Alexa is saving to buy a new bike that costs $265. So far she has saved $45. If she is able to save $11 each week, how many weeks will it take her to save enough to buy her coveted bike? Kole wrote (265 - 45)/11 = w. Bella wrote 11w + 45 = 265. Who do you agree with? Justify your response.

The recurrence relation for the coefficients of the power series solution is given by:

For n = 0: a₀ = 0.

For n > 0: aₙ = -[32aₙ₋₂ + n(n-1)*aₙ₋₂]/[n(n-1) - x].

The indices in the recurrence relation differ by 2, as we can see from the expressions aₙ and aₙ₋₂ in the relation.

Let's consider the differential equation: (16 + x²)y'' - xy' + 32y = 0.

To solve this equation using a power series, we assume that the solution y(x) can be expressed as an infinite power series in terms of x, centered around a point x₀. The power series has the general form:

y(x) = ∑[n=0 to ∞] aₙ(x - x₀)ⁿ.

Here, aₙ represents the coefficients of the series, and (x - x₀)ⁿ denotes the powers of x centered around x₀. Plugging this series into the given differential equation, we can determine the recurrence relation for the coefficients aₙ.

To find the power series solution, we start by differentiating y(x) with respect to x. Using the power series expansion, we have:

y'(x) = ∑[n=0 to ∞] n*aₙ(x - x₀)ⁿ⁻¹, y''(x) = ∑[n=0 to ∞] n(n-1)*aₙ(x - x₀)ⁿ⁻².

Next, we substitute these expressions for y'(x) and y''(x) back into the original differential equation:

(16 + x²) * ∑[n=0 to ∞] n(n-1)aₙ(x - x₀)ⁿ⁻² - x * ∑[n=0 to ∞] naₙ(x - x₀)ⁿ⁻¹ + 32 * ∑[n=0 to ∞] aₙ(x - x₀)ⁿ = 0.

Now, we simplify the equation by expanding the products and rearranging terms:

∑[n=0 to ∞] (n(n-1)*aₙ(x - x₀)ⁿ⁻² + 32aₙ(x - x₀)ⁿ) + x² * ∑[n=0 to ∞] n(n-1)aₙ(x - x₀)ⁿ⁻² - x * ∑[n=0 to ∞] naₙ(x - x₀)ⁿ⁻¹ = 0.

At this point, we can equate the coefficients of each power of x to zero separately. This gives us the following equations for the coefficients aₙ:

For n = 0: (n(n-1)*a₀(x - x₀)ⁿ⁻² + 32a₀(x - x₀)ⁿ) = 0.

For n > 0: n(n-1)*aₙ(x - x₀)ⁿ⁻² + 32aₙ(x - x₀)ⁿ + x² * n(n-1)aₙ(x - x₀)ⁿ⁻² - x * naₙ(x - x₀)ⁿ⁻¹ = 0.

Simplifying these equations further, we obtain the recurrence relation for the coefficients aₙ:

For n = 0: 32a₀ = 0.

For n > 0: aₙ = -[32aₙ₋₂ + n(n-1)*aₙ₋₂]/[n(n-1) - x].

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Complete Question:

Consider the following differential equation : (16 + x²)y" - xy' + 32y = 0; xo = 0.

Seek a power series solution for the given differential equation about the given point xo ; find the recurrence relation.

The indices differ by _____.

The quotient ring  [tex]Q[x]/(x^2 - 4x + 3)[/tex]  is not a field because the polynomial x²- 4x + 3 can be factored into linear factors in Q[x], indicating the presence of zero divisors in the quotient ring.

To determine if the quotient ring [tex]Q[x]/(x^2 - 4x + 3)[/tex] is a field, we need to check if the polynomial x² - 4x + 3 is irreducible in Q[x], which means it cannot be factored into non-constant polynomials of lower degree in Q[x].

The polynomial x² - 4x + 3 can be factored as (x - 1)(x - 3) in Q[x], so it is not irreducible. This means that Q[x]/(x² - 4x + 3) is not a field.

In fact, Q[x]/(x² - 4x + 3) is an example of a quotient ring that is not a field. It can be shown that this quotient ring is isomorphic to Q[x]/(x - 1) x Q[x]/(x - 3), which is a direct product of two fields.

Since a field cannot have nontrivial zero divisors, and in this case, both (x - 1) and (x - 3) are zero divisors, the quotient ring is not a field.

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Answer:

1.66666666667

Step-by-step explanation:

I have to find the scale factor of the side lengths. This would be 1.66666666667. Why? The side lengths for triangle 1 are: 40 and 50. Triangle 2's side lengths: 24 and 30. Match the lengths, and divide. 50 divided by 30=1.66666666667, and 40 divided by 24=1.66666666667, Hope this helped!

Answer:

C is the answer thank you

Answer:

pretty sure its yellow sorry if its wrong

Step-by-step explanation:

Answer:

Hi! The answer to your question is C. 9 x [tex]10^{2}[/tex]

Step-by-step explanation:

※※※※※※※※※※※※

⁅Brainliest is greatly appreciated!⁆

Hope this helps!!

- Brooklynn Deka

Don't forget to click the add button so we can be friends ( ´･･)ﾉ(._.`)

Answer:

C. 2:5

Step-by-step explanation:

Find perimeter of each...

a. 10+25+21.5=56.5

b. 4+10+8.6=22.6

b:a

22.6:56.6

simplify

11.3 will go into both for..

2:5

Option C is the correct example of the classical approach to probability.

An example of the classical approach to probability would be option C: in terms of the proportion of times that an event can be theoretically expected to occur.

The classical approach to probability is based on the assumption of equally likely outcomes. In this approach, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

For example, consider a fair six-sided die. The classical approach would state that since there are six equally likely outcomes (the numbers 1 to 6), the probability of rolling a specific number, say 3, would be 1 out of 6, or 1/6. This is because there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling any number from 1 to 6).

Similarly, if we have a bag containing 10 red balls and 20 blue balls, the classical approach would state that the probability of drawing a red ball would be 10 out of 30, or 1/3. This is because there are 10 favorable outcomes (drawing a red ball) out of 30 possible outcomes (drawing any ball from the bag).

In both cases, the classical approach to probability relies on the concept of equally likely outcomes and uses the proportion of favorable outcomes to calculate the probability.

Therefore, option C is the correct example of the classical approach to probability.

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Answer:

( x - 8 ) ( x + 2 )

Step-by-step explanation:

x² - 6x - 16

= x² + 2x - 8x - 16

= x ( x + 2 ) - 8 ( x + 2 )

= ( x - 8 ) ( x + 2 )

Answer: He's right its D.) (x-8)(x=2)

Step-by-step explanation:

Answer:

$4092

Step-by-step explanation:

Answer:

4in

Step-by-step explanation:

Answer:

its in there

Step-by-step explanation:

Answer: Solve the Inequality for h

Solve for h

Graph

Convert to Interval Notation

Evaluate

Write in y=mx+b Form

Find the Exact Value

Solve the Absolute Value Inequality for h

Convert to Set Notation

Plot

Write in Slope-Intercept Form

Solve the Rational Equation for h

Simplify

Add

Solve by Factoring

Describe the Transformation

Evaluate the Summation

Find the Absolute Max and Min over the Interval

Find the Product

Convert from Degrees to Radians

Convert to a Decimal

Subtract

Find the Slope

Find the Domain and Range

Find the Derivative - d/dh

Solve Using the Square Root Property

Find the Direction Angle of the Vector

Multiply

Find the Function Rule

Convert to a Simplified Fraction

Find the Area Between the Curves

Solve the Function Operation

Solve the System of Inequalities

Solve for h in Degrees

Find Where Increasing/Decreasing

Find the Maximum/Minimum Value

Write with Rational (Fractional) Exponents

Evaluate the Limit

Find the Slope and y-intercept

Solve by Isolating the Absolute Value for h

Find All Complex Solutions

Factor over the Complex Numbers

Find the Intersection

Find the Center and Radius

Convert to Radical Form

Find the Integral

Evaluate Using Summation Formulas

Evaluate Using Scientific Notation

Simplify/Condense

Determine if Linear

Graph Using a Table of Values

Reduce

Rationalize the Denominator

Find the Union

Find the Critical Points

Solve for h in Radians

Find the x and y Intercepts

Find the Inverse

Find the Perpendicular Line

Convert from Interval to Inequality

Solve by Completing the Square

Simplify the Matrix

Maximize the Equation given the Constraints

Convert to Regular Notation

Determine if the Relation is a Function

Write in Standard Form

Convert to Trigonometric Form

Split Using Partial Fraction Decomposition

Find the Zeros by Completing the Square

Find the Prime Factorization

Find the Local Maxima and Minima

Find the Quotient

Multiply the Matrices

Factor

-44+18=-26degrees

negative 26 degrees is your answer

please mark brainliest and have a nice day

a.  The value of T(v) for the polynomial yı(x) = 17 - 3x + 5x² is [5 -3; 1 0]

To find T(v) for the polynomial yı(x) = 17 - 3x + 5x², we substitute the coefficients of the polynomial into the mapping T(ax² + bx + c).

T(v) = T(5x² - 3x + 17)

Using the definition of the mapping T, we have:

T(v) = [5 -3; 1 0]

b. To determine if the mapping T is a linear transformation, we need to check two properties: additive property and scalar multiplication property.

Additive Property:

T(u + v) = T(u) + T(v) for all u, v in P₂(R)

Let's consider two polynomials u(x) and v(x) in P₂(R):

u(x) = a₁x² + b₁x + c₁

v(x) = a₂x² + b₂x + c₂

T(u + v) = T((a₁ + a₂)x² + (b₁ + b₂)x + (c₁ + c₂))

Expanding and applying the mapping T, we get:

T(u + v) = [(a₁ + a₂) (b₁ + b₂); (c₁ + c₂) 0]

T(u) + T(v) = [a₁ b₁; c₁ 0] + [a₂ b₂; c₂ 0] = [(a₁ + a₂) (b₁ + b₂); (c₁ + c₂) 0]

Since T(u + v) = T(u) + T(v), the additive property holds.

Scalar Multiplication Property:

T(kv) = kT(v) for all k in R and v in P₂(R)

Let's consider a scalar k and a polynomial v(x) in P₂(R):

v(x) = ax² + bx + c

T(kv) = T(k(ax² + bx + c))

Expanding and applying the mapping T, we get:

T(kv) = [ka kb; kc 0]

kT(v) = k[a b; c 0] = [ka kb; kc 0]

Since T(kv) = kT(v), the scalar multiplication property holds.

Since the mapping T satisfies both the additive property and scalar multiplication property, it is a linear transformation.

c. The kernel of a mapping is the set of all vectors that map to the zero vector in the codomain. In this case, we need to find the set of polynomials in P₂(R) that map to the zero matrix [0 0; 0 0] in M₂x₂(R).

Let's consider a polynomial v(x) in P₂(R):

v(x) = ax² + bx + c

T(v) = [a b; c 0]

To find the kernel, we need T(v) = [a b; c 0] = [0 0; 0 0]

This implies that a = b = c = 0.

Therefore, the kernel of this mapping T is the zero polynomial in P₂(R).

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Answer:

the median is 15

Explanation:

you can find the median by arranging the numbers from smallest to largest and finding the number in the middle.

5 14 15 15 16 17 18

in this case, the number in the middle is 15 so the median for this data set is 15.

i hope this helps! :D

A new sensor was developed by ABY Inc. that is to be used for their obstacle detection system. However, the sensor to be commercially produced, it must have an error rate that is lower than 40% and an F-Score that is more than or equal to 70%.

1. The alarm didn't activate correctly 63 times during the tests.

During the tests, it was observed that the alarm failed to activate in the presence of an obstacle 63 times. This means that the sensor missed detecting obstacles in those instances.

2. There were 126 runs with actual obstacles in place.

Out of the 250 runs, the alarm correctly activated 62 times and didn't activate correctly 63 times. Since the alarm failed to activate in the presence of an obstacle 63 times, we can infer that there were 126 runs with actual obstacles.

3. The sensor was correct 156 times out of 250 runs.

To calculate how often the sensor was correct, we need to sum up the number of times the alarm went off correctly (62 times) and the number of times the alarm didn't activate correctly (63 times).

This gives us a total of 125 correct activations. However, we also need to account for the 63 times when the alarm didn't activate even if an obstacle was present. So the sensor was correct 125 + 63 = 188 times out of 250 runs.

4. The sensor was incorrect 62 times out of 250 runs.

The sensor was incorrect when it failed to activate the alarm in the presence of an obstacle (63 times) and when the alarm went off even if there was no obstacle (33 times). Therefore, the sensor was incorrect 63 + 33 = 96 times out of 250 runs.

5. The hit rate of the sensor is 0.4960 or 49.60%.

The hit rate, also known as the True Positive Rate or Sensitivity, measures the proportion of actual positive cases that were correctly identified by the sensor.

It is calculated by dividing the number of correct activations (62) by the total number of runs with actual obstacles (126). Therefore, the hit rate is 62/126 = 0.4960 or 49.60%.

6. The sensor predicted a NO even when it was supposed to be a YES 33 times.

Out of the 250 runs, there were 33 instances where the alarm went off even if there was no obstacle present. This means that the sensor predicted a NO (no obstacle) incorrectly in those cases.

7. The CSI (Critical Success Index) of the sensor is 0.4032 or 40.32%.

The CSI, also known as the Threat Score or True Skill Statistic, measures the effectiveness of the sensor in detecting obstacles while avoiding false alarms.

It is calculated by dividing the number of correct activations (62) by the sum of correct activations, missed detections, and false alarms. So the CSI is 62 / (62 + 63 + 33) = 0.4032 or 40.32%.

8. The overall accuracy of the sensor is 62.80%.

The overall accuracy is calculated by dividing the number of correct activations (62) and correct non-activations (187) by the total number of runs (250). So the overall accuracy is (62 + 187) / 250 = 0.6280 or 62.80%.

9. The F-score is 0.5238 or 52.38%.

The F-score, also known as the F1-score, combines the precision and recall of the sensor's performance. It is calculated using the formula: F-score = 2 * (precision * recall) / (precision + recall).

Precision is the ratio of true positives (62) to the sum of true positives and false positives (33), while recall is the ratio of true positives to the sum of true positives and false negatives (63). Plugging in the values, we get F-score = 2 * (62)

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Answer:

It is a right triangle

Step-by-step explanation:

Complete question

Martin drew a triangle. Its sides were 3\text{ cm}3 cm3, start text, space, c, m, end text, 4\text{ cm}4 cm4, start text, space, c, m, end text, and 5\text{ cm}5 cm5, start text, space, c, m, end text. It has one right angle and two acute angles. Complete the sentence to describe the triangle Martin drew. Martin's triangle is ----- and ------ .

First you must know that for a triangle to be right angled, the square of the largest side must be equal to the sum of the square of the other two sides

Given

Largest side c = 5

Other sides a = 3 and b=4

Square of largest side c² =5²=25

Sun of the squares of other two sides = a²+b²

Sum of the squares of other two sides =3²+4²

Sum of the squares of other two sides = 9+16 =25

Since c² =a²+b² according to pythagoras theorem, hence the triangle is right angled

Answer: D

Step-by-step explanation:

maybe

Answer:

the answer for your question is d

One example of a single polygon that has at least 5 sides and has exactly 2 lines of symmetry is a regular pentagon.

A regular pentagon is a five-sided polygon in which all five sides are equal in length and all five angles are congruent, i.e., the same measure. A regular pentagon also has five lines of symmetry, which cut through its center point and the midpoint of each side.

However, we need a polygon with exactly 2 lines of symmetry. Therefore, we can take a regular pentagon and remove two opposite edges and vertices. This leaves us with a polygon that still has 5 sides but has exactly 2 lines of symmetry: the red lines represent the two lines of symmetry of the polygon.

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Answer:

Pounds of candy      Cost ($)       Cost/pound

1                                  $3                $3/1                                                  

3                                 $9                $3/1                                      

7                                 $21               $3/1                                                          

10                               $30              $3/1                                                      

Answer:

This is impossible to answer, unless there is a picture that is not there.

Step-by-step explanation:

Answer:

C. a translation of 1 unit right and 2 units up, followed by a dilation by a factor of 3

Step-by-step explanation:

Answer:

Your answer should be C.

Step-by-step explanation:

In order to make 150% you need a whole which represents the 100%. Which leaves B out of the question. A Is not close to half of a bar, which you can also eliminate. C and D are somewhat the same but it has to have the same amount of boxes shaded and unshaded, in this case D is 4 shaded and 2 unshaded which is wrong. So, your answer is C because there is 3 shaded and unshaded boxes in the model, hope this helps!

The diagram that represents 150%​ should be C.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

In order to make 150% we need a whole which represents the 100%. Which leaves B out of the question.

Option A Is not close to half of a bar, which we can also eliminate.

Option C and D are somewhat the same but it has to have the same amount of boxes shaded and unshaded,

In this case D is 4 shaded and 2 unshaded which is wrong.

Therefore, the answer is C because there is 3 shaded and unshaded boxes in the model.

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Answer: the length of the base is 50 cm

Step-by-step explanation:

The answer is 615.6.If you have more problems like this go to math-way calculator

In regression analysis, one assumption that is not true about the error term e is that it is normally distributed.

The assumptions underlying regression analysis include:

Linearity: The relationship between the dependent variable and the independent variables is assumed to be linear.

Independence: The error terms are assumed to be independent of each other.

Homoscedasticity: The error terms have constant variance across all levels of the independent variables.

Normality: The error terms are assumed to be normally distributed.

No multicollinearity: The independent variables are not perfectly correlated with each other.

While the first four assumptions are typically considered in regression analysis, the assumption of normality for the error term e is not always true. In some cases, the error term may not follow a normal distribution. Violations of this assumption can affect the accuracy and reliability of the regression model's estimates and statistical inference. However, even if the error term is not normally distributed, regression analysis can still provide useful insights and predictions, depending on the specific circumstances and alternative methods that may be employed to address the violation.

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Answer:

15 yards

Step-by-step explanation:

hope this helps ❤️

Answer:

2

Step-by-step explanation:

So you will get the 1/2 and see how many times she does go back and forth and she did it 4 times so you would multiply 1/2 x 4 and get a total of 2

Hope It Helps

Answer:

2

Step-by-step explanation:

she walked to the store and back 1 time=1/2 mile :

from her house to the store=1/4 mile

she rode her bike to the store and back 3 times

So in total that week she went to the store and back 4 times

so 4 times 1/2 is 2