The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. Choose two pregnancies independently and at random.
A) What is the expected difference in the lengths of the two pregnancies?
B) What is the standard deviation of difference in the lengths of the two pregnancies?
C) Find the probability that the difference in the lengths of the two pregnancies is greater than 25 days.

Answer:

576

Step-by-step explanation:

6 papers an hour. 7 hours spent grading.

So 7•6 = 42

618-42

576

Hope this helps

The probability of 2 cars crossing the bridge from X to Y in a 1-minute period is:

P(X = 2) = ((λ^x) / x!) * e^(-λ)

P(X = 2) = ((XX/100 * 10)^2 / 2!) * e^(-XX/100 * 10)

P(X = 2) = (XX/500) * e^(-XX/100 * 10)

P(X = 2) = (XX/500) * 0.000045

a) Let X be the number of cars that cross the bridge in a 1-minute period.

Since the Poisson process with a rate of µ = 600/hour, the rate of cars crossing the bridge is

λ = 600/60

= 10/min.

The probability that two cars will cross the bridge during the 1-minute period can be calculated by the following formula:

P(X = 2) = ((λ^x) / x!) * e^(-λ)

P(X = 2) = ((10^2) / 2!) * e^(-10)

P(X = 2) = 0.0045

b) Let Y be the number of cars that travel from X to Y in a 1-minute period.

Since the probability that a car travels from X to Y is p = 0.XX,

The probability that a car travels from Y to X is 1 - p.

As per the Poisson process, the probability of

λ = 10/min.

Let X be the number of cars that cross the bridge from X to Y in a 1-minute period.

Then X follows a Poisson distribution with a rate of

µ = 10*p

= XX/100 * 10.  

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The average number of full-time students in samples of size 16 is B) 3.5.

Because of the extraordinarily huge population, this can be regarded a binomial distribution if all students globally are considered. A normal distribution is commonly used to approximate the binomial distribution. As a result, the mean equals the expectation:

E[x] = np = (16)(0.22) = 3.52

μ = 3.52

The likelihood of success raised to the power of the number of successes is multiplied by the probability of failure raised to the power of the difference between the number of successes and the number of trials. The product is then multiplied by the sum of the number of trials and successes.

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The value of the test statistic is  x² = 3.841.

Therefore option B is correct.

Expected frequency for "Health insurance" and "Men"

= (80 * 70) / 110= 50.909

Expected frequency for "Health insurance" and "Women"

= (30 * 70) / 110 =  19.091

Expected frequency for "No health insurance" and "Men"

= (80 * 40) / 110

= 29.091

Expected frequency for "No health insurance" and "Women"

= (30 * 40) / 110 =  10.909

We find the chi-square statistic

χ² = Σ [(O - E)² / E]

χ² = [(50 - 50.909)² / 50.909] + [(20 - 19.091)² / 19.091] + [(30 - 29.091)² / 29.091] + [(10 - 10.909)² / 10.909]

= (0.081² / 50.909) + (0.909² / 19.091) + (0.909² / 29.091) + (0.081² / 10.909)

=  0.00131 + 0.04537 + 0.02784 + 0.00604

= 0.08056

We find  the critical value for a 0.05 significance level and 1 degree of freedom = 3.841.

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complete question:

A survey conducted in a small business yielded the results shown in the table. Test the claim that health care coverage is independent of gender. Use a 0.05 significance level. What is the value of the test statistic?

                                    Men          Women

Health insurance           50              20

No health insurance      30               10

OA. x^2=0.1637

OB. x^2=8.263

OC. x^2 =3.841

OD. x^2 =5.821

Answer:

The area of the circle is 28.26 m

Step-by-step explanation:

A = π r^2

A = (3.14) × 3^2

A = 28.26

Area of the circle = 28.26 m

(I'm sorry but I think you made a mistake, PI is 3.14 not 3.15) :)

Answer:

x=6

Step-by-step explanation:

x+2=8

subtract 2 from both sides

x=6

The interval of convergence, I, is (-∞, +∞), which means the series converges for all real values of x.

To find the radius of convergence, use the ratio test. The ratio test states that for a power series of the form:

Σ(aₙ × xⁿ)

where aₙ is the nth term of the series, the radius of convergence R is given by:

R = lim(n→∞) |aₙ / a_(n+1)|

In this case, the series:

Σ(n!) × xⁿ

Apply the ratio test to find the radius of convergence:

|aₙ / a_(n+1)| = |(n!) × xⁿ / ((n+1)!) × xⁿ⁺¹|

= |x / (n+1)|

Taking the limit as n approaches infinity:

lim(n→∞) |x / (n+1)| = |x / ∞| = 0

Since the limit is 0, the series converges for all values of x. This means that the radius of convergence, R, is infinite (R = ∞).

Now, let's find the interval of convergence, I. Since the radius of convergence is infinite, the series converges for all values of x. Therefore, the interval of convergence, I, is (-∞, +∞), which means the series converges for all real values of x.

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Answer:

1x + 15?

Step-by-step explanation:

a) the value of the integral 1.664. b) the coefficient of x4 is (3/1280). c) the value of the integral  2.14 d) the percentage error in the approximation is -28.67%.

a) To evaluate the integral exactly, we make a substitution in the form of ax = sin 0 where a = (1/2).

Substitute x = (sin θ)/2, dx = (cos θ)/2 dθ, and 1 - 4x² = cos² θ in the integral to get it in terms of θ.

∫5√(1-4x²)dx = ∫(5/2) cos²θ dθApply the identity cos²θ = (1 + cos 2θ)/2 to simplify the integrand as shown.∫(5/2) cos²θ dθ = (5/4)∫(1 + cos2θ) dθ = (5/4)θ + (5/8)sin 2θ

Evaluate the above expression from 0 to π/2 to get the value of the integral.

(5/4)θ + (5/8)sin 2θ = (5/4) π/2 + (5/8) sin π = 1.664

b) The integrand is f(x) = 5√(1-4x²).We can write it as shown below, using the binomial series. f(x) = 5(1 - 4x²)^(1/2) = 5∑_(n=0)^∞〖(1/2)_n (2n)!/n! (1/16)^n x^(2n) 〗

The above expression is the Maclaurin Series expansion of f(x) as required.In the expansion, the coefficient of x4 is (1/2)_2 (2.4)/(2!) (1/16)^2 = (3/1280)

c) Integrating each term of the expansion, we obtain the following expression.(5/4)θ + (5/8)sin 2θ = (5/4) π/2 + (5/8) sin π = 1.664

We approximate the value of the integral using the first three terms of the series expansion, and then add the values of the integrated terms.

The terms up to x4 are included in this calculation. I=5[1+(1/2) (-4x²) +(1/2)_2 (-4x²)²]I=5[1-2x²+3x^4/4] = (5/4) (π/2 + (5/16)π²) ≈ 2.14

d) The percentage error in the approximation is given by:%Error = [(Exact value - Approximation value)/ Exact value] x 100Substitute the appropriate values to calculate.%Error = [(1.664 - 2.14)/1.664] x 100 = -28.67% (correct to 3 significant figures)Thus, the percentage error in the approximation is -28.67%.

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Answer:

1.

Step-by-step explanation:

base formula

is length × height so that would be 11×4=44

base= 44

height=4

volume= 132

2.

base formula

since its a cube it would be length× hight = 36

base= 36

hight=6

volume =216

3.

base formula

pie×radius^2 so that would be 3.14×1.5^2= 14.80

base 14.80

hight 4

volume= 59.2

4

Answer:

Option B will be your answer

Step-by-step explanation:

V=2 1/2×1/2×2

=2.5 cube

volume of 1/2 cubic units =)(1/2×1/2×1/2=0.125cube^3

2.5/0.125=20

Hope it helps...

v = 2½

number of half unit cubes = 20

Answer:

2 real solutions

Step-by-step explanation:

x=6i, -6i

Answer:

15°, 16°, 46°, 59°

Step-by-step explanation:

1.) so the entire angle is 89°, then you take off the 44° and the 30°

89° - 44° - 30° = 15°

So the answer to 1 is x = 15°

2.) 90° - 74° = 16°

3.) 180° - 134° = 46°

4.) the angles are vertical, so they're equal:

x = 59°

hope this helps:)

Answer:2 11/24

Step-by-step explanation:

Answer:

2.4583

Step-by-step explanation:

I helped you.

First

5÷6 and 7÷8 and again similarly 3÷4 and sum the all outcome come from these eqations

The number 8.7104 belongs to the set of real numbers. The sets of natural numbers, whole numbers, integers, rational numbers, and real numbers are ordered from most specific to most inclusive.

Natural numbers: Also known as counting numbers, they include positive whole numbers starting from 1 (1, 2, 3, 4, ...).

Whole numbers: Similar to natural numbers, they include all positive integers starting from 0 (0, 1, 2, 3, ...).

Integers: This set includes both positive and negative whole numbers, including zero (-∞, ..., -3, -2, -1, 0, 1, 2, 3, ..., +∞).

Rational numbers: These are numbers that can be expressed as fractions, where the numerator and denominator are both integers. Rational numbers can be written as terminating or repeating decimals.

Real numbers: This set includes all rational and irrational numbers. Real numbers can be represented on the number line and include all possible decimal values, including non-terminating and non-repeating decimals.

In the case of the number 8.7104, it is a decimal number that can be expressed as a terminating decimal. Therefore, it falls within the set of real numbers. Real numbers encompass all possible decimal values, both terminating and non-terminating, making them the broadest set in terms of representation on the number line.

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The probability P(Z < -1.06) is approximately 0.142. The probability P(Z > 2.386) is about 0.008. The probability P(-0.777 < Z < 0.777) is approximately 0.456.

The probability P(X < 9.8) ≈ 0.211. The probability P(X > 10.2) =  = 0.212. The probability P(X < 9.8 or X > 10.2) = 0.423.

To locate the distribution of X and the indicated possibilities for the given instances, we need to use the residences of the everyday distribution. Given that the populace has a median (μ) of 10 and a widespread deviation (σ) of 2.5, we will continue as follows:

a. N = 7, P(X < 9):

For a pattern size of seven, the distribution of X follows a normal distribution with the equal mean (10) however a trendy deviation of σ/sqrt(n) = 2.5/[tex]\sqrt{7}[/tex] ≈ 0.944.

To discover P(X < nine), we need to standardize the cost of 9 with the use of the Z-rating formula: Z = (X - μ) / σ.

Substituting the values, we get Z = (9 - 10) / 0.944 ≈ -1.06.

Using a standard regular distribution table or calculator, we are able to locate that the chance P(Z < -1.06) is approximately 0.142.

B. N = 12, P(X > 11.5):

For a sample length of 12, the distribution of X follows a regular distribution with the same suggestion (10) but a well-known deviation of σ/[tex]\sqrt{n}[/tex] = 2.5/[tex]\sqrt{12}[/tex] ≈ 0.7217.

To discover P(X > 11.5), we standardize the value of 11.5 for the usage of the Z-rating method: Z = (X - μ) / σ.

Substituting the values, we get Z = (11.5 - 10) / 0.7217 ≈ 2.386.

Using a trendy everyday distribution table or calculator, we will locate that the chance P(Z > 2.386) is about 0.008.

C. N = 15, P(9.5 < X < 10.25):

For a sample size of 15, the distribution of X follows a normal distribution with identical implies (10) however a popular deviation of σ/sqrt(n) = 2.5/[tex]\sqrt{15}[/tex]≈ 0.6455.

To discover P(9.5 < X < 10.25), we need to standardize the values using the Z-score components.

Z1 = (9.5 - 10) / 0.6455 ≈ -0.777, and Z2 = (10.25 - 10) / 0.6455 ≈ 0.777.

Using a widespread ordinary distribution desk or calculator, we can locate that P(-0.777 < Z < 0.777) is approximately 0.456.

D. N = 100, P(X < 9.8 or X > 10.2):

For a sample size of 100, the distribution of X follows a regular distribution with the equal implies (10) however a general deviation of σ/sqrt(n) = 2.5/[tex]\sqrt{100}[/tex] = 0.25.

To find P(X < 9.8 or X > 10.2), we need to calculate the probabilities for each person's case and subtract them from 1.

P(X < 9.8) = P(Z < (9.8 - 10) / 0.25) ≈ P(Z < -0.8) ≈ 0.211.

P(X > 10.2) = P(Z > (10.2 - 10) / 0.25) ≈ P(Z < -0.8) ≈ 1 - P(Z < 0.8) ≈ 1 - 0.788 = 0.212.

Therefore, P(X < 9.8 or X > 10.2) ≈ P(X < 9.8) + P(X > 10.2) ≈ 0.211 + 0.212 = 0.423.

Remember to consult a trendy everyday distribution desk or use a calculator to locate the possibilities associated with the Z-scores.

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Answer:

C and D

Step-by-step explanation:

Got it right on the test.

1 hexagon and 6 rectangles and 4 squares and two rectangles that are not squares are sets of shapes which can be used as the net of a three-dimensional figure. Option A and option D are correct.

Hexagon and 6 rectangles: This combination of shapes can be used to create the net of a hexagonal prism.

The hexagon will be used as the base of the prism, and the six rectangles can be attached to the sides of the hexagon to form the remaining faces of the prism.

When folded along the edges, the net will result in a hexagonal prism.

4 squares and two rectangles that are not squares: This combination can be used to create the net of a rectangular prism or a cuboid.

The four squares will be used as the top, bottom, and side faces of the prism, while the two rectangles (which are not squares) can be attached to the remaining sides to complete the net.

When the net is folded along the edges and assembled, it will form a rectangular prism or cuboid.

Hence, Option A and option D are correct. 1 hexagon and 6 rectangles and 4 squares and two rectangles that are not squares are sets of shapes which can be used as the net of a three-dimensional figure.

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Answer:

AC = 8 The classification is isosceles

Step-by-step explanation:

Answer:

$85.2

Step-by-step explanation:

Answer:

85.2 dollar

Step-by-step explanation:

Tax is 5.2 because 80 times 0.065 is that, then you add them up

Answer:

A) Experimental probability = 0.12

B) Theoretical probability = 1/6

Step-by-step explanation:

A) Experimental probability is based on the total number of times an event occurs with respect to the total outcome of the experiment in question.

Now, we are told that the die was rolled 100 times and that 6 was gotten 12 times for the 100 rolls.

Thus;

Experimental probability = 12/100

Experimental probability = 0.12

B) Theoretical probability is the number of ways that an event can occur in relation to the total outcomes.

Here, the number of ways 6 can occur is 1 and the total outcome is 6 possible due numbers.

Thus,

Theoretical probability = 1/6

Answer: A: y=5x+7

Step-by-step explanation: Hope this help :D

Without yield management, the theatre's revenues would be $176,100.

To calculate the theatre's revenues without yield management, we need to determine the number of tickets sold for each fare class and multiply it by the corresponding ticket price. The number of low fare class tickets sold is not provided in the information, so we cannot determine the exact revenue for that fare class. However, since there is ample demand for the low fare class, it is reasonable to assume that all 1761 seats are sold at the discounted price of $75. Therefore, the revenue from the low fare class would be 1761 seats × $75 = $132,075. For the high fare class, the demand is normally distributed with a mean of 1200 and a standard deviation of 150. To maximize revenues, the theatre should sell as many high fare class tickets as possible. Assuming all remaining seats (1761 - number of low fare class tickets) are sold at the high fare of $100, the revenue from the high fare class would be (1761 - number of low fare class tickets) × $100. To calculate the exact number of high fare class tickets sold, we need to know the cutoff point for the demand distribution that separates high fare demand from low fare demand. Since this information is not provided, we cannot determine the exact revenue from the high fare class. However, the only answer option that is close to the estimated revenue considering all high fare class tickets sold is $176,100.

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Answer: No. Pennant Sports Shop did not sell the same ratio of defense sticks to total lacrosse sticks on both days.

Step-by-step explanation:

On Friday, there were 25 lacrosse sticks sold, 10 of which were defense sticks. The ratio of defense sticks to lacrosse will be:

= 10/25 = 2/5 = 2:5

On Saturday, there were 50 lacrosse sticks sold, 15 of which were defense stick. The ratio of defense sticks to lacrosse will be:

= 15/50 = 3/10 = 3:10

Based on the calculation above, Pennant Sports Shop did not sell the same ratio of defense sticks to total lacrosse sticks on both days

Answer:

the second option

Step-by-step explanation:

pretty sure it's the second option

hope this helped ;)

Answer:

Step-by-step explanation:

[tex]\sf 30-24x[/tex]

30 → 6 * 5

24 → 6 * 4

[tex]\sf 6* \:5-6* \:4x[/tex]

[tex]\sf 6\left(5-4x\right)[/tex]

Answer:

13 + 1 1/2 - 1/4

Step-by-step explanation:

1 gallons = 4 quarts

3 1/4 = 13/4 x 4 = 13

Quarts left = original quart + quart added - quart drunk

13 + 1 1/2 - 1/4

Answer:

9.1 units

Step-by-step explanation:

formula of a distance of two points:

[tex]\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex] where x and y indicate the coordinates of the points

[tex]\sqrt{(4+5)^2 + (-1)^2} = \sqrt{81 + 1} = \sqrt{82} = 9.1 units[/tex]