(B) 5 (C) 6 (D) 9 What is the solution set for the absolute value equation |2x-4|=20?

1) a) ω = 2πf = 2π(50) = 100π radians per second

b) 96.78m/s.

2) (a) T = 1/f = 1/12 seconds,

(b) ω = 2πf = 2π(12) = 24π radians per second.

3) original length of the pendulum is 9.0m.

4)  original length of the spiral spring is 20cm.

5)  the initial velocity of the football is 17.32m/s At the highest

Angular speed is the speed of the object in rotational motion. Distance traveled is represented as θ and is measured in radians. The time taken is measured in terms of seconds. Therefore, the angular speed is articulated in radians per second or rad/s.

1. (a) The angular speed of a body vibrating at 50 cycles per second is:

ω = 2πf = 2π(50) = 100π radians per second

(b) The stone is projected horizontally, so its initial vertical velocity is zero. The time taken for the stone to fall from the top of the tower to the ground is given by:

t = √(2h/g) = √(2×75/10) = √15

The horizontal distance traveled by the stone is:

d = vxt = (25m/s)×(√15) ≈ 96.78m

Therefore, the speed with which the stone strikes the ground is approximately 96.78m/s.

2. (a) The period of the motion is:

T = 1/f = 1/12 seconds

(b) The angular speed of the motion is:

ω = 2πf = 2π(12) = 24π radians per second

(c) The velocity at the middle of oscillation is zero, since this is the point of maximum displacement and therefore maximum potential energy.

(d) The acceleration at the end of oscillation is given by:

a = -ω²x = -(24π)²(0.02) = -11.52 m/s²

where x is the amplitude of the motion.

3. The period of a simple pendulum is given by:

T = 2π√(L/g)

where L is the length of the pendulum and g is the acceleration due to gravity. Therefore, we can write:

17 = 2π√(L/g) (1)

8.5 = 2π√[(L-1.5)/g] (2)

Dividing (2) by (1), we get:

1/2 = √[(L-1.5)/L]

Squaring both sides and simplifying, we get:

L = 9.0m

Therefore, the original length of the pendulum is 9.0m.

4. (a) Let the original length of the spiral spring be x. Then, using Hooke's law, we have:

5N = k(25cm - x) (1)

10N = k(30cm - x) (2)

where k is the spring constant. Solving for k in equation (1), we get:

k = 5N/(25cm - x)

Substituting into equation (2), we get:

10N = [5N/(25cm - x)](30cm - x)

Simplifying and solving for x, we get:

x = 20cm

Therefore, the original length of the spiral spring is 20cm.

(b) The pressure of the trapped air column in the capillary tube is balanced by the pressure of the atmosphere. When the tube is held horizontally, the length of the air column is the same as its length in the vertical position. Therefore, the length of the air column is 15cm.

When the tube is held vertically with the open end underneath, the length of the air column is given by:

L = 76cm - 20cm = 56cm

Therefore, the length of the air column is 56cm.

5. The horizontal and vertical components of the initial velocity of the football are:

v₀x = v₀cos(60°) = (20m/s)cos(60°) = 10m/s

v₀y = v₀sin(60°) = (20m/s)sin(60°) = 17.32m/s

At the highest

Hence, the answer to each question:

1) a) ω = 2πf = 2π(50) = 100π radians per second

b) 96.78m/s.

2) (a) T = 1/f = 1/12 seconds,

(b) ω = 2πf = 2π(12) = 24π radians per second.

3) original length of the pendulum is 9.0m.

4)  original length of the spiral spring is 20cm.

5)  the initial velocity of the football is 17.32m/s At the highest

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The number of cubic centimeters of space that 3 ping pongs would have is 339. 29 cm ³

A ping pong ball takes the shape of a sphere and the volume of a sphere is ;

= 4 / 3 x π x radius ³

Given the radius of 3 cm, the volume of one ping pong ball is :

= 4 / 3 x π x 3 ³

= 113. 09734 cm ³

If there are three ping pong balls, the volume would then be :

= 113. 09734  x 3 ping pongs

= 339. 29 cm ³

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Answer:

[tex]\frac{\sqrt{x+3} }{x+1}[/tex]

Step-by-step explanation:

nothing further can happen.

The number from oldest to youngest is - 5 - 4 - 2 - Fault B- Unconformity A - 6 - 1 - 3 , the layer 5 is older than the layer 3 and line "B" represent - Fault .

How to do ordering of rock layers ?

Ordering of rock layers, also known as stratigraphy, is a process of arranging rock layers in a specific order based on their age and location. There are several principles that geologists use to determine the relative ages of rock layers:

Law of superposition: In an undisturbed sequence of rocks, the oldest rocks are at the bottom and the youngest rocks are at the top.

Principle of original horizontality: Layers of sediment are originally deposited horizontally, and any deformation of these layers must have occurred after deposition.

Principle of cross-cutting relationships: Any feature that cuts across a rock or rock layer is younger than the rock or layer that it cuts across.

Principle of inclusions: Any rock fragments included in another rock layer must be older than the rock layer that contains them.

Ordering of given rock layers :

The number from oldest to youngest is given below -

5 - 4 - 2 - Fault B- Unconformity A - 6 - 1 - 3

The age of layer 5 is older than the layer 3 .

The line "B" represent - Fault . A fault in rock is a fracture or break in the Earth's crust where rock on either side has moved relative to the other side.

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Answer:

0.26x

Step-by-step explanation:

If x is decreased by 74% then new value of x

= x - 74% of x

74% as decimal = 74/100 = 0.74

New value of x
= x - 0.74x

=x(1 - 0.74)

=0.26x

A population consists of five members 2,3,6,8,1). consider all possible samples of size two which can be doamn with replacement from this positioning population.  The mean is  4 and standard deviation of the population is 1.67. The mean and standard error of sample mean (x) from the sampling distribution of x is 4 and 1.18 respectively

i) The mean and standard deviation of the population:

Mean = (2+3+6+8+1)/5 = 20/5 = 4

Standard deviation = √[(2-4)²+(3-4)²+(6-4)²+(8-4)²+(1-4)²]/5 = √14/5 = 1.67


ii) The mean and standard error of sample mean (x) from the sampling distribution of x:

Mean of sample mean = Mean of population = 4

Standard error of sample mean = Standard deviation of population/√n = 1.67/√2 = 1.18


The mean of a population is calculated by adding up all the values and dividing by the number of values in the population. The standard deviation of a population is calculated by finding the difference between each value and the mean, squaring those differences, adding them up, and then dividing by the number of values in the population.

The mean of the sample mean is the same as the mean of the population, and the standard error of the sample mean is the standard deviation of the population divided by the square root of the sample size.

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To find the composite functions, we simply substitute one function into the other.

For example, f[g(x)] means we substitute g(x) into f(x) wherever there is an x. So, f[g(x)] = 3(g(x)) + 4 = 3(2x^2 − 5x − 9) + 4 = 6x^2 − 15x − 23.Similarly, we can find the other composite functions: g[f(x)] = 2(f(x))^2 − 5(f(x)) − 9 = 2(3x+4)^2 − 5(3x+4) − 9 = 18x^2 + 7x - 7f[f(x)] = 3(f(x)) + 4 = 3(3x+4) + 4 = 9x + 16

For the last part, f/g means we divide f(x) by g(x):f/g = (3x+4)/(2x^2−5x−9)The domain of this function is all real numbers except for the values of x that make the denominator equal to zero.

To find these values, we set the denominator equal to zero and solve for x:2x^2−5x−9 = 0(2x+3)(x-3) = 0x = -3/2, 3 So the domain of f/g is (-∞, -3/2) ∪ (-3/2, 3) ∪ (3, ∞) in interval notation.

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Answer:

6

Step-by-step explanation:

[tex]1\frac{1}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] × [tex]\frac{4}{1}[/tex] = [tex]\frac{12}{2}[/tex] = 6  

Answer:

x = -3 to x = 2

Step-by-step explanation:

The function is decreasing where the slope is negative, seen when the y-values decrease as the x-values increase. Your answer is correct.

Answer:

X is - 3 to x is 2

Step-by-step explanation:

Look at the x axis, the point where the curve slopes down is the decreasing point

Where x is - 3 is a peak point, it begins to slope from there and rises when x is 3

The smallest number among the given options is 0.125.

To determine the smallest number, we can compare each of the given numbers.

0.625 > 0.25 > 0.375 > 0.5 > 0.125

As we can see, the smallest number is 0.125, which is option E.

Comparison symbols are those that tell us whether one number is greater than, less than, or equal to another. The symbols are:

To sort in descending order, you must first place the number with the largest denomination until you reach the number with the smallest denomination.

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So, the coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.

The coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.

A coefficient is the number that is multiplied by a variable in an expression. In this case, the x^(2) term is -4x^(2), so the coefficient is -4.

To find the coefficient of a specific term in an expression, you can simply look at the number that is directly in front of the variable and its exponent. For example, in the term 5x, the coefficient is 5, and in the term 2, the coefficient is 2 (since there is no variable, the coefficient is simply the number itself).

In the expression 5x-4x^(2)+2, the x^(2) term is -4x^(2), so the coefficient is -4. This means that the x^(2) term is being multiplied by -4 in the expression.

So, the coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.

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Answer:

60

Step-by-step explanation:

24 + 36 = 60

You can use the Gold Digger for the distributive property! * Factor as if you want to find the Greatest Common Factor.

The system of equations that does not have a solution is {(x-2y=-3),(-2x+4y=6):}.

To see why, let's first look at the other two systems of equations:

{(4x+6y=12),(6x+9y=12):}

If we divide the first equation by 2, we get:

{(2x+3y=6),(6x+9y=12):}

If we then multiply the first equation by -3, we get:

{(-6x-9y=-18),(6x+9y=12):}

If we add these two equations together, we get:

{0= -6}

This is a false statement, so there is no solution for this system of equations.

Similarly, for the system of equations {(x+y=-1),(4x-3y=24):}, we can multiply the first equation by -4 and add the two equations together to get:

{-4x-4y=4, (4x-3y=24):}

{-7y=28}

This equation has a solution, so this system of equations does have a solution.

However, for the system of equations {(x-2y=-3),(-2x+4y=6):}, if we multiply the first equation by -2 and add the two equations together, we get:

{-2x+4y=6, (-2x+4y=6):}

{0=0}

This equation is always true, so there are an infinite number of solutions for this system of equations. Therefore, this system of equations does not have a unique solution.

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There is a significant relationship between the variables (H-value = 2 and P-value = 0.994)

The test for significant relationship is used to determine whether there is a statistically significant relationship between two or more variables. In this case, the test can be used to determine whether there is a statistically significant relationship between the number of daily passenger trips (in thousands) for subways and commuter rail service. Based on the H-value and P-value, the result of this test indicates that there is a significant relationship between the variables (H-value = 2 and P-value = 0.994). Therefore, option (a) is correct and option (d) is incorrect.

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Answer:

1.5x + 2y = 12

Step-by-step explanation:

The equation representing Serena’s spending on snacks today would be 1.5x + 2y = 12, where x represents the number of drinks purchased and y represents the number of bags of chips purchased.

Therefore, the equation is 1.5x + 2y = 12.

Answer:

4x+3y

Step-by-step explanation:

Combining like terms, we get:

5x - x + 4y - y = 4x + 3y

Therefore, 5x+4y-x-y simplifies to 4x+3y.

The value of x for each rectangle is given as follows:

5) x = 7.

7) x = 10.

The area of a rectangle of base b and height h is given by the multiplication of these two dimensions, as follows:

A = bh.

Hence, for item 5, the value of x is given as follows:

3(5x - 2) = 99

5x - 2 = 33

5x = 35

x = 7.

For item 7, the value of x is obtained as follows:

3(4x - 3) = 111

4x - 3 = 37

4x = 40

x = 40/4

x = 10.

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The lateral surface and the total surface areas of the prism are 96 in² and 2304 in² respectively.

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given is prism, we need to find the lateral surface and the total surface areas,

Lateral surface area = (perimeter of base) × length

Perimeter of base = 3 × 4 = 12 in

length = 8 in

The lateral surface area = 12 × 8 = 96 in²

Total surface area = (perimeter of base) × length × 2(base area)

= 96 × 2(3×4)

= 96 × 24

= 2304 in²

Hence, the lateral surface and the total surface areas of the prism are 96 in² and 2304 in² respectively.

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Therefore, the rate per period (i) is 0.00708333 and the number of periods (n) is 84. The future value of the annuity is $34563.89.

To find i (the rate per period) and n (the number of periods) for the given annuity, we need to use the formula for the future value of an annuity:

FV = PMT × [(1 + i)^n - 1] / i

Where FV is the future value, PMT is the periodic payment, i is the rate per period, and n is the number of periods.

Given:
PMT = $305
i = 8.5% / 12 = 0.00708333 (since the interest is compounded monthly)
n = 7 × 12 = 84 (since there are 12 months in a year and the deposits are made for 7 years)

Plugging these values into the formula, we get:

FV = $305 × [(1 + 0.00708333)^84 - 1] / 0.00708333

FV = $305 × [1.80722 - 1] / 0.00708333

FV = $305 × 0.80722 / 0.00708333

FV = $34563.89

Therefore, the rate per period (i) is 0.00708333 and the number of periods (n) is 84. The future value of the annuity is $34563.89.

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Answer:

Step-by-step explanation: First lets multiply the numerators, so 3*3 is 9, then we multiply the denominators, so 4*5 is 20. 9/20 or 0.45 will be your answer.

The probability of needing exactly 4 rolls to get doubles is 0.12.

What is meant by probability?

An event's probability is a numerical representation of how likely it is that the event will take place. In mathematical notation, it is written as a number between 0 and 1, or as a percentage between 0% and 100%. The higher an event's probability, the more likely it is to occur. In a sample space, there is a probability of 1 for each event. The probability formula states that the ratio between the number of favourable outcomes and the total number of outcomes determines the likelihood that an event will occur. Sets are used in the terminology of probability theory. A set is a grouping of various things.

From the figure,

The number of times we get doubles in 1 roll = 5

The number of times we get doubles in 2 rolls = 4

The number of times we get doubles in 3 rolls = 4

The number of times we get doubles in 4 rolls = 3

The number of times we get doubles in 5 rolls = 3

The number of times we get doubles in 6 rolls = 2

The number of times we get doubles in 7 rolls = 3

The number of times we get doubles in 8 rolls = 0

The number of times we get doubles in 9 rolls = 1

Total number of outcomes = 5+4+4+3+3+2+3+1  = 25

Number of doubles in 4 rolls = 3

The probability of needing exactly 4 rolls to get doubles = 3/25 = 0.12

Therefore the probability of needing exactly 4 rolls to get doubles is 0.12.

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1) a) X approaches negative infinity, f(x) approaches positive infinity.

b) The degree of f(x) is 3.

c) The maximum number of turning points for f(x) is 2.

d) The leading coefficient of f(x) is -1.

e) The end behavior of f(x) is "as x approaches infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches positive infinity.

2) a) a) The end behavior of g(x) is determined by the leading term x⁴. As x approaches infinity, g(x) approaches positive infinity. As x approaches negative infinity, g(x) approaches positive infinity.

b) The degree of g(x) is 4.

c) The maximum number of turning points for g(x) is 3.

d)The leading coefficient of g(x) is 1.

e)The end behavior of g(x) is "as x approaches infinity, g(x) approaches positive infinity; as x approaches negative infinity, g(x) approaches positive infinity.

Given f(x)=-x³ + 6x³ - 9x
a) The end behavior of f(x) is determined by the leading term -x³. As x approaches infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches positive infinity.
b) The degree of f(x) is 3, as the highest exponent in the polynomial is 3.
c) The maximum number of turning points for f(x) is 2, as it is one less than the degree of the polynomial.
d) The leading coefficient of f(x) is -1, as it is the coefficient of the leading term -x³.


Given g(x)=x(x+2)(x-2)²
b) The degree of g(x) is 4, as the highest exponent in the polynomial is 4.
c) The maximum number of turning points for g(x) is 3, as it is one less than the degree of the polynomial.
d) The leading coefficient of g(x) is 1, as it is the coefficient of the leading term x⁴.

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According to the information we can infer that the statement that establishes a correct interpretation of the model is the model associates a score of 80 with 2 hours of studying.

To select the correct statement we must replace the value of (t) in the equation and check the relationship between the results of the students in the test and the hours spent studying.

According to the above, if we replace t by two we can infer that the result would be y = 80 as shown below:

So the correct answer would be statement C.

On the other hand, to identify the percentage to which the number of seventh grade students who have a laptop is equivalent, we must add the total number of students in this grade and then find the percentage with a rule of three:

So the correct answer would be 42% because this value is the closest and we could approximate it.

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The new function after the parent function f(x)=2^(x) is horizontally shrunk by a factor of two, translated right by 10 and translated 5 units down is f(x) = 2^((x-10)/2) - 5.

- Horizontal shrink by a factor of two: This means that the x-value of each point on the graph will be divided by 2. To achieve this, we can multiply the x-value inside the function by 1/2, or divide it by 2. So, the function becomes

f(x) = 2^((x/2))

- Translation right by 10: This means that the entire graph will shift 10 units to the right. To achieve this, we can subtract 10 from the x-value inside the function. So, the function becomes

f(x) = 2^((x-10)/2)

- Translation 5 units down: This means that the entire graph will shift 5 units down. To achieve this, we can subtract 5 from the entire function. So, the function becomes

f(x) = 2^((x-10)/2) - 5

Therefore, the new function is f(x) = 2^((x-10)/2) - 5

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The domain of the piecewise function g of x is all real numbers, except for x = 2, which is the point at which the two functions overlap. Therefore, the domain is (–∞, 2) ∪ (2, ∞).

A domain is a collection of computers and devices connected to one another through a network. It is a logical grouping of computers and devices, such as a local area network (LAN) or a wide area network (WAN). Each device within the network is assigned a unique address, allowing it to communicate with other devices within the network. Domains can also be used to control access to resources, such as files, folders, printers, and databases. Domains can be used to authenticate users and set permissions, which determine the type of access a user has to the domain’s resources. This is commonly used in businesses and organizations to ensure that only authorized personnel have access to sensitive information.

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Let A, B, and C be 3x3 matrices such that det(A) =2, det(C) = 4, and 2A^TB^-1 = C the determinant of matrix B is 4.

To find the determinant of matrix B, we can use the property of determinants that states that det(AB) = det(A)det(B). We can rearrange the given equation 2A^TB^-1 = C to get B = 2A^T C^-1. Then, we can take the determinant of both sides to get det(B) = det(2A^T C^-1).

Using the property of determinants, we can expand the right side of the equation to get det(B) = det(2)det(A^T)det(C^-1). Since the determinant of a scalar multiple of a matrix is the scalar multiple of the determinant, det(2) = 2^3 = 8. Also, the determinant of the transpose of a matrix is the same as the determinant of the original matrix, so det(A^T) = det(A) = 2.

Finally, the determinant of the inverse of a matrix is the reciprocal of the determinant of the original matrix, so det(C^-1) = 1/det(C) = 1/4.

Substituting these values back into the equation, we get det(B) = 8*2*(1/4) = 4. Therefore, the determinant of matrix B is 4.
det(B) = 4.

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Answer:

The answer is  3

The forecasted sales volume is 34.116 thousand Euro if the investment volume is planned to be 30 thousand Euro.

Let's solve this problem step by step:

Calculate the correlation coefficient (r) using the formula:
r = (ΣXY - (ΣX)(ΣY)/n) / sqrt([(ΣX^2 - (ΣX)^2/n)(ΣY^2 - (ΣY)^2/n)])

Plug in the given values into the formula:
r = (126.54 - (22)(66)/12) / sqrt([(45.8 - (22)^2/12)(369.94 - (66)^2/12)])

Simplify the formula and solve for r:
r = (126.54 - 121) / sqrt([(45.8 - 40.333)(369.94 - 363)])
r = 5.54 / sqrt[(5.467)(6.94)]
r = 5.54 / 4.967
r = 1.115

Make conclusions about the closeness of the linear relationship based on the value of r:
Since the value of r is close to 1, this indicates a strong positive linear relationship between the investments (X variable) and the main product's sales (Y variable).

Find the linear regression from variable Y to the X using the formula:
Y = a + bX

Calculate the slope (b) using the formula:
b = (ΣXY - (ΣX)(ΣY)/n) / (ΣX^2 - (ΣX)^2/n)

Plug in the given values into the formula and solve for b:
b = (126.54 - (22)(66)/12) / (45.8 - (22)^2/12)
b = 5.54 / 5.467
b = 1.013

Calculate the intercept (a) using the formula:
a = (ΣY - b(ΣX))/n

Plug in the given values into the formula and solve for a:
a = (66 - 1.013(22))/12
a = 44.714/12
a = 3.726

Plug in the values of a and b into the linear regression formula:
Y = 3.726 + 1.013X

Forecast the sales volume if the investment volume is planned to be 30 thousand Euro by plugging in the value of X into the linear regression formula:
Y = 3.726 + 1.013(30)
Y = 3.726 + 30.39
Y = 34.116

Therefore, the forecasted sales volume is 34.116 thousand Euro if the investment volume is planned to be 30 thousand Euro.

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The correct answer is option C. A graphic image showing a pair of similar polygons with an X-axis showing the value range from 0 to 16 and a Y-axis values from 0 to 16.

Polygons are two-dimensional shapes with straight sides that are joined together. They are closed shapes, meaning all the sides are connected. Polygons can have anywhere from three sides to an infinite number of sides. The most common types of polygons are triangles, quadrilaterals, pentagons, hexagons, and octagons.

This correct image is showing two polygons that are similar, or which have the same shape. This means that the sides of the two polygons are equal in length and each angle is the same. In other words, they are exactly the same shape, but can be different sizes. The X-axis and Y-axis values shown in the image are the coordinates of the points that make up the polygons. The X-axis values indicate the horizontal distance from the origin, while the Y-axis values indicate the vertical distance from the origin. By looking at the coordinates of the points that make up the polygons, we can see that the two polygons are similar.

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