create a box and whisker plot for the following set of data

We can say that f(x) has a local maximum at A and a local minimum at B.

A function is a mathematical rule that assigns a unique output value to each input value. It describes the relationship between the input and output variables.

Critical numbers of a function are the values of the independent variable where the derivative is zero or undefined, indicating possible extrema or inflection points.

According to the given information:

To find the critical numbers of the function f(x), we need to find the values of x where f'(x) = 0 or f'(x) is undefined.

f(x) = cos(x) + √2/2

f'(x) = -sin(x)

Setting f'(x) = -sin(x) = 0, we get sin(x) = 0, which is true for x = nπ, where n is an integer. However, we only need to consider the values of x in the interval [0,2].

For n = 0, x = 0 is a critical number.

For n = 1, x = π is a critical number.

For n = 2, x = 2π is not in the interval [0,2], so we don't need to consider it.

Therefore, the critical numbers of f(x) in the interval [0,2] are A = 0 and B = π.

To find the nature of the critical points, we need to find the second derivative of f(x).

f''(x) = -cos(x)

Evaluating f''(x) at A and B, we get:

f''(A) = -cos(0) = -1, which means that f(x) has a local maximum at A.

f''(B) = -cos(π) = 1, which means that f(x) has a local minimum at B.

Therefore, we can say that f(x) has a local maximum at A and a local minimum at B.

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Answer:

Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.

On Thursday, she practiced for 5 minutes according to the table.

On Friday, she practiced for 9 minutes according to the table.

Adding these two times together, we get:

5 minutes + 9 minutes = 14 minutes

Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.

It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to√(0.861(1.0.861)/410) = 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

What is a proportion?

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to[tex]\sqrt{\frac{0.861(1.0.861)}{410)}[/tex]= 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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x ≤ 4, -2≤ y ≤ 2  are the domain and range of the graph of this function.

What is the domain and domain of the function in the graph?

Another way to identify domains and feature sets is with graphs. Domain refers to the set of possible input values, so a chart's domain consists of all input values ​​displayed on the x-axis.

                                    A range is the set of possible output values ​​plotted on the y-axis. To find the domain and domain of the equation y = f(x), find the value of the independent variable x for which the function is defined. 

y = f(x)

according to the graph value of y

 x ≤ 4,

-2≤ y ≤ 2

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The expression x^4 + 5x^2 - 8 in quadratic form is: (x^2 + 8)(x^2 - 1)

It should be noted that to express the given expression x^4+5x^2 - 8 in quadratic form, we need to identify a suitable substitution that will allow us to rewrite the expression as a quadratic in a new variable.

One possible substitution is to let u = x^2, so that we can write:

x^4 + 5x^2 - 8 = u^2 + 5u - 8

We can then factor this quadratic expression as:

u^2 + 5u - 8 = (u + 8)(u - 1)

Substituting back u = x^2, we get:

x^4 + 5x^2 - 8 = (x^2 + 8)(x^2 - 1)

Therefore, the expression x^4 + 5x^2 - 8 in quadratic form is:

(x^2 + 8)(x^2 - 1)

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Answer:

y = 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 3 ← is in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes , then

slope of line AB is m = 2

line AB crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 2x + 4 ← equation of line AB

When the two sections are combined, the total number of circles would be ten, representing the value of 5 times 2, which is 10.

Number is a mathematical concept used to quantify or measure a quantity. It is a symbol or group of symbols that stands for a quantity, such as 2, 4, 5, 10, and so on. Numbers are used to express amounts, to count, and to measure. They are also used to represent relationships between quantities and to compare quantities.

A place value disk can be used to represent the value of 5 times 2, which is equal to 10. The disk would have two sections, one representing the number 5 and the other representing the number 2. The number 5 would be represented by five single circles in the “ones” section, and the number 2 would be represented by two single circles in the “ones” section. When the two sections are combined, the total number of circles would be ten, representing the value of 5 times 2, which is 10.

The place value disk is a useful visual tool to help students understand the concept of multiplication. It allows them to clearly see how the number of circles in each section are multiplied to get the final answer. This can help them better understand the concept of multiplication and how it works.

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Complete questions as follows-

Answer:

1

Step-by-step explanation:

1/3 + 8/12 ⬅️(factor out by common factor, 4)

= 1/3 + 2/3

=1+2/ 3

=3/3 or 1

Answer:

k = 10

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ MYZ is an exterior angle of the triangle , then

4k + 5 + 6k + 10 = 115

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

Answer:

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

Exterior angle of a triangle is equal to the sum of remote interior angles.

In the given picture, the exterior angle is 115°, and remote interior angles are (4k + 5)° and (6k + 10)°.

Set up equation and solve for k:

Therefore the value of k is 10.

Answer:

≈ 0.153

Step-by-step explanation:

using the rules of logarithms

log x - log y ⇔ log ([tex]\frac{x}{y}[/tex] )

[tex]log_{b}[/tex] b = 1

then

[tex]log_{c}[/tex] ( [tex]\frac{4}{c}[/tex] )

= [tex]log_{c}[/tex] 4 - [tex]log_{c}[/tex] c

= 1.153 - 1

= 0.153

Answer: Total distance of the swimming competition is 55.56 km.

Step-by-step explanation:

Let x be the total distance of the swimming competition.

On the first day, Angie covered 25% of the total distance, which means she swam 0.25x km.

On the second day, she covered one-third of the remaining distance, which is (1 - 0.25)x = 0.75x km.

So, she swam (1/3) * 0.75x = 0.25x km on the second day.

On the third day, she covered 25% of the remaining distance, which is (1 - 0.25 - 1/3)x = 0.42x km.

So, she swam 0.25 * 0.42x = 0.105x km on the third day.

On the final day, she swam half of the remaining distance,

which is (1 - 0.25 - 1/3 - 0.5)x = 0.125x km.

The total distance she swam is the sum of the distances swum on each day:

0.25x + 0.25x + 0.105x + 0.125x = 0.73x

We know that the total distance of the competition is x - 15 km (since she still has 15 km left to swim).

So we can set up the equation:

0.73x = x - 15

Solving for x, we get:

x-0.73x = 15

0.27x = 15

x = 55.56

Therefore, the total distance of the swimming competition is 55.56 km.

Answer:

height= 3cm

Step-by-step explanation:

to find the base of each triangle just half the bottom to get 4cm

a^2+b^2=c^2

a^2+4^2=5^2

a^2+16=25

a^2=9

a=√9

a=3

The correct option is: No. Because the interval does not contain $35, the manager would not be issued the bonus.

An interval refers to a range of values between two points on a numerical scale. It can be represented by two numbers, called endpoints, and includes all the values that lie between these endpoints.

The two common types of intervals are closed intervals and open intervals.

According to the given information:

In a confidence interval, the range of values within which the true population parameter (in this case, the mean amount of money each customer spends per visit) is likely to fall is estimated. A 95% confidence interval means that there is a 95% probability that the true population parameter falls within the interval.

In this case, the confidence interval is ($10.53, $31.89), which means that we are 95% confident that the true mean amount customers spend per visit falls between $10.53 and $31.89. Since the interval does not contain $35, it is not reasonable to believe that the manager will receive a bonus, as the estimated mean amount spent per visit is below $35 according to the confidence interval.

The correct answer is: No. Because the interval does not contain $35, the manager would not be issued the bonus.

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Answer:

yes it is pretty hard but I believe I. you

Is the graph increasing, decreasing, or constant: C. Constant.

In Mathematics and Geometry, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

By critically observing the graph shown above, we can reasonably infer and logically deduce that the graph is constant because it assumes only one y-value, which is represented by this equation y = 3.

In conclusion, the above is constant, rather than increasing or decreasing.

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91.3 pounds of fruit are left

Jason bought = 91.5 pounds

class ate = 0.2 pounds

You subtract the amount the class ate from the amount Jason bought to get the amount of fruit left.

91.5 - 0.2 = 91.3 pounds

I'm afraid you forgot to add a picture?

Answer:

To evaluate the composite functions (f◦g), (g◦f), (f◦f), and (g◦g), we need to substitute one function into the other and simplify the resulting expression.

(a) (f◦g)(4):

To find (f◦g)(4), we need to first find g(4) and then substitute it into f(x):

g(4) = 7 - 1/2(4)^2

= 7 - 8

= -1

Now we substitute g(4) = -1 into f(x):

(f◦g)(4) = f(g(4))

= f(-1)

= 3(-1)^2 - 2

= 1

Therefore, (f◦g)(4) = 1.

(b) (g◦f)(2):

To find (g◦f)(2), we need to first find f(2) and then substitute it into g(x):

f(2) = 3(2)^2 - 2

= 10

Now we substitute f(2) = 10 into g(x):

(g◦f)(2) = g(f(2))

= g(10)

= 7 - 1/2(10)^2

= -43

Therefore, (g◦f)(2) = -43.

(c) (f◦f)(1):

To find (f◦f)(1), we need to find f(f(1)):

f(1) = 3(1)^2 - 2

= 1

Now we substitute f(1) = 1 into f(x):

(f◦f)(1) = f(f(1))

= f(1)

= 1

Therefore, (f◦f)(1) = 1.

(d) (g◦g)(0):

To find (g◦g)(0), we need to find g(g(0)):

g(0) = 7 - 1/2(0)^2

= 7

Now we substitute g(0) = 7 into g(x):

(g◦g)(0) = g(g(0))

= g(7)

= 7 - 1/2(7)^2

= -17/2

Therefore, (g◦g)(0) = -17/2.

The correct answer is: Decrease total assets and net income.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

The recognition of uncollectible accounts expense for Year 2 will decrease total assets and net income.

When uncollectible accounts expense is recognized, it is recorded as a debit to the allowance for doubtful accounts and a credit to the uncollectible accounts expense account. This reduces the balance of accounts receivable, which is a current asset, and thus decreases total assets. Additionally, recognizing this expense reduces net income by the same amount.

Therefore, the correct answer is: Decrease total assets and net income.

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The equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

The equation of a circle with center (a,b) and radius r is given by the equation:

(x - a)^2 + (y - b)^2 = r^2

Using the given values, the equation of the circle with center (1/2, 0) and radius 2 is:

(x - 1/2)^2 + (y - 0)^2 = 2^2

Expanding and simplifying, we get:

(x - 1/2)^2 + y^2 = 4 - 1/4

Therefore, the equation of the circle is:

(x - 1/2)^2 + y^2 = 15/4

So, the equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

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The volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

In general, volume refers to the amount of space occupied by a three-dimensional object. In physics, volume is a measure of the amount of space an object takes up, typically measured in cubic meters (m³) or cubic centimeters (cm³).

In mathematics, volume is often used to refer to the measure of the size of a solid object or region in three-dimensional space. This measure can be calculated using various methods depending on the shape of the object or region, such as integration, formulae, or counting.

For example, the volume of a cube can be calculated by multiplying its length, width, and height together. The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius of the sphere.

In finance, volume can also refer to the number of shares or contracts traded in a particular market or stock exchange over a given period of time. High trading volume often indicates a more active market, while low trading volume may indicate less interest or activity in a particular security or market.

The formula for calculating the volume of air passing through a filter is:

Volume = Filter Area x Airflow Velocity

Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:

Filter Area = Length x Width

Filter Area = 4 ft x 2 ft

Filter Area = 8 square feet

Now we can substitute the values into the formula:

Volume = Filter Area x Airflow Velocity

Volume = 8 sq ft x 100 ft/min

Volume = 800 cubic feet per minute (CFM)

Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

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Solving the system of equations using matrices is : = -66, y = 163, and z = 11.

To solve this system of equations using matrices, we can write it in the form AX = B, where:

A = coefficient matrix

X = variable matrix (containing x, y, and z)

B = constant matrix (containing the constants on the right-hand side of each equation)

So, we have:

| 2  -1  3 |   | x |   | 180 |

| -4  2  3 | x | y | = | 225 |

| 3  -4  0 |   | z |   | 270 |

We can solve for X by multiplying both sides of the equation by the inverse of A:

X = A^-1 * B

First, we need to find the inverse of A. We can do this by using the formula:

A^-1 = (1 / det(A)) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate (transpose of the cofactor matrix) of A.

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

det(A) = 2(20 - 3(-4)) - (-1)(-40 - 33) + 3(-4*(-1) - 2*3) = 16

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

The cofactor matrix is:

| 2  9  6 |

| 12  0  -2 |

| 13  -9  8 |

Taking the transpose of the cofactor matrix gives us the adjugate of A:

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

So, we have:

A^-1 = (1 / det(A)) * adj(A) = (1 / 16) *

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

Multiplying A^-1 by B gives us:

| x |   | -66 |

| y | = | 163 |

| z |   | 11  |

Therefore, x = -66, y = 163, and z = 11.

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Answer: 104%

Step-by-step explanation: 26% times 4 years

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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Answer:

B

Step-by-step explanation:

The answer are in angle m∠5+m∠6=180°,m∠2+m∠3=m∠6,m∠2+m∠3+m∠5=180°.

Angle is a geometric concept that is used to describe the relationship between two lines or planes. It is measured in degrees, with a full circle being 360 degrees. Angles are used in mathematics to measure the size of a shape and the amount of turn between two lines. In physics, angles are used to describe the force of friction, the direction of a force, and the direction of light. Angles can also be used to describe the orientation of objects in space.

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary by angles

m∠4=180°-m∠3 ----> equation B

substitute the equation- B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

therefore

Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary to angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

therefore

This option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of any of tAnswer:

Step-by-step explanation:

he interior angles that of a triangle must be equal to 180 degrees

therefore

This option is true for sure

case E) we have

m∠2+m∠3+m∠5=180°.

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The surface area of this figure is determined as 980.5 m².

The total surface area of the figure is the sum of all the area of the six faces and it is calculated as follows;

Area of top face = 12.7 m x 11 m = 139.7 m²

Area of bottom face = 9.5 m x 16 m = 152 m²

Area of far right face = 12.7 m x 14 m = 177.8 m²

Area of far left face = 9.5 m x 14 m = 133 m²

Area of front face = 16 m x 14 m = 224 m²

Area of back face = 11 m x 14 m = 154 m²

Total surface area = 139.7 m² + 152 m² + 177.8 m² + 133 m² + 224 m² + 154 m²

= 980.5 m²

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Angle A equals 41.81°

c: