Please show work. It’s really urgent too! Thanks :) Sorry if it’s bad quality.

The third-order Taylor polynomial for a function f with derivatives at x=0 is given by:
P_3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3
P_3(x) = 5 - 3x + (8/2)x^2 + (24/6)x^3
P_3(0.4) = 5 - 3(0.4) + 4(0.4)^2 + 4(0.4)^3 ≈ 4.296
So, the approximation of f(0.4) using the third-order Taylor polynomial is approximately 4.296.

The partial sum containing the first n + 1 terms of the Taylor series is an n-order polynomial called the nth-order Taylor polynomial of the function. Taylor polynomials are generally approximate for functions that get better as n increases. Taylor's theorem provides a quantitative estimate of the resulting error using this approach. If the series of Taylor functions converge, the sum is the limit of an infinite number of Taylor polynomials. A function can diverge from the equation of the Taylor series even if the Taylor series converges.

The third-order Taylor polynomial for f at x=0 is given by:
f(x) = f(0) + f'(0)x + (f''(0)/2)x^2 + (f'''(0)/6)x^3

Substituting the given values, we get:
f(x) = 5 - 3x + 4x^2 + 4x^3

To approximate f(0.4), we plug in x=0.4 into the polynomial:
f(0.4) ≈ 5 - 3(0.4) + 4(0.4)^2 + 4(0.4)^3
≈ 4.4688

Therefore, using the third-order Taylor polynomial, we can approximate f(0.4) to be approximately 4.4688.

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Answer:

-4x-1

Step-by-step explanation:

combine 4x and -8x to make -4x and combine -2 and 1 to make -1

The sample size which is required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03 is equals to the 382.

We have provide that the state education commission wants to draw an estimate on the fraction of tenth grade students that have reading skills at or below the eighth grade level.

Population proportion, p = 0.21

confidence level = 85%

Margin of error = 0.03,

We have to determine the sample size. For determining sample size for estimating a population propotion, using the below formula,

n = (Zα/2)² ×p×(1-p) / MOE²

where MOE is the margin of error

Using the distribution table, Zc for 85% for confidence level where α = 0.15 or α/2 = 0.075 equals to the 1.439.

Substituting all known values in formula we

n = 1.439² × 0.21( 0.79)/ (0.03)²

=> n = 382.2336 ~ 382

Hence, required sample size is 382.

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Answer:

The answer I'm not too sure but I think you don't have to chear to know.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Pretty obvious this is an exponential decay graph, so it's either 'divide' or 'multiply'.

The length of the shortest straight  is approximately 28.01 ft.

What is the right triangle?

A right triangle is" a type of triangle that has one angle measuring 90 degrees (a right angle). The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees".

To find the length of the shortest straight beam,we can use the Pythagorean theorem.

Let's denote the length of the beam as L and  a right triangle formed by the beam, the wall, and the ground. The wall is 28 ft tall, and the distance from the wall to the building is 1 ft.

Using the Pythagorean theorem,

\(L^2 = (28 ft)^2 + (1 ft)^2\)

Simplifying the equation:

\(L^2 = 784 ft^2 + 1 ft^2\\ L^2 = 785 ft^2\)

\(L = \sqrt{785}ft\)

Calculating the value of L:

L ≈ 28.01 ft

Therefore, the length of the shortest straight beam  is approximately 28.01 ft.

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The solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.

It follows from the task content that the solution to the equation is to be determined and expressed in its simplest form.

Given;

-1/2 -1/2(4/5x+1) = -2 -3x

By distributing the coefficients: we have;

-1/2 - 2/5x - 1/2 = -2 -3x

Hence, by collecting like terms; we have;

-1/2 - 1/2 + 2 = -3x + (2/5)x

1 = -13x/5

Therefore; by cross-multiplication; we have;

5 = -13x

Divide both sides by; -13.

x = -5/13.

Ultimately, the solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.

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Order Of Operation — Also known as BODMAS says to solve Bracket first then Roots or Exponents, Divide, Multiply, Add and finally Subtract.

However, while solving an equation we need to multiply before subtraction isn't always necessary.

For Example :-

Here we need to solve the brackets first and in order to solve the brackets we need to subtract before multiplying.

As we know (12 - 6 = 6) so,

➔ 3 + 2 × 6

➔ 3 + 12

➔ 15

In the equation above, we subtracted 6 from 12 before multiplying 2 with it that was because (12 - 6) were inside brackets.

Taking Another Example :-

Solving Brackets first, (1 + 2 = 3)

➔ 10 - 6 ÷ 3

➔ 10 - 2

➔ 8

In the second example, we added 1 & 2 before dividing 6 by it that was because (1 + 2) were inside brackets.

Thus,

Following Order Of Operation (BODMAS) doesn't always means to multiply before subtraction, we can Subtract first if the number to be subtracted is inside Brackets.

\(\begin{gathered}\begin{gathered}\: \begin{gathered}\begin{gathered} \footnotesize{\boxed{\boxed{\begin{array}{cc} \\ \\ \bf{ \: \: \: B = Bracket \: \: \: } \\ \\ \bf{ \: \: \: O = Order \: \: \: } \\ \\ \bf{ \: \: \: D = Divide \: \: \: } \\ \\ \bf{ \: \: \: M = Multiply \: \: \: } \\ \\ \bf{ \: \: \: A = Add \: \: \: } \\ \\ \bf{ \: \: \: S = Subtract \: \: \: } \\ \\ \: \end{array}}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\)

\(\bf{\pmb{\underline{\rule{170pt}{5pt}}}}\)

Answer:

7

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Step-by-step explanation:

The correct answer is:

c. The z-value for a standard normal distribution can be either positive or negative.

The z-value, also known as the standard score, measures the distance between a data point and the mean of its distribution in units of standard deviation. It is calculated by subtracting the population mean from the data point and then dividing the result by the standard deviation.

Since the mean of a standard normal distribution is zero, the z-value simply represents the number of standard deviations a data point is from the mean. As a result, the z-value can be either positive or negative, depending on whether the data point is above or below the mean, respectively.

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Quick sort will be guaranteed to run in O(n log n) time when the pivot element is chosen in a way that partitions the array into approximately equal halves.

Quick sort is a sorting algorithm that uses divide-and-conquer to sort an array or list of elements. The algorithm works by partitioning the array into two subarrays, one containing all elements smaller than a chosen pivot element, and the other containing all elements larger than the pivot.

The pivot element is then placed between the two subarrays and the process is repeated recursively on each subarray until the entire array is sorted.

Quick sort is generally considered to have an average case time complexity of O(n log n), which means that the algorithm will take proportional to n log n time to sort an array of n elements on average. However, in the worst case, the time complexity of quick sort can be O(n^2), which can occur when the pivot is consistently chosen as the smallest or largest element in the array, leading to an unbalanced partitioning of the array.

To guarantee that quick sort will run in O(n log n) time, it is important to choose a good pivot element that is representative of the entire array and leads to a balanced partitioning of the elements. This can be done by using a randomized pivot selection or by choosing a median-of-three pivot selection that takes the median of the first, middle, and last elements of the array as the pivot. Additionally, choosing a good partitioning scheme that minimizes the number of comparisons and swaps required can also improve the time complexity of the algorithm.

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Answer:

x = -8

Step-by-step explanation:

2 - (3x + 5) = 5 - 2x

Subtract 2 from each side.

-(3x + 5) = 3 - 2x

Apply the negative sign in front of the parentheses.

-3x - 5 = 3 - 2x

Add 5 to both sides.

-3x = 8 - 2x

Add 2x to both sides.

-x = 8

We can't have a negative x value, so we'll need to multiply each side by -1.

x = -8

Hopefully, this helped and wasn't too confusing!

Answer:

Solution given;

2-(3x+5)=5-2x

2-3x-5=5-2x

-3-5=3x-2x

x=-8 is your answer

The pairwise comparisons that need to be made for this anova result will be b.3

In order to determine the number of pairwise comparisons needed for a one-way between-subjects ANOVA with three groups, we can use the formula:

N = (k * (k-1)) / 2

Where N represents the number of pairwise comparisons and k represents the number of groups. In this case, k = 3.

Plugging in the values:

N = (3 * (3-1)) / 2

N = (3 * 2) / 2

N = 6 / 2

N = 3

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The simple interest is $24.75.

The simple interest that is paid on an amount of money is a function of the amount deposited, time and interest rate.

Simple interest = amount deposited x time x interest rate

$375 x 0.022 x 3 = $24.75

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Hayato spent approximately 16,383.13 Japanese Yen. Rounded to the nearest yen, the answer is (d) 16384.

To find out how much Hayato spent in Japanese Yen, we need to multiply the amount he spent in USD by the exchange rate:

$203 * 80.71 = 16,383.13

So, Hayato spent approximately 16,383.13 Japanese Yen. Rounded to the nearest yen, the answer is (d) 16384.

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Answer:

Step-by-step explanation:

6) Slope = 5

(5 , 40) ; m =5

y - y1 = m(x -x1)

y - 40 = 5 (x - 5)

y -40 = 5x - 25

     y = 5x - 25 + 40

y = 5x + 15

7)  slope = 2

m =2 ;  (-2 , 0)

y - y1 = m(x -x1)

y - 0 = 2(x -[-2])

      y = 2(x +2)

y = 2x +4

8) D) It takes 6 miles to travel a mile

In the XY plane, the circles with equations (x-3) + y = 11 and (x+2) + y = r are externally tangent. the value of r is -6.

Generally, To find the value of r, we can start by solving for the centers and radii of the two circles.

The equation of the first circle is of the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. We can rewrite the equation of the first circle as (x - 3)² + y² = 11², so the center of the circle is (3, 0) and the radius is 11.

The equation of the second circle is also of the form (x - h)₂ + (y - k)₂ = r². We can rewrite the equation of the second circle as (x + 2)² + y² = r², so the center of the circle is (-2, 0) and the radius is r.

Since the two circles are externally tangent, the distance between their centers is equal to the sum of their radii. Therefore, the distance between the centers is equal to 11 + r. We can use the distance formula to find the distance between the centers:

distance = √((h₂ - h₁)^2 + (k₂ - k₁)²)

Plugging in the coordinates of the centers, we get:

distance = √((-2 - 3)^2 + (0 - 0)^2) = √(5^2 + 0^2) = √(25) = 5

Since the distance between the centers is equal to the sum of the radii, we can set up the equation:

5 = 11 + r

Solving for r, we get:

r = 5 - 11 = -6

Therefore, the value of r is -6.

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Answer:

y=15

Step-by-step explanation:

The significance level is 0.05. In hypothesis testing, the significance level, also known as the alpha level, represents the probability of rejecting the null hypothesis when it is actually true.

It indicates the maximum tolerable probability of making a Type I error, which is the incorrect rejection of the null hypothesis.

In this scenario, the critical value is given as 4±1.4. Since the alternative hypothesis is two-sided (μ ≠ 4), we divide the significance level equally into two tails. Therefore, each tail has a probability of 0.025. The critical value of 4±1.4 corresponds to a range of (2.6, 5.4). If the sample mean falls outside this range, we would reject the null hypothesis.

The significance level of 0.05 means that there is a 5% chance of observing a sample mean outside the critical region, assuming the null hypothesis is true. It represents the maximum probability at which we are willing to reject the null hypothesis and conclude that the population mean is not equal to 4.

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Searching it up gives your answer right then and there.

