(x4 – x² – 30) ÷ (x² + 5)

The solution of a compound inequality is the common region or intersection region of two inequalities.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

A sentence having two inequality statements connected by the words 'or' Or 'and' is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence.

For example, if in a compound inequality we get x > 3 and x > 5 so the final conclusion is x > 5.

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Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

The length of the rectangular garden given the area and width is 8/7 miles

A rectangle is a form of quadrilateral having opposing sides parallel and four right angles. The area of a rectangle can be calculated by multiplying the length by width.

Area of a rectangular garden = length × width

16 = x × 14

16 = 14x

x = 16 / 14

x = 8/7 miles

Therefore, the length of the rectangular garden given the area and width is 8/7 miles.

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Rollaway Skates is cheaper when the number of people is less than or equal to 4. For example, the cost for 2 people at Rollaway Skates is $10, while the cost for 2 people at Wheelie's Skates and Stuff is $106.

Wheelie's Skates and Stuff is cheaper when the number of people is greater than or equal to 5. For example, the cost for 6 people at Rollaway Skates is $30, while the cost for 6 people at Wheelie's Skates and Stuff is $118.

I hope this helps! Do you have any other questions?

Answer:

The median is 6.5

Step-by-step explanation:

To find the median, first organize the numbers from least to greatest:

1, 4, 6, 6, 7, 8, 9, 10

The median is always the number in the middle, but since there are eight numbers here, there will be two numbers in the middle: 6 and 7.

To solve for this, we have to find the average of the numbers.

Add the two numbers together and then divide by 2 (we divide by 2 because we are averaging two numbers).

(6 + 7)/2

13/2

6.5

The Binomial probability of x = 3 for the given parameters is 0.2048

The Binomial probability relation can expressed as :

\(P(x) = nCx * p^{n} * q^{n-x}\)

where :

for x = 3

We substitute x into the equation thus :

P(x = 3) = 17C3 * (1/8)³ * (1 - 1/8)¹⁴

P(x = 3) = 0.2048

Therefore, the probability of x = 3 in the scenario given is 0.2048

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Answer: 3 11/15  please mark brainliest If I helped you.

the question is kayar and 12 by 5 miles on Monday and 21 by three miles on Tuesday what is the total distance in miles kayuren during those two days first phone on Monday how much run that was 12 by 5 miles on Tuesday Shirin to 1 by 3 minus now this whole part and fractional part are written separately so this can be converted into a mixed fraction like when a number is of the form of p by see that is one whole number and fraction then it is written as a + b by c so we can write Monday that was 12 by 5 miles that is

12 by 1 + 2 by 5 that will be 5 will be LCM of 5 + 2 will be 7 by 5 MI and Tuesday it will be 21 by 3 that is 2 + 1 by 3 3 will be the LCM of 3 and 22 will be 6 plus one that is 7 by 3 minus in question is asked that what was the total distance kayar and thus during today's so Monday plus Tuesday will be the total total 27 by 5 + 7 by 3 that will be equal to LCM will be 15 this will be X 307 into 3 + 7 and 25 that

is 21 + 45 upon 15 that will be equal to 56 upon 15 Now since we have to give answer in mixed fraction in whole number and fraction this a bi bi can be divided into a whole number and fraction part when divided by be the remainder is remainder is written here b is written here and question is written here so 56 by 15 can be written as 15 and 23 is 45 three years question remainder will be 11:00 that is 56 - 45 and below will be the denominator will be 15 so this is our answer and the correct

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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An equation has terms, variables, constants and coefficients.

A term is the part of the equation that is separated by addition or subtraction signs.

A variable is usually symbolized by a letter in place of an unknown value.

The coefficient is the number before the variable, the ones that multiply it.

The constans are the known values or numbers that appear in the equation.

For example:

3X+16

This equation has two terms "3X" and "16"

One variable "X"

One coefficient "3"

One constant "16"

The exponential function giving the number of bacteria after x hours is given as follows:

\(y = 250(2)^x\)

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 250, b = 2.

Hence the function is given as follows:

\(y = 250(2)^x\)

The problem asks for the exponential function giving the number of bacteria after x hours is given as follows:

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Answer:

Step-by-step explanation:

It is a linear equation. If we solve it, the result step by step is given by:

6x+2-x=12

6x-x=12-2

5x=10

\(x=\frac{10}{5}\)

x=2

On applying higher-order thinking skills, it can be seen that Joel does not count the numbers 82 82 62 80 while counting backwards from 79 to 65.

What is Higher-Order Thinking?

Higher-order thinking is a concept of educational reform based on learning taxonomies (like Bloom's taxonomy). Higher-order thinking skills are also known as higher order thinking skills (HOTS). The theory holds that some forms of learning have more universal advantages while requiring more cognitive effort than others.

Joel counts back from 79 to 65.

The numbers in descending order from 79 to 65 is -

79 78 77 76 75 74 73 72 71 70 69 68 67 66 65

The numbers go from right to left on a number line.

The options for the numbers are -

77 72 70 82 70 82 67 62 80

After applying HOTS the numbers which do not lie in between 79 and 65 when counting backwards is -

82 82 62 80

Therefore, the numbers which can be eliminated are 82 82 62 80.

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Answer:

The sequence is increasing by 5 at each step. So, we can write:

a1 = 30

a2 = 30 + 5 = 35

a3 = 30 + 25 = 40

a4 = 30 + 35 = 45

a5 = 30 + 4*5 = 50

We notice that the nth term is given by:

an = 30 + (n-1)5

So, the explicit formula for the nth term is:

an = 25n + 5

Answer:

Step-by-step explanation:

To find the equation for the nth term in the sequence, we need to determine the pattern or rule that generates the sequence.

From the given information, we can see that the sequence is not arithmetic because the differences between consecutive terms are not constant. Instead, the sequence appears to be quadratic because the second difference between consecutive terms is constant.

Using the given values of a₁, a₃, and a₅, we can find the first few differences:

a₃ - a₁ = 4 - (-6) = 10

a₅ - a₃ = 14 - 4 = 10

So, the first difference is 10, which indicates a linear term in the equation for an. We can now use the given value of a₁ and the first difference to find the constant term in the quadratic equation. Let d be the common difference, then we have:

a₂ = a₁ + d = -6 + 10 = 4

a₄ = a₃ + d = 4 + 10 = 14

a₆ = a₅ + d = 14 + 10 = 24 - 1

a₇ = a₆ + d = 24 - 1 + 10 = 33

Now, we can find the second difference between consecutive terms:

a₄ - 2a₃ + a₂ = 14 - 2(4) + (-6) = 0

a₆ - 2a₅ + a₄ = 19 - 2(14) + 4 = -5

a₇ - 2a₆ + a₅ = 33 - 2(19) + 14 = 9

Since the second difference is constant (-5), this confirms that the sequence has a quadratic term in its equation. Let's assume the equation for the nth term is:

an = an² + bn + c

Substituting the values we know, we get three equations:

a₁ = a₁² + b₁ + c --> -6 = c

a₃ = a₃² + b₃ + c --> 4 = 9a + b + c

a₅ = a₅² + b₅ + c --> 14 = 25a + 5b + c

Solving this system of equations, we get:

a = 1/2, b = 19/2, and c = -6

Therefore, the equation for the nth term in the sequence is:

an = (1/2)n² + (19/2)n - 6.

Answer: BC<MN

Step-by-step explanation:

Answer: BC <MN

Step-by-step explanation: i just took the test on eginuity

Answer:

  52,227.4 square feet

Step-by-step explanation:

The area of the field not covered by the silo is the difference between the area of the rectangular field and the area of the circular base of the silo.

The field area is given by the formula ...

  A = LW . . . . where L and W represent length and width

The area of the circular base of the silo is given by the formula ...

  A = πr² . . . . where r represents the radius of the silo (half the diameter)

__

The desired difference is ...

  A = LW - πr² = (160 ft)(330 ft) -π(13.5 ft)² ≈ 52800 ft² -572.6 ft²

  A ≈ 52,227.4 ft²

About 52,227.4 square feet are left for planting.

_____

Additional comment

Sometimes, you are expected to round the answer to a precision matching the precision of the contributors. Here, that would be 2 significant figures:

  52,000 ft²

You may be expected to give your answer rounded to a precision other than either of the values shown above.

Answer:

9 1/7

Step-by-step explanation:

This is the answer because 64 divided by 7 is 9.142... this means that there are 9 whole numbers and 1/7 remaining after the 9 whole numbers

All circles are similar because their shape is same but sizes vary.

Similar figures are those figures which have the same shape, but sizes are different.

To prove the given statement, consider two circles C and C' with radius r and r' respectively.

r can be greater than or less than r'.

Circle C can be dilated to a certain value to get the circle C'.

The shape of both the circles remain same.

But the size is different.

This is the case for any arbitrary circles.

Hence all circles are similar.

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When the pyramid is cut out of the prism, it has a volume of 36 cubic meters and the same base and height.

It is also known as the object's capacity. The fundamental equation for volume is length, width, and height, as opposed to the fundamental equation for the area of a rectangular shape, which is length, breadth, and height. The math is the same regardless of how you refer to the different dimensions. For example, you can substitute "depth" for "height." Volume is used to describe an object's capacity.  Volume can also be used to describe how much space a three-dimensional object occupies.

given

The ratio of their volumes is always one to three

Since the volume of a prism is 108 cubic meters,

a pyramid's volume is 1/3 * 108, or 36 cubic meters.

When the pyramid is cut out of the prism, it has a volume of 36 cubic meters and the same base and height.

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Answer: 1600 cents or 16 US dollars

Step-by-step explanation:

Given information

20 cent coin is 1.2 mm thick

The total length is 21.6 cm

Set variables

Let x be the number of 20-cent coins

Set equation

1.2x = 216

Divide 1.2 on both sides

1.2x / 1.2 = 216 / 1.2

x = 80

Find the value of the pile

Number of coins × Coin value

= 80 × 20 cent

= \(\boxed{1600\ cents}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

maximum is 16,853 cell phones

≤  18.853

Step-by-step explanation:

1,176,912.42.   per quarter budget

247,638.00    per quarter fixed cost

We subtract then divide the amount cost of phones and ensure its less or rounded down.

1,176,912.42 -247,638 = 929274.42

929274.42 / 55.14 = 16853

16,852 < m ≤ 16,853

The amount of money earned by Zach each week will be equal to $9 per week.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given data in the question,

Total amount earned by Zach = $36

The time taken to earn the amount = 4 weeks

Then, the amount earned each week will be.

= $36/4

= $9 per week

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Answer:

None

Step-by-step explanation:

Truly, I'm not sure what type of problem this is, but most people don't favor all the seasons. If there is more to the problem, I would be glad to help further.

Answer:

One possible way to estimate how many people out of 20 would say that they like all seasons is to use a simple random sample. A simple random sample is a subset of a population that is selected in such a way that every member of the population has an equal chance of being included. For example, one could use a random number generator to assign a number from 1 to 20 to each person in the population, and then select the first 20 numbers that appear. The sample would then consist of the people who have those numbers.

Using a simple random sample, one could ask each person in the sample whether they like all seasons or not, and then calculate the proportion of positive responses. This proportion is an estimate of the true proportion of people in the population who like all seasons. However, this estimate is not exact, and it may vary depending on the sample that is selected. To measure the uncertainty of the estimate, one could use a confidence interval. A confidence interval is a range of values that is likely to contain the true proportion with a certain level of confidence. For example, a 95% confidence interval means that if the sampling procedure was repeated many times, 95% of the intervals would contain the true proportion.

One way to construct a confidence interval for a proportion is to use the formula:

p ± z * sqrt(p * (1 - p) / n)

where p is the sample proportion, z is a critical value that depends on the level of confidence, and n is the sample size. For a 95% confidence interval, z is approximately 1.96. For example, if out of 20 people in the sample, 12 said that they like all seasons, then the sample proportion is 0.6, and the confidence interval is:

0.6 ± 1.96 * sqrt(0.6 * (1 - 0.6) / 20)

which simplifies to:

0.6 ± 0.22

or:

(0.38, 0.82)

This means that we are 95% confident that the true proportion of people who like all seasons in the population is between 0.38 and 0.82. Therefore, based on this sample and this confidence interval, we would expect between 8 and 16 people out of 20 to say that they like all seasons in the population.

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We are asked to determine what percentage is 50 of the given ones.

We have that:

The 3rd and 4th expressions cannot be simplified using the quotient rule for exponents

The quotient rule for exponents states that if you have two exponents, and you want to divide them, you can do so by subtracting the exponent of the denominator from the exponent of the numerator.

The general form of the quotient rule:

xᵃ / xᵇ = xᵃ⁻ᵇ

Given:

(3²9⁻¹2³)/(8⁵7⁻²)

(3²9⁻¹2³)/(8⁵7⁻²) = (3² × 3²⁽⁻¹⁾ × 2³)/(8⁵×7⁻²)

                        = (3² × 3⁻² × 2³)/(2³⁽⁵⁾ ×7⁻²)

                        = (3²⁺⁽⁻²⁾ × 2³)/(2¹⁵ × 7⁻²)

                        = (3⁰ × 2³)/(2¹⁵ × 7⁻²)

                        = (1 × 2³)/(2¹⁵ × 7⁻²)

                        = (2³)/(2¹⁵ × 7⁻²)

                       = 2³⁻¹⁵ × 7²    ( quotient rule is used here)

                       = (2⁻¹²) (7²)

(4⁻²x⁻¹)/(4⁻¹x⁻²)

(4⁻²x⁻¹)/(4⁻¹x⁻²) = 4⁻²⁻⁽⁻¹⁾ × x⁻¹⁻⁽⁻²⁾  ( quotient rule is used here)

                       = 4⁻²⁻⁽⁻¹⁾ × x⁻¹⁻⁽⁻²⁾

                       = (4⁻¹) (x¹)

(6x⁻⁸z²)(6⁵x⁻¹z²)

(quotient rule cannot be used to simplify this expression because the two expressions are multiplying each other)

(q⁻⁵r¹¹)/(s⁶t⁻¹⁵)

(quotient rule cannot be used here  because there are no like bases)

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The experimental effect highlighted by the scenario described would most likely be an example of placebo effect.

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Answer:

The one you have selected is correct. 9.5(w+5.7)=77.9

Step-by-step explanation:

Area is length x width, but the length is the same. So, the 9.5 is not in the parentheses. The existing width (w) is having 5.7 yards added on before being multiplied for area calculations. Because of the order of operations, (w+5.7) must be in parentheses so it is done before multiplication.

Answer:

9.5(w+5.7)=77.9

Step-by-step explanation:

took the test

Answer:

\(B(x,y) = (-2,-4)\)

\(O(x,y) = (6,-6)\)

\(Y(x,y) = (13,1)\)

Step-by-step explanation:

Given

\(Translation: (-3,6)\)

\(B': (-5,2)\)

\(O':(3,0)\)

\(Y': (10,7)\)

Required

Determine the coordinates of B, O and Y

Recall that the given translation is:

\((x,y) = (-3,6)\)

Calculating the x coordinates of B:

\(B_x + x = B'_x\)

Where \(B': (-5,2)\)

This gives

\(B_x -3 = -5\)

\(B_x = -5 + 3\)

\(B_x = -2\)

Calculating the y coordinates of B:

\(B_y + y = B'_y\)

This gives

\(B_y + 6 = 2\)

\(B_y = 2 - 6\)

\(B_y = -4\)

Hence:

\(B(x,y) = (-2,-4)\)

Calculating the x coordinates of O:

\(O_x + x = O'_x\)

Where \(O':(3,0)\)

This gives

\(O_x -3 = 3\)

\(O_x = 3 + 3\)

\(O_x = 6\)

Calculating the y coordinates of O:

\(O_y + y = O'_y\)

This gives

\(O_y + 6 = 0\)

\(O_y = 0 - 6\)

\(O_y = - 6\)

Hence:

\(O(x,y) = (6,-6)\)

Calculating the x coordinates of Y:

\(Y_x + x = Y'_x\)

Where \(Y': (10,7)\)

This gives

\(Y_x -3 = 10\)

\(Y_x = 10 + 3\)

\(Y_x = 13\)

Calculating the y coordinates of Y:

\(Y_y + y = Y'_y\)

This gives

\(Y_y + 6 = 7\)

\(Y_y = 7 - 6\)

\(Y_y = 1\)

Hence:

\(Y(x,y) = (13,1)\)