the relationship between x and y is proportional. when x is 3 and y is 15. what is x when y is 60? what is the value of x.

a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700 then average total cost is $ 0.61

The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:

1. 1,000 units per day at a total cost of $700.

ATC = Total cost/output

ATC = $700/1000

ATC = $0.58

2. If the firm produced 500 units per day, its total cost would be $450.

ATC = Total cost/output

ATC = $450/500

ATC = $0.45

3. If it produced 700 units per day, its total cost would be $425.

ATC = Total cost/output

ATC = $425/700

ATC = $0.61

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The correct option is (c) 10x−6x²  for the given set of equations that occur in Al-Khowarizmi's work. x10−x + 10−x x = 6 13

The given equation is :

x^(10-x) + (10-x)/x = 6/13.

Rewriting the given equation by multiplying the whole equation by x gives us:

x^(11-x) + (10-x) = 6x/13

Rearranging, 13x^(11-x) + 130 - 13x = 6x^2

As we observe, the equation can not be factorized.

We'll find the least common denominator of the three fractions that are present in the given equation.

To do so, the denominator of each fraction should be expressed in its prime factors as follows:

x is a common factor in the denominator.

13 is a prime factor that is only found in the denominator of the first fraction.

2 is a prime factor that is only found in the denominator of the third fraction.

LCD = 2 * 13 * x^(11-x)

       = 26x^(11-x).

Hence, the correct option is (c) 10x−6x².

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Answer:

not sure if it's a or b but I think it's a

Answer:

2

Step-by-step explanation:

Kate will have to pay $56.25 out of pocket for her doctor visit.

The formula for calculating coinsurance is Coinsurance = (Cost of Service x Coinsurance Percent) / 100.If Kate has not met her deductible yet, she will need to pay the full $25 deductible plus 25% of the remaining bill.

The formula for calculating the amount Kate needs to pay is as follows:

Cost to Patient (C) = Deductible (D) + Coinsurance (C) * (Bill – Deductible)  In this case, Kate would need to pay (125 x 25) / 100 = $31.25. The extra $25 is the deductible, which is the amount she must pay before her insurance kicks in.This amount is due immediately upon the visit, regardless of whether or not she has met her deductible So in total, Kate would have to pay $25 + $31.25 = $56.25. In summary, Kate will have to pay $56.25 out of pocket for her doctor visit.

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The distance of point from the axis of rotation of the second hand is 8.2 cm.

Here,

A point located on the second hand of a large clock has a radial acceleration of 0.09 cm/s2.

We have to find the distance of point from the axis of rotation of the second hand.

What is Rotation?

The circular motion of an object around the circle is called Rotation.

Now,

Let us consider the equation for the centripetal acceleration given by;

\(a_{c} = \frac{v^{2} }{r}\)

where, v is the velocity and r is the radius.

Now, the velocity can be expressed as;

\(v = wr = \frac{2\pi r}{T}\)

where, ω is the angular velocity and T is the period.

Solving for the radius using these equations given as;

\(a_{c} = \frac{v^{2} }{r}\\\\v^{2} = a_{c} r\\\\(\frac{2\pi r}{T} )^2 = a_{c} r\\\\\frac{4\pi ^{2}r^{2} }{T^{2} } = a_{c} r\\\\r = \frac{T^{2} a_{c} }{4\pi ^{2} } \\\\r = \frac{(60s)^2(0.09 cm/s^2)}{4\pi ^{2} } \\\\r = 8.2 cm\)

Hence, The distance of point from the axis of rotation of the second hand is 8.2 cm.

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Answer:

A and C

Step-by-step explanation:

The angles and their images are congruent.

330 ways can the instructor choose the first group of four education students.

What is probability in math?

Given:

12 students

3 groups consisting of 4 students.

Mark can't be in the first group.

The combination formula that I used is =  n! / r!(n-r)!

where: n = number of choices ; r = number of people to be chosen.

This is the formula I used because the order is not important and repetition is not allowed.

