-3x+y=2
-x+y-4=0
solving a system of linear equations by substitution

The coordinates of B' are (14, 19) when coordinate of B are (4, 15)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

Translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

Given that after translation the point A(-4,7) to the point A'(6,11)

(x,y)---->(x+10, y+4)

A(-4,7)---->(-4+10, 7+4)=A'(6, 11)

Now we need to find coordinates of B' when B is (4, 15)

(4,15)--->(4+10, 15+4)=(14, 19)

Hence, the coordinates of B' are (14, 19) when coordinate of B are (4, 15)

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We make distinct dot plots for every predictor variable.

x₂=6.3368+0.7604×x₄

x₂=6.67+0.04×x₆

x₂=7.718+0.04×x₁₂

Given that,

Refer to Appendix C.1's SENIC data collection. All additional variables in the data set, with the exception of medical school affiliation and area, are included in the list of potential predictor variables for length of stay (Y). It is anticipated that the best model will have logio Y as the response variable, first-order terms for the predictor variables, and no interaction terms. Take examples 57–113 into consideration as the model-building data set for the subsequent studies.

We have to make distinct dot plots for every predictor variable. Do these storylines have any significant elements.

We know that,

Average length of stay = x₂

Infection risk = x₄

X-ray ratio = x₆

Available Services = x₁₂

57–113 into consideration as the model-building data set for the subsequent studies.

By using, regression equation for x₂ as dependent variable and regression equation for x₄ as independent variable..

Then,

x₂=6.3368+0.7604×x₄

x₂=6.67+0.04×x₆

x₂=7.718+0.04×x₁₂

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Answer:

angle congruence just watch some videos about it explaining that

Answer:

4 cupcakes

Step-by-step explanation:

Answer:

4

cupcakes

Step-by-step explanation:

This is because it says the cupcakes are 3$ each. if you buy 7 items for 15$

3x4=12.

The interest rate required to accumulate a simple interest of $ 1,711.11 in 220 days is approximately 20%.

The simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for interest rate r.

I = P × r × t

$1711.11 = $14000  × r × 220/365yr

1711.11  = 616000/73 × r

r = 1711.11 ÷ 616000/73

r = 0.20227776

Rate R = r × 100%

Rate R = 0.20227776 × 100%

Rate R = 20%

Therefore, rate of the investment is 20%

Option A is the correct answer.

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Answer:

Step-by-step explanation:

You and a friend race each other. you give your friend a 50-foot head start. the distance y (in feet) your friend runs after x seconds is represented by the linear function y=14x+50 . the table shows the distances you run. time (seconds) x :  2, 4, 6, 8 distinct (feet) y :  38, 7...

Let A be a diagonalizable matrix. If c₁ and c₂ are solution to system

x⃗' (t) = A x⃗ ( t )

the possible values of c₁ is 1 and c₂ is 2 .

So, the correct option is option(a) and (e).

We have given that A is 2 × 2 diagonalizable matrix and x⃗ (t) = ( 3eᵗ + eᶜ₁t , 3e²ᵗ + eᶜ₂ᵗ) is a solution of system, x⃗ '(t) = A x⃗(ᵗ) .

A Solution of system always satisfied the equation of system.

Now, Differenating x⃗ (t) wih respect to t we get, x⃗' (t)=( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ)

So, ( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ)= A ( 3eᵗ + eᶜ₁t , 3e²ᵗ + eᶜ₂ᵗ) where A is diagonalizable and A = [a 0 0 b].

Then, ( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ) = ( 3aeᵗ + aeᶜ₁t , 3be²ᵗ + b eᶜ₂ᵗ)

equating the coefficients on both sides we get, 3eᵗ + c₁ eᶜ₁t = 3aeᵗ + aeᶜ₁t 6e²ᵗ + c₂ eᶜ₂ᵗ = 3be²ᵗ + b eᶜ₂ᵗ

after equating the corresponding equations , 3 = 3a and c₁ = a and 6 = 3b and c₂ = b after solving all we get a = 1 and b = 2 which implies c₁ = 1 and c₂ = 2. Hence, the possible values are c₁ = 1 and c₂ = 2.

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Complete question:

Let A be a diagonalizable matrix. If c₁ and c₂ are solution to system x⃗ (t) = A x⃗

then check all the possible values of c₁ and c₂ and below.

(a) c₁ = 1

(b) c₁ = 3

(c) c₁ = 2

d) c₂ = 1

(e)c₂ =2

(f) c₂ = 3

The option that is not true about the given radical function is; d. f'(x) exists for all x

We are given the function;

f(x) = 1 + x^(2/3)

a) All odd radical functions are continuous for all numbers, this is,  exists for every x ∈ ℝ. A set of real numbers.

b) From the graph attached, the function f(x) has an absolute minimum at x = 0.

c) f(x) increases for x > 0 and x < 0.

d)  First derivative does not exists for x = 0

e) The first and second derivatives of the function are f'(x) = ²/₃x^(-1/3) and  f"(x) = -²/₉x^(-4/3)

Thus, the first derivative f"(x) does not exist for x = 0

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Answer:

You can split the 36 into base 10 blocks and tell them 3 means three 10 blocks.

Using simple percentage rule, the answer is 25%,52% and 16.67%.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent symbol, %, or the abbreviation "pct" are frequently used to indicate percentages. The term "percent" derives from "percent," a shortened form of "per centum," which meaning per hundred.

The required formula is:

percentage (%) = Change/total * 100

Percentage Decrease = [tex]\frac {80-60}{80} * 100[/tex]

=25%

Percentage Decrease=[tex]\frac {500-240}{500} * 100[/tex]

=52%

Percentage Decrease = [tex]\frac {144-120}{144} * 100[/tex]

=16.67%

We calculated the percentage decrease using the above-mentioned formula.

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(a)let A=event that first k-1 draws will get r-1 red balls

let B=event that last (kth) draw will get rth red ball

P(kth draw is the rth red ball)= P(A AND B) = P(A)xP(B)

(b)P(A)=  # of  ways to draw r-1 red balls in k-1 trail

         # of ways to draw k-1 balls

RBBB *R is one way to achieve P(A AND B)

BBBR *R is another way.

(c)There are n−(r−1) red left, and a total of (m+n)−(k−1) balls left, so the (conditional) probability of drawing a red on the kth trial is n−r+1/m+n−k+1 Thus our required probability is

So,  P(A)= nC(r-1) x mC(n-r) x 1/(n+m)C(k-1)

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Answer:

somone in my class is literally a new York rat

Step-by-step explanation:

Exactly one-ninth of the original water is left after 8 pourings.

Given data,

Model the container's remaining contents as follows;

After the first pour, 1⁄2 is left, after the second, half * two-thirds, etc.

This is the final result. 1/2 * 2/3 * 3/4 * . . . . 8/9 * 9/10

Because the terms cancel out, 9/10 remains.

The numerators form an arithmetic sequence with a common difference of 1 and endpoints (1, 8), thus all that is left to do is count the terms or pour.

Therefore, 8 pourings do exactly one-ninth of the original water remain.

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Answer: .29

Step-by-step explanation:

Therefore, the equation having solution x=5 are option b) x+2=7 ,Option c) 3x=15 and Option e)x-5=0

equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics.

Here,

A.)20 - x = 5

B) x + 2 = 7

C) 3x = 15

D) 5x = 15

E) x- 5 = 0

So, the equation which has solution as x=5 are:

Option b) x+2=7

=>x+2=7

=>x=7-2

=>x=5

Option c) 3x=15

=> 3x=15

=> x=15/3

=> x=5

Option e)x-5=0

=>x-5=0

=>x=5

Therefore, the equation having solution x=5 are option b) x+2=7 ,Option c) 3x=15 and Option e)x-5=0

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The integer minus four to vector input integers:

# Python program to count positive and negative numbers in a List
# list of numbers
list1 = [10, -21, 4, -45, 66, -93, 1]
pos_count, neg_count = 0, 0
# iterating each number in list
for num in list1:
  # checking condition
  if num >= 0:
      pos_count += 1
  else:
      neg_count += 1
print("Positive numbers in the list: ", pos_count)
print("Negative numbers in the list: ", neg_count)

What is loop in python?

A for loop is used for iterating over a sequence (that is either a list, a tuple, a dictionary, a set, or a string). This is less like the for keyword in other programming languages, and works more like an iterator method as found in other object-orientated programming languages.
Using a for loop, count both positive and negative numbers from a specified list. Use a for loop to iterate each member in the list, then check to see if the positive number test is true by seeing if num >= 0.
Increase the positive count if the condition is true; else, increase the negative count.

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The difference between the normal low temperature and the record low temperature is 31°F.

The physical concept of temperature indicates in numerical form how hot or cold the weather is. A thermometer is used to determine temperature.

When the temperature is hot the measure of temparature will be in positive when the temperature is cold the measure of temparature will be negative.  

The formula for the difference between the normal low temperature and the record low temperature is given by

Here we have

The coldest temperature ever recorded in Mathville was - 16° F

This happened on January 30th, 1984. The normal low for that day is 15°F.

Here we need to find the difference between the normal low temperature and the record low temperature.

The formula for the difference is given by

Difference = (record low temperature) - (normal low temperature)  

From the given data,

Difference will be = - 16°F - (15°F) = -16°F - 15°F = - 31°F  

Therefore,

The difference between the normal low temperature and the record low temperature is 31°F.

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Check the picture below, so that's the triangle hmmmm a bit non-right-triangle or irregular per se, so let's use Heron's formula on this one, so we'll have to first find the length of each side

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ J(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill JK=\sqrt{(~~ 0- (-2)~~)^2 + (~~ 3- 1~~)^2} \\\\\\ ~\hfill JK=\sqrt{( 2)^2 + ( 2)^2} \implies JK=\sqrt{ 8 }[/tex]

[tex]K(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad L(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill KL=\sqrt{(~~ 3- 0~~)^2 + (~~ -4- 3~~)^2} \\\\\\ ~\hfill KL=\sqrt{( 3)^2 + ( -7)^2} \implies KL=\sqrt{ 58 } \\\\\\ L(\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\qquad J(\stackrel{x_2}{-2}~,~\stackrel{y_2}{1}) ~\hfill LJ=\sqrt{(~~ -2- 3~~)^2 + (~~ 1- (-4)~~)^2} \\\\\\ ~\hfill LJ=\sqrt{( -5)^2 + (5)^2} \implies LJ=\sqrt{ 50 }[/tex]

now let's use those three lengths for Heron's

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{8}\\ b=\sqrt{58}\\ c=\sqrt{50}\\ s=\frac{\sqrt{8}+\sqrt{58}+\sqrt{50}}{2}\\\\ \qquad \frac{\sqrt{58}+7\sqrt{2}}{2} \end{cases}[/tex]

[tex]A=\sqrt{\frac{\sqrt{58}+7\sqrt{2}}{2}\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{8} \right)\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{58} \right)\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{50} \right)} \\\\\\ ~\hfill {\Large \begin{array}{llll} A=10 \end{array}}~\hfill[/tex]

Answer:

C. 20

Step-by-step explanation:

60 = 2x + 20  ==> solve for x

60 - 20 = 2x + 20 - 20  ==> subtract 20 on both sides to isolate x

40 = 2x  ==> simplify

x = 40/2  ==> divide both sides by 2 to isolate x

x = 20 degrees

Answer: C. 20

Answer: 27.5 gallons in a full tank

Step-by-step explanation:

Let's call "x" the entire tank.

After adding 11 gallons, in the end, he has 2/5 tanks full

so the equations would be

11=2/5x

solve for x

x=55/2

x=27.5

27.5 gallons

Irrational numbers are all real numbers that are not rational numbers in mathematics. Irrational numbers, on the other hand, cannot be stated as the ratio of two integers.

Irrational numbers are all real numbers that are not rational numbers in mathematics. Irrational numbers, on the other hand, cannot be stated as the ratio of two integers. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.

The decimal part in 8.25635... is a nonrepeating nonterminating type number then it can not be written in the form of fractions like p/q.

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Answer:

Walnuts cost $3.25 a point and chocolate chips cost $1.50 a pound

Step-by-step explanation:

Let w =  the cost of walnuts per pound

Let c = the cost of chocolate chips per pound.

2w + 3c = 11

4w + 8c = 25

Multiply the first equation by -2 and then add it to the second equation

-4w - 6c + = -22

4w + 8c = 25

        2c = 3  Divide both sides by 2

          c = [tex]\frac{3}{2}[/tex] = $1.50

The chocolate chips cost $1.50 per pound

Substitute 1.50 for c into either the of the 2 original equations

2w +3(1.50) = 11

2w + 4.50 = 11  Subtract 4.50 from both sides

2w = 6.50  Divide both sides by 2

w = 3.25

The walnuts cost 3.25 per pound

Check

2w + 3c = 11

2(3.25) +3(1.50) = 11

6.50 + 4.50 = 11

11 = 11

4w + 8c = 25

4(3.25) + 8(1.50) = 25

13 + 12 = 25

25 = 25

The money he will have in this account if he keeps it for 5 years is $333, if the interest rate is compounded semiannually.

Compound interest is the term used to describe interest on savings that is calculated using both the initial principal and interest that has accrued over time. You can earn interest on interest, which is known as compound interest. Mathematically, if you have $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will have $110.25 by the conclusion of the second year.

Given,

P=$300

Time t=5 years

Interest rate=2.1%

Hence, the amount will have in his account is:

=[tex]P(1+(10/2000)^{2t}[/tex]

Here, the interest is compounded semiannually.

=[tex]300(1+(2.1/200))^{10}[/tex]

=$333

Therefore, the money he will have in this account if he keeps it for 5 years is $333, if the interest rate is compounded semiannually.

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Answer:

A. 336

B. 210

Step-by-step explanation:

To solve, we need to first multiply 126 by 2, which gives us 252. This is how many pages we had left after the first day. Then, since we read one-quarter on the first day, 252 is three-quarters, or 75% of the book. To find what number 252 is 75% of, we multiply both sides by 100 and divide by 75. This gives us 336, and the total amount. Next, we need to find how many pages we read on the first day. To do this, we find 25% of 336, which is 84. Then add 84 (how much we read on the first day) to 126 (how much we read on the second day), which gives us 210.

Answer:

(a) 336 pages

(b) 210 pages

=======================================================

Work Shown:

Part (a)

x = number of pages

x/4 = amount read on day 1

3x/4 = amount left to read after day 1 is over

(1/2)*(3x/4) = 3x/8 = amount read on day 2

(x/4) + (3x/8) = (2x/8)+(3x/8) = 5x/8 = amount read on days 1 and 2

x - (5x/8) = 8x/8 - (5x/8) = 3x/8 = amount left after day 2 is over

3x/8 = 126

3x = 8*126

3x = 1008

x = 1008/3

x = 336

There are 336 pages total

-------------------

Check:

336 pages total.

You read one-quarter of that on day one, so you read 336/4 = 84 pages on the first day.

There are 336-84 = 252 pages left (note that 3/4 * 336 = 252)

Then on day two, you read half of what's left, so you read 252/2 = 126 pages. The other half (126) is the last 126 pages mentioned for day 3, so the answer to part (a) is confirmed.

-------------------

There are at least three ways we can solve part (b)

Either way, 210 pages have been read by the end of the 2nd day.

with the correct sampling method, you expect to obtain a sample mean exactly the same as the population mean is false statement.

Sampling is an important tool used to collect data from a population. It is a process by which a subset of individuals from the population is selected to represent the population as a whole. Sampling allows researchers to collect data more quickly and efficiently than if data were collected from the entire population. It is also cost-effective and time-saving. However, it is important to note that no sampling method can guarantee that the sample mean will be exactly the same as the population mean. This is because of the random nature of sampling, which means that a sample mean could be slightly different from the population mean. Therefore, it is important to use appropriate sampling techniques and to be aware of the potential for sampling bias.

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The difference in the mean of the two major automobile manufactures is equal to option c. 2.0.

As given in the questions,

Number of samples selected for each manufactures = 8

For manufacturers A :

Mean of manufacturer A

=(Sum of all the eight data) / ( Number of data)

= ( 32+ 27 + 26 + 26 + 25 + 29 + 31 + 25 ) / 8

= 221 / 8

= 27.625

Mean of manufacturer B

=(Sum of all the eight data) / ( Number of data)

= ( 28 + 22 + 27 + 24 + 24 + 25 + 28 + 27 ) / 8

= 205 / 8

= 25.625

Difference in the mean of manufacturer A and B

= 27.625 - 25.625

= 2.0

Therefore, the difference in the mean of both manufacturer is given by Option C. 2.0.

The complete question is :

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.

Driver              Manufacturer A                 Manufacturer B

1                             32                                    28

2                            27                                    22

3                            26                                    27

4                            26                                    24

5                            25                                    24

6                            29                                    25

7                             31                                    28

8                             25                                   27

A) The mean for the differences is __________

a. 0.50               b. 1.5                 c. 2.0              d. 2.5

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Answer:

g(12) = -7

Step-by-step explanation:

g(x) = 3 - 5/6x

g(x) = 3 - 5x/6

g(12) = 3 - 5(12)/6  ==> plug in 12 for x

g(12) = 3 - 5*12/6

g(12) = 3 - 60/6 ==> simplify

g(12) = 3 - 10

g(12) = -7

Answer:

-7

Step-by-step explanation:

g(12) = 3 - [tex]\frac{5}{6}[/tex](12)

g(12) = 3 -10

g(x)  = -7

Answer:

P.E = mgh

For 10m cliff

Now,

P.E. = mgh

P.E. = 40 × 9.8 × 10

P.E = 3920 Joule

For 5m cliff

Now,

P.E. = mgh

P.E. = 40 × 9.8 × 5

P.E = 1960 Joule

Answer:4000 for the first one, for the second one it is 2000

Step-by-step explanation:

Mass=40kg

Height=10m

Gravity=10Nkg.(always taken)

Thus,

40×10×10

=4000

Mass=40kg

Height=5m

Gravity=10Nkg.(again, it is always taken)

Thus,

40 x 5 x 10

=2000

The value of n in the equation, 3n - 8 = 32 - n will be 10. The value is obtained by rearranging the equation and adding the like term.

the equation is :-

3n-8=32-n

take all the values of n one side-

3n+n = 32+8

4n = 40

n = 40/4

n = 10

so the value of the n in the equation is 10.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

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