A man drove 14 mi directly east from his home, made a left turn at an intersection, and then traveled 3 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

The probability that the sample mean will be between 181 and 185 is 0.3039.

Given,

The mean of a population, μ = 180

Standard deviation, σ = 36

Number of sample observations, n = 84

We have to find the probability that the sample mean will be between 181 and 185;

Lets convert 181 and 185 into z scores;

z = (x - μ) / (σ/√n)

z = (181 - 180) / (36/√84)

z = 1/3.93

z = 0.25

z = (185 - 180) / (36/√84)

z = 5 / 3.93

z = 1.27

Lets look z score table;

The area to the left of z = 0.25 is 0.5987

The area to the left of z = 1.27 is 0.8980

The probability that the z is between 0.25 and 1.27 would be 0.8980 – 0.5887 = 0.3039.

That is,

The probability that the sample mean will be between 181 and 185 is 0.3039.

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Answer:

90 calories

Step-by-step explanation:

Calories : quantity of food

there are 300 calories in 100 g of a certain food

300 calories : 100 g food

how many calories are there in a 30 g portion of food​

Let x = number of calories

x calories : 30 g food

Equate both ratios

300 calories : 100 g food = x calories : 30 g food

300/100 = x/30

300 * 30 = 100 * x

9000 = 100x

x = 9000/100

x = 90

x = number of calories = 90 calories

The factorization of x²-x will be x(x - 1 ).

Factorization or factoring in mathematics is the process of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

Given that the quadratic expression is  x² - x.

To factorize x² - x, we can first factor out the common factor of x:

x² - x = x(x - 1)

So the fully factorized form of x² - x is:

x(x - 1)

Therefore, the factorized form of the expression x²-x is, x(x - 1).

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The major methods of recording unstructured observational data are Narrative Description, Field Notes, Audio or Video Recording, Photography, Diagrams or Maps.

The major methods of recording unstructured observational data are:

1. Narrative Description: This method involves writing a detailed, chronological account of the observed events or behaviors, capturing the context and interactions as they occur naturally.

2. Field Notes: In this method, the observer takes brief, concise notes during the observation, focusing on key events, behaviors, or interactions. These notes can be expanded and organized later for further analysis.

3. Audio or Video Recording: Using audio or video equipment, the observer captures the events and interactions in their entirety. This allows for a more accurate record and the ability to review and analyze the data multiple times.

4. Photography: Taking photographs during the observation can provide a visual record of the events and behaviors. These images can supplement other data collection methods and help to illustrate specific aspects of the observation.

5. Diagrams or Maps: Drawing diagrams or maps of the observation setting can help capture the spatial relationships between individuals and objects, as well as the overall layout of the environment.

These methods can be used individually or in combination, depending on the research question and the specific needs of the study. Remember to always respect participants' privacy and obtain informed consent when necessary.

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Answer:

1. C

2. A

Step-by-step explanation:

Step 1: Write equation

3x - 1 = 7

3x = 8

Step 2: Use 1st equation and solve

3x = 8

x = 8/3

Step 3: Use 2nd equation and solve

3x = 8

x = 8/3

Both equations have equivalent solutions and the 2nd equation is the simplified version of the 1st.

Answer: 52x+4

Step-by-step explanation: Do 16(2x-1)+4(5x+5) and get 52x+4.

Answer:

The far left one

Step-by-step explanation:

When you graph it it intercepts the point (-56,0) the other es are wrong because the x and y points are mixed up.

Answer:

(-4,-3)

Step-by-step explanation:

Answer:

answer is 80

Step-by-step explanation:

25% = 1/4

you'll need four lines in the diagram, each having 20.

I dont know what diagram your having to use, but I hope this helped!

The value of LE is 18 units.

We are given an image of a number line, we have to find the value of LE.

Number line

Number lines are the horizontal straight lines in which the integers are placed in equal intervals. All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

All (natural numbers) positive numbers occupy the right side of the zero whereas negative numbers occupy the left side of zero on the number line. As we move on to the left side value of a number decreases.

Observing from the number line, we can say that L = -11 and E = 7

Hence, LE =  7-(-11) = 7 + 11 = 18 units.

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The 20th percentile of the given probability density function is 10 + 2 ln 0.8 or approximately 11.22. The value of P(X < 17) is 0.9332. Using the given values, P(X < 17|X < 1.2004) is found to be 0.2.1.

Calculation of the 20th percentile cumulative distribution function of the given probability density function is

f(x) = {0 for x < 10 ; (1 - e^(-0.5(x - 10))) for 10 ≤ x < 20; 1 for x ≥ 20 }

Here, we need to find the 20th percentile.

For 0 < P < 1, the Pth percentile of X is given by:

xP = F^(-1)(P), where F(x) is the cumulative distribution function.

F(x) = P[X ≤ x]For P = 0.2, the 20th percentile of X is given by:

20P = F^(-1)(0.2)

Let F(x) = y

∴ 20 = y ⇒

y = 0.2

The inverse of the cumulative distribution function, F^(-1)(y), is the solution of F(x) = y.

So, F(x) = 0.2

0.2 = 1 - e^(-0.5(x - 10))

⇒ e^(-0.5(x - 10))

= 0.8⇒ -0.5(x - 10)

= ln 0.8⇒ x - 10

= -2 ln 0.8

⇒ x = 10 + 2 ln 0.8

Hence, the 20th percentile of X is 10 + 2 ln 0.8 or approximately 11.22.

Calculation of P(X < 17)The probability density function of X is: f(x) = 1/2 e^(-|x|/2)

The probability P(X < 17) is given by:

P(X < 17) = ∫f(x) dx from -∞ to 17

= ∫(1/2 e^(-|x|/2)) dx from -∞ to 17

= 0.9332...

Now, P(X < 17) > 0.2

Therefore, P(X < 17) > P(X < 17|X < b)for any b < 17.

Hence, P(X < 17|X < b) < 0.2.

Now, using conditional probability:

P(X < 17|X < b) = P(X < 17, X < b)/P(X < b)

= P(X < 17)/P(X < b)

Here, b is any value such that P(X < b) > 0. The function is symmetric about 0, so let b = -a where a > 0. Then:

P(X < b) = P(X < -a)

= ∫f(x) dx from -∞ to -a

= ∫(1/2 e^(-|x|/2)) dx from -∞ to -a

= 1/2 (1 - e^a/2)

So, P(X < 17|X < b) = P(X < 17)/P(X < b)

P(X < 17|X < -a) = [0.9332]/[1/2 (1 - e^a/2)]

= 0.366e^(a/2)

Now, we need to find a such that

P(X < 17|X < -a) = 0.2.

Let g(a) = 0.366e^(a/2)

= 0.2⇒ e^(a/2)

= 0.546

It can be simplified as:

a = 2 ln 0.546

= -1.2004

Hence,

=  P(X < 17|X < -a)

= P(X < 17|X < 1.2004)

= 0.2.

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The one-sample z-statistic for evaluating the hypothesis that unvaccinated people get COVID-19 is not 0.03 is -85.7. This statistic tested the hypothesis that unvaccinated people do not get COVID-19 at 0.03%.

In order to compute the one-sample z-statistic, we must first do a comparison between the observed proportion of COVID-19 instances in the placebo group and the expected proportion of 0.03. (p - p0) / [(p0(1-p0)) / n is the formula for the one-sample z-statistic. In this formula, p represents the actual proportion, p0 represents the predicted proportion, and n represents the sample size.

The observed proportion of COVID-19 instances among those who received the placebo is 162/18325 less than 0.0088. According to the received wisdom, the proportion that should be anticipated is 0.03. The total number of people sampled is 18325. After entering these numbers into the formula, we receive the following results:

z = (0.0088 - 0.03) / √[(0.03(1-0.03)) / 18325] ≈ (-0.0212) / √[(0.0291) / 18325] ≈ -85.7

As a result, the value of the z-statistic for just one sample is about -85.7. This demonstrates that the observed proportion of COVID-19 cases in the unvaccinated population is significantly different from the expected proportion of COVID-19 cases in that population.

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The upper and lower control limits for the X-bar chart are approximately 53.87 and 50.78,

The upper and lower control limits for the X-bar chart, we need to calculate the sample mean (X-bar) and the sample standard deviation (S) of the data. Once we have these values, we can use the formulas for control limits.

From the given table, let's calculate the X-bar and S:

Sample Size (n) = 5

Sample Values: 51, 52, 53, 55, 50

The X-bar (sample mean)

X-bar = (Sum of sample values) / n

X-bar = (51 + 52 + 53 + 55 + 50) / 5

X-bar = 261 / 5

X-bar = 52.2

The range (R)

R = Maximum value - Minimum value

R = 55 - 50

R = 5

The average range (R-bar)

R-bar = (Sum of ranges) / n

R-bar = (5 + 5 + 5 + 5 + 5) / 5

R-bar = 25 / 5

R-bar = 5

The standard deviation (S)

S = R-bar / d2

(d2 is a constant depending on the sample size, in this case, n = 5)

Using the d2 value for n = 5 from the control chart constants table, we find d2 = 2.326.

S = 5 / 2.326

S ≈ 2.15

Now that we have X-bar and S, we can calculate the control limits:

Upper Control Limit (UCL) = X-bar + (A2 × S /√(n))

Lower Control Limit (LCL) = X-bar - (A2 × S / √(n))

Using the appropriate constant A2 for n = 5 from the control chart constants table, we find A2 = 0.577.

UCL = 52.2 + (0.577 × 2.15 / √(5))

UCL ≈ 53.87

LCL = 52.2 - (0.577 × 2.15 / √(5))

LCL ≈ 50.78

Therefore, the upper and lower control limits for the X-bar chart are approximately 53.87 and 50.78, respectively.

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The value of x is 35.

The given angles are (x+12) degree and (4x-7)degree,

Since the two lines being crossed are Parallel  lines,

And Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation.

Sum of internal angles is 180 degree,

Therefore,

⇒ x + 12 + 4x - 7 = 180.

⇒ 5x + 5 = 180

⇒ 5x = 175

⇒   x = 35

Hence,

⇒   x = 35

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The complete question is:

given m||n, fine the value of x.

(X+12)° & (4x-7)°.

Answer:

The time it will take for the ball to reach maximum height of 64 feet is 2 seconds

Step-by-step explanation:

The given equation for the height, h, in feet the ball reaches is given by the function;

h(t) = -16·t² + 64·t

To reach maximum height, \(h_{max}\), we have;

At \(h_{max}\), we have;

\(\dfrac{\mathrm{d} h}{\mathrm{d} t} = 0\)

\(\dfrac{\mathrm{d} \left (-16\cdot t^{2} + 64\cdot t \right )}{\mathrm{d} t} = 0\)

Which gives;

64 -32·t = 0

64 = 32·t

t = 64/32 = 2 seconds

Therefore, it will take 2 seconds for the ball to reach maximum height

The maximum height reached is given as follows;

h(2) = -16×2² + 64×2 = 64 feet

The time it will take for the ball to reach maximum height of 64 feet is 2 seconds.

The area of the sector of a circle with a radius of 100 inches and a central angle of 1/3 radian is approximately 5,235.99 square inches.

To find the area of a sector, we can use the formula: Area = (θ/2π) × πr², where θ is the central angle and r is the radius of the circle. In this case, the central angle is 1/3 radian and the radius is 100 inches.

First, we convert the central angle to degrees. Since 2π radians is equal to 360 degrees, we can set up a proportion: (1/3 radian) / (2π radians) = θ / 360 degrees. Solving for θ, we find θ = (1/3 radian) × (360 degrees) / (2π radians) ≈ 19.471 degrees.

Next, we substitute the values into the formula: Area = (19.471 degrees / 360 degrees) × π × (100 inches)². Simplifying this expression, we get Area ≈ (0.05409) × π × 10,000 square inches ≈ 5,235.99 square inches.

Therefore, the area of the sector is approximately 5,235.99 square inches.

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Answer:

Wouldn't it be just 2 since it's already solved

Answer:

a=9.4cm

b=12.0cm

Step-by-step explanation:

Answer:

Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer

These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

To solve the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0, we need to simplify and rearrange the equation to its standard form and then solve for p.

Combining like terms, the equation becomes:

3p^2 - 10p + 5 = 0

Now, we can use the quadratic formula to solve for p. The quadratic formula states:

p = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -10, and c = 5. Substituting these values into the quadratic formula, we have:

p = (-(-10) ± √((-10)^2 - 4 * 3 * 5)) / (2 * 3)

Simplifying further:

p = (10 ± √(100 - 60)) / 6

p = (10 ± √40) / 6

p = (10 ± 2√10) / 6

Now, we can simplify and find the two possible values of p:

p₁ = (10 + 2√10) / 6

p₂ = (10 - 2√10) / 6

These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

In simplified form, the solutions are:

p₁ = (5 + √10) / 3

p₂ = (5 - √10) / 3

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The correct interpretation is that a 1% increase in x1 leads to a 0.0085 increase in y. Hence, a one unit change in x1 would result in a 0.85 increase in y.

In the given linear regression model, y = 1 + 0.85 ln(x1) + ε, a 1% increase in x1 results in a 0.0085 increase in y.

The coefficient in front of ln(x1) in the regression model is 0.85. This implies that a 1% increase in x1 leads to a 0.0085 (0.85% of 1%) increase in y. The natural logarithm function introduces a non-linear relationship between x1 and y. Therefore, the effect of a 1% increase in x1 on y is not directly proportional but rather influenced by the logarithmic transformation.

It is important to note that the interpretation of the effect of x1 on y depends on the context of the data and the assumptions of the model. In this case, since the model includes a logarithmic term, it suggests that the relationship between x1 and y is not linear but rather exhibits diminishing returns. As x1 increases, the impact on y becomes smaller due to the logarithmic transformation.

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For the region under f(x) = 4x^2 on [0, 2], the sum of the areas of the upper approximating rectangle approaches 32/3, or lim n→∞ rn = 32/3.

To show this, we can use the Riemann sum, which approximates the area under the curve by dividing it into a finite number of subintervals and using rectangles to approximate the area of each subinterval. The upper Riemann sum is obtained by using the height of the rectangle with the maximum value of the function in each subinterval.

For this specific function and interval, the width of each subinterval is 2/n, and the height of the upper rectangle in each subinterval is f(i(2/n)), where i is the index of the subinterval. The sum of the areas of the upper rectangles is then given by:

(2/n)Σ[1≤i≤n]f(i(2/n))

Substituting the function f(x) = 4x^2 and simplifying, we get:

(8/n^3)Σ[1≤i≤n]i^2

Using the formula for the sum of squares of the first n natural numbers, Σ[1≤i≤n]i^2 = n(n+1)(2n+1)/6, and simplifying further, we get:

(8/n^3) * n(n+1)(2n+1)/6 = (4/3) * (n+1/2) * (2n+1)/n^2

Taking the limit as n approaches infinity, we get:

lim n→∞ (4/3) * (n+1/2) * (2n+1)/n^2 = 32/3

Therefore, the sum of the areas of the upper approximating rectangles approaches 32/3 as the number of subintervals approaches infinity, or lim n→∞ rn = 32/3.

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Answer: (d)- 1.76 kg

Step-by-step explanation:

Given

The first laptop mass was 11 kg

The rate of mass decreases by 4.7% per year

In 1982, it was

\(\Rightarrow 11-11\times 4.7\%=11-11\times 0.047\\\Rightarrow 11(1-0.047)\ kg\)

In 1983, it was

\(\Rightarrow 11(1-0.047)-11(1-0.047)\times 0.047=11(1-0.047)^2\)

In 2019 i.e. after 38 years, it is

\(\Rightarrow 11(1-0.047)^38=11\times 0.953^{38}=1.76\ kg\)

The best prediction is that the college will have about 480 students who prefer cookies.

According to the table, 27 out of 225 students prefer cookies. To find the prediction for the number of cookies the college will need, we can set up a proportion:

27/225 = x/4000

Where x is the predicted number of students who prefer cookies.

Solving for x, we get:

x = (27/225) * 4000

x ≈ 480

Therefore, the best prediction is that the college will have about 480 students who prefer cookies.

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Answer: 1.8 L/h

Step-by-step explanation:

To convert the rate of water dripping from a tap from millilitres per second (ml/sec) to litres per hour (L/h), we need to use conversion factors.

Step 1:

First, let's convert the rate from millilitres per second to litres per second.

There are 1000 millilitres in a litre, so we can divide the rate in millilitres per second by 1000 to get the rate in litres per second:

\(\LARGE \boxed{\textsf{0.5 ml/sec $\div$ 1000 = 0.0005 L/sec}}\)

Step 2:

We can convert the rate from litres per second to litres per hour. There are 3600 seconds in an hour, so we can multiply the rate in litres per second by 3600 to get the rate in litres per hour:

\(\LARGE \boxed{\textsf{0.0005 L/sec $\times$ 3600 = 1.8 L/h}}\)

Therefore, the rate of water dripping from the tap is 1.8 L/h.

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answer:

choice letter b

Step-by-step explanation:

a² + b² = c²

4² + 3² = 25²

Square root of 25 = 5

C = 5 yards

Equation that relates D = 0.5 + 20x + 0.5v

Initial distance covered d1 = 0.5km

If she rode a bicycle for x hours at an average speed of 20 kilometers per hour, then her distance during this period is:

Speed = Distance/Time

Speed is defined as the rate that an object travels through space; it is the distance traveled in a certain amount of time. A familiar example from our daily lives can be seen when we drive to work or school. Our speed is measured by how fast or slowly we drive. Our car is said to have a speed of 60 miles per hour (mph) if it will travel a distance of 60 miles in exactly 1 hour.

Distance d2 = speed × time

d2 = 20x

If she ran for 0.5 hour at an average speed of v kilometers per hour, her distance this time will be;

Distance d3 = 0.5v

If her total distance is D, then;

D = d1+d2+d3

D = 0.5 + 20x + 0.5v

Hence an equation that relates D, x, and v is D = 0.5 + 20x + 0.5v

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