Consider the following piecewise-defined function. F(x) = {22

- 5,x < 3

(2x + 5,x > 3

Find f(-4)

Refer to the attachment for figure:

The height of the rectangle = 11 inches

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x= height

Width becomes x+49

Diagonal BD=61 inches

By pythagoras theorem,

BD²=BC²+CD²

61²= (x+49)²+x²

3721=x²+98x+2401+x²

On simplification,

x²+49x-660=0

Find the factors

(x+60)(x-11)=0

x=-60, x=11

Consider positive value for height

height = 11 inches

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Answer:

multiply 12 by 16, and 8 by 18

Step-by-step explanation:

basically, you take the top of one, and multiply it by the bottom of the opposite fraction.

To dilate a point at a point, you start by selecting a center of dilation and a scale factor.

Then, for each point that you want to dilate, you do the following:

For example, if you wanted to dilate point P by a scale factor of 2, with the center of dilation at O, you would draw a line segment from O to P, double its length, and then draw a new line segment from O to the new point, using the new length that you calculated. The new point would be the point that you arrive at when you complete this line segment.

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Answer:

e

Step-by-step explanation:

Answer:

Step-by-step explanation:

I am assuming the tank starts empty. It means that in 1 hour the tank has half that water, or 3600 gallons. And the good thing of lines passing through 0.0 is that the value at 1 IS the slope we need. ie 3600.

At this point it's easy to find that if in 2 hours it filled 1/10th of the tank, in 20 hours the tank will be full.

Graph done with paint, obviously not to scale.

Answer:

3/4 is 0.75 and 1 is 1

Step-by-step explanation:

:\

Answer:

26.88

Step-by-step explanation:

32% of 84

= \(\frac{32}{100}\) × 84

= 0.32 × 84

= 26.88

Answer:

Step-by-step explanation:

84 : 100 = 0.84

0.84 × 32 = 26.88

84 : 100 × 32 = 26.88

There is no real number solution to this equation. Therefore, it is not possible to find an equation relating a, b, and c that guarantees the given linear system to be consistent for any values of a, b, and c.

To ensure that the given linear system is consistent for any values of a, b, and c, we need to find an equation that guarantees the existence of a solution.

This can be achieved by setting up a condition on the coefficients of the system such that the determinant of the coefficient matrix is zero.

Let's consider the coefficient matrix A:

A = [[1, 2, -3],

[2, 3, 3],

[5, 9, -6]]

We want to find an equation relating a, b, and c such that the determinant of A is zero.

det(A) = 0

Using the properties of determinants, we can expand the determinant along the first row:

det(A) = 1 * det([[3, 3], [9, -6]]) - 2 * det([[2, 3], [5, -6]]) + (-3) * det([[2, 3], [5, 9]])

Simplifying further, we have:

det(A) = 1 * (3*(-6) - 39) - 2 * (2(-6) - 35) + (-3) * (29 - 3*5)

det(A) = -54 + 2*(-12) - 3*3

det(A) = -54 - 24 - 9

det(A) = -87

Setting the determinant equal to zero, we get:

-87 = 0

However, there is no real number solution to this equation. Therefore, it is not possible to find an equation relating a, b, and c that guarantees the given linear system to be consistent for any values of a, b, and c.

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The median of the given list of numbers is 87.

To find the median of a list of numbers, we arrange them in ascending order and identify the middle value.

If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

First, let's arrange the numbers in ascending order:

65.9, 68, 70, 74, 75, 78, 84, 86, 87, 90, 93, 93, 95, 96, 97, 380, 486, 680

There are 17 numbers in the list, which is an odd number. The middle number is the 9th number in the list, which is 87.

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Answer:

y = 5/3x + 13/3

Step-by-step explanation:

slope intercept form is y = mx + b

to find the slope of a line using two points, you use the formula

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

(-2,1) (1,6)

(6 - 1)/(1 + 2)

5/3 is the slope

to solve for b, you take one of the points in the given and the slope (m) and solve for b

y = mx +b

y = 5/3x + b

6 = 5/3(1) + b

6 = 5/3 + b

18/3 = 5/3 + b

13/3 = b

now put the entire equation together

y = 5/3x + 13/3

a. FALSE: The x-intercept is (-10, 0) and the y-intercept is (0, -4). b. TRUE: A stochastic matrix meets all the given conditions. c. FALSE: A regular matrix is a stochastic matrix that, when raised to a positive power.

a. The x-intercept occurs when y = 0, so by substituting y = 0 into the equation 2x - 5y = 20, we get 2x = 20, which gives x = 10. Therefore, the x-intercept is (10, 0), not (0, 10). Similarly, the y-intercept occurs when x = 0, so substituting x = 0 into the equation gives -5y = 20, which results in y = -4. Therefore, the y-intercept is (0, -4), not (-4, 0).

b. A stochastic matrix is defined as a square matrix where all entries are greater than or equal to 0, and the sum of the entries in each column is 1. Therefore, the statement is true.

c. A regular matrix is a stochastic matrix where, when raised to a positive power, all entries remain positive. The statement mentions "all positive nonzero entries," which is incorrect. Therefore, the statement is false.

d. A polynomial interpolant is a model that can be obtained by using an exact number of data points, n+1, for a polynomial of degree n. This statement is true as it corresponds to the definition of polynomial interpolation, where a polynomial function is constructed to pass through the given data points.

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Answer:

x=18

Step-by-step explanation:

Isolate the variable

2/3 x=12

divide by 2/3

x=18

\(6^{2}=3*x\\36=3x\\x=12\\\)

Answer:

29°

Step-by-step explanation:

all triangles = 180° so if you add 118 + 33 = 151

subtract 180 - 151 = 29

therefore your 3rd angle is 29°

To find the area of the surface that lies within the cylinder x² + y² = 9, we need to find the limits of integration for x and y.

Since the surface is defined as z = xy, we can rewrite the equation of the cylinder as y = √(9 - x²).
To find the limits of integration for x, we need to determine the range of x-values for which y is defined. From the equation y = √(9 - x²), we can see that y is defined as long as 9 - x² ≥ 0. Solving this inequality, we have x² ≤ 9, which means -3 ≤ x ≤ 3.
Now, to find the limits of integration for y, we need to determine the range of y-values for which x is defined. From the equation x² + y² = 9, we can see that y is defined as long as x² + y² ≤ 9. Therefore, -√(9 - x²) ≤ y ≤ √(9 - x²).
Using these limits of integration, we can set up the double integral to find the area of the surface:
A = ∬(R) √(1 + (∂z/∂x)² + (∂z/∂y)²) dA
where R is the region defined by -3 ≤ x ≤ 3 and -√(9 - x²) ≤ y ≤ √(9 - x²).
Unfortunately, it is not possible to calculate the exact value of this integral without further information. However, you can use numerical integration methods or software to approximate the area.

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Answer:

Y=1/3x-6

Step-by-step explanation:

Answer:

Subtract x from both sides.

-3y = -x + 18

Divide everything by -3.

y = -1/3 - 6

^There ya go. ^

If researchers use statistical tests and determine that there is a low probability that their experimental results occurred purely by chance, then their results are considered statistically significant.

Statistically significant results suggest that the observed effects in the experimental group are unlikely to have happened by chance and are likely to reflect a real effect of the treatment or intervention being tested.

However, it's important to note that statistical significance does not necessarily mean practical significance or real-world importance. For example, a small effect may be statistically significant but still not large enough to have practical implications.

Additionally, it's important to be aware of potential sources of error and bias in the experimental design and data analysis, and to consider the results in the context of other relevant evidence. Statistical significance should not be used as the sole criterion for accepting or rejecting research results, and should always be accompanied by a thorough evaluation of the quality of the evidence and the implications of the results.

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In the context of topology, the relationship between a topological space, a normal subgroup, and a continuous function are discussed here.

These can be understood as follows:

1. Topological space: A topological space is a set equipped with a collection of subsets called open sets, which satisfy certain properties. These properties include that the empty set and the entire set are open, any union of open sets is open, and the intersection of finitely many open sets is open. Topological spaces provide a framework for studying concepts like convergence, continuity, and compactness.

2. Normal subgroup: In group theory, a subgroup is a subset of a group that is itself a group. A normal subgroup is a special kind of subgroup that has the property that it is preserved under conjugation by elements of the group. In other words, if H is a normal subgroup of a group G, and g is any element of G, then the conjugate of H by g, denoted by gHg⁻¹, is also a subgroup of G.

3. Continuous function: In topology, a function between two topological spaces is said to be continuous if the preimage of every open set in the codomain is open in the domain. Intuitively, this means that small changes in the input result in small changes in the output. Continuous functions play a fundamental role in topology, as they preserve the topological structure of the spaces involved.

Now, let's establish the relationship between these concepts in the topological and metrical senses:

1. In the topological sense:
  - A topological space can have a normal subgroup if it is equipped with an underlying group structure. However, the properties of the topological space alone do not directly determine the existence or nature of a normal subgroup.
  - A continuous function between two topological spaces may or may not respect the group structure. The continuity of a function is determined solely by the open sets in the two spaces, without considering any underlying group structure.

2. In the metrical sense:
  - A topological space can be equipped with a metric, which is a function that measures the distance between elements of the space. In this case, the topological structure is induced by the metric, and concepts like convergence and continuity can be defined in terms of the metric.
  - A normal subgroup in the metrical sense would refer to a subgroup that is preserved under the metric. However, the metric alone does not determine the existence or nature of a normal subgroup.
  - A continuous function in the metrical sense would mean that small changes in the input result in small changes in the output, as measured by the metric.

In summary, the relationship between a topological space, a normal subgroup, and a continuous function depends on the underlying structures and properties involved. While a topological space can have a normal subgroup in the context of an underlying group structure, a continuous function is determined solely by the open sets in the spaces involved, without considering any group structure. In the metrical sense, the metric can induce a topological structure and affect the behavior of normal subgroups and continuous functions.

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Step-by-step explanation:

In my opinion 125 is an outlier because it is the only 3 digit number

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Answer:

Step-by-step explanation:

according to the question

2(-1)³+9(-1)+k=0

=>2(-1)+9(-1)+k=0

=>-2-9+k=0

=>-11+k

therefore

k=11

The area of the lawn in the scale drawing is approximately 996 square feet.

1. Measure the length and width of the lawn in inches on the scale drawing.

Length = 16.5 inches

Width = 15.5 inches

2. Convert the measurements to feet by dividing the inches by 12.

Length = 16.5/12 = 1.375 feet

Width = 15.5/12 = 1.291 feet

3. Calculate the area of the lawn by multiplying the length and width.

Area = 1.375 x 1.291 = 1.75 square feet

4. Multiply the area by the scale factor (in this case, 560) to get the actual area.

Area = 1.75 x 560 = 996 square feet

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Answer:

19.7

Step-by-step explanation:

a^2+b^2=c^2

so 18^2+8^2=x^2

324+64=388

x is about 19.7

The equation for the regression line that predicts the probability of default in percent using the credit score as the explanatory variable can be given as follows: Probability of Default in Percent = a + b(Credit Score)

where a is the y-intercept and b is the slope of the regression line. The y-intercept represents the value of the dependent variable when the independent variable is zero, while the slope represents the rate of change in the dependent variable for every one-unit increase in the independent variable.

For instance, a credit score of 650 can have a probability of default of 5%. This implies that the probability of default in percent can be predicted as:

Probability of Default in Percent = a + b(650)

where the coefficient of determination (r²) can be used to assess the degree of relationship between the probability of default in percent and credit score.

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Answer: y=2/5x+b

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

(x-3)=5

add 3 to 5= 8

another way is to do:

subtract -3 to 5 = -2

Answer:

x=8

Step-by-step explanation:

The value of the expression when x = 2, y = -3, and z = 4 is -18 + 8Ω.

The expression to evaluate is:

6ν + XZ Ω

Substituting x = 2 and z = 4, we get:

6ν + (2)(4) Ω

Simplifying the right side, we get:

6ν + 8Ω

Substituting y = -3, we get:

6(-3) + 8Ω

Simplifying the left side, we get:

-18 + 8Ω

Therefore, the value of the expression when x = 2, y = -3, and z = 4 is:

-18 + 8Ω.

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Answer:

184

Step-by-step explanation:

SA = 2LW + 2LH + 2WH

SA = 2(5 × 4) + 2(5 × 8) + 2(4 × 8)

SA = 2(20) + 2(40) + 2(32)

SA = 40 + 80 + 64

SA = 184

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YW

To provide Logical Proofs with line-by-line justifications for the following arguments,

Let's use the first 4 rules of inference.

Given below is the justification for each step of the proof with the applicable rule of Inference.

E > M1. A > (E > ~F) Premise2. H v (~F > M) Premise3. A Premise4. ~H  Premise5. A > E > ~F 1, Hypothetical syllogism6.

E > ~F 5,3 Modus Ponens 7 .

~F > M 2,3 Disjunctive Syllogism 8.

E > M 6,7 Hypothetical SyllogismIf

A is true, then E must be true because A > E > ~F.

Also, if ~H is true, then ~F must be true because H v (~F > M). And if ~F is true,

Then M must be true because ~F > M. Therefore, E > M is a valid  based on the given premises using the first four rules of inference.

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