I don't get it my teacher tried to help me but I still don't get it

The value of derivative f '(x) can be simplified to f '(x) = -20x³+4x²+8x+1.Yes the answer agrees.

To find the derivative of f(x) = (1 + 4x²)(x - x²) using the product rule, we first take the derivative of the first term, which is 8x(x-x²), and then add it to the derivative of the second term, which is (1+4x²)(1-2x). Simplifying this expression, we get f '(x) = 8x-12x³+1-2x+4x²-8x³.  

To find the derivative by multiplying first, we would have to distribute the terms and then take the derivative of each term separately, which would be a more tedious process and would not necessarily give us the same answer as using the product rule. .

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Answer:

what you  have is right

Step-by-step explanation:

Step-by-step explanation:

The answer is d . all your doing is multiplying the 8 and the 1/2 and then use ( ) and multiply by 1/3

The area of the garden that is grass is 30 square meters.

The square garden has a side length of 6 meters.

The triangular pond has a base of 4 meters and a height of 3 meters.

The area of the garden that is grass.

The area of the square garden is 6 x 6 = 36 square meters.

The area of the triangular pond is (1/2) x 4 x 3 = 6 square meters.

Therefore, the area of the garden that is grass is 36 - 6 = 30 square meters.

The area of the garden that is grass is 30 square meters.

Here are the steps in detail:

Calculate the area of the square garden: 6 m * 6 m = 36 square meters

Calculate the area of the triangular pond: (1/2) * 4 m * 3 m = 6 square meters

Subtract the area of the pond from the area of the square to find the area of the grass: 36 square meters - 6 square meters = 30 square meters

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Answer:

Answer:

$0.11

Step-by-step explanation:

2 packs of toy cars cost $0.22.

1 pack of toy cars will cost:

0.22/2=$0.11

0.11 dollars.

After closely analyzing the line graph, it can be seen that the number of pygmy marmosets weighing more than 1/2 ounce are 8.

To create a line plot, we plot each weight of the each pygmy marmosets on the y-axis and the pygmy marmoset number on the x-axis, which will be ultimately being connected using the points with a line.

After ploting the each mentioned weights (in ounces ) and taking a close study of the plotted line graph,  we can see that there are total 8 pygmy marmosets which are weighing more than 1/2 ounce.

Therefore, the total number of pygmy marmosets with weight more than 1/2 ounces are 8.

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The complete question is :

The table shows the weights of 10 newborn pygmy marmosets make a line plot to display the data. How many pygmy marmosets weigh more than 1/2 ounce ?

Pygmy Marmoset      Weight (ounces)

1                                 0.4

2                                 0.5

3                                 0.6

4                                 0.7

5                                 0.8

6                                 0.9

7                                 1.0

8                                 1.1

9                                 1.2

10                                 1.3

The laptop will be worth $594.48 in two years.

To find the value of the laptop in two years, we need to substitute the given values into the formula:

Value = P x (1 - r)ⁿ

In this case, the original value of the laptop is $700, and it depreciates at a rate of 0.08 per year (which is 8% expressed as a decimal). We want to find the value in two years, so t = 2.

Substituting the values into the formula:

Value = $700 x (1 - 0.08)²

Value = $700 x (0.92)²

Value ≈ $700 x 0.8464

Value ≈ $594.48

Therefore, the laptop will be worth $594.48 in two years.

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Answer:

2y² + 14y - 15

Step-by-step explanation:

(2y² + 8y - 9) - (- 6y + 6)

Remove first parenthesis and distribute second by - 1

= 2y² + 8y - 9 + 6y - 6 ← collect like terms

= 2y² + 14y - 15

This question is incomplete, the complete question is;

Listed below are the lead concentrations in u​g/g measured in different traditional medicines. Use a  0.01 significance level to test the claim that the mean lead concentration for all such medicines is less than  18u​g/g.

22.5 , 9 , 18.5 , 22 , 16 , 18.5 , 15 , 3 , 8, 6

a) what is the null and alternative hypothesis

b) determine the test statistic

Answer:

a)

the null and alternative hypothesis will be;

Null hypothesis            H₀ : Ц = 18 ug/g

Alternative hypothesis  H₁ : Ц < 18 ug/g

b) the Test Statistic = -1.47

Step-by-step explanation:

Given data;

x = 22.5 , 9 , 18.5 , 22 , 16 , 18.5 , 15 , 3 , 8, 6

number of observation n = 10

level of significance ∝ = 0.01

a)

the null and alternative hypothesis will be;

Null hypothesis             H₀ : Ц = 18 ug/g

Alternative hypothesis  H₁ : Ц < 18 ug/g

b)

Test statistics;

using the formula;

t = (x" - Ц) / (s/√n)

x" is the sample mean

s is the standard deviation

Ц is the population mean ( 18 )

n is the number of observation ( 10 )

for first we get our mean x"

mean x" = ∑x / n

mean x" = (22.5  + 9  + 18.5  + 22  + 16  + 18.5  + 15  + 3  + 8 + 6) / 10

mean x" = 138.5 /10

mean x" = 14.85

Next we find the standard deviation s    

standard deviation s = √[ (∑(x-x")²) / (n - 1)]

x                     (x - x")                    (x - x")²

22.5                7.65                       58.5225

9                      -5.85                      34.2225

18.5                  3.65                       13.3225

22                    7.15                         51.1225

16                     1.15                          1.3225

18.5                  3.65                        13.3225

15                    0.15                         0.0225

3                      -11.85                       140.4225

8                     -6.85                        46.9225

6                     -8.85                        78.3225

total                                                437.525

so we substitute to get our standard deviation

standard deviation s = √[ (   437.525 / (10 - 1)]

= √[ 437.525 / 9]

= √48.6138

standard deviation s = 6.9723

Finally our we substitute our values into the Test statistics formula

t = (x" - Ц) / (s/√n)

t =  (14.85 - 18) / (6.9723/√10)

t = -3.25 /  2.2048

t =  -1.47

Therefore the Test Statistic = -1.47

Answer:

\(\textsf{1.} \quad 3x^2-4x+12\)

\(\textsf{2.} \quad 3x^2-8x+4\)

\(\textsf{3.} \quad 6x^3-8x+32\)

\(\textsf{4.} \quad \dfrac{3x^2-6x+8}{2x+4}\)

\(\textsf{5.} \quad 12x^2+36x+32\)

Step-by-step explanation:

Given functions:

\(\begin{cases}f(x)=3x^2-6x+8\\g(x)=2x+4\end{cases}\)

Function composition is an operation that takes two functions and produces a third function.

The composite function (f + g)(x) means to add function f(x) and g(x):

\(\begin{aligned}\implies (f+g)(x) & = f(x)+g(x)\\&=(3x^2-6x+8)+(2x+4)\\ &=3x^2-6x+2x+8+4\\ &=3x^2-4x+12\end{aligned}\)

The composite function (f - g)(x) means to subtract function g(x) from function f(x):

\(\begin{aligned}\implies (f-g)(x) & = f(x)-g(x)\\&=(3x^2-6x+8)-(2x+4)\\&=3x^2-6x+8-2x-4\\ &=3x^2-6x-2x+8-4\\ &=3x^2-8x+4\end{aligned}\)

The composite function f(x) · g(x) means to multiply functions f(x) and g(x):

\(\begin{aligned}\implies f(x)\cdot g(x) & =(3x^2-6x+8)(2x+4)\\ &=3x^2(2x+4)-6x(2x+4)+8(2x+4)\\&=6x^3+12x^2-12x^2-24x+16x+32\\&=6x^3-8x+32\end{aligned}\)

The composite function f(x)/g(x) means to divide function f(x) by function g(x):

\(\begin{aligned}\implies \dfrac{f(x)}{g(x)} & = \dfrac{3x^2-6x+8}{2x+4}\\\end{aligned}\)

The composite function f(g(x)) means to substitute the function g(x) in place of the x in function f(x):

\(\begin{aligned}\implies f(g(x))&=3(g(x))^2-6(g(x))+8\\&=3(2x+4)^2-6(2x+4)+8\\&=3(2x+4)(2x+4)-12x-24+8\\&=3(4x^2+16x+16)-12x-16\\&=12x^2+48x+48-12x-16\\&=12x^2+48x-12x+48-16\\&=12x^2+36x+32\end{aligned}\)

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The number that he must bowl in his third game to have an average of at least 200 is 236.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the third game be illustrated as x.

Since Ben bowled 152 and 212 in his first two games, the average will be illustrated thus:

(152 + 212 + x) / 3 ≥ 200

152 + 212 + x ≥ (200 × 3)

152 + 212 + x ≥ 600

364 + x + x ≥ 600

x ≥ 600 - 364

x ≥ 236

In conclusion, Ben must bowl at least 236.

