*F7 Consider the curve y 2x sin(x). Find the equation of the tangent line at the poin when x = π/2

*check attachment for options given

Answer:

Ariel (150 words per minute)

Step-by-step explanation:

We are given the different rate at which each student reads number of words against time.

To select which student reads the fastest (greatest number per minute), let's calculate for each student the number of words they can read per minute using the information given to us about the 3 students in the options.

==>Tamar:

Let "a" be the number of words Tamar reads per minute

500 words = 5 minutes

a = 1 minutes

Cross multiply

500*1 = 5*a

500 = 5a

500/5 = a

a = 100 words per minute.

==>Levi:

From the table given for Levi, he reads 280 words in 2 minutes

Let "b" be the number of words he would read per minute

280 = 2

b = 1

280*1 = 2*b

280 = 2b

280/2 = b

140 = b

b = 140 words per minute

==>Ariel:

From the graph given for Ariel, 300 words is read in 2 minutes.

Let c = words read per minute

300 = 2

c = 1

300*1 = 2*c

300 = 2c

300/2 = c

150 = c

c = 150 words per minute

The student that reads fastest is Ariel (150 words per minute)

Answer:

ariel

Step-by-step explanation:

Khanacademy

Trust

The vertex form of a quadratic function is given by:

�

(

�

)

=

�

(

�

−

ℎ

)

2

+

�

f(x)=a(x−h)

2

+k

where $(h, k)$ is the vertex of the parabola.

Substituting the given vertex $\left(-2,\ -6\right)$, we get:

�

(

�

)

=

�

(

�

−

(

−

2

)

)

2

−

6

f(x)=a(x−(−2))

2

−6

Simplifying:

�

(

�

)

=

�

(

�

+

2

)

2

−

6

f(x)=a(x+2)

2

−6

To find the value of $a$, we use the fact that the function passes through the point $\left(-1,\ 2\right)$:

2

=

�

(

−

1

+

2

)

2

−

6

2=a(−1+2)

2

−6

Solving for $a$:

\begin{align*}

2 + 6 &= a(1)^2 \

a &= 8

\end{align*}

Therefore, the quadratic function in vertex form that satisfies the given conditions is:

�

(

�

)

=

8

(

�

+

2

)

2

−

6

f(x)=8(x+2)

2

−6

Answer:

Step-by-step explanation:  (10)(A) Add and subtract polynomials of degree one and degree two. (10)(B) Multiply polynomials of degree one and degree two. (10)(C) Determine the quotient

Hope it helps =}

Answer:

b

Step-by-step explanation:

Answer: p = 9h

Step-by-step explanation:

     If she makes 9 dollars of every hour of work, this will be a linear equation. We will write it as the following:

      p = 9h

Answer:

9h/p

Step-by-step explanation:

9 x # of hours = total pay

$9 is the dollars for each hour, so you multiply that by how many hours Maria works. You will get the total pay.

a. We can use the following equation y = b₀ + b₁ * x₂

b. The p-value indicates the significance of the relationship.

c. We can use the following equation y = b₀ + b₁ * x₃

d. Similar to part (b), we need to analyze the statistical measures such as R-squared and p-value to determine if the equation developed in part (c) provides a good fit for the observed data.

e. We can use the following equation y = b₀ + b₁ * x₁ + b₂ * x₂ + b₃ * x₃

f. A p-value below the significance level (0.05) would indicate a significant relationship.

g. The results and interpretation of this test can provide insights into the contribution of the repairperson to the overall model.

The correlation coefficient illustrates how closely two variables are related to one another. This coefficient's range is from -1 to +1. This coefficient demonstrates the degree to which the observed data for two variables are significantly associated.

a) To develop the estimated simple linear regression equation to predict the repair time (y) given the type of repair (x₂), we can use the following equation:

y = b₀ + b₁ * x₂

where y represents the repair time and x₂ is the type of repair (0 for mechanical, 1 for electrical).

b) To determine if the equation developed in part (a) provides a good fit for the observed data, we need to analyze the statistical measures such as R-squared and p-value. R-squared measures the proportion of variance in the dependent variable (repair time) explained by the independent variable (type of repair). The p-value indicates the significance of the relationship.

c) To develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service (x₃), we can use the following equation:

y = b₀ + b₁ * x₃

where y represents the repair time and x₃ is the repairperson (0 for Bob Jones, 1 for Dave Newton).

d) Similar to part (b), we need to analyze the statistical measures such as R-squared and p-value to determine if the equation developed in part (c) provides a good fit for the observed data.

e) To develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service (x₁), the type of repair (x₂), and the repairperson (x₃), we can use the following equation:

y = b₀ + b₁ * x₁ + b₂ * x₂ + b₃ * x₃

where y represents the repair time, x₁ is the number of months since the last maintenance service, x₂ is the type of repair, and x₃ is the repairperson.

f) To test whether the estimated regression equation developed in part (e) represents a significant relationship between the independent variables and the dependent variable, we can perform a hypothesis test using the F-test or t-test and examine the p-value associated with the test. A p-value below the significance level (0.05) would indicate a significant relationship.

g) To determine if the addition of the independent variable x₃ (repairperson) is statistically significant, we can perform a hypothesis test specifically for the coefficient associated with x₃. The p-value associated with this coefficient will indicate its significance. A p-value below the significance level (0.05) would suggest that the repairperson variable has a statistically significant effect on the repair time. The results and interpretation of this test can provide insights into the contribution of the repairperson to the overall model.

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Answer:

3rd quadrant.

Step-by-step explanation:

We know that

4x + 7 < -3

5 - 3*y ≥ 11

We should isolate both of the variables in these inequalities:

for the first one we get:

4x + 7 < - 3

4x < -3 - 7

4x < -10

x < -10/4

So x is smaller than a negative number, then we know that x is negative, from this we already know that the point will be on quadrants 2 or 3.

For the other inequality we get:

5 - 3*y ≥ 11

5 - 11 ≥ 3y

-6 ≥ 3y

-6/3 ≥ y

-2 ≥  y

So we can see that y is equal to or smaller than a negative number, then y is a negative number.

So both values, x and y, are negatives.

This means that the point P(x, y) is in the 3rd quadrant.

Answer:

i is d i think so

Step-by-step explanation:

Answer:

it is A area of trapezoid = 1/2 × h( base1+base2) so it is 1/2× 8×(13+19)

Both \(f(x) = -x^2\) and \(f(x) = -2x^3 + 5x^2 - 3x + 7\) approach negative infinity as x approaches infinity.

As x approaches infinity, the dominant term of the function determines its behavior. In the case of \(f(x) = -x^2\), the term \(x^2\) becomes infinitely large and negative, causing the entire function to approach negative infinity. Similarly, in the case of \(f(x) = -2x^3 + 5x^2 - 3x + 7\), the term \(-2x^3\) dominates and becomes infinitely negative as x approaches infinity, causing the entire function to approach negative infinity. This is because the negative exponent on \(x^3\) causes the value of the term to become increasingly negative as x increases without bound.

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The speed of boat is 5/6 meter per second and height of boat is 50\(\sqrt{3}\) meter.

An angle is a shape created by two rays or lines that meet at the same terminal. The Latin word "angulus" (which means "corner") is where the term "angle" first appeared. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "" is used to denote angles. The Greek letter,,, etc. can be used to represent the angle between the two beams.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

After solving the figure:

The speed of boat is 5/6 meter per second and height of boat is 50\(\sqrt{3}\) meter.

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The speed of the boat from point C to point B is approximately 10.82 meters per second.

What is speed ?

Speed is a measure of how fast an object is moving. It is the rate at which an object covers distance.

We can use trigonometry to solve for h and the speed of the boat. Let's start with h:

From the right triangle CLB, we have:

tan 30° = h / CB

where CB is the distance between points C and B, which is given as 50 meters. Solving for h, we get:

h = CB * tan 30° = 50 * tan 30° ≈ 28.87 meters

So the height of the lighthouse is approximately 28.87 meters.

Now let's find the speed of the boat. We know that the boat travels from point C to point B in 1 minute, which is equivalent to 60 seconds. Let's define the speed of the boat as v, in meters per second. Then we have:

v = CB / t

where t is the time it takes for the boat to travel from point C to point B. We can find t using the distance formula:

\(CB = \sqrt{(x_B - x_C)^2 + (y_B - y_C)^2\)

where x and y are the coordinates of each point. From the diagram, we can see that:

\(x_C = 0\)

\(y_C = 0\)

\(x_B = BL * cos \theta\)

\(y_B = BL * sin \theta\)

where BL is the distance from point B to the foot of the lighthouse, which is equal to h / tan θ. Therefore:

CB \(= \sqrt{((BL * cos \theta)^2 + (BL * sin \theta)^2)\)

     \(= \sqrt{(BL^2 * (cos^2 \theta + sin^2 \theta))\)

     \(= BL = h / tan \theta\)

Substituting the values we have found, we get:

v = CB / t = (h / tan θ) / 60 ≈ 10.82 meters per second

Therefore, the speed of the boat from point C to point B is approximately 10.82 meters per second.

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Answer:

daughter = 9yrs

mother = 27yrs

Step-by-step explanation:

let age of daughter be x

age of mother = 3x

by qsn,

three yrs ago,

4 (x-3) = 3x-3

4x-12 = 3x-3

4x-3x = -3+12

× = 9 yrs (age of daughter )

3x = 3×9 = 27 yrs ( age of mother)

Taking the ratio of similar sides of the triangle, y has a value of √21

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

In math, This is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.

To find the value of y, we have to take the ratio of  sides of the two similar triangles

7 / y = y / 3

7 × 3 = y × y

21 = y²

y = √21

The value of y is √21

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The issue of too many proficient business-savvy programmers is least likely to arise in machine learning(ml) and artificial intelligence(ai).

What is machine learning?

The process by which computers learn to recognize patterns, or the capacity to continuously learn from and make predictions based on data, then make adjustments without being specifically programmed to do so, is known as machine learning (ML), a subcategory of artificial intelligence.

The operation of machine learning is quite complicated and varies according to the task at hand and the algorithm employed to do it. However, at its foundation, a machine learning model is a computer that analyzes data to spot patterns before using those realizations to better fulfill the work that has been given to it. Machine learning can automate any task that depends on a set of data points or rules, even the more difficult ones.

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===================================================

Work Shown:

c(b) = 5b

h(b) = b+4

h(c(b)) = c(b)+4 ... replace every b with c(b)

h(c(b)) = 5b+4 ... replace c(b) on the right hand side with 5b

For the sake of simplicity, let's call "h(c(b))" as k

k = h(c(b))

k = 5b+4

that way we can use it later in the next section

---------------

a(b) = b^2 + 7

a(k) = k^2 + 7 ... replace b with k

a(k) = (5b+4)^2 + 7 ... plug in k = 5b+4

a(k) = 25b^2+40b+16+7 .... use FOIL rule

a(k) = 25b^2+40b+23

a( h(c(b)) ) = 25b^2+40b+23

In that last step, I replaced k with h(c(b)) so that we get to the original format your teacher wanted.

The calculations below show that Z-score of 10 is –1.25; Z-score of 20 is 1.25; Z-score of 12 is –0.75; Z-score of 17 is 0.50; and Z-score of 16 is 0.25.

The following notations and formulas will be used in these calculations:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

SD = Standard deviation = Variance^0.5

Z-score = (x - Mean) / SD

Where;

n = number of values = 5

x = each value

Therefore, we have:

Mean = (10 + 20 + 12 + 17 + 16) / 5 = 15

Variance = ((10-15)^2 + (20-15)^2 + (12-15)^2 + (17-15)^2 + (16-15)^2) / (5-1) = 64 / 4 = 16

SD = Standard deviation = Variance^0.50 = 16^0.5 = 4

Z-score of 10 = (10 – 15) / 4 = –1.25

Z-score of 20 = (20 - 15) / 4 = 1.25

Z-score of 12 = (12 - 15) / 4 = –0.75

Z-score of 17 = (17 - 15) / 4 = 0.50

Z-score of 16 = (16 - 15) / 4 = 0.25

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Answer:

a

Step-by-step explanation:

You can only be going 70 mph, or below (to a certain point) or you'll get pulled over / get a ticket.

The simple interest rate that will ensure that Bob's investment of R6,500 equals Alice's 3% compound interest per year investment is 3.2%.

The difference between simple interest and compound interest is that simple interest computes interest on the principal only for each period.

Compound interest computes interest on both the principal and accumulated interest for each period.

