[5] find the unit tangent vector t (t) to the curve r(t) = hsin t, 1 t, costi when t = 0.

The first partial derivative of f(x,y) with respect to x is:

∂f/∂x = a(bx - ad) + c(cx + dy)

The first partial derivative of f(x,y) with respect to y is:

∂f/∂y = b(cx + dy) + c(cx + dy)

Answer:

Range is 53

Step-by-step explanation:

The range is the difference between the maximum and minimum values in a data set.

The minimum value in the data set is 45, and the maximum value is 98.

Therefore, the range is:

98 - 45 = 53

So the answer is 53.

A. The probability of hitting the black circle inside the target is closer to 1.

B. The probability of hitting the white portion of the target is closer to 0. This is because the area of the white portion of the square is 91 (100-9π), while the area of the circle is 9π. Therefore, the probability of hitting the white portion of the target is (91/100), which is closer to 0.

Part A: Area of the black circle: 9π

Area of the square: 100

Probability of hitting the black circle: (9π/100) = (3/10)

Part B: Area of the white portion of the square: 91 (100-9π)

Area of the circle: 9π

Probability of hitting the white portion of the target: (91/100)

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Yes, the construction demonstrates how to copy a segment correctly by hand.

The specific construction steps that show this are:

The construction is correct because it follows the steps for copying a segment correctly by hand. The compass is used to measure the length of the original segment, and then the compass is used to draw an arc with the same length.

The line segment CD is drawn through the intersection of the arc and the original segment, and this line segment is congruent to the original segment.

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The rate per mile in this problem is given as follows:

0.88 minutes per mile.

The rate per mile in this problem is obtained applying the proportions in the context of the problem.

A proportion is applied as the rate per mile is given by the division of the number of minutes by the number of miles.

The parameters for this problem are given as follows:

Hence the rate per mile in this problem is given as follows:

30/34 = 0.88 minutes per mile.

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Molly is the only student who rewrote the equation correctly into slope-intercept form. Her equation is:

y = -4x + 3

Jared, Ali, and Mia made mistakes in their simplifications by not dividing the entire equation by 3 when isolating the term with y.

Let's analyze each student's attempt to rewrite the equation 12x + 3y = 9 into slope-intercept form.

Jared:

Jared's attempt is incorrect. He started correctly by isolating the term with y, but he made a mistake in simplifying it. Instead of dividing the entire equation by 3, he only divided the constant term. The correct simplification would be:

3y = 9 - 12x

y = (-12/3)x + 3

y = -4x + 3

Molly:

Molly's attempt is correct. She correctly isolated the term with y and divided the entire equation by 3 to solve for y. The simplified equation is:

y = (-12/3)x + 3

y = -4x + 3

Ali:

Ali's attempt is incorrect. He attempted to move the term with x to the other side of the equation but made a mistake in the process. Instead of subtracting 12x from both sides, he mistakenly subtracted 4x from both sides. The correct simplification would be:

12x + 3y = 9

3y = 9 - 12x

y = (-12/3)x + 3

y = -4x + 3

Mia:

Mia's attempt is incorrect. She made the same mistake as Jared by dividing only the constant term by 3. The correct simplification would be:

3y = 9 - 12x

y = (-12/3)x + 3

y = -4x + 3

From the analysis, we can see that Molly is the only student who rewrote the equation correctly into slope-intercept form. Her equation is:

y = -4x + 3

Jared, Ali, and Mia made mistakes in their simplifications by not dividing the entire equation by 3 when isolating the term with y.

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The calculated value of the commission percentage is 4%

From the question, we have the following parameters that can be used in our computation:

Hourly rate = $15

Commission = x%

So, the function of the earnings is

f(x) = x% * 1400 + Hourly rate * Number of hours

This gives

When the total earning is 176, we have

x% * 1400 + 15 * 8 = 176

This gives

x% * 1400 + 120 = 176

So, we have

x% * 1400= 56

Divide

x = 4

Hence, the commission percentage is 4%

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Answer:

top left

Step-by-step explanation:

the line has a similar amount of dots above and below it,

The area between Z= -2.68 and Z= -0.99 for the standard normal distribution is 0.3389. (option c)

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The area under the curve of the standard normal distribution represents the probability of a random variable taking a certain value or falling within a certain range.

