75
25
Simplify fraction to a mixed number

Answer:

\(n(x) = 8 \: n(y) = 12 \\ n(x\: u \: y) = 8 + 12 \\ n = 20\)

The correct option 2 that is 30 children's tickets and 7 adult tickets were sold.

Given : A graph which has adult tickets in the x - axis

and children tickets in the y - axis

The marked point is  ( 30, 7 )

this means that the value of x axis 30 and y axis is 7

thus from the above information it is clear that there are 30 children's tickets and 7 adult tickets were sold.

So the correct option is Option 2

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Answer:

Graph B

Step-By-Step Explanation:

Answer:

The correct answer is B

Step-by-step explanation:

Answer: 121 meters

Step-by-step explanation:

In picture

Answer:

6

Step-by-step explanation:

6/1 is an improper fraction which is also equal to 6.

Answer:

48

Step-by-step explanation:

if 5 students out of 60 choose enchiladas we can calculate the percentage of students who chose enchiladas. We get 8.33% So in order to find the no. of Students who would choose enchiladas out of 576 students, we simply have to multiply 8.33% with 576. we would get 47.98. As people's no. cannot be in decimal we have to change it to whole number which is 48 out of 576.

Answer:

13x+6

Step-by-step explanation:

The volume of a rectangular prism with a base length of 4 cm, a base width of 2 cm, and a height of 6 cm is 48 cubic cm. If we triple the size of the prism, then the new base length would be 12 cm, the new base width would be 6 cm, and the new height would be 18 cm. Therefore, the volume of the new prism would be:

Volume = (12 cm) x (6 cm) x (18 cm) = 1296 cubic cm

So the volume of the prism would be increased to 1296 cubic cm by tripling the size of the original prism.

To find the volume of a rectangular prism, we simply need to multiply the length, width, and height of the prism together. In this case, we were given the dimensions of the original rectangular prism and asked to find the volume of the new prism if we tripled its size. To do this, we simply multiplied each dimension by 3 to get the new dimensions and then calculated the new volume by multiplying those dimensions together.

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Answer:

A is the answer

Step-by-step explanation:

The derivative of the function at point P₀ in the direction of A is 17√2.

What is derivative?

In calculus, the derivative represents the rate of change of a function with respect to its independent variable. It measures how a function behaves or varies as the input variable changes.

To find the derivative of the function at point P₀ in the direction of vector A, we need to calculate the directional derivative. The directional derivative is given by the dot product of the gradient of the function with the unit vector in the direction of A.

Given:

\(f(x, y) = 5xy + 3y^2\)

P₀(-9, 1)

A = -√2i - √2j

First, let's find the gradient of the function:

∇f(x, y) = (∂f/∂x)i + (∂f/∂y)j

Taking the partial derivatives:

∂f/∂x = 5y

∂f/∂y = 5x + 6y

So, the gradient is:

∇f(x, y) = 5y i + (5x + 6y)j

Next, we need to find the unit vector in the direction of A:

\(|A| = \sqrt((-\sqrt2)^2 + (-\sqrt2)^2) = \sqrt(2 + 2) = 2\)

u = A/|A| = (-√2i - √2j)/2 = -√2/2 i - √2/2 j

Finally, we can calculate the directional derivative:

Df(P₀, A) = ∇f(P₀) · u

Substituting the values:

Df(P₀, A) = (5(1) i + (5(-9) + 6(1))j) · (-√2/2 i - √2/2 j)

= (5i - 39j) · (-√2/2 i - √2/2 j)

= -5√2/2 - (-39√2/2)

= -5√2/2 + 39√2/2

= (39 - 5)√2/2

= 34√2/2

= 17√2

Therefore, the derivative of the function at point P₀ in the direction of A is 17√2.

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Answer:

1/50

Step-by-step explanation:

1/30 * 3/5 = 3/150

Reduce

1/50

Answer:

2/5

Step-by-step explanation:

Sequence of similarity transformations :

Reflect JKL across y-axis -- ----> Dilation ------> 90 degree counterclockwise rotation about the origin

What is rotation ?

The rotation of a point with regard to the origin is described by the rotation formula. To get the position of the point after rotation, apply the rotation formula. Rotation is a circular movement about the specific axis or point of rotation. In general, there are two common directions for rotation: clockwise and anti-clockwise or counter-clockwise.

An object moving in a circle around its center is said to as rotating. Rotation can occur in a variety of ways. Earth's rotative motion

First, do the reflection of JKL across y-axis.

Then, do the dilation

Then , do the 90 degree counterclockwise rotation about the origin

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In order to view more detail in the condensed data columns, we can expand the columns by clicking on the arrow icon located on the right side of the column header.

By clicking on the arrow icon located on the right side of the column header, this can expand column and show more detailed information of the fever report.

Effectively, the feature allows to easily access all the relevant data without having to switch between different views or reports which makes it more efficient and user-friendly. Also, we can also customize the columns and choose which data to display based on your preferences and needs.

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The correct option for the range of the piecewise function g(x) is (-∞, +∞).

Thus, option (A) is correct.

In the given piecewise function, g(x), we have two parts:

Part 1: g(x) = \(x^2 - 5\) for x < -3

Part 2: g(x) = 2x for x ≥ -3

For Part 1, the function g(x) = \(x^2 - 5\) represents a downward-opening parabola with the vertex at (-∞, -5)

and, the range extending from -5 to +∞.

So, for x < -3, the range is [-5, +∞).

For Part 2, the function g(x) = 2x represents a linear function with a slope of 2.

As x approaches -3 from the right (x ≥ -3), the function extends from -∞ to +∞.

So, for x ≥ -3, the range is (-∞, +∞).

To find the overall range of the piecewise function, take union of the ranges from both parts.

Thus, the overall range is (-∞, +∞).

Therefore, the range is (-∞, +∞).

Thus, option (A) is correct.

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\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:   I'm gonna go with B. hours worked; weekly pay; 30 to 35 hours; $360 to $420, because I had something similar to this

Wendy is paid $9 per hour and plans to work between 20 and 25 hours per week. Identify the independent and dependent quantity in the situation. Find reasonable domain and range values.

weekly pay; hours worked; 20 to 25 hours; $180 to $225

hours worked; weekly pay; 20 to 25 hours; $180 to $225

weekly pay; hours worked; $180 to $225; 20 to 25 hours

hours worked; weekly pay; 20 to 25 hours; $9 to $225

Step-by-step explanation:

The independent quantity is her pay and the dependent quantity is the hours she works in a week.

I believe the range would be 30 to 35 hours and the domain would be $360 to $450.

...................................................................................................................................................

Answer:

Part a) The independent quantity is the variable x (the number of hours) and the dependent quantity is the variable y (total paid)

Part b) Domain  

Part c) Range  

Step-by-step explanation:

Let

x------> the number of hours

y-----> total paid

The linear equation that represent this situation is

so

Part a)

The independent quantity is the variable x (the number of hours)

The dependent quantity is the variable y (total paid)

Part b) Find the domain

The domain is the interval-------->  

All real numbers greater than or equal to  hours and less than or equal to  hours

Part c) Find the range

For  

find the value of y

For  

find the value of y

The range is the interval------->  

All real numbers greater than or equal to  and less than or equal to  

...............................................................................................................................................

The dependent quantity would be the $12 per hour, while the independent quantities are 30 hrs/ week to 35 hours/ week.

The $12 per hour would become $360/week to $420/week.

The domain of the problem, with the unit of hrs/week, would be :30,31,32,33,34,35.

The Range of the problem, with the unit of $/week, would be : 360, 372, 384, 396, 408, 420.

...............................................................................................................................................

The least appropriate measure of central tendency for a data set that contains outliers is the mean. This is because the mean is calculated by taking the sum of all the values in the data set and dividing it by the number of values. This means that the mean is heavily influenced by outliers, as they are included in the calculation.

The median, 2nd quartile, and 50th percentile are all more appropriate measures of central tendency for a data set that contains outliers, as they are not affected by the presence of outliers. The median is calculated by taking the middle value of the data set, the 2nd quartile is calculated by taking the median of the upper half of the data set, and the 50th percentile is calculated by taking the value at the 50th percentile of the data set.

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Step-by-step explanation:

Given function:

The transformation of f(x) is g(x):

The graph of g(x) is attached below

The standard form of the Polynomial would be \(x^{4}\)  -x³ /2 -8

The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial.

We must consider each term's degree in order to write any polynomial in standard form.

Given the polynomial -8 -x³ /2 -xx³ with the highest degree comes first, followed by x raise to power 4, and then the constant, -8, comes last.

Thus, we would have:

\(x^{4}\)  -x³ /2 -8

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The probability that you choose a consonant followed by a vowel is given by P ( A ) = 3/10

Given data ,

There are 3 consonants in the bag: B, C, and D

There are 2 vowels in the bag: A and E

The total number of tiles in the bag is 5

Probability of choosing a consonant

There are 3 consonants out of 5 tiles in the bag

So, the probability of choosing a consonant on the first draw is 3/5.

Probability of choosing a vowel

After putting the first tile aside, there are now 4 tiles remaining in the bag, out of which 2 are vowels

So, the probability of choosing a vowel on the second draw, given that a consonant was chosen on the first draw, is 2/4

Probability of choosing a consonant followed by a vowel = (3/5) * (2/4) = 6/20 = 3/10

Hence , the probability of choosing a consonant followed by a vowel is 3/10

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An equation for the line of best fit that models the data points is y = 1.31x + 0.02.

In order to determine a linear equation for the line of best fit that models the data points described above, we would use a scatter plot on Microsoft Excel.

In this scenario, the width (in centimeters) would be plotted on the x-axis of the scatter plot while the length (in centimeters) would be plotted on the y-axis of the scatter plot.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the width and length, a linear equation for the line of best fit is given by:

y = 1.31x + 0.02.

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Question

The graph shows a scatter plot for a set of data.

Scatter plot with x-axis labeled width in centimeters and y-axis labeled with length in centimeters. The 20 points graphed are 1.3 and 1.7, 1.4 and 1.9, 1.4 and 1.8, 1.5 and 1.9, 1.9 and 2.3, 2.1 and 3.5, 2.1 and 2.8, 2.1 and 2.7, 2.2 and 3, 2.2 and 2.7, 2.3 and 3, 2.4 and 3.2, 2.4 and 2.9, 2.5 and 3.5, 2.5 and 3.3, 2.6 and 3.5, 2.6 and 3.4, 2.6 and 3.4, 2.7 and 3.2, and 2.8 and 3.8.

Determine the equation for a line of fit for the data.

Answer: The graph shows no correlation, and it is neither linear nor exponential.

Step-by-step explanation:

try doing a line of fit you're ALWAYS. gonna be ignoring other dots/points/coorids.

Why it's not a correlation is because nothing is together. You could consider a lot of dots on the edge.

If that doesn't make sense to you lets go through each answer

The graph shows a negative correlation, and it is a linear model.

The coordinates don't form any specific line

None of the coordinates are together

there's no slope since there's no line of fit.

it's THE SAME FOR THE OTHER ANSWER CHOICES BESIDES:

'The graph shows no correlation, and it is neither linear nor exponential.'

Answer: 2 5/6 I think.

Wait no. I just did the math and it would be 2 1/2

Using numerical integration methods, we find that R5 is approximately equal to 65.00.

To the nearest two decimal places, we have to calculate R5 for f(x) = x³ + 1 on [0, 4].

We will use Simpson's Rule for the calculation.

Simpson's rule for approximating the value of integral states that;

Rn(f) = [b-a/3n][f(x0) + 4Σ[i=1, n/2](fi) + 2Σ[i=1, n/2-1](fi*) + f(xn)

]Where fi = f(xi), fi* = f(xi + xi+1), xi = a + i(Δx), Δx = (b-a)/n, x0 = a and xn = b.

In our case, n = 5 since we want to calculate R5. Therefore, Δx = (4-0)/5 = 0.8

The values of xi will be;x0 = 0x1 = 0.8x2 = 1.6x3 = 2.4x4 = 3.2x5 = 4

Now, we will calculate the values of fi = f(xi);

f(x0) = f(0) = 0³ + 1 = 1

f(x1) = f(0.8) = 0.8³ + 1 = 1.512

f(x2) = f(1.6) = 1.6³ + 1 = 5.696

f(x3) = f(2.4) = 2.4³ + 1 = 15.584

f(x4) = f(3.2) = 3.2³ + 1 = 34.368

f(x5) = f(4) = 4³ + 1 = 65

Now we calculate the values of fi* = f(xi + xi+1);

f(x0+x1) = f(0+0.8) = 0.8³ + 1 = 1.512

f(x1+x2) = f(0.8+1.6) = 1.6³ + 1 = 5.696

f(x2+x3) = f(1.6+2.4) = 2.4³ + 1 = 15.584

f(x3+x4) = f(2.4+3.2) = 3.2³ + 1 = 34.368

Now we can substitute these values in Simpson's formula;

R5(f) = [4-0/3(5)][f(x0) + 4Σ[i=1, n/2](fi) + 2Σ[i=1, n/2-1](fi*) + f(xn)]

R5(f) = 0.8/3[1 + 4(1.512 + 15.584) + 2(5.696 + 34.368)]

R5(f) = 23.63466667 ≈ 23.63

Therefore, the nearest two decimal places value of R5 for f(x) = x³ + 1 on [0, 4] is 23.63.

Hence, option A is the correct answer; \boxed{44.96}.

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The total pressure of a mixture of two gases is the finalized value of the summation of the total pressure of each of the gases.

The total pressure of a mixture of two gases can be expressed in the form of an equation, as below,

Total Pressure = Pressure of Gas 1 + Pressure of Gas 2

It is noteworthy to be mentioned that the partial pressure of an individual gas is completely in contrast to that of the individual pressure of a gas. It can be expressed in the form of an equation, as below,

Partial Pressure = Total Pressure of Gas x Mole Fraction of Gas

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Answer:

the roots of f(x) = (x+5)3(x-9)2(x+1) are -5 (with a multiplicity of 3), 9 (with a multiplicity of 2)

Step-by-step explanation:

To find the roots of f(x) = (x+5)3(x-9)2(x+1), we need to set the polynomial equal to zero and solve for x.

f(x) = (x+5)3(x-9)2(x+1)

Setting f(x) equal to zero, we get:

0 = (x+5)3(x-9)2(x+1)

The roots of the polynomial are the values of x that make f(x) equal to zero. Therefore, the roots of the polynomial are:

-5 (with a multiplicity of 3), 9 (with a multiplicity of 2), and -1

Therefore, the roots of f(x) = (x+5)3(x-9)2(x+1) are -5 (with a multiplicity of 3), 9 (with a multiplicity of 2),

Answer:

171

Step-by-step explanation:

Range without outlier = 85 maximum - 38 minimum = 47

Range with outlier = 256-38 = 218

increase = 218-47 = 171

Using the standard deviation value of these interarrival times, the coefficient of variation is 0.012.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

The standard deviation to mean ratio, or coefficient of variation (CV), illustrates the degree of variability in proportion to the population mean. The dispersion increases with increasing CV.

Formula is given by:

\(CV = \frac {\sigma}{\mu}\)

\(\sigma = 0.02\)

Mean for the time of 0.02 sec is = 79 * 0.02

=1.58

CV= 0.02/1.58

=0.012

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