. You have 17 birthday gifts! 9 came from your
family, the rest came from your friends. How many
gifts did your friends give you?

Answer:

160 females 96 males

Step-by-step explanation:

find multiples of 256

multiply 5/3 by those multiples

40/24 times 8/8= 160/96

add=

256

Answer:

10 years

Step-by-step explanation:

Given :

Population of Canyon falls = 22500

Rate of decrease = 740 per year

Population after x years :

f(x) = 22500 - 740x ; x = number of years

Population of Swift Creek = 15200

Rate of Increase = 1500 per year

Population after x years :

f(x) = 15200 + 1500x ; x = number of years

Number of years when, population of swift creek will be twice that of Canyon falls

15200 + 1500x = 2(22500 - 740x)

15200 + 1500x = 45000 - 1480x

15200 - 45000 = - 1480x - 1500x

-29800 = - 2980x

x = 29800 / 2980

x = 10

After 10 years

The electric potential, V, is 73.63 N and the magnitude of the electric field is 12.00 V/m.

The given electric potential is,V=2xy²z³+3ln(x²+2y²+3z²) N

The components of the electric field can be found as follows,

E=-∇V=- (∂V/∂x) i - (∂V/∂y) j - (∂V/∂z) k

(a) To determine the potential at P(3, 2, -1), substitute x=3, y=2, and z=-1 in the given potential,

V=2(3)(2²)(-1)³ + 3 ln [(3)²+2(2)²+3(-1)²]= 72.32 N

(b) The magnitude of the potential is given by,

|V|= √ (Vx²+Vy²+Vz²)

The electric potential, V, is a scalar quantity. Its magnitude is always positive. Therefore,

|V|= √ [(2xy²z³)² + (3ln(x²+2y²+3z²))²]= √ [(-72)² + (16.32)²]= 73.63 N

(c) To determine the electric field E at P(3,2,-1), find the partial derivatives of V with respect to x, y, and z, and then substitute x=3, y=2, and z=-1 to obtain Ex, Ey, and Ez.

Ex = -(∂V/∂x)= -2y²z³/(x²+2y²+3z²) = -4.8 V/m

Ey = -(∂V/∂y)= -4xyz³/(x²+2y²+3z²) = -10.67 V/m

Ez = -(∂V/∂z)= -6xyz²/(x²+2y²+3z²) = 5.33 V/m

Therefore, the electric field E at P(3,2,-1) is, E=Exi+Eyj+Ezk=-4.8 i - 10.67 j + 5.33 k

(d) The magnitude of the electric field is given by,

|E|= √ (Ex²+Ey²+Ez²)= √ [(4.8)²+(10.67)²+(5.33)²]= 12.00 V/m

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Answer:

Step-by-step explanation:

Difference quotient formula is f(x+h) - f(x) / h

(-3 - 2(x+h)²) - (-3 - 2x²) / h

(-3 - 2(x²+2xh+h²) - (-3 - 2x²) / h

(-3 - 2x² - 4xh - 2h²) - (-3 - 2x²) / h

-4xh - 2h² / h

h(-4x - 2h) / h

-4x-2h

Answer:

4x + 7y = 3365

x + y = 578

x = matinees

y = regular

Step-by-step explanation:

Given

$4 = matinees

$7 = regular

Total tickets = 578

Money collected = $3365

If one calls the amount of matinees that when "x" and the amount of regulars that went "y", then one can form the system;

4x + 7y = 3365

x + y = 578

Solving the system;

Multiply the second equation by (-4)

4x + 7y = 3365

-4x - 4y = -2312

Add the equations

4x + 7y = 3365

-4x -4y = -2312

3y = 1053

Inverse operations

3y = 1053

/3        /3

y = 351

x = 227

For moviegoers who are younger than 12 years old, the ticket price is a fixed amount of $5. This is represented by the first rule of the piecewise function

For moviegoers who are 12 years old or older, but younger than 55, the ticket price is also a fixed amount, but this time it is $9. This is represented by the second rule of the piecewise function

For moviegoers who are 55 years old or older, a special rate is available, and the ticket price is $7. This is represented by the third rule of the piecewise function

So, for a 16 year-old, the ticket price would be $9.

For a 12 year-old, the ticket price would also be $5.

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Answer:

5.5

Step-by-step explanation:

Sales tax = tax rate × Cost of meal

Sales tax = $1.32

Tax rate = x%

Cost of meal = $24

Sales tax = tax rate × Cost of meal

1.32 = x% × 24

1.32 = x/100 × 24

1.32 = 24x/100

1.32 * 100 = 24x

132 = 24x

x = 132/24

x = 5.5%

= 5.5

The terms and properties of operations that complete the statement and reasons for the equivalent expressions are;

3. Same

4.The properties of operations to write the equivalent expressions are; (-4), (-4) Distributive property

(-4), (-4), Associative property

(-4), (-3) Distributive property

5. When x = 2, and y = -5 -28·x + 12·y is -116 = -116

Equivalent expressions are expressions that have the same value for the values of the input variable.

3. The completed statement is presented as follows;

Equivalent expressions evaluate to the same value when a given set of values of x and y are substituted into both expressions.

4. The expressions in the question can be expanded to collect like terms as follows;

Expression; -28·x + 12·y

The common factor of 28 and 12 is 4, therefore, we get;

-28·x + 12·y = (4 × (-7))·x + (4 × 3)·y

To make the coefficient of the leading term positive, we get;

-28·x + 12·y = (-4 * 7)·x + (-4 * (-3))·y; Distributive property

Factoring the algebraic expression on the right, where the common factor is -4, we get;

(-4 * 7)·x + (-4 * (-3))·y = -4 × (7·x) + -4 × (-3·y);  Associative property

= -4 × ((7·x) + (-3·y));

Therefore; -28·x + 12·y = -4 × (7·x + -3·y); Distributive property

5. Evaluation of the left and right side of the expression, where; x = 2, and y = 5, we get;

-28 × 2 + 12 × -5 = -116

(-4) × ((7 × 2) + (-3 × -5)) = -4 × 29 = -116

The completed equations are therefore;

-28·x + 12·y = -4 × (7·x + -3·y)

-28 × 2 + 12 × (-5) = -4 × (7 × 2 + -3 × (-5))

-116 = -116

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Answer:

Width: 8; Length: 10

Step-by-step explanation:

Every square meter in the room is worth 90, and the room is worth 7200 total. Given this information, if we divide the total, 7200, by the value per square meter, 90, we get that there are 80 square meters in this room. We also know that the value of the second room, 3600, is half of the first room. And if subtracting 5 from the first room's length halves the value, then we know that the subtraction halved the length.

Since we now know that the Length = 10, we have a much simpler equation of 10W = 80, 10 being the length, W being the width, and 80 being the total square meters, and after a quick simplification, we have W = 8.

The function 4x / ( x -16 ) is shown in the graph having a range from 0 to ∞.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The given function 4x / ( x -16 ) is shown in the graph as having a range from 0 to ∞.

The graph of the function  4x / ( x -16 ) is attached with the answer below.

Therefore, the function 4x / ( x -16 ) is shown in the graph having a range from 0 to ∞.

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Answer:

Step-by-step explanation:

Given that \(f(x)=-3x+8\).

The new function,g, whose graph is a transalation of 1 unit up is,

\(g=f+1\)

\(\Rightarrow g(x)=(-3x+8)+1\)

\(\Rightarrow g(x)=-3x+9\)

Thee factory is able to provide 94.38 boxes per hour to the warehouse.

Rate = (2000 - 1245) / 8 = 94.38 boxes per hour

Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.

Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2

Therefore, the inventory at the end of a 40-hour work week would be:

1245 + 3775.2 = 5020.2 boxes

rate = (50000 - 1245) / time

Simplifying this equation, we get:

time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).

Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,

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Answer: \(\frac{40}{3}\)

Step-by-step explanation:

     To see how many groups of 3/4 are in 10, we can divide 10 by 3/4.

           \(\displaystyle 10 \;/\; \frac{3}{4} =\frac{10}{1} *\frac{4}{3} =\frac{40}{3}\)

Answer:

30in²

Step-by-step explanation:

Area of a triangle = ( base length times height ) / 2

Given base length = 10 in

Given height = 6 in

Area = ( 6 * 10 ) / 2 = 60 / 2 = 30in²

Answer:

30in²

Step-by-step explanation:

area of triangle= base×height/2

Interactions involving dummy variables can provide insights into the different effects of independent variables across categories.

1. Dummy variables are binary variables that represent categorical variables in a regression analysis. When interactions are included between dummy variables and other independent variables, it allows for differential effects of the independent variables based on the different levels of the categorical variable.

For example, let's consider a regression model to predict income based on education level and gender. We can include an interaction term between education level (represented by dummy variables for different levels) and gender. This interaction term allows us to examine whether the effect of education level on income differs between males and females. It helps capture any gender-specific differences in the relationship between education and income.

1.2 The linear probability model (LPM) is a common approach to estimate the probability of an event occurring using a linear regression framework. However, it has several problems:

1. The predicted probabilities from the LPM can fall outside the [0, 1] range: Since the LPM does not impose any restrictions on the predicted probabilities, they can sometimes exceed the valid probability range. This violates the assumption of probabilities being bounded between 0 and 1.

2. Heteroscedasticity: The LPM assumes constant error variance across the range of the predictors. However, in practice, the variability of the error term may change with different levels of the predictors, resulting in heteroscedasticity. This violates the assumption of homoscedasticity.

3. Non-linearity: The LPM assumes a linear relationship between the predictors and the probability of the event. However, this may not always be the case, and using a linear model can result in misspecification.

To remedy these problems, an alternative to the LPM is to use logistic regression or probit regression models. These models explicitly model the probability of an event occurring and address the issues mentioned above. They provide predicted probabilities that fall within the valid range of 0 to 1, account for heteroscedasticity, and allow for non-linear relationships between the predictors and the probability of the event.

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Answer:

See Explanation

Step-by-step explanation:

Given

\(Sides:\ 9cm\ and\ 8cm\)

The question is incomplete, as what is required is not state. However, a possible question could be to determine the possible side length of the third side.

To do this, we make use of the triangle inequality theorem which states that:

Given three sides (a, b and c) of a triangle, the following inequalities exist.

\(a + b > c\)

\(a + c > b\)

\(b + c > a\)

Let a and b represent the two sides such that:

\(a = 9\)

\(b = 8\)

The inequalities become:

\(9 + 8 > c\)

\(9 + c > 8\)

\(8 + c > 9\)

Solve for c in each:

\(9 + 8 > c\)

\(17 > c\)

\(c < 17\)

\(9 + c > 8\)

\(c > 8 - 9\)

\(c > - 1\)

\(8 + c > 9\)

\(c >9 - 8\)

\(c >1\)

The value of c must be positive, so, we consider;

\(c >1\) and \(c < 17\)

Rewrite:

\(1 < c\) and \(c < 17\)

Combine both

\(1 < c < 17\)

Hence, the value of c is:

\(c = (1,17)\)

Answer:

20.4 pounds

Step-by-step explanation:

Given that:

Weight of a coin = 7^-2 pounds

Weight of 1000 coins will be :

Weight per coin * number of coins

7^-2 * 1000

0.0204081 * 1000

= 20.408 pounds

= 20.4 pounds

Answer:

Step-by-step explanation:

Because 2 1/4=2 2/8

so 2 2/8 - 1 1/8 equals 1 1/4

:)

Moses is currently 3996 years old.

Let's denote Methuselah's current age as "M" and Moses's current age as "M2".

"Moses is twice as old as Methuselah was when Methuselah was one-third as old as Moses will be when Moses is as old as Methuselah is now." This can be written as:

M2 = 2 × (M - (1/3) × M2)

We can simplify this equation by multiplying both sides by 3:

3 × M2 = 6 × (M - (1/3) × M2)

3 × M2 = 6M - 2 × M2

5 × M2 = 6M

"If the difference of their ages is 666" can be written as:

M2 - M = 666

We can use equation (5) to substitute for M2 in equation (6):

5 × M2 = 6M

5 × (M + 666) = 6M

5M + 3330 = 6M

M = 3330

Therefore, Methuselah is currently 3330 years old. We can use equation (6) to find Moses's current age:

M2 - M = 666

M2 - 3330 = 666

M2 = 3996

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m = (Y2 - Y1)/(X2 - X1)

m = (1 - (-3))/(1 - (-2))

m = (1 + 3)/(1 + 2)

m = 4/3 <==> 1 ⅓

Answer:

Hope the picture helps

Step-by-step explanation:

The perimeter of ΔABC is 14.35 units where O ∈ AB.

A geometric figure known as an angle is created by two rays or lines that have a shared termination. The two rays or lines that meet at the same place are referred to as the angle's sides or legs, and the angle's common terminal is known as the vertex.

When a circle has an inscribed angle that cuts out a semi-circle, then the inscribed angle is a right angle. So m∠C = 90°

The length of AB = 2r = 2(3) = 6 units

By using law of Sines,

cos A / cos C = AC/AB

AC = cos(35/90)(AB)

AC = cos (35/90)(6) = 4.91 units

sin(35/90) = BC/AB

BC = sin(35/90)(6) = 3.44 units

Perimeter of ΔABC = AB + BC + AC

                                = 6 + 3.44 + 4.91

                                = 14.35 units

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Answer:

8$ in tax will be paid

Step-by-step explanation:

5% sales tax means 0.05 cents on the dollar will be taxed so take 0.05 times 160 you get 8$ in tax

Answer:

3.5

Step-by-step explanation:

The scale factor of these shapes are 3.5 because they are being increased by being multiplied by 3.5.

4 × 3.5 = 14

6 × 3.5 = 21

Answer:

Di ko po alam grade 4palang po ako

Step-by-step explanation:

I'm so sorry po

(a) The economic loading of unit 4 and B are 11.54 MW and 138.46 MW, respectively.

To find the economic loading of the two units when the total load to be supplied by the power station is 150 MW, we need to minimize the total fuel cost. Let x be the power generated by unit 4 and y be the power generated by unit B. Then, we have:

x + y = 150 (total load)

The total fuel cost C is given by:

C = F4(x) + Fb(y)

where F4(x) and Fb(y) are the fuel costs for units 4 and B, respectively. Using the given relations, we have:

F4(x) = 0.06x^2 + 11.4x

Fb(y) = 0.07y^2 + 10y

Substituting x = 150 - y, we get:

C(y) = 0.06(150-y)^2 + 11.4(150-y) + 0.07y^2 + 10y

Expanding and simplifying, we get:

C(y) = 0.013y^2 - 3.6y + 1710

To minimize C(y), we take its derivative with respect to y and set it equal to zero:

dC/dy = 0.026y - 3.6 = 0

y = 138.46 MW

Substituting y back into x = 150 - y, we get:

x = 11.54 MW

(b) The negative value that is  -1297.5 indicates that there is a net decrease in fuel cost per hour if the load is equally shared by the two units.

To find the net increase in fuel cost per hour if the load is equally shared by the two units, we need to calculate the fuel cost for each unit when they generate half of the total load (i.e., 75 MW). Using the given relations, we have:

F4(75) = 0.06(75)^2 + 11.4(75) = 1282.5

Fb(75) = 0.07(75)^2 + 10(75) = 1312.5

Therefore, the total fuel cost is:

C = F4(75) + Fb(75) = 2595

If the load is equally shared by the two units, each unit generates 75/2 = 37.5 MW. The fuel cost for each unit is:

F4(37.5) = 0.06(37.5)^2 + 11.4(37.5) = 641.25

Fb(37.5) = 0.07(37.5)^2 + 10(37.5) = 656.25

Therefore, the total fuel cost is:

C' = F4(37.5) + Fb(37.5) = 1297.5

The net increase in fuel cost per hour is:

ΔC = C' - C = 1297.5 - 2595 = -1297.5

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The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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