Which number is not a whole number ? A. 8. B. -10. C. 0. D.18/3

The equation of the parabola is gotten as;

 y = -4x² + 24x - 32

We are given the coordinates of a parabola to be;

(3, 4) ; (4,0) ; (2,0)

The general form of equation of a parabola is given by;

y = ax² + bx + c

Let's plug in the x and y coordinates as given to us from the question.

(3²)a + 3b + c = 4

9a + 3b + c = 4  ----(eq 1)

(4²)a + 4b + c = 0

16a + 4b + c = 0  ----(eq 2)

(2²)a + 2b + c = 0

4a + 2b + c = 0  ----(eq 3)

       y = -4x² + 24x - 32

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The number of cups of rice the restaurant would need for 20 cups of veggies is 5.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

The recipe calls for 1/4 cup of rice for every 1 cup of veggies.

Now,

1cup veggie = 1/4 cup rice

20cup veggies= 1/4 * 20 cup rice

=5

Therefore, by algebra the count of cups of rice will be 5.

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The answer of the given question based on the Voltage drop the answer is , the voltage dropped across R3 is 277.11 V.

Ohm's law is  fundamental principle in electrical engineering and physics that describes  relationship between voltage, current, and resistance in  electrical circuit. It states that current through conductor between two points is directly proportional to voltage across  two points, and inversely proportional to resistance between them.

To determine the voltage dropped across R3, we need to use Ohm's law and Kirchhoff's circuit laws. First, we can calculate the total resistance in the circuit:

Rtotal = R1 + R2 || R3

R2 || R3 = (R2 * R3) / (R2 + R3) (parallel resistance formula)

Rtotal = R1 + (R2 || R3)

Rtotal = 152 + ((18 * 362) / (18 + 362))

Rtotal = 149.89 Ω (rounded to 2 decimal places)

Next, we can use Ohm's law to calculate the current flowing through the circuit:

I = ET / Rtotal

I = 120 / 149.89

I = 0.8004 A (rounded to 4 decimal places)

Finally, we can use Kirchhoff's voltage law to determine the voltage dropped across R3:

ET = IR1 + IR2 || IR3 + IR3

ET = I(R1 + R2 || R3) + IR3

ET - I(R1 + R2 || R3) = IR3

R3 = (ET - I(R1 + R2 || R3)) / I

R3 = (120 - (0.8004 * (152 + ((18 * 362) / (18 + 362))))) / 0.8004

R3 = 277.11 V (rounded to 2 decimal places)

Therefore, the voltage dropped across R3 is 277.11 V.

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The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Managers, goods, services, and technology are all needed in developing countries, and therefore, they provide new markets for companies that can supply these essentials.

Developing countries often have growing economies and increasing consumer demands. As these countries strive for development and improvement, they require effective management to drive their businesses and organizations. Managers play a crucial role in overseeing operations, implementing strategies, and maximizing efficiency.

Additionally, developing countries require goods and services to meet the needs of their populations. This includes basic necessities such as food, clothing, and shelter, as well as other essential products and services like healthcare, education, infrastructure development, and transportation. Companies that can provide these goods and services have an opportunity to enter new markets and cater to the demands of the growing population.

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Using the formula of volume of rectangular prism;

1. The volume of the rectangular prism is 3672cm³

2. The volume of the rectangular prism is 630in³

3. The volume of the rectangular prism is  3744ft³

The volume of a rectangular prism can be calculated by multiplying its length (l), width (w), and height (h). The formula for the volume of a rectangular prism is:

Volume = length × width × height

V = l × w × h

By substituting the given values for the length, width, and height into the formula, you can calculate the volume of the rectangular prism.

1. To find the volume of the rectangular prism, we have to substitute the value into the formula;

v = 9 * 24 * 17

v = 3672cm³

2. The volume of the rectangular prism is given as;

v = 4.5 * 14 * 10

v = 630in³

3. The volume of the rectangular prism is given as;

v = 8 * 12 * 39

v = 3744ft³

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Answer:

Ok so I think the answer is 4.8 points per minute

Step-by-step explanation:

Why because Uncle Drew scored 28 points in 5 \frac{5}{6} minutes. We have to convert the mixed fraction first:

t = 5 \frac{5}{6}=\frac{5\cdot 6+5}{6}=\frac{35}{6}

So, the time is 35/6 minutes.

In order to find the number of points he scored in a minute, we have to divide the total number of points by the number of minutes, so:

mean = \frac{28}{35/6}=28 \cdot \frac{6}{35}=4.8

So, he scored 4.8 points per minute.

I hope you foundthis helpful.

Answer:

Uncle Drew averaged  5/24  ​points per minute.

Answer:

x = 2

Step-by-step explanation:

-12 = -3x²

divide through by -3

-12/-3 = -3x²/-3

4 = x²

square root both sides

[4]^½ = x²× x^½

so therefore: 2 = x

Answer: 4 terms and 8 factors

Step-by-step explanation:

^

For a line having a slope of -1/9, the value for y is obtained as -1.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

We can use the point-slope form of the equation of a line to solve this problem.

The point-slope form is -

y - y1 = m(x - x1)

where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) is any other point on the line.

We are given that the line has a slope of -1/9.

Let's use the point (-2, y) as our (x1, y1) point.

Plugging in the values in the equation -

y - y1 = m(x - x1)

y - y1 = (-1/9)(x - (-2))

y - y1 = (-1/9)(x + 2)

Now we can use the other given point, (7, -2), and plug in the values for x and y -

-2 - y1 = (-1/9)(7 + 2)

-2 - y1 = (-1/9)(9)

-2 - y1 = -1

Solving for y1, we get -

y1 = -2 + 1

y1 = -1

Therefore, the value of y is -1.

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Answer:

The answer is

B

D

F

Step-by-step explanation:

Squaring a fraction is like squaring a whole number really so you just square the fraction by multiplying it by itself.

To model the cost of renting an economy car for x days, you can use a linear equation. A linear equation can be represented in the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. In this case, y represents the cost of renting the car, and x represents the number of days.

To find the equation of the line, we need to use the given information to find the slope and y-intercept. We know that the cost of renting the car increases by a certain amount for each additional day, so the slope will be the daily rate. We also know that the cost of renting the car for 1 day is $90, which means that $90 is the y-intercept.We can use the two points (1, 90) and (3, 170) to find the slope:Slope = (y2 - y1) / (x2 - x1)

Slope = (170 - 90) / (3 - 1)Slope = 80 / 2Slope = 40Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:y - y1 = m(x - x1)We can use the point (1, 90) as our reference point:y - 90 = 40(x - 1)Simplifying this equation gives y = 40x + 50Thus, the function to model the cost of renting an economy car for x days is given by the equation y = 40x + 50, where y represents the cost and x represents the number of days.

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Thats all, now pay up the 50 points,lol

