Write an equation and solve. Round to the nearest hundredth where necessary. What is 35% of 63?

The standard form of the given equation f(x) = 6x² − x + 1 is:

\(f(x)=6\left(x-\frac{1}{12}\right)^2-\frac{23}{24}\)

So, f(x) = 6x² − x + 1:

We must convert this to standard form, which is provided by:

Where x² is the co-efficient of the leading term and (h, k) is the curve's vertex (minimum and maximum point).

The formula h = -b/2a can be used to calculate h.

We can find k by determining f(h), as k=f (h).

\(\begin{aligned}&k=f\left(\frac{1}{12}\right)=6\left(\frac{1}{12}\right)^2-\frac{1}{12}+1 \\&k=\left(6 \times \frac{1}{141}\right)-\frac{1}{12}+1 \\&k=\frac{1}{24}-\frac{1}{12}+1 \\&k=\frac{1-2+24}{24}=\frac{23}{24}\end{aligned}\)

Therefore, the standard form of the given equation f(x) = 6x² − x + 1 is:

\(f(x)=6\left(x-\frac{1}{12}\right)^2-\frac{23}{24}\)

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The correct question is given below:

Write the quadratic function in standard form.

f(x) = 6x² − x + 1

Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

Answer:

19

Step-by-step explanation:

The probability that a customer ordered a cold drink given that he or she ordered a large is 32%.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

P(Small | Cold) = n(Small and Cold)/n(Cold)

From the table:

P(Small | Cold) = 8/(8 + 12 + 5)

P(Small | Cold) = 0.32

or

P(Small | Cold) = 32%

Thus, the probability that a customer ordered a cold drink given that he or she ordered a large is 32%.

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Answer:

Step-by-step explanation:

If the shape is a parallelogram, that means the two parallel sides are equal in length so, we get the equation:

\(3x-4 =65\\y-4 = 91\\\)

After solving for x and y, we get that

x = 23 and y = 95

Hope that helps!

Opposite sides of ap parallelogram are parallel and equal

And

Answer:

answer A is correct because the formula of equation in point slope is

y-y1=m(x-x1)

where,(x1,y1)point is given that is (6,-2)

slope=m=3

equation in point-slope form of the line that passes through the point (6, −2) and has a slope of 3 is  y + 2 = 3(x − 6)

statement of equality between two expressions consisting of variables and/or numbers.

As, equation line is:

y-y1=m(x-x1)

We have,

coordinates (6, −2) and slope=3

So,

y+2=3(x-6)

y+2=3x-18

y-3x= -20

Hence,  equation in point-slope form of the line that passes through the point (6, −2) and has a slope of 3 is y+2=3(x-6).

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

a, 10% of 300 = 30 b, 300 - 30 = 270

Step-by-step explanation:

1. 300 x 10 = 3,000

2. Move decimal place 2 to the left = 30.00

3.  Subtract 30 from 300 which is 270

The equations of each line are:

a. y = -3x + 3

b. y = -2/3x - 3

In slope-intercept form, the equation of a line is written as, y = mx + b, given that:

Note: the slope values of parallel lines are the same.

a. The slope of y = -3x - 1 is, -3. The line that is parallel to it will have the same slope (m) of -3.

Substitute m = -3 and (x, y) = (2, -3) into y = mx + b to find b:

-3 = -3(2) + b

-3 = -6 + b

-3 + 6 = b

3 = b

b = 3

Substitute b = 3 and m = -3 into y = mx + b

y = -3x + 3

b. Rewrite 2x + 3y = 6 in the slope-intercept form

3y = -2x + 6

y = -2/3y + 2

The slope of y = -2/3y + 2 is, -2/3. The line that is parallel to it will have the same slope (m) of -2/3.

Substitute m = -2/3 and (x, y) = (0, 5) into y = mx + b to find b:

5 = -2/3(0) + b

-3 = 0 + b

-3 = b

b = -3

Substitute b = -3 and m = -2/3 into y = mx + b

y = -2/3x - 3

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The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Answer:

see explanation

Step-by-step explanation:

(a)

given y varies directly with T and  inversely with x² , then the equation relating them is

y = \(\frac{kT}{x^2}\) ← k is the constant of variation

to find k use the condition y = 5 when T = 2 and x = 4

5 = \(\frac{2T}{4^2}\) = \(\frac{2k}{16}\) ( multiply both sides by 16 )

80 = 2k ( divide both sides by 2 )

40 = k

y = \(\frac{40T}{x^2}\) ← equation of variation

(b)

when T = 3 and x = 4 , then

y = \(\frac{40(3)}{4^2}\) = \(\frac{120}{16}\) = 7.5

The electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.

In the analogy of a circuit with resistance, we can compare it to an obstacle race. Here's how we can relate the different elements:

Circuit: The entire obstacle race course represents the circuit itself. It includes all the components and paths that the participants will go through.

Obstacles: The obstacles in the race represent the resistors in the circuit. Just like resistors impede the flow of electrical current in a circuit, obstacles in the race impede the progress of the participants.

People/Participants: The people participating in the race represent the flow of electric current in the circuit. They are the "charge" moving through the circuit, encountering and overcoming obstacles (resistors) to reach the finish line.

The goal of the participants (people) is to navigate through the obstacles (resistors) and complete the race (circuit) by reaching the finish line.

Similarly, in an electrical circuit, the goal is for the electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.

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There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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The remainder theorem indicates that remainder when the polynomial x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) is 8

The remainder theorem specifies the relationship between the division of a polynomial by a linear factor to the value of the polynomial at a specified point

The remainder when the polynomial expression; x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by x - 1, can be found using the remainder theorem by plugging in x = 1 in the function as follows;

f(1) = 1⁵ - 3 × 1⁴ - 2 × 1³ - 5 × 1² + 5 × 1 + 12 = 8

The remainder when x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) therefore is 8

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Answer:

\(b1=1b2=1h=7b1=1b2=6h=2b1=6b2=9h=2\)

Answer:

Step-by-step explanation

Answer:

-7

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To find the value of t, we can use the formula for the slope of a line:

m = (y2 - y1) / (x2 - x1)

Given that the slope of the line is 0, we have:

0 = (-7 - t) / (5 - 3)

To solve for t, we can cross-multiply:

0 * (5 - 3) = -7 - t

0 = -7 - t

To isolate t, we can add 7 to both sides:

7 = -t

Dividing both sides by -1, we get:

t = -7

Therefore, the value of t is -7.

Answer:

if one hour is 0.09

24hours is 0.09x24=2.16 a day

a month is 2.16x30= 64.8

4months =64.8x4= $259.2

that's the answer.

Answer:

P(X=0)=0.732

P(X=1)=0.1962

P(X=2)=0.0526

P(X=3)=0.0141

P(X=4)=0.0038

P(X=5)=0.001 0

P(X≥6)=0.0004

Step-by-step explanation:

We want to find the probability distribution of X, where X is the number of items that must be tested before finding the first defective 10-year old widget.

This means that if X=2, the first two items are not defective and the third item is defective.

The probability of finding a defective item is p=0.732 for each trial.

Then, the probability for X=k can be written as:

\(P(X=k)=(1-p)^k\cdot p=(1-0.732)^k\cdot0.732=0.278^k\cdot 0.732\)

Then, we can write:

\(P(X=0)=0.268^0\cdot 0.732=0.732\\\\P(X=1)=0.268^1\cdot 0.732=0.1962\\\\P(X=2)=0.268^2\cdot 0.732=0.0526\\\\P(X=3)=0.268^3\cdot 0.732=0.0141\\\\P(X=4)=0.268^4\cdot 0.732=0.0038\\\\P(X=5)=0.268^5\cdot 0.732=0.001\\\\P(X\geq6)=0.0004\\\\\)

Answer:C

Step-by-step explanation:

That’s most likely the answer

A variable in mathematics is a number that can change depending on the issue. Several mathematical statements and equations use the generic letters x, y, and z. In other words, a variable is a symbol that stands for an unknowable numeric value. Say that x Plus 5 equals 10. The "x" variable is used here.

The variable "model of car driven" is qualitative because it is an attribute characteristic. Qualitative variables are those that are not numerical in nature but rather represent characteristics or categories that can be observed or measured through attributes. In this case, the model of the car driven is a type of attribute that describes the make and model of the car, such as Honda Civic, Toyota Corolla, etc.

Therefore, option B is the correct answer.

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Optiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

A qualitative variable is a type οf variable in statistics that describes a characteristic οr quality οf an οbject οr phenοmenοn. It is alsο called a categοrical variable, and it can be nοminal οr οrdinal. Nοminal variables have categοries that have nο inherent οrder, while οrdinal variables have categοries with a natural οrder οr ranking.

The variable "Mοdel οf car driven" is qualitative because it is an attribute characteristic. Qualitative variables are variables that are nοt numerical in nature but are based οn attributes οr characteristics. In this case, the mοdel οf the car driven is a categοrical variable that describes a particular characteristic οf the car, such as its make οr mοdel. This variable cannοt be measured quantitatively οr numerically, but rather it can be categοrized based οn specific attributes οr features.

Therefοre, οptiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

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Answer: hey

Step-by-step explanation:

The simplified expression is \(-4x^2 + 3x + 1\), which is a quadratic polynomial. Option D.

To simplify the expression \((8x^2 + 3x) - (12x^2 - 1)\), we can distribute the negative sign to each term within the parentheses:

\(8x^2 + 3x - 12x^2 + 1\)

Next, we can combine like terms by adding or subtracting coefficients of similar powers of x:

\((8x^2 - 12x^2) + 3x + 1\)

Simplifying further, we have:

\(-4x^2 + 3x + 1\)

The resulting polynomial \(-4x^2 + 3x + 1\) is a quadratic polynomial since it has a highest power of x^2 (the exponent of x is 2), which is\(-4x^2.\)Quadratic polynomials are polynomials of degree 2 and can be represented by a parabola when graphed.

In summary, the simplified expression \((8x^2 + 3x) - (12x^2 - 1)\) simplifies to \(-4x^2 + 3x + 1\) , which is a quadratic polynomial. So Option D is correct

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Note the complete question is

Answer:

5 is the answer

Step-by-step explanation:

hope this helps

The steady-state matrix X for the given Markov chain is [-1.0 -1.5].

To find the steady-state matrix X for an absorbing Markov chain, we need to follow these steps,

Rearrange the given transition probability matrix P so that it is in standard form, where the absorbing states (if any) are in the lower right corner and the transient states are in the upper left corner.

Partition the standard form matrix P into submatrices Q and R, where Q contains the transient states and R contains the absorbing states.

Find the fundamental matrix N = (I - Q)^(-1), where I is the identity matrix.

Find the matrix B = N*R.

The steady-state matrix X is the bottom row of the matrix B, padded with zeros if necessary.

Now, let's apply these steps to the given matrix P,

The matrix P is already in standard form, with the absorbing states (states 2 and 3) in the lower right corner.

We can partition P into the submatrices Q and R as follows:

Q = [0.6 0.4]

      [0.2 0.5]

R = [1 0]

      [0 1]

The fundamental matrix N is:

N = (I - Q)^(-1)

   = ([[-0.625  0.5  ]

        [ 0.25  -0.6 ]])^(-1)

    = [[-2.4 -1.6]

        [-1.0 -1.5]]

The matrix B is:

B = N*R

  = [[-2.4 -1.6]

       [-1.0 -1.5]] * [[1 0]

                          [0 1]]

  = [[-2.4 -1.6]

      [-1.0 -1.5]]

The steady-state matrix X is the bottom row of B, padded with zeros if necessary. Since there are two absorbing states, the steady-state matrix X will be a row vector of length 2. Therefore, X = [ -1.0 -1.5  ]

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Answer:

you have to make x-3 and x-7 equal to zero...

x = 3 or x=7

"A"

Step-by-step explanation:

Answer:

A 3, 7

Step-by-step explanation:

Using the zero product property

x-3 = 0    x-7 =0

x-3+3 =0+3      x-7+7 = 0+7

x=3,  x=7

Step-by-step explanation:

rectangle l = 6 units

b = 3 units

area = 18 units ^ 2

parallelogram l = 6 units

b = 1 unit

area = 6 unit ^2

total area = 24 units ^2

Answer:

166 1/2 or 166.5

Step-by-step explanation:

The formula for finding area is length*width. This can also just be written as A=l*w. Our area is still unknown, so it'll stay as A in this equation. Here, our length and width don't matter all that much, so we can input them where we please.

Now, we have the equation A=18*9 1/4

So, let's solve! 18*9 1/4 is equal to 166 1/2 or 166.5

With this, the area is equal to 166 1/2 or 166.5