Find the mean, median, mode, and range for each data set given.
a. 7, 12, 1, 7, 6, 5, 11
b. 85, 105, 95, 90, 115
c.15, 11, 11, 16, 16, 9
Which of the data sets from Exercise 2 are skewed?

Answer:

The constant of a polynomial function is the coefficient of the term with the highest degree (the term with the highest power of x), which in this case is 0. Therefore, the constant of the polynomial function f(x)=-(x+3(x+7)²(x-1)⁵(x+1)⁷(x-4) is 0.

Answer: The pH of blood is a measure of its acidity or basicity and is related to the concentration of hydrogen ions (H+) in the blood. The pH of 7.371 indicates that the blood is slightly basic. Carbonic acid (H2CO3) is a weak acid that dissociates into bicarbonate (HCO3-) and hydrogen ions (H+) in water. The carbonic acid concentration of 1.5 indicates the concentration of H2CO3 in the blood.

The concentration of bicarbonate (HCO3-) in the blood can be approximated by using the relationship between the pH, carbonic acid concentration and the bicarbonate concentration. The Henderson-Hasselbalch equation, which relates the pH and the pK of a buffer, to the ratio of the buffer's conjugate base to its acid form is:

pH = pK + log [HCO3-]/[H2CO3]

The pK of carbonic acid is 6.1 and the concentration of H2CO3 is given as 1.5.

Plugging these values into the Henderson-Hasselbalch equation,

7.371 = 6.1 + log [HCO3-]/1.5

Solving for [HCO3-],

[HCO3-] ≈ 25.8 mM

The approximate concentration of bicarbonate (HCO3-) in the person's blood is 25.8 mM.

Please note that this is an approximation, the actual value may vary depending on the person's health condition.

Step-by-step explanation:

Answer:

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

Step-by-step explanation:

If the distribution of the monthly utility bill for gas or electric energy can be considered mound-shaped and symmetric, we can use the standard normal distribution table to find the percentage of homes that have a monthly utility bill of more than $83.

To use the standard normal distribution table, we need to standardize the variable by subtracting the mean and dividing by the standard deviation:

(83 - 91) / 8 = -0.875

This means that a monthly utility bill of $83 is 0.875 standard deviations below the mean.

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

As per the triangles ABC and SDC are similar triangles then Gilligan can conclude that triangles ABC and SDC are similar and Gilligan can conclude that the distance of the ship from the shore is 509 feet.

The term called triangle in math is defined as a three-sided polygon, which has three vertices

Here from the question we understand points S, C and A are collinear, here we have know that line AB and SD are vertical and parallel lines at the either sides of point C.

So we can conclude that triangles ABC and SDC are similar.

The distance from the ship is calculated as,

=> SD: 130 = AB: 23

Here we have to substitute 90 for AB, then we get,

=> SD: 130 = 90: 23

When write it as,

=>SD/130 = 90/23

When we simplify this then we get  Gilligan can conclude that the distance of the ship from the shore is 509 ft

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Answer:

525 minutes

Step-by-step explanation:

Let us find the temperature of each furnace after 't' minutes.

Furnace1:

Temperature in furnace1 is reducing at rate of 3.5°C per minute.

Rate of cooling after t minute = 3.5*t = 3.5t

We have to subtract 3.5t from 1200°C as it is cooling.

Temperature of furnace1 after 't' minutes = 1200 - 3.5t

Furance2:

Temperature in furnace2 is increasing at rate of 0.5°C per minute.

Rate of heating after t minute = 0.5*t = 0.5t

We have to add 3.5t from 900°C as it is getting heated.

Temperature of furnace1 after 't' minutes = 900 +0.5t

After some minutes, both furnace reach the same temperature.

              900 + 0.5t = 1200 - 3.5t

    900 + 0.5t + 3.5t = 1200

                           4t   = 1200 + 900

                           4t   = 2100

                             t =  2100 ÷ 4

                             [tex]\boxed{t = 525 \ minutes}[/tex]

The height of the room is 5 m.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Length = 7 m

Width = 2 m

Height = x

Four walls of a room will have,

Two walls of length x height.

Two walls of Width x height.

Now,

Area four walls of the room = 90 m

2 (length x height) + 2 (Width x height) = 90

2 (7x) + 2 (2x) = 90

14x + 4x = 90

18x = 90

x = 5

Thus,

Height of the room = 5 m.

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Step-by-step explanation:

The area of a rectangle is given by the formula:

Area = length * width

In this case, the length of the rectangle is given by x + 3 and the width is given by x - 4.

