Determine the range of the function g(x)= 5x^2-2x+1. Enter your answer in interval notation. This is a parabola that turns upward.

About 95.45% of the area is between z = -2 and z = 2, which is also within 2 standard deviations of the mean.

The mean is a measure of central tendency, which represents the average value of a set of numbers. It is calculated by adding up all the numbers in the set and dividing the sum by the total number of values.

The formula for calculating the mean of a set of n numbers x1, x2, x3, ..., xn is:

mean = (x1 + x2 + x3 + ... + xn) / n

For example, suppose we have a set of numbers {5, 7, 3, 2, 8}. To find the mean of this set, we add up all the numbers and divide by the total number of values:

mean = (5 + 7 + 3 + 2 + 8) / 5 = 25 / 5 = 5

Therefore, the mean of the set {5, 7, 3, 2, 8} is 5.

In the given question,

Assuming that we have a normal distribution, about 95% of the data falls within 2 standard deviations of the mean. Therefore, the area between z = -2 and z = 2 represents about 95% of the total area under the curve.

We can use a standard normal distribution table or a calculator to find the area under the curve between z = -2 and z = 2. From the table or calculator, we can find that the area between z = -2 and z = 2 is approximately 0.9545 or 95.45%.

Therefore, about 95.45% of the area is between z = -2 and z = 2, which is also within 2 standard deviations of the mean.

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Answer:

1/3

Step-by-step explanation:

since number 2 card was not replaced, we have;

probability of picking a second card, 3;

let S be number of sample space

n(S)= 4

n(3)= 1

Pr(3/2)= 1/3

(because since one was already chosen and n, the sample space would reduce)

We use the PEMDAS rule to answer our question which says in an arithmetic operation the order of precedence is the following.

parenthesis > Exponents > Multiplication/ division > addition/ subtraction.

Having that in mind, we see that there is no parenthesis in our expression, and therefore, we proceed to simplify the exponents. Doing this gives

Next up is multiplication and division, meaning 9 × 8 ÷ 2 is to be simplified.

Since, 9 × 8 ÷ 2 = 36, the expression becomes

Now we do addition and subtraction from left to right and we get

Hence, our expression simplifies to 82.

The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.

To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.

The PDF of V is defined as:

f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.

The expected value of V, denoted as E(V), can be calculated as:

E(V) = ∫v * f(v) dv

To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.

E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.

E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.

E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.

E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].

E(V) = (0.25) * [(49 / 2) - (9 / 2)].

E(V) = (0.25) * (40 / 2).

E(V) = (0.25) * 20.

E(V) = 5.

Therefore, the expected value of the continuous random variable V is 5.

The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.

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Answer:

8

Step-by-step explanation:

I'm using this equation: a^2+b^2=c^2

x^2+6^2=10^2

x^2+36+100

x^2= 64

x=sqrt64

x=8

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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Answer:

Lets start with the top row.

First, add the two values.

5+14=19

Now, divide each value by the total.

5/19=0.26315789473

Round the decimal to the nearest hundredth.

5/19=0.26

14/19=0.73684210526

Round it to the nearest hundredth.

14/19=0.74

Now, The second row.

Add the two values.

16+7=23

Divide the first value by the total.

16/23=0.69565217391

Round it to the nearest hundredth.

16/23=0.70

Divide the second value by the total.

7/23=0.30434782608

Round to the nearest hundredth.

7/23=0.30

Done!

Answer:

Row 1: 0.26 0.74

Row 2: 0.70 0.30

Step-by-step explanation:

Khan

Answer:

y =-x-3

Step-by-step explanation:

slope intercept/ y-intercept form is y=mx+b

you have to isolate y here

x+y=-3      subtract x from both sides

y=-x-3

Answer:

2 2/5

Step-by-step explanation:

Answer:

y =2x

Step-by-step explanation:

Slope intercept form is

y= mx+b where m is the slope and b is the y intercept

y = 2x+0

y = 2x

Answer:

Step-by-step explanation:

e

Answer:

\(2.0 \times {10}^{4} \)

Step-by-step explanation:

\( \frac{2.8 \times {10}^{7} }{1.4 \times {10}^{3} } \\ 2 \times {10}^{7 - 3} \\ 2 \times {10}^{4} \)

The equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

\(\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\)

\(\rm c = \dfrac{\sum y -m \sum x}{n}\)

The line of best fit;
y = mx + c

m = 16.89

c = 134.95

y = 16.89x + 134.95

Plug x = 2010 - 2002 = 8

y = 16.89(8) + 134.95

y = $2700.07

Thus, the equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07

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Answer:

Step-by-step explanation:

Answer:

Figure 1: 4

Figure 2: 8

Figure 3: 16

Figure 4: 20

Step-by-step explanation:

Go around each figure and count how many cube lengths it takes to go around.

The midpoint formula and the normal vector of the plane can be used to determine the equation of the plane that contains all points equidistant from the points (1,0,-2) and (3,4,0).

Given by: The midpoint of the two points is:

M = [(1 + 3)/2, (0 + 4)/2, (-2 + 0)/2] = (2, 2, -1) (2, 2, -1)

The following vector runs between the two points:

V = (3 - 1, 4 - 0, 0 - (-2)) = (2, 4, 2) (2, 4, 2)

The cross product of two non-parallel plane vectors yields the normal vector to the plane. The midpoint M to a point on the plane is one such vector, while the other is the vector V. Consider the point P = (2, 2, -1) + t(2, 4, 2) as an illustration, where t is a scalar.

The normal vector is then provided by:

N = V x (P - M) = (2, 4, 2) x (2t, 4t, 2t -1), which equals (12t, -8t, 4t + 2)

The point-normal form, which makes use of the normal vector N and the point M, can be used to determine the equation for the plane:

(x - 2) * 12t = (y - 2) * -8t = (z + 1) * 4t + 2

The final equation of the plane is obtained by multiplying both sides of the equation by t and setting t 0.

12(x - 2) = -8(y - 2) = 4(z + 1) + 2

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To find the margin of error, we need to first determine the formula for it. The margin of error (ME) is calculated by multiplying the critical value of the confidence level (in this case 90%) with the standard error (SE) of the sample mean.

The critical value for a 90% confidence interval can be found using a t-distribution table with n-1 degrees of freedom (where n is the sample size). For a sample size of 30, the degrees of freedom would be 29. Using the table, the critical value for a 90% confidence interval is approximately 1.697.

Next, we need to calculate the standard error. The formula for the standard error of the sample mean is the standard deviation of the population divided by the square root of the sample size. However, we don't know the standard deviation of the population, so we will use the sample standard deviation as an estimate.

Assuming that the sample is representative of the population, we can assume that the sample standard deviation is an unbiased estimate of the population standard deviation. Therefore, we can use the formula:

SE = s / sqrt(n)

where s is the sample standard deviation and n is the sample size.

Since we are not given the sample standard deviation, we cannot calculate the standard error. However, we can use the range of the confidence interval to estimate it. The range of the confidence interval is equal to the margin of error multiplied by 2. Therefore:

ME = (51.3 - 48.7) / 2 = 1.3

Using the formula for the margin of error, we can solve for the standard error:

ME = t*SE

1.3 = 1.697*SE

SE = 0.767

Therefore, the margin of error is approximately 1.3 inches.

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The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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The computation (u x v) × w will result in a vector quantity.

Among the given computations, (u x v) × w will result in a vector quantity. Let's break down each computation to understand their outcomes.

(u x v) × w: The cross product of vectors u and v results in a new vector, and then this vector is crossed with vector w. Both cross-products yield vector quantities, so the final result will also be a vector.

(u x v) - (w x 2): The cross product of u and v is subtracted from the cross product of w and 2. Cross products yield vector quantities, but the subtraction operation will result in a vector if the magnitudes and directions are different. Otherwise, it will be a scalar.

Therefore, the computation (u x v) × w will definitely result in a vector quantity, while the computation (u x v) - (w x 2) may or may not result in a vector, depending on the specific vectors involved.

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Answer:

C. (0.3452, ∞)

Step-by-step explanation:

The interval of t when the population of algae will be greater than 500 is (3.452, ∞)

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

The amount of algae in a bloom, P, can be modeled by the equation \(P = t^4 + 6t^3+ 7t^2 + 8t\) where t is measured in weeks.

We need to find the find the interval of t will the population of algae be greater than 500

So, we get an inequality,

\(\Rightarrow P > 500\\\\\Rightarrow t^4 + 6t^3+ 7t^2 + 8t > 500\\\\\Rightarrow t (t^3 + 6 t^2 + 7 t + 8) > 500\\\\\Rightarrow t [t [t (t + 6) + 7] + 8] > 500\\\\\Rightarrow t > 3.45~~and ~~t < -6.759\\\\\)

But time is measured in weeks.

So, t will not have the values from the interval (−∞, −6.759)

Therefore, the interval of t when the population of algae will be greater than 500 is (3.452, ∞)

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The elevation of Mt. Wilson is 17362.31 feet.

An equation is a a mathematical statement formed when two algebraic expressions are equated by an equal sign.

It is given in the question

the various heights of the peak ,

It has been asked to form an equation

Snow Crest is 11,127 feet higher than Mt.Wilson

The equation to find the elevation of Mt. Wilson is

Let the height of Mt.Wilson be x

Then

28489.31 - x = 11127

x = 17362.31

The elevation of Mt. Wilson is 17362.31 feet.

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Answer:

It's B , or #2

2x-3y<7

Step-by-step explanation:

So answer is true For deductive arguments, you answer true to the question “Do the premises provide enough logical support for the conclusion

A valid argument is a deductive argument that succeeds in providing decisive logical support.

A valid argument is thus a deductive argument an argument that attempts to establish conclusive support for its conclusion  that succeeds.

An invalid argument is a deductive argument that fails in providing conclusive support.

For deductive arguments, you answer “yes” to the question “Do the premises provide enough logical support for the conclusion?” if the argument is valid, and you answer “no” if otherwise.

So answer is true For deductive arguments, you answer true to the question “Do the premises provide enough logical support for the conclusion

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The expression that shows a way to factor 16 + 72 is 8(2 + 9)

From the question, we have the following parameters that can be used in our computation:

16 + 72

Express the terms of the expression as products

So, we have the following representation

16 + 72 = 8 * 2 + 8 * 9

Factor out 8 from the expression

This gives

16 + 72 = 8 * (2 +  9)

Hence, the factored expression of 16 + 72 is 8 * (2 +  9)

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Answer: either x=0 or x+10=0

Step-by-step explanation:

The statement  either x = 0 or 3 + 10 = 0 is also true according to the zero product property

Two or more expressions with an Equal sign is called as Equation.

If the equation (x + 10) x = 0 is true

x plus ten times of x equal to zero

According to the zero product property

if the equation (x + 10)x = 0 is true, then either x + 10 = 0 or x = 0.

So the statement "either x = 0 or 3 + 10 = 0" is true.

Hence, the statement  either x = 0 or 3 + 10 = 0 is also true according to the zero product property

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The bg - (a v b) ► g is proved using Axiom 9 and other axioms.

To prove a → g and bg - (a v b) ► g using Axiom 9, we will follow these steps:

1. Start with a → g (assumption).
2. Apply Axiom 1 to a → g: (a → g) → ((a → g) → g) → (a → g).
3. Apply Modus Ponens on (1) and (2): ((a → g) → g) → (a → g).
4. Apply Axiom 1 again to a → g: (a → g) → ((a → g) → g).
5. Apply Modus Ponens on (3) and (4): (a → g) → g.
6. Given bg - (a v b), apply Axiom 9 to get (a v b) → g.
7. Apply Axiom 1 to a v b: (a v b) → ((a v b) → g) → (a v b).
8. Apply Modus Ponens on (6) and (7): ((a v b) → g) → (a v b).
9. Apply Modus Ponens on (5) and (8): (a v b).

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We can conclude that ¬(a v b) ►g ¬a, and hence, the statement a →g. bg - (a v b) ►g is true.

However, I can still help you outline proof based on your given information.

1. assume that a →g. bg is true. Then, by applying the first part of Axiom 9, we get: (a →g. ¬(a v b)) →g. ¬a.
You want to prove that: a → g, bg - (a ∨ b) ► g.

2. You're provided with a hint to use Axiom 9.

3. Given that we can use any result in page 36 of the cheat sheet, I'll assume we have access to various axioms and rules of inference.

To outline a proof, we could follow these steps:

Step 1: Write down the given information: a → g and bg - (a ∨ b) ► g.

Step 2: Use Axiom 9 in conjunction with other axioms from the cheat sheet to make deductions.
we need to prove that a →g. ¬(a v b) is true. Assume the negation of this statement, which is (a →g. ¬(a v b)) ►g ¬g. a. This can be rewritten as ¬(¬g. a) ►g ¬(¬g. ¬(a v b)), which is equivalent to g. a ►g (a v b).

Step 3: Continue making deductions using rules of inference from the cheat sheet until you reach the desired conclusion, which is (a ∨ b) ► g.
Now, by using the second part of Axiom 9 with g. a as a and ¬(a v b) as b, we get: (g. a →g. ¬¬(a v b)) →g. (g. a →g. (a v b)) →g. ¬g. g. a.

Simplifying the double negation in the first part, we get g. a →g. (a v b). Substituting this in the second part, we get: (g. a →g. (a v b)) →g. ¬g. g. a.

Unfortunately, without knowing the content of your cheat sheet and Axiom 9, I can't provide a more detailed answer. However, I hope the outline above helps guide you in constructing your proof.

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Answer:

17

Step-by-step explanation:

Since there is no variables in the equation they are all like terms. So just do addition or subtraction. But if it wants you to separate addition and subtraction the answer would be 31-12.

If this is for Imagine Math:

Question:

Simplify the expression by combining like terms.

15+12−5+4−7

Answer:

7x +4y + 8

Answer: To find the value of the car after 8 years, we can use the given information to create a linear equation in the form:

y - y1 = m(x - x1)

Where:

y is the value of the car after 8 years (what we want to find)

y1 is the value of the car after a given time (either 3 or 5 years)

x is the given time (either 3 or 5 years)

x1 is the starting time (when the car was purchased)

m is the rate of decrease (slope of the line)

We can use the two given data points to find the slope of the line:

m = (y2 - y1) / (x2 - x1)

m = (11,000 - 15,000) / (5 - 3)

m = -2,000 per year

Now, we can use one of the data points to solve for the y-intercept of the line:

y - y1 = m(x - x1)

y - 15,000 = (-2,000)(3 - x1)

y - 15,000 = (-2,000)(3 - x1)

y - 15,000 = (-6,000 + 2,000x1)

y = 2,000x1 - 6,000 + 15,000

y = 2,000x1 + 9,000

So the linear equation that represents the value of the car after x years is:

y - 15,000 = (-2,000)(x - 3)

Simplifying this equation gives:

y - 15,000 = -2,000x + 6,000

Now, we can use x = 8 to find the value of y:

y - 15,000 = -2,000(8) + 6,000

y - 15,000 = -2,000

y = $13,000

Therefore, the value of the car after 8 years will be $13,000.

So the completed expression is:

y - 15,000 = -2,000(x - 3)

The value of the car after 8 years will be $13,000.

Step-by-step explanation:

The econometric specification for a regression of Y and D using the pre-post method is: [ Y_{it} = \beta_0 + \beta_1D_{it} + \epsilon_{it} \]

Pooled Cross Section Data:

To estimate the pre-post method, we will use the data for individuals who have observations in both years, i.e., individuals for whom we have data in both year t (before) and year t+1 (after).

Assumed Counterfactual:

The assumed counterfactual in this model is that the outcome for each individual in year t+1, had they not enrolled in the program, would be the same as their outcome in year t.

Weaknesses of the Assumed Counterfactual:

The assumed counterfactual relies on the assumption that the outcome for each individual would remain constant from year t to year t+1 in the absence of program enrollment.

However, this assumption may not hold true if there are other factors that could affect the outcome. Unobserved time-varying factors or changes in individuals' circumstances over time can introduce biases and violate the assumption of a constant counterfactual.

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The econometric specification for a regression of Y and D using the pre-post method is given by:

Yi = β0 + β1Di + εi

In this econometric specification, Yi represents the outcome of interest for individual i. Di is a binary variable that indicates enrollment (1) or non-enrollment (0) of individual i in the program. β0 is the intercept term, β1 is the coefficient that captures the average treatment effect of the program on the outcome, and εi is the error term.

To estimate the pre-post method, we will use the pooled cross-section data for year t (before program implementation) and year t+1 (after program implementation). This means that we will have observations for both individuals who were enrolled in the program (Di = 1) and those who were not (Di = 0) before and after the program.

The pre-post method assumes that the difference in outcomes between the two time periods for individuals who were not enrolled in the program (Di = 0) represents the counterfactual or what would have happened to the treatment group (Di = 1) had they not been enrolled. This assumption is based on the idea that the only difference between the treatment and control groups is the enrollment in the program.

However, there are several weaknesses in the assumed counterfactual. First, there may be unobserved factors that differ between the treatment and control groups, which can bias the estimated treatment effect. Second, the pre-post method assumes that there are no time-varying confounders that change between the two time periods, which may not hold true in practice. Finally, the assumption of parallel trends between the treatment and control groups before program implementation is crucial for identifying the causal effect, but it can be difficult to verify.

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Answer:

exact form-512/7

decimal form-73.1

Mixed number form-73 1/7

Step-by-step explanation: