What is 6/14 + 1/5 equal to?

The correct answer is C. The dependent variable is not typically the explanatory variable in a regression model.

In regression analysis, we aim to understand the relationship between a dependent variable and one or more independent variables. The dependent variable is the variable we are trying to explain or predict, while the independent variables are the ones we use to explain or predict the dependent variable.

In a regression model, the intercept coefficient is typically interpreted. It represents the predicted value of the dependent variable when all the independent variables are equal to zero. So, statement A is not true.

The estimates of the slope coefficients are indeed found from sample data. These coefficients represent the change in the dependent variable associated with a one-unit change in the corresponding independent variable. Therefore, statement B is true.

Finally, the regression line is constructed in a way that it minimizes the sum of squared errors, also known as the residuals. The residuals are the differences between the actual values of the dependent variable and the predicted values from the regression model. So, statement D is true.

In summary, statement C is the only statement that is not true about a regression model. The dependent variable is not typically the explanatory variable in regression analysis.

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Applying the knowledge of quotient and fractions, we have:

The number of soda each person will drink is: \(1\frac{2}{3} \) glasses.

The fraction of sugar to be used per cupcake is: \(1\frac{3}{5} \)

Problem 1:

The expression that matches the situation is: 7 ÷ 3 (quotient of 7 and 3)

7/3 = \(1\frac{2}{3} \)

The number of soda each person will drink is: \(1\frac{2}{3} \) glasses.

Problem 2:

The expression that matches the situation is: 8 ÷ 5 (quotient of 8 and 5)

8/5 = \(1\frac{3}{5} \)

The fraction of sugar to be used per cupcake is: \(1\frac{3}{5} \)

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The radius of the cone is 3 times the radius of the cylinder, given that they have equal volumes and radii of equal length.

The height of the cylinder is also 24 centimeters since the radii are equal.

To find the volume of the cylinder, use the formula V = πr^2h, where r is the radius and h is the height.

To find the volume of the cone, use the formula V = (1/3)πr^2h, where r is the radius and h is the height.

Since the volumes are equal, you can set up the equation (1/3)πr^2(24) = πr^2(24) and solve for r.

Simplifying the equation, you get (1/3) = 1.

This means that the radius of the cone is 3 times the radius of the cylinder.

Therefore, the radius of the cone is 3 times the radius of the cylinder, given that they have equal volumes and radii of equal length.
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By definition of area of a rectangule,  the width of the field is 2/3 mile.

The area is the measure of a space delimited by a contour called the perimeter. In other words, area is the measure of the surface of a figure; that is, the measure of its interior region.

A rectangle is a flat geometric figure with four sides, of which two sides that are opposite parallel to each other have the same length and the remaining two have another length.

The area of ​​a rectangle is calculated from the two different sides, and it is calculated by multiplying the length (L) by the width (W):

Area= L×W

In this case, the length of a rectangular shaped field is 3/4 mile. If the area of the field is 1/2 mile², then the width can be calculated as:

1/2 mile²= 3/4 mile× W

Solving:

1/2 mile²÷ 3/4 mile= W

2/3 mile= W

Finally, the width of the field is 2/3 mile.

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The perpendicular distance x of Mount Krasha from the road is approximately 297.33 km.

One of the most significant areas of mathematics, trigonometry has a wide range of applications.

We can solve this problem using trigonometry. Let's draw a diagram to help us visualize the situation:

Let's let the point where the direction toward Mount Krasha makes an angle of 33 degrees with the road be point A, and let the point 16 km farther along the road where the angle is 35 degrees be point B. Let's also let the perpendicular distance from Mount Krasha to the road be x.

From the diagram, we can see that:

- The distance from point A to point B along the road is 16 km.

- The angle between the road and the perpendicular line from Mount Krasha to the road is (90 - 33) = 57 degrees at point A, and (90 - 35) = 55 degrees at point B.

Using trigonometry, we can set up two equations:

```

tan(57) = x / d     (where d is the distance from the starting point to point A)

tan(55) = x / (d + 16)   (where d + 16 is the distance from the starting point to point B)

```

We want to solve for x, so we can rearrange each equation to isolate x:

```

x = d * tan(57)

x = (d + 16) * tan(55)

```

Now we can set these two equations equal to each other and solve for d:

```

d * tan(57) = (d + 16) * tan(55)

d * 1.5403 = (d + 16) * 1.4281

1.5403d = 1.4281d + 22.8496

0.1122d = 22.8496

d = 203.76 km

```

Therefore, the distance from the starting point to point A is 203.76 km. We can now substitute this value into either equation for x to solve for x:

```

x = d * tan(57)

x = 203.76 km * tan(57°)

x ≈ 297.33 km

```

Therefore, the perpendicular distance x of Mount Krasha from the road is approximately 297.33 km.

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Answer:

a) Sinusoidal functions are y = a sin [b(x-h)] + k    (or)                                        

y = a cos [b(x-h)] + k

Where a is amplitude a= (max-min)/2=(16-2)/2=7

period p= 2π/b

            b=2π/30

            Horizontal transformation to 10 units right h=10

            k= (max+min)/2=(16+2)/2=9

h = 7 cos [π/15(t-10)]+ 9

b) t=10min=600 sec

substitue in the above equation

h=5.5m

Answer:

so67 =9

Step-by-step explanation:

The angle of elevation of the road is approximately 9.48 degrees.

To calculate the angle of elevation of the road, we need to use the tangent function, which relates the opposite side (vertical change) to the adjacent side (horizontal distance). In this case, the vertical change is 100 feet and the horizontal distance is 0.6 miles, which we need to convert to feet.

Convert 0.6 miles to feet

Since 1 mile is equal to 5,280 feet, we can calculate:

0.6 miles * 5,280 feet/mile = 3,168 feet

Step 2: Calculate the angle of elevation

Using the tangent function:

To find the angle, we take the inverse tangent (arctan) of this ratio:

Finally, we convert the angle from radians to degrees:

Rounded to two decimal places, the angle of elevation of the road is approximately 9.48 degrees.

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Initially, only one person had heard the rumor.

The answer is b.

We have the following information available from the question is:

The function  \(N(t) =\frac{300}{1+299e^ \\,0.36t}\) describes the spread of a rumor among a group of people in an enclosed space.

Where,

N represents the number of people who have heard the rumor,

and t is measured in minutes since the rumor was started.

Now, According to the question:

The function is:

\(N(t) =\frac{300}{1+299e^ \\,0.36t}\)

And, we put t = 0 we get :

\(N(0) =\frac{300}{1+299e^ \\,0.36(0)}\)

\(N(t) =\frac{300}{1+299e^ \\0}\)

\(N(t) =\frac{300}{1+299}\\\\N(t) =\frac{300}{300} = 1\)

Hence, Initially, only one person had heard the rumor.

The answer is b.

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Complete question is:

The function N(t)=300/(1+299e^-0.36t) describes the spread of a rumor among a group of people who have heard the rumor, and (t) is measured in minutes since the rumor was started. Which of the following statements are true?

a. The rate at which the rumor spreads speeds up over time.

b. Initially, only one person had heard the rumor.

c. It will take approx. 14 mins for 100 people to hear the rumor.

d. There are 299 people in the enclosed space.

Answer:

Angles: Y=S and Z=T

Sides YZ=ST and XZ=RT

Step-by-step explanation: trus

Addition of a positive and negative number always means that you are going to subtract the number e. g. 4+-1 = 3. However, multiplication of a positive and negative number means the answer is always negative e. g. 5 x - 3 = - 15.

The addition of positive and negative number will always subtract with sign of maximum value.

The multiplication of positive and negative number will have a negative sign always.

When two numbers which have different sign are added, they will always be subtracted from each other. The sign will vary accordingly.

Example: Consider two number -5 and 4

= -5 + 4

= -1

Here, 5 is the larger value. So, the sign comes is negative.

Example: consider two number 5 and -4.

= 5 + (-4)

= 1

Here, 5 is the large number. So, the sign comes is positive.

When two numbers with opposite signs are multiplied, the answer is always a negative number.

Example; Consider two numbers 4 and -5.

On multiplication,

4×(-5) = -20

Thus, the multiplication of two numbers with different signs will always give a negative number.

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The set of all pure and mixed strategy Nash Equilibria of the given two-person game is {(U, D), (D, U), (1/3, 2/3), (2/3, 1/3)}.

The given two-person game is shown in the given table below.Player 2Player 1UDUD2,20,00,20,4The given two-person game has two pure strategy Nash equilibria, (U, D) and (D, U).Mixed strategy Nash EquilibriaIn this game, if player 1 selects U with a probability of q, then the expected payoff of player 2 will be: U = 2q + 0 (1 - q) = 2q where 1 - q is the probability of selecting D.

Similarly, if player 1 selects D with a probability of q, then the expected payoff of player 2 will be: D = 0q + 4 (1 - q) = 4 - 4q where 1 - q is the probability of selecting U.

Similarly, if player 2 selects U with a probability of p, then the expected payoff of player 1 will be: U = 2p + 0 (1 - p) = 2p where 1 - p is the probability of selecting D.

Similarly, if player 2 selects D with a probability of p, then the expected payoff of player 1 will be: D = 0p + 2 (1 - p) = 2 - 2p where 1 - p is the probability of selecting U.

If player 1 mixes his strategies, then the best response of player 2 can be obtained as: U = 2q and D = 4 - 4q.

Similarly, if player 2 mixes his strategies, then the best response of player 1 can be obtained as: U = 2p and D = 2 - 2pThe following table can be drawn for the best response of each player.

Best Responses Player 2 Player 1 U D U D BR21 1 2 2 BR12 1/2 1/2 2 0.

By solving the above best responses, the set of all pure and mixed strategy Nash equilibria can be obtained.

SolutionThe pure strategy Nash equilibria are (U, D) and (D, U).Now we will find the mixed strategy Nash equilibria of the given two-person game by solving the best response correspondences of each player.

The set of all pure and mixed strategy Nash equilibria of the given two-person game is {(U, D), (D, U), (1/3, 2/3), (2/3, 1/3)}.

The given two-person game has been given in the table shown below.Player 2Player 1UDUD2,20,00,20,4The two-person game given above can have a pure strategy Nash Equilibrium and mixed strategy Nash Equilibrium, which can be found by plotting the best response correspondences of each player.

The Nash equilibrium can be defined as a state where no player can increase its payoff by changing its strategy given the other player's strategy.The mixed Nash equilibrium can be solved by considering the probability with which each player is playing each of its strategies.

The expected payoff of the player is calculated by multiplying the payoff of each outcome with its probability and then adding up all the values of each outcome after multiplication. Each player tries to choose the strategy that maximizes its expected payoff given the strategy of the other player.

The best response of each player can be plotted on a graph. If the best response of each player coincides, then it is a Nash Equilibrium.

The set of all pure and mixed strategy Nash Equilibria of the given two-person game is {(U, D), (D, U), (1/3, 2/3), (2/3, 1/3)}. The Nash equilibrium can be defined as a state where no player can increase its payoff by changing its strategy given the other player's strategy. The best response of each player can be plotted on a graph. If the best response of each player coincides, then it is a Nash Equilibrium.

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Answer:

AC = 70

BG = 38

GC = 28

AE = 63

Step-by-step explanation:

The given parameters are;

The centroid of ΔABC = G

The length of FC = 35

The length of AG = 42

The length of BF = 57

The length of DG = 14

Given that the centroid is the intersection of the medians, we have;

FA = FC = 35 Definition of median line FB, (point F is the midpoint of AC)

AC = FA + FC = 35 + 35 = 70 by segment addition postulate

AC = 70

BG = 2/3 × BF = 2/3 × 57 = 38 Definition of median line BF

BG = 38

DG = 14 = 1/3 × DC Definition of median line

∴ DC = 3 × DG = 3 × 14 = 42

GC = 2/3 × DC = 2/3 × 42 = 28 Definition of median line DC

GC = 28

AG = 42 = 2/3 × AE Definition of median line AE

∴ AE = 3/2 × 42 = 63

AE = 63.

The equation of the ellipse with focus at (-2,0) and vertices at (±7, 0) is given as follows:

x²/49 + y²/45 = 1.

The equation of an ellipse of center (h,k) is given by the equation presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

The center of the ellipse is given by the mean of the coordinates of the vertices, as follows:

Hence:

x²/a² + y²/b² = 1.

The vertices are at x + a and x - a, hence the parameter a is given as follows:

a = 7.

Considering the focus at (-2,0), the parameter c is given as follows:

c = -2.

We need the parameter c to obtain parameter b as follows:

c² = a² - b²

b² = a² - c²

b² = 49 - 4

b² = 45.

Hence the equation is given as follows:

x²/49 + y²/45 = 1.

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Explanation:

We have to multiply -4 by itself 3 times: (-4)³ = (-4)x(-4)x(-4)

The first time we'll have a positive number, because the product of two negative numbers is a positive number:

Now we just have to solve 16x(-4). The result will be a negative number, because the product between a positive and a negative number is negative:

Answer:

(-4)³ = -64

Answer:

B. 45

Step-by-step explanation:

If im wrong please let me know

Have a nice day :)

Answer:

17.32 cm

Step-by-step explanation:

hope this helps

Answer:

-5/-3

Step-by-step explanation:

first y intercept=

-5/-3

The density , weight , specific weight of a body with mass 0.600 kg and volume 400cm^3 is equal to  1.5 g/ cm³ , 5.88 Newton , and 14.7 grams respectively.

Let 'ρ' be the density of the body with specific weight.

Mass of the body 'm' is equal to 0.600kg

1kg = 1000grams

⇒0.600 kg = 600 grams

Volume of the body is equal to 400cm³

Standard density formula is equal to

Density = Mass / volume

⇒ ρ = 600 / 400

⇒ ρ = 1.5 g/ cm³

Weight 'w' = mass × acceleration due to gravity

⇒ w = 0.600 × 9.8 kg m/s²

⇒ w = 5.88 Newton

Specific weight  = density × gravity

                         =(1.5 × 9.8) ×1000

                         = 14700kg

                          = 14.7 grams

Therefore, the density , weight , specific weight of a given body is equal to 1.5 g/ cm³ , 5.88 Newton , and 14.7 grams respectively.

The above question is incomplete , the complete question is :

Calculate the density, the weight and the specific weight of a body whose mass is 0.600kg and its volume is 400cm^3.

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To find the value of x, we set HB equal to HA and solve for x: 2x - 46 = 24, therefore x = 35.

To find the value of x, we can set HA equal to HB and solve for x.

Given that HA = 24 and HB = 2x - 46, we can set up the equation:

24 = 2x - 46.

To isolate the variable x, we can start by adding 46 to both sides of the equation:

24 + 46 = 2x - 46 + 46

70 = 2x

Next, we divide both sides of the equation by 2 to solve for x:

70 / 2 = 2x / 2

35 = x

Therefore, the value of x is 35.

By substituting x = 35 back into the original equation, we can verify the solution:

HA = 24 and HB = 2x - 46

HA = 24

HB = 2(35) - 46

HB = 70 - 46

HB = 24

Since HA and HB are equal, and the value of x = 35 satisfies the equation, we can conclude that x = 35 is the correct value.

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Answer:

381.05 ft

Step-by-step explanation:

A right triangle can be formed with the bottom of the tree, the top of the tree, and you. In a right triangle, for any angle θ, tanθ=opposite/adjacent.

Let \(h\) represent the height of the tree. The angle 60° has opposite side \(h\) and adjacent side is 220.

Set up the following equation;

tan(60°)=h/220

Multiply both sides by 220:

h=220tan(60°)≈381.05 ft (rounded to the nearest hundredth, ans)

Answer:

0.375

Step-by-step explanation:

One more than two-thirds of a number is no less than 25 is x = -30.

An equation is a mathematical expression that contains two algebraic expressions on either side of the "equals (=)" sign. It shows the equality between the words written to the left and the words written to the right. In all mathematics there is L.H.S = R.H.S (left side = right side). Equations can be solved to find the values ​​of unknown variables that represent unknown quantities or numbers. If there is no "equals" sign in the expression, it means it is not equal. It will be treated as a guide.

let the no. be x

According to the question:-

2/3 × x = 1/2× (x-5)

⇒ 2x/3 = x/2- 5

⇒ 2x/3 - x/2 = -5

⇒ (4x- 3x)/6 = -5

⇒ x/6  = -5

⇒ x = -30.

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1) The area of trapezoid is,

⇒ A = 40.5 cm²

2) The area of triangle is,

⇒ A = 16.69 cm²

We have to given that;

First figure shows a trapezoid

And, Second shows triangle.

Since, We know that;

Area of Trapezoid is,

A = (6 + 12) x 4.5 / 2

A = 18 x 4.5 / 2

A = 40.5 cm²

And, For second figure,

Area of triangle is,

A = 1/2 × Base × Height

A = 1/2 × 7.3 × 4.6

A = 16.69 cm²

Therefore, We get;

1) The area of trapezoid is,

⇒ A = 40.5 cm²

2) The area of triangle is,

⇒ A = 16.69 cm²

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Given equation is a first-order nonlinear ordinary differential equation (ODE): y' - (x + y - 1)^2 = 0

What is differential equation ?

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

This equation can be solved using various methods, such as numerical methods or analytical methods like the implicit function theorem or the method of characteristics. However, finding an exact solution can be challenging and may not always be possible.

If you would like to find an approximate solution to this ODE, you could use numerical methods such as Euler's method, Runge-Kutta method, or the finite difference method. These methods can provide a numerical approximation to the solution for a given range of x and a specified initial condition.

The given equation is a first-order nonlinear ordinary differential equation (ODE):

y' - (x + y - 1)^2 = 0

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