5x + 6 = 2(2x - 3)
help

Answer:

  (b)  Both vertical and horizontal reflection

Step-by-step explanation:

The figure will be a horizontal reflection of itself about any vertical line through two of the smaller 6-pointed stars.

The figure will be a vertical reflection of itself about any horizontal line through two of the smaller 6-pointed stars.

  the pattern has both vertical and horizontal reflection

__

Additional comment

A pattern will have horizontal reflection if there exists a vertical line about which the pattern can be reflected to itself. That is, there exists one (or more) vertical lines of symmetry.

Similarly, the pattern will have vertical reflection if there is a horizontal line about which the pattern can be reflected to itself. Such a line is a horizontal line of symmetry.

Answer

1+21

Step-by-step explanation:

Hope this helps :D

From the given graph

The x-axis represents the number of hours

The y-axis represents the amount earned

The common solution of the two lines is the point of intersection

Since the point of intersection is (4, 40), then

They will earn the same amount of money $40 in 4 hours

After 4 hours they will the same amount of money

If a series an is defined by the equations a1 = 2 an+1 = 3 + cos(n) / √n · an, then  Σan is absolutely convergent. Therefore, the answer is: a) absolutely convergent.

To determine whether Σan is absolutely convergent, conditionally convergent, or divergent, we need to analyze the behavior of the series as n approaches infinity.

First, let's look at the absolute value of the terms in the series:

|an| = |2 × (3 + cos(n) / √n · an-1)|
    = |6 + 2cos(n) / √n · an-1|

Next, we can use the Comparison Test by comparing the series to a known convergent or divergent series. Let's compare the series to the p-series:

∑1/n^p

where p = 3/2. This series is known to converge by the p-test.

Now, we can rewrite the absolute value of an in terms of the p-series:

|an| = |6 + 2cos(n) / √n · an-1|
     ≤ |6 + 2 / √n · an-1|          (since cos(n) ≤ 1)
     ≤ 6 + 2 / √n · |an-1|           (using the triangle inequality)

Therefore, we have:

|an| ≤ 6 + 2 / √n · |an-1|

If we take the limit of both sides as n approaches infinity, we get:

lim n→∞ (6 + 2 / √n · |an-1|) / |an-1|
= lim n→∞ (6 / |an-1|) + (2 / (√n · |an-1|))
= 6 / lim n→∞ |an-1| + 0

Since lim n→∞ |an-1| exists (as an is a well-defined series), we can conclude that the limit is a finite number. Therefore, by the Comparison Test, Σ|an| converges.

Finally, we can use the Ratio Test to determine whether Σan converges absolutely or conditionally:

lim n→∞ |an+1 / an|
= lim n→∞ |(3 + cos(n+1) / √(n+1) · an) / an|
= lim n→∞ |(3 + cos(n+1)) / (√(n+1) · an)|

Using L'Hopital's Rule, we can show that the limit of the cosine term is 0, and the limit of the denominator is infinity. Therefore, the limit of the ratio is 0.

Since the limit of the ratio is less than 1, we can conclude that Σan converges absolutely.

Therefore, the answer is: a) absolutely convergent.

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Answer:

x = 6

Step-by-step explanation:

2 + 7x = 5x + 14

7x - 5x = 14 - 2

2x = 12

x = 12 : 2

x = 6

Good luck !

The acceleration of gravity on the surface of planet Nos'kere is about 21.16 m/s².

Since we know that,

The formula for the period of a pendulum is,

⇒ T = 2π√(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

We can rearrange this formula to solve for g,

⇒ g = 4π²L/T²

Substituting the given values, we get,

⇒ g = 4π²(3.4 m)/(2.9 s)²

⇒ g ≈ 21.16 m/s²

Therefore,

On the surface of the planet Nos'kere, gravity accelerates at a rate of around 21.16 m/s².

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Answer:

Volume of a rectangular prism =length×width×height

= 4x3x7

=84

volume = 84

Answer: The answer would be 84

Step-by-step explanation:

To get the volume of a rectangular prism you need to times the width hight and length

Width x Hight x Length = Volume

4 x 3 x 7 = 84  

Given:

1 chocolate chip cookie recipe = 12 cup of chocolate chips per batch.

