Find the equation of the linear function represented by the table below in slope-intercept form.

The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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Answer:

72+20sqrt3

Step-by-step explanation:

check the attached file

The domain is set of all real numbers and the range is y ≥ -4

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

The equation is given as

g(x) = |x + 4|

The domain

The above equation is an absolute value equation

An absolute value equation can take any value as its input

This means that the domain is the set of all real numbers

When represented as an interval, we have

The domain is (-∝, ∝)

Also, we have

-∝ < x < ∝

Hence, the domain is the set of all real numbers

The range

Here, we have

g(x) = |x + 4|

The above equation is an absolute value function

An absolute value function represented as

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

Vertex = (-4, 0)

Remove the x value

y = -4

Because the leading coefficient is positive, then the vertex is a minimum

i.e.

[-4, ∝)

Another representation is

y ≥ -4

So, the range is y ≥ -4

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Answer:

b

Step-by-step explanation:

i know

The solution is Option B.

The translation of triangle MNP along T < 2 , -9 > is

M’(−1, −2), N’(2, −5), P’(4, −3)

What is Translation?

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

The notation for translation is T(h, k) where T is the translation, h is the change in the x-axis, and k is the change in the y-axis

Given data ,

Let the translated triangle be represented as ΔM'N'P'

Now , the translation rule is T < 2 , -9 >

Let the coordinates of the triangle ΔMNP be

The coordinates of M = M ( -3 , 7 )

The coordinates of N = N ( 0 , 4 )

The coordinates of P = P ( 2 , 6 )

Now , applying the translation rule of T < 2 , -9 > for the triangle MNP , we get

The coordinates of M' = M' ( -3 + 2 , 7 - 9 )

The coordinates of M' = M' ( -1 , -2 )

The coordinates of N' = N' ( 0 + 2 , 4 - 9 )

The coordinates of N' = N' ( 2 , -5 )

The coordinates of P' = P' ( 2 + 2 , 6 - 9 )

The coordinates of P' = P' ( 4 , -3 )

Hence , the coordinates of triangle M'N'P' is M’(−1, −2), N’(2, −5), P’(4, −3)

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The probability that a randomly chosen person from the united states can donate blood to maria is 0.50

considering blood to be of types A,B,AB and O

further all blood groups are equi probable

Probability of blood type A  = probability of blood type B = probability of blood type AB = probability of blood type O = x

Probability of blood type A  + probability of blood type B + probability of blood type AB + probability of blood type O = 1

⇒ 4x = 1

⇒ x = 1/4

Probability that a random person will have blood of type B or O = x+x

= 1/4 + 1/4

= 1/2

= 0.50

Hence we get the required answer.

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Answer:

Girls: 7 points each

Boys: 11 points each

Step-by-step explanation:

The value of x is 91/9.

What is the value of X triangle?

The two angles' combined angles are subtracted from 180 degrees. A triangle's total angles are always equal to 180 degrees. When you remove the total of the two angles from 180 degrees, note the difference you discovered. This is what X is worth. The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.

(9x+1)+ 88

Remove parentheses: (a)=a

9 x+1+88=180

Add the numbers: 1+88=89

9 x+89=180

Move 89 to the right side

9 x=91

Divide both sides by 9

[tex]\frac{9 x}{9}=\frac{91}{9}$$[/tex]

Simplify

[tex]x=\frac{91}{9}$$[/tex]

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Answer:

  x = 5

Step-by-step explanation:

You want the value of x where one of the base angles in an isosceles triangle is marked (9x+1)° and the vertex angle is marked 88°.

Each base angle of an isosceles triangle is the complement of half the vertex angle. This one is ...

  9x +1 = 90 -(88/2)

  9x = 45 . . . . . . . . . . subtract 1

  x = 5 . . . . . . . . . divide by 5

Answer:

The measure of arc FG is 148°

Step-by-step explanation:

Since the measure of an arc is equal to the measure of the central angle that subtends it, and the measure of central angle CG is 148°, the measure of arc FG is 148°. This is because the arc FG is subtended by the central angle CG.

Answer:

Step-by-step explanation:

Rocio ha gastado mas. El cubo de Jaime esta mas lleno.

Rocio gasto otro poco mas porque 3 esta mas grande que 2

Answer:

42

Step-by-step explanation:

150+102=252

252/6=42

The values of x is x = 6 Or x = - 4 when the expression - 3x² + 6x + 72 will be zero.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Here in the problem, we have to find the roots of the quadratic equation

- 3x² + 6x + 72 = 0.

3x² - 6x - 72 = 0.

x² - 2x - 24 = 0.

x² - 6x + 4x - 24 = 0.

x(x - 6) + 4(x - 6) = 0.

(x - 6)(x + 4) = 0.

x = 6 Or x = - 4 are the values of x when the expression will be zero.

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Number of years since 2003 x=5 years and number of jobs in thousand y=288.

In this method two equation are added or subtracted depending on the sign of variables. After adding or subtracting we create a new equation with one variable. Therefore, we easily get the solution.

while using addition method of algebra, we either add or subtract two equations to obtain a new equation by eliminating one variable. Hence, this method is called elimination method.

Given equation, 7.4x-y= -254

                         12.4x-y = -231

          using addition method

                -5x= -23

                  after solving x=4.6

            x= 5 (nearest whole number)

                     y = 288.04

                y =288

   hence, number of years 5

 number of jobs in thousand =288

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The complete table will be;

Minutes              15   30

Cages cleaned   2    4

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.

Now,

Since, The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes to clean 2 hamster cages.

Hence, By definition of proportion we get;

Let the time to clean 4 hamster cages = x

So, We get;

⇒ 15 / 2 = x / 4

⇒ 15×4 / 2 = x

⇒ 30 = x

⇒ x = 30

Thus, It take 30 minutes to clean the 4 hamster cages.

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The total cost of the rental if Dana drives the car for 15 miles is $90.2

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

C = 73.25 + 1.13m

Where

m = number of miles

This means that

m = 15

SO, we have the following equation

C = 73.25 + 1.13 * 15

Evaluate

C = 90.2

Hence, the total cost is $90.2

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"Dana and her family are going to Six Flags Great America the sum- mer after her Sophomore year. She is excited, because she will be doing all driving: After doing some complicated analysis, she calcu; lates that it will cost a certain amount per mile to pick up everyone and drive to the park, plus flat amount for everyone's admission tickets. The equation below models the total cost, €,and the variable m represents the number of miles driven: C = 73.25 + 1.13m

Answer: x = 6, y = 10; as a point, that would be (6, 10).

Step-by-step explanation:

To do it graphically, you would just graph the equations 25x + 15y = 300 and x + y = 16. Then, you would find the intersecting point.

To do this, you should convert to point-slope format.

15y = -25x + 300 and x + y = 16

1) y = -5/3x + 20 and 2) y = -x + 16

Now, for equation 1, you start at the y-intercept (0, 20) and for every increase of 1 on the x-axis, you decrease -5/3 on the y-axis. To graph this in the software, you click on the point (0, 20) and on another point on the line y = -5/3x + 20. (Any will do, but it should be an integer. (3, 15) works.)

Do the same for equation 2. Start at the y-intercept (0, 16) and decrease 1 for every increase of 1 on the x-axis.

Look for the point(s) where the lines intercept. It is (6, 10). If you have the time, you can verify this algebraically.

The polynomial expression are P(x) = (x - 1)(x + 1)[(x - 3)² + 1] and P(x) = x⁴ - 6x³ + 9x² + 6x - 10

Factored form

The given parameters are

There are complex numbers in the above zeros

This means that, the other zero is

Zeros = 3 + i

The equation of the polynomial is then calculated as

P(x) = Leading coefficient * (x - zero)^multiplicity

So, we have

P(x) = (x - 1) * (x + 1) * (x - (3 + i)) * (x - (3 - i))

This gives

P(x) = (x - 1) * (x + 1) * (x - 3 - i) * (x - 3 + i)

Evaluate the products

P(x) = (x - 1) * (x + 1) * [(x - 3)² - (i)²]

So, we have

P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]

P(x) = (x - 1)(x + 1)[(x - 3)² + 1]

The standard form

In (a), we have

P(x) = (x - 1) * (x + 1) * [(x - 3)² + 1]

Expand

P(x) = (x² - 1) * (x² - 6x + 9 + 1)

So, we have

P(x) = (x² - 1) * (x² - 6x + 10)

Remove the brackets

P(x) = x⁴ - 6x³ + 10x² - x² + 6x - 10

Evaluate the like terms

P(x) = x⁴ - 6x³ + 9x² + 6x - 10

Hence, the equation is P(x) = x⁴ - 6x³ + 9x² + 6x - 10

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Answer:

1155.52cm²

Step-by-step explanation:

A cylinder's volume is π r² h, and its surface area is 2π r h + 2πr²

radius(r) = 8cm

π = 3.14

height(h) = 15

2πrh + 2πr²

=2πr(h + r)

= 2 × 3.14 × 8 ( 15 + 8)

= 50.24(23)

= 1155.52cm²

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An increasing exponential function is modeled as follows:

A(t) = A(0)(1 + r)^t.

The parameters of the exponential function are given as follows:

She borrows 12,000 at 12% annual percentage rate, hence the initial value and the growth rate are given as follows:

A(0) = 12,000, r = 0.12.

Then the function that describes her loan is given as follows:

A(t) = 12000(1.12)^t.

After six years, the value of the loan is calculated as follows:

A(6) = 12000(1.12)^6 = $23,686.

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Answer:

Step-by-step explanation:

Sorry if this is different, but based on what I read, here is the answer.

100 x 0.85 = 85

therefor it is 85%, which is significantly more than 80%

The price of the chair in the furniture store is $94.

Given that the wholesale price for a chair is $169 and that a certain furniture store marks up the wholesale price by 16%.

The price of the chair in the furniture store will be:

= $169 + (16% × $169)

= $169 + $27.04

= $196

The price is $194.

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Answer:

D

Step-by-step explanation:

base area = (6 · 4)/2 = 24/2 = 12 cm²

half base length = 6 : 2 = 3 cm

leg = [tex]\sqrt{3^2+4^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex] cm

perimeter = (5·2) + 6 = 10 + 6 = 16 cm

lateral area = 16 · 20 = 320 cm²

surface area = (2 · 12) + 320 = 24 + 320 = 344 cm²

Bob lifts a 15N rock through a distance of 1.7m, 25.5 J work does Bob do

An item should be converted to energy before being moved. The use of force is one way to transfer energy. The amount of energy used by a force to move an item is referred to as the work done.

The amount of the displacement and the component of the applied force of the object in the displacement direction is the work done by a force. Pushing a block with force "F" causes the body to move more quickly, meaning that work has been completed.

Work done (W) = F × s

Where, F = force

s = displacement

Now putting the values, we get-

or, W = 15 N × 1.7 m

or, W = 25.5 N-m or Joule

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Answer:

Step-by-step explanation:

You want equations of lines parallel and perpendicular to y = 2x -1 through the point (-7, 2).

The given equation is written in slope-intercept form:

  y = mx + b

where m = 2, and b = -1.

The slope of the line is m, the x-coefficient. For the given line, the slope is 2.

A parallel line will have the same slope: 2.

A perpendicular line will have the opposite reciprocal slope: -1/2.

When you have a point and slope, it is useful to use the point-slope form of the equation for a line:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

For both of the desired lines, the point is (h, k) = (-7, 2). Using this point and the above slopes, we have ...

Answer:

Fraction: 4 1/4 = 17/4

Decimal: 17/4 = 4.25

Step-by-step explanation:

The given linear equation (1/3)x+ y=2 in the slope-intercept form is

y=(-1/3)x+2.

Where m is the slope and b is the y-intercept, the slope-intercept form is represented as y = mx+ b. By utilizing y=mx+ b, a line is typically simple to graph. The point-slope form and standard form of linear equations are further types. Example 1: A line with a slope of 1/2 and a y-axis crossing at (0, -3). Calculate the line's equation. It is y = x/2 - 3 that determines the line's equation. Example 2: Determine the equation utilizing the y-y-intercept axis's and the horizontal line's slope intercept formula (0, 8).

Finding the slope between two points on a line and then solving for the y-intercept in the slope-intercept equation y=mx+ b allow us to build an equation for that line.

Given linear equation is:

(1/3)x+ y=2

The following is the slope-intercept form of the given linear equation:

y=(-1/3)x+2

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The equation of each of the lines are:

1. y = 1/3x - 1

2. y = 3x + 1

3. y = 2/3x - 1

4. y = 3x

5. y = -2/3x - 1

6. y = 1/3x - 1

7. y = -3x + 2

To write the equation of a line, find the following:

1. Slope (m) = rise/run = 1/3

y-intercept (b) = -1.

To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:

y = 1/3x - 1

2. Slope (m) = rise/run = 3/1 = 3

y-intercept (b) = 1.

To write the equation, substitute m = 3 and b = 1 into y = mx + b:

y = 3x + 1

3. Slope (m) = rise/run = 2/3

y-intercept (b) = -1.

To write the equation, substitute m = 2/3 and b = -1 into y = mx + b:

y = 2/3x - 1

4. Slope (m) = rise/run = 3/1 = 3

y-intercept (b) = 0.

To write the equation, substitute m = 3 and b = 0 into y = mx + b:

y = 3x

5. Slope (m) = rise/run = -2/3

y-intercept (b) = -1.

To write the equation, substitute m = -2/3 and b = -1 into y = mx + b:

y = -2/3x - 1

6. Slope (m) = rise/run = 1/3

y-intercept (b) = -1.

To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:

y = 1/3x - 1

7. Slope (m) = rise/run = -3/1 = -3.

y-intercept (b) = 2.

To write the equation, substitute m = -3 and b = 2 into y = mx + b:

y = -3x + 2

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Answer:

Bellow

Step-by-step explanation:

QS =√c2 - b2

= √202 - 15.0941916044552

= √172.16537980799

= 13.12118

Store B offers better $0.85 per-roll price than store A.

One type of operation is division in mathematics. The phrases or numbers are divided into the same number of components during this operation.

Given, two stores sell identical sandwich rolls in different size packages.

Store A sells a six-pack for $5.28.

To find the unit price,

we take division of 5.28 with number 6.

The unit price of sandwich roll for store A,

= 5.28 / 6

= $0.88

To find the unit price of sandwich roll for store B,

we take division of 3.40 with number 4.

= 3.40 / 4

= $0.85

And $0.85 < $0.88.

Therefore, Store B offers better per-roll price.

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No. Tom is not correct.

If the money were split equally everyone would've gotten £200.

But, if everyone went by the mentioned distribution, then,

Rachel would get = 2/5 x 600 = £280

Remainder money = 600 - 280 = £320

Samina would get = 1/4 x 320 = £80

Tom would get the remaining money = 600 - (280 + 80)

                                                              = 600 - 360

                                                              =  £240      

Since, £240 > £200, Tom would be incorrect in saying he would have had more money if he had split the money equally.

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