The following statistics represent crime rates per 1000 population for a random sample of 46 Denver neighborhoods. The mean crime rate, * = 64.2 and standard deviation, s = 27.9 crimes per 1000 population a) Let us say that the data are representative of the population crime rates in Denver neighborhoods. Compute the margin of error, E for an 80% confidence interval for , the population mean crime rate for all Denver neighborhoods. (5 pts) (11) Compute an 80% confidence interval for y, the population mean crime rate for all Denver neighborhoods. (4 pts) b) Suppose you are advising the police department about police patrol assignments. One neighborhood has a crime rate of 57 crimes per 1000 population. Do you think that this rate is below the average population crime rate and that fewer patrols could safely be assigned to this neighborhood? Explain. Use the confidence interval to justify your answer. (3 pts) c) Another neighborhood has a crime rate of 75 crimes per 1000 population average? Does this crime rate seem to be higher than the population average? Would you recommend assigning more patrols to this neighborhood? Explain. Use the confidence interval to justify your answer. (3 pts) PART 3. (see chapter 83 for help) Sunspots have been observed for many centuries. Records of sunspots from ancient Persian and Chinese astronomers go back thousands of years. Some archaeologists think sunspot activity may somehow be related to prolonged periods of drought in the southern United States. Let x be a random variable representing the average number of sunspots observed in a four-week period. A random sample of 40 such periods from Spanish colonial times gave a sample mean, * = 47.0.

Answer:

A.

two rays that share a common endpoint called the vertex

Step-by-step explanation:

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

The best statement which defines an angle is "Two rays that shares a common endpoints called vertex".

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

From the definition of an angle, a figure which is formed by two rays or lines that shares a common endpoints is called an angle.

Hence, the best statement which defines an angle is "Two rays that shares a common endpoints called vertex".

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Answer: 168

Step-by-step explanation: f(51)= 3(51)+15, 3(51)=153.  153+15=168

Answer:

x = 12

Step-by-step explanation:

given

f(x) = 51

f(x) = 3x + 15

51 = 3x + 15

3x = 51 - 15

3x = 36

x = 12

Step-by-step explanation:

Answer:

the answer is angle 4 is congruent to angle 3 and the measure of angle 4 is angle to angle 54, while, the congruent of angle 4 is angle 2 and, the supplement angle of angle 3 is angle 1 and the sum of all is angle 162

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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The total materials cost before sales tax is $297.21.

The total materials cost is the result of the addition of the total cost of posts, wire mesh, gate, and staples, as follows.

The length of the rectangular space = 6 meters

The width of the space = 10.5 meters'

The perimeter of the space = 33 meters [2(6 + 10.5)]

The space between posts = 1.5 meters

The number of posts = 22 (33 ÷ 1.5)

The cost per post = $2.69

a) The cost of the posts = $59.18 ($2.69 x 22)

The cost of wire mesh:

Cost per meter = $5.96

The number of meters of wire mesh = 33 meters

b) Total cost of the wire mesh = $196.68 ($5.96 x 33)

c) Cost of the gate = $25.39

Cost of Staples:

The number of staples per post = 7

The total number of staples required = 154 (22 x 7)

The number of boxes of staples = 4

The cost per box = $3.99

d) The total cost of staples = $15.96 (4 x $3.99)

The total cost of materials = $297.21 ($59.18 + $196.68 + $25.39 + $15.96)

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Answer:

day eight!!

Step-by-step explanation:

Josh --> starts with $40, saving $10

Sal --> starts with $160, spending $5

day one: josh: $50, sal: $155

day two: josh: $60, sal: $150

day three: josh: $70, sal: $145

day four: josh: $80, sal: $140

day five: josh: $90, sal: $135

day six: josh: $100, sal: $130

day seven: josh: $110, sal: $125

day eight: josh: $120, sal: $120

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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a. The probability of getting exactly 1 girl in 8 births is given as follows: 0.0313 = 3.13%.

b. The probability of getting 1 or fewer girls in 8 births is given as follows: 0.0352 = 3.52%.

c. The relevant probability for significantly low is given as follows: B. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability.

d. The correct option regarding whether the probability is significantly low is: D. Yes, since the appropriate probability is less than 0.05, it is a significantly low number.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

The mass probability formula is given as follows:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are listed as follows:

The relevant probabilities for this problem are given as follows:

Hence the probability of 1 or fewer, used to verify if the event is significantly low, is:

P(X <= 1) = P(X = 0) + P(X = 1)

P(X <= 1) = 0.0352.

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The probability of rolling a one on the first die and a six on the second die is 1/36.

Probability measures the likelihood or chance of an event happening.

A number between 0 and 1, where 0 represents an impossibility and 1 represents certainty, is used to express it.

By dividing the number of favourable outcomes by the total number of possible outcomes, one can determine the probability of an event.

The probability of rolling a one on the first die is 1/6, and the probability of rolling a six on the second die is also 1/6.

Since the two events are independent, we can use the multiplication rule of probability to find the probability of both events occurring together:

P(rolling a one on the first die and a six on the second die) = P(rolling a one on the first die) × P(rolling a six on the second die)

= (1/6) × (1/6)

= 1/36

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Answer: length and width

Step-by-step explanation:

The most common starting point in elementary school when one is discussing the concept of area is length (longer side) and width (shorter side) of a regular size object.
Book or notebook can be the best example that does have length and width.
Suppose the length of a book cover is 10 inches and width of that book cover is 6 inches. So what is the area of that book cover?

We know Area= length X width

So area of book cover = 10 inches X 6 inches = 60 square inches ( inches X inches = square inches).

Before discussing area must have to to have knowledge about length and width.

This is an example of a sample survey or a sampling method.

Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study. If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.

In the given scenario, you are conducting a sample survey to determine the proportion of each color of Peanut Butter M&Ms. A sample survey is a method used to collect data from a subset of a larger population in order to make inferences about the entire population.

Instead of counting every single Peanut Butter M&M in existence, which would be impractical and time-consuming, you decide to take a smaller representative sample. You purchase 10 packages of Peanut Butter M&Ms, each weighing 1.69 ounces, and count the number of M&Ms of each color in those packages.

By analyzing the data collected from this sample, you can estimate the proportion of each color of Peanut Butter M&Ms in the larger population. This approach is more feasible and provides a reasonable approximation of the overall distribution of colors without having to examine every individual item.

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Answer:

79ft²

Step-by-step explanation:

find the unknow side a

a = √(18² - 14²)

a = √(324 - 196)

a = √128

a = 11.31 ft

---------------------

find area

(11.31 * 14) : 2 =

79.17ft²

so your answer is 79ft²

The ratio of two thirds to four is given as follows:

1 : 6.

The ratio between two amounts a and b is obtained applying a proportion.

A proportion is applied because the ratio is given by the division of the amount a by the amount b.

The parameters for this problem are given as follows:

Hence the ratio of two thirds and four is calculated as follows:

(2/3)/4 = 2/3 x 1/4 = 2/12 = 1/6.

In ratio notation, it is given as follows:

1 : 6.

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The circumference of the moon is  2158π miles.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know the perimeter or the circumference of a circle is 2πr, Where r is the radius.

Therefore, The perimeter or the circumference of the moon with a radius of 1079 miles is,

= 2×π×1079 miles.

= 2158π miles.

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Answer:

r=d/t

r=360 cm / 9 sec= 40 cm per second

Hope that helps :)

Answer:

40 centimeters per second.

Step-by-step explanation:

360 divided by 9= 40

ChIcKeN nUgGeTs :>

Answer:

c

Step-by-step explanation:

Answer:

(4,2) and (2,0)

Step-by-step explanation:

To find two linearly independent solutions of the differential equation y" + 7xy = 0 in the form of power series, we substitute the given form of solutions into the differential equation and equate the coefficients of like powers of x to find the values of the coefficients.

Let's substitute the given form of y₁ and y₂ into the differential equation:

For y₁: y₁" = 42a₆x⁴ + 18a₃x

The equation becomes: (42a₆x⁴ + 18a₃x) + 7x(1 + a₃x³ + a₆x⁶) = 0

For y₂: y₂" = 24b₇x⁵ + 12b₄x³

The equation becomes: (24b₇x⁵ + 12b₄x³) + 7x(x + b₄x⁴ + b₇x⁷) = 0

By equating the coefficients of like powers of x to zero, we can solve for the coefficients.

For the coefficients a₃, a₆, b₄, and b₇, we need to solve the following equations:

For x³: 18a₃ + 7a₃ = 0

This gives a₃ = 0.

For x⁴: 42a₆ + 7b₄ = 0

This gives b₄ = -6a₆.

For x⁵: 24b₇ = 0

This gives b₇ = 0.

For x⁶: 42a₆ = 0

This gives a₆ = 0.

So, the coefficients a₃ and a₆ are both zero, and the coefficients b₄ and b₇ are zero as well.

Therefore, the first few coefficients are:

a₃ = 0

a₆ = 0

b₄ = 0

b₇ = 0

This means that the power series solutions y₁ and y₂ have no terms involving x³, x⁴, x⁶, and x⁷.

In summary, the linearly independent solutions of the given differential equation are:

y₁ = 1 + a₆x⁶ + ...

y₂ = x + b₄x⁴ + ...

Since a₃ = a₆ = b₄ = b₇ = 0, the power series solutions are simplified to:

y₁ = 1

y₂ = x

These solutions do not contain any terms with x³, x⁴, x⁶, or x⁷, which is consistent with the values we found for the coefficients.

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In ideal projectile motion, when the positive -axis is chosen to be vertically upward, the -component of the velocity of the object during the ascending part of the motion and the -component of the velocity during the descending part of the motion are b) negative, positive respectively.

In ideal projectile motion, the initial velocity of an object can be separated into its x-component (horizontal) and y-component (vertical). When the positive y-axis is chosen to be vertically upward, the object experiences a constant acceleration due to gravity.

This results in a negative y-component of velocity during the ascending part of the motion (as the object is moving upwards against gravity) and a positive y-component during the descending part of the motion (as the object is falling downwards with gravity).

To summarize, the y-component of velocity is negative during the ascending part of the motion and positive during the descending part. This is because gravity acts downwards, causing the object to slow down as it rises and speed up as it falls.

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Answer:

Coding: if s then w , else d

Math Logic: (s -> w) & (~s -> d)

Step-by-step explanation:

In a logical and/or coding concept this would be solved as the following

Coding: if s then w , else d

Math Logic: (s -> w) & (~s -> d)

Both of these statements are basically stating that if you are subscribed to the service then you can simply how ahead and use the wireless network in the airport, but if you are not a subscriber then you have to pay the daily fee in order to be able to use the network.

The relative maximum value of f occurs at x = b) 0.20.

We can find the relative maximum value of f by finding the critical point of f, which is the value of x where the derivative of f is equal to 0.

f'(x) = e^x - 3x^2 = 0

e^x = 3x^2

ln(e^x) = ln(3x^2)

x = sqrt(ln(3x^2))/sqrt(3)

That is not a real value, however, we can find the relative max by finding the second derivative test, which is the sign of the second derivative of f at x. If the second derivative is positive, the x is a relative max.

f''(x) = e^x - 6x

To find the relative max we have to evaluate the second derivative at each option point a,b,c,d,e

a) -0.46 f''(-0.46) is negative

b) 0.20 f''(0.20) is positive

c) 0.91 f''(0.91) is negative

d) 0.95 f''(0.95) is negative

e) 3.73 f''(3.73) is negative

Therefore, the relative maximum value of f occurs at x = b) 0.20

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The point e. x = 5, y = 0 satisfies the two linear constraints simultaneously. We have two linear constraints which are given as;

2x + 5y ≤ 10 (Equation 1)

10x + 6y ≤ 42 (Equation 2)

We need to find the point which satisfies both equations. Let us plug in the values one by one to check which one satisfies the two equations simultaneously.

a. x= 6, y = 2

In Equation 1:2x + 5y = 2(6) + 5(2) = 17

In Equation 2:10x + 6y = 10(6) + 6(2) = 66

Thus, this point does not satisfy equations 1 and 2 simultaneously.

b. x=6, y=4

In Equation 1:2x + 5y = 2(6) + 5(4) = 28

In Equation 2:10x + 6y = 10(6) + 6(4) = 72

Thus, this point does not satisfy equations 1 and 2 simultaneously.

c. x=2, y = 1

In Equation 1:2x + 5y = 2(2) + 5(1) = 9

In Equation 2:10x + 6y = 10(2) + 6(1) = 26

Thus, this point does not satisfy equations 1 and 2 simultaneously.

d. x=2, y = 6

In Equation 1:2x + 5y = 2(2) + 5(6) = 32

In Equation 2:10x + 6y = 10(2) + 6(6) = 52

Thus, this point does not satisfy equations 1 and 2 simultaneously.

e. x = 5, y = 0

In Equation 1:2x + 5y = 2(5) + 5(0) = 10

In Equation 2:10x + 6y = 10(5) + 6(0) = 50

Thus, this point satisfies both equations simultaneously.

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Answer:

Step-by-step explanation:7.48521878104

Step-by-step explanation:

The given equations are :

-x+6y = 16 ...(1)

8x-6y = -2 ...(2)

The y-variable will be eliminated when adding the system of  equations.

Adding equations (1) and (2).

-x+6y+8x-6y = 16+(-2)

7x = 14

x = 2

Put the value of x in equation (1).

-2+6y = 16

6y = 16+2

y = 3

There is only one solution to the system of equations i.e. (2,3).

The possible values of x as required to be determined in the task content are; ±½.

It follows from the task content that the possible values of x are to be determined from the given task content.

The given equation can be written algebraically as;

√(8x) • √(10x) • √(3x) • √(15x) = 15

√3600x² = 15

60x² = 15

x² = 15 / 60

x² = 1/4.

x = ± ½.

Ultimately, the possible values of x as required in the task content are; +½ and -½.

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The initial value problem calculator is a tool used to calculate differential equations.

An instrument for solving ordinary differential equations with initial conditions is an initial value problem calculator. Finding a function that solves a given differential equation and a set of initial conditions is the goal of this calculator, a particular kind of differential equation problem. The differential equation, the beginning conditions, and other pertinent parameters are entered into the calculator, which then generates a solution that fulfils the initial conditions.

Usually, the answer is provided as a function that specifies how the system behaves over time. In disciplines like physics, engineering, and economics, where differential equations are regularly employed to represent dynamic systems, these calculators are widely used. They can be helpful for obtaining an understanding of a system's behavior and for predicting its upcoming trends

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