Part 1: Let f(x)=2x−1 and g(x)=−x2+x−3. Which equation shows h(x), where h(x)=f(x)⋅g(x)?

h(x)=x2+x+3

h(x)=−x2+3x−4

h(x)=−2x3+x2−5x−3

h(x)=−2x3+3x2−7x+3
Part 2: Is function f even, odd, or neither?





Part 3: Is function g even, odd, or neither?

The confidence interval for the proportion of students attending a football game is [0.6592, 0.7044].

Confidence interval can be calculated by below formula

\(Pcap - Z_{\alpha /2}\sqrt{\frac{Pcap(1 - Pcap)}{n} } < p < Pcap + Z_{\alpha /2}\sqrt{\frac{Pcap(1 - Pcap)}{n} }\)

where the left part is the lower interval and right side is the higher interval.

Pcap = 750/1100

Pcap = 0.6818

Again to calculate \(Z_{\alpha /2}\) , as we know that the level of confidence is 90 percent so its value will be 1.645

now putting the values on the both side we can get ,

0.6818 - 1.645 x 0.014 < p  <  0.6818 + 1.645 x 0.014

0.6818 - 0.023  < p < 0.6818 + 0.023

0.6588 < p < 0.7048

the nearest value is [0.6592, 0.7044]

Hence the confidence interval for the proportion of students attending a football game is [0.6592, 0.7044]

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Answer:

6/10 | 60% | 0.60

¾ | 75% | .75

23/100 | 23% | .23

⅛ | 12.5% | .125

9/50 | 18% | .18

⅔ | 67% | .67

The distribution for X is a negative binomial distribution, denoted as nb(x;6, 188​), with parameters r = 6 (number of successes), p = 8/18 (probability of success in each trial).

To compute the probabilities:

P(X = 2): nb(2;6, 8/18)

P(X ≤ 2): nb(0;6, 8/18) + nb(1;6, 8/18) + nb(2;6, 8/18)

P(X ≥ 2): 1 - P(X < 2) = 1 - P(X ≤ 1)

To calculate the mean value and standard deviation of X:

Mean (μ) = r * (1 - p) / p

Standard Deviation (σ) = sqrt(r * (1 - p) / (p^2))

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Answer:

Post them individually

Step-by-step explanation:

1. B

2. 4th option ,----> Megan's at 2.5 per week

Megan's plant:

slope = 7-4.5/2-1 = 2.5= growth rate

Suzanne's plant:

slope = 7-5/2-1= 2 = growth rage

3.D

4 2nd option , $2 for each song

Rate of change = 6-4/3-2 = 2

The function satisfies the properties of being continuous and differentiable everywhere and having a horizontal asymptote at y = 2. However, it does not satisfy the conditions for f'(x) < 0 everywhere it is defined and f''(x) < 0 on the intervals (-∞,1) and (2,4), and f''(x) > 0 on the intervals (1,2) and (4,∞).

To sketch a graph that satisfies all the given properties, we can consider the following function:

\(f(x) = 2 - e^(-x)\)

Let's analyze each property:

a. Continuous and differentiable everywhere:

The function \(f(x) = 2 - e^(-x)\) is continuous and differentiable for all real numbers. The exponential function is continuous and differentiable for any x, and subtracting it from 2 maintains continuity and differentiability.

b. f′(x) < 0 everywhere it is defined:

Taking the derivative of f(x), we have:

\(f'(x) = e^(-x)\)

Since \(e^(-x)\) is always positive for any x, f'(x) is always positive, which means f(x) does not satisfy this property.

c. A horizontal asymptote at y = 2:

As x approaches infinity, the term approaches 0. Therefore, the limit of f(x) as x approaches infinity is:

lim(x→∞) f(x) = lim(x→∞)\((2 - e^(-x))\)

= 2 - 0

= 2

This shows that f(x) has a horizontal asymptote at y = 2.

d. f′′(x) < 0 on (−∞,1) and (2,4), f′′(x) > 0 on (1,2) and (4,∞):

Taking the second derivative of f(x), we have:

\(f''(x) = e^(-x)\)

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The correct statements are:

ln( yx​)= ln(y)ln(x)​

log 5​(xy)=log 5​(x)⋅log 5​(y)

log 2​( yx​)=log 2​(x)−log 2​(y)

log 4​(xy)=log 4​(x)+log 4​(y)

The true statements from the given options are:

1. ln( yx​) = ln(y)ln(x) (This is the property of logarithms known as the power rule for natural logarithms.)

