What are the 7 laws of logarithms?.

We'll begin with a three-dimensional coordinate system where the x-axis comes toward us on the left.

The y-axis moves out toward the right, and the z-axis is absolutely vertical in order to plot points in three-dimensional coordinate space. When we need to take into account negative values of x, y, or z, then we should be aware that the negative x-axis moves out to the left.

The negative y-axis moves out to the right, and the negative z-axis is absolutely vertical and extends out below the positive z-axis.

In three-dimensional space, up until we reach our coordinate point, we advance along the x-axis, then parallel to the y-axis, then parallel to the z-axis.

Similar to how we find our point by going parallel to the y-axis after moving outside along the x-axis to our x value in two-dimensional coordinate space.

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We can use the proportion:

measurement in the drawing / scale = actual measurement

We know that the scale is 5 millimeters : 3 meters and the actual width of the parking lot is 42 meters. To find the width of the parking lot in the drawing, we can set up the proportion as:

width in drawing / 5 millimeters = 42 meters / 3 meters

To solve for the width in the drawing, we can cross-multiply and divide:

width in drawing = (42 meters * 5 millimeters) / 3 meters

Converting millimeters to meters:

width in drawing = (42 * 5 * 10^-3) / 3

width in drawing = (210 * 10^-3) / 3

width in drawing = 70 * 10^-3 meters = 0.07 meters

So the width of the parking lot in the drawing is 0.07 meters or 70 millimeters.

Based on the information provided, 95% of the number is equivalent to 342.

To find the 95% of the number, let's use the rule of three with the information provided to find the 100%.

Based on this, let's create a simple equation:

Therefore, 100% of this number is 360, now using this information, let's find the 95% of the same number.

You can double check this result using the 70% as follows

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The inverse of a function in standard form can be determined by substituting the function in the standard form

Every function does not have an inverse. A function needs to be a one-to-one function, which means there can't be repeated output for distinct inputs, in order to have an inverse. When a quadratic function is in vertex form, if the leading coefficient (a) is not zero, the function has an inverse. The various steps to find the inverse of a function in standard form can be noted as -

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Answer:

Step-by-step explanation:

the answer to the first puzzle being choose will be 100 pieces is 8 out of 100

The total cost of the fence will be £841. The solution is obtained using the concept of perimeter of triangle.

What is perimeter of triangle?

Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.

We are given a right-angled triangle with one angle 59° and the adjacent side as 145 meters.

We know that tan θ = Opposite side/Adjacent side

⇒ tan 59° = Opposite side/145

⇒ 1.66 = Opposite side/145

⇒ 241 meters(approx) = Opposite side

Now, using pythagoras theorem,

⇒Hypotenuse^2 = Base^2 + Perpendicular^2

⇒Hypotenuse^2 = 241^2 + 145^2

⇒Hypotenuse^2 = 58,081 + 21,025

⇒Hypotenuse^2 = 79,106

⇒Hypotenuse = 281 meters(approx)

Perimeter of triangle = Sum of three sides

⇒ Perimeter = 145 + 241 + 281

⇒ Perimeter = 667 meters

The fence costs £ 1.26 per meter

Total cost of fence = 1.26 * 667 = £840.42 = £841

Hence, the total cost of the fence will be £841.

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Answer: I believe it would be 25 minutes

Step-by-step explanation: longest amount of time minus shortest amount of time.

Answer:

= 7  7/8

Step-by-step explanation:

3 3/8 = 3 + 3/8 = 24/8 + 3/8 = (24+3)/8 = 27/8

2 1/3 = 2 + 1/3 = 6/3 + 1/3 = (6+1) / 3 = 7/3

Then:

3 3/8 x 2 1/3 = 27/8 x 7/3 = (27x7) / (8x3)

= 189 / 24 = 168/24 + 21/24 = 7 + 21/24

= 7 + 7/8

= 7 7/8

Draw a circle over the number to begin plotting an inequality, such as x>9, on a number line (e.g., 9). If the sign also says equal to (or), then complete the circle.

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solved, 3x+2/x+7 = 3x²+21x+2/x+7

solution:

3x+2/x+7

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times x+7/x+7

we get,

3x(x+7)/x+7 + 2/x+7

since 3x(x+7)/x+7 and 2/x+7  have the same denominator, add them by adding their numerators.

we get,

3x (x+7) +2/x+7

Do the multiplications in 3x(x+7)+2.

we get, 3x²+21x+2/x+7

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The formula for the sum rule is: P(A or B) = P(A) + P(B) - P(A and B)

The sum rule, also known as the addition rule of probability, states that the probability of any two events occurring together is the sum of the probability of each event occurring individually, minus the probability of them both occurring at the same time. The formula for the sum rule is:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are two events and P(A) and P(B) are the probabilities of each event occurring individually, and P(A and B) is the probability of both events occurring at the same time.

The sum rule is used when the two events are mutually exclusive, meaning that they cannot happen at the same time. In this case, P(A and B) = 0, so the formula becomes:

P(A or B) = P(A) + P(B)

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Answer:Kids grow at their own pace. Big, small, tall, short — there is a wide range of healthy shapes and sizes among children. Genetics, gender, nutrition, physical activity, health problems, environment, and hormones all play a role in a child's height and weight. And many of these things can vary widely from family to family.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know the slope and y-intercept of the line shown in the graph.

The line crosses the y-axis at y = 7. This is the y-intercept, the added constant in the equation. That is, b = 7.

In addition to passing through the point (0, 7), the line can also be seen to pass through the point (1, 4). This means the line has a "rise" of -3 for the corresponding "run" of +1.

The slope is ...

  m = rise/run = -3/1 = -3

The slope-intercept equation for the line is ...

  y = mx + b

  y = -3x +7

__

Additional comment

We chose to determine the y-intercept first, because it usually is found on a grid intersection. For determining slope, it is convenient to find two points on grid intersections. That way, the slope can be most precisely determined. It can be less accurate to interpolate values when determining points that are not on grid intersections.

Since the y-intercept is a grid intersection point, we only need to find another point where the line crosses a grid intersection to make our slope calculation as simple and accurate as possible.

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The percent of 8th graders estimated they spend less than an hour a day on social media  47% .

What do you mean by percentage ?

Percentage is a way of expressing a number as a fraction of 100. It is basically denoted using the percent sign, "%". For example, 45% means 45 out of 100, or 0.45. Percentage can be used to express how much of something is present or has been completed.

From the given table,

For 7th grade,

26 / 37  * 100

= 70%

For 8th grade,

26/55 * 100

= 47% (approx)

Total ,

52 / 92  *  100

= 5200 / 92

= 57 %

Hence, the percent of 8th graders estimated they spend less than an hour a day on social media  47% .

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The required number of actual meters represented by 18 centimeters on the blueprint is 3.6 meters.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
A scale on a blueprint drawing of a house shows that 10 centimeters represent 2 meters.

Scale factor,
10 centimeter: 2 meters = 1 centimeters : 0.2 meters

So,
18 centimeters = 18 × 0.2 meters = 3.6 meters.

Thus, the required number of actual meters represented by 18 centimeters on the blueprint is 3.6 meters.

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The surface area of a cylinder is given by the formula 2πr (r + h) where r is the radius and h is the height.

Plugging in the given values, we get: 2π(6) (6 + 3) = 2π(6)(9) = 108π.

Rounded to the nearest thousandth, this is approximately 342.8.

The surface area of an object is the total area that the object's surface occupies. It is a measure of the total area of all the exposed surfaces of an object. It is typically measured in square units, such as square meters or square inches. The surface area of an object can be calculated using various formulas, depending on the shape of the object. For example, the surface area of a cube is the area of all six faces of the cube, while the surface area of a sphere is the area of the spherical surface. The surface area is an important property of an object in fields such as engineering, physics, chemistry, and architecture.

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The distance between points (2, 3) and (-4, 5) is 6.3 units.

As we know according to the distance formula the distance between points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]

Here we have been given points (2,3) and (-4,5)

Let us assume that  (x₁, y₁) = (2, 3)

and (x₂, y₂) = (-4, 5)

Let d represents the distance between points (2,3) and (−4,5)

Using above distance formula the distance d between given points would be,

[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow d = \sqrt{[(-4 - 2)^2 + (5 - 3)^2]}\\\\\Rightarrow d = \sqrt{[(-6)^2 + (2)^2]}\\\\\Rightarrow d = \sqrt{36+4}\\\\\Rightarrow d = \sqrt{40}\\\\\Rightarrow d = 6.3~units[/tex]

Therefore, the distance is 6.3 units.

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The complete question is:

What is the distance between points (2,3) and (−4,5)  ?

Answer: x = 6 and y = -9

Step-by-step explanation:

Solve by reduction method

7x + 2y = 24

8x + 2y = 30

We will multiply the first equation by 8, and the second equation by -7, then both equations must be added.

8(7x + 2y = 24)

-7(8x + 2y = 30)

Add these equations to eliminate x

  2y = -18

Then we solve 2y = -18 for y. (We divide by 2)

      2y/2 = -18/2

      y = -9

We place the found value of y , in one of the original equations y in order to solve for x.

7x + 2y = 24

7x + 2(-9) = 24

7x - 18 = 24

We add 18 to both sides.

  7x - 18 + (18) = 24 + (18)

       7x = 42

We add 18 to both sides.

 7x/7 = 42/7

  x = 6

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The given equations 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines if the value of k is 2.

Given the pair of equations is

3x - y + 8 = 0

6x - ky = -16 describes coincident lines.

We have to calculate the value of k.

We know that,

For a pair of linear equations in two variables a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,

If a₁/a₂ = b₁/b₂ = c₁/c₂, then the pair of linear equations is dependent and consistent.

We have, a₁ = 3, b₁ = -1, c₁ = 8

a₂ = +6, b₂ = -k, c₂ = +16

So, a₁/a₂ = 3/6 = 1/2

b₁/b₂ = -1/-k = 1/k

c₁/c₂ = 8/16 = 1/2

a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2

1/k = 1/2

k = 2

Therefore, the value of k is 2.

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The probability that an individual got the flu given that they received the  vaccine is 0.739130435.

What is probability ?

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.

Bayes' theorem to solve for the probability that an individual got the flu given that they received the vaccine. Bayes' theorem states that:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

The probability of event B given that event A has occurred, P(B|A), can be calculated as the general chance of both events happening, which is .27278402.

So, using Bayes' theorem:

P(A|B) = P(B|A) * P(A) / P(B) = .27278402 * .33208489 / .06803995 = .739130435

Therefore, the probability that an individual got the flu given that they received the vaccine is 0.739130435.

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The probability that an individual got the flu is approximately 1.09.

Let's call the probability of receiving a placebo "P(placebo)" and the probability of not getting the flu "P(no flu)". Then, using the information given, we have:

P(placebo) = 0.33208489

P(no flu) = 0.93196005

P(placebo and no flu) = 0.27278402

To find the probability of getting the flu given that they received the vaccine (not a placebo), we can use the formula for conditional probability:

P(flu | vaccine) = P(flu and vaccine) / P(vaccine)

Since the individual either received a placebo or a vaccine (but not both), the probability of receiving a vaccine is given by:

P(vaccine) = 1 - P(placebo) = 1 - 0.33208489 = 0.66791511

The probability of getting the flu and receiving a vaccine is equal to the complement of the probability of getting the placebo and not getting the flu, which is:

P(flu and vaccine) = 1 - P(placebo and no flu) = 1 - 0.27278402 = 0.7272159

Finally, substituting these values into the formula for conditional probability, we get:

P(flu | vaccine) = P(flu and vaccine) / P(vaccine) = 0.7272159 / 0.66791511 = 1.09103623

So, the probability of getting the flu given that an individual received the vaccine is approximately 1.09.

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The exponential function f (t) = e is a mathematical function that describes a relationship between a number and its power.

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The value of each variable in a parallelogram can be found by measuring the lengths of the sides, the angles between the sides, and the area of the shape. The measurements should be rounded to the nearest tenth, if necessary.

The value of each variable in a parallelogram can be determined by taking measurements of the various components of the shape. The first step is to measure the lengths of the sides. These are typically labeled as a, b, c, and d. The angles between the sides can then be measured, which are typically labeled as A, B, C, and D. The area of the parallelogram can be calculated using the formula A=ab sin C. All of these measurements should be rounded to the nearest tenth, if necessary. Once all of the measurements have been taken, the values of the variables can then be determined. This is done by using the values found to solve for the unknowns in the formula. For example, if the lengths of the sides are known, the angles can be calculated using the Law of Cosines. Knowing all of the measurements of the parallelogram can allow you to solve for the values of the variables.

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The complete question is

Find the value of each variable in the parallelogram. Round your answers to the nearest tenth, if necessary labeled as A,B,C and D.

The percentage of data within 2 standard deviations of the mean is given as follows:

100%.

Using a calculator, the measures for this problem are given as follows:

The bounds within two standard deviations of the mean are given as follows:

All the measures in this problem are within these bounds, hence the percentage is of 100%.

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The point (7, 10.5) is on the graph of both equations and satisfies the system of equations.

To find the solution to a system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

The system of equations is:

y = 2x - 3.5

x - 2y = -14

We can begin by solving one of the equations for one of the variables, for example, we can solve the first equation for y:

y = 2x - 3.5

Next, we can substitute this expression for y into the second equation:

x - 2(2x - 3.5) = -14

This gives us:

x - 4x + 7 = -14

-3x = -21

x=7

Now we can substitute this value of x back into the first equation to find the corresponding value of y:

y = 2(7) - 3.5

y = 10.5

So the solution to the system of equations is x = 7, y = 10.5.

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[tex]-\cfrac{1}{2}x+\cfrac{1}{8}y=\cfrac{3}{4}\implies -\cfrac{x}{2}+\cfrac{y}{8}=\cfrac{3}{4}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8\left( -\cfrac{x}{2}+\cfrac{y}{8}\right)=8\left( \cfrac{3}{4} \right)} \\\\\\ -4x+y=6\implies y=4x+6[/tex]

Check the picture below.

From the work out of the expressions, we have;

a.  4 1/5

b. 7 7/24

A fraction can be defined as any expression which consists of a numerator and denominator. The three major types are: proper fraction, improper fraction and mixed fraction.

To work out the given expressions;

a.  7/9 × 5 2/5

convert both to a proper fraction,

7/9 x 27/ 5 = (7 x 27)/ (9 x 5)

                   = 189/ 45

                   = 4 1/5

b. 1 3/4 × 4 1/6

express in a proper fraction

7/ 4 x 25/ 6 = (7 x 25)/ (4 x 6)

                   = 175/ 24

                  = 7 7/24

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The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³. That is why the mole is also called Avogadro's number.

The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)

So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A

atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.

We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).

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The number of sets of one hot dog and one soda  he can buy is; 5 sets

We are given;

Cost of hotdog = $3

Cost of soda = $4

Total amount grant has = $38

Now, we are told that he wants to buy same set of hotdog as that of sodas. Thus, let the amount be x and we have the algebraic expression;

3x + 4x = 38

7x = 38

x = 38/7

x = 5³/₇

We will pick the whole number to get 5 sets

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Complete question is;

Grant is at a basket ball game and wants to buy as many $3 hotdog and $4 Sodas as he can. If grant has $38 and wants to buy as many sets of one hot dog and one soda as he can how can he buy?

Answer:

8

Step-by-step explanation:

[tex]x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8[/tex]