What point on the line 3x – y = 4 is closest to the point A(–2, 3)?

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

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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The probability that the sum of the numbers rolled is even or greater than 9 is 25/36.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, two number cubes at the same time. Each cube has sides numbered 1 through 6.

There are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Probability of getting sum as even number:

Number of favourable out comes = 18

Total number of outcomes = 36

Now, probability = 18/36

Probability of getting sum as greater than 9:

Number of favourable out comes = 7

Total number of outcomes = 36

Now, probability = 7/36

So, the probability of event is 18/36 + 7/36

= 25/36

Therefore, the probability that the sum of the numbers rolled is even or greater than 9 is 25/36.

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Answer: 12

Step-by-step explanation:

Answer:

[tex] \sf \: x = 12[/tex]

Step-by-step explanation:

Given equation,

→ x - 9 = 3

Now the value of x will be,

→ x - 9 = 3

→ x = 3 + 9

→ [ x = 12 ]

Hence, the value of x is 12.

The time it takes for the balance to reach $1000 depends on the frequency of compounding:

This is calculated using the formula for compound interest: A = P * (1 + r/n)^(nt), where P is the initial deposit, r is the annual interest rate, n is the number of times compounded in a year, and t is the number of years.

I calculated the time it takes for the balance to reach $1000 using the formula for compound interest:

A = P * (1 + r/n)^(nt),

where A is the final balance, P is the initial deposit ($100), r is the annual interest rate (6%), n is the number of times compounded in a year (annually, semi-annually, quarterly, or monthly), and t is the number of years.

I solved for t, keeping all other variables constant, by taking the natural logarithm of both sides of the equation and rearranging the terms:

t = (ln(A/P)) / (ln(1 + r/n) * n)

I used a mathematical software or calculator to perform the calculations and obtain the values for t for each given frequency of compounding.

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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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The area of the parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet is,

⇒ four hundred thirty-three and one-eighth ft²

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.

Now, We know that;

Area of a parallelogram = Base × Height

Substitute the given values, we get;

⇒ Area of a parallelogram = Base × Height

⇒ Area of a parallelogram = 22 1/2 × 19 1/4

⇒ Area of a parallelogram = 45/2 × 77/4

⇒ Area of a parallelogram = 3465/8

⇒ Area of a parallelogram = 433 1/8 ft²

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The same process is used to build an inscribed square and an inscribed regular hexagon: creating the circle.

A square that fits inside a specific shape and has sides that are perpendicular to it is said to be inscribed. The sides of the square that is inscribed are as long as they can be while still fitting entirely inside the provided shape and being perpendicular to it.

A regular hexagon that fits inside another shape so that its vertices contact it is called an inscribed regular hexagon. The sides of the inscribed hexagon are as long as they can be while still fitting entirely inside the predetermined shape and being perpendicular to it.

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The required solution of the expression y = 8x + 8 at x = 3 3/4 is given as after simplification is 38.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
y = 8x + 8

We are given that to determine the solution of the given expression at x = 3 3/4, Since x = 3 3 /4 = 15 / 4

Now, put x = 15/4 in the given expression,
y = 8 (15/4) + 8
y = 30 + 8
y = 38

Thus, the required solution of the given expression is y = 38.

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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.

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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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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The skill of inspecting produce properly requires much training and expertise.

Mashgichim must be knowledgeable with the halakhas of slaughtering meat, preparing meat and fish[13], and separating meat and dairy, depending on the task. She or he must be familiar with the operation of boilers and shipping boats, as high temperatures and extended storage durations might jeopardize the kosher status of meals.

However, one of the most important tasks of mashgichim is the checking in and verification of shipments. Before using a food product, Mashgihcim must confirm that it has a dependable hekhsher (certification). When a product is out of stock, suppliers frequently substitute non-kosher goods. These alternatives would normally be tolerated by non-kosher institutions.

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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 total cost for the truck rental will be $495.75

The cost of the truck rental can be calculated using the formula:

Cost = Daily rate + Per mile rate * Total miles

where:

Daily rate = $39.95 per day

Per mile rate = 64 cents per mile = $0.64 per mile

Total days = 5 days

Total miles = 460 miles

Substituting the values in the formula, we get:

Cost = $39.95 * 5 + $0.64 * 460

Cost = $199.75 + $296

Cost = $495.75

Therefore, the total cost for the truck rental will be $495.75.

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The total cost for the truck rental will be $495.75

The cost of the truck rental can be calculated using the formula:

Cost = Daily rate + Per mile rate * Total miles

where:

Daily rate = $39.95 per day

Per mile rate = 64 cents per mile = $0.64 per mile

Total days = 5 days

Total miles = 460 miles

Substituting the values in the formula, we get:

Cost = $39.95 * 5 + $0.64 * 460

Cost = $199.75 + $296

Cost = $495.75

Therefore, the total cost for the truck rental will be $495.75.

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Answer:

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

Answer: 20

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

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:

I finished

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.52

Mia earned a total of 6x + 4 from the two children. Both Paolo and Carla wrote equivalent expressions to calculate the amount Mia earned.

Paolo added 3(x + 2) to itself and subtracted 8 to calculate the total amount of money Mia earned from both children. Since she cared for two children for three hours each, she earned 3(x + 2) for each child for a total of 6(x + 2). He then subtracted the 8 dollars that Mia spent on materials for the activities.

Mia earned a total of 6x + 4 from the two children. Both Paolo and Carla wrote equivalent expressions to calculate the amount Mia earned. By simplifying the expressions, it was determined that they were indeed equivalent.

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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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The indefinite integral is   [tex]\frac{x^6}{3} +c[/tex].

What is indefinite integral?

An integral is considered to be indefinite if it has no upper or lower bounds.

The most generic anti-derivative of f(x) is known as an indefinite integral and denoted, in mathematics, by F(x), which is any anti-derivative of f(x).

[tex]\int[/tex]f(x) = F(x) + C

Here the given integral is [tex]\int{2x^5} dx[/tex]

=> [tex]\int{2x^5} dx[/tex]

=> [tex]2\int x^5 dx[/tex]

We know that [tex]\int x^n dx = \frac{x^{n+1}}{n+1}+c[/tex] where c is constant then,

=> [tex]2[\frac{x^{5+1}}{5+1} ]+c[/tex]

=> [tex]2\frac{x^6}{6} +c[/tex]

=> [tex]\frac{x^6}{3} +c[/tex]

Now take [tex]\frac{x^6}{3}[/tex] and differentiate to check the results then,

=> [tex]\frac{d}{dy}[\frac{x^6}{3} ][/tex]

=> [tex]\frac{1}{3} \frac{dx^6}{dy}[/tex]

We know that [tex]\frac{d}{dy} x^n = nx^{n-1}[/tex] then

=> [tex]\frac{1}{3}\times6x^{6-1}[/tex]

=> [tex]2x^5[/tex]

Hence the indefinite integral is  [tex]\frac{x^6}{3} +c[/tex].

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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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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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The multiplication problem that matches the model is, 3/5 x 3/10. So Option D is correct

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

Given that,

Two models

One having,

3 blue color filled sections and 2 blank sections

Another one having,

3 blue color filled semi-sections and 7 blank sections

we have to make analogy between multiplication of ratio of filled to total sections and multiplications of numbers,

Total sections in model 1 = 5

Total semi-sections in model 2 = 10

Ratio in 1 = filled/total = 3/5

Ratio in 2 = filled/total = 3/10

Now multiplying both the ratio,

⇒  3/5 × 3/10

Hence, the analogy is 3/5 × 3/10

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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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Let's call the weight of pears sold x.

So the weight of apples sold would be 7.8 - x.

And we know that x = 7.8 * 1/4 = 1.95 kilograms.

Therefore, the weight of apples sold is 7.8 - 1.95 = 5.85 kilograms.

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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Answer:

a . a²-9

b.x²-y²

c.n²-25

d.z²-4