find the area and circumference of the following circles and show ur working
a)circle of radius 3cm
b)circle of 10 inch
c) circle of radius 12m
d)circle of radius 3km
e) circle of radius 9.8cm
f) circle radius 23.4mm​

The trigonometry functions when calculated are sin(A) = 18/34 and cos(A) = 30/34

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

The right triangle

Where we have

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

sin(A) = 18/34

cos(A) = 30/34

Hence, the values are sin(A) = 18/34 and cos(A) = 30/34

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The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The vertex is classified as a maximum or minimum depending on the term a, which multiplies x², as follows:

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The time takes by car to cover the distance between two cities by car varies inversely with the speed of car. Total 5 hours will consume to complete the trip with a car moving at 40 mph.

Time is taken in traveling a particular distance is proportional to the distance traveled which means more distance covered in more time.

The speed of an object is defined as the 'distance traveled per unit time'. Formula is written as [tex]Speed(s ) = \frac{Distance(d)}{Time(t)}[/tex]

Now, Speed of car (s) = 50 miles per hour

Car takes 4 hours to complete the trip. Let the distance travelled by car in 4 hour during the trip be 'x'. Applying the speed formula, [tex]50 mph = \frac{ x}{4 \: \: hours}[/tex]

=> x = 4 × 50 miles

=> x = 200 miles

Now, if the speed of car (s') = 40 mph in the trip. We have to determine the time taken by car to complete the trip with 40 mph speed. So, we know the speed of car and total distance travelled by car on trip. Using the time formula,[tex]time ( t') = \frac{distance (x) }{ speed( s')} [/tex]

=> [tex] time (t') = \frac{ 200 \: miles}{ 40 \: mph}[/tex]

= 5 hours.

Hence, required value of time is 5 hours.

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Complete question :

The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes four hours for a car moving at 50 mph. How long does the trip take for a car moving at 40 mph?

Ricardo used w/100 Ccf of water.

Given that, Ricardo household used w cubic feet of water in a month of summers,

we need to express the number of ccf of water they used algebraically,

Ccf = A CCF is a unit of measurement of volume.

The CCF is used to measure gas consumption, used in the billing of natural gas and water delivered to households.

1 CCF = 100 cubic feet

CCF means Centum Cubic Feet.

1 cubic feet = 0.01 Ccf

Therefore,

w cubic feet = 0.01 × w Ccf

= w / 100

Hence, Ricardo used w/100 Ccf of water.

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The walking distance that is saved by cutting across the lot is 55.

A right triangle, also known as a right-angled triangle, is a triangle that has one angle that measures 90° (a right angle). The remaining two angles are acute, or less than 90°

Apply right angle triangle rules;

⇒ 38² = (x+14)² + x²

⇒ 1444 = x² + 196 + 28x + x²

⇒ 2x² + 28x - 1248 = 0

⇒  x = 19 and x = -33

Therefore, the walking distance that is saved by cutting across the lot is:

⇒ x + x + 14

⇒ 19 + 19 + 14

⇒ 52

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Answer:

-34x+29

Step-by-step explanation:

[tex]7(5-x)-3(9x+2)=7.5-7x-3.9x-3.2=35-7x-27x-6\\=-34x+29[/tex]

Answer:

[tex]x=[/tex] ±[tex]\sqrt{10wy} - t[/tex]

Step-by-step explanation:

[tex](x+t)^2=10wy[/tex]

[tex]x+t=[/tex] ±[tex]\sqrt{10wy}[/tex]

[tex]x=[/tex] ±[tex]\sqrt{10wy} - t[/tex]

Answer:

The vertices of the image after rotating triangle uvw 90 degrees counterclockwise are u′(0, −2), v′(1, −3), w′(3, −3).

Step-by-step explanation:

The exponential function to represent the number of new participants of the challenge as a function of the day number, is f(x) = 12 × 4ˣ.

Let f(x) be the number of new participants on day x.

On day 0 (today), Aliyah, Kim, and Reese are the only participants. They each send selfies to 4 friends, so there will be 3 x 4 = 12 new participants on day 1.

From day 1 onwards, each new participant will send selfies to 4 friends. Therefore, the number of new participants will quadruple each day. This gives us an exponential growth function:

f(x) = 12 × 4ˣ

where f(x) represents the number of new participants on day x.

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Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.

To complete the basic step of the proof, we need to show that the statement p(n) is true for the smallest positive integer n, which is 1.

Let's plug n = 1 into the statement p(n):[tex]1^3 = (\frac{1(1 + 1))}{2})^2[/tex]

Simplifying the equation, we get:
[tex]1^3 = (1(2)/2)^2\\1^3 = (1^2)^2\\1 = 1[/tex]

Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.

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The statement is true for n=1, and we have completed the basis step of the proof.

To complete the basis step of the proof for the statement p(n), we need to show that it is true for the smallest positive

integer n, which is 1.

Our statement is:

[tex]1^3 + 2^3 + 3^3 + ... + n^3 = (n(n+1)/2)^2.[/tex]

For the basis step, let n = 1:

Left side: [tex]1^3 = 1[/tex]

Right side:[tex](1(1+1)/2)^2 = (1(2)/2)^2 = (1)^2 = 1[/tex]

Since the left side and the right side are equal, we have successfully completed the basis step of the proof for the statement p(n).

Therefore, the statement is true for n=1, and we have completed the basis step of the proof.

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Therefore, angles ZACB and ZAXB are congruent, and since they are complementary to angles ZAO and ZBO, respectively, they must be supplementary.

The Circumscribed Angle Theorem states that an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs. More formally, if two chords of a circle intersect at point P, then the measure of the angle formed by the chords (let's call it angle ABC) is equal to half the sum of the measures of the arcs intercepted by the angle.

Here,

To prove that ZAXB and ZACB are supplementary, we need to show that the sum of their measures is 180 degrees. Here's the proof:

Given: ZAXB is a circumscribed angle of circle C.

To Prove: ZAXB and ZACB are supplementary.

Proof:

Draw circle C with center O and circumscribed angle ZAXB.

Draw radii OA, OB, and OC to the points of intersection A, B, and C.

Since XA and XB are tangent to circle C at points A and B, respectively, we know that angles OAX and OBX are right angles.

Therefore, angles ZAO and ZBO are complementary to angles ZAC and ZBC, respectively.

By the Inscribed Angle Theorem, we know that angles ZAO and ZBO are congruent to angle ZAXB.

Therefore, angles ZACB and ZAXB are congruent, and since they are complementary to angles ZAO and ZBO, respectively, they must be supplementary.

Thus, we have proven that ZAXB and ZACB are supplementary.

Therefore, the proof is complete.

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The Riemann sum that represents the illustration on the graph is the second option as i goes from 1 to 4:

[tex]1∑2 {(xᵢ)}^{2} [/tex]

The Riemann sum is a mathematical concept used to approximate the area under a curve. It is named after the German mathematician Bernhard Riemann.

The idea behind the Riemann sum is to divide the area under the curve into a series of rectangles, where the height of each rectangle is determined by the function being integrated, and the width of each rectangle is determined by the size of the intervals used to divide the domain of the function. The area of each rectangle is then calculated and added together to get an approximation of the total area under the curve.

The Riemann sum is written in the following form:

[tex]∑f(xᵢ)Δxᵢ[/tex]

where f(xᵢ) is the value of the function at the ith point in the interval, Δxᵢ is the width of the ith rectangle, and the sum is taken over all i intervals.

Thus, the Riemann sum that represents the illustration on the graph as i goes from 1 to 4 is:

[tex]1∑2 {(xᵢ)}^{2} [/tex]

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Using the above information, we can calculate the missing figures in the table and this is shown on the table attached.

For the "Shorts" row: It's given that 42 people were wearing shorts.

Therefore, the "Close-Toed Shoes" column in the "Shorts" row is also 42, and the "Total" column is the sum of open-toed and closed-toed shoes, which is 84.

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See text below

30 people surveyed were wearing open-toed shoes.

1/3 of the people with open-toed shoes were wearing

pants.

• 42 people were wearing shorts.

Twice as many people were wearing closed-toed shoes

than open-toed shoes.

Complete the table using the information given.

                   Open-Toed Shoes              Close-Toed Shoes         Total

Shorts                     -------                           ------                               --------

Pants                         ------                           ----------                            ------

Total                          ------                           ----------                            ---------

Answer: 77

Step-by-step explanation: You could set up a proportion for this question. 1.5 centimeters = 3.5 meters x centimeters = 180 meters 1.5 x 180 / 3.5 Rounded to the nearest whole number, the answer is 77.

Each person would receive 10.67π square inches of pizza.

If 12 friends shared 8 small pizzas equally, we need to determine the amount of pizza each person would receive. To do this, we can start by calculating the total amount of pizza in all 8 small pizzas.

Assuming that each small pizza has the same size, we can divide the total amount of pizza by the number of people sharing it to get the amount of pizza each person would get.

Let's assume that each small pizza has an area of 10 square inches, for a total area of 80 square inches for 8 small pizzas. Dividing this area equally among 12 people, each person would receive approximately 6.67 square inches of pizza.

Alternatively, if we assume that each small pizza has a diameter of 8 inches, we can use the formula for the area of a circle to calculate the total area of each small pizza:

Area = π x (radius)^2

Area = π x (4 inches)^2

Area = 16π square inches

For 8 small pizzas, the total area would be:

Total area = 8 x 16π = 128π square inches

Dividing this area equally among 12 people, each person would receive approximately 10.67π square inches of pizza.

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The scale factor that takes triangle C to triangle D is 3/10.

Scale factor is a number by which the size a geometrical figure or shape can be changed with respect to its original size.

To find the scale factor that takes triangle C to triangle D, we use the formula below

Formula:

Where:

From the diagram in the question,

Given:

Substitute these values into equation 1

Hence, the scale factor is 3/10.

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Answer:

A(-6,0) B(-1,0) C(0,6)

Step-by-step explanation:

The measure of angle ZCOD is 27°.

Since A, O, and B are collinear, angles AOC and COB form a linear pair, which means their sum is 180°. Therefore:

x + 50° = 180°

Solving for x, we get:

x = 130°

Next, we can use the fact that angles AOC and BOA are vertical angles, which means they are congruent. Therefore:

x = 103°

Substituting x with 130°, we get:

130° = 103° + COD

Solving for COD, we get:

COD = 27°

Finally, since angles AOD and COB are alternate interior angles, they are congruent. Therefore:

77° = 50° + ZCOD

Solving for ZCOD, we get:

ZCOD = 27°

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--The complete question is, Given that points A, O, and B are collinear, find the measure of angle ZCOD, where:

Angle AOC is denoted by x and measures 90°

Angle BOA measures 103°

Angle AOD measures 77°

Angle COB measures 50°.

Please note that point O is located between points A and B.--

The optimal measure of variability is the IQR, which equals 4. The proper measure of variability for the data is C.

The difference among the third and the first quartile is defined by the interquartile range. The entire series is divided into four equally sized pieces by the partitioned values referred to as quartiles. Three quartiles are present.

The spread of the middle 50% of the data, which is less susceptible to outliers than the range, is measured by the interquartile range (IQR), which is the best measure of variability for these data.

The IQR is calculated by deducting the third quartile ([tex]Q_3[/tex]) from the first quartile ([tex]Q_1[/tex]). We can see from the box plot that [tex]Q_1[/tex] is roughly

17 and [tex]Q_3[/tex] is roughly 21.

Therefore,

[tex]IQR=Q_3-Q_1\\\\IQR=21-17\\\\IQR=4[/tex]

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Answer: 4

Step-by-step explanation:

Given:

   [tex]2log_62+3log_63+log_612[/tex]

Rewrite using the power property:

   [tex]log_62^2+log_63^3+log_612[/tex]

Rewrite by adding the logarithms together (multiplying) since they all have a common base of 6:

   [tex]log_6(2^2*3^3*12)[/tex]

Simplify by multiplying:

   [tex]log_6(4*27*12)[/tex]

   [tex]log_6(1,296)[/tex]

Evaluate the logarithm:

   [tex]log_6(1,296)[/tex]

   4

The probability that the man will hit his target at least once in 4 shots is calculated using the complementary probability of him missing all 4 shots. Since he hits his target 25% of the time, he misses it 75% of the time.

The probability of missing all 4 shots is (0.75)^4 = 0.3164.

Now, to find the probability of hitting the target at least once, subtract the probability of missing all shots from 1:

1 - 0.3164 = 0.6836 or 68.36%.

So, the probability that the man will hit his target at least once in 4 shots is approximately 68.36%.

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The equation of the line 2x + 3y + 1 = 0 after it has been reflected across y = -1 and rotated about O(2,3) by 180 degrees is -2x + y = 15.

To reflect the line 2x + 3y + 1 = 0 across the line y = -1, we need to subtract twice the y-coordinate of each point on the line from the equation of the line.

This is because the reflection of a point across a line is obtained by reflecting it across the line's perpendicular bisector, which is also the line with the same x-coordinates and twice the distance from the point to the line.

Subtracting twice the y-coordinate, we get:

2x + 3(-2y - 1) + 1 = 0

Simplifying the equation, we get:

2x - 6y - 5 = 0

Now, to rotate the line about the point O(2,3) by 180 degrees, we can use the rotation formula:

x' = 2a - x

y' = 2b - y

where (x,y) are the coordinates of a point on the original line, and (x',y') are the coordinates of the same point after rotation about the point (a,b).

Substituting the coordinates of two points on the line, we get:

(0,-1) → x' = 2(2) - 0 = 4, y' = 2(3) - (-1) = 7

(-1/2,0) → x' = 2(2) - (-1/2) = 4 1/2, y' = 2(3) - 0 = 6

Now, we can use the two points (4,7) and (4 1/2,6) to find the equation of the rotated line using point-slope form:

slope = (6-7) / (4 1/2 - 4) = -2

y - 7 = -2(x - 4)

y = -2x + 15

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Answer:

The center of the circle is at (-6, 14), and the radius is 15, so we have this equation:

[tex] {(x + 6)}^{2} + {(y - 14)}^{2} = 225 [/tex]

If the  volume of a volleyball is approximately 113 in³, then the diameter of the volleyball is approximately option (D) 5 inches.

The formula for the volume of a sphere is

V = (4/3)πr³

where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.

We are given the volume of the volleyball as 113 in³, so we can solve for the radius as follows

113 = (4/3)πr³

r³ = 113 / ((4/3)π)

r³ ≈ 21.50

r ≈ 2.8

To find the diameter, we double the radius:

d = 2r ≈ 5.6

Rounding this to the nearest whole number

d = 5 in

Therefore, the correct option is (D) 5 in

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Answer:

Step-by-step explanation:

the 32 pack because it costs just slightly more

We need at least 3.465 gallons of paint to paint the walls of this room.

The area of the two rectangular faces on either end of the prism is:

length x height = 17 x 12 = 204 square feet

The area of the two rectangular faces on the sides of the prism is:

width x height = 15 x 12 = 180 square feet

The area of the top and bottom faces of the prism is:

length x width = 17 x 15 = 255 square feet

The total surface area of the prism is:

2(204) + 2(180) + 2(255) = 1386 square feet

Now, we divide surface area by coverage of one gallon of paint:

1386 / 400 = 3.465

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In an expression using the logical operator And Also, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false.

The And Also operator is a short-circuiting operator that is used to combine two or more Boolean expressions. It evaluates the left-hand expression first and then the right-hand expression only if the left-hand expression evaluates to true

. If the left-hand expression evaluates to false, then the right-hand expression is not evaluated at all. This helps to improve the performance of the code by avoiding unnecessary evaluations of expressions that would not change the outcome of the overall condition.

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In an expression using the logical operator And Also , as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. Therefore option c. And Also correct.

This is because the AndAlso operator employs short-circuit evaluation, meaning it stops evaluating once it encounters

the first false condition since the overall result will definitely be false.

In an expression using AndAlso, if the first condition is false, the entire expression is evaluated as false without testing

any further conditions. This is also known as short-circuit evaluation.

In contrast, the OrElse operator evaluates to true as soon as one of the compound conditions is true, without testing

any further conditions. The Nor and Xor operators are less commonly used and have different behavior.

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A congruence transformation that maps triangle RST to triangle UVW is a reflection along the line y = 1, followed by a translation 2 units right and down by 1 units.

A congruence transformation that maps triangle RST to triangle UVW is a rotation of 180°, followed by a translation 2 units left and down by 5 units.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-images underwent a sequence of congruence transformations to produce the images.

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Answer:

Step-by-step explanation:

The absolute value (or modulus) | 5 - 3x | of a real number  5 - 3x is the non-negative value of 5 - 3x without regard to its sign.

| 5 - 3x| + 2 = 19

| 5 + 3x | = 19 - 2

| 5 + 3x | = 17

Ans: D

Answer: First choice 480t = 300t + 900

Step-by-step explanation:

A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.  

On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.

Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.

ANS

Let say t is time in hrs for Which Both Assembly line worked

M made 300 toys per hr on Tuesday

Toys made on Tuesday at Assembly line M = 300 × t  = 300t  toys

N made 480 toys per hr on Tuesday

Toys made on Tuesday at Assembly line N = 480 × t  = 480t  toys

Toys Made by N on Tuesday  = Toys made by M on Tuesday + Toys made by M on Monday

480t = 300t + 900

=> 180 t = 900

=> t = 900/180

=> t = 5 hr

N capacity on tuesday Per hour * t  = M capacity on tuesday per hour  * t  + Toys made by M on Monday

N = N capacity on tuesday Per hour

M = M capacity on tuesday Per hour

=> t (N - M ) = 900

=> t = 900/(N-M)