To find the area between two values of the standard normal distribution, we can use a standard normal table or a calculator with a standard normal distribution function. In this case, we can use a standard normal table to find the area between Z= -2.68 and Z= -0.99.

The table gives us the area to the left of Z= -2.68 as 0.0038 and the area to the left of Z= -0.99 as 0.1611. To find the area between Z= -2.68 and Z= -0.99, we subtract the area to the left of Z= -2.68 from the area to the left of Z= -0.99:

0.1611 - 0.0038 = 0.1573

Therefore, the area between Z= -2.68 and Z= -0.99 for the standard normal distribution is approximately 0.1573 or 0.3389 when rounded to four decimal places.

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Answer:

3201.3ft³

Step-by-step explanation:

V=πr²h

Large container:

V=π·11²·19

V=7222.52

Small container

V=π·8²·20

V=4021.24

7222.52-4021.24=3201.28

Rounded to the nearest tenth is 3201.3

Francisca prefers less rainfall, she might choose City B, as it generally has fewer rainy days during the two-week period.

Here are the results for the number of rainy days during a two-week period over the past 10 years for the two cities:

City A:

Year 1: 8 rainy days

Year 2: 10 rainy days

Year 3: 7 rainy days

Year 4: 9 rainy days

Year 5: 6 rainy days

Year 6: 10 rainy days

Year 7: 8 rainy days

Year 8: 9 rainy days

Year 9: 7 rainy days

Year 10: 6 rainy days

City B:

Year 1: 4 rainy days

Year 2: 5 rainy days

Year 3: 6 rainy days

Year 4: 4 rainy days

Year 5: 5 rainy days

Year 6: 7 rainy days

Year 7: 3 rainy days

Year 8: 6 rainy days

Year 9: 5 rainy days

Year 10: 4 rainy days

Based on this information, Francisca can compare the number of rainy days between the two cities to make her decision. If she prefers less rainfall, she might choose City B, as it generally has fewer rainy days during the two-week period. However, other factors such as temperature, attractions, or personal preferences may also influence her decision.

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During the twelfth week, there will be about 204,800 butterflies in the research area.

To solve the problem, we can use the formula:

[tex]N = N_0 * (2^t)[/tex]

Where:

N is the number of butterflies after t weeks

[tex]N_0[/tex] is the initial number of butterflies

t is the number of weeks

We are given that N0 = 50 and t = 12. We can substitute these values into the formula and solve for N:

[tex]N = 50 * (2^{12})\\\\N = 50 * 4096\\\\N = 204,800[/tex]

Therefore, there will be approximately 204,800 butterflies in the study area during the twelfth week.

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(a) The selling price is $6.25.

(b)  The net profit is the difference between the selling price and the cost is $4.35.

(c)  The cost is $1.90.

We have,

Let's denote the cost of producing one bag of corn chips as "C", the selling price as "S", and the net profit as "P".

We can then use the given information to set up the following equations:

Overhead percent = 20% of the selling price

=> 0.2S = $1.25

Markup = Selling price - Cost

=> $4.35 = S - C

We can solve these two equations simultaneously to find the values of S and C:

0.2S = $1.25

=> S = $6.25 (dividing both sides by 0.2)

$4.35 = S - C

=> $4.35 = $6.25 - C (substituting the value of S)

=> C = $1.90 (subtracting $4.35 from both sides)

(a)

The selling price is $6.25.

(b)

The net profit is the difference between the selling price and the cost:

P = S - C

= $6.25 - $1.90

= $4.35.

(c)

The cost is $1.90.

Thus,

(a) The selling price is $6.25.

(b)  The net profit is the difference between the selling price and the cost is $4.35.

(c)  The cost is $1.90.

