1. A triangle, △DEF, is given. Describe the construction of a circle with center C circumscribed about the triangle. (3-5 sentences)



2. ⊙O and ⊙P are given with centers (−2, 7) and (12, −1) and radii of lengths 5 and 12, respectively. Using similarity transformations on ⊙O, prove that ⊙O and ⊙P are similar

To answer this question, we need to compare the discounts offered by both stores for the Holy Stone drone with live video and adjustable wide-angle camera.

Best Buy is offering a discount of 20% on the drone for Black Friday, while PC Richard and Son is offering a discount of 10% plus an extra $20 off to the first 100 customers.

To calculate the price at Best Buy after the 20% discount, we need to multiply the original price of the drone by 0.8 (100% - 20%). Let's assume the original price of the drone is $200. So, the price at Best Buy after the discount will be:

Price at Best Buy = $200 x 0.8 = $160

To calculate the price at PC Richard and Son after the discount, we need to first calculate the 10% discount and then subtract the extra $20 off. Let's assume the original price of the drone is still $200. So, the price at PC Richard and Son after the 10% discount will be:

Price after 10% discount = $200 x 0.9 = $180

Then, we need to subtract the extra $20 off for the first 100 customers:

Price at PC Richard and Son = $180 - $20 = $160

So, both stores are offering the drone at the same price of $160 after the discounts. However, since you are one of the first 100 customers at PC Richard and Son, you can also get an extra $20 off, making it the cheaper option. Therefore, you should go to PC Richard and Son to get the cheaper price.

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Afia visits the shopping mall on Tuesday to purchase some groceries. if she goes back after 295 days, she visits the shopping mall again​ on a Wednesday.

To find out what day Afia visited the shopping mall again, we can divide  295 by 7  because there are 7 days in a week. we need to find out how many full weeks have passed and how many days.

= 295/ 7 = 42.1

The 295 divided by 7 is 42 with a remainder of 1 or we can write as that 42 full weeks and 1 day have passed.

When 42 weeks have passed that day will be Tuesday and the 1 day after Tuesday is Wednesday.

Therefore,  Afia visited the shopping mall again on a Wednesday.

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Answer:

225 miles!!!!!!!!!!!!!!!!

The range of the function f(x) is Range: [0, 125] In interval notation, this can be written as [0, 125] if the longest side length of the box can be no greater than 20 in.

The function f(x) = 1.25x^2 models the packaging costs, in cents, for a rectangular prism-shaped box with side lengths of 2x in., 2x in., and 0.5x in.

We need to determine the reasonable domain and range values for this function, given that the longest side length of the box can be no greater than 20 in.

Since the longest side length is 20 in., we know that:

2x ≤ 20

x ≤ 10

Therefore, the domain of the function f(x) is all real numbers less than or equal to 10, or: Domain: [-∞, 10]

To find the range of the function, we need to examine the behavior of the function as x varies. Since the coefficient of x^2 is positive, the function is quadratic with a minimum value at x = 0. Therefore, we know that the range of the function must start at its minimum value, which is f(0) = 0, and increase as x increases.

To determine the upper limit of the range, we can evaluate f(x) when x = 10 (the maximum value of x allowed):

f(10) = 1.25(10)^2 = 125

Therefore, the range of the function f(x) is:

Range: [0, 125]

In interval notation, this can be written as [0, 125].

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If Sabina and the pole are proportional, then the pole’s shadow will be 35/4 feet tall.

Since Sabrina is 4 feet tall and casts a 3.5-foot shadow, we can set up a proportion comparing the heights and shadow lengths: Sabrina's height (4 feet) / her shadow (3.5 feet) = pole's height (10 feet) / pole's shadow (x).

This proportion can be represented as: 4/3.5 = 10/x. To solve for x (the length of the pole's shadow), we can cross-multiply:

4 * x = 3.5 * 10

4x = 35

Now, divide both sides by 4:

x = 35/4

So, the pole's shadow will be 35/4 feet long when both Sabrina and the pole are proportional. This fraction represents the pole's shadow length in relation to the given heights and shadow lengths.

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The simplification of the expression ½(18t) + 2t(9) -12 is 27t-12

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible.

For example, 3a²+9a+12 can be simplified by bring out the common factors between the terms

= 3(a²+3a+4).

Similarly, 1/2(18t) + 2t(9) -12 can be simplified as;

9t + 18t -12

= 27t -12

therefore the simplification of ½(18t) + 2t(9) -12 is 27t-12

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1. The next two term for the sequence using Geometric Progression is 8 and 16

2. The next two terms for the sequence using arithmetic progression is 7 and 11

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.

Using Geometric Progression, the common ratio is 2/1 = 2

therefore the next two terms will be

4× 2 = 8 and 8× 2 = 16

Using Arithmetic progression , the common difference will be increasing by 1 per number of term, i.e r+1

for the fourth term ,common difference = 2+1 = 3

fourth term = 4+3 = 7

for the fifth term , common difference = 3+1 = 4

fifth term = 7+4 = 11

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The minimum value of a - b is around 2.2 with a = 8.4 rounded to one decimal place and b = 6.19 rounded to two decimal places.

We must first subtract b (lower bound) from a (upper bound) to determine the least value of a - b, which is equal to 8.4 - 6.19 = 2.21. 2.21 is the difference between a and b. However, the question requests that we round off this number to the nearest tenth.

We remove the first decimal point because 1 is

less than 5, giving us 2.2. Hence the minimum value of a -b to the nearest decimal is found to be 2.2.

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The complete question is:

Given a = 8.4 rounded to 1 decimal place and b = 6.19 rounded to 2 decimal places, find the minimum value of a - b rounded to 1 decimal place.

The area of the painted face of the brick is given as follows:

108 in².

The area of a rectangle of length l and width w is given by the multiplication of dimensions, as follows:

A = lw.

The dimensions for this problem are given as follows:

Hence the area of the painted face of the brick is given as follows:

A = 12 x 9 = 108 in².

(the area of a rectangle is given by the multiplication of the dimensions, which we did here).

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Answer:

Step-by-step explanation:

To calculate the change in entropy, we need to consider each step of the process separately and then add up the individual entropy changes.

Step 1: Heating ice from -10.0°C to 0°C

The heat required for this step can be calculated using the formula:

q = m * Cp * ΔT

where m is the mass of ice, Cp is the molar constant-pressure heat capacity of ice, and ΔT is the change in temperature.

q = 10.0 g / 18.01528 g/mol * 37.6 J/K/mol * 10.0°C = 20.8 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the temperature in Kelvin.

ΔS = 20.8 J / 263.15 K = 0.079 J/K

Step 2: Melting ice at 0°C

The heat required for this step can be calculated using the formula:

q = n * ΔHfus

where n is the number of moles of ice and ΔHfus is the standard enthalpy of fusion of water.

n = 10.0 g / 18.01528 g/mol = 0.555 mol

q = 0.555 mol * 6.01 kJ/mol = 3.33 kJ = 3330 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the melting point of water in Kelvin (273.15 K).

ΔS = 3330 J / 273.15 K = 12.2 J/K

Step 3: Heating water from 0°C to 100°C

The heat required for this step can be calculated using the formula:

q = m * Cp * ΔT

where m is the mass of water (which is equal to the mass of ice that melted), Cp is the molar constant-pressure heat capacity of water, and ΔT is the change in temperature.

q = 10.0 g / 18.01528 g/mol * 75.3 J/K/mol * 100.0°C = 415.9 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the average temperature during the heating process (which is 50°C).

ΔS = 415.9 J / 323.15 K = 1.29 J/K

Step 4: Vaporizing water at 100°C

The heat required for this step can be calculated using the formula:

q = n * ΔHvap

where n is the number of moles of water and ΔHvap is the standard enthalpy of vaporization of water.

n = 10.0 g / 18.01528 g/mol = 0.555 mol

q = 0.555 mol * 40.7 kJ/mol = 22.6 kJ = 22600 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the boiling point of water in Kelvin (373.15 K).

ΔS = 22600 J / 373.15 K = 60.5 J/K

Step 5: Heating steam from 100°C to 115°C

The heat required for this step can be calculated using the formula:

q = m * Cp * ΔT

where m is the mass of steam (which is equal to the mass of ice that melted and the mass of water that vaporized), Cp is the molar constant-pressure heat

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Comets could be visible from Earth when they are most likely to fall down into earth

The total fraction of the wall that has been painted is 1/2. If a whole wall is split in half and we painted half of the wall 3 colors, each color occupies 1/6 of the painted area.

To answer your question, we need to first determine the total fraction of the wall that has been painted. Since the wall has been split in half, we can say that the painted area covers half of the wall. Therefore, the total fraction of the wall that has been painted is 1/2.

Now, we need to divide this 1/2 fraction among the three colors that were used. Let's say the three colors are red, blue, and green. We can represent the fraction of the wall occupied by each color as follows:

- Red: 1/3 x 1/2 = 1/6
- Blue: 1/3 x 1/2 = 1/6
- Green: 1/3 x 1/2 = 1/6

So each color occupies 1/6 of the painted area, which is equivalent to 1/12 of the whole wall. This means that if the wall was not split in half and we painted the entire wall with the same 3 colors, each color would occupy 1/12 of the total wall area.

In summary, if a whole wall is split in half and we painted half of the wall 3 colors, each color occupies 1/6 of the painted area, which is equivalent to 1/12 of the whole wall.

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The radius of the circle to the nearest 10th is 5.4

The formula for calculating the length of an arc of a circle is:

length of arc = radius x angle in radians

l = rθ

where

r = radius of the circle

l = length of arc

θ = angle in radians

From the question, we are given:

length of arc = 11.9

angle in radians (θ) = 2.2radians

The we can plug in the values

11.9 = r x 2.2

make r the subject of the formula

r = 11.9/2.2

r = 5.41 (to 2 decimal places)

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The minimum surface area of the box is 68 cm², which corresponds to option (d).

Let the side length of the square base be x and the height of the box be h. Then, we have:

Volume of the box = x²h = 32

h = 32/x²

The surface area of the box is given by:

S = x² + 4(xh) = x² + 4x(32/x²) = x² + 128/x

To find the minimum surface area, we can differentiate S with respect to x, set the derivative equal to zero, and solve for x:

dS/dx = 2x - 128/x² = 0

2x = 128/x²

x⁴ = 64

x = 2 cm

Note that we need to check that this critical point gives us a minimum surface area. We can do this by checking the second derivative:

d²S/dx² = 2 + 256/x³

d²S/dx² at x = 2 is positive,

indicating that this critical point gives us a minimum surface area.

Substituting x = 2 in the equation for S, we get:

S = 2² + 128/2 = 4 + 64 = 68

Therefore, the minimum surface area of the box is 68 cm², which corresponds to option (d).

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The rate of change of cost when the number of magazines printed per day is 17 is 752 dollars per print. The correct option is C.

The function C(x) = 25x² - 98x represents the cost of printing magazines per day at a printing press. To find the rate of change of cost when 17 magazines are printed per day, we need to calculate the derivative of the function with respect to x (the number of magazines printed), which represents the rate of change at a given point.

The derivative of C(x) with respect to x can be found using the power rule for differentiation. For a function of the form f(x) = [tex]ax^n[/tex], its derivative is f'(x) = [tex]n*ax^{(n-1)[/tex].

Applying the power rule to our function, we get:
C'(x) = 2(25x) - 98 = 50x - 98.

Now, we need to evaluate C'(x) when x = 17 (the number of magazines printed per day):
C'(17) = 50(17) - 98 = 850 - 98 = 752.

Therefore, the rate of change of cost when the number of magazines printed per day is 17 is 752 dollars per print. So, the correct answer is: C. 752$/print.

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The area of the regular figure of side length 24 cm is 1496.45 square centimeter.

The given regular figure is a hexagon.

A hexagon is a polygon with six sides and six angles.

It is a two-dimensional shape formed by connecting six straight line segments.

The side length of hexagon is 24 cm..

The formula for the area of a regular hexagon is 3√3/2 a².

Where a is the side length of hexagon.

Area =  3√3/2 a².

Plug in a value as 24:

Area = 3√3/2 ×24²

= 3√3×576/2

=2992.9/2

=1496.45 square centimeter.

Hence, the area of figure is 1496.45 square centimeter.

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Find the area of the regular figure below:​

The probability that the drug lasts less than 220 minutes for a random sample of 10 people is 0.0571, or about 5.71%.

To solve this problem, we need to use the normal distribution formula and the central limit theorem. The formula for the standard normal distribution is:

z = (x - μ) / σ

where z is the z-score, x is the observed value, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability that the drug lasts less than 220 minutes (3 hours and 40 minutes) for a random sample of 10 people. To do this, we first need to calculate the sample mean and the sample standard deviation.

The sample mean is the same as the population mean, which is 240 minutes:

μ = 240 minutes

The sample standard deviation is given by the formula:

σ = population standard deviation / sqrt(sample size)

σ = 40 minutes / sqrt(10) = 12.65 minutes (rounded to the nearest hundredth)

Now, we can calculate the z-score for a drug duration of 220 minutes:

z = (220 - 240) / 12.65 = -1.58 (rounded to the nearest hundredth)

We can use a standard normal distribution table or a calculator to find the probability that the z-score is less than -1.58. The probability is approximately 0.0571 (rounded to the nearest ten-thousandth).

Therefore, the probability that the drug lasts less than 220 minutes for a random sample of 10 people is 0.0571, or 5.71%.

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Answer:

y=9

Step-by-step explanation:

The opposite angles of 2 intersecting lines are equal.

11y-36⁰=63⁰

11y=63⁰+36⁰

11y=99⁰

y=9

Hope this helps!

Answer:

Step-by-step explanation:

To find the percentage of her total spending that she spent on Fun, we need to first find her total spending. We add up the amounts she spent in each category:

\begin{align*}

\text{Total spending} &= \text{Rent} + \text{Food} + \text{Fun} + \text{Other} \\

&= 1200 + 500 + 300 + 200 \\

&= 2200

\end{align*}

So Kara spent a total of $2200 this month.

To find the percentage of her spending that went towards Fun, we divide the amount spent on Fun by the total spending and then multiply by 100 to convert to a percentage:

300/2200 x 100 ≈ 13.6%

So Kara spent approximately 14% of her total spending on Fun.

Kritim's percentage profit is 8.5%.

Milan bought the table for Rs 3600 and sold it to Kritim at a profit of Rs 205. Hence, Kritim paid Rs 3600 + Rs 205 = Rs 3805 for the table. Kritim then sold the table to Aayush for Rs 4968.

To find Kritim's profit percentage, we need to calculate the profit percentage on the cost price. The cost price for Kritim is Rs 3805, and the selling price is Rs 4968. Hence, the profit earned by Kritim is Rs 4968 - Rs 3805 = Rs 1163.

Profit percentage = (Profit / Cost price) x 100%

Profit percentage = (1163 / 3805) x 100%

Profit percentage = 0.3055 x 100%

Profit percentage = 30.55%

Therefore, Kritim's profit percentage is 8.5%.

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The probability that at least one value is observed more than once when rolling a regular 6-sided die 5 times is approximately 0.598.

The total number of possible outcomes when rolling a die 5 times is 6⁵ = 7776 (since there are 6 possible outcomes for each roll and there are 5 rolls). To calculate the number of outcomes where no value is repeated, we can use the permutation formula: P(6,5) = 6! / (6-5)! = 6! / 1! = 720, since there are 6 possible outcomes for the first roll, 5 for the second roll (since one outcome has been used), and so on.

So, the probability of not observing any repeated values is P(no repeats) = 720 / 7776 ≈ 0.0926. Therefore, the probability of observing at least one repeated value is P(at least one repeat) = 1 - P(no repeats) ≈ 0.9074.

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Answer:

(x-4)^2+(y-1)^2=9

Step-by-step explanation:

diameter = 6

radius = diameter/2 = 3

center (h,k) = (4,1)

standard equation of a circle (x-h)^2 + (y-k)^2=r^2

(x-4)^2+(y-1)^2=9

The total area of the composite figure is 576 square meters

From the question, we have the following parameters that can be used in our computation:

The composite figure

The total area of the composite figure is the sum of the individual shapes

So, we have

Surface area = Rectangle + Trapezoid

Using the area formulas, we have

Surface area = 29 * 16 + 1/2 *(14 + 18) * (36 - 29)

Evaluate

Surface area = 576

Hence. the total area of the figure is 576 square meters

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Complete question

Find the area of the polygon.

See attachment

The area of the polygon is ____ square meters.

Answer:

To solve this problem, we need to find an integer to multiply the first equation by so that when we add the two equations together, the x term is eliminated. Let's first rearrange the equations to make them easier to work with:

1/18 x + 4/5 y = 10

-5/6 x - 3/4 y = 3

To eliminate the x term, we need to multiply the first equation by a certain integer so that when we add it to the second equation, the x terms cancel out. To do this, we need to find a common multiple of the denominators of the x coefficients in both equations, which are 18 and -6. The least common multiple of 18 and -6 is 18, so we can multiply the first equation by 18:

18(1/18 x + 4/5 y = 10)

Simplifying this equation, we get:

x + 72/5 y = 180

Now we can add this equation to the second equation:

x + 72/5 y = 180

-5/6 x - 3/4 y = 3

Multiplying the second equation by 15 to get rid of the fractions, we get:

-25/2 x - 45/4 y = 45

Now we can add the two equations together to eliminate the x term:

-25/2 x + x + 72/5 y - 45/4 y = 180 + 45

Simplifying this equation, we get:

-13/20 y = 225/4

Multiplying both sides by -20/13, we get:

y = -450/13

Therefore, the integer we need to multiply the first equation by is 18, which corresponds to option B.

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Considering the figures the scale factor is 1/4

Area of parallelogram QRST

= 9 square units

Area of parallelogram Q'R'S'T'

= 144 square units

The scale factor is solved using a reference side say QR and Q'R'

with QR = 12 and Q'R' = 3

the relationship is

QR * scale factor = Q'R'

12 * scale factor = 3

scale factor = 3/12 = 1/4

Area of parallelogram QRST

= base * height

= 3 * 3

= 9 square units

Area of parallelogram Q'R'S'T'

= 12 * 12

= 144 square units

The relationship between the areas are

9 square units * ( scale factor)² = 144

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The value of mean is 5.5 and the value of standard deviation is 1.44.

Now, we need to find the mean and standard deviation of this random variable. The mean of a uniformly distributed random variable can be found by taking the average of the lower and upper bounds of the distribution. In this case, the lower bound is 3 and the upper bound is 8, so the mean would be:

Mean = (3+8)/2 = 5.5

So, the expected number of tickets purchased by an individual is 5.5.

Next, we need to find the standard deviation. The standard deviation is a measure of the deviation or spread of the data from the mean. For a uniform distribution, the formula for standard deviation is:

Standard Deviation = (Upper Bound - Lower Bound) / √12

Plugging in the values, we get:

Standard Deviation = (8-3) / √(12) = 1.44

This means that on average, the number of tickets purchased by an individual is expected to deviate from the mean by about 1.44 tickets.

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We know that after 36 months, Martin will have to pay Richard P193,969.

Hi! Based on your question, Richard lends P154,600 to Martin at an 8.5% simple interest rate per annum, and the debt is payable after 36 months. To find out how much Martin will have to pay Richard after 36 months, we'll first calculate the interest.

Simple Interest = Principal × Rate × Time
Interest = P154,600 × 8.5% × (36 months / 12 months per year)
Interest = P154,600 × 0.085 × 3
Interest = P39,369

Now, add the interest to the principal to find the total amount Martin needs to pay Richard:
Total Amount = Principal + Interest
Total Amount = P154,600 + P39,369
Total Amount = P193,969

After 36 months, Martin will have to pay Richard P193,969.

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the distance between the two planes is |x - 19|. Since we don't have any information about the value of x, we cannot compute the exact distance. We can only give the answer in terms of |x - 19|, rounded to three decimal places.

To verify that the two planes are parallel, we need to check if their normal vectors are parallel. The normal vector of the first plane is <2, 0, 0> and the normal vector of the second plane is <2, 0, -4>. We can see that these vectors are parallel because they have the same direction but different magnitudes. Therefore, the two planes are parallel.

To find the distance between the planes, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the variables x, y, and z in the equation of one of the planes, and d is the constant term.

Let's use the first plane: 2x - 42 = 4

We can rewrite this as 2x - 38 = 0, which means that a = 2, b = 0, c = 0, and d = -38.

Substituting these values into the formula, we get:

distance = |2x + 0y + 0z - 38| / √(2² + 0² + 0²)
distance = |2x - 38| / 2
distance = |x - 19|

Therefore, the distance between the two planes is |x - 19|. Since we don't have any information about the value of x, we cannot compute the exact distance. We can only give the answer in terms of |x - 19|, rounded to three decimal places.

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The intermediate step in completing the square for x^2= -16x-37 is (x+8)^2=27.

To complete the square for the given equation, we need to add a constant value to both sides of the equation such that we can factor the left-hand side as a perfect square.

x^2 + 16x = -37

To determine the constant value we need to add to both sides, we take half the coefficient of x (which is 16/2 = 8) and square it to get 64. Then we add 64 to both sides of the equation:

x^2 + 16x + 64 = 27

Now we can factor the left-hand side as a perfect square:

(x + 8)^2 = 27

So the intermediate step in completing the square for x^2= -16x-37 is (x+8)^2=27.

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Answer:

---------------------------------

5) Use the combination formula:

In this case, n = 15 (total students) and r = 5 (students in a group).

Substitute and calculate:

The teacher can combine the students in 3003 ways for the first group.

6) After the first group of five is selected, there are 10 students remaining.

Again use the combination formula, with n = 10 and r = 5:

The teacher can combine the remaining students in 252 ways for the second group.