Given the list of functions. calculate each of the following
F(x)=x-2 g(x)=-3x + 2 h(x)=1/5x -6

Find g(-2)

A. g(-1) =6 B. g(-1)=-6 C. g(-1) =8 D. g(-1)=-8

Answer:

the equation is 5x + 4y = 80,

False. The triple exponential smoothing method does consider seasonality variations in the analysis of the data, along with trend and level components, to provide accurate forecasts.

The statement is false. Triple exponential smoothing, also known as Holt-Winters method, is a time series forecasting method that incorporates trend and seasonality variations in the analysis of the data, but it does not specifically use seasonality variations.

Triple exponential smoothing extends simple exponential smoothing and double exponential smoothing by introducing an additional component for seasonality. It is commonly used to forecast data that exhibits trend and seasonality patterns. The method takes into account the level, trend, and seasonality of the time series to make predictions.

The triple exponential smoothing method utilizes three smoothing equations to update the level, trend, and seasonality components of the time series. The level component represents the overall average value of the series, the trend component captures the systematic increase or decrease over time, and the seasonality component accounts for the repetitive patterns observed within each season.

By incorporating these three components, triple exponential smoothing can capture both the trend and seasonality variations in the data, making it suitable for forecasting time series that exhibit both long-term trends and repetitive seasonal patterns.

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Answer:

x + 2y = 14

Step-by-step explanation:

That’s the answer

Answer:

p(p+q-qr)

Step-by-step explanation:

p^2+pq-pqr​

Factor out a p

p(p+q-qr)

Answer:

p(p+q-qr)

Step-by-step explanation:

p^2 +pq-pqr

= p(p+q-qr)

The probability that the gambler has strictly more than $32 after playing the game five times is 68.75%.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. In this problem, we are dealing with a gambler who is playing a game with equal probability of doubling or reducing their stake to half.

The gambler's initial stake is $32. Let us consider the possible outcomes after one play of the game. The stake can either double to $64 or reduce to $16, each with equal probability. If the stake doubles, the gambler has more than their initial stake. If the stake is reduced to half, the gambler has less than their initial stake.

Now, let us consider the possible outcomes after two plays of the game. There are four possible outcomes:

(1) the stake doubles twice and the gambler has

=> $64 * 2 = $128,

(2) the stake doubles then reduces to half and the gambler has

=> $32 * 2 * 0.5 = $32,

(3) the stake reduces to half then doubles and the gambler has

=> $32 * 0.5 * 2 = $32,

(4) the stake reduces to half twice and the gambler has

=> $32 * 0.5 * 0.5 = $8.

We can represent these outcomes using a tree diagram. Each branch represents a possible outcome, and the probability of that outcome is written next to the branch.

After five plays of the game, there are 32 possible outcomes.

We can calculate the probability of the gambler having more than their initial stake by adding up the probabilities of all the outcomes where the gambler has more than $32. This turns out to be 0.6875 or 68.75%.

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The approximate area of the trapezoid is determined as  13.95 unit².

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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Answer:

\(7\%\)

Step-by-step explanation:

Initial temperature = 85 degrees Fahrenheit

Final temperature = 79 degrees Fahrenheit

Percentage change in temperature is given by

\(\dfrac{|\text{Final temperature}-\text{Initial temperature}|}{\text{Initial temperature}}\times 100\%\\ =\dfrac{|79-85|}{85}\times 100\%\\ =7.05\approx 7\%\)

The change in the high temperature from Saturday to Sunday is \(7\%\).

Answer:

speed of James is: 3.75 miles/hour.

Step-by-step explanation:

We need to find the speed of James in miles per hour(mi/hr)

we know that 1 mile=5280 feet

James takes 120 steps in 1 minute so he will cover 120×60 steps in 1 hour.

i.e. he takes 7200 steps in 1 hour.

also each step of James=2.75 feet

total distance covered by James in 1 hour=2.75×7200 feet=19800 feet

\(19800feet=\frac{19800}{5280} miles=3.65miles\)

hence speed of James= (distance covered by james in 1 hour)/1 hour

speed of James=3.75 miles/hour.

