The mean SAT score in mathematics, μ, is 53. The standard deviation of these scores is 41. A special preparation course claims that its graduates will score higher, on average, than the mean score 503. A random sample of 70 students completed the course, and their mean SAT score in mathematics was 505. At the 0. 05 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 41.

A. ) Null Hypothesis: B. ) Alternative Hypothesis:C. ) The Value of the test statistic:D. ) The P-Value:

We don't know if she will reject the null hypothesis without knowing the level of significance. But if the p-value is smaller than the level of significance, she would reject the null hypothesis

The correct explanation for the P-value is option B: "If the​ P-value for a particular test statistic is ​, she expects results at least as extreme as the test statistic in about of 100 samples if the null hypothesis is true."

This means that if the null hypothesis is true, there is a certain probability (represented by the P-value) that we would observe a test statistic as extreme or more extreme than the one we observed in our sample.

As for the conclusion, we cannot determine whether or not the researcher would reject the null hypothesis based solely on the P-value. The decision to reject or not reject the null hypothesis depends on the level of significance (alpha) chosen by the researcher. If the P-value is smaller than the chosen alpha, then the researcher would reject the null hypothesis.

Otherwise, she would fail to reject it. Without knowing the level of significance chosen, we cannot determine the conclusion.

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if it has a diameter of 28, its radius is half that or 14.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=14\\ h=7.5 \end{cases}\implies V=\pi (14)^2(7.5) \\\\\\ V=1470\pi \implies V=1470(\frac{22}{7})\implies V=4620~m^3[/tex]

Vince is 16 years old, his sister is 8 years old, and their mother is 48 years old, where Vince is twice his sister's age and their mother is twice the sum of their ages.

Let's start by assigning variables to the unknown ages. Let V be Vince's age, S be his sister's age, and M be their mother's age. Then we can set up three equations based on the given information:

V = 2S (Vince is twice his sister's age)

S = 8 (His sister is 8 years old)

M = 2(V + S) (Their mother's age is twice the sum of their ages)

Using equation 1 and substituting S = 8, we can solve for Vince's age:

V = 2S

V = 2(8)

V = 16

So Vince is 16 years old.

Using equation 3 and substituting V = 16 and S = 8, we can solve for their mother's age:

M = 2(V + S)

M = 2(16 + 8)

M = 2(24)

M = 48

So their mother is 48 years old.

Therefore, Vince is 16 years old, his sister is 8 years old, and their mother is 48 years old.

To summarize:

Vince is twice his sister's age, and his sister is 8 years old.

Using this information, we can calculate that Vince is 16 years old.

Their mother's age is twice the sum of their ages, so using Vince and his sister's ages, we can calculate that their mother is 48 years old.

Therefore, Vince is 16 years old, his sister is 8 years old, and their mother is 48 years old.

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Here, option (a) is correct i.e., MNOP is a trapezoid because exactly one pair of opposite sides is parallel.

In Euclidean geometry, a trapezoid is defined as a convex quadrilateral by definition. The bases of the trapezoid are parallel sides. The formula to find the area will be:

Area = 1/2 x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides

Perimeter = is the sum of lengths of sides of the trapezoid

Quadrilateral MNOP is a trapezoid because exactly one pair of opposite sides is parallel.

To see the image please see the graph given below.

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The sampIe mean has a 0.9992 chance of being Iess than $453.

A measure οf a grοup οf vaIues' variance οr dispersiοn in statistics is caIIed the standard deviatiοn. When the standard deviatiοn is Iοw, the vaIues are mοre IikeIy tο faII within a narrοw range, aIsο knοwn as the expected vaIue, whereas when the standard deviatiοn is high, the vaIues tend tο be cIοser tο the mean.

The sampIing distributiοn οf the sampIe mean is apprοximateIy nοrmaI with mean μ = $450 and standard deviatiοn [tex]\sigma/ \sqrt{(n)} = \$40/\sqrt{(625)} = \$1.6[/tex].

(a) Tο find the prοbabiIity that the sampIe mean wiII be Iess than $453, we standardize the sampIe mean:

[tex]z = (x - \mu) / (\sigma / \sqrt{(n)}) = (453 - 450) / (40 / \sqrt{(625)}) = 3.125[/tex]

Using a standard nοrmaI tabIe, we find that the prοbabiIity οf getting a z-scοre οf 3.125 οr Iess is 0.9992.

Therefοre, the prοbabiIity that the sampIe mean wiII be Iess than $453 is 0.9992.

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It would take the newer pump 36 minutes to drain the pool working alone.

Let's call the time it takes the newer pump to drain the pool "t". Then, we know that the older pump takes 5t to drain the pool.

If they work together, their combined rate is the sum of their individual rates. Let's call the rate of the newer pump "r" (in units of pool drained per hour). Then, the rate of the older pump is 1/5 of that, or r/5. Together, their rate is:

r + (r/5) = (6/3) = 2

We can simplify this equation by multiplying both sides by 5:

5r + r = 10

Simplifying, we get:

6r = 10

Dividing both sides by 6, we get:

r = 10/6 = 5/3

So the rate of the newer pump is 5/3 of the pool drained per hour.

To find the time it takes the newer pump to drain the pool, we can use the formula:

rate = work / time

Where "work" is the amount of pool drained (which we can assume is 1, since we're talking about draining the entire pool).

So we can write:

5/3 = 1 / t

Multiplying both sides by t, we get:

5t / 3 = 1

Multiplying both sides by 3/5, we get:

t = 3/5 hours, or 36 minutes

Therefore, it would take the newer pump 36 minutes to drain the pool working alone.

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To find the quotient and remainder if

�

(

�

)

f(x) is divided by

�

(

�

)

p(x), first, we need to divide the polynomials. Division of polynomials can be done by long division method. So, let's solve the problem and find the quotient and remainder of the polynomial.

In long division, first, we divide the first term of dividend by the first term of divisor.

3x^4/x^2 = 3x^2

Now we multiply this result (3x^2) with divisor and subtract from dividend.

3x^4 + 2x^3 - x^2 - x - 6 - (3x^2(x^2 + 1))= -3x^3 - x - 6

Next, we bring down the next term of the dividend. And repeat the process until we cannot divide further.

-3x^3/x^2 = -3x

Now, we multiply this result (-3x) with divisor and subtract from the last dividend.

-3x^3 - x - 6 - (-3x(x^2 + 1))= 3x^2 - x - 6

Now, we again bring down the next term of the dividend.

3x^2/x^2 = 3

Next, we multiply this result (3) with divisor and subtract from the last dividend.

3x^2 - x - 6 - (3(x^2 + 1))= -x - 9

-x/x^2 = -

Now, we multiply this result (-1) with divisor and subtract from the last dividend.

-x - 9 - (-1(x^2 + 1))= -x - 10

So, the quotient and remainder if

�

(

�

)

f(x) is divided by

�

(

�

)

p(x) are:

quotient = 3x^2 - 3

remainder = -x - 10

QUAD is not relevant to this question.

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Answer:

x = 114 degrees

Step-by-step explanation:

Angle x and the exterior angle form a straight line, which is 180 degrees. Because of this, we can subtract 66 from 180, equaling 114.

Answer:

the third option

Step-by-step explanation:

The minimum value of the function is 9, and the function never stops increasing.

The given function is y=(x−9)²+9.

We need to find the minimum and maximum value of the function. The given function is a quadratic function whose graph is a parabola. Since the coefficient of x² is positive, the graph of the quadratic function will be in the form of an upward parabola whose vertex is at the point (h,k).

The vertex form of the quadratic function is given byy = a(x - h)² + k, where(h,k) is the vertex of the parabola.

a is the coefficient of (x - h)².

In the given function,y = (x-9)² + 9, the vertex of this function is (9,9) and a=1.

Therefore, the minimum value of the function is 9 at x=9, which is the vertex of the parabola.

The function y=(x−9)²+9 is an upward parabola, and hence it never stops increasing, which means that the function has no maximum value.

Thus, the minimum value of the function is 9, and the function never stops increasing.

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Answer:

[tex]s=170\frac{\sqrt{m} }{q}[/tex]

Step-by-step explanation:

since varies directly with square root of m and inversely with q ( [tex]\sqrt{m}[/tex] goes in the numerator and [tex]q[/tex] in the denominator)

[tex]s=a\frac{\sqrt{m} }{q}[/tex]

notice a is a constant, we need to find it!

since s=340 when m=36 and q=3

 [tex]340=a\frac{\sqrt{36} }{3}=a\frac{6}{3} =2a[/tex]
[tex]a=340/2=170[/tex]

so equation is:
[tex]s=170\frac{\sqrt{m} }{q}[/tex]

There is 360 mg of drug in 30 mL of the 60 mg/5 mL elixir.

The amount of drug in a given volume of a medication can be calculated using the following formula: Amount of drug (mg) = Volume (mL) x Concentration (mg/mL). In this case, we have 30 mL of a 60 mg/5 mL elixir, so the amount of drug in 30 mL can be calculated as follows: Amount of drug (mg) = 30 mL x 60 mg/5 mL = 360 mg. Therefore, there is 360 mg of drug in 30 mL of the 60 mg/5 mL elixir.

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Answer:

160m².

Step-by-step explanation:

In this case, the prism has two identical rectangular faces with dimensions of 5m by 4m, and four identical rectangular faces with dimensions of 5m by 6m.

Therefore, the surface area of the prism can be calculated as follows:

Surface Area = 2(5m x 4m) + 4(5m x 6m)

Surface Area = 40m² + 120m²

Surface Area = 160m²

So the surface area of the prism is 160m².

Cοmparing the given equatiοn with the standard form, we can see that the center is at [tex]$(-17.5, 15.\bar{3})$[/tex], and the radius is [tex]$\sqrt{18.1}$[/tex].

The standard form of the equatiοn of a circle is:

[tex]$$(x - h)^2 + (y - k)^2 = r^2$$[/tex]

where (h, k) is the center of the circle and r is the radius. This form of the equation is useful because it prοvides information about the center and radius οf the circle in a straightforward way. To use the standard form to graph a circle, we can plοt the center (h, k) on the coordinate plane and then draw a circle with radius r centered at (h, k).

To find the center and radius of the circle with equatiοn [tex]$(x+17.5)^2 + (y - 15.\bar{3})^2 = 18.1$[/tex], we can use the standard fοrm of the equation of a circle:

[tex]$$(x - h)^2 + (y - k)^2 = r^2$$[/tex]

where (h, k) is the center οf the circle and r is the radius.

Comparing the given equatiοn with the standard form, we can see that the center is at [tex]$(-17.5, 15.\bar{3})$[/tex], and the radius is [tex]$\sqrt{18.1}$[/tex]. Therefοre, we can write:

Center [tex]$= \left(-17.5, 15.\bar{3}\right)$[/tex]

Radius[tex]$= \sqrt{18.1}$[/tex]

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A circle in the xy-plane has the equation (x+17.5)²+(y-15(3))² = 18.1. Which of the following pairs is its center and radius.

a. (17, 15.3) and √18

b. (19, 14) and √9

c. (17, 15.3) and 9

d. (19, 14) and 18

Therefore , the solution of the given problem of expression comes out to be  the response is j + 8.

Calculations like variable multiplication, splitting, joining, and presently removing are required. Combining them would result in the following: An equation, some statistics, and a mathematical formula. A declaration of truth is composed of values, components, mathematical processes like additions, subtractions, errors, and subdivisions as well as arithmetic formulas. Words and phrases can be evaluated and analysed.

Here,

We must first determine the difference between 10 and 2, which is: before we can add the distinction of 10 and 2 to j.

=> 10 - 2 = 8

Now, by writing only the expression: we can add 8 to j.

=> j + 8

Consequently, the response is j Plus 8.

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Therefore the total cost for 18 months of membership is[tex]$742.50[/tex].The equation to find the cost of initiation and x months of membership is y + 59x = 742.50

The equation to find the cost of initiation and x months of membership is y + 59x = 742.50. Since the cost for one year of membership is known, the cost for initiation can be found by subtracting 59x from both sides of the equation, resulting in y = 742.50 - 59x. To find the total cost for 18 months of membership, we plug x = 18 into the equation, resulting in y + 59(18) = 742.50. This can be simplified to y + 1062 = 742.50, which means that y = -319.50. Therefore, the total cost for 18 months of membership is[tex]$742.50 - $319.50[/tex], which equals [tex]$423.00[/tex]. This calculation can be represented by the equation y + 59x = 742.50, where y is the cost of initiation and x is the number of months of membership. Plugging in the number of months of membership (x = 18) gives us the total cost for 18 months of membership (y + 1062 = 742.50). Simplifying this equation yields y = -319.50, and therefore the total cost for 18 months of membership is[tex]$742.50.[/tex]

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Step-by-step explanation:

To determine whether the ice cream scoop will fit in the cone or overflow, we need to compare the volume of the scoop to the volume of the cone. If the volume of the scoop is less than or equal to the volume of the cone, the scoop will fit in the cone. If the volume of the scoop is greater than the volume of the cone, the scoop will overflow.

The formula for the volume of a sphere is:

V_sphere = (4/3)πr³

where r is the radius of the sphere. In this case, the radius of the ice cream scoop is 3 cm, so:

V_sphere = (4/3)π(3 cm)³ ≈ 113.1 cm³

The formula for the volume of a cone is:

V_cone = (1/3)πr²h

where r is the radius of the base of the cone and h is the height of the cone. In this case, the radius of the cone is also 3 cm and the height of the cone is 5 cm, so:

V_cone = (1/3)π(3 cm)²(5 cm) ≈ 47.1 cm³

Therefore, the volume of the ice cream scoop is greater than the volume of the cone, and the ice cream will overflow when it melts.

To explain this result, we can note that the volume of the ice cream scoop is determined by its shape and size, which cannot be changed. However, the volume of the cone is determined by both its shape and size, as well as the amount of space available inside it. When the ice cream melts, it will fill up the cone and displace the air inside, increasing the volume of the cone. However, the volume of the ice cream scoop will not change, so it will overflow the cone.

a) The system of equations modeling this scenario is as follows:

C = 11.50 + 0.9n

C = 13.25 + 0.55n.

b) The number of toppings where the cost is the same at either Pizza Palace or Tasty Pizza is 5.

A system of equations is two or more equations solved concurrently.

A system of equations is also called simultaneous equations because the equations are solved at the same time or simultaneously.

                               Pizza Palace    Tasty Pizza

Pizza cost per unit       $11.50             $13.25

Topping cost per unit  $0.90              $0.55

Let the number of toppings = n

Let the total cost for the pizza at each pizza place = c

The total cost at Pizza Palace C = 11.50 + 0.9n... Equation 1

The total cost at Tasty Pizza, C = 13.25 + 0.55n... Equation 2

For the total cost, c, to be the same at the pizza places, Equation 1 must equate Equation 2:

That is, C = C.

Substituting the values of C:

11.50 + 0.9n = 13.25 + 0.55n

0.35n = 1.75

n = 5

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Answer:

1.)  51.515%  2.) 48.485%

Step-by-step explanation:

In this question we know 66 is 100% of the fraction, so we can start the process of converting a fraction into a percent, by figuring out how to adjust the fraction so that the denominator will be 100. First, divide 100 by the denominator.

100/66 = 1.515

Now we want to multiply denominator and numerator by 100.

34 × 1.515 = 51.515

66 × 1.515 = 100

Therefore, 34/66 as a percentage will be 51.515%

Now we want to convert 32/66. We will do the same for this equation.

100/66 = 1.515

32 × 1.515 = 48.485

66 × 1.515 = 100

Therefore 32/66 as a percentage will be 48.485

Hope this helps : )

Answer:

113.10 square inches

Step-by-step explanation:

Base shape = Circle

r = radius of Base shape

 = 3 in

l = slanted height

 = 9 in

Surface Area of cone = [tex]\pi r^{2} + \pi rl[/tex]

                                    = [tex][\pi (3)^{2} + \pi (3) (9)] in^{2}[/tex]

                                    = [tex][9\pi + 27\pi] in^{2}[/tex]

                                     = [tex]36\pi[/tex] square inches

                                     = 113.10 square inches (Rounded to the nearest    hundredth place)

Given:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex]{ \star{ \boxed{ \textsf{ \purple{Surface area of cone = πr² + πrs}}}}}[/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

The set of sample means generated by Mark may not be representative of the population of the city.

This is because Mark's sampling method is not random and may introduce bias into the sample. By only surveying bypassers in the central street, the sample may not be representative of the whole population of the city. On the other hand, Judy's random sampling method has a higher chance of capturing a representative sample of the population.

To confirm this, we can compare the sampling distributions generated by both methods. We can calculate the mean and standard deviation of the sample means for each method and compare them. If the means and standard deviations are significantly different, it may suggest that Mark's sampling method is biased.

To calculate the standard deviation of the sampling distribution, we can use the formula:

Since the population standard deviation is not given, we can use the sample standard deviation as an estimate. Assuming the sample standard deviation is 2, we can calculate the standard deviation of the sampling distribution as follows:

For Judy's method:

For Mark's method:

Assuming that the central street has a population size of 1000, we can calculate the standard deviation as:

The standard deviation of Mark's sampling distribution is much larger than Judy's, indicating that Mark's sampling method may not be representative of the whole population of the city.

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A function assigns values. The phase shift of a periodic function is the horizontal translation of the function.

A function assigns the value of each element of one set to the other specific element of another set.

The Phase Shift of a periodic function is the horizontal shift of the function from its normal position. The shift is either left or right.

For example, if the value of c in the function of sine is negative then the function will move towards the right side by the value of c, while if the value of c is positive then the function will towards the left.

Thus, the phase shift of a periodic function is the horizontal translation of the function.

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Answer:

(1)
Let x represent the number of HD Big View TV models produced
let y represent the number of MegaTeleBox models produced

(2)
2x + 3y ≤ 192       manpower constraint
x + y = 72             production capacity constraint
x ≥ 0                     Non-negativity constraint
y ≥ 0                     Non-negativity constraint

(3)
See attached graph

Step-by-step explanation:

(1)
Let x represent the number of HD Big View TV models produced
let y represent the number of MegaTeleBox models produced

(2)

Constraints
There are a total of 192 person hours per day to manufacture both models so this is the upper limit on the person-hours resource

Each unit of HD Big View takes 2 person-hours so x units will require 2x person-hours

Each unit of MegaTeleBox   takes 3 person-hours so y units will require 3y person-hours

Total person-hours to produce x and y units
= 2x + 3y
and this cannot exceed 192.

Therefore the first inequality is manpower resource constraint:
2x + 3y ≤ 192     [1]

Total manufacturing capacity is 72 units. The actual total production is
x + y and this cannot exceed 72

Second inequality is
x + y = 72             [2]

In addition the number of units produced cannot be less than zero. These are the non-negativity constraints:
x ≥ 0, y ≥ 0    [3]

Plugging in all these constraints we get the following system of inequalities

2x + 3y ≤ 192       [1]  manpower constraint
x + y = 72             [2]  production capacity constraint
x ≥ 0                     Non-negativity constraint
y ≥ 0                      Non-negativity constraint

(3) See attached graph for this part of the question

The dark shaded region shows the solution set

To show that the company cannot make a negative number of television sets we only consider values on the positive x and y axes

Option E would be (10+5 square root would be 2) cm, which is also incorrect as it does not represent the correct perimeter of the square.

In the figure attached, ABC is a square, AC is diagonal and measures 10 cm. What is the perimeter of the square? A) 20 cm. B) 40 cm. C) (10+10 square root would be 2) cm. D) (5+10 square root would be 2) cm. E) (10+5 square root would be 2) cm.The perimeter of a square is equal to the sum of all four sides. Since ABC is a square, the sides are equal in length. Since AC is the diagonal of the square, it is equal to the length of the two consecutive sides. Therefore, the length of each side AB and BC is equal to 10 cm. Therefore, the perimeter of the square ABC is 20 cm (10 cm x 2). This is option A, 20 cm. The other options are not correct as they do not represent the correct perimeter of the square. Option C would be (10+10 square root would be 2) cm, which is incorrect as it does not represent the correct perimeter of the square. Option D would be (5+10 square root would be 2) cm, which is also incorrect as it does not represent the correct perimeter of the square. Lastly, Option E would be (10+5 square root would be 2) cm, which is also incorrect as it does not represent the correct perimeter of the square.

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The numbers when decomposed using their prime factors are 72: 2³ × 3², 204: 2² × 3 × 17, 1800: 2³ × 3² × 5² and  42336: 2⁵ × 3 × 11² × 17

To decompose a number into its prime factors, we need to find the prime numbers that multiply together to give the original number.

The numbers are given as  72, 204, 1800, and 42336

So, we have

Let's decompose each of the given numbers:

72 = 2 × 2 × 2 × 3 × 3

Prime factorization: 2³ × 3²

204 = 2 × 2 × 3 × 17

Prime factorization: 2² × 3 × 17

1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5

Prime factorization: 2³ × 3² × 5²

42336 = 2 × 2 × 2 × 2 × 2 × 3 × 11 × 11 × 17

Prime factorization: 2⁵ × 3 × 11² × 17

Therefore, the prime factorization of each number is:

72: 2³ × 3²

204: 2² × 3 × 17

1800: 2³ × 3² × 5²

42336: 2⁵ × 3 × 11² × 17

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The best description of how close the prediction was to the actual population in 2013 is option (A) with in 100 people

To solve this problem, we can use the exponential growth formula:

P(t) = P0 × e^(rt)

where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.718.

We can use the given data to find the growth rate r:

58,000 = 42,000 × e^(r×30)

Dividing both sides by 42,000:

e^(r×30) = 58,000/42,000 = 1.38

Taking the natural logarithm of both sides:

r×30 = ln(1.38)

r = ln(1.38)/30

r ≈ 0.0106

Now we can use this growth rate to predict the population in 2013:

P(53) = 42,000 × e^(0.0106×53) ≈ 74,480

So the predicted population of 74,480 is within 520 people of the actual population of 75,000

Therefore, the correct option is (A) Within 100 people.

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The can measure exactly 4 litres by having 1 2/3 in the 5litres container and 2 2/3 in the 7 litres container

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and been asked to imagine how you would solve it using math.

These word problems are interpreted into mathematical equation or expression.

If the woman wants to have the water in two containers with a good ratio, then we say;

The ratio of container 1 to container 2 is 5:7

therefore;

the amount of water in 5litres container = 5/12 × 4 5/3 = 1 2/3 litres

the amount of water in 7 litres = 7/12 × 4 = 7/3 = 2 2/3 litres

Therefore to measure it, she will have 1 2/3 in the 5litres container and 2 2/3 in the 7 litres container

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The volume of the right circular cone is approximately 1819.1 cubic centimeters.

Volume is the measure of the amount of space occupied by a three-dimensional object or shape. It is expressed in cubic units, such as cubic centimeters, cubic meters, or cubic inches, depending on the system of measurement being used. The formula for volume varies depending on the shape of the object, but for many common three-dimensional shapes, such as cubes, spheres, cylinders, and cones, there are well-known formulas for calculating their volumes.

According to the given information :

The formula for the volume of a right circular cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.

Substituting the given values, we get:

V = (1/3)π(9.6 cm)²(19.9 cm)

V ≈ 1819.1 cubic centimeters (rounded to the nearest tenth)

Therefore, the volume of the right circular cone is approximately 1819.1 cubic centimeters.

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