Which point on the number line has the least absolute value?​

To find the critical points of f(x) = x - 18x² + 96x, we need to find the values of x where f'(x) = 0.

f'(x) = 1 - 36x + 96

Setting f'(x) = 0, we get:

-36x + 97 = 0

x = 97/36

So the critical point is (97/36, f(97/36)).

To use the Second Derivative Test, we need to find f''(x):

f''(x) = -36

At the critical point x = 97/36, f''(97/36) = -36 < 0.

Since f''(97/36) is negative, the Second Derivative Test tells us that the critical point corresponds to a local maximum.

Therefore, the critical point (97/36, f(97/36)) is a local maximum.
To find the critical points of the function f(x) = x - 18x² + 96x, we first need to find its first derivative, f'(x), and then set it to zero to find the critical points.

1. Find the first derivative, f'(x):
f'(x) = d/dx (x - 18x² + 96x) = 1 - 36x + 96

2. Set f'(x) to zero and solve for x:
0 = 1 - 36x + 96
36x = 95
x = 95/36

Now, let's use the Second Derivative Test to determine if this critical point corresponds to a local minimum or maximum.

3. Find the second derivative, f''(x):
f''(x) = d/dx (1 - 36x + 96) = -36

4. Evaluate f''(x) at the critical point x = 95/36:
f''(95/36) = -36

Since f''(95/36) is negative, the Second Derivative Test tells us that the critical point x = 95/36 corresponds to a local maximum.

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Answer:

After selling 98 cups, she made $98

Step-by-step explanation:

If she sold 98 cups, and each one went for $1, then you can set up an equation:

98(1)=98

Answer:

Ashley made $98.

Step-by-step explanation:

If 1 cup = $1, then you multiply the cups by 98 meaning you also must multiply $1 by 98 to get a total of $98.

Answer:

x=32°

Step-by-step explanation:

3x-2=2x+30

x-2=30

x=32°

To determine the scale factor of the dilation between the green parallelogram and the black parallelogram, you would need to compare the corresponding side lengths of the two parallelograms. For example, if the green parallelogram has a side length that is half of the black parallelogram's side length, the scale factor would be 1/2 (Option B).

If the green parallelogram's side length is twice the black parallelogram's side length, the scale factor would be 2 (Option C). And if the green parallelogram's side length is one-third of the black parallelogram's side length, the scale factor would be 1/3 (Option A). Without specific measurements or a visual representation, it is not possible to accurately identify the scale factor between the two parallelograms. Please provide the side lengths or a diagram to help determine the correct scale factor.

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There may be a difference on speed based on various factors

Though it would be reasonable to conclude that if it takes less time for a car to move 50 centimeters than 150 centimeters, they must be traveling faster; we do not know exactly when they did this and whether their speed changed accordingly.

Furthermore, it could have taken the same time covering both distances; thus leaving unanswered questions regarding their relative speeds.

Due to variables affecting car speed such as changes in terrain or obstacles in its path, we cannot accurately predict its speed without more information regarding these two runs.

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Answer:

i think it would be...5^-5, 5^0, 5^4

Step-by-step explanation:

pls mark brainliest

The function h(x) can be represented by -3x-9 .

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+6. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=7 and b=6.

The question gives two linear equations that represent two functions: f(x)=-2x+7 and g(x)=5x-16.

For solving this you should sum both equations. See below

h(x)=f(x)+g(x)

h(x)=-2x+7 +5x-16

h(x)=-3x-9

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Answer:

Subtract 1 from both sides.

Answer:

subtract 1 from both sides. because taking out the 1 from 1 and 1 from 17 will equal 16. which leaves t/4=16

The derivative of y with respect to x when y = e⁻¹⁷ˣ  is dy/dx = -17eˣ

Find the derivative?

To find the derivative of y with respect to x when y = e⁻¹⁷ˣ, we'll use these terms: "derivative", "respect", and "with".