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Answer:

795 toys

Step-by-step explanation:

if she gives away 25 toys each week for 22 weeks, that will be a total of 550 toys in 22 weeks

And now we simply minus 550 from 1345 to get 795 toys remaining after 22 weeks

Answer:

-6

Step-by-step explanation:

-8=-2x+4    -8-4=2x   -12=2x  x= -12:2   x= -6

Answer:

HM

Step-by-step explanation:

dddd

Answer:

permutations: order matters

combinations: order doesn't matter

Answer:

A combination doesn't need to be in a specific order, unlike permutation which needs to go in order.

Step-by-step explanation:

Answer:

\(\sqrt{13}\)

Step-by-step explanation:

Given a vector < x, y > then its magnitude is

\(\sqrt{x^2+y^2}\)

Given the directed line segment

P (0, 0 ) → Q (3, 2 ) then

PQ = q - p = (3, 2 ) - (0, 0 ) = < 3 - 0, 2 - 0 > = < 3 , 2 >

| PQ | = \(\sqrt{3^2+2^2}\) = \(\sqrt{9+4}\) = \(\sqrt{13}\)

Answer:

3.398

Step-by-step explanation:

log(10) 2500 = log(10) (5^2*10^2) = log(10) 5^2 + log(10) 10^2 = 2*log(10) 5 + 2=3.398

Answer:

12

Step-by-step explanation:

2xy+15x

Let x=4 and y= -9

2(-4)(-9) + 15(-4)

Multiply

72 -60

Subtract

12

Answer:

-12

Step-by-step explanation:

2(4)(-9)+15(4) is what it should look like.

Answer:

Perimeter of the final star = 40 cm²

Step-by-step Explanation:

The perimeter of the six-pointed star is the sum of the sides of the 6 equilateral triangles that form a boundary around the star.

1 triangular tiles gas a perimeter of 10cm.

Only 2 out of the 3 equal sides of each of the 6 equilateral triangles form the boundary of the final star.

Therefore, perimeter of the final star = ⅔ of the total perimeter of 6 triangular tiles

= ⅔ of (10*6)

= ⅔*60

= 2*20

Perimeter of the final star = 40 cm²

Answer:

Step-by-step explanation:

x2–5x+6 x2-x-2

x2+x-12 x2 +5x+4

i) x² - 5x + 6

⇒ x² - 3x - 2x + 6

⇒ x(x - 3) -2(x - 3)

⇒ (x - 2) (x - 3)    

Answer:

45 sq cm

Step-by-step explanation:

A triangle has an area of half of a rectangle if it has the same base and height.

The equation of the parallel line to y = 2x - 1, that passes through (-3, 1) is: y = 2x + 7.

Two lines that are parallel to each other would always have the same slope (m). In the slope-intercept form of the equation that represents a line, y = mx + b, the slope of the line is represented as "m", while the y-intercept is represented as b.

Given:

A point (-3, 1)

Equation, y = 2x - 1. The slope (m) = 2. Since parallel lines have the same slope (m), therefore, the line that passes through (-3, 1) also have a slope (m) = 2.

Substitute (x, y) = (-3, 1) and m = 2 into y = mx + b:

1 = 2(-3) + b

1 = -6 + b

1 + 6 = b

b = 7

To write the equation of the parallel line to y = 2x - 1, substitute m = 2 and b = 7 into y = mx + b:

y = 2x + 7.

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Answer:

\(y=-8x+80\)

Step-by-step explanation:

\(Slope=\frac{y_2-y_1}{x_2-x_1}=\frac{32-64}{6-2}=\frac{-32}{4}=-8\)

\(y=mx+b\)

\(y=-8x+b\)

\(64=-8(2)+b\)

\(64=-16+b\)

\(80=b\)

Therefore, the estimated line of best fit is \(y=-8x+80\)

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Answer:

-3/10

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-6-(-9))/(-3-7)

m=(-6+9)/-10

m=3/-10

m=-3/10

Answer: here it is

Step-by-step explanation:

Statement A is an example of inductive statement, whereas, statement B is a example of deductive statement.

Inductive reasoning is a method of reasoning in which a body of observations is considered to derive a general principle. It consists of making broad generalizations based on specific observations.

For example,

The last few times I’ve driven past the beach on a sunny day, the parking lot was nearly full. Therefore, on sunny days, the beach parking lot will be nearly full.

Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be false.

For example,

On Thursdays, the trash gets picked up at the curb of the driveway. Today is Thursday. Therefore, the trash will get picked up at the curb of the driveway today.

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Answer:

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

According to the Angles of Intersecting Chords Theorem, the angle between two chords is half the sum of the intercepted arc measures :

Substitute and solve for x: