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The sum of n natural numbers is three digits number and all digits are the same. The same digits is 6 and the sum is 666.

A three-digit number with the same digits is the sum of n natural numbers.

Let's say the sum of n natural numbers is bbb.

Then,

n( n + 1) / 2 = bbb

n( n + 1) / 2 = b( 111 )

n( n + 1) / 2 = b ( 3 × 37 )

n( n + 1) = 6b × 37

Now, the left-hand side of the equation is the product of two consecutive natural numbers.

Therefore, the right-hand side of the equation is also the product of two consecutive natural numbers.

Hence, 6b = 36

b = 36/ 6

b = 6 and n = 36

As a result, 36 numbers have been added together, and their total is 666.

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Answer:

2+0.12x=time on scooter bill

x is minutes and x is 157 minutes on the scooter

Step-by-step explanation:

The sample proportion, p-hat, of engineers who have master's degrees is   68.5% out of 200 engineers.

p-hat proportion:

In this proportion,  "p" denotes the probability of a certain event occurring or a certain parameter being true for a certain population, but when a population is large, it may be impractical or impossible to measure it directly. So, we have used the proportion for that cases.

The general form for calculating p-hat proportion is,

[tex]\hat{p}=\frac{x}{y}[/tex]

where

x  is the number of successes in the sample, and

y is the size of the sample.

Given,

In a random sample of 200 engineers, 137 have a master's degree.

Here we need to find the the sample proportion, p-hat, of engineers who have master's degrees

According to the question,

x = 137 (number of successes in the sample)

and y = 200 (size of the sample)

Now apply the value on the formula then we get,

[tex]\hat{p}=\frac{137}{200}[/tex]

So, the value of p-hat is

[tex]\hat{p}=0.685[/tex]

The results are usually reported as a percentage, which in this case would be

=> 0.685 x 100 = 68.5%

Therefore, the sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.

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Answer:The final balance is $28,043.4.

The total compound interest is $10,043.4.

Step-by-step explanation:

https://www.omnicalculator.com/finance/compound-interest?c=USD&v=var1:1,subject:1138535033,var2:1,subject2:1,FinalBal:20000,FinalBal_adj:20000,apy:1.95!perc,infl:0,PeriodicDep:50,q:1000!!l,type:1,DepositBal:0,PrincipalBal:0,g:0!perc,first_day:19255,select1:1,TableFreq:111,InitialDep:18000,r:3!perc,t:180!yrsmos,m:1,ct1:1,ct2:0,compound_frequency:21,ct3:3,represent:13

Answer:

Leon has $15 and Laci has $61

Step-by-step explanation:

Let x = the amount Leon has.  So 4 times that plus $1 would be 4x+1.  Our equation is:

x + (4x+1) = 76

Combine like terms

5x + 1 = 76

Subtract 1 from both sides

5x = 75

Divide both sides by 5

x = 15.  This is Leon.  Laci is 4(15) +1, or 61.

The algebraic expression of the mathematical statement given as "The difference of a number squared and 6" is  x^2 - 6

Expressions are mathematical statements that are represented by variables, coefficients and operators

The mathematical statement is given as

The difference of a number squared and 6

Represent the number with x

So, the mathematical statement becomes

The difference of a number squared and 6 ⇒ The difference of x squared and 6

x squared implies x^2

So, the mathematical statement becomes

The difference of a number squared and 6 ⇒ The difference of x^2 and 6

difference means minus (-)

So, the mathematical statement becomes

The difference of a number squared and 6 ⇒  x^2 - 6

Hence, the algebraic expression of the mathematical statement given as "The difference of a number squared and 6" is  x^2 - 6

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Using proportions, it is found that Belinda's map uses a scale of 0.025 inches : 100 feet = 0.00025 inches : 1 feet.

A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

Scale problems are solved using proportions. Elvis’s map uses a 1/4 scale of 1 inch to 100 feet, hence:

Belinda's map has the same area, hence they use the same scale, hence she uses a scale of 0.025 inches : 100 feet = 0.00025 inches : 1 feet.

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The equation that makes it easy to find the number of pounds of jalapenos is j = (12.65​ - 2.99t)/1.33.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Tomatoes cost $2.99​ per pound and jalapenos cost $1.33​ per pound. Anna spent $12.65​ buying tomatoes and jalapenos.

2.99t + 1.33j = 12.65​

Make the subject as j and solve the equation for j:

1.33j = 12.65​ - 2.99t

j = (12.65​ - 2.99t)/1.33

Thus, the equation that makes it easy to find the number of pounds of jalapenos is j = (12.65​ - 2.99t)/1.33.

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Your answer is x=1/3

Good luck with your test!~ ^^

Answer:

Hello,

Step-by-step explanation:

1) Conjecture: The sum of any two odd numbers is even
(2a+1)+(2b+1)=2a+2b+2=2(a+b+1) is even

2) Conjecture: The product of any two odd numbers is ODD
(2a+1)*(2b+1)=4ab+2b+2a+1=2(2ab+a+b)+1 is ODD
1*1=1

1*5=5

7*9=63

9*11=99

13*21=273

3) Conjecture: The product of a number (x-1) and the number (x+1) is always equal to the difference of the square of x between 1

(x-1)(x+1)=x²-x+x-1=x²-1

Answer: 450 is divisible by 2, 3, 5, 6, and 9

Step-by-step explanation: 450 is divisible by 2 because the last digit (0) is an even number.

Divisible by three because the sum of all the digits in 450 is a multiple of three: 4+5+0 = 9 which is 3*3.

Divisible by 5 because it ends with a 0 (could also end in 5)

Divisible by 6 because it is divisible by both 2 and 3 (2*3=6)

Divisible by 9 because 45 is divisible by 9.

Answer:

82,337

Step-by-step explanation:

   76,749

      5565

+         23
   82,337

Hope it helps!!!

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The value of both the interior angles of the triangle is calculated as 70° and 35°.

If a triangle side is formed, the exterior angle made is equal to the sum of a 2 interior opposite angles.

Now, as per the given question;

The exterior angle of a triangle is 105°.

Let one of the interior angle is 'x'.

Then, the other interior angle is 35 degree less; x - 35°.

By the exterior angle property.

Sum of interior angles = exterior angle

x + x - 35° = 105°

2x = 105° + 35°

2x = 140°

x = 70°

The other interior angle is; x - 35°

= 70° - 35°

= 35°

Therefore, the two interior angles of the triangles are estimated as 70° and 35°.

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The specified value of n for trapezoidal rule, the midpoint rule, and simpson's rule is 10.36 , 10.72 and 10.52.

Trapezoidal Rule: In Calculus, “Trapezoidal Rule” is one of the important integration rules. The name trapezoidal is because when the area under the curve is evaluated, then the total area is divided into small trapezoids instead of rectangles. This rule is used for approximating the definite integrals where it uses the linear approximations of the functions.

The trapezoidal rule is mostly used in the numerical analysis process. To evaluate the definite integrals, we can also use Riemann Sums, where we use small rectangles to evaluate the area under the curve.

Midpoint rule : In mathematics, the midpoint rule, also known as the midpoint Riemann sum or midpoint method, is a method of estimating the integral of a function or the area under a curve by dividing the area into rectangles of equal width. The midpoint rule formula is. The midpoint method formula works by summing the areas of each of the rectangles to produce an estimate for the area under a curve.

Simpson's Rule: Simpson's rule is used to find the value of a definite integral (that is of the form b∫ₐ f(x) dx) by approximating the area under the graph of the function f(x). While using the Riemann sum, we calculate the area under a curve (a definite integral) by dividing the area under the curve into rectangles whereas while using Simpson's rule, we evaluate the area under a curve is by dividing the total area into parabolas. Simpson's rule is also known as Simpson's 1/3 rule (which is pronounced as Simpson's one-third rule).

Now,

a=1,b=4,Δx =(b-a)/n =3/6 =1/2

f(x)=4√(ln(x))

trapezoidal rule:

∫4√(ln(x)) dx =(Δx /2)[f(1)+2*[f(1.5)+f(2)+f(2.5)+f(3)+f(3.5)]+f(4)]

∫4√(ln(x)) dx =((1/2) /2)[4√(ln(1))  +2*[4√(ln(1.5)) +4√(ln(2)) +4√(ln(2.5)) +4√(ln(3)) +4√(ln(3.5))] +4√(ln(4))]

∫4√(ln(x)) dx =10.365336

midpoint rule :

∫4√(ln(x)) dx =(Δx)[f(1.25)+f(1.75)+f(2.25)+f(2.75)+f(3.25)+f(3.75)]]

∫4√(ln(x)) dx =(1/2)[4√(ln(1.25))  +4√(ln(1.75)) +4√(ln(2.25)) +4√(ln(2.75)) +4√(ln(3.25)) +4√(ln(3.75)) ]

∫4√(ln(x)) dx =10.724182

simpsons rule:

∫4√(ln(x)) dx =(Δx /3)[f(1)+4*f(1.5)+ 2*f(2)+ 4*f(2.5)+  2*f(3)+  4*f(3.5)]+f(4)]

∫4√(ln(x)) dx =((1/2) /3)[4√(ln(1))  +4*4√(ln(1.5)) +  2*4√(ln(2))  +4*4√(ln(2.5))  +2*4√(ln(3)) + 4*4√(ln(3.5)) +4√(ln(4))]

∫4√(ln(x)) dx =10.527905

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Answer:

AC = 18

Step-by-step explanation:

AC = AB + BC = 7 + 11 = 18

Answer:

Pretty sure it’s x>12

Step-by-step explanation:

Answer x > 12

thats the whole thing

Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by Continuous random variables.

What is Continuous Random Variable ?

A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.

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Answer:

13 1/3

____

         [tex]1\:2/3 = 5/3\\1/8 = 1/8\\\\5/3 \div 1/8\\=\frac{5\cdot8}{3\cdot1}\\= \frac{40}{3}\\= 13\:1/3[/tex]

When working with mixed numbers that are being divided, you know where to start. Start by converting mixed numbers to fractions, then multiply the fractions together to divide them. Simplify your improper fraction by counting how many times it surpasses the denominator.

Answer:

16 1/4

Step-by-step explanation:

4*10=40, add one more 1/4 and you get 41. So simplified, 41/4 = 10 1/4

Add the 6 and you get 16 1/4

[tex]-7,5 + 4,2 = -3.3[/tex]

[tex]-0,9 \cdot 2,7 = -2.43[/tex]

Blank bank as well as Thank bank earn equal interest.

In this question, Blank Bank offers an annual rate of r% for y years.

and Thank Bank offers a rate of ry% for 1 year.

Assuming $x is deposited into a savings account, we need to determine which bank earn more interest.

We know that, Interest = principal × rate × time

Now we convert the rates to decimals and to do that we divide by 100.

So, the annual rate of the Blank bank = 0.0r

And the annual rate of the Thank Bank = 0.0ry

Using above formula of interest,

For Blank bank, the interest would be,

I_B = x × 0.0r × y

I_B = xy(0.0r)

I_B = 0.0rxy                         ....................(1)

here, we find the interest for 'y' years

And for the Thank Bank, the interest would be,

I_T = x × 0.0ry × 1

I_T = I_B = 0.0rxy              ....................(2)

From (1) and (2),

I_B = I_T

Both the banks earn equal interest.

Therefore, Blank bank as well as Thank bank earn equal interest.

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Answer:

Step-by-step explanation:

Yes, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

Here,

The differential equation (1-xy)y' = y^2

And,  y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2.

What is Differential equation?

A differential equation is a mathematical equation that relates some function with its derivatives.

Now,

To show y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2, we have to find the solution of differential equation.

The differential equation is;

[tex](1-xy)y'=y^2\\\\\\\\[/tex]

[tex](1-xy) \frac{dy}{dx} = y^2[/tex]

[tex]\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }[/tex]

It is form of  [tex]\frac{dx}{dy} + Px = Qy[/tex],

Where, P is the function of y and Q is the function of x.

Hence, Integrating factor = [tex]e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y[/tex]

The solution is;

[tex]x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c[/tex]

[tex]xy = lny + c[/tex]

Take c = 0, we get;

[tex]xy = lny\\\\y = e^{xy}[/tex]

Hence, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

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The dimensions of her scale drawing is 9 centimeters high and 101.25 centimeters long.

As we are informed from the question -

Measurement in real = measurement on scale

The 4 feet height measures 3 centimeters on scale

So, height of 12 feet on scale will be = (3/4) × 12

Performing multiplication and division to find the height of scale drawing

Height 12 feet on scale = 9 centimeters

The length of 135 feet will measure on scale = (3/4) × 135

Performing multiplication and division to find the height of scale drawing

Length 135 feet on scale = 101.25 centimeters

So, the dimensions of scale drawing will be 9 centimeters high and 101.25 centimeters long.

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Answer:  Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm. You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm². Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm.

Step-by-step explanation:

Answer:

y = -2x - 3

Step-by-step explanation:

The slopes of two perpendicular lines are negative reciprocals of each other. So slope of s is -2

using m = -2, x = 2, y = -7

y = mx + b

-7 = (-2)(2) + b

-7 = -4 + b

b = -3

y = -2x - 3