A harried chef can't keep up with his breakfast orders and decides to automate the process with a "butter gun." The gun provides a 10 gram burst of butter spray with each hit of the trigger. He starts with a rack that holds one piece of toast 1 meter away. The demand again exceeds supply and he realizes he can use the same gun to produce more toast by placing a larger rack at a greater distance. He finds that a four-slice rack works at a distance of 2 meters. Pleased with profits he carries the idea a step further and puts a holder 3 meters away, maintaining a 10 gram spray. See figure below.a) If 1 spray entirely covers the area of a single slice at 1 meter, can it entirely cover the area of 4 slices at 2 meters? Why or why not?b) How many slices can one spray cover with a 3 meter arragnement?c) How do these changes affect the amount of butter on each piece of toastd) Our up-and-coming chef moves the fun back to 5 meters. Predict how much toast he can spray and how much better each piece gets.e) Explain how he could duplicate the original single-slice toast at 5 meters from the gun.

The only function whose range includes all real values and is both odd and even is the constant function f (x) = 0, which is precisely zero.

The constant function that is precisely zero, f (x) = 0, is the only function whose range encompasses all real values and is both odd and even. When two functions are added together, they are either even or odd.

F(x) = 0, which is defined for all real numbers, is the unique function that is both even and odd. This is merely a line that is located on the x-axis. A function that is even is the result of two even functions. An even function is the result of two odd functions. An odd function is created when an even function and an odd function are combined.

Neither an even nor an odd function is a function f(x) in which f(x) ≠ f(−x) and −f(x) ≠ f(−x) for any value of x. These functions aren't symmetrical either about the origin or the y-axis on a graph.

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By using the unitary method, we can determine that 5 people are needed in the group, with 12 holes and 5 pigeons.

The Pigeonhole Principle is a mathematical theorem that states that if you have more objects than containers and all objects are placed in containers, then at least one container must have more than one object.

In the context of determining the minimum number of people needed in a group for five people to have been born in the same month, we can use the unitary method. The unitary method involves dividing the total number of possibilities by the number of objects we want to place in each container.

So, if we have 12 months in a year and we want to place 5 people in containers take one person per container, we need at least

=> 5/12 = 5/1 = 5 people in the group.

In this case, there are 12 holes and 5 pigeons. So, we need 5 people in the group to ensure that 5 of them were born in the same month.

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Therefore , the solution of the given problem of polynomial comes out to be  quotient comes out to be (p³ + 2p² + 6p -10) .

A polynomial is a mathematical statement with coefficients or uncertainty that uses only additions, erasures, multiplications, and powers of positive integer variables. There is just one indeterminate x polynomial identified by the formula x2 4x + 7. The term "polynomial" refers to a phrase in mathematics that consists of variables (sometimes referred to as "indeterminates") and coefficients that can be added, deducted, multiplied, then raised to negative number powers of non-variables.

Here,

Given :

=> (p⁴ -7p³ - 12p² - 64p + 90 )  / (p-9)

=> (p-9) * (p³ + 2p² + 6p -10)  / (p-9)

=>  (p³ + 2p² + 6p -10)

Thus , quotient comes out to be (p³ + 2p² + 6p -10) .

Therefore , the solution of the given problem of polynomial comes out to be  quotient comes out to be (p³ + 2p² + 6p -10) .

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As per the definition of  Laplace equation, none of the functions satisfy the Laplace equation.

The equation ∇²z/∇x² + ∇²z/∇y² = 0 is known as the Laplace equation, which describes the behavior of a scalar field that is in a state of equilibrium, meaning it is not changing over time.

When examining the two functions, z = ey (y cos x - x sin y) and z = e (y cos x - x sin x), it is important to determine if they satisfy the Laplace equation.

For the first function, z = ey (y cos x - x sin y), the partial derivatives can be calculated as follows:

∇²z/∇x² = e^y (cos x + x cos y - y sin x)

∇²z/∇y² = e^y (x sin x - sin y - y cos y)

By adding these two partial derivatives together, we can see that the first function does not satisfy the Laplace equation, as the result is not equal to zero.

For the second function, z = e (y cos x - x sin x), the partial derivatives can be calculated as follows:

∇²z/∇x² = -e (cos x + x cos x - y sin x)

∇²z/∇y² = -e (x sin x - sin y - y cos x)

Once again, by adding these two partial derivatives together, we can see that the second function also does not satisfy the Laplace equation, as the result is not equal to zero.

Therefore, none of the given functions satisfy the Laplace equation.

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Answer:

Step-by-step explanation:20 10x2=20

Answer: 20

Step-by-step explanation: 2 times 10 = 20

Numerical data are information about people, places, and things that can measured with numbers.

What are numbers?

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.

The system of numbers -

Is a helpful collection of numbers.

It reflects the number's algebraic and mathematical structure.

It offers a common depiction.

People utilise numbers, such as 1, 2, 3, 4, etc., to count various things or objects. Since thousands of years ago, people have used numerals to count objects.

Numbers are used to measure numerical data that are information about people, places, and things.

Therefore, the measurement is done by numbers.

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Answer:

Step-by-step explanation:

0.52

Answer: 17.63698

Step-by-step explanation:

8 kilogram is equal to 17.63698096 pounds. If You want convert kilograms to pounds, multiply the kilogram value by 2.2046226218.

Answer:

8 kg is equal to 17.6 lbs.

Step-by-step explanation:

Since 2.2 lbs is equal to 1 kg, you would have to multiply 2.2 by 8.

2.2 x 8 = 17.6

Because 2.2 multiplied by 8 is 17.6 that means 8 kg is the same as 17.6 lbs.

Answer: 4 yards x 4 yards

Step-by-step explanation:

All squares have the same perimeter and area

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,

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

[tex]$+4 f\left(x_1\right)+2 f\left(x_2\right)+\cdots \\[/tex]

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

[tex]$\quad \text { where } \Delta x=\frac{b-a}{n} \\[/tex]

[tex]$\quad \text { and } x_i=a+i \Delta x[/tex]

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:

if all you want is a multiple of 5 then here are a few; 5, 10, 15, and 20

Step-by-step explanation:

a multiple of 5 is any number that 5 can go into without having a remainder. it's the same for all numbers.

Answer:

it has 1 solution

Step-by-step explanation:

Answer:

Salary after 9 years: $86,000

Salary after t years: ($2,000×t)+$68,000

The basis for the solution space is then {[1, -4, 6]}.

To find a basis for the solution space of a homogeneous system of linear equations, we can perform row operations on the augmented matrix to obtain the reduced row echelon form.

The augmented matrix for the system of linear equations is:

| 1 4 -3 | 0 |

| -2 -8 6 | 0 |

Performing row operations, we get:

| 1 4 -3 | 0 |

| 0 0 24 | 0 |

From the reduced row echelon form, we can see that the non-trivial solution is x = t, y = -4t, z = 6t for any scalar t. This means that the solution space is spanned by the single non-trivial vector [1, -4, 6].

The dimension of the solution space is 1, meaning that it is a one-dimensional subspace of the three-dimensional space of all possible solutions. The basis for the solution space is then {[1, -4, 6]}.

Therefore, The basis for the solution space is then {[1, -4, 6]}.

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Answer: Stem and leaf plots have one advantage over histograms-- they display the original data, while histograms merely summarize them.

Step-by-step explanation:

​Stem-and-leaf plots contain original data values while histograms do not.

In order to categorise discrete or continuous variables, a stem and leaf plot, also known as a stem plot, is used. Data collection and organisation are done using a stem and leaf plot.

A bar graph is a good analogy for a stem and leaf plot. Because every number in the data is divided into a stem and a leaf, the name stem and leaf was chosen. The number's entirety - all but the final digit—is contained in the stem. There will always be one digit in the number's leaf. A stem and leaf plot's main benefit is the grouping of the data and the display of all the original data.

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36 observations are produced by multiplying $6 by 6 when two fair dice are rolled.

When two fair dice are rolled, $6 multiplied by 6 results in 36 observations.

[tex]& P(X=2)=P(1,1)=\frac{1}{36} \\[/tex]

[tex]& P(X=3)=P(1,2)+P(2,1)=\frac{2}{36}=\frac{1}{18} \\[/tex]

[tex]& P(X=4)=P(1,3)+P(2,2)+P(3,1)=\frac{3}{36}=\frac{1}{12} \\[/tex]

[tex]& P(X=5)=P(1,4)+P(2,3)+P(3,2)+P(4,1)=\frac{4}{36}=\frac{1}{9} \\[/tex]

[tex]& P(X=6)=P(1,5)+P(2,4)+P(3,3)+P(4,2)+P(5,1)=\frac{5}{36} \\[/tex]

[tex]& P(X=7)=P(1,6)+P(2,5)+P(3,4)+P(4,3)+P(5,2)+P(6,1)=\frac{6}{36}=\frac{1}{6} \\[/tex]

[tex]& P(X=9)=P(3,6)+P(4,5)+P(5,4)+P(6,3)=\frac{4}{36}=\frac{1}{9}[/tex]

[tex]& P(X=10)=P(4,6)+P(5,5)+P(6,4)=\frac{3}{36}=\frac{1}{12} \\[/tex]

[tex]& P(X=11)=P(5,6)+P(6,5)=\frac{2}{36}=\frac{1}{18} \\[/tex]

[tex]& P(X=12)=P(6,6)=\frac{1}{36}[/tex]

Therefore, the required probability distribution is as follows.

Then, E(X) = [tex]\sum \mathrm{X}_{\mathrm{i}} \cdot[/tex] [tex]\mathrm{P}\left(\mathrm{X}_{\mathrm{i}}\right)$[/tex]

[tex]& =2 \times \frac{1}{36}+3 \times \frac{1}{18}+4 \times \frac{1}{12}+5 \times \frac{1}{9}+6 \times \frac{5}{36}+7 \times \frac{1}{6}+8 \times \frac{5}{36}+9 \times \frac{1}{9}+10 \times \frac{1}{12}+ \\[/tex]

[tex]& 11 \times \frac{1}{18}+12 \times \frac{1}{36} \\[/tex]

[tex]& =\frac{1}{18}+\frac{1}{6}+\frac{1}{3}+\frac{5}{9}+\frac{5}{6}+\frac{7}{6}+\frac{10}{9}+1+\frac{5}{6}+\frac{11}{18}+\frac{1}{3} \\[/tex]

=7

[tex]& \mathrm{E}\left(\mathrm{X}^2\right)=\sum \mathrm{X}_{\mathrm{i}}^2 \cdot \mathrm{P}\left(\mathrm{X}_{\mathrm{i}}\right) \\[/tex]

[tex]& =4 \times \frac{1}{36}+9 \times \frac{1}{18}+16 \times \frac{1}{12}+25 \times \frac{1}{9}+36 \times \frac{5}{36}+49 \times \frac{1}{6}+64 \times \frac{5}{36}+81 \times \frac{1}{9}+ \\[/tex]

[tex]& 100 \times \frac{1}{12}+121 \times \frac{1}{18}+144 \times \frac{1}{36} \\[/tex]

[tex]& =\frac{1}{9}+\frac{1}{2}+\frac{4}{3}+\frac{25}{9}+5+\frac{49}{6}+\frac{80}{9}+9+\frac{25}{3}+\frac{121}{18}+4 \\[/tex]

[tex]& =\frac{987}{18}=\frac{329}{6}=54.833 \\[/tex]

[tex]& \text { Then, } \mathrm{V} \text { ar }[/tex][tex](\mathrm{X})=\mathrm{E}\left(\mathrm{X}^2\right)-[\mathrm{E}(\mathrm{X})]^2 \\[/tex]

[tex]& =54.833-(7)^2 \\[/tex]

= 54.833 - 49

=5.833

[tex]& \therefore \text { Standard deviation }=\sqrt{\mathrm{V} \text { ar }(\mathrm{X})} \\[/tex]

[tex]& =\sqrt{5.833} \\[/tex]

= 2.415

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A boxplot consists of several components including a box that shows the interquartile range (IQR) of the data, a line in the box representing the median, and "whiskers" that extend out from the box to show the range of the data.

If the box part of boxplot A is shorter in length than the box part of boxplot B, it suggests that the data in the first dataset (A) has a smaller interquartile range (IQR) compared to the data in the second dataset (B).

This means that the middle 50% of the data in dataset A is more tightly clustered together compared to the middle 50% of the data in dataset B. This can be due to the presence of outliers in the second dataset.

Boxplots are commonly used in statistical analysis and data visualization, but it is not used on a daily basis in every field. They are particularly useful in fields such as finance, biology, and engineering where large amounts of data need to be analyzed and visualized to draw insights and make decisions.

In these fields, they may be used daily or several times a week, depending on the specific use case and the data that needs to be analyzed. However, in other fields such as the arts, humanities, or some service industries, boxplots may not be used as frequently.

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the length of side a'b' will be greater than the length of side ab. The length of side a'b' is 12 units.

Rectangle abcd is a 4-sided shape with sides of length a, b, c, and d. When a rectangle is dilated, it is enlarged or scaled up. The length of the sides of the new rectangle, a', b', c', and d', will be greater than the original sides of the rectangle abcd. Therefore, the length of side a'b' will be greater than the length of side ab. The length of side a'b' is 12 units.

The length of side ab of the new rectangle (a'b'c'd) is 12 units, since it was dilated from 4 units and 6 units (abcd).

The complete question is :

Rectangle abcd has side lengths of 4 units and 6 units. It was dilated to create rectangle a'b'c'd. What is the length of side ab of the new rectangle?

6 units

7. 6 units

9. 5 units

12 units.

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A, b, c, and d-length sides make up the four-sided rectangle abcd. A rectangle is expanded or scaled up when it is dilated. The new rectangle's sides, a', b', c', and d', will all be longer than the rectangle's initial sides, abcd. As a result, side a'b' will have a length that is longer than side ab. Side a'b' measures 12 units in length.

6 units

7. 6 units

9. 5 units

12 units.

The board weighs approximately 8.05 pounds. Hence, its density is 46.80  lb/ ft³

The density of something is a measure of how heavy it is in relation to its size. When a thing is more dense than water, it sinks; when an object is less dense than water, it floats. Density is a feature of a substance that is independent of the amount of substance.

The formula for density is given by:

ρ = m/V

Where:

ρ = density

m = mass

V = volume

In this case, the dimension of the oak board is:

wide = 5.5 inches = 0.458 feet

thick = 1.5 inches = 0.125 feet

length = 3 feet

Hence, the volume of the board is:

V = 0.458 x 0.125 x 3 = 0.172 ft³

The weight is 8.05 pounds, therefore, the density:

ρ = 8.05/0.172  lb/ ft³

ρ = 46.80  lb/ ft³

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Using three equal subintervals and a right riemann sum, left riemann sum, and a midpoint sum is -6.4, 3.8, -1.0.

1) Integral with left end points:

         A-left = -3.4*2 + (-0.6)*2 + 0.8*2 = -6.4

2) Integral with right end points:

        A-right = -0.6*2 + 0.8*2 + 1.7*2 = 3.8

3) Integral with midpoints:

         A-mid = -2.2*2 + 0.2*2 + 1.5*2 = -1.0

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

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The change in demand is $15 per barrel.

Given is that the price of oil increases from 20 to 5 per barrel.

So we can write the change in demand as -

$20 per barrel - $5 per barrel

$15 per barrel

Therefore, the change in demand is $15 per barrel.

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The mean of the distribution would be lower than the median of 82.5.

The median for the 400 observations shown in the histogram can be estimated as follows:

Since there are 400 observations, the median will be the 200th observation. The histogram shows that there are 55 observations between 90 and 100 and 155 observations between 80 and 90. Approximately 210 observations are between 80 and 100, and 140 observations are between 85 and 100.

Therefore, the 200th observation is likely to be between 80 and 85. The median can be calculated as the average of 80 and 85, which is (80 + 85) / 2 = 82.5.

The histogram shows that the distribution is skewed to the left, so the mean is expected to be lower than the median. The mean of the distribution would be lower than the median of 82.5.

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The mean of the distribution would be lower than the median of 82.5.

The median for the 400 observations shown in the histogram can be estimated as follows:

Since there are 400 observations, the median will be the 200th observation. The histogram shows that there are 55 observations between 90 and 100 and 155 observations between 80 and 90. Approximately 210 observations are between 80 and 100, and 140 observations are between 85 and 100.

Therefore, the 200th observation is likely to be between 80 and 85. The median can be calculated as the average of 80 and 85, which is (80 + 85) / 2 = 82.5.

The histogram shows that the distribution is skewed to the left, so the mean is expected to be lower than the median. The mean of the distribution would be lower than the median of 82.5.

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Answer: the sales price is $35.70

Step-by-step explanation:

42(0.15) to get the answer of how much the price is being reduced by. when you solve that you get 6.3.

42-6.3= 35.70

The measure of 6.16798 feet are equal to 188 cm.

a dimension in US measurements that is 12 inches long (or wide). The definition of a foot in the Metric System is 0.3048 metres (the foot is defined that way).

The word "foot," which refers to the sole unit of measurement, is pluralized as "foot." In this sense, how far or how long you are measuring determines the mathematical difference between a foot and a foot.

The measurements in feet and feet are often used. They enable us to estimate the size of a person or a group. They can also help us calculate the separation between two spots. The word "foot," which refers to the sole unit of measurement, is pluralized as "foot."

          =188 cm = 6.16798.

           =188 cm = 6.17

Divide the length value by 30.48

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The measure of the arc PN, arc QN, arc RP, arc RM, arc RZ, and arc RPN will be 65°, 128°, 125°, 120°, 55°, and 215°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

The measure of the arc MZ is given as,

arc MZ + arc MN = 90

arc MZ + 25 = 90°

arc MZ = 65°

The measure of the arc QN is given as,

arc QN = 38° + 90°

arc QN = 128°

The measure of the arc RP is given as,

arc PR = 87° + 38°

arc PR = 125°

The measure of the arc RZ is given as,

arc RZ + 87° + 38° + 90° + 25° + 65° = 360°

arc PR = 55°

The measure of the arc RM is given as,

arc RM = 55° + 65°

arc RM = 120°

The measure of the arc RPN is given as,

arc RPN = 87° + 38° + 90°

arc RPN = 215°

The measure of the arc PN, arc QN, arc RP, arc RM, arc RZ, and arc RPN will be 65°, 128°, 125°, 120°, 55°, and 215°, respectively.

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The percentage of the data X = [2 4 6 8 10 12 14 16] lie between 4 and 8 hours about 50%.

A boxplot is a graphical representation of the data in a set, and it can be used to quickly identify patterns in a data set. In this example, we have a set of numbers X = [2, 4, 6, 8, 10, 12, 14, 16]. A boxplot of this data set would show a box that contains the middle 50% of the data and the whiskers that extend out to the maximum and minimum values.

From the boxplot, we cannot determine what percentage of the data lie between 4 and 8 hours. However, we can estimate that approximately 25% of the data lie between 4 and 8 hours, as this is a quarter of the middle 50% of the data.

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If this column has a square cross-section, the width of the square cross-section is 1 km.

Let's call the width of the square cross-section "w".

The volume of the column can be calculated as the area of the cross-section multiplied by its height.

w * w * 400,000 km = 400,000 km^3

Solving for w:

w^2 * 400,000 km = 400,000 km^3

w^2 = 400,000 km^3 / 400,000 km = 1 km^2

w = √(1 km^2) = 1 km

So, the width of the square cross-section is 1 km.

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Answer:

Step-by-step explanation:

Maybe just add or multiply the number by something to get the answer

The required probabilities are:-

a) P(8 of the players numbers are drawn) = 1.3×10⁻⁸

b) P(7 of the players number are drawn) = 3.33×10⁻⁶

c) P(at least 6 of the players number were drawn) = 1.84×10⁻⁴

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, In a state lottery, a player must choose 8 of the numbers from 1 to 40. The lottery commission then performs an experiment that selects 8 of these 40 numbers.

Players has 8 combinations of numbers from 1-40. The outcome S contains all the combinations of 8 out of 40

a) P(8 of the players numbers are drawn) = 1/40/8 = 1.3×10⁻⁸

b) Number of ways of drawing 78 selected numbers from 1-40 = 8×(40-7)8×32

P(7 of the players number are drawn) = 8×32/40 =3.33×10⁻⁶

c) P(at least 6 players numbers are drawn)= 32/2×(8/6) ways to draw.

P(at least 6 players numbers are drawn) = P(all 8 chosen are drawn) + P(7 players numbers drawn) + P(6 chosen are drawn) = 1+8 x32/40/8 +[8\6 ×32/2]

P(at least 6 players numbers are drawn) = 1.84×10⁻⁴

Hence, the required probabilities are:-

a) P(8 of the players numbers are drawn) = 1.3×10⁻⁸

b) P(7 of the players number are drawn) = 3.33×10⁻⁶

c) P(at least 6 of the players number were drawn) = 1.84×10⁻⁴

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