Locate the absolute extrema of the function on the closed interval:
y = 3x^(2/3) - 2x, [-1, 1]

By using the distance formula, the length of BB' on the graph is equal to [tex]\sqrt{29}\;units.[/tex]

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

[tex]Distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points B (0, 2) and B' (5, 4) into the distance formula, we have the following;

[tex]Distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\\\\Distance \;BB'= \sqrt{(5-0)^2 + (4-2)^2}\\\\Distance \;BB'= \sqrt{(5)^2 + (2)^2}\\\\Distance \;BB'= \sqrt{25 + 4}\\\\Distance \;BB'= \sqrt{29}\;units[/tex]

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Since the variance is the square of the standard deviation, the variance here is 6.3.

In statistics, the variance shows how much the values spread out around the mean. The standard deviation is obtained as the square root of the variance of a given value.

Now;

[tex]s = \sqrt{v}[/tex]

s = 2.5

[tex]v = s^2[/tex]

[tex]s = (2.5)^2 =[/tex]6.3

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Answer:

For trapezoids, we have some rules:

The angles always need to ad up to 360°

We also have that the base angles are suplementary, so they need to ad to 180°. (one smaller or equal than 90° and the other greater or equal than 90°)

Then, if the angles are one equal to 60° and the other 45°.

The other two angles are:

a1 = 180° - 60° = 120°

a2 = 180° - 45° = 135°

and now we have: 120° + 60° + 45° + 135° = 360°

for the other we have an angle of 60° and other of 120°.

This two angles can be one next to the other, so may be suplementary.

this mens that the other two angles may be any angles that add to 180° (again, one is less or equal than 90° and the other is greater or equal than 90°)

So we can have:

a1 = 110°

a2 = 70°

for example.

The value of k in the given function is k =3

From the question, the given function is F(x)= kx2

This can be properly written as

[tex]f(x) =kx^{2}[/tex]

Also, from the question, we have that f(2) = 12

Since [tex]f(x) =kx^{2}[/tex]

∴ [tex]f(2) =k(2)^{2}[/tex]

This becomes

[tex]f(2) = k \times 4[/tex]

[tex]f(2) = 4k[/tex]

Now, to determine the value of k, we will input the value of f(2), that is f(2)=12 in the above equation, that is

[tex]f(2) = 4k[/tex] becomes

[tex]12= 4k[/tex]

Now, divide both sides by 4

[tex]\frac{12}{4} = \frac{4k}{4}[/tex]

[tex]3 = k[/tex]

∴ [tex]k = 3[/tex]

Hence, the value of k in the given function is k =3

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The rate at which the epidemic is growing after 10 years is approximately 0.79.

Using the provided formula for the derivative of the population function with respect to time and evaluating it at ( t = 10), we have:

[tex]\[ \frac{dP}{dt} \Bigg|_{t=10} = \frac{-500(20,000)(-0.549)e^{-5.49}}{(1 + 20,000e^{-5.49})^2} \][/tex]

[tex]\[ \approx \frac{-500(20,000)(-0.549)e^{-5.49}}{(1 + 20,000e^{-5.49})^2} \][/tex]

[tex]\[ \approx \frac{-500(20,000)(-0.549)(0.004088)}{(1 + 20,000(0.004088))^2} \][/tex]

[tex]\[ \approx \frac{-500(20,000)(-0.549)(0.004088)}{(1 + 81.76)^2} \][/tex]

[tex]\[ \approx \frac{-500(20,000)(-0.549)(0.004088)}{(82.76)^2} \][/tex]

[tex]\[ \approx \frac{-500(20,000)(-0.549)(0.004088)}{6856.8976} \][/tex]

[tex]\[ \approx \frac{5431.56}{6856.8976} \][/tex]

[tex]\[ \approx 0.7926 \][/tex]

Rounding to two significant digits, the rate at which the epidemic is growing after 10 years is approximately 0.79.

Answer:

To find the rate of growth of the epidemic after 10 years, we'll first differentiate the epidemic curve equation with respect to time (t) and then plug in t = 10 to find the growth rate.

Therefore, after 10 years, the epidemic is growing at a rate of approximately -0.082 (rounded to two significant digits).

Step-by-step explanation:

To determine the rate of growth of the epidemic after 10 years, we'll first differentiate the given epidemic curve equation with respect to time (t) using the quotient rule and the chain rule of differentiation.

Let [tex]\( P = \frac{500}{1 + 20,000e^{-0.549t}} \)[/tex].

To differentiate P with respect to t, we'll use the quotient rule:

[tex]\[ \frac{dP}{dt} = \frac{d}{dt} \left( \frac{500}{1 + 20,000e^{-0.549t}} \right) \]\[ = \frac{0 - 500 \times \frac{d}{dt}(1 + 20,000e^{-0.549t})}{(1 + 20,000e^{-0.549t})^2} \][/tex]

Now, we'll find [tex]\( \frac{d}{dt}(1 + 20,000e^{-0.549t}) \)[/tex] using the chain rule:

[tex]\[ \frac{d}{dt}(1 + 20,000e^{-0.549t}) = 0 - 20,000 \times (-0.549)e^{-0.549t} \]\[ = 10,980e^{-0.549t} \][/tex]

Substituting this back into the differentiation of P:

[tex]\[ \frac{dP}{dt} = \frac{-500 \times 10,980e^{-0.549t}}{(1 + 20,000e^{-0.549t})^2} \][/tex]

Now, we'll find the growth rate after 10 years by plugging in [tex]\( t = 10 \)[/tex] into [tex]\( \frac{dP}{dt} \)[/tex]:

[tex]\[ \frac{dP}{dt} \bigg|_{t=10} = \frac{-500 \times 10,980e^{-0.549 \times 10}}{(1 + 20,000e^{-0.549 \times 10})^2} \]\[ \approx \frac{-500 \times 10,980 \times e^{-5.49}}{(1 + 20,000e^{-5.49})^2} \]\[ \approx \frac{-500 \times 10,980 \times 0.004056}{(1 + 20,000 \times 0.004056)^2} \]\[ \approx -0.082 \][/tex]

Thus, after 10 years, the epidemic is growing at a rate of approximately -0.082 (rounded to two significant digits).

Answer:

No, it is 3x-5 and r=0

Step-by-step explanation:

We can do it by long division method  the required quotient is 3x-5 and r=0

not 3x-1 , r=1

multiply the divisor with 3x  we will get [tex]3x^2+9x[/tex]to cancel out the first term of dividend

Now after solving we will get [tex]-5x-15[/tex]

Now, multiply the divisor by -5 we will get -5x-15 which will cancel the entire dividend.

Answer:  The correct option is

(B) $122.08.

Step-by-step explanation:  Given that Ira bought a tennis racquet that cost $112 and the sales tax rate is 9 percent.

We are to find the total amount that Ira paid.

The total amount Ira paid is the sum of the cost price and the sales tax.

The sales tax paid by Ira is given by

[tex]S_t=9\%\times 112=\dfrac{9}{100}\times112=\dfrac{1008}{100}=10.08.[/tex]

Therefore, the total amount paid by Ira will be

[tex]A_p=112+S_t=112+10.08=122.08.[/tex]

Thus, the total amount paid by Ira is $122.08.

Option (B) is CORRECT.

Answer:

The correct option is

(B) $122.08.

Step-by-step explanation:

Plzz visit my profile and help me with my questions.

Answer:64 %

Step-by-step explanation:

Given if it rains John Plays piano is 0.8

i.e. if it rains probability that john will not play is 0.2

If it not rain Then probability that john will play piano is 0.4

he will not play is 0.6

Given if there is 60 % chance that it will rain tomorrow  

Thus Pobability that john will play is

[tex]=Probability\ that\ it\ will \times Probability\ john\ will\ play+Probability\ it\ will\ not\ rain\times Probability john will play[/tex]

[tex]=0.6\times 0.8+0.4\times 0.4=0.48+0.16=0.64[/tex]

Answer:

the answer is a hope it helps.

Step-by-step explanation:

Answer:

Plane Z

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct answer is the number of minutes the students studied. The student's grades is dependent on how long they studied. The domain is the independent variable or the amount of time.

Final answer:

The domain in a scatterplot of study time versus test grades represents all the reported study times of the students. It is visualized by plotting this data on a dot plot or analyzing the distribution to see the correlation between study time and grades.

Explanation:

The domain of a function in mathematics represents the set of all possible input values it can accept, typically the x-values on a graph. In the context of a scatterplot of time studying versus test grades created by a math teacher, the domain would consist of the various amounts of time that students reported studying. Analyzing the distribution of these values can showcase how study time correlates to test performance, assuming that this is a function with a one-to-one correspondence between study time and grade received, passing the vertical-line test.

To create a dot plot, as suggested in a collaborative classroom exercise, you would align a number line with the possible amounts of study time and place a dot above the corresponding value for each student's reported study time. Through this process, you could visualize the amount of study time on the x-axis and gain insights into the study habits of the class.

In a given scenario like the one described for Ms. Phan studying for an economics exam, the total benefit and the expected total gain in her score could be plotted to visualize the marginal benefits of additional study hours. This helps to understand the concept of diminishing returns in relation to study time and test score improvement.

To solve this linear differential equation, we can use the method of characteristic equation. The general solution is y = (c1 + c2x + c3x^2)e^(2x), where c1, c2, and c3 are constants.

To solve this linear differential equation, we can use the method of characteristic equation. Let's assume that the solution is of the form y = e^(rx). Substituting this in the given equation, we get the characteristic equation as r^3 - 6r^2 + 12r - 8 = 0. This can be factored as (r - 2)^3 = 0. So, the characteristic roots are r = 2, 2, and 2.

Since we have repeated roots, the general solution is given by y = (c1 + c2x + c3x^2)e^(2x), where c1, c2, and c3 are constants.

Therefore, the general solution to the linear differential equation y''' - 6y'' + 12y' - 8y = 0 is y = (c1 + c2x + c3x^2)e^(2x), where c1, c2, and c3 are constants.

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Answer: 36.1 hours

Step-by-step explanation:

Given: The amount someone earns for each hour worked = [tex]\$6.25[/tex]

The expected amount to earn by work = [tex]\$225.65[/tex]

Now, to find the number of hours work to earn the expected value , we divide the expected value by the hourly rate, we get

The  number of hours work to earn [tex]\$225.65\ =\frac{225.65}{6.25}=36.104\approx36.1[/tex]  

Hence, the number of hours work to earn  [tex]\$225.65[/tex] about 36.1 hours.

Ann could pick from 1800 different 4-digit numbers that are multiples of 5, considering the range of possible digits for each position and the requirement that it must be a multiple of 5.

To determine how many different 4-digit numbers that are multiples of 5 Ann could pick, we need to consider three things:

The first digit can be anything from 1 to 9 (since the number cannot start with zero).

The second and third digits can be anything from 0 to 9.

The fourth digit must be either 0 or 5 (since the number is a multiple of 5).

For each of the first three digits, we have 9 possible choices (1-9 for the first digit, 0-9 for both the second and third digits), and for the last digit, we have 2 possible choices (0 or 5). Using the counting principle, we multiply the number of choices for each digit together to find the total number of possible 4-digit multiples of 5 Ann can pick:

9 (first digit) × 10 (second digit) × 10 (third digit) × 2 (fourth digit) = 1800 different 4-digit multiples of 5.

So, Ann could pick from 1800 different 4-digit numbers that are multiples of 5.

Answer:

Linear

Step-by-step explanation:

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