) +P(2)]

= 1/2 x [1/6 +1/6]

= 1/6.

Therefore ,the required probability of getting tails and a number less than 3 is  equal to 1/6.

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The slope-intercept form of a linear equation is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

Given that the slope of the line is 1 and it passes through the point (8, –1), we can use the point-slope form of a linear equation to write the equation in slope-intercept form. The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Substituting the values given in the problem into the point-slope form, we get:

y - (-1) = 1(x - 8)

Expanding the right side and rearranging the terms, we get:

y + 1 = x - 8

y = x - 9

This is the equation of the line in slope-intercept form. The y-intercept is (-9, 0), which is the point at which the line crosses the y-axis.

Answer:

AngleCAB = 44°

AngleHAB = 66°

Step-by-step explanation:

AngleEAF is a right angle, equal to 90°.

EH and DC are just two intersecting lines. They form a couple of pairs of vertical angles. Vertical angles are equal to each other. We'll use the vertical angles, AngleEAD and CAH.

Angle EAD and CAH are equal to each other.

EAD = CAH

90°+20° = 2x + 3x

Combine like terms.

110° = 5x

Divide by 5

110/5 = x

22 = x

Angle CAB

= 2x

= 2(22)

= 44

AngleCAB = 44°

AngleHAB

= 3x

= 3(22)

= 66

AngleHAB = 66°

The probability that exactly one of the next three vehicles fail is 0.737 .

Given :

64% of all vehicles examined at a certain emissions inspection station pass the inspection. assuming that successive vehicles pass or fail independently of one another .

probability that exactly one of the next three vehicles fail is :

P = 1 -  probability that all of the next three vehicles passes .

= 1 - 64 % * 64 % * 64 %

= 1 - 64/100 - 64/100 - 64/100

= 1 - 0.64 * 0.64 * 0.64

= 1 - 0.4096 * 0.64

= 1 - 0.262

= 0.737

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Answer:

x=−10,y=−5

Step-by-step explanation:

Answer: 980

Step-by-step explanation: 20 = 2 x 2 x 5

245 = 5 x 7 x 7

70 = 2 x 5 x 7

= 2 x 2 x 5 x 7 x 7

= 980.

Greatest common divisor: 5

The velocity at which the diver hits the water is 45.96 feet/s.

The velocity of an object is in feet per sec after it has fallen a distance of d feet is approximated by the function v(d) = √64.4d

Given that, height of olympic diving platform d = 10 m = 32.8 feet

We know that, v(d) = √64.4d and d = 32.8

So, substituting in the above function, we have

v(d) = √64.4d

⇒ √64.4 * 32.8

⇒ √ 2112.32

⇒ 45.96 feet/s

Thus, the velocity at which the diver hits the water is 45.96 feet/s.

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The probability of P(X = 48) and P(Y =2) is 0.1056 and 0.2642 respectively.

Suppose 10 percent of households earn over 80,000 dollars a year,and 0.25 percent of households earn over 450,000.

a random sample of 400 house-holds has been chosen

N = 400

P = 25%

n*p = 400*0.25 = 100

n(1-p) = 400 * 0.75 = 300

100 and 300 are greater than 5 so we use the normal distribution here to estimate further.

mean = n*p = 100

sd = √(np(1 - p))

sd = √(100(1 - 0.25))

sd = √(100 x 0.75)

sd = √75

sd = 8.66

p(X≥48)

= p(X≥47.5)

P(z <  (47.5 - 40)/6)

P(z < 1.25)

= 0.8944

1 - 0.8944

= 0.1056

FOR Y

N = 400 p = 0.25% = 0.0025

400 * 0.0025 = 1

1 is less than 5 so we use poisson distribution.

using the excel function,

1 - BINOMDIST(1, 400, 0.0025, TRUE)

= 1 - 0.735759074

= 0.2642

Therefore, the probability of P(X = 48) is  0.1056 and P(Y =2) is 0.2642

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Answer:

Before we declare what happens, we must have an understanding of outliers and standard deviation. Outliers are certain points that are x deviations away from the mean. Standard deviation is a measurement of dispersion in relations to the mean you are identifying. Given this information, when outliers are removed, the standard deviation becomes a lower amount, because you have to think of standard deviation as a population measurement in a way. So imagine the outliers are a prestigious group of people, and if they leave the community, the population is indeed lower. Outliers affect deviation by a measure of extremity. The more extreme an outlier, the more or less a standard deviation will be affected. When outliers are removed, they will lower the standard deviation, which changes the data in respect to population. A high outlier, however, will increase both mean and median no matter what.

Hope this helps!

Answer:

Step-by-step explanation:

f vesadfc

Let T be a binary search tree with n nodes, in which n > 0. When I is linear, the search algorithm makes n key comparisons, in unsuccessful case.

The BST (Binary Search Tree) is a tree where all nodes on the left and right sides of a given node are larger and less than each other.

The nodes of the BST are not kept in a continuous location because it is a non-linear data structure. The element is absent from the list in the best-case scenario, making it a worst-case scenario.

The worst-case temporal complexity for linear structures is O. (n).

In the worst scenario, there will be n key comparisons.

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The right question is:

Let T be a binary search tree with n nodes, in which n > 0. When I is linear, the search algorithm makes.......................... key comparisons, in unsuccessful case.

The estimate of the number of students studying abroad in 2003 is 169 and the estimate of the number of students studying abroad in 2018 is 433

a. Estimate the number of students studying abroad in 2003.

The function is given as:

y = 123(1.065)^x

Where x represents years from 1998 to 2013

2003 is 5 years from 1998.

This means that

x = 5

Substitute the known values in the above equation

y = 123(1.065)^5

Evaluate the exponent

y = 123 * 1.37008666342

Evaluate the product

y = 168.520659601

Approximate

y = 169

Hence, the estimate of the number of students studying abroad in 2003 is 169

b. Assuming this equation continues to be valid in the future, use this equation to predict the number of students studying abroad in 2018.

2018 is 20 years from 1998.

This means that

x = 20

Substitute the known values in the above equation

y = 123(1.065)^20

Evaluate the exponent

y = 123 * 3.52364506352

Evaluate the product

y = 433.408342813

Approximate

y = 433

Hence, the estimate of the number of students studying abroad in 2018 is 433

Answer:

150-3x

Step-by-step explanation:

Use distrubitive property:

180-6x +3x-30

Factor:

150-3x

Answer:

-3x+150

Step-by-step explanation:

6(30-x)+3(x-10)

6(30)+6(-x)+3(x)+3(-10)

180-6x+3x-30

180-3x-30

-3x+150

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Answer:

............................

Answer:

Step-by-step explanation:

90% confidence interval for positive difference between means that there is a 90% probability that the confidence interval will contain the true population mean

The difference in sample means is used to calculate the difference in population means. A confidence interval reveals how accurate the estimate is.

We will make three assumptions in order to build a confidence interval:

1. The variance between the two populations is equal. The second assumption of homogeneity of variance is what this premise is known as.

3. The populations are evenly distributed.

4. Each value is sampled separately from every other value.

The following formula is used to construct a confidence range for the mean difference:

[tex]Lower Limit = M_1 - M_2 -(t_{CL})(S_{M1} - S{M2})\\Upper Limit = M_1 - M_2 +(t_{CL})(S_{M1} - S{M2})[/tex]

where [tex]S_{M1} - S{M2}[/tex] is the expected standard error of the difference between sample means, tCL is the desired level of confidence, and M1 - M2 is the difference between sample means.

The given question is incomplete So, I've answered in general according to my knowledge

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There are no crictical numbers of the given function 12-5e^(-x).

Let's Consider

[tex]f(x) = 12 - 5*e^-x[/tex].

What is critical number of a function.

If a number causes the derivative of an expression to equal 0, it is critical.

As a result, we must set the derivative of the expression to 0.

Local Maxima and Local Minima points are also consider as critical number of a function.

f`(x) = 0 or f`(x) =1/0 by solving both equation we can find all the critical points of a function f(x).

Derivative of given funciton f(x) is f`(x).

f`(x) = [tex]0 - 5*(e^-x)*(-1).[/tex]

f`(x) = [tex]5*(e^-x)[/tex].

f`(x) = 0

[tex]5*e^-x[/tex] = 0

[tex]e^-x[/tex] = 0

[tex]e^-x[/tex] never going to zero because e^-x is an exponential decreasing function.

So there are no crictical numbers of the given function f(x).

So We enter none in this question.

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fn is an integrable function on [a, b]. further, assume that the sequence (fn) converges uniformly to f on [a, b]. f is integrable on integral [a, b].

Let ε > 0. Since (fn) converges uniformly to f on [a, b], there exists an N such that |fn(x) - f(x)| < ε for all x ∈ [a, b] and all n ≥ N.

