Which property of equality is used to solve m+18= -9

The predicted value of f(3) is 108 using the third-order Taylor series expansion, and the true percent relative error for each approximation is ε₀ = 134.83%, ε₁ = 32.02%, ε₂ = 40.45%, and ε₃ = 39.33%.

The Taylor series expansion of the given function f(x) = 25x³ - 6x² + 7x - 88 about a base point x = 1 is given by:

Taylor series expansion for a function is given as:

f(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)² + (f'''(a)/3!)(x - a)³ + ... + Rn(a)

Where, a = 1, f(a) = 25(1)³ - 6(1)² + 7(1) - 88 = -62.

The first three derivatives of the function are:

f'(x) = 75x² - 12x + 7

f''(x) = 150x - 12f'''(x) = 150

The zeroth-order approximation is the same as f(1), i.e., -62.

The first-order approximation is given by:  

f₁(x) = f(a) + f'(a)(x - a)f₁(3) = -62 + [75(1)² - 12(1) + 7](3 - 1) = 121

The second-order approximation is given by:

f₂(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)²

f₂(3) = -62 + [75(1)² - 12(1) + 7](3 - 1) + [150(1) / 2!](3 - 1)² = 106

The third-order approximation is given by:

f₃(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)² + (f'''(a)/3!)(x - a)³

f₃(3) = -62 + [75(1)² - 12(1) + 7](3 - 1) + [150(1) / 2!](3 - 1)² + [150 / 3!](3 - 1)³= 108

The true value of the function f(3) = 25(3)³ - 6(3)² + 7(3) - 88 = 178

The true percent relative error, ε is given by:

ε = |(Approximate value - True value) / True value| × 100

For zeroth-order approximation, ε₀ = |(-62 - 178) / 178| × 100 = 134.83%

For first-order approximation, ε₁ = |(121 - 178) / 178| × 100 = 32.02%

For second-order approximation, ε₂ = |(106 - 178) / 178| × 100 = 40.45%

For third-order approximation, ε₃ = |(108 - 178) / 178| × 100 = 39.33%

Hence, the predicted value of f(3) is 108 using the third-order Taylor series expansion, and the true percent relative error for each approximation is ε₀ = 134.83%, ε₁ = 32.02%, ε₂ = 40.45%, and ε₃ = 39.33%.

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The value of x is 10.

Given triangle is a right-angled triangle.

Let the lengths of not mentioned lengths be 2p(hypotenuse) and 2q (other side).

There are two triangles in the given picture.

Consider the smaller triangle.

Apply Pythagoras theorem to that i.e.,

\(p^{2}\) = \((3x)^{2} + q^{2}\)

(Here, total hypotenuse is 2p length and the smaller triangle has half of its length. So, length is p. Similarly in case of q)

\(p^{2} = 9x^{2} + q^{2}\)  (Equation 1)

Now, consider the large triangle.

Apply Pythagoras theorem to that i.e.,

\((2p)^{2} = (4x + 20)^{2} + (2q)^{2}\)

\(4p^{2} = (16x^{2} + 160x + 400) + 4q^{2}\)

Substitute \(p^{2}\) from Equation 1

\(4(9x^{2} + q^{2} ) = 16x^{2} + 160x + 400 + 4q^{2}\\\)

\(36x^{2} + 4q^{2} = 16x^{2} + 160x + 400 + 4q^{2}\)

\(36x^{2} = 16x^{2} + 160x + 400\)  (\(4q^{2}\) from both sides got cancelled)

\(20x^{2} - 160x - 400 = 0\)

Solving the quadratic equation,

\(20x^{2} - 200x + 40x - 400 = 0\)

\(20x(x - 10) + 40(x - 10) = 0\)

\((20x+ 40)(x - 10) = 0\)

So, 20x + 40 = 0 or x - 10 = 0

i.e., x = -2 or 1o

But \(x \neq -2\) because angles cannot be negative.

So, x is 10.

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Therefore, the prism's base can be either 9 x 9 inches, 6 x 6 inches, or

4 x 4 inches in size.

.

The amount of space that an object's surface takes up in total is measured by its surface area. It is usually expressed in square units, such as square inches or square metres.The surface area of a three-dimensional object can be determined by adding up the areas of all of its faces.

For instance, the surface area of a rectangular prism can be calculated using the formula below:

A = lw + lh + lw

The formula SA = 2lw + 2lh + 2wh, where l is the prism's length, w is its width, and h is its height, determines the surface area of a rectangular prism. Inputting the values provided yields:

306 is equal to 2l + 2(24) + 2(24) + 48

306 - 48l = 2w(l+24) 153 - 24

l = wl + 48w 153 - 48w = l(w+24) 153 - 24l - 48w = wl

We can identify all potential values of l and w that meet this equation because they are both whole numbers. Since it is a rectangular prism with a square base, we know that l > w. Given that the surface area cannot be more than 306, we also know that l(w+24) 153. We may therefore begin by identifying all variables of (153-48w) bigger than w.and equal to or less than 12 (since w cannot be greater than 12). We get:

W=1, L=9, L=2, L=6, and L=3

Therefore, the prism's base can be either 9 x 9 inches, 6 x 6 inches, or 4 x 4 inches in size.

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Answer:

200

Step-by-step explanation:

0.75X = 150

X = 200

so 200 is the answer

Answer:

200

150 is 75% of 200

Step-by-step explanation:

150 is 75% of what number

we can change this so it is simpler to understand.

150 = 75% of x

whenever it says "of" it is telling you to multiply

150 = 75% * x

now we simplify

150 = 75/100 * x

150 = 75x/100

*100       *100

15000 = 75x

/75          /75

200  = x

150 is 75% of 200

Answer:

g(x)= 9 cos (x - \(\frac{\pi}{3}\)) +7

Step-by-step explanation:

What is given is f(x) = g cos (x - pi/2) + 3

Note that the standard form of cosine function is a cos (bx + c) + d

a= amplitude

-c/b = phase shift

d = vertical shift

After moving pi/6 to the left --

x = pi/2 - pi/6 = pi/3

once moving pi/6 left, it is at pi/3

moving 4 units up just means adding 4 + 3, and that equals 7, that would be the vertical shift once applied.

So the equation that represents g(x) is C. 9 cos (x - pi/3) + 7

The equation that represents the function g(x) is \(g(x)=9 \cos (x- \frac{\pi}{3})+7\)

The function is given as:

\(f(x)=9 \cos (x-\frac{\pi}{2})+3\)

The function f(x) is first translated \(\frac{\pi}{6}\) units left.

The rule of this translation is:

\((x,y) \to (x + \frac{\pi}{6},y)\)

So, we have:

\(f'(x)=9 \cos (x+ \frac{\pi}{6}-\frac{\pi}{2})+3\)

Take LCM

\(f'(x)=9 \cos (x+ \frac{\pi - 3\pi}{6})+3\)

\(f'(x)=9 \cos (x- \frac{2\pi}{6})+3\)

Divide 2 by 6

\(f'(x)=9 \cos (x- \frac{\pi}{3})+3\)

Next, we translate f'(x) 4 units up.

The rule of this translation is:

\((x,y) \to (x,y+4)\)

So, we have:

\(g(x)=9 \cos (x- \frac{\pi}{3})+3 +4\)

\(g(x)=9 \cos (x- \frac{\pi}{3})+7\)

Hence, the equation that represents the function g(x) is \(g(x)=9 \cos (x- \frac{\pi}{3})+7\)

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Answer:

they're all 0

Step-by-step explanation:

N/A

Answer:

550.5323531336038

Step-by-step explanation:

I have a hint: if you ever need help with triangle trigonometry questions go to carbside depot trigonometry calculator it is a literal life savor

Probability of an event is the measure of its chance of occurrence. The mean of the given probability distribution is 3

Expectation can be taken as a weighted mean, weights being the probability of occurrence of that specific observation.

Thus, if the random variable is X, and its probability mass function is given as:  f(x) = P(X = x), then we have:

\(E(X) = \sum_{i=1}^n( f(x_i) \times x_i)\)

(n is number of values X takes)

For the given case, we have:

X = project grade (from 1 to 5, thus, 1, 2,3,4, or 5 as its values.)

The probability distribution of X is given as:

\(\begin{array}{cc}x&P(X = X)\\1&0.1\\2&0.2\\3&0.4\\4&0.2\\5&0.1\end{array}\)

Using the aforesaid definition, we get the mean of random variable X as:

\(E(X) = \sum_{i=1}^n( f(x_i) \times x_i)\\\\E(X) = 1 \times 0.1 + 2 \times 0.2 + 3 \times 0.4 + 4 \times 0.2 + 5 \times 0.1\\E(X) = 0.1 + 0.4 + 1.2 + 0.8+0.5 = 3\)

Thus, the mean of the given probability distribution is 3

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Answer:

its not shwon btw

Step-by-step explanation:

Answer:

Step-by-step explanation:

Do you have a picture I can see?

The following time Joey's age is greater than Zoe's, his two numbers add up to 11 years.

Consider Chloe to be c years old and Joey to be c+1 years old. After n years, Chloe and Zoe will be n + c and n + 1 respectively.

Based on the given conditions,

(n + c) ÷ (n + 1) = 1 + [(c - 1) ÷ (n + 1)]

n is an integer for 9 non-negative integers.

C – 1 hence has 9 positive divisors.

Either \(p^{8}\) or \(p^{2} q^{2}\) is the prime factorization of c-1 < 100

Since c - 1 < 100, is

c - 1 = \(2^{2} *3^{2}\)

c - 1 = 36,

c = 36 + 1

We can calculate the coefficient,

c = 37

We can infer that Joey is 38 years old as of right now.

Assume that after k years, Joey's age is multiplied by Zoe's age, making Joey and Zoe k + 38 and k + 1 years old, respectively.

So,

We can write,

(k + 38) ÷ (k + 1) = 1 + [(38 - 1) ÷ (k + 1)]

K is an integer for some positive integers.

Since 37 can be divided by k + 1,

k = 36 is the only viable option.

Using the assumption that Joey will be k + 38 = 74 years old, the result is 7 + 4 = 11.

Therefore,

11 years is the sum of Joey's two digits the next time his age is a multiple of Zoe's age.

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Answer:

the answer is A

Step-by-step explanation:

Answer:

(C).Graph C

Step-by-step explanation:

The value of cos(Z) is 12/13.

Since both triangles are similar, △ABC ~ △XYZ, the corresponding angles are congruent. It means:

m∠C = m∠Z, and

cos C = cos Z

The ratio for cosine is adjacent/hypotenuse. In a right triangle, the hypotenuse is the longest side, while an opposite side is the one across from a given angle, and an adjacent side is the one next to a given angle.

Since the side marked 12 is adjacent to angle C and 13 is the hypotenuse of this triangle; so, we know that:

cos C = 12/13

Thus, because of the angles and cosines for C and Z will be the same, it makes:

cos Z = cos C = 12/13

Hence, the value of cos(Z) is 12/13.

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Answer:

The clock shows 8:18

Step-by-step explanation:

Answer:

8:18

Step-by-step explanation:

Based on the given information, the cost per ounce of the 16 oz jar and the 12 oz jar is not provided. Therefore, it is not possible to determine which jar of mayonnaise Sigmund should buy.

In order to compare the cost of the two jars of mayonnaise and determine which one Sigmund should buy, we need to know the price per ounce for each jar. Without this information, we cannot make a conclusive decision.

The cost per ounce is essential because it allows us to compare the prices accurately. For example, if the 16 oz jar costs $3 and the 12 oz jar costs $2.50, we can calculate the cost per ounce for each jar. The cost per ounce for the 16 oz jar would be $3 divided by 16 oz, which is $0.1875 per ounce. Similarly, the cost per ounce for the 12 oz jar would be $2.50 divided by 12 oz, which is approximately $0.2083 per ounce.

With this information, we can determine that the 16 oz jar is more cost-effective as it has a lower cost per ounce compared to the 12 oz jar. However, without the specific prices per ounce provided in the given information, it is impossible to determine which jar of mayonnaise Sigmund should buy.

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up one over 14 or 1/14

Answer:

see explanation

Step-by-step explanation:

∠ a and 150° are a linear pair and sum to 180° , then

∠ a + 150° = 180° ( subtract 150° from both sides )

∠ a = 30°

the sum of the 3 angles in a triangle = 180° , then

∠ b + ∠ a + 60° = 180° , that is

∠ b + 30° + 60° = 180°

∠ b + 90° = 180° ( subtract 90° from both sides )

∠ b = 90°

Answer:

About 17 weeks

Step-by-step explanation:

Given

Ryan:

\(Initial = 150\)

\(Additional = 10\) (weekly)

Sarah:

\(Initial = 233\)

\(Additional = 5\) (weekly)

Required

Determine the number of weeks they have the same cards

Represent the number of weeks with w:

For Both individuals, number of card at any given week is:

\(Initial + Additional * w\)

So,

For Ryan, the expression is:

\(150 + 10 * w\)

\(150 + 10w\)

For Sarah, the expression is:

\(233 + 5 * w\)

\(233 + 5 w\)

To determine the number of weeks, we have to equate both equations:

\(150 + 10w= 233 + 5 w\)

Collect Like Terms

\(10w - 5w = 233 - 150\)

\(5w = 83\)

Solve for w

\(w = 83/5\)

\(w = 16.6\)

16.6 implies about 17 weeks, because 16.6 approximates to 17

Conclusively, Ryan and Sarah will have the same number of balls in about 17 weeks

Answer:

108πin³

Step-by-step explanation:

The volume of a cone = ⅓ of the volume of a cylinder

Thus, volume of cylinder = 2πr²h

Where, r = radius, h = height of cylinder.

Volume of cone = ⅓×πr²h

So therefore, the volume of a cone given = ⅓ of the volume of a cylinder with the same height and and base of the cone

Thus,

If Volume of cone = 36πin³ , volume of cylinder would be 3 × 36πin³

Volume of cylinder = 108πin³

Answer:

3 and 4

Step-by-step explanation:

13 is between the perfect squares of 9 and 16, which are 3^2 and 4^2 respectively.

The ratio of the height to the diameter that maximizes the volume of the cylindrical can is: 0.886 approximately.

Let the radius of the cylindrical can be denoted by r, and its height by h. The surface area of the can is given by:

S = 2π\(r^2\)+ 2πrh

Simplifying this expression, we get:

h = (S - 2π\(r^2\))/(2πr)

The volume of the cylindrical can is given by:

V = π\(r^2\)h

Substituting the expression for h obtained earlier, we get:

V = π\(r^2\)(S - 2π\(r^2\))/(2πr)

Simplifying this expression, we get:

V = (S/2π - \(r^2\))πr

To maximize the volume of the cylindrical can, we need to find the value of r that maximizes the above expression. We can do this by differentiating the expression with respect to r, setting it equal to zero, and solving for r:

dV/dr = (S/2π - \(2r^2\))π = 0

Solving for r, we get:

r = √(S/4π)

Substituting this value of r back into the expression for h, we get:

h = (S - 4π\(r^2\))/(4πr) = (S - S/2)/(2√(S/4π)) = √(Sπ)/2

Therefore, the ratio of the height to the diameter that maximizes the volume of the cylindrical can is:

h/2r = (√(Sπ)/2)/(2√(S/4π)) = √(π/4) = 0.886 approximately.

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In classification analysis, we are determining the probability of an observation belonging to a specific class or category.

In classification analysis, we aim to assign observations to predefined classes or categories based on their features or characteristics. This analysis involves training a model on a labeled dataset, where each observation is associated with a known class.

During the training phase, the classification model learns patterns and relationships in the input data to make predictions about the class labels of unseen observations. The model estimates the probability of an observation belonging to each class based on the learned patterns.

To determine the probability of an observation belonging to a specific class, the classification model calculates a score or probability value for each class. These scores indicate the model's confidence in the prediction. The probability values are often derived from a probabilistic algorithm or a mathematical function such as logistic regression or a decision tree.

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Answer:

red) area = 59.2 km²

Step-by-step explanation:

area of bottom 4 x 4 = 16

area of 4 sides = 4 (1/2)(4)(5.4) = 43.2

16 + 432 = 59.2 km²

Answer:

Step-by-step explanation:

lateral area = 2(base)(slant height) = 2·4·2 = 16 km²

base area = base² = 4² = 16 km²

surface area = 16 + 16 = 32 km²

Answer:

b=-a

Step-by-step explanation:

Becaude when b is positive a will be negative

And when b is negative a will be positive.

If you perform multiple t-tests, the Type I error increases.

When conducting multiple t-tests, each individual test has a certain probability of committing a Type I error, which is the probability of incorrectly rejecting the null hypothesis when it is actually true. The standard threshold for Type I error is typically set at 5% (or 0.05).

However, when multiple tests are performed, the probability of committing at least one Type I error across all the tests increases. This is known as the problem of multiple comparisons or multiple testing.

The more tests you perform, the higher the likelihood of observing a significant result by chance alone, leading to an increased Type I error rate.

To address this issue, it is common to adjust the significance level (e.g., using Bonferroni correction) or conduct post hoc comparisons using methods such as Tukey's test or Bonferroni adjustment.

These methods help control the overall Type I error rate when multiple comparisons are made.

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Answer:

C

4y=20

Hope this helped

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

Diameter =30

radius=30/2=15

area =πr²

=π×15²

= π×(15)(15)

=225π cm² or 706.95cm²

circumference C=πD

C=3.142×30cm

C=30πcm or 94.26cm

To construct a 98% confidence interval for B₁, we can use the t-distribution since the sample size is small (n = 12).

Given the sample mean (B₁ = 46), sample standard deviation (s = 5.7), and sum of squares (SSzz = 57), we can calculate the confidence interval.

The formula for a confidence interval is:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

For a 98% confidence level and n = 12, the critical value is approximately 2.681 (obtained from a t-distribution table).

The standard error is calculated as the sample standard deviation divided by the square root of the sample size (s / √n).

Plugging in the values:

Standard Error = 5.7 / √12 ≈ 1.647

Confidence Interval = 46 ± (2.681 * 1.647)

Therefore, the 98% confidence interval for B₁ is approximately (42.21, 49.79).

In conclusion, we can be 98% confident that the true value of B₁ falls within the range of 42.21 to 49.79 based on the given sample data.

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Answer:

42 units^2

Step-by-step explanation:

the area of the triangle is 7x12/2 = 42

The surface area of the given regular pyramid is 84 cm^2.

To find the surface area of a regular pyramid, we need to calculate the area of each face and add them together. A regular pyramid has a base that is a regular polygon, and its lateral faces are triangles that meet at a common vertex. We can use the Pythagorean theorem to find the slant height of the pyramid, which is the height of each lateral face.

Let's assume that the base of the regular pyramid is a square with side length 6 cm, and the slant height is 4 cm.

First, we need to find the area of the base of the pyramid:

Area of the base = (side length)^2

                = 6 cm x 6 cm

                = 36 cm^2

Next, we need to find the area of each triangular lateral face. Since the pyramid is a regular pyramid, all the triangular faces are congruent.

We can find the area of each triangular face using the formula:

Area of a triangle = (1/2) x base x height

The base of each triangular face is equal to the side length of the square base, which is 6 cm. The height of each triangular face is equal to the slant height, which is 4 cm.

Area of each triangular face = (1/2) x 6 cm x 4 cm

                            = 12 cm^2

Since the pyramid has 4 triangular faces, we need to multiply the area of one triangular face by 4 to get the total area of all the triangular faces:

Total area of the triangular faces = 4 x 12 cm^2

                                 = 48 cm^2

Finally, we can find the total surface area of the pyramid by adding the area of the base and the area of the triangular faces:

Total surface area = Area of the base + Total area of the triangular faces

                  = 36 cm^2 + 48 cm^2

                  = 84 cm^2

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