24) Evaluate the expression with its given values.

x/4 + 3y; x = 12, y = 2

Answer:

-9

Step-by-step explanation:

[tex]f(-2)=2(-2)=-4 \\ \\ g(-2)=|-2-3|=5;\\ \\ (f-g)(2)=-4-5=-9[/tex]

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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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: To answer this question, we need to perform a hypothesis test. The null hypothesis is that the standard deviation of the process is 2 mg or less, and the alternative hypothesis is that the standard deviation of the process is over 2 mg.

To test this hypothesis, we need to calculate the test statistic, which is the z-score. The z-score tells us how many standard deviations a given data point is from the mean. In this case, the z-score is calculated by subtracting the mean of the sample from the hypothesized mean of the population, and dividing that difference by the standard deviation of the sample:

z = (20.2 - 20) / 2.4 = 0.1

Since the z-score is positive, we know that the mean of the sample is greater than the hypothesized mean of the population. However, we need to compare this z-score to the critical value to determine whether it is statistically significant.

The critical value is the z-score that marks the cutoff between the region of acceptance and the region of rejection of the null hypothesis. For a 1% level of significance, the critical value is the z-score that marks the 99th percentile of the normal distribution. Since the normal distribution is symmetrical, this means that the critical value is 2.58 standard deviations from the mean.

Since the z-score we calculated is less than the critical value, we cannot reject the null hypothesis. This means that we cannot assert that the standard deviation of the process is over 2 mg at a 1% level of significance.

Answer:

y(0.1) = 0.05, y(0.2) = 0.09

Modified Euler's method is a numerical method used to solve ordinary differential equations (ODEs). It is a variation of Euler's method that is more accurate than the original, but still relatively simple to implement. It works by taking a single iteration of the Euler method, then using the midpoint between the current and previous points to calculate the next point in the sequence. This is done in order to reduce the error.

Solution

We have, y(0) = 0

dy/dt = 1 – y

h = 0.1

Using modified Euler's method,

y(0.1) = y(0) + (1/2) h (f(t0, y0) + f(t0 + h, y0 + hf(t0, y0)))

= 0 + (1/2) (0.1) [(1 - 0) + (1 - 0 + 0.1)]

= 0.05

Similarly,

y(0.2) = 0.1 + (1/2) (0.1) [(1 - 0.05) + (1 - 0.1 + 0.1)]

= 0.0975

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The different possibilities

The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its position in the number, which might result in a number having two comparable digits with distinct values.

Given:

5.4  

Now, filling with different possibilities

Tens       Ones     Tenths     Hundredths

0                5               4                     0

0                5               3                    10

0                5               2                   20

0                 5              1                   30

0                 5              0                   40

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Answer:

Step-by-step explanation:

You want the solution to scalene triangle ABC with AC = 23, BC = 15, and ∠A = 40°.

When two sides of a triangle are given, along with an angle not between them, the Law of Sines can be used to solve the triangle. It tells you ...

  sin(B)/AC = sin(C)/AB = sin(A)/BC

When the given angle is opposite the shortest given side, there are generally 2 solutions.

  sin(B)/23 = sin(40°)/15 . . . . . fill in given values to find angle B

  B = arcsin(23/15·sin(40°)) = 80.3° or 99.7°

Angle C will have the value that makes up the difference from 180°:

  C = 180° -40° -{80.3°, 99.7°} = {59.7°, 40.3°}

The length of side AB can be found using the same Law of Sines proportion:

  AB = BC·sin(C)/sin(A) = 15/sin(40°)·sin({59.7°, 40.3°})

  AB = {20.2, 15.1}

The solutions are ...

Arguably, the second solution is not a "scalene" triangle. It is (nearly) isosceles. (See the comment below.)

__

Additional comment

Since answers are requested to be rounded to tenths, both solutions are scalene triangles. If we rounded to integers, then only the first solution would be a scalene triangle.

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)

Because the range is supplied as the difference between the side and the total of the sides given, option C, which is 9 cm<x<17 cm, is the right choice.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Here,

The range of possible lengths for the third side,

13-4<x<13+4

9<x<17

The correct option is C that is 9 cm < x < 17 cm because the range is given in difference between the side and sum of sides given.

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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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Answer:

y = [tex]\frac{3}{4}[/tex] x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and c the y- intercept )

given

- 3x + 4y = 4 ( add 3x to both sides )

4y = 3x + 4 ( divide through by 4 )

y = [tex]\frac{3}{4}[/tex] x + 1 ← in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{3}{4}[/tex] x + b ← is the partial equation of the parallel line

to find b substitute (4, 0 ) into the partial equation

0 = 3 + b ⇒ b = 0 - 3 = - 3

y = [tex]\frac{3}{4}[/tex] x - 3 ← equation of parallel line

The slope of line is -3,  the equation of line is y=-3x+2 and the graph is not proportional.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given graph let us take two points (0, 5) and (1,2).

m=2-5/1=-3.

Now let us find the y intercept.

2=-0+b

2=b

So the equation of line is y=-3x+2.

As the graph is not passing through the origin, then the graph is not proportional.

Hence, -3 is the slope of line and  y=-3x+2 is the equation of line and the graph is not proportional.

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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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We need to see how far the figure has moved in translation and directions and angles in rotational transformation.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

Given is a triangle ABC,

In translation transformation, the original image is congruent to the transformed one hence, we need to see  how far the shape has moved to the left or right and how many it has moved up or down.

In rotational transformation, the original figure is not necessarily congruent to the image hence, we need to see direction (clockwise CW or counterclockwise CCW) angle in degrees and Center point of rotation (turn about what point)

Hence, we need to see how far the figure has moved in translation and directions and angles in rotational transformation.

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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

The constant of proportionality of the given linear graph is; 3/5

The constant of proportionality is defined as the ratio of two proportional values that is said to be in a constant value.

Now, in this case where we have a graph, the constant of proportionality is equivalent to the slope of the graph.

The slope will be gotten using two coordinates (x₁, y₁) and (x₂, y₂) with the formula;

m = (y₂ - y₁)/(x₂ - x₁)

Let us use two coordinates on the graph (0.5, 0.3) and (1, 0.6)

m = (0.6 - 0.3)/(1 - 0.5)

m = 0.3/0.5

m = 3/5

This is same as the constant of proportionality.

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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]

Answer: 8√2

Step-by-step explanation:

The correct proportion used to prove that HJ || KL is [tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex].

What is the proportion theorem of two similar lines?

According to this theorem, if you draw a line parallel to one side of a triangle that divides the other sides into two separate points, the line will proportionally divide the other sides. In addition, a line is parallel to the third side if it divides any two triangle sides in the same ratio.

We have,

HJ || KL

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

And in the given triangle,  HJ is parallel to KL, So HJ divided the two sides in proportion, that is

[tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex]

The correct option is the fourth option.

So, The correct proportion could be used to prove that HJ || KL

[tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex]

Hence, the correct proportion used to prove that HJ || KL is [tex]\frac{GK}{HK} = \frac{GL}{LJ}[/tex].

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The exact coordinates of the terminal point (x,y) is = (-2.212185 , 2)  .

In the question ,

it is given that ,

the measure of the angle in the figure is = 2.4 radians ,

From graph ,

we can see that the y - coordinate is = 2 unit , So , y = 2 .

Now , for the x - coordinate ,

we draw a right triangle ABO ,

where the height is 2 units and hypotnuse is = 3 units (radius) ,

the angle 2.4 radian in degree is = 137.51° ,

So , from the trigonometric ratio ,

Cos(θ) = base/hypotnuse ,

Cos(137.51) = x/3 ,

x = 3*Cos(137.51)

x = 3*(-0.737395)

x = -2.212185

Therefore , the exact point (x,y) is = (-2.212185 , 2) .

The given question is incomplete , the complete question is

The angle below measures 2.4 radians, and the circle centered at the angle's vertex has a radius 3 units long. Determine the exact coordinates of the terminal point (x , y) .

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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:

(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 )

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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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

Answer:

The price of the Penthouse is $2.4 million

Down Payment is $2.1 Million

So the amount that must be financed is $2.4 million - $2.1 million = $0.3 million or $300,000

Step-by-step explanation:

Answer:

<A ≅ <X

<B ≅ <Y

Method

AAS Congruence Theorem

Step-by-step explanation:

Answer:

Not a triangle.

Criteria for it to be a triangle:

3 = A

6 = B

2 = C

A + B > C

B + C > A

A + C > B

What this says, is that if you add any two sides of the triangle, it needs to be bigger than the one you left out.

3 + 6 > 2 This one works

6 + 2 > 3 This one works

3 + 2 > 6 This one doesn't work because 5 is less than 6

Since the last one didn't work, it's not a triangle.

Answer: 110

Step-by-step explanation: If the drama class sold 20 more adult tickets than student tickets to the fall play, and adult tickets cost $8, then the number of adult tickets sold can be calculated by adding 20 to the number of student tickets sold and multiplying by $8. We can set up an equation to represent this relationship, where A represents the number of adult tickets sold and S represents the number of student tickets sold:

A = S + 20

A * 8 = $880

We know that the total amount collected from ticket sales was $880, and we know that adult tickets cost $8, so we can divide $880 by $8 to find the number of adult tickets sold:

A = $880 / $8

A = 110

Therefore, the drama class sold 110 adult tickets to the fall play.

Answer:

$275

Step-by-step explanation:

25600-2500=23100 how much is left to pay

7*12=84 months left till college

23100/84=275 he would have to save per month