Therefore, the area of the rectangle is:

Area = (x + 3) * (x - 4)

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

In this case, the length of the rectangle is given by x + 3 and the width is given by x - 4.

Therefore, the perimeter of the rectangle is:

Perimeter = 2 * ((x + 3) + (x - 4)) = 2x - 2

So the area of the rectangle is (x + 3)(x - 4) and the perimeter is 2x - 2.

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Answer: Area= x^2-x-12  ,  Perimeter = 4x-2

Step-by-step explanation: According to the question,

Length = x+3

Breadth = x-4

Area of a rectangle = Length * breadth

Area = (x+3)(x-4)

Area = x^2-x-12

Perimeter of rectangle = 2*(length+ breadth)

Perimeter = 2* (x+3+x-4)

                 = 2*(2x-1)

                 = 4x-2

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The two non-right angles in a right angled triangle balance each other out because the right angle already takes up 90 degrees of the triangle's 180 total angles. We refer to two angles as complementing each other when their sums equal 90 degrees.

The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The sum of the other two inner angles is 90 degrees. Base and perpendicular are the names of the other two sides that are close to the right angle. The Pythagorean Theorem is a triangle formula.

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Answer:

x=-1 y=-1

Step-by-step explanation:

i am lazy to type

Answer:{x = -1}{y = -1}

Step-by-step explanation:

subtract the two equations

{6x - 5y = -1                       ^

{6x + 4y = -10                      ^

determine the sign

6x - 5y - (6x +4y) = -1 - (-10) ^

simplify

6x - 5y - 6x - 4y = -1 + 10 ^

substitute

y = -1      ^

solve the equation

6x + 4 x (-1) = -10  ^

write the solution

x = -1                     ^

The net external force acting on the freely falling ball is 43.12 N.

We are provided with the following information:

Mass of bowling ball (m) = 5.5kg

Distance travelled by the ball (h) = 12m

Time taken by the ball = 1.75 s

To calculate the net force acting on the ball, we first need to calculate the acceleration experienced by the ball under free fall.

We can determine the acceleration using the formula,

d= ut + (1/2)at^2

since, the ball was initially at rest, u=0.

Thus, formula becomes,

d= (1/2)at^2.

Therefore, a= 2d/t^2

=> a= 2*12/(1.75)^2

=> a=24/ 3.0625

=> a= 7.84 m/s^2

Now, according to Newton's 2nd law of Motion,

[tex]F_{net} = mass * acceleration[/tex]

[tex]F_{net}[/tex] = 5.5 * 7.84 N =  43.12 N

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The solution of equation f(x)=g(x) is 2.

a formula that illustrates the relationship between the two expressions on either side of a sign. Usually, it has one variable and an equal sign. similar to 2. 2x - 4 = 2. The equals sign (=) in equations indicates that two expressions are equal. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.

The "left hand side" and "right hand side" of the equation refer to the expressions on each side of the equals sign. The right side of an equation is frequently thought of as zero.

Given : f(x)=g(x)

          1/x = (x-1)^2-1

          1 = x (x-1)² - 1

          x (x-1)² = 2

         x ( x² + 1 - 2x ) = 2

         x³ + x - 2x² = 2

         x³ + x - 2x² - 2 = 0

         x³ - 2x² + x - 2= 0

        x²(x-2) + 1(x-2) = 0

       (x² +1) + (x-2) = 0

So,   x = 2 .

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The trigonometric equation 7cos(9x) - 1 = 17 has an undefined solution.

The trigonometric equation for this problem is defined as follows:

7cos(9x) - 1 = 17

Isolating the cosine, we have that:

7cos(9x) = 18

cos(9x) = 18/7

Now we isolate x applying the arc cosine, which is the inverse of the cosine, as follows:

9x = arccos(18/7)

9x = undefined.

The solution is undefined because the arccosine only exists for values between -1 and 1, as the cosine of an angle is always going to assume a value between -1 and 1.

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Probability that 2 or more of the statistics courses are in same slot is 0.28.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

probability that 2 or more of the statistics courses are in same slot

=1-P(all 3 are in different slots)

=1-P(select 3 from 10 slots and arrange them)

=1-(10*9*8)/10^3

=0.28

Therefore, probability that 2 or more of the statistics courses are in same slot is 0.28.

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The area in square meters will the oil slick cover is 9.5×10⁶ m².

15 barrels of diesel spilt into the ocean, where each barrel contains 42 gallons. Thereby the total volume of the oil spilt by 15 barrels is calculated as follows:

The total volume of the oil spilt by 15 barrels = 15× 42 gallons.

