Classify each number below as a rational number or an irrational number.

Answer:

he do be running tho

Answer:

He burned a total of 735 calories.

Step-by-step explanation:

4 miles + 3 miles = 7 miles

105 calories/1 mile = 7 miles/ ? calories

105 calories times 7= 735 calories

While using bisection method to find the solution of the equation f(x)=x⁴ +3x-2=0 on interval [0, 1], after the first step of the bisection method, the interval becomes [0.5, 1].

To use the bisection method to find the solution of the equation f(x) = x⁴ + 3x - 2 = 0 on the interval [0, 1], we start by evaluating the function at the endpoints of the interval.

f(0) = 0⁴ + 3(0) - 2 = -2

f(1) = 1⁴ + 3(1) - 2 = 2

Since the function changes sign on the interval [0, 1] (f(0) < 0 and f(1) > 0), we can conclude that there is at least one root within this interval.

The bisection method involves iteratively dividing the interval in half and selecting the subinterval where the function changes sign. In each iteration, we calculate the midpoint of the interval and evaluate the function at that point.

After the first step, we find the midpoint of the interval [0, 1]:

midpoint = (0 + 1) / 2 = 0.5

We then evaluate the function at the midpoint:

f(0.5) = (0.5)⁴ + 3(0.5) - 2 = -0.375

Since f(0.5) is negative, we can update our interval to [0.5, 1]. The new interval now contains the root of the equation.

This updated interval allows us to continue the bisection method and refine our approximation of the root of the equation f(x) = x⁴ + 3x - 2 = 0 within the specified interval.

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The probability as a decimal rounded to 4 decimal places is 0.5398.

For a standard normal distribution, find: P(z < 0.1) Express the probability as a decimal rounded to 4 decimal places.

The standard normal distribution has a mean of 0 and a standard deviation of 1.

To find P(z < 0.1), we need to find the area to the left of z = 0.1 on the standard normal distribution curve.

Using a standard normal distribution table or a calculator with a standard normal distribution function, we find that P(z < 0.1) = 0.5398.

Therefore, the probability as a decimal rounded to 4 decimal places is 0.5398.

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Answers:

==========================================================

Explanation:

x = smaller number

2x-5 = larger number, since it's five less than twice the smaller number

The sum of both values is 43, so,

(smaller)+(larger) = 43

(x) + (2x-5) = 43

3x-5 = 43

3x = 43+5

3x = 48

x = 48/3

x = 16 is the smaller number

2x-5 = 2*16-5 = 32-5 = 27 is the larger number

Check: 16+27 = 43

The answer is confirmed.

Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

27 = 3 x 3 x 3 = 3³

log3 27

= log3 3³

= 3 log3 3

= 3 x 1

= 3

Note : -

Formulas : -

Logn n = 1

Logn n^n = n Logn n

The present value of the new drug is $6.951 million (Round to three decimal places).

The present value of an investment represents the current worth of its future cash flows, taking into account the time value of money. To calculate the present value of the new drug, we need to discount the projected future profits back to their present value using the given interest rate of 10% per year.

In this case, the drug is expected to generate $2 million in profits in its first year, and this amount will grow at a rate of 5% per year for the next 17 years. To determine the present value, we discount each year's profit by the appropriate discount factor.

Using the formula for the present value of a growing annuity, we can calculate the discount factor for each year. The formula is as follows:

PV = CF1 / (1 + r) + CF2 / (1 + r)² + ... + CFn / \((1 + r)^n\)

Where PV is the present value, CF is the cash flow for each year, r is the discount rate, and n is the number of years.

In this case, we have CF1 = $2 million, r = 10% (0.10), and n = 17. The cash flows for subsequent years will be calculated by multiplying the previous year's profit by the growth rate of 5% (0.05).

By plugging in the values and performing the calculations, we find that the present value of the new drug is $6.951 million (rounded to three decimal places).

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a) The average slope or rate of change between (0, 1) and (2, 4) is 3/2.

b) The average slope or rate of change between (-2, 1/4) and (-1, 1/2) is 1/4.

c) The slope or rate of change is not constant between these two pairs of points, since the average slopes are different.

d) The function connecting these pairs of points is not a linear function.