Since Mark can't be considered in the first group, the value of n would be 11 instead of 12. value of r is 4.

numerator: n! = 11! = 39,916,800

denominator: r!(n-r)! = 4!(11-4)! = 4!*7! = 120,960

Combination = 39,916,800 / 120,960 = 330

Therefore, There are 330 ways that the instructor can choose 4 students for the first group.

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The solution is:  The required value of x is - 2.

We are given the following two functions :

f(x)=x^2-2x and g(x)=6x=4

We are to find the value of x for which (f + g)(x) = 0.

We know that for any two functions p(x) and q(x), the following property holds true :

p(x) + q(x) = (p+q)x

We have

(f + g)(x) = 0

x^2 - 2x + 6x + 4 = 0

x^2 + 4x + 4 = 0

(x + 2)^2 = 0

x + 2 = 0

x = -2

Thus, the required value of x is - 2.

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complete question:

If f(x)=x2-2x and g(x)=6x=4, for which value of x does (f+g)(x)=0

Answer:

Yes

Step-by-step explanation:

3/5, 1/2, 2/3, and 3/4 must be 3 or lower if added together.

We need to find the LCM of the denominators. The LCM, or lowest common multiple, of the denominators is 60. So we have to multiply the fractions by the LCM and add them up.

36 + 30 + 40 + 45 = 151.

60 x 3 = 180.

151 isn't up to 180, so yes. And also, if you divide 151 by 60, you would get 2.52 approximately.

The ratios that can be used to illustrate how many heads of lettuce,X, he would need to head 275 guests would be = 37/100 = X/275. That is option A.

The number of heads of lettuce needed to feed 100 guest = 37

The number of heads of lettuce that will be needed for 275 guests = X.

Mathematically;

100 guests = 37

275 guests =X

That is,

X * 100 = 37 ×275

Which is the same as = 37/100 = X/275

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With 98% confidence interval, all teenagers' mean number of hours watching TV per week will be (26.6,29.4).

98% confidence interval can be calculated as

Point estimate± Error margin

Point estimate=mean number of hours watching TV

students=28.

Error margin=1.4.

As per given data, the 98% confidence interval for all teenagers is

=28± 1.4

=(28-1.4,28+1.4)

=(26.6,29.4)

Statisticians use confidence intervals to assess the level of uncertainty in a sample variable. For instance, a researcher may select numerous samples at random from the same population and compute a confidence interval for each sample to estimate how each sample may correctly reflect the true value of the population variable. With certain intervals including the true population parameter and others not, each produced dataset is distinct. Confidence intervals are a set of values that are constrained by the mean of the statistic and are likely to include an unidentified population parameter. The confidence level is the proportion of likelihood, or certainty, that, after multiple draws from a random sample, the confidence interval would contain the true population parameter.

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The equation of the straight line is y = -2x - 4, the value of x₁ is -1 and the value of y₁ is -2.

To find the equation of a straight line given its slope and one point, we use the point-slope form of the equation:

−y − y₁​ = m(x−x₁ )

where m is the slope of the line, and (x₁, y₁) is the given point.

In this case, m = -2 and the point is (-1, -2). So we have:

x₁ = -1

y₁ = -2

m = -2

Substituting these values into the point-slope form, we get:

y−(−2)=−2(x−(−1))

Simplifying and rearranging terms, we get the equation of the line:

y + 2 = -2x - 2

y = -2x - 4

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Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

The deer population in 5 years is approximately 294 deer.

A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay. Over time, exponential functions monitor constant growth. Examples from the actual world include radioactive decay, compound interest, and bacterial proliferation.

a. To solve the differential equation dP/dt = −0.1P, we can separate the variables and integrate:

dP/P = −0.1 dt

Integrating both sides gives:

ln|P| = −0.1t + C

where C is the constant of integration. To solve for C, we can use the initial condition that P = 495 when t = 0:

ln|495| = −0.1(0) + C

C = ln|495|

Substituting this value of C back into the equation gives:

ln|P| = −0.1t + ln|495|

Simplifying using logarithm properties, we get:

ln|P/495| = −0.1t

Exponentiating both sides gives:

|P/495| = e^−0.1t

Taking the absolute value off and multiplying both sides by 495, we get:

P = 495e^−0.1t

To find the deer population in 5 years, we can substitute t = 5 into the equation:

\(P = 495e^{-0.1(5)} = 294\) deer (rounded to the nearest deer).

Therefore, the deer population in 5 years is approximately 294 deer.

b. To find an equation for the deer population P(t) in terms of t and k for the period after 5 years, we can use the differential equation:

dP/dt = k(650−P)

Separating the variables and integrating, we get:

∫dP/(650−P) = ∫k dt

Using partial fraction decomposition and integrating, we get:

ln|650−P| = −kt + C

where C is the constant of integration. To solve for C, we can use the initial condition that P = 294 when t = 5:

ln|650−294| = −k(5) + C

C = ln|356| + 5k

Substituting this value of C back into the equation gives:

ln|650−P| = −kt + ln|356| + 5k

Simplifying using logarithm properties, we get:

ln|(650−P)/356| = −kt

Exponentiating both sides gives:

\(|(650-P)/356| = e^{-kt\)

Taking the absolute value off and multiplying both sides by 356, we get:

\(650-P = 356e^{-kt\)

Solving for P gives:

\(P = 650-356e^{-kt\)

Therefore, the equation for the deer population P(t) in terms of t and k for the period after 5 years is P = 650−356e^−kt.

c. Using the growth model from part b), if the deer population is 350 one year later, we can substitute t = 1 and P = 350 into the equation and solve for k:

350 = 650−356e^−k

Solving for \(e^{-k\) gives:

\(e^{-k = (650-350)/356 = 3/2\)

Taking the natural logarithm of both sides gives:

−k = ln(3/2)

Solving for k gives:

k = −ln(3/2) ≈ 0.4055

Therefore, k ≈ 0.4055.

d. Using the growth model from part b) and the value of k from part c), the long-term behavior of the deer population as t → ∞ is determined by the limit:

lim P(t) as t → ∞

We can use the fact that \(e^{-kt\)approaches 0 as t →

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To determine the length of the supports, we first need to determine the dimensions of the Pokéball. Since a Pokéball is a sphere, we know that its volume can be calculated using the formula:

V = (4/3)πr^3

where V is the volume and r is the radius.

Since the volume is given as 22 cubic feet, we can solve for r:

22 = (4/3)πr^3

r^3 = (22*3)/(4π)

r = 1.91 feet

Next, we need to determine the length of the supports. Since they will be perpendicular to the base of the Pokéball, they will form a right triangle with the radius of the sphere as the hypotenuse. We can use the Pythagorean theorem to solve for the length of the supports:

a^2 + b^2 = c^2

where c is the radius of the sphere and a and b are the lengths of the supports.

Solving for a or b, we get:

a = sqrt(c^2 - b^2)

or

b = sqrt(c^2 - a^2)

Since we want the supports to be the same length, we can set a = b and solve for that length:

a^2 + b^2 = c^2

2a^2 = r^2

a = sqrt(r^2/2)

Plugging in r = 1.91 feet, we get:

a = sqrt(1.91^2/2) = 1.35 feet

Therefore, each support must be 1.35 feet long.

This statement is true

A probability is a numerical value that indicates the chance, or likelihood, of a specific event occurring. Probability is the measure of the likelihood of a random event happening, and it is expressed as a number between 0 and 1, with 0 implying that the event would never occur and 1 implying that it is certain to happen.

The probability of an event happening is referred to as its likelihood. Probability can be expressed as a fraction, percentage, or decimal, and it is a vital tool in statistics. It is frequently utilized in mathematics to estimate real-world situations that involve random variables such as coin flips, weather patterns, stock market trends, and even sporting events.

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Answer:

I. Not a function

II. Not a function

III. Yes, function

IIII. Yep!

(I messed up the numbering in the explanations, sorry 3 is 4 and 4 is 3)

Step-by-step explanation:

Hi!

For a function, every x value must have exactly 1 y value.

f(2) can't equal both 0 and 10. It can only equal 0 or 10. So, because of this, we have a test called the vertical line test. Basically, you drag a line through a graph, and if there is any x value that goes to two (or more) different y-values, then that graph is not the graph of the function.

Let me try to give a practical explanation.

I.

In this graph, everything looks fine until we reach x=6. (I'm assuming the graph goes by ones). Do you see the problem? Yep! x has two different y values.

y= 4 and y= 6.

So, this isn't a function. Why? Because there are two y values for each x value (aka, this doesn't pass the V.L.T)

II.

(1,2), (2,5) , (3,8) , (2,-5) (1,-2)

We have two groups of problem points.

(2,5) and (2,-5) and (1,2) and (1,-2)

Here, each x value goes to a different y value. Therefore, this isn't a function

III. y=x^2

This is your typical parabola. See the graph that I attached.

Notice that -2 and 2 both go to 4. Two different x-values going to the same y-value is fine, but one x can't go to to different y values.

IIII.

(-4,1) , (0,3) , (4,5) , (6,6)

Check 1: Does any x-value go to multiple y values? Nope! So, this is a function.

Approximately 99.7% ( or 99.73% ) population  lies within  3 standard deviation   ( μ - 3σ , μ + 3σ ) = ( 38, 68 ) .

Why is there a standard deviation?

Empirical rule holds only for normal populations and states that

approximately 68% ( or 68.27%) population lies within  standard deviation

                          ( μ - σ , μ + σ ) = ( 48 , 58 )

Approximately 95% ( or 95.45% ) population  lies within 2  standard deviation  

                    ( μ - 2σ , μ + 2σ ) = ( 43, 63 )

Approximately 99.7% ( or 99.73% ) population  lies within  3 standard deviation  

                        ( μ - 3σ , μ + 3σ ) = ( 38, 68 )

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The volume of the solid that results when the region enclosed by y = √x, y = 0, and x = 9 is revolved about the line x = 9 is 54π/5 cubic units.

We can use the method of cylindrical shells to find the volume of the solid that results when the region enclosed by y = √x, y = 0, and x = 9 is revolved about the line x = 9.

First, we need to find the height of each cylindrical shell. Since we are revolving the region about the line x = 9, the radius of each shell will be 9 - x.

The height of each shell will be the difference between the upper and lower bounds of the region, which is y = √x and y = 0:

height = √x - 0

= √x

So the volume of each cylindrical shell will be:

dV = 2π(9 - x)√x dx

To find the total volume of the solid, we integrate this expression from x = 0 to x = 9:

V = ∫(from 0 to 9) 2π(9 - x)√x dx

We can simplify this integral by making the substitution u = √x, which gives us:

V = 2π∫(from 0 to 3) (9 - u^2)u^2 du

Expanding the integrand and integrating term by term, we get:

V = 2π(27/5 - 9/3)

= 2π(27/5 - 27/9)

= 2π(162/45 - 135/45)

= 54π/5

Therefore, the volume of the solid that results when the region enclosed by y = √x, y = 0, and x = 9 is revolved about the line x = 9 is 54π/5 cubic units.

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Answer:

3.) B

How to solve:

Just get the cubed root of all the numbers inside the fraction

Answer:

21

Step-by-step explanation:

An isosceles triangle has 2 sides of the same length, those sides being the sides that aren't the base. The perimeter is the total length of all 3 sides of the triangle. We know that the base is 5 inches, and that one side is 8. Because the triangle is isosceles, we know that the others ide is also 8 inches. Therefore, the perimeter is 8+8+5, which is 21.

Answer:

21 in.

Step-by-step explanation:

If the triangle is isosceles, then two of its three sides are of equal length.  We can assume that the side lengths are 5 in., 8 in and 8 in.  Summing these up, we get total length 21 in.  That's the perimeter of the triangle.

Roberto's z-score is approximately 2.29. This means that his score is about 2.29 standard deviations above the mean.

A z-score (also known as a standard score) is a measure of how many standard deviations a data point is away from the mean of a distribution. It is used to standardize data so that we can compare values from different distributions.

For example, if a student's score on a test is 80 and the mean score is 75 with a standard deviation of 5, the z-score for the student's score would be:

z = (80 - 75) / 5

z = 1

This means that the student's score is one standard deviation above the mean.

To find Roberto's z-score, we can use the formula:

(x - μ) / σ

where x is Roberto's score, μ is the mean of the test, and σ is the standard deviation of the test.

We are given that the mean was 69 and the standard deviation was 7. Roberto scored 85. So we can plug in these values into the formula and solve for z:

z = (85 - 69) / 7

z = 16 / 7

z ≈ 2.29

Therefore, Roberto's z-score is approximately 2.29.

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Answer:

-6a²b+2ab²+8ab

Step-by-step explanation:

a²b + 2ab² +8ab - 7a²b

a²b-7a²b+2ab²+8ab

-6a²b+2ab²+8ab

In this the correct choice is: D. There are no relative maxima and no relative minima.

The given function is y = \(x^{3}\) - 12x + 3. To find the relative maxima and minima, we need to calculate the first and second derivatives of the function.

First, let's find the first derivative: y' = 3\(x^{2}\) - 12

Now, let's find the second derivative: y'' = 6x

To apply the second-derivative test, we need to determine the critical points by setting the first derivative equal to zero and solving for x:

3\(x^{2}\) - 12 = 0

\(x^{2}\)- 4 = 0

(x - 2)(x + 2) = 0

From this equation, we find that x = 2 and x = -2 are the critical points.

Now, let's evaluate the second derivative at these critical points:

y''(2) = 6(2) = 12

y''(-2) = 6(-2) = -12

Since the second derivative at x = 2 is positive (12 > 0) and the second derivative at x = -2 is negative (-12 < 0), the second-derivative test tells us that there are no relative maxima or minima. Therefore, the correct choice is D. There are no relative maxima and no relative minima for the given function.

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The complete question is:

Test for relative maxima and minima. Use the second-derivative test, if possible. y=x3 - 12x + 3 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The relative maxima occur at x = 2. The relative minima occur at -2. (Type integers or simplified fractions. Use a comma to separate answers as needed.) The relative maxima occur at x=-2. There are no relative minima. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O C. The relative minima occur at x = 2 . There are no relative maxima. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OD. There are no relative maxima and no relative minima.

Falcons had a more effective overall record because of the higher median. Thus, the answer is option B.

The median is usually used for the comparison of two data sets instead of the mean, as it is not affected by outliers.

Compare the total points earned by each team.

The Eagles data set is given below:

3, 7, 10, 10, 13, 14, 17, 21, 24, 24, 27, 27, 37, 40, 55.

As the data set has an odd cardinality, the median is the middle element, therefore it is for:

21.

For the Falcons, we use the same approach and obtain a median about:

24.

Therefore, we can say that the Falcons had a more effective overall record because of the higher median and the best measure of center to compare would be mean.

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Answer:

A 19.8

Step-by-step explanation:

Still 5 seconds.

(Assuming the Earth around that building is flat.

Answer:

they're both 60 degrees.

Step-by-step explan

Answer:

D   (0, 3)

Step-by-step explanation:

To go from B (8, 3) to C (3, 8)

subtract 5 from x, add 5 to y

A (5, -2)

subtract 5 from x,   x = 0

add 5 to y,   y = 3

D (0, 3)

If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are equal then the two lines are parallel.

The four sets of opposing angles that each have their own vertex point, are on different sides of the transversal and are both either internal or exterior are called alternate angles.

In geometry, a transversal line is one that cuts across the plane in two places. It does so at two spots where two lines meet. Many right angles are produced when two transverse lines meet. There are four types of similar angles: matching, alternative interior, alternate exterior, and co-interior.

In geometry, two lines are considered parallel if and only if all pairs of alternative interior angles in any transversal are equal.

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