Use π = 22/7 to find the circumference and area of the following circle. r = 2 1/2 cm C = ____ A = ______​

Answer:

  1) a1 = -5, a(n) = a(n-1) + 2

Step-by-step explanation:

The explicit formula for an arithmetic sequence can be written ...

  an = a1 +d(n -1)

The corresponding recursive formula is ...

  a(1) = a1, a(n) = a(n -1) +d

__

Comparing the above explicit formula to the one you're given, you see that ...

  a1 = -5, d = 2

Using these values in the recursive formula gives you ...

  a(1) = -5, a(n) = a(n-1) +2

Answer:

(x-2)^2-2

Step-by-step explanation:

x^2-4x+2

take the x out

x(x-4) + 2

(x-2)^2-2

because (x-2)^2 is

x^2-4x+4

its like completing the square

Answer:

(x-2)² -2

Step-by-step explanation:

Consider that (a+b)² = a²+2ab+b²

To find the form (x-A)²+B compare  x²-4x+2 with a²+2ab+b²

x² - 4x +2

a² + 2 a b+ b², so a= x and b = (-2)

x²+ 2· x ·(-2)+ (-2)² -  2  = (x-2)² -2 is in the form (x-A)²+B

Check our answer:

(x-2)² -2= (x²-2·2x+4)-2 = x²-4x +2 ✅

Answer: maggie is right

Step-by-step explanation:

because the first number is 7 and the first number in the sentence is 7

9514 1404 393

Answer:

Step-by-step explanation:

X'∩Y includes those elements of Y that are not in X. That would be {f, g}.

__

(X∩Y)' is all the elements that are not in the intersection of X and Y. That intersection is {d, e}, so this is the complement of that set; {a, b, c, f, g, h}.

__

X'∩Y' is the same as (X∪Y)'. There is only one element not in X or Y: {h}.

Answer: These events are independent.

Step-by-step explanation:

Two events are considered independent if the outcome of one event does not affect the outcome of the other event. In this case, getting a 5 or 6 on a dice toss and getting at most 3 on a dice toss are independent events.

This is because the probability of getting a 5 or 6 is 2/6 or 1/3, which is completely unrelated to the probability of getting at most 3, which is 3/6 or 1/2. The outcome of getting a 5 or 6 does not affect the probability of getting at most 3, and vice versa. Therefore, these events are independent.

Answer:

1778.68 I think

Step-by-step explanation:

Answer:

605

I just got confused sorry.

The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.

Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.

The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.

The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).

Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.

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Answer:

The formula for finding the area of a circle using its radius is:

The formula for finding the area of a circle using its radius is:A = πr²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14

Step-by-step explanation:

Hope it Helps

The formula for finding the area of a circle using its radius is π * r².

The formula for finding the area of a circle using its diameter is (π/4) * d².

The formula for finding the area of a circle using its radius is:

A = π * r²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

r represents the radius of the circle.

If you have the diameter of the circle instead of the radius, you can use the following formula:

A = (π/4) * d²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

d is the diameter of the circle.

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a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

\( A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} \)

The initial amount occurs at t = 0.

\( A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} \)

\( A(0) = 934 (\dfrac{1}{2})^0 \)

\( A(0) = 934 \times 1 \)

\( A(0) = 934 \)

After 80 years, t = 80.

\( A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} \)

\( A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} \)

\( A(80) = 934 (0.15749) \)

\( A(80) = 147 \)

Set up two limits of the function

\(\lim_{x \to \infty} f(x)= \lim_{x \to \infty} 9x=\infty\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} 9x=-\infty\)

This answer makes sense because f(x) has a positive correlation with x. This means as x increases so does f(x). If we make x infinitely negative, f(x) will also get infinitely negative. Same logic for driving x to positive infinity.

Also, just look at the graph of f(x)=9x. We can see that is a continuous function that grows without bounds. So, it makes sense that if x goes to infinity so will the function and if x goes to -infinity the function will go to -infinity.

Step-by-step explanation:

we good and you.........

Answer:

Im doing great:) Just finishing up school work! And you ?

Step-by-step explanation:

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

Let's find the mean, median, and mode for each set of numbers:

Set: 40, 38, 29, 34, 37, 22, 15, 38

Mean: To find the mean, we sum up all the numbers and divide by the total count:

Mean = (40 + 38 + 29 + 34 + 37 + 22 + 15 + 38) / 8 = 273 / 8 = 34.125

Median: To find the median, we arrange the numbers in ascending order and find the middle value:

Arranged set: 15, 22, 29, 34, 37, 38, 38, 40

Median = (29 + 34) / 2 = 63 / 2 = 31.5

Mode: The mode is the number(s) that appear(s) most frequently in the set:

Mode = 38 (appears twice)

Set: 26, 32, 12, 18, 11, 14, 21, 12, 27

Mean: Mean = (26 + 32 + 12 + 18 + 11 + 14 + 21 + 12 + 27) / 9 = 173 / 9 ≈ 19.222

Median: Arranged set: 11, 12, 12, 14, 18, 21, 26, 27, 32

Median = 18

Mode: No mode (all numbers appear only once)

Set: 3, 3, 4, 7, 5, 7, 6, 7, 8, 8, 8, 9, 8, 10, 12, 9, 15, 15

Mean: Mean = (3 + 3 + 4 + 7 + 5 + 7 + 6 + 7 + 8 + 8 + 8 + 9 + 8 + 10 + 12 + 9 + 15 + 15) / 18 ≈ 8.611

Median: Arranged set: 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 12, 15, 15

Median = 8

Mode: Mode = 8 (appears 4 times)

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

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Answer:

She'll have $661 in the account in 2022.

Step-by-step explanation:

Compound interest:

The amount of money earned in compound interest after t years is given by the following equation:

\(A(t) = A(0)(1+r)^t\)

In which A(0) is the initial amount and r is the interest rate, as a decimal.

Rachael started off with $400. It earns 3% interest each year.

This means that \(A(0) = 400, r = 0.03\)

So

\(A(t) = A(0)(1+r)^t\)

\(A(t) = 400(1+0.03)^t\)

\(A(t) = 400(1.03)^t\)

She wants to know how much money she'll have in the account in 2022.

17 years after 2005, which means that this is A(17). So

\(A(17) = 400(1.03)^{17} = 661\)

She'll have $661 in the account in 2022.

The slope of the line that passes through the points (7,-4) and (11,-4) is 0.

The slope of a line is found by using the formula:

slope = (change in y)/(change in x)

To find the change in y, subtract the y-coordinate of one point from the y-coordinate of the other point:

-4 - (-4) = 0

To find the change in x, subtract the x-coordinate of one point from the x-coordinate of the other point:

11 - 7 = 4

Now we can use the formula to find the slope:

slope = 0/4 = 0

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Answer:

41.6 km/h

Step-by-step explanation:

Nao drives 95mi/2.5hr or 38 miles per hour, or 60.8 km/h

1 hr 15 min is the same as 1.25 hours

Arban drives 128km/1.25hr or 102.4 km/h

The difference is 102.4-60.8 = 41.6

Answer:

Round both numbers to 1 significant figure.

400+400=800

800 is the answer.

With a triangle, the sum of any two side lengths must be greater than the third side length. If this is not true, then the side lengths cannot make a triangle. Let's go through each set of side lengths and determine which would and wouldn't work.

a. 3, 4, 8 - will not make a triangle

3 + 4 = 7 > 8 = false

3 + 8 = 11 > 4 = true

4 + 8 = 12 > 3 = true

b. 7, 6, 12 - will make a triangle

7 + 6 = 13 > 12 = true

7 + 12 = 19 > 6 = true

6 + 12 = 18 > 7 = true

c. 5, 11, 13 - will make a triangle

5 + 11 = 16 > 13 = true

5 + 13 = 18 > 11 = true

11 + 13 = 24 > 5 = true

d. 4, 6, 12 - will not make a triangle

4 + 6 = 10 > 12 = false

4 + 12 = 16 > 6 = true

6 + 12 = 18 > 4 = true

e. 4, 6, 10 - will not make a triangle

4 + 6 = 10 > 10 = false

4 + 10 = 14 > 6 = true

6 + 10 = 16 > 4 = true

Hope this helps!

the 3 correct statements are:

For a function f(x), we define the inverse function f⁻¹(x):

This means that, if for a given value of x = x₀ we have:

f(x₀) = y₀

Then:

f⁻¹(y₀) = x₀

From this, we can conclude that the domain of f(x) is the range of the inverse, and the range of f(x) is the domain of the inverse.

Then the statements that are correct are:

These 3 are the 3 correct statements.

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Answer:

180 degrees rotation about the origin

Explanation:

First, we need to identify the coordinates of DOG and D'O'G' as follows

D(-2, 1) ---> D'(2, -1)

O(-3, 3) ---> O'(3, -3)

G(1, 1) ---> G'(-1, -1)

Therefore, the rule for the transformation is

(x, y) ---> (-x, -y)

This rule is the rule for a 180 degrees rotation about the origin. So, the transformation is a 180 degrees rotation about the origin.

Answer:

The binomial that completes the factorization is 3p + 4q.

Step-by-step explanation:

We can start by recognizing that the given expression has two terms, which are both perfect cubes:

27p^4 is the cube of (3p)^2, and

64pq^3 is the cube of (4q)^2.

Therefore, we can use the formula for the sum of two cubes:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

to factorize the given expression:

27p^4 + 64pq^3 = (3p)^2 + (4q)^2)(9p^2 - 12pq + 16q^2)

Now, we want to find the binomial that completes the factorization. We notice that the first factor (3p + 4q)(9p^2 - 12pq + 16q^2) is not a binomial, but a product of two binomials. So we focus on the second factor, which is a trinomial. We want to see if we can factor it further.

We can try to factor out a common factor of 3 from the first two terms and a common factor of 4 from the last two terms:

9p^2 - 12pq + 16q^2 = 3(3p^2 - 4pq) + 4(4q^2)

Now we can see that we have the difference of two squares:

3p^2 - 4pq = (p(3p - 4q))

4q^2 = (2q)^2

So we can write:

9p^2 - 12pq + 16q^2 = 3p(3p - 4q) + 4q^2

= (3p - 4q)(3p + 4q) + 4q^2

Now we can substitute this back into our original expression:

27p^4 + 64pq^3 = (3p + 4q)((3p)^2 - 3p(4q) + (4q)^2) + 4q^2

= (3p + 4q)(9p^2 - 12pq + 16q^2) + 4q^2

So the binomial that completes the factorization is 3p + 4q.

Answer:

C. volume

Step-by-step explanation:

The response variable in this scenario would be the volume of the usable lumber. That is because this variable depends completely on the height of the cherry trees that are being measured. The higher that the cherry trees are the more volume can be expected to get from cutting these trees down. The opposite goes for trees that are smaller, they would decrease the total expected volume that will be received from the usable lumber since there would be less amount of tree to cut down.

Option (b) is the correct answer: Perpendicular segments.

Perpendicular rays, perpendicular segments, perpendicular lines, and parallel lines are important concepts in geometry that describe the relationship between lines and line segments.

1. Perpendicular Rays: Perpendicular rays are two rays that intersect at point and form a right angle (90 degrees) at the point of intersection. The rays extend indefinitely in opposite directions from the point of intersection.

2. Perpendicular Segments: Perpendicular segments are line segments that intersect at a right angle. They share a common endpoint but do not extend indefinitely like rays. The right angle is formed at the point of intersection.

3. Perpendicular Lines: Perpendicular lines are lines that intersect at a right angle. They continue indefinitely in opposite directions and form four right angles at the point of intersection. Perpendicular lines are often denoted by a symbol ⊥.

4. Parallel Lines: Parallel lines are lines that never intersect. They remain equidistant from each other at all points. Parallel lines have the same slope and do not converge or diverge. In Euclidean geometry, parallel lines are denoted by a double vertical line symbol (||).

Understanding these concepts is fundamental in geometry as they help define angles, shapes, and spatial relationships. The properties of perpendicular and parallel lines play a crucial role in various geometric theorems and applications.

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Answer:

To graph the line with slope -1 passing through the point (-2,4), we can use the point-slope form of the equation of a line, which is:

where m is the slope of the line, and (x1, y1) is the given point on the line. Substituting the given values, we get:

Simplifying this equation, we get:

Now we can graph this line by plotting the given point (-2,4), and then using the slope of -1 to find one or more additional points on the line. We can do this by starting at the given point and then moving one unit down (since the slope is negative) and one unit to the right (since the slope is -1). This gives us the point (-1,3). We can then connect these two points to graph the line.

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Answer:

\(y=-\frac{1}{3}x -8\)

Step-by-step explanation:

1) Write down the standard form of an equation of a line and the formula to find m.

\(y=mx+b\)

\(m=\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

2) Find m using the formula then substitute it into \(y=mx+b\).

\(m=\frac{-5 - (-6) }{-9 - (-6)}\\m=\frac{-5 +6 }{-9 +6}\\m=\frac{1}{-3} \\m=-\frac{1}{3}\)

So, \(y=-\frac{1}{3}x +b\).

3) Find b by substituting a pair of coordinates the line goes through.

\(-6=-\frac{1}{3}(-6) +b\\-6=2+b\\-6 - 2=b\\-8=b\)

4) Substitute b into \(y=-\frac{1}{3}x +b\) to get your final answer.

\(y=-\frac{1}{3}x -8\)

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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