Suppose a ball is being twirled at the end of a string and the center of rotation is the origin of a coordinate system. If the string breaks, the initial path of the ball is on a line that is perpendicular to the radius of the circle. Suppose the string breaks when the ball is at the point whose coordinates are P(1, 2). Find the equation of the line on which the initial path lies.

Thus, the solution set of the given absolute value inequalities is found as: 0 ≥ x ≥ -1

The comparison of the connection here between variable and its value is a compound inequality. In a compound inequality, a variable is compared across two ranges which may provide the variable's range by satisfying either one or both of the limitations .

The given absolute value inequalities :

|(x+1)/2 - x/2| < 1/2

Removing the modulus sign will for 2 equations:

(x+1)/2 - x/2 < 1/2  and  (x+1)/2 - x/2 < - 1/2

Simplifying each:

(x+1)/2 - x/2 < 1/2  

x/2 + 1/2 - x/2 < 1/2

Both values will get cancelled:

0 < 0

But 0 = 0

and  (x+1)/2 - x/2 > - 1/2

x/2 + 1/2 - x/2 > -1/2

0 > -1 (correct)

here also the terms are getting completely cancelled to

Thus, the solution set of the given absolute value inequalities is found as: 0 ≥ x ≥ -1

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Complete question:

Find the set of the solutions of the following absolute value inequalities.

|(x+1)/2 - x/2| < 1/2

To find the length and width of each room on the blueprint, we need to use the given scale of 1 in. : 4 ft. This means that every 1 inch on the blueprint represents 4 feet in the actual house.

To find the length and width of each room on the blueprint, we can multiply the actual length and width of each room by 1/4 (or divide by 4). This gives us:

Living room: Length = 12 ft. ÷ 4 = 3 in., Width = 8 ft. ÷ 4 = 2 in.

Kitchen: Length = 16 ft. ÷ 4 = 4 in., Width = 16 ft. ÷ 4 = 4 in.

Office: Length = 16 ft. ÷ 4 = 4 in., Width = 8 ft. ÷ 4 = 2 in.

Bedroom: Length = 20 ft. ÷ 4 = 5 in., Width = 20 ft. ÷ 4 = 5 in.

Bedroom: Length = 10 ft. ÷ 4 = 2.5 in., Width = 20 ft. ÷ 4 = 5 in.

Bathroom: Length = 16 ft. ÷ 4 = 4 in., Width = 8 ft. ÷ 4 = 2 in.

Therefore, the length and width of each room on the blueprint are:

Living room: 3 in. x 2 in.

Kitchen: 4 in. x 4 in.

Office: 4 in. x 2 in.

Bedroom: 5 in. x 5 in.

Bedroom: 2.5 in. x 5 in.

Bathroom: 4 in. x 2 in.

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Answer:

2^6 = 64

Step-by-step explanation:

2^6 = 2⁶ = 2*2*2*2*2*2

= 64

Using graphing technology, we have came to know that the range οf the given functiοn is f(x )≤ 7.

The set οf all resulting values οf a functiοn is called the range οf a functiοn.

Fοr example if the functiοn is f(x)= 2x.

Fοr the given set οf values x={ 1,2,3 and sο οn} the range will be {2,4,6 and sο οn}

Given functiοn is f(x)= -|x|+7

The range οf an absοlute function οf the fοrm -c| [tex]ax+b[/tex]| is f(x) ≤ k

here k=7

sο the range will be f(x) ≤ 7

Hence range οf the given functiοn  will be f(x) ≤ 7.

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The recursive relationship that describes how the number of Marco's followers is changing each day is Pt = Pt-1 + 32.

It should be noted that after 5 days, Marco will have 597 followers.

The relationship is Pt = Pt-1 + 32 where Pt is the number of followers on day t and Pt-1 is the number of followers on the previous day.

In this case, to calculate how many followers Marco will have after 5 days, we can use this recursive relationship starting with P0 = 437 (the initial number of followers):

P1 = P0 + 32 = 437 + 32 = 469

P2 = P1 + 32 = 469 + 32 = 501

P3 = P2 + 32 = 501 + 32 = 533

P4 = P3 + 32 = 533 + 32 = 565

P5 = P4 + 32 = 565 + 32 = 597

Therefore, after 5 days, Marco will have 597 followers.

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The signs of the coordinates of ΔS'T'U' the x-coordinate is positive and the y-coordinate is negative.

Coordinates are a set of numbers or values that define the position of a point or object in space or on a surface. They are used to locate a point or object in a specific location relative to a reference point, axis, or plane.

The coordinate system is divided into four quadrants, numbered from I to IV, which are separated by the x- and y-axes. The origin is located at the intersection of the x- and y-axes, and has coordinates (0, 0)

The ΔSTU lies in Q3 if it reflected then ΔS'T'U' lies in Q4, it means that the point is located in the fourth quadrant of the Cartesian coordinate system. In this quadrant, the x-coordinates are positive and the y-coordinates are negative.

More specifically, if we assume that the point ΔS'T'U' is represented by the coordinates (x, y), then we have:

x > 0 (because it lies to the right of the y-axis)

y < 0 (because it lies below the x-axis)

For example, if the point ΔS'T'U' has coordinates (3, -2), then it lies in Q4, since the x-coordinate is positive and the y-coordinate is negative.

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Answer:

first box, first box, second box

Step-by-step explanation:

Answer:

0.4 seconds or

0.00667 minutes

Step-by-step explanation:

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pi times radius times 2 = circumference

pi times 10 inches times 2 = 62.83 inches = circumference

In one revolution, the wheel covers a distance equal to its circumference. So, at a speed of 22 revolutions per minute, the wheel covers a distance of:

22 x 62.83 inches inches per minute

1382.26 revolutions per minute

The wheel travels 1383.8 ft. in 60 seconds.

The wheel travels 1 ft. in (60 /  1383.8) seconds.

The wheel travels 10 ft. in (60 /  1383.8) * 10 seconds = 0.4 seconds

= 0.4 seconds divided by 60 = 0.00667 minutes

Answer:

14.0°

Step-by-step explanation:

[tex]\frac{sin(35)}{19} = \frac{sin(B)}{8}[/tex]

There is a B next to sin, but it represents m∠B. Note that both angles are in degrees.

Cross multiply the above equation.

8sin(35) = 19sin(B)

m∠B = [tex]sin^-1(\frac{8sin(35)}{19} )[/tex]

m∠B = 0.24391 rad

        ≅ 14.0°

Based on the probability distribution, the score that is most likely is 3, since it has the highest probability of 0.48.

By answering the presented question, we may conclude that Therefore, triangle the measure of BCD is 120°.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles.

Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides.

Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees).

The region of a triangle may be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

Since triangle ABC is isosceles with AB = BC, angles A and C are also equal to each other. Let x be the measure of angles A and C. Then we have:

angle A + angle B + angle C = 180° (sum of angles in a triangle)

x + 60° + x = 180°

2x + 60° = 180°

2x = 120°

x = 60°

So angles A and C each measure 60°, making triangle ABC an equilateral triangle.

Now, angle BCD is an exterior angle of triangle ABC. By the Exterior Angle Theorem, the measure of angle BCD is equal to the sum of angles A and C:

angle BCD = angle A + angle C = 60° + 60° = 120°

Therefore, the measure of BCD is 120 degrees.

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The given expression [tex]g^2/3h[/tex] is equivalent to the option (c) [tex]8g^2/24h[/tex]as we have multiplied 8 in both numerator and denominator.

The given expression is [tex]g^2/3h[/tex].

Now, to further simplify the expression, we can multiply both numerator and denominator by 8. This gives us:

[tex](g^2/3h) * (8/8)[/tex]

Simplifying further, we get:

[tex](8g^2)/(24h)[/tex]

Therefore, the expression equivalent to [tex]g^2/3h[/tex] is [tex](8g^2)/(24h)[/tex].

Thus, the given expression [tex]g^2/3h[/tex] is equivalent to the option (c) [tex]8g^2/24h[/tex] as we have multiplied 8 in both numerator and denominator.

The numerator is the top part of a fraction, which represents the number of equal parts being considered. It is the value that is above the fraction bar and represents the quantity being divided into equal parts.

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The complete question is :

Which expression is equivalent to [tex]g^2/3h[/tex]?

Click on the correct answer.

(A) [tex]g^2+5/3h+5[/tex]

(B) [tex]6g^2/15h[/tex]

(C) [tex]8g^2/24h[/tex]

173 units2 is the area of the figure.

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

Hence, 173 units2 is the area of the figure.

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let's keep in mind that arc's get their angle value from the central angle they cover, so in this case whatever angle value the arcAFB has, will also be the same for the ∡AFB.

Check the picture below.

Answer:

Step-by-step explanation:

a) (x-1)(2x-5)

b) x=-1 x=-2.5      x+1=0 x=-1        2x-5=0      2x=5     x=2.5

c) The degree is even so the ends of the graph will point in the same direction, the leading coefficient is positive so both ends will point up

d) First plot the x intercepts, then plug f(0) into the equation to get the y intercept. Plot the y intercept and then connect the points

e)

According to the given information, the number of vowels in the first word is 3x = 3(2) = 6.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, a left-hand side and a right-hand side, separated by an equal sign. The left-hand side and the right-hand side of an equation contain expressions that may include variables, constants, coefficients, and mathematical operations.

Let the number of vowels in the first word be 3x (since the ratio of vowels in the first word to the second word is 3:5)

Then, the number of vowels in the second word is 5x (since the ratio of vowels in the first word to the second word is 3:5)

Given that the second word contains 10 vowels. So, 5x = 10

Hence, x = 2

Therefore, according to the given information, the number of vowels in the first word is 3x = 3(2) = 6.

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After answering the presented question, we can conclude that As a range result, the class breadth in this frequency distribution table is one.

The variable's range is calculated by taking its maximum observed value and subtracting its minimum observed value (minimum). Possible range or variational bounds: a variety of steel costs; a variety of styles; The scope or magnitude of a method or action: perception. The maximum or anticipated range of a weapon's projectile. A list or set's range is the number between the lowest and maximum. Align all of the numbers before identifying the region. Next, subtract (reduce) the lowest number from the highest number. The solution includes the range of the list. The solution specifies the range of the list.

To calculate the class width, we must first determine the range of values within each class interval.

The class intervals are as follows:

[tex]0-1\s2-3\s4-5\s6-7[/tex]

8-9

0-1 interval range: 1-0 = 1

2-3 interval range: 3-2 = 1

5-4 = 1 interval range of 4-5

7-6 = 1 interval range of 6-7

8-9 interval range: 9-8 = 1

The intervals all have the same range of one.

To calculate the class width, subtract the upper limit of the first interval from the lower limit of the first interval.

Higher limit of first interval - Lower limit of first interval = class width

1 - 0 class width

1 class width

As a result, the class breadth in this frequency distribution table is one.

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0.006678 rounded to 3 decimal places is 0.0067.

We have,

To round 0.006678 to 3 decimal places, we need to look at the fourth decimal place (the digit 7).

Since 7 is greater than or equal to 5, we round up the last digit (8) by adding 1 to it.

Now,

The rounded number is 0.0067

So 0.006678 rounded to 3 decimal places is 0.0067.

Thus,

0.006678 rounded to 3 decimal places is 0.0067.

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1. The transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.

2. stretching by a factor of 2 along the y-axis

3. reflection

4. shift

5. reflection

6. stretch

7. stretch

8. reflection

The transformation of a function f represented by g is the process of modifying the function f to create a new function g. This can be done in a number of ways, such as shifting the graph, stretching it, or reflecting it in some way.

1. f(x) = √x, g(x) = √(x+1)+8, the transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.

2. f(x) = √x, g(x) = 2√(x - 1), the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift by -1 along the x-axis.

3. f(x) = ³√x, g(x) = −³√x-1, the transformation of f is a reflection across the x-axis, followed by a shift of -1 along the x-axis.

4. f(x) = ³√x, g(x) = ³√(x +4)-5, the transformation of f is a shift of 4 units along the x-axis, followed by a shift of -5 units along the y-axis.

5. f(x) = x^½, g(x) =1/4(-x)^½, the transformation of f is a reflection across the y-axis, followed by a stretching by a factor of 1/4 along the y-axis.

6. f(x) = x^⅓, g(x) =1/3x^⅓+6, the transformation of f is a stretching by a factor of 1/3 along the y-axis, followed by a shift of 6 units along the y-axis.

7. f(x)= ⁴√x, g(x) =2 ⁴√(x+5)-4, the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift of 5 units along the x-axis, followed by a shift of -4 units along the y-axis.

8. f(x)= ⁵√x, g(x) =⁵√(-32x)+3, the transformation of f is a reflection across the x-axis, followed by a stretching by a factor of 32 along the x-axis, followed by a shift of 3 units along the y-axis.

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19. The transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.

20. The transformation of f is a stretching by a factor of 2 along the y-axis

21. The transformation of f is a reflection across the x-axis.

22. The transformation of f is a shift of 4 units along the x-axis, followed by a shift of -5 units along the y-axis.

23. The transformation of f is a reflection across the y-axis.

24. The transformation of f is a stretching by a factor of 1/3 along the y-axis.

25. The transformation of f is a stretching by a factor of 2 along the y-axis.

26. The transformation of f is a reflection across the x-axis, followed by a stretching by a factor of 32 along the x-axis

The transformation of a function f represented by g is the process of modifying the function f to create a new function g. This can be done in a number of ways, such as shifting the graph, stretching it, or reflecting it in some way.

19. f(x) = √x, g(x) = √(x+1)+8, the transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.

20. f(x) = √x, g(x) = 2√(x - 1), the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift by -1 along the x-axis.

21. f(x) = ³√x, g(x) = −³√x-1, the transformation of f is a reflection across the x-axis, followed by a shift of -1 along the x-axis.

22. f(x) = ³√x, g(x) = ³√(x +4)-5, the transformation of f is a shift of 4 units along the x-axis, followed by a shift of -5 units along the y-axis.

23. f(x) = x½, g(x) =1/4(-x½, the transformation of f is a reflection across the y-axis, followed by a stretching by a factor of 1/4 along the y-axis.

24. f(x) = x⅓, g(x) =1/3x⅓+6, the transformation of f is a stretching by a factor of 1/3 along the y-axis, followed by a shift of 6 units along the y-axis.

25. f(x)= ⁴√x, g(x) =2 ⁴√(x+5)-4, the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift of 5 units along the x-axis, followed by a shift of -4 units along the y-axis.

26. f(x)= ⁵√x, g(x) =⁵√(-32x)+3, the transformation of f is a reflection across the x-axis, followed by a stretching by a factor of 32 along the x-axis, followed by a shift of 3 units along the y-axis.

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Answer:

r=9

Step-by-step explanation:

the radius is half of the circumference because the equation for circumference is 2 X radius, so dividing the circumference by 2 will undo the problem.

(18/2 = 9 )

The probability that the sample mean will be greater than M = 10 pounds is 0.9525.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating the event is impossible and 1 indicating it is certain. Probability is used in many fields, including mathematics, statistics, science, and finance.

To solve this problem, we need to use the central limit theorem (CLT), which states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough.

Since the sample size is small (n = 4), we need to use the t-distribution instead of the normal distribution. However, since the population standard deviation is known, we can use the standard normal distribution with a z-score.

First, we need to calculate the standard error of the mean:

SE = σ / sqrt(n) = 6 / sqrt(4) = 3

Next, we can calculate the z-score:

z = (M - µ) / SE = (10 - 15) / 3 = -1.67

Finally, we can use a standard normal distribution table or calculator to find the probability of a z-score greater than -1.67:

p(M > 10) = P(z > -1.67) = 0.9525 (rounded to four decimals)

Therefore, the probability that the sample mean will be greater than M = 10 pounds is 0.9525.

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The minimum annual interest rate Kyoko should aim for rounding to the nearest hundredth of a percent is [tex]$6.76%$.[/tex]

What is meant by interest rate?

An interest rate is the percentage of principal charged by a lender or received by a depositor in exchange for the use of money, usually expressed as an annual percentage rate (APR). It is the amount of interest charged on a loan or earned on an investment.

Given that Kyoko has [tex]$10,000[/tex] that she wants to invest and her goal is to have [tex]$15,000[/tex] by the time she finishes graduate school in 6 years. Let the minimum annual interest rate be denoted by [tex]$r$[/tex] (in decimal form).

Using the compound interest formula, we have:

[tex]$A = P(1 + \frac{r}{n})^{nt}$[/tex]

where

A is the future value of the investment (which is [tex]$15,000$[/tex] in this case)

P is the present value of the investment (which is [tex]$10,000$[/tex] in this case)

r is the annual interest rate (what we need to find)

n is the number of times the interest is compounded per year (which is 365 since the interest is compounded daily)

t is the time (in years)

Plugging in the given values, we get:

[tex]$15000 = 10000(1 + \frac{r}{365})^{365\times 6}$[/tex]

Taking natural logarithm on both sides, we get:

[tex]$\ln(1.5) = \ln(1 + \frac{r}{365})^{365\times 6}$[/tex]

Using the property of logarithms, we can write the exponent on the right-hand side as:

[tex]$6\cdot 365\cdot \ln(1 + \frac{r}{365})$[/tex]

Dividing both sides by [tex]$6\cdot 365$[/tex] and simplifying, we get:

[tex]$\ln(1.5) = \ln(1 + \frac{r}{365})$[/tex]

[tex]$1.5 = 1 + \frac{r}{365}$[/tex]

[tex]$r = 365\times (1.5-1) = 365\times 0.5 = 182.5$[/tex]

Therefore, the minimum annual interest rate Kyoko should aim for is [tex]$r=182.5%$.[/tex] Rounding to the nearest hundredth of a percent, we get [tex]$6.76%$.[/tex]

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Answer:

V = 27

Step-by-step explanation:

62 = −19 + 3v

Swap sides so that all variable terms are on the left-hand side.

−19 + 3v = 62

Add 19 to both sides.

3v = 62 + 19

Add 62 and 19 to get 81.

3v = 81

Divide both sides by 3.

v = 81/3

​Divide 81 by 3 to get 27.

v = 27

I hope this will help you! :)

Thus, the total area of the figure made by square grids paper in three-dimensional figure is found as: 48 in².

Three-dimensional (3D) shapes have three dimensions, like length, breadth, and height. Prisms and spheres are two examples of 3D shapes. Multidimensional and physically holdable 3D forms.

The three - dimensional dimensions comprising width, height, and depth are referred to as three dimensions, or 3D. The physical world is three dimensional, as is everything that can be seen there.

For the given net of 3-D figure.

Each  square of grip represents 1 in².

Total area = rectangle area + 2*triangle area

Total area = length*breadth + 2*(1/2*base*height)

Total area = 12*3 + 3*4

Total area =  48 in².

Thus, the total area of the figure made by square grids paper in three-dimensional figure is found as: 48 in².

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A water bottle

Step-by-step explanation:

It's a water bottle because you cannot measure volume with a dollr bill or postage stamp.

NO IDEA i'm only in 5th grade sorry.