in a random sample of 310 cars driven at low altitudes, 41 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. in an independent random sample of 95 cars driven at high altitudes, 21 of them exceeded the standard. compute the test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.

Answer:

-3/2

Step-by-step explanation:

Count the rise = -3

Count the run= 2

Rise/run= -3/2

Answer:

-7/-4 or 1.75

Step-by-step explanation:

Another formula for the slope of a line is (y2-y1)÷(x2-x1)

So all we need is to find the points (x1, y1) and (x2, y2)

Point 1: (1, -3)

Point 2: (-3, 4)

Sub this into the equation:

(-3-4) ÷ (-3-1) = -7 ÷ -4 = 1.75

since r is so widely used, it is appropriate to calculate r for nonlinear data: False.

The calculation of r (Pearson's correlation coefficient) is based on the assumption that the relationship between the two variables is linear. Therefore, it is not appropriate to calculate r for nonlinear data as it may give misleading results.

In summary, it is not appropriate to calculate r for nonlinear data as it assumes a linear relationship between the variables. Other methods such as Spearman's rank correlation or Kendall's tau may be used for nonlinear data.


n: The correlation coefficient 'r' is specifically designed to measure the strength and direction of a linear relationship between two variables. While it is widely used, calculating 'r' for nonlinear data is not appropriate, as it will not accurately capture the true nature of the relationship between the variables.

When dealing with nonlinear data, it is better to use other statistical methods designed for such data, rather than relying on the correlation coefficient 'r'.

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Answer:

567.06 in.²

Step-by-step explanation:

The mat is a semicircle.

The straight side is a diameter.

d = 38 in.

r = d/2 = 19 in.

Area of circle = πr²

Area of semicircle = πr²/2

A = 3.14159 × (19 in.)² / 2

A = 567.06 in.²

Answer:

Store B has more expensive lawn mowers.

Step-by-step explanation:

The median price is the price in the middle of the possible prices which means that if you double the median price you will get about what the highest price can be.

What can be inferred from the data is store B has more expensive lawn mowers.

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order. Median is a measure of central tendency.  For example 3 is the median in this dataset: 1, 3, 6

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The ERD for the described situation would include entities such as county jails, mental health facilities, shelters, hospitals, and a coordinating database. Relationships between these entities would allow for coordination and prediction of the type of assistance individuals may need to reduce their involvement in the justice system.

The ERD for the Miami-Dade County court system's database would include the following entities:

County Jails: Represents the jails within the county system where individuals may be incarcerated.

Mental Health Facilities: Represents the facilities that provide mental health services and support.

Shelters: Represents the shelters that offer temporary housing and assistance to those in need.

Hospitals: Represents the healthcare institutions where individuals receive medical treatment.

Coordinating Database: Represents the central database that coordinates activities and stores information from all the other entities.

The relationships between these entities would be established through appropriate connections:

County Jails to Coordinating Database: This relationship would allow for the exchange of information about individuals in the jail system, including their personal history and involvement in the justice system.

Mental Health Facilities to Coordinating Database: This relationship would facilitate the sharing of information regarding individuals' mental health needs and treatment plans.

Shelters to Coordinating Database: This relationship would enable the coordination of housing services and assistance programs for individuals in the justice system.

Hospitals to Coordinating Database: This relationship would allow for the integration of medical records and healthcare services for individuals involved in the justice system.

These relationships and the information stored in the coordinating database would serve as the foundation for algorithms to predict the type of help individuals might require to reduce their involvement in the justice system.

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Chelsea made a mistake in simplifying the equation 3(x-3). To find the solution to 4x-5=2(3(x-3)), we first simplify the expression inside the parentheses.

Now, to isolate the variable x, we need to move the terms with x to one side of the equation. Let's subtract 4x from both sides, which gives us -5-4x=6x-18-4x. Simplifying this, we get -5-4x=2x-18.

Next, let's move the constant terms to the other side. Adding 18 to both sides, we get -5-4x+18=2x-18+18. Simplifying this, we get -4x+13=2x.

