-6(2x-3)=-2(8x-1)
Helpp

The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.

Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point

\(r(x) = f(g(x))\)therefore the derivative of r is given by \(r'(x) = f'g(x)\times g'(x)\)

\(r'(1) = f'(g(1))\times g'(1)\) from the graphs

r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0

Similarly s'(1) = g'(f(1))\times f'(1) from the graphs

 f(1)=1.5, f'(1)

=\dfrac{ (3-0)}{(0-2)}

= -3/2 , g'(3/2) = 0

s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0

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Complete question:

let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).

Answer:

12. The formula to estimate the amount of material required to cover firm 1's structure not including the floor is π·r² + π·r·h

13. 10445.8 unit²

Step-by-step explanation:

12. The given parameters are;

The shape of the firm 1's structure = Cylindrical shape

The radius of the firm 1's structure = 35

Height of firm 1 structure = 60

The amount of material to cover the firm 1 structure not including the floor = The surface area of a cylinder excluding the base

The formula for the surface area of a cylinder = 2·π·r² + π·r·h

Removing the area of the base, we have

The surface area of a cylinder excluding the case  = 2·π·r² + π·r·h - π·r² = π·r² + π·r·h

The formula to estimate the amount of material required to cover firm 1's structure not including the floor = π·r² + π·r·h

13.

The amount of material to cover firm 1's structure not including the floor = π × 35² + π × 35 × 60 = 10445.8 unit².

Overloading in object-oriented programming enables class methods with different parameter lists and return types to perform distinct tasks based on input parameters, improving readability and reducing code complexity.

In the object-oriented model, if class methods have the same name but different parameter lists and/or return types, they are said to be Overloaded.

In object-oriented programming (OOP), overloading refers to the ability of a function or method to be used for a variety of purposes that share the same name but have different input parameters (a parameter is a variable that is used in a method to refer to the data that is passed to it).In object-oriented programming, method overloading allows developers to use the same method name to perform distinct tasks based on the input parameters. The output of the method is determined by the input parameters passed. This enhances the readability of the program and makes it easier to use because it minimizes the number of method names used for distinct tasks.The overloaded method allows the same class method to be used to execute a variety of operations.

It's a great feature for developers because it lets them write fewer lines of code. Overloaded methods are commonly employed when the same task can be completed in multiple ways based on the input parameters.

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Refer to the attachment for the diagram:

The length of HC rounded to 1 DP = 9.3 cm²

What is a cuboid?

A cuboid is a solid shape or a three-dimensional shape in geometry. A cuboid is a convex polyhedron that has eight vertices, twelve edges, and six rectangular faces. A rectangular prism is another name for a cuboid. A cube is an object with six square faces on a cuboid.

From the figure,

length (l)= 5.4 cm = AB

width (w)=3.4 cm = BC

height (h)= 6.7 cm = CG

Formula:

Length of diagonal = √(l²+w²+h²) = √(5.4²+3.4²+6.7²) = 9.25 cm²

Rounded to 1 decimal point:

9.3 cm²

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Answer:

3 is A 2 is 7 or around 32 and then 1 you gotta figure it out.

Step-by-step explanation:

This may not be correct but hopefully it is..

The nurse should teach the parents to administer 2.5 teaspoons of the acetaminophen liquid suspension per dose.

The prescribed dosage of acetaminophen is 300 mg every 4 hours as needed. The liquid suspension provides 120 mg of acetaminophen per 5 mL (1 teaspoon). To determine the number of teaspoons required for the prescribed dosage, we can set up a proportion:

120 mg / 5 mL = 300 mg / x mL

Cross-multiplying, we get:

120 mg * x mL = 5 mL * 300 mg

Simplifying, we have

120x = 1500

Dividing both sides by 120, we find:

x = 1500 / 120 = 12.5 mL

Since there are 5 mL (1 teaspoon) in each dose, we can convert 12.5 mL to teaspoons:

12.5 mL / 5 mL = 2.5 teaspoons

Therefore, the nurse should teach the parents to administer 2.5 teaspoons of the acetaminophen liquid suspension per dose to ensure the child receives the prescribed dosage of 300 mg.

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Answer:

24

Step-by-step explanation:

The total number of students in the three sections is 36 + 40 + 48 = 124.

To find the maximum number of students in each row, we need to divide the total number of students by the number of rows, rounded down to the nearest integer.

Let's call the maximum number of students in each row "x". Then, we can write the equation:

x * n = 124

To find the maximum value of x, we need to find the maximum value of n such that the result of x * n is less than or equal to 124.

Starting with n = 1, we can increment n and calculate x for each value of n until x * n is greater than 124.

For n = 1, x * n = 124, so x = 124.

For n = 2, x * n = 62, so x = 62.

For n = 3, x * n = 41, so x = 41.

For n = 4, x * n = 31, so x = 31.

For n = 5, x * n = 24.8, which is not an integer, so we round down to 24.

Therefore, the maximum number of students in each row is 24, with a total of 5 rows.

Answer:

Step-by-step explanation:

Let's call the maximum number of students in each row "r". To find this value, we need to divide the total number of students by the number of rows. To ensure that all the students can fit into the rows, the number of students in each section must be divisible by the number of rows.

First, we find the least common multiple (LCM) of the number of students in each section, which will be the total number of students if we arrange them in the same number of rows. The LCM of 36, 40, and 48 is 240.

Next, we divide the LCM by the number of students in each section to find the number of rows:

r = LCM / 36 = 240 / 36= 6.67 (rounded down to 6)

So, the maximum number of students that can be in each row is 24

Answer:

OK SO THE OTHER THING DOES NOT LET US TEXT SOOO HERES THE OTHER ONE

Step-by-step explanation:

Answer:

2.71428571429

Step-by-step explanation:

lol

Answer:

The answer D is false because The 1st 1 is true The fish is poisonous When When it goes up into a ball there goes the answer B is also true and b is true as well because they blink to Communicate.therefore the false answer is D

Step-by-step explanation:

The Master Theorem can be applied to solve the recurrence relation T(n) = 4T(n/2) + nlogn using Case 2, but it cannot be applied to the other two recurrence relations.

For the first recurrence relation, T(n) = T(n-1) + 5, the Master Theorem cannot be directly applied. The Master Theorem is applicable for divide-and-conquer recurrence relations of the form T(n) = aT(n/b) + f(n), where a ≥ 1, b > 1, and f(n) is an asymptotically positive function.

Similarly, for the second recurrence relation, T(n) = 3T(n/3) + n, the Master Theorem cannot be directly applied as it does not match the form required for its application.

In the case of T(n) = 4T(n/2) + nlogn, the Master Theorem can be applied. This recurrence relation follows the form T(n) = aT(n/b) + f(n), where a = 4, b = 2, and f(n) = nlogn. Comparing the function f(n) with n^log_b(a), we see that f(n) = nlogn falls into Case 2 of the Master Theorem. Therefore, the solution to this recurrence relation would be in the form of Θ(n^log_b(a) * log^k n), where k is a non-negative integer.

For T(n) = 2T(n/3) + 2n, the Master Theorem cannot be directly applied as it does not match the required form for its application.

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Answer:

Step-by-step explanation:

pt=y TR=3x+1 QT=3y TS=5x+11

71°.

.

.

................

In the given diagram, the value fοr the measure οf angle HIK is οbtained as 71°.

An angle is a figure in plane geοmetry that is created by twο rays οr lines that have a shared endpοint. The Latin wοrd "angulus," which meaning "cοrner," is the sοurce οf the English term "angle." The shared terminus οf twο rays is knοwn as the vertex, and the twο rays are referred tο as sides οf an angle.

The measure οf angle HIJ is given as 117°.

The measure οf angle KIJ is given as 46°.

In the diagram it can be seen that when ∠KIJ and ∠HIK is added it fοrms the ∠HIJ.

Mathematically it can written as -

∠KIJ + ∠HIK = ∠HIJ

Substitute the value in the equatiοn -

46° + ∠HIK = 117°

Subtract tο find the value οf ∠HIK -

∠HIK = 117° - 46°

∠HIK = 71°

Therefοre, the measure οf angle ∠HIK = 71°.

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Part a: The probability that a given battery will last between 2.3 and 3.6 years is 80.41%.

Part b: The probability that a given battery will last longer than 24 months is 97.72%.

For the given question,

The data for the storage battery are-

Part a: The probability that a given battery will last between 2.3 and 3.6 years.

Find z score for x = 2.3 years.

z(2.3) = (x - μ )/σ

Put the values,

z(2.3) = (2.3 - 3.0)/0.5

z(2.3) = -1.4

Use negative z score table;

P(z = -1.4) = 0.0808

Similarly, for x = 3.6

z = (3.6 - 3)/0.5

z = 1.2

Use positive z table;

z = 0.8849

P(2.3<x<3.6) = 0.8849 - 0.0808

P(2.3<x<3.6) = 0.8041

Thus, the probability that a given battery will last between 2.3 and 3.6 years is 80.41%.

Part b: The probability that a given battery will last longer than 24 months = 2 years.

x = 2 years

z (2) = ( 2 - 3.0 )/ 0.5

z = 2

P(x > 2) = 0.9772

Thus, the probability that a given battery will last longer than 24 months is 97.72%.

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Answer:

Slope can be found by determining the ratio of the rise (vertical change) to the run (horizontal change).

In this case miles is the rise, and 3 hours is the run

It should rise 12 and go over 3

I cannot really make out what's on your screen but it's likely it would be D.

The line has to pass 3, it cannot be off 3 by a bit.

And it should be lower than 20 because it rises 12.

Answer:

36 1/4 in³

Step-by-step explanation:

v = 3 5/8 * 2 1/2 * 4

Convert to improper fractions

v = 29/8 * 5/2 * 4/1

Cancel

v = 29/2 * 5/2 * 1/1

Multiply

v = 145/4

Reduce

v = 36 1/4 in³

The summary of the calculations for the given data set is as follows: The median is 48, the mean is approximately 46.42, the variance is approximately 120.52, the standard deviation is approximately 10.98, and the quartiles are Q₁ = 42, Q₂ = 48, and Q₃ = 52.

1. Median:

Arrange the data in ascending order: 21, 27, 28, 29, 32, 35, 35, 36, 41, 41, 42, 42, 43, 44, 44, 45, 46, 46, 46, 47, 47, 48, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 54, 54, 56, 56, 56, 58, 64.

The median is the middle value, which is 48.

2. Mean:

Sum all the values: 45 + 52 + 48 + 41 + 56 + 46 + 44 + 42 + 48 + 53 + 51 + 53 + 51 + 32 + 56 + 21 + 49 + 56 + 28 + 35 + 64 + 48 + 46 + 43 + 52 + 50 + 54 + 47 + 44 + 47 + 50 + 49 + 52 + 28 + 36 + 54 + 41 + 29 + 35 + 58 + 42 + 46 + 27 = 1998.

Divide the sum by the number of data points (43): 1998 / 43 = approximately 46.42.

3. Variance:

Calculate the mean: 46.42 (from the previous step).

For each data point, subtract the mean, square the result, and sum all the squares.

Sum of squares: (45 - 46.42)² + (52 - 46.42)² + ... + (27 - 46.42)² = 52680.34.

Divide the sum by the number of data points (43): 52680.34 / 43 = approximately 1225.12.

4. Standard Deviation:

Take the square root of the variance: √1225.12 = approximately 35.00.

5. Quartiles:

Q₁: The median of the lower half of the data set is the 22nd value, which is 42.

Q₂: The overall median is the 22nd value, which is 48.

Q₃: The median of the upper half of the data set is the 32nd value, which is 52.

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Answer:

2/3

Step-by-step explanation:

use rise over run. you may pick two y values and 2 x values and say (y2-y1)/(x2-x1). here I used (3-1)/(3-0)

Answer:

2/3

Step-by-step explanation:

y2-y1/x2-x1

is the formula for point slope.

so plug in points that meet and put the rise over the run.

Therefore, the series `sum_(n=1)^(infty) 6*(-4)^n/(n!)` is conditionally convergent.

The series to determine is:\(`sum_(n=1)^(infty) 6*(-4)^n/(n!)`\)

Here, \(`n! = n*(n-1)*(n-2)*...*2*1`\)is the factorial of n. It is defined as the product of all positive integers from 1 to n.

Let's first check the convergence of the absolute value of the series.

Since all terms of the series are positive, the absolute value of the series is the series itself.

\(`sum_(n=1)^(infty) |6*(-4)^n/(n!)| = sum_(n=1)^(infty) 6*(4/3)^n/n!`\)

The ratio of successive terms is:\(`|a_(n+1)/a_n| = 4/3`\)

The limit of the ratio of successive terms is:`\(lim_(n- > infty) |a_(n+1)/a_n| = 4/3 < 1`\)

Since the limit of the ratio of successive terms is less than 1, the series converges absolutely.

Therefore, the series is absolutely convergent.

Let's now check the convergence of the series.

\(`sum_(n=1)^(infty) 6*(-4)^n/(n!) = 6 + 96 - 288/2 + 1536/6 - 12288/24 + ...`\)

The series can be rewritten as:\(`sum_(n=1)^(infty) (-1)^(n+1) 6*(4)^n/(n!)`\)

The series is the alternating harmonic series \(`sum_(n=1)^(infty) (-1)^(n+1)/n`\)multiplied by 6*4^n.

The alternating harmonic series is conditionally convergent and its absolute value is the harmonic series, which diverges.

The correct option is conditionally convergent.

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Answer:

             B.   m∠A + m∠C = m∠B + m∠D

Step-by-step explanation:

To inscribe a quadrilateral in a circle, the sums of its opposite angles must be equal (each sum of its opposite angles equals 180 °)

The best response for a person handling biohazards with an open wound on their hands is to not  work with biohazards until the cut is healed or cleared by a healthcare professional to work with the use of waterproof bandages and double gloves.

Biohazards are extremely dangerous because they can get into the human body and cause a lot of damage.

This is why a person with an open would or existing cut should not handle a biohazard until they are cleared to to so by a trained healthcare professional.

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The correct answer is C. Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has fewer solution variables than equations:

x_2 = 4

x_1 + x_2 = 6

To illustrate this, let's solve the system of equations:

From the first equation, we have x_2 = 4.

Substituting this value into the second equation, we get:

x_1 + 4 = 6

Simplifying, we find:

x_1 = 2

Therefore, the solution to the system of equations is x_1 = 2 and x_2 = 4. This ordered pair satisfies both equations, making the system consistent.

In this case, even though we have more equations (2 equations) than unknowns (2 unknowns), the equations are not contradictory or incompatible. The system has a unique solution, and it is consistent.

It is important to note that not all overdetermined systems are consistent. If the equations are contradictory or incompatible, the system will be inconsistent. Inconsistent overdetermined systems typically have more equations than unknowns and lead to contradictions.

In summary, an overdetermined system can be consistent if the equations allow for a solution that satisfies all the equations. The consistency of the system depends on the specific equations involved and their relationship to one another.

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So on solving the provided question, we can say that - in the circle angle DGF = 59 .

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

in the circle

angle AGC = angle DGF

so angle DGF = 59

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Answer:

x = 18/7

Step-by-step explanation:

First, you want to combine like terms

3x + 2 + 4x - 20

7x - 18

If the equation is equal to zero, then you would get x by itself.

7x - 18 = 0

7x = 18

x = 18/7

Answer:

Step-by-step explanation:

Here you go mate

Step 1

3x+2+4x-20  Equation/Question

Step 2

3x+2+4x-20  simplify by taking terms

(3x+4x)+(2+(-20))

answer

7x-18

The expression is 2z+0.67

From the question, we have

During the first year that she owned the stock, it decreased by 35%. During the second year the value of the stock decreased by 32%.

z-35%+z-32%

=z-7/20+z-8/25

=2z+0.67

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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Answer:

≈93.6

Step-by-step explanation:

percent right = answers right/ anwers wrong

Answers right= 47-3=44

%=44/47

≈93.6

Answer: \((z+6)(z+14)\)

Answer:

First one: function

Second one: not a function

Step-by-step explanation:

A function is a relationship where each input has it's own unique output. If an input has more than one output then the relationship is not a function

For the first one no x value repeats meaning each input has it's own output therefore it is a function

For the second one the x value 8 has more than 1 output therefore the second one is not a function

Answer:   \(\bold{\dfrac{4}{49}z^2-\dfrac{12}{35}xz+\dfrac{9}{25}x^2}\)

Step-by-step explanation:

\(\bigg(\dfrac{2}{7}z-\dfrac{3}{5}x\bigg)\bigg(\dfrac{2}{7}z-\dfrac{3}{5}x\bigg)\\\\\\=\dfrac{2}{7}z\bigg(\dfrac{2}{7}z-\dfrac{3}{5}x\bigg)-\dfrac{3}{5}x\bigg(\dfrac{2}{7}z-\dfrac{3}{5}x\bigg)\\\\\\=\dfrac{4}{49}z^2-\dfrac{6}{35}xz-\dfrac{6}{35}xz+\dfrac{9}{25}x^2\\\\\\=\dfrac{4}{49}z^2-\dfrac{12}{35}xz+\dfrac{9}{25}x^2\)

The second pump takes 48 hours to fill the pool by itself.

Given,

One pump can fill a pool in 16 hrs.  

let's consider it will fill a pump at a rate of '' x'' per hour and the rate at which the second pump fills the pool "y". per hour.

Let us consider two equations:

x = 1 pool / 16 hours  ⇒ 1

(x+ y) = 1 pool / 12 hours ⇒ 2

we need to find the value of ''y''

So we substitute the value of "x'' in  equation 2

y = (1 pool / 12 hours) - (1 pool / 16 hours)

Simplifying this expression, we get:

y = (4/48) - (3/48)

y = 1/48

So the second pump can fill the pool by itself at a rate of 1 pool every 48 hours.

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Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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