As a hive of bees makes and uses its honey, the bees are adding honey at a rate described by the function h(t) over the first 2 years, at what time t is the amount of honey in the hive the most? What is the maximum value?

Answer:

Step-by-step explanation:

Tangent line is:

Perpendicular line to this has a slope of -3 and passes through  point (1, 2).

Its equation is:

Using the second line passing through the center, find the coordinates of the center:

Solve the system by elimination:

Then

The center is (0, 5) and radius is the distance from center to point (1, 2):

The equation of circle:

Number of ways to roll 5 distinct dice and get 3 of a kind is 7200

To find the number of ways to roll 5 distinct dice and get 3 of a kind:

Choose which number appears three times. There are 6 possible choices.

Choose which three dice will show the chosen number. There are 5 ways to choose the first die, 4 ways to choose the second die, and 3 ways to choose the third die, for a total combinations 5 x 4 x 3 = 60 ways.

Choose the numbers that the remaining two dice will show. There are 5 choices for the first die and 4 choices for the second die, but the order in which we choose them doesn't matter, so we need to divide by 2 to correct for overcounting. This gives us (5 x 4) / 2 = 10 ways.

Choose which of the two remaining dice will show the first chosen number. There are 2 choices.

Multiply all of the choices together: 6 x 60 x 10 x 2 = 7,200.

Therefore,  there are 7,200 ways to roll 5 distinct dice and get 3 of a kind.

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Answer:  Choice (3)

2 + log(a) + 2*log(b)

======================================================

Work Shown:

The log rules we'll use are

So,

c = log(100ab^2)

c = log(100) + log(a) + log(b^2) ......... use log rule 1

c = log(10^2) + log(a) + log(b^2)

c = 2*log(10) + log(a) + 2*log(b) ......... use log rule 2

c = 2*1 + log(a) + 2*log(b) .................... use log rule 3

c = 2 + log(a) + 2*log(b)

Note: The use of rule 3 assumes that all logs shown are in base 10, which is the default assumed base. Rule 3 doesn't work for any general base. The more generalized rule is \(\log_b(b) = 1\). If b = 10, then we get rule 3 above.

Answer:

The expression from part B is = (1 • 2) • (106 • 10-8).

Multiply the first factors.

1 • 2 = 2

Multiply the powers of 10 using this property of exponents: anam = an + m.

106 • 10-8 = 106 + (-8) = 10-2

The expression is 2 × 10-2.

Step-by-step explanation:

This is Plato and edmentumm sample response. Please paraphrase other wise you will get in trouble. I'm sorry if I'm late!

Answer: Mean is 7 and median is 7

Step-by-step explanation:

2+6+3+10+9+8+10+6+6+10/10

=7

2,3,6,6,6,8,9,10,10,10

6+8/2

=7

Answer:

Terry= mean is 7, median is 7

David= mean is 4.4, median is 4

Step-by-step explanation:

I do not really understands what it means by compare them.

Answer:

p(2) = 0

Step-by-step explanation:

p(2) = 3(2)(2-2)

p(2) = 6(2-2)

p(2) = 6(0)

p(2) = 0

Answer:

152

Step-by-step explanation:

The composition (fog)(5) is equal to 38. We substitute 5 into g(x) to find g(5) = -6. Then, substituting -6 into f(x), we get f(-6) = 38.

To find (fog)(5), we need to substitute the value of 5 into g(x) and then use the resulting expression as the input for f(x).

Evaluate g(5)

We substitute x = 5 into g(x) to find g(5):

g(5) = -(5) - 1

g(5) = -6

Evaluate f(g(5))

Now that we know g(5) is equal to -6, we substitute -6 into f(x):

f(g(5)) = f(-6)

f(-6) = (-6)² + 2

f(-6) = 36 + 2

f(-6) = 38

Simplify the result

The final step is to simplify the result to the nearest tenth. In this case, the value is already a whole number, so we don't need to make any further adjustments. Therefore, (fog)(5) = 38.

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Answer:what is the questionStep-by-step explanation:

The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer: Real, equal, rational.

Step-by-step explanation:

\(-x^2-8x-16=0\\-(x^2+8x+16)=0\\Multiply \ the\ left \ and\ right \ sides\ of\ the\ equation\ by \ -1:\\x^2+8x+16=0\\x^2+2*x*4+4^2=0\\(x+4)^2=0\\x+4=0\\x=-4.\)

Both the median and the range changed, the correct option is A.

