Find the derivative of the following function. f(w)=5w⁶+8w⁵+7w
f′(w)=

Mode

2 x 5 = 10

6 x 5 = 30

5 x 5 = 25

3 x 5 = 15

7 x 5 = 35

8 x 5 = 40

9 x 5 = 45

2 x 5 = 10

4 x 5 = 20

7 x 5 = 35

4 x 5 = 20

7 x 5 = 35

The mode is 35 because it is repeated 3 times.

Answer:

g(x)=x+2

Step-by-step explanation:

took the test and found out the right answer.

The graph of the Cartesian equation y = (x - 6)^2 indicates the portion of the graph traced by the particle and the direction of motion. It forms a U-shaped curve opening upwards, with the vertex at (6, 0). The particle moves along this curve in the direction away from the vertex, as indicated by the positive coefficient of the squared term.

The given parametric equations are x = 5t + 6 and y = 25t^2, where t is in the interval (-∞, ∞). To find the Cartesian equation for the particle's path, we eliminate the parameter t by expressing t in terms of x and substituting it into the equation for y.

From the equation x = 5t + 6, we can solve for t as t = (x - 6)/5. Substituting this value into the equation for y, we have y = 25((x - 6)/5)^2.

Simplifying the expression, we get y = 25(x - 6)^2/25 = (x - 6)^2.

Therefore, the Cartesian equation for the particle's path is y = (x - 6)^2.

Graphing this equation, we obtain a parabolic curve with its vertex at (6, 0). The graph represents the path of the particle as it moves along the curve. The direction of motion can be determined by observing the sign of the coefficient of the squared term. In this case, since the coefficient is positive, the particle moves upwards from the vertex.

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We need to find the length of the longest side of an arrowhead.

Length of the longest side of the tip is \(14.14\ \text{units}\).

The length of one of the legs of the isosceles right triangle is 10 units.

Since, it is a isosceles right triangle, two sides will have equal lengths.

So, the other side of the triangle will also be 10 units and the angle between these two sides will be \(90^{\circ}\).

So, the Pythagoras theorem can be used to find the third side which will be the longest.

\(h=\sqrt{10^2+10^2}=\sqrt{200}\\\Rightarrow h=10\sqrt{2}=14.14\ \text{units}\)

The length of the longest side of the tip is \(14.14\ \text{units}\).

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Answer:

3

Step-by-step explanation:

81^(¼) can also be witten as the fourth root of 81, which happens to be 3.

Answer:

3

Step-by-step explanation:

(3*(to the fourth power))1/4

1. To get Equation B from Equation A, we add/subtract the same quantity to/from both sides.

2. Equation A is equivalent to Equation B

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

Here, we have

1.  We are given the equation :

2x - 1 = 5x .............(A)

To get Equation B from A, we would subtract 2x from both sides of the equation.

2x - 2x - 1 = 5x - 2x

- 1 = 3x...... (B)

Hence, to get Equation B from Equation A, we add/subtract the same quantity to/from both sides.

2. Based on the previous answer,

2x - 1 = 5x  is equal to  -1 = 3x.

Hence, both Equation A and Equation B are equivalent expressions.

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The value today of a money machine that will pay $1,488.00 per year for 18 years, with the first payment starting in 2 years, is approximately $16,033.52.

To determine how much Derek will need in his retirement account on his 65th birthday, we can use the concept of present value. Since Derek wants to withdraw $130,476.00 per year for 20 years (from his 66th to 85th birthday) and the interest rate is 9%, we can calculate the present value of this annuity.

By using the present value of an annuity formula, the calculation yields a retirement account balance of approximately $1,187,672.66 on his 65th birthday.

For the second scenario, to find the value today of a money machine that pays $1,488.00 per year for 18 years, starting 2 years from today, we can again use the concept of present value. With an interest rate of 10%, we calculate the present value of this annuity.

Using the present value of an annuity formula, the calculation shows that the value today of this money machine is approximately $16,033.52.In both cases, the present value calculations take into account the time value of money, which means that future cash flows are discounted back to their present value based on the interest rate.

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Sal will pay to tile his entryway by calculating the area of the entryway in square feet and multiplying it by the cost of the tile per square foot.

To determine the cost of tiling Sal's entryway, we need to calculate the area of the floor plan. Since each unit length represents 1 foot, we can consider the dimensions of the floor plan in terms of feet. Let's say the length is 'L' feet and the width is 'W' feet. The area can be found by multiplying L by W, giving us the total area in square feet.

Once we have the area, we can multiply it by the cost per square foot, which is $1.15. This will give us the total cost of the tiles needed to cover the entryway.

It's important to note that rounding the final answer to the nearest cent is necessary to provide a precise cost value.

Therefore, by calculating the area of the entryway and multiplying it by the cost per square foot, we can determine the total amount Sal will pay to tile his entryway.

In conclusion, to calculate the cost, we need to find the area of the entryway by multiplying the length and width in units, convert it to square feet, and then multiply it by the tile cost per square foot.

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The graph of the function f(x) = ex - 2x has a horizontal tangent line at x = 0.693.

To find the values of x for which the graph of the function f(x) = ex - 2x has a horizontal tangent line, we need to determine when the derivative of the function is equal to zero. A horizontal tangent line occurs when the slope of the function is zero, which corresponds to the critical points of the function.

To find the critical points, we differentiate f(x) with respect to x. The derivative of ex is ex, and the derivative of -2x is -2. Setting the derivative equal to zero, we have ex - 2 = 0.

Adding 2 to both sides, we get ex = 2. Taking the natural logarithm of both sides, we have ln(ex) = ln(2), which simplifies to x = ln(2).

Therefore, the graph of f(x) = ex - 2x has a horizontal tangent line at x = ln(2) or approximately x = 0.693. At this point, the slope of the function is zero, indicating a horizontal tangent line.

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The rectangular form of n = (2.80∠–29.9°) is n = 2.45 – 1.38j.

To convert the polar form of n = (2.80∠–29.9°) to rectangular form, we can use the following equations:

a = r*cos(θ)
b = r*sin(θ)

where r is the magnitude of the complex number and θ is its angle in polar form.

Using the given values, we have:

r = 2.80
θ = –29.9°

Converting θ to radians:

θ = –29.9° * π/180 = –0.522 radians

Substituting the values in the equations, we get:

a = 2.80*cos(–0.522) = 2.45
b = 2.80*sin(–0.522) = –1.38

Therefore, the rectangular form of n = (2.80∠–29.9°) is:

n = 2.45 – 1.38j

So,  The rectangular form of n = (2.80∠–29.9°) is n = 2.45 – 1.38j.

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In this case, the inflection point occurs at 2 years with a population level of 333. Since the inflection point represents half of the carrying capacity, you can calculate the carrying capacity by multiplying the population level at the inflection point by 2: Therefore, the carrying capacity of this population is 666.

To answer this question, we first need to understand what is meant by carrying capacity. Carrying capacity refers to the maximum number of individuals that can be supported by an ecosystem or environment without causing negative impacts on that ecosystem. It is the point at which the resources available in the environment can no longer support any additional growth in the population.
Given that the population is growing logistically, we can assume that it is following the logistic growth model, which takes into account the carrying capacity of the environment. The inflection point in the graph occurs when the population growth rate starts to slow down, indicating that the carrying capacity has been reached.
At the inflection point, the population level is 333, and we know that this is happening at 2 years. However, without more information about the growth rate or carrying capacity, it is not possible to calculate the carrying capacity. We would need additional data points from the graph or information about the growth rate to determine the carrying capacity.
In summary, we need more information about the growth rate or additional data points from the graph to determine the carrying capacity. Answering this question with more than 100 words, we can also emphasize the importance of understanding carrying capacity in population growth and how it is critical for sustainable growth and conservation efforts.
A population growing logistically experiences an S-shaped curve on its graph, where the carrying capacity is the maximum population size that the environment can sustain. In a logistic growth model, the inflection point is the point at which the population's growth rate is at its maximum, which usually occurs when the population reaches half of the carrying capacity.
In this case, the inflection point occurs at 2 years with a population level of 333. Since the inflection point represents half of the carrying capacity, you can calculate the carrying capacity by multiplying the population level at the inflection point by 2:
Carrying Capacity = 333 * 2 = 666
Therefore, the carrying capacity of this population is 666.

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Answer:

Step-by-step explanation:

q log a is equivalent to log a^q.  Note:  This assumes that the base of your logarithmic system is 10.

-3 log b is equivalent to log b^(-3)

and so   q log a -3 log b  in condensed logarithm form is

log {a^q*b^(-3)}

                 a^q

or log  -----------------

                 b^3    

Answer:

3.75 cups

Step-by-step explanation:

Given that :

5 cups of liquid lemonade concentrate is mixed with 2.5 cups of water to make lemonade

5 cups of lemonade = 2.5 cups of water

Ratio :

5 / 2.5

For 2.5 cups of lemonade :

5 / 2.5 = 0.5

Multiply :

5 / 2.5 * 0.5 / 0.5

2.5 / 1.25

Hence, 2.5 cups + 1.25 cups = 3.75 cups of lemonade will be made with 2.5 cups of liquid lemonade concentrate

We are asked to factor out the expression:

4 x^3 - 10 x

So we extract a factor of "2" from the numerical factors "4" and "10", and also a factor of "x" from each term,leading to:

2 x ( 2 x^2 - 5)

Therefore, please select the first answer option they give you in the list.

your answer would be 33.

step 1

2(+14)−1(2−5)

2+28−1(2−5)

step 2 distribute

2+28−1(2−5)

2+28−2+5

step 3 then add the numbers

2+28−2+5

2+33−2

combine

2+33−2

ANSWER IS

33

Answer:

60

Step-by-step explanation:

edge

To find the measure of angle B, we can use the inverse tangent function:

tan(B) = opposite / adjacent = a / b

tan(B) = 500 / 300

B = arctan(500 / 300)

B ≈ 59.0 degrees

Therefore, the measure of angle B is approximately 59 degrees (rounded to the nearest degree).

The measure of length RQ and RS are 3.

We have,

∠QRS = 90

QS = 3√2

Now,

In ΔQRS,

From trigonometry,

Where the two angles are 45 and one angle is 90.

We know that,

RS = 1

QS = √2

RQ = 1

But,

QS = 3√2

This means,

We multiply 3 on all sides.

So,

RS = 3

QS = 3√2

RQ = 3

Thus,

The measure of length RQ and RS are 3.

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Answer:

I think the answer would be :

b = 0.375 a

Hope it was helpful for you ^^ .

Answer:

2/7 or 29%

Step-by-step explanation:

you add all the numbers than you put the blue marble on top and there it is.

Answer:

2/7

Step-by-step explanation:

Hello there.

1. First, you would add all the numbers up to get the total.

3 + 2 + 2 = 7 total marbles

2. Of those 7 marbles, 2 are blue. This would be 2/7 in fraction form.

Hence, there is a 2 in 7 chance that Sandra will choose a blue marble from the bag.

Hope this helps.

- Angelo

The Probability that the system does not fail for 2 days is 0. 053

Given ,

Mean (u) = 37 hours .

Step  1 : Calculate the rate parameter, λ.

λ = 1/ mean

λ = 1/ 37 = 0.02703

Step 2 : Find the probability that the system does not

fall for two days, P ( x\(\leq\)2 )  

P ( x\(\leq\)2 ) .= 1 - e power (lamda(x))

       = 1 - e - 2(lamda)

        = 1 - e power  -2(0. 02703 )

By solving,

P ( x\(\leq\)2 ) = 0.05263

P ( x\(\leq\)2 ) = 0. 053 [ upto three decimals]

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The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

Substitute the x and y values from the ordered pairs into the equation, one by one, until both sides of the equation are equal.

Step-by-step explanation:

A. (-2,-3)

3 * (-2) - 4 * (-3) = 21

-6 + 12 = 21

6 = 21 not equal

B. (0,7)

3 * 0 - 4 * 7 = 21

0 - 28 = 21

- 28 = 21 not equal

C. (7,0)

3 * 7 - 4 * 0 = 21

21 - 0 = 21

21 = 21 equal

Answer: It is linear

Step-by-step explanation:

When you graph the equation, it is a straight line, meaning it is linear.

If you graphed the equation and it wasn't a straight line, it would be nonlinear.

Answer:

c is the answer ....

mark me brainliest

Answer:

1.price(dollars) and soccer ball

2.y=30 and x=5

3. I think 5 or 30

Step-by-step explanation:

pa follow po

pa brainlest po

pa heart and 5 star

The given expression is √8aᵇ / √108 and the simplified expression is (√2 * aᵇ) / (3√3).

To simplify this expression, we can start by simplifying the square roots:

√8aᵇ = √(4 * 2) * aᵇ = 2√2 * aᵇ

√108 = √(36 * 3) = 6√3

Now, we can substitute these simplified square roots back into the original expression:

(2√2 * aᵇ) / (6√3)

To simplify further, we can divide both the numerator and denominator by their greatest common factor, which in this case is 2:

(2√2 * aᵇ) / (6√3) = (√2 * aᵇ) / (3√3)

The simplified expression is (√2 * aᵇ) / (3√3).

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The absolute value of any number is never negative. Absolute value represents distance, and negative distance is not possible (it doesn't make any sense to have a negative distance). Specifically, it is the distance from the given number to 0 on the number line.

The result of an absolute value is either 0 or positive.

Examples:

| -22 | = 22

| -1.7 | = 1.7

| 35 | = 35

The vertical bars surrounding the numbers are absolute value bars

Answer:

C and D

Step-by-step explanation:

a = 10.8 - 8/1.5 - 1 = 4.2

rate of change: 4.2

y = 4.2x + b

x = 1, y = 8

8 = 4.2 (1) + b

8 - 4.2 = b

b = 3.8

Initial value: 3.8