Identify the following as an identity, a contradiction, or a conditional equation.
3(x + 2) = 3x + 2

Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Answer:

Step-by-step explanation:

Answer:

Here ig

Step-by-step explanation:

Answer:The legislative branch

Step-by-step explanation:

The least value is 11.

\($$\begin{aligned}&\mathrm{S}=\frac{1}{1-(1 / 2)}=2 \\&\mathrm{~S}_{\mathrm{n}}=\frac{1-(1 / 2)^{\mathrm{n}}}{1-(1 / 2)}=2-\frac{1}{2^{\mathrm{n}-1}}\end{aligned}$$\)

\($$\mathrm{S}-\mathrm{S}_{\mathrm{n}}=\frac{1}{2^{\mathrm{n}-1}} < \frac{1}{1000} \text { or } 2^{\mathrm{n}-1} \geq 1000$$\)

Now \($2^{10}=32 \times 32=1024$\)

\($$\therefore n-1 \geq 10 \text { or } n \geq 11$$\)

Hence the least value is 11.

If you have a positive term in your quadratic equation, it will also have a minimum value. This minimum value can be found by graphing the function or solving one of the two equations. If you have the equation y = a\(x^2\) + bx + c, you may use the equation min = c - \(b^2\)/4a to determine the minimum value.

A quadratic equation is a second-order polynomial equation in a single variable x a\(x^2\)+bx+c=0. with a ≠ 0 . The fundamental theorem of algebra assures that it has at least one solution because it is a second-order polynomial equation.

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Answer:

80cm3

Step-by-step explanation:

volume of the composite solid=volume of the

pyramid+

volume of the

cuboid

volume of the pyramid=1/3* base area*height

=1/3*5*4*6

=40cm3

volume of the cuboid=base area *height

=5*4*2

=40cm3

volume of the composite solid=40cm3+40cm3

=80cm3

9514 1404 393

Answer:

Step-by-step explanation:

f(x) is copied from the problem statement.

g(x) is a symbolic representation of the English wording, using x to represent "a number."

h(x) is the exponential function that corresponds to the geometric sequence in the table. It has a common ratio of 3, and a multiplier of 1 at x=0.

Answer:

768

Step-by-step explanation:

a gallon = 128 fluid ounces so 6 gallons would be 768 fluid ounces

Answer:

Step-by-step explanation:

As you can see below, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

The associative law in mathematics states that the grouping of numbers in an addition or multiplication operation does not affect the result. In other words, you can regroup terms within parentheses without changing the value of the expression.

Using the associative law, we can regroup the terms in the expression s + (r + 75) by removing the parentheses and rearranging the terms:

s + (r + 75) = (s + r) + 75

The expression (s + r) + 75 is equivalent to s + (r + 75) because the addition operation is associative.

Let's take an example to illustrate this:

Suppose s = 10 and r = 20.

Using the original expression:

s + (r + 75) = 10 + (20 + 75) = 10 + 95 = 105

Using the expression with regrouped terms:

(s + r) + 75 = (10 + 20) + 75 = 30 + 75 = 105

As you can see, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

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Answer:

200 (12+3)

Step-by-step explanation:

They sold 200 tickets at a price of (12+3)

200 (12+3)

The solution is Option A.

The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the coordinate of the triangle be represented as A

Now , the coordinate A = A ( -4 , 1 )

Now , the coordinate of the triangle after translation is A' ( 0 , -3 )

when there is a translation of the coordinate A by 4 units to the right , we get

A to 4 units right = A ( -4 + 4 , 1 )

The new coordinate of A = A ( 0 ,  1 )

Now , A to 4 units down , we get

The coordinate of A' = A' ( 0 , 1 - 4 )

The coordinate of A' = A' ( 0 , -3 )

Hence , the translated coordinate is A' ( 0 , -3 )

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Answer:

y=-2x-4

Step-by-step explanation:

Given that,

Slope, m = -2

It passes through the point (1,-6).

We need to find the equation of line that passes throgh the given point. It can be calculated as:

\(y-y_1=m(x-x_1)\)

Put y₁ = -6, x₁ = 1 and m = -2

\(y-(-6)=(-2)(x-1)\\\\y+6=-2x+2\\\\y+2x+6-2=0\\\\y=-2x-4\)

Hence, the equation of line is y=-2x-4.

Answer:

1/2

Step-by-step explanation:

Find the domain of the inequality: \(\left \{ {{b > 0} \atop {b\neq 1}} \right.\)

Solve the inequality: b > 0

Convert inequality to equation: b = 1

Solve the equation: b = 1

Convert equation to inequality: b ≠ 1

Find the intersection: 0 < b < 1 or b > 1

The domain of the inequality is: \(\text{log}_b3=\frac{1}{4} ,0 < b, < b < 1\) or\(b > 1\)

Convert logarithm to exponential form: \(b^{\frac{1}{4} }\) = 3, 0 <b<b1 or b > 1

Power on both sides: (b^1/4)^4=3^4, 0<b<1 or b > 1

Simplify using exponent rule (a^n)^m = a^nm:

b = 3^4, 0<b<1 or b > 1

Calculate the power:

b = 81 , 0<b<1 or b > 1

Find the intersection: b = 81

Substitute: \(\text{log}_{81}9\)

Factorize the argument: \(\text{log}_{81} 3^2\)

Express the logarithm of a power of an expression as the power times the logarithm of the expression: \(2*\text{log}_{81} 3\)

Factorize the base: \(2*\text{log}x_{3^4} 3\)

Rewrite the expression using the formula: \(\text{log}_{a^n} b\)

to \((\frac{1}{n} ) \text{log}_ab:\) \(2*\frac{1}{4} *\text{log}_33\)

Apply the power law of logarithm to simplify the expression:

\(2*\frac{1}{4}\)

Reduce the expression to the lowest form:

\(\frac{1}{2}\)

Answer: 1/2

Answer:

\(\log_b9=\dfrac{1}{2}\)

Step-by-step explanation:

\(\textsf{Given}: \quad\log_b3=\dfrac{1}{4}\)

\(\textsf{To find }\log_b9, \textsf{ rewrite 9 as 3}^2:\)

\(\implies \log_b9=\log_b3^2\)

\(\textsf{Apply the Power log law}: \quad \log_ax^n=n\log_ax\)

\(\implies \log_b3^2= 2\log_b3\)

\(\begin{aligned}\textsf{If }\log_b3& =\dfrac{1}{4}\\\\ \implies 2 \log_b3 & =2 \times \dfrac{1}{4}\\\\ & = \dfrac{2}{4}\\\\ & = \dfrac{1}{2}\end{aligned}\)

\(\textsf{Therefore}: \quad\log_b9=\dfrac{1}{2}\)

Answer:

A. 261

B. 347

c. 1176

d. 1715

Step-by-step explanation:

Answer:

The width is 13

Step-by-step explanation:

Use the formula p=2(l+w)

w=P/2 - l = 90/2 - 32 = 13ft

The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

Nate has a deductible of $1,000, which means he is responsible for paying that amount out of pocket before his insurance coverage kicks in. The cost of repairing his car is $7,000, which exceeds his deductible.

However, Nate's collision coverage limit is $5,000, which is the maximum amount his insurance will cover for repairs.

Since the cost of repairs exceeds Nate's coverage limit, he will have to pay the difference between the coverage limit and the actual repair cost.

In this case, Nate's out-of-pocket expenses would be $7,000 (repair cost) - $5,000 (coverage limit) = $2,000.

Therefore, Nate will have to pay a total of $2,000 out of pocket for this claim, which includes his $1,000 deductible and the additional $1,000 that exceeds his coverage limit.

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Answer:

75%

Step-by-step explanation:

To find the percent decrease, use the percent change formula:

(difference / original) x 100

8 - 2 = 6, so the difference is 6.

Plug in the difference and original:

(6 / 8) x 100

= 75

So, the percent decrease is 75%

The probability of a false positive test result is approximately 0.1702 or 17.02%.

The person who will suffer from a false positive are the subjects who aren't drug users.

From the given data, we can see that there are a total of 46 + 1 = 47 positive test results, out of which 8 are false positives (i.e., the subject is not a drug user).

The probability of a false positive test result is:

Probability of false positive = Number of false positives / Total number of positive test results.

Probability of false positive = 8 / 47

Probability of false positive = 0.1702

Therefore, the probability of a false positive test result is approximately 0.1702 or 17.02%.

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Step-by-step explanation:

C. 3X + 2=8is the correct answer

hope it helps you have a good day

please mark me as brain list it is 100% correct

Answer:

Your answer is C

Step-by-step explanation:

(3 * 2) + 2

6 + 2 = 8

Answer:

8 people bought economy and 2 bought first class

Step-by-step explanation:

there are 10 person and total is 1580 so 250+ 9(135)=1460 which is wrong so we gonna try adding 2(250) and 8(135) which got us 1580

The perimeter and area of the figure are 41.50mm and 18.50mm².

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.

The perimeter of an enclosed space is referred to by the word. A house's property line is found on its outside.

Length of BD=√13²-2²

BD=√165

Length of DC=√36-4

=√32

Area of ABC=Area of ADB+ Area of ADC

=(1/2)(BD)(AD)+ (1/2)(DC)(AD)

=(1/2)(√165)(2)+(1/2)(√32)(2)

Area=√165+√32

=18.50

Perimeter=Perimeter of ADB+ Perimeter of ADC

=(13+2+√165)+(6+2+√32)

=23+√165+√32

=41.50

Therefore, the perimeter and area of the figure are 41.50mm and 18.50mm².

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An equation of a direct proportion is: A. y = 8x.

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a direct proportion can be represented the following equation:

y = kx

Where:

In this context, we can reasonably infer and logically deduce that an equation of a direct proportion is y = 8x.

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The period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π

The function is given as:

y = 2∕3 cos(4∕7x) + 2.

The above function is a cosine function

A cosine function is represented as:

y = A cos(B(x + C)) + D

Where the period is

Period = 2π/B

By comparing the equations, we have

B = 4/7

Substitute B = 4/7 in Period = 2π/B

Period = 2π/(4/7)

Express as product

Period = 2π * 7/4

Divide 4 by 2

Period = π * 7/2

Evaluate the product

Period = 7/2π

Hence, the period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π

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Answer:

28 m below the surface to catch its prey

scale factor of triangle is 20/7 = 2.8571 .

To get the scale factor of two triangles, follow these steps:

1. Check that the two triangles are similar.

2-If the triangles are similar, identify the sides that match.

3. Subtract any known angle from the triangle and multiply the result by the matching (also known) angle in the second triangle.

As a result,

4- the scale factor is equalized by the division.

∵ To find scale factor of two triangle we divide the sides of the both sides

∴ the scale factor of triangle given will be 20/7 = 2.8571 .

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The total amount paid by the customer will be $32,262.5 and the amount of the interest will be $ 2,262.5.

APR on a credit card is the way of saying that the interest you are charged over a year is equal to roughly of your balance.

Suppose you walk in to buy a $30,000 car, and you are able to put $3,000 down.

Your dealer initially offers $3,000 for your trade.

You couldn't get to your bank in time, so you finance through the dealer.

They are currently able to offer you a 4% interest rate for 48 months.

After the down payment, the amount will be

P = $ 27,000

r = 4% = 0.00333

n = 48 months

Then the cost of the monthly payment will be

\(\rm MP = P r \times \dfrac{(1+r)^n}{(1+r)^n - 1}\\\\MP = 27000 \times 0.0033 \times \dfrac{(1 + 0.0033)^{48}}{(1+0.0033)^{48} - 1}\\\\MP = 609.63\)

Then the total amount paid by the customer will be

Total amount = 3000 + 609.63 × 48

Total amount = $ 32,262.5

Then the amount of the interest will be given as

Interest amount = $32,262.5 - $30,000

Interest amount = $ 2,262.5

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Answer:

Plug in 1ft/12in

This will give you 36 ft

Step-by-step explanation:

After plugging in, multiply across and simplify/divide and you get your answer