Does anyone understand how to do this? If you do can you explain how I solve it and receive the answer?

The average rate of change of the function over the interval [-6,4] is 3.4.

To determine the average rate of change of the function over the interval -6 ≤ x ≤ 4, we first need to calculate the values of h(x) at -6 and 4.

After finding the values of h(x) at these points, we will use the formula of average rate of change of the function to determine the answer.

Step-by-step explanation Let's calculate the value of h(-6).h(x) = -x² + x - 4h(-6) = -(-6)² + (-6) - 4h(-6) = -36 - 6 - 4h(-6) = -46 Similarly, let's calculate the value of h(4).h(x) = -x² + x - 4h(4) = -(4)² + 4 - 4h(4) = -16 + 4 - 4h(4) = -12.

The formula for average rate of change of the function over the interval [-6,4] is:(h(4) - h(-6)) / (4 - (-6))Substituting the values in the formula, we get:(-12 - (-46)) / (4 - (-6))= 34 / 10= 3.4.

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Answer:

= 1/2

Step-by-step explanation:

√25 / √100

= 1/2

The correct answer is: 1/2

The difference between the mean and the median of the data is 1

Given data:

11, 12, 8, 12, 8, 8, 11, 11, 9

= (11 + 12 + 8 + 12 + 8 + 8 + 11 + 11 + 9) / 9

= 90 / 9

= 10

Arrange in ascending order

8, 8, 8, 9, 11, 11, 11, 12, 12

The middle number is 11

Therefore, the difference between the mean and the median of the data is 11 - 10 = 1

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Looking at the first system of equations,

16x - 10y = 10

-8x - 6y = 6

If we multiply both sides of the second equation by 2, the coefficient of x is exactly the negative of the coefficient of x in the first equation.

-8x - 6y = 6

⇒   2 (-8x - 6y) = 2 (6)

⇒   -16x - 12y = 12

By combining this new equation with the first one, we can eliminate x and solve for y :

(16x - 10y) + (-16x - 12y) = 10 + 12

⇒   -22y = 22

⇒   y = -1

Then we just solve for x by replacing y in either equation.

16x - 10y = 10

⇒   16x - 10 (-1) = 10

⇒   16x + 10 = 10

⇒   16x = 0

⇒   x = 0

The main idea behind elimination is combining the given equations in just the right amount so that one of the variables disappears. The "right amount" involves using the LCM of the coefficients of a given variable. In this example, the x-coefficients had LCM(8, 16) = 16, so we only had to scale one of the equations (the one with -8x) to cancel all the x terms.

If we wanted to eliminate y first instead, we first note that LCM(6, 10) = 30. To get 30 as a coefficient on y, in the first equation we would have multiplied by 3:

16x - 10y = 10

⇒   3 (16x - 10y) = 3 (10)

⇒   48x - 30y = 30

And in the second equation, we would have multiplied by -5 (negative so that upon combining the equations, we end up with -30y + 30y = 0):

-8x - 6y = 6

⇒   -5 (-8x - 6y) = -5 (6)

⇒   40x + 30y = -30

Now combining the two scaled equations gives

(48x - 30y) + (40x + 30y) = 30 + (-30)

⇒   88x = 0

⇒   x = 0

We then solve for y :

16x - 10y = 10

⇒   -10y = 10

⇒   y = -1

so we end up with the same solution as before.

Answer: The standard answer would be 4.612258099 × 10.

Step-by-step explanation: Pls give me brainliest. It might help w/ my depression. :\

The y-intercept, which represents the point the graph crosses the y-axis, is the point where x = 0, or the usual start of a time based function

The true statements about the y-intercept are;

B. The y-intercept is 10

D. The y-intercept tells me that they paid the babysitter $10 to buy her lunch

Reasons:

The points on the graph are;

\(\begin{array}{|c|cc|} \mathbf{Time }&&\mathbf{Cost}\\0&&10\\1&&20\\2&&30\\3&&40\\4&&50\\5&&60\end{array}\right]\)

The slope of the graph is therefore; \(\dfrac{60 - 50}{5 - 4} = 10\)

The equation of the graph is y - 60 = 10·(x - 5)

y = 10·x - 50 + 60 = 10·x + 10

The y-intercept is give by the point where the x-value is zero

At the start when x = 0, the amount paid to the baby sitter is y = 10×0 + 10 = 10

Therefore, the y-intercept which is $10, represent the amount the family

paid to the babysitter at the start for her lunch

The correct statements are therefore;

Option B; The y-intercept = 10

Option D; The y-intercept indicates the amount given to the babysitter for

her lunch

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Answer:

d and b i did the quiz

Step-by-step explanation:

Answer:

The value of -2 is LESS THAN the value of 1.5 because -2 lies to the LEFT of 0 and 1.5 lies to the RIGHT of 0 on the number line

Step-by-step explanation:

the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

To form a third-degree polynomial function with real coefficients such that the complex number 6 + i and the real number 7 are zeros, we can use the fact that complex zeros come in conjugate pairs.

Given that 6 + i is a zero, its conjugate 6 - i will also be a zero. Thus, the zeros of the polynomial are 6 + i, 6 - i, and 7.

To find the polynomial function, we start by forming the factors corresponding to each zero:

(x - (6 + i))   --> This corresponds to the zero 6 + i

(x - (6 - i))   --> This corresponds to the zero 6 - i

(x - 7)        --> This corresponds to the zero 7

To simplify the factors, we multiply them out:

(x - (6 + i))(x - (6 - i))(x - 7)

= ((x - 6) - i)((x - 6) + i)(x - 7)

= ((x - 6)² - i²)(x - 7)

= ((x - 6)² + 1)(x - 7)

Expanding the squared term:

= (x² - 12x + 36 + 1)(x - 7)

= (x² - 12x + 37)(x - 7)

Therefore, the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

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the equivalent expressions are:

And the expression in scientific notation is the last one in the bullet points.

Here we start with the expression:

(9.6*10³)*(6.7*10)

Where both numbers are in scientific notation, notice that we can write that product as:

(9.6*10³)*(6.7*10) = (9.6*6.7)*(10³*10) = 64.32*10⁴

Now, remember that in scientific notation, we only can have a single digit in the left of the decimal point, so we can rewrite:

64.32*10⁴ = 6.432*10⁵

So the equivalent expressions are:

And the expression in scientific notation is the last one in the bullet points.

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Answer:

height of the man is ≈ 6.5

Step-by-step explanation:

shadow of the man/ shadow of the tree = height of the man/ height of the tree

4/11 = x/18                   cross multiply

11x = 4(18)

11x = 72

  x = 6.5

Answer:

2

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

3x5=15

+1(2-4x5)=2-20-18

15-18=-3

Answer:

-3

Step-by-step explanation:

Given equation for reference: 3x + (2 - 4x)

3(5) + (2 - 4(5)) is with x substituted for 5.

Next, we just follow PEMDAS like any other expression

First off, parentheses.

2 - 4(5), starting with multiplication, and then subtraction

The result of the parentheses is -18

3(5) - 18 is the result when we put that back into the expression.

Next, we multiply 3 by 5; the result being

15 - 18

Now, we just subtract 18 from fifteen, getting -3

Hope this helps!

The parallelogram have the value of x = 3, angle m∠XWY = 30° and m∠X = 115°

A parallelogram is a geometric shape with four sides, where opposite sides are parallel and have equal lengths. Its opposite angles are also equal in measure.

The sides WV and XY are equal in length so;

3x = 9

x = 9/3

x = 3

angles m∠XWY and m∠VYW are alternate angles and are equal so;

m∠VYW = 180 - (35 + 115)

m∠VYW = 30° = m∠XWY

opposite angles are also equal in measure so;

m∠V = m∠X = 115°

In conclusion, the parallelogram have the value of x = 3, angle m∠XWY = 30° and m∠X = 115°

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Answer:

the new coords are (2,-3) the new y coord is -3

Step-by-step explanation:

Step-by-step explanation:

Of course the new coordinates are (2,-3)

Hope it helps....

'cause you know better.....

Answer:

56 cola flavored gumboils

Step-by-step explanation:

Bob's 40 count of gumballs has 16 cola gumballs

Therefore the probability of a gumball being cola based on the sample size of Bob's purchase = 16/40 = 2/5

There are 140 gumballs left in the machine so we can expect that, on an average, 2/5 of them should be cola gumballs

So number of cola gumballs left is expected to be  2/5 x 140 = 56

This is only a prediction based on Bob's sample of 40 cola gumballs

The source of internal invalidity reflected in this example is experimental mortality, as the drop in sample size due to soldiers being reassigned to different stations across the U.S. can lead to a decrease in statistical power and increased risk of bias in the results.

This example reflects the source of internal invalidity known as c) experimental mortality. Experimental mortality refers to the loss of participants during an experiment, which may cause issues with the overall validity of the results. In this case, the reassignment of soldiers to different stations across the U.S. caused the sample size to drop, potentially affecting the outcome of the study on the effect of group size on group morale.

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Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

             Statements                                  Reasons

1). AD ≅ BC                                           1). Given

2). ∠D ≅ ∠C                                          2). Given

3). ∠DEA ≅ ∠CEB                                 3). Vertically opposite angles

4). ΔADE ≅ Δ BCE                                4). AAS postulate of congruence

5). AE ≅ BE                                           5). CPCTC

Hence, proved.

The conclusion of Clairaut's theorem holds for the given function u = exy sin y.

To verify that Clairaut's theorem holds for the given function u = exy sin y, we need to compute the partial derivatives uxy and uyx and check if they are equal.

First, we compute the partial derivative of u with respect to x:

ux = ey sin y

Next, we compute the partial derivative of ux with respect to y:

uxy = e^y cos y + ey cos y

Now, we compute the partial derivative of u with respect to y:

uy = exy cos y + exy sin y

Finally, we compute the partial derivative of uy with respect to x:

uyx = exy cos y + exy cos y

Thus, we have:

uxy = e^y cos y + e^y cos y = 2e^y cos y

uyx = exy cos y + exy cos y = 2exy cos y

Since 2e^y cos y = 2exy cos y for all x and y, we can conclude that uxy = uyx. Therefore, the conclusion of Clairaut's theorem holds for the given function u = exy sin y.

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The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.

If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050

The population is given to be increasing exponentially, which means it will follow the equation:

\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.

We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:

\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)

Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.

Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:

\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)

where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)

where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)

Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)

To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):

\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.

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The reliability corresponds to the design factor of 1. 2 is R=0.9616 and d=1.02, for 1.5 R=0.9999 and d=1.14.

To find the reliabilities we first have to find z. There is a formula to find z.

\(z=\frac{n_d-1}{\sqrt{n_d^2C_s^2+C_s_d^2} }\)

Factor c is defined as:

C=sd/u

For the strength, this is simply because we are given μs and sd's so we have

\(C_s=\frac{6.59kpsi}{95.5kpsi}\)

Cs=0.069

For the stress, it's a bit different since we are given the μp and sd p:

sd=4P/πd².

