Explain why Sa f(x)dx = 0 (Hint: Use the First Fundamental Theorem of Calculus) 4. A student made the following error on a test: Sve"" dx = $x* Sea? = *e* +C. A : Identify the error and explain how to correct it.

Answer:

-228

Step-by-step explanation:

calculator :)

Answer:

-156

Step-by-step explanation:

[4(-6)](3+5)+ (-6)^2

-24(3+5)+36

-25(8)+36

-196+36

-156

(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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By taking the difference between the two times, we will see that he has 28 minutes to get ready.

To find this, we need to take the difference between the hour at which he needs to leave (first value that we need to write in the number line) and the hour at which he wakes up (second value in the number line)

The time that he has to get ready is just the distance between these two points on the number line, or we can get it by taking the difference.

He wakes up at 7:47 am = 7 hours and 47 minutes.

He needsto leave at 8:15 am = 8 hours and 15 minutes.

The differnece is:

(8h and 15m) - (7h and 47m)

(8h - 7h) + (15m - 47m)

1h + ( -32m)

And we know that 1 hour = 60 min, then:

1h + ( -32m) = 60 min - 32 min = 28min

He has 28 minutes to get ready.

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The number of non-fiction books sold on Friday will be two-and-a-half times the number of arts and crafts books sold on Friday. Therefore, option B is the correct answer.

We can see from the table that on Thursday, 7 sports and trivia books and 19 arts and crafts books were sold, for a difference of 12.

On Thursday, 13 non-fiction books and 19 arts and crafts books were sold. If we assume that the same ratio will hold on Friday, then we can predict that the number of non-fiction books sold will be (19/2)×2.5 = 23.75, which is not a whole number. Therefore, this prediction is not supported by the data.

Therefore, option B is the correct answer.

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Answer:

Step-by-step explanation:

all values are true

Answer:

6

Step-by-step explanation:

this is so simple brother

Answer:

The cube root of 8x27 is 54

Step-by-step explanation:

Observe the following pattern (1×2)+(2×3)=2×3×43, (1×2)+(2×3)+(3×4)=3×4×53, (1×2)+(2×3)+(3×4)+(4×5)=4×5×63 and find the value of  (1×2)+(2×3)+(3×4)+(4×5)+(5×6)

Answer:

1. 10 rainy days

2. 24 points

3. 4 cups

Explanation:

Divide thirty by three to get ten rainy days.

Divide 15 by 90, then multiply the product by four to get 24 points.

divide the volume value by 8.

a) The campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.

b) A Chi-Square goodness of fit test.

a) A campaign manager would like to show that the distribution of individuals within several social economic categories is different than what a newspaper reported and that's why we know that the campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.

Chi-Square goodness of fit is used to find out how the observed value of a given phenomenon is significantly different from the expected value. In Chi-Square goodness of fit test, the sample data is divided into intervals.

In this case, we have one categorical variable which is the distribution of individuals within several social groups. We want to see if the actual distribution of the variable is significantly different from the distribution within several social groups as claimed(expected) by the newspaper.

Hence, we will use chi-square goodness of fit test for this case.

b) A Chi-Square goodness of fit test.

Here the variable is the distribution of individuals purchasing season pass at an amusement park. The variable has 4 categories based on the age group of the individuals.

A tourist company wants to test the actual distribution of individuals within each age group and wants to check if it is significantly different from the expected distribution i.e the one claimed by the amusement park.

The tourist company randomly sampled 200 individuals entering the park.

The proportion of individuals within each group as claimed by the amusement park is given.

Hence, we will use chi-square goodness of fit test to test if the actual distribution within each group is significantly different or not from the claimed distribution.

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Therefore, the derivative of the function \(y = 5t^6 - 4√t + 6/t\) is \(y'(t) = 30t^5 - 2t^(-1/2) - 6/t^2.\)

To find the derivative of the function \(y = 5t^6 - 4√t + 6/t\), we can differentiate each term separately using the rules of differentiation.

Let's calculate the derivative step by step:

For the term \(5t^6\), we can use the power rule of differentiation. According to the power rule, if we have a term of the form \(f(t) = ct^n\), then its derivative is f'(t) = nct^(n-1). Applying this rule, we get:

\(d/dt (5t^6) = 6(5)t^(6-1) = 30t^5.\)

For the term -4√t, we can use the chain rule. The derivative of √t with respect to t is (1/2)t*(-1/2) according to the power rule. Applying the chain rule, we have:

d/dt (-4√t) = -4(1/2)t^(-1/2) * (d/dt)(t) = -2t*(-1/2).

For the term 6/t, we can use the power rule of differentiation with a negative exponent. The derivative of \(t^(-1) is (-1)t^(-1-1) = -t^(-2)\). However, since the term is 6/t, we need to multiply the derivative by 6:

\(d/dt (6/t) = 6(-t^(-2)) = -6/t^2.\)

Now, let's put all the derivatives together to get the derivative of the function y = 5t^6 - 4√t + 6/t:

\(y'(t) = 30t^5 - 2t^(-1/2) - 6/t^2.\)

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The proportion of the 30 sampled bottles are more than 12 ounces is 0.30. The value is most affected by the error will be mean.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint.

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The distance between the two points in simplest radical form. (-1, 3) and (7, 5) is 68

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²)

using the formula for distance between two points;

d = \(\sqrt{(x1-x2)^2 + (y1 - y2)^2}\)

Substituting for the values

d = \(\sqrt{(-1-7)^2 + (3 - 5)^2}\)

d = \(\sqrt{(-8)^2 + (-2)^2}\)

d = \(\sqrt{64 + 4}\)

d= \(\sqrt{68}\)

d = 8

Hence, the distance between the two points is 8

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Answer:

3,696

Step-by-step explanation:

7x24x22 equals 3,696

24x7=168

168x22=3,696

Using LaTeX code, the expression for \((f + g)(x)\) is as follows:

\(\((f + g)(x) = f(x) + g(x) = (2x^2 + 11x - 7) + (-3x^2 - 10x + 2)\)\)

Now, let's simplify the expression:

\(\((f + g)(x) = 2x^2 - 3x^2 + 11x - 10x - 7 + 2\)\)

Combining like terms:

\(\((f + g)(x) = -x^2 + x - 5\)\)

Therefore, the correct answer is a) \(\(-x^2 + x - 5\)\).

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By solving linear equation we get total cost  C = 2.97 r

Where r is a number of reams and C is the total cost.

A linear equation in one variable is one that is written in the form ax + b = 0, where a, and b are real numbers and the coefficients of x and constant, i.e. a and b, are not equal to zero.

Given:

Writing on linear equations that represent the proportional relationships

y = mx

Where y = total cost

m = unit cost

x = number of reams

So as per the question linear equation will be,

For 4 reams = 11.88

So, 1 ream = 11.88/4

    = 2.97

Similarly for 6 reams = 17.82

So, 1 ream  = 17.82/ 6

     = 2.97

By solving linear equation we get total cost  C = 2.97 r

Where r is the number of reams and C is the total cost.

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Answer:

Sin 18° = cos 72° and sin 72° = cos 18°

Step-by-step explanation:

According to trigonometry identity;

sin Ф = cos(90 - Ф)

for Sin 18° = cos 72

Ф = 18°

Substitute into the expression

sin Ф = cos(90 - Ф)

sin 18 = cos(90 - 18)

Sin 18 = cos 72

Hence the statement id true

For sin 72° = cos 18

Ф = 72°

Substitute into the expression

sin Ф = cos(90 - Ф)

sin 72 = cos(90 - 72)

Sin 72 = cos 18

Hence this statement too is correct

The two correct statements are Sin 18° = cos 72° and sin 72° = cos 18°

The given statement is correct.

Hence it is true.

We have a statement regarding the quadratic equations.

We have to verify whether it is true or not.

Since we know that,

A quadratic equation is an equation with a single variable of degree 2. Its general form is ax² + bx + c = 0, where x is variable and a, b, and c are constants, and a ≠ 0.

According to the question, we are provided with the standard form of the quadratic equation as -  ax² + bx + c = 0.

If we compare the statement given in the question with the definition discussed above, then it can be concluded that the given statement is true. Equation ax² + bx + c = 0 is the standard form of a quadratic equation with a, b, and c as constant real numbers.

The constant 'a' cannot be 0, as this would reduce the degree of the equation to 1.

Hence, the given statement is correct.

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The tension in the string connecting blocks 2 and 3 depends on the masses of the blocks and the acceleration of the system.

The tension in the string is determined by the net force acting on block 2. Since block 3 is on a smooth table with negligible friction, the only horizontal force acting on block 2 is the tension in the string. According to Newton's second law, the net force on an object is equal to the mass of the object multiplied by its acceleration. In this case, the acceleration of the system is determined by the weight of block 2 and block 3 and the force of static friction between block 1 and the floor. By considering the forces acting on block 2, we can set up an equation using the relationship between tension and the mass and acceleration of block 2 to solve for the tension in the string.

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"What is the significance of the invention of the printing press in the 15th century, and how did it impact the spread of knowledge and information during that time?"

Answer:

the answer is d

Step-by-step explanation:

Can i have brainliest?

Answer:

=−16x+8 for -2(8x-4)

Step-by-step explanation:

What is the solution to -2(8x-4)= -8x

What is the solution to 2x+5= 7x

so that means -2(8x-4) is less than 2x+5.

Answer: x > 1/6

Step-by-step explanation:

-2(8x - 4) < 2x + 5

Distribute:

-16x + 8 < 2x + 5

Subtract 2x from both sides:

-18x + 8 < 5

Subtract 8 from both sides:

-18x < -3

Divide both sides by -18:

x > 3/18 BUT this simplifies to:

x > 1/6

The reason the inequality flipped is because you divided both sides by a negative number.

The inequality ONLY flips when you divide or multiply both sides by a NEGATIVE number.

Hope this helps!

Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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Answer:

Step-by-step explanation:

radius of bed = 8 m

area of bed = 64π m²

radius of bed and sidewalk = 8+4 = 12 m

area of bed and sidewalk = 144π m²

area of sidewalk = 144π - 64π = 80π ≈ 251.2 m²

Answer:

0.44%

Step-by-step explanation:

1. We know that 2/455 is the same as 2÷455.

2. Once, you do 2÷455 it gives you 0.0044.

3. Then multiply by 100, 0.0044×100= 0.44%

Or just bring the decimal back two places to find this.

The overall supply of money in an economy depends on the amount of central bank money (base money or high powered money) through the money multiplier effect. An increase in foreign output (Y*) has a positive effect on the domestic income level (Y) in an open economy setting.

i) In an open economy setting, an increase in foreign output (Y*) affects the domestic income level (Y) through the expenditure approach. The equation used to explain this relationship is the expenditure-output (income) equation, which is a fundamental component of aggregate demand. The equation is:

Y = C + I + G + (X - M)

where:

Y = Domestic income level

C = Consumption

I = Investment

G = Government spending

X = Exports

M = Imports

When there is an increase in foreign output (Y*), it implies an increase in exports (X). This increase in exports leads to an increase in the net exports term (X - M) of the equation. Net exports represent the difference between exports and imports. As net exports increase, the equation suggests that the domestic income level (Y) also increases.

The increase in foreign output (Y*) implies that more goods and services are being produced by the foreign economy. This, in turn, leads to an increase in the demand for imports (M) from the foreign economy.

As a result, the net exports term (X - M) in the equation becomes larger, contributing positively to the domestic income level (Y). This is due to the increased demand for exports, which leads to an increase in net exports and ultimately boosts the domestic income level.

ii) The overall supply of money in an economy depends on the amount of central bank money, also known as base money or high powered money (H), through the money multiplier effect. The central bank can change the overall supply of money without changing the amount of central bank money through open market operations and changes in reserve requirements.

The overall supply of money in an economy is determined by the money multiplier effect. The money multiplier represents the ratio between the overall supply of money and the amount of central bank money. It shows how much commercial banks can expand the money supply through the lending process.

The money multiplier formula is:

Multiplier = 1 / Reserve Requirement

Reserve requirement refers to the percentage of deposits that banks must hold as reserves and not lend out. When the central bank changes the reserve requirement, it affects the money multiplier and, consequently, the overall supply of money. Lowering the reserve requirement increases the money multiplier, leading to a higher overall supply of money. Conversely, increasing the reserve requirement decreases the money multiplier and reduces the overall supply of money.

Additionally, the central bank can change the overall supply of money through open market operations. Open market operations involve the buying or selling of government securities by the central bank. When the central bank buys government securities, it injects money into the economy, increasing the overall supply of money.

Conversely, when it sells government securities, it withdraws money from the economy, reducing the overall supply of money. However, the central bank can change the overall supply of money without changing the amount of central bank money by adjusting the reserve requirement or conducting open market operations.

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A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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The fact that the cards are replaced means that the probability of picking an ace exactly two times after replacing the card 5 times is 0.47%

As the cards are replaced, this makes this an independent probabilities problem.

The probability of getting an ace exactly two times is:

= Probability of getting ace once x Probability of getting ace once x Probability of not getting ace³

Solving gives:

= 4/52 x 4/52 x (48/52)³

= 0.00465

= 0.47%

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