A random sample of the price of gasoline from 40 gas stations in a region gives the statistics below. Complete parts a) through c). y = $3.49, s = $0.21 a) Find a 95% confidence interval for the mean price of regular gasoline in that region. (Round to three decimal places as needed.)

Answer:

Step-by-step explanation:

2x-1+7x=175c

9x-1=175c

9x=175c+1

x=175/9c +1/9 ,C

Answer:

The equation of the line that passes through the given points is:

Hence, option D is correct.

The graph of the line equation is also attached below.

Step-by-step explanation:

Given the points

Finding the slope between (-5, 10) and (5, -10)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(-5,\:10\right),\:\left(x_2,\:y_2\right)=\left(5,\:-10\right)\)

\(m=\frac{-10-10}{5-\left(-5\right)}\)

\(m=-2\)

Using the point-slope form to determine the line equation

Point slope form:

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (-5, 10)

\(y-10=-2\left(x-\left(-5\right)\right)\)

\(y-10=-2\left(x+5\right)\)

Add 10 to both sides

\(y-10+10=-2\left(x+5\right)+10\)

simplify

\(y=-2x\)

Thus, the equation of the line that passes through the given points is:

Hence, option D is correct.

The graph of the line equation is also attached below.

The smallest positive solution for the given equation is x ≈ 0.121 radians.

To solve the equation sin(2x)cos(5x) - cos(2x)sin(5x) = -0.35 for the smallest positive solution, we can use the following steps:

Step 1: Use the angle subtraction formula for sine.
The given equation can be written using the angle subtraction formula: sin(A - B) = sin(A)cos(B) - cos(A)sin(B).

Therefore, the equation becomes sin(2x - 5x) = -0.35.

Step 2: Simplify the equation.
Simplify the equation to sin(-3x) = -0.35.

Step 3: Use the property sin(-x) = -sin(x).
Applying this property, we get sin(3x) = 0.35.

Step 4: Find the value of 3x using the arcsin function.
To find the value of 3x, take the inverse sine (arcsin) of both sides: 3x = arcsin(0.35).

Step 5: Solve for x.
Divide both sides of the equation by 3 to find x: x = (arcsin(0.35))/3.

Using a calculator, we find that x ≈ 0.121 radians. This is the smallest positive solution for the given equation.

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The length of the midsegment of the trapezoid ABCD is 4.15 units

From the question, we have the following parameters that can be used in our computation:

Parallel sides =  7.3 and 5.5

The length of the midsegment of the trapezoid ABCD is calculated as

Midsegment = 1/2(Sum of parallel sides)

Substitute the known values in the above equation, so, we have the following representation

Midsegment = 1/2 * (7.3 + 5/5)

Evaluate

Midsegment = 4.15

Hence, the Midsegment is 4.15

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Answer:

f(x) = (x + 1)((x - 1)^2)(x - 3)

Answer:

13- 60, 14- 30

Step-by-step explanation:

number 13 is a 60, 60,60 triangle

number 14 has two identical edges 2 of the corners are the same:

30, 30, 120

Answer:

for 13 its x=60 and for 14 its x=120

Step-by-step explanation:

for 13 its a equilateral triangle meaning all sides are the same so the answer x=60

for 14 its a obtuse isosceles triangle meaning it has 2 angles that are the same and 1 obtuse angle so the other angles would be 30 and 120. hope this helps :)

Answer:

For an nth term in an arithmetic sequence

U(n) = a + ( n-1)d

a = first term

d = common difference

n = number of terms.

Considering the above picture

a = 9

d = 6 - 9 = - 3

For an nth term of the sequence

U(n) = 9 + (n - 1)-3

= 9 - 3n + 3

= 12 - 3n

Hope this helps

In the given definitions, there are several difficulties and violations of the rules for definition by genus and difference. These include ambiguity, lack of specificity, and the inclusion of irrelevant information.

The rules being violated include the requirement for clear and concise definitions, inclusion of essential characteristics, and avoiding irrelevant or subjective statements.

12. The definition of a raincoat as an outer garment of plastic that repels water is too broad. It lacks specificity regarding the material and construction of the raincoat, as not all raincoats are made of plastic. Additionally, the use of "outer garment" is subjective and does not provide a clear distinction from other types of clothing.

13. The definition of a hazard as anything that is dangerous is too broad and subjective. It fails to provide a specific category or characteristics that define what qualifies as a hazard. The definition should include specific criteria or conditions that identify a hazard, such as the potential to cause harm or risk to safety.

14. The definition of sneezing as emitting wind audibly by the nose is too narrow and lacks clarity. It excludes other aspects of sneezing, such as the involuntary reflex and the expulsion of air through the mouth. The definition should encompass the essential characteristics of sneezing, including the reflexive nature and expulsion of air to clear the nasal passages.

15. The definition of a bore as a person who talks when you want him to listen is subjective and relies on personal preference. It does not provide objective criteria or essential characteristics to define a bore. A more appropriate definition would focus on the tendency to dominate conversations or disregard the interest or input of others.

In conclusion, these definitions violate the rules for definition by genus and difference by lacking specificity, including irrelevant information, and relying on subjective or ambiguous criteria. Clear and concise definitions should be based on essential characteristics and avoid personal opinions or subjective judgments.

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The coordinates of the vertices of the reflected image are

A' ( 6,5) , B' ( 5,1), C' ( 8,2)

given that

a triangle has vertices A ( -6,5 ) , B (-5, 1) , C( -8,2 )

it is reflected over Y axis

we have to find the coordinates of the vertices of the reflected image

since it is reflected over Y axis then only the sign of x coordinates changes

the rule for a reflection over the Y axis is (x, y) -> ( -x , y)

the y coordinate in this case is unchanged

the vertices changes and it become

A( -6, 5) -> A' ( 6,5)

B ( -5, 1) -> B' ( 5,1)

C ( -8,2) -> C' ( 8,2)

preimage of coordinates attached below

Hence the coordinates of the vertices of the reflected image are

A' ( 6,5) , B' ( 5,1), C' ( 8,2)

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Answer:

3:5 or 3/5

Step-by-step explanation:

We know that there are -->

56 Females

84 Males

We need to find the total amt. of ppl

56 + 84 = 140

Males/140 --> Plug 84 in => 84/140

Since it wants simplified, divide both by 7 as 7 is a factor of both -->

12/20 --> Divide by 4

3/5 => This is the most simplified we can get and -->

thus, our answer is 3:5 or 3/5

Hope this helps!

Answer:

the answer is D less than or equal to

Step-by-step explanation:

Answer:

Day 4 and 6

Step-by-step explanation:

The numerical length of PQ is 20

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that the line segments are: -

OQ=11  O P = 9

The numerical value of PQ will be calculated as below.

OP+OQ=PQ

11+9=PQ=11+9=PQ

Therefore PQ=20=PQ

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The slope (m) of the line is 19 and the y-intercept (b) is -4. The equation of the line can be expressed as y = 19x - 4.

The slope (m) of a straight line can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Using the given points (3, 53) and (5, 91), we can substitute the values into the formula:

m = (91 - 53) / (5 - 3)

m = 38 / 2

m = 19

Therefore, the slope (m) of the straight line is 19.

To determine the y-intercept (b), we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

Using the point (3, 53) and the slope we just calculated (m = 19), we can substitute the values into the equation:

53 = 19(3) + b

53 = 57 + b

Now, solving for b:

b = 53 - 57

b = -4

Therefore, the y-intercept (b) of the straight line is -4.

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The United States abortion rate based on the given function is decreasing. The estimated abortion rate for 2008 is 13.46 abortions per 1000 women and the estimated abortion rate for 2013 is 16.5 abortions per 1000 women. The year when the abortion rate will be 12 is approximately 2024.

The function given for the United States abortion rate is R(x) = -0.58x + 23.9, where x is the year since 1990 and R(x) is the abortion rate. To determine if the rate is increasing or decreasing, we need to look at the slope of the function. The slope is -0.58, which is negative, so the rate is decreasing over time.

To find the estimated abortion rate for 2008, we can substitute x = 18 into the function since 2008 is 18 years after 1990. Therefore,R(18) = -0.58(18) + 23.9 ≈ 13.46 abortions per 1000 women.To find the estimated abortion rate for 2013, we can substitute x = 23 into the function since 2013 is 23 years after 1990. Therefore, R(23) = -0.58(23) + 23.9 ≈ 16.5 abortions per 1000 women.

To find the year when the abortion rate will be 12, we need to set R(x) = 12 and solve for x.-0.58x + 23.9 = 12-0.58x = -11.9x ≈ 20.52. Since x is the year since 1990, the year when the abortion rate will be 12 is approximately 2010 + 20.52 = 2030. Rounded to the nearest year, this is 2024. Therefore, the year when the abortion rate will be 12 is 2024.

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Answer:

(x² + 2)(2x - 5)

Step-by-step explanation:

assuming the expression has to be factorised

2x³ - 5x² + 4x - 10 ← rearranging terms as indicated

= 2x³ + 4x - 5x² - 10 ( factor the first/second and third/fourth terms )

= 2x(x² + 2) - 5(x² + 2) ← factor out (x² + 2) from each term

= (x² + 2)(2x - 5) ← in factored form

The total weight of the truck with 20 tons refrigerated on is 35 tons.

It should be noted that the weight simply means the.mass that's contained in a body.

From the information, the truck weighs 15 tons when empty and we want to know the total weight of the truck with 20 tons refrigerated on.

In this case, the weight will be:

= Weight when empty + Added weight

= 15 + 20

= 35 tons.

This illustrates the weight.

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The people who are interviewed constitute a convenience sample.

If the survey company is interviewing anyone who is available in the shopping mall without using any systematic method for selecting the participants, it would be considered a convenience sample.

