Let f(x)=7x^5 ln(x) + 1/3 x^3


f’(x)=


I’m stuck on this calculus problem. If anyone could help me work this out. I would appreciate if you showed all your steps.

ANSWERS ARE AT THE BOTTOM.

To find the probability of 2 events happening in a row, we need to multiply their probabilities.

For example, if a friend bet: "If you roll a six on a dice and filp and coin and get heads, then I'll give you 500 bucks. However, if you don't roll a six and flip and coin and get heads in a row, then you have to give me 500 bucks."

You want to know the probability of you winning this bet.

So, we need to multiply the probability of rolling a six, and the probability of flipping a coin and landing heads.

This is 1/6 * 1/2

That is 1/12

You probably should't take this bet, because you only have a 1/12 chance of winning.

Lets go back to your problem. The jar contains 16 red marbles and 28 blue marbles. The probability of picking a red marble right now is 16/28, or 4/7. Assume we picked a red marble on our first try. Now, there are only 15 red marbles. The probability of picking a red marble right now is 15/28.

Probability of picking a red marble on your first try:  4/7

Probability of picking a red marble on your second try:  15/28

Now, we need to multiply the probabilities.

4/7 * 15/28

60/196

15/49

ANSWER:

15/49

Here....

The length is given 15 feet and the width is 12 feet...Now let's find the Perimeter..

Perimeter = 2 ( l + b )

= 2 ( 15 + 12 )

= 2 × 27

= 54 feet

[tex]...[/tex]

:)...

Answer:

  x = y = 4

Step-by-step explanation:

A 2-variable linear programming problem is nicely solved by graphing. The solution will be one of the vertices of the solution set. The attached graph shows that means it is one of (x, y) = [(0, 0), (0, 6), (4, 4), (6, 2), (7, 0)}.

__

Evaluating the objective function at each of these vertices will show you the solution that maximizes it.

(0, 0) -- P = 40·0 +50·0 = 0

(0, 6) -- P = 40·0 +50·6 = 300

(4, 4) -- P = 40·4 +50·4 = 360

(6, 2) -- P = 40·6 +50·2 = 340

(7, 0) -- P = 40·7 +50·0 = 280

_____

Additional comment

The solution set would ordinarily be the area that is covered by the shading that signifies the solution set of each of the 5 inequalities. 5 different overlapping shadings can make the graph quite messy, so we have elected to shade the areas that are NOT part of the solution set. In doing so, we have made the boundary lines dashed when they are part of the solution set

The possible solutions are the vertices of the white space on the graph.

The black line on the graph is the line corresponding to the maximum value of the objective function. To maximize the objective function, we want that line as far from the origin as possible. It is shown intersecting the vertex of the solution space that meets that condition.

Answer:

Run 4 hours, Walk 8 hours.

Step-by-step explanation:

Let R be the running time

Let W be the walking time

Distance = Speed x Time

48 = 6R + 3W (equation 1)

12 = R + W (equation 2)

We will use elimination method to solve for these simulteanous equations.

Multiply Equation 2 by 3.

12x3 = 3(R+W)

36 = 3R + 3W (equation 3)

now subtract equation 3 from equation 1.

48-36 = 6R - 3R + 3W - 3W

12 = 3R

R = 12/3

= 4hours

now Substitute R into equation 2.

12 = 4 + W

W = 12 - 4

= 8

Therefore Michael plan to run for 4 hours and walk for 8 hours.

Answer: C

Step-by-step explanation:

The slope is positive, so m>0.

The y-intercept is negative, so b<0.

Answer:

y = -7x

Explanation:

Take two points from table: (-4, 28), (-3, 21)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope\ (m): \dfrac{21-28}{-3-(-4)} = -7[/tex]

Now find equation:

[tex]\sf y - y_1 = m (x - x_1)[/tex]

[tex]\rightarrow \sf y - 21 = -7(x - (-3))[/tex]

[tex]\rightarrow \sf y = -7(x +3) + 21[/tex]

[tex]\rightarrow \sf y = -7x -21 + 21[/tex]

[tex]\rightarrow \sf y = -7x[/tex]

Slope

Equation of line

Answer:

The first sequence is correct being (6)^k

Step-by-step explanation:

To find a ratio divide a term by its previous member such as 36/6 to give you r=6.

a) The ratio of the perimeters is the same as the scale factor, so the ratio is the perimeters is 2/3.

b) The perimeter of triangle ABC is [tex]36\left(\frac{3}{2} \right)=\boxed{54 \text{ ft}}[/tex]

c) The ratio of the areas is the scale of the scale factor. In this case, the ratio is [tex](2/3)^{2}=\boxed{4/9}[/tex]

d) The area of FDE is [tex]36(4/9)=\boxed{16 \text{ ft}^{2}}[/tex]

Answer:

.

Step-by-step explanation:

.

The standard deviation is a better measure of spread for movies than it is for basketball games.

A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

As, Movies is more centric to mean and not skewed on a particular side whereas basketball games is not centric to mean but is skewed right then left.

Now, Standard deviation just measures the deviation or spread with respect to mean of collected data.

So, In the movies the data is more collected. Thus standard deviation is best suited for movie data.

Now, interquartile range. IQR relies on if the data is skewed.

So, in the basketball data the standard deviation will not give the information.

Hence, the  standard deviation is a better measure of spread for movies than it is for basketball games.

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Answer:

I have no clue what I could answer that question with other than (-6,-10)

The pieces of rope measuring a yard can he divide his rope into1/4 would be 96.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Chad has a rope that is 24 yards long. He wants to divide the rope so each piece will be 1/4 yards

= 24÷1/4

= 24× 4

= 96

Hence he can divide the rope into 96 pieces.

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Answer:

339.47

Step-by-step explanation:

100 - 24 = 76

258 = 76 percent

3.39473684211 = 1 percent

339.47 = 100 percent

Answer:

The decrease in price is $61.92

The sale price is $196.08

Step-by-step explanation:

24% × 258 = 61.92

258 decrease 24% =

258 × (1 - 24%) = 258 × (1 - 0.24) = 196.08

x= -.55

6x+14x=11

20x=-11

x=-11/20

Answer:

24

Step-by-step explanation:

the question translates to asking how many times does 7/8 fit in 21, so 21 divided by 7/8.

when we divide by a fraction, we can multiply by it's inverse, so 21 divided by 7/8, is 21 multiplied by 8/7. so:

21×8/7 = (21×8)/7 = (21/7)×8 = 3×8 = 24

The expressions show the total number of furniture legs in aisle 2 is 4t + 4c + 3s.

A quantity obtained by the addition of a group of numbers.

Given number of tables = t, chairs = c and stools = s.

The total number of furniture legs = 4 * t + 4 * c + 3 * s.

                                                         = 4t + 4c + 3s.

Therefore, the expressions which show the total number of furniture legs in aisle 2 is 4t + 4c + 3s.

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A function assigns the values. The value of (p·p)(x) is x⁴ + 10x³ + 30x² + 25x.

A function assigns the value of each element of one set to the other specific element of another set.

Given p(x)= x²+5x, therefore, the value of (p·p)(x) can be written as,

(p·p)(x) = p(p(x))

            = (x²+5x)²+5(x²+5x)

            = x⁴ + 25x² + 10x³ + 5x² + 25x

            = x⁴ + 10x³ + 30x² + 25x

Hence, the value of (p·p)(x) is x⁴ + 10x³ + 30x² + 25x.

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The next number in the sequence 7, 11, 2, 18, -7, would be -11.

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

Given sequence;

7, 11, 2, 18, -7,

We can see that the fifth term is similar to the first term, except for the negative.

So, we can conclude that the integers start from the fifth term and leads to the next term as a negative of the second one.

Therefore, The next number in the sequence 7, 11, 2, 18, -7, would be -11.

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Answer:

[tex]f(4)=e^{4}-3[/tex]   or   [tex]f(4)\approx51.5981500331...[/tex]

Step-by-step explanation:

The following is a general explanation of functions, what they mean, and how to evaluate them.  The simplifications and calculations at the end are based on the clarification from your comments that [tex]f(x)=e^{x}-3[/tex] .  If [tex]f(x)[/tex] is equal to something else, the simplifications/calculation will obviously be a little different, and the answer will likely be different, but the general process will be the same.

In the equation [tex]f(x)=e^{x}-3[/tex] , the left side of the equation is saying several things at once.

Names

The first character, "f", is the name of the function.

The name of a function tells you which set of directions you should look for to apply to an input.  Some functions have names that are more than one letter, and even might give a hint as to what they do, for instance I might name a certain function [tex]squareroot[/tex], and based on the name, you might guess what the equation for [tex]squareroot(x)[/tex] might look like.

Mathematicians often use "f" as a function name between different problems over and over and over again, unless they come up with a special function that is worth giving a special name to.  

Input

The rest of the characters after the name of the function, are "(x)" which is a pair of parentheses to contain the input, and the input itself.

Again, mathematicians often use "x" as a generic input over and over and over again, until we actually know which number we want to put into the function.

Output

Even though we've already discussed every character in the notation on the left, there is actually one more thing that the left side of the equation is saying:  Altogether, "f(x)" is the output of the function, when the input "x" is put in.  I feel it's worth stating, because it's often glossed over.

The equation itself

Next in the equation is the equals sign, which means that the left side of the equation, which is the output "f(x)", is equal to the stuff on the right.

The right side of the equation is the rule to follow describing what f(x) does to an input, and can help you calculate the output.

For instance, if I asked what p(4) was, it is clear that there is an input of 4, but without knowing what the function "p" does, there's no way to know what the function will give as an output when one inputs "4".  This is why the right-hand side of the equation for a function is important.

To evaluate any function, we take an input, apply the function, and simplify/calculate the output.

In this case, the question asks for [tex]f(4)[/tex], meaning that the "input" is "4".  

In this case, the question gives an explanation of what the function does through a rule given in equation form.

Given your clarification of the given function,  [tex]f(x)=e^{x}-3[/tex] , meaning a generic input (in this case "x") is put into the function "f" and the output is found by doing the arithmetic on the right side of the equation (exponentiating the number by "e", and then subtracting 4)

Notice that in the expression  [tex]f(4)[/tex], the "x"  was replaced with "4".  So, we need to substitute "4" where we see an "x" in the rule on the right hand side of the equation rule, and simplify and/or calculate (calculate, like with a calculator)

So, to evaluate the expression [tex]f(4)[/tex], simply substitute, and simplify/calculate.

Simplifying (no calculator)

To simplify without a calculator, we substitute "4".  Any time you make a substitution, use parentheses.  Then, try to simplify.

[tex]f(4)=e^{(4)}-3[/tex]

[tex]f(4)=e^{4}-3[/tex]

As it turns out, this is as much as we could simplify things here (without a calculator).  So, if an exact answer is needed, this would be it.

Calculating (with a calculator)

To calculate with a calculator, we substitute "4".  Any time you make a substitution, use parentheses.  Then, try to simplify.

[tex]f(4)=e^{(4)}-3[/tex]

[tex]f(4)=e^{4}-3[/tex]

[tex]f(4)=54.5981500331...-3[/tex]

[tex]f(4)=51.5981500331...[/tex]

So calculating with a calculator, the output of the function "f", for an input of "4", is approximately 51.598.

Answer:

10

Step-by-step explanation:

15 ÷ 1.5 = 10

Answer:

33, 792

Step-by-step explanation:

first convert the 8 miles to feet because our answers are in feet.

1 mile= 5280 feet

therefore 8 miles= 5280×8

= 42240

Dale and son covered 4/5 of the 42240 feet

= 4/5×42240

= 33,782 feet

Answer:

Step-by-step explanation:

A function is defined so that for each input, there is no more than one output.

Answer:

11.65

Step-by-step explanation:

3x+99x=102x

1188/102=11.65

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3x + 99x = 1,188}[/tex]

[tex]\large\textbf{COMBINE the LIKE TERMS}[/tex]

[tex]\mathsf{(3x + 99x) = 1,188}\\\mathsf{3x + 99x = 1,188}\\\mathsf{\bold{102x} = 1,188}[/tex]

[tex]\large\textbf{DIVIDE 102 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{102x}{102} = \dfrac{1,188}{102}}[/tex]

[tex]\large\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathsf{x = \dfrac{1,188}{102}}[/tex]

[tex]\mathsf{x = 11.64705882}[/tex]

[tex]\large\textbf{AND IF YOU'RE ROUNDING}[/tex]

[tex]\mathsf{x \approx 12}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x \approx 12}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The constant of the proportional relationship graphed in this problem is of 10.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the points on the graph are: (0,0), (2,20), (4,40), ..., hence the constant is:

k = 40/4 = 20/2 = 10.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: slope = not \:\: defined [/tex]

with closest value = [tex] \sf{\infin} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: slope = \cfrac{rise}{run}[/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{ - 8 - ( - 9)}{1 - 1} [/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{ - 8 + 9}{0} [/tex]

[tex]\qquad \tt \rightarrow \: m \: \: is \: \: not \: \: defined[/tex]

[ Any real number divided by 0 is not defined ]

You can also assume it's closest value if possible, that is infinity ([tex]\sf{\infin}[/tex])

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The missing values are shown in the attached picture, and 41 degrees F = 5 degrees C.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

We have:

[tex]\rm F = \dfrac{9}{5}C + 32[/tex]

Make subject C and solve:

[tex]\rm \dfrac{5}{9}(F-32) = \dfrac{5}{9}\times\dfrac{9}{5}C[/tex]

[tex]\rm \dfrac{5}{9}(F-32) = C[/tex]

Plug F = 41

[tex]\rm \dfrac{5}{9}(41-32) = C[/tex]

[tex]\rm \dfrac{5}{9}(9) = C[/tex]

41 degrees F = 5 degrees C

Thus, the missing values are shown in the attached picture, and 41 degrees F = 5 degrees C.

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Answer:

[tex]\sqrt{1}[/tex]

Step-by-step explanation:

We know that a rational number cannot have roots. All of the answer choices cannot be simplified except for [tex]\sqrt{1}[/tex], which can become 1. Therefore, our answer is [tex]\sqrt{1}[/tex].

Answer:

small piece = 28 inches

large piece = 56 inches

Step-by-step explanation:

The carpenter has one piece of wood 84 inches long. He wants to cut that piece of wood into two pieces. One piece will be 2 times as long as the other. Let's let x = the small piece of wood

2x + x = 84

In this equation, the longer piece is 2 times the shorter piece and the shorter piece is added, which equals 84 inches. Lets solve:

2x + x = 84

3x = 84

3x/3 = 84/3

x = 28

This means that the shorter piece is 28 inches. To find the longer piece, multiply 28 by 2 because the longer piece is twice the shorter piece. Therefore the longer piece is

28 × 2 = 56

Finally, we figured out that the short piece is 28 inches and the longer piece is 56 inches

We can double check this by doing 56 + 28 and making sure it equals 84