An image formed by a circular spotlight has a radius of 124 centimeters. What is the area of the circular image? Use 3.14 for pi (TT).A. 48,280.64 cm2B. 23,768 25 cm2C. 44,728 15 cm2D. 39,824 88 cm2

The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.

Part A: The absolute value inequality that describes the range of the actual weight of the object is:

|w - 125.8| ≤ 0.4

Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:

w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4

Solving the first inequality:

w - 125.8 ≤ 0.4

Add 125.8 to both sides:

w ≤ 126.2

Solving the second inequality:

-(w - 125.8) ≤ 0.4

Multiply by -1 and distribute the negative sign:

-w + 125.8 ≤ 0.4

Subtract 125.8 from both sides:

-w ≤ -125.4

Divide by -1 (note that the inequality direction flips):

w ≥ 125.4

Combining the solutions, we have:

125.4 ≤ w ≤ 126.2

The object is 125.4 ≤ w ≤ 126.2.

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Answer:

206 ft

Step-by-step explanation:

Each wire is a hypotenuse of a right triangle in which the height of the tower is one leg and the distance from the anchor of the wire to the base of the tower is the other leg.

Leg 1: 200 ft

Leg 2: 50 ft

Hypotenuse: x

200² + 50² = x²

x² = 40,000 + 2,500

x² = 42,500

x = √42,500

x = 206

Answer: 206 ft

Answer:

  \(\left(\dfrac{1}{2},-\dfrac{\sqrt{3}}{2}\right)\)

Step-by-step explanation:

An angle is co-terminal with the same angle that has any multiple of 360° added to it.

__

The angle -420° is co-terminal with (-420° +720°) = 300°. The attached unit circle chart shows the coordinates of the terminal side of that angle.

These coordinates are ...

  (x, y) = (cos(300°), sin(300°))

  (x, y) = (1/2, -√3/2)

To find arcsin, we need to use the identity:

sin(arcsin(x)) = x

Since arcsin is negative, sin(arcsin) is also negative. Therefore, we can say:

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

where (cos)^2 = 8/17

Substituting, we get:

sin(arcsin) = -sqrt(1 - (8/17))

Simplifying, we get:

sin(arcsin) = -sqrt(17/17 - 8/17)

Simplifying further, we get:

sin(arcsin) = -sqrt(9/17)

Therefore, arcsin = -sqrt(9/17)

To find arctan, we need to use the identity:

tan(arctan(x)) = x

Substituting, we get:

tan(arctan) = -8/17

Therefore, arctan = -8/17

So, arcsin is -sqrt(9/17) and arctan is -8/17.

Answer:

4-6x

Step-by-step explanation:

let the number be =x

4-6x

The mathematical expression is,

⇒ 6m - 4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

“four less than six times a number m”

Now,

Since, The algebraic expression is,

“four less than six times a number m”

Hence, We can formulate the mathematical expression as;

⇒ 6 × m - 4

⇒ 6m - 4

Thus, The mathematical expression is,

⇒ 6m - 4

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If the total height between two floors is 9'0 1/2" and 14 risers are to be used in a set of stairs, the height of each riser would be approximately 7.75 inches.

To find the height of each riser in a set of stairs given the total height between two floors, we need to divide the total height by the number of risers.

First, let's convert the total height to a consistent unit. The distance between two floors is given as 9'0 1/2". We can convert this to inches by multiplying the feet by 12 and adding the remaining inches:

9 feet = 9 * 12 = 108 inches

0 1/2 inch = 0.5 inch

Total height = 108 + 0.5 = 108.5 inches

Next, we divide the total height by the number of risers (14) to find the height of each riser:

Height of each riser = Total height / Number of risers

Height of each riser = 108.5 inches / 14

Using a calculator, we can compute:

Height of each riser ≈ 7.75 inches

Therefore, the height of each riser in the set of stairs would be approximately 7.75 inches.

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Answer: D

Step-by-step explanation:

Answer:

Step-by-step explanation:

sin = opposite / hypotenuse

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer: He is incorrect.

Step-by-step explanation:

The question says:

"tea drinkers in Canada is 4:1"

We only have that, so i guess that this means:

"The ratio of nonregular tea drinkers to regular tea drinkers in Canada is 4:1"

The ratio 4:1 means that for each 4 non-regular tea drinkers, there is one regular tea drinker.

Now let's multiply both by 100.

For each 400 nonregular tea drinker, there are 100 regular tea drinkers, if we add them we have a total of 500

Then the statement would be if 500 people were surveyed, 100 of the would most likely be regular tea drinkers.

Answer:

3/15, 1/5, or 0.2 probability. Highly unlikely

Explanation:

12/15 is the shown probability. The leftover is 3/15, so 3/15 is the chance of missing the basket.

~Hope this helps~

Step-by-step explanation:

11.

As all the exterior angles of a pentagon add up to 360, [ because exterior angle of a polygon = n(360/n) where n = no. Of sides, As the number of sides in a pentagon is 5, n=5. Thus, the sum of exterior angles of a pentagon = 5(360°/5) = 360°.]

THEN,

56 + 2x + 85 + 57 + 4x = 360

6x + 198 = 360

6x = 360 - 198

X = 162/6 = 27

Ans : x = 27

12.

Let the missing angle be x,

As we know that all exterior angles in a pentagon add up to 360 ( Write the same thing written above),

Then,

83 + 83 + 26 + 46 + x = 360

238 + x = 360

X= 360 - 238

X = 122

Answer : the fifth exterior angle = 122°

Hope this helps

The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.

Determine the slope (m) of the line using the formula:

   m = (y2 - y1) / (x2 - x1)

For the given points (5, -3) and (-2, -4), we have:

   m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7

Use the point-slope form of a linear equation:

   y - y1 = m(x - x1)

Using the point (5, -3), we have:

   y - (-3) = (1/7)(x - 5)

Simplifying:

   y + 3 = (1/7)(x - 5)

Convert the equation to standard form:

Multiply both sides of the equation by 7 to eliminate the fraction:

   7y + 21 = x - 5

Rearrange the equation to have the x and y terms on the same side:

   x - 7y = 26

The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.

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Answer:

approximately glof glorf hundred

Step-by-step explanation:

if u subtract eighty from gloof glife you get glof glorf hundred

Step-by-step explanation:

There are 11 prime numbers : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

Answer:

  about 5368.6 miles per day

Step-by-step explanation:

The units "km/hour" has hours in the denominator. To get days in the denominator, you need a fraction with hours in the numerator and days in the denominator: hours/day. To keep the same value, that fraction must have the same time period in the numerator as the denominator: (24 h)/(1 da).

  {360 km/h)×(24 h)/(1 da) = (360×24) km/da = 8640 km/da

Similarly to replace km in the numerator with miles, you need to multiply by a fraction that has miles in the numerator and km in the denominator.

  (8640 km/da)×(1 mi)/(1.609344 km) = 8640/1.609344 mi/da

  ≈ 5368.6 mi/da

Three ordered pairs that could represent the location of another vertex of the square are (7, 2), (-5, 2), (1, 8).

To find the possible locations of the other vertices of the square, we need to determine the distance from point K to any other vertex of the square. Since the perimeter of the square is 20 units, each side of the square has a length of 20/4 = 5 units.

One way to find the other vertices is to draw a circle with center at K and radius 5 units, and then look for points on the circle that have integer coordinates. Alternatively, we can use the distance formula to calculate the distance from K to another point (x, y), which must be 5 units, and then solve for y in terms of x.

Using the distance formula, we get:

\(\sqrt{(x-1)^{2} +(y-1)^{2} }\) = 5

Simplifying and squaring both sides, we get:

(x-1)^2 + (y-2)^2 = 25

Expanding the left side and simplifying, we get:

\(x^{2}\) - 2x + \(y^{2}\) - 4y + 20 = 0

Completing the square for x and y, we get:

\((x-1)^{2}\)  + \((y-1)^{2}\)  = \(6^{2}\)

This is the equation of a circle with center at (1, 2) and radius 6 units. Any point on this circle that has integer coordinates could be a vertex of the square, since it will be exactly 5 units away from K.

Using this method, we can find several possible locations of the other vertices of the square. Three of them are:

(7, 2), (-5, 2), (1, 8)

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Answer:

A)x^2-x-6

B)2x^2-12x+12

C)x^2-4

Step-by-step explanation:

A) Lets break this problem into portions the first part we trying  to distribute is  x(x-3)

X times X is X^2 and X times 3 is 3x so x^2-3x

Lets work on the second part

2(x-3)

2 times x =2x and 2 times -3 = -6 so 2x-6

And since you are supposed to add them its 2x-6+x^2-3x

x^2 can't be combined so that is seperate but 2x(+)-3x (negative overpowers positiveis) so we have -x and then -6 cant be joined with anything so

x^2-x-6

B) I'm going to go a little faster but it's essentially the same

2x(x-4)-3(x-4)

Multiply2x*x= 2x^2

2x*-4=-8x

combinde these two (2x^2-8x)

Pt.2

-3*x= -3x

-3*-4(negative and negative cancels out and it becomes positive)=12

join  (-3x+12)

and then 2x^2-8x-3x+12

you can only combine -8x-3x so -12x

2x^2-12x+12

C) this is level 3

x(x-2) + 2(x-2)

(x^2-2x) +(2x-4)

only like terms is 2x and-2x so combine and its 0

x^2-4

Given statement solution is :-  For the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

To calculate Patricia's pay for the third week of April, we'll need to determine her regular pay, overtime pay, and gross pay.

Regular Pay:

Patricia worked 53 hours, but only 40 hours are considered regular hours. Therefore, the regular pay is calculated as follows:

Regular Pay = Regular Hours x Hourly Rate

Regular Pay = 40 hours x $11.90/hour

Regular Pay = $476

Overtime Pay:

Since Patricia worked 53 hours in total and 40 of those are regular hours, the remaining 13 hours are considered overtime hours. Overtime pay is calculated by multiplying the overtime hours by 1.5 times the hourly rate.

Overtime Pay = Overtime Hours x (Hourly Rate x 1.5)

Overtime Pay = 13 hours x ($11.90/hour x 1.5)

Overtime Pay = 13 hours x $17.85/hour

Overtime Pay = $231.45

Gross Pay:

Gross Pay is the sum of Regular Pay and Overtime Pay.

Gross Pay = Regular Pay + Overtime Pay

Gross Pay = $476 + $231.45

Gross Pay = $707.45

Therefore, for the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

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A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function.

A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. Accordingly, the likelihood of any specific outcome of y is the same, and the likelihood of any range of outcomes is equal to the length of the range. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function. Accordingly, the length of the range multiplied by the likelihood of any specific occurrence yields the cumulative probability of any range of outcomes. Since the likelihood of any specific result in that range is 1 and the range's length is 0.5, for instance, the cumulative probability of 0 y 0.5 is 0.5. Since the likelihood of any given result within that range is still 1, but the range's length is 0.5, the cumulative probability of 0.5 y 1 is 0.75. The chance of any range of outcomes for y1 and y2 if they are independent random variables both having the uniform(0,1) distribution is just the sum of their respective cumulative probabilities.

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Answer:

\(3 \geq x\)

Step-by-step explanation:

\(1\geq \frac{x}{3}\)

Multiply each side by 3.

\(3 \geq x\)

A. The equation that relates these variables is:

d = s * t. B. The biker would travel 10 miles in 20 minutes. C. The biker would bike for 96 minutes to travel 48 miles. Rounded to the nearest tenth, this is 96.0 minutes.

a. Let's define the variables:

t = time in minutes

d = distance traveled by the biker in miles

s = speed of the biker in miles per minute

The equation that relates these variables is:

d = s * t

b. If the biker travels for 20 minutes, we can use the equation above to find the distance traveled:

d = s * t

d = s * 20 (since t = 20 minutes)

We need to know the speed of the biker to calculate the distance traveled. Let's assume that the biker's speed is 0.5 miles per minute (which is equivalent to 30 miles per hour):

d = 0.5 * 20

d = 10

Therefore, the biker would travel 10 miles in 20 minutes.

c. If the biker traveled 48 miles, we can rearrange the equation above to find the time:

d = s * t

t = d / s

We need to know the speed of the biker to calculate the time. Let's assume that the biker's speed is still 0.5 miles per minute:

t = 48 / 0.5

t = 96

Therefore, the biker would bike for 96 minutes to travel 48 miles. Rounded to the nearest tenth, this is 96.0 minutes.

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Answer:

y = 31

Step-by-step explanation:

2y-5+123=180

123 - 5 = 118

2y+118=180

subtract 118 from both sides

2y+118 - 118 = 180 - 118

180 - 118  = 62

2y = 62

divide 2 by both sides

2y/2 = 62/2

y = 31

Answer:

Step-by-step explanation:

2y+−5+123=180

Step 1: (Combine Like Terms)

(2y)+(−5+123)=180

Step 2:  (Subtract 118 from both sides)

2y+118−118=180−118

2y=62

Step 3: Divide both sides by 2

2y/2= 62/2

y=31

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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Answer:

D. 2.19

Step-by-step explanation:

ok so the formula for the surface area of a sphere is 4\(\pi\)\(r^2\)

We see that 4\(\pi\)\(r^2\)=60.

To find the radius we must isolate r on one side of the equations.

\(r^2\)=60/4\(\pi\)

\(r^2\) = 4.77464829276

r = \(\sqrt{4.77464829276}\)

That is approximately equal to 2.19

Answer: 9

Step-by-step explanation:

72÷9=8

9÷9=1

72/9 = 8/1