If f(x) = (x^2-3x-4); g(x) = (2x^2+5x+2)
what is (f + g)(-1)?

Answer:

2

Step-by-step explanation:

\(16^{\frac{1}{4} }\) = \(\sqrt[4]{16}\) = 2.  To find the fourth root, find the number that repeats itself four times using multiplication. 2 x 2 x 2 x 2 = 16

Answer:

x=1

Step-by-step explanation:

it is

After 4 hours of discharging, the volume left in the tank would be 500 liters. The correct option is C.

Initially, the tank has a water capacity of 1500 liters.

After three hours of discharging, half of the water is discharged, which means 1500/2 = 750 liters have been removed from the tank.

To find the volume left after 4 hours of discharging, we need to subtract the additional amount discharged in the fourth hour.

Since the discharge rate remains the same, we can calculate the amount discharged in one hour as 750/3 = 250 liters.

Therefore, in the fourth hour, 250 liters would be discharged. Subtracting this from the remaining water after three hours (750 liters), we get 750 - 250 = 500 liters.

Therefore, the correct answer is c. 500 liters.

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Answer:

idek

Step-by-step explanation:

Answer:

\(4x^3+7x^2+5x+2\)

Step-by-step explanation:

Given:

\(f(x)=4x^2+5x-3\)

\(g(x)=4x^3+3x^2+5\)

\(\begin{aligned}\implies (f+g)(x)=f(x)+g(x) & = (4x^2+5x-3) + (4x^3+3x^2+5) \\& = 4x^2+5x-3+4x^3+3x^2+5 \\& = 4x^3+4x^2+3x^2+5x-3+5 \\& = 4x^3+7x^2+5x+2 \\\end{aligned}\)

Answer:

4 <(less than or Equal to) y (less than or Equal to) 13

Step-by-step explanation:

The correct answer is True.  The range of the graph of the equation y = x^5 + 11x - 14x² - 12 is not (-7, +∞), but rather (-∞, +∞). The graph of the equation y = x5 + 11x - 14x² - 12 has a range of (-7, +[infinity]).

The range of a function or equation is the set of all possible output values (y-values) that the function can produce. In other words, it is the vertical spread of the graph. For example, if the range of a graph is (-3, 5), it means that the y-values of the graph can be any number between -3 and 5, inclusive. Next, let's look at the given equation y = x5 + 11x - 14x² - 12. To determine the range of this equation, we need to find the maximum and minimum y-values that it can produce. One way to do this is by finding the vertex of the parabola formed by the quadratic term -14x². The x-coordinate of the vertex is given by -b/2a, where a and b are the coefficients of the quadratic term. In this case, a = -14 and b = 11, so the x-coordinate of the vertex is x = -11/(-2*-14) = 11/28.

The statement that the range of the graph of the equation y = x5 + 11x - 14x² - 12 is (-7, +[infinity]) is true. This is because the equation is a polynomial of odd degree and has no maximum y-value. The minimum y-value that it can produce is -71/28, which is greater than -7. Therefore, any y-value greater than -7 is possible.
Your question is about the range of the graph of the equation y = x^5 + 11x - 14x² - 12 and whether the given range, (-7, +∞), is true or false.

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The length of VZ (distance across the lake) is 3222 feet.

Properties of similar triangle.

Similar triangles are two or more triangles which have common corresponding properties. Thus the corresponding sides or angles can be compared.

But note that similarity of given shapes does not imply that they are congruent i.e equal in all respect.

To determine the distance across the lake, Jarvis needs to compare the similar triangles ΔXYW and ΔAZV.

Thus on comparing the length of corresponding sides of the triangles, it can be deduced that:

WY/ VZ = XY/ XZ

1074/ VZ = 2148/ 6444

VZ = (1074*6444)/ 2148

     = 3222

VZ = 3222 feet

Therefore, the distance across the lake i.e VZ is 3222 feet.

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Answer:

6/25

Step-by-step explanation:

Answer:

Step-by-step explanation:

2(x - 3) = 10

or. 2x - 6 = 10

or. 2x = 10 + 6 = 16

or. x = 16/2 = 8

Answer:

3/2

Step-by-step explanation:

9514 1404 393

Answer:

  2.  13√2

Step-by-step explanation:

You can consider the radical as though it were some (non-numeric) symbol.

Using Ф for √2, this becomes ...

  2Ф +4Ф +7Ф = (2+4+7)Ф = 13Ф

Using √2 for Ф, this becomes ...

  = 13√2

__

In short, do not be intimidated by the radical expression. Treat it as you would any other symbol for purposes of collecting terms. (Of course, you can only combine "like" radicals.)

The maximum value is the largest number in the set, which is 57. These five values provide a summary of the distribution of the data set.

The five-number summary of the given data set is as follows:

Minimum (smallest value): 6

Lower quartile (QL): 18

Median: 31

Upper quartile (QU): 48

Maximum (largest value): 57

To calculate the five-number summary, the data set is first arranged in ascending order. The minimum value is the smallest number in the set, which is 6. The lower quartile (QL) is the median of the lower half of the data set, which is 18. The median is the middle value of the data set, which is 31. The upper quartile (QU) is the median of the upper half of the data set, which is 48. The maximum value is the largest number in the set, which is 57. These five values provide a summary of the distribution of the data set.

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The average amount of water in the reservoir from 4 to 10 hours is 3500.

The graph shows the amount of water in a reservoir over a 12-hour period.

To estimate the average amount of water in the reservoir from 4 to 10 hours, we need to take the mean of the heights of the points at 4 and 10 hours.

The water level is plotted on the y-axis while the hours are plotted on the x-axis.

The horizontal line at y = 4000 represents the maximum amount of water the reservoir can hold.

Since the graph never goes above that line, we can assume that the reservoir is always at maximum capacity.

Therefore, the average amount of water in the reservoir from 4 to 10 hours is:

Average amount of water = (height at 4 hours + height at 10 hours)/2

To estimate the height at 4 hours, we can look at where the line intersects the y-axis when x = 4.

We can see that the height is approximately 3250.

To estimate the height at 10 hours, we can look at where the line intersects the y-axis when x = 10.

We can see that the height is approximately 3750.

Therefore, the average amount of water in the reservoir from 4 to 10 hours is:

(3250 + 3750)/2

= 3500

Therefore, the average amount of water in the reservoir from 4 to 10 hours is 3500.

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Answer:

The answer is

Step-by-step explanation:

Area of a circle is given by

where r is the radius of the circle

From the question

r = 7 inches

So the area of the circle is

A = 3.14(7)²

= 3.14 × 49

We have the final answer as

Hope this helps you

Here, we are given with a circle whose radius = 7 inches, and we are asked to find the area of the circle. Taking value of π = 3.14

We know,

Here,

So, let's find the area,

➝ Area of the circle = πr²

➝ Area of the circle = 3.14 × 7²

➝ Area of the circle = 3.14 × 49

➝ Area of the circle = 153.86 inch²

Hence, Area of the circle:

\( \huge{ \boxed{ \bf{153.86 \: {inch}^{2} }}}\)

And we are done !!

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(i) The relationship between the OLS estimators of α₂ and ᵝ₂ can be determined by considering the relationship between the consumption function and the savings function. Since X = Y + Z, we can substitute this into the consumption function equation to obtain Y = α₁ + α₂(Y + Z) + e. Simplifying the equation, we get Y = (α₁/(1 - α₂)) + (α₂/(1 - α₂))Z + (e/(1 - α₂)). Comparing this equation with the savings function Z₁ = ᵝ₁ + ᵝ₂X + u₁, we can see that the OLS estimator of ᵝ₂ is related to the OLS estimator of α₂ as follows: ᵝ₂ = α₂/(1 - α₂).

(ii) The residual sum of squares (RSS) will not be the same for the two models of Y₁ = α₁ + α₂X₁ + e and Z₁ = ᵝ₁ + ᵝ₂X₁ + u₁. This is because the error terms e and u₁ are different for the two models. The RSS is calculated as the sum of squared differences between the observed values and the predicted values. Since the error terms e and u₁ are different, the predicted values and the residuals will also be different, resulting in different RSS values for the two models.

(iii) The R² terms of the two models cannot be directly compared. R² is a measure of the proportion of the total variation in the dependent variable that is explained by the independent variables. Since the consumption function and the savings function have different dependent variables (Y and Z, respectively), the R² values calculated for each model represent the goodness of fit for their respective dependent variables. Therefore, the R² terms of the two models cannot be compared directly.

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Answer:

after 80 years, approximately 2.15 grams of the initial 16 grams of cesium-137 would remain. This means that about 13.4 grams would have decayed during this time period.

Answer:

(-4,3)

Step-by-step explanation:

Answer:

x = 46

Step-by-step explanation:

Hello there!

The following angles are corresponding angles

One of the properties of corresponding anlges is that they are congruent

That being said we can use this equation to solve for x

2x + 4 = 4x - 88

step 1 subtract 2x from each side

2x -2x cancels out

4x - 2x = 2x

now we have

4 = 2x - 88

step 2 add 88 to each side

-88 + 88 cancels out

4 + 88 = 92

now we have 92 = 2x

step 3 divide each side by 2

92 / 2 = 46

2x/2= x

we're left with x = 46

Answer:

60.000 x 10 to the power of 3

Step-by-step explanation:

The number of simple events in this experiment is 16.

The correct answer to the given question is option c.

The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes. A simple event is one in which only one of the outcomes can occur. For example, if a coin is tossed, a simple event would be the outcome of the coin being heads or tails.

The total number of possible outcomes in the experiment of tossing 4 unbiased coins simultaneously is 2⁴, since there are two possible outcomes for each coin. Thus, the total number of possible outcomes is 16.

Each coin has two possible outcomes: heads or tails. If all four coins are flipped, there are two possible outcomes for the first coin, two possible outcomes for the second coin, two possible outcomes for the third coin, and two possible outcomes for the fourth coin. Therefore, the total number of possible outcomes is 2 × 2 × 2 × 2 = 16.

Therefore, the number of simple events in this experiment is 16, which is option (c).

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Answer:

c

Step-by-step explanation:

i know

Answer:

The data set has a range of 8 instruments

Step-by-step explanation:

Answer:

Vertex form: y = (x+4)^2 - 9

Minimum y-value of function: [-9, ∞)

Step-by-step explanation:

Vertex form: y = a(x-h)^2 + k

To convert standard form into vertex form, you will need to complete the square. To find the minimum y-value, you will need to find the vertex and see the y-value (as it is a parabola and nothing goes above/below it).

Step 1: Move 7 over to the other side (or subtract 7)

y - 7 = x^2 + 8x

Step 2: Complete the Square

y - 7 + 16 = x^2 + 8x + 16

Step 3: Factor and combine like terms

y + 9 = (x + 4)^2

Step 4: Move 9 back to the right (or subtract 9)

y = (x + 4)^2 - 9

Final Answer: y = (x + 4)^2 - 9

Your vertex is located at (h, k), so at (-4, 9). Since the highest degree coefficient is positive, the parabola is facing up. Nothing will go below the y-value of 9.

The coefficient of determination is the ratio of the sum of squares regression and the ssy

The sum of squares regression is 27

The given parameters are:

Coefficient of determination, R^2 = 0.12

SSy = 225

The coefficient of determination is calculated as:

R^2 = SSR/SSY

So, we have:

0.12 = SSR/225

Make SSR the subject

SSR = 0.12 * 225

Evaluate the product

SSR = 27

Hece, the sum of squares regression is 27

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The sum of squares regression is 27

The coefficient of determination or R squared method is the proportion of the variance in the dependent variable that is predicted from the independent variable.

The coefficient of determination is calculated by using the following formula;

\(\rm R^2 = \dfrac{SSR}{SSY}\\\\ 0.12= \dfrac{SSR}{225}\\\\ SSR = 225 \times 0.12 \\\\ SSR = 27\)

Hence, the sum of squares regression is 27.

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Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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If the derivative of a function is positive, then the function is increasing. If the derivative of a function is negative, then the function is decreasing.

1. Take a function, f(x).

2. Take the derivative of the function, f'(x).

3. If f'(x) is greater than 0, then the function is increasing.

4. If f'(x) is less than 0, then the function is decreasing.

To determine if a function is increasing or decreasing, the derivative of the function must be found. The derivative of a function is written as f'(x). If the derivative is greater than 0, then the function is increasing. If the derivative is less than 0, then the function is decreasing. This is because an increasing function has a positive slope, and a decreasing function has a negative slope. The derivative is the slope of the function, so if the derivative is positive, the function is increasing, and vice versa.

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The correct option is D. Behavioral economics studies the influence of cognitive biases and irrational decision-making on consumer behavior.

Behavioral economics combines insights from psychology and economics to understand how individuals make choices that deviate from the assumptions of classical economics. It recognizes that human behavior is often influenced by emotions, cognitive biases, and heuristics.

leading to deviations from rational decision-making. Behavioral economists study these behavioral patterns to develop more realistic models and theories that better capture the complexities of decision-making in real-world situations.

By incorporating psychological factors into economic analysis, behavioral economics provides a broader understanding of human behavior and its implications for economic outcomes.

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Answer:

D.) This system has infinitely many solutions

Step-by-step explanation:

y = -4x - 6

-4x - y - 6 = 0

-4x - y - 6 = 0

-y = 4x + 6

-y/-1 = 4x/-1 + 6/-1

y = -4x - 6

There are infinitely many solutions, because both of the lines are exactly the same. As show below ! Hope this helps once again ^w^