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Which rights did the states have and which rights did the federal golprnment have under the Articles of Confederation?
Run post office
Declare war
All other powers not specified
in document
Negotiate with foreign powers Collect taxes
Control militia
State | Federal Government

Answer:

Financial Freedom

Step-by-step explanation:

In my personal opinion, the biggest reason/incentive for saving would be Financial Freedom. This is the ability to not have to depend on a full-time job in order to survive and be able to live off of the passive income being produced by the money that you saved. If you save enough money and invest it correctly you can live off of the interest that is being generated from those investments. This allows you to not have to work a full-time job and instead free's up your time to pursue meaningfull hobbies or even travel. I believe that is true freedom and it is something that motivates me to save money.

Answer:

A: 74.9

B: 51.4

C: 53.7

Sorry I don't have enough time for the rest

Step-by-step explanation:

all angles should add up to 180

Answer:

The average monthly payment would be most affected by Mark's observation of one significantly lower payment. The reason is that the average is calculated by summing all the payments and dividing by the total number of payments, so any extreme values (such as the significantly lower payment) can have a substantial impact on the average value.

Step-by-step explanation:

a) Sample space: {1,2,3,4,5,6} for the first toss of the die. If the result is even, then another toss is made, resulting in the sample space {2,4,6} for the second toss. If the first toss is odd, a coin is tossed, resulting in the sample space {H, T} for the coin toss.

b) Each outcome in the sample space has an equal probability of 1/6, except for the outcomes in {2,4,6}, which have a probability of 1/18 for the second toss.

c) P(a) = P(H) = 1/6, P(b) = 1/2.

d) ac: {5H}, bc: {1,3,5}, ab: { }, a∪b: {1,3,5,H}.

e) P(ac) = 1/6, P(bc) = 3/6 = 1/2, P(a∩b) = 0, P(a∪b) = 4/6 = 2/3, P(a|b) = P(ab)/P(b) = 0/1/2 = 0, P(b|a) = P(a∩b)/P(a) = 0/1/6 = 0.

f) a and b are not mutually exclusive events because there is a possibility that both events can occur together. They are not independent because the outcome of  the first toss affects the likelihood of the second toss or coin toss.

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The measure of exterior angle in the following triangle is A, 125°.

Because the given triangle is a right-angled triangle, ΔABC.

Considering the angles

m∠A = 35°

m∠C = 90°

A triangle's angles add up to 180°.

So,

180° = mA + mB + mC

mA = 35° and mC = 90° are substituted in the equation

35° + m∠B + 90° = 180°

125 + m∠B = 180°

Take 125 off both sides.

125 + m∠B - 125 = 180° - 125

m∠B = 55°

As a result, the angle B is measured as follows:

m∠B = 55°

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it. In a triangle with a 90° angle, the sum of the other two angles is:

180° - 90° = 90°. So, the measure of the exterior angle is 90° + 35° = 125°.

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Complete question:

find the measure of exterior angle in the following triangle 35°

The integral test states that if a series is a sum of terms that are positive and decreasing, and if the terms of the series can be expressed as the values of a continuous and decreasing function, then the series converges if and only if the corresponding improper integral converges.

Let's apply the integral test to the given series. We need to find a continuous, positive, and decreasing function f(x) such that the series is the sum of the values of f(x) for x ranging from 2 to infinity.

For the first series, we have:

∑n=2∞n(lnn)p

Let f(x) = x(lnx)p. Then f(x) is continuous, positive, and decreasing for x ≥ 2. Moreover, we have:

f'(x) = (lnx)p + px(lnx)p-1

f''(x) = (lnx)p-1 + p(lnx)p-2 + p(lnx)p-1

Since f''(x) is positive for x ≥ 2 and p > 0, f(x) is concave up and the trapezoidal approximation underestimates the integral. Therefore, we have:

∫2∞f(x)dx = ∫2∞x(lnx)pdx

Using integration by substitution, let u = lnx, then du = 1/x dx. Therefore:

∫2∞x(lnx)pdx = ∫ln2∞u^pe^udu

Since the exponential function grows faster than any power of u, the integral converges if and only if p < -1.

For the second series, we have:

∑n=2∞1/n(ln⁡n)²

Let f(x) = 1/(x(lnx)²). Then f(x) is continuous, positive, and decreasing for x ≥ 2. Moreover, we have:

f'(x) = -(lnx-2)/(x(lnx)³)

f''(x) = (lnx-2)²/(x²(lnx)⁴) - 3(lnx-2)/(x²(lnx)⁴)

Since f''(x) is negative for x ≥ 2, f(x) is concave down and the trapezoidal approximation overestimates the integral. Therefore, we have:

∫2∞f(x)dx ≤ ∑n=2∞f(n) ≤ f(2) + ∫2∞f(x)dx

where the inequality follows from the fact that the series is the sum of the values of f(x) for x ranging from 2 to infinity.

Using the comparison test, we have:

∫2∞f(x)dx = ∫ln2∞(1/u²)du = 1/ln2

Therefore, the series converges if and only if p > 1.

In summary, the series ∑n=2∞n(lnn)p converges if and only if p < -1, and the series ∑n=2∞1/n(ln⁡n)² converges if and only if p > 1. For values of p such that -1 ≤ p ≤ 1, the series diverges.
To find the values of p for which the series converges or diverges using the integral test, we will first write the series and then perform the integral test.

The given series is:

∑(n=2 to infinity) [1/n(ln(n))^p]

Now, let's consider the function f(x) = 1/x(ln(x))^p for x ≥ 2. The function is continuous, positive, and decreasing for x ≥ 2 when p > 0.

We will now perform the integral test:

∫(2 to infinity) [1/x(ln(x))^p] dx

To evaluate this integral, we will use the substitution method:

Let u = ln(x), so du = (1/x) dx.

When x = 2, u = ln(2).
When x approaches infinity, u approaches infinity.

Now the integral becomes:

∫(ln(2) to infinity) [1/u^p] du

This is now an integral of the form ∫(a to infinity) [1/u^p] du, which converges when p > 1 and diverges when p ≤ 1.

So, for the given series:

- It converges when p > 1.
- It diverges when p ≤ 1.

In conclusion, using the integral test, the series ∑(n=2 to infinity) [1/n(ln(n))^p] converges for values of p > 1 and diverges for values of p ≤ 1.

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Solution

-8 r + 8r =0

And the correct answer would be:

Inverse property of addition

Answer:

a. h(-6)=10

b. x=6

Step-by-step explanation:

a.

To find h(-6), you want to plug in x=-6 into h(x).

\(h(-6)=6-\frac{2}{3}(-6)\)          [multiply]

\(h(-6)=6+4\)                  [add]

\(h(-6)=10\)

Now, we know that h(-6)=10.

------------------------------------------------------------------------------------------------------

b.

To find the value of x, we want to set h(x) equal to 2.

\(2=6-\frac{2}{3} x\)                        [subtract both sides by 6]

\(-4=-\frac{2}{3}x\)                         [multiply both sides by -3/2]

\(x=6\)

Now, we know that x=6.

The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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Step-by-step explanation:

The solution is in the above photo

The given values indicate that the relationship between the number of

DVDs and the weight of the bookcase is not proportional but linear.

The number of DVDs the bookcase can hold is 300 DVDs.

Reason:

Weight of bookcase with 10 DVDs = 30.4 pounds

Weight of the bookcase with 45 DVDs = 38.8 pounds

Let C represent the weight of the bookcase with no DVDs on it, and let x

represent the weight of one DVD, we have;

30.4 = 10·x + C...(1)

38.8 = 45·x + C...(2)

Subtracting equation (1) from (2) gives;

45·x - 10·x = 38.8 - 30.4

35·x = 8.4

\(x = \dfrac{8.4}{35} =0.24\)

The weight of each DVD, x = 0.24 pounds

From equation (1), we get;

30.4 = 10·x + C

C = 30.4 - 10·x

C = 30.4 - 10× 2.4 = 28

The weight of the bookcase, C = 28

Let n represent the maximum number of DVDs the bookcase can hold,

which together with the bookcase weigh 100 pounds, we have;

100 = 0.24·n + 28

0.24·n = 100 - 28 = 72

\(n = \dfrac{72}{0.24} = 300\)

The number of DVDs the bookcase can hold, n = 300 DVDs

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Answer:

last option

Step-by-step explanation:

It was correct I told my teacher

The solution to the inequality is x > -1. represented by graph (B)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operations.

Inequality is an expression that shows the non equal comparison of numbers and variables.

From the inequality:

16x - 80x < 37 + 27

-64x < 64

-x < 1

x > -1

The solution to the inequality is represented by graph (B)

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The acceleration of the object is 2 m/s²

From the question, we are to determine the acceleration of the object

From Newton's second law of motion, we have that

F = ma

∴ a = F/m

Where F is the net force

m is the mass

and a is the acceleration

From the given information,

m = 5kg

From the diagram,

Net force = 30 N - 20N

Net force = 10 N

Then,

a = F/m

a = 10/5

a = 2 m/s²

Hence, the acceleration of the object is 2 m/s²

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Answer:

the line represents the average slope in which the dots line up. in other words, it shows where most of the options/solutions are on the plot

Step-by-step explanation:

nice pfp

Answer:

Step-by-step explanation:

If the polynomial function has rational coefficients, then the missing root must be conjugate with 3 + √11, which is achieved by reversing the sign of root:

\( \LARGE{ \underline{\underline{ \purple{ \bf{Required \: answer:}}}}}\)

Since 3 roots are rational but one of the four is irrational. Then, there must be a conjugate pair for that which we can do by reversing the sign between the rational and the non-rational part.

Hence, Another root of the polynomial function f(x) will be ofcourse the conjugate pair of 3 + √11 i.e. 3 - √11 (Ans)

Answer:

The Graphs are in the picture below. ⬇️

25 days is value of discount period.

What does a math discount mean?

The difference in price between the item's purchase price and par value is the discount. Discounts are different types of price reductions or deductions from a product's cost.

                               The selling price of the goods is lowered as a result of the discount, which increases its allure for the consumer. The customer is psychologically impacted by the price reduction, which prompts them to buy. Trade discounts and cash discounts are the two different sorts of discounts available.

Date of note = April 12

Length of note = 45 days

Date of discount = May 2

Days passed before discount = May 2 - April 12 = 20 days

Discount period for the bank to wait to receive its money = Length of note - Days passed before discount

= 45 days - 20 days = 25 days

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The power to which a number or expression is raised is called the exponent.

1. An exponent is a mathematical notation that represents the power to which a number or expression is raised. It is written as a superscript number or variable placed above and to the right of the base number or expression.

2. The base number or expression is the number or expression that is being multiplied repeatedly by itself, raised to the power of the exponent.

3. The exponent tells us how many times the base number or expression should be multiplied by itself. For example, in the expression \(2^3\), the base is 2 and the exponent is 3. This means that 2 should be multiplied by itself three times: 2 * 2 * 2 = 8.

4. The exponent can be a positive whole number, a negative number, zero, or a fraction. Each of these cases has different interpretations:

  - Positive exponent: Indicates repeated multiplication. For example, \(2^4\)means 2 multiplied by itself four times.

  - Negative exponent: Indicates the reciprocal of the base raised to the positive exponent. For example, \(2^{-3\) means 1 divided by \(2^3\).

  - Zero exponent: Always equals 1. For example, \(2^0\) = 1.

  - Fractional exponent: Represents a root. For example, \(4^{(1/2)\)represents the square root of 4.

5. Exponents follow certain mathematical properties, such as the product rule \((a^m * a^n = a^{(m+n)})\), the quotient rule \((a^m / a^n = a^{(m-n)})\), and the power rule \(((a^m)^n = a^{(m*n)})\).

Remember to use these rules and definitions to correctly interpret and evaluate expressions involving exponents.

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False. The Six Sigma DMAIC approach is one of many problem-solving methods that can be used, and is most appropriate when the problem is complex and the potential solutions are not immediately evident.

Six Sigma DMAIC (define, measure, analyze, improve, control) is a strategy used to improve processes and products. It is designed to help companies identify and eliminate defects and reduce variability in their processes. It is not the best way to attack all problems, as there are many other problem-solving methods, such as Design Thinking and Lean, that may be more suitable solution depending on the complexity of the problem.

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If the perimeter of the rectangle is 4646 centimeters and its length is 88 centimeters then its width would be 2235 centimeters

The perimeter of a form in geometry is defined as the entire length of its border. A shape's circumference is calculated by summing the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

In daily life, people constantly employ the idea of perimeter. For instance, we measure the perimeter of the area to be fenced in or decorated for Christmas to determine how much wire you will need.

We are aware that a regular polygon has equal-length sides.

A regular polygon's perimeter is equal to the product of all of its sides, which is equal to the quantity o sides times the length of a side.

How to solve?

width = 4646 - 2*88 =4470

width of one side = 4470/2 = 2235 centimeters

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Answer:

35° and 55°

Step-by-step explanation:

Complementary angles sum to 90°

let one angle be x and the other x + 20 , then

x + x + 20 = 90

2x + 20 = 90 ( subtract 20 from both sides )

2x = 70 ( divide both sides by 2 )

x = 35°°

x + 20 = 35 + 20 = 55

The 2 angles are 35° and 55°

Answer:

........................  x = −27

The answer would be

\(w = \frac{jk - 5}{6} \)

Hope the attachment can help!

Answer:

i dont have an exact answer but i can give an explanation to what i believe. 1, you'd have to find the second digit after 6. 2, divide that by k and your answer is j.

The angle between sides GM and MT is ∠M.

The 2 sides that include ∠T are MT and GT.

The angle between sides GT and MG is ∠G.

There's not much to say about this, but I can answer questions if you have any.

since the now has a value of ten so the p is equalled to 59

Answer:

12

Step-by-step explanation:

Answer:

Not necessarily...

Step-by-step explanation:

3 abosolute value is 3

Answer:

1)  C.  $13.90 per pound

2)  B. 93.75

3)  B. 399.42

4)  B. 87

Step-by-step explanation:

Given:

Therefore, one pound of cat food costs:

\(\sf \implies \dfrac{\$65.60}{4}=\$16.40\)

If the customer applied a coupon for $2.50 off per pound, then the new price per pound of the cat food is:

⇒ Price after discount = $16.40 - $2.50 = $13.90 per pound

To calculate 37.5 divided by 0.4, multiply both numbers by 10.

Therefore, divide 375 by 4:

\(\large \begin{array}{ccclcc}&0&9&3.&7&5\\\cline{2-6}4 & \!\!\!\big) 3&7&5&&\\&0& \downarrow\\\cline{2-6} &3&7\\ -& 3 & 6 & \downarrow \\ \cline{2-6} & 0 & 1 & 5\\-&&1&2\\ \cline{2-6} & & 0 & 3.&0 \\ - &&&2. & 8\\ \cline{2-6} &&&&2&0\\ - &&&&2 & 0\end{array}\)

Therefore:

⇒ 37.5 ÷ 0.4 = 93.75

The product of two numbers means to multiply them.

When multiplying decimals, remove the decimal points and multiply the numbers as if there were no decimals:

\(\begin{array}{ccccccc} && &4 & 7 & 5 & 5 \\ \times &&& &&8 & 4\\ \cline{2-7} &&1 & 9 & 0 & 2 & 0\\ &3 & 8 & 0 & 4 & 0 & 0\\ \cline{2-7} & 3 & 9 & 9 & 4 & 2 & 0\\ \cline{2-7}\end{array}\)

Finally, put the decimal point back in the answer - it will have as many decimal places as the decimal places of the two original numbers combined.

Therefore, 47.55 × 8.4 = 399.420 = 399.42

To calculate 17.4 divided by 0.2, multiply both numbers by 10.

Therefore, divide 174 by 2:

\(\large \begin{array}{cccl}&0&8&7\phantom{)}\\\cline{2-4}2 & \!\!\!\big) 1&7&4\phantom{)}\\&0& \downarrow\\\cline{2-4} &1&7\\ -& 1 & 6 & \downarrow \phantom{)}\\ \cline{2-4} & 0 & 1 & 4\phantom{)}\\-&&1&4\\ \cline{2-4} & & & 0 \end{array}\)

Therefore:

⇒ 17.4 ÷ 0.2 = 87

The power series representation of f(x) = Σn=1∞ (-1)ⁿ⁻¹ 6ⁿ x²ⁿ+¹ where Σ represents the summation notation.

The power series representation of the given function, centered at x = 0, is:

f(x) = x / (6x² + 1)f(x) = x (1 / (6x² + 1))

We can represent the denominator of the fraction in the form of a power series as follows:

1 / (6x² + 1) = 1 - 6x² + 36x⁴ - 216x⁶ + ...

This is obtained by dividing 1 by the denominator and expressing it as a geometric series with first term 1 and common ratio -(6x²).

Now we can substitute the power series for 1 / (6x² + 1) in the original expression of f(x) to get the power series representation of f(x) as follows:

f(x) = x (1 / (6x² + 1))f(x) = x (1 - 6x² + 36x⁴ - 216x⁶ + ...)

f(x) = x - 6x³ + 36x⁵ - 216x⁷ + ...

∴ The power series representation of f(x), centered at x = 0, is:

f(x) = Σn=1∞ (-1)ⁿ⁻¹ 6ⁿ x²ⁿ+¹ where Σ represents the summation notation.

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