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Answer:

We need to find the speed of James in miles per hour(mi/hr)

we know that 1 mile=5280 feet

James takes 120 steps in 1 minute so he will cover 120×60 steps in 1 hour.

i.e. he takes 7200 steps in 1 hour.

also each step of James=2.75 feet

total distance covered by James in 1 hour=2.75×7200 feet=19800 feet

19800feet=\frac{19800}{5280} miles=3.65miles19800feet=

5280

19800

miles=3.65miles

hence speed of James= (distance covered by james in 1 hour)/1 hour

Value of mean is, 40.2

Value of median is, 45

Value of mode is, 28

Value of range is, 25

Given that;

Data set is,

⇒ 28, 45, 53, 28, 47

Now, We can arrange into ascending order as;

⇒ 28, 28, 45, 47, 53

Hence, Value of mean is,

⇒ (28 + 28 + 45 + 47 + 53) / 5

⇒ 40.2

And, The value of median is,

⇒ (5 + 1) / 2

⇒ 6/2

⇒ 3rd term

⇒ 45

The value of mode =28

And, The value of range is,

⇒ 53 - 28

⇒ 25

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Answer:

\( y= cx^2 +dx +e\)

We see that:

\( c = a, d= 2a , e= 3\)

The axis of symmetry is defined by this formula:

\( X= - \frac{d}{2c}\)

And replacing we got:

\( X= -\frac{2a}{2a}= -1\)

Thn the axis of symmetry would be X=-1

Step-by-step explanation:

For this case we have the following function:

\( y = ax^2 +2ax +3\)

If we compare this function with the general expression of a quadratic formula given by:

\( y= cx^2 +dx +e\)

We see that:

\( c = a, d= 2a , e= 3\)

The axis of symmetry is defined by this formula:

\( X= - \frac{d}{2c}\)

And replacing we got:

\( X= -\frac{2a}{2a}= -1\)

Thn the axis of symmetry would be X=-1

Since this equation must hold for all values of x, we can substitute x = i and x = -i to get two equations: 2A + 3i = -5i=> 2A - 3i = 5i=> A = -3/2Therefore, A is equal to -3/2.

A polynomial is a mathematical statement with coefficients and uncertainty that uses only additions, subtractions, multiplications, and powers of positive integer variables. There is just one indeterminate x polynomial identified by the formula x2 4x + 7. The term "polynomial" refers to an expression in mathematics that consists of variables (sometimes referred to as "indeterminates") and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression having variables and coefficients. Only addition, subtraction, multiplication, and non-negative integer exponents are permitted in expressions. The word for these expressions is polynomials.

To find A, we need to perform polynomial long division of P(x) by \(x^2 + 1\)and get the remainder equal to -5x.

          x

   --------------

\(x^2 + 1 | x^3 + 3x^2 - 2Ax + 3\)

         \(x^3 + 0x^2 + x\)

          --------------

               \(3x^2 - 2Ax\)

           \(3x^2 + 0x - 3i\)

                ------------

                    \(2Ax + 3i\)

                \(2Ax + 0x - 2iA\)

                       -----------

                        \(3i + 2iA\)

The remainder of the division is (2A + 3i) when the divisor is \(x^2 + 1\). We know that this remainder is equal to -5x, so we can set up the equation:

2A + 3i = -5x

Since this equation must hold for all values of x, we can substitute x = i and x = -i to get two equations:

2A + 3i = -5i

2A - 3i = 5i

A = -3/2

Therefore, A is equal to -3/2.

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Answer:
Cluster : 60,61,62,63
Gaps: 64,65 , 69,70
Outlier: 71
This is what I learned so don't blame me please!

Step-by-step explanation:

Cluster is numbers all on one side. Outlier can be the largest number or lowest. Normally the alone one.

Answer:

You are correct! But note the syntax:

the computer wants you to type in the box

2/3 x - 2

because "y =" is already written!

Step-by-step explanation:

Answer:

your P will be equal to 8 x

Answer:

C). Circle Graph

Step-by-step explanation:

As per the question, a 'circle graph' would be most adequate to display that the majority of the teenagers prefer to do their study and homework in their bedrooms. A circle graph or pie-chart represents the data in a visually appealing manner using colors to display various proportions of the data that makes it easy to understand for the readers. Thus, more than half of the circle filled with the same color will clearly hint that most of the teenagers love doing their studies in their bedroom. Thus, option C is the correct answer.

This is because the number of pounds can take on an infinite number of values within a range.

The following table shows a series of experiments and associated random variables:ExperimentRandom Variable (x)Values

Continuous or Discrete

a. Take a 15-question examinationNumber of questions answered correctlyDiscreteb. Observe cars arriving at a tollbooth for 1 hourNumber of cars arriving at tollboothDiscretec. Audit 50 tax returnsNumber of returns containing errorsDiscreted. Observe an employee's workNumber of nonproductive hours in a nine-hour workdayDiscretee. Weigh a shipment of goodsNumber of poundsContinuous

The random variable in experiment a is discrete. This is because the number of questions answered correctly can only take on a finite number of values.The random variable in experiment b is also discrete. This is because the number of cars arriving at the tollbooth can only take on a finite number of values.The random variable in experiment c is also discrete. This is because the number of returns containing errors can only take on a finite number of values.The random variable in experiment d is discrete. This is because the number of nonproductive hours in a nine-hour workday can only take on a finite number of values.The random variable in experiment e is continuous.

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Answer:

Step-by-step explanation:There are a total of 20 sweets in the bag (5 red + 6 blue + 9 yellow).

To find the probability that Sarah takes two sweets of the same color, we need to find the probability of her choosing a sweet of a specific color on her first pick and then the probability of her choosing another sweet of that same color on her second pick.

For example, if she chooses a red sweet on her first pick, the probability of that happening is 5/20, or 1/4. Then the probability of her choosing another red sweet on her second pick, given that she already picked one, is 4/20, or 2/10. Therefore the probability of her choosing two red sweets in a row is (1/4) * (2/10) = 1/20.

Similarly, the probability of her choosing two blue sweets in a row is (6/20) * (5/20) = 3/50.

The probability of her choosing two yellow sweets in a row is (9/20) * (8/20) = 9/100.

The probability of her choosing two sweets of the same color is the sum of the probability of her choosing two red sweets, two blue sweets, or two yellow sweets in a row.

P(Two same color) = 1/20 + 3/50 + 9/100 = 11/50

So, the probability of her choosing two sweets of the same color is 11/50.

The price of the rechargeable drill in the home improvement stores is P(m) = 1.2m + 4, where m is the manufacturing total cost.

P(m) = 1.2m + 4

P(m) = 1.2(manufacturing cost) + 4

P(m) = 1.2m + 4

The manufacturer of tools charges $4 more than its manufacturing cost for a rechargeable drill to a chain of home improvement stores. Following that, the chain sells each drill for 120 percent of what it paid the manufacturer.. Therefore, the price of the rechargeable drill in the home improvement stores can be represented by the function P(m), where m is the manufacturing cost of the drill. The equation P(m) = 1.2m + 4 shows that the price of the rechargeable drill in the home improvement stores is equal to 1.2 times the manufacturing cost plus $4. This equation indicates that the manufacturer of tools charges $4 more than its manufacturing cost and the home improvement stores then increase the price of the drill by 20% of the price they paid to the manufacturer. Therefore, the total cost of the rechargeable drill in the home improvement stores is 1.2m + 4, where m is the manufacturing cost of the drill.

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Answer:

z=53 y=37 and x=90

Step-by-step explanation:

Since there's a transversal, x is 90 because of alternate angles. Also alternate exterior angles are z so z=53 degrees. 180-(90+53)=37 degrees is y.

Answer:

data given

Universal set 40people

people who can sew 14

people who can knit 12

people who can do both 5

Step-by-step explanation:

•people who can sew only

=14-5

=9

•people who can knit only

=12-9

=7

Union of people who can sew and the one who can knit

=9+7+5

=21

who do neither

=40-21

=19

: .people neither sew or knit are 19

The degrees of freedom in the given regression model is 33.

In a regression model that has 40 observations, 6 independent variables and one intercept, the degrees of freedom can be calculated using the formula below:

Degrees of freedom = (number of observations) - (number of independent variables + 1)

Degrees of freedom = 40 - (6 + 1)Degrees of freedom = 33

Therefore,

the correct answer is option (a) 33.Explanation:

In the given scenario, the number of observations is 40, the number of independent variables is 6, and the model has one intercept.

To find the degrees of freedom, we can use the formula given above.

Degrees of freedom = (number of observations) - (number of independent variables + 1)Substituting the given values in the formula, we get:

Degrees of freedom = 40 - (6 + 1)Degrees of freedom = 40 - 7Degrees of freedom = 33

Therefore, the degrees of freedom in the given regression model is 33.

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Answer:

\(x=\pm5\)

Step-by-step explanation:

First, add 75 to each side.

\(3x^2-75+75=0+75\\3x^2=75\)

Next, divide each side by 3.

\(x^2=25\)

Now, you can take the square root.

\(x = \pm\sqrt25}\)

\(x=\pm 5\)

Answer:

35 feet

Step-by-step explanation:

The problem is a right angle triangle problem and we have to solve it using pythagoras theorem

Let the length of the wire be x

So;

x^2 = 34^2 + 8^2

x = √34^2 + 8^2

x = 35 feet

False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.

To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).

Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.

Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:

f'(x) = 5cos(x) - sin(x).

This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).

In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).

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Answer:

24

Step-by-step explanation:

GCF means greatest common factor.

Factors of 24:  1, 2, 3, 4, 6, 8, 12, 24

Factors of 48:  1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The greatest common factor between both sets is 24, so the GCF of 24 and 48 is 24.

Answer:

C

Step-by-step explanation:

A is wrong because as an example take 14. The last digit 4 is divisible by 4 but the number 14 is not evenly divisible by 4.

B is wrong because as an example take 26. 26 is even but is not evenly divisible by 4.

D is wrong because as an example take 10. The last digit in 10 is zero but 10 is not evenly divisible by 4.

Answer:

Step-by-step explanation:

-60 -60 -60 0 0