In his history class, Han's homework scores are:

100 100 100 100 95 100 90 100 0
The history teacher uses the mean to calculate the grade for homework. Write an argument for Han to explain why median would be a better measure to use for his homework grades.

Answer:

a. To find the inverse of the function c = w + 3, we can follow the steps below:

Step 1: Replace c with y.

y = w + 3

Step 2: Swap the positions of w and y.

w = y + 3

Step 3: Solve for y.

y = w - 3

Therefore, the inverse function is w = y - 3.

b. To find the inverse of the function y = x - 2, we can follow the steps below:

Step 1: Replace y with f(x).

f(x) = x - 2

Step 2: Swap the positions of x and f(x).

x = f(x) - 2

Step 3: Solve for f(x).

f(x) = x + 2

Therefore, the inverse function is f(x) = x + 2.

c. To find the inverse of the function y = 5x, we can follow the steps below:

Step 1: Replace y with f(x).

f(x) = 5x

Step 2: Swap the positions of x and f(x).

x = 5f(x)

Step 3: Solve for f(x).

f(x) = x/5

Therefore, the inverse function is f(x) = x/5.

d. To find the inverse of the function w = D/7, we can follow the steps below:

Step 1: Replace w with f(D).

f(D) = D/7

Step 2: Swap the positions of D and f(D).

D = f(D)/7

Step 3: Solve for f(D).

f(D) = 7D

Therefore, the inverse function is f(D) = 7D.

Answer:

x = 15

Step-by-step explanation:

Given m||n, the angles indicated with (6x+20) and (8x-10) are alternate angles and their measures are equal.

So, to find the value of x, we can write the following equation:

8x - 10 = 6x + 20

8x - 6x = 20 + 10

2x = 30

x = 15

We can solve the given equation using differentiation techniques.

                Differentiation is a method of finding the derivative of a function.Differentiation in mathematics is a function's derivative with respect to an independent variable. Calculus's concept of differentiation can be used to calculate the function per unit change in the independent variable.

              [tex]f(x)=2x^{4}-8e^{x}[/tex]

              [tex]f'(x)=2 * (4x^{3} )-8e^{x}[/tex]

                       =[tex]8x^{3} - 8e^{x}[/tex]

             substitute x= 5

            [tex]f'(5)= 8 * (5)^{3} -8 e^{5} \\ = 1000 - 8 e^{5}[/tex]

      and for f''(x) we have to again derivate the f'(x)

          [tex]f''(x)=24 x^{2} - 8 e^{x}\\ sub x=5 \\-- > f''(5)=24 * 5^{2} - 8 e^{5}\\ = 600 - 8 e^{5}\\[/tex]

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On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:

x = 1.49y

-1.49y + x = 0

-149y + 100x = 0

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The linear equation in the required form is: x - 1.49y = 0

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."

Using this information, we can write:

x = 1.49y

To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.

Subtracting 1.49y from both sides, we get:

x - 1.49y = 0

So the linear equation in the required form is:

x - 1.49y = 0

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In this case, the given sample mean of 25.3 is only slightly higher than the population mean of 25, and is well within one standard deviation from the population mean. Therefore, the probability of a sample mean being less than 25.3 is 0.9582.

In statistics, the mean is a measure of central tendency that represents the sum of all values in a dataset divided by the total number of values in that dataset. It is also commonly referred to as the average.

Here,

To find the required probability, we need to calculate the z-score first:

z = (x - μ) / (σ / √n)

z = (25.3 - 25) / (1.3 / √68)

z = 1.73

Looking at the standard normal table, the probability of a z-score being less than 1.73 is 0.9582.

To determine whether the given sample mean would be considered unusual, we need to compare it to the population mean and standard deviation. A sample mean is considered unusual if it falls outside the range of values that are expected to occur with a high probability based on the population mean and standard deviation.

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A) 52 ft

B) 3640 ft²

C) $12,740

a. The house has a square base with a side length of 50 feet, and the roof extends 1 foot beyond the walls on all sides. To find the length of each side of the base of the roof, we need to add 1 foot on each side of the square base.

