Question: The pages of a book are numbered consecutively, beginning with 1. The digit 7 is
printed 25 times in numbering the pages. What is the largest number of pages the
book can have?

The sample variance is 2482.6375 and the sample standard deviation is 49.79 (rounded to four decimal places). The sample variance and standard deviation can be calculated using the following formula:

Sample variance:

s^2 = (1 / (n-1)) * ∑ (x_i - x)^2

Sample standard deviation:

s = √(s^2)

Where:

x_i is each data point,

x is the sample mean,

n is the number of data points,

∑ represents the sum of all terms.

First, we need to calculate the sample mean:

x = (86 + 102 + 130 + 160 + 180 + 195 + 135 + 145 + 214 + 105 + 145 + 154 + 153 + 135 + 87 + 99 + 94 + 119 + 129) / 20 = 140.95

Next, we can use the sample mean to calculate the sample variance:

s^2 = (1 / (20-1)) * ( (86-140.95)^2 + (102-140.95)^2 + (130-140.95)^2 + (160-140.95)^2 + (180-140.95)^2 + (195-140.95)^2 + (135-140.95)^2 + (145-140.95)^2 + (214-140.95)^2 + (105-140.95)^2 + (145-140.95)^2 + (154-140.95)^2 + (153-140.95)^2 + (135-140.95)^2 + (87-140.95)^2 + (99-140.95)^2 + (94-140.95)^2 + (119-140.95)^2 + (129-140.95)^2)

Finally, we can take the square root of the sample variance to find the sample standard deviation:

s = √(s^2) = √(2482.6375) = 49.79

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The total length is 115 km.

Let "x" be the complete lengh. So, in order to find 20% of that length we need to multiply by 0.2, which equals 20%. And it needs to equal 23 km. Hence the equation should be the following:

[tex]0.2x=23[/tex]

[tex]\frac{0.2x}{0.2} =\frac{23}{0.2} \\ \\x=115[/tex]

To verify the answer, calculate 20% of the result (115), and it should equal 23 km. Let's see!

[tex]115*0.2=\\ \\23[/tex]

The total length is 115 km.

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Answer:

Step-by-step explanation:

Absolute Change:

The absolute change in the politician's support is calculated as the difference between the final support percentage (53%) and the initial support percentage (32%):

53% - 32% = 21 percentage points

So, the absolute change in the politician's support is 21 percentage points.

Relative Change:

The relative change in the politician's support is calculated as the absolute change divided by the initial support percentage, multiplied by 100 to express it as a percentage:

(21 / 32) * 100 = 65.625%

Rounding to the nearest tenth of a percent, the relative change in the politician's support is 65.6%.

So, the absolute change in the politician's support is 21 percentage points, and the relative change is 65.6%.

In this case, the absolute change in the politician's support is an increase of 21 percentage points, and the relative change is an increase of 65.6%.

In this situation, the absolute change in the politician's support can be calculated by subtracting the original value from the new value. So, 53% (new value) - 32% (original value) = 21%. Thus, the absolute change in support is 21 percentage points.

The relative change is the absolute change divided by the original value. So, 21% (absolute change) ÷ 32% (original value) = 0.65625. To get the relative change as a percentage, we need to multiply this decimal by 100, and round to the nearest tenth of a percent, which gives us 65.6%.

Therefore, the politician's support has increased by an absolute change of 21 percentage points, and a relative change of 65.6%.

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Answer:

Step-by-step explanation:

The expression "6x power of 2" represents a polynomial expression in the variable x. The term "6x" is a linear term, and the term "2" is a constant term. So, the expression "6x power of 2" can be classified as a degree 1 polynomial with one variable.

Answer:

  monomial of degree 2 with one variable

Step-by-step explanation:

You want to classify 6x².

A polynomial is a sum of terms consisting of the product of a constant and one or more variables raised to non-negative integer powers. Special names are given to polynomials consisting of one, two, or three terms.

The given term has a coefficient of 6, and one variable, x, raised to the power of 2. The "degree" of the term is the sum of powers of all of the variables in the term, so the degree of x² is 2.

A single-term polynomial is called a "monomial."

  6x² is a monomial of degree 2

The two lines have same slope with opposite signs thus, the linear routes are perpendicular, and Ty and Leo will pass through a common coordinate.

A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle. If two segments PQ and RS connect at right angles, we may say that they are perpendicular to one another.

For the given coordinates of Ty and Leo let us calculate the slope of the line.

The slope of the line is given as:

m = (y2 - y1) / (x2 - x1)

For Ty:

m = (1 - 3) / (0 + 1) = -2

For Leo:

m = (2 - 4) / (0 - 1) = 2

The two lines have same slope with opposite signs thus, the lines are perpendicular, and Ty and Leo will pass through a common coordinate.

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Answer:

92

Step-by-step explanation:

2x49=98-6=92

Answer:

f(7) = 92

Step-by-step explanation:

To find f(7), substitute x = 7 into the given function.

[tex]\begin{aligned}f(7)&=2(7)^2-6\\&=2(49)-6\\&=98-6\\&=92\end{aligned}[/tex]

The rate law for the overall reaction is:[tex]rate = k[A]^2[B][C][/tex]

The rate law describes the relationship between the rate of a reaction and the concentrations of the reactants. In this case, the overall reaction is the combination of three elementary reactions: (i): 2 a b c (slow), (ii): b d e (fast), and (iii): e c f (fast).

We can determine the rate law for the overall reaction by combining the rate laws from each of the elementary reactions. The rate law for reaction (i) is[tex]rate = k[A]^2[B][C],[/tex] since it is a second order reaction with respect to A and first order with respect to B and C. Reaction (ii) is first order with respect to B, and reaction (iii) is first order with respect to E and C.

Combining the rate laws, we get: [tex]rate = k[A]^2[B][C][/tex]. This is the rate law for the overall reaction.

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The equation x^3+y^3+z^3=k has no general algebraic solution

From the question, we have the following parameters that can be used in our computation:

x^3+y^3+z^3=k

Where

k = 1, 2, ...., 99, 100

There is no general solution to the equation, and it can only be solved by assumptions

Take for instance: k = 1

The solutions for k = 1 are (1, 0, 0), (0, 1, 0) and (0, 0, 1)

There are multiple solutions for other values too

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a)

The class modal interval is 24 ≤ a < 26.

b)

The Mean age of the employee is 23.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Age                 Frequency (f)      Midpoint (x)    fx

18 ≤ a < 20       3                            19                 57

20 ≤ a < 22      2                           21                  42

22 ≤ a < 24      7                           23                  161

24 ≤ a < 26      8                           25                  200

26 ≤ a               0                

Now,

Sum of all the frequencies.

N = 3 + 2 + 7 + 8 = 20

Sum of fx.

= 57 + 42 + 161 + 200

= 460

Now,

Mean = 460/20

Mean = 23

Now,

Class modal interval.

= 24 ≤ a < 26

Because in the class interval, the frequency is the highest.

Thus,

The class modal interval is 24 ≤ a < 26.

The Mean is 23.

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Bode plots depict the frequency response, or the magnitude and phase changes as a function of frequency. This is accomplished using two semi-log scale plots. Using MATLAB, plot Bode diagrams of G1(s) and G2(s) given below.

(a) The first function is:

G1(s) = (1 + s)/(1 + 2s)

MATLAB Code:

%G1(s)

n1 = [1 1]                %coefficients of numerator

d1 = [2 1]               %coefficients of denominator

sys1 = f(n1,d1)      %the transfer function

bode(sys1)           %bode plot

grid on

Command Window:

>> Untitled

n1 = 1 1

d1 = 2 1

sys1 = (1 + s)/(1 + 2s)

Continuous-time transfer function.

(b) The second function is:

G(s) = (1 - s)/(1 - 2s)

MATLAB Code:

%G2(s)

n2 = [-1 1]                    %coefficients of numerator

d2 = [2 1]                   %coefficients of denominator

sys2 = f(n2, d2)       %the transfer function

bode(sys2)               %bode plot

grid on

Command Window:

>> Untitled

n2 = -1 1

d2 = 2 1

sys2 = (1 - s)/(1 - 2s)

Continuous-time transfer function.

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The complete question is:

Using MATLAB, plot Bode diagrams of G1(s) and G2(s) given below:

G1(s) = (1 + s)/(1 + 2s)

G2(s) = (1 - s)/(1 - 2s)

Note that the second transfer function is a non-minimum phase system; meaning it has a zero on the right-half plane. Note how the phase plot is affected.

Answer:

108 m^2

Step-by-step explanation:

9*4*3= 108 m^2

The volume of the solid generated is V=8π and 32/5π

Given functions are  x=y²,  x=2  and  y=0

The equation y=x² is a parabola opening to right and has a vertex at  O(0,0)

and another y=0 is the x-axis and  x=2  is a line parallel to the y-axis

The region bounded by the above will be formed once their intersection points are known.

y²=2⟹y=±√2

OFB is bounded by  O(0,0), F(2,0) and  B(2,√2)

Let  V be the volume of solid generated when the region  OFB  is revolved around line x=2.

[tex]V=\pi \int\limits^2_0 {x^4} \, dx \\[/tex]

V=π[x⁵/5]²₀

V=π[(2)⁵/5]

V=32/5 π.

[tex]V=\pi \int\limits^4_0 {(2^2)_2-(\sqrt{y}^2)_3 } \, dy\\\\ V=\int\limits^4_0 {(4-y)} \, dx[/tex]

V=8π.

when the shaded region revolves the bout x-axis:

[tex]V=\pi \int\limits^b_a {y^2} \, dx \\\\V=\pi \int\limits^2_0 {y^2} \, dx =\pi \int\limits^2_0 {x^4} \, dx =\pi [\frac{1}{5}.x^5]_0^2\\\\ V=\pi [\frac{32}{5}-0][/tex]

V=32/5

when the shaded region revolves the bout y-axis:

[tex]V=\pi \int\limits^c_d [(x^2)_2-(x^2)_1} \, dx \\V=\pi \int\limits^4_0 [(2^2)_2-(\sqrt{y} ^2)_1} \, dy \\V=\pi \int\limits^4_0 {(4-y)} \, dy =\pi [4y-\frac{1}{2}y^2]_0^4[/tex]

V=π[16-8]

V=8π

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In the attachment......

Answer:

Stefan borrowed $8000 on his car loan and $4000 on his student loan.

Step-by-step explanation:

a. Let x be the amount of money Stefan borrowed on his car loan and y be the amount he borrowed on his student loan. According to the problem, Stefan borrowed twice as much on his car loan as on his student loan, so x = 2y.

b. The annual interest on the car loan is $360 more than the interest on the student loan. We can set up an equation as follows:

0.08x - 0.07y = 360

c. Substituting x = 2y from equation (a) into equation (b), we get:

0.08(2y) - 0.07y = 360

0.16y - 0.07y = 360

0.09y = 360

y = 4000

So, Stefan borrowed $4000 on his student loan. Using equation (a), we can find the amount he borrowed on his car loan:

x = 2y = 2(4000) = 8000

Therefore, Stefan borrowed $8000 on his car loan and $4000 on his student loan.

There are 120 different ways to the five sentences be arranged.

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

In an encyclopedia of language, the author presents five sentences that make a reasonable paragraph regardless of their order.

And, The sentences are listed below.

1) Mark had told him about the foxes.

2) John looked out of the window.

3) Could it be a fox?

4) However, nobody had seen one for months.

5) He thought he saw a shape in the bushes.

Since, There are 5 sentence.

Hence, Number of different ways to the five sentences be arranged is,

⇒ 5!

⇒ 5 × 4 × 3 × 2 × 1

⇒ 120

Thus, There are 120 different ways to the five sentences be arranged.

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Answer:

The sine function for the given parameters is y = 4 sin ( pi/2 * x ) + 1. The period is 12, the amplitude is 4, the midline is y = 1 and the y-intercept is (0, 1). The function is not a reflection of its parent function over the x-axis.

Step-by-step explanation:

To solve a sine function with the given features, one must first identify the midline, amplitude, period, and phase shift of the function. The midline is the average of the maximum and minimum values of the graph, while the amplitude is half of the difference between these two values. The period is the length of one cycle in radians, and the phase shift is how much it has been shifted from its parent function over the x-axis.

The equation is satisfied for the gcd(30, 21) and it is: -30 + 21 = 3.

For the gcd(a, b) values in exercise 1.9, the extended Euclidean algorithm (Theorem 1.11) can be used to find integers u and v such that au + bv = gcd(a, b).

We start by using the Euclidean algorithm to calculate the gcd(a, b). We then iteratively calculate the remainder, quotient, and coefficients for each step. We use the equation a = qb + r, where q is the quotient and r is the remainder. We then use the equation r = a - qb to find the value of u and v.

For example, consider gcd(30, 21). We use the Euclidean algorithm to calculate the gcd. We get that gcd(30, 21) = 3. We then use the equation a = qb + r to calculate the remainder, quotient, and coefficients. We get that 30 = 1(21) + 9. We then use the equation r = a - qb to find the values of u and v. So, 9 = 30 - 1(21), which gives us that u = -1 and v = 1. This means that the equation is satisfied for the gcd(30, 21) and it is: -30 + 21 = 3.

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The translation applied is:

(x, y) → (x - 1, y - 5)

It is a translation of 1 unit to the left and 5 units down.

To find the translation from MNOP to M'N'O'P' we just need to take the difference between any two correspondent vertices.

For example, we can see that:

M = (-1, 3)

M' = (-2, -2)

Taking the difference we will geT:

(-2, -2) - (-1, 3) = (-2 + 1, -2 - 3) = (-1, -5)

Sothat the translation is:

(x, y) → (x - 1, y - 5)

The translation one unit to the left and 5 units down.

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Answer:

Denise will cost less.

Step-by-step explanation:

20×9=180.

therefore Jesse will cost $180 for the 9hour job whereas denise:

15×9=135.

135+40=175.

denise will cost $175.

This shows denise is $5 cheaper.

Answer:

Step-by-step explanation:

1. multiply 15x9  and then add 40

2. 20x9

now which one cost less jesse or denisse?

Answer:

36.4

Step-by-step explanation:

1. rule is

[tex]\frac{AB}{BH} =\frac{BC}{BD}; \ or \ \frac{z}{BH} =\frac{BC}{BD};[/tex]

2. according to the rule above

[tex]z=\frac{BH*BC}{BD}; \ = > \ z=\frac{15(20+14)}{14}=\frac{15*34}{14}=36.42857.[/tex]

3. finally, z=36.4

PS. additional details are in the attachment.

Answer:

m∠Y = 60

WY = 7 in

Step-by-step explanation:

It's an isosceles triangle (2 sides are equal), therefore m∠W = m∠Y because the base angles of an isosceles triangle are equal.

Sum of interior angles of a triangle is 180.

let x = m∠W = m∠Y

2x + 60 = 180

2x = 180 - 60 = 120

x = 120/2 = 60

m∠Y = 60

Since all 3 angles = 60, now we know it's an equilateral triangle, therefore WY = 7 in

40 dollars. Aunt sponsored me with 2 dollars per minute, and I walked for 20 minutes, so I have raised 40 dollars for charity.

My aunt is a very generous and kind person. She offered to sponser me for a charity walk, telling me that she would give me 2 dollars per minute I walked. I was really excited to get involved in this walk and help out a good cause. I decided to commit to walking 20 minutes, which meant I would be raising 40 dollars for charity. I was really proud of myself for being able to help out, and I was also really thankful for my aunt's generous sponsership. Over the 20 minutes, I was really motivated to keep going, knowing that I was helping out a charity and also earning money. After the 20 minutes were up, I had raised 40 dollars for charity, thanks to my aunt's sponsership. It was a really rewarding experience and I'm glad I got to take part.

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The radius of the sphere is half of its diameter, so the radius is 30/2 = 15 inches.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.

Substituting the given values, we get:

V = (4/3)π(15)³

V = (4/3)π(3375)

V = 4500π

Therefore, the volume of the sphere is 4500π cubic inches.

Hence, Reese would need 2/5 yards of blue ribbon for every yard of gold ribbon. Thus, the correct option will be (c)

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as:

1 : 3 (for every one boy there are 3 girls)

and if there is 2 pen and 4 copy in your bag the the ratio is

1 : 2 (for every 1 pen there is 2 copy)

We know that

Reese needs 1/4 yards of blue ribbon for every 5/8 yards of gold ribbon.

To know the total blue ribbon she would need for each yard of gold ribbon, we use the following proportion.

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

the x = 5/8 = 4x

x = 2/5

Reese needs 1/4 yards of blue ribbon for every 5/8 yards of gold ribbon.

To know the total blue ribbon she would need for each yard of gold ribbon, we use the following proportion.

Then, we solve for x.

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The question is incomplete, the complete question is:

Standard based practice compare two fractions jasmine cut 3/8 yard of blue ribbon and 1/3 yard of red ribbon to decorate will be:

a) 0

b) 4/7

c) 2/5

d) 3/9

Answer:

Variables:

x = number of lollipops sold

y = number of candy bars sold

Inequality: 2x + 4y ≥ 180

Answer:

$12,000

Step-by-step explanation:

2000([tex](1 + \frac{.05}{2}) ^{2(3)}[/tex]

12,000

all the applications are true.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

Solution: Start by using:

2012 indicates that x=1

So A = 900 (1.05) = 900 × 1,05=945

B = 1100 (1.038) = 1100 × 1038 = 1141.8 \sC = 5000 (0,85) = 5000 x0.85 = 4250 \s4250 1141.8945

So, Ture is the first applicant.

Applying the second: 1.05-1=0.055% Ture

The third application is 1-0.85=0.15=15%. False

Applying the fourth: A 1.05+=0.05=5%

B: \s11038-1=0.038=3.8% \s5% > 3.8% Ture

Hence all the apply are true.

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The journal entry for the business receiving $ 6, 000 for a 10 month service contract is :

Date                     Account and Explanation               Debit           Credit

December 1          Cash                                           $ 6, 000

                            Unearned Service Revenue                             $ 6, 000

                            Being revenue received for services

                             not yet rendered

When a business receives money for a service that it is yet to perform for the client, this is called unearned service revenue. The amount is to be debited to the cash account as it is an asset and assets are debited when they increase.

Unearned service revenue will then be credited by the same amount because it represents a liability that the company owes to the client.

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The tan(t−π) = 74of the given trigonometric function, tan(t−π), is 74

From the question, we are to determine the value of trigonometric function tan(t−π) using the given information.

The given information is tan(t) = 74

We can use the following identity to solve this problem:

tan(t - π) = tan(t) - tan(π) / 1 + tan(t)tan(π)

Since tan(π) = 0

This can be simplified into

tan(t - π) = tan(t) / (1 - 0)

tan(t - π) = tan(t)

Thus,

We just need to find tan(t)

Given that tan(t) = 74.

Hence, tan(t−π) = 74

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Answer:

the awnser is C

Step-by-step explanation: