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The rate of change for the interval between 0 and 2 for the quadratic equation f(x) = 2x^2 + x - 3, represented in the table, is 6.

To find the rate of change for the interval between 0 and 2 for the quadratic equation f(x) = 2x^2 + x - 3, we can use the values provided in the table.

First, let's calculate the values of f(x) for x = 0 and x = 2:

For x = 0: f(0) = 2(0)^2 + 0 - 3 = -3

For x = 2: f(2) = 2(2)^2 + 2 - 3 = 9

Now, we can find the rate of change by calculating the difference in the values of f(x) divided by the difference in x for the interval [0, 2]:

Rate of change = (f(2) - f(0)) / (2 - 0)

Substituting the values we found:

Rate of change = (9 - (-3)) / (2 - 0)

= (9 + 3) / 2

= 12 / 2

= 6

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Answer:

This is possible and the answer is (-1,0,1)

Step-by-step explanation:

It’s difficult to write out matrices here.

I apologize!

Answer:

3a(1+3b)

Step-by-step explanation:

First step is to find the greatest common factor between these two terms, which is 3a. Next you'll need to divide the two terms by that factor, which would give you what would be in the parenthesis, placed the factor in front to signify the multiplication of those terms and voila, you got the fully factored form.

Answer:

6:5

Step-by-step explanation:

Step 1: we need to match the b portions of each ration, use a lcm calculator, we see that the least common factor of 1 and 2 is 2

Step 2: For our a:b ratio of 3:1 we need to multiply each portion of the ration by 2 divided by 1 is 2

2 times 3:2 times 1 = 6: 2 our new a b ratio

Step 3: for our bc ratio of 2: 5 we need to multiply each portion of the ratio by 2 divided by 2 equals 1

1 times 2: 1 times 5 = 2:5 our new b:c ratio

since the b portions of each ratio match, we just take a: c = 6:5

GOOD LUCK!

Answer: x =1/2

y = [tex]\sqrt{3}[/tex]/2

Step-by-step explanation:

Answer:

The answer would be 1/4. I explained below if you don't get how you get the answer. Good luck!

Step-by-step explanation:

1. Find the LCM of 4 and 10

4, 8, 12, 16, 20

10, 20

The LCM of 4 and 10 is 20.

2. Divide 4 and 10 by 20.

20 ÷ 4 = 5

20 ÷ 10 = 2

3. Multiply the numbers by the answer you got in step 2.

3 x 5 = 15

5 x 2 = 10

4. Put it together.(example:number you got in step 3/20)

15/20

10/20

5. Subtract

15/20 - 10/20 = 5/20

You get the answer of 5/20 or 1/4. I would write 1/4 though.

Answer:

1/3

Step-by-step explanation:

1/3

Answer:

3

Step-by-step explanation:

11/1 divided by 11/3

keep change flip to get:

11/1 x 3/11

and multiply to get:

33/11

Simplify to get:

3/1 or 3

Answer:

3

Step-by-step explanation:

step one is to make the fraction into a unbalanced fraction

step two is to make it a proper fraction by switching the values (I am talking about 2 2/3s so you know)

Then remove the greatest common factor, so 11, and only three remains

Answer:

275

Step-by-step explanation:

Answer:

Total Cost = $275

Step-by-step explanation:

25% = 0.25

Multiply $220 by 0.25 to get 25% of $220.

0.25 × $220 = $55

Now add $220 and $55 to get the total cost.

$220 + $55 = $275

Answer:

1.) [tex]\frac{5}{4\\}[/tex]

2.) [tex]\frac{4}{3}[/tex]

3.) 1

4.) [tex]\frac{2}{3}[/tex]

5.) [tex]\frac{9}{8}[/tex]

6.) [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

The 2 steps for all of these is to get common denominators and then add and simplify.

1.) 3/4 + 1/2 (common denominator) 3/4 + 2/4 = 5/4

2.) 5/6 + 1/2 (common denominator) 5/6 + 3/6 = 4/3

3.) 3/6 + 1/2 (common denominator) 3/6 + 3/6 = 6/6 (simplify) = 1

4.) 1/6 + 4/8 (common denominator) 8/48 + 24/48 =  32/48 (simplify) = 2/3

5.) 7/8 + 1/4 (common denominator) 7/8 + 2/8 = 9/8

6.) 3/8 + 1/2 (common denominator) 3/8 + 4/8 = 7/8

Answer:

n=8/11

Step-by-step explanation:

Answer:

C) n=8/11

Step-by-step explanation:

3/4n=6/11

n=6/11÷3/4

invert and multiply

n=6/11x4/3

n=24/33

n=8/11

Answer:

137 degrees since it says 47

Step-by-step explanation:

Answer:

4 (2x + 12) = 0

8x + 48 = 0

8x = - 48

x = -48/8

x = - 6 (option 2)

Answer:

[tex]3.6 * 10^{3} \\\\[/tex]

Step-by-step explanation:

Answer:

The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval. The variance is the same as the mean.

Average rate of 56 calls per hour:

This means that [tex]\mu = 56n[/tex], in which n is the number of hours.

Find the average and standard deviation of the number of service calls in a 15-minute period.

15 minute is one fourth of a hour, which means that [tex]n = \frac{1}{4}[/tex]. So

[tex]\mu = 56n = \frac{56}{4} = 14[/tex]

The variance is also 14, which means that the standard deviation is [tex]\sqrt{14} = 3.74[/tex]

The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.

Answer:

20.83 yard

Step-by-step explanation:

Calculate Cubic Yards

Calculate your area

Calculate your volume: Multiply area times the depth to get volume in cubic feet

Calculate your cubic yards: Divide cubic feet by 27 to convert to cubic yards and this is your answer

Where ft2 = square foot, ft3 = cubic foot, yd3 = cubic yard

Total yards = 5[x] + x + 8  

Solve

133 = 6x + 8

6x = 125

x = 20.83 yard

Therefore, the Cyclone cleared 20.83 yards on the first day.

Answer:

t = 42857.14 h

Step-by-step explanation:

Given that,

The speed of space shuttle, v = 28000 km/h

We know that, the distance between the Saturn and the Earth is 1,200,000,000 km.

Let t be the time.

As we know, speed = distance/time

So,

[tex]t=\dfrac{d}{v}\\\\t=\dfrac{1,200,000,000}{28000}\\\\t=42857.14\ h[/tex]

So, the required time is equal to 42857.14 hours.

Based on the graphs provided its is seen that, a power model could be appropriate because the scatter plot of log height versus log weight is roughly linear. Therefore, option C is the correct answer.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

Based on the graphs provided its is seen that, a power model could be appropriate because the scatter plot of log height versus log weight is roughly linear. The next step is to look at the residual plot.

Therefore, option C is the correct answer.

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Answer:

Step-by-step explanation:

Distance = 6 miles

Time = 3 hours

Speed = Distance ÷ Time

Speed = 6 ÷ 3

Speed = 2 miles/hour

....................................................

Speed = 2 miles/hour

Distance = 7.5 miles

Time = Distance ÷ Speed

Time = 7.5 ÷ 2

Time = 3.75 hours

3.75 hours = 3 hours & 45 minutes

Answer:

Step-by-step explanation:

Time taken to travel 6 miles = 3 hours

Time taken to travel 1 mile = 3 ÷ 6 = [tex]\frac{3}{6}=\frac{1}{2} hour[/tex] = 30 minutes

Time taken to travel 7.5 miles = 30 * 7.5 = 225 minutes = 3.45 hours

Answer:

4cm

Step-by-step explanation:

Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

A regular decagon is a polygon with ten sides of equal length and ten angles of equal measure.

To find the length of each of the other sides, we can use the fact that a regular decagon can be divided into ten congruent isosceles triangles.

The isosceles triangle can be split into two right triangles by drawing an altitude from the vertex opposite the base to the midpoint of the base.

Let's call the length of one of the equal sides of the isosceles triangle "s", and let's call the length of the altitude "h".

Then we can use the Pythagorean theorem to find the length of the other side:

s² = h² + (s/2)²

We can solve for "h" in terms of "s" as follows:

h² = s² - (s/2)²

h² = (4s²)/4 - s²/4

h² = (15s²)/16

h = (s√15)/4

Since the altitude divides the isosceles triangle into two congruent right triangles, each with a hypotenuse of "s",

We can use the Pythagorean theorem again to find the length of each of the other sides of the regular decagon:

s² = h² + (s/2)²

s² = [(s√15)/4]² + (s/2)²

s² = (15s²)/16 + (s²)/4

s² = (15s² + 4s²)/16

s^2 = (19s²)/16

s = √(19/16) s

s = (√19/4) cm

Therefore,

Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.

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Answer:

$61.76

Step-by-step explanation:

So I can't answer how much do you have left or did you make enough money, but I can calculate the money you made. Since it's $9.15 per hour and you worked 6.75, you simply multiply the numbers together. The money you made was $61.76.

Answer:

SA = 240

Step-by-step explanation:

SA = (10*10) + (8*10) + (6*10)

SA = 240

Answer:

The 80% confidence interval for the proportion of all college students who drove a car the day before the survey was conducted is (0.479, 0.621).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

A random sample of 80 college students showed that 44 had driven a car during the day before the survey was conducted.

This means that [tex]n = 80, \pi = \frac{44}{80} = 0.55[/tex]

80% confidence level

So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 1.28\sqrt{\frac{0.55*0.45}{80}} = 0.479[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 + 1.28\sqrt{\frac{0.55*0.45}{80}} = 0.621[/tex]

The 80% confidence interval for the proportion of all college students who drove a car the day before the survey was conducted is (0.479, 0.621).