Find the area of the stained glass window shown if the diameter of the semi-circle is 61 inches. Use 3.14 for , round your answer to the nearest square inch, and enter the number only.

The solution of the inequality is -1 ≤ x ≤ 3.

To solve the inequality |2x(x-1)+12| ≤ 18, we can break it down into two separate inequalities:

2x(x-1) + 12 ≤ 18

-(2x(x-1) + 12) ≤ 18

Solving the first inequality:

2x(x-1) + 12 ≤ 18

2x² - 2x + 12 ≤ 18

2x² - 2x - 6 ≤ 0

Solving the second inequality:

-(2x(x-1) + 12) ≤ 18

-2x(x-1) - 12 ≤ 18

-2x² + 2x - 12 ≤ 18

2x² - 2x + 30 ≤ 0

Now, let's solve each inequality separately.

For the first inequality, 2x² - 2x - 6 ≤ 0:

We can factor this quadratic equation:

(2x + 2)(x - 3) ≤ 0

To determine the sign of the inequality, we need to consider the intervals where the expression is positive or negative. We set each factor equal to zero to find the critical values:

2x + 2 = 0 => x = -1

x - 3 = 0 => x = 3

Plotting these critical values on a number line and testing intervals, we find that the solution is -1 ≤ x ≤ 3.

For the second inequality, 2x² - 2x + 30 ≤ 0:

This quadratic equation does not have real solutions, so there are no solutions to this inequality.

Combining the solutions from both inequalities, we have -1 ≤ x ≤ 3.

To graph the solution, we plot the interval -1 ≤ x ≤ 3 on the number line. The shaded region on the number line represents the solution set.

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The value of tan (A-B) is equal to 715/2052.

To find the value of tan(A - B), we can use the trigonometric identity:

tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))

Given that tan(A) = 40/9 and sin(B) = 45/53, we can determine the values of cos(B) and tan(B) using the Pythagorean identity:

sin^2(B) + cos^2(B) = 1

cos(B) = sqrt(1 - sin^2(B))

cos(B) = sqrt(1 - (45/53)^2)

cos(B) = sqrt(1 - 2025/2809)

cos(B) = sqrt(784/2809)

cos(B) = 28/53

tan(B) = sin(B)/cos(B)

tan(B) = (45/53)/(28/53)

tan(B) = 45/28

Now we can substitute the values into the formula for tan(A - B):

tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))

tan(A - B) = (40/9 - 45/28)/(1 + (40/9)(45/28))

tan(A - B) = [(1120/252 - 405/252)] / (1 + (1800/252))

tan(A - B) = (715/252) / (2052/252)

tan(A - B) = 715/2052

Therefore, tan(A - B) is equal to 715/2052.

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Answer:

471.1 square units

Step-by-step explanation:

A regular nonagon is a 9-sided polygon with sides of equal length.

The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.

Therefore, the given diagram shows a regular nonagon with an apothem of 12 units.

The side length (s) of a regular polygon can be calculated using the apothem formula:

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Given values:

Substitute the given values into the formula to create an expression for the side length (s):

[tex]12=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{9}\right)}[/tex]

[tex]12=\dfrac{s}{2 \tan\left(20^{\circ}\right)}[/tex]

[tex]s=24 \tan\left(20^{\circ}\right)[/tex]

The standard formula for an area of a regular polygon is:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]

Substitute the found expression for s together with n = 9 and a = 12 into the formula and solve for A:

[tex]A=\dfrac{9 \cdot 24 \tan(20^{\circ}) \cdot 12}{2}[/tex]

[tex]A=1296\tan(20^{\circ})[/tex]

[tex]A=471.705423...[/tex]

[tex]A=471.7\; \sf square\;units\;(nearest\;tenth)[/tex]

Therefore, the area of a regular nonagon with an apothem of 12 units is 471.1 square units, rounded to the nearest tenth.

Answer:

Step-by-step explanation:

Step 1: Group the first two terms together and then the last two terms together. Step 2: Factor out a GCF from each separate binomial. Step 3: Factor out the common binomial. Note that if we multiply our answer out, we do get the original polynomial.

Answer: To find a 2 numbers that multiply to the value of C and Add to the value of b.

Step-by-step explanation: They Have to multiply to C and add to B and after that you can just continue simplifying the polynomial.

Answer:

mean, 25.8 median 23

Step-by-step explanation:

Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.

The mean of a set of numbers is the sum divided by the number of terms.

You cannot have 1 imaginary solution because the quadratic equation must have either two real solutions or two complex solutions

In mathematics, the discriminant (D = b2 - 4ac) aids in identifying the kind of solutions to quadratic equations of the form ax2 + bx + c = 0.

There are two unique real solutions if the discriminant is positive. There is only one viable option if the discriminant is zero. There are no practical solutions, however, if the discriminant is negative.

The quadratic equation in this instance has two complex solutions that are conjugates of one another. Because the quadratic equation must have either two real solutions or two complex solutions, there can never be just one hypothetical solution.

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Answer:

Step-by-step explanation:

The sum of 100,000 + 10,000,000,000,000 is 10,000,100,000,000.

The designer can choose from 84 possible combinations of tiles, and they can create 6 different sample designs using the 3 chosen tiles when placing them side by side.

To determine the number of possible combinations of tiles that the designer can choose, we can use the concept of combinations.

Since the designer has 9 different kinds of tiles and wants to choose 3 of them, we can calculate the number of combinations using the formula for combinations, which is [tex]nCr = n! / (r! \times (n - r)!).[/tex]

Number of combinations of tiles = 9C3 [tex]= 9! / (3! \times (9 - 3)!)[/tex]

Simplifying further:

[tex]9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1[/tex]

[tex]3! = 3 \times 2 \times 1[/tex]

[tex](9 - 3)! = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1[/tex]

Plugging these values into the formula:

Number of combinations of tiles[tex]= 9 \times 8 \times 7 / (3 \times 2 \times 1 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)[/tex]

Simplifying the expression:

Number of combinations of tiles = 84

The designer can choose from 84 possible combinations of tiles, and they can create 6 different sample designs using the 3 chosen tiles when placing them side by side.

Therefore, the designer can choose from 84 possible combinations of tiles.

Now, let's calculate the number of different sample designs the designer can make using the 3 chosen tiles.

Since the tiles are placed side by side, the order of the tiles matters.

To calculate the number of different arrangements, we can use the concept of permutations.

Number of sample designs = 3!

Calculating:

[tex]3! = 3 \times 2 \times 1 = 6[/tex]

Therefore, the designer can create 6 different sample designs using the 3 chosen tiles when placing them side by side.

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The solution is: the value of the angles a, b and c are : a = 60, b = 90, c = 100.

Here,

We have that in line CHF, it has two given and one unknown angle.

The total angle of one straight line is 180.

Given that:

a = 180 - 50 -70 = 60

The angle intersecting the CHFD line can be computed by the the total angle inside the triangle.

Angle on EFH would give 180-40-60 = 80 and on EFD the angle would be 100 from 180-80.

Since angle C is congruent to the angle EFD.

c = 100

Take note that in a 4 sided polygon (GEFH), the total exterior angle is 360 degrees.

The different angle would be

angle GHF = 50 + a = 50+60 = 110

angle EFH = 80

angle FEG = 180- c = 180-100 = 80

ANGLE EGH = 360 - GHF -EFH -FEG = 360 - 110-80-80 = 90

since angle AG is congruent to EGH, we can calculate for the angle b which is congruent to its opposite. This would give us formula of

360 = (90+90) + (b) +(b)

360 = 180 +2b

b = 90

Hence, The solution is: the value of the angles a, b and c are : a = 60, b = 90, c = 100.

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Answer:

  b. 5.9 mL

Step-by-step explanation:

You want the value that represents the 99th percentile of a normal distribution with a mean of 5 mL and a standard deviation of 0.4 mL.

The inverse of the normal CDF function is used to find the X value for a given area. Here, we want X such that P(x < X) = 0.99 for μ = 5 and σ = 0.4.

The attached calculator output shows that is about X = 5.9305. Rounded to 1 decimal place, the volume is ...

  5.9 mL

<95141404393>

Answer:

x+1

DOMAIN: x [tex]\neq[/tex] -5

Step-by-step explanation:

We can factor [tex]x^{2}[/tex]+6x+5 as (x+1)(x+5) since this expands to [tex]x^{2}[/tex]+5*x+1*x+5*1, which is [tex]x^{2}[/tex]+6x+5.

Now, we have:

[tex]\frac{(x+1)(x+5)}{(x+5)}[/tex]  

We can cancel out x+5, because this expression is the same as (x+1)*[tex]\frac{x+5}{x+5}[/tex], which is (x+1).

HOWEVER, the denominator cannot be equal to zero because that will make the expression undefined (you can't divide by zero). So, since x+5[tex]\neq[/tex]0, x[tex]\neq[/tex]-5.

Answer:

Step-by-step explanation:

It's c

-4 1/6

Plug in the number for a and you get -2 1/3 - 11/6

make the first number into a fraction, so -7/3

-7/3 - 11/6

common denominator, so, -14/6 - 11/6, which equals -25/6

simplify: -4 1/6

Hope that helps!

Answer:

The answer is

[tex] \frac{ - 25}{6} [/tex]

-4⅙

Step-by-step explanation:

[tex]a - \frac{ - 11}{6} [/tex]

[tex]a = - 2 \times \frac{1}{3} [/tex]

[tex] \frac{ - 7}{3} - \frac{ - 11}{6} [/tex]

[tex] = \frac{ - 25}{6} [/tex]

The value of R and θ is 6.18 and 53.13 degrees, under the condition that a circle C has center at the origin and radius 5 .

In order to  evaluate the equation of the circle K. The diameter of K has endpoints at the origin and (0,15). Then, the center of K is at (0,7.5) and its radius is 7.5. Therefore, the evaluated equation of K is
x² + (y-7.5)² = 56.25.
The equation of circle C is x² + y² = 25.
The two circles intersect at two points. Now we have to evaluate the coordinates of these points.
Staging y = 5 - x² in the equation of K,
we get
x² + (5-x²-7.5)² = 56.25.
Applying simplification on this equation
x⁴ - 10x² + 31.25 = 0.
Calculating this quadratic equation gives us
x² = 5 ± √(10)/2.
If P lies in the first quadrant,
we choose x² = 5 + √(10)/2 and y = √(25-x²) to get P in Cartesian coordinates.
Converting P to polar coordinates gives us
r = √(x²+y²) and θ = arctan(y/x).
Staging x = √(5+√(10)/2) and y = √(25-x²) in these equations gives us
r ≈ 6.18 and θ ≈ 0.93 radians.
Using this formula to convert into degree
Rad × 180/π
= 0.93 × 180/π
≈ 53.13 degrees
Therefore, r ≈ 6.18 and θ ≈ 53.13 degrees.
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The given text presents a map of South Africa with various locations marked. However, important information such as the scale of the map and the number of provinces is missing. Without the scale, we cannot accurately determine distances or calculate probabilities. Similarly, the absence of information regarding the provinces prevents us from calculating the probability of selecting a specific province. Therefore, based on the given text, we can only answer the first two questions, which involve the type of scale and the general direction between two locations.

1. The type of scale given in the diagram is a ratio scale, specifically a linear scale. It represents the relationship between map distance and actual distance in a straight line.

Interpretation of the given scale:

The scale on the map is not clearly visible in the provided text. However, it is typically written as a fraction or ratio, where the numerator represents the map distance and the denominator represents the corresponding actual distance on the ground. For example, a scale of 1:1,000,000 means that 1 unit on the map represents 1,000,000 units in the real world.

2. The general direction of Badplaas from Colesburg is to the northeast.

3. To determine the actual straight-line distance between East London and Bloemfontein, we would need the scale from the map. However, the scale is not provided in the given text, making it impossible to calculate the distance accurately.

4. Stellenbosch is located in the Western Cape province on the map.

5. To calculate the probability of randomly selecting the Western Cape province in South Africa, we would need the total number of provinces in South Africa and the number of provinces that belong to the Western Cape. However, this information is not provided in the given text, so it is not possible to calculate the probability.

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t = (6 + 3k)/(k - 2) is the formula for t in the equation k=2(t+3)/t-3.

The given equation is k=2(t+3)/t-3.

We need to isolate t on one side of the equation.

Let's start by cross-multiplying:

k(t - 3) = 2(t + 3)

Expanding the brackets:

kt - 3k = 2t + 6

Now, let's gather all the terms with t on one side and all the constant

terms on the other side:

kt - 2t = 6 + 3k

Factoring out t on the left side:

t(k - 2) = 6 + 3k

Finally, we can solve for t by dividing both sides of the equation by (k - 2):

t = (6 + 3k)/(k - 2)

Therefore, t is the subject of the formula, and it is given by t = (6 + 3k)/(k - 2).

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Band B-1 is a band of the electromagnetic spectrum that is used for cellular communications. It is located in the 2100 MHz frequency range.

Band B-2 is also a band of the electromagnetic spectrum that is used for cellular communications. It is located in the 1900 MHz frequency range.

The main difference between band B-1 and band B-2 is their range. Band B-1 has a longer range than band B-2. This is because it is located in a higher frequency range. Higher frequency ranges have shorter wavelengths, which means that they can travel through objects more easily. This makes them better for use in areas where there are a lot of obstacles, such as buildings and trees.

Band B-2 has a shorter range than band B-1, but it is better for use in areas where there are a lot of people. This is because it is located in a lower frequency range

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Answer:

2/3

Hope this helps

Answer:

23.35 minutes

Step-by-step explanation:

Brendan finished in 22.5 minutes. Tobias finished 85 seconds after. Just add 85 seconds to 22.5 minutes. There are 100 second in 1 minute. Since Brendan is already at 22.5, there is only 0.5 left to get to 23. 0.5 in this case means 50 seconds. You do 85 - 50 = 35. Now, you are at 23 minutes. Add 35 seconds to that to get to 23.25 minutes.

No, I disagree because a good line of fit has to minimize the sum of the squared distance between all the points in the data.

A line of fit is used to mathematically model the relationship between variables in a data. A line of fit is drawn such that the best line would minimize the sum of the squared distances between the plotted points.

This means that, the line of fit should not aim to go through the middle of the data points but minimize the sum of the squared distances between them.

Hence, Alfred's reasoning is Incorrect .

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The accounting equation is:

Assets (Rs. 1,75,000 - Rs. 35,000) = Liabilities (Rs. 45,000 + Rs. 5,000) + Capital (Rs. 20,000)

We have,

Based on the given transactions, we can prepare the accounting equation as follows:

a. Started business with Cash Rs. 250,000.

Assets: Cash = Rs. 250,000

b. Purchased goods amounting to Rs. 45,000 on credit from Harish.

Assets: Cash = Rs. 250,000, Inventory = Rs. 45,000

Liabilities: Accounts Payable = Rs. 45,000

c. Goods costing to Rs. 80,000 was sold for Rs. 1,25,000 on credit.

Assets: Cash = Rs. 250,000, Accounts Receivable = Rs. 1,25,000

Inventory: Rs. 45,000 - Rs. 80,000 = Rs. -35,000 (Assuming no additional purchases or returns)

Liabilities: Accounts Payable = Rs. 45,000

Capital: Retained Earnings = Rs. 1,25,000 - Rs. 80,000 = Rs. 45,000

d. Salaries outstanding Rs. 5,000.

Liabilities: Salaries Payable = Rs. 5,000

e. Rent paid Rs. 50,000.

Assets: Cash = Rs. 250,000 - Rs. 50,000 = Rs. 2,00,000

f. Withdrawn by owner for personal use Rs. 25,000.

Assets: Cash = Rs. 2,00,000 - Rs. 25,000 = Rs. 1,75,000

Capital: Retained Earnings = Rs. 45,000 - Rs. 25,000 = Rs. 20,000

Now, let's summarize the accounting equation:

Assets:

Cash = Rs. 1,75,000

Inventory = Rs. -35,000 (negative value indicates loss or returns)

Liabilities:

Accounts Payable = Rs. 45,000

Salaries Payable = Rs. 5,000

Capital:

Retained Earnings = Rs. 20,000

Therefore,

The accounting equation is:

Assets (Rs. 1,75,000 - Rs. 35,000) = Liabilities (Rs. 45,000 + Rs. 5,000) + Capital (Rs. 20,000)

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Answer:

x / 2 = 17

Step-by-step explanation:

Since we're told that there are 2 friends, they split the cost evenly, and they  each paid $17 individually, we'd have to use the equation x / 2 = 17 to find the total cost.

If you were to solve, you'd find that the total cost was $34 as 2 * 17 = 34 and 34 / 2 = 17

Answer:

75 points ( more than?? you didn't add the drop-down list ) today's score.

Hope this helps!

Step-by-step explanation:

y = mx + b

y = 5x + b

(50) = 5(6) + b  -> b = 20

y = 5x + 20

If Carlos plays the game today for 0 min, he will get a score of 20 ( odd...  how is that possible )

But tomorrow, he plans to play for an extra 15 min, so he will get a score of 95 ( ( 5 × 15 ) + 20 ). The question asks for how much his score will change so his score will change by 75 points ( 95 - 20 ).

You could also just do 15 × 5 to get 75 :)

The average rate of change for the snowfall amount is given as follows:

2.4 inches per hour.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The change in the output is given as follows:

8.1 - 3.3 = 4.8.

(output is the amount of snow).

The change in the input is given as follows:

2 - 0 = 2.

(input is the time in hours).

Hence the average rate of change of the snowfall over time is given as follows:

4.8/2 = 2.4 inches per hour.

(change in the snowfall divided by the change in time).

The table is given by the image presented at the end of the answer.

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Using balanced billing, the monthly payment is $278

Using balanced billing to determine their monthly payment, we simply need to divide their total annual payment by the total number of months in a year. This will result to dividing the entire annual bill by 12 to determine the monthly payment.

Given that the Ross family spent $3,336 for electricity last year, we can calculate their monthly payment as follows:

Monthly payment = Total cost / Number of months

Monthly payment = $3,336 / 12

Monthly payment  = $278

Therefore, the Ross family's monthly payment for balanced billing will be approximately $278.

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The initial deposit needed for the account is given as follows:

$19,257.37.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]A = 22000, t = 3, r = 0.0447, n = 4[/tex]

Hence the initial deposit P is obtained as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]22000 = P\left(1 + \frac{0.0447}{4}\right)^{4 \times 3}[/tex]

1.142657P = 22000

P = 22000/1.142657

P = $19,257.37.

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Using the mean value theorem in  f(x) = 1/2x² + 7, c =  2√3

The mean value theorem states that let f be continuous over the closed interval  [a,b] and differentiable over the open interval  (a,b). Then, there exists at least one point c ∈(a,b) such that f'(c) = [f(b) - f(a)]/(b - a)

To find c using the mean value theoren for f(x) = 1/2x² + 7 over the interval [0, 6], we proceed as follows.

Uisng the mean value theorem, we know that

f'(c) = [f(b) - f(a)]/(b - a)

⇒ f(c) = 1/(b - a)∫ₐᵇ[f(x)

Now over the interval [a, b] = [0,6]

f(c) = 1/(6 - 0)∫₀⁶[f(x)

Now, since f(x) = 1/2x² + 7

Substituting this into the equation, we have that

f(c) = 1/(6 - 0)∫₀⁶[f(x)

f(c) = 1/(6 - 0)∫₀⁶(1/2x² + 7)

f(c) = 1/6∫₀⁶(1/2x² + ∫₀⁶7)

f(c) = 1/6[1/2x³/3 + 7x]₀⁶

f(c) = 1/6[x³/6 + 7x]₀⁶

f(c) = 1/6[6³/6 + 7(6)] - [0³/6 + 7(0)]

f(c) = 1/6[6²+ 42] - [0 + 7(0)]

f(c) = 1/6([36 + 42] - [0 + 0])

f(c) = 1/6(78 - 0)

f(c) = 1/6(78)

f(c) = 13

Now, since f(x) = 1/2x² + 7

f(c) = 1/2c² + 7

1/2c² + 7 = 13

1/2c² = 13 - 7

1/2c² = 6

c² = 2 × 6

c² = 12

c = √12

c = 2√3

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Answer:

23p -6k - 42p + 30k - 5p

23p - 42p - 5p + 30k - 6k

23p - 47p + 24k

-24p + 24k

24(- p + k)

24( k - p)

Answer:

The answer is

60p + 24k

Step-by-step explanation:

1: Expand

=23p - 6k + 42p + 30k - 5p

step2: collect like terms

=42p + 23p - 5p - 6k + 30k

step 3: add/subtract them to get your answer

=60p + 24k

your answer☝

Answer:

  23/41

Step-by-step explanation:

You want to know the fraction who failed, given they predicted they would fail.

The attached 2-way table shows the given numbers (black) and the numbers that make the totals correct (blue).

It shows 23 of the 41 who thought they would fail actually did. That fraction is ...

  23/41 . . . . failed who thought they would

<95141404393>