In a convenience sample, the sample is selected based on ease of access to the participants, and it may not be representative of the entire population. This type of sampling can lead to bias in the sample, as the views of people who happen to be available in the mall at the time may not be representative of the views of the entire population.

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Answer:

the slope is 5. 5/1

Step-by-step explanation:

Use rise over run to find slope. It is the easiest way to find slope

You rise 5 and 1 to the right

Answer:

The slope is 5

Step-by-step explanation:

So you're just trying to find the slop. We're going to choose 2 points to use which are already marked on the graph.

(0, 2) and (-1, -3)

So to find the slope, we have to find (the difference in y) / (the difference in x)

So we're going to do

-3-2/-1-0

Which is

-5/-1

So since there are two negatives, it become positive, and it'll simplify into 5.

So the slope of the line is 5

Answer:

2−12x+36

Step-by-step explanation:

Answer:

(x-6)² = (x-6)(x-6) = x² - 12x + 36

Step-by-step explanation:

When a 30-inch segment is cut into two parts whose lengths have the ratio 3 to 5, the length of the shortest part is 11.25 inches.

Therefore, the answer is 11.25in.

A line segment is cut into two parts, say of length x and y in inch. As they are cut in ratio 3 is to 5, x/y = 3/ 5.

Therefore, 5x = 3y implies x = 3y/5 = 0.6y

Also total length of the line segment is 30in, that is x + y = 30.

Therefore, 0.6y + y = 30

y = 30/ 1.6

= 18.75

Thus, x = 0.6y = 11.25

Therefore the 30in line segment is divided into lengths of 11.25in and 18.75in.

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The triangles AEB and DEC describes AA similarity .

What is AA Similarity ?

Two triangles are said to be congruent by AA Similarity when two angles in one triangle are congruent to two angles in another triangle .

In the question ,

a figure is given .

in triangle AEB and triangle DEC ,

we can see that ,

∠AEB ≅ ∠DEC    ,   because they are vertically opposite angles .

On rotating triangle CED by  180° around the point E, then the translate point D to point A confirms  ∠EAB ≅ ∠EDC.

Since two angles are Congruent

So , By AA Similarity , triangles AEB and DEC are Congruent .

Therefore , the triangles AEB and DEC are Congruent .

The given question is incomplete , the complete question is

Which of the following triangles in the given figure describes AA similarity ?

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Answer:

Step-by-step explanation:

these triangles are not similar,  you can tell, b/c the one given angle and that they are both right triangles, so you also know that the other angle , that is not given is not the same, in the two.   hence the sides are not the same lengths or ratios of each other.  they are NA

If ker(A)=im(B), the product of the two matrices AB will be the zero matrix.

A linear transformation is a function that can be represented as a matrix transformation, and the kernel is the set of all inputs which produce an output of 0. In this example, the kernel of the linear transformation is the line spanned by A = 1 in R3.

If we consider an n x p matrix A and a p x m matrix B, and if the kernel of matrix A (ker(A)) is equal to the image of matrix B (im(B)), then the product of the two matrices AB will be the zero matrix. This is because all elements in the product matrix will be the result of multiplying a row vector of A by a column vector of B. But, since the kernel of A is equal to the image of B, this means that all of the row vectors of A and all of the column vectors of B are equal, so the result of multiplying any of them together will be the zero vector.

To summarize, if the kernel of A is equal to the image of B, the product of the two matrices AB will be the zero matrix.

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The main idea behind statistical inference is that through the use of sample data, we are able to draw conclusions about the population from which the data was drawn (option c).

Statistical inference allows us to make inferences and draw conclusions about a larger population based on the analysis of a smaller representative sample.

By collecting data from a sample, we can use statistical methods to analyze and summarize the information. These methods include estimating population parameters, testing hypotheses, and making predictions.

The key assumption underlying statistical inference is that the sample is representative of the larger population, allowing us to generalize the findings to the population as a whole.

Statistical inference provides a way to make reliable and informed decisions, identify patterns and relationships, and make predictions about future observations based on the available data. It allows researchers, scientists, and decision-makers to make evidence-based conclusions and draw meaningful insights from limited observations.

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Answer: \(U_{n} =(40)+(n-1)(10)\)

Step-by-step:

\(U_{n} =a+(n-1)d\)

a = 40

d = 10

\(U_{n} =(40)+(n-1)(10)\) is the formula for nth hour

The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

A and B are typically subitized, which means that they can be immediately recognized without counting. C and D are more likely to be counted.

Counting is the process of determining the number of items in a set by successively adding one. Subitizing, on the other hand, is the ability to immediately recognize the number of items in a small set without counting. The capacity for subitizing is limited to small sets typically ranging from 1 to 5 items, depending on the individual's age and mathematical ability. The answer to this question would be option C, 3. For most individuals, recognizing the number of items in a set of 3 would require counting rather than subitizing, as 3 is at the upper limit of the typical range for subitizing.

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