A rectangular trame has a width that is ¾ its length.
The area of the trame is 192 square inches. What are the dimensions ot the frame?

7 lbs 8 oz more weight can the trolley hold the trolley can hold 20 lbs of groceries and Annie put 12 lbs 8 oz of groceries on the trolley. This can be obtained by converting the values to oz and subtracting them.

We know that, 1 lbs = 16 oz

Capacity of the trolley = 20 lbs

                                     = 20 × 16 oz

                                     = 320 oz

Weight put in the trolley = 12 lbs 8 oz

                                        = ( 12 × 16 ) + 8 oz  

                                        = 192+8 oz

                                        = 200 oz

Remaining weight that the trolley can hold = 320 oz - 200 oz

                                                                       = 120 oz

                                                                       = (7 × 16) + 8 oz

                                                                       = 7 lbs 8 oz

Hence 7 lbs 8 oz more weight can the trolley hold the trolley can hold 20 lbs of groceries and Annie put 12 lbs 8 oz of groceries on the trolley.

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False. A data set can have the same mean and median, but not necessarily the same mode.

The mean, median, and mode are measures of central tendency used to describe a data set. The mean is the average of all the values in the data set, the median is the middle value when the data set is arranged in ascending or descending order, and the mode is the value that appears most frequently.

While it is possible for a data set to have the same mean and median, it is not necessary for the mode to be the same as well. For example, consider a data set with the values [1, 2, 3, 3, 4, 5]. In this case, the mean is 3, the median is 3, and the mode is also 3 because it appears twice, which is more frequently than any other value. However, there are scenarios where the mode can be different from the mean and median, such as in a bimodal distribution where there are two distinct peaks in the data set.

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The midpoint (W) of XY is also on segment PQ, so PQ is the bisector of XY.

Hope it helps you :)

Assuming the population standard deviation is known and the standard deviation of the sample mean x : option (b) is correct : the standard error of the sample mean decreases.

In probability theory, the central limit theorem (CLT) states that the distribution of a sample variable approximates a normal distribution (i.e., a “bell curve”) as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population's actual distribution shape.

Standard deviation is a calculation of the dispersion or variation in a set of numbers. If the standard deviation is a small number, it means the data points are close to their average value. If the deviation is large, it means the numbers are spread out, further from the mean or average.

There are different ways to write out the steps of the population standard deviation calculation into an equation. A common equation is:

                          σ = ([Σ(x - u)2]/N)1/2

Where:

σ is the population standard deviation

Σ represents the sum or total from 1 to N

x is an individual value

u is the average of the population

N is the total number of the population

A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set. The sample mean can be applied to a variety of uses, including calculating population averages.

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Answer:

Step-by-step explanation:

Answer to first question = her mistake was that she wrote the constant to be 10 whereas the constant is actually -10 once you rearrange the equation to look like a quadratic equation.

Quadratic equations are written in form of ax^2 + bx + c = 0

You are given x^2 + 3x = 10, first you need to bring the constant c (10) to the left side (by subtracting 10 on both sides).

x^2 + 3x - 10 = 0

c = -10

Answer to second part:

x = 2, -5

Answer:

y' = 1 / sinxcosx

Step-by-step explanation:

Given :

y = sinx + cosx / sinx - cosx

Applying quotient rule :

y' = [(sinx - cosx)(cosx - sinx) - (sinx + cosx)(cosx + sinx)] / (sinx -

cosx)²

y' = [sinxcosx - cos²x - sin²x + sinxcosx - (sinxcosx + cos²x + sin²x + sinxcosx)] / (sinx - cosx)²

y' = 2sinxcosx - 2sinxcosx - 2cos²x - 2sin²x / (sinx -cosx)²

y' = -2(sin²x + cos²x) / (sinx - cosx)²

y' = -2 / (sinx - cosx)²

y' = -2 / sin²x - 2sinxcosx + cos²x

y' = -2 / -2sinxcosx

y' = 1 / sinxcosx  [⇒ Final answer]

Answer:

⇒\(y'=-\frac{2}{(six-cosx)^{2} }\)

Step-by-step explanation:

⇒Answer in the attachment.

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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Answer: 31

Step-by-step explanation:

9 + 2 = 11. 11 is how old Kelly is in 2 years.

1/3 of 33 is 11. Kelly's mother is 33 in two years, meaning two years ago, Kelly's Mother is 31.

Here is the full equation.   K = Kelly.    M = Kellys Mom

9k = m

2k + 9k = m + 2m

11k = m + 2

11k = \(\frac{m}{3}\)

M + 2 = 33

     -2    -2

m = 31

In order to calculate the surface area of a prism, it is necessary to sum up the areas of all its sides. One can obtain this number by using the ensuing formula:

Surface Area = 2B + Ph

The value B represents the area of the base of the prism, P refers to the perimeter, and h pertains to its height. To find the amount of space on the outside of a cylinder, one needs to add up the areas of its curved exterior, along with both circular tops.

The following method may be employed for such a computational process:

Surface Area = 2πr² + 2πrh

In this context, r indicates the radius of the circular foundation, whereas h denotes its altitude measurement.

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Given the information on the problem, we can use the law of cosines to find the length of p with the following equation:

substituting the values at hand, we get the following:

therefore, the length of p is 111 cm

Answer:

We have the quadratic \(x^{2} - 6x + 9\) which can factor into \(\boxed{(x - 3)(x - 3)}\)

Hope this helps!

Answer:

the answer would be d

which is 0.006

Answer:

x = 2 , y = 1

Step-by-step explanation:

For the triangles to be congruent then the hypotenuse and leg must be congruent, that is

x = y + 1 → (1)

4y = x + 2 → (2)

Substitute x = y + 1 into (2)

4y = y + 1 + 2

4y = y + 3 ( subtract y from both sides )

3y = 3 ( divide both sides by 3 )

y = 1

Substitute y = 1 into (1)

x = y + 1 = 1 + 1 = 2

The integral of a function between two limits, a and b, can be approximated numerically using Simpson's Rule. It is based on understanding the region beneath a parabola or other flat curve. h = (b - a) / N and N is an even integer in this rule. 

Simpson's Rule equation is,

\($\int_a^b f(x) x^{\prime} \approx \frac{\Delta x}{3}\left(f\left(x_0\right)\right. \\\)

\($+4 f\left(x_1\right)+2 f\left(x_2\right)+\cdots \\\)

\($\left.+4 f\left(x_{n-1}\right)+f\left(x_n\right)\right) \\\)

\($\quad \text { where } \Delta x=\frac{b-a}{n} \\\)

\($\quad \text { and } x_i=a+i \Delta x\)

n = it is an even subdivisions of the function.

a = point at the function graph's beginning

b = point at the function graph's tip

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Answer:

Step-by-step explanation:

I think it is helpful to set this up as a proportion as it is the easiest way in my opinion.

1st step: 396/18 and x/11

This is the way you set up the proportion.

2nd Step: You would have to multiply 396 and 11 then divide the value by 18.

396x11 = 4,356

4,356/18 = 242

x=242 Dollars

Answer: 242 dollars

Therefore, Alan would make 242$ while working at the same rate for 11 hours.

Answer:

(326-6) ÷ 8 = s

40 = s

Step-by-step explanation:

326-6=320 This was done so we get to know the total amount of students in busses, since six rode in cars.

Then we divide the amount of students in busses by the amount of busses to get 40. 40 students in each bus.

False. The claim that any linear programming (LP) problem with four variables and four constraints can be solved graphically due to duality is incorrect.

Duality in linear programming refers to the relationship between a given LP problem (called the primal problem) and its associated dual problem. The duality theorem states that if the primal problem has an optimal solution, then the dual problem also has an optimal solution, and the optimal objective values of both problems are equal. However, the ability to solve a specific LP problem graphically depends on its complexity and the number of variables and constraints involved.

While graphical methods can be useful for understanding and visualizing LP problems with two variables and two constraints, they become increasingly impractical as the number of variables and constraints grows. Graphical methods rely on representing the feasible region and finding the optimal solution by identifying the corner points of the feasible region. However, as the number of dimensions increases, the feasible region becomes difficult to visualize, making graphical methods inefficient.

Therefore, it is not generally true that any LP problem with four variables and four constraints can be solved graphically using duality. In practice, more efficient methods such as the simplex algorithm or interior point methods are typically employed for solving LP problems of this size.

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Answer:

B). to show the general tendency of the points in a scatterplot

Step-by-step explanation:

The purpose of a regression line is to show the general tendency of the points in a scatterplot option (B) is correct.

A regression line is a graph that illustrates the pattern of a group of statistics. In other words, it shows the data's best pattern.

It is given that:

The regression line is a line of best fit.

From the definition of the regression line, line is a graph that illustrates the pattern of a group of statistics and to show the general tendency of the points in a scatterplot.

Thus, the purpose of a regression line is to show the general tendency of the points in a scatterplot option (B) is correct.

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Answer:?

Step-by-step explanation:?

The population is the entire group of individuals that the neighborhood association wants to gather information about, in this case, the residents of the neighborhood.

The officers of a neighborhood association are interested in knowing if residents are willing to contribute towards beautifying the neighborhood and how much money they are willing to contribute. The officers are considering two methods for gathering data: Method A involves calling and surveying every tenth resident on the association's roster, while Method B involves randomly selecting and surveying 10 residents from among those who attend the neighborhood block party.

To properly design a survey, it is important to identify the population, which in this case is the entire neighborhood or community being served by the association. Identifying the population is necessary to ensure that the sample selected is representative of the population and can provide reliable results. The officers should also consider the potential biases associated with each sampling method and determine which one is more appropriate for their specific needs.

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Answer:

$90

Step-by-step explanation:

First you find the total area of the shape:

9ft times 6 ft times 5 ft= 270 ft

divide 270 ft by 3 to get the amount of money that Maya will pay.

270 divided by 3 is 90

so the answ er is $90

The correct option is B.

The value will be  = 25

What is the Angles of the triangle?

The sum of the two interior angles that are not adjacent to it equals the exterior angles of a triangle, but the interior angles of a triangle always add up to 180°. Subtracting the angle of the desired vertex from 180° is another method for determining a triangle's exterior angle.

∠ACE = (2x+2)°

∠ECB = (5x+ 3)°

Angles ACE and ECB are additional angles according to the linear postulate, as seen in the attached diagram.

Therefore:

∠ACE+∠ECB = 180°

(2x+2)+(5x+3) = 180

2x+ 5x+ 2+ 3 = 180

7x + 5 = 180

7x = 175

x= 175/7

x = 25

Thus the value will be  = 25

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I understand that the question you are lookin for is :

Lines de and ab intersect at point c. lines d e and a b intersect at point c. angle a c e is (2 x 2) degrees. angle e c b is (5 x 3) degrees. what is the value of x?

A.12

B. 25

C. 38

D. 52

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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Step-by-step explanation:

step 1. we will denote the average rate of change as r.

step 2. r = (f(5) - f(3))/(5 - 3)

step 3. r = (375 - 81)/2

step 4. r = 294/2

step 5. r = 147.

step 6. note: this is just like finding m. m = (y2 - y1)/(x2 - x1)

Answer: 1 cup

Step-by-step explanation:

he has already put in 4, and he needs 5

5-4 = 1

Answer:

Step-by-step explanation:

I more cup

In a triangle one side that lies on an extended line segment,  statement about x is true, x = 62 because 147−85=62 and 85 + 62 = 147. So Option B is correct

In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°

Given that,

A triangle, which has one interior angle 85° and one exterior angle 147°

Another exterior angle x = ?

It is already known that,

Sum of complementary angles are 180

So,

⇒  Y + 147 = 180

⇒  Y  = 180 - 147

⇒  Y = 33

sum of all the interior angles of the triangle is 180°

X + Y + 85 = 180

X = 180 - 85 - 33

X = 62

Hence, the value of x is 62

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Answer:

78m

Step-by-step explanation:

6×13

78

not too sure tho

The regression line that forecasts home equity using the FICO credit score as the explanatory variable has the equation Y' = 1798X + 0.

Due to the fact that this linear regression model includes two parameters that need to be estimated from training data, it has two degrees of freedom. One additional column in the data (one additional input variable) would provide the model one extra degree of freedom.

An equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable, represents a linear regression line. A line's intercept (the value of y when x = 0) is equal to the slope of the line, which is b.

Hence we get the required answer.

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