(Graph attached)
Please show work
What is the average speed of the runner at 4 seconds
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Answer:

To graph the line with slope -1 passing through the point (-2,4), we can use the point-slope form of the equation of a line, which is:

where m is the slope of the line, and (x1, y1) is the given point on the line. Substituting the given values, we get:

Simplifying this equation, we get:

Now we can graph this line by plotting the given point (-2,4), and then using the slope of -1 to find one or more additional points on the line. We can do this by starting at the given point and then moving one unit down (since the slope is negative) and one unit to the right (since the slope is -1). This gives us the point (-1,3). We can then connect these two points to graph the line.

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Answer:

6 / 51

Step-by-step explanation:

It is false.

Reason:

The probability of picking a black card at first is:

26 / 52 = 1/2

There are now 25 black cards and 51 cards in total.

The probability of picking another black card, if there's no replacement is now:

25 / 51

Now, there are 24 black cards and 50 cards left in total.

The probability of picking a black card without replacement now becomes:

24 / 50 = 12 / 25

Hence, the probability of picking three black cards without replacement is:

1/2 * 25/51 * 12 / 25 = 300 / 2550

In simplest form, it is 6 / 51

0.2019 is a fraction of the toasters that can be expected to fail during the fourth year of use  for  the given statistical studies

As it is the fraction of toasters that can be expected to fail during the fourth year of use. This is determined from a statistical study, which indicates that the fraction of electric toasters manufactured by a certain company that is still in working condition after t years of use is approximately 0.3012. To calculate the fraction of toasters expected to fail during the fourth year of use, we simply subtract 0.3012 from 1, which gives us 0.2019. This means that, according to the statistical study, approximately 20% of the electric toasters manufactured by the company can be expected to fail during the fourth year of use.

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Answer:
The factors correlate with the x-intercepts. For example, with the factor (x - 3), there is an x-intercept at (3, 0). Likewise, with the factor (x + 2), there is an x-intercept at (-2, 0). This suggests that the opposite sign of the factors are the x-intercepts in the graph.

Answer: C. "How do you like this great new TV show?"

The term "great" put in there skews the question to make people think the show is great, when it may not be. So people may have a tendency to say they really like the show when they may not.

Or perhaps they may like the show (somewhat) but the fact that they can sense the bias built into the question makes them decide to say opposite and say they don't like the show. Maybe this sort of scenario would have them rebel in a way.

Either way, the use of "great" is likely to alter the opinion of people answering the question.

Answer:

F

Step-by-step explanation:

Simplify then graph it, find the x-intercept.

y = 3.75 + 1.5 (x - 1)

y = 1.5x + 2.25

When graphed, the x-intercept is 1.5

So it is, $1.50 per mile

Answer:

F. $1.50 per mile

Step-by-step explanation:

In order to solve this, you can first change it to slope-intercept form to find the slope, or rate of change, easier:

y = 3.75 + 1.5(x - 1) (given)

y = 3.75 + 1.5x - 1.5 (multiply 1.5 by each term in the parenthesis)

y = 2.25 + 1.5x (subtract 1.5 from 2.25)

y = 1.5x + 2.25 (order the terms by exponent value)

In slope-intercept form, the m (slope) of this equation is 1.5, so the rate of change is $1.50 per mile (with an initial fee of $2.25).

Initial explanation

We want to find a point C that lies on the line AB.

Its distance to B must be three times its distance to A.

We have that the coordinates of C correspond to the division of the x axis and the y axis:

on th

Answer:

The x,y that start with 1,4

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

(x1 + x2) , (y1+y2)

   2              2

Step-by-step explanation:

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The solution to the system is x = -6 and y = 4.

To solve the system by the addition method, we want to add the equations together in a way that will eliminate one of the variables.

Let's start by multiplying the first equation by -3 to get -3x - 9y = -18, and then add the second equation to it:

-3x - 9y = -18

+ 3x + 4y = -2

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    -5y = -20

Now we can solve for y by dividing both sides by -5:

y = 4

We can substitute y=4 into one of the original equations, say x+3y=6, to solve for x:

x + 3(4) = 6

x + 12 = 6

x = -6

So the solution to the system is x = -6 and y = 4.

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Answer:

2 days 5 minuts 14 seconds

Step-by-step explanation:

 1 1   1 1    1

 18   19   26

+25  45  48

1 24   05  14

Answer:

It is not possible

Step-by-step explanation:

Given

0.8km

Required

Convert to minutes

In conversion, only units of the same metric can be converted.

i.e.

You can convert meters to miles (they both measure distance)

You can convert seconds to hours (they both measure time)

You can convert kilogram to pounds (they both measure weight)

But in the given question, you attempt to convert from distance to time.

This is not possible, because time and distance are different measurements

Answer:

the answer is 77

Step-by-step explanation:

A measures 32 and B measures 109 so you subtract 109 and 32 and your answer will be 77

The function u(t) which governs the motion of the mass is a simple harmonic oscillator equation u(t)=10cos(2πt/T)+12, where T=2π√m/k is the period of oscillation and m,k are the mass and spring constant respectively.

1. Calculate the angular frequency of the mass:

ω = sqrt(4/1)

= 2 rad/s

2. Calculate the displacement equation for the mass:

u(t) = 10 cos(2t) + 12 sin(2t) - 1t

3. Substitute a value of t into the displacement equation:

u(1s) = 10 cos(2*1) + 12 sin(2*1) - 1*1

= 8.8 + 11.7 - 1

= 18.5 cm

The motion of the mass can be modelled as a simple harmonic oscillator, which is a system that follows Hooke's law. This law states that the restoring force exerted by a spring is directly proportional to the displacement of the spring. In this case, the spring is stretched by a force of 4 N, and the mass  attached  to it is given an initial downward displacement of 12 cm. The equation governing this motion is a simple harmonic oscillator equation, which is given by u(t)=10cos(2πt/T)+12, where T=2π√m/k is the period of oscillation and are the mass and spring constant respectively. The equation is derived from the forces acting on the system, which are the spring force and the gravitational force. The equation shows how the displacement of the mass varies with time, and it also takes into account the initial velocity of the mass (1 m/s). The equation thus provides a complete description of the motion of the mass.

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part a.

There is  a 49.1% chance that HRC finds a sample mean between $477 and $527.

part b.

There is a 20.9% chance that the sample mean falls between $492 and $512.

The standard error (SE) of the sample mean.

SE = σ / √(n)

σ = $80 and n = 68.

SE = 80 / √(68)

z1 = (X1 - μ) / SE

z2 = (X2 - μ) / SE

for first scenario:

X1 = $477, X2 = $527, and μ = $499.

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

For the range $477 to $527:

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

z1 = -0.275

z2 = 0.35

Probability 1 =  0.4909 = 49.1%

We have a 49.1% chance that HRC finds a sample mean between $477 and $527.

For the second scenario

X1 = $492, X2 = $512, and μ = $499.

z1 = (492 - 499) / Standard Error

z2 = (512 - 499) / SE

We have a 20.9% chance that the sample mean falls between $492 and $512.

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Answer:

No

Step-by-step explanation:

You cant have 2 y values

Answer:

it is indeed a function

Step-by-step explanation:

Answer:

The sampling distribution of X, for a sample of size 16, will be approximately normal with mean 2 mm and standard deviation 0.01 mm.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For the population:

Mean 2 mm, standard deviation 0.04 mm

Describe the sampling distribution of X (for a sample of size 16).

Sample of size 16 means that \(n = 16\)

By the Central Limit Theorem, approximately normal with mean 2 and standard deviation \(s = \frac{0.04}{\sqrt{16}} = 0.01\)

Answer:

10

Step-by-step explanation:

4(folk songs) × $9 = 36

36 + $49 = 85

85 - 75 = 10

Answer:   No  He will need $10.00 more.

Step-by-step explanation:

4 books X  $9. = $36.000

$75. - 36. = $39.00

He will need $10.00 more to buy the $49.00 music stand.

The solution of equation as ordered pairs can be given as {0, 3/2, 3, 6, 15/2}.

Domain may be defined as the input variable x for any of the given function which gives a suitable set of output variables y. The input variable is called the independent variable whereas the output variable is called the dependent variable. The equation given in the question 3x - 2y = -6 can also be expressed as y = (3x + 6)/2. The ordered pairs of Domain are {-2, -1, 0, 2, 3}. Now if we put these values as values of x we get the values of y as,

At x = -2, y = 0, at x = -1, y = 3/2, at x = 0, y = 3, at x = 2, y = 6 and at x = 3, y = 15/2.

These are the values of outputs, and the ordered pair will be expressed as

{0, 3/2, 3, 6, 15/2}.

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The four winning numbers are 24, 32, 27 and 37 respectively

It is important to note the following;

From the information given;

a. First number =  square root of 576

This is represented as

First number = √576

First number = 24

b. Second number =  multiple of 8 between 30 and 39

Second number = 32

c. Third number =  cube of 3

This is represented as;

Third number =  3³

Third number =  37

d. largest prime number less than 40

Fourth number = 37

Hence, the numbers are 24, 32, 27 and 37

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Answer:

c is the best one to choose because it makes the most since

Answer:

4 apartments per floor

Answer: 4

Step-by-step explanation:

If there are 36 apartments in the building with 9 on each floor, you can find the answer by simply doing the equation 36/9=4.

If \(f^{-1}(x)\) is the inverse of \(f(x)\), then

\(f\left(f^{-1}(x)\right) = x\)

We're given a domain for \(f(x)\) of \(x\ge0\), so \(f\left(f^{-1}(x)\right) = x\) is valid only for \(f^{-1}(x)\ge0\).

Now,

\(f\left(f^{-1}(x)\right) = \left(f^{-1}(x) + 1\right)^2 + 2 = x\)

Solve for the inverse :

\(\left(f^{-1}(x) + 1\right)^2 = x - 2 \\\\ \sqrt{\left(f^{-1}(x)+1\right)^2} = \sqrt{x-2} \\\\ \left|f^{-1}(x) + 1\right| = \sqrt{x-2}\)

Since \(f^{-1}(x)\ge0 \implies f^{-1}(x)+1 \ge0\), by definition of absolute value we have

\(\left|f^{-1}(x)+1\right| = f^{-1}(x) + 1\)

Then we end up with

\(f^{-1}(x) + 1 = \sqrt{x-2} \\\\ \boxed{f^{-1}(x) = \sqrt{x-2}-1}\)

Answer:

Acceleration

Step-by-step explanation:

The Newton's second law of motion can be expressed as;

F = ma

Where F is the force acting on an object, m is the mass of the object and a is the acceleration of the object.

For an object of mass 2kg and acceleration of 5 m/\(s^{2}\), we have;

\(F_{1}\) = 2 × 5 = 10 N

If we triple the mass,

m = 2 × 3 = 6 kg

Therefore,

\(F_{2}\) = 6 × 5 = 30 N

Thus, at constant acceleration, \(F_{2}\) = 3 × \(F_{1}\)

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2