Since fn is integrable on [a, b], it follows that

∫a b|fn(x)|dx < ∞ for all n ≥ N.

We have

∫a b|f(x)|dx ≤ ∫a b|fn(x)|dx + ∫a b|fn(x) - f(x)|dx

Since |fn(x) - f(x)| < ε, it follows that

∫a b|f(x)|dx ≤ ∫a b|fn(x)|dx + ε(b - a)

Since the right hand side is finite, it follows that ∫a b|f(x)|dx is finite. Hence, f is integrable on integral [a, b].

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The percent change is -25% that is decreased.

What is percent change ?

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent , half of it is 50 percent , none of something is 0 percent.

Percent change equals the change in value divided by absolute value of original value and multiplied by 100.

Negative precent change :

When the change goes on decreasing, i.e. final value is less than original.

Positive percent change :

When the change goes on increasing i.e. final value is more than original.

In given que,

initial value = 8

final value = 6

change in value = 6-8

                           = -2

So, percent change = -2/8 *100 = -25%

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Answer:The only rational root of x3−3x2+4x−12=0 is 3.

Step-by-step explanation:

{1,−1,2,−2,3,−3,4,−4,−6,12,−12} , if at least one root is rational.

hope this helps

The scenario that describes a pattern of exponential decay is option (D) i.e, an elimination chess tournament has half the number of players on each successful round.

What is Exponential Decay ?

     Where, N is the quantity

                  λ (lambda) is a positive rate called the exponential decay  constant, disintegration constant, rate constant, or transformation constant.

Hence, the answer is option(D) i.e, an elimination chess tournament has half the number of players on each successful round.

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Is there any other information provided in the given question? For instance, is there data showing what each of the given letters represent?

The flagpoles are 40 feet, and the wires cross at E, which is directly above point F on the ground. Then EF is 5.142 feet.

The maximum height for flagpoles is twenty (20) feet. (3) When next to or encircled by residential lots, the flagpole may not be erected in any side or rear yard setback.

It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.

by applying similar triangles on triangles we get the equation on ABC and EFC

40y+9x=360

by applying similar triangles on triangles, we get the equation on DBC and EBF

y=3/10x

x=120/7

putting values in the very first equation we get

y=3/10x(120/7)

y=5.142

EF=5.142 feet.

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Using simple percentage rule, the answer is 25%,52% and 16.67%.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent symbol, %, or the abbreviation "pct" are frequently used to indicate percentages. The term "percent" derives from "percent," a shortened form of "per centum," which meaning per hundred.

The required formula is:

percentage (%) = Change/total * 100

Percentage Decrease = [tex]\frac {80-60}{80} * 100[/tex]

=25%

Percentage Decrease=[tex]\frac {500-240}{500} * 100[/tex]

=52%

Percentage Decrease = [tex]\frac {144-120}{144} * 100[/tex]

=16.67%

We calculated the percentage decrease using the above-mentioned formula.

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Answer:

C'(9,5)

Step-by-step explanation:

C(5,6)

Add or subtract how much you translate (move) left/right to the x-coordinate

Add or subtract how much you translate (move) up/down to the y-coordinate

C(5+x, 6+y) = C'

C(5+4, 6-1) = C'

C'(9,5)

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The equation of the linear relationship between x and y is: y = 4x - 1.

If we are given a table of values that shows the relation of x to y, to find the equation, find the value of the slope (m) and the value of the y-intercept (b), then plug their values into the equation, y = mx + b.

Given the table:

x   0   1   2   3   4

y   -1   3  7   11  15

Using two points from the table, (0, -1) and (1, 3), find the slope (m):

Slope (m) = change in y / change in x = (-1 - 3) / (0 - 1)

Slope (m) = -4/-1

m = 4

The y-intercept (b) = -1 [this is the value of y when x = 0, as seen in the table]

Substitute m = 4 and b = -1 into the equation, y = mx + b:

y = 4x - 1

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The amount Sally’s share would be;

⇒ $30,000

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

John, Sally and Jane form a partnership. They agree to distribute profits using a 2:3:2 ratio.

And, The profits are $70,000.

Now,

Since, The profits are $70,000.

Hence, We get;

⇒ 2x  + 3x + 2x = $70,000

⇒ 7x = $70,000

⇒ x = $10,000

So, The amount of Sally’s share would be;

⇒ 3x = 3 × 10,000

         = $30,000

Thus, The amount Sally’s share would be;

⇒ $30,000

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