what is the expression in from 4^n

The derivative of the function f(x) = 4x³ - 8x, evaluated at x = 4, is f'(4) = 184. This means that at x = 4, the rate of change of f(x) is 184 units per unit of x.

The derivative of a function measures the rate at which the function is changing at a specific point. In this case, we are given the function f(x) = 4x³ - 8x and asked to find its derivative at x = 4, denoted as f'(4).

To find the derivative of f(x), we can apply the power rule of differentiation. According to the power rule, if we have a term of the form axⁿ, the derivative is given by d/dx(axⁿ) = naxⁿ⁻¹. Applying this rule to each term in f(x), we get:

f'(x) = d/dx(4x³) - d/dx(8x)

      = 3(4)(x²) - 8

      = 12x² - 8

Now, to find f'(4), we substitute x = 4 into the derivative expression:

f'(4) = 12(4)² - 8

     = 12(16) - 8

     = 192 - 8

     = 184

Therefore, the main answer is f'(4) = 184.

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To prove that 3 divides n^3 + 2n for any positive integer n, we need to show that there exists an integer k such that n^3 + 2n = 3k.

Let's proceed with the proof using mathematical induction:

Base case:

For n = 1, we have 1^3 + 2(1) = 1 + 2 = 3, which is divisible by 3. So the statement holds true for n = 1.

Inductive hypothesis:

Assume that the statement holds true for some positive integer k, i.e., k^3 + 2k = 3m, where m is an integer.

Inductive step:

We need to prove that the statement holds true for k + 1, i.e., (k + 1)^3 + 2(k + 1) = 3p, where p is an integer.

Expanding the expression (k + 1)^3 + 2(k + 1):

= k^3 + 3k^2 + 3k + 1 + 2k + 2

= (k^3 + 2k) + 3k^2 + 3k + 3

= 3m + 3k^2 + 3k + 3

= 3(m + k^2 + k + 1)

From the inductive hypothesis, we know that k^3 + 2k = 3m. Substituting this in the above expression:

= 3m + 3k^2 + 3k + 3

= 3(m + k^2 + k + 1)

We can see that the expression is a multiple of 3, with (m + k^2 + k + 1) as the coefficient.

Since m, k, and 1 are integers, (m + k^2 + k + 1) is also an integer. Therefore, (k + 1)^3 + 2(k + 1) is divisible by 3.

By using mathematical induction, we have proved that for any positive integer n, 3 divides n^3 + 2n.

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Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

Answer:

1/45

Step-by-step explanation:

There are 10 marbles

P ( yellow) = yellow marbles / total = 2/10 = 1/5

We do not replace the marble

There are 9 marbles, 1 of which is yellow

P ( yellow) = yellow marbles / total = 1/9

P ( yellow, no replacement, yellow) = 1/5 * 1/9 = 1/45

Answer:

x = -4

Step-by-step explanation:

15x = -60

move 15 over and divide 60 by it

x = -60/15

then solve

x = -4

Answer:

x=-4

Step-by-step explanation:

first let's solve 15x for 60 so solving for the valuable "x" we move all terms containing x to the left and all other terms to the right. Dividing each side by 15 so x is negative 4

Answer:

x = ± √ 22 − 3

Step-by-step explanation:

Answer:

(x-6y)(x-4y)

Step-by-step explanation:

Answer:

Angle 7 is equal to angle 1

Answer:

Step-by-step explanation:

The expression -2x³ + 13x² + 3x + 50 is equivalent to 10 - (2x³ + 11x² - 2x - 35) + (x + 5) + 6(4x²

An algebraic expression is an expression which consists of variables, coefficients, constants, and mathematical operators such as addition, subtraction, multiplication and division. Generally, if two things are the same, then it is called equivalent. Similarly, in mathematics, the equivalent expressions are the expressions that are the same, even though the expression looks different. But if the values are plugged in the expression, both the expressions give the same result.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

In the given expression;

10 - (2x³ + 11x² - 2x - 35) + (x + 5) + 6(4x²); this can be reduced or simplified to -2x³ + 13x² + 3x + 50

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Answer: 11/8

Step-by-step explanation:

1. Multiply the whole number by the denominator: 8•1=8

2. Add the numerator to the sum of the whole number and denominator: 8+3=11

3. Put the original denominator as the denominator, again: 11/8

hope this helps a bit lol

The required difference of the polynomial functions is -9s^2 + 4s - 2

Given the following difference of polynomial expressed as:

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

We are to find the difference

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

Expand

–6s^2 + 12s – 8 - 3s^2 - 8s + 6

Collect the like terms

–6s^2- 3s^2 + 12s - 8s - 8 + 6

-9s^2 + 4s - 2

Hence the required difference of the polynomial functions is -9s^2 + 4s - 2

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complete question

Find each difference.

(–6s2 + 12s – 8) – (3s2 + 8s – 6) =

–9s2 + 4s – 14

–9s2 + 4s – 2

–9s2 + 20s – 14

–9s2 + 20s – 2

The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

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first I needa know what the starting temp is? is it 4? or?? because if it's 4 then its -12

The required equation function j which is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

As we can see in the graph the functions j and f are similar but the graph of j is 2 units left of f. So, function f(x) has a domain of real number greater than equal to zero, while as the function j is 2 units left of f then its equation is given as  \(j(x)= (x+2)^{1/2}\)  where the domain of j is all real numbers greater then or equal to -2.

Thus, the equation of function j is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

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In the question the graph is missing, a graph has been added on behalf of the incomplete question.

The constant of proportionality is 2.02.

According to the concept of proportion, two ratios are in proportion when they are equal.

Two ratios or fractions are equal when an equation or a declaration to that effect is utilised. A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Four dozen gourmet donuts cost a total of $96.96.

So, if y be the total cost of the donuts and x be the number of donuts.

then the proportionality is

y= kx

k= y/x

k = 96.96 / (4 x 12)

k= 96.96/ 48

k= 2.02

Hence, the constant of proportionality is 2.02.

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Answer:

Its 1.45, you didn't have to ask a question just look it up

Step-by-step explanation:

7.25-5c

Answer:

Step-by-step explanation:

Ok:

1. This is a percent problem!

45/100*15=

675/100=

6.75

2. Subtract:

15-6.75=

8.25$

Answer: 8.25$

Answer:

975

Step-by-step explanation:

Answer:

975 what kind of question of that

The equation that represents the relationship between the total number of hours and days is h = 8d.

A straight line on a coordinate plane is described by a linear equation. It has the mathematical formula y = mx + b, where m denotes the line's slope and b its y-intercept. The largest power of the variable (in this example, y) in a linear equation with degree 1 is 1.

Given that, total number of hour the chef spends making cakes, h, and the number of days chef spends making cakes, d.

Thus, Total number of hours = (Number of cakes per day) x (Number of hours per cake) x (Number of days)

h = 4 x 2 x d

h = 8d

Hence, the equation that represents the relationship between the total number of hours and days is h = 8d.

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Answer:

Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.

Step-by-step explanation:

:)

Answer: True, because 8 + 0.5 = 8.5, which is a rational number since fractions and decimals are counted as rational numbers.

To get a sample mean of customers during this 5 weekdays period are 1.79.

The term standard deviation refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given that,

A small hair salon in Denver, Colorado, averages about 32 customers on weekdays with a standard deviation of 5. This means that

She reports that her strategy has worked since the sample mean of customers during this 5 weekday period jumps to 36.

We also have to find a standard deviation of the sample(that is, the 5 days),

S= \(\frac{σ}{\sqrt{5} }\)

S=\(\frac{5}{\sqrt{5} }\)

S= 2.24

\(Z=\frac{X- μ}{σ}\)

Z= 36-32/2.24

Z= 1.79

Therefore, to get a sample mean of customers during this 5 weekdays period are 1.79.

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Answer:

24

Step-by-step explanation:

25%= 1/4 of the class

1/4 *x=6

x=24

The number of green beads left over = 15

Walter:

Number of green beads = 476

Number of red beads = 32

Agnes:

Number of green beads = 104

Number of red beads = 16

Holly:

Number of green beads = 281

Number of red beads = 80

Total number of red beads = 32+16+80 = 128 beads

Number of red beads required for making one lizard = 16

Since 128/16 = 8 , there will be no red beads left after making 8 lizards.

Total number of green beads = 476+104+281 = 861 beads

Number of green beads required for making one lizard = 94

Now 861/94 = \(9\frac{15}{94}\)

That is , 15 is the remainder when 861 is divided by 94

So there will be 15 green beads left after making 9 lizards.

Therefore, the number of green beads left over = 15

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Answer:

The length of the leg is 11 units.

Step-by-step explanation:

The triangle 45 - 45 - 90 theorem states that the length of the hypotenuse is \(\sqrt{2}\) times of the length of any of the legs. Hence, we get the following expression:

\(h = \sqrt{2} \cdot l\) (1)

Where:

\(l\) - Length of the leg, in units.

\(h\) - Hypotenuse, in units.

If we know that \(h = 11\sqrt{2}\), then the length of the leg is:

\(l = \frac{h}{\sqrt{2}}\)

\(l = 11\)

The length of the leg is 11 units.

Answer:

we know the smaller cone's height is 1/4 of 12, namely 3

Step-by-step explanation:

Because we know the radius and height of both cones, we can calculate the area of the larger one by subtracting the area of the smaller one; the Frustum's area remains.

Answer:

The definition of implied is something that was hinted at or suggested, but not directly stated. When a person looks at his watch and yawns multiple times as you are talking, this is an example of a situation where boredom is implied.

The product of (3 - √5)(7 - √5) simplifies to 26 - 10√5.

To multiply and simplify the expression (3 - √5)(7 - √5), we can use the distributive property of multiplication over addition. Here are the steps:

1. Start by multiplying the first terms in each set of parentheses: 3 * 7 = 21.

2. Then multiply the outer terms: 3 * (-√5) = -3√5.

3. Next, multiply the inner terms: -√5 * 7 = -7√5.

4. Finally, multiply the last terms: -√5 * -√5 = 5.

Now we can combine these terms to simplify the expression:

21 + (-3√5) + (-7√5) + 5

Combine the like terms: 21 + 5 - 3√5 - 7√5

Combine the constants: 21 + 5 = 26.

Combine the radical terms: -3√5 - 7√5 = -10√5.

The final simplified expression is: 26 - 10√5.

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