circle $c$ has radius 6 cm. how many square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle $c$?

Answer:

I and III

Step-by-step explanation:

substitute 2 for y in each equation.

-9 + 27 = 18

-18 + 27 = 9

5(27) = 135

2(27) = 54

The set of vectors that form an

orthonormal basis

for R² is B. {[1,0]ᵀ,[0,1]ᵀ}.

To determine which of the sets of vectors form an orthonormal basis for R², we need to check if the vectors are orthogonal and have a length of 1. For set A, we can calculate the dot product of the two vectors and see that it is not equal to zero, so they are not orthogonal. For set C, the dot product of the two vectors is also not equal to zero, so they are not orthogonal. For set D, we can calculate the length of the vectors and see that they are not equal to 1, so they do not have a length of 1. Therefore, the only set of vectors that form an orthonormal basis for R² is set B, which consists of the standard basis

vectors

{[1,0]ᵀ,[0,1]ᵀ}.

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The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.

The given function is f(x) = e^x near x = 0.

To find the best linear approximation, L(x), we use the formula:

L(x) = f(a) + f'(a)(x-a),

where a is the point near which we are approximating.

Let a = 0, so that a is near the point x = 0.

f(a) = f(0) = e^0 = 1

f'(x) = d/dx (e^x) = e^x;

so f'(a) = f'(0) = e^0 = 1

Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1

Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.

For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.

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Answer: x = 1

Step-by-step explanation:

( π=3,14 , r= d/2= 7.6/2= 3,8m )

C= 2πr
C= 2·π·3.8
C≈23.87m

Answer:

Look Below

Step-by-step explanation:

The formula for a circle is πr².

Therefore, we can divide the area of the circle by 3.14, and then square root it. 490.63/3.14=156.25... If you square root that, you get 12.5. Same thing with the other circle. 219.45/3.14=69.888... If you square root that, you get 8.36. Now that we have the radius, we can multiply that by two to find the diameter. And we're done.

Feel free to tell me if I did anything wrong! :)

Numeric data can be used to present facts, show relationships between variables, and support an argument.

Numeric data is a powerful tool that can be used to present facts, demonstrate relationships between variables, and support an argument. It is often used to provide evidence for a particular point of view, and it can be used to persuade an audience or inform them about a particular topic. Numeric data can be presented in various forms such as graphs, tables, and charts, and when used effectively, it can be a very effective tool for conveying information. It is important to understand how to interpret numeric data correctly, as it can be used to draw false conclusions if the data is misinterpreted.

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It is important to consider the scale of measurement and the specific characteristics of the variables when selecting an appropriate statistical test.The tests can be classified as follows:

1. A researcher measures the proportion of schizophrenic patients born in each season.

This test is nonparametric. The scale of measurement is categorical, as the seasons (spring, summer, fall, winter) represent distinct categories rather than continuous numerical values. Therefore, parametric assumptions, such as normality and equal variances, do not apply to this measurement.

2. A researcher measures the average age that schizophrenia is diagnosed among male and female patients.

This test is parametric. The scale of measurement is continuous and numerical (age in years). Parametric tests, such as t-tests or ANOVA, can be applied when working with continuous data, assuming the data meet the required assumptions (e.g., normality, independence, and equal variances).

3. A researcher tests whether frequency of Internet use and social interaction are independent.

This test can be both parametric or nonparametric, depending on the measurement scale and the specific statistical test used. If the variables are measured on a nominal or ordinal scale, nonparametric tests, such as the chi-square test, would be appropriate. If the variables are measured on a continuous scale, parametric tests, such as logistic regression, could be employed.

4. A researcher measures the amount of time (in seconds) that a group of teenagers uses the Internet for school-related and non-school-related purposes.

This test is parametric. The scale of measurement is continuous (time in seconds), and parametric tests, such as t-tests or ANOVA, can be utilized to compare means or variances, assuming the required assumptions are met.

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As per the reflection rule, the location of point A is (-2,7)

Reflection rule:

(i) Change the sign of x-coordinate.

(ii) Retain the  y-coordinate.

Therefore, when a point is reflected over the y-axis, the sign of its x - coordinate changes.

Given,

Here we have the graph and in the graph we have the point A as (2,7).

Now, we need to find the new location when the point is reflected across y axis.

Here we know that, the point A is reflected over the y axis.

When we apply the reflection over y axis rule, that is,

( x ,y) →→ ( -x , y)

When we looking at the rule, the sign of the x coordinate is changed.

Thus makes the point that reflected across the y axis as,

=>  point A ( 2, 7) →→ ( -2 , 7)

Therefore,  point A ( 2, 7) has the new location ( -2 , 3) after reflection.

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The math topics covered in the grade 6 math worksheets are algebra,geometry,measurement, number operation.

1. Number sense and operations: This includes understanding numbers, fractions, decimals, and integers, as well as performing operations with them.

2. Algebra: This includes understanding algebraic expressions and equations, and using them to solve problems.

3. Geometry: This includes understanding basic geometric concepts, such as lines, angles, and shapes, and using them to solve problems.

4. Measurement: This includes understanding measurement concepts, such as length, area, and volume, and using them to solve problems.

5. Data analysis and probability: This includes understanding basic concepts of statistics, such as mean, median, and mode, and using them to analyze data and make predictions.

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The time necessary for p dollars to double when it is invested at interest rate r compounded annually is given by the formula:

t = (ln 2) / (r ln (1 + r))

When compounded monthly, the formula becomes:

t = (ln 2) / (12 r ln (1 + r/12))

When compounded daily, the formula becomes:

t = (ln 2) / (365 r ln (1 + r/365))

When compounded continuously, the formula becomes:

t = ln 2 / (r)

Note that ln is the natural logarithm function.

To use these formulas, you need to know the value of the interest rate r. For example, if r is 5%, then:

When compounded annually, t = (ln 2) / (0.05 ln 1.05) = 13.86 years
When compounded monthly, t = (ln 2) / (12 x 0.05 ln 1.0041) = 14.21 years
When compounded daily, t = (ln 2) / (365 x 0.05 ln 1.000137) = 14.27 years
When compounded continuously, t = ln 2 / (0.05) = 13.86 years

Therefore, the time necessary for p dollars to double depends on the interest rate and the frequency of compounding. Generally, the more frequently the interest is compounded, the shorter the time necessary for p dollars to double.

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The functions that correctly identify the transformation of f(x) = x² shifted three units to the left and five units up is

g(x) = (x + 3)² + 5

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The function that correctly identifies the transformation of f(x) = x² shifted three units to the left and five units up is:

g(x) = (x + 3)² + 5

To see why, we can use the following steps:

To shift a function three units to the left, we replace "x" with "(x + 3)".

This is because for any value of "x", "x + 3" represents a point that is three units to the left of "x".

To shift a function five units up, we add 5 to the entire function.

This is because for any value of "x", the value of the function is increased by 5 units.

Combining these transformations, we get:

g(x) = (x + 3)² + 5

This function represents a parabola that is shifted three units to the left and five units up from the original function f(x) = x^2.

Thus,

The functions that correctly identify the transformation of f(x) = x² shifted three units to the left and five units up is

g(x) = (x + 3)² + 5

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The area of the rectangle is 12 square units which vertices are P(2, 3), Q(4, -1), R(-8, -7), and S(-10, -3).

To find the area of the rectangle, we need to first find the side lengths of the rectangle. We can do this by using the coordinates of the points to find the distances between them.

The side length of the rectangle along the x-axis is the distance between points P and Q, which is 4 - 2 = 2 units.

The side length of the rectangle along the y-axis is the distance between points P and S, which is 3 - (-3) = 6 units.

Now that we know the side lengths of the rectangle, we can use the formula for the area of a rectangle, which is length x width, to find the area.

The area of the rectangle is 2 x 6 = 12 square units.

Therefore, the answer is 12 square units.

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Answer:

One of us is lying

Step-by-step explanation:

Answer:

my favorite book is: A Curious Tale of the In-Between

Totally recommended

The total number of votes registered in all is 571289.

To find out how many votes were registered in all, we need to add the number of valid votes, invalid votes, and the number of people who did not cast their votes.

So, the total number of votes registered in all is:

The problem asks to find out how many votes were registered in all in an election given the number of valid votes, invalid votes, and the number of people who did not cast their votes.

We can start by adding the number of valid votes and invalid votes because those are the votes that were cast, regardless of whether they were valid or not.

This gives us:

498656 (valid votes) + 6768 (invalid votes)

= 505424 votes.

498656 (valid votes) + 6768 (invalid votes) + 83865 (people who did not vote)

= 571289 votes.

The total number of votes registered in all is 571289

However, we also need to add the number of people who did not cast their votes, which is given as 83865.

Therefore, the total number of votes registered in all is:

505424 (valid and invalid votes) + 83865 (people who did not vote)

= 571289 votes.

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The months when both of these plans would pay off the same amout of money for the new phone is 8 months.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

Let the number of months be x

You can pay a one-time charge of 200$ and then an additional $15 per month. This will be 200 + 15x. The second option is not paying any money at this time and having a monthly bill of 40$ a month. This will be 40x.

The equation will be

200 + 15x = 40x

Collect like terms

40x - 15x = 200

25x = 200

Divide

x = 200/25

x = 8

The number of months is 8.

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The probability for the given event is P = 0.5

The probability is given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.

Here the condition is "rolling a number greater than 4 or rolling a 2"

The outcomes that meet the condition are {2, 5, 6}

And all the outcomes of the six-sided die are {1, 2, 3, 4, 5, 6}

So 3 out of 6 outcomes meet the condition, thus, the probability is:

P = 3/6 = 1/2 = 0.5

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Answer:

a = 2\(w^{2}\) + 3w

Step-by-step explanation:

Area = length time width

A= (2w + 3) w

a = 2\(w^{2}\) + 3w

68 68 70 61 67 71 63 67



Step 1: Write the formula of standard deviation

n = 8

Step 2: Find the mean

Step 3: find the standard deviation

Next, substitute to find the standard deviation

standard deviation = 3.14

Final answer

The number of data within the standard deviation of the mean = 5

Step-by-step explanation:

We have,

\(y=7x^2-3\)

It is required to find the value of the discriminant. It is given by :

\(D=b^2-4ac\)

Here, a = 7 b = 0 and c = -3

So,

\(D=(0)^2-4\times 7\times (-3)\\\\D=84\)

The discriminant is positive here, it means that it has two distinct real number solutions.

Let V be the volume of the tank. The inlet pipe fills the tank at a rate of

V / (5 hours) = 0.2V / hour

and the outlet pipe drains it at a rate of

V / (8 hours) = 0.125V / hour

With both valves open, the net rate of water entering the tank is

(0.2V - 0.125V ) / hour = 0.075V / hour

If t is the time it takes for the tank to be full, then

(0.075V ) / hour • t = V

Solve for t :

t = V / ((0.075V ) / hour)

t = 1/0.075 hour

t ≈ 13.333 hours

Answer:

22.5 cm^2

Step-by-step explanation:

Amount of paper is going to be measured in area, so we want the surface area of the cone.  Since it is a cub it doesn't have a base, so we don't need to count it.  

Area of the cone without the base, or what is called the lateral area is pi*r*s where r is the radius and s is the slant height.  and of course radius is d/2 where d is the diameter.  so let's plug it in.  We know diameter is 6 and slant height is 7.5

SA = pi * r * s

SA = pi * d/2 * s

SA = pi * 6/2 * 7.5

SA = 22.5 cm^2

So you will need 22.5 square centimeters of paper.

Answer:

6

Step-by-step explanation:

Since the  x coordinate is the same, we only have to look at the y coordinate

3 - -3 = 3 +3 = 6

The distance is 6

Answer:

6

Step-by-step explanation:

Notice that x does not change.  We do go from y = -3 to y = 3, so the distance between these two y-values is 3 - (-3) = 6

The Answer Is 7.5

Tangent and 8 makes a right triangle, which is great because you could find the diameter and divide it by 2 to find the radius.

64+d^2=289

d^2=225

d=15

15/2=7.5

Answer: The answer is 25.

Answer:

1. 80

2. 2400

Step-by-step explanation:

1. what is the change in Dan's total pay for each copy of math is fun he sells?

2. what is Dan's total pay if he doesn't sell any copies of math is fun?

Given

y=80x + 2400

When x=0

y=80(0)+2400

=0+2400

=2400

When x=1

y=80x + 2400

=80(1) + 2400

=80+2400

=2480

change in Dan's total pay for each copy of math is fun he sells is

= 2480 - 2400

=80

2. Dan's total pay if he doesn't sell any copies of math is fun?

y=80x+2400

When x=0

y=80(0)+2400

=0+2400

=2400

The minimum value of the given equation is 5.

The minimum value of the expression x² + y² - 6x + 4y + 18 for real x and y can be found using the method of completing the square.

To find the minimum value of x² + y² - 6x + 4y + 18, we need to convert the expression to the standard form of a quadratic expression.

First, let's collect the like terms: x² - 6x + y² + 4y + 18

Now, let's complete the square for the x terms: x² - 6x = (x - 3)² - 9

And, let's complete the square for the y terms: y² + 4y = (y + 2)² - 4

Now, let's substitute these back into the original expression:x² + y² - 6x + 4y + 18 = (x - 3)² - 9 + (y + 2)² - 4 + 18= (x - 3)² + (y + 2)² + 5

Now, we can see that the minimum value of this expression is 5, which is obtained when (x - 3)² = 0 and (y + 2)² = 0, i.e., when x = 3 and y = -2. Therefore, the minimum value of the expression is 5.

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The takt time for the given system, where the total time per shift is 430 minutes, there is one shift, workers have two 18-minute breaks, and 40 minutes for lunch, and the daily demand is 356 units, is 1.21 minutes per cycle.

Takt time is calculated by dividing the available production time by the customer demand. In this case, the available production time is the total time per shift minus the break and lunch times.

Total time per shift = 430 minutes

Break time = 2 breaks * 18 minutes = 36 minutes

Lunch time = 40 minutes

Available production time = Total time per shift - Break time - Lunch time

= 430 minutes - 36 minutes - 40 minutes

= 354 minutes

To calculate the takt time, we divide the available production time by the daily demand:

Takt time = Available production time / Daily demand

= 354 minutes / 356 units

≈ 0.9944 minutes per unit

Rounding the takt time to 2 decimal places, we get approximately 1.21 minutes per cycle.

Therefore, the takt time for the given system is 1.21 minutes per cycle.

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The equation of a line into slope-intercept form is represented as:

y = mx + c

where m = slope of the line

c = y-intercept of the line

On simplifying 8x - 20y = 40, the equation will be:

⇒ 2 (4x - 10y) = 2 (20)

⇒ 4x - 10y = 20

⇒ 2x - 5y = 10

⇒ 2x - 10 = 5y

⇒ 5y = 2x + (-10)

⇒ y = 2x/5 + (-10/5)

⇒ y = 2x/5 + (-2)

The slope of this line = 2/5

y-intercept of the line = -2

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In linear equation,   20x + 45y = 440 ,     y = 2x  Where x is the number of small boxes sent and y  is the number of large boxes sent.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this

                 20x + 45y = 440

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation

              y = 2x

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is

                20x + 45y = 440

                      y = 2x

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