Write the equation of the parabola that has its vertex at (-2,7) and passes through (-1,3).

We need to find the d/dt of the curve, then evaluate at t=0, and finally normalize the result to get the unit tangent vector. The derivative can be found using the chain rule, and after putting t=0, we get the point (0, 0, 10). The magnitude of this vector is 10, so the unit tangent vector is (0, 0, 1).

Explanation:

The unit tangent vector T(t) is defined as the derivative of the position vector r(t), divided by its magnitude. In other words, T(t) = r'(t)/|r'(t)|. To find the derivative of the curve r(t), we need to use the chain rule, as follows:

r'(t) = (5e^(-t) - 5te^(-t), 10/(1+t^2), 10e^t)

Now, we can evaluate r'(t) at t=0 to get the tangent vector at that point:

r'(0) = (5, 10, 10)

The magnitude of r'(0) is given by:

|r'(0)| = sqrt((5)^2 + (10)^2 + (10)^2) = 10sqrt(3)

Therefore, the unit tangent vector at t=0 is:

T(0) = r'(0)/|r'(0)| = (5/sqrt(3), 10/sqrt(3), 10/sqrt(3))

However, this vector can be simplified to:

T(0) = (0, 0, 1)

since the first two components are zero and the third component is equal to 1. This is the final answer for the unit tangent vector at the point where t=0.

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Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.

The ordered pairs are given as:

(-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11)

Now, First, look at the values of the abscissas: -3, -2, -1, 0, and 1.

The values form an arithmetic sequence with common difference of 1.

On the other hand the values of the ordinates: 1, 3, 5, 7, and 9 also form an arithmetic sequence with common difference of 2.

Since the coordinates form arithmetic sequences

Hence, From the ordered pair above:

We can see that, as x increases by 1, the value of y increases by 2

The above is a property of a linear function

Hence, the true statement is (c)

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Complete question is,

The ordered pairs below represent a relation between x and y. (-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11). Could this set of ordered pairs have been generated by a linear function?. A) Yes, because the distance between consecutive x-values is constant. B) No, because the distance between consecutive y-values is different than the distance between consecutive x-values. C) Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it. D) No, because the y-values decrease and then increas

By Pythagorean theorem, the missing sides of right triangles are listed below:

Case 1: x = 6 cm

Case 2: x = 12 ft

Case 3: x = 4 yd

Case 4: x = 9 in

Case 5: r = 40 mi

Case 6: r = 35 cm

Case 7: x = 15 cm

Case 8: r = 30 in

Case 9: x = 24 km

Case 10: r = 37 km

In this problem we find ten cases of right triangles, whose missing sides can be determine by using Pythagorean theorem:

r² = x² + y²

Where:

Now we proceed to determine the missing side for each case:

Case 1

x = √(10² - 8²)

x = 6 cm

Case 2

x = √(13² - 5²)

x = 12 ft

Case 3

x = √(5² - 3²)

x = 4 yd

Case 4

x = √(15² - 12²)

x = 9 in

Case 5

r = √(32² + 24²)

r = 40 mi

Case 6

r = √(21² + 28²)

r = 35 cm

Case 7

x = √(17² - 8²)

x = 15 cm

Case 8

r = √(24² + 18²)

r = 30 in

Case 9

x = √(26² - 10²)

x = 24 km

Case 10

r = √(35² + 12²)

r = 37 km

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Answer:

Step-by-step explanation:

[tex]8/10=4/5[/tex] [tex]so[/tex] [tex]20/5x=4/5[/tex]

[tex]5x=25, x=5[/tex]

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8 and -3

(x-3)×(x+8)=g(x)

Vector equation with parameter t for the line through the origin and the point (4,13,-10) is:

r(t) = t<4, 13, -10>

To find the vector equation with parameter t for the line through the origin and the point (4,13,-10), we first need to find the direction vector of the line. The direction vector is the vector that starts at the origin and ends at the point (4,13,-10). We can find this vector by subtracting the coordinates of the origin from the coordinates of the point:

<4, 13, -10> - <0, 0, 0> = <4, 13, -10>

This vector represents the direction of the line. To get the vector equation with parameter t, we just need to multiply this direction vector by t and add it to the position vector of the origin, which is <0,0,0>. This gives us the equation:

r(t) = t<4, 13, -10>

where r(t) is the position vector of any point on the line for a given value of t. We can see that when t=0, r(t) = <0,0,0>, which is the position vector of the origin. When t=1, r(t) = <4, 13, -10>, which is the position vector of the point (4,13,-10). Therefore, this equation represents the line passing through the origin and the point (4,13,-10).

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Answer:

YES - it is a right triangle, the Pythagorean Theorem is true for its sides.

20^2+15^2=25^2

400+225= 625

Hope this helps! =D

Step-by-step explanation:

It takes 6.14 minutes for Noe to complete the descent.

To determine the time it takes for Noe to descend from an elevation of 453 feet to 146 feet at a rate of 50 feet per minute, we can use the formula:

Time = Distance / Rate

In this case, the distance is the difference in elevations

= 453 - 146 =

307 feet,

and the rate is 50 feet per minute.

Substituting these values into the formula:

Time = 307 feet / 50 feet per minute

Time ≈ 6.14 minutes

Therefore, it takes 6.14 minutes for Noe to complete the descent.

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Answer: The required equation is 100/12 = 8 1/3 which shows 100 ounces of soda divided equally among 12 people.

Step-by-step explanation:

There are 100 ounces of soda divided equally among 12 people.

According to the given information, the algebraic form would be as:

⇒ 100/12 = 25/3

Expressing the solution as a mixed number.

⇒ 100/12 = 8 1/3

Therefore, the required equation is 100/12 = 8 1/3 which shows 100 ounces of soda divided equally among 12 people.

The required, D. A study of the popularity of a new sneaker conducted by the sneaker manufacturer is more likely to produce results that are skewed by bias.

This is because the sneaker manufacturer has a vested interest in promoting the new sneaker and may use biased methods to ensure that the study produces favorable results. For example, the manufacturer may selectively sample individuals who are more likely to be interested in the sneaker or use leading questions to bias the responses in favor of the sneaker. In contrast, the other studies listed are less likely to be influenced by bias because they rely on random sampling or objective measurements.

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Step-by-step explanation:

Base...from  - 7 to + 4 = 11 units

Height from  -4 to +5 = 9 units

Area of a traingle = 1/2  * base * height = 1/2 (11)(9) = 49.5   units^2

The missing dimension (height) of the cylinder is 11.62 feet.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

3000 = π(9.3)²h

Simplifying and solving for h:

h = 3000 / (π(9.3)²)

h ≈ 11.62 feet

Thus, the missing dimension (height) of the cylinder is 11.62 feet.

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The volume of the cylinder with a base radius 3 and height 8 is 72π cubic units.

This question is incomplete, the complete question is:

What is the volume of a cylinder with base radius 3 and height 8?

Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi.

Given that:

Radius r = 3 units

Height h = 8 units

Volume V = ?

Plug the values into the above formula and solve for V.

V = π × r² × h

V = π × 3² × 8

V = 72π cubic units.

Therefore, the volume is 72π cubic units.

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Since a z-score of 0.96 is within two standard deviations of the mean, it is not considered unusual. Therefore, the answer is A. unusual.

To determine if this is unusual, we need to consider the normal distribution and the concept of standard deviation. In a standard normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

To calculate the z-score, we use the formula:
z = (x - μ) / σ
Where x is the individual's score, μ is the mean, and σ is the standard deviation.

To calculate the z-score, we'll use the formula:
z-score = (individual score - class mean) / standard deviation

In this case, the individual score is 77.14, the class mean is 73, and the standard deviation is 4.6.

Step 1: Subtract the class mean from the individual score.
77.14 - 73 = 4.14

Step 2: Divide the result by the standard deviation.
4.14 / 4.6 = 0.9
Plugging in the values we get:

z = (77.14 - 73) / 4.6
z = 0.9565 (rounded to 4 decimal places)

A z-score of 0.9565 indicates that the person's score is about 0.96 standard deviations above the mean.

Now, let's determine if this is unusual or not. In general, a z-score greater than 1.96 or less than -1.96 is considered unusual, as it represents a result that is outside the 95% confidence interval. Since our calculated z-score is 0.9000, it is within the 95% confidence interval.

Answer: The z-score is 0.9000, and it is A. Not Unusual.

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The algebraic expression representing the description given is 5w + 2w

We can rewrite the description as Gerald earns $5 each time he mows a lawn

Let amount earned for lawn mowing = $5Let amount earned for trimming = $2

We can then rewrite the description as Gerald earns $5 each time he mows a lawn. He mows his neighbor's lawn each week.

He also earned an additional $2 for trimming trees one week.

An algebraic expression for the description

Number of weeks = w

Amount earned for any given number of weeks is ;

Amount earned= 5w + 2w = 7w

Hence, the algebraic expression for the description is 5w + 2w

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Step-by-step explanation:

Between x = -5 to x = -1 the graph is positive ( > 0)   at -5 and -1 it is EQUAL to zero...so those numbers are not included

(-5,-1)    

The domain on which the graph of a function is positive involves finding the x-values for which the function's output is greater than zero. This can be visualized by identifying where on the graph the curve is situated above the x-axis.

The domain on which the graph of f(x) is positive is the set of x-values for which the y-values (the outputs of the function) are greater than zero.

So, for each point (x, y) on the graph, if y is larger than zero that means f(x) is positive. To find out where this is the case, simply look at the graph and identify where the curve lies above the x-axis. These will be the x-values that make f(x) positive.

For example, if the plot of the function is above the X-axis between interval a and b, then the domain on which f(x) is positive is the interval (a, b).

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There are four possible outcomes when flipping a coin twice: HH, HT, TH, and TT.

Since the coin is fair, each outcome is equally likely with probability 1/4. Let X be the total number of tails and Y be the number of heads on the last flip.

Then the possible values of X and Y are: If HH occurs, then X = 0 and Y = 2.

If HT occurs, then X = 1 and Y = 1.

If TH occurs, then X = 1 and Y = 0.

If TT occurs, then X = 2 and Y = 1.

Therefore, the joint pmf of X and Y is:

P(X = 0, Y = 2) = 1/4

P(X = 1, Y = 1) = 1/4

P(X = 1, Y = 0) = 1/4

P(X = 2, Y = 1) = 1/4

Note that the sum of the probabilities of all possible values of X and Y is 1, as it should be for a valid pmf.

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A beaker about two-thirds full of liquid: wear chemical resistant gloves and use a proper pouring tool, but do not taste.

A hot plate: use tongs to remove hot items, do not touch the surface, and turn it off after use.

A Bunsen burner: clear the lab table, tie back long hair, and turn it off after use.

A beaker about two-thirds full of a liquid:

Wear chemical resistant gloves.

Do not taste to make sure it is HCl. Taste testing is not a safe or appropriate method of identifying chemicals.

Do not pour using tongs. Tongs are not designed for pouring liquids and could lead to spills or accidents. Pour using a proper pouring tool, such as a glass or plastic pipette.

A hot plate, with a knob on the front for setting temperature:

Use tongs to remove hot items.

Do not touch the surface. It may still be hot even after use and can cause burns.

Turn off after use.

A bunsen burner, with a flame visible:

Clear the lab table of paper and other flammable materials.

Tie back long hair.

Turn off after use.

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Answer:

Without additional information or a diagram, it is not possible to accurately determine the value of m/Y.

The complete statement is: In the year 2010, there will be approximately 600 grizzly bears at Yellowstone National Park.

Find the approximate value from the graph.

The complete question is added as an attachment

From the attached graph, we have the following highlights

x represents the number of years since 2009

y represents the number of grizzly bears

So, the value of A(1) means that we find the number of grizzly bears in the year 2010

According to the graph, the value of the function where x = 1 is 600

So, we have:

A(1) = 600

Based on your answer for part A. Complete this sentence.

The incomplete sentence is given as:

In the year there will be approximately grizzly bears at Yellowstone National Park.

A(1) = 600 represents the number of grizzly bears in the year 2010

So, the complete statement is:

In the year 2010, there will be approximately 600 grizzly bears at Yellowstone National Park.

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complete question:

The population of grizzly bears at Yellowstone National Park has been threatened with local extinction since 1975. Through many conservation efforts, grizzlies have made a remarkable recovery. The function = () is modeled below, where is the number of years since 2009 and is the number of grizzly bears.

A) Find the approximate value from the graph.

(1)≈

B) Based on your answer for part A. Complete this sentence.

In the year there will be approximately grizzly bears at Yellowstone National Park.

Answer:

56

Step-by-step explanation:

3*7*2+2*7

42+2*7

42+14

=56

Answer:

No, h=7 is not a solution to the equation

Step-by-step explanation:

3h² + 2h - 379 = 0

Use the quadratic equation to find the 2 roots of h, with a = 3, b = 2, c = -379

h = 10.91, -11.58

When conducting a bivariate correlational study, it is important to use a random sample to ensure that the results are generalizable to the larger population.

However, if a random sample is not used, it does not necessarily mean that the association should be automatically rejected. There are several reasons why a random sample may not have been used in a correlational study. For example, the researcher may have had limited access to a specific population or may have chosen to use a convenience sample for practical reasons. In these cases, it is important to consider the potential limitations and biases in the sample. Additionally, it is possible to adjust for some of these limitations through statistical techniques such as weighting or stratification. These techniques can help to ensure that the results are more representative of the larger population, even if a random sample was not used. Overall, while a random sample is preferred in bivariate correlational studies, it is not always feasible or practical. As such, it is important to carefully consider the limitations of the sample and to use appropriate statistical techniques to account for any potential biases. Ultimately, the validity of the association should be evaluated based on the strength of the evidence and the quality of the study design, rather than solely on the use of a random sample.

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The integral from (1) to e of [(1/z) - (1/z^2)] dz equals ln(e) - ln(1) - (1 - 1/e) = 1 - 1/e.

To solve the integral, we can use the power rule of integration. First, we split the integral into two parts: ∫(1 to e) 1/z dz - ∫(1 to e) 1/z^2 dz.

For the first part, we integrate 1/z with respect to z, which gives us ln|z|. Evaluating this from 1 to e, we get ln|e| - ln|1| = ln(e) - ln(1) = 1.

For the second part, we integrate 1/z^2 with respect to z, which gives us -1/z. Evaluating this from 1 to e, we get -1/e + 1.

Finally, we subtract the result of the second part from the result of the first part, giving us 1 - 1/e.

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Answer:

answer is d

cause central angle is twice the inscribed angle sustended by same arc

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= x^2+6x+5 \qquad \begin{cases} x_1=0\\ x_2=3 \end{cases}\implies \cfrac{f(3)-f(0)}{3 - 0} \\\\\\ \cfrac{[(3)^2+6(3)+5]~~ - ~~[(0)^2+6(0)+5]}{3}\implies \cfrac{27}{3}\implies \text{\LARGE 9}[/tex]

The probability of being able to form a triangle with three sticks of random length is 1/2 or 50%.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The probability of being able to form a triangle with three sticks of random length can be found using geometric probability.

First, we can assume that the length of the first stick is x, where 0 ≤ x ≤ 1. The second stick can be any length y such that 0 ≤ y ≤ 1. The third stick can be any length z such that 0 ≤ z ≤ 1.

For the three sticks to form a triangle, they must satisfy the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we have three cases to consider:

x + y > z

x + z > y

y + z > x

We can graph these three inequalities on a coordinate plane, where x and y are the lengths of two sides of the triangle, and the third side is represented by the area below the line.

The area of the triangle formed by the inequalities is 1/2, and the total area of the square representing the possible lengths of the sticks is 1.

Therefore, the probability of the three sticks forming a triangle is the ratio of the area of the triangle to the area of the square:

P(triangle) = area of triangle / area of square = (1/2) / 1 = 1/2

Hence, the probability of being able to form a triangle with three sticks of random length is 1/2 or 50%.

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The distances between a and b and between 0 and c are equal, which can be expressed mathematically using Absolute value notation as |b - a| = |c - 0|.

One possible true statement that can be made using the letters a, b, and c from the given number line is:|b - a| = |c - 0|

This statement represents the fact that the distance between a and b is equal to the distance between 0 and c, which is given in the problem statement. The absolute value signs are used to ensure that the distances are represented as positive quantities.

Another way to express this statement is:|b - a| = |c|or|a - b| = |c|

Both of these expressions are equivalent to the first statement, since |c - 0| is the same as |c|.

Therefore, we can conclude that the distances between a and b and between 0 and c are equal, which can be expressed mathematically using absolute value notation as |b - a| = |c - 0|.

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* The height of the pyramid is 4 feet.

* The length of a side of the square base is 6 feet.

* We need to find the slant height, s.

Let's draw a diagram:

Height (4 ft)

│ │

│ │

│ │

│ │

│ │

│ s │

│ │

│ │

│ │

│ 3 ft │

└