Here is an R script that explores three visual and statistical measures of the logistic regression association between the variable mpg (Miles/(US) gallon)(independent variable) and the var:

```{r}library(ggplot2)

library(dplyr)

library(tidyr)

library(ggpubr)

library(ggcorrplot)

library(psych)

library(corrplot)

# Load datasetmtcars

# Run the logistic regressionmodel <- glm(vs ~ mpg, data = mtcars, family = "binomial")summary(model)#

# Exploration of the association between mpg and vs# Plot the dataggplot(mtcars, aes(x = mpg, y = vs)) + geom_point()

# Plot the logistic regression lineggplot(mtcars, aes(x = mpg, y = vs)) + geom_point() + stat_smooth(method = "glm", method.args = list(family = "binomial"), se = FALSE, color = "red")

# Plot the residuals against the fitted valuesggplot(model, aes(x = fitted.values, y = residuals)) + geom_point() + geom_smooth(se = FALSE, color = "red")

# Create a correlation matrixcor_matrix <- cor(mtcars)corrplot(cor_matrix, type = "upper")ggcorrplot(cor_matrix, type = "upper", colors = c("#6D9EC1", "white", "#E46726"), title = "Correlation matrix")

# Test for multicollinearitypairs.panels(mtcars)

# Test for normalityplot(model)```

Explanation:

The script begins by loading the necessary libraries for the analysis. The mtcars dataset is then loaded, and a logistic regression model is fit using mpg as the predictor variable and vs as the response variable. The summary of the model is then printed.

Next, three visual measures of the association between mpg and vs are explored.

The first plot is a scatter plot of the data. The second plot overlays the logistic regression line on the scatter plot. The third plot is a residuals plot. The script then creates a correlation matrix and plots it using corrplot and ggcorrplot. Lastly, tests for multicollinearity and normality are conducted using pairs. panels and plot, respectively.

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Answer:

\(k = (-162)\).

Step-by-step explanation:

A point of the form \((x_{0},\, y_{0})\) belongs to the graph of this function, \(y = k / x\), if and only if the equation of this function holds after substituting in \(x = x_{0}\) and \(y = y_{0}\).

The question states that the point \((-9,\, 18)\) belongs to the graph of this function. Thus, the equation of this function, \(y = k / x\), should hold after substituting in \(x = (-9)\) and \(y = 18\):

\(y = k / x\).

\(18 = k / (-9)\).

Solve this equation for the constant \(k\):

\(\begin{aligned}k &= 18 \times (-9) \\ &= (-162)\end{aligned}\).

Thus, \(k = (-162)\).

The value of tan (P) is determined as  4/3.

The value of tan (P) is calculated by applying trig ratio as follows;

The trig ratio is simplified as;

SOH CAH TOA;

SOH ----> sin θ = opposite side / hypothenuse side

CAH -----> cos θ = adjacent side / hypothenuse side

TOA ------> tan θ = opposite side / adjacent side

The value of adjacent side of tan (P) is calculated as follows;

h = √ ( 10²  -  8² )

h = 6

The value of tan (P) is calculated as follows;

tan ( P ) = 8/6

tan (P) = 4/3

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The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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Answer:

9

Step-by-step explanation:

Because x = 2 we can re arrange this too 3x2^2 - 2x2 + 1

after doing this we can simplify it too 12-4+1 which when we do it is just 9.

Part A

The transformation of f(x) to g(x) is a translation

two types

First

translation in x direction

the rule is

(x,y) ------> (x+k1,y)

second

translation in y direction

(x,y) -----> (x,y+k2)

Part B

solve for k

First

(x,y) ------> (x+k1,y)

the x-intercept of f(x) is 5

the x-intercept of g(x) is -3

so

(x,y) ------> (x-8,y)

the translation is 8 units to the left

k1=-8

Second

(x,y) -----> (x,y+k2)

the y-intercept of f(x) is -10

the y-intercept of g(x) is 6

so

(x,y) -----> (x,y+16)

the translation is 16 units up

k2=16

Part C

write an equation for each type of transformation

First

(x,y) ------> (x-8,y)

so

g(x)=f(x+8)

second

(x,y) -----> (x,y+16)

so

g(x)=f(x)+16

Answer:

0.583

Step-by-step explanation:

We know that

\(\frac{7}{12}\)

is the same as

7÷12

Then using

Long Division for 7 divided by 12

and rounding to a Max of 3 Decimal Places gives us

=0.583

By the principle of mathematical induction, the statement cn = 32n is true for all integers n ≥ 0.

To show that the sequence cn = 32n for all integers n ≥ 0, we can use mathematical induction.

Step 1: Base case

Let's first verify the statement for the base case when n = 0.

c0 = 3 (given)

32n = 3^0 = 1

So, the statement holds true for the base case.

Step 2: Inductive hypothesis

Assume that the statement is true for some arbitrary positive integer k, i.e., ck = 32k.

Step 3: Inductive step

We need to show that the statement is true for the next integer, k + 1.

We know that ck+1 = (ck)^2.

Substituting the inductive hypothesis into the equation:

ck+1 = (32k)^2 = 32(2k).

By the laws of exponentiation, (32)^2 = 32*2 = 32^2 = 32(1+1) = 32(2).

Therefore, ck+1 = 32(2k) = 32(2) = 32(1+1) = 32^2 = 32(2).

So, the statement holds true for k + 1.

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Answer:

Question 16: 44 inches

Question 18: 10, 24, 26

Step-by-step explanation:

Question 16:

Pythagoras Theorem: c^2 = a^2 + b^2, where c is the hypotenuse and the longest side.

125^2 = 117^2 + b^2

15,625 = 13,689 + b^2

15,625 - 13689 = b^2

1936 = b^2

√1936 = b

44 = b

Question 18:

Pythagoras Theorem: c^2 = a^2 + b^2, where c is the hypotenuse and the longest side. You have to try all the possibilities. The ones that match are the lengths.

The answers are 10, 24, 26

c^2 = a^2 + b^2

26^2 = 10^2 + 24^2

676 = 100 + 576

676 = 676

The present worth (PW) of each project is calculated based on the given cash flows and the firm's minimum attractive rate of return (MARR) of 10% per year.

To calculate the PW of each project, we discount the cash flows at the MARR of 10% per year. The PW for each project is determined as follows:

Project 1: EOY 0: -\(10,000 + (5,125 / (1 + 0.10)^1) + (5,125 / (1 + 0.10)^2) + (5,125 / (1 + 0.10)^3) = $10,682.13\)

Project 2: EOY 0: -\(8,500 + (4,450 / (1 + 0.10)^1) + (4,450 / (1 + 0.10)^2) + (4,450 / (1 + 0.10)^3) = $9,202.79\)

Project 3: EOY 0: \(11,000 + (5,400 / (1 + 0.10)^1) + (5,400 / (1 + 0.10)^2) + (5,400 / (1 + 0.10)^3) = $9,834.71\)

The project with the highest PW is recommended. In this case, Project 1 has the highest PW of $10,682.13, so it would be the recommended project.

The IRR for each project can be determined by finding the discount rate that makes the PW equal to zero. Using the cash flows provided, the IRR for each project can be calculated using a trial-and-error approach or financial software. Let's assume the IRRs are as follows:

Project 1: IRR ≈ 17.5%

Project 2: IRR ≈ 15.3%

Project 3: IRR ≈ 13.8%

The project with the highest PW may differ from the project with the largest IRR due to the timing and magnitude of cash flows. The PW takes into account the timing of cash flows and discounts them to the present value. It represents the total value created by the project over its lifetime. On the other hand, the IRR considers the rate of return that equates the present value of cash inflows to the initial investment. It represents the project's internal rate of return.

Therefore, a project with a higher PW indicates higher overall value, while a project with a larger IRR implies a higher rate of return. These measures can lead to different rankings depending on the cash flow patterns and the MARR.

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Answer:

x = 17, MN = 11

Step-by-step explanation:

Given 2 secants from an external point to a circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.

(5)

7(7 + x) = 8(8 + 13) = 8 × 21 = 168 ( divide both sides by 7 )

7 + x = 24 ( subtract 7 from both sides )

x = 17

(6)

9(9 + 2x - 7) = 10(10 + 8)

9(2x + 2) = 10 × 18 = 180 ( divide both sides by 9 )

2x + 2 = 20 ( subtract 2 from both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Then

MN = 2x - 7 = 2(9) - 7 = 18 - 7 = 11

Using the sine rule we estimate the value of b to be approximately 4.6 units.

The sine law, often referred to as the sine formula, sine rule, or law of sines, is a trigonometrical equation that connects the lengths of any triangle's sides to its sines.

The sine rule states that \(\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}\) , where A ,B and C are the three vertices of the triangle and a, b and c are the three side lengths.

Given A = 50° and B = 62 ° and a = 4 .

Now we use the given values to :

\(\frac{4}{sin50} =\frac{b}{sin62}\)

or, b = 4.6104...

or , b ≈ 4.6

Hence the length of b is 4.6

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Answer:

I think it is 55

Answer:

Step-by-step explanation:

138° - 80° = 58°

Step-by-step explanation:

To determine if a system of two equations with two unknowns has infinite solutions using matrices, you can perform Gaussian elimination or row reduction on the augmented matrix of the system. If the reduced form of the matrix is the identity matrix, then the system has a unique solution. If the reduced form is a row of zeros except for the last column, then the system has no solution. If the reduced form has a row with all zeros except for the last column being non-zero, then the system has an infinite number of solutions.

In other words, the system has infinite solutions if the row reduced form of the augmented matrix has a row of the form [0 0 c], where c is a non-zero scalar. This means that there is a non-trivial solution that satisfies the equation, indicating that there are infinitely many solutions.