Alice:

Principal investment = R6,500

Compound interest rate per year = 3%

Investment period = 5years

Future value = R7,535.28 (R6,500 x 1.03⁵)

Total Interest R1,035.28 (R7,535.28 - R6,500)

Bob:

Principal invested = R6,500

The simple interest rate = r

Investment period = 5years

The future value of the simple interest investment, A = P(1+rt)

7,535.28 = 6,500(1 + 5r)

Dividing each side b 6,500:

1.15927 = (1 + 5r)

5r = 0.15927

r = 0.031854

r - 0.032

r = 3.2% (0.32 x 100)

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Calculate r, giving your answer correct to 1 decimal place.

Hi! Based on the information provided, using homework 10 data with a significance level (α) of 0.05 and a p-value of 0.038, your conclusion is that you would reject the null hypothesis.

This is because the p-value (0.038) is less than the significance level (0.05), indicating that there is significant evidence to suggest that the alternative hypothesis is true. Therefore, the conclusion is made based on the evidence to suggest that there is a statistically significant difference between the groups being compared in the study analyzed in homework 10.

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The motion of the particle follows a periodic pattern as t varies from -2 to 2. It moves horizontally between x = -1 and x = 1 while its y-coordinate stays non-negative, reaching a maximum value of y = 1 at t = 0.

In physics, periodic motion is movement that repeats at regular intervals. A swing in motion, a rocking chair, a bouncing ball, a tuning fork vibrating, the Earth orbiting the Sun, and a water wave are all examples of periodic motion.

The motion of the particle can be described by its position (x, y) as t varies in the interval -2 ≤ t ≤ 2, where x = sin(t) and \(y = cos^2(t)\).

As t varies from -2 to 2, the x-coordinate of the particle's position varies according to the function x = sin(t). The sine function oscillates between -1 and 1 as t varies, so the particle moves horizontally back and forth between x = -1 and x = 1. The particle reaches its maximum displacement in the positive x-direction at t = π/2 and its maximum displacement in the negative x-direction at t = -π/2.

The y-coordinate of the particle's position is given by \(y = cos^2(t)\). The cosine function also oscillates between -1 and 1, but squaring it makes the values positive. Therefore, the particle's y-coordinate is always non-negative. It reaches its maximum value of y = 1 at t = 0 and its minimum value of y = 0 at t = ±2.

Overall, the motion of the particle follows a periodic pattern as t varies from -2 to 2. It moves horizontally between x = -1 and x = 1 while its y-coordinate stays non-negative, reaching a maximum value of y = 1 at t = 0.

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The explicit formula is a_n = 3+4n

From the question, we have

a1 = 7

We know that,

a_n = a_1 +(n-1)d

a_n = 7 +(n-1)4

a_n = 7+4n-4

a_n = 3+4n

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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The change in electrical potential when moving along the x-axis from x = 5.0 m to x = 1.0 m. The result depends on the values of A, B, and C, which are given as 1.5 V/m^(-3), 0.45 V/m^(-2), and -15 V/m^(-1) respectively.

To calculate the change in electrical potential, we need to integrate the electric field along the path of motion. In this case, we are moving along the x-axis, so only the x-component of the electric field is relevant.

The electric potential difference (ΔV) between two points A and B is given by the formula:

ΔV = ∫ E · dl

where E is the electric field and dl is an infinitesimal displacement along the path of motion. Since we are only concerned with the x-component of the electric field, the integral simplifies to:

ΔV = ∫ (Ax^2 + Bz) dx

Integrating with respect to x from x = 5.0 m to x = 1.0 m, we can find the change in electrical potential.

ΔV = ∫ (Ax^2 + Bz) dx = ∫ (1.5x^2 + Bz) dx

Evaluating the integral, we get the change in electrical potential when moving along the x-axis from x = 5.0 m to x = 1.0 m in the given electric field.

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Answer: 6750.50

Step-by-step explanation: 6750.50 because I did the math and got it correct on FLVS

Use the PeRT equation and just solve it algebraically to find P the principal investment

Answer:

The correct answer on EDG-2020 is:

c) ≈471 in.2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

credit to the first guy

The width of each class interval from the given grouped frequency distribution table is 9.

In a frequency distribution, the numerical width of a class is referred to as the class interval. Data is organised into classes in a grouped frequency distribution. The class interval is determined by the difference between the upper and lower class limits.

The give class intervals are 20-29, 30-39, 40-49 and 50-59.

The size, or width, of a class interval is the difference between the lower and upper class boundaries and is also referred to as the class width, class size, or class length.

So, class width = Upper class - Lower class

29-20=9

39-30=9

Therefore, the width of each class interval is 9.

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Answer:

1. D= 46 degrees

2. X= 50 degrees

3. X= 180-118 = 62 degrees

4. X = 90-75 = 15 degrees.

Step-by-step explanation:

Answer:

Going by the order from the first row left to right and then second row left to right

1) D=46

2) x=62

3) x=50

4) x=15

5) b=40

Step-by-step explanation:

So for the first column for the first question its a complementary angle which means 2 or more angles added up to from a 90 degrees angle. We got 44 degrees already and an unknown angle which will lead to 90-44= 46 and that 46 degrees is your answer. D will be equal to 46.

For the second question on the first column, you have 2 angles forming a straight line. This is a s upplementary angle which means 2 or more angles added up to from 180 degrees. You have 1 angle already which is 118 and to find the other angle, 180-118 which will be 62. X will equal to 62

For the thrid question which is the first question on the SECOND column, you have another supplementary angle. You have 130 and 180-130=50 and X will equal to 50.

For the 4th question you have a complementary and one angle is 75. You do 90-75 and get 15. X will equal to 15.

The last question which is the huge rectangle on the right, you have 2 intersecting lines. We know one side is 40. Well the only thing that makes sense here is B=40 since its vertical to the one angle given. Vertical angles are equal so therfore the answer is b=40

Answer:

step 1: distribute -1

step 2: combine like terms

step 3: subtract 4 on both sides

step 4: divided both sides by -8, so u can isolate M alone

M=-2

Step-by-step explanation:

The total product average product and marginal product are important to operate efficiently and maximize profits. Option D is the correct answer.

Being able to calculate the total product, average product, and marginal product is important for businesses to operate efficiently and maximize profits.

The total product is the overall output produced by a business, while the average product is the output per unit of input, and the marginal product is the change in output resulting from a change in input.

These calculations can help businesses optimize their production processes by identifying the most efficient levels of input and output.

By maximizing their output while minimizing their input costs, businesses can increase their profitability and gain a competitive advantage in the market.

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The question is -

Being able to calculate the total product average product and the marginal product is important:

a. for determining demand and supply.

b. when filing taxes.

c. to keep competition in check.

d. to operate efficiently and maximize profits.

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Carmen invested her saving in fund B as $11,000.

For the given question;

Let 'x' be the amount invested by Carmen in fund B.

The, the amount invested in fund A is x - 5000.

The profit on fund A is 2% = 2%(x - 5000).

the profit on fund B is 5% = 5%(x).

Then, the total profit is $670.

The equation will be .

2%(x - 5000) +  5%(x) = 670

2(x - 5000)/100 +  5(x)/100 = 670

2x - 10,000 + 5x = 67,000.

Further simplifying.

7x = 67,000 + 10,000

7x = 77,0000

x = 11,000

Thus, amount invested in fund B is $11,000.

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using the fifth partial sum of the exponential series, the approximation for e^(-2.5) is approximately 1.649 (rounded to three decimal places).

To approximate the value of e^(-2.5) using the fifth partial sum of the exponential series, we can use the formula:

e^x = 1 + x + (x^2 / 2!) + (x^3 / 3!) + (x^4 / 4!) + ... + (x^n / n!)

In this case, we have x = -2.5. Let's calculate the fifth partial sum:

e^(-2.5) ≈ 1 + (-2.5) + (-2.5^2 / 2!) + (-2.5^3 / 3!) + (-2.5^4 / 4!)

Using a calculator or performing the calculations step by step:

e^(-2.5) ≈ 1 + (-2.5) + (6.25 / 2) + (-15.625 / 6) + (39.0625 / 24)

e^(-2.5) ≈ 1 - 2.5 + 3.125 - 2.60417 + 1.6276

e^(-2.5) ≈ 1.64893

Therefore, using the fifth partial sum of the exponential series, the approximation for e^(-2.5) is approximately 1.649 (rounded to three decimal places).

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