Work Shown:
[tex]\sqrt{200} \times \sqrt{2}\\\\\sqrt{200 \times 2}\\\\\sqrt{400}\\\\\sqrt{20^2}\\\\20\\\\\text{Therefore, }\sqrt{200} \times \sqrt{2}=20\\\\[/tex]
The rules I used were:
[tex]\sqrt{A}*\sqrt{B} = \sqrt{AB}\\\\\sqrt{A^2} = A \ \ \text{ where } A \ge 0\\\\[/tex]
can someone help me i don't know how to do this.
Graph −1/2x+1/8y=3/4.
[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.
7x + 2y = 24
8x + 2y = 30
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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For what value of k do the equations 6x Ky =- 16 and 3x y 8 0 represent coincident line?.
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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y=_x + _
what is the slope?
Answer:
slope: -3y-intercept: +7equation: y = -3x +7Step-by-step explanation:
You want to know the slope and y-intercept of the line shown in the graph.
InterceptThe line crosses the y-axis at y = 7. This is the y-intercept, the added constant in the equation. That is, b = 7.
SlopeIn 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
EquationThe 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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Why is mole Avogadro's number?.
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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Shelley drew a scale drawing of the high school. She used the scale 5 millimeters : 3 meters. If the actual width of the parking lot is 42 meters, how wide is the parking lot in the drawing?
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.
There are eight different sizes of puzzles. Each person takes a turn selecting and keeps it. What is the probability that the first puzzle chosen is a 100-peice and the second is a 1000-piece puzzle
Answer:
Step-by-step explanation:
the answer to the first puzzle being choose will be 100 pieces is 8 out of 100
1. Craig borrowed $1,200 from his parents to buy a stereo. His parents charged him 5% simple interest for 3 years. How much interest did he pay his parents?
How do you find the inverse of a function in standard form?.
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 -
The function should first be written in standard form as follows: y = f(x) = a*x + b, where a and b are constants.Substituting y for x and x for y in the equation: x = f(y)(a*y + b)(y)Isolate y on one side of the equation and solve for it: y = (x-b)/aIf required, make the equation simpler.The original function f(x) = a*x + b is now the inverse function f-1(y) = (x-b)/a.Read more about standard form on:
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How do you plot 3 coordinates?.
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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Suppose that y varies jointly with w and x and inversely with z and y = 150 when w = 5, x = 15 and z = 3. Write the equation that models the relationship. Then find y when w = 3, x = 2 and z = 2.
sorry for bad handwriting :)
unit 1 geometry basics homework 2 segment addition postulate
The geometry questions attached are: UV = 67, x = 67, BD = 88, BC = 26 and CD = 61
What is meant by line segment?In contrast to a line, which can be extended endlessly on both ends, a line segment has endpoints.
An area or portion of a line with two endpoints is known as a line segment. A line segment has a set length as opposed to a line. Both metric measurements, such as millimeters and centimeters, as well as conventional units, such as feet or inches, can be used to measure the length of a line segment.
A line segment, in geometry, is a portion of a straight line that is constrained by two clearly defined end points and contains every point on the line that is situated in between those endpoints. The Euclidean distance between two line segments' ends determines the length of the segment.
5.)
UW = 6x - 35
UW = UV + VW (total length of a line segment)
UV = 19
VW = 4x - 20
6x - 35 = 19 + 4x - 20
simplifying the above equation, we get
6x - 4x = 19 - 20 + 35
2x = 34
x = 34 / 2
x = 17
UW = 6x - 35 = 6(17) - 35 = 67
6.)
HJ = 7x - 27
HJ = HI + IJ (total length of a line segment)
Substitute the values in the above equation, we get
7x - 27 = 3x - 5 + x - 1
simplifying the above equation, we get
7x - 3x - x = - 5 - 1 + 27
3x = 21
x = 21 /3
x = 7
7.)
BD = 7x - 10, BC = 4x - 29 and CD = 5x - 9
BD = BC + CD (total length of a line segment)
7x - 10 = 4x - 29 + 5x - 9
simplifying the above equation, we get
7x - 4x - 5x = - 29 - 9 + 10
-2x = - 28
x = 14
Therefore, the geometry questions attached are:
BD = 7(14) - 10 = 88
BC = 4(14) - 29 = 27
CD = 5(14) - 9 = 61
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Can someone tell me what number on the number line is greater than -9 for an inequality?
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.
What is inequality in math example?An inequality compares two values and indicates whether one is lower, higher, or just not equal to the other. It is implied by the expression a b that a and b are not equal. If a b, then a must be smaller than b. When a > b, an is greater than b.A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance.When resolving an inequality, you can either add or subtract the same amount from each side, or multiply or divide each side by the same positive amount. The inequality sign appears if each side is multiplied or divided by a negative number.To learn more about inequality refer to:
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What is the difference between the largest 6 digit number and smallest 4 digit number?.
The difference between the largest 6-digit and the smallest 4-digit numbers is 998999.
The aim is to find the smallest 4-digit and largest 6-digit numbers, and then we need to determine the difference between these two values.
Let's start by finding the smallest 4-digit number.
We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit, 1; therefore, it can be used in the highest place value.
Thus, we can create the required 4-digit smallest number with 0 and 1.
Hence, the smallest 4-digit number is 1000.
Now, we will discover the largest 6-digit number.
As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 6-digit number with the digit 9.
Thus, the largest 6-digit number is 999999.
Now, find the difference between these two values.
So, we can determine the difference between the smallest 4-digit and the largest 6-digit numbers by subtracting the smallest from the largest.
Thus, we get,
⇒999999−1000
⇒998999
Hence, 9989999 is the difference between the smallest 4-digit and the largest 6-digit numbers.
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Find the value of each variable in the parallelogram. Round your answers to the nearest tenth, if necessary.
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.
What percent of the 8th graders estimated they spend less than an hour a day on social media? Round your answer to the nearest tenth of a percent.
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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Jan 19, 4:48:05 PM
What is the surface area of the cylinder with height 3 m and radius 6 m?
Round your answer to the nearest thousandth.
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.
What is surface area?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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Work out x^2- 2x
when x =4
Answer:
8
Step-by-step explanation:
[tex]x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8[/tex]
For the following set of data, find the percentage of data within 2 population standard deviations of the mean, to the nearest 10th of a percent. 90, 40, 63, 62, 65, 67, 63, 68 90, 40, 63, 62, 65, 67, 63, 68
The percentage of data within 2 standard deviations of the mean is given as follows:
100%.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.Using a calculator, the measures for this problem are given as follows:
Mean: 64.75.Standard deviation: 12.65.The bounds within two standard deviations of the mean are given as follows:
64.75 - 2 x 12.65 = 39.45.64.75 + 2 x 12.65 = 90.05.All the measures in this problem are within these bounds, hence the percentage is of 100%.
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Hey i dont know leave step by step
The exponential function f (t) = e is a mathematical function that describes a relationship between a number and its power.
What is the value for b?It is also known as the exponential growth function, as it models the continuous growth of a quantity over time.The exponential function f (t) = e can be expressed in the form f (t) = b, where b is a constant. The constant b is the base of the exponential function and determines how quickly the quantity grows or decays. The value of b for the exponential function f (t) = e is 2.718281828459045. This constant can be derived using the Taylor series expansion of the exponential function. The Taylor series is an infinite sum of terms, where the terms are the derivatives of the exponential function at the origin.The value of b for the exponential function f (t) = e is important because it helps to determine the rate of growth or decay of a quantity over time. Knowing the value of b for the exponential function allows us to easily calculate the value of a quantity at a given time, given its initial value. In summary, the value of b for the exponential function f (t) = e is 2.718281828459045. This constant can be derived using the Taylor series expansion of the exponential function and is used to determine the rate of growth or decay of a quantity over time.To learn more about The exponential function refer to:
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Evaluate 0.5^3 and 0.5^-3 as fraction
Answer:
Step-by-step explanation:
0.5^3 = 0.5*0.5*0.5
= 0.125
= 125/1000
= 1/8.
0.5^-3
= 1 / 0.5^3
= 1 / 1/8
= 8.
If 25% of a number is 90 and 70% of the same number is 252, find 95% of that number.
Based on the information provided, 95% of the number is equivalent to 342.
How to find the number?To find the 95% of the number, let's use the rule of three with the information provided to find the 100%.
25% = 90 100% = xBased on this, let's create a simple equation:
x = 100 x 90 / 25 = 360Therefore, 100% of this number is 360, now using this information, let's find the 95% of the same number.
360 / 100 x 95 = 342You can double check this result using the 70% as follows
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Determine if each expression is or is not equivalent to −0.5g + 2.5.??
where is the expressions?
One hose can fill a small swimming pool in 75 minutes. A larger hose can fill the pool in 50 minutes. How long will it take the two hoses to fill the pool working together?
Answer: I believe it would be 25 minutes
Step-by-step explanation: longest amount of time minus shortest amount of time.
What is 3 3/8 x 2 1/3
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
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
The number of sets of one hot dog and one soda he can buy is; 5 sets
How to solve Algebra Word problems?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?
You know that the general chance that a randomly selected individual got a placebo is. 33208489. You also know that the general chance that an individual did not get the flu is. 93196005. Finally, the chance of both happening is. 27278402. Question 1 Given that they received the vaccine, what is the probability that an individual got the flu
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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what is The quotient of a number and nine is lessthan the number. In algebraic expressions
Answer:
Step-by-step explanation:
The quotient is the result you get when dividing numbers.
Let the number be n then the expression is:
n / 9 < n.
so like i nee help asap
Step-by-step explanation:
[tex] {h}^{2} + {r}^{2} = {l}^{2} \\ {h}^{2} = {l }^{2} - \: {r}^{2} \\ {h }^{2} = {13}^{2} - {12}^{2} \\ {h}^{2} = 169 - 144 \\ {h}^{2} = 25 \\ h = 5[/tex]
:. h = 5 in ...
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work out
a) 7/9×5 2/5 b) 1 3/4×4 1/6
From the work out of the expressions, we have;
a. 4 1/5
b. 7 7/24
Types of fraction?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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