Identify the function. In this case, y = e⁻¹⁷ˣ

Find the derivative (dy/dx) of the function with respect to x. To do this, we'll apply the chain rule, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

The outer function is e^(u) (where u is the inner function), and its derivative with respect to u is e^(u). The inner function is -17x, and its derivative with respect to x is -17.

Apply the chain rule. The derivative of y with respect to x (dy/dx) is the product of the derivative of the outer function and the derivative of the inner function: (e^(u)) * (-17).

Substitute u with the inner function (-17x). So, dy/dx = (e⁻¹⁷ˣ * (-17).

The derivative of y with respect to x when y = e⁻¹⁷ˣ  is dy/dx = -17eˣ

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The radius of the pond is 32 feet, under the condition  that 43 feet from the bank and 75 feet from the point of tangency.

Let us consider that  the center of the circle O, the point of tangency T, and Federico's position P.
We can utilize these two points to form a line. The point of tangency is the place where Federico is closest to the pond. The radius of the pond is considered perpendicular to this line and passes through the point of tangency.

Firstly, we have to  the distance between Federico's position P and covers passes through points T and B (the bank). This distance is equivalent to the given  radius of the circle. We have to apply the formula for the distance between a point and a line to find this distance.

Let us assume this distance as  d.
d = (|BT x BP|) / |BT|

Here
|BT| = line segment length of  BT,
|BP| = line segment length of  BP,
BT x BP = vectors cross product of  BT and BP.

Here we evaluate  |BT| applying the Pythagorean theorem
|BT|² = 75²+ r²

Here,
r = radius concerning the circle.
Then,

|BP|² = 43² + r²
Staging these values into our formula for d:
d = (|BT x BP|) / |BT|
 = (|BT| × |BP|) / |BT|
 = |BP|
 = √(43² + r²)

We want to solve for r, so we can square both sides:

d² = 43² + r²

r² = d² - 43²

r = √(d² - 43²)

Placing in d = 75,

r = √(75² - 43²)
≈ 32 feet
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The function that represents the total cost (y) of buying x shirt online of $3.50 each and shipping charges of $9.50 is 3.50x + 9.50 = y

Cost of each shirt = $3.50

The fee for shipping the shirts is = $9.50

Total number of shirts bought by shirt online = x

The total cost of buying x shirts is represented by y

The total cost will be the sum of each cost of the shirt and shipping charges

y = 3.50x + 9.50

Hence, the function that represents the total cost y of buying x shirt online of $3.50 each and shipping charges of $9.50 is 3.50x + 9.50 = y

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The question is incomplete complete question is :

The teacher could buy the shirt online at 3.50 each she would also pay a fee of 9.50 for shipping the shirts. Write a function that can be used to find y the total cost in dollars of buying x shirts online.

2x+14=30

2x =30-14

2x=16

x =8

Answer:

8

Step-by-step explanation:

Twice means 2 so twice a number,n, means 2 times n thus 2n

sum means add so, 2n + 14

"is" means equal so 2n + 14 = 30

Solve for n:

2n=16

N=8

Answer: 10, 911,000,000

Step-by-step explanation:

10,911,000,000 < 11,000,000,000

10,911,000,000 > 10,910,099,999

Answer:

Step-by-step explanation:

The probability of drawing 2 red cards from a standard 52-card deck can be calculated as follows:

There are 26 red cards in the deck, so the probability of drawing a red card on the first draw is 26/52.

After the first card is drawn, there are 25 red cards remaining in the deck out of 51 total cards, so the probability of drawing a red card on the second draw is 25/51.

To find the probability of both events happening together (drawing 2 red cards), we multiply the probabilities of each event:

(26/52) * (25/51) = 0.245 or approximately 24.5%

Therefore, the probability of drawing 2 red cards in a standard 52 card deck is approximately 24.5%.