2. log 5​(xy) = log 5​(x)⋅log 5​(y) (This is the product rule for logarithms with base 5.)

3. log 2​( yx​) = log 2​(x)−log 2​(y) (This is the quotient rule for logarithms with base 2.)

4. log 4​(xy) = log 4​(x)+log 4​(y) (This is the product rule for logarithms with base 4.)

Therefore, the true statements are:

ln( yx​)= ln(y)ln(x)​

log 5​(xy)=log 5​(x)⋅log 5​(y)

log 2​( yx​)=log 2​(x)−log 2​(y)

log 4​(xy)=log 4​(x)+log 4​(y)

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Answer:

12

Step-by-step explanation:

8+8+9+11+24=60

60/5=12

\(\huge\textsf{Hey there!}\)

\(\large\text{Well, you know that mean means average. You have to find the}\\\large\text{sum of all of the number in the data set and divide the sum by}\\\large\text{by the total numbers in the data.}\)

\(\mathsf{\dfrac{8+8+9+11+24}{5}}\)

\(\mathsf{8 + 8 + 9 + 11 + 24}\\\mathsf{8 + 8 = \boxed{\bf 16}}\\\mathsf{= 16 + 9 + 11 + 24}\\\mathsf{16 + 9 = \boxed{\bf 25}}\\\mathsf{= 25+11+24}\\\mathsf{25+11=\boxed{\bf 36}}\\\mathsf{36+ 24}\\\boxed{= \mathsf{\bf 60}}\)

\(\mathsf{\dfrac{60}{5}}\\\\\\\mathsf{= \dfrac{60\div5}{5\div5}}\\\\\\\mathsf{= 60\div5\rightarrow\boxed{\bf 12}}\\\\\\\mathsf{= 5\div5\rightarrow\boxed{\bf 1}}\\\\\mathsf{\rightarrow \dfrac{12}{1}= \boxed{\bf 12}}\)

\(\boxed{\boxed{\large\textsf{Answer: \huge Your \bf {MEAN is 12}}}}\huge\checkmark\)

\(\large\textsf{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:1/2(1/t+6)1/2t^2

Step-by-step explanation:

Find the derivative by using the chain and power rules.

The derivative of the function f(t) = √t/\(t^{2\)+6 is given by the expression -1/2\(t^{(1/2)/(t^{2 + 6)^{2\).

To find the derivative, we need to apply the power rule for derivatives. The power rule states that for a function

f(x) = \(x^{n\) the derivative is given by \(n*x^{(n-1)\).

In this case, we have a fraction and a square root of t. The fraction is of the form x/\(x^{n\), so we can rewrite it as x/\(x^{n\). Now, applying the power rule, the derivative of the fraction is given by 1*\(x^{(1-n)/x^{n\)or \(1/x^{(n-1)\).

For the square root, we can rewrite it as √\(t^{1\), so applying the power rule, the derivative of the square root is given by \(1/2t^{(1/2)\).

Now, putting everything together, we have the following expression for the derivative: -1/2\(t^{(1/2)/(t^{2 + 6)^{2\).

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Answer:

x = 18/7

Step-by-step explanation:

First, you want to combine like terms

3x + 2 + 4x - 20

7x - 18

If the equation is equal to zero, then you would get x by itself.

7x - 18 = 0

7x = 18

x = 18/7

Answer:

Step-by-step explanation:

Here you go mate

Step 1

3x+2+4x-20  Equation/Question

Step 2

3x+2+4x-20  simplify by taking terms

(3x+4x)+(2+(-20))

answer

7x-18

The derivatives of ws and wt in terms of s and t are 4/3 and 10/3, respectively. This is calculated using the chain rule and the derivatives of w, s, and t.

To find the derivatives of ws and wt, we will use the chain rule. First, we need to rewrite w in terms of s and t: w = 2(s+3t) - 2(s-3t)/3st + 2(s-3t). Then, for the derivative of ws, we can rewrite it as dw/ds, and for the derivative of wt, we can rewrite it as dw/dt.We will use the chain rule to find the derivatives of ws and wt. The chain rule states that if we have a function f(g(x)) and we want to find its derivative with respect to x, we can take the derivative of f with respect to g, multiplied by the derivative of g with respect to x.For ws, the derivative of w with respect to s is 2 - 2/3st + 2. The derivative of s with respect to s is 1. So, the derivative of ws is 2 - 2/3st + 2.For wt, the derivative of w with respect to t is 6 - 2/3st + 2. The derivative of t with respect to t is 1. So, the derivative of wt is 6 - 2/3st + 2.Therefore, the derivatives of ws and wt, in terms of the independent variables s and t, are 2 - 2/3st + 2 and 6 - 2/3st + 2, respectively.

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Answer:

No they are not equivalent.

Step-by-step explanation:

2(x - 2) + 3

First distribute the 2. It goes to both the x and also to the - 2

= 2x - 4 + 3

Add - 4 + 3

= 2x - 1

This is not equal to 2x - 7

Answer:

5

0

5

10

Step-by-step explanation:

Since the question is asking the absolute value of h, the only number that changes is -5 to 5.

Step-by-step explanation:

The blanks on the R are just the absolute values of the numbers on the L

x     f(x)

-5     5

0      0

5       5

10     10           that's it

Answer:

It is a metaphor.

Step-by-step explanation:

Hope it helps

To find a recursive Nevill's method when interpolating a table using a polynomial at x = 4.1, we can use the following steps:

Step 1: Set up the given data in a table with two columns, one for f(x) and the other for x.

f(x)             x

36               1.16164956

3.80201036       4.0

0.30663842       4.2

0.35916618       -123926000.4

Step 2: Begin by finding the first-order differences in the f(x) column. Subtract each successive value from the previous value.

Δf(x)            x

-32.19798964     1.16164956

-3.49537194      4.0

-0.05247276      4.2

Step 3: Repeat the process of finding differences until we reach a single value in the Δf(x) column. Continue subtracting each successive value from the previous one.

Δ^2f(x)          x

29.7026177       1.16164956

3.44289918       4.0

Step 4: Repeat Step 3 until we obtain a single value.

Δ^3f(x)          x

-26.25971852     1.16164956

Step 5: Calculate the divided differences using the values obtained in the previous steps.

Divided Differences:

Df(x)             x

36                1.16164956

-32.19798964     4.0

29.7026177       4.2

-26.25971852     -123926000.4

Step 6: Apply the recursive Nevill's method to find the interpolated value at x = 4.1 using the divided differences.

f(4.1) = 36 + (-32.19798964)(4.1 - 1.16164956) + (29.7026177)(4.1 - 1.16164956)(4.1 - 4.0) + (-26.25971852)(4.1 - 1.16164956)(4.1 - 4.0)(4.1 - 4.2)

Solving the above expression will give the interpolated value at x = 4.1.

Q2: To construct an approximation polynomial using the Hermite method, we follow these steps:

Step 1: Set up the given data in a table with three columns: f(x), f'(x), and x.

f(x)             f'(x)              x

2.572152         7.615964          1.2

3.602102         13.97514          1.3

5.797884         34.61546          1.4

14.101442        199.500           1.5

Step 2: Calculate the divided differences for the f(x) and f'(x) columns separately.

Divided Differences for f(x):

Df(x)            \(D^2\)f(x)           \(D^3\)f(x)

2.572152         0.51595           0.25838

Divided Differences for f'(x):

Df'(x)           \(D^2\)f'(x)

7.615964         2.852176

Step 3: Apply the Hermite interpolation formula to construct the approximation polynomial.

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Given that Viggo is 9 years old and his sister Wren is 6 years old. And €75 is divided between them in the ratio of their ages. We need to find out how much money Viggo will get.

To find the amount of money Viggo gets, we need to understand the concept of ratio. Ratio is the quantitative relation between two numbers showing the number of times one value contains or is contained within the other. To find the amount of money Viggo gets, we need to find out the ratio of his age to the total age of both Viggo and Wren.

Age of Viggo = 9 years Age of Wren = 6 years Total age of both = 9 + 6 = 15So, the ratio of Viggo's age to the total age of both is 9 : 15 or 3 : 5.Now, we can divide the €75 in the ratio 3 : 5. This is done by dividing the total amount into 3 + 5 = 8 parts. Then, the amount that Viggo gets can be found by multiplying his share (3 parts) with the total amount (€75) and dividing by the total number of parts (8).Amount received by Viggo = (3/8) × €75= €28.The amount of money that Viggo will get is €28.

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Any data that can be represented numerically is called data is quantitative.

The correct option is (a)

Quantitative data is data that can be counted or measured in numerical values.

Qualitative data is non-numeric information, such as in-depth interview transcripts, diaries, anthropological field notes, answers to open-ended survey questions, audio-visual recordings and images.

Qualitative data describes qualities or characteristics. It is the descriptive and conceptual findings collected through questionnaires, interviews, or observation.

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A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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Answer:

No it's not a function

Step-by-step explanation:

Because it doesn't pass the vertical line test.

Answer:

Mary should be correct because -0 doesn't exist.

Answer:

The answer is 2

Step-by-step explanation:

-5-(-7) = 5 + ?

-5-(-7)

-5 + 7 = 2

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Answer:

1

Step-by-step explanation:

K(x)=5^(x+2)

Let x = -2

K(-2)=5^(-2+2)

       = 5^0

      = 1

Answer:

k(- 2) = 1

Step-by-step explanation:

Substitute x = - 2 into k(x) , that is

k(- 2) = \(5^{-2+2}\) = \(5^{0}\) = 1 [ \(a^{0}\) = 1 ]

As the variance/mean ratio is significantly greater than 1, the population is found to be a clumped distribution.

A clumped distribution, also known as an aggregated distribution, is a pattern of dispersion or arrangement of individuals within a population where they are found in groups or clusters. This means that individuals within a population are more likely to be found in certain areas, while other areas may have few or no individuals.

From the table in the attached image, it can be seen that

the variance= sum of (x -  0.6)^2/ sum of frequency

= 362.88/288

= 1.26

Variance/mean = 1.26/0.6 = 2.1 which is greater than 1

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Answer:

a = - 3

Step-by-step explanation:

r² - 6r + 9

consider the factors of the constant term (+ 9) which sum to give the coefficient of the r- term (- 6)

the factors are - 3 and - 3 , since

- 3 × - 3 = + 9 and - 3 - 3 = - 6 , then

r² - 6r + 9

= (r - 3)(r - 3)

= (r - 3)² ← in the form (r + a)²

with a = - 3

The value of x = -4

The given linear function is f(x) = -4x+8

We have to find the x corresponding to f(x) = 24

For our convenience, let f(x) = y

Then y = -4x + 8

This equation implies y in terms of x.

Isolating x to one side of the equation, we get,

x = (y - 8)/-4 = (8-y)/4

This equation gives x in terms of y.

So when f(x) = y = 24,

x = (8-24)/4

⇒ x = -4

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2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

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Answer:

4.5

Step-by-step explanation:

15% of 30 is 4.5

30/100=0.3

0.3*15=4.5

Answer:

This is my answer is

Force=mass × acceleration.

120=mass × 2.

120=2m.

mass=60kg

Answer:

B. 642.22 units squared

Step-by-step explanation:

Knowing that QP ║ MN and ∠QLP = ∠MLN, then ΔQLP ~ ΔMLN.

That means corresponding sides and heights have the same ratios.

We know that QP = 25, which corresponds to MN = 34. Also, the height of ΔQLP, LS, corresponds to the height of ΔMLN, LR = LS + SR = LS + 10. Let's say LS = x.

We can now write:

QP / MN = LS / LR

25 / 34 = x / (x + 10)

Cross-multiply:

34 * x = 25 * (x + 10)

34x = 25x + 250

34x - 25x = 250

9x = 250

x = 250/9 ≈ 27.78 units

So, LS = 27.78 units and LR = LS + SR = 27.78 + 10 = 37.78 units.

The area of a triangle is denoted by A = (1/2) * b * h, where b is the base and h is the height.

Here, the base of ΔLMN is MN = 34, and the height is LR = 37.78. Plug these in:

A = (1/2) * b * h

A = (1/2) * 34 * 37.78 ≈ 642.22 units squared

The answer is thus B.

~ an aesthetics lover