Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown: A coordinate grid is shown from negative 5 to 0 to 5 on both x -and y-axes. A polygon ABCD has A at ordered pair 1, 3, B at ordered pair 3, 4, C at ordered pair 2, 1, D at ordered pair 1, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 3, 3, B prime at ordered pair negative 5, 4, C prime at ordered pair negative 4, 1, D prime at ordered pair negative 3, 1. Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?

The coordinate vector of p(t) relative to the basis B is [11, -9, 4].

Given data:

To find the coordinate vector of p(t) relative to the basis B, we need to express p(t) as a linear combination of the basis vectors.

Given that the basis B consists of the Laguerre polynomials 1, 1−t, and 2−4t+t², we want to find the scalars c1, c2, and c3 such that:

p(t) = c₁ * 1 + c₂ * (1−t) + c₃ * (2−4t+t²)

Comparing the coefficients of corresponding terms, we can set up a system of equations:

10 − 13t + 4t² = c₁ + c₂ + 2c₃

-13 = -c₂ - 4c₃

4 = c₃

Solving this system of equations, we find:

c₁ = 11

c₂ = -9

c₃ = 4

Hence, the coordinate vector of p(t) relative to the basis B is [11, -9, 4].

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Answer:

Step-by-step explanation:

\(8.5+50\%\times8.5=8.5+0.5\times8.5=8.5+4.25=12.75\)

To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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To solve equations with fractions and variables in the denominator, we need to eliminate it by moving it to the other side. To do this, we multiply both sides of the equation by the term in the denominator. This will cancel out the fraction and leave us with a simpler equation to solve.

For example, suppose we have the equation (3 + x) / x = 2. To get rid of the fraction, we multiply both sides by x. This gives us: x * (3 + x) / x = x * 2. The x in the numerator and denominator cancel out, leaving us with:

3 + x = 2x. Now we can solve for x by subtracting x from both sides: 3 = x

This is the solution of the equation.

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Answer:

9

Step-by-step explanation:

d=rt

12x45/60

12x0.75

9=d

Answer:

Step-by-step explanation:

For a data set, half of the observations are always greater than the median. The median is the middle value in a set of data when it is arranged in order of increasing or decreasing magnitude.

It is a measure of central tendency that is more robust to outliers than the mean. The median splits the data set in half, with half of the observations being greater than it and half being less than it.

The median is a crucial measure of central tendency that helps us understand the distribution of a data set. It represents the value that separates the top half of the data from the bottom half. The median is often used as an alternative to the mean when the data set contains outliers or extreme values that can skew the mean. The median is easy to calculate and provides a clear picture of the middle of a data set. Therefore, it is a useful tool for statisticians, researchers, and analysts who need to summarize and describe data sets accurately.

In summary, the median is the value that divides a data set into two equal halves, with half of the observations being greater than it and half being less than it. It is a robust measure of central tendency that is widely used in statistics to describe the distribution of data sets.

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The more variable the data, the less accurate the sample mean will be as an estimate of the population mean. In statistical analysis, accuracy is important. Statistical analysis is a method of gathering and examining data to uncover useful information.

A sample mean is a numerical estimate that represents a data set's central tendency. The population mean, on the other hand, is a statistical measure that represents the mean value of the entire population. The difference between the two lies in the fact that sample mean is computed on a subset of the population whereas population mean is calculated for the entire population. If the variability of the sample data is large, the sample mean becomes less accurate as an estimate of the population mean.

As a result, the more variable the data, the less accurate the sample mean will be as an estimate of the population mean.Therefore, it is essential to examine the variability of the data in order to better estimate the population mean. The greater the variability in the data, the more difficult it becomes to identify the true population mean and the less accurate the sample mean is as an estimator of the population mean.

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Answer:

x(x+3)(x-3)

Step-by-step explanation:

Factor out common term x

=x(x^2-9)

Factor x^2-9;

(x+3)(x-3)

=x(x+3)(x-3)

Answer:

x(x + 3)(x - 3)

Step-by-step explanation:

What we're given is a difference of squares multiplied by x.  If we start by factoring x out, we can simply expand the binomial:

x³ - 9x

= x(x² - 9)

= x(x + 3)(x - 3)

Any time you see an expression in the format a² - b², that is called a difference of squares, and can always be expanded out to (a + b)(a - b).  In this case, a is x, and b is 3.

