Which number line represents the solution set for the inequality 2x - 62 6(x-2) + 8?​

Answer:

29/14

Step-by-step explanation:

Start by working out the LCM of these (or any common denominator). A common denominator for 4 and 7 is 28 cuz 4 x 7 = 28.

3/4 = 21/28

4/7 = 16/28

3/4 = 21/28

(21+16+21)/28 = 58/28 which can simplify to 29/14

hi

Golden rule : you can only add or substract fraction if and only if they have the same denominator.

so two solutions :

you see that one denominator is a multiple of the second. so you multiply all the fraction by this multiple.

ex : 1/3 + 5/6

here I can easely convert 1/3 into a fraction with 6 as 6 is 3x2.

so : 1x2 = 2 and 3x2 = 6

1/3 is 2/6

so. 1/3 +5/6 = 2/6 +5/6

fraction have same denominator, I add numerators : 2/6 +5/6 =7/6

if it not that evident, you multiply fraction A up and down by denominator of fraction B.

and you multiply up and down fraction B by denomonator of fraction A

let' s see with your exemle :

3/4 +4/7+3/4 = ?

first I add fraction with same denominator :

3/4+3/4+4/7 = 6/4 +4/7

fraction A is 6/4.

I multiply up and down by denominator fractiok B which is " 7"

so. 6/4 = 6x7/4×7 = 42/28

let's apply method to fraction B whixh is 4/7 . let' multiply up and down by denominator of fraction A which is " 4"

so : 4/7 = 4x4 /7x4 = 16/28

now we have :

6/4 +4/7 = 42/28 +16/28

both my fractions have same denominator "28" so I add numerator :

42/28 +16/28 = 58/28

Now must wonder if 58/28 can be simplify. Good trick is to decompose numbers, and in prime number is the best way to do

58 = 2x29

28 = 7x2x2

so 58/28= (2×29)/ (7x2x2)

when there is same number up and down I can cross it out .

so here one "2" up and down can be rule out

so 58/28 = 2x29 /7×2×2 = 29/7x2 =29/14

I can not symplify more, so calculus is over.

in short :

3/4+4/7+3/4 = 6/4+4/7

= 42/28 +16/28

=58/28

= 29/14

We need to evaluate the given function at these x values:

f(x) = 6x + 12

Just plug in the x-values into x of the functional expression. Simple!

a)

x = 4

f(4) = 6(4) + 12 = 24 + 12 = 36

b)

x = -13

f(-13) = 6(-13) + 12 = -78 + 12 = -66

c)

x = 12/31

Answer:

In order of the questions asked, the answers are, C, D, A, C

Step-by-step explanation:

After three half-lives have elapsed, 12.5% of the original nuclide remains, so the answer is C.

if 17 % is daughter nuclide, then 83% is parent nuclide, so , the answer is D

the isotope for dating organic remains is A. carbon-14

for 25% of original, 2 half-lives must have passed, so we get (2)(5730) = 11460

so the answer is C

The total number of groupings that is possible amounts to 62.

It is required that each one of the tourists must choose either of the two guides. This means, therefore, the possible number of groupings is: \(2^{6} \)64.

However, if we subtract the 2 people (recall that the guides decided to split) the answer becomes calculable as follows:

Totaling each scenario, we can say:

(6 x2) + (15x2) + 20 = 62

Another way to express this is

\(2^{6} \) - 2= 62

This refers to the various possible ways in which a given amount or number of items, or persons, may be arranged.

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The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.

Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.

Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.

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Using the formula for the population growth with given value of rate and the condition for the population to reach, The answer is 87 years.

The country, territory, or geographic area's yearly average rate of change in population size over a certain time period. It expresses the proportion, usually multiplied by 100, between the annual growth in population size and the total population for that year.

The rise in the number of people on Earth is referred to as population growth. The majority of human history saw a relatively steady population size. Energy, food, water, and medical care, however, became more accessible and dependable as a result of innovation and industrialization.

rate = 0.8%

\(2P = P * (1 + \frac {0.8}{100})^{n}\)

\(2= (1.008)^{n}\)

n=86.98 years

approximately 87 years.

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Step-by-step explanation:

Let x be the number of pages that were skimmed through.

Time taken to skim through = 10 * (x/15) = 2/3 x min.

Time taken to read through = 15 * [(275-x)/10] = 1.5(275-x) min.

We have 2/3 x + 1.5(275-x) = 350.

Therefore 412.5 - 5/6 x = 350 and x = 75.

