If g(x) = 1 – 2x + 3x2, find the average rate of change of the function as x varies from 2 to 5

Answer:

  5240 kg/m³

Step-by-step explanation:

You want the average density of a planet with radius 6052 km and mass 4.87×10^27 g.

The mass is given in grams, and the corresponding unit in the desired answer is kilograms. There are 1000 g in 1 kg, so 4.87×10^27 g = 4.87×10^24 kg.

The radius is given in km, and the corresponding unit in the desired answer is meters. There are 1000 meters in 1 km, so 6052 km = 6052×10^3 m. (We could adjust the decimal point, but we choose to let the calculator do that.)

The units of density tell you it is computed by dividing the mass by the volume:

  ρ = mass/volume

The volume of the sphere is found using the given formula, so the density is ...

  ρ = (4.87×10^24 kg)/(4/3π(6052×10^3 m)^3)

  ρ ≈ 5240 kg/m³

The average density of the planet is about 5240 kg/m³.

__

Additional comment

This is comparable to the average density of Earth, which is about 5520 kg/m³.

The statement that best describes the chord of a circle is a chord is any segment in which the end points are found on the arc of the circle. (option a).

A chord of a circle is a line segment that connects two points on the circle. The two endpoints of the chord are called the endpoints of the chord, and they lie on the circumference of the circle.

Therefore, option (a) that states that a chord is any segment in which the endpoints are found on the arc of the circle is the correct answer.

It is important to note that a chord does not have to pass through the center of the circle. If a chord passes through the center of the circle, it is called a diameter. A diameter is the longest chord of a circle, and it divides the circle into two equal parts called semicircles.

The correct answer to the question is option (a), which states that a chord is any segment in which the endpoints are found on the arc of the circle.

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Complete Question:

which of the following best describes the chord of a circle?

a) a chord is any segment in which the endpoints are found on the arc of the circle.

b) a chord is a triangle inside of a circle.

c) a chord is the arc formed from the segment.

d) a chord is a square inside of a circle.

There are 300 ways a person can go from P to Q and return by a different bus.

To find the number of ways a person can go from P to Q and return by a different bus, we can use the combination formula:

nCr = n! / (r! × (n-r)!)

where n is the total number of options, and r is the number of choices we want to make.

In this case, there are 25 buses running between P and Q, so the total number of options for going from P to Q and returning by a different bus is 25 × 24 (since we have 25 choices for the first leg of the journey, and 24 choices for the second leg).

To find the total number of ways to make this choice, we can use the combination formula with n = 25×24 and r = 2

nCr = (25×24)! / (2! × (25×24-2)!)

= (25 × 24)! / (2! × 23!)

= (25×24) / 2

= 300

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The equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.

An exponential decay function can be written as f(x) = ab^x where b is the base of the exponential function and a is the initial value. If b is between 0 and 1, the function will exhibit exponential decay. Since we need a vertical shrink of 3/4, we can set b = 3/4.

We also need a vertical shift of 10 units, so we add 10 to the function. The resulting function is: f(x) = 10 - (3/4)^x. Therefore, the equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.

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Answer: 40/7 or 5.7

Step-by-step explanation:

using angle bisector theorem we get,

x/5 = 8/7

Upon substituting our given values in above equation, we will get:

x/5 X 5 = 8/7 X 5

x = 40/7 or 5.7

Answer:

3.3

Step-by-step explanation:

Angle bisector theorem: In a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.

       [tex]\dfrac{x}{8-x}=\dfrac{5}{7}[/tex]

Cross multiply,

    x *7 = 5*(8 - x)

        7x = 40 - 5x

   7x + 5x = 40

        12x   = 40

             [tex]x = \dfrac{40}{12}\\\\x = 3.3[/tex]

When we write out the system of equations, we will get:

[tex]x+y=18[/tex]

[tex]x-y=-8[/tex]

We can then use elimination to get just one variable.

[tex]x+y=18[/tex]

[tex]x-y= -8[/tex]

Which gives us: [tex]2x=10[/tex]

We then divide by 2 and get: [tex]x=5[/tex]

We next plug that into one of the two equations and solve for the other variable: [tex](5)+y=18[/tex]

We subtract 5 from both sides and get: [tex]y=13[/tex]

So the two numbers are 13 and 5.

Answer:

(-3, 6.4)

Step-by-step explanation

First draw a line across the y axis about 4.2 blocks in

Then go to doing your reflections with ease

If Point T is graphed at T(-3, 2) and is reflected across the line y = 4.2 then the coordinates of T' are (-3, 6.4)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The line y = 4.2 is a horizontal line that is 1.8 units above the x-axis (since the y-coordinate of T is 2).

