1. ESSENTIAL QUESTION How do you rewrite rational expressions to find sums and differences

Two numbers that are in both sequences are the numbers 17 and 32.

A sequence can be described as a set of numbers each with a defined interval between one another. For example, in the sequence 2, 4, 6, 8, 10, the interval is 2.

To find two common numbers, let's expand the sequences as it is shown below:

First sequence: In this sequence, the interval is 5.

2 7 12 17 22 27 32

Second sequence: In this sequence, the interval is 3.

-4 -1 2 5 8 11 14 17 20 23 26 29 32

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If a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.

What is inequality?

In mathematics, an inequality is a statement that describes a relationship between two values, expressing that one value is greater than, less than, or equal to the other value. Inequalities are denoted by symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).

The inequality 10 < y means that "y" is greater than 10. To determine whether a given value of "y" is a solution to this inequality, we simply need to check whether that value is indeed greater than 10.

For example:

If y = 11, then 10 < y is true, because 11 is greater than 10.

If y = 10, then 10 < y is false, because 10 is not greater than 10 (they are equal).

If y = 9, then 10 < y is false, because 9 is not greater than 10.

Hence, if a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.

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Answer:

you see

Step-by-step explanation:

Answer:

-9+3x

Step-by-step explanation:

(-3x2 + x + 5) − (4x2 − 2x)

(-6+x+5)-(8-2x)

(-1+x)-8+2x

-1+x-8+2x

-9+3x

The IQR is the best measure of variability, and it equals 45.

Data variation can be caused by a variety of sources. Variability is also known as data spread. The standard deviation is a measure of variability since it measures the spread of data.

The range is the best measure of variability for the data shown, and its value is 45.

The range is defined as the difference between the largest and smallest values in a set of data.

In this case, the largest score is 88 and the smallest score is 20, so the range is 88 - 20 = 68.

The IQR (interquartile range) is another measure of variability, but it is not the best measure for this data set because the data set has only a few values and does not form a normal distribution. The IQR is a more appropriate measure for larger data sets that form a normal distribution.

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Answer:

Step-by-step explanation: 34 quarts

1 Liter = approximately 1.06 quarts

so 34 x 1.06 is about 36.04 quarts

7/8 of sixteen times a half of 30 is 210.

What is a PEMDAS rule?

PEMDAS is an acronym that stands for the order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

To calculate this, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

Start with the expression inside the parentheses: half of 30 is 15.

Multiply 16 by 15: 16 times 15 is 240.

Find 7/8 of 240:

7/8 of 240 = (7/8) x 240

                  = 210

Hence, 7/8 of sixteen times a half of 30 is 210.

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Answer:

285.76 kilograms       1.1 cubic yard

Step-by-step explanation:

Answer:

1.11121 cubic yards.

Step-by-step explanation:

First, let's convert the weight of 1 bag of garden soil from pounds to kilograms:

1 lb = 0.45359237 kg

42 lbs = 42 * 0.45359237 kg = 19.05 kg

So, the weight of 1 bag of garden soil is 19.05 kilograms.

Next, let's find the weight of 15 bags of garden soil:

15 bags * 19.05 kg/bag = 285.75 kg

So, 15 bags of garden soil weigh 285.75 kilograms.

Next, let's find the volume of 15 bags of garden soil in cubic yards:

1 cubic foot = 0.037037 cubic yards

2 cubic feet * 15 bags = 30 cubic feet

30 cubic feet = 30 * 0.037037 cubic yards = 1.11121 cubic yards

So, 15 bags of garden soil have a volume of 1.11121 cubic yards.

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Answer:

You figure out the slope

Step-by-step explanation:

Rise/Run is a formula that calculates the slope.  This determines the direction of the line and how steep it is.

Answer:

its a math term yw my boy

Step-by-step explanation:

The domain of the function for this situation is given as follows:

B. All whole numbers greater than or equal to 0 and less than or equal to 7.

The domain of a function is the set that contains all the values assumed by the input of the function.

Hence, on a graph, the domain is given by the values assumes on the horizontal axis of the graph.

The values that compose the domain of the graph are given as follows:

0, 1, 2, 3, 4, 5, 6 and 7.

Which is best described by option B.

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Step-by-step explanation:

To plot the integer -7 on the number line, we can place it to the left of 0. The number line would look like this:

-10 -8 -7 -6 -4 -2 0 2 4 6 8 10

The distance between 0 and -7 is 7 units, since 0 is 7 units to the right of -7.

The absolute value of -7 is 7, since the absolute value of a number is its distance from 0 on the number line.

The magnitude of -7 is also 7, which is the same as its absolute value. The magnitude of a number refers to its size or absolute value, regardless of its sign. In this case, the magnitude of -7 is 7.

The image of the point M(4, -1) after reflection in the line y = 3 would have the x-coordinate of 4.

When you reflect, you are giving something serious thought. [written] I continued my thoughtful stroll to the car while contemplating the unfortunate honeymooners. Synonyms: thoughtful, ponderous, contemplative, and pensive More reflective's opposites.

Cogitate, deliberate, reason, conjecture, and think are a few words that frequently replace the word reflect. All of these terms indicate "to utilise one's faculties of imagination, reasoning, or inference," but reflect denotes thoughtful deliberation over a memory that has just come to mind.

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Using the formula of simple interest, the time it will take to accumulate to $3200 at a rate of 4.5% is 71.35 years

Simple interest is a method of calculating the interest charge on a loan or deposit. It is based on the principle of earning interest only on the initial amount (principal) that was borrowed or deposited.

The formula for simple interest is:

I = P * r * t

where:

I is the interest amount

P is the principal amount

r is the interest rate (expressed as a decimal)

t is the time period (in years)

Substituting the values into the formula;

A = P(1 + rt)

3200 = 760(1 + 0.045(t))

3200 = 760 + 34.2t

34.2t = 3200 - 760

34.2t = 2440

t = 2440 / 34.2

t = 72.35 years

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The measure of each angle in the regular polygon is 154.3 degrees

From the question, we have the following parameters that can be used in our computation:

Number of sides, n = 14

The measure of each angle is calculated as

Angle = ( n − 2 ) × 180/n

substitute the known values in the above equation, so, we have the following representation

Angle = (14 − 2) × 180/14

Evaluate

Angle = 154.3

Hence, the angle is 154.3

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a) The required margin of error and lower and upper limits are:-

E =0.124

Lower limit =3.026

Upper limit =  3.274

b) sample size is n = 27.

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

The margin of error will be calculated as:-

a) Margin of error (E) :

[tex]E = Z_c\times \dfrac{\sigma}{\sqrt{n}}[/tex]

E =0.124

Margin of error = E =0.124

The lower and upper limits are calculated as:-

Lower limit = x-E

L= 3.15 - 0.124

L= 3.026

Lower limit =3.026

Upper limit = x + E

U= 3.15 + 0.124

U= 3.274

Upper limit =  3.274

b) The following equation may be used to calculate the right number of samples, n when is already known:

Margin of error = 0.13

Sample size (n):

[tex]n = (\dfrac{Z_c\sigma}{E})^2[/tex]

[tex]n = (\dfrac{1.28\times 0.36}{0.09})^2[/tex]

n = 26.21

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Convert the problem to standard form and write the initial tableau with slack variables:

Maximize

[tex]Z = 7*3 + 6*4 + 18*5 + 14*6 - 3*1 - 3*2 - 4*5 - 4*6[/tex]

Subject to:

[tex]x1 + x2 + s1 = 4000\\x3 - (1/3)*1 + (1/3)*5 = 0\\x4 - (1/3)*2 + (1/2)*6 = 0\\x3*1 + 3*2 + 3*3 + 3*4 + 3*5 + 2*6 + s2 = 6000[/tex]

All variables are non-negative.

Tableau

 x1  x2  x3  x4  x5  x6  s1  s2   b

Z -3 -3 7 6 18 14 0 0 0

s1 1 1 0 0 0 0 1 0 4000

s2 3 3 3 3 3 2 0 1 6000

x5 0 0 1 0 1/3 0 0 0 0

x6 0 0 0 1 0 1/2 0 0 0

The basic variables are s1, s2, x5, and x6.

Step 1: Choose  entering variable. The most positive coefficient in objective row is 18, corresponding to x5. x5 enters the basis.

Step 2: Choose the leaving variable. The minimum ratio of right-hand side to coefficient of x5 is 12000/(1/3) = 36000,

corresponding to s1. s1 leaves the basis.

Step 3: Perform, pivot operation to make x5 the basic variable for s1. Divide, pivot row by 1/3 and subtract appropriate multiples of the pivot row from other rows to make other entries in column 5 zero.

 x1    x2    x3    x4     x5     x6   s1    s2       b

Z -3 -3 7 6 18 14 0 0 0

x5 0 0 1 0 1/3 0 0 0 0

s2 3 3 3 3 2 2/3 2/3 0 1/3 24000

x3 1 0 1/3 0 1/3 0 -1/3 0 0

x4 0 1 0 1/3 0 1/2 -1/6 0 0

The basic variables are x5, x3, x4, and s2.

Step 4: Choose the entering variable. The most positive coefficient in the objective row is 7, corresponding to x3. x3 enters the basis.

Step 5: Determine the leaving variable. The right-hand side's minimum ratio to the coefficient of x3 is 0, indicating that x3 can be increased without bound. This implies that the optimal solution is unbounded and that there is no finite optimal value for the problem.

As a result, the simplex algorithm demonstrates that the given linear programming problem lacks a feasible solution. This means that it is not possible to meet all of the constraints at the same time.

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Answer:

YES, x = 8

Step-by-step explanation:

plug in 8 for x and see if both sides are equal

3/4 times 8 = 24/4 or 6

Answer:

Step-by-step explanation:

If we solve it as....

[tex]\mathrm{\cfrac{3}{4}x=6}[/tex]

[tex]\mathrm{4\times\cfrac{3}{4}x=6\times\:4}[/tex]

[tex]\mathrm{3x=24}[/tex]

[tex]\mathrm{\cfrac{3x}{3}=\cfrac{24}{3}}[/tex]

[tex]\mathrm{x=8}[/tex]

Yes, 8 would be the solution!

___________________

Hope this helps!

Answer:

The total possible outcomes that exist are:

                            2400

Step-by-step explanation:

We are given four dices:

first is a standard 6-faced die.

The second die has 4 faces.

Third dice has 10 faces.

Fourth dice has 10 faces.

Now when all the dice are thrown together then the total number of possible outcomes are:

( Since there are 4 numbers possible for the first die, 6 for second and 10 each for third and fourth)

                   The answer is:

                          2400

Answer:

he weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.

Step-by-step explanation:

To find the weight of 15 bags in kilograms, we can first convert the weight of one bag from pounds to kilograms and then multiply by the number of bags:

1 pound = 0.453592 kilograms

So the weight of one bag in kilograms is:

42 pounds * 0.453592 kilograms/pound = 19.05 kilograms

The weight of 15 bags in kilograms is:

15 bags * 19.05 kilograms/bag = 285.75 kilograms

To find the volume of 15 bags in cubic yards, we can first convert the volume of one bag from cubic feet to cubic yards and then multiply by the number of bags:

1 cubic yard = 27 cubic feet

So the volume of one bag in cubic yards is:

2 cubic feet / 27 cubic feet/cubic yard = 2 / 27 = 0.07407 cubic yards

The volume of 15 bags in cubic yards is:

15 bags * 0.07407 cubic yards/bag = 1.111 cubic yards

Therefore, the weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.

The equation of the line which is parallel to the line x = -4 will be x = -3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation of the line is x = -4. The y-intercept is zero for the line.

The equation of the line parallel to the equation will be,

x = -3

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Answer:

perimeter of rectangle = 2(length +breadth)

=2(20+80) m

=200 m

∴perimeter of rectangle is 200 m

Answer:

35 mph

Step-by-step explanation:

5×5=25

60-25=35.

If "a" is a root of a polynomial, then (x-a) is a factor of the polynomial.

If the multiplicity of a root a is "p", then (x-a)^p is a factor of the polynomial.

Based on the roots and multiplicity, we have:

    P(x) = k · (x-2)^2 · (x-0) · (x - (-2))

    P(x) = k · (x-2)^2 · (x-0) · (x+2)

We need that "k" up front to account for any vertical stretch or compression to hit the exact point (5,189).

To find "k", we plug in that point and solve for "k":

     189 = k · (5-2)^2 · (5-0) · (5+2)

     189 = k · (3)^2 · (5) · (7)

     189 = k · 315

     0.6 = k

So the final answer is: P(x) = 0.6 · (x-2)^2 · (x-0) · (x+2)

The values of the piecewise functions at the indicated limits using the equations obtained from the graph are;

[tex]\lim \limits_{x \to2^+}\frac{f(x) - 4}{f(x+ 3)} = \underline{-\frac{2}{3} }[/tex]

[tex]\lim \limits_{x\to 3^-}[/tex] f(f(x) + 4) = 7

[tex]\lim\limits_{h\to 0} \frac{f(2+ h)-f(2)}{h}[/tex] DNE

A piecewise function is a function that has rules or definition based on the interval of reference of the function.

The graphed function, f(x), comprising of several piecewise functions, indicates that as x → 2⁺, we get;

The points on the line of the graph are;

(1, 1), and (3, 3)

The slope of the graph as x tends to 2⁺ is therefore;

Slope = (3 - 1)/(3 - 1) = 1

The equation of the line is therefore;

y - 1 = x - 1

y = f(x) =  x

Therefore;

f(x) - 4 = x - 4

f(x + 3) = x + 3

[tex]\lim \limits_{x\to 2^+} \frac{f(x) -4}{f(x + 3)} = \frac{x - 4}{x + 3} | x = 2[/tex]

The piecewise function for the interval, x → 3⁻ is; f(x) = x, therefore;

f(f(x) + 4) = f(x + 4) = x + 4

[tex]\lim \limits_{x\to 3^-}f(f(x) + 4)[/tex] = x + 4, where; x = 3, therefore;

[tex]\lim \limits_{h\to 0} = \frac{f(2 + h)-f(2)}{h}[/tex], can be found as follows;

The equation of the function at x = 2 is; y = f(x) = x

f(2 + h) = 2 + h

f(2) = 2

Therefore;

[tex]\frac{f(2 + h)-f(2)}{h}[/tex] = (2 + h - 2)/h = h/h

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-1/10 should be subtracted from 1/2 to get 4/10.

A fraction is of the form → (x/y).

For example, we can write fractions as → 2/3.

Fractions and ratios represent the same aspect. We can write -

2 : 3 = 2/3

4 : 7 = 4/7

Given is to solve the expression -

(1/2) - ? = 4/10

We can write the expression as -

(1/2) - (x) = (4/10)

(x) = 4/10 - 1/2

(x) = 4/10 - 5/10

(x) = -1/10

Therefore, -1/10 should be subtracted from 1/2 to get 4/10.

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{Question in English -

What fraction subtracted from 1/2 equals 4/10?}

Answer:

Given that s = 1.5, the expressions that have a value of 13.5 are:

(1) 5s + 8 = 5 × 1.5 + 8 = 13.5

(2) 2s^2 + 9 = 2 × 1.5^2 + 9 = 13.5

Note: The value of any other expression will depend on the specific formula and the value of other variables used in the expression.

After 40 years, the account has a total balance of $49.450.80.

Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.

Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.

The total contributions would be $100 x 480 = $48,000.

The interest earned on the account balance can be calculated as follows:

Interest = Account balance * Interest rate

At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:

Year 1: $48,000 * 1.5% = $720

Balance = $48,000 + $720 = $48,720

Year 2: $48,720 * 1.5% = $730.80

Balance = $48,720 + $730.80 = $49,450.80

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