Median, in statistics, is the middle value of the given list of data, when arranged in an order.

The data set that contains the outlier is given as:

4, 14, 15, 15, 16, 16, 18, 19, 20, 20, 21

The minimum value of the data is: 4

The median or middle quartile i.e. \(\rm Q_2\)  is the central tendency of the data and exists in the middle of the data.

The median is: 16

Also, the lower set of data is:

4,14,15,15,16

The lower quartile i.e. \(\rm Q_1\)  is the median of the lower set of data.

The  lower quartile i.e. \(\rm Q_1\) = 15

Similarly, the upper set of data is:

18, 19, 20, 20, 21

the upper quartile i.e. \(\rm Q_3\)  is the median of the upper set of data.

upper quartile i.e. \(\rm Q_3\) = 20

Also, the interquartile range is:

\(\rm Q_3-Q_1=20-15=5\)

The maximum value of the set is 21.

Range = Maximum value-Minimum value =21 - 4 = 17

As we know that 4 is the outlier of the data as it is the smallest as compared to all the data points.

After removing the outlier the data set is:

14, 15, 15, 16, 16, 18, 19, 20, 20, 21

The minimum value of the set =14

The maximum value of set =21

Range = Maximum value-Minimum value =21-14 = 7

Hence, Both the median and the range changed.

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Answer:

  2048/3 π cubic units

Step-by-step explanation:

You want the exact volume of a sphere with radius 8 units.

The volume of a sphere is given by the formula ...

  V = 4/3πr³

  V = 4/3π(8³) = 2048/3·π . . . . cubic units

The volume of the sphere is 2048/3·π cubic units.

__

Additional comment

That's (682 2/3)π.

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Equivalent to the original implication, "if you win the lottery, then you will be rich," are statements (d), (h), (j), and (1). Equivalent to the converse of the implication are statements (b), (e), (i), and (k).

The original implication states that winning the lottery leads to being rich. The equivalent statements are those that express the same relationship, while the converse of the implication reverses the order of the events.

Equivalent to the original implication:

(d) You will be rich if you win the lottery.

(h) You will be rich only if you win the lottery.

(j) If you are rich, you must have won the lottery.

(1) You will win the lottery if and only if you are rich.

Equivalent to the converse of the implication:

(b) Either you don't win the lottery or else you are rich.

(e) You will win the lottery if you are rich.

(i) Unless you win the lottery, you won't be rich.

(k) If you are not rich, then you did not win the lottery.

Not equivalent to either the implication or its converse:

(a) Either you win the lottery or else you are not rich.

(c) You will win the lottery and be rich.

(f) It is necessary for you to win the lottery to be rich.

(g) It is sufficient to win the lottery to be rich.

These statements do not capture the exact relationship between winning the lottery and being rich or its converse.

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well, let's take a looksie, hmm the sector is really a sector with a central angle of 90°, wait a second!! a circle has a total of 360°, so 90°+90°+90°+90° = 360°, so 90°is really just one quarter that of a circle.

Now, if we just get the whole area of the circle, then grab only one quarter of that, we'll be set, yeahhhh!!

\(\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies A=\pi (9)^2 \\\\\\ \stackrel{\textit{one quarter of that}}{\cfrac{1}{4}\cdot \pi (9)^2}\implies \cfrac{81\pi }{4}\implies \cfrac{81(3.14)}{4} ~~ \approx ~~ \text{\LARGE 63.6}\)

Answer:

-25

Step-by-step explanation:

-10--25=15

Answer:

Step-by-step explanation:

If 60cm is the outer diameter of the rim, then the rim without a tire would travel 188.50 (not 188.4) cm per revolution. There will of course be a tire, and the extra diameter of wheel+tire will increase the distance traveled by the bike. If e.g. the tire is 3cm from bead to outermost tread (and is properly inflated), then the extra circumference would be 2 x 3cm x pi = 18.850cm of distance traveled, for a total of just over 207.3 cm per revolution.

Answer:

False I believe

Step-by-step explanation:

Scaling transformation onto the x co ordinate by a factor of 5.

A co-ordinate system represents two points one for x axis and another for y axis in a ordered pair (x,y)

According the given question Point (w, z) is transformed by the rule (w5, z).

Here w represents x co-ordinate points and z represents y co-ordinate points.

We can observe that the x co-ordinate point have been scaled by a factor of 5.We can think of that after this transformation the line has become less steeper from origin.

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The final equation of the curve is y = -x + (1/2)x^3 - 2/3 log(x^3 - y) + 2/3 log(x^3) + 2/3.

To find a curve y = y(x) through the point (1, -1) such that the tangent to the curve at any point (x0, y(x0)) intersects the y-axis at y = x0^3, we can use the method of differential equations.

Let the curve be represented by y = f(x).

Then, the slope of the tangent line at any point (x0, y(x0)) on the curve is given by dy/dx evaluated at x = x0.

We know that the tangent line intersects the y-axis at y = x0^3.

Hence, the point of intersection is (0, x0^3).

The equation of the tangent line can be written in the point-slope form as follows: y - y(x0) = (dy/dx)|x

=x0 * (x - x0)

Using the point of intersection (0, x0^3),

we get: x0^3 - y(x0) =

(dy/dx)|x=x0 * (-x0)Simplifying the above equation,

we get: (dy/dx)|x=x0

= (y(x0) - x0^3) / x0

Now, we can write this equation in the differential form as follows: dy/dx = (y - x^3) /x Integrating both sides of the above equation, we get

∫[1, x] dy / (y - x^3)

= ∫[1, x] dx / x

Using partial fractions, we can write the left-hand side as follows:

A / (y - x^3) + B / y = 1 / x

Multiplying both sides by xy(y - x^3),

we get: Axy + Bxy - Bx^3

= y - x^3

Solving for A and B, we get:

A = 1 / x^3 and B = -1 / (x(x^3 - y))

Hence, we get the following integral equation:∫[-1, y] dy / (y - x^3) + ∫[1, x] dx / x = 0

Solving the above equation for y, we get: y = -x + Cx^3 - 2/3 log(x^3 - y) + 2/3 log(x^3) + 2/3

where C is a constant of integration. Using the initial condition y(1) = -1,

we get:C = -1/2

Hence, the equation of the curve is:y = -x + (1/2)x^3 - 2/3 log(x^3 - y) + 2/3 log(x^3) + 2/3: We started by assuming that the curve can be represented by y = f(x).

Then, we used the fact that the slope of the tangent line at any point (x0, y(x0)) on the curve is given by dy/dx evaluated at x = x0.

We know that the tangent line intersects the y-axis at y = x0^3. Hence, the point of intersection is (0, x0^3).Using the point-slope form of the equation of a line, we derived an expression for the slope of the tangent line at any point (x0, y(x0)).

Then, we used this expression to write the differential equation dy/dx = (y - x^3) / x that the curve must satisfy.

We then integrated both sides of this equation to obtain the integral equation ∫[-1, y] dy / (y - x^3) + ∫[1, x] dx / x = 0. Solving this equation for y, we obtained the equation of the curve. Using the initial condition y(1) = -1, we determined the constant of integration C.

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Explanation:

Let's go over the possible choices to see which statements are true and which are false.

To summarize, only choice B is true. The rest are false.

The answer is (f . g)(x) = - (34k + 17k⁷ + 17k⁵ + 40k³ + 20k² + 60).

Remember that :

(f . g)(x) = f(x) × g(x)

Hence :

at initial the number of dogs were , 18 dogs

final number of dogs is 18 - 6 = 12

so the percentage change is

so the change is 33.33%.

The distribution for X is a negative binomial distribution, denoted as nb(x;6, 188​), with parameters r = 6 (number of successes), p = 8/18 (probability of success in each trial).

To compute the probabilities:

P(X = 2): nb(2;6, 8/18)

P(X ≤ 2): nb(0;6, 8/18) + nb(1;6, 8/18) + nb(2;6, 8/18)

P(X ≥ 2): 1 - P(X < 2) = 1 - P(X ≤ 1)

To calculate the mean value and standard deviation of X:

Mean (μ) = r * (1 - p) / p

Standard Deviation (σ) = sqrt(r * (1 - p) / (p^2))

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each toss results in 2 possible outcomes, head or tail so the number of possible outcomes for 7 would be

Answer:

2^7

2x2x2x2x2x2x2 = 2^7

Answer:

the answer is 16 hahaha