Find the center and radius of a circle with the equation below.

(x+3)2+(y−2)2=144

Answer:

∠ E = 70° , ∠ F = 40° , ∠ G = 70°

Step-by-step explanation:

given EF = FG then Δ EFG is isosceles with base angles congruent, that is

∠ G = ∠ E = 5n

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

4n - 16 + 5n + 5n

14n - 16 = 180 ( add 16 to both sides )

14n = 196 ( divide both sides by 14 )

n = 14

Then

∠ E = 5n = 5(14) = 70°

∠ F = 4n - 16 = 4(14) - 16 = 56 - 16 = 40°

∠ G = 5n = 5(14) = 70°

The probability that the archer gets exactly 4 bull's-eyes out of 8 shots is approximately 0.191

This is an example of a binomial distribution problem, where the archer has a probability of hitting the bull's-eye of 0.49 for each arrow and we want to know the probability of getting exactly 4 bull's-eyes out of 8 shots.

The probability of getting exactly 4 bull's-eyes out of 8 shots can be calculated using the binomial probability formula

P(X = k) = (n choose k) × p^k × (1-p)^(n-k)

where

X is the number of successes (bull's-eyes)

k is the specific number of successes we want (4 in this case)

n is the total number of trials (8 in this case)

p is the probability of success on a single trial (0.49 in this case)

(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (also written as "nCk")

Plugging in the numbers, we get

P(X = 4) = (8 choose 4) × 0.49⁴ × (1-0.49)⁴

= (8! / (4! × 4!)) × 0.49⁴ × 0.51⁴

≈ 0.191

Learn more about probability here

brainly.com/question/11234923

#SPJ4

Step-by-step explanation:

yes, the inequality is almost correct.

this is the fully correct one :

27 <= 12 + 6x

we want to get at least 27 gallons in the pool.

that means, if we hit exactly 27 gallons, it is a valid solution. therefore we need the "<=".

we want to get at least 27 gallons by starting with already existing 12 gallons and then adding 6 gallons for every minute (e.g. 5 minutes give us 5×6 = 30 gallons additional water).

so, now, let's solve :

27 <= 12 + 6x

15 <= 6x

15/6 <= x

2.5 <= x

therefore, it will take at least 2.5 minutes to fill the pool with at least 27 gallons.

Answer:

37.5 liters of water

Step-by-step explanation:

We Know

Mrs.Lim bought 25 bottles of water.

Each bottle contained 1[tex]\frac{1}{2}[/tex] liter of water.

How many liters of water did she buy altogether?

We Take

1.5 · 25 = 37.5 liters of water

So, she bought 37.5 liters of water.

The domain of f^(-1)(x) is [1, infinity), and the range of f^(-1)(x) is all real numbers.

We are given that;

Function f(z) = Y² + 1.

Now,

Step 1: Replace f(z) with y

y = z^2 + 1

Step 2: Swap x and y

z = y^2 + 1

Step 3: Solve for y

y^2 = z - 1

y = sqrt(z - 1)

Step 4: Replace y with f^(-1)(x)

f^(-1)(x) = sqrt(x - 1)

This is the inverse function of f(z).

Therefore, by domain and range answer will be all real numbers, and the range of f(z) is [1, infinity).

Learn more about the domain and range of the function:

brainly.com/question/2264373

#SPJ1

The probability of selecting two different counters that are of two different colors is 0.193

In the given question, we have a total of 20 counters, 8 are yellow and 12 are green.

The probability of choosing a 2 different colors will be;

P = 7/20 * 11/20

P = 77 / 400

P = 0.193

This is because the first probability of choosing a green is 11/20 and the second probability of choosing a yellow is 7/20. This is an example of probability without replacement

When we multiply both together to determine the probability of choosing different colors, we would have 0.193

Learn more on probability here;

https://brainly.com/question/23286309

#SPJ1

The surface area of the triangular pyramid is approximately 435.66 square millimeters.

The surface area of the triangular pyramid can be calculated by finding the area of the equilateral triangle base and the area of the three triangular faces, and then adding them together.

To find the area of the equilateral triangle base, we use the formula A = (√(3)/4) * a², where a is the length of one of the legs.

A = (√(3)/4) * 11.7² = 72.9444 mm²

To find the area of each triangular face, we use the formula

A = (1/2) * base * height

where the base is the side length of the equilateral triangle and the height is the slant height of the pyramid.

A = (1/2) * 11.7 * 12.3 = 71.9425 mm²

So, the surface area of the triangular pyramid is:

SA = 3A(Base) + 3A(face)

SA = 3(72.9444) + 3(71.9425)

SA = 435.6621 mm²

Therefore, the surface area of the triangular pyramid is approximately 435.66 square millimeters.

Learn More about surface area

https://brainly.com/question/16519513

#SPJ4

Required value of f(g(x)), g(f(x)), f(f(x)) are 2x²- 4x + 2 , 2x² -1 and 8x⁴ respectively.

the range of f(g(x)) is [0, ∞), the range of g(f(x)) = = 2x²-1 is [-1,∞) and the range of f(f(x)) is [0, ∞).

What is composition of functions?

Suppose we are given two functions f(x), g(x). We construct a new function h(x) as follows. plug 'x' into g(x) and find its value. then plugin this value into f(x), that is find f(g(x)). Now set h(x) = f(g(x)). This new function h(x) is called the composition of functions f(x) and g(x).

a. f(g(x)) = 2 * (x - 1)² = 2(x² - 2x + 1) = 2x²- 4x + 2 Since fg(x)) is a polynomial its domain is all real numbers. to find the range note that f(g(x)) = 2 * (x - 1) ² . and the range of the square is all non-negative real numbers. So the range of f(g(x)) is [0, ∞).

b. g(f(x)) = (2x²) - 1 =2x² -1.g(f(x)) is a polynomial function, so the domain of g(f(x)) is (-∞, ∞). Note that the range of 2x² is [0, ∞). So the range of g(f(x)) = 2x²-1 is [-1,∞)

c. f(f(x)) = 2 * (2x²)² = 2(4x⁴) = 8x⁴ . Since this is a polynomial function, the domain is (-∞, ∞), and clearly the range is [0, ∞).

To know more about composition of functions, visit:

https://brainly.com/question/5614233

#SPJ1

Answer: Cant really show you but use the picture below

Step-by-step explanation:

The slope is 2/5 or basically use the rise over run method. I would start with using x as 0. If so the y would be 3 as seen. So one point is (0,3). From there you can use another number and input it.

The area of this figure based on the information will be 10mm²

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

From the information, the shape gas sides 5mm and 2mm. The area of this figure will be:

= Length × Width

= 5mm × 2mm

= 10mm²

In conclusion, the area of this figure based on the information will be 10mm²

Learn more about area on:

brainly.com/question/2607596

#SPJ1

A shape gas sides 5mm and 2mm. What is the area of this figure 9mm 7mm 2mm 3mm 10mm

In the above case, the  law of joint proportionality is the one I am going to use to write the equation that stands for the above  situation:

V = k x h  x g²

Note that from the equation written:

V =  the volume of wood produced by the tree

h  = the height of the tree

g =  the circumference of the tree

k = a constant of proportionality.

For one to know the  value of k, we have to make use the data given in the problem.

Since h = 40 m

g = 1.5 m

V = 288 m³

Hence the volume of wood produced is:

288 = k   x  40 x (1.5)²

Simplifying this equation, we have:

288 = k    x  90

When we Divide both sides by 90, we have :

k = 3.2

So one can say  the equation that stands the situation is:

V = 3.2 x   h x  g²

Learn more about volume  from

https://brainly.com/question/27710307

#SPJ1

Answer:

y=41/3 and x = -14

Step-by-step explanation:

system of the linear equation :

-3y-4x=15       eq[i]

9y+7x=25      eq[ii]

multiplying eq[i] by -7 and eq[ii] by 4,we get

21y+28x= -105    eq[iii]

36y+28x= 100     eq[iv]

subtracting eq[iii] from eq[iv],we get

15y=205

y=205/15=41/3

and x= -14

The surface area of the given shape above would be = 47.2

To determine the surface area of the solid shape above,the surface area of a cone and a cylinder is first determined and then added together.

The formula for the surface area (SA) of cone = πrs + πr²

where;

r = 1

s = 6

S.A = 3.14×1×6 + 3.14×1×1²

= 18.84+3.14

= 21.98

Formula for Surface area of cylinder = 2πr(r+h)

where;

r = 1

h = 3

SA = 2×3.14×1 (1+3)

= 25.12

Therefore, the surface area of the solid shape = 21.98+25.22 = 47.2

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

The volume of the hemisphere whose radius is 6.8 ft. is 658.2 ft³ rounded to the nearest tenth

The radius of each hemisphere = 6.8 ft.

Volume of sphere = 4/3 πr³

A hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape

So by dividing the equation in half we get

Volume of hemisphere = (4/3 πr³ )/2

Volume of hemisphere = 2/3 πr³

Putting the value of r in the equation

Volume of hemisphere = 2/3 × 3.14 × (6.8)³

Volume of hemisphere = 658.2 ft³

To learn more about volume click here :

https://brainly.com/question/1578538

#SPJ4

The percentage of students that type less than 30 words per minute are given as follows:

30.61%.

An histogram is a graph that shows the number of times each element of x was observed, or the number of observations in each range of a data-set.

For the histogram in this problem, we have that:

The total number of students is given as follows:

5 + 10 + 14 + 20 = 49.

15 students type less than 30 words per minute, hence the percentage is given as follows:

P = 15/49 x 100%

P = 30.61%.

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

More can be learned about histograms at https://brainly.com/question/27436357

#SPJ1

The value of x as given in the above triangle is x = 12

A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle, in geometry.

The Pythagorean theorem, states that the square of the length of the hypotenuse is the same as the sum of the squares of the lengths of the other two sides, may be utilized in the calculation the length of the hypotenuse.

Since we have a 45-45-90 triangle, so the sides opposite of the 45-degree angle are the same, while the hypotenuse is √2

6√2(√2) = 6(2) = 12

x = 12

Recall that two of the same roots will become one whole number, for example

√2(√2) = 2

√3(√3) = 3

Learn more about Triangle:
https://brainly.com/question/2773823
#SPJ4

The number of dummy variables to be entered into a regression model is always equal to the number of groups (k) minus 1 because of a statistical concept known as "dummy variable trap" or "multicollinearity".

In the regression analysis we use the variable of dummy to represent a whole group and sort them into group that could be used further in the analyses. A dummy variable takes the value of 0 or 1, depending on whether the observation, belongs to a particular group or not in a data.

Let us assume that we have k groups, so we will need k-1 dummy variable to present the entire group where we create a situation when the sum of all the dummy variable is equal to 1. This creates a perfect multicollinearity, which makes the regression model impossible to estimate.

So, to avoid this problem, we eliminate one group from the model and use k-1 dummy variables to represent the remaining groups for the purpose of easiness in the analysis of the data that we are using for research.

To know more about multicollinearity, visit,

https://brainly.com/question/15856348

#SPJ4

The probability of pulling two skittles of the same colour in a row is 4/13.

Finding the likelihood that the first skittle will be any colour and then the likelihood that the second skittle will be the same colour as the first will allow you to calculate the likelihood of pulling two Skittles of the same colour in a row.

There are a total of 27 Skittles in the bag because there are 9 of each colour there. As a result, there is a one-in-one chance that the first skittle will be of any hue.

There will be a total of 26 skittles left in the bag when the first skittle is pulled, along with 8 skittles of the same colour. The likelihood that the second skittle will be the same colour as the first is thus

Probability = 8/26 or 4/13.

By adding these probabilities, we obtain:

1 x 4/13 = 4/13

Therefore, the probability of pulling two Skittles of the same colour in a row is 4/13.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

The Z-Score value for a particular sample with mean 70.07 and the standard deviation is 10.27 is equals to 0.97.

In statistics, the z-score is the numeric number of standard deviations by which t a raw score lies above or below the mean value. Positive z score represents value above the mean. We have a sample with sample mean, μ = 70.07

Standard deviations, σ = 10.27

We have to determine z score that corresponds to a raw score of 80. That is value of X = 80. Using the Z-Score formula, [tex]z = \frac{ X - \mu }{\sigma} [/tex]

where X --> raw value

μ --> mean

σ--> standard deviations

Substituents all known values in above formula, [tex]z =\frac{ 80 - 70.07}{10.27} [/tex]

[tex]z= \frac{ 9.93 }{10.27} [/tex]

= 0.97

Hence, required value is 0.97.

For more information about Z-score, refer:

https://brainly.com/question/28096232

#SPJ4

Area = 18 cm^2

Main steps:

Step 1: Identify the shape

Step 2: Use the correct formula for Area

Step 1: Identify the shape

First, we must identify that the shape is a trapezoid.  A trapezoid is a 4-sided shape that has one pair of parallel sides.  The two sides that are parallel to each other are called the "bases".

Observe that the top line and the bottom line have an arrow on each of them which denotes that those two sides are parallel.

Therefore, the shape is a trapezoid.

Step 2: Use the correct formula for Area

The area of a trapezoid is given by the following formula:

[tex]A_{Trapezoid} = \frac{1}{2}(b_1+b_2)h[/tex], where b1 and b2 are the two "bases", and h is the height (the perpendicular distance between the two parallel sides).  This amounts to finding the average of the two bases, and multiplying by the height.

[tex]A_{Trapezoid} = \frac{1}{2}(b_1+b_2)h[/tex]

[tex]A_{Trapezoid} = \frac{1}{2}((2 cm)+(4 cm))(6 cm)[/tex]

[tex]A_{Trapezoid} = \frac{1}{2}(6 cm)(6 cm)[/tex]

[tex]A_{Trapezoid} = 18 cm^2[/tex]

The correct formula to calculate the surface area of the cylinder is:

[tex]SA = 2\pi(1.2)^2 + 1.2\pi(3.8)[/tex]

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of a circular base and a curved surface that is formed by a set of parallel lines that are equidistant from the base. The base can be a circle, and the cylinder can have different heights.

To find the surface area of a cylinder, we use the formula:

[tex]SA = 2\pi r^2 + 2\pi rh[/tex]

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is pi (approximately 3.14).

The diameter of the cylinder is given as 2.4 centimeters, so the radius (r) is half of that, which is 1.2 centimeters. The height of the cylinder is given as 3.8 centimeters.

Therefore, the correct formula to calculate the surface area of the cylinder is:

[tex]SA = 2\pi(1.2)^2 + 1.2\pi(3.8)[/tex]

This simplifies to:

SA = 2π(1.44) + 4.56π

SA = 2.88π + 4.56π

SA = 7.44π

Finally, to find the amount of wrapping paper needed, we multiply the surface area by the number of cylinders we need to cover.

To learn more about cylinder visit:

https://brainly.com/question/30390407

#SPJ1

Answer:

67 miles per hour

Step-by-step explanation:

We can set up a proportion to find how many miles per hour this person travels:

268/4

=67

So, the rate is 67 miles per hour.

Hope this helps :)

— driving 268 miles in 4 hours is a total rate of 67 miles per hour

why???

268/4 = 67

The statements that are true about the plant are:

The plant did grow 4. 77 cm in two weeks as shown below :

= 2. 8 cm in first week + 1. 97 cm in second week

= 2. 8 + 1. 97

= 4. 77 cm

The plant grew faster in the first week than the second as the plant grew 2.8 cm in the first week and 1.97 cm in the second week, indicating a slower growth rate in the second week compared to the first week.

Find out more on length at https://brainly.com/question/24168462.

#SPJ4

Options for this question include:

The plant has grown a total of 4.77 cm in two weeks

The plant grew at a faster rate in the first week than the second week

The plant will be 100 cm tall after 50 weeks

The plant will require at least 5 cm of water per week to continue growing

The plant will die if it doesn't receive enough sunlight each day

About 1144π cubic inches (or approximately, 3591 cubic inches) of additional air is needed to fully fill the sphere-shaped balloon.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius.

In this case, the radius is 8 inches, so the volume of the balloon is:

V = (4/3)π(8^3)

V = 2144π cubic inches

The balloon already has 1000 cubic inches of air, so the amount of air still needed to fill the balloon is:

2144π - 1000 = 1144π cubic inches (rounded to the nearest whole number, this is approximately 3591 cubic inches).

For more information about volume, visit:

https://brainly.com/question/463363

#SPJ11

Answer:

  (a)  4.2

Step-by-step explanation:

You want an estimate of √18 to one decimal place.

The squares on either side of 18 are 4² = 16 and 5² = 25. The value 18 is about (18 -16)/(25 -16) = 2/9 of the way between these numbers. So, an estimate of the square root is ...

  4 + 2/9 ≈ 4.2

__

Additional comment

A fast way to improve the estimate is to take the average of this value and the quotient of 18 and this value:

  (4.2 +18/4.2)/2 ≈ 4.2429

Compare this to the actual root of 4.2426.

Using that same method again gives a value that matches the root when rounded to 8 decimal places.

The correct statement regarding the meaning of the conditional probability P(B|A) is given as follows:

C. The probability that the sum is 11, given that the first number cube shows a 6.

Conditional probability is the probability of one event happening, considering the result of a previous event.

The notation is P(B|A), which is read as the probability of B happening, considering that A has happened.

The events in this problem are given as follows:

Hence the correct statement regarding the meaning, that is, B given A = sum of 11 given that a six was rolled first, is given by option C.

More can be learned about conditional probability at https://brainly.com/question/10739997

#SPJ1

Concave hexagon with two pairs of congruent sides is:

   /\

   /  \

  /    \

 /      \

/        \

/_____\

\        /

\      /

 \    /

  \  /

   \/

A hexagon is a six-sided polygon. A concave hexagon is a hexagon with at least one interior angle greater than 180 degrees.

We can start with a regular hexagon, which has six congruent sides and six interior angles of 120 degrees each.

We can then extend two opposite sides of the regular hexagon outwards to create two pairs of congruent sides. The extended sides should not be parallel to each other, but rather at an angle, so that the resulting hexagon is concave.

Here is an example of a concave hexagon with two pairs of congruent sides:

   /\

   /  \

  /    \

 /      \

/        \

/_____\

\        /

\      /

 \    /

  \  /

   \/

In this hexagon, sides AB and CD are congruent, and sides EF and GH are also congruent. However, the angles at vertices A and H are greater than 180 degrees, making this a concave hexagon.

Learn more about congruent sides.

brainly.com/question/28911587

#SPJ11

The statement which is true include the following: B. The y-coordinates of the solutions to the system and the zeroes of the equation are not equal.

In Mathematics and Geometry, a polynomial graph simply refers to a type of graph that touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Generally speaking, the zero of a polynomial function simply refers to a point where it crosses or cuts the x-axis of a graph.

By critically observing the graph of the polynomial function shown in the image attached below, we can logically deduce that the y-coordinates of the solutions to the system of equations and the zeros of the equation are not equal;

3x³ + x = 2x + 1

P(x) = 3x³ + x - 2x - 1

3x³ + x - 2x - 1 = 0

Read more on polynomial here: https://brainly.com/question/4174466

#SPJ1