Write an absolute value inequality and a compound inequality for a length of 8.9mm with a tolerance of 0.15mm

The formula for estimating the nth term of an arithmetic sequence is:

a n = a₁ + (n-1)d

The first five terms of a n = -2n + 3 = 1, -1, -3, -5, -7

A succession of numbers merged together to make a sequence exists comprehended as an arithmetic sequence.

A series of numbers named an arithmetic progression or arithmetic sequence (AP) contains a constant difference between the terms.

The formula for estimating the nth term of an arithmetic sequence exists:

a n = a₁ + (n-1)d

The four quantities in the formula exist a n, a₁, n, d.

The first 5 terms are a n = -2n + 3

a₁ = -2 + 3 = 1

a2 = -4 + 3 = -1

a3 = -6 + 3 = -3

a4 = -8 + 3 = -5

a5 = -10+3 = -7

Therefore, the first 5 terms of the sequence  be 1, -1, -3, -5, -7.

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If 22 is the geometric mean of a number and four times the number, then the number is 11.

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Let x = x1 = unknown number

y = x2 = four times the number = 4x

Using the formula in solving geometric mean, plug in the values and variables.

GM = n√x1 x2 . . . xn

22 = √xy

22 = √x(4x)

22 = √4x^2

22 = 2x

x = 11

y = 4x

y = 44

Hence, the number is 11. 22 is the geometric mean of 11 and 44.

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Answer: x=27    y=4

Step-by-step explanation:

Let the larger of two numbers is x and the smaller of two numbers is y

Hence,

[tex]\displaystyle\left \{ {x-5y=7} \atop {x+y=31}} \right.\\\\\left \{ {{x-5y=7} \atop {x+y-y=31-y}} \right. \\\\\left \{ {{x-5y=7\ \ \ \ \ (1)} \atop {x=31-y}\ \ \ \ (2)} \right. \\[/tex]

Substitute equation (2) into equation (1):

[tex]31-y-5y=7\\31-6y=7\\31-6y+6y=7+6y\\31=7+6y\\31-7=7+6y-7\\24=6y\\[/tex]

Divide both parts of the equation by 6:

[tex]4=y\\Hence,\\x=31-4\\x=27[/tex]

rob has 8 dimes and 17 nickels in $1.65

There is only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All the points fall on the same line when the values that together make a linear equation true are determined and plotted on a coordinate grid.

Let n represent nickels & d dimes

given: n + d = 25 #1 (number of coins)

given: .05n + .10d = 1.65 #2 (amount in dollars)

n = 25 - d #3 (rewrite of #1)

.05(25 -d) + .10d = 1.65 (substitute #3 in #2)

1.25 - .05d + .10d = 1.65 (multiply out the left side)

.05d = .40 (collection of like terms)

d = 8 (divided both sides by.05)

n + 8 = 25 (substitute answer for d in #1)

n = 17 (subtract both sides by 8)

There are 8 dimes and 17 nickels.

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Answer:

105.47 hours

Step-by-step explanation:

1300x0.13=172.9

172.9+1300=1502.9

1502.9/14.25=105.47

Answer:

Thus the value of the car decreases by $2,750 every year.... Making it $19,250 in the first year and $16,500 in the second

Step-by-step explanation:

12.5/100×22,000

2750

Answer:

Associative.

Step-by-step explanation:

The associative property is the property that means an equation's result will be the same regardless of grouping the factors together or reversing the equation.

e.g

[tex](a - b) \times c = c \times (b-a)[/tex]

The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. The circumcenter, centroid, and orthocenter are all collinear.

The circumcenter, centroid, and orthocenter are all collinear.

The centroid separates the line connecting the circumcenter and orthocenter in the proportion of 2 :1

i.e, CSOC = 21.

Where, C-Coordinate of the centroid. O-Coordinate of the orthocenter.

The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. A centroid is the point at which the lines drawn from the midpoints of each side of a triangle intersect at the opposite vertex.

Any triangle's orthocenter, centroid, and circumcenter are collinear. The centroid divides the distance between the orthocenter and the circumcenter in a 2:1 ratio. The line connecting these three points is known as the triangle's Euler line. to represent the ABC triangle's circumcircle.

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The given sequence is geometric, with common ratio = 0.4.

Now, Given: 10, 4, 1.6, 0.64, ....

Here, [tex]\frac{4}{10}=\frac{1.6}{4}=\frac{0.64}{1.6}=0.4[/tex]

That is, the given sequence follows the only necessary condition for a sequence to be geometric.

Hence, The given sequence is geometric, with common ratio = 0.4.

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Answer:

It will take 22 hours

Step-by-step explanation:

10925 ÷ 500 = 21.9 = 22 hours

Answer:

630 rock cards

Step-by-step explanation:

aight so 40 % of 1400 is 560 , and 15% of 1400 is 210 . add those and you get 770 . so you got 770 water and rare . you subtract that by 1400 and you got 630 !!

Answer: 476 rock type pokemon cards

Step-by-step explanation: Let's do this! 40% of 1400 is 560, and 15% of 560 is 84. 560 - 84 = 476.

Answer:

x= -3

Step-by-step explanation:

[tex]2(2x + 3) = x - 3 \\ 4x + 6 = x - 3 \\ 4x = x - 3 - 6 \\ 4x - x = - 3 - 6 \\ 3x = - 9 \\ x = \frac{ - 9}{3} \\ x = - 3[/tex]

Answer:

[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]

Step-by-step explanation:

Given absolute value equation:

[tex]2|2x+3|=|x-3|[/tex]

The absolute value of a number is its positive numerical value.

Therefore, the expressions inside the bars should be set to both positive and negative.  Rewrite the absolute value equation as four equations without absolute value bars and simplify:

[tex]\textsf{Positive = Positive}: \quad 2(2x+3)=x-3[/tex]

[tex]\textsf{Positive = Negative}: \quad 2(2x+3)=-(x-3)[/tex]

[tex]\begin{aligned}\textsf{Negative = Positive}: \quad -2(2x+3) &=x-3\\ \implies 2(2x+3) &=-(x-3)\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Negative = Negative}: \quad -2(2x+3) &=-(x-3)\\ \implies 2(2x+3)&=x-3\end{aligned}[/tex]

From inspection of the equations:

so there are only two unique equations to be solved.

Equation 1

[tex]\begin{aligned}2(2x+3) & =x-3\\4x+6 & = x-3\\4x+6-x&=x-3-x\\3x+6&=-3\\3x+6-6&=-3-6\\3x & =-9\\\dfrac{3x}{3} & = \dfrac{-9}{3}\\ x&=-3 \end{aligned}[/tex]

Equation 2

[tex]\begin{aligned}2(2x+3)&=-(x-3)\\4x+6&=-x+3\\4x+6+x&=-x+3+x\\5x+6&=3\\5x+6-6&=3-6\\5x &=-3\\ \dfrac{5x}{5}&=\dfrac{-3}{5}\\x &=-\dfrac{3}{5} \end{aligned}[/tex]

Therefore, the solutions are:

[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]

For the following function, we have that:

In a graph:

Hence, for the graph in this problem, we have that:

Hence:

We have to look at the values of y on the interval, hence:

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Answer: $7 per book

Step-by-step explanation:

$77 for 11 books, so we do 77 ÷ 11 = 7

Answer:

$34,000.00

Step-by-step explanation:

[tex]2,780,000/82 = 33,902.439\\33,902.439 ~ 34,000.00[/tex]

The average hockey player makes per game is an amount of $34,000.00 which is the correct option would be option (A).

In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.

For example 4/2 = 2

The average professional hockey player makes $2.78 million a year.

$2.78 million = $2,780,000

They play an average of 82 games.

The average hockey player makes per game = 2,780,000 / 82

Apply the division operation to get the answer.

The average hockey player makes per game = 33,902.439

The average hockey player makes per game = $33,900.00

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for the first one x = 12

second one is 2

Answer:

x = 12

x = 2

Step-by-step explanation:

Basically the triangles are congruent. Therefore, the sides are equal to each other. Set both equations equal to each other and solve for x.

A Figure ABCD is a rhombus. The angles of A and C are equal by alterenate interior angle. The value of x in the figure ABCD rhombus is 9 degree.

We know that rhombuses are a particular type of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal.

The Solution to an equation is finding values of the variable in the considered equation for which the equation considered evaluates to be true.

For a solution, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, thus solution to a system is the intersection of all its equation at single point

WE know that the diagonals of a rhombus bisect each other, we know that triangle DEC is a right triangle.

Since the side lengths of a rhombus are equal, so the angles of A and C are equal by alterenate interior angle.

Now, 5x-8 = 3x + 10

i.e. 5x - 3x = 10 + 8

i.e. 2x = 18

i.e. x = 9

Therefore the value of x in the figure ABCD is 9 degree.

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Answer:

for real even great Britain cant get this because ya

Step-by-step explanation:

Answer:

35, the population size is 2.

The example that illustrates public scientific communication is D. a federal government agency publishes an article in a professional scientific journal detailing technical details of a new virus.

Communication simply had to do with how messages are passed from the sender to the audience or the other party.

In this case, the example that illustrates public scientific communication is a federal government agency publishes an article in a professional scientific journal detailing technical details of a new virus.

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The following volume quantities are listed below:

a) 2 pints, 1 qt

b) 12 pints, 6 qt

c) 5 pints, 2.5 c

d) 6.75 pints, 3.375 fl oz

In this question we must transform a quantity in a unit to another quantity in a unit of the same kind. For instance, if we have a quantity in a mass unit, then we only can convert it into another mass unit.

Herein we have four unit conversion cases for volumes, both pints and quarts are volume units commonly used in the United States. There are the following equivalencies:

Now we proceed to convert each quantity to pints and quarts by cross multiplication:

a) 32 fl oz × 2 pints / 32 fl oz = 2 pints, 32 fl oz × 1 qt / 32 fl oz = 1 qt

b) 24 c × 2 pints / 4 c = 12 pints, 24 c × 1 qt / 4 c = 6 qt

c) 10 c × 2 pints / 4 c = 5 pints, 10 c × 1 qt / 4 c = 2.5 c

d) 108 fl oz × 2 pints / 32 fl oz = 6.75 pints, 108 fl oz × 1 qt / 32 fl oz = 3.375 fl oz

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 The rationalized expression in general term is given by: (-8 -4√2) / 3

  Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.

  As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.

(8√2 / 6-3√8 ) Multiply by  ( 6+3√8)/( 6+3√8)

(8√2 / 6-3√8 )( 6+3√8)/( 6+3√8)

8√2(6+3√8) / (6-3√8)²  Expand the denominator using the FOIL method.

8√2(6+3√8) / (36 - 18√8 + 18√8 - 72)

8√2(6+3√8) / -36

48√2 + 24√2√8 / -36  ::::.   √8 = 2√2

48√2 + 96 / -36

-12(4√2 + 8) / 12x3

(-8 -4√2) / 3 is the result.

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Answer: n=-7

Step-by-step explanation:

5n - 7n = 14

(5-7)n=14

-2n=14

-2n/(-2)=14/(-2)

n=14/(-2)

n=-7

The equation is,

→ 5n - 7n = 14

Solving for the value of n,

→ 5n - 7n = 14

→ -2n = 14

→ n = -(14//2)

→ [ n = -7 ]

Thus, the value of n is -7.

The equation written in standard form is expressed as 3x - y = -11

The standard form of a linear equation is expressed as Ax + By = C

Given the equation below;

y - 8 = 3(x+1)

Expand

y- 8 = 3x + 3

Collect the like terms

y-3x = 3 + 8

y - 3x = 11

-3x + y = 11

3x - y = -11

Hence the equation written in standard form is expressed as 3x - y = -11

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The maximum​ displacement, the​ frequency, and the time required for one cycle are 1/5 inch, 1/π Hz and π sec.

A displacement is a vector in geometry and mechanics that has a length equal to the shortest distance between a point P's initial and final positions. It calculates the length and angle of the net motion, or total motion, in a straight line from the starting point to the destination of the point trajectory. The translation that links the starting point and the ending point can be used to spot a displacement.

Therefore, the instantaneous speed is different from velocity, which is the rate at which the distance traveled along a particular path changes over time. The temporal rate of change of the position vector can also be used to describe velocity.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per \underline{month}} \end{array}\dotfill &1\\ t=\underline{months}\dotfill &10 \end{cases} \\\\\\ A=50\left(1+\frac{0.03}{1}\right)^{1\cdot 10} \implies A=50(1.03)^{10}\implies A \approx \text{\LARGE 67.20}[/tex]

well, let's check how long till you'd have $100 first

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$100\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per \underline{month}} \end{array}\dotfill &1\\ t=\underline{months} \end{cases}[/tex]

[tex]100=50\left(1+\frac{0.03}{1}\right)^{1\cdot t} \implies 100=50(1.03)^t\implies \cfrac{100}{50}=1.03^t \\\\\\ 2=1.03^t\implies \log(2)=\log(1.03^t)\implies \log(2)=t\log(1.03) \\\\\\ \stackrel{\textit{about 23 months and 13 days}}{\cfrac{\log(2)}{\log(1.03)}=t\implies \text{\LARGE 23.45}\approx t}[/tex]

The distance from the sun to the other focus is 5.01 × 10⁹ m.

(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;

2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.

(b) To express this in terms of solar radii, we set up a ratio;

(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2

Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.

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Complete question is;

The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.

The sum of the finite series  [tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex]  is 20

Given a finite series:

[tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex]

Recall the properties of summation notation:

Σₙ b. f(n) = b Σₙ f(n) where b is a constant.

Σ (a + b) = Σ a +  Σ b

[tex]\sum\limits^p_{n=1} {b} =b.p[/tex]  where b is a constant

Using the above summation properties, we can write:

[tex]\sum\limits^{8}_{n=1} {(7-n)}=\sum\limits^{8}_{n=1} {7}-\sum\limits^{8}_{n=1} {n}[/tex]

=7 . 8 - (1+2+3+ ...+8)

= 56 - 8/2 (1+8)

= 56 - 4 . 9

= 56 - 36 = 20

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