The lifespan of a certain make of electric light bulb is known to be normally distributed with a mean life of 2000 hours and a standard deviation of 120 hours. Find the probability that the lifespan of such bulbs will be i) greater than 2150 hours ii) greater than 1910 hours iii) less than 2500 hours iv) at least 3000 hours v) within the range of 1850 hours to 2090 hours

(a) ( x_{t+1}=\frac{1}{2} x_{t}+3 ), the solution to this difference equation is x_t = 2^t + 3, The difference equations in this problem are both linear difference equations with constant coefficients.

This can be found by solving the equation recursively. For example, the first few terms of the solution are

t | x_t

--- | ---

0 | 3

1 | 7

2 | 15

3 | 31

The general term of the solution can be found by noting that

x_{t+1} = \frac{1}{2} x_t + 3 = \frac{1}{2} (2^t + 3) + 3 = 2^t + 3

(b) ( x_{t+1}=-3 x_{t}+4 )

The solution to this difference equation is

x_t = 4 \cdot \left( \frac{1}{3} \right)^t + 4

This can be found by solving the equation recursively. For example, the first few terms of the solution are

t | x_t

--- | ---

0 | 4

1 | 5

2 | 2

3 | 1

The general term of the solution can be found by noting that

x_{t+1} = -3 x_t + 4 = -3 \left( 4 \cdot \left( \frac{1}{3} \right)^t + 4 \right) + 4 = 4 \cdot \left( \frac{1}{3} \right)^t + 4

The difference equations in this problem are both linear difference equations with constant coefficients. This means that they can be solved using a technique called back substitution.

Back substitution involves solving the equation recursively, starting with the last term and working backwards to the first term.

In the first problem, the equation can be solved recursively as follows:

x_{t+1} = \frac{1}{2} x_t + 3

x_t = \frac{1}{2} x_{t-1} + 3

x_{t-1} = \frac{1}{2} x_{t-2} + 3

...

x_0 = \frac{1}{2} x_{-1} + 3

The general term of the solution can be found by noting that

x_{t+1} = \frac{1}{2} x_t + 3 = \frac{1}{2} (2^t + 3) + 3 = 2^t + 3

The second problem can be solved recursively as follows:

x_{t+1} = -3 x_t + 4

x_t = -3 x_{t-1} + 4

x_{t-1} = -3 x_{t-2} + 4

...

x_0 = -3 x_{-1} + 4

The general term of the solution can be found by noting that

x_{t+1} = -3 x_t + 4 = -3 \left( 4 \cdot \left( \frac{1}{3} \right)^t + 4 \right) + 4 = 4 \cdot \left( \frac{1}{3} \right)^t + 4

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Her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h

Let's assume that the total distance of the round trip is d kilometers and that she drove at a constant speed of v km/h for the entire trip. The time it takes for her to travel the entire distance at speed v is given by t = d/v.

Since she drove back home using the same path she took out to the university, her average speed for the entire trip must be equal to her speed on the way out and back. Therefore, the total time it took for her to complete the round trip is 2t = 2d/v.

Since the total time it took for her to complete the round trip is 7.1 hours, we can set up an equation:

2d/v = 7.1 hours

Converting hours to seconds and solving for v, we have:

v = 2d / (7.1 * 3600) km/s

Finally, converting to km/h, we get:

v = 2d / (7.1 * 3600) * 3600 km/h

Therefore, her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h

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The main difference between the denominator of the F-ratio (the error term) for a repeated-measures ANOVA and an independent-measures ANOVA lies in the way variability is accounted for within the groups.

In a repeated-measures ANOVA, the same participants are exposed to multiple conditions or measured at different time points. Therefore, this design accounts for individual differences, leading to a smaller error term in the denominator of the F-ratio.

The error term in repeated-measures ANOVA represents the variability due to individual differences and the residual error, but not the variability between participants. In contrast, an independent-measures ANOVA involves separate groups of participants for each condition, meaning that variability between participants is included in the error term.

As a result, the error term for the independent-measures ANOVA is larger than that of the repeated-measures ANOVA. This difference in the denominator of the F-ratio affects the sensitivity of the statistical test, with the repeated-measures ANOVA being more sensitive due to its smaller error term.

In summary, the denominator of the F-ratio (the error term) differs for a repeated-measures ANOVA compared to an independent-measures ANOVA in terms of the variability accounted for within groups. The repeated-measures ANOVA error term is smaller, as it controls for individual differences, while the independent-measures ANOVA error term is larger because it includes variability between participants.

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Answer:

A and D

Step-by-step explanation:

Got it right on Edge hope this helped!

Answer:

A&B

Step-by-step explanation:

its right on edg

Carl made a mistake by multiplying the two values in the quotient rather than dividing them.

So, the result of 4 divided by 2 1/3 and an explanation of Carl's error:

Thus, if we divide 4 2/3 by 2 1/3, we get:

Carl made the error of assuming his quotient (2) was equal to the value of the terms it contained.

Therefore, Carl made a mistake by multiplying the two values in the quotient rather than dividing them.

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Answer:

90 Confidence Interval for the proportion = [ 0.216,0.334]

Step-by-step explanation:

The confidence interval for proportion formula =

p ± z × √p(1 - p)/n

Where p = x/n

x = 42

n = number of samples = 153

p = 42/153

p = 0.2745098039 ≈ 0.275

z = z score of 90% confidence interval = 1.645

Confidence interval =

0.275 ± 1.645 × √0.275 - ( 1 - 0.275)/153

= 0.275 ± 1.645 × √0.0013031046

= 0.275 ± 0.0593820985

Confidence Interval

= 0.275 - 0.0593820985

= 0.2156179015

≈ 0.216

= 0.275 + 0.0593820985

= 0.3343820985

≈ 0.334

90 Confidence Interval for the proportion = [ 0.216,0.334]

Answer:

The fraction of people for 4th movie is 0.1167

Step-by-step explanation:

The number of people that bought a comedy movie ticket = 2/3

The number of people that bought the horror movie ticket = 1/4

The number of people that bought kids movie ticket = 3/10

Total number people for three movies = 2/3 + ¼ + 3/10 = 0.8833

The fraction of people for 4th movie = 1 – 0.8833 = 0.1167

Answer:

Unknown.

Step-by-step explanation:

Need more info.

As the age of the bus increases, the annual maintenance cost generally increases as well. Therefore, the estimated regression model is: y = a + bx = 883.5 + 253.17x where y is the annual maintenance cost and x is the age of the bus.

(a) The correct scatter chart is (i) which has age of bus as the independent variable. The scatter chart indicates there may be a linear relationship between age of bus and annual maintenance cost.

(b) To develop an estimated regression equation, we can use the following steps:

X = (1+2+2+2+2+3+4+4+5+5)/10 = 3

Y = (350+370+480+520+590+550+750+800+790+950)/10

= 643

Calculate the deviations of age of bus (x) and annual maintenance cost (y) from their respective means (X and Y).

x - X: -2, -1, -1, -1, -1, 0, 1, 1, 2, 2

y - Y: -293, -273, -163, -123, -53, -93, 107, 157, 147, 307

Calculate the sum of the product of the deviations of x and y.

∑[(x - X)(y - Y)] = (-2)(-293) + (-1)(-273) + (-1)(-163) + (-1)(-123) + (-1)(-53) + (0)(-93) + (1)(107) + (1)(157) + (2)(147) + (2)(307)

= 4,557

Calculate the sum of the squared deviations of x.

∑[(x - X)²] = (-2)² + (-1)² + (-1)² + (-1)² + (-1)² + 0² + 1² + 1² + 2² + 2²

= 18

Calculate the estimated slope of the regression line, b.

b = ∑[(x - X)(y - Y)] / ∑[(x - X)²]

= 4,557 / 18

= 253.17

Calculate the estimated intercept of the regression line, a.

a = Y - bX

= 643 - (253.17)(3)

= 883.5

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Answer:

cos W = 7/15

Step-by-step explanation:

Mathematically the cosine of an angle is the ratio of the adjacent to the hypotenuse side

From the diagram given, 14 is adjacent to vertex w and 30 faces the right angle which makes it the hypotenuse

So, we have it that;

cos W = 14/30

cos W = 7/15

Answer:

z=8/5

Step-by-step explanation:

2(4z-1)=3(z+2)

distribute the 2 and 3

8z-2=3z+6

move 2 to the other side by adding 2

8z=3z+8

move 3 to the other side by subtracting 3

5z=8

divide both sides by 5

z= 8/5

The equivalent value of the expression is z = 8/5 = 1.6

Given data ,

Let the equation be represented as A

Now , the value of A is

2 ( 4z - 1 ) = 3 ( z + 2 )

On simplifying the equation , we get

2 ( 4z - 1 ) = 3 ( z + 2 )

So , the left hand side of the equation is equated to the right hand side by the value of 3 ( z + 2 )

Opening the parenthesis on both sides , we get

2 ( 4z ) - 2 = 3z + 6

8z - 2 = 3z + 6

Subtracting 3z on both sides , we get

5z - 2 = 6

Adding 2 on both sides , we get

5z = 8

Divide by 5 on both sides , we get

z = 8/5

z = 1.6

Therefore , the value of z = 8/5 = 1.6

Hence , the expression is z = 8/5 = 1.6

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Answer:

20/3

Step-by-step explanation:

By the property of equal intercepts made by transversals on parallel lines.

\( \frac{4x - 3}{x + 17} = \frac{1}{1} \\ \\ 4x - 3 = x + 17 \\ \\ 4x - x = 17 + 3 \\ \\ 3x = 20 \\ \\ x = \frac{20}{3} \\ \\ \)

N(t) approaches 550.

The equation N(t) = 550 / (1 + 49e^(-0.7t)) models the number of people in a town who have heard a rumor after t days. The equation describes the growth of the number of people who have heard the rumor over time. The e^(-0.7t) term in the denominator represents the rate of decay or the slowing down of the spread of the rumor as t increases. As t increases without bound, the exponential term approaches 0, so the fraction approaches 550 / (1 + 49 * 0) = 550 / 1 = 550.

This means that as time goes on, the number of people who have heard the rumor will approach 550, the limit or maximum value of N(t). This value is not limited by any of the factors mentioned in the options (b) to (e).

The number of people who started the rumor is not given in the equation and cannot be determined from the information provided.

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Answer:

3XY

Step-by-step explanation:

Answer:

∠ADB = 35°

Step-by-step explanation:

The angle at the circumference in a semicircle is a right angle.

⇒ ∠ABC = 90°

Interior angles in a triangle sum to 180°

⇒ ∠BAC + ∠ABC + ∠BCA = 180°

⇒ 55° + 90° + ∠BCA = 180°

⇒ ∠BCA = 35°

The angles at the circumference subtended by the same arc are equal (angles in the same segment are equal)

⇒ ∠ADB = ∠BCA

⇒ ∠ADB = 35°

y=-2x+[-1]

Hope it is correct

Answer:

P(candy chosen is red) = 58/200

Step-by-step explanation:

0.29 is the probability that a candy chosen at random will be red.

The probability exists the branch of mathematics involving numerical descriptions of how likely an event exists to happen, or how likely it exists that a proposition stands true. The probability of an event exists in a number between 0 and 1, where, roughly speaking, 0 reveals the impossibility of the event, and 1 demonstrates certainty.

A machine contains = 76 green candies

B machine contains = 42 orange candies

C  machine contains = 58 red candies

D  machine contains = 24 yellow candies

Probability = 58 / 76 + 42+ 58+ 24

                  = 58 / 200

                  = 0.29

0.29 is the probability that a candy chosen at random will be red.

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Answer:

49 is the answer

thank you

If the rates are the same ones, the tank will be filled in 15 minutes.

Let's define R as the rate at which we fill the tank, we know that we can fill a volume V in 6 minutes, then:

R*6 min = V

R = V/6min

Then r is the rate at which we empty the tank, we know that a volume V is emptied in 10 minutes, then:

r*10 min = V

r = V/10min

If both valves are open, the rate at which we will fill the tank is:

R - r

Now we need to find the value of time T such that:

(R - r)*T = V

(V/6min - V/10min)*T = V

(1/6min - 1/10min)*T = 1

(5/30min - 3/30min)*T = 1

(2/30 min)*T = 1

T = (30min/2)

T = 15 minutes.

The tank will be filled in 15 minutes.

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Answer:

try 7

Step-by-step explanation:

Using trigonometric ratio, the tangent of X is tan θ = YZ / XY

Trigonometric ratios are ratios of the sides of a right triangle, defined in terms of the angles of the triangle. There are six trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

The sine of an angle is defined as the ratio of the side opposite the angle to the hypotenuse (the side opposite the right angle).

The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

In this problem, the tangent of angle X will be given as;

tan X = opposite / adjacent

tan X = YZ / XY

Substituting the value of θ in place of x;

tan θ = YZ / XY

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Answer:

20$

Step-by-step explanation:

220 ÷ 11 = 20

Therefore, It costs 20$ for each Teen to go to the pool

Hope this helps (:

To calculate the cost of driving a diesel tractor trailer truck for 175.0 miles, we need to determine the number of gallons of fuel required and then multiply it by the cost per gallon.

Calculate the number of gallons of fuel needed. Given that the truck gets 8.500 miles per gallon, we divide the total distance (175.0 miles) by the fuel efficiency: 175.0 miles / 8.500 miles per gallon

= 20.59 gallons (approximately)

Calculate the cost of the fuel.Since diesel fuel costs $3.599 per gallon, we multiply the number of gallons needed by the cost per gallon: 20.59 gallons x $3.599/gallon = $73.89 (approximately) Therefore, it will cost you approximately $73.89 to drive the diesel tractor trailer truck for 175.0 miles, assuming it gets 8.500 miles per gallon and diesel fuel costs $3.599 per gallon.

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Answer:

Quick! Multiply the first number by 4 and see if it gives you the second number!

Step-by-step explanation:

0*4 does not equal 3

3*4 does not equal 0

Etc etc

Answer:

4(3x+7)

Step-by-step explanation:

12x+28

Bot numbers are divisible by 4

4*3 *x + 4*7

Factor out the 4

4(3x+7)

Answer:

62,144

Step-by-step explanation:

60,000 x (1 + 2%)^2 : growth in 2 years

+ 750: in migrants

- 410: out migrants

- 620: died

Answer:

62,144

Step-by-step explanation:

\(60,000 \times (1 + 2\%)^{2} \)

➡️ \( = 62,424\)

In-migrants:

➡️ \(750 - 410 = 340\)

now:

\(62,424 + 340 - 620\)

➡️ \( = 62,144\)

So, the present of the municipality is 62,144

Answer:  x = -12

Steps: 17 + x = 5

Subtract 17 from both sides: 17 + x - 17 = 5 - 17

Simplify: x = -12

The 95% confidence interval estimate of the mean for the DNA samples is approximately (0.32, 7.46), and the practical use of the confidence interval is to provide a range of values where the true population mean is likely to lie.

To construct a 95% confidence interval estimate of the mean for the given DNA samples, we can use statistical methods.

Calculate the sample mean (X) of the DNA samples:

X = (2 + 2 + 14 + 3 + 3 + 3 + 3 + 4 + 1) / 9

= 35 / 9

≈ 3.89

Calculate the sample standard deviation (s) of the DNA samples:

s = √[(Σ(x - X)²) / (n - 1)]

= √[( (2 - 3.89)² + (2 - 3.89)² + (14 - 3.89)² + (3 - 3.89)² + (3 - 3.89)² + (3 - 3.89)² + (3 - 3.89)² + (4 - 3.89)² + (1 - 3.89)² ) / (9 - 1)]

≈ √[(36.22 + 36.22 + 91.33 + 0.79 + 0.79 + 0.79 + 0.79 + 0.01 + 6.43) / 8]

≈ √[173.25 / 8]

≈ √21.66

≈ 4.65

Calculate the standard error of the mean (SE):

SE = s / √n

= 4.65 / √9

= 4.65 / 3

≈ 1.55

Determine the critical value for a 95% confidence level, which corresponds to a t-distribution with n-1 degrees of freedom. Since n = 9, the degree of freedom is 9-1 = 8. Using a t-table or statistical software, the critical value for a 95% confidence level with 8 degrees of freedom is approximately 2.306.

Calculate the margin of error (ME):

ME = Critical value × SE

= 2.306 × 1.55

≈ 3.57

Construct the 95% confidence interval:

Confidence interval = X ± ME

= 3.89 ± 3.57

≈ (0.32, 7.46)

The practical use of the confidence interval is that it provides an estimate of the range within which the true population means is likely to fall with a certain level of confidence (in this case, 95%). It helps to quantify the uncertainty associated with the sample mean and allows for making inferences about the population based on the sample data.

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