Solve the inequality
22 + 4x - 32 < 0

Answer:

any nuber less then 3.5  and 5th awnser

Step-by-step explanation:

x is less then 3.5 so any    number less then 3.5

5th one is true too because you can go into negitves  and tehre is are infanite negitives

Answer:

The following statements and graphs are true:

x < 3.5

Any number that is less than 3.5 is a solution.

There are an infinite number of solutions.

The statement "x ≤ 3.5" is not true because the original inequality states that x is strictly less than 3.5, not less than or equal to 3.5. The statement "Any number that is greater than 3.5 is a solution" is also not true for the same reason. Finally, 3.5 is not a solution to the inequality because the inequality is strict: it only includes values of x that are strictly less than 3.5.

________________________________________________________

The difference between strict and non-strict inequalities is that strict inequalities use "<" or ">" symbols, which exclude the boundary values, while non-strict inequalities use "≤" or "≥" symbols, which include the boundary values.

For example, the inequality x < 5 is a strict inequality, which means that x can be any number less than 5, but it cannot be 5 itself. On the other hand, the inequality x ≤ 5 is a non-strict inequality, which means that x can be any number less than or equal to 5.

Similarly, the inequality y > -3 is a strict inequality, which means that y can be any number greater than -3, but it cannot be -3 itself. The inequality y ≥ -3 is a non-strict inequality, which means that y can be any number greater than or equal to -3.

Inequalities are used in a variety of real-life applications, including:

Business and economics: Inequalities are used to represent constraints in optimization problems, such as maximizing profits subject to resource limitations.

Engineering and physics: Inequalities are used to represent physical constraints, such as maximum and minimum values for quantities like speed, acceleration, and force.

Health and social sciences: Inequalities are used to represent inequalities in health outcomes and access to healthcare, as well as social inequalities related to income, education, and other factors.

Computer science and optimization: Inequalities are used to represent constraints in optimization problems, such as scheduling, routing, and allocation of resources.

Probability and statistics: Inequalities are used to bound the probability of events and to represent relationships between random variables.

Inequalities are also used in various fields of mathematics, including algebra, geometry, and analysis. They are important tools for proving theorems and solving problems in these areas.

Step-by-step explanation:

1. the number of parts that the dividend is being divided into

2. opposite operations that undo one another

3. the result of dividing two numbers

4. the number being divided

5. the quotient of any number and zero

:)

Answer:

1. The number being divided

2. opposite operations that undo one another

3. The result of dviding two numbers

4. The number of parts that the dividened is being divided into

5.The quotient of any number and zero

Step-by-step explanation:

Answer:

2x³ + 5x + 2

Step-by-step explanation:

2x + 3x + 2 + 2x³

You can only add together terms that have the same type of variable. For example, x is different from x² or x³.

(2x + 3x) + 2 + 2x³

5x + 2 + 2x³

Order it like this:

2x³ + 5x + 2

Answer:

2.4 or  \(\frac{12}{5}\)

Step-by-step explanation:

In the divisor (the second fraction) we flip the numerator and the denominator. This is known as the reciprocal and basically it means the reverse of the fraction. When we find the reciprocal, we also have to change the division sign to a multiplication sign.

Once you've flipped the second fraction and changed the symbol from divide to multiply, we can multiply the numerators together and the denominators together and we have our solution:

\(\frac{12}{5}\)

Answer:

You didn't provide any choices or options to pick from but here are the possible answers is:

- Encourage the use of the incentive spirometer every 2 hours

-Instruct to splint incision when coughing and deep breathing.

-Reposition the client every 2 hours

-Assist with early ambulation.

Step-by-step explanation:

Hope I could help!

In the plan of care to prevent postoperative atelectasis, interventions should not include the use of tobacco products or exposure to secondhand smoke.

The nurse should include several interventions in the plan of care to prevent postoperative atelectasis, but there are specific interventions that should not be included. Atelectasis is the partial or complete collapse of the lung, and preventing it is crucial after surgery. Here are some interventions that should be included:

Incentive Spirometry: The nurse should encourage the client to use an incentive spirometer to promote deep breathing and lung expansion.

Early Ambulation: Encouraging the client to get out of bed and walk as soon as possible after surgery helps improve lung function.

Pain Management: Adequate pain control measures should be in place to ensure the client can take deep breaths without discomfort.

Coughing and Deep Breathing Exercises: The nurse should teach and encourage the client to perform regular coughing and deep breathing exercises to clear the airways and prevent mucus buildup.

Positioning: Proper positioning, such as elevating the head of the bed, can aid lung expansion.

What should not be included in the plan of care is the use of tobacco products or exposure to secondhand smoke, as smoking and smoke exposure are detrimental to lung health and can worsen atelectasis. These should be strictly avoided to prevent postoperative complications.

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The average miles per hour that John and his family travel is 55 mph.

American drivers now log a total of 14,263 miles in a single year on average. Around 1,200 miles are driven per month on average, according to this information.

We must divide the whole distance travelled by the total time taken by John and his family in order to determine their average miles per hour:

Total distance x Total time equals average speed.

In this instance, their total journey distance was 137.5 miles, and their total travel duration was 2.5 hours. Hence, we can enter the following values into the formula:

Average speed = 137.5 miles / 2.5 hours

137.5 divided by 2.5 results in:

Average speed is 55 miles per hour.

John and his family therefore travel at an average speed of 55 mph.

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The probability that they all have different birthdays is 0.903 or 90.3%.

1. Calculate the number of days in a year.

There are 365 days in a year.

2. Calculate the number of possible combinations for 3 people.

There are 365 x 365 x 365 = 4,738,625 possible combinations for 3 people.

3. Calculate the number of combinations where all 3 people have different birthdays.

There are 365 x 364 x 363 = 4,324,320 combinations where all 3 people have different birthdays.

4. Calculate the probability.

The probability that they all have different birthdays is 4,324,320 / 4,738,625 = 0.903 or 90.3%.

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Answer:

The arithmetic sequence formula to find the sum of n terms is given as follows: Sn = n/2 (a1 + an) Where Sn is the sum of n terms of an arithmetic sequence.

The dimension of the smallest flowering plant is 59/2500 in. long and 129/10,000 in. wide.

To convert Decimal into Fraction form:

Do the following Steps:

Step 1: Make a fraction with the decimal number as the numerator and a 1 as the denominator.

Step 2: Remove the decimal places by multiplication.

Step 3: Reduce the fraction.

Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Given,

The smallest flowering plant is the flowering aquatic duckweed found in Australia.

And it is 0.0236 inch long and 0.0129 inch wide.

Here we need to write these dimensions as fractions in simplest form.

Rewrite the decimal number as a fraction with 1 in the denominator

So,

=> 0.0236/1 and 0.0129/1

Now, Multiply to remove 4 decimal places. Here, you multiply top and bottom by 10⁴ = 10000.

Then we get,

=> 236/10000 and 129/10000

Now, reduce the fraction by dividing both numerator and denominator by GCF = 4,

=> 59/2500

But the fraction 129/10000 is not reducible.

Therefore, the fraction form is,

=> 59/2500 in. long and 129/10,000 in. wide.

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Considering the given situation, it is found that:

a. The absolute value inequality is: |x - 131745| > 15000.

b. The possibilities for the price of car B are of x < $116,745 or x > x > $146,745.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It gives the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.

In this problem, the difference between the price of car B of x and the price of car A of $131,745 is greater than $15,000, hence the absolute value inequality that models this situation is:

|x - 131745| > 15000.

Hence the possibilities for the price of car B are:

The complete problem is given by:

"Two of the most expensive cars in the world are car A and car B. The prices of these two cars differ by more than $15,000. The price of car A is $131,745. a. Assuming that you do not know which model is more expensive, write an absolute value inequality that describes this situation. Use x for the cost of car B. b. What are the possibilities for the price of car B?"

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Answer:#2

Step-by-step explanation:

Answer:

not sure but i think the answer is 9.40

Step-by-step explanation:

Answer:

420

Step-by-step explanation:

volume = length x width x height

12 x 5 x 7 = 420

The first number, 5 x \(10^22,\) can be written as 5 followed by 22 zeros:

5,000,000,000,000,000,000,000

To simplify means to make something easier to understand or do by reducing complexity, removing unnecessary details, or using simpler language or concepts.

The second number , 5 × 10², can be written as 5 followed by 2 zeros: 500

The third number, 3.7 x 10⁵³, can be written as 3.7 followed by 53 zeros:

370,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

or in scientific notation as 3.7 x 10⁵³

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Simplify

2. 5 x 10^22. 5 × 10 2 and 3. 7 x 10^53. 7 × 10 5

Answer:

B

Step-by-step explanation:

The y- intercept is the point on the y- axis where the line crosses it

This point is y = 2

with coordinates (0, 2 ) → B

The line is  crossing the y axis at (0,2)

The x - intercept is where a line crosses the axis and the y intercept is the point where  the line crosses the y - axis .

observing the graph it can be concluded that ,

The line is  crossing the y axis where x = 0 and y = 2 , so the point is (0,2)

correct answer is c) (0,2)

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Answer:

Step-by-step explanation:

I think you mean 0.5 in:20 mi

2 in × (20 mi)/(0.5 in) = 80 mi

2 inches on the map corresponds to 80 miles.

8 miles is the real distance that corresponds to the 2 inch map measurement.

We can utilize the map's scale to get the actual distance that corresponds to the 2 inch map distance.

The scale is presented as 0:5 in:20 mi, which implies that each 5 inches on the map corresponds to 20 miles in actual travel distance.

Let's establish a ratio to determine the actual distance:

5/2 = 20/x

If we cross-multiply, we obtain:

5x = 2(20)

5x = 40

When we multiply both sides by 5, we get:

x = 40 / 5

x = 8

Therefore, 8 miles is the real distance that corresponds to the 2 inch map measurement.

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Answer:

(-1,-2)

Step-by-step explanation:

See attached graph.

The probability of selecting a black marble followed by a red marble with replacement is option A: 4.7%.

Based on the question, for one to calculate the probability of selecting a black marble followed by a red marble, we need to look at the two independent events which are:

So, the probability of selecting a black marble on the first draw is:

2 black marbles out of a total of 16 marbles (6 red + 3 yellow + 2 black + 5 pink)

= 2/16 approximately 1/8.

Based on the fact that the marble is replaced, the probabilities for each draw will have to remain the same.

So, the probability of selecting a red marble on the second draw =  6 red marbles out of a total of 16 marbles

= 6/16

= 3/8.

To know the probability of both events occurring, we need to multiply the sole probabilities:

P(black marble and then red marble) = P(black marble) x  P(red marble)

= (1/8) x (3/8)

= 3/64

So one can Convert the probability to a percentage, and it will be:

P(black marble and then red marble) = 0.047

                                                               = 4.7%

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see text below

A bag contains 6 red, 3 yellow, 2 black, and 5 pink marbles. What is the probability of selecting a black marble followed by a red marble? The first one is replaced.

4.7%

12.5%

78.3%

75%

Answer:

267.95 in³

Step-by-step explanation:

volume = 4/3 × 3.14 × 4³

= 4/3 × 3.14 × 64

= 267.95 in³

Waterways should retain the old backhoes equipment.

To determine whether it is more favorable to purchase new backhoes or overhaul the old ones, we will evaluate the net present value (NPV), profitability index (PI), and internal rate of return (IRR) for both options.

Net Present Value (NPV):

For the new backhoes:

The initial cost of investment = Purchase cost when new - Salvage value now

= $199,994 - $15,200 = $184,794

The net cash flow generated each year for the new backhoes remains unspecified, so we cannot calculate its NPV.

For the old backhoes:

Initial investment = Cost of the overhaul = $41,400

Net cash flow generated each year = $15,200

Using the provided PV table, we can calculate the NPV for the old backhoes:

NPV = Net cash flow generated each year * PV factor for 8 years - Initial investment

= $15,200 * 5.76162 - $41,400 ≈ $55,689.69

Since the NPV for the old backhoes is positive, retaining the old equipment is favorable.

Profitability Index (PI):

The profitability index is calculated by dividing the present value of cash inflows by the initial investment.

For the new backhoes:

Since the net cash flow generated each year is unspecified, we cannot calculate the PI.

For the old backhoes:

PI = (Net cash flow generated each year * PV factor for 8 years) / Initial investment

= ($15,200 * 5.76162) / $41,400 ≈ 2.11

The profitability index for the old backhoes is 2.11.

Based on the PI, the old backhoes have a higher profitability index than the new backhoes, indicating that retaining the old equipment is more profitable.

Internal Rate of Return (IRR):

The IRR factor for the new and old backhoes is not provided, so we cannot calculate the exact IRR.

In summary, based on the net present value (NPV) and profitability index (PI), it is more favorable for Waterways to retain the old backhoes equipment.

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The equivalent form of expression 15(p+ 4) - 12(2q + 4) is,

⇒ 15p - 24q + 12

We have to given that;

The value of expression is,

⇒ 15(p+ 4) - 12(2q + 4)

Now, We can simplify as;

⇒ 15(p+ 4) - 12(2q + 4)

⇒ 15p + 60 - 24q - 48

⇒ 15p - 24q + 12

Thus, The equivalent form of expression 15(p+ 4) - 12(2q + 4) is,

⇒ 15p - 24q + 12

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Answer:

Answer choice : 3

Step-by-step explanation:

To put fractions in order from least to greatest, you need to compare their values by finding the common denominator.

Step 1: Find a common denominator for all the fractions.

Step 2: Convert each fraction to an equivalent fraction with the common denominator.

Step 3: Compare the numerators of the equivalent fractions. The fraction with the smallest numerator is the smallest fraction, and the fraction with the largest numerator is the largest fraction.

Step 4: If two or more fractions have the same numerator, compare their denominators. The fraction with the smallest denominator is the smallest fraction, and the fraction with the largest denominator is the largest fraction.

Step 5: Write the fractions in order from least to greatest.

For example, let's say you need to put the fractions 1/3, 2/5, and 3/8 in order from least to greatest.

Step 1: The common denominator for 3, 5, and 8 is 120.

Step 2: Convert each fraction to an equivalent fraction with a denominator of 120.

1/3 = 40/120

2/5 = 48/120

3/8 = 45/120

Step 3: Compare the numerators of the equivalent fractions: 40 < 45 < 48

Step 4: Since 40 is not equal to 45 or 48, we don't need to compare the denominators.

Step 5: Write the fractions in order from least to greatest: 1/3 < 3/8 < 2/5.

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Answer:

c) -2

Explanation:

The limit required is the value of f(x) when we are going close to -2 but from the rigth of -2. We can see in the graph, that when we go to -2 from the right, the value of f(-2) approaches -2.

Therefore, the answer is C) -2.

Answer:

  82/99

Step-by-step explanation:

1. Notice the length of the repeating pattern.

  the pattern is 82 repeating, a 2-digit pattern

2. Notice where the repeating pattern starts, relative to the decimal point.

  the repeating starts at the decimal point

3. If the repeating starts at the decimal point, use a pattern of repeating 9s of the same length as the denominator of the fraction

  2 nines are the denominator: 82/99

4. Reduce the fraction if possible

  this fraction cannot be reduced

As a simplified fraction, 0.828282... = 82/99

_____

Comment on more complicated cases

If the repeat does not start at the decimal point, or if the number contains an integer part, then the numerator of the fraction is found in a slightly different way. Let n be the number of repeating digits of the number x. The fraction is then ...

  (10^n·x -x)/(10^n -1)

Example:

  1.2345345345...        a number with a 3-digit repeat not starting at the decimal point

  (1234.5345... -1.2345...)/(1000 -1) = 1233.3/999  = 4111/3330

The multiplication by 10^n aligns the repeating parts so they cancel when you do the subtraction.

=========================================================

Explanation:

We can prove this by contradiction.

Let's say

and

A+B = C

We'll show that a contradiction happens based on this.

If A is rational, then A = p/q where p,q are two integers. The q cannot be zero.

If C is rational, then C = r/s for some other integers. We can't have s be zero.

Note the following

A+B = C

B = C - A

B = r/s - p/q

B = qr/qs - ps/qs

B = (qr - ps)/qs

B = (some integer)/(some other integer)

This shows B is rational. But this is where the contradiction happens: We stated earlier that B was irrational. A number cannot be both rational and irrational at the same time. The very definition "irrational" literally means "not rational".

In short, I've shown that if A+B = C such that A,C are rational, then B must be rational as well.

The template is

rational + rational = rational

Therefore, we've shown that if A is rational and B is irrational, then C cannot possibly be rational. C is irrational.

Another template is

rational + irrational = irrational

Given all the weights and the total capacity of the elevator, we have the following expression:

where 'x' denotes the weight of the third case.

Solving for x, we get the following:

therefore, the third case must weigh 60.3 kg or less.

Answer:

$21.78

Step-by-step explanation:

2.79 X 5 = 13.95

13.95 + 7.83 = 21.78