When a point is reflected across a horizontal line, its y-coordinate is negated with respect to the line.

So, the y-coordinate of the reflected point T' will be:

y-coordinate of T' = (-3, 6.4)

Hence, if Point T is graphed at T(-3, 2) and is reflected across the line y = 4.2 then the coordinates of T' are (-3, 6.4)

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I hoped this helped!  

: )

Step-by-step explanation:

originally - (6,-1)     After translation - (1,4)

originally - (8,-1)     After translation - (3,4)

originally - (4,-7)     After translation - (-1,-2)

originally - (7,-9)     After translation - (3,-4)

originally - (9,-9)     After translation - (4,-4)

Therefore, the observed value of the test statistic for testing the null hypothesis H0: p = 0.5 versus the alternative hypothesis H1: [tex]p > 0.5[/tex]is z= 1.8. The correct answer is (e) z=[tex]0.59— 0.5/√0.5(0.5)/100.[/tex]

In this particular question, the observed value of the test statistic for testing the null hypothesis H0: p = 0.5 versus the alternative hypothesis H1: p > 0.5 is to be determined. The question provides a random sample of 100 likely voters in a small city, which produced 59 voters in favor of Candidate A. The formula for calculating the test statistic is as follows:

z= (p- P) / sqrt[P(1-P) / n]

where p is the sample proportion, P is the hypothesized population proportion, and n is the sample size.

Substituting the given values into the formula, we get:

z= [tex](0.59- 0.5) / sqrt[0.5(0.5) / 100][/tex]

z= [tex]0.09 / 0.05[/tex]

z=[tex]1.8[/tex]

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The estimated joint probability for the "low income and 21-35 age group" cell is 0.108.

In the table given, individuals are cross-classified by their income level and age group. We have to find the estimated joint probability for the "low income and 21-35 age group" cell. The joint probability of the low income and 21-35 age group is calculated as follows;

From the given table, the number of people in the "low income and 21-35 age group" cell is 120.The total number of people in the sample = 120 + 100 + 75 + 150 + 160 + 100 + 160 + 180 + 160 = 1105.

The estimated joint probability for the "low income and 21-35 age group" cell is:P(Low income, 21-35 age group) = 120/1105P(Low income, 21-35 age group) = 0.108. Therefore, the estimated joint probability for the "low income and 21-35 age group" cell is 0.108.

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Therefore, the order of the samples from smallest to largest amount (moles) of OY is: Go, Y, Na, Mn.

In order to list the samples in order of the amount (moles) from smallest to largest OY, we need to calculate the number of moles of each element. Let's start with the given samples:Na -[tex]0.10 gY - 0.10 gGo - 0.10 gMn - 0.10 g[/tex]

Now, let's find the number of moles of each element:Na: The molar mass of Na is 22.99 g/mol.Number of moles of Na = mass of Na/molar mass of Na= 0.10 g/22.99 g/mol= 0.00435 molY: The molar mass of Y is 88.91 g/mol.Number of moles of Y = mass of Y/molar mass of Y= 0.10 g/88.91 g/mol= 0.00112 molGo: The molar mass of Go is 118.71 g/mol.Number of moles of Go = mass of Go/molar mass of Go= 0.10 g/118.71 g/mol= 0.00084 molMn: The molar mass of Mn is 54.94 g/mol.

Number of moles of Mn = mass of Mn/molar mass of Mn= 0.10 g/54.94 g/mol= 0.00182 molNow, we can list the samples in order of the amount (moles) from smallest to largest OY:Go (0.00084 mol) < Y (0.00112 mol) < Na (0.00435 mol) < Mn (0.00182 mol)

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Therefore , the solution of the given problem of percentage comes out to be the initial annual heating cost was about £1438,26 before the 15% increase.

A number or statistic that is stated as an amount of 100 is referred to as "a%" in statistics. The forms "pct," "pct," or "pc" are additionally uncommon. The common way to indicate it is with a representation "%," though. The ratio to the total sum is flat, and there are no indicators. Percentages are actually integers because they almost always add up to 100. To suggest that a number indicates a percentage, either the word "fraction" or a representation for percentage (%) must come before the number.

Here,

Assume that the annual heating expense was x prior to the 15% increase.

=> x + 0.15x = 1.15x was the new bill after the 15% price rise.

We can write: Because we are aware that the new price following the increase is £1654:

=> 1.15x = 1654

We must find x in order to determine the initial bill before the increase:

=> x = 1654/1.15

=> x ≈ 1438.26

Therefore, the initial annual heating cost was about £1438,26 before the 15% increase.

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Therefore , the solution of the given problem of unitary method comes out to be the parking lot has 60 trucks.

It is possible to accomplish the objective by using this widespread convenience, pre-existing variables, or all significant components from the initial Diocesan adaptable survey that adhered to a specific methodology. If it doesn't, both of the essential components of a term confirmation outcome will undoubtedly be lost, but if it is, there is going to be another opportunity to contact the entity.

Here,

Let's begin by giving the unknowns variables:

x = number of vehicles

Van count = 4 times

Since there are 205 cars overall, the number of lorries is equal to (205 - 11x).

The value of x can be determined using the second bit of knowledge:

=> 4x/3 = (205 - 11x)/2

When we simplify this solution, we obtain:

=> 8x = 3(205 - 11x)

=> 8x = 615 - 33x

=> 41x = 615

=> x = 15

We can now determine the quantity of vans:

Van count = 4x = 4(15) = 60

Consequently, the parking lot has 60 trucks.

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Answer: 131.95 cm

Step-by-step explanation:

The diameter of the semicircle is 42 cm, which means the radius is half of that:

r = d/2 = 42/2 = 21 cm

The circumference of a full circle with radius "r" is given by the formula:

C = 2πr

Since this is a semicircle, we need to divide the circumference by 2:

C/2 = πr

Substituting the value of "r" we found above, we get:

C/2 = π(21)

Simplifying:

C/2 = 21π

C = 2(21π)

C ≈ 131.95

Rounding to the nearest hundredth, we get:

C ≈ 131.95 cm

Therefore, the circumference of the semicircle is approximately 131.95 cm.

Answer: Jills fourth number is 28

Step-by-step explanation:

The probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615. This is because out of the 13 balls, 6 of them have even numbers.

To calculate the probability, we use the formula:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

In this case, the favorable outcomes would be the number of even numbers, which is 6. The total number of outcomes would be 13 (the total number of balls in the bag). Therefore, the probability of selecting a ball that has an even number is 6/13.

Another way to look at this is to think of the probability as the ratio of favorable outcomes to total possible outcomes. In this case, the ratio is 6:13, which can be simplified to 3:6 or 1:2. Since one out of every two outcomes is favorable, the probability is 0.5, which is the same as 6/13.

To further understand the concept of probability, consider the example of a fair coin. If a fair coin is flipped, the probability of getting either heads or tails is 50%. This is because the ratio of favorable outcomes (one head and one tail) to total possible outcomes (two heads and two tails) is 1:2.

In conclusion, the probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615.

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Answer: 65

Step-by-step explanation:

Based on the past week's sales data, the baker can expect to sell Option C 220 caramel, 130 gingerbread, and 420 mint choco chip cookies.

The population in statistics refers to the total set of people or things that we are attempting to analyse and make conclusions about. Typically, this group is too big to see or measure directly, so we use statistical methods to infer some of its features from a smaller collection of people or things, known as a sample. A representative portion of the population was selected for the sample in order to learn more about the population as a whole. The purpose of statistical analysis is to draw conclusions about the population using data from the sample.

The number of weeks in a month= 4.

Using the given table the estimated number of sales for the month are:

Salted caramel: 51 x 4 = 204

Gingerbread: 31 x 4 = 124

Mint: 99 x 4 = 396

Hence, based on the past week's sales data, the baker can expect to sell Option C 220 caramel, 130 gingerbread, and 420 mint choco chip cookies.

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Answer:

linear

Step-by-step explanation:

gradient 1 = [tex]\frac{-3-12}{6-3}[/tex] = -5

gradient 2 = [tex]\frac{-18+3}{9-6}[/tex] = -5

therefore, the graph is linear as the gradient is constant

Answer:

14 = 2 x 7

28 = 2² x 7

56 = 2³ x 7

Answer:

The volume is 1474.45 mm^2

Step-by-step explanation:

First, you have to find the radius. To do this, you divide the diameter by 2. This means that the radius is 8.

Then you use the formula V=3.14*r^2*(h/3)

V=3.14*8^2*(22/3)=1474.45 mm^2

Answer:

The equation of a vertical line in the graph, which is parallel to y-axis is x = a. The slope of a vertical line is infinity or undefined as it has no y-intercept and the denominator in the slope formula is zero.