Length of each side of the base of the roof = 50 ft + 1 ft + 1 ft = 52 ft

b. The slant height of the roof is 35 feet. To find the sum of the areas of the lateral faces of the pyramid, we can use the formula for the lateral area of a pyramid:

Lateral Area = (Perimeter of the base * Slant Height) / 2;

Since the base of the roof is a square, the perimeter is:

Perimeter = 4 * Side Length = 4 * 52 ft = 208 ft;

Now we can find the lateral area:

Lateral Area = (208 ft * 35 ft) / 2 = 3640 ft²;

c. The cost of installing a metal roof covering is $350 for every 100 square feet of roof. To find the cost of installing a metal roof covering on the house, we can use the following formula:

Cost = (Lateral Area / 100) * Cost per 100 square feet;

Cost = (3640 ft² / 100) * $350 = 36.4 * $350 ≈ $12,740;

The cost of installing a metal roof covering on the house is approximately $12,740.

Olivia swam farther. This is because 5/8 of a mile is greater than 7/12

Carl swam 7/12 of a mile

Olivia swam 5/8 of a mile

= 7/12

= 0.58

= 5/8

= 0.625

From the calculation above, 5/8 is greater than 7/12

Hence Olivia swam faster than Carl because 5/8 of a mile is greater than 7/12 of a mile

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As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

For a normally distributed data set with a mean of 0 and a standard deviation of 0.5, the proportion of values between -1 and 1 is most closely related to 68%.

Approximately 68% of the data in a normal distribution lies within one standard deviation of the mean, which explains why. One standard deviation below the mean is -0.5, and one standard deviation above the mean is 0.5 since the mean is 0 and the standard deviation is 0.5. As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

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The probability that Alex makes at least four free throws in the next six attempts is 9/15 or 0.6.

The probability is determined from the simulation as follows:

Alec spins a spinner with four equal sections and lets the numbers 1-3 represent making a free throw.

The number of spins that result in Alec making at least four free throws in the next six attempts is given below:

9 out of the 15 spins resulted in Alec making at least four free throws in the next six attempts.

The probability based on the simulation = 9/15 or 0.6

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Complete question:

Alec makes 75% of his free throws. He wants to know the probability that he makes at least four of his next six free throws. Alec runs a simulation. He spins a spinner with four equal sections and lets the numbers 1-3 represent making a free throw. Based on the simulation, what is the probability that Alec makes at least four of his next free throws? Explain.

232344

231342

121123

441432

311221

343133

341414

412312

141111

423131

432234

143132

423233

411332

143314

Based on the tabulated level of significance, the correct answer is:

A two-sample t-test with is used to test whether the difference in means is significant at a 5% level of significance.

The null hypothesis is that there is no difference in the means.

The test statistic for the two-sample t-test is given as:

where;

Substituting the given values:

t = (1245 - 1208) / (√(1346 * (1/12 + 1/11)))

t = 2.29

The calculated t-value (2.29) is greater than the tabulated t-value at a 5% level of significance for 21 degrees of freedom, hence, we reject the null hypothesis and conclude that the means are different.

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The volume of the model of the Earth is approximately 69.115 cubic centimeters.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a sphere can be found using the formula V = (4/3)πr³, where r is the radius of the sphere. Since the diameter of the Earth model is 4.8 cm, the radius is half of that, or 2.4 cm.

Plugging in this value, we get:

V = (4/3)π(2.4 cm)³

V ≈ 69.115 cm³

Therefore, the volume of the model of the Earth is approximately 69.115 cubic centimeters.

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Answer:

Step-by-step explanation

multiply every term by the least common denominator to remove fractions

Hence, the piece-wise function to  represent the number of  buses required to  transport 380, 9th graders is :

f(x) = { 1, if 0 < 380 ≤60x

          2, if 60x < 380≤120x

          3, if 120x < 380≤180x

          4, if 180x < 380 ≤ 240x

          5, if 240x < 380≤300x

          6, if 300x < 380 ≤ 360x

          7, if 360x < 380 }

In mathematics, a piece-wise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different  interval in the domain. Piece-wise definition is actually a way of expressing  the function, rather than a characteristic of the function itself.

Let 'x' be the  number of buses required to transport all the 9th graders. We can write the function in two parts, for 1st part  when the number of  students is less than or equal to 60 ( that is the capacity of one bus)  and for 2nd part  when it is greater than 60.

For x buses, each with a capacity of 60, we have:

Therefore,  the piece-wise function to  represent the number of  buses required to  transport 380, 9th graders is :

f(x) = { 1, if 0 < 380 ≤60x

          2, if 60x < 380≤120x

          3, if 120x < 380≤180x

          4, if 180x < 380 ≤ 240x

          5, if 240x < 380≤300x

          6, if 300x < 380 ≤ 360x

          7, if 360x < 380 }

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Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

The next step to take in copying the angle is:  place the compass at point C and open the compass to the distance between B and C.

The steps that we take in copying an angle are:

1). Draw a working line with the help of a straightedge.

2). Now we put a point A as the vertex of the angle.

3). Construct an arc with a radius 'r' (any length ) from vertex A which intersects the working line say at C.

4). With the same radius we draw an arc from point E which intersects the line ED and EF at G and H respectively.

5). Mark an arc from point G which intersects line EF at I.

6). Measure the distance between points G and I with compass and mark an arc from point C which intersects the previous arc say at U.

7). Now join the points S and U.

Hence we copy any angle.

Thus, looking at the given image, the next step is to place the compass at point C and open the compass to the distance between B and C.

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Answer:Creativity is important in constructing scientific questions because the obvious questions do not always lead to interesting results. Scientists need to be able to think outside the box and come up with new and original questions to investigate.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the mean/average of each child:  Add all their times and divide by the number of times there are.

Nelson=(108+130+106+121+126+124+110+124+122)/9

   =119

Tyrese=(117,119,118, 120, 136, 118, 118,120, 123)/9

=121

Nelson-Tyrese = 119-121 = -2

For median list numbers in order and pick middle number

Nelson

106, 108, 110, 121, 122, 124, 124, 126, 130

Nelson median=122

Tyrese

117, 118, 118, 118, 119, 120, 120, 123, 136

Tyrese median =119

Based on the data Tyrese is more likely to finish 120 or less.  Most of his times are under that, even though nelson has a better average.

The angle between the two kayakers is given as follows:

83º.

The cosine of the angle between two vectors a and b is obtained according to the equation presented as follows:

[tex]\cos{\theta} = \frac{ab}{|a||b|}[/tex]

In which:

The dot product of the two vectors in this problem is given as follows:

190 x 128 - 160 x 121 = 4960.

The norm of each vector is given as follows:

Hence the angle is obtained as follows:

cos(x) = 4960/(248.4 x 176.1)

cos(x) = 0.1134

x = arccos(0.1134)

x = 83º.

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Answer: - 7.5

Step-by-step explanation:

Answer:

The value of the given equation is 2.

Step-by-step explanation:

Evaluate and simplify the expression

when x = 5 and z = 3.

[tex]\longrightarrow{\sf{\dfrac{2x - 3(x - z)}{z - 1}}}[/tex]

substituting the given values in the equation :

[tex]\longrightarrow{\sf{\dfrac{2x - 3(x - z)}{z - 1}}}[/tex]

[tex]\longrightarrow{\sf{\dfrac{2 \times 5 - 3(5 - 3)}{3 - 1}}}[/tex]

[tex]\longrightarrow{\sf{\dfrac{10 - 3(5 - 3)}{3 - 1}}}[/tex]

[tex]\longrightarrow{\sf{\dfrac{7(2)}{2}}}[/tex]

[tex]\longrightarrow{\sf{\dfrac{7 \times 2}{2}}}[/tex]

[tex]\longrightarrow{\sf{\dfrac{7 \times \cancel{2}}{\cancel{2}}}}[/tex]

[tex]\longrightarrow{\sf{\underline{\underline{2}}}}[/tex]

Hence, the value of the given equation is 2.

Morgan's supply of raisins is approximately 4.62 pounds.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

Let's start by setting up an equation based on the given information:

14/48 + 38/48 = 5/x

Here, x represents the total supply of raisins in pounds.

To solve for x, we can first combine the fractions on the left-hand side of the equation:

52/48 = 5/x

Next, we can simplify by cross-multiplying:

52x = 48 x 5

52x = 240

Finally, we can solve for x by dividing both sides by 52:

x = 240/52

x ≈ 4.62

Therefore, Morgan's supply of raisins is approximately 4.62 pounds.

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The logarithmic function can be written exponentially as follows.[tex]t = 8^y.[/tex]

Exponents and logarithms are inverse operations of one another. We can rewrite an equation in logarithmic form as log_a(b) = x if it has the form axe = b. A number's logarithm is the exponent that must be raised in order to obtain that number. For instance, since 102 = 100, log_10(100) = 2. Similar to this, we can express an equation in exponential form, such as axe = b, if it is in logarithmic form, such as log_a(b) = x. The inverse function of the logarithmic function is the exponential function. As a result, when we apply a logarithm to an exponential expression, the original exponent is returned, and the opposite is true.

The given logarithmic expression is [tex]log_{8}(t) = y.[/tex]

We know that if we have an equation in the form [tex]a^x = b[/tex], we can rewrite it in logarithmic form as [tex]log_a(b) = x[/tex] and vice versa.

Thus, [tex]log_{8}(t) = y[/tex]

[tex]t = 8^y[/tex]

Hence, the logarithmic function can be written exponentially as follows.[tex]t = 8^y.[/tex]

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Answer:

2.8

Step-by-step explanation:

The formula for calculating simple interest is:

I = Prt

Where I is the interest earned, P is the principal amount, r is the interest rate per year, and t is the time period in years.

In this case, we know that Nick invested $1,000 and earned $112 in interest over a period of 4 years. We can use this information to calculate the interest rate:

112 = 1000 * r * 4

Simplifying the equation, we get:

r = 112 / (1000 * 4)r = 0.028

Multiplying by 100 to convert to a percentage, we get:r = 2.8%

Therefore, Nick's interest rate was 2.8% to the nearest tenth.

The test statistic (37.96) is greater than the critical value (11.345), we can reject the null hypothesis and conclude that there is a significant relationship between admission date and birthday.

The test statistic for this test is calculated by summing the squared differences between the observed and expected frequencies in each category, divided by the expected frequency in that category. This formula is:

X² = ∑(observed - expected)² / expected

The degrees of freedom for this test are equal to the number of categories minus one (4-1=3). Using a significance level of 0.01, the critical value for this test is 11.345.

To calculate the test statistic for this sample, we first need to calculate the expected frequencies. Each category should have an expected frequency of 196/4 = 49.

Category 1: expected frequency = 49, observed frequency = 12

Category 2: expected frequency = 49, observed frequency = 22

Category 3: expected frequency = 49, observed frequency = 65

Category 4: expected frequency = 49, observed frequency = 97

Using the formula above, we can calculate the test statistic:

X² = [(12-49)²/49] + [(22-49)²/49] + [(65-49)²/49] + [(97-49)²/49]

X² = 37.96

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Complete Question:

An article focuses on the existence of any relationship between the date of patient admission for treatment of alcoholism and the patient's birthday. Assuming a 365-day year (i.e., excluding leap year), in the absence of any relation, a patient's admission date is equally likely to be any one of the 365 possible days. The investigators established four different admission categories: (1) within 7 days of birthday, (2) between 8 and 30 days, inclusive, from the birthday, (3) between 31 and 90 days, inclusive, from the birthday, and (4) more than 90 days from the birthday. A sample of 196patients gave observed frequencies of 12, 22, 65, and 97 for categories 1, 2, 3, and 4, respectively. State and test the relevant hypotheses using a significance level of 0.01. Calculate the test statistic.

Answer:

To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:

EAR = (1 + r/n)^n - 1

where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.

For daily compounding, n = 365 (since there are 365 days in a year), so we have:

EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%

To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:

EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%

Therefore, the effective annual rate for hourly compounding is approximately 7.27%.

Answer:

To find the location of point L, we need to use the fact that point K lies on the perpendicular bisector of segment JL.

The perpendicular bisector of a segment is a line that passes through the midpoint of the segment and is perpendicular to the segment.

First, we can find the midpoint of segment JL:

Midpoint of JL = ((-5 + x)/2, (-8 + y)/2)

where (x, y) is the location of point L.

Since point K lies on the perpendicular bisector of JL, the line passing through K and the midpoint of JL will be perpendicular to JL.

The slope of the line passing through K and the midpoint of JL is:

m = (2 - (-8))/(-9 - (-5 + x)/2) = 10/(-9 - (5 - x)/2) = -4/(x - 7)

where we have used the fact that the line passing through K and the midpoint of JL is perpendicular to JL, so its slope is the negative reciprocal of the slope of JL.

Now, we can use the fact that the line passing through K and the midpoint of JL contains point K(-9, 2) to write the equation of the line:

y - 2 = m(x + 9)

Substituting the expression we found for m, we get:

y - 2 = (-4/(x - 7))(x + 9)

Simplifying this equation, we get:

y = -4x/ (x - 7) - 2

Now, we can substitute the x-coordinates of the answer choices to see which one gives us a valid y-coordinate:

A. (1, -2): y = -4(1)/(-6) - 2 = -1 --> Incorrect

B. (-1, -12): y = -4(-1)/(-8) - 2 = 1/2 --> Incorrect

C. (-3, -2): y = -4(-3)/(-10) - 2 = 6/5 --> Incorrect

D. (-3, -12): y = -4(-3)/(-10 - 4) - 2 = -26/7 --> Correct

Therefore, the location of point L is (-3, -12), which is answer choice D.

(x - 3)(x + 6) can be written in vertex form as y = (x - (-3/2))² - 20.25

What is the vertex form?

The vertex form of a quadratic function is a way of writing a quadratic function in form f(x) = a(x - h)² + k where (h, k) is the vertex of the parabola, a is a coefficient that determines the shape and direction of the parabola, and x is the input variable.

Expanding (x - 3)(x + 6), we get:

x² + 6x - 3x - 18 = x² + 3x - 18

To write this expression in vertex form, we need to complete the square. To do this, we add and subtract (3/2)² = 2.25 inside the parentheses:

x² + 3x - 18 + 2.25 - 2.25 = (x² + 3x + 2.25) - 20.25

Now, we can write the expression in vertex form:

y = (x - (-3/2))² - 20.25

Therefore, (x - 3)(x + 6) can be written in vertex form as:

y = (x - (-3/2))² - 20.25

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Answer:

multiple of 3

Step-by-step explanation:

I think that it will least likely land on a multiple of 3 because none of them are multiples of 3.

The length of the segment HI is 32.9

The Circle identities refer to a set of fundamental identities in trigonometry that relate to the some trigonometric functions of an angle in a right-angled triangle.

We know that the equation or formula of secant-tangent;

HI² = KI × JI

Given values:

KI = KJ + JI

KI = 21 + 24 = 45

JI = 24

put the all values in the secant-tangent equation above,

HI² = 45 × 24

HI² = 1080

Take the square root of both sides

HI = 32.9

Hence, the length of the segment HI is 32.9

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Question figure-

Thus, the missing side lengths are :x = 9 feet: y = 6 feet:

A blueprint is a collection of two-dimensional drawings that shows exactly how an architect intends a project to look. Typically, a building's dimensions, materials, and precise location of every component are described in the blueprints.

Given that-

The blue print for the pool of the backyard is prepared which is shown in given diagram.

A figure's longest side is its length, its shortest side is its width, and its highest point is its height.

For the given dimensions in the diagram:

x = 11 + 3 - 5 = 9 ft

y = 8 + 4 - 6 = 6  ft

Thus, the missing side lengths are :x = 9 feet: y = 6 feet:

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Complete question:

You have also decided to put a pool in your backyard, and the builder has shown you the blue print below that shows the pool from above.

Determine the missing side lengths:x = __ feet: y = ___feet:

Diagram for the question is attached.