You interview four people. You find that person A is a married 24​-year-old white female with 2 pets and whose college GPA was 2.4. Person B is a single 44​-year-old Asian female with 5 pets and whose college GPA was 2.5. Person C is a single 35​-year-old Hispanic male with 4 pets and whose college GPA was 2.2. Person D is a single 48​-year-old Asian male with 3 pets and whose college GPA was 3.8. Construct a data file for the characteristics number of pets and ethnic group for this sample.

Answer:

  x 2 −2 3 −3

  y 4 4 9 −9

Step-by-step explanation:

A table does not represent a function if any x-value is repeated. The table shown above is the only one with unique x-values.

The coordinates provided represent vertices of a triangle on a 2-dimensional grid like a city map. Visualizing the points and connecting them creates a right triangle. Vectors can express the sides of this triangle in terms of magnitude and direction.

This is a problem pertaining to geometry and the use of coordinate systems. In the question, we're given vertices of a triangle on a coordinate grid. The coordinates, (1, 1), (1, 4), and (-3, 4), denote specific points on this two-dimensional grid system. Just as in a city map, these coordinates help define the exact location of the points in a well-defined and universally understood manner.

To visualize the triangle formed by these coordinates on a city map, we can consider (1, 1) as a starting point. From this point, move 3 units north to reach (1, 4), then move 4 units to the left to reach (-3, 4), and finally move back 3 units south to reach the starting point (1, 1). This forms a right triangle, with (1, 4) as the right-angle vertex.

Similar to the concept of directional travel mentioned in the supplementary text, vectors can also be utilized in such coordinate systems to describe movement or distance between different points on the map. In our triangle example, each side of the triangle can be represented by a vector, with its magnitude (length) and direction.

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To find the area of the triangle park, we can calculate the lengths of the sides using the distance formula and then use Heron's formula to find the area. The area of the triangle park is 6 square units.

The given question is about a city planner mapping out a triangle park on a grid paper using coordinates. The vertices of the park are given as (1, 1), (1, 4), and (-3, 4). The subject of this question is Mathematics, and the grade level is High School.

To find the area of the triangle park, we can use the formula for the area of a triangle. We connect the vertices with line segments and calculate the lengths of the sides. Then, using the Heron's formula, we can calculate the area.

First, we calculate the lengths of the sides using the distance formula. The length of AB is sqrt((1-1)^2 + (4-1)^2) = sqrt(9) = √9 = 3. The length of BC is sqrt((1-(-3))^2 + (4-4)^2) = sqrt(16) = √16 = 4. The length of AC is sqrt((1-(-3))^2 + (4-1)^2) = sqrt(25) = √25 = 5.

Next, we use Heron's formula to calculate the area. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by: Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (s = (a+b+c)/2).

In this case, a = 3, b = 4, and c = 5. Therefore, s = (3+4+5)/2 = 12/2 = 6. Plugging in the values, the area of the triangle is given by: Area = sqrt(6(6-3)(6-4)(6-5)) = sqrt(6*3*2*1) = sqrt(36) = √36 = 6.

Therefore, the area of the triangle park is 6 square units.

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Answer:

  "closed"

Step-by-step explanation:

A set is closed with respect to an operation if the operation on members of the set produces a member of the set.

Answer: D. [tex]\dfrac{qd}{(q+2)}[/tex]

Step-by-step explanation:

Given : q workers can paint a house in d days.

Let [tex]d_1[/tex] be the number of days taken by q+2 workers to paint the same house.

Since there is inverse relationship between the number of workers and the number of days to do same work ( condition - all workers paints at the same rate), as the number of workers increases the number of days to complete it decreases.

