What multiples to 16 and adds to -8

a. the linear approximating polynomial L(x) is 1+x

b. the quadratic approximating polynomial Q(x) is 1 + x + x^2

a. The linear approximating polynomial for a function f(x) centered at the point a can be found using the formula:

L(x) = f(a) + f'(a)(x - a)

where f'(a) is the derivative of the function evaluated at the point a.

b. The quadratic approximating polynomial for a function f(x) centered at the point a can be found using the formula:

Q(x) = f(a) + f'(a)(x - a) + (1/2)f''(a)(x - a)^2

where f''(a) is the second derivative of the function evaluated at the point a.

c. To approximate the quantity 1/(1-x) using the linear and quadratic approximating polynomials obtained in parts a. and b., we need to first find the values of f(a), f'(a), f''(a) at the given point a.

Let's assume a = 0 for simplicity.

a. Linear Approximation:
To find the linear approximating polynomial, we need to evaluate f(0) and f'(0).

f(x) = 1/(1-x)

f(0) = 1/(1-0) = 1

To find f'(0), we need to take the derivative of f(x) and evaluate it at x = 0.

f'(x) = 1/(1-x)^2

f'(0) = 1/(1-0)^2 = 1

Using the linear approximation formula, we can now find the linear approximating polynomial L(x):

L(x) = f(0) + f'(0)(x - 0) = 1 + 1(x - 0) = 1 + x

b. Quadratic Approximation:
To find the quadratic approximating polynomial, we need to evaluate f''(0).

f''(x) = 2/(1-x)^3

f''(0) = 2/(1-0)^3 = 2

Using the quadratic approximation formula, we can now find the quadratic approximating polynomial Q(x):

Q(x) = f(0) + f'(0)(x - 0) + (1/2)f''(0)(x - 0)^2 = 1 + 1(x - 0) + (1/2)2(x - 0)^2 = 1 + x + x^2

Now, we can use these linear and quadratic approximating polynomials to approximate the given quantity 1/(1-x). For example, if we want to approximate the value of 1/(1-x) at x = 0.1, we can substitute x = 0.1 into both L(x) and Q(x) to get the approximate values.

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Answer:

There are many times in algebra when you need to simplify an expression. The properties of real numbers provide tools to help you take a complicated expression and simplify it.

The associative, commutative, and distributive properties of algebra are the properties most often used to simplify algebraic expressions. You will want to have a good understanding of these properties to make the problems in algebra easier to work.

Step-by-step explanation:

Commutative Property of Multiplication

For any real numbers a and b, a · b = b · aOrder does not matter as long as the two quantities are being multiplied together. This property works for real numbers and for variables that represent real numbers.

just as subtraction is not commutative, neither is division commutative. 4 ÷ 2 does not have the same quotient as 2 ÷ 4.Associative Property of Addition

For any real numbers a, b, and c, (a + b) + c = a + (b + c).

Associative Property of Multiplication

For any real numbers a, b, and c, (a • b) • c = a • (b • c).Multiplication has an associative property that works exactly the same as the one for addition. The associative property of multiplication states that numbers in a multiplication expression can be regrouped using parentheses. For example, the expression below can be rewritten in two different ways using the associative property.

The parentheses do not affect the product, the product is the same regardless of where the parentheses are.

The distributive property of multiplication is a very useful property that lets you rewrite expressions in which you are multiplying a number by a sum or difference. The property states that the product of a sum or difference, such as 6(5 – 2), is equal to the sum or difference of products, in this case, 6(5) – 6(2).

   6(5 – 2) = 6(3) = 18

 65) – 6(2) = 30 – 12 = 18

The distributive property of multiplication can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2.3(10 + 2) = ?

According to this property, you can add the numbers 10 and 2 first and then multiply by 3, as shown here: 3(10 + 2) = 3(12) = 36. Alternatively, you can first multiply each addend by the 3 (this is called distributing the 3), and then you can add the products. This process is shown here.

3 (10 + 2) = 3(12) = 36

3(10) + 3(2) = 30 + 6 = 36

The products are the same.

since multiplication is commutative, you can use the distributive property regardless of the order of the factors.

Answer:

2x^3(5x + 1) (2x + 5)

Step-by-step explanation:

I used a website called math.way, u should try it too!

Answer:

x = 3 +√43, x = 3 - √43

Step-by-step explanation:

x^2 - 6x - 34 = 0

move the 34 across

x^2 - 6x = 34

take -6 and divide by two, then square it

(-6/2)^2 = 9

add the product to your equation

x^2 - 6 + 9 = 34 + 9

solve

(x - 3)^2 = 43

x - 3 = ± √43

x = 3 ± √43

The 95% confidence interval for the population mean SAT score is given as follows:

(1340, 1460).

The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.

The bounds are obtained according to the equation defined as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which the variables of the equation are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

\(\overline{x} = 1400, n = 64, s = 240\)

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.

Then the lower bound of the interval is of:

1400 - 1.998 x 240/sqrt(64) = 1340.

The upper bound of the interval is of:

1400 + 1.998 x 240/sqrt(64) = 1460.

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Answer: Yes

Step-by-step explanation: The sum of the length of the 2 smaller side must be greater than the biggest side (hypotneus) So yes, 9+2=11 which is greater than 10.

The number of cars which can be made by using 4 tires, a main chassis, and 5 lithium-ion batteries are 4.

Using hit and trial method :

→ assuming tires as limiting substance

4 tires → 1 car

17 tires → 17/4 ×1 car

= 4.25 cars {reducing it to greatest integer value}

→ Assuming chassis as limiting theorem:

1 chassis → 1 car

5 chassis → 5 cars

→ Assuming batteries as limiting theorem substance:

5 batteries → 1 car

22 batteries → 22/5 × 1 car

= 4.4 → 4 cars

Therefore, 4 cars can be made by the given substance.

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The statement is true. A network's physical topology refers to the arrangement of devices and cables that determine how signals travel electronically.

The physical topology of a network describes the physical arrangement of devices, cables, and other components that make up the network infrastructure. It defines how these elements are connected and how signals flow between them. The physical topology is concerned with the actual layout and structure of the network.

There are different types of physical topologies, including bus, star, ring, mesh, and hybrid topologies. In a bus topology, devices are connected to a central cable, and signals travel along the cable to reach their destination. In a star topology, devices are connected to a central hub or switch, and signals are transmitted from the source device to the hub/switch, which then distributes the signal to the destination device. A ring topology connects devices in a circular manner, where signals travel in one direction around the ring.

The physical topology determines factors such as signal propagation, fault tolerance, scalability, and network performance. It plays a crucial role in determining how efficiently and effectively signals travel electronically within a network. Therefore, the statement that a network's physical topology describes how signals travel electronically is true.

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The value of the triple integral is -16.

Triple integral is a mathematical concept used in calculus to calculate the volume of three-dimensional objects. It extends the concept of a single integral to functions of three variables and integrates over a region in three-dimensional space.

The triple integral of a function f(x, y, z) over a region E in three-dimensional space is denoted by:

∭E f(x, y, z) dV

We can set up the triple integral as follows:

∫∫∫ 16y dV

Where the limits of integration are:

0 ≤ x ≤ 2

0 ≤ y ≤ (2- \(x^2\)z)/(2y)

0 ≤ z ≤ 2/\(x^{2y\)

Note that the upper bound of integration for y is not a constant, but depends on both x and z.

Integrating with respect to y first, we get:

∫∫∫ 16y dV = ∫0^2 ∫\(0^(2-x^2z)/(2x)\)∫\(0^(2/x^2y) 16y dz dy dx\)

= ∫\(0^2\) ∫\(0^(2-x^2z)/(2x) 32/x dx dz\)

= ∫\(0^2\) [16(\(2-x^2z)/x^2\)] dz

= ∫\(0^2 (32/x^2 - 16z)\) dz

= 32∫\(0^2 x^-2 dx - 16\)∫\(0^2\)z dz

= 16 - 16(2)

= -16

Therefore, the value of the triple integral is -16.

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Answer:

5(4) - 6 + 5(4) - 6

Step-by-step explanation:

k(x) = 5x - 6

(k+k)(x) = 5x - 6 + 5x - 6

(k+k)(4) = 5(4) - 6 + 5(4) - 6

=> Option D is correct

Hope this helps!

The expression is equivalent to (k+k) (4) will be 5(4) - 6 + 5(4) - 6. The correct option is B.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The expression will be solved as below:-

k(x) = 5x - 6

(k+k)(x) = 5x - 6 + 5x - 6

(k+k)(4) = 5(4) - 6 + 5(4) - 6

Therefore, the expression is equivalent to (k+k) (4) will be 5(4) - 6 + 5(4) - 6. The correct option is B.

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Answer: Use distributive practice rather than massed practice. ...

Study in triads or quads of students at least once every week. ...

Don't try to memorize formulas (A good instructor will never ask you to do this). ...

Work as many and varied problems and exercises as you possibly can. ...

Look for reoccurring themes in statistics.

Venn diagram:

The percentage of students that studied mathematics = 25%
The percentage of students that studied electronics = 20%
The percentage of students that studied Communications = 55%
The percentage of students that studied both electronics and Communications subjects = 10%

P(studied Communications or electronics or both subjects)
= P(studied Communications) + P(studied electronics) - P(studied both electronics and Communications subjects)
= 55% + 20% - 10%
= 65%

Therefore, the probability that a student studied Communications or electronics or both subjects is 65%.

P(studied mathematics and Communications subjects)
= P(studied mathematics) × P(studied Communications)
= 25% × 55%
= 13.75%

Therefore, the probability that a student studied mathematics and Communications subjects is 13.75%.

Drawing a Venn diagram, we have 25% studying Mathematics (M), 20% studying Electronics (E), and 55% studying Communications (C).10% studied both Electronics and Communications.

Therefore, the percentages become as follows: M = 25% - 10% = 15% E = 20% - 10% = 10% C = 55%.

Part 2 - To obtain the probability that a student studied Communications or Electronics or both subjects

P(Communication or Electronics) = P(Communication) + P(Electronics) - P(Communication and Electronics) = 55% + 20% - 10% = 65%.

The probability that a student studied Communications or Electronics or both subjects is 65%.

Part 3 -To obtain the probability that a student studied Mathematics and Communications subjects,

P(Mathematics and Communications) = P(Mathematics) * P(Communications) = 25% * 55% = 13.75%.

The probability that a student studied Mathematics and Communications subjects is 13.75%.

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To solve the given problem using arrays, we need to follow the given steps:Step 1: Define an empty array to hold the objectsStep 2: Define an empty array to hold the objects collected by the collector. Step 3: Define a variable to count the number of trials.

Step 4: Define a variable to count the number of unique objects collected by the collector.Step 5: Define a loop that will continue until all unique objects are collected. The given problem is to pick objects from a set of object. Let's say the set of objects is a set of 10 objects, then we need to pick these objects randomly until we have collected all of them.The solution to the given problem using arrays is defined in the following steps:Step 1: Define an empty array to hold the objects.

This array will hold all the objects that are present in the given set. For instance, if there are 10 objects, then this array will hold all the 10 objects.Step 2: Define an empty array to hold the objects collected by the collector.This array will hold all the objects that are collected by the collector. Initially, it will be an empty array.Step 3: Define a variable to count the number of trials.This variable will keep track of the number of trials required to collect all the objects. Initially, it will be 0.Step 4: Define a variable to count the number of unique objects collected by the collector.This variable will keep track of the number of unique objects collected by the collector. Initially, it will be 0.Step 5: Define a loop that will continue until all unique objects are collected.

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Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

The area under the standard normal curve where P(Z > -0.5) is 0.6915. To find this, we can use a standard normal distribution table or a calculator with a normal distribution function.

First, we need to find the z-score associated with -0.5. We know that the mean of the standard normal distribution is 0 and the standard deviation is 1. So, the z-score can be calculated as z = (x - μ) / σ = (-0.5 - 0) / 1 = -0.5. Now, we can look up the area to the right of the z-score -0.5 in a standard normal distribution table. The area is 0.6915, which means that the probability of getting a z-score greater than -0.5 is 0.6915.

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The probability of the asked events is 1/220

Probability is the study of the mathematics of calculating the likelihood that particular events will happen.

Given that, a bag contains three red marbles, three green ones, one fluorescent pink one, four yellow ones, and two orange ones. Susan grabs four at random.

There are 13 marbles in total, and she will pick 4, if we are given that she already has fluorescent pink, therefore, now probability of getting 3 red marbles out of 12,

The number of favorable case is 1, and the total outcome = ¹²C₃ = 220

So, the probability = 1/220

Hence, the probability of the asked events is 1/220

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A score on a test that can be standardized with respect to the mean and standard deviation of the data referred to as z-score.

A z-score (also known as a standard score) is a standardized form of measurement that reflects the number of standard deviations a raw score is above or below the mean of its distribution. In simple terms, a z-score represents the distance between a score and the mean in units of standard deviation.

For example, a z-score of +1.5 indicates that a score is 1.5 standard deviations above the mean, whereas a z-score of -2.0 indicates that a score is 2.0 standard deviations below the mean. The z-score transformation allows scores from different distributions to be compared and evaluated on the same scale.

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Answer:

4

Step-by-step explanation:

If you replace x with 3 in the expression you will get an indefenite form (0/0)

So there two methods.

The easiest one is applying The hospital rule

Derivate the expression firsr but separatly.

● (x^2 -2x -3)' = 2x - 2

● (x-3)' = 1

When x tends to 3

Lim(x^2-2x-3/x-3) = lim (2x-2/1) = 6-2 = 4

The roots of the nominator are:

\( \frac{ 2 ( + - ) \sqrt{4 + 12}}{2} = \frac{ 2 ( + - ) 4}{2} = 3 \: and \: - 1\)

Which means that the nominator can be written as:

\( {x}^{2} - 2x - 3 = (x - 3)(x + 1)\)

Thus we compute the limit as shown below:

\(lim( \frac{ {x}^{2} - 2x - 3}{x - 3})(x - > 3) = lim( \frac{(x - 3)(x + 1)}{x - 3})(x - > 3) = lim( x + 1)(x - > 3) = 4\)

Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.

The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.

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Answer:

15k+88-8k

7k+88 is the solution

Answer:

Look below

Step-by-step explanation:

THe screenshot is proof

The 90th percentile of the thermometer readings is approximately 1.282 degrees Celsius.

To find the 90th percentile of the thermometer readings, which are normally distributed with a mean of 0 degrees and a standard deviation of 1 degree Celsius, follow these steps:

1. Look up the z-score corresponding to the 90th percentile in a standard normal distribution table or use a calculator. The z-score for the 90th percentile is approximately 1.282.

2. Since the mean (µ) is 0 and the standard deviation (σ) is 1, use the z-score formula to find the temperature reading at the 90th percentile:

X = µ + z × σ.

3. Substitute the values:

X = 0 + 1.282 × 1.

4. Calculate the result:

X ≈ 1.282 degrees Celsius.

Thus, the 90th percentile of the thermometer readings is approximately 1.282 degrees Celsius.

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Answer:

kevin is 7

Rob is 48 yo

Step-by-step explanation:

According to the question the total distance traveled by the body from t = 0 to t = 4 is 52 units.

To find the body's acceleration when the velocity is 0, we need to differentiate the position function with respect to time to obtain the velocity function and then differentiate the velocity function with respect to time to obtain the acceleration function.

To find the total distance traveled by the body from t = 0 to t = 4, we need to calculate the definite integral of the absolute value of the velocity function over the interval [0, 4].

The velocity function is given by:

\(\[ v = 3t^2 - 24t + 45 \]\)

Integrating the absolute value of the velocity function over the interval \([0, 4]:\)

\(\[ \text{Distance} = \int_{0}^{4} |v| \, dt \]\)

We split the integral into two intervals where v is positive and negative:

\(\[ \text{Distance} = \int_{0}^{4} v \, dt + \int_{0}^{4} -v \, dt \]\)

Substituting the expression for v:

\(\[ \text{Distance} = \int_{0}^{4} (3t^2 - 24t + 45) \, dt + \int_{0}^{4} (-3t^2 + 24t - 45) \, dt \]\)

Evaluating the integrals:

\(\[ \text{Distance} = \left[ t^3 - 12t^2 + 45t \right]_{0}^{4} + \left[ -t^3 + 12t^2 - 45t \right]_{0}^{4} \]\)

Simplifying further:

\(\[ \text{Distance} = \left(4^3 - 12(4)^2 + 45(4)\right) - \left(0^3 - 12(0)^2 + 45(0)\right) + \left(-(4^3) + 12(4)^2 - 45(4)\right) - \left(-(0^3) + 12(0)^2 - 45(0)\right) \]\)

Calculating the values:

\(\[ \text{Distance} = (64 - 192 + 180) - (0 - 0 + 0) + (-64 + 192 - 180) - (0 - 0 + 0) \]\)

Simplifying further:

\(\[ \text{Distance} = 52 \]\)

Therefore, the total distance traveled by the body from t = 0 to t = 4 is 52 units.

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Answer:

The answer is 65.97 yd^3

Step-by-step explanation:

The volume of a cone is: v = \(\pi r^{2}\frac{h}{3}\)

So, v = \(\pi\)(3^2)(7/3) = 65.97345 yd^3

You can use the Pythagoras theorem for this since a right triangle is formed.

\(c^2 = a^2 + b^2\)

C = 12

A = 4

B = x

Input values:

\(12^2 = 4^2 + x^2\)

\(144 = 16 + x^2\)

\(128 = x^2\)

\(x = \sqrt{128}\)

\(x = 11.3137...\)

So, about 11ft.

The change in the accounts receivable is -$373,816.23 if the firm's management wanted its to be done in 35 days.

Here we have to find the change in the accounts receivable.

The given data:

Sales = $ 9,745,923

inventory = $ 2,237,435

cash = $ 755,071

day's sales outstanding(DSO) = 49 days

Formula to find DSO:

DSO = 365/ accounts receivable turnover

        = 365/ ( net sales/ accounts receivable)

        = 365 × accounts receivable/ net sales

Account receivables = DSO × net sales / 365

                                 = 49 × 9,745,923 / 365

                                 = $1,308,356.70

Target DSO = 35 days

Net accounts received = DSO × net sales / 365

                                      = 35 × 9,745,923 / 365

                                      = $934,540.56

ΔAccounts received = $1,308,356.79 - $ 934,540.56

                                  = - $373,816.23

Therefore change in accounts received is -$373,816.23.

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The amount of paper used for the label on the can of tune is 12.57 in²

Here, the shape of the can of can is cylindrical.

The area of the cured surface of cylinder is given by formula,

A = 2πrh

where r is the radius of the cylinder

and h is the height of the cylinder

Here, r = 2 in and h = 1 in

so, the area of the lateral surface of cylinder would be,

A = 2 × π × r × h

A = 2 × π × 2 × 1

A = 4 × π

A = 12.57 sq. in.

Therefore, the required amount of paper = 12.57 in²

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The data sufficiency question if t and x are integers, so on finding the value of x both the given statements are not sufficient.

It is given that t and x are integers

Statement 1: x²/t² = 4/9

Let us test some values. There are many values of x and t that satisfy statement 1.
Here are two cases:

Case a: Taking x = 2 and t = 3. Noticing that x²/t² = 2²/3² = 4/9. So, here in this case x = 2

Case b: Taking x = 20 and t = 30. Noticing that x²/t² = 20²/30² = 400/900 = 4/9. So, here in this case x = 20

Since we cannot answer the given question with certainty, so statement 1 is NOT SUFFICIENT

Statement 2: It is given that x > 0 and t > 0 Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined

There are many values of x and t that satisfy BOTH statements. Here are two cases:

Case a: Taking x = 2 and t = 3. Noticing that x²/t² = 2²/3² = 4/9. So, here in this case x = 2

Case b: Taking x = 20 and t = 30. Noticing that x²/t² = 20²/30² = 400/900 = 4/9. So, here in this case x = 20

Since we cannot answer the given question with certainty, the combined statements are NOT SUFFICIENT

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