The parametric equations for the tangent line to curve C at point P are: x = -t y = 6t - 1 z = 8t + 6

To find the parametric equations for the tangent line to curve C at point P, we need to first find the derivative of the curve at P.

Taking the derivative of each component of the curve, we get:

dx/dt = -1

dy/dt = -6t

dz/dt = 8

At point P = (0, -1, 6), t = -1.

Plugging this into the derivative, we get:

dx/dt = -1

dy/dt = 6

dz/dt = 8

So, the tangent vector to curve C at point P is < -1, 6, 8 >.

To get the parametric equations for the tangent line, we can use the point-slope form: r(t) = P + t< -1, 6, 8 > Plugging in the coordinates of point P, we get: r(t) = <0, -1, 6> + t< -1, 6, 8 > Expanding this out, we get: r(t) = <-t, 6t - 1, 8t + 6>

So, the parametric equations for the tangent line to curve C at point P are: x = -t y = 6t - 1 z = 8t + 6

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Answer:

The formula for the volume of a cone is ⅓ r2h cubic units, where r is the radius of the circular base and h is the height of the cone.The volume of any sphere is 2/3rd of the volume of any cylinder with equivalent radius and height equal to the diameter.The formula for the volume of a sphere is 4⁄3πr³. For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h

Step-by-step explanation:

The formula for volume is: Volume = length x width x height

Answer:

Step-by-step explanation:

Volume of a sphere:  4/3 π r³

4/3 (3.14) (2.5)³ =

4/3 (3.14) (15.625) = 65.42 units³

Volume of a cylinder = π r² h

(3.14) (2.5)² (4)

(3.14) (6.25)(4) = 78.5 units²

Volume of a Cone = 1/3 π r² h

(1/3)(3.14)(2.5)²(4) =

(1/3)(3.14)(6.25)(4) = 26.17 units²

The boat must move 785.82 m closer to the cliff  for the angle of depression to become 19°.

We need to find how much closer to the cliff the boat must move for the angle of depression to change from 7° to 19°.

Calculate the distance from the boat to the base of the cliff at 7° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(7°) = 150m/distance
distance = 150m/tan(7°)

distance=1221.49

Calculate the distance from the boat to the base of the cliff at 19° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(19°) = 150m/distance
distance = 150m/tan(19°)

distance=435.6665

Calculate the difference between the two distances to find out how much closer the boat must move.
difference = distance at 7° angle of depression - distance at 19° angle of depression

Plugging in the values from Steps 1 and 2, we get:
difference = (150m/tan(7°)) - (150m/tan(19°))

difference=1221.49-435.6665

difference=785.8235

After calculating, we find that the boat must move approximately 785.82 meters closer to the cliff for the angle of depression to change from 7° to 19°.

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In this case, the mean absolute deviation of 8.5 indicates that, on average, the data points deviate from the mean by about 8.5 units.

Mean absolute deviation (MAD) is a statistical measure that represents the average distance between each data point and the mean of the data set. It is calculated by finding the absolute value of the difference between each data point and the mean, and then taking the average of these absolute differences. MAD is a useful measure of the variability or spread of a data set, and is often used as an alternative to the more common measure of standard deviation. Like standard deviation, MAD gives an indication of how spread out the data is, but unlike standard deviation, MAD is less sensitive to extreme values or outliers.

Here,

To find the mean absolute deviation of the data, we first need to calculate the mean (average) of the data:

Mean = (46 + 54 + 43 + 57 + 50 + 62 + 78 + 42) / 8

Mean = 52

The mean of the data is 52.

Next, we need to calculate the absolute deviation of each data point from the mean. The absolute deviation is simply the absolute value of the difference between each data point and the mean:

|46 - 52| = 6

|54 - 52| = 2

|43 - 52| = 9

|57 - 52| = 5

|50 - 52| = 2

|62 - 52| = 10

|78 - 52| = 26

|42 - 52| = 10

Now, we can calculate the mean absolute deviation by taking the average of the absolute deviations:

Mean Absolute Deviation = (6 + 2 + 9 + 5 + 2 + 10 + 26 + 10) / 8

Mean Absolute Deviation = 8.5

The mean absolute deviation of the data is 8.5.

Interpretation: The mean absolute deviation represents the average distance between each data point and the mean of the data. In this case, the mean absolute deviation of 8.5 indicates that, on average, the data points deviate from the mean by about 8.5 units. This means that the data points are relatively spread out, with some points being much higher or lower than the mean.

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There are now 260 cows on the farm.

Let's start through calculating the amount of milk produced with the aid of the original cows before any modifications were made.

If every of the unique cows was producing 12.8 liters of milk in keeping with day, and there had been "x" cows, then the entire amount of milk produced by means of the original cows could be:

12.8x liters per day

After the adjustments, the farmer has 60 more cows and all cows produce 15 liters of milk per day. So, the full amount of milk produced with the aid of all cows after the modifications would be:

15(x + 60) liters per day

we're told that the new milk production is 1340 liters more according to day than before the changes. So, we can set up an linear equation:

15(x + 60) = 12.8x + 1340

Simplifying the equation, we get:

15x + 900 = 12.8x + 1340

2.2x = 440

x = 200

therefore, there were at first 200 cows on the farm. After the changes, the full number of cows would be:

x + 60 = 200 + 60 = 260 cows

So, there are now 260 cows on the farm.

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The distance between the two points (8,6) and (3,-6) in simplest radical form is √169 units.

The complete question is :

Find the distance between the two points in simplest radical form.

(8,6) and (3,−6)

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given that. the two points are (8,6) and (3,-6).

Substituting the values into the formula, we get:

d = √((3 - 8)² + (-6 - 6)²)

Simplifying the expression inside the square root:

d = √((-5)² + (-12)²)

d = √(25 + 144)

d = √169

Therefore, the distance is √169 units.

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The probability of no heads is given as follows:

P(No Heads) = 17.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of outcomes is given as follows:

200.

The desired outcomes, those without heads, are Tails, Tails, which happened 35 times, hence the probability is given as follows:

p = 35/200

p = 0.175

p = 17.5%.

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The required probability is approximately 0.1253 or 12.53%.

We can use the central limit theorem to approximate the sampling distribution of the mean of the weights of clothes washed by 50 families of four. According to the central limit theorem, the sampling distribution of the mean will be approximately normal if the sample size is large enough (n > 30), regardless of the shape of the population distribution.

The mean of the sampling distribution of the mean will be equal to the population mean, which is 2000 lbs

[tex]SEM=\frac{\sigma}{\sqrt{n} }[/tex]

σ = population standard deviation

n = sample size.

[tex]SEM=\frac{187.5}{\sqrt{50} }[/tex]

= 26.5

Now we need to find the z-scores corresponding to the two values of the mean.

[tex]z_1=\frac{1980-2000}{26.5}[/tex]

= -0.75

[tex]z_2=\frac{1990-2000}{26.5}[/tex]

= -0.38

Using a standard normal table, we can find the probability that a z-score is between -0.75 and -0.38.

P(-0.75 < Z < -0.38) = 0.1253

Therefore, the required probability is approximately 0.1253 or 12.53%.

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In one month, a total of 447 people stayed at the hotel.

In one month, a hotel had 382 adults and 65 children staying as guests.

To find out the total number of people who stayed at the hotel, we simply need to add the number of adults and children together.

In one month, a total of 447 people (382 adults and 65 children) stayed at the hotel.

Overall, this problem is a simple example of addition in action. By adding the number of adults and children together, we can determine the total number of people who stayed in the hotel.

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Karen's last class will end at three in the afternoon.

Given that Kevin has three classes in a row, each lasting two hours, we can calculate the total duration of his classes. Three classes, each two hours long, amount to a total of 6 hours.

Since Kevin's first class starts at seven in the morning, we add 6 hours to that time, resulting in the conclusion of Karen's last class at three in the afternoon.

Understanding schedules and timetables is essential for effective time management. In academic settings, students often have multiple classes with varying durations throughout the day.

Calculating the end time of a class or event based on its start time and duration helps individuals plan their activities and allocate their time efficiently.

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The probability that an M&M picked at random is brown is 30% if m&m picked brown at random. Probability refers to the measure of the likelihood of an event occurring.

To find the probability that an M&M picked at random is brown, we need to consider the given percentages of the other colors. Given that 20% are yellow, 20% are red, 10% are orange, 10% are blue, and 10% are green. First, let's add these percentages together:
20% + 20% + 10% + 10% + 10% = 70%

Since the total percentage should add up to 100%, we can find the percentage of brown M&Ms by subtracting the sum of the other colors' percentages from 100%:
100% - 70% = 30%
So, the probability that an M&M picked at random is brown is 30%.

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The factored form of 21r-56 is: 21r-56 = 7r(-5) or 7r*(-5)

Factoring is the process of finding the factors (or divisors) of a given mathematical expression or number. In algebra, factoring involves breaking down an expression into simpler parts (called factors) that can be multiplied together to obtain the original expression. The goal of factoring is to simplify the expression or solve an equation by expressing it in terms of its factors.

In the given question,

To factor 21r-56, we first need to find the greatest common factor (GCF) of the two terms. The GCF of 21 and 56 is 7. We can also factor out r since it is a common factor of both terms. Therefore, we can write:

21r-56 = 7r(3-8)

Simplifying the expression inside the parentheses, we get:

21r-56 = 7r(-5)

Therefore, the factored form of 21r-56 is:

21r-56 = 7r(-5) or 7r*(-5).

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The volume of the cylinder is 4004 cubic metres.

The diameter of the cylinder is 28 metres and the height of the cylinder is 6.5 metres.

Therefore, the volume of the cylinder can be found as follows:

Hence,

volume of a cylinder = πr²h

where

Therefore,

volume of the cylinder =  22 / 7 × 14² × 6.5

volume of the cylinder = 22 / 7 × 196 × 6.5

volume of the cylinder = 28028 / 7

volume of the cylinder = 4004 cubic metres

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To find the first derivative of the equation x cos(14x + 13y) = y sin x, we will need to use the chain rule and product rule.

First, we will differentiate each term separately:

d/dx(x) = 1

d/dx(cos(14x + 13y)) = -sin(14x + 13y) * d/dx(14x + 13y)
= -sin(14x + 13y) * 14

d/dx(y) = 0 (since y is a constant)

d/dx(sin(x)) = cos(x)

Next, we will apply the product rule to differentiate the left-hand side of the equation:

d/dx(x cos(14x + 13y)) = cos(14x + 13y) + x * (-sin(14x + 13y) * 14)

Now, we can set this expression equal to the derivative of the right-hand side of the equation and solve for the first derivative:

cos(14x + 13y) - 14x sin(14x + 13y) = y cos(x)

Our final answer for the first derivative is:

cos(14x + 13y) - 14x sin(14x + 13y) = y cos(x)

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The student used 30.0 mL of 3.00 M HCl to make the 50.0 mL sample of 1.80 M HCl.

To find the volume of 3.00 M HCl needed to make a 50.0 mL sample of 1.80 M HCl, we can use the equation:

M₁V₁ = M₂V₂

Where M₁ is the initial concentration, V₁ is the initial volume, M₂ is the final concentration, and V₂ is the final volume.

We are given M₁ = 3.00 M, M₂ = 1.80 M, and V₂ = 50.0 mL. We can rearrange the equation to solve for V₁:

V₁ = (M₂V₂) / M₁

V₁ = (1.80 M * 50.0 mL) / 3.00 M

V₁ = 30.0 mL

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