Equation of inverse variation between x and y  : [tex]x_1y_1=x_2y_2[/tex]

Substitute , [tex]x_1=q ,\ y_1=d[/tex] and  [tex]x_2=q+2 ,\ y_2=d_2[/tex] , we get

[tex]qd=(q+2)d_2\\\\\Rightarrow\ d_2=\dfrac{qd}{(q+2)}[/tex]

Therefore , the number of days it will take  q+2 workers to paint the same house = [tex]\dfrac{qd}{(q+2)}[/tex]

Hence, the correct answer is : D. [tex]\dfrac{qd}{(q+2)}[/tex]

Final answer:

The point in Quadrant I with an x-value 2 units from the origin and a y-value 7 units from the origin has coordinates (2, 7).

Explanation:

The student is asked to determine the coordinates of a point that lies in Quadrant I of the Cartesian coordinate system, with an x-value that is 2 units from the origin and a y-value 7 units from the origin.

The Cartesian coordinate system is divided into four quadrants, and Quadrant I is where both x and y values are positive.

Therefore, a point located 2 units away from the origin on the x-axis, and 7 units away on the y-axis, would have coordinates (2, 7).

Remember, the origin is the point where the x-axis and y-axis intersect, (0,0). Moving 2 units to the right, you reach an x-value of 2. Then, moving up 7 units, you achieve a y-value of 7.

Thus, the coordinates are (2, 7).

The limit of the given expression as x approaches negative infinity is 1. This is computed by simplifying and rationalizing the expression, then applying the limit, which leads to a result of 1.

To solve the given limit problem, we will first rationalize the expression. Given the expression as: (1-x⁴) / (x²+4x), we can simplify this by factoring out an x² from both the numerator and the denominator. The expression then becomes: (1/x²- 1) / (1+ 4/x). Taking the limit as x approaches negative infinity, we will have: lim (1/x² - 1)⁵/ (1+4/x)⁵. Factoring out x² from the numerator and x from the denominator, we have: lim (1 - 1/x^2)⁵/ (1+ 4/x)⁵ As x approaches negative infinity, the terms 1/x²and 4/x approaches 0, hence the limit becomes (1⁵)/(1⁵) = 1.

Learn more about Limit here:

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The limit as x approaches -∞ of [(1 - x^4) / (x^2 + 4x)]^5 is -1. This is calculated by dividing each term in the fraction by x^2, and observing the resulting behaviours of the terms as x approaches -∞.

Finding the limit of a function as x approaches -∞ is a fundamental concept in Calculus. In order to find the limit of (1 - x^4) / (x^2 + 4x) all raised to the power of 5 as x approaches -∞, divide each term in the fraction by x^2. This results in Limit x → -∞ (1/x^2 - 1)((1 + 4/x)^-5). We then can observe that as x approaches -∞, the expression 1/x^2 and 4/x will become zero.

Consequently, the limit of the fraction is (-1)^5, which equals -1. As a result, the limit as x approaches -∞ of [(1 - x^4) / (x^2 + 4x)]^5 is -1. This limit-finding process works because of the application of laws of limits and the behaviour of polynomials, particularly their asymptotic behaviours as demonstrated in concepts like infinite limit and powers.

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Answer:

A. 2.8 minutes

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Solution to the problem

Let X the random variable that represent the length of time it takes a college student to find a parking spot in the library parking of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(3.5,1)[/tex]  

Where [tex]\mu=3.5[/tex] and [tex]\sigma=1[/tex]

And we need to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.758[/tex]   (a)

[tex]P(X<a)=0.242[/tex]   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.242 of the area on the left and 0.758 of the area on the right it's z=-0.700. On this case P(Z<-0.700)=0.242 and P(z>-0.700)=0.758

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.242[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.242[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=-0.700<\frac{a-3.5}{1}[/tex]

And if we solve for a we got

[tex]a=3.5 -0.700*1=2.8[/tex]

So the value of height that separates the bottom 24.2% of data from the top 75.8% is 2.8 minutes.  

The point in time where 75.8% of students exceed when finding a parking spot is calculated using Z-scores in a normal distribution. The time is approximately 2.8 minutes.

The process to find the point in the distribution where 75.8% of the students exceed the required time to find a parking spot in the library parking lot is essentially to calculate the Z-score corresponding to a given cumulative probability (or area) in the standard normal curve.  If the area to the left of the Z-score is 75.8%, then the area to the right of the Z-score is 100%-75.8% = 24.2%.

We then find the Z-score corresponding to 24.2% in the Z-tables. In this case, the corresponding Z-score is approximately -0.7 (since the tables usually give the area to the left, and we are dealing with the area to the right of the Z-score, we consider the negative of the found Z-score).

To convert this back to the time it takes to find a parking spot, we use the formula for converting Z-scores back to raw scores: X = μ + Zσ, where X is the raw score (time to find a parking spot), μ is the mean time to find a parking spot, Z is the Z-score, and σ is the standard deviation of the time to find a parking spot.

Substituting the given values, we get X = 3.5 + (-0.7)*1 = 2.8.

Thus, the time at which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot is 2.8 minutes (option A).

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Answer:

View Image

Step-by-step explanation:

Solve for y.

You have a ≥ so it's a solid line and you shade above that line.

Answer:

Solution

(x, y) = (2, 3)

Step-by-step explanation:

The function that represents the number of E.coli bacteria cells per 100 mL of water as t years elapses, and is missing in the question, is:

[tex]A(t)=136(1.123)^{4t}[/tex]

Answer:

   Option A. 59%

Explanation:

The base, 1.123, represents the multiplicative constant rate of change of the function, so you just must substitute 1 for t in the power part of the function::

Then, the multiplicative rate of change is 1.590, which means that every year the number of E.coli bacteria cells per 100 mL of water increases by a factor of 1.590, and that is 1.59 - 1 = 0.590 or 59% increase.

You can calculate it also using two consecutive values for t. For instance, use t =1 and t = 1

[tex]t=1\\\\ A(1)=136(1.123)^4\\\\\\t=2\\ \\ \\A(2)=136(1.123)^8\\ \\ \\A(2)/A(1)=1.123^8/1.1123^4=1.123^4=1.590[/tex]

Answer:

a) [tex]P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039[/tex]  

[tex]P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469[/tex]  

[tex]P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211[/tex]  

[tex]P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422[/tex]  

[tex]P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316[/tex]

b) [tex] E(X) = np = 4*0.75=3[/tex]

c) [tex] Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866[/tex]

d) [tex] P(X \geq 3) \geq 0.98[/tex]

And the dsitribution that satisfy this is [tex]X\sim Binom(n=9,p=0.75[/tex]

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=4, p=1-0.25=0.75)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

Part a

[tex]P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039[/tex]  

[tex]P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469[/tex]  

[tex]P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211[/tex]  

[tex]P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422[/tex]  

[tex]P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316[/tex]

Part b

The expected value is givn by:

[tex] E(X) = np = 4*0.75=3[/tex]

Part c

For the standard deviation we have this:

[tex]Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866[/tex]

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

[tex] P(X \geq 3) \geq 0.98[/tex]

And the dsitribution that satisfy this is [tex]X\sim Binom(n=9,p=0.75[/tex]

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

To find the probabilities of different numbers of successes ranging from 0 to 4 in a group of parolees, we can use the binomial probability formula. The expected number of parolees who will not be repeat offenders can be calculated by multiplying the probability of success by the total number of parolees. The standard deviation can also be calculated using a formula. To be about 98% sure that three or more parolees will not become repeat offenders, Alice should counsel a group size of at least 13 parolees.

To find the probabilities of different numbers of successes, we can use the binomial probability formula. Given that the probability of success is 0.25 and the number of trials is 4, we can calculate the probabilities as follows:

The expected number of parolees who will not be repeat offenders can be calculated by multiplying the probability of success (0.25) by the total number of parolees (4), which gives an expected value of 1 parolee. The standard deviation can be calculated using the formula sqrt(n * p * (1-p)), where n is the number of trials and p is the probability of success. In this case, the standard deviation is sqrt(4 * 0.25 * (1-0.25)) ≈ 0.866.

To determine the size of the group that Alice should counsel to be about 98% sure that three or more parolees will not become repeat offenders, we can use the binomial cumulative distribution function. We need to find the smallest value of n (the number of trials) such that P(X ≥ 3) > 0.98, where X represents the number of successes. Solving this inequality, we find that Alice should counsel a group size of at least 13 parolees.

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Answer:

The parents who didn't answer with either naughty and nice are 6.

Step-by-step explanation:

Given:

150 parents were surveyed. 26% said that the kids were naughty and 70% said their kids were nice.

Now, to find parents who didn't answer with either naughty and nice.

So, as given in question:

70% said that their kids are naughty.

26% said that their kids are nice.

So, to get the percentage of parents who didn't answer we subtract.

Thus, the percentage of  parents who didn't answer with either naughty and nice:

100% - (70% + 26%)

100% - 96% = 4%.

Hence, 4% of parents didn't answer.

Now, to get how many  parents didn't answer we calculate the percentage of the total who didn't answer:

Total parents surveyed = 150.

Parents who didn't answer =  4% of the total parents surveyed.

[tex]Parents\ who\ didn't\ answer = 4\% of 150.[/tex]

[tex]Parents\ who\ didn't\ answer = \frac{4}{100}\times 150.[/tex]

[tex]Parents\ who\ didn't\ answer = \frac{600}{100}.[/tex]

[tex]Parents\ who\ didn't\ answer = 6.[/tex]

Therefore, the parents who didn't answer with either naughty and nice are 6.

Explanation:

a. The line joining the midpoints of the parallel bases is perpendicular to both of them. It is the line of symmetry for the trapezoid. This means the angles and sides on one side of that line of symmetry are congruent to the corresponding angles and sides on the other side of the line. The diagonals are the same length.

__

b. We observe that adjacent pairs of points have the same x-coordinate, so are on vertical lines, which have undefined slope. KN is a segment of the line x=1; LM is a segment of the line x=3. If the trapezoid is isosceles, the midpoints of these segments will be on a horizontal line. The midpoint of KN is at y=(3-2)/2 = 1/2. The midpoint of LM is at y=(1+0)/2 = 1/2. These points are on the same horizontal line, so the trapezoid is isosceles.

__

c. We observed in part (b) that the parallel sides are KN and LM. The coordinate difference between K and L is (1, 3) -(3, 1) = (-2, 2). That is, segment KL is the hypotenuse of an isosceles right triangle with side lengths 2, so the lengths of KL and MN are both 2√2.

_____

For part (c), we used the shortcut that the hypotenuse of an isosceles right triangle is √2 times the leg length.

Step-by-step explanation:

the answer is

Y=2.5

X=3.75

Answer:

6 brownies and 2 cupcakes.

Step-by-step explanation:

Let the number of brownies be b and the number of cupckes be c.

We have the following system:

b = 3c

1.5b + 3c = 15

Substituting for  b in the second equation:

4.5c  + 3c = 15

7.5c = 15

c =  2.

Thus b = 3c = 6.

Step-by-step explanation:

9.5 × 10^(5) is greater than 1.2 × 10^(4) is greater than 8.1 × 10^(-6) is greater than -7.2×10^(-4)

D > C > B > A

To order the numbers from least to greatest, one must compare the exponents in scientific notation. The correct sequence from least to greatest is B, A, C, D.

The question asks to order the given numbers from least to greatest. The numbers are provided in scientific notation, which is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. To compare these numbers, we look at their power of 10, as this indicates the number's scale or size.

'A' is 7.2*10^-4 which is a small positive number.

'B' is 8.1*10^-6 which is even smaller, given the more negative exponent.

'C' is 1.2*10^4 which is a large positive number.

'D' is 9.5*10^5 which is larger than 'C', given the larger exponent.

Therefore, when ordered from least to greatest, the sequence is: B, A, C, D.

Answer:

[tex] x= 5*400 ft = 2000 ft[/tex]

Step-by-step explanation:

For this case we can use the figure attached and we are interested in order to find the value of x.

We have two similar triangles (DEC and ABC) and we can find the scale factor like this:

[tex]Factor= \frac{EC}{BC}=\frac{500ft}{100ft}=5[/tex]

And now we can apply proportions in order to find the value of x using the two sides DE and BA, since we have the ratio between the triangle DEC and ABC we have this:

[tex]Factor=5=\frac{x ft}{400 ft}[/tex]

And solving for x we got:

[tex] x= 5*400 ft = 2000 ft[/tex]

And then the distance across the lake would be 2000 ft

Answer:

ewq

Step-by-step explanation:

Answer:

Measure of arc ZWX is 230°.

Step-by-step explanation:

Given:

arc WX = 50°

Now

The diameter divide a circle into two equal parts

so

[tex]arc\ ZWX=arc\ ZRW+arc\ WX[/tex]

Since WZ is diameter of the circle.

[tex]arc\ ZRW=180\°[/tex]

substituting in above equation we get

[tex]arc\ ZWX=180\°+50\°=230\°[/tex]

Hence Measure of arc ZWX is 230°.

Answer:

B. 230

Step-by-step explanation:

Just took the test

Answer:

Step-by-step explanation:

1.

A

2.

A

3.

A

4.

Let the number=x

double=2x

add 6

2x+6

divide by 2

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

subtract 3

x+3-3=x

which is the original number

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

Answer:

130000m^2

Step-by-step explanation:

a = 800m

b = 800m

c= 650m

α = 30°

4th he triangular trench is an isosceles triangle.

Area of a triangle = 1/2(bcsinA)

= 1/2(800*650*sin30°)

= 130,000m^2

Answer:

The area enclosed by the trenches is 130 000[tex]m^{2}[/tex]

Step-by-step explanation:

The two given sides of the trenches are 800m and 650m. Since the included angle of the two sides are given, then the area covered by the trenches can be calculated using the formula;

     Area of a triangle = [tex]\frac{1}{2}[/tex] × abSin C

where: a is the length of one side and b the length of the second side and C represents the value of the included angle.

Thus,

    a = 800m, b = 650m and C = 30°

So that,

Area enclosed by the trenches  = [tex]\frac{1}{2}[/tex] × abSin C

                                                          =  [tex]\frac{1}{2}[/tex] × 800 × 650 × Sin30°

                                                          = [tex]\frac{1}{2}[/tex] × 800 × 650 × 0.5

                                                          = 130 000

The area enclosed by the trenches  is 130 000[tex]m^{2}[/tex].

No options given in the question are equivalent to the original system of equations because none of them retain the same solutions as the original system.

The equivalent system for the given system of equations can be found by manipulating the original system of equations. The original system of equations is:

2x + 3y = 7

4x − 2y = 4.

Equations are equivalent if one is a multiple of the other. We can see that if the second equation is multiplied by 2, it will become:

8x - 4y = 8,

which is not an option given in your question. Therefore, none of the presented options (A-D) are equivalent to the initial system of equations. Always remember that an equivalent system retains the same solutions as the original system.

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The function's derivative, f'(x) = x²(x + 1)³3(x - 4)³, has 2 relative maximum and minimum points.

So, the correct answer is C) 2.

The function's derivative, f'(x) =  x²(x + 1)³3(x - 4)³, gives us information about the critical points of the function. Relative maximum and minimum points occur where the derivative is zero or undefined. To find these points, we set the derivative equal to zero and solve for x:  x²(x + 1)³3(x - 4)³ = 0. By analyzing the signs of the factors, we can determine the number of relative maximum and minimum points:

Therefore, the total number of relative maximum and minimum points is 2.

So, the correct answer is C) 2.

Answer:

Option 3)

[tex]x^3-9^3 = (x-9)(x^2 + 9x + 81)[/tex]

Step-by-step explanation:

We use the identities:

[tex]a^3 + b^3 = (a+b)(a^2-ab+b^2)\\a^3-b^3 = (a-b)(a^2+ab+b^2)[/tex]

1.

[tex](x + 7)(x^2 -7x + 14)[/tex]

It is not a sum or difference of cubes because it does not satisfies the identity.

2.

[tex](x + 8)(x^2 + 8x + 64)[/tex]

It is not a sum or difference of cubes because it does not satisfies the identity.

3.

[tex](x - 9)(x^2 + 9x + 81)\\\text{Comparing with the identity:} \\a^3-b^3 = (a-b)(a^2+ab+b^2)\\\text{We get}\\a = x\\b = 9\\x^3-9^3 = (x-9)(x^2 + 9x + 81)[/tex]

Thus, it can be expressed as a difference of cubes.

4.

[tex](x - 10)(x^2 - 10x + 100)[/tex]

It is not a sum or difference of cubes because it does not satisfies the identity.

Answer:

C

Step-by-step explanation:

Answer:

Statements (1) and (2) TOGETHER are NOT sufficient.

Explanation:

As in the equation (327)(510)(z) = (58)(914)(xy) there are THREE variables in total i.e. "x", "y" and "z" hence minimum three equations are required to find out values of all variables. Hence,

If the given number of equations is equal to total variable used in any of the equation, values of all the variables can be find out otherwise there can be unlimited number of solutions.

So, value of "x" cannot be determined with the given data.

Answer:

80% People Decreased after 3 Stops.

Step-by-step explanation:

Given:

Total Number of People on the bus =60

Number of people decreased = 48

We need to find the the percent of decrease in the number of people on the bus.

The percent of decrease in the number of people on the bus can be calculated by dividing Number of people decreased on the bus with Total Number of people on the bus and then multiplied with 100.

Framing in equation form we get;

percent of decrease in the number of people on the bus = [tex]\frac{\textrm{Number of people decreased on the bus}}{\textrm{Total Number of people on the bus}}\times100[/tex]

Substituting the values we get;

percent of decrease in the number of people on the bus = [tex]\frac{48}{60}\times100 = 80\%[/tex]

Hence 80% People Decreased after 3 Stops.

Answer:

$150

Step-by-step explanation:

Dad gives the girl 50 and she save 20 so 50-20 = 30. Then u multiply that by the number of months given...so 30*5= 150

Answer: 150

Step-by-step explanation:

50-20=30

30x5=150

the reason that these are inverses is because if you switch x with z

and g(f(x))=x, then (x-9)/(x+5) is (z-9)/(z+5)=x. which implies that:

(z+5) - 14/(z+5)=1-(14/(z-5))=x.

(1/(1 - x) * 14) + 5 = z = g(x) maybe i messed up?

Step-by-step explanation:

f(x) = (x − 9) / (x + 5)

g(x) = (-5x − 9) / (x − 1)

To find f(g(x)), substitute g(x) into f(x).

f(g(x)) = [(-5x − 9) / (x − 1) − 9] / [(-5x − 9) / (x − 1) + 5]

Multiply top and bottom by x − 1.

f(g(x)) = [(-5x − 9) − 9(x − 1)] / [(-5x − 9) + 5(x − 1)]

Simplify.

f(g(x)) = (-5x − 9 − 9x + 9) / (-5x − 9 + 5x − 5)

f(g(x)) = (-14x) / (-14)

f(g(x)) = x

To find g(f(x)), substitute f(x) into g(x).

g(f(x) = [-5(x − 9) / (x + 5) − 9] / [(x − 9) / (x + 5) − 1]

Multiply top and bottom by x + 5.

g(f(x) = [-5(x − 9) − 9(x + 5)] / [(x − 9) − (x + 5)]

Simplify.

g(f(x) = (-5x + 45 − 9x − 45) / (x − 9 − x − 5)

g(f(x) = (-14x) / (-14)

g(f(x) = x

Answer:

3 necklaces.

Step-by-step explanation:

According to the Question,

Elise is having 15 Purple beads and 12 Yellow beads ,

All necklace should be the same ,

So, She wants to form group such that in each group , equal number of Purple and Yellow beads will be present.

Now , the maximum number of such necklaces can be calculated from the HCF of 15 and 12 as we want to break them in equal groups .

Now , HCF of 15 and 12 comes out to be 3.

Thus ,

a maximum of 3 necklaces can be made.

Final answer:

The common multiple of the heights of the two stacks is 72 inches which will also be the same height of stack

Explanation:

The boxes that are being stacked have different heights - 18 inches and 24 inches. To find the shortest height at which the two stacks will be the same height, we need to determine the common multiple of 18 and 24.

18 and 24 have a common multiple of 72. Therefore, the two stacks will be the same height when they reach 72 inches.

Answer: The shortest height at which the two stacks will be the same height is 72 inches.

Answer:

72 yrs old.

Step-by-step explanation:

The combined age

D+O=96

The owner is 3 times older than dog

O=3D

D+3D=96

4D = 96

D= 24

Now substitute the value of D in O=3D

O=3.24= 72

The owner is 72 years old.

To solve this problem, we can use algebra. Let's define the dog's age as 'd' and the owner's age as 'o'. By solving the two equations (o + d = 96 and o = 3d), we can determine that the dog is 24 years old and the owner is 72 years old.

The question asks us to find the age of a dog's owner, given that the combined ages of the owner and the dog are 96 years, and the owner's age is three times the age of the dog. We can use algebra to solve this problem.

Let's define the dog's age as 'd' and the owner's age as 'o'. We know that o = 3d (the owner's age is three times the dog's age) and o + d = 96 (the combined ages of the owner and the dog are 96).

To find the owner's age, substitute '3d' for 'o' in the second equation: 3d + d = 96. This simplifies to 4d = 96. Dividing both sides of the equation by 4 gives us d = 24, meaning the dog is 24 years old. Now we substitute d = 24 into the equation o = 3d, resulting in o = 72. Therefore, the owner is 72 years old.

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Answer:

Maximum 3 socks (minimum 2) to be taken out to have a pair of same color.

Step-by-step explanation:

Well, it can be assumed that for example there are 4n black and 5n brown socks in a drawer (which satisfies ratio of 4/5). If first sock is taken out the probability of this sock being black is 4/9 (4n/(4n+5n)) or being brown is 5/9 (5n/(4n+5n)). If the first sock is black, the probability of second attempt being black is (4n-1)/(9n-1), but being brown is (5n)/(9n-1). f the first sock is brown, the probability of second attempt being brown is (5n-1)/(9n-1), but being black is (4n)/(9n-1). In either case, there is a probability of taking out different colors of socks in two attempts (taking black first then brown or vice-versa). So maximum 3 (minimum 2) attempts required to make sure you have a pair of the same color of socks.

To ensure you have a pair of the same color socks, you must take out a minimum of 5 socks from the drawer containing a mix of black and brown socks in a ratio of 4 to 5.

If you have black socks and brown socks in your drawer, mixed in a ratio of 4 to 5, you need to consider the worst-case scenario to ensure you have a pair of the same color. If you take out 4 black socks, one by one, you may still not have a matching pair if they are all black—so you need to take out another sock. If this fifth sock is brown, you now have one pair of brown socks. If it's black, then you already had a pair from the four black socks. Thus, you must take out a minimum of 5 socks to guarantee a matching pair.