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A coin is biased such that it results in 2 heads in every 3 coin flips, on average. The sequence is most probable for the biased

Tomtit [17]

33% Probability of displaying tails.

5 0

3 years ago

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A college entrance exam company determined that a score of 2222 on the mathematics portion of the exam suggests that a student i

kolbaska11 [484]

Answer:

Yes, Students are scoring above 2222 on the math portion of the exam.

Step-by-step explanation:

We are given that a college entrance exam company determined that a score of 2222 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics i.e., population mean is 22.

Null Hypothesis, $H_0$ : $\mu$ = 22 {Students are scoring equal to 2222 on the math portion of the exam}

Alternate Hypothesis, $H_0$ : $\mu$ > 22 {Students are scoring above 2222 on the math portion of the exam}

Also, a random sample of 150 students who completed this core set of courses results in a mean math score of 22.7 on the college entrance exam with a standard deviation of 3.93 i.e.;

Sample mean, $Xbar$ = 22.7 and Sample standard deviation, s = 3.93

The Test statistics is given by;

Z = $\frac{Xbar -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

Test Statistics = $\frac{22.7 -22}{\frac{3.93}{\sqrt{150} } }$ ~ $t_1_4_9$

= 2.1815

Since, we are not given with the significance level, so we assume it to be 5%. At 5% significance level t table gives critical value of 1.6578 at 149 degree of freedom. Since our test statistics is more than the critical value so we reject null hypothesis as our test statistics fall in the rejection region.

Therefore, we conclude that Students are scoring above 2222 on the math portion of the exam.

7 0

3 years ago

Find the missing factor 6s^2-7s-5=(3s-5)()

victus00 [196]

Answer: 2s + 1

Explanation:

1) Given expression: 6s² - 7s- 5 = (3s - 5) ( )

2) The missing factor ( ) is such that when it is multiplied by (3s - 5) the product is 6s² - 7s- 5.

3) Since the first term of the first factor starts with 3s, the first term of the second factor shall be 2s (since they have to yield 6s²). Then, you can write:

6s² - 7s- 5 = (3s - 5) (2s + )

4) The second term of the missing factor is positive because the product (+)(-) = (-) which is the sign of the third term of the polynomial.

5) The second term is such that when multiplied by - 5 is equal to the last term of the polynomial (also - 5), so this second terms is +1.

And you get: 6s² - 7s- 5 = (3s - 5) (2s + 1)

6) You can expand, using distributive property to confirm the result:

(3s - 5) (2s + 1 ) = (3s)(2s) + (3s)(1) - (5)(2s) -(5)(1) = 6s² - 7s- 5, which confirms the result.

3 0

3 years ago

A water tank is in the shape of a right circular cone as shown above. The diameter of the cone is 10 feet, and the height is 15

Vsevolod [243]

Answer:

The rate at which the height of the water tank is changing is approximately 0.4244 ft/hour

Step-by-step explanation:

The given parameters are;

The diameter of the cone = 10 feet

The height of the cone = 15 feet

The rate at which water is leaking from the tank, (dV/dt) = 12 ft³/h

The volume of water in the tank = 27·π cubic feet

The volume V of a right circular cone with radius r and height h = 1/3×π×r²×h

The rate of change of the volume, dV, with time dt is given as follows;

The radius of the cone when the volume of the water in the tank is 27·π cubic feet is given as follows;

1/3×π×r²×h = 27·π ft³

The ratio of the height to the radius of the cone is h/r = 15/5 = 3

h/r = 3

∴ r =h/3

The volume of the cone, V = 1/3×π×r²×h = 1/3×π×(h/3)²×h = 1/27×π×h³ = h³/27×π

dV/dt = dV/dh × dh/dt

Which gives;

12 = d(h³/27×π)/dh × dh/dt = π×h²/9 × dh/dt

dh/dt = 12/(π×h²/9)

At 27·π ft³ = 1/27×π×h³ ft³, we have;

27 = 1/27×h³

27² = h³

h = ∛27² = 9

∴ dh/dt = 12/(π×h²/9) = 12/(π×9²/9) = 12/(π×9) = 4/(3·π) ≈ 0.4244 ft/hour

The rate at which the height of the water tank is changing ≈ 0.4244 ft/hour.

6 0

3 years ago

What value of x makes the equation true?<br> -1=1 – 4(-5+4x) – 4x

cluponka [151]

Answer:

x = 11/10

Step-by-step explanation:

we have from statement:

-1=1 - 4(-5+4x) – 4x

we apply distributive property:

-1 = 1 -4*(-5) -4*(4x) -4x

so we have:

-1= 1+20 -16x -4x

-1 = 21 -20x

-22=-20x

so we have:

x=22/20

x=11/10

we can substitute the x value found:

-1 = 1 - 4(-5+4*(11/10)) – 4*(11/10)

-1 = 1+20 -17.6 -4.4

-1 =21 -22

so we have:

-1 = -1

4 0

4 years ago