Evaluate (f + g)(x) if f(x) = 2x and g(x) = 3X - 2
when x = 3

The derivatives of the functions are listed below:

(a) [tex]f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}[/tex]    

(b) [tex]f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }[/tex]

(c) f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)²    

(d) f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)]

(e) f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶

(f) [tex]f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}][/tex]

(g) [tex]f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)[/tex]

(h) f'(x) = cot x + cos (㏑ x) · (1 / x)

In this question we must obtain the first derivatives of each expression by applying differentiation rules:

(a) [tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}[/tex]

(b) [tex]f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}[/tex]

(c) f(x) = (sin x - cos x) / (x² - 1)

(d) f(x) = 5ˣ · ㏒₅ x

(e) f(x) = (x⁻⁵ + √3)⁻⁹

(f) [tex]f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}[/tex]

(g) [tex]f(x) = \arccos^{2} x - \arctan (\sqrt{x})[/tex]

(h) f(x) = ㏑ (sin x) + sin (㏑ x)

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The true statements are;

-Both graphs are logarithmic functions

-Both graphs have been shifted and flipped (B and D).

A graph is a plot of information on the cartesian coordinates. The function is plotted on an x - y cartesian plane. Given the nature of function, we can understand the shape of the graph as shown.

In this case, the graph shows a flipped logarithmic function. As such, the following are true about the function;

-Both graphs are logarithmic functions

-Both graphs have been shifted and flipped

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Answer:

100°

Step-by-step explanation:

basically, in this situation, whatever number or angle you're given, and the number diagonally across from it are supposed to add up to 180°.

(i think its called a cyclic quadrilateral, so do with that what you will.)

The given expression is factored as [tex]4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]

Given expression: [tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}[/tex]

In order to factorize the given expression, take out the common terms and then simplify further.

[tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}=4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]

In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftover.

A number can have either positive or negative factors.

A number has a finite number of factors.

A number's factor will never be more than or equal to the provided number.

Every number contains at least two factors, 1 and the actual number, with the exception of 0 and 1.

Finding a number's factors involves using the division and multiplication operations.

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Answer: C

Step-by-step explanation:

The zeros of a graph are where the graph intersects the x-axis.

Using the Central Limit Theorem, the standard error of the distribution of differences in sample means is of 1.97.

According to the Central Limit Theorem, it is given by the standard deviation of the sample divided by the square root of the sample size, hence:

It is given by the square root of the sum of the standard errors of each sample squared, hence:

s = sqrt(1.1² + 1.63²) = 1.97.

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The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.

The definition of a prime number is a natural number larger than 1 that is not the sum of two lesser natural numbers. A composite number is any natural number that is more than 1 but not a prime.

The only two components in prime numbers are 1 and the number itself.

Any whole number greater than one is a prime number.

It has exactly two factors—1 and the actual number.

There is just one 2-digit even prime number.

Every pair of prime numbers is always a co-prime.

The product of prime numbers can be used to represent any number.

Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960

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Answer: [tex]\Large\boxed{\dfrac{3}{8} }[/tex]

Step-by-step explanation:

Given information

[tex]b=2[/tex]

[tex]c=-\dfrac{7}{4}[/tex]

Given expression

[tex]b-(-\dfrac{1}{8}) +c[/tex]

Substitute values into the expression

[tex]=(2)-(-\dfrac{1}{8}) +(-\dfrac{7}{4} )[/tex]

Convert the fractions into the common denominator

Least Common Multiple (LCM) of 8 and 4 = 8

[tex]=(2)-(-\dfrac{1}{8}) +(-\dfrac{7\times2}{4\times2} )[/tex]

[tex]=(2)-(-\dfrac{1}{8}) +(-\dfrac{14}{8} )[/tex]

Simplify the parenthesis

[tex]=2+\dfrac{1}{8} -\dfrac{14}{8}[/tex]

Simplify by addition

[tex]=\dfrac{16}{8} +\dfrac{1}{8} -\dfrac{14}{8}[/tex]

[tex]=\dfrac{17}{8} -\dfrac{14}{8}[/tex]

Simplify by subtraction

[tex]\Large\boxed{=\dfrac{3}{8} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: 288

Step-by-step explanation:

(16x9)x2

Answer:

2/7 = 29% (nearest percent)

Step-by-step explanation:

Calculate the totals and add them to the table:

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} & \sf Freshman & \sf Sophmore & \sf Juniors & \sf Seniors & \sf Total \\\cline{1-6} \sf Male & 4 & 6 & 2 & 2 & 14\\\cline{1-6} \sf Female & 3 & 4 & 6 & 3 & 16\\\cline{1-6} \sf Total & 7 & 10 & 8 & 5 & 30\\\cline{1-6}\end{array}[/tex]

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Let P(A) = probability that the student is a freshman

Let P(B) = probability that the student is male

Use the given table to calculate the probability that the student is male:

[tex]\sf \implies P(B)=\dfrac{14}{30}[/tex]

And the probability that the student is a freshman and male:

[tex]\implies \sf P(A \cap B)=\dfrac{4}{30}[/tex]

To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of A given B is:

[tex]\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}[/tex]

Substitute the found values into the formula:

[tex]\implies \sf P(Freshman|Male)=\dfrac{\dfrac{4}{30}}{\dfrac{14}{30}}=\dfrac{4}{14}=\dfrac{2}{7}=0.28571...=29\%[/tex]

Therefore, the probability that the student is a freshman given they are male is 29% (nearest percent).

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The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.

According to the statement

we have given that the some numbers of the songs which are added by the larrisa in her playlist.

And we have to tell the ways which are formed with the help of the combination and permutations.

So, For this purpose we know that the

The first condition we have given that the

"play no more than 4 blues songs" - indicates playlist can contain 0, 1, 2, 3, or 4 blues songs. You need to analyze five different cases and add them up together in the end. From 7 blues songs, you can either "pick" 0, 1, 2, 3, or 4. Since order matters, it's a permutation, not a combination.

Afterwards, it gets tricky. Consider the first case, where we have 0 blues songs. This means that there are 10 spaces for the remaining (3+5+7 = 15) songs, which means that they can be arranged in (7P0 ∙ 15P10) ways.

For the next case, where we have 1 blues songs, it means that there are 9 spaces for the remaining 15 songs, which means that they can be arranged in (7P1 ∙ 15P9) ways. Continue doing this for the cases of 2, 3, and 4 blues songs and add up all the cases together.

And from this way we get the all combinations which are formed.

So, For this purpose

n = (7P0 ∙ 15P10) + (7P1 ∙ 15P9) + (7P2 ∙ 15P8) + (7P3 ∙ 15P7) + (7P4 ∙ 15P6) = 4.43459016×1010,

which rounded to the hundredths place, is 4.43 x 10^10 possible playlists.

So, The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.

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Answer:

Step-by-step explanation:

Answer: 19/40

Step-by-step explanation:

First Write 0.475 as 0.4751Multiply both numerator and denominator by 10 for every number after the decimal point0.475 × 10001 × 1000 = 4751000. Reducing the fraction gives The answer

Answer:

2^1 × 5^2 × 7^1 = 350

Step-by-step explanation:

2, 5, 7 are prime

first step is to divide the number 350 with the prime factor 2

continue dividing the number 175 by the next smallest prime factor

stop until you can't divide anymore

https://www.cuemath.com/numbers/factors-of-350/

so hmmm on average on the last 7 test, you get 82, so hmmm we could say that on each of the 7 tests you got 82, so you got 82, 7 times.

now, let's say in the 8th test, you get a grade of "g", now, if we were to get an average of all 8 tests, that means the average will simply be (82*7) + "g", and we know that's 84, so

[tex]\cfrac{(\stackrel{\textit{sum of all first seven tests}}{82+82+82+82+82+82+82})~~ + ~~g}{8}~~ = ~~84\implies \cfrac{(82\cdot 7)~~ + ~~g}{8}~~ = ~~84 \\\\\\ \cfrac{574+g}{8}=84\implies 574+g=672\implies g=672-574\implies g=98[/tex]

You must score 98 on the eighth test to raise your average to 84.

Average = Sum of all scores / Number of scores

The average score is given as 82, so the sum of the first 7 test scores would be 82 multiplied by 7.

The average to 84, we need to find the sum of all 8 test scores. Let's represent the score we need on the eighth test as "x."