The average slope or rate of change between two points (x1, y1) and (x2, y2) on a line is given by

average slope = (y2 - y1) / (x2 - x1)

For the points (0, 1) and (2, 4), the average slope is

average slope = (4 - 1) / (2 - 0) = 3/2

For the points (-2, 1/4) and (-1, 1/2), the average slope is

average slope = (1/2 - 1/4) / (-1 - (-2)) = 1/4

The slope or rate of change is not constant between these two pairs of points, since the average slopes are different. Therefore, the function connecting these pairs of points is not a linear function.

Note that a linear function has a constant slope, so if the slope is changing, then the function cannot be linear.

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Answer:

Step-by-step explanation:4

Okay uhm.. guessing, guessing..-

1 = D

2 = E

3 = A

4 = B

5 = F

6 = C

If these are not right, sorry. :<

Hope this helps?

The correct matching of the graph to the statement will be A-2, B-5, C-4, D-1, E-3, and F-6.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

Let's match the statement to the graph, then we have

1. The tree takes a certain amount of time then its height increases. So, the graph is D.

2. The volume of a cube is cubic of edge length. So, the graph is A.

3. The amount of fuel gets exhausted with time. So, the graph is E.

4. The area is proportional to height. So, the graph is C.

5. The temperature first increases and then decreases. So, the graph is B.

6. The number of cars can be washed easily but with time man gets tired. So, the graph is F.

The correct matching of the graph to the statement will be A-2, B-5, C-4, D-1, E-3, and F-6.

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Answer:

it will just. e (a/b)^7

Step-by-step explanation:

since its divide, according to the rule of indices, it will just be to the power of 9-2 =7

could you give me brainliest thanks!

Answer:

12

Step-by-step explanation:

Based on the area of the Mojave desert and the area of the scale drawing, the scale of the map is 1 square inches : 2,500 square miles.

The scale of a map is used to find out how the distance on the map relates to the distance on the ground. It is usually shown as a ratio.

The fact that the area of the Mojave desert is 25,000 square miles but only 10 square inches on the scale drawing means that every 10 square inches on the map is equal to 25,000 actual square miles.

The scale is:

10 square inches : 25,000 square miles

In its simplest form, this is:

10 / 10 square inches : 25,000 / 10 square miles

1 square inch : 2,500 square miles

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The system of linear equations 6x - 2y = 8 and 12x - ky = 5 does not have a solution if and only if k = 12. This means that when k takes the value of 12, the system of equations becomes inconsistent and there is no set of values for x and y that simultaneously satisfy both equations.

In the given system, the coefficient of y in the second equation is directly related to the condition for a solution. When k is equal to 12, the second equation becomes 12x - 12y = 5, which can be simplified to 6x - 6y = 5/2. Comparing this equation to the first equation 6x - 2y = 8, we can see that the coefficients of x and y are not proportional. As a result, the two lines represented by the equations are parallel and never intersect, leading to no common solution. Therefore, when k is equal to 12, the system does not have a solution. For any other value of k, a unique solution or an infinite number of solutions may exist.

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The observation is located to the left of the mean by a distance of 1.2 standard deviations.

The z-score of an observation represents the number of standard deviations the observation is away from the mean.

If the z-score for a particular observation is z = -1.2, this means that the observation is 1.2 standard deviations below the mean.

If the mean is represented by μ and the standard deviation by σ, then we can express this observation as:

observation = μ + (z * σ)

observation = μ + (-1.2 * σ)

This means that the observation is located to the left of the mean by a distance of 1.2 standard deviations.

For example, The z-score represents the number of standard deviations an observation is above or below the mean of the distribution.

In this case, a z-score of -1.2 indicates that the observation is 1.2 standard deviations below the mean height of the group.

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The speed of the river is 7.5 kilometers per hour.

Let the speed of boat in still water = u = 14 km/h

Let the speed of river = v = x km/h

Upstream speed = u - v = 14 - x

Downstream speed = u + v = 14 +x

Distance paddled upstream = \(D_{1}\) = 5 km

Distance paddled downstream = \(D_{2}\) = 10 km

Time taken (upstream) = \(T_{1}\) = \(\frac{D_{1} }{u-v}\)

Time taken (downstream) = \(T_{2}\) = \(\frac{D_{2} }{u+v}\)

According to question,

        \(T_{1}\) = \(T_{2}\)

      \(\frac{D_{1} }{u-v}\) = \(\frac{D_{2} }{u+v}\)

     \(\frac{5}{14-x}\) = \(\frac{10}{14+x}\)

5(14 + x) = 10(14 - x)

   14 + x = 2(14 - x)

   14 + x = 28 - 2x

  x + 2x = 28 - 14

        3x = 14

          x = \(\frac{14}{3}\)

          x = 7.5

Hence, Speed of river is 7.5 km/h.

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SOLUTION:

For parallelograms; opposite sides are congruent;

Thus;

The shorter opposite sides must be equal too, thus;

Thus, for the figure to be a parallelogram, x = 6 and y = 10

The general term of the given sequence {8, 4, 8, 4, ...} can be represented by the formula: an = 8 - 4 * ((n - 1) mod 2), where n is the position of the term in the sequence.

we need to analyze the pattern in the given terms and try to identify a formula that generates those terms. Let's examine the given sequence {8, 4, 8, 4, ...}.

From the first few terms, we can observe that the sequence alternates between the numbers 8 and 4. The first term is 8, the second term is 4, the third term is 8 again, and so on. This pattern repeats indefinitely.

We can express the alternating pattern more formally by using the modulo operation. The modulo operation calculates the remainder when a number is divided by another number. In this case, we'll use the modulo 2 (mod 2) operation, which returns either 0 or 1.

If we consider the position of each term in the sequence, we can notice that the terms at even positions (2nd, 4th, 6th, ...) are equal to 4, and the terms at odd positions (1st, 3rd, 5th, ...) are equal to 8.

To represent this pattern mathematically, we can define a formula for the general term of the sequence:

an = 8 - 4 * ((n - 1) mod 2)

In this formula, 'an' represents the 'n-th' term of the sequence. The expression ((n - 1) mod 2) evaluates to 0 for even values of 'n' and 1 for odd values of 'n'. By multiplying this expression by 4 and subtracting it from 8, we get the desired alternating pattern of 8s and 4s.

For example, let's find the 7th term of the sequence using the formula:

a7 = 8 - 4 * ((7 - 1) mod 2)

  = 8 - 4 * (6 mod 2)

  = 8 - 4 * 0

  = 8

Therefore, the 7th term is 8, which aligns with the pattern of the sequence.

By using this formula, you can find any term in the sequence by plugging in the corresponding value of 'n'.


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Answer:

just a and b

Step-by-step explanation:

The Secant method is a numerical method used to find the root of a mathematical equation. The method is based on the tangent line approximation of the function at a point.

To calculate the root of the function f(x) = x2 – 3x + 9 using the Secant method, perform the following steps:Step 1: Choose the initial guesses, co = 1, and x1 = 0. Step 2: Use the formula given below to compute the next approximation, xn+1:$$x_{n+1}=x_n-\frac{f(x_n)(x_n-x_{n-1})}{f(x_n)-f(x_{n-1})}$$ Step 3: Compute the approximate derivative (dfap) using the formula below:$$dfap=\frac{f(x_n)-f(x_{n-1})}{x_n-x_{n-1}}$$ Substituting the given values into the above equations, we have; $$f(x) = x^2 – 3x + 9$$$$c_0 = 1$$$$x_1 = 0$$$$x_2=x_1-\frac{f(x_1)(x_1-c_0)}{f(x_1)-f(c_0)}$$$$x_2=0-\frac{(0^2 - 3 \times 0 + 9)(0-1)}{(0^2 - 3 \times 0 + 9)- (1^2 - 3 \times 1 + 9)}$$$$x_2 = 1.5$$$$dfap = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$$$$dfap = \frac{(1.5^2 - 3 \times 1.5 + 9) - (0^2 - 3 \times 0 + 9)}{1.5 - 0}$$$$dfap= -0.0033$$Hence, the approximate derivative (dfap) used in the first iteration of the Secant method is -0.0033.

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The approximate derivative (dfap) used in that iteration is 22.

The secant method is an iterative root-finding algorithm that utilizes a succession of roots of secant lines to better approximate a root of a function.

The secant method is a root-finding algorithm that doesn't require the function's derivative to be determined. This is a considerable advantage because computing derivatives can be difficult and can frequently take more time than computing a function value.

\(f(x) = x2 – 3x + 9\)

To solve for the root of the function using secant method, we are given two initial guesses,

x0=1 and x1=0

Now, find the value of x2

The formula for calculating x2 is

\(x2 = x1 - f(x1)(x1-x0)/(f(x1)-f(x0))\)

Now, we are given x0=1, x1=0

We need to calculate f(x0), f(x1) and dfap (approximate derivative)

First calculate f(x0) and f(x1)

\(f(x0) = x02 – 3x0 + 9f(1) \\= 1-3+9 \\= 7\)

\(f(x1) = x12 – 3x1 + 9f(0) \\= 0-0+9 \\= 9\)

So, using these values we calculate x2 which is

\(x2 = x1 - f(x1)(x1-x0)/(f(x1)-f(x0))\\= 0 - 9(0-1)/(9-7)\\= -9/2\)

Next we calculate the approximate derivative, \(dfapdfap = f(x1)/dx\)

Now, \(dx = (x2-x1) \\= (-9/2-0) \\= -9/2\)

Therefore, \(dfap = f(x1)/dx\\= (f(x2) - f(x0))/(x2-x0)\\= ((-9/2)2 - 3(-9/2) + 9 - 7)/(-9/2-1) \\= 22\)

So, the approximate derivative (dfap) used in that iteration is 22 (approx)

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The equation \(3(5^{n-1}) 4\) holds true whenever n is a positive integer.

To prove this equation, we can use mathematical induction.

Base Case (n = 1):

When n = 1, the equation becomes 3(5) = 3(5^0) * 4, which simplifies to 15 = 12. This is true.

Inductive Step:

Assume the equation holds for some positive integer k, i.e., 3 * 3(5) * \(3(5^2) * ... * 3(5^k) = 3(5^(k-1)) * 4.\)

We need to prove that it holds for k + 1, i.e.,\(3 * 3(5) * 3(5^2) * ... * 3(5^k) * 3(5^(k+1)) = 3(5^k) * 4.\)

Starting with the left side of the equation:

\(3 * 3(5) 3(5^2) * ... * 3(5^k) * 3(5^(k+1))= (3 *3(5) 3(5^2) * ... * 3(5^k)) * 3(5^(k+1))\)

= \((3(5^(k-1)) * 4) * 3(5^(k+1))\) (using the assumption)

=\(3(5^k) * 4.\)

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A regular polygon is a polygon with all sides and angles congruent. It exhibits symmetry and uniformity in its sides and angles, creating a visually appealing shape.

A polygon with all sides and angles congruent is called a regular polygon. In a regular polygon, all sides have the same length, and all angles have the same measure. This uniformity in the lengths and angles of the polygon's sides and angles gives it a symmetrical and balanced appearance.

Regular polygons are named based on the number of sides they have. Some common examples include the equilateral triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), and so on. The names of regular polygons are derived from Greek or Latin numerical prefixes.

In a regular polygon, each interior angle has the same measure, which can be calculated using the formula:

Interior angle measure = (n-2) * 180 / n

Where n represents the number of sides of the polygon.

The sum of the interior angles of any polygon is given by the formula:

Sum of interior angles = (n-2) * 180 degrees

Regular polygons have several interesting properties. For instance, the

exterior angles of a regular polygon sum up to 360 degrees, and the measure of each exterior angle can be calculated by dividing 360 degrees by the number of sides.

Regular polygons often possess symmetrical properties and are aesthetically pleasing. They are commonly used in design, architecture, and various mathematical applications.

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Answer:

4/81

Step-by-step explanation:

8/9 divided by 18

I WILL USE THE REASONS CORRESPONDING ANGLES AND ANGLES ON THE STRAIGHT LINE. SINCE THE DIAGRAM LACKS FULL LABELLING THAT MAKES ME UNABLE TO EXPLAIN MORE USING DEMONSTRATION

\(3x - 3 + (4x - 6) = 180 \\ 3x + 4x - 3 - 6 =180 \\ 7x - 9 = 180 \\ 7x = 180 + 9 \\ 7x = 189 \\ \frac{7x}{7} = \frac{189}{7} \\ x = 27\)

ATTACHED IS THE SOLUTION x=27°

Answer:

x = 27

Step-by-step explanation:

3x - 3 and 4x - 6 are same- side exterior angles and sum to 180° , that is

3x - 3 + 4x - 6 = 180

7x - 9 = 180 ( add 9 to both sides )

7x = 189 ( divide both sides by 7 )

x = 27

Answer:

D. sqt5

Step-by-step explanation:

The best process is to start eliminate answers. It can not be C because

-8 + 8 =0. 0 is not an irrational number. Sqt4 is 2, 2+8=10. 10 is a real rational number. 5/9 is not an irrational number because it is a ratio of 5 to the non-zero quotient of 9. Sqt5 is the only irrational number, and when added to 8, it is still irrational.

The set that represents the intersection of sets B and C is option d. {1, d, e}.

The intersection of two sets, B and C, consists of the elements that are common to both sets. Looking at the given sets, B = {1, {2, 3}, d, e} and C = {1, 3, d, e}, we can identify the elements that are present in both sets.

Set B contains the elements 1, {2, 3}, d, and e. Set C contains the elements 1, 3, d, and e. To find the intersection of B and C, we need to identify the elements that are present in both sets.

From the given sets, we can see that the elements {2, 3} and 3 are only present in set B and not in set C. Therefore, they are not part of the intersection.

The elements that are common to both sets B and C are 1, d, and e. These elements are present in both sets B and C. Hence, the intersection of B and C is {1, d, e}.

Therefore, option d. {1, d, e} represents the set B ∩ C.

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The missing premise is "all dogs are non-cats." Therefore, the argument is true.

The given information and analyze the argument step-by-step.

1. Some non-poodles are not non-cats: This statement means that there are some animals that are not poodles and are also cats.

2. No cats are dogs: This statement means that there is no overlap between cats and dogs.

Now, let's try to determine if "some poodles are dogs" can be concluded from these premises:
Since no cats are dogs, it doesn't matter whether some non-poodles are not non-cats. Poodles are a breed of dog, so it's already a fact that poodles are dogs.

So, the answer is True: some poodles are dogs.

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Using the fourth-order Runge-Kutta method, the solution to the given differential equation y' = Y - T² + 1 with the initial condition Y(0) = 0.5 and a step size h = 0.5 for 0 ≤ T ≤ 2 is:

Y(0.5) ≈ 1.7031

Y(1.0) ≈ 2.8730

Y(1.5) ≈ 4.3194

Y(2.0) ≈ 6.0406

To solve the given differential equation using the fourth-order Runge-Kutta method, we need to iteratively calculate the values of Y at different points within the given interval. Here's a step-by-step calculation:

Step 1: Define the initial condition:

Y(0) = 0.5

Step 2: Determine the number of steps and the step size:

Number of steps = (2 - 0) / 0.5 = 4

Step size (h) = 0.5

Step 3: Perform the fourth-order Runge-Kutta iteration:

Using the formula for the fourth-order Runge-Kutta method:

k₁ = h * (Y - T² + 1)

k₂ = h * (Y + k₁/2 - (T + h/2)² + 1)

k₃ = h * (Y + k₂/2 - (T + h/2)² + 1)

k₄ = h * (Y + k₃ - (T + h)² + 1)

Y(T + h) = Y + (k₁ + 2k₂ + 2k₃ + k₄)/6

Step 4: Perform the calculations for each step:

For T = 0:

k₁ = 0.5 * (0.5 - 0² + 1) = 1.25

k₂ = 0.5 * (0.5 + 1.25/2 - (0 + 0.5/2)² + 1) ≈ 1.7266

k₃ = 0.5 * (0.5 + 1.7266/2 - (0 + 0.5/2)² + 1) ≈ 1.8551

k₄ = 0.5 * (0.5 + 1.8551 - (0 + 0.5)² + 1) ≈ 2.3251

Y(0.5) ≈ 0.5 + (1.25 + 2 * 1.7266 + 2 * 1.8551 + 2.3251)/6 ≈ 1.7031

Repeat the same process for T = 0.5, 1.0, 1.5, and 2.0 to calculate the corresponding values of Y.

Using the fourth-order Runge-Kutta method with a step size of 0.5, we obtained the approximated values of Y at T = 0.5, 1.0, 1.5, and 2.0 as 1.7031, 2.8730, 4.3194, and 6.0406, respectively.

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Answer:

-3/4

rise

-----

run

Answer:

hi :]

Step-by-step explanation: