The table contains some input-output pairs for the functions \( f \) and \( g \). Evaluate the following expressions. a. \( f(g(7))= \) b. \( f^{-1}(10)= \) c. \( g^{-1}(10)= \)

Answer:

Jose stretched the taffy the farthest and Maria stretched it the least

Step-by-step explanation:

Distance stretched by George = 3 feet

Distance stretched by Jose is \(1\dfrac{1}{3}\) times as much as George so

\(3\times 1\dfrac{1}{3}=3\times\dfrac{4}{3}=4\ \text{feet}\)

Distance stretched by Jose is \(4\ \text{feet}\)

Maria streched the taffy \(\dfrac{2}{3}\) times as George

\(3\times \dfrac{2}{3}=2\ \text{feet}\)

Maria stretched the taffy by \(2\ \text{feet}\)

Sally stretched it \(\dfrac{6}{6}\) so \(1\ \text{feet}\)

So, Jose stretched the taffy the farthest and Maria stretched it the least.

Marco's data points have a better line of best fit based on a comparison of Correlation coefficients.

Marco is incorrect in stating that his data points have a better line of best fit than Landon based solely on the comparison of correlation coefficients. The magnitude of the correlation coefficient alone does not determine the quality or strength of the line of best fit.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1. A positive correlation coefficient (such as 0.85) indicates a positive linear relationship, while a negative correlation coefficient (such as -0.85) indicates a negative linear relationship. The closer the correlation coefficient is to -1 or +1, the stronger the relationship. A correlation coefficient of 0 indicates no linear relationship.

In the case of Landon and Marco, both correlation coefficients have the same absolute value of 0.85, suggesting a strong linear relationship. However, the negative sign for Landon's correlation coefficient indicates a negative linear relationship, while the positive sign for Marco's correlation coefficient indicates a positive linear relationship.

The comparison between -0.85 and 0.85 should not be made in terms of greater or lesser quality of the line of best fit. The choice of a positive or negative correlation depends on the context and nature of the variables being analyzed.

The appropriateness of the line of best fit and the goodness-of-fit of the model should be evaluated based on additional factors such as the data points' distribution around the line, residuals, and the overall context of the analysis. These aspects provide more comprehensive insights into the quality of the fit and the reliability of the relationship being represented.

Therefore, Marco's data points have a better line of best fit solely based on a comparison of correlation coefficients. The interpretation of the correlation coefficient requires considering the nature of the variables and other factors influencing the analysis.

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To estimate the number of sandwiches the deli manager should anticipate selling when 178 customers visit the deli, we can analyze the given data and approximate it using a linear function.

By observing the table, we notice that the number of sandwiches sold varies with the number of customers. This indicates a relationship between the two variables.

To estimate the number of sandwiches, we can fit a line to the data points and use the linear function to make predictions. Using a statistical software or a spreadsheet, we can perform linear regression analysis to find the equation of the best-fit line. However, since we are limited to text-based interaction, I will provide a general approach.

Let's assume the number of customers is the independent variable (x) and the number of sandwiches is the dependent variable (y). Using the given data points, we can calculate the equation of the line.

After calculating the linear equation, we can substitute the value of 178 for the number of customers (x) into the equation to estimate the number of sandwiches (y).

Please provide the data points for the number of sandwiches sold corresponding to each number of customers so that I can perform the linear regression analysis and provide a more accurate estimate for you.

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Answer:54

Step-by-step explanation: You simply minus $66 from $120. I am fairly sure that i am right. If my answer is wrong, then please forgive me.

Answer:

\(\frac{68285}{44}\) or \(1551.93181818...\)

Step-by-step explanation:

\(\frac{9755}{2(\frac{22}{7})}\\\\\)

The volume = LBH = x²y

.°. If a pyramid and a prism have the same base and height, their volumes are always in the ratio of 1/3xVolume of prism.

The volume of Pyramid = 1/3*x²y

h = 3 *1/3x²y/x²

h = 3*1/3x²y*1/x²

h = 3*1/3y

Answer: possibly 3/5?

Step-by-step explanation: Well y=Mx+b

m= slope

b= y intercect

b= 3

and if you follow the cordantes your secound dot is 3/5

Answer:

Explanation:You can dowly/3fcEdSxnload the answer here. Link below!

bit.

Answer:

.20 per minute.If you dives 1 mile by 5 min u will get .20

Answer:

A. The probability of a temperature from 30 degrees to 90 degrees

Step-by-step explanation:

The range of the graph is from 60 to 160 degrees, so we're looking for options that fit within that range.

A. 30 degrees is lower than 60, outside the range

B. Fits

C. Need more information

D. 30 degrees is too low, outside the range

Answer: 0

Step-by-step explanation:

The slope of a line that contains the points (13, -2) and (3, -2) would be 0, since the y-coordinate of both points is the same. The slope of a line is determined by the difference in the y-coordinates of the two points, divided by the difference in their x-coordinates. In this case, the difference in the y-coordinates is 0, so the slope is 0.

The unit rate of running 2.3 km in 7 minutes is 5.48 metres per second.

Unit rate can be defined as a measure used to represent how many units of one type of quantity corresponds to one unit of anther type of quantity.

Here the distance is given in kilometres (km) which can be converted into metres by multiplying by 1000 as,

2.3 km = 2.3*1000 metres

= 2300 metres

Here the time taken to cover 2.3 km is 7 minutes which can be converted ito seconds by multiplying by 60 as,

7 minutes= 7*60 seconds

= 420 seconds

Hence the unit rate of running 2.3 km in 7 minutes expressed in metre per second is calculated as = 2300 metres / 420 seconds

= 5.4761 metres per second

= 5.48 metres per second (approximately)

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A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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Answer:

C: 122

Step-by-step explanation:

as in angle C (which is empty) is 122 degrees because I did the math.

The C in pentagon ABCDE is 122.

We know that each angle should be 90 degrees

Since there is 4 angles so total should be 450 degrees

So,

= 450 - 105 - 86 - 137

= 122 degrees

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Answer:

xem

Step-by-step explanation:

Compute the length of the curve r(t)=3ti+2tj+(t2−4)k over the interval 0≤t≤8 HINT use the formula ∫t2+a2​dt=21​tt2+a2​+21​a2ln(t+t2+a2​)+C

To compute the length of the curve given by the vector function r(t) = 3ti + 2tj + (t²2 - 4)k over the interval 0 ≤ t ≤ 8, we can use the arc length formula:

L = ∫√(dx/dt)²2 + (dy/dt)²2 + (dz/dt)²2 dt

First, let's find the derivatives of x, y, and z with respect to t:

dx/dt = 3

dy/dt = 2

dz/dt = 2t

Now, we can substitute these derivatives into the arc length formula:

L = ∫√(3²2 + 2²2 + (2t)²2) dt

L = ∫√(9 + 4 + 4t²2) dt

L = ∫√(13 + 4t²2) dt

To integrate this expression, we can use the hint given:

∫√(13 + 4t²2) dt = 1/2 ∫(1 + 4t²2)²(1/2) dt

                  = 1/2 [t√(1 + 4t²2) + (1/4)ln(t + √(1 + 4t²2)) + C]

Now we can evaluate this expression over the interval 0 ≤ t ≤ 8:

L = 1/2 [(8√(1 + 4(8²2)) + (1/4)ln(8 + √(1 + 4(8²2)))) - (0√(1 + 4(0²2)) + (1/4)ln(0 + √(1 + 4(0²2))))]

Simplifying further will give the length of the curve.

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Finding the length of the curve C from (0, 0, 4) to (π, 2, 0)We are given the vector function of curve C and we need to find the length of the curve C from (0, 0, 4) to (π, 2, 0).

To find the required length, we integrate the magnitude of the derivative of the vector function with respect to t (that is, the speed of the particle that moves along the curve), that is, Finding the parametric equation for the tangent lines that are parallel to the z-axis at the point on curve C. The direction of the tangent line to a curve at a point is given by the derivative of the vector function of the curve at that point.

Since we are to find the tangent lines that are parallel to the z-axis, we need to find the points on the curve at which the z-coordinate is constant. These points will be the ones that lie on the intersection of the curve and the planes parallel to the z-axis. So, we solve for the z-coordinate of the vector function of curve we have the points on curve C at which the z-coordinate is constant. Now, we need to find the derivative of r(t) at these points and then the direction of the tangent lines to the curve at these points.

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Answer:

37.6991

Step-by-step explanation:

25.1327 + 12.5664

Answer:

History of mathematics

Several civilizations — in China, India, Egypt, Central America and Mesopotamia — contributed to mathematics as we know it today. The Sumerians were the first people to develop a counting system. Mathematicians developed arithmetic, which includes basic operations, multiplication, fractions and square roots. The Sumerians’ system passed through the Akkadian Empire to the Babylonians around 300 B.C. Six hundred years later, in America, the Mayans developed elaborate calendar systems and were skilled astronomers. About this time, the concept of zero was developed.

Step-by-step explanation:which includes basic operations, multiplication, fractions and square roots. The Sumerians’ system passed through the Akkadian Empire to the Babylonians around 300 B.C. Six hundred years later, in America, the Mayans developed elaborate calendar systems and were skilled astronomers. About this time, the concept of zero was developed.

Answer: 3 sq. m

Step-by-step explanation:

assuming you are solving for the large, solid triangle, you can subtract the whole minus the part

to solve for the whole, (3 + 1) [base] x 2 [height] / 2 = 4

to solve for the dotted part, 1 [base] x 2 [height] / 2 = 1

whole - part, or 4 - 1, equals 3

Answer: y=2.17(2.96)

Step-by-step explanation: i took the test

The number of blue tickets is 50 tickets. The result is obtained by using the concept of operation with fractions.

In a hat, we have:

Find the number of blue tickets!

Let's say all tickets is a. Then,

The remaining section (pink tickets) is

= 1 - (green + white + blue) tickets

= 1 - (1/10 + 1/2 + 1/4)

= 1 - (2/20 + 10/20 + 5/20)

= 20/20 - 17/20

= 3/20

All tickets are

3/20 = 30/a

a = (20 × 30)/3

a = 20 × 10

a = 200 tickets

The blue tickets are

= 1/4 a

= 1/4 (200)

= 50 tickets

Hence, the blue tickets in the hat are 50 tickets.

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Answer:

439.6

Step-by-step explanation:

r times 2 (Because 70 is half of the...)=140 times pie or just round it to 3.14

So= 70 times 2 times 3.14

Answer:

-7 and 10

Step-by-step explanation:

\(2x^2-6x-140=0\)

Divide both sides by 2

\(x^2-3x-70=0\)

From the possible solutions given, we know this equation can easily be factored.

\((x-10)(x+7)=0\)

\(\therefore x_1=-7 \text{ and } x_2=10\)

A conditional equation is neither an identity nor a contradiction. It is a statement that is only true under certain conditions.

A conditional equation is an equation that expresses a condition. It has two parts: a hypothesis (or antecedent) and a conclusion (or consequent). The hypothesis states that a certain condition must be met in order for the conclusion to be true. For example, the equation "if x = 4, then x + 1 = 5" is a conditional equation. If the condition (x = 4) is true, then the conclusion (x + 1 = 5) is also true. However, if the condition is false, then the conclusion is also false. Therefore, a conditional equation is neither an identity nor a contradiction, but rather a statement that is only true under certain conditions.

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Answer:

The first one

\( log_{11} \: (x)\)

Step-by-step explanation:

f(x) = 11^x

Here are the steps to find the inverse of a function:

1. Let f(x)=y

2. Make x the subject of formula.

3. Replace y by x.

\(11 {}^{x} = y \\ \: log(11 {}^{x} ) = log(y) \\ x log(11) = log(y) \\ x = \frac{ log(y) }{ log(11) } = log_{11}(y) \\ f {}^{ - 1} (x) = log_{11}(x) \)

Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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Our final rational function becomes: g(x) =\([(x + 4)(ax + b)(x + 3)^2(x + 1)] / [(x + 4)(cx + d)(x - 1)^2]\)

To create a rational function g(x) that satisfies the given properties, we can start by considering the horizontal asymptote and the hole.

Given that the horizontal asymptote is y = 0, we know that the degree of the polynomial in the numerator is less than or equal to the degree of the polynomial in the denominator.

Considering the hole at (-4, -3/19), we can introduce a factor of (x + 4) in both the numerator and denominator to cancel out the common factor. This will create a hole at x = -4.

So far, we have:

g(x) = [(x + 4)(ax + b)] / [(x + 4)(cx + d)]

Next, let's consider the local minimum at (-3, -1/6) and the local maximum at (1, 1/2).

To ensure a local minimum at x = -3, we can make the factor (x + 3) squared in the denominator, so that it does not cancel out with the numerator. We can also choose a positive coefficient for the factor in the numerator to create a downward-facing parabola.

To ensure a local maximum at x = 1, we can make the factor (x - 1) squared in the denominator, and again choose a positive coefficient for the factor in the numerator.

Adding these factors, we have:

g(x) =\([(x + 4)(ax + b)(x + 3)^2] / [(x + 4)(cx + d)(x - 1)^2]\)

Finally, we consider the x-intercept at x = -1 and the y-intercept at y = 1/3.

To achieve an x-intercept at x = -1, we can set the factor (x + 1) in the numerator.

To achieve a y-intercept at y = 1/3, we set the numerator constant to 1/3.

Multiplying these factors, our final rational function becomes:

g(x) = \([(x + 4)(ax + b)(x + 3)^2(x + 1)] / [(x + 4)(cx + d)(x - 1)^2]\)

Where a, b, c, and d are coefficients that can be determined by solving a system of equations using the given properties.

Please note that without additional information or constraints, there are multiple possible rational functions that can satisfy these properties. The function provided above is one possible solution that meets the given conditions.

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

Please check explanations for answer

Step-by-step explanation:

Here, we want to fill out the properties of the given expression

1. Polynomial

Yes, it is a polynomial as it satisfies the properties

2. Degree

The degree is the highest power

we have a raiders to 2 and b raised to 1 giving the total power as 3

3. It has just two terms

4. It is a monomial

Answer:

its (b^2+a^2) (x^2+y^2)