Answer:8pages

Step-by-step explanation:

10minutes/350minutes×275=7.85~8pages

Answer:

y intercept is (0,-1)

Step-by-step explanation:

the Nash equilibrium is not necessarily the best or most desirable outcome for the players involved. It simply represents a stable state where no player has an incentive to unilaterally deviate from their chosen strategy.

To determine the Nash equilibria in a game, we need to analyze the strategies of each player and identify the combinations of strategies where no player has an incentive to unilaterally deviate.

Given the options:

1. (P1=Shot, P2=Shot)

2. (P1=No shot, P2=No shot)

3. (P1=Shot, P2=No shot)

4. (P1=No shot, P2=Shot)

Let's analyze each combination:

1. (P1=Shot, P2=Shot):

If both players choose to shoot, they both face the risk of being shot and getting injured. Neither player has an incentive to deviate from this strategy, as changing to "No shot" would expose them to the risk of being shot without being able to retaliate. Therefore, (P1=Shot, P2=Shot) is a Nash equilibrium.

2. (P1=No shot, P2=No shot):

If both players choose not to shoot, they avoid the risk of being injured. Again, neither player has an incentive to unilaterally deviate from this strategy, as changing to "Shot" would expose them to the risk of being injured without gaining any advantage. Therefore, (P1=No shot, P2=No shot) is a Nash equilibrium.

3. (P1=Shot, P2=No shot):

If Player 1 chooses to shoot while Player 2 chooses not to shoot, Player 1 has an advantage and can potentially eliminate Player 2 without being injured. In this scenario, Player 2 may have an incentive to deviate from "No shot" and switch to "Shot" to protect themselves. Therefore, (P1=Shot, P2=No shot) is not a Nash equilibrium.

4. (P1=No shot, P2=Shot):

Similarly, if Player 1 chooses not to shoot while Player 2 chooses to shoot, Player 2 has an advantage and can potentially eliminate Player 1 without being injured. In this scenario, Player 1 may have an incentive to deviate from "No shot" and switch to "Shot" to protect themselves. Therefore, (P1=No shot, P2=Shot) is not a Nash equilibrium.

Based on the analysis, the Nash equilibria in this game are:

- (P1=Shot, P2=Shot)

- (P1=No shot, P2=No shot)

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The probability that these two spins added together would equal 7 is 1/25.

The probability that each spin will land on a specific number is 1/5. Since the spins are independent, we can multiply the probability of each spin landing on the desired number to find the probability of both spins landing on the desired numbers.

To get the sum 7, Charlie's spinner needs to land on 4, which is (1/5) and Libby's spinner needs to land on 3 which is also (1/5).

The probability of both spins landing on the desired numbers is (1/5) * (1/5) = 1/25.

It is important to note that the probability is low because the spins are independent events, meaning that the outcome of one spin does not affect the outcome of the other spin.

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Answer:

= 16m2o−8mno

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

From the diagram, we find,

(2x - 16) + (x - 8) = 9

=> 2x - 16 + x - 8 = 9

=> 2x + x - 16 - 8 = 9

=> 3x - 24 = 9

=> 3x = 9 + 24

=> 3x = 33

=> x = 33/3

=> x = 11

The reasonable estimate of the probability that Todd runs 5/13.

We know that,

Experimental probability = Number of favorable outcomes/total number  of outcomes.

Experimental probability, also called empirical probability, is based on real experiments and rational records of what happened. A series of real-world experiments are conducted to determine the occurrence of events. Experiments with undetermined results are called random experiments. The results of such experiments are uncertain. Repeat the random experiment several times to determine its probability. Experiments are repeated a specified number of times, and each repetition is called a trial. Mathematically, the formula for experimental probability is defined as:

Probability of event P(E) =

frequency of occurrence of event / total number of trials.

According to the question:

The number of favorable outcomes are 5.

The total number of outcomes are 2 + 3 + 3 + 5 = 13.

Therefore, the reasonable estimate of the probability that Todd runs is 5/13.

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Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

This estimation is speculative and may not accurately reflect the actual probability in the given context.

To determine the probability that a person is using a 3-month new member discount given that they have been a member for more than a year, we would need additional information such as the total number of members, the number of members using the discount, and the distribution of membership lengths.

Without this information, it is not possible to calculate the probability directly. However, we can make some assumptions to provide a general idea.

Assuming that the new member discount is only available to new members for the first three months of their membership and that the number of members who have been a member for more than a year is significant, we can estimate that the probability of a person using the 3-month new member discount in this scenario is likely to be low.

This assumption is based on the understanding that the longer a person has been a member, the less likely they are to still be eligible for or make use of a new member discount.

It's important to note that without specific data or a more detailed understanding of the membership characteristics and behavior, this estimation is speculative and may not accurately reflect the actual probability in the given context.

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Answer:

my guess is the flagpole is 164 in tall

Step-by-step explanation:

if she 60 in tall then her shadow is 36 in taller

the flagpole's shadow is 200in so subtract 36 from 200

To evaluate each integral in terms of areas, we need to understand that the integral represents the area under the curve of a function, f(x), between two points on the x-axis.

Let's discuss each integral:

(a) ∫₀⁸ f(x) dx: This represents the area under the curve of f(x) from x = 0 to x = 8. The integral calculates the accumulated area along this interval.

(b) ∫₀²⁰ f(x) dx: Similarly, this represents the area under the curve of f(x) from x = 0 to x = 20. It's a broader interval than (a), so it covers more area under the curve.

(c) ∫²⁰²⁸ f(x) dx: This integral represents the area under the curve of f(x) between x = 20 and x = 28. It's important to note that the interval is now shifted to the right compared to (a) and (b).

(d) ∫¹²²⁸ f(x) dx: This integral calculates the area under the curve of f(x) from x = 12 to x = 28. The interval here is larger than in (c), covering more area under the curve.

(e) ∫¹²²⁸ |f(x)| dx: This integral evaluates the area under the absolute value of f(x) from x = 12 to x = 28. The absolute value ensures that negative function values contribute positively to the area calculation, preventing any cancelation of areas.

(f) ∫₀⁸ f(x) dx: This integral is the same as (a), representing the area under the curve of f(x) from x = 0 to x = 8.

Each integral evaluates the area under the curve of f(x) for different intervals on the x-axis, providing insights into the total accumulated area in those intervals.

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The potential error in the measurements made on this scale, where it reads 0.01g when it is empty, is systematic error.

Systematic errors are consistent and repeatable errors that occur in the same direction and magnitude for each measurement. In this case, the scale consistently reads 0.01g even when there is no weight on it. This indicates a systematic error in the scale's calibration or zeroing mechanism.

Random errors, on the other hand, are unpredictable and can vary in both direction and magnitude. They do not consistently affect measurements in the same way.

Since the error in this case consistently affects the measurements in the same way (always reading 0.01g), it is classified as a systematic error.

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Answer:

136

Step-by-step explanation:

GEMDAS

G - groupings

E - exponents

M - multiply

A - add

S - subtract

The perimeter of the composite figure would be = 21 (to the nearest tenth).

Perimeter is defined as the quantity that is used to evaluate the total length of the sides of an object.

From the given diagram, the composite figure is made up of 6 sides. The addition of these sides is the figures perimeter.

The sides of the composite figure are:

a = 6; b = 12; c = 9; d = 9; e = -9; f = -6.

The perimeter = a + b + c + d + e + f.

= 6 + 12 + 9 +9+ (-9) + (-6)

= 27 - 6

= 21 ( to the nearest tenth)

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Answer:

c. is the correct answer

Answer:

volume = 85.095cm³

Step-by-step explanation:

Volume of cone is ¹/³ πr ²h

volume = ¹/³ x 3.142 x (2.5)² x 13

volume = 85.095cm³

Answer:  D.

Step-by-step explanation:

V(cone)=(1/3)\(\pi r^{2} h\)     they gave diameter=5 but radius is half of that

                                    r=2.5     h=13

V(cone)=\((1/3)\pi (2.5)^{2} 13\)    to get an answer like the choices.  multiply everything in calculator except pi

so

V(cone)=27.083\(\pi\)

In Chapter 6, Problem 10P, the constraints are derived based on the given problem scenario and the objective of the optimization problem. Without specific details about Problem 10P in Chapter 6, it is challenging to provide a precise explanation.

However, I can provide a general understanding of how constraints are typically formulated in optimization problems. In optimization problems, constraints are used to represent the limitations or restrictions on the decision variables. These constraints can arise from various sources, such as physical constraints, resource constraints, budget constraints, or technical constraints. To derive the constraints, you need to carefully analyze the problem statement and identify the conditions or limitations that must be satisfied. These conditions are then translated into mathematical inequalities or equations that relate the decision variables. For example, if the problem involves allocating limited resources among different activities, the constraints would represent the availability of those resources and ensure that the total allocation does not exceed the available amount. Similarly, if the problem involves production planning, constraints might include demand requirements, capacity limitations, or inventory constraints. In general, the process of formulating constraints requires careful consideration of the problem's requirements, objectives, and limitations. It often involves translating real-world constraints into mathematical expressions to create a well-defined optimization problem that can be solved using appropriate techniques.