Average = Sum of all scores / Number of scores

Using this equation, we can write:

84 = (Sum of the first 7 test scores + x) / 8

Multiply both sides of the equation by 8:

8 * 84 = Sum of the first 7 test scores + x

672 = Sum of the first 7 test scores + x

Subtract:

672 - Sum of the first 7 test scores = x

Substitute the sum of the first 7 test scores (82 * 7) into the equation:

x = 672 - (82 * 7)

x = 672 - 574

x = 98

Therefore, you must score 98 on the eighth test to raise your average to 84.

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Answer:

======================

Find the cost, x:

Find the price to get 12% profit:

Answer: 45%

Step-by-step explanation:

Given:

Find:

The number of groups which contains 9 is 9 and the total number of groups are 20.

So,

P = 9 / 20 = 0.45 = 45%

Therefore, the experimental probability is 45%

Step-by-step explanation:

the probability of 1 tested insect is killed is 60% or 0.6.

the probability that it is not killed is then 1-0.6 = 0.4.

when we test 7 insects and exactly 4 survive is the event that

3 insects are killed, 4 insects survive.

the probability for one such case is

0.6×0.6×0.6 × 0.4×0.4×0.4×0.4

how many such cases do we have ?

as many as ways we can select 4 insects out of the given 7.

these are 7 over 4 combinations :

7! / (4! × (7-4)!) = 7! / (4! × 3!) = 7×6×5/(3×2) = 7×5 = 35

so, the probability that exactly 4 out of 7 tested insects survive is

35 × 0.6³ × 0.4⁴ = 0.193536 ≈ 0.1935

See below for the distance between the points and the lines

Question 2

The line and the points are given as:

x = y

P = (4, -2)

Rewrite the equation as:

y = x

The slope of the above equation is

m = 1

The slope of a line perpendicular to it is

m = -1

A linear equation is represented as:

y = mx + b

Substitute m = -1

y = -x + b

Substitute (4, -2) in y = -x + b

-2 = -4 + b

Solve for b

b = 2

Substitute b = 2 in y = -x + b

y = -x + 2

So, we have:

x = y and y = -x + 2

Substitute x for y

x = -x + 2

Solve for x

x = 1

Substitute x = 1 in y = x

y = 1

So, we have the following points

(1, 1) and (4, -2)

The distance between the above points is

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(1 - 4)² + (1 + 2)²

Evaluate

d = 3√2

Hence, the distance between x = y and P = (4, -2) is 3√2 units

Question 3

The line and the points are given as:

y = 2x + 1

Q = (2, 10)

The slope of the above equation is

m = 2

The slope of a line perpendicular to it is

m = -1/2

A linear equation is represented as:

y = mx + b

Substitute m = -1/2

y = -1/2x + b

Substitute (2, 10) in y = -1/2x + b

10 = -1/2 * 2 + b

Solve for b

b = 11

Substitute b = 11 in y = -1/2x + b

y = -1/2x + 11

So, we have:

y = 2x + 1 and y = -1/2x + 11

Substitute 2x + 1 for y

2x + 1 = -1/2x + 11

Solve for x

x = 4

Substitute x = 4 in y = 2x + 1

y = 9

So, we have the following points

(4, 9) and (2, 10)

The distance between the above points is

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(4 - 2)² + (9 - 10)²

Evaluate

d = √5

Hence, the distance between the line and the point is √5 units

Question 4

The line and the points are given as:

y = -x + 3

R = (-5, 0)

The slope of the above equation is

m = -1

The slope of a line perpendicular to it is

m = 1

A linear equation is represented as:

y = mx + b

Substitute m = 1

y = x + b

Substitute (-5, 0) in y = x + b

0 = 5 + b

Solve for b

b = -5

Substitute b = 5 in y = x + b

y = x + 5

So, we have:

y = x + 5 and y = -x + 3

Substitute x + 5 for y

x + 5 = -x + 3

Solve for x

x = -1

Substitute x = -1 in y = x + 3

y = 2

So, we have the following points

(-1, 2) and (-5, 0)

The distance between the above points is

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(-1 + 5)² + (2 - 0)²

Evaluate

d = 2√5

Hence, the distance between the line and the point is 2√5 units

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]

( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )

[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]

[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]

[tex]\qquad❖ \: \sf \:6x = 168[/tex]

[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]

Next,

[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]

[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]

[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]

[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]

( x = 28° )

[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

Answer:

Length = 52 ft

Width = 40 ft

Step-by-step explanation:

Given information:

Scale

[tex]\implies \sf 3 \: in : 8 \: ft[/tex]

[tex]\implies \sf 1 \: in : \dfrac{8}{3} \: ft[/tex]

To find the length and width of the studio in feet, multiply the length and width in inches by 8/3:

[tex]\sf Length = 19.5 \times \dfrac{8}{3}=52\:ft[/tex]

[tex]\sf Width = 15 \times \dfrac{8}{3}=40\:ft[/tex]

Therefore, the length of the actual studio is 52 ft and the width of the actual studio is 40 ft.

Scale is 3in:8ft

So

Length

Width

Answer:

33 units²

Refer to the attached page

I've shown the complete calculation over there.

Answer: 33

Step-by-step explanation:

one easy way to do it is by finding the area of the 4 triangles.

because the top two and the bottom two are the same that helps a lot. The first triangle is 9 times three and then cut your answer in half. Do the same thing for the other 9 times three triangle you will end up with 27. for the top two you would multiply 3 times two to get 6 cut 6 in half to get 3. do the same or the other triangle and now you just have to add.

3 plus 3 plus 13.5 plus 13.5

to get 33

Answer:

L

Step-by-step explanation:

interior angle formula so

(number of sides - 2)*180

2*180 = 360

you can also just take an example from a square 4*90 = 360

360-121-58-70 = 111

6.665 grams of the 13 grams remain after 8 hours.

The decay equation for the 13 grams of iron-52 is:

[tex]N(t) = 13g*e^{(-ln(2)/8.3h)*t}}[/tex]

Where N is the amount of iron-52, and t is the time in years.

Where we used the fact that the half-life is exactly 8.3 hours.

Now, the amount that is left is given by N(8h), so we just need to replace the variable t by by 8 hours, so we get:

[tex]N(8h) = 13g*e^{(-ln(2)/8.3h)*8h}} = 6.665g[/tex]

So 6.665 grams of the 13 grams remain after 8 hours.

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Answer:

The value of C will be -1.

Step-by-step explanation:

Greetings !

[tex]f(1) = - 6 \\ thus \: substitute \: in \: the \: equation \: \\ f(x) = 3x {}^{2} - 8x + c \\ - 6 = 3(1) {}^{2} - 8(1) + c \\ - 6 = 3 - 8 + c \\ - 6 = - 5 + c \\ - 1 = c \\ c = - 1 \\ therefore \: f(x) = 3x {}^{2} - 8x - 1 \\ f(1) = 3(1) {}^{2} - 8(1) - 1 \\ f(1) = 3 - 8 - 1 \\ f(1) =3 - 9 \\ f(1) = - 6[/tex]

Once you detect that there is a delay or disability, then you should continue to be the reliable partner in child care to the family so this is True.

The observation and screening process can lead to a child care partner discovering a delay or disability.

When this happens, you should report to your supervisor to check if the child is eligible for federal and state programs related to their condition. Whatever the case, you should remain accessible to the family as their partner in child care.

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Answer:

5

Step-by-step explanation:

Gradient (slope) of the curve can be found by deriving a curve function.

In this scenario, the given function is a polynomial function which we can use Power Rules to derive it.

Power Rules

[tex]\displaystyle{y=ax^n \to y' = nax^{n-1}}[/tex]

Thus, using the power rules, we will have:

[tex]\displaystyle{y'=3x^2-4x+5}[/tex]

Note that deriving a constant will always result in 0.

Then the problem gives us that we want to find the slope or gradient at where the curve crosses y-axis.

The curve crosses y-axis at x = 0 only. Therefore, we substitute x = 0 in a derived function.

[tex]\displaystyle{y'(0) = 3(0)^2-4(0)+5}\\\\\displaystyle{y'(0) = 5}[/tex]

Therefore, the slope at the point where a curve crosses y-axis will be 5.

The chance or probability of landing on a number divisible by 2 is 1/2.

The likelihood of an event occurring is defined by probability. By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

According to the question,

Total number of outcomes = 6

Favorable number of outcomes = 3

Thus, the required Probability = 3/6 =1/2

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Step-by-step explanation:

4W-8=3W+6

4W-3W=6+8

W=14°

lets find the value of W in this straight line

4W-8°=180°(angle on a straight line)

collect like terms

4W=180°+8°

4W=188°

divide both sides by the coefficient of W which is 4

W=47°

if i am correct pls rate it

Answer:

I believe its 20.8, but I may be wrong

Step-by-step explanation: