The number of miles a motorcycle, x, will travel on one gallon of gasoline is modeled by a normal distribution with mean 44 and standard deviation 5. With one gallon of gasoline in the motorcycle, find the probability that mike can travel more than 50 miles without refueling. Round your answer to four decimal places.

Answer: Tyler has 22 cards

Step-by-step explanation:

To begin, we know that Morgan has 12 less than 5x Tyler's cards, so...

12+98=110

Now that we had 110, we then read that it is the PRODUCT of 5 and the number that Tyler has, so we will show that algebraically.

110=5x

Now, divide 110 by 5 to find X.

110/5=22

Tyler has 22 cards.

In linear equation, the solution of equations is ( -2 , 1)

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

y = 2x + 5

y = 1/2x + 2

the solution of equations is ( -2 , 1)

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The error Percentage is 20%

What is Percentage?

A percentage is a component of a whole stated as a number between 0 and 100 rather than as a fraction. All of anything is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the fraction of the entire by the whole itself and multiply by 100.

Solution:

We gussed that LeBron James would score 35 points, but he only scored 28 points

So, the difference was of 7 points (35-28)

Error Percentage = 7/35 * 100

Error Percentage = 1/5 *100

Error Percentage = 20%

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Answer:

(10,6) and (-5, -3)

Step-by-step explanation:

The slope of the line is given by rise/run between (0,0) and (5,3)
Rise = y2 - y1 = 3 - 0 = 3

Run = x2 - x1 = 5 - 0 = 5

Slope m 3/5

Slope intercept form of a line is

y = mx + b

where m is the slope and b is the y-intercept

Since the line passes through (0,0) the y-intercept is 0

So we get

[tex]y = \dfrac{3}{5}x + 0 \\\\or\\\\y = \dfrac{3}{5}x[/tex]

This means for any x value, the corresponding y value should be 3/5th of that x value

Only the first and third choices have this requirement fulfilled

The equation of the circle with center (−1,−2) containing the point (0,6).

(x + 1)^2 + (y + 2)^2 = 65

Remember that the equation of a circle with radius R and center (a, b) is written as:

(x - a)^2 + (y - b)^2 = R^2

Here we know that the center of the circle is (-1, -2), then our equation is something like:

(x + 1)^2 + (y + 2)^2 = R^2

We know that our circle contains the point (0, 6), replacing these values in the equation above we get:

(0 + 1)^2 + (6 + 2)^2 = R^2

1 + 8^2 = R^2

65 = R^2

Then the circle equation is:

(x + 1)^2 + (y + 2)^2 = 65

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The shadow of the ball moving over the ground at 150 feet per second after 1 second.

How can I determine the shadow of the ball's speed?

Assuming the ball drops the distance indicated by this sentence:

S = 16t²

Additionally, the height (h) of the ball's shadow one second later is provided by

h = 30 - S

The term for the shadow of the ball would then be as follows:

OX/30 = (20 + XQ)/30 = XQ/h

30XQ = 20h + hXQ

20h = 30XQ - hXQ

20h = (30 - h)XQ

XQ = 20h/(30 - h)

Substituting the value of h, we have:

XQ = 20(30 - S)/(30 - 30 - S)

Substituting the value of S, we have:

XQ = 20(30 - 16t²)/(30 - 30 - 16t²)

XQ = 20(30 - 16t²)/16t²

XQ = (600 - 320t²)/16t²

XQ = 600/16t² - 320t²/16t²

XQ = 600/16t² - 20

Differentiating with respect to t, we have:

d(XQ)/dt = 600/16t² - 20

d(XQ)/dt = 600 (-64t/(16t²)²)

d(XQ)/dt = 600 (-64t/256t⁴)

d(XQ)/dt = 600 (-0.5/2t³)

d(XQ)/dt = -300/2t³

Then,

At t = 1, we have:

Speed = 300/2(1)

Speed = 150 ft/s.

That is,

After one second the ball's shadow was travelling over the ground at a speed of 150 feet per second.

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The equation of the line in slope-intercept form is: y = 5x + 3.

If the value of the slope of a line, m, is known, and the value of its y-intercept, b, is known, the equation of the line in slope-intercept form would be written as:

y = mx + b.

Given the following:

To write the equation of the line in slope-intercept form, substitute m = 5 and b = 3:

y = 5x + 3

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Question:

A line's slope is 5, and its y -intercept is 3. What is its equation in slope-intercept form?

A good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up is count all the bytes of the data in the struct.

Rule:

In math rule refers a numerical pattern is a sequence of numbers that has been created based on a formula or rule called a pattern rule

Given,

Here we need to find a good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up.

According to the rule of thumb, the count all the bytes of the data in the struct.

and then we need to find the nearest power of 2, 4 or 8 based on the largest Data Type in your struct.

So, if the total number of bytes is larger than that power, then the struct will be the next power in size.

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Answer:

y = (-2/3)x + (19/3)

Step-by-step explanation:

3x - 2y = 5

-2y + 3x = 5

      -3x        -3x

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

-2y = -3x + 5

-2      -2    -2

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

       3            5

y = -------x - -------

       2            2

                            -2

Perpendicular:  -------- x

                             3

                     -2

(2, 5);  m =  --------

x₁ y₁               3

y - y₁ = m(x - x₁)

y - 5 = (-2/3)(x - 2)

y - 5 = (-2/3)x + (4/3)

   +5                 +5

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

y = (-2/3)x + (19/3)

I hope this helps!

The simplified form of  (m + 3n + 8)(m + 3n - 8) is  m^2 + 3n^2 + 6mn - 64.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given,  (x+2)(x+3) = x^2+5x+6.

∴ (m + 3n + 8)(m + 3n - 8).

= m^2 + 3mn - 8m + 3mn + 3n^2 - 24n + 8m + 24n - 64.

= m^2 + 3n^2 + 6mn - 64.

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Answer: 250 meters

Step-by-step explanation: Find the unit rate. 2000 divided by 8 will get you a unit rate of 250 meters per minute.

Answer: 225

Step-by-step explanation:

Answer:

5 hours

Step-by-step explanation:

To figure this out we will do the total she earned yesterday divided by the hours she worked. So, 84/7=12. So know we know how much she earns in an hour, $12. So if she is earn $60 today then we should do 60/12 to figure out how many hours she worked. 60/12=5. So she worked 5 hours.

I hope this helps!!!

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The requried area under the standard normal curve that lies to the right of z = 0.11 and to the left of z = 0.41 is approximately 0.1153.

To find the area under the standard normal curve that lies to the right of the z-score 0.11 and to the left of the z-score 0.41, we can use a standard normal table or a statistical calculator.

The area to the right of z = 0.11 can be found by subtracting the cumulative area to the left of z = 0.11 from 1.

The area to the left of z = 0.41 can be directly read from the standard normal table.

Using a standard normal table or a calculator, we find:

The area to the left of z = 0.11 is approximately  0.5438.

The area to the left of z = 0.41 is approximately 0.6591.

Now, let's find the area between these two z-scores:

Area = (Area to the left of z = 0.41) - (Area to the left of z = 0.11)

Area = 0.6591 - 0.5438

Area ≈ 0.1153

So, the area under the standard normal curve that lies to the right of z = 0.11 and to the left of z = 0.41 is approximately 0.1153.

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Step-by-step explanation:

1[tex] {10}^{ - 8} = \frac{1}{10^{8} } [/tex]

[tex]7 \times \frac{1}{ {10}^{8} } = \frac{7}{ {10}^{8} } [/tex]

2)

[tex]6 \times {10}^{ - 8} = 6 \times \frac{1}{ {10}^{8} } = \frac{6}{ {10}^{8} } [/tex]

The probability that you picked the fair coin given that the outcome of the toss was heads is 1/3.

There is a one in two chance of drawing the fair coin. The chances of flipping heads again are 1 in 2. As a result, there is a 1 in 4 chance that the coin will land on heads.

There is a one in two chance of drawing the trick coin. The probability of flipping heads is then 2 to 1. As a result, there is a 2 in 4 chance that the coin will land on heads.

When each is multiplied by four, the resulting integers are

fair: 1 and trick: 2

and overall results: 3. (fair and tails is not counted)

The likelihood of a fair coin is one in three.

The likelihood that the chosen coin will show heads and be the fair coin is 33.333%.

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Answer: 130 cookies are left

Step-by-step explanation:

3/4 of 520 = 390

520 - 390 = 130

Answer:

130 cookies are left.

Step-by-step explanation:

1. Turn 3/4 into a decimal

3 ÷ 4 = 0.75

2. Multiply

0.75 x 520 = 390

3. Subtract

520 - 390 = 130

Solution:

130 cookies are left.

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The resulting regression was predicted GPA is 3.1 Predict the outcome of one variable from the outcome of a second variable.

The variable we are predicting is called the reference variable and is denoted as Y. The variable on which the prediction is based is called the predictor and is denoted as X. The magnitude of the correlation coefficient indicates the strength of the association. A prediction is a statement intended to tell you something about the future.

Predicted grades are qualifying grades that an applicant's school or college is expected to achieve under favorable circumstances. These predicted grades are used by colleges as part of the admissions process to help understand an applicant's potential. The expected result of an experiment is derived from a hypothesis or theory. This is a guess at the possible outcome of the scenario.

GPA= 3.1+3.6+1.6+3.1+4.1/ 5= 15.5/5 = 3.1

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A solution that does not simultaneously satisfy all constraints is called an infeasible solution.

Option (C) is correct.

What is linear programming?

Linear programming, also known as linear optimization, is a method for achieving the best result in a mathematical model with requirements represented by linear relationships. Linear programming is a special case of mathematical programming.

In linear programming, a solution that does not simultaneously satisfy all constraints is called an infeasible solution.

In some cases, there is no feasible solution area, i.e., there are no points that satisfy all constraints of the problem. An infeasible LP problem with two decision variables can be identified through its graph. For example, let us consider the following linear programming problem.

Minimize z = 200x1 + 300x2

subject to

2x1 + 3x2 ≥ 1200

x1 + x2 ≤ 400

2x1 + 1.5x2 ≥ 900

x1, x2 ≥ 0

The region located on the right of PQR includes all solutions, which satisfy the first and the third constraints. The region located on the left of ST includes all solutions, which satisfy the second constraint. Thus, the problem is infeasible because there is no set of points that satisfies all three constraints.

Hence, a solution that does not simultaneously satisfy all constraints is called an infeasible solution.

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The function which describes the arithmetic sequence is f(x) = −0.6x + 8.6.

The correct answer option is option D

Given the sequence:

8, 7.4, 6.8, 6.2, 5.6, …

Check all the options

Where,

x = number of term

A. f(x) = 0.6x + 8

When x = 1

f(x) = 0.6x + 8

= 0.6(1) + 8

= 0.6 + 8

= 8.6

B. f(x) = 0.6x + 8.6

When x = 1

= 0.6(1) + 8.6

= 0.6 + 8.6

= 9.2

C. f(x) = −0.6x + 8

When x = 1

= -0.6(1) + 8

= 0.6 + 8

= 8.6

D. f(x) = −0.6x + 8.6

When x = 1

= -0.6(1) + 8.6

= -0.6 + 8.6

= 8

Hence, f(x) = −0.6x + 8.6 is the function which describes the sequence.

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If each is a 4-digit number beginning with 1 that has exactly two identical digits , then there are 432 such numbers .

In the question ,

Suppose  that the two identical digits are both 1.

and since the thousands digit must be 1, only one of the other three digits can be 1. This means that the  possible forms for the required numbers are

11xy , 1x1y , 1xy1  ,

Because the number must have exactly two identical digits, x ≠ y, x ≠ 1, and y ≠ 1.

Hence, Of this form there are 3 × 9 × 8 = 216 numbers .

Now suppose that two identical digits are not 1 , we will have the following possibilities:

1xxy , 1xyx , 1yxx

Again, x ≠ y , x ≠ 1 , and y ≠ 1 .

Of this form there are 3 × 9 × 8 = 216 numbers .

So , the total numbers are 216 + 216 = 432 .

Therefore , the total  numbers are 432 .

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The height of the object after 1.00 seconds launched is 24 feet.

Quadratic function is a function where the maximum power of x variable is 2. Simply you can write quadratic function as:

y = ax^2 + bx + c

y is height in feet and x is time in second.

Known 2 conditions from the question:

From second condition (0 feet in 0 second), we can substitute 0 both in y and y:

y = ax^2 + bx + c

0 = a(0)^2 + b(0) + c

0 = 0 + 0 + c

0 = c

And this, we know that the constant (c) of the function is 0.

Just substitute c with 0 in previous function.

y = ax^2 + bx + c

y = ax^2 + bx + 0

y = ax^2 + bx

From first condition (25 feet in 1.25 seconds), we can substitute x with 1.25 and y with 25:

y = ax^2 + bx

25 = a(1.25)^2 + b(1.25)

25 = 1.56625a + 1.25b

Maximum/minimum point of quadratic function can be found with dy/dx = 0, dy/dx is differential:

y = ax^2 + bx

dy/dx = 2ax + b

0 = 2ax + b

0 = 2a(1.25) + b

0 = 2.5a + b

-2.5a = b

After we know the ratio a and b, we can substitute b with -2.5a in previous equation:

25 = 1.5625a + 1.25b

25 = 1.5625a + 1.25(-2.5a)

25 = 1.5625a - 3.125a

25 = -1.5625a

15/-1.5635 = a

a = 15/-1.5625

a = 16

We got a = 16. Then we just substitute it in a b ratio equation:

b = -2.5a

b = -2.5(-16)

b = 40

After we know a, b, c, just substitute that three numbers in the function:

y = ax^2 + bx + c

y = -16x^2 + 40x

So, the function can be used in launching of the object is y = -16x^2 + 40x.

Where is the object in 1.00 seconds after launched? Just substitute x with 1.

y = -16x^2 + 40x

y = -16(1)^2 + 40(1)

y = -16 + 40

y = 24 feet

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x = 1+i or x = 1-i are the complex roots of the graph

Below are the steps for determining the complex roots of a graph or curve:

1. Draw a vertical line passing through the vertex of the parabola or curve

2. The value of x where the line intersects the x-axis gives the real part of the root

3.  Draw a horizontal line of height twice the height of the vertex from the x-axis

4. Draw a vertical line from this point of intersection to intersect the x-axis

5. The distance of this point from the real part of the root gives you the imaginary part of the root

(Check the attached image for the labeling)

From the image attached:

Real part of the root: a = 1

Imaginary part of the root: b = 1

Remember: complex root is of the form x = a±bi

Therefore, the complex roots of the graph are x = 1+i or x = 1-i

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Answer:

25

Step-by-step explanation:

450 divided by 18 is 25

Answer: 25 miles

Step-by-step explanation:
450/18 = 25
25 miles with 1 gallon of gas

Answer:

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

Step-by-step explanation:

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

[tex]3zy = 4x[/tex]

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

Answer:

z = (4x)/(3y)

Step-by-step explanation:

Given equation,

→ x = (3yz)/4

Now the value of z will be,

→ x = (3yz)/4

→ (3yz)/4 = x

→ 3yz = x × 4

→ z × 3y = 4x

→ [ z = 4x/3y ]

Hence, value of z is 4x/3y.

The family of all least polynomials with roots at - 4, - 3, 0, 2 is represented by the polynomial y = a · (x + 4) · (x + 3) · x · (x - 2), where a is the lead coefficient.

Herein we must determine the family of all least polynomials whose roots must be the real numbers - 4, -3, 0, 2. Polynomials are algebraic expressions, whose factor form is described below:

y = a · Π (x - rₙ), for n = {1, 2, 3, 4, ..., m - 1, m}

Where:

In accordance with all these assumptions and definition, the function is defined below:

y = a · (x + 4) · (x + 3) · x · (x - 2)

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Answer:

33

Step-by-step explanation:

-4(-6) + 9

24 + 9

33