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Answer:

x=20

Step-by-step explanation:

The speed of the curve at t=4 is approximately 40.63.

We have a given curve as follows:

¯ r ( t ) = ⟨ 5 t 2 − 6 , 7 t − 6 , t 3 8 t ⟩ at t = 4

To find the speed of the curve at t=4, we need to evaluate the magnitude of its velocity vector at t=4.

Velocity vector is the derivative of the curve with respect to time.

Hence, we start by finding the derivative of the curve. The derivative of the curve can be obtained as follows:¯ r'(t) = ⟨10t, 7, (3/8)t² - (3/8)⟩We can now evaluate the velocity vector at t=4:

¯ r'(4) = ⟨10*4, 7, (3/8)(4²) - (3/8)⟩= ⟨40, 7, 1.5⟩

To find the speed of the curve at t=4, we need to evaluate the magnitude of the velocity vector at t=4. The magnitude of a vector can be obtained using the formula:

|v| = √(v₁² + v₂² + v₃² +...)

Therefore, the speed of the curve ¯ r ( t ) = ⟨ 5 t 2 − 6 , 7 t − 6 , t 3 8 t ⟩ at t = 4 is:

|¯ r'(4)| = √(40² + 7² + 1.5²)= √(1600 + 49 + 2.25)= √1651.25≈ 40.63

The speed of the curve at t=4 is approximately 40.63.

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Based on the information in the graph, we can infer that the range of dilation between black and red is 1:2 and between black and green is 2:1.

To find the range of dilation between the triangles we must find their dimension ratio. In this case we must count how many squares the base of the original triangle (black) has. According to the above, this triangle has 8 units.

Then we count the units that have the red and green triangles. In the case of red it has 16 and green has 4. So we could say that for each unit of black, red has two units and green has half a unit, so the ranges would be: 1:2 between black and red and 2:1 between black and green.

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Answer:

1.3

Step-by-step explanation:

Hope this is correct, if not sorry

Answer:

t = 6162  years

Step-by-step explanation:

Apparently you are asked to use the constant k = 0.0001 instead of the most common 0.00012. We'll answer the problem using such number you typed, but make sure that there is no omission in your typing.

The equation to use is that for carbon decay:

\(N(t)=N_0\,e^{-0.0001\,\,t}\)

If the skull contains 54% of its original amount of C14, then that means that :

\(N(t)=0.54 \,\,N_0\)

we use this to solve for the time (t) in our equation:

\(0.54\,\,N_0=N_0\,e^{-0.0001\,\,t}\\\frac{0.54\,\,N_0}{N_0}=e^{-0.0001\,\,t}\\0.54=e^{-0.0001\,\,t}\\ln(0.54)=-0.0001\,\,t\\t=\frac{ln(0.54)}{-0.0001} \\t=6161.86\,\,years\)

which rounded to the nearest year as requested gives :

t = 6162  years

Answer:

The guy on top is correct so thank u so much!! the answer is 6162

Step-by-step explanation:

I did the test

Plant B produced 28,000 panels. Plant B produced 28,000 panels.  

Let's assume that Plant B produced x number of panels. Since 10% of the panels from Plant A were defective, then 90% of the panels were good.

Hence, the number of good panels produced by Plant A is 90% of 16,000 = 0.9 × 16,000 = 14,400 panels. Similarly, 97% of the panels produced by Plant B were good, since 3% of them were defective. Hence, the number of good panels produced by Plant B is 97% of the number of panels produced, or 0.97x.

Therefore, the total number of good panels produced from both plants is:14,400 + 0.97xThe total number of defective panels from both plants is 7% of the total number of panels produced.

Therefore:0.07 (16,000 + x) = 1,120 + 0.03x Simplifying the equation, we get:1,120 + 0.03x = 0.07 × 16,000 + 0.07x1,120 + 0.03x = 1,120 + 1,120 + 0.04x0.03x - 0.04x = 1,120x = 28,000

Therefore, Plant B produced 28,000 panels. Plant B produced 28,000 panels.  

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