The standard deviation is:

σ=4/πd²*σP

From this we have:

Cσ=σP/⁻P

=5kip/65kip

Cσ=1/13

For nd=1.2 we have:

\(z=-\frac{1.2-1}{\sqrt{1.2^2(0.069)^2+(1/13)^2} }\)

z=-1.77

from table A-10 we see that the probability of failure is 0.0384, meaning the reliability is

R=1-F

R=1-0.0384

R=0.9616

We can express the diameter from 2 equations for stress:

\(\frac{4P}{\pi d^2} =\frac{S}{n_d} - > d=\sqrt{\frac{4Pn_d}{\pi S} } \\\\d=\sqrt{\frac{4.65kips.1.2}{\pi .95.5kpsi} }\)

d=1.02

from nd=1.5 we have:

\(z=-\frac{1.5-1}{\sqrt{1.5^2(0.069)^2+(1/13)^2} }\)

z=-3.88

from table A-10 we see that the probability of failure is 0.0001, meaning the reliability is:

R=1-F

R=1-0.0001

R=0.9999

The diameter is:

\(d=\sqrt{\frac{4.65kips.1.5}{\pi .95.5kpsi} }\)

d=1.14

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Hypothesis test used to test the batting average of the two given team national league and American league is given z-test.

As given in the question,

Given : Mean batting for American league is not equal to Mean batting for National league.

Therefore, hypothesis test used to test the batting average of the national league and American league is given z-test.

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Answer:

∠D'A'B'

Step-by-step explanation:

Answer:

The value of ? is 1004.

Step-by-step explanation:

I'll use x instead of ?:

\(9^x+9^x+9^x=3^{2009}\\3\cdot9^x=3^{2009}\\3\cdot(3^2)^x=3^{2009}\\3\cdot3^{2x}=3^{2009}\\3^{2x+1}=3^{2009}\\2x+1=2009\\2x=2008\\x=1004\)

Answer:

.. f (x) = 3x7 – x4 + 2x3 – 5x2 – 4.

Step-by-step explanation:

Answer:

16

Explanation:

The segment with a length equal to 12 is tangent to the circle, It means that it forms an angle of 90 degrees with the line of the missing length.

So, the formed triangle is a right triangle and we can apply the Pythagorean theorem to solve the question.

Then, since 20 is the hypotenuse of the triangle, we get that the missing side can be calculated as:

So, solving the expression, we get:

Therefore, the segment length is 16.

Answer:

0

Step-by-step explanation:

\(m=\frac{-21-(-21)}{-14-36}\)

Answer: slope = 0  

Step-by-step explanation:

slope = Δy ÷ Δx = (-21 - (-21)) / (-14 -36) = 0 / -5 = 0

It's a horizontal line

Considering that y is between x and z, we have that:

We consider that y is between x and z, hence the length of the segment is given by:

xz = xy + yz

The separate lengths are given as follows:

Hence:

4k + 38 = 3k - 2 + 7k + 4.

4k + 38 = 10k + 2

6k = 36

k = 6.

Hence the length of yz is given by:

yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.

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Answers: Options A and D

Answer:

A. The slope of m is -2/5

and

D. The slope of p is -5/2

Step-by-step explanation:

The slope is defined as the "change in y" over the "change in x" of a line. If you pick two points on a line --- (x1,y1) and (x2,y2) --- you can calculate the slope by dividing y2 - y1 over x2 - x1.

Line m goes through the points (-2,7) and (3,5). Slope = (y2 - y1)/(x2 - x1) = (5 - 7 )/(3 - -2) = -2/5

Line q goes through the points (6,15) and (0,0). Slope = (y2 - y1)/(x2 - x1) = (0 - 15 )/(0 - 6) = -15/-6 = 2.5 = 2 1/2 = 5/2

Line n goes through the points (-5,0) and (0,-2). Slope = (y2 - y1)/(x2 - x1) = (-2 - 0 )/(0 - -5) = -2/5

Line p goes through the points (6,15) and (10,5). Slope = (y2 - y1)/(x2 - x1) = (5 - 15 )/(10 - 6) = -10/4 = -2.5 = -2 1/2 = -5/2

Therfore the only true options are A and D

Step-by-step explanation:

Using Pythagoras theorem:

\( = \sqrt{{20}^{2} - {12}^{2} } \)

\( = \sqrt{400 - 144}\)

\( = \sqrt{256} \)

\( = 16\)