Two functions are ________ equivalent if they produce the same output for a specific input value.
Always
Sometimes
Never

The expected value of X is 7, and the standard deviation of X is 2.42 respectively.

The average of X's potential values is the expected value of X. We must first determine the sum of all potential x values multiplied by each value's associated probability before we can determine the expected value.

Calculate the expected value of X

Expected value = (2×(1/36)) + (3×(2/36)) + (4×(3/36)) + (5×(4/36)) + (6×(5/36)) + (7×(6/36)) + (8×(5/36)) + (9×(4/36)) + (10×(3/36)) + (11×(2/36)) + (12×(1/36))

Expected value = 7

Calculate the variance of X

Variance = (2-7)2×(1/36) + (3-7)2×(2/36) + (4-7)2×(3/36) + (5-7)2×(4/36) + (6-7)2×(5/36) + (7-7)2×(6/36) + (8-7)2×(5/36) + (9-7)2×(4/36) + (10-7)2×(3/36) + (11-7)2×(2/36) + (12-7)2×(1/36)

Variance = 5.83

Calculate the standard deviation of X

Standard deviation = √(variance)

Standard deviation = 2.42

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Complete Question:

Consider the roll of two dice. Let X be a random variable representing the sum of the number of dots appearing on each of the dice. The probabilities of each possible value of X are as follows:

x             P(x)

2            1/36

3            2/36

4            3/36

5            4/36

6            5/36

7            6/36

8            5/36

9            4/36

10           3/36

11            2/36

12            1/36

Determine the expected value and standard deviation of X.

In this case, the terminal velocity can be determined as v_terminal = sqrt(g/k). The velocity of a ball dropped from a great height can be described by an expression that takes into account the force of air resistance acting on it.

In this case, with a drag coefficient of 0.1 and a force proportional to the square of velocity, the expression for velocity at any time t is v(t) = (g/k)(1 - e^(-kt)), where g is the acceleration due to gravity and k is the product of the drag coefficient and mass of the ball. The limiting or terminal velocity of the ball is the maximum velocity it reaches when the force of gravity and the drag force balance each other out.

When a ball is dropped from a great height, it initially accelerates due to the force of gravity. However, as the ball gains velocity, the force of air resistance starts to oppose its motion. The drag force is proportional to the square of the velocity and acts in the opposite direction.

The net force acting on the ball can be expressed as F_net = mg - kv^2, where m is the mass of the ball, g is the acceleration due to gravity, and k is the drag coefficient. According to Newton's second law, F_net is equal to the mass times the acceleration, so we have mg - kv^2 = ma.

Rearranging the equation, we get ma + kv^2 = mg. Dividing both sides by m, we have a + (k/m)v^2 = g. Since a = dv/dt (acceleration is the derivative of velocity with respect to time), we can rewrite the equation as dv/dt + (k/m)v^2 = g.

This is a first-order linear ordinary differential equation that can be solved using various methods, such as separation of variables. Solving this equation leads to the expression v(t) = (g/k)(1 - e^(-kt)), where e is the base of the natural logarithm.

The terminal velocity is the point at which the velocity of the ball no longer increases. At terminal velocity, the force of gravity and the drag force balance each other out, resulting in zero acceleration. Mathematically, we set dv/dt = 0 in the equation dv/dt + (k/m)v^2 = g. Solving for v, we find v_terminal = sqrt(g/k), which represents the maximum velocity the ball will reach under the given conditions.

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The angle 1 can be named as follows:

∠RST

∠TSR

∠S

There are various ways to name an angles. You can name an angle by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.

Therefore, let's name the angle 1 indicated on the diagram as follows:

Hence, the different ways to name the angle 1 is as follows:

∠RST or ∠TSR

Or

∠S

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Answer:

( x - 4 )^2 + ( y + 5 )^2 = 9^2

Step-by-step explanation:

equation of a circle: ( x - h )^2 + ( y - k )^2 = r^2

( h, k ) is the center and r is the radius.

\(\boxed{c.\:n\:=\:18}\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\( \frac{6}{n} = \frac{14}{42} \\ ⇢ n = \frac{6 \times 42}{14} \\ ⇢ n = \frac{252}{14} \\ ⇢ n = 18\)

\({ \bf{ \underbrace{To\:verify:}}}\)

\( \frac{6}{n} = \frac{14}{42} \\ ⇢  \frac{6}{18} = \frac{14}{42} \\ ⇢  \frac{1}{3} = \frac{1}{3} \\ ⇢ L.H.S.=R. H. S\)

Hence verified.

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.ඞ}}}}}\)

Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

Answer:

\(h=\frac{2A}{b}\)

Step-by-step explanation:

In this problem, we will rearrange the equation to isolate \(h\).

We start with the given equation:

\(A=\frac{1}{2} bh\)

I will work the \(\frac{1}{2}\) and the \(b\) out of the right side so that \(h\) is left by itself.

First I multiply both sides by 2 to get rid of the \(\frac{1}{2}\) :

\((2)A = (2)\frac{1}{2} bh\)

2 is the same as \(\frac{2}{1}\), so its numerator and denominator cancel the \(\frac{1}{2}\) .

Simplifying, we now have:

\(2A=bh\)

Now we can divide both sides by \(b\):

\(\frac{2A}{b} =\frac{bh}{b}\)

We can cancel the \(b\) in the fraction on the right side, and we're left with:

\(\frac{2A}{b} =h\)

which is the same as:

\(h=\frac{2A}{b}\)

Hope this helps! Let me know if you have any questions.

Camille will have walked for 5 days when she and Hiroki have walked the same number of miles.Let's call the number of days Camille walks "x". After the first day, she walks 3 miles each day, so her total distance after x days is 7 + 3(x - 1) miles.

Hiroki starts walking later, but he walks 5 miles each day. To make up for the two days he missed, he walks 5 miles each day for x - 2 days. His total distance after x days is 5(x - 2) miles.

For Camille and Hiroki to have walked the same number of miles, their distances must be equal:

7 + 3(x - 1) = 5(x - 2)

Expanding the right side:

7 + 3x - 3 = 5x - 10

Combining like terms:

3x + 7 = 5x - 3

Subtracting 3x from both sides:

7 = 2x - 3

Adding 3 to both sides:

10 = 2x

Dividing both sides by 2:

5 = x

So, Camille will have walked for 5 days when she and Hiroki have walked the same number of miles.

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Answer:(-7, -8), (-7,5), (-6,0),(-1,8)

Step-by-step explanation:

Functions are relations with one output (y) for any unique input (x).

The first set has two values of y when x = -7:  -8 and 5.

The other sets have unique values for each x.

The rocket hits the ground after 9 seconds (t = 9).

To determine when the rocket hits the ground, we need to find the time when the height (h(t)) equals zero.

Given the equation for the height of the rocket as h(t) = -16t^2 + 144t, we can set it equal to zero:

-16t^2 + 144t = 0

We can factor out a common term of -16t:

-16t(t - 9) = 0

Setting each factor equal to zero gives us two possible solutions:

-16t = 0, which implies t = 0.

t - 9 = 0, which implies t = 9.

Since time (t) cannot be negative in this context, we discard the t = 0 solution.

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Answer:

y = 2/3

Step-by-step explanation:

14 = 6(2) + 3y

14 = 12 + 3y

2 = 3y

y = 2/3

It will take forty seven minute (i.e., 47 minute later) for the digits displayed next to form an arithmetic sequence again.

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers where each term is the sum of the previous term and a constant difference. It is also known as an arithmetic sequence.

At 2:58 p.m., the digits displayed on the clock are 2, 5, and 8, and they form an arithmetic sequence with a common difference of 3.

The next time the digits will form an arithmetic sequence is when the time is 3:45 p.m.

At 3:45 p.m., the digits displayed on the clock are 3, 4, and 5, and they also form an arithmetic sequence with a common difference of 1.

Therefore, it will take forty seven minute (i.e., 47 minute later) for the digits displayed next to form an arithmetic sequence again.

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Answer:84.84m^2

Edit: I redid it doing the base separate and got 84.847 because Pythagorean theorem tells you the sides of the three triangles are 6.998 which is ever so slightly smaller than the base triangle.

Step-by-step explanation:

This is assuming the triangles are equal. 1/2bh gives you 21.21 for the triangle with the given height and then multiplying that by four for all the sides gives you 84.84m^2. The question doesn’t specify what type of pyramid it is so again I’m assuming it’s equal. Not 100% positive hope it can help at all.

Given data:

The given ratio is 16g:72g.

The expression for the given ratio is,

Thus, the given ratio can be written as 2/9.

The  breakdown is as follows:

A: The entire green box represents the overall chemical equation.

B: The blue box represents the reactant, which is 2H2O (water)

C: The arrow represents the chemical reaction or the process of breaking down the reactant into the products.

D: The pink box represents the products, which are 2H2 (hydrogen) and O2 (oxygen)

So the chemical equation is 2 H2O --> 2 H2 + O2

The entire green box represents the chemical equation, the blue box represents the reactant (water) and the pink box represents the products (hydrogen and oxygen) and the arrow represents the chemical reaction.

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Answer:

-53

Step-by-step explanation:

if m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5 , and t = − 2

-| 10 - 7r + 8m + 2p |

Substitute the given values into the equation.

-| 10 - 7(5) + 8(-4) + 2(2) |

Simplify

-| 10 - 35 + -32 + 4) |

-| -53 |

= -53

Absolute value of -53 is 53 however there is a negative sign outside of it, so the answer is -53

Answer:

y = 2x + 18

Step-by-step explanation:

This is slope intercept form: y = mx + b

m = slope

b = y-intercept

We are already given the slope, 2

y = 2x + b

Now we just need to find b, so plug in the given coordinates

2 = 2(-8) + b

2 = -16 + b

Add 16 to both sides

2 = -16 + b

+ 16  + 16

b = 18

Now place in the new b into the the equation

y = 2x + 18

The type of data described in the scenario is categorical data. Categorical data represents qualitative variables that can be divided into distinct categories or groups.

In this case, the data represents the outcome of the treatment for patients with Type 2 Diabetes.The two possible outcomes, "no longer needed to use insulin" and "still needed to use insulin," indicate distinct categories or groups into which the patients can be classified based on their response to the treatment.

The data is categorical because it involves the assignment of patients to two different groups (metformin and rosiglitazone) and the classification of their outcomes into two discrete categories. It does not involve numerical measurements or continuous variables. By categorizing the patients' responses to the treatment, researchers can analyze and compare the effectiveness of the two drugs, evaluate the proportion of patients who achieved the desired outcome, and make conclusions about the potential benefits of each treatment option for patients with Type 2 Diabetes.

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Complete Question : Diabetes 17 Points A clinical trial was performed on 465 patients, aged 10-17, who suffered from Type 2 Diabetes These patients were randomly assigned to one of two groups Group 1 met) was treated with a drug called metformin Group 2 frosi) was treated with a drug called rosiglitazone At the end of the experiment, there were two possible outcomes. Outcome 1 is that the patient no longer needed to use insulin Outcome 2 is that the patient still needed to use insulin 232 patients were assigned to the met treatment, and 112 of them no longer needed insulin after the treatment 233 patients were assigned to the ros treatment, and 143 of them no longer needed insulin after the treatment. What type of data is this?

a) The exact solutions on [0, 2π) are t = π/3, π, and 5π/3. b) The exact solution on the interval [0, π) is t = 2π/3. c) The solutions are θ = π/3 and θ = 5π/3. d) The exact solutions on the interval [0, 2π) are: t = arcsin[(-1 +  \(\sqrt{41}\))/4] and t = 2π - arcsin[(-1 +  \(\sqrt{41}\))/4] using trigonometric identities.

a) We can rewrite the equation as:

2\(cos^{2}t\) + cos(t) - 1 = 0

Using the quadratic formula, we get:

cos(t) = [-1 ± \(\sqrt{1-4(2)(-1)}\) ] / (4)

cos(t) = [-1 ± \(\sqrt{9}\)]/4

cos(t) = [-1 ± 3]/4

Thus, we have two solutions:

cos(t) = 1/2, which gives us t = π/3 and t = 5π/3

cos(t) = -1, which gives us t = π

Therefore, the exact solutions on [0, 2π) are t = π/3, π, and 5π/3.

b) We can use the identity \(tan^{2}t\) + 1 = \(sec^{2}t\) to rewrite the equation as:

\(tan^{2}t\) = - \((3/2)^{2}\)

Taking the square root of both sides and remembering that tan(t) is negative in the third quadrant, we get:

tan(t) = -3/2

Using the identity tan(t) = sin(t)/cos(t), we can rewrite this as:

sin(t)/cos(t) = -3/2

Multiplying both sides by cos(t) and rearranging, we get:

sin(t) = -3cos(t)/2

Squaring both sides and using the identity \(sin^{2}t\) + \(cos^{2}t\) = 1, we get:

9\(cos^{2}t\)/4 + \(cos^{2}t\) = 1

Expanding and simplifying, we get:

13 \(cos^{2}t\) /4 = 1

\(cos^{2}t\)  = 4/13

Taking the square root of both sides and remembering that cos(t) is negative in the third quadrant, we get:

cos(t) = -2\(\sqrt{13}\) /13

Using the identity  \(sin^{2}t\) +  \(cos^{2}t\)  = 1, we can solve for sin(t) as:

sin(t) = -3/2 cos(t) = 3\(\sqrt{13}\) /13

Therefore, the exact solution on the interval [0, π) is t = 2π/3.

c) We can use the identity sin(2θ) = 2sin(θ)cos(θ) to rewrite the equation as:

sin(θ) = 2sin(θ)cos(θ)

Dividing both sides by sin(θ) (assuming sin(θ) is non-zero), we get:

1 = 2cos(θ)

cos(θ) = 1/2

Therefore, the solutions are θ = π/3 and θ = 5π/3.

d) We can use the identity cos(2t) = 1 - 2 \(sin^{2}t\)  and rearrange the equation as:

2 \(sin^{2}t\)  + sin(t) - 5 = 0

Solving this quadratic equation using the quadratic formula, we get:

sin(t) = [-1 ± \(\sqrt{41}\)]/4

Since the sine function has a range of [-1, 1], only the positive solution is possible, so we have:

sin(t) = (-1 + \(\sqrt{41}\))/4

Using the identity \(cos^{2}t\) = 1 -  \(sin^{2}t\) , we can solve for cos(t) as:

cos(t) =\(\sqrt{1-sin^{2}t}\) = \(\sqrt{17-\sqrt{41} }/4\)

Therefore, the exact solutions on the interval [0, 2π) are:

t = arcsin[(-1 +  \(\sqrt{41}\))/4] and t = 2π - arcsin[(-1 +  \(\sqrt{41}\))/4]

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The percentage increase in the value of the house each of the three years is 11.49%.

The equation that can be used to represent the percentage change in the value of the house is:

(100x - 10%) + 3x% = 55.52%

90% + 3x = 55.52%

90% - 55.52% = 3x

34,48% = 3x

x = 34.48/3

x = 11.49%

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Answer:

1,216 dollars

Step-by-step explanation:

Do 32 x 38 = 1,216

Answer:

D

Step-by-step explanation:

The parabola opens to the right

therefor it will be of the form x = +y^2

The probability that demand during this period will exceed 25 gallons depends on the distribution of demand.

To calculate the probability of a stockout during the replenishment lead-time, we need to consider the distribution of demand during this period. If the demand follows a known probability distribution, such as the normal distribution, we can use statistical methods to estimate the probability.

First, we need to determine the parameters of the distribution, such as the mean and standard deviation of the demand during the lead-time. Once we have these parameters, we can calculate the probability of demand exceeding 25 gallons using the cumulative distribution function (CDF) of the chosen distribution.

For example, if the demand during lead-time follows a normal distribution with a mean of 20 gallons and a standard deviation of 5 gallons, we can use the normal distribution table or statistical software to find the probability of demand exceeding 25 gallons.

Alternatively, if we have historical data on demand during lead-time, we can use that data to estimate the probability. We can calculate the proportion of instances where the demand exceeded 25 gallons and use this as an estimate of the probability of a stockout during the lead-time.

Overall, the probability of a stockout during replenishment lead-time depends on the distribution of demand and can be determined using statistical techniques or historical data.

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Answer:

x>-8

Step-by-step explanation:

7x+11>5x-5

2x+11>-5

2x>-16

x>-8

the > sign acts like an equal sign :)

Answer:

\( x > - 8\)

Step-by-step explanation:

\(7x + 11 > 5x - 5 \\ 7x - 5x > - 11 - 5 \\ 2x > - 16 \\ x > - 8\)

The equation that represents the sentence "28 is the quotient of a number and 4" is 28 = n/4.

In the given sentence, "28 is the quotient of a number and 4," we can break down the sentence into mathematical terms. The term "quotient" refers to the result of division, and "a number" can be represented by the variable "n." The divisor is 4.

1) Define the variable.

Let's assign the variable "n" to represent "a number."

2) Write the equation.

Since the sentence states that "28 is the quotient of a number and 4," we can write this as an equation: 28 = n/4.

The equation 28 = n/4 represents the fact that the number 28 is the result of dividing "a number" (n) by 4. The left side of the equation represents 28, and the right side represents "a number" divided by 4.

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In the given problem, we calculated the price of a bond with a $1,000 face value, a $50 annual coupon, and six years to maturity when the interest rate is 4%. The price of the bond was found to be $1,160.79.

The calculation of the price of the bond can be done using the following formula:

Price = (Annual Coupon Payment / Interest Rate) x (1 - 1 / (1 + Interest Rate) ^ Years to Maturity) + Face Value / (1 + Interest Rate) ^ Years to Maturity.

The annual coupon payment is $50, the interest rate is 4% or 0.040 and the face value is $1,000. Therefore, the price of the bond is given as:Price = ($50 / 0.040) x (1 - 1 / (1 + 0.040) ^ 6) + $1,000 / (1 + 0.040) ^ 6Price = ($1,250) x (1 - 1 / 1.281) + $747.26Price = $1,160.79.

Therefore, the price of the bond is $1,160.79. The bond offers an annual coupon of $50 and has a face value of $1,000. It has six years to maturity and the interest rate is 4%.

Using the bond pricing formula, we can calculate that the price of the bond is $1,160.79.

In finance, a bond is a type of debt security in which the issuer owes the holders a debt and is obliged to pay interest or repay the principal at a later date, known as maturity.

A bond can be issued by a company, municipality, or government entity as a means of raising capital. The price of a bond is determined by several factors, including its face value, coupon rate, and interest rate.

In the given problem, we are asked to calculate the price of a bond with a $1,000 face value, a $50 annual coupon, and six years to maturity when the interest rate is 4%.

Using the bond pricing formula, we found that the price of the bond is $1,160.79.

This means that if an investor were to buy the bond for this price, they would receive the annual coupon payments of $50 for the next six years and then receive the face value of $1,000 at maturity.

In conclusion, the price of a bond can be calculated using the bond pricing formula. The price of a bond depends on several factors, including its face value, coupon rate, and interest rate. In the given problem, we calculated the price of a bond with a $1,000 face value, a $50 annual coupon, and six years to maturity when the interest rate is 4%. The price of the bond was found to be $1,160.79.

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To test the difference between two independent population means with two samples, you need to calculate the degrees of freedom (df). Here's a step-by-step explanation:

1. Identify the sample sizes: The first sample has a size of 28 (n1 = 28), and the second sample has a size of 27 (n2 = 27).

2. Calculate the degrees of freedom for each sample: For each sample, subtract 1 from the sample size. For sample 1, df1 = n1 - 1 = 28 - 1 = 27. For sample 2, df2 = n2 - 1 = 27 - 1 = 26.

3. Combine the degrees of freedom: Add the degrees of freedom from each sample together to get the total degrees of freedom: df = df1 + df2 = 27 + 26 = 53.

In this case, you will use 53 degrees of freedom to find the critical value for testing the difference between the two independent population means.

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Answer:

-11.5

Step-by-step explanation:

I just did it on the calculator :)

A key requirement for the process of testing hypotheses in the scientific method is experimentation. A hypothesis is an idea or explanation for a phenomenon that is grounded in existing knowledge or observations, and the scientific method involves testing those hypotheses through experimentation.

The process of testing hypotheses requires the development of a testable hypothesis, the design of experiments to test the hypothesis, and the collection and analysis of data from those experiments to evaluate the hypothesis. The experiments must be designed carefully, with appropriate controls and variables to ensure that the results are reliable and valid. Scientists also need to communicate their findings to the scientific community, which involves publishing their results in scientific journals and presenting their work at conferences.

This helps to ensure that other scientists can replicate their experiments and validate their findings, which is a critical part of the scientific process. Ultimately, the process of testing hypotheses is essential for advancing scientific knowledge and understanding how the world works.

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