The first record of zero was founded in Mesopotamia 3 B.C

Inventor:

The Mayans invented it independently circa 4 A.D

Then it was only then during mid-fifth century it spread to Cambodia

Near the end of seventh century it went to China, and Islamic counties at the end of the eighth century.

(Correct me if I'm wrong not all website's are reliable,So sorry if I'm wrong.)

Answer:

Our domain is -5 < x < 5 or (-5,5) in interval notation form.

Step-by-step explanation:

Domain is a set of all x-values. If we want to find the domain through the graph, we will just look whenever if the graph has an open-dot/closed-dot or not. The following that you'll commonly see in finding domain through graph:

    1. Closed Dots

They are dots that have solid color (generally black) to indicate that the interval there do include that x-value. An example is if there's a closed dot or solid dot at x = 4 then the value x = 4 is included in.

    2. Opened Dots

They are white dots - they only have outlines but no color of the dot. They work quite similar to the closed dots, except that the value at that point will not be included in. An example is if there's an opened dot at x = 4 then the value x = 4 will not be included in.

However, x = 4.0001 or values that are very close to x = 4 will be included in, just not x = 4.

----------------------------------------------------------------------------------------------------------

Now since we are finding the domain through interval, we will ignore all y-values and y-axis. We will only be looking at x-axis and x-values.

The initial opened dot starts at x = -5 and the final opened dot ends at x = 5 as shown in the graph. Keep in mind that graphing visualization is a mandatory skill in mathematics!

The domain's interval has structure of initial x-value < x < final x-value (Only for opened dots, for closed dots, use ≥ or ≤) so from the structure, we can conclude that:

Our domain is -5 < x < 5 or (-5,5) in interval notation form.

Answer:

2

Step-by-step explanation:

Currently, Peter has run a total distance of \(400\cdot 23 =9200\:\text{m}\). His goal is 10 km, as stated in the problem, which equates to 10,000 meters. Thus he will need to run \(10,000-9,200=800\) more meters to achieve his goal. Since the track is 400 meters, he needs to run around the track \(\frac{800}{400}=\boxed{2}\) more times to achieve his goal.

Answer:

9 > b

Step-by-step explanation:

-13 > 5 - 2b

-13 - 5 > -2b

-18/-2 > b

9 > b

The length of side LJ in triangle JKL is approximately 12.27 centimetre .

To determine the length of side LJ in triangle JKL, we can use the concept of similarity between triangles. When two triangles are similar, their corresponding sides are proportional.

Length of side XY in triangle XYZ: 8.7

Length of side XZ in triangle XYZ: 8.2

Length of side YZ in triangle XYZ: 7.8

Length of side JK in triangle JKL: 13.05

Let's set up the proportion using the corresponding sides:

XY / JK = XZ / LJ = YZ / KL

Substituting the given values:

8.7 / 13.05 = 8.2 / LJ = 7.8 / KL

Now, we can solve for LJ:

8.2 / LJ = 8.7 / 13.05

Cross-multiplying:

8.2 * 13.05 = 8.7 * LJ

106.71 = 8.7 * LJ

Dividing both sides by 8.7:

LJ = 106.71 / 8.7

LJ ≈ 12.27

Therefore, the length of side LJ in triangle JKL is approximately 12.27cemtimetre .

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:

The answer is (-2,3)

Step-by-step explanation:

x=-2 and y=3

Answer:

Step-by-step explanation:

I've already answered this question.

Answer: 83.3%

Step-by-step explanation:

It is 83.3% because the other answers don't have the same information as Option D

Answer:

see explanation

Step-by-step explanation:

using the identity

tan²x = sec²x - 1

consider the left side

(tanx + secx)² ← expand using FOIL

= tan²x + 2tanxsecx + sec²x

= sec²x - 1 + 2tanxsecx + sec²x ← collect like terms

= 2sec²x + 2tanxsecx - 1

= right side , thus proven