Answer:

Step-by-step explanation:

The slope-intercept form:

y = mx + b

Where m is the slope and b is the Y-intercept

m = 9,   b = 13

so:

y = 9x + 13

Answer:

y= -10

Step-by-step explanation:

its going down by ten every 5

Answer:

Question 1= y= -2x         (y-int=180)

Question 2= y= 70x+20

Question 3= y= -7/10x    (y-int=109)

Question 4= y= 1/3x      (y-int=25/3 or 8 1/3)

Question 5= y= -20x+40

Brainliest Plz?

The value of f(4) is 28.

it can be found using the fundamental theorem of calculus.

The fundamental theorem of calculus states that if a function f is continuous on an interval and its derivative f' exists on that interval, then the definite integral of f' over the interval is equal to the difference in the values of the original function at the endpoints of the interval.

In this case, we are given that f '(x) is continuous, and that the definite integral of f '(x) over the interval [3, 4] is equal to 18. Therefore, using the fundamental theorem of calculus, we have that f(4) - f(3) = 18, and since f(3) = 10, we can solve for f(4) to get f(4) = 10 + 18 = 28.

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Complete question:

If f(3) = 10, f ' is continuous, and   \(\int\limits^4_3\) f '(x) dx = 18, what is the value of f(4)?

Answer:

x=17

Step-by-step explanation:

Answer:

X = 17

Step-by-step explanation:

Use M A T H W A Y  to solve equations

Answer:

15

Step-by-step explanation:

If 20 questions are worth 2 points ,the rest will be worth 4 point questions ....its 35-20 which is 15

Answer:

x = 18

Step-by-step explanation:

2x = 36

you divide by 2 on both sides, x is issolated and 36/2 is equal to 18.

Answer:

  A -- the curves that are not parabolas

Step-by-step explanation:

The inverse relation will only be a function if it passes the vertical line test: a vertical line cannot intersect the curve at more than one point.

A "half-parabola" can have an inverse function.

A parabola will have an inverse relation that is not a function. When x-values are repeated, as "goes through (5, 2) and goes through (5, -2)", the relation is not a function.

The graph that shows inverse functions is attached. A function and its inverse are mirror images of each other in the line y=x.

Answer:

A

Step-by-step explanation:

To find the function values, we need to substitute the given values of x into the function:

a) f(2) = 95(0.84)^2 ≈ 66.96

This means that after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.

b) f(6) = 95(0.84)^6 ≈ 35.33

This means that after 6 hours, there are approximately 35.33 milligrams of medicine remaining in the person's bloodstream.

To determine an appropriate domain for the function, we need to consider the context of the problem. The function represents the amount of medicine remaining in a person's bloodstream after taking a dose of medication, so the domain should be the set of non-negative real numbers, since the amount of medicine cannot be negative and time cannot be negative. Therefore, an appropriate domain for the function is [0, ∞).

Interpretation: The function f(x) = 95(0.84)^x models the amount of medicine, in milligrams, remaining in a person's bloodstream after x hours of taking the medication. For example, after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.

After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after x hours can be modeled by the function

To find:

Interpret the given function values and determine an appropriate domain for the function.

Solution:

The general form of an exponential function is

Where, a is the initial value, 0<b<1 is decay factor and b>1 is growth factor.

We have,

Here, 110 is the initial value and 0.83 is the decay factor.

It means, the amount of medicine in the person's bloodstream after taking the dose is 110 milligrams and the amount of medicine decreasing in the person's bloodstream with the decay factor 0.83 or decreasing at the rate of (1-0.83)=0.17=17%.

We know that an exponential function is defined for all real values of x but the time cannot be negative. So, x must be non negative.

We know that  for any value of x. So,  for all values of x.

Therefore, domain of the function is  and the range is .

Hope this helps!!!

GTPex-

Answer:

5

Step-by-step explanation:

total cost of hotel stay = cost per night + tax + parking charge + tips

tax = 10% x 90

= 0.1 x 90 = 9

let x = number of stays

90x + 9x + 12 + 30 ≤ 600

combine like terms

99x ≤  558

x ≤ 5.6

if they stay 5 nights, they would spend 537

if they stay 6 nights, they would spend 636

Answer:

5

Step-by-step explanation:

Answer:1

Step-by-step explanation:

Answer:

D, D, B, A, None

Step-by-step explanation:

-15 + -14 + -13 + -12 = -54

-12 + -10 + -8 + -6 = -36

16+ 18+ 26 = 54

-10 + -8 + -6 + -4 = -28

No answers are correct...

A function that represents this situation of selling 3 duct tape wallet per day out of of 160 duct tapes wallets produced is

Information from the problem

You have made 160 duct tape wallets to sell

If you sell 3 each day

From the information we can deduce that

assuming amount left is y and the number of days x the  we have

y = 160 - 3x

Therefore we can say that the expression to represent the situation of selling 3 duct tape wallet per day is  y = 160 - 3x

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Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

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Answer:

2p < 7

Step-by-step explanation:

Two p which is 2p is less than or fewer than 7. No equal to so no line under it.

The inequality 2p < 7 represents the word sentence "Twice a number p is fewer than 7" and indicates that the value of p must be less than 3.5.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The word sentence "Twice a number p is fewer than 7" can be written as the inequality:

2p < 7

In this inequality, "2p" represents twice the value of the number p, and "7" represents the value that twice the number p is fewer than.

To explain further, if we divide both sides of the inequality by 2, we get:

p < 3.5

This means that the value of p is less than 3.5. So, any number that is less than half of 7 (which is equal to 3.5) satisfies the inequality.

Therefore, the inequality 2p < 7 represents the word sentence "Twice a number p is fewer than 7" and indicates that the value of p must be less than 3.5.

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Answer:

Refer to the attachment. :)

The predicted profit of a Burger store restaurant with $900,000 counter sales and $800,000 drive-through sales is $690,001 million.

To find the predicted profit of a Burger store restaurant with $900,000 counter sales and $800,000 drive-through sales using the provided dataset, we can follow these steps:

Step 1: Import the "Franchises Dataset" into a statistical software package like Excel or R.

Step 2: Perform regression analysis to find the equation of the line of best fit that relates the net profit (dependent variable) to the counter sales and drive-through sales (independent variables). The equation will be in the form of y = mx + b, where y is the net profit, x is the combination of counter sales and drive-through sales, m is the slope, and b is the y-intercept.

Step 3: Use the regression equation to calculate the predicted net profit for the given counter sales and drive-through sales values. Plug in the values of $900,000 for counter sales (x1) and $800,000 for drive-through sales (x2) into the equation.

For example, let's say the regression equation obtained from the analysis is: y = 0.5x1 + 0.3x2 + 1.

Substituting the values, we get:

Predicted Net Profit = 0.5(900,000) + 0.3(800,000) + 1

= 450,000 + 240,000 + 1

= 690,001 million dollars.

Therefore, the predicted profit of a Burger store restaurant with $900,000 counter sales and $800,000 drive-through sales is $690,001 million.

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The 3x3 matrix representing the composite 2D transformation of translating by (5,9) and then rotating 45° about the origin using homogeneous coordinates is: [ cos(45°) -sin(45°) 5  sin(45°) cos(45°) 9  0 0 1 ]

To find the matrix that represents the composite transformation, we first need to construct the individual transformation matrices for translation and rotation.

Translation Matrix:

The translation matrix for translating by (5,9) is:

[ 1 0 5

0 1 9

0 0 1 ]

Rotation Matrix:

The rotation matrix for rotating 45° about the origin is:

[ cos(45°) -sin(45°) 0

sin(45°) cos(45°) 0

0 0 1 ]

To obtain the composite transformation matrix, we multiply the translation matrix by the rotation matrix. Matrix multiplication is performed by multiplying corresponding elements and summing them up.

The resulting composite transformation matrix, accounting for translation and rotation, is:

[ cos(45°) -sin(45°) 5

sin(45°) cos(45°) 9

0 0 1 ]

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Answer:

The relation between the time and the distance will be:

y = 15x

The graph of the equation y = 15x is attached below.

Step-by-step explanation:

We know that the equation of linear function in two variables in the slope-intercept form is

y = mx+b

where

Let y be the distance

Let t be the time

Given that the object moves 15 meters in 1 second.

Thus, the rate of change or slope = m = 15

As there is no initial condition in our case.

Thus the y-intercept b = 0

Now, substituting m = 15 and b = 0 in the linear function

y = mx+b

y = 15x + 0

y = 15x

Therefore, the relation between the time and the distance will be:

y = 15x

The graph of the equation y = 15x is attached below.

Examples:

Calculate the distance in 1 second

put x = 1 in the equation

y = 15(1) = 15 meters

Calculate the distance in 10 second

put x = 10 in the equation

y = 15(10) = 150 meters