let us call a positive integer $n$ 'fortunate' if the sum of its digits is a multiple of 7, and 'superfortunate' if it is fortunate and if none of the numbers $n 1, n 2,\dots, n 12$ is fortunate. find the smallest superfortunate number.

Step 1: limx→0[f(x)+g(x)] .Rule or Limit Law used: Sum Rule for Limits.

Step 2: limx→0f(x)+limx→0g(x) .Rule or Limit Law used: Limit of a Sum Rule.

Step 1: limx→0[f(x)+g(x)]

This first step is using the sum Rule for Limits. This rule states that the limit of the sum of two functions is equal to the sum of the limits of the individual functions. So in this case, the limit of the sum of f(x) and g(x) is equal to the sum of the limits of f(x) and g(x) individually.

Step 2: limx→0f(x)+limx→0g(x)

This second step uses the Limit of a Sum Rule. This rule states that the limit of the sum of two functions is equal to the sum of the individual limits of the functions. So in this case, the limit of the sum of f(x) and g(x) is equal to the sum of the individual limits of f(x) and g(x). This is the same result as in the first step, but using a different rule.

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The formula for the sum of cubes of the first n natural numbers is:

(1^3 + 2^3 + 3^3 + ... + n^3) = (1 + 2 + 3 + ... + n)^2

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The range of the function is {0, 4, 10}. Option A. {0, 4, 10}

The concept used in finding the range of a function is called functional mapping, which maps the elements in the domain of the function to the corresponding elements in the range.

In this problem, we took a set of values in the domain of the function (which was {-2, 0, 3}) and evaluated the function for each of those values to find the corresponding outputs in the range of the function, which was {0, 4, 10}.

To find the range of the function f(x) = 2x + 4 for the domain {-2, 0, 3}, we need to calculate the output of the function for each of the values in the domain:

For x = -2: f(-2) = 2 * -2 + 4 = -4 + 4 = 0

For x = 0: f(0) = 2 * 0 + 4 = 4

For x = 3: f(3) = 2 * 3 + 4 = 10

Therefore, the range of the function is {0, 4, 10}. Option A. {0, 4, 10}

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The range of the function f(x) = 2x+4 when the domain is {-2,0,3} is {0,4,10} .

The range for this function would be {0,4,10}.

Given, Function f(x) = 2x+4

Domain = {-2,0,3}

After putting the value of x= -2 in the function f(x) =2x+4 ,

f(-2) = 2×-2+4 = -4+4= 0

After putting the value of x= 0 in the function f(x) = 2x+4

f(0)= 2×0+4 =0+4=4

After putting the value of x= 3 in the function f(x) = 2x+4

f(3) =2×3+4= 6+4= 10

Here, after putting values in function the domain will become {0,4,10}.

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Check the picture below.

The value of x for each given right angled triangle are:

Please remember that these answers are calculated using calculator.

Remember that a triangle has the sum of angles 180°; then since we have a right angled triangle, then the sum of the non-right angles in the triangle should be equal to 90°.

We use Θ as the note for the unknown non-right angle.

1. 36° + Θ = 90°

Θ = 54°

Under the Sinus Law:

x / sin 54 = 7 / sin 90

x / 0.8 = 7 / 1

x = 5.6

2. 41° + Θ = 90°

Θ = 49°

Under the Sinus Law:

x / sin 49 = 6 / sin 90

x / 0.75 = 6 / 1

x = 4.52

3. 30° + Θ = 90°

Θ = 60°

Under the Sinus Law:

x / sin 90 = 6 / sin 60

x / 1 = 6 / (√3/2)

x = 4√3

4. 37° + Θ = 90°

Θ = 53°

Under the Sinus Law:

5 / sin 53 = x / sin 90

x = 5 / 0.79

x = 6.26

5. 33° + Θ = 90°

Θ = 57°

Under the Sinus Law:

7 / sin 90 = x / sin 57

7 / 1 = x / 0.84

x = 5.87

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Answer: (-3,6)

Step-by-step explanation:

The point is 3 spaces to the left in the second quadrant on the x-axis which is negative

Then it is 6 spaces up on the y-axis which is positive

The value of x is 6

The possible error could your friend have made to get x​ = -2 is Your friend should have added 5x and 4x to get a sum of 9​x, but instead got a sum of 8x. Option C

Algebraic expressions are described as expressions that are composed of variable, terms, coefficients, factors and constants.

These expressions are also made up of mathematical or arithmetic operations. These operations include;

From the information given, we have the equation;

5x + 4x - 68 = 34 - 8x

collect like terms

5x + 4x + 8x = 34 + 68

Add or subtract the like terms

17x = 102

Divide both sides by the coefficient of the variable, we get;

17x/17 = 102/17

x = 6

Hence, the value is 6

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The slope is:

Work/explanation:

To find the slope, I use the slope formula

[tex]\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

where m = slope.

Plug in the data

[tex]\sf{m=\dfrac{-2-4}{14-(-1)}[/tex]

Simplify

[tex]\sf{m=\dfrac{-6}{14+1}}[/tex]

Simplify the denominator

[tex]\sf{m=-\dfrac{6}{15}}[/tex]

Finally, reduce the fraction to its lowest terms.

[tex]\sf{m=-\dfrac{2}{5}}[/tex]

Answer:

Below

Step-by-step explanation:

Interest = p r t    p = principle = 300   r = decimal interest = .14    t = years = 4

 Interest = 300 * .15 * 4 = 180 dollars

The student completed 9 courses of four credits each.

Let x = number of four-credit courses the student completed

If the student completed a total of 15 courses, then the expression for the number of three-credit courses the student completed is:

"15 - x"

If the student earned a total of 54 credits after completing 15 courses, then the equation to show this will be:

4x + 3(15 - x) = 54

Simplify the equation and solve for the value of x.

4x + 45 - 3x = 54

x = 9

Hence, the number of four-credit courses the student completed is 9 course.

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The distance from the base's center at that time is 18 feet.

What is function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

A function is typically represented as y = f. (x).

h(x) = 16 ft x is the distance from the base when

h(x) = 16 h(x) = -IxI + 34

when a raindrop falls from the end of the roof.

16 = -IxI + 34

IxI = 34 – 16 = 18

It might land on the roof's opposite end.

The distance from the base's center at that time is 18 feet.

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The boat is approximately 515 feet away from the lighthouse.

To find the distance from the boat to the lighthouse, we can use trigonometry. The angle of depression from the person to the boat is 28°, and the height of the lighthouse is 200 feet. Let's call the distance from the boat to the lighthouse x. Using the tangent function, we have

Solving for x, we have x = 200 / tan 28°. Approximating this value using a calculator, we have x ≈ 514.7 feet. Rounding to the nearest foot, the boat is approximately 515 feet away from the lighthouse.

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[tex]Let \: the \: two \: points \: be \: \underline{\underline{A( x_{1} ,y_{1})}} \: and \: \underline{\underline{B \: ( x_{2}, y_{2})}}[/tex]

Then ,

[tex]\boxed{d(AB) = \sqrt{ {( x_{2} - x_{1}) }^{2} + {( y_{2} - y_{1}) }^{2} } }\\ [/tex]

where , d(AB) is the distance between the two points A and B.

hope helpful! :)

Answer:

the Distance Between the two points a and b

Step-by-step explanation:

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). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

The inverse of the cosecant function is the secant function so option A is correct.

In mathematics, the inverse of a function "f" is another function "g" such that when "f" is applied to an input "x", the result is "x". And when "g" is applied to the result, the original input "x" is recovered. This relationship can be expressed as: f(g(x)) = x and g(f(x)) = x.

The cosecant function is defined as the reciprocal of the sine function, so csc(x) = 1/sin(x). The inverse of the cosecant function is the secant function, which is defined as the reciprocal of the cosine function, so sec(x) = 1/cos(x).

In other words, when the cosecant function is applied to an angle "x", the result is 1/sin(x), and when the secant function is applied to the result, the original angle "x" is recovered. This relationship can be expressed as: sec(csc(x)) = x and csc(sec(x)) = x.

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The local maximum is x = 13.5 with a value of g(13.5) = (13.5)^2 - 27 * 13.5 = g(13.5) = 125.375.

(a) To determine whether a function is even, odd, or neither, we need to check if g(x) = g(-x) for all x (even), g(x) = -g(-x) for all x (odd), or neither.

g(x) = x^2 - 27x is neither even nor odd because it does not satisfy either of the two conditions for even or odd functions.

(b) To determine the local maximum, we need to find the critical points (points where the derivative is equal to zero or undefined) and then determine if they are local maxima, local minima, or neither.

g'(x) = 2x - 27, which has critical points at x = 13.5 and x = 0. Since g'(x) > 0 for x < 0 and g'(x) < 0 for x > 0, x = 0 is a local minimum. Since g'(x) < 0 for x < 13.5 and g'(x) > 0 for x > 13.5, x = 13.5 is a local maximum.

Therefore, the local maximum is x = 13.5 with a value of g(13.5) = (13.5)^2 - 27 * 13.5 = g(13.5) = 125.375.

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The largest value of x that satisfies the inequality is approximately -1.8639.

To find the largest possible value of x that satisfies the inequality 1/(x + 2)⁶ > 1,000,000, we can start by rearranging the inequality:

1/(x + 2)⁶ > 1,000,000

Taking the reciprocal of both sides:

(x + 2)⁶ < 1/1,000,000

Now, let's take the sixth root of both sides:

x + 2 < (1/1,000,000)[tex]}^{1/6[/tex]

Calculating the right side:

x + 2 < 0.1361

Subtracting 2 from both sides:

x < 0.1361 - 2

x < -1.8639

Therefore, the largest value of x that satisfies the inequality is approximately -1.8639.

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The area of the small indoor greenhouse (herbarium) is equal to 4,250 cm².

The length of tape needed for all the 12 edges is equal to 320 cm.

Mathematically, the total surface area (TSA) of this glass panes (including base) can be calculated by using this mathematical expression:

Total surface area (TSA) = 2[lb + lh + bh]

Where:

Total surface area (TSA) = 2[(30 × 25) + (30 × 25) + (25 × 25)]

Total surface area (TSA) = 2[750 + 750 + 625]

Total surface area (TSA) = 2[2,125]

Total surface area (TSA) = 4,250 cm².

Next, we would determine the length of tape needed for all the 12 edges by using this mathematical expression:

Total length = 4(l + b + h)

Total length = 4(30 + 25 + 25)

Total length = 4(80)

Total length = 320 cm.

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The first three terms of the sequence are 2, 5, and 8.The 41st term of this sequence is 122.

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Answer:

1.725

Step-by-step explanation:

1/4 or .25 multiplied by the total of 6.9

For Deepa to find his yearly balance in a single step, he must multiply his money by 1.01

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period. Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

The following calculation must be done in order to determine what Deepa should multiply his current balance by in order to find his total balance in a year in one step if no money will be added to or removed from the investment. Deepa invests money in an account that pays a simple interest rate of 1% per year.

Current balance = X

Interest = 1% = 1/100 = 0.01

Interest + principal = 1.01

1.01X = Total balance in a year

Deepa must therefore multiply her money by 1.01 in order to determine it in a single step.

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A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Mathematical equations with two expressions on either side of the "equal to" sign are referred to as simple equations.

Let the distance he walks till turning back be 'd',

The total distance while returning back = d + 3.25 miles

Time per unit mile = 8 minutes,

Total distance he walks after already completing 3.25 miles

= 2d+3.25 miles

Therefore, total time for this distance [tex]$=(2 \mathrm{~d}+3.25) * 8=16 \mathrm{~d}+26$[/tex] minutes,

Given that it will take 50 minutes to get to the car after traveling 3.25 miles south,

Let the equation be

[tex]$$\begin{aligned}& 16 d+26=50 \\& 16 d=24 \\& d=\frac{24}{16}=1.5 \text { miles; }\end{aligned}$$[/tex]

Therefore, the required answer exists be 1.5 miles.

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[tex]\huge\begin{array}{ccc}d=\sqrt{442}=11\sqrt2\end{array}[/tex]

The formula:

[tex]A(x_A,\ y_A),\ B(x_B,\ y_B)\\\\|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]

SOLUTION:

We have:

[tex]A(-22,\ 20),\ B(-23,-1)[/tex]

Substitute:

[tex]|AB|=\sqrt{(-23-(-22))^2+(-1-20)^2}=\sqrt{(-1)^2+(-21)^2}\\\\=\sqrt{1+441}=\sqrt{442}=\sqrt{121\cdot2}=\sqrt{121}\cdot\sqrt2=\boxed{11\sqrt2}[/tex]

Answer:

2) 1885 km

3) 795 h 46 m 29 s

Step-by-step explanation:

2)

C = 2πr

C = 2 × 3.14159 × 300 km

C = 1885 km

3)

(1000000 km)/ (1885 km/tour) = 530.16477 tours

1 tour = 1 h 30 m = 1.5 h

530.16477 tours = 530.16477 × 1.5 h = 795.7747155 h = 795 h 46 m 29 s

Answer:

4x-4 that's what I gottt

The five-number summary for the given data include the following:

In Mathematics, a box-and-whisker plot can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided above, the five-number summary for the given data set include the following:

By critically observing the box-and-whisker plots or boxplot (see attachment), we can logically deduce that it has a median of 309 with an interquartile range (IQR) as follows;

Interquartile range (IQR) = Q₃ - Q₁

Interquartile range (IQR) = 335.25 - 310.5

Interquartile range (IQR) = 24.75

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Complete Question:

Determine the five-number summary for the given data. Prices in dollars of smartphones:

311, 309, 312, 314, 399, 312

The percentage of correct answers=70

what i the percentage of the correct answer?

Number of correct answers=35

number of incorrect answers=15

total number of questions=number of correct answers + number of total   incorrect answers

                                            =35+15

                                              =50

Percentage of correct answers = number of correct answers×100/Total  i                                                                                                number of question

                                          =35×100/50

                                        =  3500/50

                                          =70

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After the loop has finished executing, the 'newstr' variable should contain 'abcdxxxxxXXXXX'. The newstr variable is set to an empty string and alphabetic, numerical, and symbol characters are replaced with 'x'.

newstr = "abcdxxxxxXXXXXX

1. Initialize a new string variable called 'newstr' set to an empty string.

2. Loop through each character in the 'checkstr' variable.

3. If the character is an alphabetic character, add it to the 'newstr' string.

4. If the character is not an alphabetic character, replace it with 'x' and add it to the 'newstr' string.

5. After the loop has finished executing, the 'newstr' variable should contain 'abcdxxxxxXXXXX'.

The newstr variable is set to an empty string and alphabetic, numerical, and symbol characters are replaced with 'x'.

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As a result, we obtain the frequency and relative frequency distributions:

Data               Relative Frequency          

A                           0.5

B                           0.19

C                           0.31

The relative frequency is the ratio of the frequency to the total frequency corresponding to each entry.

Here,

Here we have a total sample as: 120

Also, the frequency corresponding to A is: 60

Corresponding to B is: 23

and corresponding to C is: 37

Hence, the Frequency table is as follows:

Data               Frequency

A                          60  

B                           23

C                           37

The relative frequency table is given by:

Data               Relative Frequency          

A                      60/120=0.5

B                       23/120=0.19  

C                       37/120=0.31

Hence, we get the frequency and relative frequency distributions:

Data               Relative Frequency          

A                           0.5

B                           0.19

C                           0.31

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Answer: Quotient is 3.6*10^10/5 and the standard form is 7.2*10^9

Step-by-step explanation:

Answer:

Step-by-step explanation:

3.6×10∧10÷5=0.72×10∧10

standard form=7.2×10∧9