A fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the standard deviation to be 1.8. She thinks the mean is 5.7 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.12 at the 85% level of confidence? Round your answer up to the next integer.

Answer:

25.02% probability that exactly 19 men and 18 women are chosen

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the men and the women are selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

Desired outcomes:

19 men, from a set of 25

18 women, from a set of 22

[tex]D = C_{25,19}*C_{22,18} = \frac{25!}{19!6!}*\frac{22!}{18!4!} = 1295486500[/tex]

Total outcomes:

37 people from a set of 25 + 22 = 47. So

[tex]T = C_{47,37} = \frac{47!}{37!10!} = 5178066751[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{1295486500}{5178066751} = 0.2502[/tex]

25.02% probability that exactly 19 men and 18 women are chosen

Answer:

8 years old.

(3x+9)

(3(8)+9)=33

Answer

i think its federal income tax increase. 2nd one i believe

Step-by-step explanation:

The President of the United States proposes a new national plan to reduce water pollution.

Which of these would most likely provide the revenue to pay for this new public service?

Step-by-step explanation:

answer is :

Answer:

1. 60 in cubed.

2. 36 m cubed.

3. 96 m cubed.

4. 60 yds cubed.

5. 120 in cubed.

Step-by-step explanation:

Alright, we need to know what the formula is for the volume of a triangular prism. Before that, here is the formula to find the volume of all shapes. Some formulas may be different for cones, spheres, and pyramids, but this is the general formula.

The formula is V=Bh.

V is your volume

B is the area of the base

h is the height of the prism..

The formula for calculating the volume for a triangular prism is 1/2bh times h. 1/2bh is the formula for finding the area of your triangle which is the base shape for a triangular prism. The other h is the height of your prism.

For number 1, they already calculated the area of the base for you, so just multiply that number with the height. 20 times 3 is 60.

That is 60 meters cubed.

Number 2, they haven't calculated the area of the base, so you have to do that. The length of the triangle is 4 and the height of the triangle is 3. Lets find the area of the triangle or the base, Do 4 times 3 which is 12 and divide it by 2 or multiply it by half. it is the same thing. You get 6, and that is the area of your base. Multiply that area by the height of the prism. You get 36 meters cubed. The reason why it is cubed is because meter times meter times meter is meter cubed.

Hope this helps!

Answer:

11 - 9 = 2 trick-or-treaters out of 11 were not dressed as pirates so the proportion is 2/11.

Answer: Ratio is 2:11

Step-by-step explanation:

So your ratio of pirates to non-pirates would be 9:11

So you subtract number of pirates from total trick-or-treaters and get 2.

So the proportion of non-pirates would be 2:11.

Step-by-step explanation:

solution.

if variable d increases then w reduces

w=k.u ×1/d

=ku/d

therefore w=k.u/d

Answer: 0.5

Step-by-step explanation:

To find the slope of a line with two given points, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

[tex]m=\frac{2-1}{4-2}=\frac{1}{2}=0.5[/tex]

The slope is 0.5.

Answer:

√6

Step-by-step explanation:

√6 = 2.44948974278...

The number never ends and the values don't repeat therefore, the correct answer is √6.

Hope this helps! :)

Answer:

B. The square root of 5

Step-by-step explanation:

You can only square root a number that can be the answer to an equation like x*x=5, which it is not.

Answer:

[tex]\frac{2}{12}[/tex] simplified to [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

4 = [tex]\frac{1}{12}[/tex]

2 = [tex]\frac{1}{12}[/tex]

[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{12}[/tex] = [tex]\frac{2}{12}[/tex] ÷ 2 = [tex]\frac{1}{6}[/tex]

Answer:

The graph g(x) is the graph f(x) vertically stretched by a factor of 7.

Step-by-step explanation:

Quadratic Equation: f(x) = a(bx - h)² + k

Since we are modifying the variable a, we are dealing with vertical stretch (a > 1) or vertical shrink (a < 1). Since a > 1 (7 > 1), we are dealing with a vertical stretch by a factor of 7.

Answer:

The graph g(x) is the graph f(x) vertically stretched by a factor of 7.

Step-by-step explanation:

Quadratic Equation: f(x) = a(bx - h)² + k

Since we are modifying the variable a, we are dealing with vertical stretch (a > 1) or vertical shrink (a < 1). Since a > 1 (7 > 1), we are dealing with a vertical stretch by a factor of 7.

Answer:

0, 10

Step-by-step explanation:

The given function is:

[tex]g(y) = \frac{y-5}{y^2-3y+15}[/tex]

According to the quotient rule:

[tex]d(\frac{f(y)}{h(y)}) = \frac{f(y)*h'(y)-h(y)*f'(y)}{h^2(y)}[/tex]

Applying the quotient rule:

[tex]g(y) = \frac{y-5}{y^2-3y+15}\\g'(y)=\frac{(y-5)*(2y-3)-(y^2-3y+15)*(1)}{(y^2-3y+15)^2}[/tex]

The values for which g'(y) are zero are the critical points:

[tex]g'(y)=0=\frac{(y-5)*(2y-3)-(y^2-3y+15)*(1)}{(y^2-3y+15)^2}\\(y-5)*(2y-3)-(y^2-3y+15)=0\\2y^2-3y-10y+15-y^2+3y-15\\y^2-10y=0\\y=\frac{10\pm \sqrt 100}{2}\\y_1=\frac{10-10}{2}= 0\\y_2=\frac{10+10}{2}=10[/tex]

The critical values are y = 0 and y = 10.

Answer:

0.45 ft/min

Step-by-step explanation:

Given:-

- The flow rate of the gravel, [tex]\frac{dV}{dt} = 35 \frac{ft^3}{min}[/tex]

- The base diameter ( d ) of cone = x

- The height ( h ) of cone = x

Find:-

How fast is the height of the pile increasing when the pile is 10 ft high?

Solution:-

- The constant flow rate of gravel dumped onto the conveyor belt is given to be 35 ft^3 / min.

- The gravel pile up into a heap of a conical shape such that base diameter ( d ) and the height ( h ) always remain the same. That is these parameter increase at the same rate.

- We develop a function of volume ( V ) of the heap piled up on conveyor belt in a conical shape as follows:

                                [tex]V = \frac{\pi }{12}*d^2*h\\\\V = \frac{\pi }{12}*x^3[/tex]

- Now we know that the volume ( V ) is a function of its base diameter and height ( x ). Where x is an implicit function of time ( t ). We will develop a rate of change expression of the volume of gravel piled as follows Use the chain rule of ordinary derivatives:

                               [tex]\frac{dV}{dt} = \frac{dV}{dx} * \frac{dx}{dt}\\\\\frac{dV}{dt} = \frac{\pi }{4} x^2 * \frac{dx}{dt}\\\\\frac{dx}{dt} = \frac{\frac{dV}{dt}}{\frac{\pi }{4} x^2}[/tex]

- Determine the rate of change of height ( h ) using the relation developed above when height is 10 ft:

                              [tex]h = x\\\\\frac{dh}{dt} = \frac{dx}{dt} = \frac{35 \frac{ft^3}{min} }{\frac{\pi }{4}*10^2 ft^2 } \\\\\frac{dh}{dt} = \frac{dx}{dt} = 0.45 \frac{ft}{min}[/tex]

Answer:

We failed to reject H₀

t < 2.06

1.5 < 2.06

We do not have significant evidence at significance level α=0.05 to show that the mean G.P.A. of CC students transferring to Sac State is above 3.3

Step-by-step explanation:

Set up hypotheses:

Null hypotheses = H₀: μ = 3.3

Alternate hypotheses = H₁: μ > 3.3

Determine type of test:

Since the alternate hypothesis states that mean G.P.A. of CC students transferring to Sac State is above 3.3, therefore we will use a upper-tailed test.

Select the test statistic:  

Since the sample size is very small (n < 30) therefore, we will use t-distribution.

Determine level of significance and critical value:

Given level of significance = 5% = 0.05

Since it is a upper tailed test,

At α = 0.05 and DF = n – 1 =  25 - 1 = 24

t-score =  2.06

Set up decision rule:

Since it is a upper tailed test, using a t statistic at a significance level of 5%

We Reject H₀ if t > 2.06

Compute the test statistic:

[tex]$ t = \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n} } } $[/tex]

[tex]$ t = \frac{ 3.45- 3.3 }{\frac{0.5}{\sqrt{25} } } $[/tex]

[tex]t = 1.5[/tex]

Conclusion:

We failed to reject H₀

t < 2.06

1.5 < 2.06

We do not have significant evidence at significance level α=0.05 to show that the mean G.P.A. of CC students transferring to Sac State is above 3.3

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ equal to 100000

For the alternative hypothesis,

H1: µ greater than 100000

This is a right tailed test

Since the population standard deviation is nit given, the distribution is a student's t.

Since n = 200

Degrees of freedom, df = n - 1 = 200 - 1 = 199

t = (x - µ)/(s/√n)

Where

x = sample mean = 103157

µ = population mean = 100000

s = samples standard deviation = 27498

t = (103157 - 100000)/(27498/√200) = 1.62

We would determine the p value using the t test calculator.

p = 0.053

Alpha = 10% = 0.1

Since alpha, 0.1 > than the p value, 0.053, then

b) At the 10% significant level, the p-value/statistics is 0.053, so we should not reject the null hypothesis.

c) Hence, we may conclude that the average has not increased and the probability that our conclusion is correct is at least 90 percent.

Answer:

x>0

Step-by-step explanation:

The domain are the possible values of x you can use.

For ln functions, x must be positive (the ln of a negative number does not exist).

So, x must be larger than 0. No part of the graph will be left of the y axis.

Answer:

The answer is option A.

Hope this helps you

Answer:

Step-by-step explanation:

To get the missing values in the table, we will factorize the given expression and compare the factored expression with the expression containing the missing constants.

1) For the expression x²+2x-8, on factorizing we have;

x²+2x-8

= (x²+4x)-(2x-8)

Factoring out the common terms from both parenthesis;

= x(x+4)-2(x+4)

= (1x+4)(1x-2)

=  (1x-2)(1x+4)

Comparing the resulting expression with (ax+b)(cx+d)

a = 1, b = -2, c = 1 and d = 4

2) For the expression 2x³+2x²-24x

Factoring out the common term we will have;

= 2x(x²+x-12)

= 2x(x²-3x+4x-12)

= 2x{x(x-3)+4(x-3)}

= 2x{(x+4)(x-3)}

=  2x(1x-3)(1x+4)

Comparing the resulting expression with 2x(ax+b)(cx+d)

a = 1, b = -3. c = 1 and d = 4

3) For the expression 6x²-15x-9 we will have;

On simplifying,

= 6x²+3x-18x-9

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

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

Comparing the resulting expression with (ax+b)(cx+d)

a = 3, b = -9, c = 2 and d = 1

Answer:

see picture attachment

Step-by-step explanation:

Answer:

1/10 per sec

Step-by-step explanation:

When he's walked x feet in the eastward direction, the angle Θ that the search light makes has tangent

tanΘ = x/18

Taking the derivative with respect to time

sec²Θ dΘ/dt = 1/18 dx/dt.

He's walking at a rate of 18 ft/sec, so dx/dt = 18.

After 3seconds,

Speed = distance/time

18ft/sec =distance/3secs

x = 18 ft/sec (3 sec)

= 54ft. At this moment

tanΘ = 54/18

= 3

sec²Θ = 1 + tan²Θ

1 + 3² = 1+9

= 10

So at this moment

10 dΘ/dt = (1/18ft) 18 ft/sec = 1

10dΘ/dt = 1

dΘ/dt = 1/10 per sec

At 1/10 per second is the rate when the light turns 3 seconds after he started walking east.

It is given that a man starts at point A and walks 18 feet north. He then turns and walks due east at 18 feet per second.

It is required to find at what rate is the light turning 3 seconds after he started walking east.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

The [tex]\rm tan\theta[/tex] is the ratio of the perpendicular to the base.

When he started walking eastward direction, the searchlight makes an angle [tex]\theta[/tex]

Let the distance is x

And the  [tex]\rm tan\theta = \frac{x}{18}[/tex]

After performing the derivate with respect to time, we get:

[tex]\rm sec^2\theta\frac{d\theta}{dt} = \frac{1}{18} \frac{dx}{dt}[/tex] ...(1)    ( the differentiation of [tex]\rm tan\theta \ is \ sec^2\theta\\[/tex])

He walking at the rate of 18 ft per second ie.

[tex]\rm \frac{dx}{dt} = 18[/tex]  

After 3 seconds  [tex]\rm Speed=\frac{Distance}{Time}[/tex]

By using speed- time formula we can calculate the distance:

Distance x = 18×3 ⇒ 54 ft.

[tex]\rm tan\theta = \frac{54}{18}[/tex]  ⇒3

We know that:

[tex]\rm sec^2\theta = 1+tan^2\theta[/tex]

[tex]\rm sec^2\theta = 1+3^2\\\\\rm sec^2\theta = 10\\[/tex]

Put this value in the (1) equation, we get:

[tex]\rm 10\frac{d\theta}{dt} = \frac{1}{18} \times18[/tex]    ∵ [tex]\rm (\frac{dx}{dt} =18)[/tex]

[tex]\rm 10\frac{d\theta}{dt} = 1\\\\\rm \frac{d\theta}{dt} = \frac{1}{10} \\\\[/tex]per second.

Thus, at 1/10 per second what rate is the light turning 3 seconds after he started walking east.

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Answer:

5

Step-by-step explanation:

Answer:

Jet= 420 mph     Wind = 10mph

Step-by-step explanation:

The speed of the plane in a tailwind can be modeled by x+y where x is the speed of the plane and y is the speed of the wind. Dividing 1290 by 3 gets you the average speed of the jet in a tailwind, which is 430.

The speed of the plane in a headwind can be modeled by x-y where x is the speed of the plane and y is the speed of the wind. Dividing 1230 by 3 gets you the average speed of the jet in a tailwind, which is 410.

This can be modeled by a system of equations, where x+y=430 and x-y=410. Solving the equation you get x=420 and y=10.

So, the speed of the jet is 420 mph and the speed of the wind is 10 mph.

Answer:

The answer is: 325 517 424 395 494

Step-by-step explanation:

Answer:

The real and imaginary parts of the result are [tex]\frac{1441}{1601}[/tex] and [tex]\frac{4}{1601}[/tex], respectively.

Step-by-step explanation:

Let be [tex]f(z) = \frac{z}{z+1}[/tex], the following expression is expanded by algebraic means:

[tex]f(z) = \frac{z\cdot (z-1)}{(z+1)\cdot (z-1)}[/tex]

[tex]f(z) = \frac{z^{2}-z}{z^{2}-1}[/tex]

[tex]f(z) = \frac{z^{2}}{z^{2}-1}-\frac{z}{z^{2}-1}[/tex]

If [tex]z = 4 - i5[/tex], then:

[tex]z^{2} = (4-i5)\cdot (4-i5)[/tex]

[tex]z^{2} = 16-i20-i20-(-1)\cdot (25)[/tex]

[tex]z^{2} = 41 - i40[/tex]

Then, the variable is substituted in the equation and simplified:

[tex]f(z) = \frac{41-i40}{41-i39} -\frac{4-i5}{41-i39}[/tex]

[tex]f(z) = \frac{37-i35}{41-i39}[/tex]

[tex]f(z) = \frac{(37-i35)\cdot (41+i39)}{(41-i39)\cdot (41+i39)}[/tex]

[tex]f(z) = \frac{1517-i1435+i1443+1365}{3202}[/tex]

[tex]f(z) = \frac{2882+i8}{3202}[/tex]

[tex]f(z) = \frac{1441}{1601} + i\frac{4}{1601}[/tex]

The real and imaginary parts of the result are [tex]\frac{1441}{1601}[/tex] and [tex]\frac{4}{1601}[/tex], respectively.

Answer:

a{(1, 3), (2, 3), (4,3), (9,3)}

Step-by-step explanation:

For the relation to be a function, each x can only go to 1 y

a{(1, 3), (2, 3), (4,3), (9,3)}

function

b{(1, 2), (1, 3), (1, 4), (1,5)}

x=1 goes to 4 different y's so not a function

c{(5, 4), (-6, 5), (4, 5), (4, 0)}

x=4 goes to 2 different y's so not a function

d{(6,-1), (1,4), (2, 3), (6, 1)}​

x = 6 goes to 2 different y's so not a function

Hey there!

To find the answer, we just need to see which point falls in this blue, which represents the inequality.

We see that the point (5,-5) is not on the blue.

We see that the point (1,5) is on the blue.

(-3,-3) is on the dotted line but not a solution of the inequality. The dotted line is excluded from the inequality. If it were a bold line, then it would be a solution of the inequality.

(3,-1) is also on the dotted line so it is not a solution.

Therefore, the answer is B. (1,5)

I hope that this helps!

We want to see which point is a solution for the graphed inequality.

We will find that the correct option is B, (1, 5)

Notice that the line that defines the inequality contains the points (-3, -3) and (3, -1)

Then the slope of that line is:

[tex]a = \frac{-1 -(-3)}{3 - (1)} = 1/2[/tex]

Then the line is something like:

y = (1/2)*x + b

To find the value of b, we use the fact that this line passes through the point (3, -1), then we have:

-1 = (1/2)*3 + b

-1 - 3/2 + b

-5/2 = b

So the line is:

y = (1/2)*x - 5/2

And we can see that the line is slashed, and the shaded area is above the line, then we have:

y > (1/2)*x - 5/2

Now that we have the inequality, we can just input the values of the points in the inequality and see if this is true.

First, options C and D can be discarded because these points are on the line, and the points on the line are not solutions.

So we only try with A and B.

A) x = 5

   y = -5

then we have:

-5 > (1/2)*5 - 5/2

-5 > 0

Which clearly is false.

B) x = 1

   y = 5

Then we have:

5 > (1/2)*1 - 5/2 = -4/2

5 > -4/2

This is true, then the point (1, 5) is a solution.

Thus the correct option is B.

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Answer:

  54.8 N·m

Step-by-step explanation:

The horizontal distance from the dumbbell to the elbow is ...

  (0.366 m)cos(15°) ≈ 0.3535 m

Then the torque due to the vertical force is ...

  (155 N)(0.3535 m) = 54.8 N·m

1) The marginal profit is [tex]4.3 - 0.7 ln(x)[/tex].

2) The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.

Thus, option (A) is correct.

C) To maximize profit 462,481 thousands of candles should be sold.

Given: [tex]P(x) = 5 x - 0.7 x[/tex] [tex]{\text}ln x.[/tex]

1) Take the derivative of the profit function P(x) with respect to x.

P(x) = 5x - 0.7x ln(x)

To find P'(x), differentiate each term separately using the power rule and the derivative of ln(x):

[tex]P'(x) = 5 - 0.7(1 + ln(x))[/tex]

       = [tex]5 - 0.7 - 0.7 ln(x)[/tex]

       = [tex]4.3 - 0.7 ln(x)[/tex]

2) Substitute x = 10 into the derivative:

P'(10) = 4.3 - 0.7 ln(10)

         = 4.3 - 0.7(2.30259)

         = 4.3 - 1.61181

         = 2.68819

Therefore, the additional profit for selling a thousand candles once 10,000 candles have already been sold.

Thus, option (A) is correct.

C) Set P'(x) = 0 and solve for x:

[tex]4.3 - 0.7 ln(x) = 0[/tex]

[tex]0.7 ln(x) = 4.3[/tex]

[tex]{\text} ln(x) = 4.3 / 0.7[/tex]

[tex]{\text} ln(x) = 6.14286[/tex]

[tex]x = e^{6.14286[/tex]

[tex]x = 462.481[/tex]

Therefore, 462,481 thousands of candles should be sold.

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1) The marginal profit, P'(x), is -0.7ln(x) + 4.3.

2) The number of thousands of candles that should be sold to maximize profit is approximately 466.9.

1) To find the marginal profit, P'(x), we need to take the derivative of the profit function, P(x), with respect to x. Using the power rule and the chain rule, we can differentiate the function:

P(x) = 5x - 0.7x ln(x)

Taking the derivative with respect to x:

P'(x) = 5 - 0.7(ln(x) + 1)

Simplifying:

P'(x) = 5 - 0.7ln(x) - 0.7

P'(x) = -0.7ln(x) + 4.3

2) To find P'(10), we substitute x = 10 into the marginal profit function:

P'(10) = -0.7ln(10) + 4.3

Using a calculator, we can evaluate this expression:

P'(10) ≈ -0.7(2.3026) + 4.3 ≈ -1.6118 + 4.3 ≈ 2.6882

The value of P'(10) is approximately 2.6882.

Now, let's interpret what P'(10) represents:

The correct interpretation is A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.

P'(10) represents the rate at which the profit is changing with respect to the number of candles sold when 10,000 candles have already been sold. In other words, it measures the additional profit (in thousands of dollars) for each additional thousand candles sold once 10,000 candles have already been sold.

Lastly, to determine the number of thousands of candles that should be sold to maximize profit, we need to find the critical points of the profit function P(x). This can be done by setting the derivative P'(x) equal to zero and solving for x.

-0.7ln(x) + 4.3 = 0

-0.7ln(x) = -4.3

ln(x) = 4.3 / 0.7

Using properties of logarithms:

x = e^(4.3 / 0.7)

Using a calculator, we can evaluate this expression:

x ≈ e^(6.1429) ≈ 466.9

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Answer:

See Explanation

Step-by-step explanation:

Given:

Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10).

(a)If we translate  quadrilateral JKLM 3 units down and 3 units left:

(x-3,y-3), we obtain: W(5,1), X(1,7), Y(9,9), and Z(11,7)

Therefore, we match it with: A translation 3 units down and 3 units left

(b)If we translate  quadrilateral JKLM 2 units right and 3 units down:

(x+2,y-3), we obtain: O(10,1), P(6,7), Q(14,9), and R(16,7)

Therefore, we match it with:A translation 2 units right and 3 units down

S(4, 16), T(10, 20), U(12, 12), and V(10, 10)

(c) If we transform quadrilateral JKLM by a sequence of reflections across the x- and y-axes, in any order, we obtain:

A(-8, -4), B(-4, -10), C(-12, -12), and D(-14, -10)

(d)If we translate  quadrilateral JKLM 3 units left and 2 units up:

(x-3,y+2), we obtain:E(5,6), F(1,12), G(9,14), and H(11,12)

Therefore, we match it with: A translation 3 units left and 2 units up

(e)S(4, 16), T(10, 20), U(12, 12), and V(10, 10)

No suitable transformation is found from JKLM to STUV.

Answer:

a translation 3 units down and 3 units left

W(5,1), X(1,7), Y(9,9), and Z(11,7)

a translation 2 units right and 3 units down

O(10,1), P(6,7), Q(14,9), and R(16,7)

a sequence of reflections across the

x- and y-axes, in any order

S(4, 16), T(10, 20), U(12, 12), and V(10, 10)

a translation 3 units left and 2 units up

E(5,6), F(1,12), G(9,14), and H(11,12)

Answer:

7

Step-by-step explanation:

Remove parentheses.

[tex]\frac{-8+4(4.5)}{6.25-8.25} \\[/tex]

Add −8 and 4.5.

[tex]\frac{4(-3.5)}{6.25 - 8.25} \\\\[/tex]

Subtract 8.25 from 6.25.

[tex]\frac{4*-3.5}{-2}[/tex]

Multiply 4 by −3.5.

[tex]\frac{-14}{-2}[/tex]

Divide −14 by −2.

= 7

Answer:

Step-by-step explanation:

the mass is 2000 mg, or 2 g.

the density is 8 g/cm^3

divide 2 by 8

0.25 cm^3

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Answer:

Theoretical probability = 50%

Experimental probability varies.

See below for explanation.

Step-by-step explanation:

This is a problem on theoretical and experimental probability. The results obtained would enable you understand their differences.

The theoretical probability is the result that is expected to happen, but it isn't always what eventually happens.

The theoretical probability of a coin landing on heads is ½ or 50%. This is same for tails.

The experimental probability is the probability obtained from carrying out the experiment. As this is the result of what actually happens, the experimental probability could be lesser  or greater than or equal to 50%.

You are required to carry out the experiment. This is because the result would vary from person to person as well as from one experiment to the other.

First, make a table for the number of trials, outcome (head and tail each) and the frequency. Pen down the result for each of the experiment carried out. You can use a tally to make it easy for compilation.

See attachment for table.

Theoretical probability of 10 trials:

Head= 5, tail = 5

Theoretical probability of 30 trials:

Head= 15, tail = 15

Theoretical probability of 100 trials:

Head= 50, tail = 50

It all amount to 50% each

So do your experiment and record the results. Afterwards compare your result  which is the experimental probability

for head and tail with the theoretical theoretical.

Also compare your result with that of your classmate.