The left and right page numbers of an open book are two consecutive integers whose sum is 27. Find these page numbers. The smaller page number is__.The larger page number is__.

Answer:

C. 18

Step-by-step explanation:

Let's say the first number is x so the second will be x+1 and the third will be x+2

x+ x+1+x+2=51

3x+3=51

3x=51-3

3x=48

3x/3=48/3

X=16 this is the first number

The second number will be x+1=16+1=17

The third number will be x+2=16+2=18

So the greatest number will be 18

Converting the force from newtons to pounds can help us determine the chances of a driver being able to stop a child. The conversion factor is 1 pound (lb) = 4.45 newtons (N).

To convert the force from newtons to pounds, we use the conversion factor of 1 lb = 4.45 N. If we have a force in newtons, we can divide it by 4.45 to obtain the equivalent force in pounds. For example, if the force is 20 N, we divide it by 4.45 to get approximately 4.49 lb.

Now, in order to assess the chances of the driver stopping the child, we need to consider various factors such as the mass and speed of the child, the friction between the driver's shoes and the ground, and the force applied by the driver. If the force applied by the driver, converted to pounds, is greater than or equal to the force exerted by the child, there is a higher chance of stopping the child.

However, it's important to note that other factors, such as the driver's reaction time and the coefficient of friction between the shoes and the ground, also play significant roles in determining the outcome. Thus, the chances of the driver stopping the child depend on a combination of these factors, making it essential to consider them comprehensively when evaluating the situation.

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Answer:

\(9n - 12 \rightarrow \frac{1}{3} (9n - 12) \\ = \frac{3}{3} (3n - 4) \\ l = 3n - 4\)

The perimeter of an equilateral triangle is 9n - 12. Write an expression to represent the length of each side.

\( = \frac{9n-12}{3} \\ = \frac{3(3n - 4)}{3} \\ = 3n - 4\)

The length of each side of the triangle is 3n-4.

Hope it helps!!

Alice gave Zack 5/32 of the chocolate bar. If Alice got 5/8 of a full bar of chocolate, this means she has 3/8 of the chocolate left after giving Zack his share.

To find out how much of her own piece Alice gave Zack, we need to subtract Zack's share from the amount Alice originally had.

Alice originally had 5/8 of the chocolate bar, so 1/4 of the full bar that Alice gave to Zack is:

(1/4) x (5/8) = 5/32

Therefore, Alice gave Zack 5/32 of the chocolate bar, which is the same as saying she kept 3/8 - 5/32 = 11/32 of the chocolate bar for herself.

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Step-by-step explanation:

6y = 4x - 18 could be the other equation of system ...

Rectangle ABCD is not similar to rectangle PQRS because their corresponding sides are not proportional, so rectangle ABCD cannot be dilated to fit exactly over rectangle PQRS.

Similar polygons are polygons that share these two features presented as follows:

The ratio between the equivalent side lengths is given as follows:

Due to the different ratios, they are not proportional, and hence the rectangles are not similar.

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Answer:

ur answer is C (x + 2)^2(x-2)

Answer:

ur answer is C (x + 2)^2(x-2)

Step-by-step explanation:

edge 2021

Answer: A=105

Step-by-step explanation: This is why:

lxwxh

so 15x14x50=105

The amount in the bank after 9 years with an interest rate of 10 percent per year, compounded annually, is $3,128.08.

What is compound annually?

Compound annually, specifically, refers to the frequency at which interest is added to the principal. In this case, the interest is compounded once a year. At the end of each year, the interest earned is added to the principal, and subsequently, interest for the following year is calculated based on the new total. This compounding process continues annually for the specified duration.

Compound interest refers to the process of earning interest not only on the initial amount (principal) but also on the accumulated interest from previous periods. In other words, it involves reinvesting the interest earned, leading to exponential growth of the principal amount over time.

To find the amount in the bank after 9 years with annual compounding, we use the formula for compound interest:

\(A = P(1 + r/n)^(nt).\)

Given:

P = $2000,

r = 10% = 0.10,

n = 1 (compounded annually),

t = 9 years.

Plugging in these values into the formula, we get:

\(A = 2000(1 + 0.10/1)^(1*9)

= 2000(1.10)^9\)

= $3,128.08 (rounded to two decimal places).

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Applying the rules for the constant, logarithm and exponents, the derivative of the given function is of:

f'(x) = 3/x - 6x² - 8/(x^5).

The function is given by:

f(x) = √2^3 + ln(x^3) - 2x^3 - log_3(729) - 2/x^4

The derivative of a sum is the sum of the derivatives, hence:

f'(x) = (√2^3)' + (ln(x^3))' - (2x^3)' - (log_3(729))' - (2/x^4)'

The derivative of a constant is of zero, hence:

Hence:

f'(x) = (ln(x^3))' - (2x^3)' - (2/x^4)'.

The derivative of the logarithm is given by:

ln(h(x))' = (1/h(x)) x h'(x).

Hence:

(ln(x^3))' = 3x²/x³ = 3/x.

The derivative of the power of x is given by:

[x^n]' = nx^(n-1).

Hence:

Hence the derivative of the function is given by:

f'(x) = 3/x - 6x² - 8/(x^5).

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State feedback controllers with integral control are useful for reducing or eliminating steady-state errors in a system. The following is a step-by-step process for designing a state feedback controller with integral control:Problem 4 Consider the plant with the following state-space representation.

0⎡⎣x˙x⎤⎦=[0−4.4−20.6]⎡⎣xu⎤⎦y=[10]Part (a)To get a 5% overshoot and 2-second settling time, we design a state feedback controller without integral control. The first step is to check the controllability and observability of the system.The rank of the controllability matrix is 2, which is equal to the number of states, indicating that the system is controllable. The system is also observable since the rank of the observability matrix is 2.

The poles of the closed-loop system can now be placed using Ackermann's formula or the coefficient matching method. Ackermann's formula is used in this example. The poles are located at -5 ± 4.83i.K = acker(A,B,[-5-4.83j,-5+4.83j])The gain matrix is calculated as:K = [4.4000 10.6000]The steady-state error for a unit step input is calculated using the following equation:ess=1+ C(A - BK)-¹Bwhere C = [1 0] and D = 0. The steady-state error for a unit step input is found to be 0.Part (b)To reduce the steady-state error to zero, integral control is added to the system. The augmented system's state vector is [x xₐ]

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Reversing the order of integration in the given double integral results in a new expression with the order of integration switched.  By reversing the order of integration of I = ∫∫ 1 dxdy we obtain ∫∫ 1 dydx.

The given double integral is written as: ∫∫ 1 dxdy.

To reverse the order of integration, we switch the order of the variables x and y. This changes the integral from being integrated with respect to y first and then x, to being integrated with respect to x first and then y. The reversed integral becomes:

∫∫ 1 dydx.

In this new expression, the integration is first performed with respect to y, followed by x.

It's important to note that the limits of integration remain the same regardless of the order of integration. The specific region of integration and the limits will determine the range of values for x and y.

To evaluate the integral, you would need to determine the appropriate limits and perform the integration accordingly.

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Answer:

Step-by-step explanation:

Given:

Angles A and C are equal. This makes triangles similar:

Ratio of corresponding sides is same:

Side measures are:

Answer:

1500

Step-by-step explanation:

75% of a 2000 km trip is 1500.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Given,

Total distance = 2000 km

We have to find the 75% of the given distance.

Let x be the 75% of the required distance.

x = 75% × 2000

x = (75/100) × 2000

x = 0.75 × 2000

x = 1500

Hence the 75% of the given distance is 1500 km.

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Answer:

B. Susan's location is cheaper for 10 people.

D. The charge for each additional person is greater for Charlie's location.

Rational zero for the \(2x^{n}-4x^{5}+3x^{2} -7x-41\) is O 2/41, 4/41, 3/41, 7/41, -2/41, -4/41, -3/41, -7/41.

According to the Rational Zero Test, which of the following might be a rational zero for the polynomial \(2x^{n}-4x^{5}+3x^{2} -7x-41\) Here n is an unknown positive integer greater than 5.

The Rational Zero Test is a theorem that determines the possible rational roots of a polynomial with integer coefficients.

In this case, we are given a polynomial with integer coefficients and are asked to identify its possible rational zeros. The possible rational zeros of the polynomial \(2x^{n}-4x^{5}+3x^{2} -7x-41\) are given by the following formula:

Possible Rational Zeros = ± (factors of the constant term) / (factors of the leading coefficient0.)In this case, the leading coefficient is 2, and the constant term is -41.

Thus, the possible rational zeros are given by:± (1, 41) / (1, 2).

Therefore, the possible rational zeros are: ± 1/2, ± 1, ± 41/2, ± 41.                                                                                                                     Now, the value of n is an unknown positive integer greater than 5. Hence, we can't determine the exact possible rational zeros. However, we can say that the possible rational zeros are  ± 1/2, ± 1, ± 41/2, ± 41.

Therefore, the correct option is O 2/41, 4/41, 3/41, 7/41, -2/41, -4/41, -3/41, -7/41.

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The height of the Key West Lighthouse in meters is approximately 26.21 meters.

Here's how you can calculate it:

- There are 3.28 feet in a meter.

- Divide the height of the lighthouse in feet by the number of feet in a meter: 86 ÷ 3.28 = 26.21 meters (rounded to two decimal places).

- Therefore, the height of the Key West Lighthouse in meters is approximately 26.21 meters.

Answer:one pen = $1.50

Step-by-step explanation:

See picture for the math if that helps

Using p for pens, h for highlighter,

A for first equation

B for second equation

I used equation A to reduce to a usable substitute by dividing all by 3

And then isolating “h”.

Now substitute the value of “h” into equation B and solve for “p”

P=$1.50

To check your work, substitute p ($1.50) into equation B and solve for “h”

h=$4.00

Now substitute the p and h values into either equation A or B and solve, they equal the numbers given

The number of bank PINs in string which exactly four digits are even is (74​)⋅57.

To determine the number of PINs with exactly four even digits, we need to consider the number of ways we can choose four even digits from the set {0, 2, 4, 6, 8}, as well as one odd digit from the set {1, 3, 5, 7, 9}.

The number of ways to choose four even digits from a set of five is given by the combination formula: (5 choose 4) = 5! / (4! * 1!) = 5.

Similarly, the number of ways to choose one odd digit from a set of five is also 5.

Since these choices are independent, we can multiply the number of ways to choose even digits by the number of ways to choose an odd digit: 5 * 5 = 25.

Once we have chosen the even digits and the odd digit, we have fixed their positions within the PIN. The remaining two digits can be chosen freely from the set of all digits (0-9), giving us 10 * 10 = 100 possible choices.

Finally, we multiply the number of choices for the even and odd digits by the number of choices for the remaining two digits: 25 * 100 = 2500.

Therefore, the total number of PINs in which exactly four digits are even is (74​)⋅57 = 2500.

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The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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The number of times his commute will be between 26 and 31 minutes is about 88.7.

The probability of Dominic's commute being between 26 and 31 minutes can be calculated using the normal distribution. The z-score of 26 minutes is

(26-32)/3.5 = -1.42,

And the z-score of 31 minutes is

(31-32)/3.5 = 0.29.

Using the z-table, we can calculate the area between the two z-scores, which is about 0.4352.

This means that about 43.52% of the day's Dominic commutes to work will take him between 26 and 31 minutes.

Since there are 205 days that Dominic commutes to work per year, the number of times his commute will be between 26 and 31 minutes is about 88.7 (rounded to the nearest whole number).

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1. The population variances are equal;
2. The samples are independent;
3. The populations are normally distributed.

All of these choices are required conditions for ANOVA:

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Answer:

8. 820 km

Step-by-step explanation:

8.

15 I per 100 km

x liter per 820 km on cross multiplication

(820 * 15) / 100 = x

12300/100 = x

123 liter =x in total 123 liter of gas will be required to travel 820 km.

Answer:

8.820

Step-by-step explanation:

hope it helps you bro

The mean and the standard deviation of the following data are 35.75 and 11.6765 respectively.

First, we'll find the mean (X) of the data:

\(X =\dfrac{(\sum x \times f) } {\sum f}\)

So, the approximate standard deviation for the monthly cell phone plan cost is 9.87.

The mean is given by

\(\mu =\frac{\sum xf}{\sum f}\)

Where x is the midpoint of the class and f is the frequency.

The calculation of mean and the standard deviation is shown in the below table:

    Hence, the mean is calculated as:

mean is   \(\mu =\frac{2359.67}{66}\)

                          =35.75

The standard deviation is calculated as:

Standard deviation =\(\sigma\) =\(\sqrt{\Dfrac{\sum f(x-\bar{x})^2}{n-1}}\)

=\(\sqrt{\dfrac{8862.12121}{65}}\)

=11.6765

Thus, the mean and the standard deviation are 35.75 and 11.6765 respectively.

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The table of standard deviation is attached below.

Answer:

€ 2932.54

Step-by-step explanation:

Rate of interest for income upto 12012 = 0.5 %

    Interest = 0.5% *12012

                  =0.05 *12012

                  = € 60.06

Rate of interest for income between 12012.01 to 19874 = 2%

    Interest = 2% * 19874

                  = 0.02 * 19874

                   =  € 397.48

Rate of interest for income between 19874.01 to 70044 = 4.5%

 Interest = 0.045 * 55000

               = € 2475

Anna's USC for the year = 60.06 + 397.48 + 2475

                                         = € 2932.54

Answer:

3/8

Step-by-step explanation:

This is the simplified version

Answer:

3/8

Step-by-step explanation:

Divide 15 and 40 by 5...

The degrees of freedom that would be used to find a confidence interval for the difference in means, when given two samples from populations G and H are 107.

A confidence interval is an estimate of the value of an unknown population parameter based on the values of a random sample of observations drawn from the population. It is an interval estimate combined with a probability statement. The probability statement indicates the level of confidence that the parameter is within the interval's boundaries.

The confidence interval is always represented in terms of the population parameter. Therefore, if one were to construct a confidence interval for a population mean, it would be in the form of (x-bar ± error), where x-bar is the sample mean and error is the margin of error.

Degrees of freedom is a statistical term that refers to the number of independent values that can be varied in a sample without changing the sample's variance. It's utilized in hypothesis testing, where it is used to determine the number of degrees of freedom for a sample's distribution.

The degree of freedom (df) for a hypothesis test is the number of observations in a sample that are free to vary after certain limitations have been imposed on the data.

In hypothesis testing, degrees of freedom are used to determine whether or not a given hypothesis is statistically significant. Degrees of freedom also influence the accuracy of statistical estimates based on a sample dataset.

The formula for degrees of freedom is (n-1), where n is the sample size.

In this case, the degrees of freedom would be:

52 + 57 - 2 = 107

Therefore, the degree of freedom would be 107.

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Answer:

the answer is option D

y =(3/4)x - (3/2)

The derivative of f(g(x)) with respect to x is  f'(1/x).

The term derivative refers to a type of financial contract whose value is dependent on an underlying asset, group of assets, or benchmark.

Given that, g(x)=ln x

Differentiation of ln x = 1/x

Hence, The derivative of f(g(x)) with respect to x is  f'(1/x).

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