Step-by-step explanation:

The three ordered pairs that are most likely the added data points are:

B: (4,10), (4,11), (4,12)

C: (8,9), (8,10), (8,11)

D: (10,10), (10,11), (10,12)

In order to determine the added data points, we first need to note that the data points have a slightly linear pattern with a negative slope. Also, a linear regression on the points will give us:  linear regression on the given data points, we obtain the equation: y = -1.2x + 10.8

In selecting the three added data points, a good criterion will be for the points to be as close as possible to the original line of best fit. The data points in option A are close to slope 1 so adding them will significantly shift the line of best fit. The data points in options B, C, and D are in a vertical line and will not shift the line of best fit. So, they are most likely the best data points to add.

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The statement "we have data that is a continuous variable. it is a measurement of time between events. this is a situation where we should evaluate a histogram for a likely exponential distribution" is true because when dealing with continuous data representing time between events, it is common to evaluate a histogram to determine if it follows an exponential distribution.

If the data represents the time between events and it is a continuous variable, it is common to evaluate the histogram to see if it follows an exponential distribution. The exponential distribution is often used to model the waiting time between independent events that occur at a constant average rate, and it has a continuous range of values that can be plotted as a histogram.

To evaluate whether the data follows an exponential distribution, you can plot a histogram and visually check if it has a single peak and a decreasing tail, which are characteristic of the exponential distribution. You can also use statistical tests such as the Kolmogorov-Smirnov test or the Anderson-Darling test to assess the goodness-of-fit between the data and the exponential distribution.

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The formula for percent from the board can be expressed this way:

The total number of students that like pineapple pizza   * 100.

      The total number of students

A (i). The part is the number of students that like pineapple pizza which is 5.

(ii). The whole is the total number of students namely; 7 + 12+ 5 + 3 + 6 = 33.

(iii). Plugging the part and whole into the equation, we will have: 5/33 * 100

(iv). Final answer is = 15.15%

A percentage is a mathematical expression that is aimed at calculating the proportion of a given quantity out of 100. In the question, we are requested to find what proportion of students like pineapple pizza.

To get the answer, we first have to determine the number of students that like pineapple pizza which is 5 according to the table. Next, we get the sum of students which is 33. The percentage will then get the fraction and multiply the result by 100. The final answer is 15.15%.

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Answer/Step-by-step explanation:

We know that sin 60° = √3/2, and we can use this information to find cos 60°:

cos 60° = √(1 - sin^2 60°) = √(1 - 3/4) = √(1/4) = 1/2.

To find the measure of angle 3, we can use the formula:

cos(180° - 2x) = -cos(2x)

We want to solve for x when cos 2x = √(√3/2) = √3/2 * 1/√2 = √3/2√2

cos(180° - 2x) = -cos(2x)

cos(2x) = √3/2√2

180° - 2x = 150° or 210°

x = 15° or 35°

Therefore, the measure of angle 3 can be either 15° or 35°.

The equation in slope-intercept form that describes the relationship in the graph is: y = -20x + 100.

An equation is a mathematical statement that shows the equality between two expressions. It contains one or more variables, and the values of these variables can be solved for to make the equation true. An equation can be represented using symbols, numbers, and operators such as addition, subtraction, multiplication, division, and exponents. Equations are used in many fields of mathematics and science, and they are a fundamental tool for solving problems and making predictions.

Here,

Part A:

The equation in slope-intercept form that describes the relationship in the graph is:

y = -20x + 100

Part B:

To determine the equation, we need to find the slope of the line passing through the two given points.

Slope, m = (change in y) / (change in x)

m = (0 - 100) / (5 - 0)

m = -20

The y-intercept can be found by substituting the slope and any point on the line into the slope-intercept form of the equation:

y = mx + b

100 = (-20)(0) + b

b = 100

Therefore, the equation in slope-intercept form is:

y = -20x + 100

Part C:

In the given situation, the slope represents the rate of decrease in the percentage of battery remaining per hour. The negative value indicates that the percentage of battery remaining decreases over time, and the magnitude of the slope (-20) indicates that the battery percentage decreases by 20% per hour.

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Answer:

8%

Step-by-step explanation:

[tex]= .08[/tex]

This is the answer as a decimal. To change a decimal to a perfect multiply the decimal by 100%

[tex].08 \times 100\% = 8\%[/tex]

Answer:

The answer is D, I'm not sure but I believe it's supposed to be

0.1(55-7)= 300

Step-by-step explanation: