{ax+3y=10

kx−3y=6

In the system of equations above, a and k are constants. If the solution to the system is (2,1) , what is the value of a+k ?

Answer:

$126

Step-by-step explanation:

Monday: 5HR X $14 = $70

Tuesday: 4HR X $14 = $56

$70+$56=$126

The solution is

a) ∠1 ≅ ∠5 by Corresponding Angles

b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles

c) ∠6 ≅ ∠4 by Alternate Interior Angles

d) ∠2 ≅ ∠8 by Alternate Exterior Angles

What are Parallel Lines Cut by Transversal?

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

From the figure , we can see that

The Corresponding angles are

Angle 1 and Angle 5

Angle 2 and Angle 6

Angle 4 and Angle 8

Angle 3 and Angle 7

The Alternate Interior angles are

Angle 4 and Angle 6

Angle 3 and Angle 5

The Co-Interior angles are

Angle 4 and Angle 5

Angle 3 and Angle 6

The Alternate exterior angles are

Angle 1 and Angle 7

Angle 2 and Angle 8

Hence , the angles from the figure that are true are

a) ∠1 ≅ ∠5 by Corresponding Angles

b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles

c) ∠6 ≅ ∠4 by Alternate Interior Angles

d) ∠2 ≅ ∠8 by Alternate Exterior Angles

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Rate of change of y =[tex]\frac{5}{4}x +1[/tex]  is 5/4.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given that the expression, y =[tex]\frac{5}{4}x +1[/tex] .

To find the rate of change,

first we make the equation in standard form.

Slope intercept form ;

(y₂ - y₁) =m (x₂ -x₁) + c

Comparing the expression to the standard form;

Here, x intercepts: ( -4/5 , 0) and y intercepts: (0,1)

Rate of change = (y₂ - y₁) / (x₂ -x₁)

Rate of change = 5/4

Therefore, rate of change of y =  is 5/4.

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The confidence interval for the average age of the population would be (18.8, 25.2).

What is the confidence interval?

In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used.

Given that,

Point estimate = sample mean = [tex]\bar x[/tex] =22

sample standard deviation = s = 6

sample size = n = 16

Degrees of freedom = df = n - 1 = 16 - 1 = 15

At 95% confidence level

[tex]\alpha[/tex] = 1 - 95%

[tex]\alpha[/tex] =1 - 0.95 =0.05

[tex]\alpha/2[/tex] = 0.025

[tex]t_{\alpha/2},df[/tex] = t 0.025 , 15 = 2.131

Margin of error = E = [tex]t\alpha/2,df * \frac{s}{\sqrt n}[/tex]

                              =2.131  * (6 / √16)

Margin of error = E = 3.20

The 95% confidence interval estimate of the population mean is,

= [tex]\bar x \pm E[/tex]

= 22  ± 3.20

= (18.8, 25.2)

Hence, the confidence interval for the average age of the population would be (18.8, 25.2).

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Jane must therefore deposit her savings in the four rivers bank.

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the data provided in the question,

Rate, r = 12%

After five years, the total amount, if Jane had saved at Mystic Bank,if Jane had saved at Mystic Bank would be:

[tex]A = P(1+\frac{r}{100} )^n[/tex]

For compounded quarterly,

n = 5 × 4

n = 20

A = 40000(1 + 12/(4 × 100))²⁰

A = 72244.44     (i)

If Jane placed her savings with the Four Rivers, then,

A = 40000(1 + 14/(2 × 100))¹⁰

A = 40000 × 1.9671

A = 78686.054  (ii)

Therefore, it is evident that case (ii) is higher than case (i). Jane must therefore deposit her savings in the four rivers bank.

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The solutions for all three questions regarding two-way frequency tables are given below.

A two-way frequency table is a method used to visually represent two sets of categorical data. Unlike one-way frequency tables which have only one categorical variable, these have two. The important parts of a two-way frequency table are the topmost rows that have the name of the category. The leftmost column also has the categories listed. The middle columns and rows contain the data (frequency).

The number in the bottom right-hand corner of a two-way frequency is used to denote the total number of data points that are there in the data set given. This is also equal to the sum of the total rows/columns.

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No, he wanted a park developed within 5 miles of his residence, yet this park is 8.30 miles away.

The horizontal and vertical distances from the two reference axes are used to define the location of a point on a coordinate plane. The x-value and y-value are often denoted as (x,y). To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate. The distance between two points is known as the x-coordinate, or abscissa, while the distance between two points is known as the y-coordinate, or ordinate.

Here,

let the house be (0,0).

coordinate of park=(3,7)

distance=√3²+7²

=√21+49

=√69

=8.30 miles.

No, He wanted a park to be built within 5 miles of his house while this park is 8.30 miles from his house.

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Absolute Value: The "unsigned" number that corresponds to the (Positive) distance between a number and zero on the number line. [tex]| - 4| = 4 and | 4| = 4;[/tex]

Positive and negative integers, fractions, rational numbers, including irrational numbers, and negative integers are all examples of real numbers. fictitious numbers,  Real numbers are those that fall between the two extremes,

Absolute Value: The "unsigned" number that corresponds to the (Positive) distance between a number and zero on the number line. | - 4| = 4 and | 4| = 4; The collection of positive numbers used to count items is known as the counting numbers, sometimes known as natural numbers. 1, 2, 3, 4, 5, ...; Fractions and decimals are not integers; rather, integers are the set of all whole numbers, along with their opposites (the positive whole numbers, the negative whole numbers, and zero). -3, -2, -1, 0, 1, 2, 3, ...; Irrational Numbers - The collection of all non-terminating, non-repeating decimal numbers; Natural Integers: The collection of positive numbers utilized in object counting (also called counting numbers). 1, 2, 3, 4, 5, ...; Unfavorable Numbers - the range of numbers on the number line that are less than zero and to the left of zero.; Number Line - a horizontal line with points representing different numbers. In a number line with just whole numbers or integers, the dots are uniformly spaced out according to the value of the number they represent.; Opposite - a number that is on the other side of zero and at the same distance from zero as a given integer. For instance, the opposites of 7 and -7 and 9 and 9 are both 7; positive figures - the group of numbers on the number line that are greater than zero and to the right of zero.

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It is occasionally accurate to say that the range of an even function is (-∞o, max), where max is the function's maximum.

the range of variation that is conceivable or the boundaries between it: pricing for various grades of steel; a variety of designs. a thing's operation or action's reach or extent: accessible to the eye. a projectile's range is how far a weapon can or will shoot it.

here the explanation

We can say that our range is any real number value between -infinity and infinity, or (,), if our range is any real number value. The range is all real numbers, but we can express this more succinctly by using the symbol R.

a position where the value of a function is highest. It is an absolute maximum if the value is larger than or equal to all other function values.

It is occasionally accurate to say that the range of an even function is (-∞o, max), where max is the function's maximum.

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According to the Mean value theorem conditions. The answer will be (a) that is Mean Value Theorem can be applied.

The Mean Value Theorem says that there exists a point c in the interval    (a, b) such that f'(c) equals the function's average rate of change throughout [a , b] if a function f is continuous on the closed interval [a , b] and differentiable on the open interval (a , b).

The name derives from the fact that an average rate of change during an interval may be considered as an average (or mean) of the instantaneous rates of change along the interval thanks to the fundamental theorem of calculus.

[tex]f(x) = 9\sin x[/tex] is continuous on [0,1] since every value for [tex]9\sin x[/tex] exist in that interval.

[tex]f(x) = 9\sin x[/tex] is differentiable on (0,1) since at every point the derivative exist that is [tex]9 \cos x[/tex] is valid in that interval.

The answer is (a) that is Yes, The Mean Value Theorem can be applied.

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Answer:

–3 4/15

or

3 4/15

Step-by-step explanation:

The probability that if I select 10 people, I will get 2 seniors and 8 freshmen is 0.00000901

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

Also from the question, we have

Number of people selected = 10

To get 2 seniors and 8 freshmen, the probability equation is

Probability = (Seniors)² * (Freshman)⁸

Substitute the known values in the above equation, so, we have the following representation

Probability = (20%)² * (35%)⁸

Evaluate

Probability = 0.0000090075

Approximate

Probability = 0.00000901

Hence, the probability is 0.00000901

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Answer: 792 Combinations

The value of the number from the equation 6A - 5 ≤ -25 is A = -3.33

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number be represented as A

Now , the value of A is calculated as

Five subtracted from the product of 6 and a number is at most -25

So , the inequality equation will be

And , substituting the values in the equation , we get

6A - 5 ≤ -25   be equation (1)

Now , adding 5 on both sides of the equation , we get

6A ≤ -25 + 5

6A ≤ -20

Divide by 6 on both sides of the equation , we get

A ≤ -3.33

Therefore , the value of A is -3.33

Hence ,

The value of the number from the equation 6A - 5 ≤ -25 is A = -3.33

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Answer: 9x

Step-by-step explanation:

-4x+y=5x

solve for x

y=9x

Answer:

To answer these questions, we need to first calculate the total number of payments you have made over the past 3 years. We can do this by multiplying the number of payments per year (12) by the number of years (3). This gives us a total of 36 payments.

Next, we can use a financial calculator or spreadsheet program to solve for the remaining balance on your loan after making 36 payments of $327.51 each. In a financial calculator, we can enter the following values:

N: 36

I: 5.8

PV: -14000

PMT: 327.51

FV: 0

Solving for PV gives us a remaining balance of $4,819.56. Therefore, the answer to part A is $4,819.56.

To find your equity in the car, we can subtract the remaining balance on the loan from the value of the car. In this case, your equity would be $7,500.00 - $4,819.56 = $2,680.44. Therefore, the answer to part B is $2,680.44.

Step-by-step explanation:

Brainliest? :>

If the supplied functions are f(x) = - 3x 2 + x - 9 and g(x) = x 3 + 6x and the value of x is -4, the value of (f + g)(- 4) is -137.

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable). Functions are typically categorized into four categories. Depending on the Element: One function to one function, many functions to one function, onto function, one function to one and onto function, into function A "vertical line test" can be used to identify whether a relation is a function when looking at a graph. If a vertical line can be drawn anywhere on the graph and cross the relation twice, the relationship is not a function.

Here,

(f+g)(x)=f(x)+g(x)

f(-4)=-3*(-4)²-4-9

f(-4)=-61

g(-4)=(-4)³-3*4

g(-4)=-76

(f+g)(-4)=f(-4)+g(-4)

=-61-76

(f+g)(-4)=-137

If the supplied functions are f(x) = - 3x 2 + x - 9 and g(x) = x 3 + 6x and x is -4, the value of (f + g)(- 4) is -137.

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the difference between Group B and Group C (-0.3) is less than the other differences, we can conclude that Group B and Group C are the means that are different.

The ANOVA test has determined that there is a difference between the means, and the Tukey's results can help to determine which mean is different. In this case, Group B (4.0) and Group C (4.3) are significantly different, meaning that one of those means is different from the other groups.

An ANOVA test has been conducted and it has been determined that there is a difference between the means. The Tukey's results can be used to identify which mean is different. In this case, Group B (4.0) and Group C (4.3) are significantly different, meaning that one of those means is different from the means of the other groups (A: 2.2 and D: 4.5). Therefore, Group B and Group C are the means that are different.

Tukey's Test

Group A vs B: 2.2 - 4.0 = -1.8

Group B vs C: 4.0 - 4.3 = -0.3

Group C vs D: 4.3 - 4.5 = -0.2

Since the difference between Group B and Group C (-0.3) is less than the other differences, we can conclude that Group B and Group C are the means that are different.

The complete question is :

suppose an analysis of variance (anova) has determined that there is a difference between means and the following tukey's results are shown. determine which mean is different.

Group A: 2.2

Group B: 4.0

Group C: 4.3

Group D: 4.5

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After evaluating f(x) = 3x - 5, the answer is f(x-2) = 3x - 11

What do you mean by functions?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). Expressions of well-known functions can be found in many frequently used mathematical formulas. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The set X is called the domain of the function and the set Y is called the codomain of the function.

Given function:

f(x) = 3x - 5

For f(x-2) substitute x as (x-2) in given function

f(x-2) = 3(x - 2) - 5 = 3x - 6 - 5 = 3x - 11

therefore, f(x-2) = 3x - 11

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Answer:

  A.  1/4 gal/scoop

  B.  w = 1/4s

  C.  line through the origin with slope 1/4; s-, w- axes labeled "scoops" and "gallons"

  D.  3 gallons

Step-by-step explanation:

Given 2 scoops of  powdered drink mix needs 1/2 gallon of water, you want (A) the constant of proportionality, (B) the equation for the relationship, (C) a description of the graph, (D) gallons for 12 scoops.

A proportional relationship between gallons of water (w) and scoops of drink mix (s) can be written as ...

  w = ks

where k is the constant of proportionality.

Solving the equation for k, we get ...

  k = w/s

Using the given values, we find k to be ...

  k = (1/2 gal)/(2 scoops) = 1/4 gal/scoop

The constant of proportionality is 1/4 gallon per scoop.

We show the equation in part A. Filling in the value of k gives ...

  w = 1/4s . . . . . . . where s is number of scoops, and w is gallons of water

The attached shows a graph. A line starts at the origin with slope 1/4; s-, w- axes are labeled "scoops" and "gallons". The practical domain is s ≥ 0, so no part of the graph is in the 3rd quadrant.

The equation tells you that 12 scoops will require ...

  w = 1/4·12 = 3 . . . . gallons

3 gallons of water are needed for 12 scoops of drink mix.

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The absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.

What is meant by absolute maximum and absolute minimum values?

A function's absolute maximum point is the point at which it can reach its highest value. A similar absolute minimum point is where the function's least possible value is obtained.

Given: [tex]f(x)=xe^{\frac{-x2}{32} }[/tex]

Differentiate the function,

[tex]f'(x)=e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }[/tex]

[tex]e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=0[/tex]

[tex]\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=e^{\frac{-x^{2} }{32} }[/tex]

[tex]\frac{x^{2} }{16} =1[/tex]

[tex]x^{2} =16[/tex]

[tex]x=[/tex] ±[tex]4[/tex]

The interval is given as: [-2,8]

This means that the value of x = -4, is out of the interval.

So, we have the following critical points:

x = (-2, 4, 8)

⇒ f(x) at x = -2

[tex]f(-2)=-2[/tex] × [tex]e^{\frac{-(-2)^{2} }{32} }[/tex]

[tex]f(-2)=-2[/tex] × [tex]e^{\frac{-4}{32} }[/tex]

[tex]f(-2)=-1.765[/tex]

⇒ f(x) at x = 4

[tex]f(4)=4[/tex] × [tex]e^{\frac{-(4)^{2} }{32} }[/tex]

[tex]f(4)=4[/tex] × [tex]e^{\frac{-16}{32} }[/tex]

[tex]f(4)=2.426[/tex]

⇒ f(x) at x = 8

[tex]f(8)=8[/tex] × [tex]e^{\frac{-(8)^{2} }{32} }[/tex]

[tex]f(8)=8[/tex] × [tex]e^{\frac{-64}{32} }[/tex]

[tex]f(8)=1.083[/tex]

Hence, by comparison, the absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.

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Answer:

10.37

Step-by-step explanation:

3 in the thousandths place is lower than 5 therefore you have to turn the thousandths into a 0 and don't change the forenumber

the given statement if a is an n x n diagonalizable matrix then each vector in R^n can be written as a linear combination of eigenvectors of a is false.

What is Diagonalizable matrix?

If there is an invertible matrix P and a diagonal matrix D such that

P^-1AP=D, or alternatively A=PDP^-1, then the square matrix A is said to be diagonalizable or non-defective in linear algebra.

If and only if the algebraic multiplicity of each of A's eigenvalues is equal to the geometric multiplicity of each eigenvalue, then A is diagonalizable. The fact that the geometric sum of the eigenvalues of A is n is an equivalent description.

The given statement is false.

If A is diagonalizable, then A had n distinct eigenvalues. It could have repeated eigenvalues as long as the basis of each eigenspace is equal to the multiplicity of that eigenvalue.

Hence, the given statement is false.

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Answer:

The Venn diagram below shows information

about the number of items in sets A and B.[asy]

label("A",(0,75));

label("B",(100,75));

label("C",(50,0));

label("D",(0,45));

label("E",(100,45));

draw(Circle((50,60), 40));

draw(Circle((50,30), 40));

draw(Circle((20,60), 20));

draw(Circle((80,60), 20));

[/asy]To find P(A'|B), we can use the formula:P(A'|B) = P(A' and B) / P(B)We can find P(A' and B) by looking at the Venn diagram. It is the number of items in the intersection of sets A' and B, which is represented by the region labeled "D" in the Venn diagram. This region contains 10 items.To find P(B), we can look at the Venn diagram and add up the number of items in both sets B and the intersection of A and B. This is represented by the regions labeled "D" and "E" in the Venn diagram, and contains a total of 20 items.Plugging these values into the formula above, we get:P(A'|B) = (10 items) / (20 items) = 1/2So, the probability that an item chosen at random belongs to A' given that it belongs to B is 1/2. This fraction is already in its simplest form.

Step-by-step explanation:

Define the function [tex]R^{+}[/tex]: N ⇒ N where R+(x) = x + [tex]x^{R}[/tex]

(a) Let A₂ = {(x,y) | [tex]R^{+}[/tex] (x) = y} language A₂ ∈L.

(b) Let A₃ = {(x,y) | [tex]R^{+}[/tex] ([tex]R^{+}[/tex] (x)) = y} language A₃ ∈L.

Given that,

For any positive integer x, let [tex]x^{R}[/tex] be the integer with the opposite of x's binary representation in terms of representation. (Assume that x's binary form has no leading 0s.) Specify the function [tex]R^{+}[/tex]: N ⇒ N where R+(x) = x + [tex]x^{R}[/tex]

(a) Let A₂ = {(x,y) | [tex]R^{+}[/tex] (x) = y}. Show A₂ ∈L.

(b) Let A₃ = {(x,y) | [tex]R^{+}[/tex] ([tex]R^{+}[/tex] (x)) = y}. Show A₃ ∈L.

We know that,

Consider the Turing machine M, which computes the inverse of x for every positive inter. The result will also be x if the computation is done using both the integer x and its inverse.

This is because the result of adding a binary number 1 to 0 is always 1. The criterion is that the binary representation of x must not contain 0. In this case, a positive integer x is converted into binary representation.

Only x values with a binary representation of 1 will be accepted by the Turing machine. Even the Turing machine will accept inverse-of-x values with binary representations of 0.

Therefore, It is proved that language A₃ ∈L.

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Answer:

5,560

Step-by-step explanation:

Answer:

Step-by-step answer should

be 5560 because if you divide 94,520 by 17 you can use calculator and the answere should be 5,560

Answer:

x=2 and y=2

Step-by-step explanation:

2x=12-4y

x=12-4y/2

x=6-2y

substitute equation on in two

2(6-2y)-y=2

12-4y-y=2

12-5y=2

5y=12-2

5y=10

y=10/5

y=2

substitute in the equation 6-2(2)=2

y=2 and x=2

Answer:

Step-by-step explanation:

.17(100)=17

17 meters

The statement that servers that exist within a data center that is publicly accessible on the internet are referred to as on-premises servers is False.

HTML5

HTML5 is a markup language used for structuring and presenting content on the World Wide Web. It is the fifth and final major HTML version that is a World Wide Web Consortium recommendation. The current specification is known as the HTML Living Standard.

On-premises servers

On-premises servers refer to the group of servers that are under the control of a private entity. This is not like the traditional cloud computing method where resources can be leased to third-party service providers.

The use of the term, on-premises refers to the local installation of these resources as against the cloud type where the resource is on the vendor's server and a client can reach the software via their internet browsers.

Hypertext Markup Language revision 5 (HTML5) is markup language for the structure and presentation of World Wide Web contents. HTML5 supports the traditional HTML and XHTML-style syntax and other new features in its markup, New APIs, XHTML and error handling.

The statement that servers that exist within a data center that is publicly accessible on the internet are referred to as on-premises servers is False.

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