1.10/11+4/5

2.1/5+1/6

The absolute extrema of the function y = 8cos(x) on the closed interval [0, 2π] are a maximum value of 8 at x = 0 and a minimum value of -8 at x = π.

To find the absolute extrema of the function y = 8cos(x) on the interval [0, 2π], we need to evaluate the function at the critical points and the endpoints of the interval.

First, let's look for critical points by finding where the derivative of the function is zero or undefined. Taking the derivative of y with respect to x, we have:

dy/dx = -8sin(x)

Setting this derivative equal to zero, we find that -8sin(x) = 0. Since sin(x) = 0 at x = 0 and x = π, these points are potential critical points.

Next, we evaluate the function y at the critical points and the endpoints of the interval. The function y = 8cos(x) evaluates to:

At x = 0: y = 8cos(0) = 8

At x = π: y = 8cos(π) = -8

At x = 2π: y = 8cos(2π) = 8

Comparing these values, we find that the maximum value of y = 8 is achieved at x = 0, and the minimum value of y = -8 is achieved at x = π.

Therefore, the absolute extrema of the function y = 8cos(x) on the closed interval [0, 2π] are a maximum value of 8 at x = 0 and a minimum value of -8 at x = π.

It's worth noting that since the cosine function oscillates between -1 and 1, the maximum and minimum values of y = 8cos(x) occur when cos(x) is at its extremes. In this case, the maximum occurs when cos(x) = 1 (at x = 0), and the minimum occurs when cos(x) = -1 (at x = π). The amplitude of the cosine function is 1, so multiplying it by 8 scales the function vertically, resulting in a maximum value of 8 and a minimum value of -8.

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Answer:

x=1.75

Step-by-step explanation:

3*2-4x+1=0 subtract 1 from both sides

3*2-4x=-1 multiply 3 and 2

6-4x=-1 Subtract 6 from both sides

-4x=-7 divide both sides by -4

x=1.75

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Answer: which question

Step-by-step explanation:

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Answer:

B//////

Step-by-step explanation:

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

The equation of the line in slope-intercept form representing the amount of money in Marus's account over time is y = mx + b.

In the slope-intercept form of a linear equation, y represents the dependent variable (in this case, the amount of money in Marus's account), x represents the independent variable (time), m represents the slope of the line, and b represents the y-intercept (the value of y when x = 0).

To determine the equation of the line, we need to know the slope and y-intercept values. The slope, m, represents the rate of change of Marus's account balance over time. If we have two points on the line, we can calculate the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Once we have the slope, we can substitute it along with the coordinates of any point on the line into the slope-intercept form equation y = mx + b to solve for the y-intercept, b. The y-intercept is the value of y when x = 0, meaning it represents the initial amount of money in Marus's account.

By determining the values of m and b, we can write the equation of the line in slope-intercept form and have a mathematical representation of how the amount of money in Marus's account changes over time.

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Answer:

-2

Step-by-step explanation:

y = 3x + 2.5

x = -1.5

y = 3 x -1.5 + 2.5

  = -4.5 + 2.5

  = -2

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

y = - 3x + 2.5

The value of the equation at x = 1 will be given as,

y = - 3 × (1) + 2.5

y = - 3 + 2.5

y = - 0.5

The value of the equation at x = - 1.5 will be given as,

y = - 3 × (-1.5) + 2.5

y = 4.5 + 2.5

y = 7

The value of the equation at x = 8.5 will be given as,

y = - 3 × (8.5) + 2.5

y = - 22.5+ 2.5

y = - 20

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

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This prompt is about being able to represent time and distance on a graph called Distance-Time Graph. See the graph attached.

A Distance-Time Graph is a sort of graph that depicts the relationship between distance and time for a moving object.

It is a handy tool for studying an object's motion since it allows one to simply ascertain the object's speed and acceleration. It is also significant because it gives a visual depiction of an object or subject's motion, making the underlying physical ideas easier to grasp.

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Full Question:

Tanisha left her house at time zero and drove to the store, which is 8 blocks away, at a speed of 4 blocks per minute. Then she stopped and went into the store for 3 minutes. From there, she drove in the same direction at a speed of 3 blocks per minute until she got to the bank, which is 12 blocks away from the store. She stopped at the bank for 7 minutes. Then she drove home at a speed of 5 blocks every 2 minutes. Make a graph of showing the number of blocks away from home that Tanisha is xx minutes after she leaves her house, until she gets back home.

Make a graph of showing the number of blocks away from home that Tanisha is x minutes after she leaves her house, until she gets back home.

Answer:

Step-by-step explanation:

d = 8 inches

r = 8/2 = 4 inches

h = 9 inches

Volume of the can = πr²h

                               = 3.1428 * 4*4 * 9

                              = 452.56 cubic inches

Answer:

121.32  Option # 1

Step-by-step explanation:

168.5 * 0.72 = 121.32

Answer:

dodndbdie9ejrnfudowp2ejdnsmwo2oeidndndoep

The simplification of 7x^2(6x + 3x^2 - 4) is 42x^3 + 21x^4 - 28x^2. The powers of x are multiplied accordingly, and the coefficients are distributed and combined.

To simplify the expression 7x^2(6x + 3x^2 - 4), we can distribute the 7x^2 to each term within the parentheses:

7x^2 * 6x + 7x^2 * 3x^2 - 7x^2 * 4

This simplifies to:

42x^3 + 21x^4 - 28x^2

Therefore, the correct simplification of the expression is 42x^3 + 21x^4 - 28x^2. The powers of x are combined accordingly, and the coefficients are multiplied accordingly. This simplification is obtained by applying the distributive property and combining like terms.

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The cost of one computer is £600 and the cost of one printer is £800.

Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, and the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer.

Let the cost of a computer be x and the cost of a printer be y.

Then, the two simultaneous equations are:5x + 4y = 6600 ---------------------- (1)

4x + 5y = 6000 ---------------------- (2)

Solving equations (1) and (2) simultaneously:x = 600y = 800

Therefore, the cost of a computer is £600 and the cost of a printer is £800..

:Therefore, the cost of one computer is £600 and the cost of one printer is £800.

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Answer:

$42 dollars is the cost per dozen.

Step-by-step explanation:

3.50 is the cost for ONE muffin and we know that 12 goes into a dozen. Simply multiple 3.50 by 12 (3.50 X 12) to get your answer 42.

Answer:

42 dollars

Step-by-step explanation:

A dozen is equal to 12. A muffin is equal to 3.5 dollars each. Therefore, you have to multiply them together. 12 times 3.5 is equal to 42. Therefore, it is 42 dollars a dozen.

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Answer:

Both answers are 47 degrees

Step-by-step explanation:

1. This is an isosceles triangle so the angle x is going to be the same as the opposite angle given which is 47. So x = 47 degrees

2. For this one, we are given the angle outside the same base angles so we take the 86 given from 180. 180-86=94. This 94 needs to be split between the two remaining angles so we divide it by 2. 94/2 = 47 degrees.

Answer:

0 Joules (No work)

Step-by-step explanation:

The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the car is 100 newtons, but the car does not move, so the distance over which the force is applied is 0 meters.

Therefore, the amount of work done on the car is 100 newtons * 0 meters = 0 joules. This means that no energy has been transferred to or from the car as a result of the force applied to it.

To ensure a zero cash flow in the portfolio, the writer needs to set up a portfolio that offsets the cash flow from selling the derivatives. The writer should have -3 underlying assets in the portfolio (meaning short sold assets)

The cash flow from selling 100 derivatives can be calculated as:

Cash Flow from selling derivatives = 100 * (Premium at time 0 - Expiry value)

Cash Flow from selling derivatives = 100 * (1.34 - 0.64) = 70

To offset this cash flow, the writer needs to include an equal and opposite cash flow from the underlying assets. Let's assume the writer buys ""x"" underlying assets.

Cash Flow from underlying assets = x * (Value at time 0 - Value at time 1)

Cash Flow from underlying assets = x * (36 - 57) = -21x

To make the cash flow from underlying assets equal to the cash flow from selling derivatives, we set up the equation:

-21x = 70

Solving this equation, we find:

x ≈ -3.33

Since the number of underlying assets must be an integer, we round -3.33 to the nearest integer, which is -3.

Therefore, the writer should have -3 underlying assets in the portfolio (meaning short sold assets).

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Hello

chinese yuan        euro           dollar

         1                    0,13              1,09

        40                                         ?

? = 40 x 1,09/1 = 43,6

43,6 Chinese yuan =  $43,6

5.6$

we have 1 yaun=0.13 euro

1 euro=1.09 dollars

so first we will convert 40 yuan into euros for that we have l yaun=0.13 euro from this if l yaun=0.13 euro then how much is 40 yuan

l yaun=0.13 euro

40 yuan = ?

crisscross then we get

?=40yuan×0.13euro÷1yuan

?=5.2 euros

1euros =1.09 dollars

5.2euros =?

?=5.2 euros ×1.09$÷1euros

?=5.67$

Answer:

D

Step-by-step explanation:

im taking the test for math on apex

Answer:

Step-by-step explanation:

The nice correct answer is D your welcome

Answer:

A prism is a three-dimensional solid figure with two parallel faces, called bases, that are congruent polygons, and lateral flat faces which are rectangles in a right prism, and are parallelograms in an oblique prism.

Sample response: A triangular prism has a 3-sided base and 3 lateral faces. A rectangular prism has a 4-sided base and 4 lateral faces. The number of sides of the base of a prism is equal to the number of lateral faces of the prism.

 Step-by-step explanation:

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The variance of a sample is 4,096. And for interquartile, the difference between the largest and smallest values. The correct answer is option D

To calculate the variance we have a small formula:

v=s^2-----(1)

v=variance

s=Standard deviation

so, given that s=64

substitute in equation(1)

v=64*64

v=4096.

variance: The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean.

Variance is denoted by a symbol: σ2.

Interquartile range (IQR) is a measure of statistical dispersion, which is used to spread the data. The IQR is also called midspread.

To calculate the IQR, the data set is divided into quartiles. These quartiles are denoted by Q1 (another name is the lower quartile), Q2 (the median), and Q3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q3 −  Q1

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In a pair of similar triangles, the corresponding sides are proportional. ... When the sides are corresponding it means to go from one triangle to another you can multiply each side by the same number. In the diagram of similar triangles the corresponding sides are the same color.

( if this is wrong I apologize)

\(\\ \rm\rightarrowtail -1/4+3/4a=-7/4a-1\)

\(\\ \rm\rightarrowtail (3/4+7/4)a=-1+1/4\)

\(\\ \rm\rightarrowtail 10/4a=-3/4\)

\(\\ \rm\rightarrowtail 10a=-3\)

\(\\ \rm\rightarrowtail a=-0.3\)

Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P\((1-r)^{n}\) = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320\((1-0.07)^{n}\) = 100

Simplifying the equation, we get:

\(0.93^{n}\) = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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Answer:

10 hours

Step-by-step explanation:

1. Create a chart.

miles    -  hours

7.5.       -   0.5 (30 minutes = 0.5 hours)

150.      -    x (let's use a variable to represent number of hours Jimmy ran)

2. Cross multiply:

7.5(x) = 150(0.5)

7.5x. = 75

3. To isolate x, divide both sides of equation by 7.5

7.5x/7.5 = 75/7.5

4. 7.5 crosses out with itself on the left side of the equation.

5. 75/7.5 = 10

x = 10

Therefore, Jimmy ran 150 miles in ten hours.

Answer:

Volume = 7,241.142 ft^3

Step-by-step explanation:

3. 7

7

Answer: CB, DA, IJ, HG

Step-by-step explanation:

As long as the lines never intersect, they are parallel

Answer:

DONT CHEAT

Step-by-step explanation:

the best estimate of the half-life, combining the two results, is approximately 13.7421 days with an uncertainty of approximately 1.3772 days.

To determine the best estimate of the half-life by combining the two results, we can use the weighted average method. The weights assigned to each measurement are inversely proportional to the squares of their uncertainties. Here's how to calculate the combined result:

Step 1: Calculate the weights for each measurement.

  w1 = 1/σ1^2

  w2 = 1/σ2^2

  Where σ1 and σ2 are the uncertainties associated with each measurement.

Step 2: Calculate the weighted values.

  w1 * t1 = w1 * (15.5 days)

  w2 * t2 = w2 * (16.2 days)

Step 3: Calculate the sum of the weights.

  W = w1 + w2

Step 4: Calculate the weighted average.

  T = (w1 * t1 + w2 * t2) / W

Step 5: Calculate the combined uncertainty.

  σ = √(1 / W)

The best estimate of the half-life is given by the value of T, and the combined uncertainty is given by the value of σ.

Let's calculate the best estimate using the given values:

For the first measurement:

σ1 = 2.3 days

For the second measurement:

σ2 = 1.5 days

Step 1:

w1 = 1/σ1^2 = 1/(2.3^2) ≈ 0.1949

w2 = 1/σ2^2 = 1/(1.5^2) ≈ 0.4444

Step 2:

w1 * t1 ≈ 0.1949 * 15.5 ≈ 3.0195

w2 * t2 ≈ 0.4444 * 16.2 ≈ 7.1993

Step 3:

W = w1 + w2 ≈ 0.1949 + 0.4444 ≈ 0.6393

Step 4:

T = (w1 * t1 + w2 * t2) / W ≈ (3.0195 + 7.1993) / 0.6393 ≈ 13.7421 days

Step 5:

σ = √(1 / W) ≈ √(1 / 0.6393) ≈ 1.3772 days

Therefore, the best estimate of the half-life, combining the two results, is approximately 13.7421 days with an uncertainty of approximately 1.3772 days.

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