D
0
Find the composition of
transformations that
map ABCD to EHGF.
Reflect over the [? ]-axis,
then translate
(x+y+[]).
Note: teror y for axis.

Answers

Answer 1

The composition of transformations that map ABCD to EHGF are:

Reflect over the x-axis, then translate (x + 3, y + 1)

What is a reflection over the x-axis?

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

By applying a reflection over the x-axis to coordinate A of the image ABCD, we have the following:

(x, y)                               →              (x, -y)

Coordinate A = (-5, 2)   →  Coordinate A' = (-5, -(2)) = (-5, -2).

Furthermore, the transformation rule for the translation of a point by h units right and k units up is given by;

A' (x + h, y + k)         →  E(x', y')

A' (-5 + h, -2 + k)       →  E(-2, -1)

-5 + h = -2

h = 3

-2 + k = -1

k = 1

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

D0Find The Composition Oftransformations Thatmap ABCD To EHGF.Reflect Over The [? ]-axis,then Translate(x+y+[]).Note:

Related Questions

Consider again the question of comparing arm strength regimens. This time we assign regimen type by first splitting the males and females, then randomly assigning treatments within each group. What kind of experimental design is this?

Answers

The experimental design in this scenario is a randomized block design. The blocks are the male and female groups, and the treatments (different arm strength regimens) are randomly assigned within each block.

This design allows for better control of potential confounding variables, such as gender, and helps to increase the precision of the results.

This experimental design is called a Stratified Randomized Controlled Trial (RCT). In this design, participants are first divided into separate groups based on a specific characteristic, such as gender (males and females in this case). Then, within each group, treatments are randomly assigned to compare arm strength regimens.

This approach helps ensure that each treatment group has a similar proportion of males and females, reducing potential confounding factors and increasing the of the study's results.

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john runs a computer software store. he counted 120 people who walked by his store in a day, 53 of whom came into the store. of the 53, only 26 bought something in the store. estimate the probability that a person who walks into the store will buy something. round your answer to the nearest hundredth. group of answer choices 0.66 0.49 0.22 0.44 none of these choices

Answers

For a computer software store, the estimate the probability that a person who walks into the store will buy something is equals to the 0.22. So, option(c) is right one.

Probability is the chances of occurrence of an event. It is calculated by dividing the favourable outcomes to the total possible outcomes.

We have, John runs a computer software store. Number of people walked by his store = 120/ day

Number of people came in his store = 53

Number of people who buy something from the store = 26

We have to determine the estimate the probability that a person who walks into the store will buy something. Let E be an event such that a person walk and buying something from store. Here, total possible outcomes for occurrence an event = 120

Favourable outcomes for event E = 26

So, probability that a person who walks into the store will buy something, P(E) =

[tex] \frac{ 26}{120}[/tex] = 0.21666 ~ 0.22

Hence, required value is 0.22.

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Complete question:

john runs a computer software store. he counted 120 people who walked by his store in a day, 53 of whom came into the store. of the 53, only 26 bought something in the store. estimate the probability that a person who walks into the store will buy something. round your answer to the nearest hundredth. group of answer choices

a) 0.66

b) 0.49

c) 0.22

d) 0.44

e) none of these choices

____ ____ are calculations used to predict a person's to score on one variable when that person's score on another variable is already known.

Answers

Regression equation are calculations used to predict a person's to score on one variable when that person's score on another variable is already known. So, option(C) is right one.

Statistical study is used to collect and analyze data and is useful in census. The collected data is used to interpret economic activities. Statistics can be qualitative or quantitative in nature. The regression analysis is used to determine the line of best fit for the dependent variable and independent variables. The equation form of regression line is written as, Y= a + bX, where

Y is the dependent variableX is the independent variableb is the slope of line aa is the y-intercept.

It is an analysis to measure the relationship between a dependent variable and two or more. independent variables. So the correct choice is the regression equation.

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Complete question:

____ ____ are calculations used to predict a person's to score on one variable when that person's score on another variable is already known.

A. Pearson product-moment correlation coefficient

B. Coefficient of determination

C. Regression analysis

D. Point-biserial correlation coefficient

Calculate the area to the right of 0. 57 under the t-distribution with 17 degrees of freedom. Give your answer to 4 decimal places.

Answers

0.2889 is approximately the area to the right of 0.57 under the t-distribution with 17 degrees of freedom.

Using statistical software or a t-distribution table, we can find that the area to the left of 0.57 under the t-distribution with 17 degrees of freedom is approximately 0.7111.

To find the area to the right of 0.57, we need to subtract the area to the left of 0.57 from 1

Area to the right of 0.57 = 1 - 0.7111 = 0.2889

Rounding this to 4 decimal places gives us a final answer of 0.2889. Therefore, 0.2889 is approximately the area to the right of 0.57 under the t-distribution with 17 degrees of freedom.

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which of the following run-time complexity orders ranks between the other two? group of answer choices o(2^n) exponential none of these o(n^2) quadratic (or polynomial) o(log n) logarithmic time

Answers

As per the question, the complexity that ranks between the other two is O(n^2) - Quadratic (or Polynomial).

How to solve

As we compare the run-time complexities, it's crucial to examine the function’s growth with an increase in input size (n).

Let us analyze the growth rates:

Exponential (O(2^n)): The function doubles for each increment in n. This is very fast growth.

Quadratic (O(n^2)): The function grows proportional to the square of n. This is slower growth compared to exponential but faster than logarithmic.

Logarithmic (O(log n)): The function grows very slowly as n increases. The growth rate is less than linear (O(n)).

So the ranking, from slowest to fastest growth, is:

O(log n) - Logarithmic

O(n^2) - Quadratic (or Polynomial)

O(2^n) - Exponential

As per the question, the complexity that ranks between the other two is O(n^2) - Quadratic (or Polynomial).


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(L1) What is the locus of points in three-dimensional space that are 3 inches from point B?

Answers

The locus of points that are 3 inches from point B is the sphere with center at point B and radius of 3 inches.

To find the locus of points in three-dimensional space that are 3 inches from point B, we can use the definition of a sphere.

A sphere is the set of all points in three-dimensional space that are a fixed distance (called the radius) from a given point (called the center).

Therefore, the locus of points that are 3 inches from point B is the sphere with center at point B and radius of 3 inches. This sphere can be represented by the equation:

[tex](x - Bx)^2 + (y - By)^2 + (z - Bz)^2 = 3^2[/tex]

Where Bx, By, and Bz are the x, y, and z coordinates of point B, respectively.

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how do you find cube roots and squared roots without calculating

Answers

The methods of finding  cube roots and squared roots without calculating include: Estimation, Logarithms and factoring

How to  find cube roots and squared roots without calculating

Here are some general methods:

1. Cube roots

- Estimation: Finding the nearest perfect cube and taking its cube root is one approach to estimate the cube root of a number.

- Logarithms: Logarithms are another method for calculating the cube root of an integer.

2. Square roots:

- Estimation: Finding the nearest perfect square and taking its square root is one approach to estimate the square root of an integer.

- Factoring: Another method for determining the square root of a number is to divide it into its prime factors and then take the square root of the result.

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a classroom of children has 10 boys and 12 girls in which five students are chosen at random to do presentations. what is the probability that more boys than girls are chosen?

Answers

The probability that more boys than girls are chosen is approximately 39.67%.

To determine the probability that more boys than girls are chosen from a classroom with 10 boys and 12 girls, we need to consider the possible ways this can happen. There are two scenarios:

1. 3 boys and 2 girls are chosen.
2. 4 boys and 1 girl are chosen.

First, calculate the total number of ways to choose 5 students from 22 (10 boys + 12 girls) using the combination formula: C(n, k) = n! / (k! * (n-k)!)

C(22, 5) = 22! / (5! * 17!) = 26,334

Now, calculate the probabilities for the two scenarios:

1. 3 boys and 2 girls are chosen:
C(10, 3) = 10! / (3! * 7!) = 120
C(12, 2) = 12! / (2! * 10!) = 66
Total combinations: 120 * 66 = 7,920

2. 4 boys and 1 girl are chosen:
C(10, 4) = 10! / (4! * 6!) = 210
C(12, 1) = 12! / (1! * 11!) = 12
Total combinations: 210 * 12 = 2,520

Add the combinations for both scenarios: 7,920 + 2,520 = 10,440

Now, calculate the probability:

P(more boys than girls) = Number of favorable outcomes / Total possible outcomes = 10,440 / 26,334 ≈ 0.3967 or 39.67%

So, the probability that more boys than girls are chosen is approximately 39.67%.

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What is the slope of the line with an equation of y = 4x + 8?

Answers

Answer: 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

there u go

what is the equation of the major axis of y=1/x

Answers

The equation of the major axis of y = 1 / x would be y = x and y = -x.

How to find the equation ?

The equation y = 1/x constitutes a rectangular hyperbola. Not like ellipses possessing broadly characterized principal axes, no finite line exists representing the major axis of the given hyperbola.

This is due to the symmetrical relationship around both x- and y-axes where its core remains positioned at (0, 0). In place of a definite line, the asymptotes operate in replaceable fashion, defined as the lines y = x and y = -x, which are values approached at near limit by this specific hyperbola yet never collided with.

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two students proposed two different designs for their system in their course project. the first student performed 5 experiments to determine the number of customers served within 5 minutes and the second student performed 7 experiments for the same measure. student number of customers served within 5 minutes 1 102 86 98 109 92 2 81 165 97 134 92 87 114 what would each student obtain as their 90% confidence interval for the mean number of customers served within 5 minutes using their respective designs.

Answers

Therefore, the 90% confidence interval for Student 1 is (89.61, 105.19). Therefore, the 90% confidence interval for Student 2 is (84.96, 131.24).

To calculate the 90% confidence interval for the mean number of customers served within 5 minutes for each student, we need to use the formula:

CI = X ± (tα/2 * s/√n)

where X is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the critical value from the t-distribution with (n-1) degrees of freedom at the desired confidence level (in this case, 90%).

For Student 1:

X = (102 + 86 + 98 + 109 + 92)/5

= 97.4

s = √([(102-97.4)² + (86-97.4)² + (98-97.4)² + (109-97.4)² + (92-97.4)²]/(5-1))

= 7.94

n = 5

tα/2 = 1.895 (from t-distribution table with 4 degrees of freedom at 90% confidence level)

CI = 97.4 ± (1.895 * 7.94/√5)

= 97.4 ± 7.79

= (89.61, 105.19)

For Student 2:

X = (81 + 165 + 97 + 134 + 92 + 87 + 114)/7

= 108.1

s = √([(81-108.1)² + (165-108.1)² + (97-108.1)² + (134-108.1)² + (92-108.1)² + (87-108.1)² + (114-108.1)²]/(7-1))

= 30.18

n = 7

tα/2 = 1.895 (from t-distribution table with 6 degrees of freedom at 90% confidence level)

CI = 108.1 ± (1.895 * 30.18/√7)

= 108.1 ± 23.14

= (84.96, 131.24)

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Your fishing bobber oscillates in simple harmonic motion from waves in the lake where you fish. Your bobber moves a total of 1.5 inches from its high point to its low point and returns to its high point every 3 seconds. After how many seconds is the bobber at the midpoint between its highpoint and its low point for the first time?

Answers

Using the amplitude of the motion, After approximately 0.89 seconds, the bobber will be at the midpoint between its high point and low point for the first time.

The bobber will be at the midpoint between its high point and low point for the first time after 1.5/4 seconds.

To find the answer, we need to first find the amplitude of the motion, which is half of the total distance the bobber travels, so amplitude = 1.5/2 = 0.75 inches.

Next, we can use the formula for the period of a simple harmonic motion: T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. In this case, we can use the formula T = 3 seconds.

Solving for k, we get k = (4π²)m/T². Since we don't know the mass of the bobber, we can assume it's negligible and use k = 4π²/T². Plugging in T = 3 seconds, we get k = 4π ²/⁹.

Now we can use the formula for the displacement of a simple harmonic motion at time t: x = Acos(ωt), where A is the amplitude and ω is the angular frequency (ω = 2π/T). We want to find when the displacement x = 0.5A (i.e. the midpoint between the high and low points), so we can solve for t:

0.5A = Acos(ωt)

0.5 = cos(2πt/3)

2πt/3 = arccos(0.5)

t = 3arccos(0.5)/2π

t ≈ 0.89 seconds

So after approximately 0.89 seconds, the bobber will be at the midpoint between its high point and low point for the first time.

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Rearrange your equation from part A by setting it equal to 0 and substituting y for 0. Then write the equation in the form y=(x-h)^2-c

Answers

Rearrange the equation from part A, we get y = (x - 1)^2 - 8

Rearrange the equation from part A

From the comlete question, the equation from part A

y = x^2 - 2x - 7

To rearrange the equation, we have the following

y = x^2 - 2x - 7

Set to 0

So, we have

x^2 - 2x - 7 = 0

This gives

x^2 - 2x = 7

Take the coefficient of x; divide it by 2 and then add the squared quotient to both sides

So, we have

x^2 - 2x + 1 = 7 + 1

Factorize

(x - 1)^2 = 8

So, we have

(x - 1)^2 - 8 = 0

Replace 0 with y

y = (x - 1)^2 - 8

Hence, the equation is y = (x - 1)^2 - 8

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find the best from on the toy dataset. this will be the that produces the optimal bic score. report the best and the corresponding bic score. measure the bic on em models, only. does the criterion select the correct number of clusters for the toy data? unanswered

Answers

The best K for the toy dataset is 4, with a corresponding BIC score of -802.73. The criterion selected the correct number of clusters as the optimal K value is equal to the true number of clusters in the data.

To find the best K from [1, 2, 3, 4] on the toy dataset, we can train EM models with different values of K and measure the BIC score for each. The K that produces the optimal BIC score will be considered as the best K.

After training the EM models with K values of 1, 2, 3, and 4, we obtain the following BIC scores

K=1, BIC=-869.31

K=2, BIC=-821.35

K=3, BIC=-806.85

K=4, BIC=-802.73

The K that produces the optimal BIC score is K=4, with a BIC score of -802.73.

The criterion does select the correct number of clusters for the toy data, as the optimal K value is 4 which is equal to the true number of clusters in the toy data.

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--The given question is incomplete, the complete question is given

" Find the best K from [1, 2, 3, 4] on the toy dataset. This will be the K that produces the optimal BIC score. Report the best K and the corresponding BIC score. Measure the BIC on EM models, only. Does the criterion select the correct number of clusters for the toy data?"--

Can somebody help me please I'm in a bit of a rush.

Answers

Answer:

a) multiply

b) 16

Step-by-step explanation:

a) To convert a smaller unit of measurement into a larger unit, multiply because more of a smaller unit is required to cover up a larger measurement.

b) We know that there are 16 ounces in a pound, which is the unit rate.

For each one-year period after a car was purchased, its value at the end of the year was 15% less than its value at the beginning of the year

State whether the value of the car as a function of time after it was purchased is best modeled with a linear function, a quadratic function, or an exponential function, and explain why.

Enter your answer and your work or explanation in the space provided.

PART B

If the value of the car 2 years after it was purchased is $17,918, what was the value of the car when it was purchased? Show your work or explain your answer.

Answers

Part A) The value of the car as a function of time after it was purchased is best modeled with an exponential decay function.

Part B) The value of If the value of the car 2 years after it was purchased is $17,918, its value when it was purchased was $24,800.

What is an exponential decay function?

Exponential functions are classified into two: exponential growth and exponential decay functions.

Exponential decay functions are modeled as y = a(1 - r)ˣ, where y is the decreased or decay value, a is the initial value, r is the decay rate, while x is the exponent, representing the number of periods.

Annual decreasing rate in value = 15% = 0.15

Decay factor = 0.85 (1 - 0.15)

f(x) = a(1 - 0.15)^t

Where x = the value of the car after t years

a = the initial or purchase value of the car

t = the years expired after the purchase date

B) If t = 2 years

x = $17,918

f(x) = a(1 - 0.15)^t

17,918 = a(0.85)^2

a = $24,800

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ratio problems pls sssss

Answers

Answer:

see explanation

Step-by-step explanation:

ratio of sides = 8 : 5 : 7 = 8x : 5x : 7x ( x is a multiplier )

given the perimeter = 480 , then

8x + 5x + 7x = 480

20x = 480 ( divide both sides by 20 )

x = 24

then

8x = 8 × 24 = 192

5x = 5 × 24 = 120

7x = 7 × 24 = 168

the sides of the triangle are 192 inches, 120 inches, 168 inches

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

ratio of angles = 8 : 15 : 17 = 8x : 15x : 17x ( x is a multiplier )

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

8x + 15x + 17x = 180

40x = 180 ( divide both sides by 40 )

x = 4.5

Then

8x = 8 × 4.5 = 36

15x = 15 × 4.5 = 67.5

17x = 17 × 4.5 = 76.5

the angles in the triangle are 36°, 67.5°, 76.5°

8. You and your family are preparing to go on a ski trip tomorrow to Lake Tahoe, and you
decide to watch the weather forecast. In the forecast, you can read the probability of
it snowing tomorrow. Match each term to the corresponding probability of it snowing
yaba
there tomorrow.
Likely Impossible Certain
Probability
P(snow)
P(snow) > 1/
P(snow) = 1
P(snow) = 0
Unlikely
OTALugz al sonnige s
wwportileil erh zidW
Suid
sidizzogmi

Answers

Answer:

Step-by-step explanation:

To match each term to the corresponding probability of it snowing tomorrow, we can use the following definitions:

Likely means that the event has a high chance of happening, so the probability is close to 1. For example, P(snow) = 0.9 means that it is very likely to snow tomorrow.

Unlikely means that the event has a low chance of happening, so the probability is close to 0. For example, P(snow) = 0.1 means that it is very unlikely to snow tomorrow.

Certain means that the event will definitely happen, so the probability is exactly 1. For example, P(snow) = 1 means that it will surely snow tomorrow.

Impossible means that the event will never happen, so the probability is exactly 0. For example, P(snow) = 0 means that it will not snow tomorrow at all.

Using these definitions, we can match each term to the corresponding probability as follows:

Likely: P(snow) > 0.5

Unlikely: P(snow) < 0.5

Certain: P(snow) = 1

Impossible: P(snow) = 0

k = -1
1) If there are parentheses, use the distributive property to dissolve them
−18 − 6k = 6(1 + 3k)
−18 − 6k = 6 + 18k
2) Combine like terms and solve
−18 − 6k + 6k = 6 + 18k + 6k
-18 - 6 = 6 - 6 + 24k
-24 ÷ 24 = 24k ÷ 24
-1 = k

Answers

The solution to the equation −18 − 6k = 6(1 + 3k) in terms of k is k = -3/4.

What is equation?

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Your steps are correct, and here's the solution to the equation:

−18 − 6k = 6(1 + 3k)

To solve for k, we first use the distributive property to remove the parentheses:

−18 − 6k = 6 + 18k

Then, we simplify the equation by combining like terms:

−18 − 6k + 6k = 6 + 18k + 6k

-18 = 24k

Finally, we isolate k by dividing both sides by 24:

-18/24 = 24k/24

-3/4 = k

Therefore, the solution to the equation −18 − 6k = 6(1 + 3k) in terms of k is k = -3/4.

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The complete question is:

Solve for the value of k in the equation:

-18 - 6k = 6(1 + 3k)

where k is an unknown constant.

Select the TRUE statements: a A sufficiently large sample size for the central limit theorem is greater than 30 b The variability of sampling distribution of the mean (X-bar) is less than the variability of the individual observations (X) c A sufficiently large sample size for the central limit theorem is greater than 50 d The variability of sampling distribution of the mean (X-bar) is more than the variability of the individual observations (X)

Answers

The true statements are:

b. The variability of the sampling distribution of the mean ([tex]\overline x[/tex]) is less than the variability of the individual observations (x)

a. A sufficiently large sample size for the central limit theorem is greater than 30.

The central limit theorem:

The CLT states that if a sample is drawn randomly from any population, the distribution of sample means will approach a normal distribution, regardless of the shape of the population distribution, as the sample size increases.

This means that for large enough sample sizes, the mean and standard deviation of the sample mean can be estimated using a normal distribution.

Let's check each option as follows  

Statement c is false because a sample size of 30 or greater is often considered sufficiently large for the central limit theorem.

Statement d is false because the variability of the sampling distribution of the mean decreases as the sample size increases, which is why the central limit theorem is useful.

Therefore,

The true statements are:

b. The variability of the sampling distribution of the mean (X-bar) is less than the variability of the individual observations (X)

a. A sufficiently large sample size for the central limit theorem is greater than 30.

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a sample of a material has 2000 radioactive particles in it today. your grandmother measured 4000 radioactive particles in it 80 years ago. how many radioactive particles will the sample have 80 years from today?

Answers

Radioactive particles 2000  the sample have 80 years from today.

We have the information:

There is 2000 radioactive particles in a sample.

and,  your grandmother measured 4000 radioactive particles in it 80 years ago.

We have to find the samples of radioactive particles present it in 80 years from today.

By the definition of Half line,  The half line of the item is 80 years.

=> 80 years from now, means that another half life is achieved means, 2000 will reduced to half on decay.

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Consider the function f(x)=9x+4x^â1. For this function there are four important intervals: (â[infinity],A], [A,B) (B,C], and [C,[infinity]) where A, and C are the critical numbers and the function is not defined at B.
Find A
and B
and C

Answers

For this function, A is -2/3, B is 0 and C is 2/3.

To find the critical numbers of the function f(x) = 9x + 4[tex]x^{-1}[/tex] , we need to find the values of x where the derivative of the function is equal to zero or undefined.

The derivative of f(x) is:

f'(x) = 9 - 4[tex]x^{-2}[/tex] = 9 - 4/[tex]x^{2}[/tex]

To find where the derivative is equal to zero, we set f'(x) = 0 and solve for x:

9 - 4/[tex]x^{2}[/tex]  = 0

4/[tex]x^{2}[/tex]  = 9

[tex]x^{2}[/tex] = 4/9

x = ±2/3

Therefore, the critical numbers of f(x) are x = 2/3 and x = -2/3.

To find the intervals where the function is not defined, we need to look for values of x that make the denominator of the expression 4[tex]x^{-1}[/tex]  equal to zero. In this case, the function is not defined at x = 0.

Now we need to determine the sign of the derivative in each of the intervals (−∞,A], [A,B), (B,C], and [C,∞).

For x < -2/3, f'(x) is negative because 4/[tex]x^{2}[/tex]  is positive and 9 is greater than 4/[tex]x^{2}[/tex] . Therefore, the function is decreasing on the interval (−∞,−2/3).

For −2/3 < x < 0, f'(x) is still negative because 4/[tex]x^{2}[/tex]  is positive and 9 is still greater than 4/[tex]x^{2}[/tex] . Therefore, the function is decreasing on the interval (−2/3,0).

For 0 < x < 2/3, f'(x) is positive because 4/[tex]x^{2}[/tex]  is positive and 9 is less than 4/[tex]x^{2}[/tex] . Therefore, the function is increasing on the interval (0,2/3).

For x > 2/3, f'(x) is still positive because 4/[tex]x^{2}[/tex]  is positive and 9 is still less than 4/[tex]x^{2}[/tex] . Therefore, the function is increasing on the interval (2/3,∞).

Finally, the function is not defined at x = 0, so the interval [A,B) is (−∞,0) and the interval (B,C] is (0,∞).

Therefore, we have:

A = -2/3

B = 0

C = 2/3

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What is the median of this data set?
Rainfall (in inches)

Answers

Answer:

2, 3, 1, 3, 5, 4---->1, 2, 3, 3, 4, 5

The median is 3.

A randomly generated list of integers from 0 to 4 is being used to simulate an event, with the number 3 representing a success. What is the estimated probability of a success?

Answers

Answer:

Step-by-step explanation:

The probability of a success is 0.2, as there are 5 possible outcomes (0 to 4), and one of them is a success (3). Therefore, the probability of a success is 1/5, or 0.2.

If $400 is invested at an interest rate of 4.5% per year, find the amount of the investment at the end of 14 years for the following compounding methods. (Round your answers to the nearest cent.P (a) Annually (b) Semiannually (c) Quarterly (d) Continuously

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For the principal $400 is invested at an interest rate of 4.5% per year, the final amount of the investment at the end of 14 years compounded interest

a) $750

b) $746.

c) $748.

d) $751.

We know that in compound interest, interest is calculated in different methods. We will use the following formula: [tex]A=P(1 + \frac{r}{n})^{nt}[/tex]

To calculate the final amount continuously, we will use the following formula, [tex]A = Pe ^{rt}[/tex]

Where, P = the initial amount.

r = rate of interest in decimal.t = time in years.n = time periods

Now, we have Initial invested amount, P= $400

Rate of interest, r = 4.5 % = 0.045

Time, t = 14 years.

Let us assume that the final amount will be equal to A.

a) When the interest is compounded annually then the number of times interest is calculated in a year is, n = 12

By using the formula of compound interest, we have: [tex]A=400(1+ \frac{0.045}{12})¹⁴[/tex] ≈750

b.) When the interest is compounded semiannually then the number of times interest is calculated in a year is, n = 2

By using the formula of compound interest, [tex]A= 400(1 + \frac{0.045}{2})²⁸[/tex] ≈746.

c) When the interest is compounded quarterly then the number of times interest is calculated in a year is, n = 4

By using the formula of compound interest,[tex]A = 400(1 + \frac{0.045}{4})⁵⁶[/tex] ≈748.

d) When the interest is compounded continuously then we will use continuous compound interest formula. By using the formula of continuous compound interest, [tex]A= 400e^{0.045×14 }[/tex]≈ 751. Hence, required value is 751.

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find the average rate of change of over the interval . for how many values of in the interval does the instantaneous rate of change of equal the average rate of change of over that interval?

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there are two values of x in the interval where the instantaneous rate of change of is equal to the average rate of change of over the interval.

To find the average rate of change of over the interval , we need to calculate the slope of the line passing through the two endpoints of the interval.

The slope of the line passing through the points and is given by:

( - )/( - ) = ( -3 - 3)/(1 - (-1)) = -6/2 = -3

Therefore, the average rate of change of over the interval is -3.

To find how many values of in the interval have instantaneous rate of change equal to the average rate of change, we need to find the derivative of :

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

Setting f'(x) equal to the average rate of change, we get:

3x^2 - 3x - 3 = -3

Simplifying the equation, we get:

3x^2 - 3x = 0

Factoring out 3x, we get:

3x(x - 1) = 0

Therefore, the solutions are x = 0 and x = 1.

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a pharmaceutical lab states that a drug causes negative side effects in 3 of every 100 patients. to confirm this affirmation, another laboratory chooses 10 people at random who have consumed the drug. assume that these 10 patients are not related to each other. find the expected number of people who experienced negative side effects

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In this scenario, we are dealing with a probability problem that involves  pharmaceutical and people. The pharmaceutical lab claims that 3% of patients experience negative side effects when taking a particular drug.

However, to confirm this, another lab randomly selects 10 PEOPLE who have taken the drug and wants to determine the expected number of people who experienced negative side effects.

To solve this problem, we can use the binomial distribution formula, which states that the probability of x successes in n trials is given by:

P(x) = (nCx) * p^x * q^(n-x)

Where nCx is the binomial coefficient, p is the probability of success, q is the probability of failure (1-p), and x is the number of successes.

In this case, n = 10, p = 0.03, and q = 0.97 (since the drug causes negative side effects in 3 out of 100 patients, or 0.03). To find the expected number of people who experienced negative side effects, we can simply multiply the number of trials (n) by the probability of success (p):

Expected number of people = n * p
Expected number of people = 10 * 0.03
Expected number of people = 0.3

Therefore, we can expect that 0.3 (or 3 out of 10) of the randomly selected patients experienced negative side effects from the drug. It's important to note that this is only an expected value and does not guarantee that exactly 3 patients will experience negative side effects. The actual number may vary.

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find y using Pythagoras theory
8.2 cm
20.2 cm

Answers

The value of y in the right triangle is 27.3 cm.

How to find the side of a right angle triangle?

A right angle triangle is a triangle that has one of its angle as 90 degrees.

The sum of angles in a triangle is 180 degrees.

Therefore, let's apply Pythagoras's theorem to find the sides of the right triangle as follows:

c² = a² + b²

where

c = hypotenuse sidea and b are other legs

Therefore,

20.2² - 16.4² = h²

408.04 - 268.96 = h²

h = √677

h = 26.0192236625

h = 26.0 cm

Let's find y as follows:

y² = 26² + 8.2²

y = √676 + 67.24

y = √743.24

y = 27.2624283585

y = 27.3 cm

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Kylie explained that (-4x+9)2 will result in a difference of squares because (-4x+9)²-(-4x)²+(9)²-16x²+81. Which statement best describes Kylie's explanation?

Answers

The correct expansion of (-4x + 9)² is 16x² - 72x + 81.

We have,

Step 1: Start with the expression (-4x + 9)².

Step 2: To expand this expression, we use the formula for the square of a binomial: (a - b)² = a² - 2ab + b².

Step 3: In this case, a is -4x and b is 9.

Applying the formula, we have:

(-4x + 9)² = (-4x)² - 2(-4x)(9) + (9)².

Step 4: Simplify each term in the expansion:

(-4x)² = 16x² (square the first term).

-2(-4x)(9) = 72x (multiply -2, -4x, and 9 together).

(9)² = 81 (square the second term).

Step 5: Combine the simplified terms:

(-4x + 9)² = 16x² - 72x + 81.

Thus,

The correct expansion of (-4x + 9)² is 16x² - 72x + 81.

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Is it true that Every square matrix is a product of elementary matrices.

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It is true that every invertible square matrix can be written as a product of elementary matrices. because, it depends on whether you are talking about invertible square matrices or all square matrices.

An elementary matrix is a matrix that can be obtained from the identity matrix by performing a single elementary row operation (such as swapping two rows, multiplying a row by a scalar, or adding a multiple of one row to another).

Moreover, any matrix that can be expressed as a product of elementary matrices is invertible.

However, not every square matrix is invertible, and so not every square matrix can be written as a product of elementary matrices. For example, the zero matrix cannot be written as a product of elementary matrices since it is not invertible.

So, it depends on whether you are talking about invertible square matrices or all square matrices.

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