A circle is centered at (4, −7) and has a radius of 5. Which of the following is the equation of this circle?

Group of answer choices

(x − 4)2 + (x + 7)2 = 5

(x − 4)2 + (x + 7)2 = 25

(x + 4)2 + (x − 7)2 = 5

(x + 4)2 + (x − 7)2 = 25

Answer:

  (-2, -1)

Step-by-step explanation:

You want the point that is 4 units left of (2, -1).

The x-coordinate of an (x, y) coordinate pair tells you the number of units to the right of the x=0 point. It increases for points farther right, and decreases for points farther left.

Moving left 4 units decreases the x-coordinate by 4 units. The x-coordinate of 2 becomes ...

  2 -4 = -2

The coordinates of the moved point are (-2, -1).

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When w = 10 and z = 2, the value of expression 2w⁻²z⁰ is equal to 1/50. So, correct option is A.

The expression 2w⁻²z⁰ can be simplified as follows:

2w⁻²z⁰ = 2/w² * z⁰

Since z⁰ = 1 for any non-zero value of z, we can simplify further:

2w⁻²z⁰ = 2/w² * 1

Now we can substitute w = 10 into the expression:

2(10)⁻² * 1 = 2/100 = 1/50

In general, when we have a negative exponent in an expression, we can rewrite it as a positive exponent in the denominator. In this case, w⁻² can be rewritten as 1/w². Additionally, any number raised to the power of 0 is always 1, so z⁰ = 1. By simplifying the expression, we can easily substitute the given values of w and z to evaluate the expression.

So, correct option is A.

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The standard form of the equation for the circle is (x - 3)² + (y - 2)² = 8.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.

Based on the information provided above, we have the following parameters:

Radius, r = √[(3 - 5)² + (2 - 4)²] = √8

Center, (h, k) = (3, 2).

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 3)² + (y - 2)² = (√8)²

(x - 3)² + (y - 2)² = 8.

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Complete Question:

A circle is shown on the coordinate plane. The graph shows a circle with the origin point A at (3, 2), and a point B on its circumference at (5, 4) and intersects the x-axis at 1 and 5 units. What is the standard form of the equation for the circle?

Answer:

Step-by-step explanation:

If the hypotenuse of a right triangle is twice the length of the shorter leg and the shorter leg is 4 cm, then the hypotenuse is 2 * 4 cm = 8 cm.

Using the Pythagorean theorem, we can find the length of the longer leg. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Letting c represent the length of the hypotenuse and a and b represent the lengths of the other two sides, we can write this as c^2 = a^2 + b^2.

Substituting in the known values for c and one of the other sides (let’s say a), we have:

8^2 = 4^2 + b^2 64 = 16 + b^2 b^2 = 48 b = sqrt(48)

So, the length of the longer leg is sqrt(48) cm, or approximately 6.93 cm.

In a circle, the measure of a central angle is equal to the measure of its intercepted arc. Since ∠RST is a central angle of circle S and its measure is 102 degrees, the measure of its intercepted arc ⌢RT is also 102 degrees.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since RS is a radius of circle S and its length is 6 units, the circumference of circle S is C = 2π * 6 = 12π units.

The length of an arc is proportional to its measure in degrees. Since the measure of ⌢RT is 102 degrees and the total measure of a circle is 360 degrees, the length of ⌢RT is (102/360) * 12π = 3.4π units.

Rounded to the nearest hundredth, this is approximately 10.68 units.

Answer:

Set 1: {10, 19, 38, 50, 51}

Step-by-step explanation:

To calculate the standard deviation of a data set, we first find the mean of the data set. The mean is simply the sum of all the values in the data set divided by the number of values. For example, the mean of Set 1 is:

(10+19+38+50+51)/5=33.6

Next, we find the variance of the data set. The variance is the average of the squared differences between each value in the data set and the mean. For example, the variance of Set 1 is:

((10−33.6)^2+(19−33.6)^2+(38−33.6)^2+(50−33.6)^2+(51−33.6)^2)/5=323.84

Finally, we take the square root of the variance to get the standard deviation. For example, the standard deviation of Set 1 is:

[tex]\sqrt{323.84}[/tex]=17.99

We can repeat this process for each of the four data sets and find that Set 1 has the largest standard deviation.

after 1000 years, there will be approximately 218.7 mg of Radium-226 remaining in the sample. use formula for radioactive decay to solve

what is radioactive decay ?

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, such as alpha particles, beta particles, and gamma rays. The decay occurs in order to achieve a more stable configuration of the nucleus.

In the given question,

The formula for radioactive decay is:

N(t) = N0 * (1/2)ᵃ⁾ᵇ

where:

N(t) is the amount of radioactive material at time t

N0 is the initial amount of radioactive material

t is the time elapsed since the initial measurement

T is the half-life of the radioactive material

We can use this formula to solve the problem as follows:

N0 = 500 mg (the initial amount)

T = 1590 years (the half-life)

t = 1000 years (the time elapsed)

N(t) = 500 * (1/2)¹⁰⁰⁰⁾ ¹⁵⁹⁰

N(t) = 500 * 0.4374

N(t) = 218.7 mg

Therefore, after 1000 years, there will be approximately 218.7 mg of Radium-226 remaining in the sample.

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The equation 5ʷ ⁺ ³ = 17 when solved for w is approximately w = 0.41 and the solution to the inequality is b ≤ 1.87

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

5ʷ ⁺ ³ = 17

Take the logarithm of both sides

So, we have

w + 3 = ln(17)/ln(3)

Evaluate the quotient

This gives

w + 3 = 2.59

So, we have

-3 + w + 3 = 2.59 - 3

Evaluate

w = 0.41

For the second expression, we have

2ᵇ ⁺ ¹ ≤ 7.31

Take the logarithm of both sides

So, we have

b ≤ ln(7.31)/ln(2) - 1

So, we have

b ≤ 1.87

Hence, the equation when solved for w is approximately w = 0.41

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The value of p in the expression is 45

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.

For example a+5 = 2 , by solving this we add the additive inverse of 5 to both sides. The additive inverse of 5 is -5

this means,

a+5-5 = 2-5

a = 2-5

a = -3

Similarly, p-42 = 3 is solved in the same way. we add the additive inverse of -42 which is +42 to both sides,

p-42+42 = 3+42

p = 3+42

p = 45

therefore the value of p is 45

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ans. 1400000

we know that

work done by gravity =  mgh

just putting values we get

= 1400x 100 x 10

= 1400000

hence,work done an elevator motor need to do to lift a 1400kg elevator a height of 100m is 1400000

Answer:

The anser is letter C)

Step-by-step explanation:

because it multiplies x3

0,5×3=1,5

1,5×10=15

10×3=30

Answer:

1cm=30m

The total charge if 138 guests attend the conference is $5450

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

Using the above as a guide, we have the following:

Total = ballroom + food * number of guests

Substitute the known values in the above equation, so, we have the following representation

Total = 620 + 35 * 138

Evaluate

Total = 5450

Hence, the total charges is $5450

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The solution of the trigonometric equation on the interval (, 360) is

A trigonometric equation is an equation that contains trigonometric ratios.

Given the trigonometric equation

2sinx = 1 - cosx, we proceed to solve for x as follows.

Since 2sinx = 1 - cosx

Using sin²x = 1 - cos²x

⇒ sinx = √(1 - cos²x )

Substituting this into the equation, we have that

2sinx = 1 - cosx

2√(1 - cos²x ) = 1 - cosx

Squaring both sides, we have that

[2√(1 - cos²x )]² = (1 - cosx)²

4(1 - cos²x ) = (1 - cosx)²

4 - 4cos²x = 1 - 2cosx + cos²x

Collecting similar terms, we have that

1 - 4 - 2cosx + 4cos²x + cos²x = 0

- 3 - 2cosx + 5cos²x = 0

Re-arranging the equation, we have that

5cos²x - 2cosx - 3 = 0

Let cosx = y

So, we have that

5y² - 2y - 3 = 0

Factorizing, we have that

5y² - 2y - 3 = 0

5y² - 5y + 3y - 3 = 0

5y(y - 1) + 3(y - 1) = 0

(5y + 3)(y - 1) = 0

⇒ 5y + 3 = 0 or y - 1 = 0

⇒ 5y = -3 or y = 1

⇒ y = -3/5 or y = 1

Since y = cosx, we have that

cosx = -3/5 or cosx = 1

cos(180° - x) = 3/5 or cos(270° - x) = 3/5 or cosx = 1

Taking inverse cosine, we have that

180° - x = cos⁻¹(3/5) or 270° - x = cos⁻¹(3/5) or x = cos⁻¹(1)

180° - x = 53.13° or 270° - x = 53.13° or x = 90°

x = 180° - 53.13° or x = 270° - 53.13° or x = 90°

x = 126.87° or x = 216.87 or x = 90°

So, the solution is

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a) Approximately 84% of the people are at least 26.5 years old. So, about 3528 people (0.84 * 4200).

b) Approximately 16% of the people are less than 26.5 years old. So, about 672 people (0.16 * 4200).

a) 26.5 years is 1.5 years (18 months) less than the mean (28 years). This is 1 standard deviation (18 months) below the mean.

The 68-95-99.7 Rule states that 68% of the data falls within 1 standard deviation of the mean. So, 100% - 68% = 32% is outside 1 standard deviation.

Since it's symmetrical, one-half of that 32% (16%) is less than 26.5 years, and the other half (16%) is older than 29.5 years.

Consequently, 100% - 16% = 84% is over 26.5 years old. If you multiply 0.84 by 4200, you get 3528 people.

b) As calculated earlier, 16% of the people are less than 26.5 years old. 0.16 * 4200 = 672 people.

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The area of the circle with a diameter of 22 in in terms of pi is 121π in².

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

Where r is radius and π is constant pi.

Given that:

The diameter of the circle is 22 inches.

Radius is half of diameter

Hence:

Radius r = diameter/2 = 22/2 = 11 in

Plug the value into the above formula and solve for area.

A = πr²

A = π × ( 11 in )²

A = 121π in²

Therefore, the area is 121π in².

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Answer:

  x < -1 or x ≥ 5

Step-by-step explanation:

You want the solution and its graph for the compound inequality ...

Adding 2 to the first inequality gives ...

  3x < -3

  x < -1 . . . . . divide by 3

Multiplying the second inequality by -1/2 gives ...

  x ≥ 5

The solution is x < -1 or x ≥ 5.

The total amount of interior angles featured on a polygon with 'n' sides can be determined through the equation (n-2)*180 degrees. This formula applies to all types of polygons, such as triangles.

In order to calculate the sum of each individual angle in the polygon, we must consider the total degree measure formed within each triangle. Every triangle consists of three different sized interior angles that together form an count of 180 degrees.

For instance, when a polygon containing 'n' sides is divided into separate triangles by interconnecting certain vertices, the overall number of triangles produced can be worked out using the equation (n-1). A square, for example, can be broken down into two distinctive triangles, whereas a pentagon structures five triangles, and finally, a hexagon results in four.

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Answer:

Step-by-step explanation:

House

B) Down Payment: $151,800

C) $607,200

D) $819,720

E) $1,426,920

F) $47,564

Car:

B) $2,902.50

C) $16,447.50

D) $3,700.6875 = $3,700.69

E) $20,148.1875 = $20,148.19

F) $335.803125 = $335.80

DONE !!! :)

The three types of rock are igneous, sedimentary, and metamorphic.

There are three types of rocks as explained below.

Igneous rocks are formed from the cooling and solidification of molten rock, either on the Earth's surface (extrusive) or beneath the surface (intrusive). Examples of igneous rocks include basalt, granite, and pumice.

Sedimentary rocks are formed from the accumulation and cementation of sediment particles (such as sand, silt, and clay) or the precipitation of minerals from a solution. Examples of sedimentary rocks include sandstone, limestone, and shale.

Metamorphic rocks are formed from the alteration of pre-existing rocks by heat, pressure, and chemical reactions. Examples of metamorphic rocks include marble, slate, and gneiss.

The rock cycle is the process by which one type of rock can be changed into another type of rock.

The rock cycle involves three main processes:

Therefore, one type of rock can be changed into another type of rock through the rock cycle by undergoing weathering, erosion, deposition, lithification, metamorphism, melting, and solidification, depending on the specific conditions and processes involved.

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Observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.

A histogram is a graph that displays the values of a numeric variable's distribution as a collection of bars.

The height of a bar represents the frequency of data points with values falling within the relevant bin; each bar typically spans a range of numerical values known as a bin or class.

Similar to a bar chart, a histogram is produced with bars of varying widths.

In a histogram, the frequency is revealed by the bar's area rather than its height.

We plot the frequency density rather than frequency on the y-axis. To figure this out, divide a group's frequency by its width.

So, the x-axis of the given histogram represents the mass of the pumpkins.

The y-axis of the histogram represents the number of pumpkins.

Then, the pumpkins with greater mass than 6 kilograms:

= 8 + 6 + 2

= 16

Therefore, observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.

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Answer:

x = 3, -5/2

Step-by-step explanation:

First, you move the 15 onto the left of the equation by subtracting it from both sides.

Second, you plug your info into the quadratic equation.  (1 +- sqrt(1+4*15*2))/4

Suppose that the production of plastic creates a social cost which is depicted in the graph above. Without any government regulation, about 650 units of plastic will be produced. (Option C)

This is because, when the market forces are left to play out, competition drives efficiency upwards, which enable suppliers to produce at lower price thus offering consumers more quantity demanded for lower prices.

Hence, without government intervention, the unit produced will be 650 at the price of 7.

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Answer:

CA - 144

AD - 98

ABD - 49

BC - 134

C - unsure

Step-by-step explanation:

Answer:

Set your calculator to degree mode.

Please sketch the figure to confirm my answer.

cos(38°) = 320/d

d•cos(38°) = 320

d = 320/cos(38°) = 406.1 feet

A sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

To estimate the sample size needed to estimate the population mean with 98% confidence to within $100, we can use the formula:

n = (z * σ / E)²

where:

n = sample size

z = z-score for the desired level of confidence (98% in this case), which can be found using a standard normal distribution table or calculator. For 98% confidence, the z-score is approximately 2.33.

σ = population standard deviation ($800 in this case)

E = margin of error ($100 in this case)

Plugging in the values, we get:

n = (2.33 * 800 / 100)²

n ≈ 432.64

Rounding up to the nearest whole number, we get a sample size of 433. Therefore, a sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

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The best approx. for mean of 10,000 sample means is equal to the population mean which is 84. The Option C is correct.

According to central limit theorem, the distribution of sample means from a large sample size will be normal regardless of the shape of the population distribution.

This is because the mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

The standard deviation of distribution of sample means will be:

= Population standard deviation / √sample size

= 7.2 / √100

= 0.72

So, the best approximation for the mean of 10,000 sample means is equal to the population mean which is 84.

Full question "Suppose we have a large population with mean = 84 and standard deviation = 7.2. 10 points Let's say we randomly sample 100 values from this population and compute the mean, then repeat this sampling process 10,000 times and record all the means we get.  Which of the following is the best approximation for the mean of our 10,000 sample means? A. 8.4 b. 100 c. 84"

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The sum of 125 (base 7) and 256 (base 7) is 404 (base 7). To compute it, we convert each number to base 10, add them, and then convert the result back to base 7.

Write each number in expanded form using powers of 7.

125 (base 7) = 1 x 7² + 2 x 7¹ + 5 x 7⁰ = 49 + 14 + 5 = 68

256 (base 7) = 2 x 7² + 5 x 7¹ + 6 x 7⁰ = 98 + 35 + 6 = 139

Add the two numbers together to get the sum in decimal form.

68 + 139 = 207

Convert the decimal sum to base 7 using repeated division by 7.

Divide 207 by 7 to get a quotient of 29 and a remainder of 4. Write down the remainder as the rightmost digit in the base 7 representation. Divide 29 by 7 to get a quotient of 4 and a remainder of 1. Write down the remainder as the next digit to the left in the base 7 representation.

Divide 4 by 7 to get a quotient of 0 and a remainder of 4. Write down the remainder as the leftmost digit in the base 7 representation.

So the sum of 125 (base 7) and 256 (base 7) is 404 (base 7).

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