What is the base of the expression 11^12

A.3

B.11

C.12

D.21

Answer:

h = 18 units

Step-by-step explanation:

(9 sqrt 2)^2 + (9 sqrt 2)^2 = h^2

162 + 162 = h^2

Sqrt 324 = h

h = 18 units

Answer:

m=4/-3

Step-by-step explanation:

the equation for slope (m) when given two points is (y2-y1)/(x2-x1)

we are given the points (9,3) and (6,7)

we can label the points:

x1=9

y1=3

x2=6

y2=7

now substitute into the equation

m=(7-3)/(6-9)

subtract

m=4/-3

the slope is 4/-3

hope this helps!

N is congruent to k+1 modulo 3, and since k+1 is not divisible by 3, N is not divisible by 3. Hence, we have shown that if the sum of the digits of a natural number is divisible by 3, then the number itself is not divisible by 3. This can be answered by the concept of Polynomial.

Suppose we have a natural number N = d_k * 10^k + d_{k-1} * 10^{k-1} + … + d_1 * 10 + d_0, where each d_i is a digit between 0 and 9 inclusive, and k is the number of digits in N minus 1. We can recognize N as the evaluation of the polynomial f(x) = d_k * x^k + d_{k-1} * x^{k-1} + ... + d_1 * x + d_0, evaluated at x = 10. Note that f(x) has integer coefficients and degree k, and thus satisfies the conditions of the theorem.

For example, let's consider a natural number N represented as a polynomial f(x) = a_nx^n + a_(n-1)x^(n-1) + … + a_0. To determine if N is divisible by 3, we can check if f(a) ≡ f(b) (mod 3) for integer values of a and b. Similarly, to determine if N is divisible by 9, we can check if f(a) ≡ f(b) (mod 9) for integer values of a and b. Using this theorem, we can deduce divisibility criteria for natural numbers by 3 or 9.

Now, suppose the sum of the digits of N is divisible by 3. Then we can write N = 3m for some integer m. Note that 10 is congruent to 1 modulo 3, so by the theorem, we have f(10) is congruent to f(1) modulo 3. But f(10) = N and f(1) = k+1, since the sum of the coefficients of f(x) is equal to k+1.

Therefore, N is congruent to k+1 modulo 3, and since k+1 is not divisible by 3, N is not divisible by 3. Hence, we have shown that if the sum of the digits of a natural number is divisible by 3, then the number itself is not divisible by 3.

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Answer:

ok so first i want to figure out what 2/5 converted to percent is......

you can find it out on a calculator or on paper by dividing 2 / 5 = 0.4

so this is 40% and if it takes him half a minute to do this, it takes him about 30 seconds to finish 40% of the essay and there is a full 60% still waiting to be done, so lets see,

40% + 40% = 80%

so that is about 1 full minute to write 80% we are still left with 20% so let's see how much time does it take to write 20% of the essay, in 40% it takes 30 seconds and in 80% it takes 60 seconds. So since 20% is half of 40% then we must divide the time in half so 30 / 2 = 15

So if we add all these numbers up it equals 1:15 minutes to write an essay

I hope this helps and please mark brainliest if i got it right!

The time taken by Ben to write a full page will be 1:15 minutes.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

you can find it out on a calculator or on paper by dividing 2 / 5 = 0.4

So this is 40% and if it takes him half a minute to do this, it takes him about 30 seconds to finish 40% of the essay and there is a full 60% still waiting to be done, so let's see,

40% + 40% = 80%

so that is about 1 full minute to write 80% we are still left with 20% so let's see how much time it takes to write 20% of the essay, in 40% it takes 30 seconds and in 80% it takes 60 seconds. So since 20% is half of 40% then we must divide the time in half so 30 / 2 = 15

Therefore, the time takes Ben to write a full page will be 1:15 minutes.

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The average number of customers in the store is 150.

To find the average number of customers in the store, we can use Little's Law, which states that the average number of customers in a system is equal to the average arrival rate multiplied by the average time they spend in the system.

Given that the average arrival rate is 100 customers per hour and the average time spent in the store is 1.5 hours, we can calculate:

Average number of customers = Average arrival rate * Average time spent

= 100 customers per hour * 1.5 hours

= 150 customers

Therefore, the average number of customers in the store is 150.

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Answer:17

Step-by-step explanation:

Answer:

he actual densities of pure, dry, geologic materials vary from 880 kg/m3 for ice (and almost 0 kg/m3 for air) to over 8000 kg/m3 for some rare minerals. Rocks are generally between 1600 kg/m3 (sediments) and 3500 kg/m3 (gabbro).

Step-by-step explanation:

Yes, we can conclude that A = B. This is because the given conditions state that the union and intersection of A and C are equal to the union and intersection of B and C, respectively.

This implies that the elements in A and B are the same, as they share the same elements with C. Therefore, A and B are equivalent, and we can conclude that A = B. The given conditions also ensure that all the elements in A and B are contained within C, so they do not affect the equality of A and B. Overall, the given conditions provide enough information to conclude that A = B. Based on the given information, we cannot definitively conclude that A = B. Although the union and intersection of A and B with C are equal, this does not guarantee that A and B are identical sets. To prove A = B, we need to show that every element in A is also in B, and vice versa. Without additional information about the specific elements in sets A, B, and C, we cannot reach a conclusion about the equality of A and B. It's possible that they are equal, but the provided conditions are not sufficient to prove it.

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Answer:

24

Step-by-step explanation:

put one fruit cup and banana in each bag

the teacher can make the greatest number of snack bags, which is 12, while ensuring that all the bags contain an equal number of fruit cups and bananas.

To find the greatest number of snack bags that the teacher can make while ensuring that all the bags are exactly the same, you need to determine the common factors of the quantities of fruit cups (36) and bananas (24). The greatest number of bags will be determined by the greatest common factor (GCF) of these two numbers.

Let's find the GCF of 36 and 24:

1. List the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

2. List the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Now, identify the common factors from both lists:

Common factors: 1, 2, 3, 4, 6, 12

The greatest common factor among these common factors is 12.

So, the teacher can make the greatest number of snack bags, which is 12, while ensuring that all the bags contain an equal number of fruit cups and bananas.

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Answer:

\( \sqrt{12a \: + \: 12b \: - \: 2ab \: + \: 2b {}^{2} } \)

Step-by-step explanation:

(a²-b²) / (a+b) = 12

a² - b² = 12(a+b)

(a-b)² + 2ab - 2b² = 12a + 12b

(a-b)² = 12a + 12b - 2ab + 2b²

a - b =

\( \sqrt{12a \: + 12b \: - 2ab \: + \: 2b {}^{2} } \)

The circumference of the circle is given by C = πd, where d is the diameter of the circle. For the beverage area, d = 50 feet, so the circumference is C = π(50) = 157.08 feet (rounded to two decimal places). Each booth needs 10.5 feet (arc length) between its center and the center of the booth next to it. To determine how many booths can fit, we need to subtract the arc length between booths from the circumference of the circle and then divide by the arc length of each booth:

Number of booths = (C - nL) / L

where n is the number of spaces between the booths and L is the arc length of each booth. We can rearrange this equation to solve for n:

n = (C - L x Number of booths) / L

Substituting the values, we get:

n = (157.08 - 10.5x) / 10.5

where x is the number of booths. To find the maximum value of x, we need to round down to the nearest whole number:

x = floor(n) = floor((157.08 - 10.5x) / 10.5) = 14

Therefore, 14 booths can fit in the beverage area.

The circumference of the circle is C = πd = π(100) = 314.16 feet (rounded to two decimal places). The angle between each pole is 15 degrees, so the angle between the centers of each booth is also 15 degrees. To find the arc length between the centers of each booth, we need to multiply the circumference of the circle by the ratio of the angle between the centers of each booth to the angle between the poles:

Arc length between centers of each booth = C x (15/360) = 13.09 feet (rounded to two decimal places)

Therefore, there will be approximately 13.1 feet between the centers of each booth.

The circumference of the circle is C = πd = π(150) = 471.24 feet (rounded to two decimal places). Each food booth needs 30 feet between its center and the center of the booth next to it. To determine how many booths can fit, we can use the same equation as in part 1:

Number of booths = (C - nL) / L

where L = 30 feet. Substituting the values, we get:

x = floor((471.24 - 30x) / 30) = 15

Therefore, there will be approximately 15 food booths.

I hope this helps!

The form of "research-data" which is likely to be used by quantitative research study than by a qualitative research study is (c) Economic data.

The Quantitative research depends on numerical data and statistical analysis to answer research questions, while

The Qualitative research depends on non-numerical data such as words, images, or observations to gain an understanding of the context of the phenomenon being studied.

The Economic data, such as data on income, expenditures, or market trends, is typically collected and analyzed using statistical methods, making it more suitable for quantitative research.

Therefore, the correct option is (c) economic data.

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The given question is incomplete, the complete question is

Which of the following forms of research or data would be more likely used by a quantitative research study than by a qualitative research study?

(a) interview data

(b) personal narrative data

(c) economic data

(d) archival data.

To find the critical numbers A and B of the function f(x) = -2x^3 + 39x^2 - 216x + 2, we need to determine the values of x where the derivative of the function is equal to zero or undefined.

First, let's find the derivative of f(x):

f'(x) = -6x^2 + 78x - 216

To find the critical numbers, we set f'(x) equal to zero and solve for x:

-6x^2 + 78x - 216 = 0

We can factor out -6 from the equation:

-6(x^2 - 13x + 36) = 0

Now, we solve the quadratic equation x^2 - 13x + 36 = 0:(x - 4)(x - 9) = 0

So, the solutions are x = 4 and x = 9.

Therefore, the critical numbers of the function f(x) = -2x^3 + 39x^2 - 216x + 2 are A = 4 and B = 9.

To find the second derivative of f(x), we differentiate f'(x):

f''(x) = -12x + 78

Now, we can find f''(A) and f''(B):

f''(A) = -12(A) + 78

= -12(4) + 78

= 30

f''(B) = -12(B) + 78

= -12(9) + 78

= -6

f''(A) = 30 and f''(B) = -6.

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The complete question is:

Consider the function f (x) = -2x^3 +39x^2- 216x + 2. This function has two critical numbers A < B:

A=?

B = ?

f " (A) = ?

f " (B) = ?

Answer: Greater than 10.

The output of the following code fragment

int x=0;

while( x < 5)

cout << x << endl;

x ++;

cout << x << endl; will be  0, 1, 2, 3, 4, 5.

The code initializes the variable x to 0, and then enters a while loop that will execute as long as x is less than 5. During each iteration of the loop, the value of x is output to the console using the cout statement, followed by a new line character.

After the cout statement, x is incremented by 1 using the x++ statement. This process is repeated until x is equal to 5, at which point the loop terminates. Finally, the value of x is output to the console using the cout statement, followed by a new line character, giving the output of 5.

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In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

Integral is a term derived form the word integration. Integration in calculus is the opposite of differentiation

Integration is used to get the whole by combining combine slices or smaller portions.

Finding areas, volumes, central points, and many other important things may be done with integration. However, it is simplest to begin by calculating the distance between a function and the x-axis.

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Answer:

ready-steady paint

Step-by-step explanation:

if he needs 12 tins, and purchased from paint -O  mine, he would spend (12/3) X 7.50 = 4 x 7.50 = £30

from ready steady, he can buy 4 for £11. he needs 12.

so he will spend (12/4) X 11 = 3 X 11 = £33. but he can get 15% off. 15% off is the same as multiplying by 0.85.

33 X 0.85 = £28.05.

so he his better purchasing from ready steady paint

Answer:

To get the answer of this, we need to multiply 2/3 by 90 centimeters to get 2/3s of the total length. Sometimes it is easier to just think, "what is a third of 90?" and then double it, but the foolproof way to get the answer is to multiply the fraction by 90/1.

2/3 * 90/1 = 180/3. Divide out and the answer is:

60 centimeters

Step-by-step explanation:

Answer:

P = 50.39 cm

Step-by-step explanation:

It is given that,

The side of a square, a = 5∛16 cm

We need to find the perimeter of the square.

Perimeter = sum of all sides.

All sides of a square are equal. Its perimeter is given by :

P = 4a

\(P=4\times 5\sqrt[3]{16} \\\\P=50.39\ cm\)

So, the exact perimeter of the square is 50.39 cm.

The new interest rate for his mortgage would be  3.75%.

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also gets additional income in terms of the recipient, known as interest, taking into account the time value of money.

Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of 1% interest reduction.

A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)

New interest rate=4.5%-0.75%=3.75%

Thus, The new interest rate for his mortgage would be  3.75%.

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The two salesperson will both charge the same amount after 5 hours

Setting up the equation for the problem thus:

Salesperson A :

50 + 5h ___(1)

Salesperson B :

15h ____(2)

Equating (1) and (2)

50 + 5h = 15h

collect like terms

50 = 15h - 5h

50 = 10h

divide both sides by 10 to isolate h

h = 5

Hence, they will both charge the same amount after 5 hours .

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The equation of the tangent line to the curve y = 2x cos(n) at the point (π, -π) is y = -2x + (2π + 2nπ sin(n) - π), where m = -2 - 2nπ sin(n) and b = 2π + 2nπ sin(n) - π.

To find the equation of the tangent line, we need to find the derivative of y with respect to x, and then evaluate it at the given point (π, -π) to find the slope of the tangent line. Then we can use the point-slope form of a line to find the equation of the tangent line in the form y = mx + b.

Taking the derivative of y with respect to x, we get:

dy/dx = 2cos(n) - 2n x sin(n)

Evaluating this derivative at x = π, we get:

dy/dx |x=π = 2cos(n) - 2n π sin(n)

Substituting x = π and y = -π into the original equation, we get:

-π = 2πcos(n)

cos(n) = -1/2

Since we want the equation of the tangent line at the point (π, -π), we can substitute x = π and y = -π into the point-slope form of a line:

y - (-π) = m(x - π)

Simplifying, we get:

y = m(x - π) - π

Substituting cos(n) = -1/2, we have:

dy/dx |x=π = 2cos(n) - 2n π sin(n) = -2 - 2nπ sin(n)

Setting this equal to the slope of the tangent line, we have:

m = -2 - 2nπ sin(n)

Substituting this value of m into the equation of the tangent line, we have:

y = (-2 - 2nπ sin(n))(x - π) - π

Therefore, the equation of the tangent line is:

y = -2x + (2π + 2nπ sin(n) - π)

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Complete question:

Find the equation of the tangent line to the curve y = 2x cos(n) at the point (π, -π). The equation of this tangent line can be written in the form y = mx + b, where m and b are constants. Find the values of m and b.

The value of x is determined as the % increase in Rake'c price.

For the given question;

Increased price of knife = 550,

Percentage increase = 10%.

Original price = y

10% of y = 550

y = 550×100/10

y = 500 (original price of knife)

Increased price of knife is 550 - 500 = 50.

Original price of rake = 600

increment  = x%

New price = 600 + x% of 600

New price = 600 + 6x

The original price of knife and rake; 500 + 600 = 1100.

Percentage increase of both tools = 170/11%.

= 170/11 × (1100/ 100) ........equation 1

Total increment on both tool = 50 + 6x .......equation 2

Equating 1 and 2.

50 + 6x = 170/11 × (1100/ 100)

On solving;

6x = 120

x = 20

Therefore, the value of (x = 20).

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The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.

The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.

To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.

The modified code for binary search in descending order would look like this:

public static int binarysearch2(int[] list, int key) {

   int low = 0;

   int high = list.length - 1;

   while (high >= low) {

       int mid = (low + high) / 2;

       if (key > list[mid])

           high = mid - 1;

       else if (key < list[mid])

           low = mid + 1;

       else

           return mid;

   }

   return -1; // Not found

}

By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.

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Answer:

$4.18 dollars per pound

Step-by-step explanation:

We can find the price in dollars per pound by dividing the cost by the number of pounds:

14.63/3.5 = 4.18

This means the price in dollars per pound is $4.18

Answer:

44.592

Step-by-step explanation:

Answer:

44.592592...

It's me, Supreme :D

Have a wonderful day! :-)

Answer:

ΔCFG is an isosceles triangle.

Step-by-step explanation:

From the picture attached,

From ΔABF and ΔEDG,

Conditions for ΔABF and ΔEDG by SSS property of congruence,

1). AB ≅ DE [Given]

2). (BC + CF) = (DF + CG)

CF = CG [Given → BC = DF]

3). FA ≅ EG

(AG + GF) ≅ (EF + GF)

AG ≅ EF

Since, two sides of ΔCFG are equal in measure

ΔCFG is an isosceles triangle.

This can be determined by property of congruency. Hence, \(\bold{2^{nd}}\)option i.e. ΔCFG is an isosceles triangle is most appropriate.

Given :

From figure ΔABF and ΔEDG  are congruence by SSS property.

Proof:

From ΔABF and ΔEDG in figure,

Conditions for ΔABF and ΔEDG by SSS property of congruence,

1). AB ≅ DE [Given]

   (BC + CF) = (DC + CG)

2). BF≅DG

     CF = CG [Given → BC = CD]

3). FA ≅ EG

     (AG + GF) ≅ (EF + GF)

    AG ≅ EF

Therefore, two sides of ΔCFG are equal in measure.

Thus,ΔCFG is an isosceles triangle.

Hence, \(\bold{2^{nd}}\) option i.e. ΔCFG is an isosceles triangle is most appropriate.

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Answer:

-10/3 < x < 2

so the answer is  x<-10/3 or x>2

Step-by-step explanation:

:)