=630 gallons

1 gallon = 3.78541 liters

Volume in L = 630 gallons × 3.78541 liters/ 1 gallon

= 2384.8083 L

1 L = 10⁻³ m³

2384.8083  L = 2384.8083 × 10⁻³ m³

= 2.3848083 m³

The area covered by the oil spill has to be determined, where the thickness of the oil spill is given to be 2.5×10² nm.

1 nm = 10⁻⁹ m

Thereby, 2.5×10² nm = 2.5×10²×10⁻⁹ m

= 2.5×10⁻⁷ m

Area (m²) = volume (m³)/thickness (m)

= 2.3848083 m³/ 2.5×10⁻⁷ m

= 0.95392×10⁷ m²

= 9.5×10⁶ m²

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The factored form of 6 + 27 is 3(2 + 9) using GCF.

The greatest common factor, which is the product of two or more numbers, is the biggest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's components have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF)

The given expression is:

6 + 27

Take the factors of the individual numbers:

6 = 1, 2, 3, 6

27 = 1, 3, 9, 17

Take the common factor from both the numbers, in this case it is 3.

Now, factor out the number from the given expression:

6 + 27

3(2 + 9)

Hence, the factored form of 6 + 27 is 3(2 + 9) using GCF.

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The value of x is 15 and the angles in the pentagon are 105,49,90,33,83

What is interior angles in a pentagon ?

The interior angles in a pentagon are the angles which are inside the pentagon and sum of the interior angles in a pentagon is 540 degrees.

Given ,

From the figure we can say that it is pentagon.

And the sum of exterior angles in a pentagon is always 360 degrees.

SO,

7x+49+6x+33+83 = 360

13x + 165 = 360

13x = 360 - 165

13x = 195

x = 195 / 13

x = 15

So, the angles could be 7x = 7*15 = 105  and 6x = 6*15 = 90

Therefore, The value of x is 15 and the angles in the pentagon are 105,49,90,33,83 .

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Answer:

1050$

Step-by-step explanation:

According to the area value, the amount required to be paid for the showroom is $2000.85

The term area in math is known as the region bounded by the shape of an object or it is the space covered by the figure or any two-dimensional geometric shape.

Here we have know that Warehouse Space A Includes 8000 sq. Ft. Of showroom and workshop space and it rents for. 85 cents per month and an additional 25. Cents per sq. Ft, per month for operations expenses.

While we looking into the question, we know that the following are known,

Area = 8000 square feet.

Rent = 85 cents.

Additional expenses = 25 cent per square feet.

Then the total expense is calculated as,

=> 85 + (8000 x 25)

=> 200085 cents.

When we convert into dollars, then we get,

=> One dollar = 100 cents.

Then the resulting value is

=> $2000.85

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A number that is less than 5 / 8 but is greater than 1 / 9 is A. 0. 5.

To find the number that is less than 5 / 8 but greater than 1 / 9, first convert both fractions to decimals.

5 / 8 in decimals is:

= 5 / 8

= 0. 625

1 / 9 in decimals is:

= 1 / 9

= 0. 111

The number from the given options that is less than 5/8 but greater than 1/9 is therefore 0. 5 as it is less than 5 / 8 but more than 1 / 9.

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The options for the question include:

The standard error of the mean for these data is 13.14 pounds..

The standard error of the mean (SEM) is a measure of the variability of the sample mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size.

To find the SEM for the given data, we first need to calculate the sample mean:

(160 + 215 + 195) / 3 = 190

Then we need to calculate the deviation of each value from the mean:

160 - 190 = -30

215 - 190 = 25

195 - 190= 5

Next, we need to square these deviations:

(-30)² = 900

25² = 625

5² = 25

Next, we need to calculate the variance:

(900 + 625 + 25) / 3 = 516 2/3

Then we need to calculate the standard deviation:

√(516 2/3) = 22.73

Finally, we can calculate the standard error of the mean:

22.73 / √(3) = 13.14

So, the standard error of the mean for these data is 13.14 pounds.

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The given scatter plot depicts the exponential function. Therefore, option 1 f(x) = 2ˣ is the correct one.

A scatter plot is a particular kind of graphic diagram that uses Cartesian coordinates to show the values of two variables for a collection of data.

We write y as the function of x as y=f(x). Here, f is considered the name of the function and x is the value of the function. To check which function depicts the given scatter plot, we have to substitute the values for x and find the function. Then, plot the graph.

By doing we get, the plot for f(x) = 2ˣ is equivalent to the given scatter plot. Because this graph depicts the exponential function where the graph passes through the point (0,1). Therefore, option 1 correctly depicts the given plot. Option 2 depicts the identity function and 4 depicts squaring or quadratic function.

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After finding the ratio, the population of Illinois than Alaska is 20 times greater.

The population of Alaska is approximately 6.5 x [tex]10^5[/tex] people.

The population of Illinois is about 1.3 x [tex]10^7[/tex] people.

We have to find how many times greater is the population of Illinois than Alaska.

We will use their population ratio to determine how many times the population of Illinois is greater than the population of Alaska.

Ratio = Population of Illinois's /Population of Alaska

Ratio = 1.3 x [tex]10^7[/tex]/6.5 x [tex]10^5[/tex]

Now simplifying.

Ratio = 0.2 x [tex]10^2[/tex]

Ratio = 20

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Answer:

1935

Step-by-step explanation:

Step 1: If 4% of a number is 77, then what is 100% of that number? Setup the equation.

77

4% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

4Y = 77 x 100

4Y = 7700

Y = 7700

100 = 1,925

Answer:

where's the graph?

Step-by-step explanation:

The polynomial for the north side of the house will be 2x^2+9x-32.

What are polynomials?

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.

Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.

Now,

As the north side will be the sum of 5x-4,x^2-23 and 4x-5

so the polynomial for north will also be the sum of  5x-4,x^2-23 and 4x-5.

Hence,

          Polynomial for north side= 5x-4 + x^2-23 + 4x-5

         Polynomial for north side   =2x^2+9x-32

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Answer:

[D] -45 + 54x

Step-by-step explanation:

Base on the given we can use the distributive property to solve this:

Distributive property ⇒ Multiply outside numbers with each term inside the parenthesis.

-9 (5 - 6 x )  → {-9 × 5 = -45 } {-9 × -6x = 54x}

Now let's put it together;

-45 + 54x

Hence, [D] -45 + 54x is the correct answer.

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The choices that describe an exact number are option b, option c, option d, and option e because they show a definite countable quantity with 100% accuracy.

The following options describe an exact number:

b. The house has four bedrooms.

c. There is one gram of salt in this beaker.

d. You drank one liter of water.

e. The little dog weighs 10 kilograms.

These numbers are exact because they are specific measurements that are not subject to uncertainty. They are countable and defined. While "you ran two miles" or "you drank one liter of water" could be approximate measurements.

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Answer:

[tex] \frac{3}{4} + \frac{1}{3} \\ \frac{ \: \: 9 \: \: + \: \: 4 \: \: }{12} \\ \frac{13}{12} [/tex]

It saves time, doesn't need to be changed if a row or column is added to the range, and adjusts the range when the function is copied to another cell.

Based on the values in another column, we'll discover how to add up a column of numerical data. We are attempting, for instance, to assess product sales based on the typical customer rating. Thus, each of our products has an average rating of 9.8, 7.2, 6.1, and so on because customers score our products on a scale of 1 to 10. The sales totals for goods with ratings of 9 to 10, 7 to 8, and so forth should be calculated.

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Upon factorization, The factors of the equation be x = 1, x = -2 + 3i, x = -2 - 3i and x = 1.

In mathematics, factorization or factoring is the process of breaking down one entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication produces the original number, matrix, etc.

Factorization is the process of shrinking the bracket of a quadratic equation, as opposed to widening the bracket and turning the equation into a product of factors that cannot be further reduced.

To solve a quadratic equation by factoring, factor the expression, set each factor equal to 0, and then solve each equation. To accomplish this, set up the terms in the equation so that the other side equals 0.

Let the given equation be f(x) = 2x³ + 6x² + 18 x - 26 and x - 1 then

2x³ + 6x² + 18x - 26 = 0

Factor 2x³ +6x² +18x-26: 2(x-1) (x²+4x+13)

2(x-1) (x²+4x+13) = 0

Using the Zero Factor Principle: If ab=0 then a=0 or b=0, x-1=0 or

Solve - 1=0:

x = 1

Solve x² + 4x + 13 = 0: x² + 3i, x = - 2 - 3i

The solutions are

x = 1, x = -2+31, x = -2 - 31

The given equation be x - 1,

x-1= 0 then x = 1.

Therefore, the factors of the equation be x = 1, x = -2 + 3i, x = -2 - 3i and x = 1.

The complete question is:

If f(x) = 2x²+6x²+18x-26 and x-1 is a factor of f(x), then find all of the zeros of f(x) algebraically.

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