p(x) = -2x – 2; Find p(-3)

The probability that the sample mean is between 7.8 and 8.2 is 0.3830

The time spent using email is normally distributed with µ = 8 min, σ = 2 min, and n = 25,

we have to find the probability that the sample mean is between 7.8 and 8.2.

Here, Mean (µ) = 8 min  

Standard deviation (σ) = 2 min

Sample size (n) = 25

We know that the distribution of the sample mean is also a normal distribution. The mean of the sample mean distribution is µ and the standard deviation of the sample mean distribution is

σ/√n = 2/√25

        = 2/5

        = 0.4.

The z-score is given by

z = (x - µ) / (σ/√n)

For the lower limit, the z-score is   z₁ = (7.8 - 8) / (0.4)

                                                              = -0.5

For the upper limit, the z-score is   z₂ = (8.2 - 8) / (0.4)

                                                               = 0.5

We have to find the probability that the sample mean is between 7.8 and 8.2. It can be represented as

P(7.8 < x < 8.2)

P(z₁ < z < z₂)

Substituting the values,

we get

P(-0.5 < z < 0.5)

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Answer:

supplementary means the angles add upto 180 degrees. The name for 2 anglew which add upto 90 degrees is "complimentary".

True. The solution of a system of linear equations in two variables is the point (x, y) where the two lines intersect. This point satisfies both equations in the system simultaneously.

A system of linear equations in two variables is a set of two equations that can be written in the form:

a₁x + b₁y = c₁
a₂x + b₂y = c₂

where x and y are the variables and a₁, b₁, c₁, a₂, b₂, and c₂ are constants. The goal is to find the values of x and y that satisfy both equations in the system.

Geometrically, each equation in the system represents a line in the two-dimensional plane. The solution of the system is the point (x, y) where the two lines intersect. This point satisfies both equations simultaneously and is the only point that does so.

To find the solution of a system of linear equations, we can use various methods such as substitution, elimination, or matrices. These methods involve manipulating the equations in the system to eliminate one of the variables and solve for the other. Once we have the value of one variable, we can substitute it back into one of the equations to solve for the other variable. The solution of the system is then the ordered pair (x, y) that satisfies both equations.

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Answer:

8/3-6/4=14/12=7/6=1 1/6 or 1.167

Step-by-step explanation:

Answer:

128 > 4*(x + 7)

Step-by-step explanation:

Given the following data;

Length = 4 meters

Width = x + 7 meters

Area = 128 m²

Mathematically, the area of a rectangle is given by the formula;

Area of rectangle = length * width

Substituting into the formula, we have;

128 > 4*(x + 7)

128 > 4x + 28

128 - 28 > 4x

100 > 4x

Dividing both sides by 4, we have;

25 > x

As per the given statement Since consumption cannot be negative, the optimal consumption amount of ham for Mandy is 0 (±5%).

To find Mandy's optimal consumption amount of ham, we need to maximize her utility subject to her budget constraint.

Given:

U = 131(Cheese) + 32(Ham)

Price of Ham (PH) = $76 per pound

Price of Cheese (PC) = $24 per pound

Income (I) = $2489

Let x represent the amount of ham consumed. The budget constraint equation is:

PH * x + PC * (I - x) = I

Substituting the given values, we have:

76x + 24(2489 - x) = 2489

Simplifying the equation:

76x + 59736 - 24x = 2489

52x = 2489 - 59736

52x = -57247

x = -57247 / 52

x ≈ -1101.29

Since consumption cannot be negative, the optimal consumption amount of ham for Mandy is 0 (±5%).

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Mandy's optimal consumption amount of ham is within a range of \($0 \pm 5\%$\)

To determine Mandy's optimal consumption amount of ham, we need to find the quantity of ham that maximizes her utility given her budget constraint.

Let \($H$\) be the quantity of ham consumed in pounds. The price of ham is \(\$76\) per pound. Mandy's income is \(\$2489\), and her utility function is given by \($U = 131C + 32H$\), where \($C$\) represents the quantity of cheese consumed in pounds.

We can set up Mandy's budget constraint as follows:

\(\[76H + 24C = 2489\]\)

To find the optimal consumption amount of ham, we can solve this equation for \($H$\). Rearranging the equation, we have:

\(\[H = \frac{2489 - 24C}{76}\]\)

Substituting the given values, we have:

\(\[H = \frac{2489 - 24C}{76}\]\)

To calculate the optimal consumption amount of ham, we can substitute different values for \($C$\) and solve for \($H$\). The optimal value will be within a range of \($0 \pm 5\%$\) due to the uncertainty in the problem statement.

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Answer:Answer:

The value of f(6) is, 18

Step-by-step explanation:

Given the function:

              .....[1]

We have to find the value of.

Put x = 6 in [1] we have;

⇒

⇒

Simplify:

Therefore, the value of f(6) is, 18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

we fill in where x is and make it 6

And I will use pemdas

f(6)=6^2÷3+6

f(6)=36÷3+6

f(6)=12+6

f(6)=18

Hopes this helps please mark brainliest

The specific values of a, b, and c, or any additional conditions or constraints, it is not possible to determine the exact function f.

To provide more specific information about the function f, to the form of the function. Typically, the height of an object in free fall modeled using a quadratic function.

A common form of a quadratic function is:

f(t) = at² + bt + c

Where:

f(t) represents the height of the ball at time t.

t represents time in seconds.

a, b, and c are constants that determine the shape and position of the quadratic curve.

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The maximum height of the ball is 18.25 meters.

Given, Sarah kicked the ball in the air. The function f models the height of the ball (in meters) as a fiction if time (in seconds) after Sarah kicked it.

The height of the ball is modeled by the function f(t) where t is time in seconds after the ball is kicked .The height of the ball can be modeled as a quadratic function given by

f(t) = -5t² + 15t + 2where, f(t) is the height of the ball (in meters) and t is the time (in seconds) after Sarah kicked the ball.

Let us find the maximum height of the ball:

Maximum height of the ball is given by the vertex of the parabola.

The vertex of the parabola is given by, x = -b / 2a

Here, a = -5, b = 15

So, x = -15 / 2 (-5) = 1.5 sec

The maximum height of the ball is given by

f(1.5) = -5 (1.5)² + 15 (1.5) + 2 = 18.25 m

Therefore, the maximum height of the ball is 18.25 meters.

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Answer:

a B and c because there the shape of the big triangles

Answer:

5 carwashes, Josh: $ 100 savings, Sandra: $100 savings

Step-by-step explanation:

First we need to find each of their formulas.

Formula for Josh: 50+10c=s

Formula for Sandra:25+15c=s

We can set these two to be equal to each other in order to find how many carwashes it takes for them to have the same amount of money.

50+10c=25+15c

25+10c=15c

25=5c

c=5

after 5 car washes, they will have the same amount of money.

now that we know that, we can plug that into each equation to find each of their savings after the 5 carwashes.

Josh's savings:

50+10c=s

plug in the amount of carwashes,

50+10*5=s

50+50=s

s=100 dollars of savings for Josh

Sandra's savings:

25+15c=s

plug in the amount of carwashes,

25+15*5=s

25+75=s

s=100 dollars of savings for Sandra

g value means that the object is experiencing an acceleration that is twice the acceleration due to Earth's gravity.

The "g value" or "g-force" is a measure of the acceleration or deceleration experienced by an object. It is defined as the ratio of the acceleration of the object to the acceleration due to Earth's gravity, which is approximately 9.8 m/s^2.

To calculate the g value of an object, you can use the following formula:

g value = acceleration of the object / acceleration due to gravity

For example, if an object experiences an acceleration of 19.6 m/s^2, the g value can be calculated as follows:

g value = 19.6 m/s^2 / 9.8 m/s^2 = 2 g

This means that the object is experiencing an acceleration that is twice the acceleration due to Earth's gravity.

It's important to note that the g value is a unitless quantity, so the units of the acceleration of the object and the acceleration due to gravity must be the same in order to obtain a correct result.

Therefore,  g value means that the object is experiencing an acceleration that is twice the acceleration due to Earth's gravity.

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The original price of the car stereo system was $82.50. Let us consider the original price of the car stereo system to be `x`.

The sale price is given as $57.75

Discount given is 30%.

Percentage of discount = 30% = 30/100 = 0.3

We know that Discount = Original price × Percentage of discount

Applying this, we get:

Original price × 0.3 = x × 0.3= 0.3x

Sale price = Original price - Discount

= x - 0.3x

= 0.7x

Given that sale price was $57.75,0.7x = $57.75

Dividing by 0.7 on both sides, we get:x = $82.50

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Answer:

36 times

Step-by-step explanation:

Given

\(Red = 4\)

\(Total = 7\)

\(n = 63\)

See attachment

Required

Predicted number of times to land on red

First, we calculate the probability of landing on red

\(Pr = \frac{Red}{Total}\)

\(Pr = \frac{4}{7}\)

The predicted number of red is the =n calculated as:

\(Red = Pr * n\)

\(Red = \frac{4}{7}*63\)

\(Red = 4 * 9\)

\(Red = 36\)

Answer:

Option B

Step-by-step explanation:

3x - 4 > 5

3x > 9

x > 3

-8x - 19 > 21

-8x > 40

x < -5

This means that we can eliminate the first option, since it includes all real numbers. We can also eliminate the last option since it doesn't include any real numbers.

The middle option is the only graph that includes numbers from -∞ to -5, and 3 to ∞

Answer:

For any exponential function in which the base is less than 1, it will be an exponential decay situation.  In this problem, the base is 0.97.  The amount that the base is less than 1  ( i.e. 1 - base) represents, in decimal form, the percent of decrease, which in this case is 0.03 or 3%.  

Step-by-step explanation:

The formula for exponential decay is y=a(1-r)x.  

r is the decay rate.

The type of transformations that maps triangle ABC onto Triangle prime ABC is a  Reflection across the line y=x ; translation 10 units to the right and 4 units up.

Note that: Triangle ABC has vertices at points  which are:

A(-6,2), B(-2,6) and C(-4,2).

Therefore, the reflection across the line y=x has the rule of"

(x, y) ---(y, x).

Hence:

A(-6,2) -- A''(2,-6);

B(-2,6)--- B''(6,-2);

C(-4,2)----C''(2,-4).

2. The translation 10 units to the right and 4 units up is:

(x, y)----(x+10,y+4).

Hence

A''(2,-6)----A'(12,-2);

B''(6,-2)----B'(16,2);

C''(2,-4)----C'(12,0).

Therefore, Points A'B'C' are said to be exactly of the vertices of that of triangle A'B'C'.

Hence, The type of transformations that maps triangle ABC onto Triangle prime ABC is a  Reflection across the line y=x ; translation 10 units to the right and 4 units up.

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Answer:

  \(A. \;\;b \;is \;greater\)

  \(B.\;\;a = 1, b = -4\)

  \(C.\;\;a = 6, c = 20\)

Step-by-step explanation:

Part A

We have the relationship

\(b = 6a - 10\)

When \(a\) is \(-2\), the value of \(b\) is

\(b = 6(-2) -10 = -12 -10 = -22\)

The corresponding value of \(c\) for \(a = - 2\) is -\(21\)

\(-21\) is greater than \(-22\) so answer is :  \(b\)  is greater

Part B

When \(c\) is \(6\), we see that the value of \(a\) from the table is \(1\)

The corresponding value of b is:

\(b = 6(1) - 10 = 6 - 10 = -4\)

Part C

When \(b = 26\), plugging this into the equation\(b = 6a - 10\) we get

\(26 = 6a - 10\\\\26 + 10 = 6a\\\\36 = 6a\\\\\)

or

\(6a = 36\) giving \(a = 36/6 = 6\)

For \(a = 6\), from the table we see that the corresponding value of \(c = 20\)(ANS)

To find the vector v with the same direction as u and a length of 3, we can scale the vector u by a factor of 3 divided by its magnitude.

Given vector u = (1, 2, -1, 0) and the desired length of v as 3, we first need to calculate the magnitude (or length) of vector u.

The magnitude of a vector is computed using the formula:

∥u∥ = √(u1² + u2²+ u3² + u4²), where u₁, u₂, u₃, and u₄ are the components of vector u.

In this case, the magnitude of vector u is √(1² + 2² + (-1)² + 0²) = √6. To find vector v with the same direction as u and a length of 3, we scale u by the factor 3/√6.

This can be done by multiplying each component of u by the scaling factor.

Therefore, vector v = (3/√6) * (1, 2, -1, 0) = (√6/2, √6, -√6/2, 0).

Hence, vector v has the same direction as u and a length of 3.

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Answer:

Angles on a straight line add up to 180 degrees so for the 129 degrees you will take 180 - 129 = 51. In the triangle you will add 51 and 55 = 106 but remember in a triangle all angles should be equal to 180. So 180 - 106 = 74. X=74degrees

Answer:

a) 25%

b) 29 - 7 = 22

c) 21

d) 26 - 15 = 11

e) 75%

Step-by-step explanation:

If the original quantity is five and the new quantity is three, then the percent decrease is 40%.

To find the percent decrease from an original quantity to a new quantity, use the following formula as shown below.

Percent decrease = [(Original quantity - New quantity)/Original quantity] x 100

Given that the original quantity is 5 and the new quantity is 3, we can use the formula to find the percent decrease as shown below.

Percent decrease = [(5 - 3)/5] x 100

= (2/5) x 100

= 0.4 x 100

= 40

Therefore, the percent decrease from an original quantity of 5 to a new quantity of 3 is 40%.

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Answer:

51 degrees

Step-by-step explanation:

As we already know that this triangle is a right triangle.

To find x, you need to subtract both angles.

90 - 39

= 51

The quadratic function in vertex form that has a vertex at (5,12) and passes through the point (8,9) is f(x) = (-1/3)(x - 5)² + 12.

Let the quadratic function in vertex form be

f(x) = a(x - h)² + k,

Where (h,k) is the vertex.

The vertex of the quadratic function is (5, 12).

Therefore, the equation of the function can be written as

f(x) = a(x - 5)² + 12.

It is given that the quadratic function passes through the point (8,9).

Therefore, we have f(8) = 9.

Substituting x = 8 and f(x) = 9 in above equation we get,

9 = a(8 - 5)² + 12.

Simplifying the equation, we get

-3 = 9a

a = -1/3

Thus, the quadratic function in vertex form that has a vertex at (5,12) and passes through the point (8,9) is f(x) = (-1/3)(x - 5)² + 12.

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The response will be A. 34 based on the details provided.

Multiplication is the reverse of division. If the three sets of 4 add up to 12, then 12 split into 3 groups of identical size results in 4 in each group. The primary objective of division is to count the number of equal groups that are created or the number of individuals in each group after a reasonable distribution.

We can divide the overall number of attendees by the number seated in each section to determine the number of sections in the auditorium:

Number of sections = Total number of attendees / Number of people in each section

Number of sections = 5,406 / 159

Number of sections ≈ 34.04

We are able to round up to the closest whole number because we are unable to have a fractional portion of a section, which results in:

Number of sections ≈ 34

Therefore, the answer is A. 34

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The given random variable process Zt is not third order stationary in distribution.

For a process to be third order stationary in distribution, its mean, variance, and third central moment must be constant over time.

Here, we can calculate the first three central moments of Zt as follows:

Mean: E[Zt] = E[(-1 raised to power of t) A] = (-1 raised to power of t E[A]. Since A has a fixed and finite mean, E[Zt] is not constant over time, and hence Zt is not first order stationary.

Variance: Var[Zt] = Var[(-1 raised to power of t) A] = Var[A]. Since A has a fixed and finite variance, Var[Zt] is constant over time, and hence Zt is second order stationary.

Third central moment: E[(Zt - E[Zt]) raised to power of 3] = E[((-1 raised to power of t) A - (-1) raised to power of t E[A]) raised to power of 3] = (-1) raised to power of t E[(A - E[A]) raised to power of 3]. Since A has a fixed and finite third central moment, E[(A - E[A]) raised to power of 3] is not constant over time, and hence E[(Zt - E[Zt]) raised to power of 3] is not constant over time, and hence Zt is not third order stationary.

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In this scenario, we have a uniformly charged thin rod extending along the x-axis from the origin (x = 0) to positive infinity (x = +∞).

The term "uniformly charged" means that the charge is distributed evenly throughout the entire length of the rod.

To analyze this situation, we can consider the following steps: 1. Determine the linear charge density (λ) of the rod. Since the rod is uniformly charged, λ remains constant along its entire length. λ is usually given in units of charge per length (e.g., coulombs per meter).

2. To find the electric field at a particular point along or outside the rod, we can break the rod into infinitesimally small segments (dx) and consider the contribution of the electric field (dE) from each of these segments.

3. Calculate the electric field (dE) produced by each segment at the desired point using Coulomb's equations , considering the linear charge density (λ) and distance between the segment and the point.

4. Integrate the electric field contributions (dE) from all segments along the entire length of the rod (from x = 0 to x = +∞) to find the total electric field (E) at the point of interest.

By following these steps, you can analyze the electric field and related properties of a uniformly charged thin rod extending along the x-axis from x = 0 to x = +∞.

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Question:

Write an algebraic statement that represents all the ways your player will win. Be sure to define your variable

Answer:

Erica:

\(0 \leq |x - y| < 10\)

Nita:

\(10 < |x - y| \leq 20\)

Step-by-step explanation:

Given

Players: Erica & Nita

Range: 0 to 20

Represent Erica with x and Nita with y

For Erica to win;

The difference between x and y must be less than 10 but greater than or equal to 0

i.e.

\(0 \leq x - y \leq 10\) or \(0 \leq y - x \leq 10\)

These two expressions can be merged together to be:

\(0 \leq |x - y| < 10\)

For Nita to win;

The difference between x and y must be greater than 10 but less than or equal to 20

i.e.

\(10 < x - y \leq 20\) or \(10 < y - x \leq 20\)

These two expressions can be merged together to be:

\(10 < |x - y| \leq 20\)

Answer:

Step-by-step explanation:

If you plot those points on a coordinate plane, you'll see that the distance from the origin up the y-axis to the point is greater than is the distance from the origin down the x-axis to the other point. That means 3 things to us: 1. the greater distance is a and the shorter is b; 2. the point (0, 11) is the vertex while the point (4, 0) is the co-vertex; and 3. this is a vertically stretched ellipse. A vertically stretched ellipse has an equation

\(\frac{(x-h)^2}{b^2} +\frac{(y-k)^2}{a^2} =1\) where h and k are the coordinates of the center, a is the greater distance (between the center and the vertex), and b is the smaller distance (between the center and the co-vertex).  Here's what we have then thus far:

h = 0

k = 0

a = 11

b = 4

Filling in our equation then looks like this:

\(\frac{(x-0)^2}{4^2} +\frac{(y-0)^2}{11^2} =1\) and simplifying:

\(\frac{x^2}{16} +\frac{y^2}{121} =1\). It appears that the last answer is the one you want, although when I teach this to my precalc students, I do not encourage them to move the x and y terms around as that answer appears to have done. But addition is also commutative so I'm sure it's acceptable (I just think it looks strange that way).

The equation of ellipse is \(\dfrac{y^2}{121}+\dfrac{x^2}{16}=1\) option D is correct.

Important information:

The standard form of an ellipse is:

\(\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1\)

Where, \((0,a)\) is vertex and \((0,b)\) is vertex.

Substitute \(a=11,b=4\) in the above equation.

\(\dfrac{x^2}{(4)^2}+\dfrac{y^2}{(11)^2}=1\)

\(\dfrac{x^2}{16}+\dfrac{y^2}{121}=1\)

\(\dfrac{y^2}{121}+\dfrac{x^2}{16}=1\)

Therefore, the correct option is D.

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