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Chelsea made a mistake when subtracting the variable term from both sides. By identifying this error and correctly following the steps, we find that the solution to the equation 4x - 5 = 2 3(x - 3) is x = -7.

Chelsea made a mistake in her work when finding the solution to the equation 4x - 5 = 2 3(x - 3). To determine where she went wrong, let's analyze her steps.

Step 1: Distribute 3 to (x - 3): 4x - 5 = 2 3x - 6.
Step 2: Combine like terms: 4x - 5 = 6x - 12.
Step 3: Move the variables to one side and the constants to the other side. Chelsea may have mistakenly subtracted 4x from both sides instead of 6x. This would result in: -5 = 2x - 12.
Step 4: Solve for x. Chelsea may have then incorrectly added 12 to both sides instead of adding 5, leading to: 7 = 2x.
Step 5: Divide both sides by 2: x = 7/2.

Upon reviewing her work, Chelsea should have subtracted 6x from both sides in Step 3, not 4x. This would have resulted in the equation 2x - 5 = -12. Correctly following the steps would lead to the correct solution: x = -7.

Therefore, Chelsea made a mistake when subtracting the variable term from both sides. By identifying this error and correctly following the steps, we find that the solution to the equation 4x - 5 = 2 3(x - 3) is x = -7.

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The probability that at least one is type O is 0.8704.

What is a binomial distribution probability?

A value's likelihood of taking one of two independent values is summarised by the statistical distribution known as the binomial distribution.

Given,  40 % of the population has type O blood and 4 people are randomly selected to be donors

Then, binomial distribution can be given by

X ~ = Binomial(n = 4, p = 0.4)

P(at least one type O)

P[X ≥ 1]

= 1- P[X < 1]

= 1- P[X = 0]

= \(1 -C(4,0) * (0.4)^{0} * (1 - 0.4)^{4-0}\)

=1-0.1296

=0.8704

Hence, the probability that at least one is type O is 0.8704.

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There are 60 different kinds of paint that can be made.

to determine the number of different kinds of paint that can be made, we need to use the multiplication principle of counting, which states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

using this principle, we can determine the number of different kinds of paint as follows:

- color: there are 5 different colors that can be used.- type: there are 2 different types of paint that can be used.

- texture: there are 3 different textures that can be used.- use: there are 2 different uses for the paint.

to find the total number of different kinds of paint, we need to multiply the number of options in each category together:

5 x 2 x 3 x 2 = 60

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Answer:

Vertically opposite angles are equal

So

x = 75°

Vertically opposite angles are equal

So

5y = 135°

Divide both sides by 5

y = 27

Hope this helps you

Adam made an error in the last step by incorrectly adding 12 - 12 as 24 instead of obtaining 0 as a result of subtracting 12 from 12.

Therefore, Robert did the correct step.

Here, we have,

To determine which students made the correct step, let's evaluate each process:

Mr. Gonzalez assign the following expression :

12 - 2x + 8y - 12 + 3x - 4y

the following process to simplify the expression by :

Robert:

12 - 12 - 2x + 3x + 8y - 4y

Combining like terms:

0 - 2x + 3x + 8y - 4y

x + 4y

Adam:

12 - 2x + 8y - 12 + 3x - 4y

Combining like terms:

12 - 12 - 2x + 3x + 8y - 4y

12-12 + 5x + 4y

24+5x + 4y

From the three processes,  Robert simplified the expression correctly to x + 4y.

However, Adam made an error in the last step by incorrectly adding 12 - 12 as 24 instead of obtaining 0 as a result of subtracting 12 from 12.

Therefore,  Robert did the correct step.

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The probability that a patient with a stiff neck has meningitis is very low at 0.002%.

To find the probability that a patient with a stiff neck has meningitis, we can use Bayes' theorem.

Let A be the event that the patient has meningitis and B be the event that the patient has a stiff neck.

We know that P(B|A) = 0.5, meaning that if a patient has meningitis, there is a 50% chance they will have a stiff neck. We also know that P(A) = 1/50,000, meaning that the probability that any patient has meningitis is 1 in 50,000. Additionally, we know that P(B) = 1/20, meaning that the probability that any patient has a stiff neck is 1 in 20.

Using Bayes' theorem, we can find the probability that a patient with a stiff neck has meningitis:

P(A|B) = P(B|A) * P(A) / P(B)
P(A|B) = 0.5 * (1/50,000) / (1/20)
P(A|B) = 0.00002 or 0.002%

Therefore, the probability that a patient with a stiff neck has meningitis is very low at 0.002%.

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Answer:

y = - 2x + 17

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 2, then

y = - 2x + c ← is the partial equation

To find c substitute (6, 5) into the partial equation

5 = - 12 + c ⇒ c = 5 + 12 = 17

y = - 2x + 17 ← equation of line

Answer: γ≈14.71deg

or

165.29deg

Step-by-step explanation:

Answer:

sorry i coldent find the anser

Step-by-step explanation:

ello

+v+

Answer:

The slope indicates that the soup kitchen uses 63 cans per day. The y-intercept shows that there were initially 825 cans at the soup kitchen.

Step-by-step explanation:

In 0.75lb (340g) of 85% lean ground beef, there are approximately 72 grams of fat.

To calculate the grams of fat in 0.75lb of 85% lean ground beef, we need to determine the fat content based on the percentage given. The term "85% lean" indicates that 85% of the weight of the ground beef is lean meat, while the remaining 15% is fat.

First, we convert 0.75lb to grams. Since 1lb is equal to 454g, multiplying 0.75lb by 454g/lb gives us 340g.

Next, we calculate the fat content by multiplying the weight of the ground beef (340g) by the percentage of fat (15%).

340g * 0.15 = 51g

Therefore, in 0.75lb (340g) of 85% lean ground beef, there are approximately 51 grams of fat.

However, the question asks for the fat content, so we subtract this value from the total weight to find the grams of fat:

340g - 51g = 289g

Therefore, there are approximately 72 grams of fat in 0.75lb (340g) of 85% lean ground beef.

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The width of a rectangle that has the length of 72 would be = 90 inches. That is option B.

A proportional rectangule represents the rectangles that have similar ratios of both length and width.

From the table given,

Rectangle with length 8 = width 10

Rectangle with length 12 = width 15

Rectangle with length 24 = width 30

We can now say that if 8 = 10 the width of length 72 = X

Make X the subject of formula;

X = 72×10/8

X = 720/8

X = 90 inches.

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Volume =  

1  πr2h

3

=  

1 ×π×42×7

3

=  117.28612573402 centimeters^3

Florence built a tower of blocks that was 171 centimeters high. She used 90 identical blocks to build the tower. The height of each block is approximately 1.9 centimeters.

To determine the height of each block, we divide the total height of the tower (171 centimeters) by the number of blocks used (90 blocks). The resulting quotient, approximately 1.9 centimeters, represents the height of each block. To find the height of each block, we divide the total height of the tower by the number of blocks used.

Height of each block = Total height of the tower / Number of blocks

Height of each block = 171 centimeters / 90 blocks

Height of each block ≈ 1.9 centimeters

Therefore, the height of each block is approximately 1.9 centimeters.

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1: no solution

2: infinitely many solutions

3: one solution

Answer:

C

Step-by-step explanation:

Just did the Unit Review

Answer:

______________________________________________

\(\green{\longmapsto}\boxed{\blue{7z - 4q = 3} }\)

______________________________________________

\(7z = 4q + 3 \\ z = \frac{4q + 3}{7} \\ \boxed{\red{z =\frac{4q}{7} + \frac{3}{7} }}\)

______________________________________________

\( - 4q = 3 - 7z \\ 4q = 7z - 3 \\ q = \frac{7z - 3}{4} \\ \boxed{\red{q = \frac{7z}{4} - \frac{3}{4} }}\)

______________________________________________

Answer:

D)

Step-by-step explanation:

A is incorrect because:  2(6) -3(-4)<9 which is 24<9 which is not true

B is incorrect because:  2(-1) -3(-9)<9 which is 25<9 which is not true

C is incorrect because: 2(2) -3(-5)<9 which is 19<9 which is not true

D is correct because: 2(-3) -3(-3)<9 which is 3<9 which is true

The correct answer is (4x^3 - 8x^2 )

Solve by using Foil's Method

Multiply (x - 3)(4x^2)

Begin, by multiplying together, the first terms of binomial

= x * 4x^2 = 4x^3

Now, multiply the last term of binomial.

= -3 * 4x^2 = -12x^2

Sum up the partial products starting from the first to last product from the first to last product and collect it:

=(4x^3 - 8x^2 )

Now, Let us know

What is Foil's Method ?

FOIL a mathematical series of steps used to multiply two binomials.

By definition we have the meaning of FOIL is given by:

F: First

O: Outer

I: Inner

L: Last

Binomial is simply an expression that consist of two variables or terms separated by either the addition sign (+) or subtraction (-).

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Answer:

lol

Step-by-step explanation:

hahahaha

The solid line has length and makes an angle with the negative y-axis, the length of the dashed line is l × cos(α).

Given, the solid line has length l and makes an angle α with the negative y-axis. By using trigonometry, we can determine the length of the dashed line using l and α. From the figure, we can see that: cos(α) = length of the adjacent side / length of the hypotenuse cos(α) = length of the dashed line / length of the solid line

Therefore, length of the dashed line = length of the solid line × cos(α)

Substituting the given values, length of the dashed line = l × cos(α)

Therefore, the length of the dashed line is l × cos(α).

The length of the dashed line is l × cos(α).

By using trigonometry, we can determine the length of the dashed line using l and α. From the figure, we can see that: cos(α) = length of the adjacent side / length of the hypotenuse cos(α) = length of the dashed line / length of the solid line. Therefore, length of the dashed line = length of the solid line × cos(α)Substituting the given values, length of the dashed line = l × cos(α).

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Their hourly wage in 3 more years (after a total of 13 years) will be 17.43 per hour.

We can solve this problem using the formula for exponential growth, which is:

\(A = P(1 + r)^t\)

Where:

A = the amount after t years

P = the initial amount

r = the annual growth rate (expressed as a decimal)

t = the number of years

Let's use this formula to solve the problem:

Find the initial amount

The initial hourly wage is 7.40, so P = 7.40

Find the annual growth rate

The wages grew from 7.40 to 14.56 in 10 years, so we can use this information to find the annual growth rate:

\(14.56 = 7.40(1 + r)^{10}\\(1 + r)^{10} = 14.56/7.40\\(1 + r)^{10} = 1.97297\\1 + r = (1.97297)^{(1/10)\)

1 + r = 1.076

r = 0.076 or 7.6%

So the annual growth rate is 7.6% (expressed as a decimal).

Find the amount after 13 years

We want to find the hourly wage in 3 more years, which is a total of 13 years (10 years of past growth + 3 more years). So t = 13.

\(A = P(1 + r)^t\\A = 7.40(1 + 0.076)^{13}\\A = 7.40(1.076)^{13}\\A = 7.40(2.355)\)

A = 17.43 (rounded to two decimal places)

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The length of the rectangle is equal to \(L < 11\;inches\).

Given the following data:

To write an equation and solve for the length of the rectangle:

Mathematically, the area of a rectangle is given by this formula:

\(A=LW\)

Where:

Substituting the given parameters into the formula, we have;

\(5L < 55\\\\L < \frac{55}{5} \\\\L < 11\;inches\)

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For the given tossing of number cube and its frequency outcome, the probability on landing a number greater than 4 is 18/60.

As given in the question

Total number of tossing a number cube = 60

Number of times greater than 4 comes up = 10 + 8 (frequency of is 10 and frequency of 6 is 8)

⇒Number of times greater than 4 comes up = 18

Probability of getting number greater than 4

=  (frequency of getting 5 and 6) / (total number of trials)

⇒ probability of getting number greater than 4  = 18 / 60                                                                      

Therefore, for the given tossing of number cube and its frequency outcome, the probability on landing a number greater than 4 is 18/60.

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18/60..............................................................