a pizza that is 12 in diameter is cut into six slices. find the length of each arc intercepted by each slice (length of the crust). find the area of each slice.

Answer:  (a-b+c)²-(b-c+a)²​

=((a-b+c)) - ((b-c+a)) ((a-b+c)) - ((b-c+a))

= (a-b+c-b+c-a) ( a-b+c+b-c+a)

= (-2b + 2c ) (2a)

= (2( -2b/2+2c/2)) (2a)

=(2(-b+c)) (2a)

=2(-b+c) (2a)

The simplification of the expression ( x^1/2)^1/6 × x^(1/3) is given by x to the 5 twelfth power.

Apply the rule of exponents representing raise a power to another power and product of the exponents with same base,

(a^m)^n= a^(mn)

( a^m ) × ( a^n ) = a^(m + n)

Here, x^(1/2) raised to the (1/6)th power.

Using the rule of exponents, we have,

x^((1/2) x (1/6))

Simplification of the product of the exponents, we get ,

= x^(1/12)

Now, multiply this by x^(1/3), so using the rule of product of exponents with same base we get,

x^(1/12) x x^(1/3)

Combining the like terms by adding the exponents, we have,

= x^((1/12) + (1/3))

Simplifying the sum of the exponents,

= x^(5/12)

Therefore, the simplification of the given expression is equal to  x to the 5 twelfth power.

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The above question is incomplete, the complete question is:

Simplify open parentheses x to the 1 half power close parentheses to the 1 sixth power. X to the 1 third power

x to the 1 fourth power

x to the 1 twelfth power

x to the 2 thirds power

x to the 5 twelfth power

The function f(x) has a decreasing end behaviour on the right when its leading coefficient is negative and its degree is greater than or equal to 2.

This means that the terms in the function must be decreasing from left to right and the last term must be negative. To illustrate, an example of a function with a decreasing end behaviour on the right could be

f(x) = -2x2 + 3x + 4.

The leading coefficient is -2, which is negative, and the degree is 2, which is greater than or equal to 2. The terms decrease from left to right, and the last term is negative, which both fulfil the requirements for the function to have a decreasing end behaviour on the right.

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The factors that could be part of the function so that the function has a decreasing end behavior on the right are as follows: - A negative coefficient of the highest degree term.

- An odd degree of the highest degree term and a negative coefficient.
- An even degree of the highest degree term and a negative coefficient.
Explanation:
A function's end behavior refers to what happens to the function's values as x approaches positive or negative infinity. A function's end behavior is said to be decreasing if the values of the function decrease as x approaches infinity, and increasing if the values of the function increase as x approaches infinity.
There are three cases when the function has a decreasing end behavior on the right:

1. If the highest degree term has a negative coefficient, the function will have a decreasing end behavior on the right. For example, the function f(x) = -2x³ - 4x² + 3x + 6 will have a decreasing end behavior on the right.
2. If the highest degree term is odd and has a negative coefficient, the function will have a decreasing end behavior on the right.

For example, the function f(x) = -x⁵ + 2x³ - x will have a decreasing end behavior on the right.
3. If the highest degree term is even and has a negative coefficient, the function will have a decreasing end behavior on the right. For example, the function f(x) = -4x⁶ + 3x⁴ - 2x² + 1 will have a decreasing end behavior on the right.

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Answer:

x > -1

Step-by-step explanation:

8x - 4 > 3x - 9

5x - 4 > -9

5x > -5

x > -1

Answer:

Choice B:  distance from home to library is length of HL

HL = 75      see calculations below

Step-by-step explanation:

use points (0,0) and (2.1, 7.2) to find HL:

HL = √(2.1 - 0)² + (7.2 - 0)² = √4.4 + 51.8 = √56.25 = 7.5

The negation of the statement "There exists an integer n such that 6n2 + 27 is prime" is "For every integer n, 6n2 + 27 is not prime."

To prove the negation, we can use algebraic manipulation to show that 6n2 + 27 is always composite.

Suppose n is any integer. We can factor out 3 from 6n2 + 27 to get 3(2n2 + 9). Since 2n2 + 9 is always odd (2 times any integer is even, and adding 9 makes it odd), we can further factor it as (2n2 + 9) = (2n2 + 6n + 9 - 6n) = [(2n+3)(n+3)] - 6n.

Substituting this expression back into 3(2n2 + 9), we get 3[(2n+3)(n+3) - 6n]. Since (2n+3)(n+3) - 6n is an integer, 3[(2n+3)(n+3) - 6n] is composite for every integer n. Therefore, 6n2 + 27 is not prime for any integer n.

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Answer:

a) 640 ml

b) 40 ml

Step-by-step explanation:

The ratio of lime to lemonade for the fizzy drink is 5 : 3 or as a fraction that would be

[tex]\dfrac{\text{Lime juice}}{\text{Lemonade}}= \dfrac{5}{3}[/tex]

[tex]\text{Therefore the ratio of lemonade to lime }\\\\ = \text{reciprocal of $ \dfrac{5}{3} $} }\\\\= \dfrac{3}{5}[/tex]

Part a)

For  all 400 ml of  lime juice we would need
[tex]\dfrac{3}{5} \times 400 \;ml = 3 \times 80 = 240 \;ml[/tex]  

Total amount of fizzy drink that can be maade
= amount of lime juice + amount of lemonade

= 400 + 240

= 640 ml

This is the answer to Part a)

Part b)

If Gianni has only 280 ml and is using all 400 ml of lime juice then the amount of lemonade used as calculated in part 1) is 240ml

That means the amount of lemonade left over = 280 - 240 = 40 ml

Answer: 41$

Step-by-step explanation:

This is because 5x6=30 (To find how much money is made)

then 11+30=41 (add both amounts)

Answer:

Step-by-step explanation:

The smaller number would be 27. If the first number is 12 greater than the 2nd number and we have to make it equal to 66. Our smaller number would be 27 becuase if we add 12 to 27 that gives us 39. 39+27= 66. Hopefully that makes sense.

The area of the walkaway is 216.66 feet squared.

The circular swimming pool has a diameter of 20 feet. A 3 foot tile walkaway is being installed around the pool.

Therefore, the area of the walkaway can be calculated as follows:

Hence,

area of the walkaway = area of the bigger circle - area of the smaller circle

area of the bigger circle = πr²

area of the bigger circle = 3.14 × 13²

area of the bigger circle  = 530.66

area of the smaller circle = πr²

area of the smaller circle  = 3.14 × 10²

area of the smaller circle = 314

area of the walkaway = 530.66 - 314  = 216.66 ft²

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Answer:

79.92m

Step-by-step explanation:

here you go hope this helps

The probability of a high school baseball player getting at least 6 hits in one game, given a 0.253 batting average, when he gets 8 at-bats, is 0.0197 or approximately 2%.


Given, the high school baseball player's batting average is 0.253, which means in 100 times he hits the ball, he will make 25.3 hits on average. We need to find the probability of getting at least 6 hits in a game when he gets 8 at-bats.

We will calculate the probability using the Binomial Probability formula. Here, the number of trials is 8, and the probability of success is 0.253. We need to find the probability of getting at least 6 hits.

P(X≥6) = 1 - P(X<6)

P(X<6) = ∑P(X=i), i=0 to 5

We can use the Binomial Probability Table to find these probabilities or use the Binomial Probability formula.

P(X<6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

= C(8,0) (0.253)^0 (1 - 0.253)^8 + C(8,1) (0.253)^1 (1 - 0.253)^7 + C(8,2) (0.253)^2 (1 - 0.253)^6 + C(8,3) (0.253)^3 (1 - 0.253)^5 + C(8,4) (0.253)^4 (1 - 0.253)^4 + C(8,5) (0.253)^5 (1 - 0.253)^3

≈ 0.9799

Therefore, P(X≥6) = 1 - 0.9799

= 0.0201 or approximately 2%.

Hence, approximately 0.0197 or 1.97% is the probability of a high school baseball player, who has a batting average of 0.253, obtaining at least 6 hits when given 8 at-bats during a single game.

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The combined area of the four removed triangles is 48 sq.units. Answer: 48

We need to find out the combined area of the four removed triangles, in square units. Given: AB = 12 units.

Let's consider the given square, and let's draw an altitude BD and also draw perpendiculars to BD from the three vertices A, C and D.

Let AB = x cm. Area of square = x² sq.cm.

Now, we are cutting a triangle with base x and height x, which is a right-angled triangle. Hence, area of each removed triangle = (1/2) * x * x = (x²/2) sq.cm.

Now, BD = x/√2. Area of rectangle = AB * BD = 12 * 12/√2 = 72√2 sq.cm.

Now, area of 4 triangles = (x²/2) + (x²/2) + (x²/2) + (x²/2) = 2x² sq.cm.

We know that, Area of rectangle = Area of 4 triangles + Area of square => 72√2 = 2x² + x² => 72√2 = 3x² => x² = 24√2 cm² => x = √(24 * 2) cm = √(48) cm = 4√3 * √2 cm.

Area of 4 triangles = 2x² sq.cm = 2 * 24 cm² = 48 sq.cm.

Hence, the combined area of the four removed triangles is 48 sq.units. Answer: 48.

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This connection makes smells particularly powerful in triggering memories and emotions.

The sense of smell is the most likely to call up mental images of specific sights, sounds, tastes, or smells. This is because the olfactory system, which is responsible for the sense of smell, is closely linked to the brain's limbic system, which is involved in emotions and memory. This connection makes smells particularly powerful in triggering memories and emotions.

The olfactory system, which is responsible for the sense of smell, is unique in its connection to the brain's limbic system, which is involved in processing emotions and memory. When we smell something, the odor molecules enter our nose and are processed by specialized sensory neurons in the olfactory epithelium. These neurons then send signals to the olfactory bulb, which is located in the brain and is the first site of olfactory processing.

From there, the olfactory information is sent to several brain regions, including the amygdala and hippocampus, which are both part of the limbic system. The amygdala is involved in processing emotions and is responsible for generating feelings of pleasure, disgust, or fear in response to smells. The hippocampus, on the other hand, is involved in forming new memories and is responsible for encoding information about the context in which a smell is experienced.

The strong connection between the olfactory system and the limbic system makes smells particularly powerful in triggering memories and emotions. For example, the scent of freshly baked bread may evoke memories of childhood mornings spent in the kitchen with a loved one, while the smell of a certain perfume may remind you of someone special. Additionally, certain smells may elicit strong emotional responses, such as the smell of smoke triggering feelings of panic and fear in someone who has experienced a fire.

Overall, the sense of smell is closely linked to our emotional and memory centers, making it a powerful tool for triggering mental images of specific sights, sounds, tastes, or smells.

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As a result, the final number or expression is g(g(1-3w)) ≈ -12w + 10 (without parenthesis).

When adding extraneous information or perhaps an afterthought to a sentence, parentheses, a pair or punctuation marks, are most frequently utilized. Two curving vertical lines can be seen in parentheses: ( ).

We must first evaluate g(1-3w) and then re-insert that result into g(x) in order to determine g(g(1-3w)).

We must first determine g(1-3w):

Substitute x with 1-3w to get g(x) ≈ 2x + 2 and g(1-3w) ≈ 2(1-3w) + 2.

g(1-3w) ≈ 2 - 6w + 2  (distribute the 2)

g(1-3w) ≈ -6w + 4 (combine similar terms) (combine like terms)

We can again again enter the result of g(1-3w) into g(x):

If you substitute g(1-3w) for x, then g(x) ≈ 2x + 2 g(g(1-3w)) ≈ 2(-6w Plus 4) + 2

g(g(1-3w)) ≈ -12w + 8 + 2 (allocate the 2) (distribute the 2)

g(g(1-3w)) ≈ -12w + 10 (combine comparable terms) (combine like terms)

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Answer:

N*r^n

Step-by-step explanation:

Let the initial number of cases at the start of year 1 be represented by N.

From the given information, we know that the number of cases increases by the same factor each year. Let this factor be represented by r.

Then, at the end of year 1, the number of cases would be N*r, since it has increased by a factor of r.

Similarly, at the end of year 2, the number of cases would be Nrr, or N*r^2.

At the end of year 3, the number of cases would be Nrrr, or Nr^3.

We can use this pattern to write a general expression for the number of cases after n years:

N * r^n

where N is the initial number of cases, r is the common factor by which the number of cases increases each year, and n is the number of years elapsed.

Step-by-step explanation:

If you take the sides you already have, 2, 7, 4, and 3, and add them together, you get 16. Lets take the portion of the perimeter you already have, and lets say this figure is a rectangle.

Divide 16 by 2 to give two sides of the rectangle a portion of the perimeter.
Since the area of a rectangle is width times height, lets create a formula:

8x = 44, 44 being the area, and 8x being the width times the variable of the height.

You get 5.5. for the height of the rectangle.

Add 8+8 to 5.5+5.5
you get 27

Answer:

[tex]\large\boxed{\textsf{Central Angles are made up of 2 Radiuses.}}[/tex]

[tex]\large\underline{\textsf{What are Central Angles?}}[/tex]

[tex]\textsf{Central Angles are angles inside of a circle. They're connected to the center of the circle.}[/tex]

[tex]\textsf{Central Angles have measures determined where the 2 endpoints meet on the circumference.}[/tex]

[tex]\textsf{Central Angles are made of 2 line segments called \underline{Radiuses}. They start at the Center.}[/tex]

[tex]\large\underline{\textsf{What are Radiuses?}}[/tex]

[tex]\textsf{Radiuses are line segments connected from the center of the circle to the circumference.}[/tex]

[tex]\textsf{Hence, Central Angles are made up of 2 Radiuses.}[/tex]

Answer:

To calculate the future value of an investment earning compound interest, we can use the formula:

FV = P(1 + r/n)^(nt)

where:

FV is the future value

P is the principal (starting amount)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

In this case, we have:

P = 6000

r = 0.18 (18% annual interest rate)

n = 12 (compounded monthly)

t = 8

Substituting these values into the formula, we get:

FV = 6000(1 + 0.18/12)^(12*8)

FV = 6000(1.015)^96

FV = 6000(3.045)

FV = 18270

Therefore, the future value of $6000 earning 18% interest, compounded monthly for 8 years, is $18,270.

The simplest form of the given expression is -20k + 126.

To find the simplest form of the expression 8(5k+7)−10(6k−7), follow these steps:
1. Distribute the numbers outside the parentheses to the terms inside the parentheses:
  8 × 5k + 8 × 7 - 10 × 6k + 10 × 7
2. Perform the multiplication:
  40k + 56 - 60k + 70
3. Combine like terms (terms with the same variable and exponent):
  (40k - 60k) + (56 + 70)
4. Simplify the expression by performing the subtraction and addition:
  -20k + 126
The simplest form of the given expression is -20k + 126.

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Answer: 3

Step-by-step explanation:

9/3=3

24/3= 8

30/3=10

Answer: $5

Step-by-step explanation:

If you sell 3 shirts for $15 you would then just divide the 3 shirts into how much all together to get the price for each shirt for $5.

The linear correlation coefficient of 0.3 indicates a moderate positive correlation between the two variables.

This suggests that when one variable increases, the other variable tends to increase too. However, there is not a strong linear relationship between the two variables, meaning that the increase in one variable does not guarantee a predictable change in the other variable.


When interpreting the findings of a correlation study, it is important to note the strength of the relationship between the two variables. A linear correlation coefficient of 0.3 indicates a moderate positive correlation, meaning that the two variables increase together but there is not a strong linear relationship between the two variables.

This means that the increase in one variable does not guarantee a predictable change in the other variable. To put it another way, the strength of the correlation means that when one variable increases, it is likely that the other will increase as well, but it is not guaranteed.

Therefore, caution should be used when making predictions based on the results of a correlation study.

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The number of iterations increases. If there is a significant difference between the two solutions, we may need to investigate the numerical method used or check for errors in our analytical solution.

Step-by-step explanation:

The differential equation is missing in your question. However, I will give a general overview of how to solve a differential equation numerically using Euler's method and how to find an analytical solution.

Numerical Solution using Euler's Method:

Suppose we have a first-order differential equation of the form y' = f(x, y), where y' represents the derivative of y with respect to x. To solve this numerically using Euler's method, we need to start with an initial condition y(x0) = y0, and we want to find the value of y at some other point x1 = x0 + h.

The Euler's method involves approximating the derivative y' by the difference quotient (y1 - y0) / h, where y1 is the value of y at x1. Rearranging this equation, we get:

y1 = y0 + h * f(x0, y0)

Using this equation, we can iteratively compute the value of y at different points by using the previous value of y. For example, to find y2, we can use the equation:

y2 = y1 + h * f(x1, y1)

We continue this process until we reach the desired endpoint.

Analytical Solution:

An analytical solution to a differential equation is an explicit expression for y(x) that satisfies the differential equation for all values of x. To find an analytical solution, we may use techniques such as separation of variables, integrating factors, or other methods specific to the type of differential equation.

For example, if we have a differential equation of the form y' = k * y, where k is a constant, we can use separation of variables to obtain:

dy / y = k * dx

Integrating both sides, we get:

ln|y| = k * x + C

where C is an arbitrary constant of integration. Solving for y, we get:

y = Ce^(kx)

where C = ±e^C is a constant determined by the initial condition.

Comparison of Solutions:

Once we have the numerical and analytical solutions, we can compare them by plotting the graphs of y(x) for each method. If the numerical solution was computed with a small enough step size, it should converge to the analytical solution as the number of iterations increases. If there is a significant difference between the two solutions, we may need to investigate the numerical method used or check for errors in our analytical solution.

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If the probability of a breakdown on assembly line 'a' is 12% and probability of a breakdown on assembly line 'b' is 16%, then the probability that assembly line 'a' or assembly line 'b' break down is equals to the 26%, i.e., 0.26.

We have the probability of a breakdown on assembly line 'a' = 12% = 0.12

The probability of a breakdown on assembly line 'b' = 16% = 0.16

The probability that both assembly lines break down = 2% = 0.02

Let's two events a breakdown on assembly line 'a' and a breakdown on assembly line 'b' be 'X' and 'Y' respectively. That is P(X) = 0.12, P(Y) = 0.16,

P(X and Y) = P(X∩Y) = 0.02

we have to calculate the probability that assembly line 'a' or assembly line 'b' break down, P( X or Y) = P(X∪Y). Using addition rule of probability, the probability that event A or event B occurs is equal to the probability that A occurs plus the probability that B occurs minus the probability that both occur. So, P( X or Y) = P(X) + P(Y) - P( X∩Y)

= 0.12 + 0.16 - 0.02

= 0.26

Hence, required probability is 0.26.

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Answer:

The value of t is 9.

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

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

In this case, we are given two points: (t, 5) and (10, -4), and the slope is given as -9. So we can set up the equation:

-9 = (-4 - 5) / (10 - t)

Simplifying, we get:

-9 = -9 / (10 - t)

Multiplying both sides by (10 - t), we get:

-9(10 - t) = -9

Expanding the left side, we get:

-90 + 9t = -9

Adding 90 to both sides, we get:

9t = 81

Dividing both sides by 9, we get:

t = 9

Therefore, the value of t is 9.

Answer:

Step-by-step explanation:

Setting A=45, we see that it is not true. However, you might find the following revealing:

sin2(45+A)=(sin45cosA+cos45sinA)2=12(1+2cosAsinA)

sin2(45−A)=(sin45cosA−cos45sinA)2=12(1−2cosAsinA)

Now, stare.

For the given following frequency table of values 351, 362, 373, 381, 391, The mode is likely to be the best measure of the center for the data set.

The given frequency table is as follows:

        Value frequency 351, 362, 373, 381, 391.

        To find the most appropriate measure of central tendency for a dataset, we need to analyze the spread of data.

The mean, median, and mode are measures of central tendency in statistics.

We can find the following measures from the given data set:

       Mean: It is calculated by summing up all the values and then dividing the result by the total number of values. This measure of central tendency is appropriate when the data are symmetrical.

      Median: It is the middle value of the data set when arranged in order. It is suitable for skewed data.

      Mode: It is the most common value in the data set. It is appropriate when data is discrete. The data in the frequency table appear to be discrete.

      Because the data are discrete, the most appropriate measure of central tendency is the mode. So, the mode is likely to be the best measure of the center for the given value frequency data set.

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Alden probably used the observational method to collect data for his box plot.

What is a case study?

A case study is an in-depth study on a particular topic collecting information in various ways in a real-world context. Using a range of data sources, a case study permits the analysis of a genuine topic within a specified framework.  Here Alden is conducting his own case study on Calories in Sodas.

In a case study, data is collected through various methods including the observational method, survey method, interview, etc. The observational method is observing the event or stimulus in real time and recording of its data. Therefore, Alden could have employed the observational method by visiting a nearby store and reading and recording the various labels of sods for their data.

And so, Alden collected the data for his box plot using the observational method.

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