Match the following terms

The name starts with letter g as the variable has highest value.

What is variable?

A variable is associate degree alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables square measure specially utilized in the case of algebraical expression or pure mathematics.

Main body:

according to question:

7j = 105

simplifying the value , we get

j = 105/7

j = 15

similarly

g - 16 = 2

simplifying the value , we get

g = 18

value of g is greater than j .

Hence the name starts with letter g.

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Answer:

q = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the roots can be found using the discriminant

Δ = b² - 4ac

• if b² - 4ac > 0 then roots are real and irrational

• if b² - 4ac = 0 then the roots are real and equal

• if b² - 4ac < 0 then the roots are not real

qx² - 6x + 18 = 0 ← is in standard form

with a = q , b = - 5 , c = 18

for one repeated (equal) real root , then

b² - 4ac = 0 ( substitute values )

(- 6)² - (4 × q × 18) = 0

36 - 72q = 0 ( subtract 36 from both sides )

- 72q = - 36 ( divide both sides by - 72 )

q = [tex]\frac{-36}{-72}[/tex] = [tex]\frac{1}{2}[/tex]

The equation of the line that has a slope of 5 and y-intercept of 9 will be y = 5x + 9.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is 5. Then the equation is given as,

y = 5x + c

The y-intercept of the line is 9. Then the equation of the line is given as,

y = 5x + 9

The equation of the line that has a slope of 5 and y-intercept of 9 will be y = 5x + 9.

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The probability that a row in the test set belongs to a Stanford student is 0.4167.

Given that,

Thomas has come up with a plan for dividing the training and test set. From the coordinates, for each row:

Students from Stanford have a 50% chance of being assigned to the test set and a 50% chance of being assigned to the train set for their rows.

20% of Berkeley students' rows are assigned to the test set, while 80% are assigned to the train set.

We have to find what is the probability that a row in the test set belongs to a Stanford student.

We know that,

Let us define events are as

B: Student in the coordinate is Berkeley student

S: Student in the coordinate is Stanford student

Tr: Rows is in the  train set

Ts: Rows is in the  test set  

Since there are 77 Berkeley student  and 23  Stanford student  in coordinate

Hence,

P(B) = Probability that Student in the coordinate is Berkeley student

= 77/(77+23) = 77/100 = 0.77

P(S) = Probability that Student in the coordinate is Stanford student  =23/(77+23) = 23/100 = 0.23

Conditional probability,

P(Ts|B) = Probability that Student placed in  the  test set   when the student is Berkeley student   = P(Ts|B) = 0.20

P(Ts|S) = Probability that Student placed in  the  test set   when the student is Stanford student   = P(Ts|S) = 0.5

Required probability,

Given that  a row is in the test se, Probability that it corresponds to a Stanford student  =

Probability of Stanford students = P(S|Ts) =

By Bayes theorem,

P(S|Ts) = P(Ts|S)×P(S)/P(Ts|S)×P(S)+P(Ts|B)×P(B)

P(S|Ts) = 0.22×0.5/0.22×0.5+0.20×0.77

P(S|Ts) = 0.4167

Therefore, The probability that a row in the test set belongs to a Stanford student is 0.4167.

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Answer: 10

Step-by-step explanation:

x + 30/7-22/7-59/7 = 19/7

Add 59/7 to both sides:

x + 30/7-22/7 = 19/7 + 59/7

Add 22/7 to both sides

x + 30/7 = 19/7 + 59/7 + 22/7

Subtract 30/7 from both sides

x = 19/7+59/7+22/7-30/7

Simplify

x = 10

The total number of feet that the plumber's helper should order for drain pipes is 19 feet.

The plumber's helper has been given the list of places in the house that will need a drain pipe. The total number of feet of pipes that he should buy should therefore be the total number of pipes that each of these places in the house need.

The number of feet of pipes is therefore:

= Kitchen sink + Bath tub + Lavatory + Laundry tub + Second lavatory

= 5  + 4 + 3 + 5 + 2

= 19 feet

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By using the concept of function, it can be calculated that-

a) [tex]\frac{g}{h}(-3) = -\frac{31}{17}[/tex]

b) The point [tex]\frac{5}{4}[/tex] is not in the domain of [tex]\frac{g}{h}[/tex]

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here,

a) The given functions are

   g(x) = 5 - 4x²

  h(x) = 5 - 4x

   [tex]\frac{g}{h}(x) = \frac{g(x)}{h(x)} = \frac{5-4x^2}{5-4x}[/tex]

   [tex]\frac{g}{h}(-3) = \frac{g(-3)}{h(-3)} = \frac{5 - 4(-3)^2}{5 - 4(-3)} = -\frac{31}{17}[/tex]

b)  [tex]\frac{g}{h}(x)[/tex] is not defined if 5 - 4x = 0

     [tex]\frac{g}{h}(x)[/tex] is not defined if  [tex]x = \frac{5}{4}[/tex]

      So the point [tex]\frac{5}{4}[/tex] is not in the domain of [tex]\frac{g}{h}[/tex].

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The following expression (-3/5)x-7-(-12)+(3/10)x can be written in the simplest form as -3/10x+5( three over 10 times x plus 5). So, option c is correct.

An expression or mathematical expression is a finite arrangement of symbols that are well-formed in line with context-dependent criteria. To help define the logical grammar and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping. A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Mathematicians have the ability to multiply, divide, add, and subtract. The following is the structure of an expression: Expression, number/variable, and mathematical operator.

(-3/5)x-7-(-12)+(3/10)x

-3/5x-7+12+3/10x

-6/10x-7+12+3/10x

-3/10x+5

Three over 10 times x plus 5

Therefore, the following expression (-3/5)x-7-(-12)+(3/10)x can be written in the simplest form as -3/10x+5( three over 10 times x plus 5).

Hence, option c is correct.

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Calculate how much you would have in 20 years if you saved $3,000 a year at an annual rate of 8 percent with the company contributing $750 a year. Use Exhibit 1-B. (Round time value factor to 3 decimal places and answer to the nearest whole dollar.)

69/100 you would save since it decreased in value

Answer:

y-intercept | -10

slope | 1

Step-by-step explanation:

plane curve | Cartesian equation -x + y = -10 | y-intercept

slope

y-intercept | -10

slope | 1

In multiple regression problem with two independent variables, value of one varible , b₁ is 2 then it means that the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, holding X₂ constant. So, second option is correct option.

Multiple Regression: Multiple regression is a statistical technique that can be used to analyze the relationship between a single dependent variable and multiple independent variables. The goal of multiple regression analysis is to use independent variables with known values to predict the value of each dependent value.

Y = b₁x₁+ b₂x₂ + … bₙxₙ + a

Here Y is the dependent variable, and X₁,…,Xₙ are the n independent variables. In calculating the weights, a, b₁,…,bₙ,

In the multiple regression b1 shows the coeffcient of independent variable X₁ in fitted model.

Here b₁ =+2.0 shows that for each unit increase in X₁, dependent variable Y is increased by 2 keeping other things constant.

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The value of x = 7 (blue)

The value of x = 6 (yellow)

The value of x = 4 (marron)

The value of x = 20 (black)

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

1,

The two angles are equal.

The sides opposite to the angles are also equal.

x = 7 (blue)

2.

The given triangle is an equilateral triangle.

All angles are equal.

The sides opposite to the angles are also equal.

x = 6 (yellow)

3.

Alternate angles are equal.

The sides opposite to the alternate angles are also equal.

x = 4 (marron)

4.

The given triangle is an isosceles triangle.

Two sides are equal.

One angle is 40.

The sum of the angles is 180.

x + x + 40 = 180

2x + 40 = 180

2x = 140

x = 20 (black)

Thus,

x = 7 (blue)

x = 6 (yellow)

x = 4 (marron)

x = 20 (black)

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The side lengths of the triangle are 11.1, 21.4, and 18.5 units.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

The given sides of the right triangle are 3m, 2m+14, and 5m.

As per the Pythagorean theorem, it follows:

(2m + 14)² = (3m)² + (5m)²

4m² + 196 + 56m = 9m² + 25m²

30m² -56m - 196 = 0

15m² - 28m - 98 = 0

[tex]m=\frac{-(-28)\pm\sqrt{(-28)^2-4(15)(-98)}}{2(15)}\\\\m=\frac{28\pm\sqrt{6664}}{2(15)}\\\\m =\frac{28\pm81.6}{2(15)}\\\\m=3.7\text{ or } m=-1.8[/tex]

Since the lengths cannot be negative, the value of m is m = 3.7.

Therefore, the side lengths of the triangle are:

3m = 3(3.7)

= 11.1

2m + 14

= 2(3.7) + 14

= 21.4

and,

5m

=5(3.7)

= 18.5

Hence, the side lengths of the triangle are 11.1, 21.4, and 18.5 units.

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Answer: 8√2

Step-by-step explanation:

The number of days in June is 30

The number of days in July = 31

The number of days in August = 31

The maturity date for a loan taken out on June 6 for 73 days is August 28.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The date on which the loan was taken = June 6.

The number of days for the loan to mature = 73 days.

Now,

The number of days in June is 30

The number of days in July = 31

The number of days in August = 31

Now,

There are (30 - 6) = 24 days remaining in the month of June.

So,

24 + 31(July) = 45 days.

Now,

73 - 45 = 28 days need to be taken from August.

So,

45(July) + 28(August) = 73 days.

This means,

The maturity date is August 28.

Thus,

The maturity date for a loan taken out on June 6 for 73 days is August 28.

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According to exponential equation 52 g sample will be left in the sample after 25 years

What is exponential equation?

The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable

Main Body:

Given =

A(t}=200 e^{-0.054t}

A)

t = 25 years

A(25}=200 e^{-0.054*25}

A(25}=200 e^{-1.35}

A(25}=200 *0.26

A(25}= 52 g

B) A = 100

A(t}=200 e^{-0.054t}

100 =200 e^{-0.054t}

e^{-0.054t} = 1/2

taking logarithm on both sides , we get

t = 12.83 years

Hence the value for each parts are as follows.

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Answer:

4x  +  1   -  2/x  +  6/(20x³ - 15x² -15x+16)

Step-by-step explanation:

                4x  +  1   -  2/x  +  6/(20x³ - 15x² -15x+16)

             ________________

5x ²-5x | 20x³ - 15x² -15x+16

1            -(20x³ - 20x²)                      ==> -15x²-(-20x²)= -15x²+20x² = 5x²

                         5x² - 15x

2                       -(5x² - 5x)                 ==> -15x-(-5x)= -15x+5x = -10x

                                 -10x+16

3                                -(10x+10)

                                           6           ==> 16-10 = 6           

1: At step 1, (4x) * (5x²-5x) = (20x³ - 20x²)

2: At step 2, 1 * (5x² - 5x) = 5x² - 5x

3: At step 3, (2/x) * (5x² - 5x) = 10x+10

The number of half gallons that that store bought with the amount of profit they made would be = 41 half gallons.

A refrigerated milk is the milk that is preserved in a refrigerator to prevent spoilage and prolong the shelf life of the milk.

A refrigerator is an electrical electronic device that is used for the preservation and storage of food and food products such as milk.

The amount that half gallon of milk was bought = $2.30 per half gallon.

The amount of half gallons of milk that was ruined= 14

The remaining milk was sold at = $3.90 per half gallon.

The profit made by the store = $105.40

The amount of half gallons that was bought,

= 105.40/3.90

= 27 + 14 ruined half gallon= 41 half gallons.

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The missing value of the distance is 8.4 feet

The relationship between two values when their ratio equals a constant number is known as a direct proportion or direct variation.  

If a and b are in direct proportion then the relation can be represented as

=>  a = kb  [ where k is constant ]

Here we have

Distance    6 feet   -     -

Time          15 sec   -    21 sec  

As we know,  

Distance will be directly proportional to Time

=> Distance ∝ Time

=> Distance = K (Time)  

=> Distance/Time = k  

Where  k is the proportionality constant

By the above calculations

If Distance and Time are directly proportional then Distance/Time must be a constant

Now use the above condition to get the missing value

At a distance of 6 feet and a time of 15 sec

=> Distance/Time = 6/15

Let the missing value is x, and the time is 21 sec

=>  Distance/Time = x/21  

As we Distance/time will be constant

=>  6/15 = x/21

=>  6(21) = x(15)

=>  x = 126/15

=>  x = 8.4

Therefore,

The missing value of the distance is 8.4 feet

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Answer:

[tex]x[/tex] is greater than 1.8

Step-by-step explanation:

Adding 1.4 to both sides of the equation yields [tex]x=3.2>1.8[/tex].

The required reasoning for the given expression is that x is greater than 1.8. Option B is correct.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial expression.

here,
Given expression,
x  - 1.4 = 1.8

The above expression refers that, when we subtract 1.4 from x it gives 1.8, which implies that x is a number greater than 1.8.
So the reasoning can be complied as x is greater than 1.8.

Thus, the required reasoning for the given expression is that x is greater than 1.8. Option B is correct.

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The minimum grade require to get grade of B is 78.6.

In the given that;

μ = 65 (average grade)

σ = 20 (standard deviation)

X ≈ N(μ, σ^{2})

Let c be the minimum grade to required to get grade of B

Percentage of data below c = 10% + 15% + 50% =75%

If we convert the percentage to probability = 75%/100% = 0.75

Now to get the value of c we solve the equation

P(X < c) = 0.75

⇒P{(X-μ)/σ < (c-μ)/σ)=0.75

Here z = (X-μ)/σ follows normal (0,1)

z is the standard normal variable

⇒P(z<(c-μ)/σ)=0.75

⇒P(z< (c-65)/20)=0.75

From z table we get, (c-65)/20 = 0.68

⇒(c-65)/20 = 0.68

⇒c= 78.6

So, minimum grade require to get grade of B is 78.6.

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The right question is given below:

To view the circle graph (pie chart) of the chungs' budget check the attached file.

What is pie chart?

A pie chart is a graphical representation technique that displays data in a circular-shaped graph.

Pie charts are often used to represent sample data with data points belonging to a combination of different categories.

Chung's budget in percentage:

Charity = 30/2145 x 100%

            = 1.39%

            = 1.4%

Clothes = 185/2145 x 100%  

             = 8.62%

Entertainment = 178/2145 x 100%

                        = 8.29%

Food = 424/2145 x 100%

         = 19.76%

Rent = 1050/2145 x 100%

        = 48.95%

Transportation = 213/2145 x 100%        

                 = 9.93%

Others = 65/2145 x 100%

           = 3.03%

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Answer:

(1.5, - 2.5 )

Step-by-step explanation:

7x + 2y = 5.5 → (1)

3x - 5y = 17 → (2)

multiplying (1) by 5 and (2) by 2 and adding will eliminate y

35x + 10y = 27.5 → (3)

6x - 10y = 34 → (4)

add (3) and (4) term by term to eliminate y

41x + 0 = 61.5

41x = 61.5 ( divide both sides by 41 )

x = 1.5

substitute x = 1.5 into either of the 2 equations and solve for y

substituting into (1)

7(1.5) + 2y = 5.5

10.5 + 2y = 5.5 ( subtract 10.5 from both sides )

2y = - 5 ( divide both sides by 2 )

y = - 2.5

solution is (1.5, - 2.5 )

Answer:  Better Deals:  for tomatoes--Farmer's Mkt.,  for cheese--Grocery, for eggs--Grocery

Step-by-step explanation:

Unit prices:

tomatoes:  $14/8 = $1.75/tomato (grocery);  $16.50/10 = $1.65 (farmers)

cheese:  $4.40/4 = $1.10/cup (grocery);  $3.45/3 = $1.15 (farmers)

eggs: $2.40/12 = $0.20/egg (grocery);  $1.75/7 = $0.25/egg (farmers)

The perimeter of the parallelogram is 24 units

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

The parallelogram is added as an attachment

When the number of units on each side of the parallelogram is counted, we have the following representation

EH = FG = 7 units

EF = GH = 5 units

The perimeter of the parallelogram is the sum of the side lengths

So, we have the following representation

Perimeter = EH + EF + FG + GH

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

Perimeter = 7 + 7 + 5 + 5

Evaluate the sum

Perimeter = 24

Hence, the perimeter is 24 units

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Using the Green's Theorem, the one along which the work done by the force is 11π/16.

In the given question we have to find the one along which the work done by the force is the greatest.

The given closed curves in the plane is

[tex]F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}[/tex]

Suppose C be a simple smooth closed curve in the plane. It is also oriented counterclockwise.

Let S be the interior of C.

Let P = [tex]\frac{x^{2}y}{4} + \frac{y^3}{3}[/tex] and Q = x

So the partial differentiation is

[tex]\frac{\partial P}{\partial y}=\frac{x^2}{4}+y^2[/tex] and  [tex]\frac{\partial Q}{\partial x}[/tex] = 1

By the Green's Theorem, work done by F is given as

W= [tex]\oint \vec{F}d\vec{r}[/tex]

W= [tex]\iint_{S}\left ( \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right )dxdy[/tex]

W= [tex]\iint_{S}\left ( 1-\frac{x^2}{y}-y^2 \right )dxdy[/tex]

Let C = x^2+y^2 = 1 and

x = rcosθ, y = rsinθ

0≤r≤1; 0≤θ≤2π

There;

W = [tex]\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )\left|\frac{\partial(x,y)}{\partial{r,\theta}}\right|d\theta dr[/tex]

and [tex]\frac{\partial (x,y)}{\partial(r, \theta)}=\left|\begin{matrix}\cos\theta &-r\sin\theta \\ \sin\theta & r\cos\theta\end{matrix} \right |[/tex] = r

Thus;

W = [tex]\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )rd\theta dr[/tex]

After solving

W = 11π/16

Hence, the one along which the work done by the force is 11π/16.

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The right question is:

Among all simple smooth closed curves in the plane, oriented counterclockwise, find the one along which the work done by the force:

[tex]F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}[/tex]

is the greatest. (Hint: First, use Green’s theorem to obtain an area integral—you will get partial credit if you only manage to complete this step.)

Answer: m = 3.1

Step-by-step explanation:

To solve for m you must divide 2.6m by 2.6m. Therefore, you must do the same on the other side of the equation.

2.6m/2.6m = 8.06/2.6m

m= 3.1

[tex]m=3.1.[/tex]

[tex]2.6m = 8.06[/tex]

[tex]\frac{2.6}{2.6} m=\frac{8.06}{2.6}\\ \\(1)m=\frac{8.06}{2.6}\\ \\m=\frac{8.06}{2.6}[/tex]

[tex]m=\frac{8.06}{2.6}\\ \\m=3.1[/tex]

[tex]2.6(3.1) = 8.06\\8.06=8.06[/tex]

That's correct!

[tex]m=3.1.[/tex]

Answer:

10?

__________________

Hope this helps? C: