Find a formula for g′(x) and determine the slope g′(−1) for the following function. g(x)=5e^x/3e^x-2

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

From the question,

We have that:

The values of each composite function are:

a) -1

b) -1

c) 2

d) 0

e) 2

f) -4

We have,

These are composite functions.

It is written as:

(f o g) (x) = f (g(x))

Now,

From the table, the values for each function f and g at specific values x are taken.

a.

(f o g)(1)

f(g(1)) = f(0) = -1

b.

(f o g) (-1)

f(g(-1)) = f(0) = -1

c.

(g o f) (-1)

g(f(-1)) = g(-2) = 2

d.

(g o f) (0)

g(f(0)) = g(-1) = 0

e.

(g o g) (-2)

g(g(-2)) = g(2) = 2

f.

(f o f) (-1)

f(f(-1)) = f(-2) = -4

Thus,

The values of each composite function are:

-1, -1, 2, 0, 2, and -4.

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Answer:

Draw open circle AT 11

Shade all numbers to the right of 11

Step-by-step explanation:

Have a great day!

Answer:

its A,B

Step-by-step explanation:

88.89 m³ of water will fill the Larger swimming pool.

The volume of a rectangular prism is given by V = lwh, where l is the length, w is the width, and h is the height. In this case, we have a pool that is in the shape of a rectangular prism and is filled with 15 m³ of water. Let's call the length of this pool "L", the width "W", and the height "H".

Then, we can write the equation:

V = LWHNow, we are told that there is a similar pool that has dimensions that are increased by a scale factor of 4/3. This means that the new length of the pool is (4/3)L, the new width is (4/3)W, and the new height is (4/3)H. We want to find out what volume of water will fill the larger swimming pool.

Let's call the volume of the larger swimming pool V', then we can write: V' = (4/3)L(4/3)W(4/3)H = (64/27)LWH

So, we can see that the volume of the larger swimming pool is (64/27) times the volume of the original swimming pool. To find out how much water will fill the larger swimming pool,

we need to multiply the volume of the larger swimming pool by the density of water. The density of water is approximately 1000 kg/m³ or 1 g/cm³, so we can use either of these values to convert the volume from cubic meters to kilograms or cubic centimeters to grams.

For simplicity, we will use the density of water in kg/m³. The volume of larger swimming pool = (64/27)LWH Volume of water needed to fill a larger swimming pool = (64/27)LWH × 1000 kg/m³= (64000/27)LWH kg= (2400/27) m³ = 88.89 m³

Therefore, 88.89 m³ of water will fill the larger swimming pool.

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The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

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The proportion of population having score between 65 to 110 is 81.85%.

We have-

Mean of population = 80

Standard deviation of population = 15

We are supposed to find the proportion of the population corresponding to scores between 65 and 110.

According to the formula of the Z-score.

z = (x-μ)/σ

X=interval, μ= population mean ,

σ= standard deviation

Here,x = 65,μ= 80,σ= 15 andz = (65-80)/15z = -1

For Z=-1, From the z-table, the area to the left is 0.1587

Now, we need to find the area in the right  It can be calculated as follows.

z = (110-80)/15 = 2.

Area to the left of Z=2.00 is 0.028

So, the area between Z= -1 and Z= 2 is

= Total Area - (area of population below 65 + area of population above 110)=1-(0.1587+0.0228)=0.8185

The proportion of the population corresponding to scores between 65 and 110 is 0.8185 or 81.85%.

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Among the given sets of vectors, the sets that can be bases for ℝ³ are (a) (2, 0, 0), (4, 4, 0), (6, 6, 6) and (b) (3, 1, -3), (6, 3, 3), (9, 2, 4). The correct options are (a) and (b).

In order for a set of vectors to form a basis for ℝ³, they must satisfy two conditions: (1) The vectors must span ℝ³, meaning that any vector in ℝ³ can be expressed as a linear combination of the given vectors, and (2) the vectors must be linearly independent, meaning that no vector in the set can be expressed as a linear combination of the other vectors.

(a) (2, 0, 0), (4, 4, 0), (6, 6, 6): These vectors span ℝ³ since any vector in ℝ³ can be expressed as a combination of the form a(2, 0, 0) + b(4, 4, 0) + c(6, 6, 6). They are also linearly independent, as no vector in the set can be expressed as a linear combination of the others. Therefore, this set forms a basis for ℝ³.

(b) (3, 1, -3), (6, 3, 3), (9, 2, 4): These vectors also span ℝ³ and are linearly independent, satisfying the conditions for a basis in ℝ³.

(c) (4, -3, 5), (8, 4, 3), (0, -10, 7): These vectors do not span ℝ³ since they lie in a two-dimensional subspace. Therefore, they cannot form a basis for ℝ³.

(d) (4, 5, 6), (4, 15, -3), (0, 10, -9): These vectors do not span ℝ³ either since they also lie in a two-dimensional subspace. Hence, they cannot form a basis for ℝ³.

In conclusion, the correct options for sets of vectors that form bases for ℝ³ are (a) and (b)

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y = 6x ,this equation represents a direct variation between y and x, where the constant of proportionality (k) is equal to 6.

What is the variation?

The table that represents a situation where y varies directly as x is:

x   y

0   0

2   12

4   24

6   36

In this table, the ratio of y to x is constant, which means that y varies directly with x. Specifically, y is always equal to 6 times x in this table, so we can write the relationship between y and x as:

y = 6x

This equation represents a direct variation between y and x, where the constant of proportionality (k) is equal to 6.

What is ratio?

A ratio is a quantitative comparison of two or more quantities or values. It expresses the relationship between two or more values, typically in the form of a fraction or a division operator. For example, the ratio of apples to oranges in a basket could be expressed as "2 to 3" or "2/3". Ratios can also be expressed in decimal or percentage form. Ratios are commonly used in mathematics, statistics, finance, and other fields to compare and analyze data.

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The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

Given that,

Because watching TV via digital streaming is becoming more and more common, tv advertising companies are having a harder time connecting with viewers. 53% of the 2343 American adults surveyed by the Harris Poll on November 13, 2012, claimed they had viewed digitally streamed television content on at least one device.

We have to find what is the sample proportion? firstly, the z-critical value is ? What is the confidence interval at 99%?

We know that,

n = 2343

Point estimate = sample proportion = \(\hat p\) = 0.530

1 - \(\hat p\) = 1 -0.530 = 0.470

At 99% confidence level

α = 1-0.99% =1-0.99 =0.01

α /2 =0.01/ 2= 0.005

Z(α /2) = Z0.005 = 2.576

Z (α/2) = 2.576 = 2.58

Margin of error = E = Z (α/2) × √((\(\hat p\) × (1 - \(\hat p\) )) / n)

=2.576 × (√(0.530×(0.470) /2343 )

= 0.027

A 99% confidence interval for population proportion p is ,

\(\hat p\)- E < p < \(\hat p\) + E

0.530 -0.027 < p < 0.530 +0.027

0.503 < p < 0.556

( 0.503, 0.556 )

Therefore, The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

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Step-by-step explanation:

multiply and the both number and divide by bytwo

Step-by-step explanation:

Look, you're taking these kinds of questions too serious and that's why you believe they're hard, now pay close attention:

the areas are defined in cm² but the radius is defined in cm, so you need find the positive root of cm².

\( \sqrt{ \frac{5500 {cm}^{2} }{220 {cm}^{2} } } = \frac{r}{5cm} = = > \\ 5 = \frac{r}{5} = = = > r = 25\)

and the question wants the base area:

\(s = \pi {r}^{2} = = = > s = 3.14 \times {(25cm)}^{2} = = > 1963.5 {cm}^{2} \)

True. The cartesian product of two sets is a set of pairs combining all elements from the first set with each of the elements in the second set.

The cartesian product of two sets A and B, denoted by A × B, is the set of all possible ordered pairs where the first element comes from set A and the second element comes from set B. In other words, each element in set A is combined with every element in set B to form a pair.

For example, let A = {1, 2} and B = {3, 4}. The cartesian product A × B would be {(1, 3), (1, 4), (2, 3), (2, 4)}, which includes all possible combinations of elements from A and B.

The cartesian product is a fundamental concept in set theory and plays a crucial role in various areas of mathematics, including algebra, combinatorics, and geometry. It allows for the systematic exploration of all possible combinations between sets and is often used in defining relations, functions, and mappings between different mathematical structures.

Therefore, it is true that the cartesian product of two sets is a set of pairs combining all elements from the first set with each of the elements in the second set.

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The amount of sales tax on Jacob’s purchase is $6.16

What is sales tax?

It is a tax which is charged by the government to raise money so it can provide public services. The tax is based on a certain percent of the price. Example: My State charges 4% sales tax. I want to buy a top advertised for $40. So the sales Tax is $40 × 4% = $1.6.

Jacob would like to purchase a coat and hat for a ski trip. The coat is $62.75, and the hat is $14.25.

So the total cost of coat and hat is $(62.75+14.25)

                                                       = $ 77

Sales tax is 8%

It means in $100 the sales tax is $8

In $100 the sales tax is $8

In $1 the sales tax is 8/100

In $77 the sales tax is (8×77)/100

                                    = $6.16

Hence, the amount of sales tax on Jacob’s purchase is $6.16.

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In summary, the radius of convergence is √2 and the interval of convergence is [-√2, √2].

To find the radius of convergence and interval of convergence of the power series, we can use the ratio test.

The given power series is:

∑ ((-1)^n (x^2)^n) / (n*2^n)

Let's apply the ratio test:

lim(n->∞) |((-1)^(n+1) (x^2)^(n+1)) / ((n+1)2^(n+1))| / |((-1)^n (x^2)^n) / (n2^n)|

Simplifying and canceling terms:

lim(n->∞) |(-1) (x^2) / (n+1)*2|

Taking the absolute value and applying the limit:

|(-1) (x^2) / 2| = |x^2/2|

For the series to converge, the ratio should be less than 1:

|x^2/2| < 1

Solving for x:

-1 < x^2/2 < 1

Multiplying both sides by 2:

-2 < x^2 < 2

Taking the square root:

√(-2) < x < √2

Since the radius of convergence is the distance from the center (x = 0) to the nearest endpoint of the interval of convergence, we can take the maximum value from the absolute values of the endpoints:

r = max(|√(-2)|, |√2|) = √2

Therefore, the radius of convergence is √2.

For the interval of convergence, we consider the endpoints:

When x = √2, the series becomes:

∑ ((-1)^n (2)^n) / (n*2^n)

This is the alternating harmonic series, which converges.

When x = -√2, the series becomes:

∑ ((-1)^n (2)^n) / (n*2^n)

This is again the alternating harmonic series, which converges.

Therefore, the interval of convergence is [-√2, √2].

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The system of equations is:

x + y = 10

4x + 3y = 36

The solution is x = 6 and y = 4.

A)

Let's define the variables:

We can write the system of equations:

x + y = 10

4x + 3y = 36

Isolate x on the first equation to get:

x = 10 - y

Replace that in the other one:

4*(10 - y) + 3y = 36

40 - 4y + 3y = 36

40 - y = 36

40 - 36 = y

4 = y

And thus, the value of x is:

x = 10 - y = 10 - 4 = 6

They bought 6 cheese wafers and 4 chocolate ones.

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Outliers are sample values that lie very far away from the majority of the other sample values.

We know that, an outlier is an observation that lies an abnormal distance from other values in a random sample from a population.

It differs significantly from other observations in a sample values.

Outlier is a value that is distant from the majority of the values in a data set.

For a scatter plot, an outlier is the point or points that are farthest from the regression line.

For example in the record of marks 25, 29, 7, 32, 85, 33, 27, 28 both 7 and 85 are outliers.

Therefore, outliers are sample values that lie very far away from the majority of the other sample values.

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Answer:

4b+4

Step-by-step explanation:

7b-3b = 4b and then you cant do anything with the four so your answer should be 4b+4!

Lengths of time it takes for new light bulbs to burn out are an example of continuous numerical data type.

Quantitative information that can be measured precisely and that can take on any value within a range is known as continuous numerical data. Measurements of length, time, weight, temperature, and many other quantifiable physical qualities are examples of continuous numerical data.

Continuous numerical data can have any value as long as it falls within a specified range, and using mathematical operations like addition, subtraction, multiplication, and division, it is possible to compare and analyze the numbers.

Since it alludes to a continuous range of precise numerical values. The duration of time in this scenario is expressed in hours, minutes, or seconds and can have any value within a specific range, for example, 0.5 hours, 1.25 hours, 2.75 hours, and so on.

Numerical data types like float and decimal can be used to represent continuous numerical data.

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Answer:

C) Alternate Exterior Angles Converse Theorem

Step-by-step explanation:

HERE IS YOUR ANS AFTER A LOT OF RESEARCH ! ^-^

19.)

\( \frac{ - 4x - 3 + 96 {a}^{2} b}{6b} \)

hope it helps

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Somebody better answer thing

According to the question 1.) False - 3 × 5 matrix columns can be linearly independent. 2.) True , 3.) True , 4.) True , 5.) True , 6.) True - 3 × 2 matrix transformation not one-to-one.

1.) True. If the set of columns of a 3 × 5 matrix is linearly dependent, it means that there exists a nontrivial linear combination of the columns that equals the zero vector.

2.) False. The effect of a linear transformation on the columns of the n × n identity matrix only determines the image of the standard basis vectors. It does not completely determine the entire transformation.

3.) False. If each row of matrix A has a pivot, it means that the rows of A are linearly independent, not linearly dependent.

4.) True. If A has a pivot in each row, it means that the rows of A are linearly independent, and the linear transformation T : Rn → Rm represented by A is one-to-one.

5.) True. Similar to statement 1, if the set of columns of a 5 × 3 matrix is linearly dependent, it means that there exists a nontrivial linear combination of the columns that equals the zero vector.

6.) True. If A is a 3 × 2 matrix, it means that the transformation x → Ax maps from R2 to R3. Since the dimensions of the domain and codomain are different, the transformation cannot be one-to-one.

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Based on the information, A.Teresa is correct. The graph of y=2xy=2x grows at an increasingly increasing rate, but the graphs of y=x2+2y=x2+2 and y=2x2y=2x2 both grow at a constantly increasing rate. Therefore, the graph of y=2xy=2x will eventually surpass both of the other graphs.

It should be noted that a graph is simply used to show the relationship that exists in the data given diagrammatically.

It should be noted that Teresa is correct as y=2ˣ grows at an increasingly increasing rate, while the other two grow at a constantly increasing rate. This means y=2ˣ will surpass the other two.

In conclusion, the correct option is A.

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Complete question

Teresa graphs the following 3 equations: y=2^x, y=x^2+2, and y=2x^2. She says that the graph of y=2^x will eventually surpass both of the other graphs. Is Teresa correct? Why or why not?

A.Teresa is correct.

The graph of y=2xy=2x grows at an increasingly increasing rate, but the graphs of y=x2+2y=x2+2 and y=2x2y=2x2 both grow at a constantly increasing rate.

Therefore, the graph of y=2xy=2x will eventually surpass both of the other graphs.

B. Teresa is not correct.

The graph of y=2xy=2x grows at an increasing rate and will eventually surpass the graph of y=x2+2y=x2+2.

However, it will never surpass the graph of y=2x2y=2x2 because the yy-value is always twice the value of x2x2.

C. Teresa is not correct.

The graph of y=2x2y=2x2 already intersected and surpassed the graph of y=2xy=2x at x=1x=1.

Once a graph has surpassed another graph, the other graph will never be higher.

Answer:

(PE) (MD) (AS)

applies to all if you must multiply or divide at the same time do the left side first

(a) The initial speed of the projectile - 28.2m/s

(b)The total time interval the projectile was in flight - 4.07s.

a) When a projectile is launched with speed \(v_{i}\) at an angle above the horizontal, the initial velocity components are \(v_{xi}\) = \(v_{i}\) cos\(θ\) and                  \(v_{yi}\)= \(v_{i}\) sin\(θ\) . Neglecting air resistance, the vertical velocity when the projectile returns to the level from which it was launched (in this case, the ground) will be \(v_{y} = - v_{yi}\) .

From this information, the total time of flight is found  \(v_{yf} = v_{yi} + a_{y}\) to be

         \(t_{total} = \frac{v_{yf} - v_{yi} }{a_{y}}\)   = \(\frac{-v_{yi} - v_{yi} }{-g}}\)  = \(\frac{2v_{yi} }{g}\)

         \(t_{total} = \frac{2v_{i}sinθ }{g}\)

Since the velocity of a projectile with no air resistance is constant, the horizontal distance it will travel in this time is given by

R = \(v_{xi} t_{total} = (v_{i} cosθ_{i}) \frac{2v_{i}sinθ }{g}\)  =  \(\frac{v^{2}_{i}}{g}( 2sinθ_{i} cosθ_{i} )\) = \(\frac{v^{2} _{i} (sin2θ_{i} ) }{g}\)

Thus, if the projectile is to have a range of R=81.1m when launched at an angle of \(θ_{i}\)=45.0°, the required initial speed is

\(v_{i} = \sqrt{\frac{81.1 * 9.80}{sin90} }\) = 28.2 m/s

Therefore, the initial speed of the projectile - 28.2m/s

b) With \(v_{i}\)=28.2m/s and \(θ_{i}\) = 45.0°, the total time of flight (as found

above) will be

        \(t_{total} = \frac{2v_{i}sinθ }{g}\)  = \(\frac{2(28.2 m/s) sin45}{9.80m/s^{2}}\) = 4.07s

∴The total time interval the projectile was in flight - was 4.07s.

c) Note that at \(θ_{i}\) =45.0° that sin(2\(θ_{i}\)) will decrease as \(θ_{i}\) is increased above this optimum launch angle. Thus, if the range is to be kept constant while the launch angle is increased above 45.0°, we see from \(v_{i}\) = \(\sqrt{\frac{Rg}{sin2θ_{i}} }\)that the required initial velocity will increase.

Observe that for \(θ_{i}\) <90°, the function sin\(θ_{i}\) increases as \(θ_{i}\) it increased. Thus, increasing the launch angle above 45.0° while keeping the range constant means that both \(v_{i}\) sins will increase. Considering the expression  \(t_{total}\) given above, we see that the total time of flight will increase.

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The correct question is :

The record distance in the sport of throwing cowpats is 81.1m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45° and neglecting air resistance, determine (a) the initial speed of the projectile and (b) the total time interval the projectile was in flight. (c) How would the answers change if the range were the same but the launch angle was greater than 45°? Explain.

The statement is true as over the last 40 years, the percentage of Americans who identify as White has been decreasing steadily.

This trend can be attributed to several factors,

Changing Demographics,

The United States has experienced significant demographic shifts in recent decades.

There has been an increase in immigration from non-European countries, resulting in a more diverse population.

Birth rates among minority populations, such as Hispanic, Asian, and African American communities,

Have been higher compared to the White population.

Multiracial Identification,

With increased recognition and acceptance of multiracial identities,

More individuals are choosing to identify with multiple racial backgrounds rather than solely as White.

This shift in self-identification contributes to the decline in the percentage of Americans identifying as solely White.

Generational Changes,

Younger generations, such as millennials and Generation Z, are more racially and ethnically diverse compared to older generations.

As younger individuals enter adulthood and the workforce, they contribute to the overall demographic changes in the country.

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Answer:

y = 150

Step-by-step explanation:

y varies inversely as x²

yx² = k

----------------

y = 6 when x = 30

6(30²) = k

6(900) = 5400

--------------------------

what is y when x = 6

y(6²) = 5400

y(36) = 5400

y = 5400/36

y = 150

Answer:

     y= 150

Step-by-step explanation:

\(y\ \alpha \ \frac{1}{x^2}\\\\y = k \times \frac{1}{x^2}\\\\\)

Given y = 6, and x = 30. Find k.

\(6 = k \times \frac{1}{30^2}\\\\6 \times 900 = k\\\\5400 = k\)

Given  x = 6 and k = 180. Find y

\(y = 5400\times \frac{1}{6^2}\\\\\)

 \(=5400 \times \frac{1}{36}\\\\=150\)

We can use the standard normal distribution table or calculate the z-score and find the corresponding area under the curve. The percentage of the population for X ≥ 124.75 is approximately 3.86%.

To find the percentage of the population for X ≥ 124.75, we need to calculate the z-score, which represents the number of standard deviations an observation is from the mean. The formula for the z-score is:

z = (X - μ) / σ

In this case, X is 124.75, μ is 100, and σ is 15. Plugging in these values, we get:

z = (124.75 - 100) / 15 = 1.65

Using the standard normal distribution table or a calculator, we can find the area under the curve to the right of the z-score of 1.65. The area represents the percentage of the population for X ≥ 124.75.

From the standard normal distribution table, we find that the area to the right of the z-score 1.65 is approximately 0.0495. Multiplying this by 100, we get 4.95%.

However, since we are interested in X ≥ 124.75, we need to consider the area to the left of the z-score of 1.65 and subtract it from 1. This gives us:

1 - 0.0495 = 0.9505

Multiplying 0.9505 by 100, we find that the percentage of the population for X ≥ 124.75 is approximately 95.05%. Therefore, the percentage of the population for X ≥ 124.75 is approximately 3.86%.

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