Which part of a cake remains if x/y has been eaten?

The equation of the least-squares regression line based on these data is, y= 106.92 +2.044x where y =predicted height of child and x = child’s foot length.

To determine the equation of the least-squares regression line, we need to fit a linear model to the data using the method of least squares. The equation of the line can be written as:

height = intercept + slope * foot length

where the intercept and slope are the parameters we need to estimate from the data. The intercept represents the predicted height when foot length is 0, and the slope represents the change in height for each unit increase in foot length.

Substituting the values form the graph,

y= 106.92 +2.044x where y =predicted height of child and x = child’s foot length.

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--The complete question is, Can we predict the heights of school-aged children from foot length? below is computer output from a regression analysis of this relationship for 15 randomly-selected canadian children from 8 to 15 years old, along with a residual plot. the explanatory variable is each child's foot length (in centimeters), and the response variable is the child's height (in centimeters).

What is the equation of the least-squares regression line based on these data?  Define any parameters used.--

Factorize: tan²A - tanA - 30

So mate, Kindly refer through the above attachment for it. Ans: ( tanA + 5 )( tanA ‐ 6 ). If you like my answer, then give a thanks ❤ and 5.0 star vote ⭐. ( And Brainliest ).

Answer:

1. 5/3 is not equal to 3/5.

2. 7-(4+3) is equal to (4+3)-7

3. (x + y) + 1 is equal to x + (y + 1)

Step-by-step explanation:

1. 5/3 and 3/5 are completely different fractions and when you switch the denominator and the numerator you get a different fraction: 5/3 = 1 2/3, 3/5

2. If you solve both of them, they are equal because 7-7 = 7-7

3. This is equal due to the associative addition property, which means that when the addition of three or more numbers, the total/sum will be the same, even when the grouping of addends are changed.

Plz mark brainliest thx

#1

\(\boxed{\dfrac{a}{b}=\dfrac{b}{a},a=b}\)

Here 5\(\neq 3\)

Hence inequality holds

#2

\(\\ \sf\longmapsto 7-(4+3)=(4+3)-7\)

\(\\ \sf\longmapsto 7-7=7-7\)

\(\\ \sf\longmapsto 0=0\)

Equality holds

#3

\(\\ \sf\longmapsto (x+y)+1=x+(y+1)\)

Equality holds

Done

The main parameter that we need to know to predict the relative importance of drift in a population is the effective population size (Ne).

Effective population size refers to the number of individuals in a population that contribute offspring to the next generation, taking into account factors such as unequal reproductive success and genetic variation.

Drift, also known as genetic drift, is the random change in allele frequencies in a population over time. It occurs due to chance events, especially in small populations, and can lead to the loss or fixation of alleles. The magnitude of genetic drift is influenced by the effective population size. In smaller populations, genetic drift tends to have a greater impact, as chance events can have a larger effect on allele frequencies. In contrast, larger populations are less susceptible to the effects of drift.

By knowing the effective population size, we can assess the relative importance of genetic drift in a population. A smaller effective population size suggests that genetic drift is more likely to play a significant role, while a larger effective population size indicates that genetic drift may have less impact compared to other evolutionary forces such as natural selection or gene flow.

Therefore, understanding the effective population size is crucial for predicting the relative importance of drift in a population and determining the genetic dynamics and evolutionary trajectory of a species.

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4. What is the main parameter that we need to know to predict the relative importance of drift in a population ??

Answer:

m=2

Step-by-step explanation:

Answer:

A.

1) 60

2) 27

B)

1.cm³

2.cm³

3.m³

Step-by-step explanation:

A)

5x3x4 =60cm³

3x3x3=27cm³

B)

1.cm³

2.cm³

3.m³

Answer:

1

Step-by-step explanation:

The Linnaean class system provides a framework for understanding the diversity of life on Earth by grouping similar organisms together based on shared characteristics.

By comparing and contrasting the definitions of each class, we can see how different groups of animals are related to each other and how they differ in terms of their biological traits.

The Linnaean class system is a way of organizing living things based on shared characteristics. Let's compare and contrast the definitions of the Linnaean classes using a Venn diagram.

First, we have the class Mammalia, which includes all animals that have hair or fur, produce milk to feed their young, and have specialized teeth. This class overlaps with the class Aves, which includes all birds, because some birds have specialized beaks and feathers that are similar to mammalian hair and teeth. However, birds do not produce milk.

Next, we have the class Reptilia, which includes animals that are cold-blooded, lay eggs, and have scales or plates on their skin. This class overlaps with both Mammalia and Aves in terms of species that lay eggs, such as monotremes (platypus and echidnas) and some birds (ostriches and emus). However, reptiles lack specialized teeth and do not produce milk.

Finally, we have the class Amphibia, which includes animals that are cold-blooded, breathe through their skin, and undergo metamorphosis from a water-dwelling larval stage to a land-dwelling adult stage. This class overlaps with Reptilia in terms of some shared characteristics, but Amphibia also lacks specialized teeth and does not lay eggs with hard shells like reptiles.

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The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333

The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:

The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.

(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.

(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:

P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

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Answer:

Check the image uploaded

The cylindrical coordinates for (-6, 6sqrt(3), 4) are (r, θ, z) = (12, -π/3, 4).

To change from rectangular to cylindrical coordinates, we use the following equations:

\(r = \sqrt\(x^2 + y^2)\)

θ = arctan(y/x)

z = z

For part (a), we have the point (-1, 1, 1).

\(r = \sqrt\((-1)^2 + 1^2) }= \sqrt2\)

θ = arctan(1/(-1)) = -π/4 (Note: We use the quadrant in which x and y are located to determine the sign of θ)

z = 1

So the cylindrical coordinates for (-1, 1, 1) are (r, θ, z) = (√2, -π/4, 1).

For part (b), we have the point\((-6, 6\sqrt\((3)}, 4)\).

\(r = √((-6)^2 + (6\sqrt\((3)}}^2) = 12\)

θ = arctan\(((6\sqrt\((3)})/(-6))\) = -π/3  (-6, 6\sqrt\((3)}, 4)

z = 4

So the cylindrical coordinates for ( (-6, 6\sqrt\((3)}, 4) are (r, θ, z) = (12, -π/3, 4).

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Answer:

147 ants

Step-by-step explanation:

7 times 3=21 21 times 7= 147

Answer:

15 309

Step-by-step explanation:

7*3^7=15309 because every week they triple

Answer: 7=6=3=2 and 8=5=4=1

Step-by-step explanation:

For 2 straight lines crossing, opposite angles are equal. And because the 2 vertical lines are parallel, both sets (1234 and 5678) of angles are the same. Let me know if that is too confusing

Answer:

f shape, I don't know if I'm correct

Answer:

Reflection

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The probability that she makes correct guesses 14 times or more is 0.0582 and this probability does not seem to verify her claim

Number of tosses of coin  n = 20

probability she guesses correctly p = 0.5

Probability she guesses incorrectly q = 1- p = 0.5

P(X < A) = P( z*σ + μ < A) = P(z < (A-μ)/σ)        (1)      ( ∵ we know z = x - μ/σ)

Mean = μ  = np = 20 * 0.5 = 10

Standard deviation = σ

Standard deviation σ = √npq = √(20 *0.5*(1-0.5) = √5 = 2.236

Probability of being correct 14 times or more

P(X ≥ 14) = 1 - P(X < 13.5)      

              = 1 - P(Z < (13.5 - 10)/2.236)         (using 1)

              = 1 - P(Z < 1.57)

               = 1 - 0.9418

               = 0.0582

Here, the probability of getting 14 or more is 0.0582 and it is usually as the probability is more than 0.05. Thus this probability does not verify her claim

Problem based on normal distribution

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A power series representation for the function, f(x) = ln(9 − x) f(x) = ln(9) − [infinity] n = 1 then, the radius of convergence, r = 1

The power series representation for the function f(x) = ln(9 − x) is given by:-

ln(1 - (x/9)) = - ∑[(xn)/n],

where n = 1 to ∞

The above is the power series representation of the function f(x) = ln(9 - x) centered at x = 0.

Now, let us determine the radius of convergence, r.

To do this, we use the Ratio Test which states that if we have a power series ∑an(x - c)n, then:

r = 1/L, where L is the limit superior of the ratio:|an+1(x - c)|/|an(x - c)|as n approaches infinity.

So, for our power series ∑[(-1)n(xn)/n], we have:|(-1)n+1(xn+1)/(n+1))/(-1)n(xn/n)|= |x|(n+1)/(n+1)|n|/n = |x|

This ratio has a limit as n approaches infinity and is equal to |x|.Now, |x| < 1 for the power series to converge.

Hence, r = 1.So, r = 1.

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Given function is:f(x) = ln(9 − x)We need to find power series representation for the given function centered at x=0.For finding power series representation for f(x), let's find first few derivatives of f(x):

\($$f(x) = ln(9-x)$$$$f'(x) = - \frac{1}{9-x}(0-1)$$$$f''(x) = \frac{1}{(9-x)^2}(0-1)$$$$f'''(x) = - \frac{2}{(9-x)^3}(0-1)$$$$f''''(x) = \frac{3 \cdot 2}{(9-x)^4}(0-1)$$Therefore, the nth derivative is given by:$$f^{n}(x) = (-1)^{n+1}\cdot \frac{(n-1)!}{(9-x)^n}$$\)

Now, we can write Taylor's series as:

\($$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x-a)^n$$$$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!}(x)^n$$So, at a=0, $$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!}(x)^n$$$$f(x) = \sum_{n=0}^\infty \frac{(-1)^{n+1}}{n!}(\frac{1}{9})^n(x)^n$$\)

Let's check the convergence of the above series using the ratio test:

$$\lim_{n \to \infty}|\frac{a_{n+1}}{a_n}| = \frac{1}{9} \lim_{n \to \infty}\frac{n!}{(n+1)!}$$This can be simplified as:$$\lim_{n \to \infty}|\frac{a_{n+1}}{a_n}| = \frac{1}{9} \lim_{n \to \infty}\frac{1}{n+1}$$As we know that,$$\lim_{n \to \infty}\frac{1}{n+1} = 0$$Therefore,$$\lim_{n \to \infty}|\frac{a_{n+1}}{a_n}| = 0$$

Thus, the above series converges for all values of x. Hence, the radius of convergence is infinity.Therefore, we can write the power series representation for the given function f(x) as$$f(x) = \ln(9) - \sum_{n=1}^\infty \frac{(-1)^n}{n}(x-9)^n$$$$f(x) = \ln(9) - \sum_{n=1}^\infty \frac{(-1)^n}{n}(9-x)^n$$The radius of convergence r is infinity.The power series representation for f(x) is f(x) = ln(9) - ∑(-1)^n (x-9)^n/n. The radius of convergence is infinity.

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Answer:

Step-by-step explanation:

1 meter = 1000 mm

So, 1 mm = \(\frac{1}{1000}\) m

To change mm to meter, divide the given mm value by 1000

Ex: 50 mm = 50 ÷ 1000 = 0.05 m

       5 mm = 5 ÷ 1000 = 0.005

Answer:

To convert millimeters to meters, multiply the number of millimeters by 0.001.

To convert meters to millimeters, multiply the number of meters by 1000.

Step-by-step explanation:

1 millimeter is 0.001 meters.

1 meter is 1000 millimeters.

To convert millimeters to meters, multiply the number of millimeters by 0.001.

Example:

This object is 100 millimeters long. How many meters long is it?

100 x 0.001 = 0.1

0.1 meters.

To convert meters to millimeters, multiply the number of meters by 1000.

Example:

This object is 100 meters long. How many millimeters long is it?

100 x 1000 = 100000

100000 millimeters.

Answer:

the answer is A. 2

Step-by-step explanation:

4x+2 has to be half of 2x+16

then 4x+2=10 and 2x+16=20 therefore it is correct

rate brainiest

The pic is your answer.

The null hypothesis states that the rate of home ownership has not increased since 2007, while the alternative hypothesis suggests that the rate of home ownership has increased since 2007.

In hypothesis testing, a Type I error occurs when the null hypothesis is rejected even though it is true. In this context, it would mean concluding that the rate of home ownership has increased since 2007 when it has actually remained the same or decreased. The consequence of a Type I error would be providing tax breaks to first-time homebuyers based on the false belief that the rate of home ownership has increased. This could lead to unnecessary financial costs for the city council.

On the other hand, a Type II error occurs when the null hypothesis is accepted even though it is false. In this scenario, a Type II error would mean failing to offer tax breaks to first-time homebuyers, assuming that the rate of home ownership has not increased since 2007 when, in reality, it has increased. The consequence of a Type II error would be missing the opportunity to incentivize first-time homebuyers and potentially boost the rate of home ownership in the city.

In this context, a more serious error would be a Type II error. If the city council fails to offer tax breaks to first-time homebuyers despite an actual increase in the rate of home ownership, it could hinder the growth of the housing market and discourage potential buyers. This may result in missed economic opportunities and hinder the city's efforts to address housing needs and stimulate growth.

For Type I error, those who would be harmed are the city council and taxpayers as they would bear the financial burden of providing tax breaks based on incorrect assumptions. For Type II error, those who would be harmed are the first-time homebuyers who could potentially miss out on tax benefits and opportunities to enter the housing market at a more affordable rate.

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The PERT expected activity time for this activity is 6 days.

To compute the PERT (Program Evaluation and Review Technique) expected activity time, we can use the formula:

Expected Time = (Optimistic Time + 4 * Most Likely Time + Pessimistic Time) / 6

Using the given values, we have:

Optimistic Time = 2 days

Most Likely Time = 5 days

Pessimistic Time = 14 days

Substituting these values into the formula:

Expected Time = (2 + 4 * 5 + 14) / 6

Expected Time = (2 + 20 + 14) / 6

Expected Time = 36 / 6

Expected Time = 6

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Answer:

6(21.25) = 127.5

It is given that the function g(x) is the inverse of f(x) so it follows:

It is given that f(-4)=9 so it follows:

So the value of g(9)-3f(-4) is given by:

Hence the value is -31.

Answer:

A. h(3) = 12

(3, 12)

B. h(-4) = -23

(-4, -23)

c.h(2/5) = -1

(2/5, -1)

Step-by-step explanation:

h(x)=5x-3

5(3)  -3 = 15 - 3 = 12

5(-4) - 3 = -20 - 3 = -23

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

Answer:

1, 3 &4

Step-by-step explanation:

The density of this sand is 1600 kg/m³.

What is the meaning of density?

The amount of something per unit of length, area, or volume: as. : the substance's mass per unit volume. In grams per cubic centimeter, density.

Given that the dimension of a cuboid is length 45 cm, width 30 cm and height 42 cm.

The volume of the cuboid is (45 × 30 × 42) cm³

                                              = 56,700 cm³

                                              = (56,700/100³) m³

                                              = 0.0567 m³

The mass of the sand is 90.72 kg.

The density of the sand is

= mass /volume

=90.72 kg / 0.0567 m³

= 1600 kg/m³

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A reflection is a figure over a line of flips in order to create a congruent image.

Each reflected point of the image should be the same distance the line of original image on the opposite side.

Pre-image: The image should being reflected, to the new image

Image The reflection of the pre-image.

What is transformation?

A transformation in mathematics and geometry is an operation performed on a given shape or graph that modifies it in some way. Translations, reflections, rotations, and dilations are frequently used transformations, and each of these transformations has unique properties.

The distance between an image and its pre-image from the line of reflection is constant. The pre-image and its image are identical if a point on the pre-image lies on the line of reflection. The segments of the line joining the corresponding vertices are parallel to the line of reflection.

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Answer:

3 months

Step-by-step explanation:

Given data

Gym A

$15 joining fee $35 monthly charge

let the number of months be x

and the total charges for x months be y

the expression for the total charges will be given as

y= 15+35x-----------------1

Gym B: No joining fee $40 monthly charge

let the number of months be x

and the total charges for x months be y

the expression for the total charges will be given as

y= 40x-----------------2

Equate 1 and 2

15+35x= 40x

collect like terms

15= 40x-35x

15= 5x

divide both sides by 5

x= 15/5

x= 3

Hence the number of months is 3 months