Let ƒ : [0, 1] → R be a strictly increasing continuous function such that f(0) = 0 and f(1) = 1. Prove that 1 lim I'll [f(x)]" dx = 0 (10 points) n→[infinity]

If after climbing 10 feet further up the pole, you measure once more, and find the angle is 24°, then the height of the building is approximately 73.59 feet.

The solution involves using trigonometry to solve for the height of the building based on the angles and distances provided.

Let's assume that the height of the pole is x, and the height of the building is y.

From the first measurement, we have \(tan(35) = \frac{y}{x}\).

From the second measurement, we have \(tan(32) = \frac{y}{x} + \frac{10}{x}\).

From the third measurement, we have \(tan(24) = \frac{y}{x} + \frac{20}{x}\).

We have three equations and three variables. We can solve for x and y.

Simplifying the second equation, we get

\(\frac{y}{x} = tan(32) - \frac{10}{x}\).

Substituting this into the first equation, we get \(tan(35) = tan(32) - \frac{10}{x}\), which simplifies to x = 69.98.

Substituting x into the second equation, we get \(tan(32) = \frac{y}{69.98}\), which simplifies to y = 73.59.

Therefore, the height of the building is approximately 73.59 feet.

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Answer:

The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.

Step-by-step explanation:

Refer the attached figure

We will use equation calculator to find the equation of given plot

\(y = 483.36 \times e^0.0264x\)

We are supposed to find the population of Namibia in the years 1940, 1997, and 2005.

x values are years

y values are population

For 1940, \(x = -10, y = y = 483.36 \times e^{0.0264(-10)} = 371.2\)

For 1997, \(x = 47, y = y = 483.36 \times e^{0.0264 \times 47} = 1671.64\)

For 2005,\(x = 55, y = y = 483.36 \times e^{0.0264 \times 55} = 2064.74\)

Hence The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.

she used 4/27 cups of cereal to make the snack mix.

Let's say the amount of cereal Nancy used was "x".

Since she used twice as many peanuts as she did cereal, the number of peanuts she used would be "2x".

Total, she used 6 3/4 cups of peanuts and cereal to make the snack mix.

Thus, we can write an equation as follows:6 3/4 = 2x + x

Convert mixed number 6 3/4 to an improper fraction:6 3/4 = (27/4)

Now we can solve the equation: (27/4) = 3x

(combining like terms)

Multiplying both sides by 4/27 gives us:1 = (4/27) * 3x

Now we can solve for "x":x = 4/27Since "x" represents the amount of cereal Nancy used,

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Approximately 34.13% of men in the Dinaric Alps region have a height between 68 and 72 inches.

To calculate this percentage, we need to find the area under the normal distribution curve between 68 and 72 inches. We can do this by standardizing the values using the z-score formula:

z = (x - μ) / σ

where x is the height value, μ is the mean height, and σ is the standard deviation.

For x = 68 inches, the z-score is:

z = (68 - 73) / 3 = -1.67

For x = 72 inches, the z-score is:

z = (72 - 73) / 3 = -0.33

Using a standard normal distribution table or a calculator with a normal distribution function, we can find that the area under the curve between z = -1.67 and z = -0.33 is approximately 0.3413 or 34.13%. Therefore, approximately 34.13% of men in the Dinaric Alps region have a height between 68 and 72 inches.

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Answer:

21 and 16

Step-by-step explanation:

x= big number

x`-5 = small number

x + x-5 = 37

2x-5 =37

2x= 42

x = 21

       21-5 = 16

21+16 = 37

Answer:

5 foot

Step-by-step explanation:

Answer:

I think + 2 plz make me brainliest

Step-by-step explanation:

Answer:

9 weeks

Step-by-step explanation:

If she took 10 quizzes over the span of 5 weeks, then she took 2 quizzes per week.

This is because:

10 quizzes ÷ 5 weeks = 2 quizzes

We can use this information to solve for 18 quizzes by setting up the equation the same way

If she takes 2 quizzes every week, and ends with 18 finished quizzes, how many total weeks did it take her ?

Variable x = total weeks

18 quizzes ÷ x weeks = 2 quizzes

With division, we can switch x weeks and 2 quizzes

18 quizzes ÷ 2 quizzes = x weeks

18 ÷ 2 = 9

9 weeks

Answer:

add everything to everything

Step-by-step explanation:

Answer:

x = 7/8 = 0.875

Step-by-step explanation:

x - 5/8 = 1/4

(Add 5/8 to both sides.)

x = 1/4 + 5/8

(Least common multiple of 4 and 8 is 8. Convert 1/4 and 5/8 to fractions with denominator 8.)

x = 2/8 + 5/8

(Since 2/8 and 5/8 have the same denominator, add them by adding their numerators.)

x = 2 + 5/8

(Add 2 and 5 to get 7)

x = 7/8

Answer: R , y>6

Step-by-step explanation:

\(a^x\)  : domain is R

Range : y > 6

Answer:

s+2=3

s=1

Step-by-step explanation:

make it braintliest please

Answer:

a) \(\sqrt{56\) → Definitely not undefined because 56 is a positive real number

b) \(-\sqrt{56\) → Definitely not undefined because 56 is a positive real number (and the negative sign is not under the square root)

c) \(\sqrt{-56\) → Definitely undefined because -56 is a negative number

__

We know that there is no real square root of a negative number because nothing multiplied by itself results in a negative number.

__

d) \(\sqrt h\) → Could be undefined because we don't know the value of \(h\); it could be positive or negative

e) \(-\sqrt {h\) → Could be undefined because we don't know the value of \(h\); it could be positive or negative (and the negative sign doesn't affect this because it is outside the square root)

f) \(\sqrt{-h\) (when \(h\) is positive) → Definitely undefined because the value inside of the square root is negative (a negative times a positive is a negative)

There are four types of rigid motions that we will consider: translation, rotation, reflection, and glide reflection

There are 3 variables present in the linear system represented by the given augmented matrix.

Option A is the correct answer.

We have,

The concept used to determine the number of variables in the linear system is based on the observation that each column in the coefficient matrix corresponds to a variable.

In a system of linear equations, the coefficient matrix represents the coefficients of the variables.

By examining the dimensions of the coefficient matrix, we can determine the number of variables in the system.

In the given augmented matrix, the coefficient matrix has 3 columns. Each column corresponds to a variable.

Therefore, we can conclude that there are 3 variables in the system.

Now,

We can see that this matrix has 3 columns.

Each column represents a variable in the linear system.

Therefore, we can conclude that there are 3 variables in the system.

Thus,

There are 3 variables present in the linear system represented by the given augmented matrix.

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The complete question:

How many variables are present in the linear system represented by the given augmented matrix, which has been reduced by elementary row operations?

Augmented matrix:

\(\left[\begin{array}{ccc}1&0&2\\-2&-3&-5\\4&1&0\\3&2&6\\6&13&-5\end{array}\right]\)

(A) 3 variables

(B) 4 variables

(C) 5 variables

(D) It is impossible to determine the number of variables.

(E) None of the above.

Answer:

divide the numerator by the denominator

Answer:

(A) x + 3y - 10

Step-by-step explanation:

This Questions tests on the concept of solving algebraic expressions.

Eg. 7x + 4y + 3y + 9x = 16x + 7y

(Note that BODMAS rule applies to algebraic expressions as well.)

Given from the question:

5x + 8 - 13y - 4x - 18 + 16y

= 5x - 4x - 13y + 16y + 8 - 18 (Regroup the terms)

= x + 3y - 10 (A)

The unit rate of Printer B = 25 pages per minute, which is greater than the unit rate of Printer A that is 15 pages per minute.

The unit rate of a graph can b determined by using any point, (x, y), on the graph and solve by finding, m, which is the ratio of y to x, if x and y represents the variables of the relationship that is graphed.

Thus, unit rate (m) = y/x.

The printing rate for Printer A is represented by the graph. To find the unit rate for Printer A, use a point on the graph, (2, 30) to find the unit rate, m.

Printer A's Unit rate (m) = y/x = 30/2

Printer A's unit rate (m) = 15 pages per minute.

The printing rate for Printer B is given as 25 pages per minute. 25 pages per minute is a greater unit rate compared to 15 pages per minute.

Therefore, we can conclude that Printer B has a greater printing rate than Printer A, because the unit rate of 25 pages per minute is greater than 15 pages per minute.

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Answer:

-7/3

Step-by-step explanation:

6d + 8 = 3d + 1 (subtract 3d from both sides)

3d + 8 = 1 (now subtract 8 from both sides)

3d = -7 (divide both sides by 3)

d = -7/3

Answer:

Step-by-step explanation:

6d+8=3d+1

3d+8=1

3d=-7

D=-7/3

Yeah, it seems fine so you're doing great so far! ^^

Answer:

D

Step-by-step explanation:

f(x)=20 cos (pi/5x + pi/2)+25

Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

Patrick's average amount of water, in cups per day is W(c) cups per day, where c is some value in [0,4].

The average amount of water Patrick drank from t=0 to t=4 days is given by the expression (1/4)∫[0,4] W(t) dt, which is the average value of W(t) over the interval [0,4]. Since W(t) is differentiable, we can apply the Mean Value Theorem for Integrals to find that this average value is equal to W(c) for some c in [0,4].

Therefore, Patrick's average amount of water, in cups per day, he drank from t=0 to t=4 days is W(c) cups per day, where c is some value in [0,4].

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The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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The weighted average cost of capital (WACC) for company C is 6.63%.

The weighted average cost of capital (WACC) is a financial metric that represents the average rate of return a company must earn on its investments to satisfy its shareholders and creditors. It takes into account the proportion of debt and equity in a company's capital structure and the respective costs associated with each.

To calculate WACC, we need to consider the cost of debt and the cost of equity. The cost of debt is the interest rate a company pays on its debt, adjusted for taxes. In this case, the pre-tax cost of debt is 2% and the tax rate is 24%. Therefore, the after-tax cost of debt is calculated as (1 - Tax Rate) multiplied by the pre-tax cost of debt, resulting in 1.52%.

The cost of equity represents the return required by equity investors to compensate for the risk associated with owning the company's stock. Here, the cost of equity for company C is 6%.

The debt represents 10% of the total capital, while the equity represents the remaining 90%. To calculate the weighted average cost of capital (WACC), we multiply the cost of debt by the proportion of debt in the capital structure and add it to the cost of equity multiplied by the proportion of equity.

WACC = (Proportion of Debt * Cost of Debt) + (Proportion of Equity * Cost of Equity)

In this case, the calculation is as follows:

WACC = (0.10 * 1.52%) + (0.90 * 6%) = 0.152% + 5.4% = 6.552%

Therefore, the weighted average cost of capital (WACC) for company C is approximately 6.63%.

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The vertex of the parabola y = f(x + 1) is (1, -1).

To find the vertex of the parabola given by the equation y = f(x + 1), we need to determine the effect of the transformation on the vertex coordinates.

The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.

In the given equation, y = f(x + 1), we can see that the transformation is a horizontal shift of 1 unit to the left. This means that the new vertex will be located 1 unit to the left of the original vertex.

Given that the original vertex is (2, -1), shifting 1 unit to the left would result in a new x-coordinate of 2 - 1 = 1. The y-coordinate remains the same.

Therefore, the vertex of the parabola y = f(x + 1) is (1, -1).

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The likely percentage that Maggie will get pregnant again 2 years after the first baby's birth is not predictable as it depends on various factors.

It's important to note that individual circumstances can vary greatly, and predicting an exact percentage of Maggie's likelihood of getting pregnant again in 2 years isn't possible. However, some factors that may influence her chances include her age, contraceptive use, and personal choices.

Teenagers have a higher fertility rate, but using effective contraceptives and making informed decisions can reduce the likelihood of a subsequent pregnancy. It's crucial for Maggie to consult with a healthcare professional for personalized advice and support.

While research suggests that the chances of getting pregnant in the first year after childbirth are relatively high, the likelihood decreases over time, and after two years, it may be lower than the chances of getting pregnant for the first time.

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The Upper Control Limit (UCL) and Lower Control Limit (LCL) are calculated for different data sets, as specified in the given values.

The UCL and LCL are statistical control limits used in process control to determine if a process is in a stable and predictable state. These limits define the range within which data points should fall if the process is under control.

In each case provided (A, B, C, D, E), the UCL and LCL values are given. These values represent the calculated control limits for the respective data sets.

To calculate the control limits, a specific statistical method such as the ± 3σ (sigma) method may have been used. This method sets the UCL and LCL at three standard deviations above and below the mean.

The UCL represents the upper threshold or upper boundary, while the LCL represents the lower threshold or lower boundary. These limits help identify any potential deviations or out-of-control situations in the data.

By applying the given values, the corresponding UCL and LCL for each data set can be calculated. These limits are important for quality control and process monitoring, ensuring that the data falls within acceptable ranges.

To calculate the UCL and LCL using ±3σ limits, we use the following formulas:

UCL = Mean + 3σ
LCL = Mean - 3σ

Here, σ represents the standard deviation of the data set. The ±3σ limits provide a range that encompasses most of the data points in a normal distribution, with approximately 99.7% of the data falling within this range.
A) For data set A:
UCL = 7.437
LCL = -2.237

B) For data set B:
UCL = 7.82
LCL = 0

C) For data set C:
UCL = 8.382
LCL = 0

D) For data set D:
UCL = 7.82
LCL = -2.22

E) For data set E:
UCL = 9.112
LCL = 0

The ±3σ limits are derived from the standard deviation (σ) of the data set. Unfortunately, the standard deviation is not provided in the given information. If you have the standard deviation available, we can proceed to calculate the UCL and LCL using the formulas UCL = Mean + 3σ and LCL = Mean - 3σ.

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Question - What are the upper control limit (UCL) and lower control limit (LCL) using a ±3σ limit for the given data sets?

A) For data set A, the UCL is 7.437 and the LCL is -2.237.
B) For data set B, the UCL is 7.82 and the LCL is 0.
C) For data set C, the UCL is 8.382 and the LCL is 0.
D) For data set D, the UCL is 7.82 and the LCL is -2.22.
E) For data set E, the UCL is 9.112 and the LCL is 0.

Congruent quadrilateral related parts are congruent.

The true statements are:

Statements 2, 4, and 6 are Not Congruent

Statements 1, 3, and 5 are Congruent

Two triangles are said to be congruent if their corresponding sides and angles are equal.

From the given figure:

Quadrilaterals 1, 2 and 4 are congruent

Quadrilateral 3 is not congruent to any of the other quadrilaterals.

The true statements are:

Quadrilateral 1 and quadrilateral 2 Congruent

Quadrilateral 1 and quadrilateral 3 Not Congruent

Quadrilateral 1 and quadrilateral 4 Congruent

Quadrilateral 2 and quadrilateral 3 Not Congruent

Quadrilateral 2 and quadrilateral 4 Congruent

Quadrilateral 3 and quadrilateral 4 Not Congruent

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