Find the average rate of change of g(x)=2x^4 + 7/x^2 on the interval [-2,4]

Answer:

As x gets smaller, pointing to negative infinity, the value of p increases, pointing to positive infinity.

As x increases, pointing to positive infinity, the value of p increases, pointing to positive infinity.

Step-by-step explanation:

To find the end behaviour of a function f(x), we calculate these following limits:

[tex]\lim_{x \to +\infty} f(x)[/tex]

And

[tex]\lim_{x \to -\infty} f(x)[/tex]

At negative infinity:

[tex]\lim_{x \to -\infty} (4x^{8} - 6x^{7} + 3x^{3} - 10)[/tex]

When the variable points to infinity, we only consider the term with the highest exponent. So

[tex]\lim_{x \to -\infty} (4x^{8} - 6x^{7} + 3x^{3} - 10) = \lim_{x \to -\infty} 4x^{8} = 4*(-\infty)^{8} = \infty[/tex]

Plus infinity, because the exponent is even.

So as x gets smaller, pointing to negative infinity, the value of p increases, pointing to positive infinity.

At positive infinity:

[tex]\lim_{x \to \infty} (4x^{8} - 6x^{7} + 3x^{3} - 10) = \lim_{x \to \infty} 4x^{8} = 4*(\infty)^{8} = \infty[/tex]

As x increases, pointing to positive infinity, the value of p increases, pointing to positive infinity.

Answer:

A - As x -> infinity, p(x) -> infinity, and as x -> -infinity, p(x) -> infinity.

Step-by-step explanation:

Answer:

3 by 19

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

Interchange x and y, then solve for y.

  [tex](x-4)^2-\dfrac{2}{3}=6y-12\qquad\text{given}\\\\(y-4)^2=6x-\dfrac{36-2}{3}\qquad\text{swap x,y; add 2/3}\\\\y-4=\pm\sqrt{6x-\dfrac{34}{3}}\\\\\boxed{y=4\pm\sqrt{6x-\dfrac{34}{3}}}[/tex]

Answer:

A= 30 sq. cm

Step-by-step explanation:

We want to find the area of both triangles seprately than add them together. For the area of a traingle, we use the equation 1/2 base times height. For triangle ABE we do this:

[tex]A = \frac{1}{2} (12)(4)[/tex]

[tex]A = (6) (4)[/tex]

[tex]A = 24[/tex]

For triangle BDC, we do this:

[tex]A = \frac{1}{2} (6) (2)[/tex]

[tex]A = (3) (2)[/tex]

[tex]A=6[/tex]

Now we have to add both areas ot get A=30 sq cm

Answer:

0.136m

Step-by-step explanation:

This is because if you draw a diagram, and label all the sides of the triangle (opp, hyp, adj), the adjacent angle is 3m. You can now use the sine rule to find the hypotenuse (length of ladder) by doing: cos 20= 3/h. You divide cos(20) by 3 and you get the answer of 0.13602m.

Answer:

(x + 5)² + (y - 7)² = 13

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (- 5, 7) and r = [tex]\sqrt{13}[/tex] , thus

(x - (- 5))² + (y - 7)² = ([tex]\sqrt{13}[/tex] )² , that is

(x + 5)² + (y - 7)² = 13 ← equation of circle

Answer:

The correct conclusion is:

"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."

Step-by-step explanation:

A doctor is measuring the average height of male students at a large college.

The doctor measures the heights, in inches, of a sample of 40 male students from the baseball team.

Using this data, the doctor calculates the 95% confidence interval (63.5, 74.4).

The following conclusions is valid:

"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."

Since we know that the confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.  

For the given case, the confidence level is 95% and the corresponding confidence interval is (63.5, 74.4) which represents the true mean of heights for male students at the college where the doctor measured heights.

Therefore, it is valid to conclude that the doctor is 95% confident that the mean height of male students at the college is within the interval of (63.5, 74.4).

Answer:

37/50

Step-by-step explanation:

So 37 out of 50 who finished the class, so 37/50 .

And you can't simplify it.

Answer:

pizza

Step-by-step explanation:

Mode is the one that appears most often

Pizza appears 4 times

Cheeseburger, spaghetti appears only 3 times

apples, hot dogs 2 times

Answer: the mode is pizza

Step-by-step explanation:

Pizza: 4

Spaghetti: 3

Cheeseburger: 3

Apples: 2

Hotdog: 2

Pizza is the most so, it is the mode.

Answer:

The combination that gives the most profit is 12 VIP rings and 12 SST rings (900 $/day).

Step-by-step explanation:

This is a linear programming problem.

The objective function is profit R, which has to be maximized.

[tex]R=40V+35S[/tex]

being V: number of VIP rings produced, and S: number of SST rings produced.

The restrictions are

- Amount of rings (less or equal than 24 a day):

[tex]V+S\leq24[/tex]

- Amount of man-hours (up to 60 man-hours per day):

[tex]3V+2S\leq60[/tex]

- The number of rings of each type is a positive integer:

[tex]V, \;S\geq 0[/tex]

This restrictions can be graphed and then limit the feasible region. The graph is attached.

We get 3 points, in which 2 of the restrictions are saturated. In one of these three points lies the combination of V and S that maximizes profit.

The points and the values for the profit function in that point are:

Point 1: V=0 and S=24.

[tex]R=40V+35S=40\cdot 0+35\cdot 24=0+840\\\\R=840[/tex]

Point 2: V=12 and S=12

[tex]R=40V+35S=40\cdot 12+35\cdot 12=480+420\\\\R=900[/tex]

Point 3: V=20 and S=0

[tex]R=40V+35S=40\cdot 20+35\cdot 0=800+0\\\\R=800[/tex]

The combination that gives the most profit is 12 VIP rings and 12 SST rings (900 $/day).

Answer:

2:3

Step-by-step explanation:

3/5 women, that makes men 2/5, and total 5/5

men to women

2:3

Answer:

a = 15

Step-by-step explanation:

Perhaps your question is:

[tex] 4^{12}= 4^{a-3}[/tex]

If it is so then let us solve:

[tex] 4^{12}= 4^{a-3}[/tex]

Since, bases are equal hence exponents will also be equal. Therefore,

12 = a - 3

12 + 3 = a

a = 15

Answer:

d) The additional training did not significantly lower the defect rate

Step-by-step explanation:

Let proportion of defective chips be = x

Null Hypothesis [H0] : Additional training has no impact on defect rate             x = 8% = 0.08

Alternate Hypothesis [H1] : Additional training has impact on defect rate          x < 8% , x < 0.08  

Observed x proportion (mean) : x' = 27 / 450 = 0.06

z statistic = [ x' - x ]  / √ [ { x ( 1-x ) } / n ]

( 0.06 - 0.08 ) /  √ [ 0.08 (0.92) / 450 ]

= -0.02 / √ 0.0001635  

= -0.02  / 0.01278

z = - 1.56

Since calculated value of z, 1.56 < tabulated value of z at assumed 0.01 significance level, 2.33

Null Hypothesis is accepted, 'training didn't have defect rate reduction impact' is concluded

Answer:

x=1

Step-by-step explanation:

1/5x = 7/35.

Multiply each side by 5

1/5 x * 5 = 7/35 *5

x = 7/7

x=1

Answer:

√157

Step-by-step explanation:

Use Pythagorean theorm.

[tex]11^2 + 6^2 = ?^2[/tex]

121 + 36 = ?^2

157 = ?^2

√157 = ?

Can't simplify.

Answer:

12.5 m

Step-by-step explanation:

You are given the lengths of the legs of a right triangle.

We can use the Pythagorean theorem to find the length of the hypotenuse.

a^2 + b^2 = c^2

(6 m)^2 + (11 m)^2 = c^2

36 m^2 + 121 m^2 = c^2

c^2 = 157 m^2

c = sqrt(157 m^2)

c = sqrt(157) m

Answer: 12.5 m

Answer:

t = 4.26

Step-by-step explanation:

Sample, n = 453

Proportion, x = 60%

Required

Test Statistic

Test statistic is calculated as follows

t = (x - p)/(σ/√n)

Where σ = √p(1 - p)

When an experiment is conducted repeatedly, the results moves close to the expected value (Law of large numbers).

Hence p = 0.5

Calculating σ

σ = √p(1 - p)

σ = √0.5(1 - 0.5)

σ = √(0.5 * 0.5)

σ = √0.5²

σ = 0.5

So,

t = (x - p)/(σ/√n) becomes

t = (60% - 0.5)/(0.5/√453)

t = (0.6 - 0.5)/(0.5/√453)

t = (0.1)/(0.5/21.28)

t = 0.1 * 21.28/0.5

t = 2.128/0.5

t = 4.256

t = 4.26 ---- Approximated

Answer:

x - 2

Step-by-step explanation:

First, we know that the area of a triangle can be found using the formula: a = 1/2(bh).

We also know that the area of this triangle can be represented by (x^2-4).

Lastly, we know that one of the legs (let's call it the base) can be represented by (2x+4).

Let's plug in those values to the original formula: x^2 - 4 = 1/2(2x + 4)h

Now, let's solve for h!

We can multiply both sides by 2, then divide each side by (2x + 4) to isolate/solve for h.

If you need help on dividing polynomials, feel free to reach out!! I'd be happy to explain.

h = (x - 2)

Answer:

7 to the power of negative 8

Answer:

  7^-8 = 1/5764801

Step-by-step explanation:

The appropriate rule of exponents is ...

  (a^b)/(a^c) = a^(b-c)

So, ...

  7^-6/7^2 = 7^(-6-2) = 7^-8 = 1/5764801

70°

Answer:

160°

Step-by-step explanation:

[tex](3x - 5) \degree + (4x + 10) \degree = 180 \degree \\ (straight \: line \: \angle s) \\ (7x + 5) \degree = 180 \degree \\7x + 5 = 180 \\ 7x = 180 - 5 \\ 7x = 175 \\ x = \frac{175}{7} \\ \huge \orange{ \boxed{x = 25}} \\ \\ m\angle BEC = (3x - 5) \degree \\ m\angle BEC = (3 \times 25 - 5) \degree \\ m\angle BEC = (75 - 5) \degree \\ \huge \red{ \boxed{m\angle BEC = 70 \degree}} \\ \\ by \: remote \: interior \: angle \: theorem : \\ m\angle ABE = m\angle BEC + m\angle BCE \\ m\angle ABE = 70 \degree + 90 \degree \\ \huge \purple{ \boxed{m\angle ABE = 160 \degree }}[/tex]

Answer:

D

Step-by-step explanation:

i did the assignment.

The correct solution of the system of the equation is -3y = 3.

The correct option is D.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A system of equations,

x – 5y = 6    {equation 1}

–x + 2y = –3    {equation 2}

In order to solve the equations, using linear combination method.

Combining the two equations 1 and 2 to eliminate one of the variables x.

Adding both the equations,

-3y = 3

y = -1.

Therefore, –3y = 3 is the solution.

To learn more about the system of equation;

brainly.com/question/13729904

#SPJ6

Step-by-step explanation:

this right ans according to your question

Answer:

6/25

Step-by-step explanation:

Because england, scotland and france are european team and they make up 3/5 of all the teams, you multiply 3/5 by 2/5 because the south american teams are brazil and argentina which make up 2/5 of the total teams. So the probability that a european team will play a south american team is 3/5*2/5 which is 6/25

Answer:

a) If the spinner is fair, then each color must have the same probability, this means that the probability for each color is the number of times that the color (in this case blue) is in the spinner divided the total amount of colors in the spinner, then the theoretical probability for each color is:

Pt = 1/5 = 0.20

The experimental probability can be found by dividing the number of times that the spinner landed on a given color (in this case for blue we have 15 times) divided the total number of spins ( 50)

Pe = 15/50 = 0.30

B) As we increment the number of spins, we should see that the experimental probability gets closer to the theoretical probability.

Answer:

median: 12   mode: 12

Step-by-step explanation:

to find the median arrange the number in ascending order and then find the one that's in the middle. to find the mode just figure out which number shows up the most

Answer:

they both are 12                                                      

100%

Step-by-step explanation:

Answer:

690

Step-by-step explanation:

587+106=690

Answer:

  (3, 8) is a solution of the system

Step-by-step explanation:

We assume your second equation is intended to be ...

  y = 2^x

This system of equations can be solved graphically or by trial and error. There are no algebraic methods for solving it.

A graph shows that (3, 8) is one of the two solutions.

Answer:

Center of the circle = (10, 5)

Radius = 10

Step-by-step explanation:

Look at the picture

Answer:

5+3 x 2=64

Step-by-step explanation:

(5+3) x 2              5^2+3^2=34 not 64

  8 x 2 = 64

Answer:

64

Step-by-step explanation:

Hope this helped