Amy solved the exponential inequality
4 Superscript 2 x minus 2 Baseline greater-than-or-equal-to 2
by first rewriting the inequality as
4 Superscript 2 x minus 2 Baseline minus 2 greater-than-or-equal-to y
and then graphing this inequality. She determines the solution set of the inequality is (infinity, 1.25 right-brace.

Which best describes Amy’s solution?

-Amy is correct. The interval (negative infinity, 1.25 right-brace is the solution set for the inequality.
-Amy did not break the inequality into two related inequalities. Her solution set only relates to one inequality.
-Amy used the incorrect inequality symbol. The solution set should be [1.25, ∞).
-Amy used the wrong variable when writing the solution. The solution set should relate to y and not x.

Answer: Rectangle

Step-by-step explanation:

The number of whole numbers whose square roots of a natural number from 1 to 200 will be 14

The natural number of square roots from 1 to 200 are mentioned below

1² = 1,

2² = 4,

3² = 9,

4² = 16,

5² = 25,

6² = 36,

7² = 49,

8² = 64,

9² = 81,

10² = 100,

11² = 121,

12² = 144,

13² = 169,

14² = 196

The number of whole numbers = 14

Above 14 the square will be greater than 200

All the whole numbers are natural number except zero. zero is a whole number not a natural number.

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Answer:

8.0

Step-by-step explanation:

Since we are trying to find the nearest tenth decimal place, we look at the hundredths place to figure it out. Since it is ≥5, we round up.

Answer:

The answer would be 8

Step-by-step explanation:

If you have a decimal and you need to round, if it is four and below, you would have just leave the number as it is if it is five and above, you round up.

re The point-slope form of a line is

The slope m of the line passing through these two points is the difference between their y coordinates divided by the difference between their x - coordinate.

Now we need only find the y-intercept.

Let us use the point (3, 4) which tells us that at x = 3, y = 4; therefore,

Hence, the question of our line in point-slope form is

Alternatively, when we have the slope of the line we would just use one of the points to quickly write the point-intercept form.

The y_1 and x_1 in the very first equation are the coordinates of one of the points on the line =. We know that one of the point on our line is (3, 4);

Answer:

3/8

Step-by-step explanation:

slope = rise/run = 3/8

The solution of the inequality is (x > - 8 and x < 2) or (x > 6 and x < 16).

Herein we find an inequality that involves two absolute values. Absolute values are defined by the following piecewise functions:

Now we proceed to solve the inequality given:

||x - 4| - 7| < 5

- 5 < |x - 4| - 7 < 5

0 < |x - 4| - 2 < 10

|x - 4| - 2 > 0 and |x - 4| - 2 < 10

Case 1: |x - 4| - 2 > 0

|x - 4| > 2

x - 4 > 2 and x - 4 < - 2

x > 6 and x < 2

Case 2: |x - 4| - 2 < 10

|x - 4| < 12

x - 4 < 12 and x - 4 > - 12

x < 16 and x > - 8

The solution of the inequality is (x > - 8 and x < 2) or (x > 6 and x < 16).

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So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:

P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)

Using the binomial formula, we can calculate each of these probabilities:

P(X=k) = (n choose k) p^k (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.

P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608

P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322

P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013

P(X=5) = (5 choose 5) (1/6)⁵ (5/6)⁰ = 0.00003

Therefore,

P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943

So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

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The expected number of passengers who showed up on time from the random sample of 235 booked passengers is 200.

we need to calculate the number of passengers who showed up on time based on the given information.

Given that 85% of people show up on time, we can find the expected number of passengers who showed up by multiplying 235 (the sample size) by 0.85 (the percentage of people who show up on time).

Expected number of passengers who showed up = 235 * 0.85 = 199.75

Since we cannot have a fraction of a passenger, we can round up the number to 200.

Airlines tend to overbook flights to maximize their revenue and minimize the chances of empty seats. They do this by selling more tickets than the actual number of seats available on the plane. This is based on the assumption that some passengers will not show up or cancel their bookings.

However, in some cases, more passengers show up than there are seats available, resulting in overbooked flights. To manage this situation, airlines may offer incentives for passengers to voluntarily give up their seats, or they may deny boarding to some passengers.

In conclusion, based on the given information, the expected number of passengers who showed up on time from the random sample of 235 booked passengers is 200. Airlines tend to overbook flights to compensate for the possibility of no-shows, but it can lead to overbooking issues if too many passengers show up.

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The answer is 143 people between the ages of 25 and 44 are at risk for heart problems, according to the relative frequency table.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.

The answer is 143 people between the ages of 25 and 44 are at risk for heart problems, according to the relative frequency table. This is calculated by adding the number of people in the 25-34 age group (87) to the number of people in the 35-44 age group (56).

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Answer:

For C i would say that it has a widely used floating-point system in which the numbers are expressed as products and it has an appropriate power.

Im new to this math so im trying to figure out a and b

Yes, there is a chance that the bottled water you are drinking is just tap water packaged in a bottle. According to a study by the Natural Resources Defense Council, 25% of bottled water is just tap water that has been packaged in a bottle. [Scientific American, July 2003]

Bottled water is drinking water that has been packaged in bottles or containers for sale. Bottled water can come from a variety of sources, such as municipal supplies, springs, wells, and other sources. In some cases, bottled water is treated or purified to remove impurities and contaminants. However, not all bottled water is purified or treated, and some may be just tap water that has been packaged in a bottle.

Purified water is water that has been treated to remove impurities and contaminants. Purified water can come from any source, including municipal supplies, wells, and other sources. Purification methods may include filtration, reverse osmosis, distillation, or other methods. Purified water is commonly used in medical and industrial applications, as well as in homes for drinking and cooking.

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P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Solution,

2x-56=8

or,2x=8+56

or,2x=64

or,X=64/2

X=32

Hope it helps

Good luck on your assignment

Answer:

x=32

Step-by-step explanation:

First I put the 56 on the other side by doing the opposite to it, so adding 56 to both sides.

2x - 56 = 8

   +56      +56

2x=64

Then divide both sides by two to single out the x and know it's value

2x=64

/2     /2

x=32

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define the given theorems

HL theorem:

LL THEOREM:

AA THEOREM

HA THEOREM

STEP 2: choose the answer

Since it can be seen from the given question image that two legs of the given triangles congruent to one another, this implies that it follows the Leg-Leg Congruence theorem.

Hence, the answer is LL

The probability of "mission accomplished" is 0.875. If the mission is accomplished, the probability of two survivors is approximately 0.2143. The PMF of total medals given out is: P(N = 0) = 0.

Let's denote the number of survivors as X, where X can take values from 0 to 4.

We know that the probability of "mission accomplished" given X survivors is given by pk = k/4, for k = 0, 1, 2, 3, 4.

Now, let's find the probability of each value of X:

P(X = 0) = probability that all X-men sacrifice = (0.5)^4 = 0.0625
P(X = 1) = probability that exactly one X-man survives = 4 * (0.5)^4 = 0.25
P(X = 2) = probability that exactly two X-men survive = 6 * (0.5)^4 = 0.375
P(X = 3) = probability that exactly three X-men survive = 4 * (0.5)^4 = 0.25
P(X = 4) = probability that all X-men survive = (0.5)^4 = 0.0625

Now, we can calculate the probability of "mission accomplished" using the law of total probability:

P("mission accomplished") = P("mission accomplished" | X = 0) * P(X = 0) +
P("mission accomplished" | X = 1) * P(X = 1) +
P("mission accomplished" | X = 2) * P(X = 2) +
P("mission accomplished" | X = 3) * P(X = 3) +
P("mission accomplished" | X = 4) * P(X = 4)

P("mission accomplished") = (0/4) * 0.0625 + (1/4) * 0.25 + (2/4) * 0.375 + (3/4) * 0.25 + (4/4) * 0.0625

P("mission accomplished") = 0 + 0.25 + 0.375 + 0.1875 + 0.0625 = 0.875

Therefore, the probability of "mission accomplished" is 0.875.

(b) If the mission is accomplished, we want to find the probability that there are exactly two survivors (P(X = 2 | "mission accomplished")).

Using Bayes' theorem, we have:

P(X = 2 | "mission accomplished") = P("mission accomplished" | X = 2) * P(X = 2) / P("mission accomplished")

P("mission accomplished" | X = 2) = 2/4 = 0.5 (as given)
P(X = 2) = 0.375 (as calculated in part a)
P("mission accomplished") = 0.875 (as calculated in part a)

P(X = 2 | "mission accomplished") = (0.5 * 0.375) / 0.875 = 0.2143 (approximately)

Therefore, the probability that there are two survivors given that the mission is accomplished is approximately 0.2143.

(c) Let's calculate the probability mass function (PMF) of N, the total number of medals given out.

The possible values of N can range from 0 to 4, corresponding to the number of survivors. For each value of X, the number of medals given out is X (the number of survivors).

P(N = 0) = P(X = 0) = 0.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the expression :

Jacob's yearly income :

2000x + 3000 ; x = number of hours worked per week.

Carlos income :

3800x - 40000

Managers prediction = 35

Jacob.: 2000(35) + 3000 = 73000

Carlos : 3800(35) - 40000 = 93000

Carlos will earn more than Jacob given the manager's prediction.

Number of hours required so they can earn the same amount :

2000x + 3000 = 3800x - 40000

3000 + 40000 = 3800x - 2000x

43000 = 1800x

x = 43000/1800

x = 23.88

x = 24 hours

Answer:

0

Step-by-step explanation:

Using slope intercept as ref (y=mx+b)

plug in the x and y x=1 and y=3 and the slope m=3

3=3(1)+b

solve for b

3=3+b

b=0

Answer:

Step-by-step explanation:

A corresponds to angle P, so angle P measues 70 degrees.

Similarly, angle Q measures 60 degrees and angle R measures 50 degrees.

The absolute change in effective federal income tax from 1940 to 2000 is 15%. This means that the tax rate for the middle class increased by 15 percentage points over this time period.

The absolute change in effective federal income tax from 1940 to 2000 can be calculated by subtracting the tax rate in 1940 from the tax rate in 2000.

To calculate the absolute change in effective federal income tax from 1940 to 2000, we subtract the tax rate in 1940 from the tax rate in 2000:

Absolute change = Tax rate in 2000 - Tax rate in 1940

              = 19% - 4%

              = 15%

Therefore, the absolute change in effective federal income tax from 1940 to 2000 is 15%. This means that the tax rate for the middle class increased by 15 percentage points over this time period.

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Answer:

(n+d=53) (.05n+.10d=4.40)   :)

The Z scores a way to standardize and compare data, as well as to identify outliers.

In simple terms, Z bases give information about how far a data point is from the means of the data set in standard deviation units. The original non-standardized heights, on the other hand, did not guarantee this information.

Z scores are used to standardize data and are useful when comparing two or more different data sets. By converting the original data to Z scores, we can compare data that is on different scales or has different units.

For example, suppose we have two data sets: one with heights measured in inches and the other with weights measured in pounds. We cannot compare these data sets directly as they are at different scales. However, by converting them to Z scores, we can compare them on the same scale.

In addition, the obtained Z's provided a way to identify outliers in the data set. Outliers are data points that are unusually far from the means of the data set. Z scores greater than 3 or less than -3 are generally considered outliers.

In general, the obtained bases are a way to standardize and compare data, as well as to identify outliers.

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Elspeth can find the circumference by dividing 9.42 centimeters by π, the mathematical constant. she can use this radius value to calculate the circumference of the circle using the formula C = 2πr.

The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius.

In this case, Elspeth knows that π times r approximately equals 9.42 centimeters. To find the circumference, she needs to divide 9.42 centimeters by π.

Dividing by π will cancel out the π on the right side of the equation, leaving only the value of the radius r. By dividing 9.42 centimeters by π, Elspeth will obtain the value of the radius.

Then, she can use this radius value to calculate the circumference of the circle using the formula C = 2πr.

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Answer:

36÷7.2=5

So this is the answer

For the parabola y = 2x² + 3x + 1,

a. i.  The x-intercepts are x = -1/2 and x = -1

a. ii. The y-intercept is y = 1

b. i. The line of symmetry is at x = -3/4

b. ii. The equation of the line of symmetry is x = -3/4

c.  The vertex is at (-3/4, -1/8)

A parabola is part of a conic section which is a curve.

Given the parabola y = 2x² + 3x + 1, we find the x- intercept when y = 0.

So, y = 2x² + 3x + 1

2x² + 3x + 1 = 0

2x² + 2x + x + 1 = 0

Factorizing, we have

2x(x + 1) + (x + 1) = 0

(2x + 1)(x + 1) = 0

2x + 1 = 0 or x + 1 = 0

2x = -1 or x = -1

x = -1/2 or x = -1

So, the x-intercepts are x = -1/2 and x = -1

Given the parabola y = 2x² + 3x + 1, we find the y- intercept when x = 0.

So, y = 2x² + 3x + 1

So, y = 2(0)² + 3(0) + 1

y = 0 + 0 + 1

y = 1

So, the y-intercept is y = 1

The line of symmetry passes through the vertex of the parabola where dy/dx = 0.

So, y = 2x² + 3x + 1

dy/dx = d(2x² + 3x + 1)/dx

= d(2x²)/dx + d3x/dx + d1/dx

= 4x + 3 + 0

= 4x + 3

So, when dy/dx = 0,we have

4x + 3 = 0

4x = -3

x = -3/4

So, the line of symmetry is at x = -3/4

The equation of the line of symmetry is x = -3/4

Since the vertex of the parabola is a t x = -3/4, substituting this into the equation, we have

y = 2x² + 3x + 1

y = 2(-3/4)² + 3(-3/4) + 1

y = 2(9/16) - 9/4 + 1

y = 9/8 - 9/4 + 1

y = (9 - 18 + 8)/8

y = (17 - 18)/8

y = -1/8

So, the vertex is at (-3/4, -1/8)

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Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:I think you can say like the most bought music in class B is alternative and the lowest one is classical and so on

Step-by-step explanation:

Answer:

2.5 × 10^-5

please correct me if im wrong.

Answer:

y=2x-6

Step-by-step explanation:

subtract 6x from each side. divide each side by -3.

In the given proof, we are provided with a series of statements and axioms. We need to use the results from page 36 of the cheat sheet (excluding Theorem 11, which is the goal of the proof) to complete the proof. Let's analyze the steps and apply the appropriate results to complete the proof:

Proof:

1. (-a) -((a+b) (a-(ab)))

2. b-a-b

3. a-a (Axiom 6, Axiom 1, Theorem 1)

We start with the first statement: (-a) -((a+b) (a-(ab))). To simplify this expression, we can use one of the results from page 36 of the cheat sheet. Let's consider Result 5, which states: "(-a)-(b-(a-(ab))) = a-ab." By comparing the given expression with Result 5, we can see that we need to make a few adjustments to match the pattern.

We have (-a) -((a+b) (a-(ab))), and we can rewrite it as (-a) - ((a+b) - (a - (ab))). Now, we can apply Result 5, which gives us (-a) - ((a+b) - (a - (ab))) = a - (ab).

So, our first statement simplifies to a - (ab).

Moving on to the second statement: b-a-b. To prove this statement, we can utilize another result from page 36. Let's consider Result 2, which states: "a - (b - a) = 2a - b." By comparing the given expression with Result 2, we see that we need to rearrange the terms.

We have b - a - b, and we can rewrite it as b - (a - b). Now, we can apply Result 2, which gives us b - (a - b) = 2b - a.

So, our second statement simplifies to 2b - a.

Finally, we have the third statement: a - a. This statement is directly derived from Axiom 6, which states: "a - a = 0."

Combining the simplified forms of the first and second statements, we have a - (ab) = 0 and 2b - a = 0. Now, we can use these two equations along with Axiom 1, which states: "a - (ab) = (a - b)a," to derive the conclusion.

From a - (ab) = 0, we can multiply both sides by a to get a^2 - a(ab) = 0. Rearranging this equation, we have a^2 = a(ab).

Next, we substitute 2b - a = 0 into the equation a^2 = a(ab). This yields a^2 = (2b)(ab), which simplifies to a^2 = 2(ab)^2.

Using Theorem 1, which states: "If a^2 = b^2, then a = b or a = -b," we can conclude that a = √(2(ab)^2) or a = -√(2(ab)^2).

Therefore, by applying the results from page 36 of the cheat sheet and the given axioms, we have derived the conclusion that a = √(2(ab)^2) or a = -√(2(ab)^2) in the given proof.

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the triangles are similar, corresponding parts of the triangles are equal in measure. Thus, it is reasonable to conclude that \(AB ≅ DE.\)

It is reasonable to conclude that \(AB ≅ DE\)because triangles ABC and DEF are similar.

This means that corresponding parts of the two triangles are equal in measure. Specifically, ∠A and ∠D are equal in measure, as are ∠B and ∠E.

Therefore, the corresponding sides AB and DE are equal in measure.

A way to show that the two triangles are similar is by using the AA Similarity Postulate.

This postulate states that if two angles of one triangle are equal in measure to two angles of a second triangle, then the two triangles are similar. In this case, \(∠A ≅ ∠D and B ≅ ∠E\), which means the two triangles are similar.

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