Alonzo wants to make 3 12 batches.

Lets's find the number of chocolate chips he will need.

Number of batches he wants to make is = 3 x 12 = 36 batches

SInce 1 chocolate chip cookie recipe calls for 12 cup of chocolate chips per batch, we have:

Answer:

LK = 3.56

ML = 8.76

m∠L = 66°

Step-by-step explanation:

tan 24 = \(\frac{LK}{8}\)

8 tan 24 = LK

LK = 3.56

cos 24 = \(\frac{8}{ML}\)

ML cos 24 = 8

ML = \(\frac{8}{cos 24}\) = 8.76

∠L and ∠M are complementary

m∠L + m∠M = 90

m∠L + 24 = 90

m∠L = 66°

Note:  You need to learn the definitions of all the trig functions and then these types of problems are easy.  

For example, Tan of an angle = oppside/adjacent side.  OK?

Step-by-step explanation:

You can remember the commutative property by thinking of the numbers "commuting," or changing places. The example shows us that "negative two plus positive four" is the same as "positive four plus negative two."

Answer:

1) 20.9

2) 896

3) 21

Step-by-step explanation:

1) 5.6÷2^3+(12.75+7.45)

---> 12.75 + 7.45 = 20.2

\(5.6\) ÷ \(2^3 + 20.2\)

--> Simplify 2^3 to 8

\(5.6\) ÷ 8 + 20.2

--> 5.6 ÷ 8 = 0.7

\(0.7+20.2\)

--> Simplify

\(20.9\)

2) 4^3 × (0.6 +3.6) ÷ 0.3

---> 0.6 + 3.6 = 4.2

4^3 * 4.2 ÷ 0.3

---> 4^3 = 64

64 * 4.2 ÷ 0.3

--> 64 * 4.2 = 268.8

268.8 ÷ 0.3

--> 268.8 ÷ 0.3 = 896

896

3) 2^4 + (2.75 +1.75) ÷ 0.9

--> 2.75 + 1.75 = 4.5

2^4 + 4.5 ÷ 0.9

--> 2^4 = 16

16 + 4.5 ÷ 0.9

--> 4.5 ÷ 0.89 = 5

16 + 5

--> Simplify

= 21

5.6 ÷ 2³ +  (12.75 + 7.45) = 20.9.

4³ × (0.6 +3.6) ÷ 0.3 =  896.

2⁴ + (2.75 +1.75) ÷ 0.9 = 21.

PEMDAS rule is the correct way of simplifying a given equation.It stands for Parentheses, exponents, multiply, divide,add and in last subtract.

According to the given question we have to simplify the given equations.

5.6 ÷ 2³ +  (12.75 + 7.45)

= 5.6 ÷ 8 + (12.75 + 7.45)

= 5.6 × 1/8 + 20.2

= 0.7 + 20.2

= 20.9.

4³ × (0.6 +3.6) ÷ 0.3

= 4³ × (4.2) ÷ 0.3

= 64 × 4.2 ÷ 0.3

= 64 × 14

= 896

2⁴ + (2.75 +1.75) ÷ 0.9

= 16 + 4.5 ÷ 0.9

= 16 + 5

= 21.

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Answer:

Divide 17 by 20.

Step-by-step explanation:

Answer is 0.85.

Answer:

Step-by-step explanation:

\(\frac{17}{20} \\\\\)

Through long division

\(\begin{matrix}\space\space\space\space\space\space\space\space\emptyspace0\space\space\space\space\space\space\space\space\space\space\space\space\\ 20\overline{|\smallspace17}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\\\)

Given

What number comes next in the sequence?

16, 8, 4, 2, 1, ?

Solution

This is a Geometric sequence, we need to find the common ratio

The formula for the common ratio is

Now

The final answer

Answer:

y = 12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

3.6y = 1.6y + 24

Step 2: Solve for y

Step 3: Check

Plug in y into the original equation to verify it's a solution.

Here we have 43.2 does indeed equal 43.2.

∴ y = 12 is the solution to the equation.

Answer:

88

Step-by-step explanation:

We know that one figure represents 8 customers. There are a total of 4 + 2.5 + 1 + 3.5 = 11 figures so the answer is 11 * 8 = 88.

Answer:

x=5

Step-by-step explanation:

2x+10=20

   -10   -10

2x=10

then divide both sides by 2

x=5

Answer:

x = 5

Step-by-step explanation:

Given

2x + 10 = 20

Subtract 10 to both sides

(2x + 10) -10 = 20 - 10

2x = 10

Divide both sides by 2

\(\frac{2x}{2} =\frac{10}{2}\)

x=5

Check your work. Substituted 5 for x

2x + 10 = 20

2(5) + 10 =20

10 + 10 = 20

20 = 20

Answer:

Step-by-step explanation:

The amounts are x (me) and y (sister).

If I give my sister 5 dollars, then we will have the same amount of money:

If she gives me 8 dollars, then I'll have twice as much money as she has:

Compare the equations and solve for y:

Find x:

The graph will have a gradual increase in speed towards the canyon, followed by a flat line during the rest, a constant positive slope while walking towards the canyon, and finally, a steep decrease in speed as Wile E. runs back to the cave.

In this scenario, let's assume that the positive direction is towards the canyon and the negative direction is towards the cave. Based on the given information, we can draw a qualitative graph of Wile E.'s speed versus time as follows:

From the start, Wile E. accelerates in the positive direction towards the canyon, so the speed gradually increases.

When Wile E. reaches the halfway point, he stops for a short rest. At this point, the graph will show a horizontal line indicating zero speed since he is not moving.

After the rest, Wile E. starts walking towards the canyon at a constant speed. The graph will show a straight line with a positive slope, representing a steady speed.

When Wile E. reaches the canyon, he realizes it's almost time for Animal Planet, so he turns around and runs back to the cave as fast as he can. The graph will show a steep line with a negative slope, indicating a rapid decrease in speed.

Overall, the graph will have a gradual increase in speed towards the canyon, followed by a flat line during the rest, a constant positive slope while walking towards the canyon, and finally, a steep decrease in speed as Wile E. runs back to the cave.

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The probability of at least 30 left-handed individuals in a sample of 100

What is boinomial probability ?

Binomial probability refers to the probability of a particular number of "successes" occurring in a fixed number of independent trials. In other words, it calculates the probability of a specific outcome happening a certain number of times in a given set of trials.

The binomial probability formula is:

P(X=k) = (n choose k) *\(p^{k}\) * \((1-p)^{(n-k)}\)

where:

P(X=k) is the probability of getting k successes in n trials

n is the number of trials

k is the number of successes

p is the probability of success on a single trial

(n choose k) is the binomial coefficient, which represent

He probability of selecting at least 30 left-handed individuals out of a sample of 100 adults in the US can be calculated using the binomial probability formula with x counting the number who are left-handed.

However, we must be careful when applying the formula to this problem because the sample is selected without replacement. The binomial distribution assumes that each trial is independent of the others, which is not the case when sampling without replacement.

In cases where the sample size is much smaller than the population size, the effect of not replacing the selected individuals is negligible. However, when the sample size is a substantial portion of the population size, as in this case, the probability of selecting an individual who is left-handed changes after each selection. This means that the probabilities of each selection are not independent, and the binomial formula cannot be used.

Therefore, to accurately calculate the probability of at least 30 left-handed individuals in a sample of 100 adults selected in the US without replacement, we need to use a different probability distribution, such as the hypergeometric distribution.

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Step-by-step explanation:

To find the angle between a line and the x-axis, we need to calculate the slope of the line first. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the points (-2, 2) and (8, 9), we can substitute the values into the formula:

m = (9 - 2) / (8 - (-2))

= 7 / 10

= 0.7

The slope of the line is 0.7. The angle between the line and the x-axis can be found using the inverse tangent (arctan) function. The tangent of an angle is equal to the slope of the line, so we can write:

tan(θ) = 0.7

Taking the inverse tangent of both sides, we find:

θ = arctan(0.7)

Using a calculator, we can evaluate this to be approximately:

θ ≈ 35.87 degrees

Therefore, the angle between the line and the x-axis is approximately 35.87 degrees.

We conclude that based on the sample data collected by Lizzy, we cannot say with confidence that the proportion of Starbucks patrons who enjoy playing board games is greater than 50%.

To answer this question, we need to perform a hypothesis test using phantoms.

Null Hypothesis: The proportion of Starbucks patrons who enjoy playing board games is equal to 50% or less (p ≤ 0.50)

Alternative Hypothesis: The proportion of Starbucks patrons who enjoy playing board games is greater than 50% (p > 0.50)

We can use a one-sample proportion z-test to test this hypothesis. First, we need to calculate the sample proportion:

p-hat = 32/57 = 0.56

Next, we need to calculate the standard error of the sample proportion:

SE = sqrt(p-hat * (1 - p-hat) / n) = sqrt(0.56 * 0.44 / 57) = 0.094

Then, we can calculate the test statistic:

z = (p-hat - p) / SE = (0.56 - 0.50) / 0.094 = 0.64

Using a significance level of 0.05, we find the critical z-value to be 1.645 (for a one-tailed test).

Since our test statistic (0.64) is less than the critical value (1.645), we fail to reject the null hypothesis. There is not enough evidence to suggest that the majority of Starbucks patrons enjoy playing board games.

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Answer:

7 m/s

Step-by-step explanation:

we do 3 1/2 times 2 since we are finding average speed which we use a whole hour so your answer will be 7. 1/2 times 2 = 1 which is why we multiply by 2.

Answer: 9.7 seconds

Step-by-step explanation:

\(16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)

The probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

The given probability distribution table shows the probabilities of having 1, 2, or 3 computers in a randomly selected home in Queens. However, the probability of having 4 or more computers is not given in the table.

To find the probability of having 4 or more computers in a randomly selected home, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is having 4 or more computers in a home, and the complement of this event is having 1, 2, or 3 computers in a home.

So, the probability of having 4 or more computers in a randomly selected home in Queens can be calculated as:

P(4 or more) = 1 - P(1 or 2 or 3)

P(1 or 2 or 3) = P(1) + P(2) + P(3) = 0.4 + 0.3 + 0.2 = 0.9

P(4 or more) = 1 - 0.9 = 0.1

Therefore, the probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

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To implement the first-best allocation rule in dominant strategies, a second-price auction would need to be modified in this example.

In a second-price auction, the highest bidder wins the auction but pays the price bid by the second-highest bidder. To implement the first-best allocation rule in dominant strategies, several modifications would be necessary. Firstly, the auction mechanism would need to incorporate information about the participants' business needs, preferences, and contract requirements. This could involve collecting detailed profiles and specifications from the members of Money Club and Money Ball. Secondly, the auction would need to consider not only the bid amount but also factors such as the participant's industry, experience, reputation, and potential synergies with other members.

These additional criteria would allow for a more comprehensive evaluation of the bidders and help determine the best allocation of contracts. Finally, the auction mechanism would need to account for potential externalities or spillover effects that arise from the interactions between members, as these can affect the overall value generated by the contracts.

By incorporating these modifications, the auction could aim to allocate contracts based on the first-best allocation rule in dominant strategies. This means that the auction would prioritize the most efficient and mutually beneficial matches between businesses, maximizing the overall welfare and value created within the network. Such modifications would require a more sophisticated auction design that considers multiple dimensions beyond just the bid price, taking into account the specific characteristics of the businesses involved and their potential for successful collaboration.

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Answer:

X=2.8 when y =14

Step-by-step explanation:

\(5x = 14 \\ x = \frac{14}{5} \\ x = 2.8 \)

The Factors of the numbers are as follows;

The common factors are 2 and 3.

Therefore, the Greatest Common Factor is (2 x 3) 6

Answer:

Blank 1: 0.12

Blank 2: 0.18

Step-by-step explanation:

Out of 50, there are 6 numbers that contain the digit 5, (5, 15, 25, 35, 45, 50)

so when you take 0.06 and multiply it by 2 (because you have to multiply 50 by 2 to get 100), you get 0.12.

For blank 2, there are 9 single digit numbers, (1, 2, 3, 4, 5, 6, 7, 8, and 9) equaling 0.09. Multiply that by 2 and you get 0.18.