help pls .............................

the equation of the tangent line to the curve y = 2 sin x at the point (π/6, 1) will be y = √3 x + 0.093.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

y = mx + b

1) m = slope of the tangent line = derivative at the point (pi/6, 1)

Function: y = 2sinx

Derivative: y ' = 2cosx

evaluate at x = pi/6=> y ' = 2cos(pi/6) = √3

2) equation using the slope and the point (pi/6, 1)

y - 1 = √3 ( x - pi/6 )

y = √3 x - √3(pi/6) +1 =√3 x + 0.093

y = √3 x + 0.093

m = √3, b = 0.093

Therefore, y = √3 x + 0.093 will be the equation of the tangent line to the curve y = 2sin x at point (π/6, 1).

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According to the information in the table, the correct options are: The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A. (option B).

To identify the correct option that matches the information in the survey table, we must read each of the options and compare it with the information in the table to establish one as true.

Based on the above, we can infer that the correct option is option B because the number of employees who voted for coffee in group B is greater than the number of employees who voted for coffee in group A.

Note: This question is incomplete because there is some information missing. Here is the complete information:

Options:

A. The estimated number of employees who would have voted for green tea is higher when based on the results of Group A rather than Group B.

B. The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A.

C. The estimates for both groups show an equal number of employees would have voted for coffee.

D. The estimated number of employees who would have voted for coffee is higher when based on the results of Group A rather than Group B.

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Answer:Let's call the two numbers x and y. We know that:

xy = 72

x + y = -38

We can use the first equation to solve for one of the variables in terms of the other:

x = 72/y

Then, we can substitute this expression into the second equation:

72/y + y = -38

y^2 + 72 = 38y

y^2 - 38y + 72 = 0

This is a quadratic equation that can be solved using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -38, c = 72.

Plugging in these values, we get:

y = (38 ± √(38^2 - 4(1)(72))) / 2(1)

y = (38 ± √(1444)) / 2

y = (38 ± 38) / 2

So, we have two solutions for y:

y = 38 / 2 = 19

y = -38 / 2 = -19

With either of these values for y, we can use the first equation to solve for x:

x = 72/y = 72/19 = 3.8

or

x = 72/-19 = -3.8

So, the two numbers whose product is 72 and whose sum is -38 are x = 3.8 and y = 19, or x = -3.8 and y = -19.

Step-by-step explanation:

Let's call the two numbers x and y. We know that:

xy = 72

x + y = -38

We can use the first equation to solve for one of the variables in terms of the other:

x = 72/y

Then, we can substitute this expression into the second equation:

72/y + y = -38

y^2 + 72 = 38y

y^2 - 38y + 72 = 0

This is a quadratic equation that can be solved using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -38, c = 72.

Plugging in these values, we get:

y = (38 ± √(38^2 - 4(1)(72))) / 2(1)

y = (38 ± √(1444)) / 2

y = (38 ± 38) / 2

So, we have two solutions for y:

y = 38 / 2 = 19

y = -38 / 2 = -19

With either of these values for y, we can use the first equation to solve for x:

x = 72/y = 72/19 = 3.8

or

x = 72/-19 = -3.8

So, the two numbers whose product is 72 and whose sum is -38 are x = 3.8 and y = 19, or x = -3.8 and y = -19.

Answer: 3

Step-by-step explanation:

Answer:

The answer to the expression is -5 + 10 - 8 = -3.

Step-by-step explanation:

Step-by-step explanation:

If you write down the amount of time Bryant spends sleeping every night, you will see a sequence of numbers between 6 and 9 hours inclusive.

Answer:

[tex]10^{7}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

then

10² × [tex]10^{5}[/tex] = [tex]10^{(2+5)}[/tex] = [tex]10^{7}[/tex]

Answer:

[tex]10^{7}[/tex]

Step-by-step explanation:

[tex]10^{2}*10^{5}=10^{2+5}=10^{7}[/tex]

The body mass index of the patient who weighs 68kg and is 60 inch tall is 29.3 kg/m².

This question is incomplete, the complete question is;

What is the body mass index IBM of a patient who weighs 68kg and is 60 inch tall?

Body mass index IBM is simply a measure of body fat of a person.

Its is calculated using the mass and height of a person.

It can be calculated using the formula;

BMI = Mass (kg) / Height² (m)

Given the data in the question;

Plug the given values into the above formula and simplify.

BMI = Mass (kg) / Height² (m)

BMI = 68kg / ( 1.524m )²

BMI = 68kg / 2.322576 m²

BMI = 29.3 kg/m²

Therefore, the BMI of the patient is 29.3 kg/m².

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From the properties of similarity, the value of x is 24.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image. More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other. This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.

By comparing corresponding sides of the shapes, we get that

6/9 = 14/21 = 2/3

So that,

16/x =2/3

multiply both sides by 3/2 we get,

(16/x)*(3/2) = 1

multiply both sides by x we get,

16*3/2 = x

⇒ x = 48/2

⇒ x = 24

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Answer:

12x-5.5 all you have to do is simplify

The rate of change of the height is approximately -1.67 meters per minute.

The volume of a cone can be written as V = (1/3)πr²h.

Differentiating with respect to time t, we get

dV/dt = (1/3)π (2rh dr/dt + r² dh/dt)

Given that the radius is decreasing at a constant rate of 1 meter per minute and the volume is decreasing at a rate of 61 cubic meters per minute, we can substitute these values into the equation to find dh/dt:

61 = (1/3)π (2rh + r² dh/dt)

dh/dt = (61 - (2rh)) / (r² * (1/3)π)

Substituting in the given values of r = 2 meters and h = 41 cubic meters, we get:

dh/dt = (61 - (2 * 2 * 41)) / (2² * (1/3)π)

dh/dt = (61 - 164) / (4 * (1/3)π)

dh/dt = -103 / (4 * (1/3)π)

Approximating π to 3.14, we get

dh/dt = -103 / (4 * (1/3) * 3.14)

dh/dt ≈ -1.67

So the rate of change of the height is approximately -1.67 meters per minute.

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Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

The intervals where the function is decreasing are:

(-3, -1) and (4, ∞)

The function is decreasing when, reading from left to right, the graph goes dondwards.

Now let's find the intervals where that happens.

First that happens between x = -3 and x = 1

And then the function starts decreasing again at x = 4 and keeps decreasing.

Then the intervals where the function decreases are:

(-3, -1) and (4, ∞)

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Answer:

Median

Step-by-step explanation:

The best measure of center in this case would be the median, as the presence of a few outliers (first-graders who were behind in language acquisition) would greatly affect the mean, while the median would provide a better representation of the typical vocabulary knowledge of first-graders in the group.

If the least value of n is 4, then the inequality best shows all the possible values of n is, n ≥ 4. So Option B is correct

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

The least value of n is 4,

Inequality representation = ?

It is known that,

Least value  of n is 4

So, Minimum possible value of n is 4

Maximum value of n should be more than 4,

In order to satisfy the condition,

So,

n  > 4

By combining both the things,

It can be written as,

n ≥ 4

Hence, the best inequality representation is n ≥ 4

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The inequalities representing the graph are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

First, we have to determine the two lines.

Line₁.

(0, 2) and (1, - 1).

m = (- 1 - 2)/(1 - 0).

m = - 3.

- 1 = - 3(1) + b.

b = 2.

y = - 3x + 2.

Line₂.

(0, - 2) and (3, 0).

m = (0 + 2)/(3 - 0).

m = 2/3.

0 = (2/3)(3) + b.

b = - 1.

y = (2/3)x - 1.

So, The two inequalities are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.

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The approximate lateral area of the cone is equal to 314 cm².

Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:

Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)

Where

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circular base = πr²

25π = πr²

Radius, r = √25

Radius, r = 5 cm.

Substituting the given parameters into the lateral area of a cone formula, we have the following;

Lateral surface area of a cone, LSA = πrl = πr4(r)

Lateral surface area of a cone, LSA = 3.14 × 5 × 20

Lateral surface area of a cone, LSA = 314 cm².

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The average amount of cliff's height that decreased each year is 1/6 inches.

The rate at which one value changes with respect to per unit change in the other value is called the unit rate. Mathematically -

{ r } = y/x                                                          .... Eq { 1 }

Given is that over the course of an 18 year research project, the height of an oceanside cliff actually dropped due to soil erosion. At the end of this period, its height was measured as -3 inches compared to what it had been at the beginning of the research project.

We can write the the average amount of cliff's height that changed each year as -

{r} = |h|/|t|

{r} = 3/18

{r} = 1/6

Therefore, the average amount of cliff's height that decreased each year is 1/6 inches.

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Answer:

70 * 12 = 840

1400 + 840 = 2240

$2,240 monthly

Step-by-step explanation:

Hope it helps! =D

Answer:

2170

Step-by-step explanation:

Write out the first 3 terms:

a 1 = 1400 ← rent in 1st year

a 2 = 1470 ← rent in 2nd year

a 3 = 1540 ← rent in 3rd year

Arithmetic Sequence: d=70

Explicit Formula:

an = a 1+(n−1)d

a 12 = 1400+(12−1)(70)

a 12 = 2170

Answer:

C

Step-by-step explanation:

Converting 40% into a decimal would be .40

Since you want to find 40% of 35, we would multiply

(35)(.40) = 14

Answer:

The annual interest you would earn on each bond depends on the bond's coupon rate, which can be calculated by dividing the bond's current yield (Column 2) by 100. For Bond A and C, the coupon rate would be 7.5%, and for Bond X and Y, it would be 8.4%. The annual interest you would earn on each bond would be the coupon rate multiplied by the bond's face value (Column 1). For Bond A and C, the annual interest would be 7.5% * $15 = $1.125, and for Bond X and Y, it would be 8.4% * $15 = $1.26.

Answer:pls brainliest :D

Step-by-step explanation:

To find the average daily balance for January, we need to find the total balance for the month and divide by the number of days in the month.

Starting balance: $700

Sofa purchase: $1100

Payment on January 14th: $550

Lamps and household items purchase: $475

Total balance: $700 + $1100 + $475 - $550 = $1825

There are 31 days in January, so the average daily balance is: $1825 / 31 = $58.87.

Answer:bro chilll

Step-by-step explanation:

The correct answer from options are,

a) x⁴ – 6x²  – 27 = 0,

d) 6(2x + 4)² = (2x + 4) + 2  and,

e) 6x⁴ = -x² + 5.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must contain at least one term of the second degree.

Given equations to find the  equations that are quadratic in form,

Standard form refers to the quadratic function f(x) = a(x - h)² + k, where a is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is the vertical line x = h.

so equations that are in form of quadratic are,

x⁴ – 6x²  – 27 = 0,

6(2x + 4)² = (2x + 4) + 2,

6x⁴ = -x² + 5

and rest all other equations are not in form of quadratic.

Hence options A, D, and E are correct.

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Answer:5 star would be greatly aprreciated

For b) Estimating the maximum heart rate, a common formula used to calculate maximum heart rate is:

Max HR = 220 - Age

Since the person is 20 years old, the maximum heart rate can be estimated as:

Max HR = 220 - 20 = 200 beats per minute.

To estimate the maximum heart rate given a resting heart rate, we can use the formula:

Max HR = Resting HR + (Max HR - Resting HR) * Percentage of Max HR

Assuming a typical range of 70-85% of maximum heart rate during exercise, the estimated maximum heart rate for a resting heart rate of 40, 60, 72, and 80 beats per minute would be:

Resting HR = 40: Max HR = 140 + (200 - 140) * 0.85 = 170 beats per minute

Resting HR = 60: Max HR = 140 + (200 - 140) * 0.80 = 176 beats per minute

Resting HR = 72: Max HR = 140 + (200 - 140) * 0.75 = 182 beats per minute

Resting HR = 80: Max HR = 140 + (200 - 140) * 0.70 = 188 beats per minute

For c) the correlation coefficient, the coefficient measures the strength and direction of the linear relationship between two variables. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates no correlation.

Step-by-step explanation:

For b) Estimating the maximum heart rate, a common formula used to calculate maximum heart rate is:

Max HR = 220 - Age

Since the person is 20 years old, the maximum heart rate can be estimated as:

Max HR = 220 - 20 = 200 beats per minute.

To estimate the maximum heart rate given a resting heart rate, we can use the formula:

Max HR = Resting HR + (Max HR - Resting HR) * Percentage of Max HR

Assuming a typical range of 70-85% of maximum heart rate during exercise, the estimated maximum heart rate for a resting heart rate of 40, 60, 72, and 80 beats per minute would be:

Resting HR = 40: Max HR = 140 + (200 - 140) * 0.85 = 170 beats per minute

Resting HR = 60: Max HR = 140 + (200 - 140) * 0.80 = 176 beats per minute

Resting HR = 72: Max HR = 140 + (200 - 140) * 0.75 = 182 beats per minute

Resting HR = 80: Max HR = 140 + (200 - 140) * 0.70 = 188 beats per minute

For c) the correlation coefficient, the coefficient measures the strength and direction of the linear relationship between two variables. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates no correlation.

To model the data with a linear function, find the slope using two points from the table, and use the slope-intercept form of the equation to find the y-intercept. To estimate the maximum heart rate for different resting heart rates, substitute the values into the equation. The correlation coefficient cannot be determined based on the given table of data.

To model the data with a linear function, we can use the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope (m). The slope is given by the formula: m = (y2 - y1) / (x2 - x1). We can choose any two points from the table to calculate the slope. Let's choose (60, 200) and (70, 180) as our two points.

Using the formula, we have m = (180 - 200) / (70 - 60) = -20 / 10 = -2.

Now, we can use the slope-intercept form of the equation to find the y-intercept (b). Let's substitute one of the points into the equation: 200 = -2(60) + b. Solving for b, we get b = 320.

Therefore, the equation of the linear function that models the data is y = -2x + 320.

To estimate the maximum heart rate for different resting heart rates, we can substitute the given values into the equation:

If the resting heart rate is 40: y = -2(40) + 320 = 240.

If the resting heart rate is 60: y = -2(60) + 320 = 200.

If the resting heart rate is 72: y = -2(72) + 320 = 176.

If the resting heart rate is 80: y = -2(80) + 320 = 160.

The correlation coefficient measures the strength and direction of the relationship between two variables. In this case, it represents the correlation between resting heart rate and maximum heart rate. The closer the correlation coefficient is to 1 or -1, the stronger the correlation. However, since we are given a table of data and not actual data points, we cannot calculate the correlation coefficient. We can only estimate it visually based on the scatter plot of the data points.

Therefore, the correlation coefficient cannot be determined and our confidence in using the regression line to estimate function values is limited.

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were going to need a lil more than that to answer :(

The event with a sample space of S = {A, B} is (d) choosing a tile from a pair of tiles, one with the letter A and one with the letter B.

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

Sample space of S = {A, B}

In probability, the sample space is the set of all possible outcomes of a random event.

In the case of choosing a tile from a pair of tiles, one with the letter A and one with the letter B, there are only two possible outcomes: A or B.

Therefore, the sample space S is {A, B}.

In contrast, for the other events listed:

In each of these events, there are more than two possible outcomes, so the sample space is a set with more than two elements.

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It took Bailey 45 days to paint the house and Andrew 11.25 days to paint the house.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, Andrew can paint the neighbor's house 4 times as fast as Bailey. Andrew and Bailey worked together, it took them 5 days.

Let the time it took Bailey to paint the house be x days, and the time it took Andrew to paint the same house be y. Then,

Establishing the system of equation,

1/x + 1/y = 1/9. . . (1)

x = 4y. . . (2)

Putting (2) into (1) gives,

1/4y + 1/y = 1/9

5/4y = 1/9

4y = 5 x 9 = 45

y = 11.25

x = 4(11.25) = 45

Hence, it took Bailey 45 days to paint the house and Andrew 11.25 days to paint the house.

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The cost of each Cappuccino and each house lattes was $2.79 and $2.99 respectively

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Let x represent the cost of each cappuccino and y represent the cost of each house lattes.

Two cappuccinos and three house lattes was $14.55, hence:

2x + 3y = 14.55   (1)

Also:

One cappuccino and two house lattes was $8.77, hence:

x + 2y = 8.77    (2)

From both equations:

x = 2.79, y = 2.99

The cost of each Cappuccino and each house lattes was $2.79 and $2.99 respectively

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Answer:

(- 9, 10 )

Step-by-step explanation:

Solve the equations simultaneously to find solution to both

- 6x + 3y = 84 → (1)

- 6x - 3y = 24 → (2)

add (1) and (2) term by term to eliminate y

- 12x + 0 = 108

- 12x = 108 ( divide both sides by - 12 )

x = - 9

substitute x = - 9 into either of the 2 equations and solve for y

substituting into (1)

- 6(- 9) + 3y = 84

54 + 3y = 84 ( subtract 54 from both sides )

3y = 30 ( divide both sides by 3 )

y = 10

solution is (- 9, 10 )