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a. The ANOVA table does not provide any information about the number of age classes. Therefore, it cannot be determined from the given table how many age classes were there.

b. The ANOVA table does not provide any information about the age-sex combination or the number of observations for each combination. Therefore, it cannot be determined from the given table how many observations were made for each age-sex combination.

c. The ANOVA table provides information about the sources of variation and their respective sum of squares, degrees of freedom, and mean squares. From this table, it can be concluded that the interaction between factors and error have a significant effect on the response variable, territory size. However, the table does not provide any information about the effect size or the direction of the effect. To draw any conclusions about the relationship between the factors and the response variable, further analysis such as post-hoc tests or effect size calculations would be required.

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The diagonal measurement as √5625 ft, which is approximately 75 feet, the correct answer is B. 75 ft 0 in.

The diagonal measurement of the rectangular slab on grade can be found using the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the length and width of the slab.

To calculate the diagonal measurement, we can apply the Pythagorean theorem:

Diagonal² = Length² + Width²

Substituting the given values, we have:

Diagonal² = (60 ft 0 in.)² + (45 ft 0 in.)²

Calculating this expression, we find:

Diagonal² = 3600 ft² + 2025 ft²

Diagonal² = 5625 ft²

Taking the square root of both sides, we obtain:

Diagonal = √5625 ft

Diagonal ≈ 75 ft

Therefore, the diagonal measurement of the rectangular slab on grade is approximately 75 feet.

To find the diagonal measurement of the rectangular slab on grade, we can use the Pythagorean theorem,

which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (length and width).

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(a) The combinations are,

Number of 6 player games = 8, if number of 2 player games = 1.

Number of 2 player games = 22, if number of 6 player games = 1.

Number of 6 player games = 7, if number of 2 player games = 4.

Number of 2 player games = 13, if number of 6 player games = 4.

(b) The number of 6 player games is 6 and the number of 2 player games is 7.

Given that total number of athletes = 50

Players needed for 6 player game = 6 and players needed for 2 player games = 2

(a) When number of 2 player games = 1,

Number of athletes left = 50 - (1 × 2) = 48

Number of 6 player games = 48/6 = 8

When number of 6 player games = 1,

Number of athletes left = 50 - (1 × 6) = 44

Number of 2 player games = 44/2 = 22

When number of 2 player games = 4,

Number of athletes left = 50 - (4 × 2) = 42

Number of 6 player games = 42/6 = 7

When number of 6 player games = 4,

Number of athletes left = 50 - (4 × 6) = 26

Number of 2 player games = 26/2 = 13

(b) Let x represents the number of 2 player games and y represents the number of 6 player games.

We get the linear equations,

x + y = 13

AND

2x + 6y = 50

From first equation,

y = 13 - x

Substituting this to second equation,

2x + 6(13 - x) = 50

2x + 78 - 6x = 50

-4x = -28

x = 7

So, y = 13 - 7 = 6

Hence the number of 2 player games played is 7 and the number of 6 player games played is 6.

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The general solution of the resulting exact differential equation is y^2 + e^(2x) = C.

To find the function N(x,y), we need to use the condition that the differential equation is exact, which means that there exists a function f(x,y) such that:

df/dx = 2x^2y + 2e^(2x)y^2 + 2x

df/dy = N(x,y)

Taking the partial derivative of df/dx with respect to y and df/dy with respect to x, we get:

∂(2x^2y + 2e^(2x)y^2 + 2x)/∂y = 2x^2 + 4e^(2x)y

∂N(x,y)/∂x = 2x^2 + 4e^(2x)y

Since these partial derivatives are equal, N(x,y) can be found by integrating one of them with respect to x:

N(x,y) = ∫(2x^2 + 4e^(2x)y) dx = (2/3)x^3 + 2e^(2x)yx + C(y)

To find C(y), we use the condition that N(0,y) = 3y, which gives:

C(y) = N(0,y) - (2/3)0^3 = 3y

Substituting this expression for C(y) into the equation for N(x,y), we get:

N(x,y) = (2/3)x^3 + 2e^(2x)yx + 3y

Next, we need to find the general solution of the resulting exact differential equation.

Since the equation is exact, we know that the solution can be obtained by integrating f(x,y) = C, where C is a constant. Using the function N(x,y) that we found, we have:

df/dx = 2x^2y + 2e^(2x)y^2 + 2x

f(x,y) = ∫(2x^2y + 2e^(2x)y^2 + 2x) dx = (2/3)x^3y + 2e^(2x)y^2 + x^2 + g(y)

Taking the partial derivative of f(x,y) with respect to y and equating it to N(x,y), we get:

∂f(x,y)/∂y = (4e^(2x)y + g'(y)) = (2/3)x^3 + 2e^(2x)y + 3y

Solving for g'(y), we get:

g'(y) = (2/3)x^3 + 4e^(2x)y + 3y

Integrating g'(y) with respect to y, we get:

g(y) = (1/3)x^3y + 2e^(2x)y^2 + (3/2)y^2 + C

Substituting this expression for g(y) into the equation for f(x,y), we get:

f(x,y) = (2/3)x^3y + 2e^(2x)y^2 + x^2 + (1/3)x^3y + 2e^(2x)y^2 + (3/2)y^2 + C

Simplifying this expression, we get:

f(x,y) = (4/3)x^3y + 4e^(2x)y^2 + x^2 + (3/2)y^2 + C

Therefore, the general solution of the exact differential equation is: (4x^2y + 2e^(2x)y^2 + 3y^2 = C)

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The equations of the lines with the given gradients and points are:

1. y = -3x + 16

2. y = -5x + 5

3. y = 4x - 20

To find the equation of a line given its gradient and a point it passes through, we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁),

where (x₁, y₁) represents the given point and m represents the gradient.

Let's calculate the equations for each given gradient and point:

1. Gradient = -3, Point Q(4,4):

Using the point-slope form:

y - 4 = -3(x - 4)

y - 4 = -3x + 12

y = -3x + 16

2. Gradient = -5, Point P(0,5):

Using the point-slope form:

y - 5 = -5(x - 0)

y - 5 = -5x

y = -5x + 5

3. Gradient = 4, Point A(6,4):

Using the point-slope form:

y - 4 = 4(x - 6)

y - 4 = 4x - 24

y = 4x - 20

Therefore, the equations of the lines with the given gradients and points are:

1. y = -3x + 16

2. y = -5x + 5

3. y = 4x - 20

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When the interval [3, 11] is divided into 16 subintervals of equal length, each of the subintervals has length (a) 2. (b)4. (b) 4. () c. 1/2

When the interval [3, 11] is divided into 16 subintervals of equal length, we can use the formula:
length of each subinterval = (length of the interval) / (number of subintervals)
Therefore, the length of each subinterval would be:
(11 - 3) / 16 = 8 / 16 = 1/2
So the answer is (c) 1/2.
This means that each of the 16 subintervals would have a length of 1/2. It's important to note that the number of subintervals does not affect the length of the interval itself, only the length of each subinterval.
It's also worth mentioning that if we had divided the interval [3, 11] into a different number of subintervals of equal length, the length of each subinterval would have been different. This formula is specific to dividing an interval into a certain number of subintervals.

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Answer:

step 1

Step-by-step explanation:

Step 1: they accidentally changed the 20 in the original prob to 2.

Answer:

step 1

Step-by-step explanation:

they wrote 2x+6=3x+2 but they wrote 2 instead of 20

it should have been 2x+6=3x+20

The measure of the angle m∠LJK subtended by the arc LK at the circumference is equal to 42°

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

arc LK = 2(m∠LJK)

Also arc LK = 84°

2(m∠LJK) = 84°

m∠LJK = 84/2 {divide through by 2}

m∠LJK = 42°

Therefore, the measure of the angle m∠LJK subtended by the arc LK at the circumference is equal to 27°

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Answer:

19.7

Step-by-step explanation:

Answer:

The required value of x is:

x = 7.3

Answer:

25%

Step-by-step explanation:

To find the experimental probability of the computer generating a 2 or a 5, we need to calculate the total number of times the outcomes 2 and 5 occurred and divide it by the total number of trials (which is 80 in this case).

Looking at the table, the outcome 2 occurred 16 times and the outcome 5 occurred 4 times.

Total number of times 2 or 5 occurred = 16 + 4 = 20

Experimental probability = (Number of times 2 or 5 occurred) / (Total number of trials) = 20 / 80 = 0.25

To express this as a percentage, we multiply the decimal value by 100:

Experimental probability = 0.25 * 100 = 25%

Therefore, the correct answer is 25%.[tex][/tex]

Answer:

Step-by-step explanation:

it is 6 because it is there 2 times

Mike initially invested $1200.

We can use the formula for simple interest to calculate the initial investment:

Interest = Principal * Interest Rate * Time

We know the interest earned is $900, the interest rate is 0.15, and the time is 5 years. Let's substitute these values into the formula:

$900 = Principal * 0.15 * 5

Simplifying the equation:

$900 = 0.75 * Principal

Now, divide both sides of the equation by 0.75 to isolate the Principal:

Principal = $900 / 0.75

Principal = $1200

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To calculate the least squares estimates of the slope and intercept of the regression line. The slope can be calculated using the formula

the sample means of the age and weight variables, respectively. Plugging in the provided values, we get:

b = (1996904.15 - (11211.00 * 44520.80 / 60)) / (543503.00 - 11211.00^2 / 60) ≈ 2.88

Next, we can use the equation for the slope and the sample means to solve for the intercept:

Plugging in the values, we get:

a = 44520.80 - 2.88 * (11211.00 / 60) ≈ 398.08

So the equation for the fitted regression line is:

y = 2.88x + 398.08

To graph the line, we can plot the sample data (age vs weight) and draw the line that best fits the data.

To predict the weight for a 25-year-old man, we can simply plug in x = 25 into the equation for the fitted line:

y = 2.88 * 25 + 398.08 ≈ 467.08 lbs

To find the residual for a 25-year-old man who weighs 170 lbs, we simply subtract the predicted weight from the observed weight:

e = 170 - 467.08 ≈ -297.08 lbs

Since the residual is negative, the prediction for the 25-year-old man was an underestimate.

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The axis of symmetry for the function f(x) = (x - 6)(x + 3) is x = 1.5.

To find the axis of symmetry of the function f(x) = (x - 6)(x + 3), we need to determine the x-value of the vertex of the parabola represented by this function.

The axis of symmetry is given by the equation x = -b / (2a), where a and b are the coefficients of the quadratic term and the linear term, respectively, in the general form of the quadratic function [tex]ax^2 + bx + c[/tex].

In this case, the quadratic term coefficient (a) is 1 and the linear term coefficient (b) is -3, so we can substitute these values into the formula:

x = -(-3) / (2 × 1)

x = 3 / 2

x = 1.5

The axis of symmetry for the function f(x) = (x - 6)(x + 3) is x = 1.5.

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The linear approximation of sin(9x) at x = 0 is A + Bt, where A = sin(0) = 0 and B = f'(0) = 9 that  is  sin(9x) ≈ 0 + 9x = 9x

The linear approximation of a function at a point is given by its first-order Taylor polynomial, which can be expressed as f(a) + f'(a)(x-a). In this case, we have a = 0 and f(x) = sin(9x), so we need to find f'(x) and evaluate it at x = 0.

Taking the derivative of sin(9x) with respect to x, we get:

f'(x) = 9cos(9x)

Evaluating this at x = 0, we get:

f'(0) = 9cos(0) = 9

So the linear approximation of sin(9x) at x = 0 is given by:

sin(9x) ≈ 0 + 9x = 9x

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The arc PS is 120

The measure of angle ∠R is 60.

We have,

If an angle is inscribed in the circle and its vertex is on the circle, then the measure of the inscribed angle is half the intercepted arc.

Now,

We see that,

∠Q and ∠R are both inscribed angles for the intercepted arc PS.

So,

Arc PS = 60 x 2 = 120

And,

∠R = 60

Thus,

The arc PS is 120

The measure of ∠R is 60.

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