Find a mathematical model that represents the statement. (Determine the constant of proportionality.)
P varies directly as x and inversely as the square of y. (P = 23 - when x = 84 and y = 12.)
LARCOLALG10 3.5.059

If the given function is f '(t) = 16/(1 + t²), the value of the function f will be f = 16 tan (t) - 24.8.

It is described as a particular kind of relationship with a set domain and range. Every value in the domain has a specific relationship with one value in the range, according to the function.

Given that,

f '(t) = 16/(1 + t²)

f(1) = 0

In order to find f integrate the function,

f = ∫(16/(1 + t²)) dt

f = 16 ∫1/(1 + t²) dt

f = 16 tan t + C

As, f(1) = 0

0 = 16 tan 1 + C

C = - 16(1.55) = -24.8

Thus, the value of function is f = 16 tan (t) - 24.8.

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Answer:cause why not

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Let x = number of people at the party.

0.9x wore red dresses.

2/25x wore green dresses.

rest of people wore white dresses

The rest of the people is

x - 0.9x - 2/25 x

x - 0.9x - 0.08x = 15

0.02x = 15

x = 750

0.9x = 675 (red)

2/25 x = 60 (green)

0.02x = 15 (white)

Answer: 60

The surface area of the cube is increasing at a rate of 49 cm²/min.

If the length of an edge of a cube is l cm.,

its volume V is l3 and surface area A is 6l2.

Differentiating V=l3 w.r.t. time,

we get,

dV/dt = 3l2dldt

dV/dt=10 cm3min,

when l=90

dl/dt=103×902

=12430

As A=6l2

dA/dt =12l×dldt

=12×90×12430

=49 cm2min

The total number of cubic units that a cube occupies in three dimensions is its volume. Six faces, twelve edges, and eight vertices make up the three-dimensional shape of a cube. Therefore, the area encircled by a cube's six faces is considered to equal its volume.

It differs from 2D shapes in that it adds a third dimension, known as height or thickness, in addition to length and breadth.

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The approximation of [tex]f_x(3,5)[/tex] using the contour diagram of f(x, y) is [tex]-\frac{2}{3}[/tex]

As per the given data we have determine the value of approximation of [tex]f_x(3,5)[/tex] using the contour diagram of f(x, y).

A contour or a contour line may be defined as the line of intersection of a level surface with the surface of ground.

This means every point on a contour line has the same altitude as that of the assumed intersecting surface.

The set of the curves f(x, y)=c

From the given contour plot the curves intersects with the line y = 5 are f( x,  y ) = 12 and f (x, y) = 10

f(x, y) = 12 intersects the line y = 5 at the point x = 3

So, f(3,5) = 12

f(x, y) = 10 intersects the line y = 5 at the point x = 6

so, f(6,5) = 10

[tex]$f_x(3,5)= \lim _{h \rightarrow 0} \frac{f(3+h, 5)-f(3,5)}{h}$[/tex]

Where approximate h = 3

[tex]f_x(3,5) & =\frac{f(3+3,5)-f(3,5)}{3}[/tex]

[tex]=\frac{f(6,5)-f(3,5)}{3}[/tex]

[tex]=\frac{10-12}{3}[/tex]

[tex]f_x(3,5) & =\frac{-2}{3}[/tex]

Therefore the answer is [tex]-\frac{2}{3}[/tex].

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Approximate  [tex]f_x(3,5)[/tex] using the contour diagram of f(x, y) shown below.

Diagram attached at the end of solution

Answer:

The correct answer would be 0.94 per pound.

Step-by-step explanation:

Answer:$785

Step-by-step explanation:

since she took money out already you have to add the to the pre existing total.

Answer:

Please read the assumptions that lead to the proposed answer of options a, b, and e being correct.  Options c and d are easily rejected.  The question is ambiguous about the locations of the angles.

Step-by-step explanation:

Parallel lines have slopes that are identical.  Lines p and q have the same slopes.

It is difficult imagining what angles are represented by x, y, and z.  There are only 2 lines, and they do not intersect.  The locations of the angles are not identified.  The lack of an intersecting point means it is free range as to where we assign the angles.

The attached graph illustrates some possibilities for x, y, and z.  It uses two simple equations as examples, with the same slope to make them parallel.  Assinment of any angles requires the use of an imaginary line that intersects the two parallel lines.  Even then, there aren't many unique locations for the angles.  To illustrate the analysis, lets assign the angles x, y, and z to thelocations shown on the graph.  

Even with this huge step, there is limited information to be able to identify which of the answer options is correct.  We can say that:

x = z

x+y=180

y+z=180

The answer options (below) appear to have similar relationships, so let's agree that the use of the imaginary line, plus the locations of x, y, and z are valid.  Looking at the answer options, we can match choices a, b, and e to the conclusions above.  d makes no sense because it is not an equation.  c says that both lines must be perpendicular to the x axis, a limitation that is relatively immaterial to whether they are parallel.  The condition of being parallel depends on those two angles being the same (e.g., 45 and 45, 22 and 22, etc.) and not require that they both be 90.

Answer Options               Guarantee Parallel?

a. x = z                                     Yes

b. x + y = 180 degree              Yes

c. x + z = 180 degree              No

d. x + y                                     No

e. y + z = 180                           Yes

The number of miles the whole trip is 15 miles

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The number of miles the whole trip is 15 miles.Given that, Liam's family has completed 40% of a trip.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of miles be x.

so, 40% of x=30

⇒ 40/100 ×x=30

⇒ 0.4x=30

⇒ x=30/0.4

⇒ x=12 miles

Therefore, the number of miles the whole trip is 15 miles.

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15 quarts are required to plan ice cream party for 60 students which is

[tex]\frac{1}{4}[/tex] th fraction of quart.

1 quarts = 4 cups

so 1 cup = [tex]\frac{1}{4}[/tex] th fraction of quart

so in  order to plan party for 60 students we need 60 cups as it is mentioned that each student gets 1 cup of ice cream.

and 1 quarts = 4 cups

so let we need x quarts for the planning of ice cream party

so total cups = 4 *x

so 4*x =60  , x= 60/4 , x=15

so 15 quarts are required for the ice cream party of 60 students  .

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The probability that the distance between the two points is more than 1/3 is 0.

The length of the given line segment is 1, so the two points chosen independently at random cannot be more than 1 unit apart.

That is, the maximum distance between the two points is 1. However, the question states that we are looking for the probability that the distance between them is more than 1/3.

Since the maximum distance between the two points is 1, and 1/3 is less than 1, it is impossible for the distance between them to be more than 1/3. Therefore, the probability that the distance between the two points is more than 1/3 is 0.

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Answer:

18

Step-by-step explanation:

[tex]6/ 1/3[/tex] =

6 x 3

18

Answer:

y = 2x - 7

Step-by-step explanation:

y = mx + b

m is known (m=2):

y = 2x + b

Since one point is known (3,-1), you can solve for b:

-1 = 2(3) + b

b = -7

So the equation is:

y = 2x - 7

The number of homes in a community of 12, 000 which would be heated by electricity, given the rate of houses heated, is c. 3,360 homes

To find the number of homes in the community which would be heated by electricity, first find the percentage of homes that are heated according to the U.S. Census :

= Number of houses heated / Total number

= 7 / 25

= 28 %

When given a community of 12, 000 homes therefore, the number of homes which would be heated are:

= Percentage of houses heated x Community size

= 28 % x 12, 000

= 3,360 homes

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Answer:

c. 3,360 homes

Step-by-step explanation:

Answer:

Step-by-step explanation:

for n=1 it is 7(1+2)=21

for n=2 it is 7(2+2)=28

for n=3 it is 7(3+2)=35

The length of shorter leg is 15 inches, length of longer leg is 36 inches and the length of hypotenuse is 39 inches.

What is right triangle?

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or formerly a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angle.

Let,

x = Longer leg of triangle

y = Shorter leg of triangle

h = Hypotenuse of triangle

Given: The length of the longer leg of a right triangle is 6inches more than twice the length of the shorter leg.

The length of the hypotenuse is 9inches more than twice the length of the shorter leg.

⇒  x = 6 + 2y

   h = 9 + 2y

The given triangle is a right angled triangle.

⇒                                 x^2 + y^2 = h^2

                         (6 + 2y)^2 + y^2 = (9 + 2y)^2

               36 + 24y + 4y^2 + y^2 = 81 + 36y + 4y^2

                         36 + 24y + 5y^2 = 81 + 36y + 4y^2

36 - 81 + 24y - 36y + 5y^2 - 4y^2 = 0

                            -45 - 12y + y^2 = 0

                              y^2 - 12y - 45 = 0

                      y^2 - 15y + 3y - 45 = 0

                       y(y - 15) + 3(y - 15) = 0

                                (y - 15)(y + 3) = 0

y - 15 = 0,   y + 3 = 0

y = 15,     y = -3

Since the length is not negative.

So, y = 15

Hence,

Shorter leg = 15 inchs

Longer leg = 6 + 2y = 6 + 2(15) = 36 inches

Hypotenuse = 9 + 2y = 9 + 2(15) = 39 inches

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Answer:

y = -6x - 4

Step-by-step explanation:

Slope intercept form:

y = mx + b

m is the slope

b is the y-intercept

To find the slope, you take two points from the line and plug them into the following equation:

[tex]\frac{y2-y1}{x2-x1}[/tex]

Let's use (0, -4) and (-2, 8):

[tex]\frac{8-(-4)}{-2-0} = \frac{12}{-2}=-6[/tex]

So m = -6

We know that the y-intercept (b) is -4, so we can plug everything into the equation:

y = -6x - 4

1) The inequality used in graph is;

⇒ x > -2

2) The solution for t will be;

⇒ t > - 2

3) The graph of - 3y > 6 is shown in figure.

4) The graph of y/2 < - 3 is shown in figure.

5) The graph of 4y > 3x - 1 is shown in figure.

A relation by which we can compare two or more mathematical expression is called an inequality.

Now,

1) By the graph, we get;

The solution of the graph is,

⇒ x > - 2

Thus, The used inequality is '>'.

2) The inequality is,

⇒ 2t + 7 > - 3 (t + 1)

Solve for t as;

⇒ 2t + 7 > - 3t - 3

⇒ 2t + 3t > - 3 - 7

⇒ 5t > - 10

⇒ t > - 2

3) The inequality is,

⇒ - 3y > 6

⇒ - y > 2

⇒ y < - 2

4) The inequality is,

⇒ y/2 < - 3

⇒ y < - 6

5) The inequality is,

⇒ 4y > 3x - 1.

Thus, The graph of 4y > 3x - 1 is shown in figure.

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The answer is 0.109, or choice B. The probability that only six of 8 Internet users buy their clothes exclusively online is 0.109.

The probability that only 6 out of 8 Internet users buy their clothes exclusively online can be calculated using the binomial distribution. The probability of a single Internet user buying their clothes exclusively online is 0.5, and the probability of an Internet user not buying their clothes exclusively online is 0.5.

The probability of 6 out of 8 Internet users buying their clothes exclusively online can be calculated using the formula:

P(X=6) = (8 choose 6) * (0.5)^6 * (0.5)^2

Plugging in the values, we get:

P(X=6) = (8 choose 6) * (0.5)^6 * (0.5)^2

= 28 * (0.5)^6 * (0.5)^2

= 28 * (0.015625) * (0.25)

= 0.109

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Complete Question:

Fifty percent of the people that use the Internet buy their clothes exclusively online. Find the probability that only six of 8 Internet users buy their clothes exclusively online. Round to three decimal places.  explain answer in 100 words.

A. 0.750

B. 0.109

C. 0.438

D. 0.004

The probability that he or she actually used steroids is 0.779.

The test is accurate 95% of the time when an athlete has taken steroids. It is 97% accurate when an athlete hasn't taken steroids. Suppose that the drug test will be used in a population of athletes in which 10% have actually taken steroids. Let's choose an athlete at random and administer the drug test.

Based on prior knowledge of conditions that might be related to the event, Bayes' theorem, which is named after Thomas Bayes and is used in probability theory and statistics, describes the probability of an event.

Using Baye's theorem:

P(steroids | positive) = P(steroids)*P(positive|steroids) / P(positive) = (0.10*0.95)/0.122 = 0.779

If the selected athlete passes the test, the probability that they used steroids: 0.779

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(complete question)

A company has developed a drug test to detect steroid use by athletes. The test is accurate 95% of the time when an athlete has taken steroids. It is 97% accurate when an athlete hasn’t taken steroids. Suppose that the drug test will be used in a population of athletes in which 10% have taken steroids. Let’s choose an athlete at random and administer the drug test.

Suppose that the chosen athlete tests positive. What’s the probability that he or she used steroids?

Answer:

Your answer is B

Step-by-step explanation:

[tex]\frac{1}{4}x-5 < -6\\\\\frac{1}{4}x < -1 \\\\[/tex]

Multiply 4 to both sides leaving x by itself.

x < -4

Remember when you divide or multiply a negative to solve for x you switch the signs of greater than to less than or vice versa.

bit strings of length 12 contain a) exactly three 1s is 220 b) at most three 1s is 2700 c) atleastthree1s is 220 d) an equal number of 0s and 1s is 66.

a) To calculate the number of bit strings of length 12 containing exactly three 1s, we can use the combination formula. The formula is nCr, where n is the total number of bits (12) and r is the number of 1s (3).The solution is 12C3 = 220.

b) To calculate the number of bit strings of length 12 containing at most three 1s, we can use the summation formula. The formula is sum of nCr, where n is the total number of bits (12) and r is the number of 1s (3). So, the answer is (12C0 + 12C1 + 12C2 + 12C3) = 2700.

c) To calculate the number of bit strings of length 12 containing at least three 1s, we can use the combination formula. The formula is nCr, where n is the total number of bits (12) and r is the number of 1s (3). The solution is 12C3 = 220.

d) To calculate the number of bit strings of length 12 containing an equal number of 0s and 1s, we can use the combination formula. The formula is nCr

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Answer:

the answer will be 4.75 units

Step-by-step explanation:

explained

The midsegment of a trapezoid is a line segment that connects the midpoints of the nonparallel sides of the trapezoid. To find the length of the midsegment, we need to first find the midpoints of the sides IJ and KL.

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. We can find the midpoint of a line segment by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.

The coordinates of the endpoints of the side IJ are (-3, -5) and (8, -5), so the midpoint of this side is:

((-3 + 8)/2, (-5 + (-5))/2) = (2.5, -5)

The coordinates of the endpoints of the side KL are (-3, -9) and (3, -9), so the midpoint of this side is:

((-3 + 3)/2, (-9 + (-9))/2) = (0, -9)

To find the length of the midsegment, we can use the distance formula to find the distance between the two midpoints:

sqrt((2.5 - 0)^2 + (-5 - (-9))^2) = sqrt(2.5^2 + 4^2) = sqrt(6.25 + 16) = sqrt(22.25) = 4.75

Therefore, the length of the midsegment of the trapezoid is approximately 4.75 units.

Answer: The first word in the alternative statistical hypothesis for an experiment with three levels of a single independent variable (IV) is "differences." This is because the alternative hypothesis typically involves the existence of differences between the levels of the IV.

Step-by-step explanation:

Here is how to formulate the alternative hypothesis for an experiment with three levels of a single IV:

Identify the independent variable (IV) and the levels of the IV. In this case, there is a single IV with three levels.

Determine the relationship between the IV and the dependent variable (DV). In other words, consider how the levels of the IV may affect the DV.

Write the alternative hypothesis in terms of the relationship between the IV and the DV. The alternative hypothesis should state that there are differences between the levels of the IV in their effect on the DV.

For example, if the IV is "type of exercise" and the levels are "running," "cycling," and "swimming," and the DV is "improvement in cardiovascular fitness," the alternative hypothesis might be "There are differences in the improvement in cardiovascular fitness between the three types of exercise."

What is the null hypothesis in an experiment?

The null hypothesis in an experiment is a statement that there is no relationship between the IV and the DV, or that there are no differences between the levels of the IV in their effect on the DV. The null hypothesis is typically denoted as H0. In the example given above, the null hypothesis might be "There is no difference in the improvement in cardiovascular fitness between the three types of exercise."

This means that the hypothesis is testing whether there are significant differences between the means of the three levels of the IV. Therefore, the first word in the alternative statistical hypothesis for any experiment with three levels of a single IV is "differences."

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The first word in the alternative statistical hypothesis for any experiment with three levels of a single IV is "difference," which refers to the difference between the means of the three levels of the IV.

What is hypothesis?

Hypothesis is an educated guess or prediction made in response to a question or problem. It is based on prior knowledge and experience, as well as available evidence. The purpose of a hypothesis is to suggest a possible explanation for an observed phenomenon and then to test the validity of the hypothesis through further research or experimentation. If the hypothesis is proven correct, it can become a theory. Hypotheses can also be disproven or modified through further testing.

This is a reference to the null hypothesis, which states that there is no difference between the means of the different levels of the IV. The alternative hypothesis is that there is a difference between the means of the different levels of the IV.

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A correct statement about sampling distributions is: Sampling distributions of means get closer to normality as the sample size increases.

The correct answer is an option (A)

In this question we have been given few statements.

We need to select a correct statement about sampling distributions.

We know that the sampling distribution is nothing but a probability distribution that is obtained through repeated sampling of a specific population.

Also according to central limit theorem, sampling distribution of means approaches normal when the sample size increases.

Therefore Sampling distributions of means get closer to normality as the sample size increases.

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A power series representation for the function is:

x^8 tan^-1(x^3) = ∑[n = 0 to ∞]  (-1)^n (x^(6n + 11)/2n + 1)

In this question we need to find a power series representation for the function.

f(x) = x^8 tan^-1(x^3)

We know that the Maclaurin series:

1/(1 - x) = ∑[n = 0 to ∞] x^n

Replacing x with -x^2 we get,

1/(1 + x^2) = ∑[n = 0 to ∞] (-x^2)^n

               = ∑[n = 0 to ∞] (-1)^n x^2n

Integrating above equation we get,

tan^-1(x) = ∑[n = 0 to ∞]  (-1)^n (x^(2n + 1)/2n + 1) + c

For x = 0 we get c = 0

so, tan^-1(x) = ∑[n = 0 to ∞]  (-1)^n (x^(2n + 1)/2n + 1)

Now we replace x by x^3, we get,

tan^-1(x^3) = ∑[n = 0 to ∞]  (-1)^n (x^3(2n + 1)/2n + 1)

Therefore, the required power series would be,

x^8 tan^-1(x^3) = ∑[n = 0 to ∞]  (-1)^n (x^(6n + 11)/2n + 1)

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Answer:

Step-by-step explanation:

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