Question 8 (1 point ) Classify the system as consistent independent, inconsistent, or coincident. 3x-6y=-12 x-2y=-4

The probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles is 25.14.

To break this problem, we need to use the standard normal distribution, assuming that the distribution of tire continuances is roughly normal. We can regularize the value of 42,000 using the formula

z = ( x- μ)/ σ

where x is the value of interest( 42,000 long hauls), μ is the mean tire continuance( 40,000 long hauls), and σ is the standard deviation( 3,000 miles). Plugging in the values, we get

z = ( 42,000- 40,000)/ 3,000 = 0.67

Using a standard normal distribution table or calculator, we can find the probability that an aimlessly named tire will last further than 42,000 long miles by looking up the area to the right of z = 0.67 under the standard average wind. This probability is roughly 25.14.

thus, the probability that a tire named arbitrarily from this brand will last more than 42,000 miles is roughly 25.14.

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The correct question is given below-

A particular brand of tires lasts an average of 40,000 miles with a standard deviation of 3,000 miles. What is the probability a tire selected at random lasts more than 42,000 miles?

Step-by-step explanation:

B        to        B'

( 7,-2)  to   (-2,-7)

(x,y)  changed to  (y,-x)    this is a 90 degree clockwise rotation

Answer:

Step-by-step explanation:

It is a 90 degree clockwise rotation.

A = (2, -5)

A' = (-5, -2)

90° clockwise will reverse the x an y points and change the sign of x.

(x, y) becomes (y, -x)

You only need to use one point to figure the rotation.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{1}}} \implies \cfrac{ 3 }{ 4 } \implies \cfrac{3}{4} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{1}}} \implies \cfrac{ -3 }{ 4 } \implies - \cfrac{3}{4} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{5}}} \implies \cfrac{ -4 }{ -3 } \implies \cfrac{4}{3}[/tex]

The correct statement regarding the circle with equation x² + y²-8x+12y+34 = 0 is given as follows:

Neither.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The equation for this problem is given as follows:

x² + y² - 8x + 12y + 34 = 0.

Completing the squares, we obtain the equation as follows:

(x - 4)² + (y + 6)² = -34 + 16 + 36

(x - 4)² + (y + 6)² = 18.

Hence the center and radius are given as follows:

The area of the circle is given as follows:

A = 2πr = 2π x 4.2 = 26 square units.

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Answer: A

Step-by-step explanation:

Answer:

There are a total of 9 customers who have entered the drawing. The probability that the first winner lives in Gaston is 2/9, since there are 2 customers from Gaston out of 9 total customers.

Once the first winner is selected, there will be 8 customers remaining, out of which 2 live in Pike. Therefore, the probability that the second winner lives in Pike, given that the first winner lives in Gaston, is 2/8 or 1/4.

To find the probability that the first winner lives in Gaston and the second winner lives in Pike, we need to multiply the probabilities of the two events:

P(Gaston first and Pike second) = P(first winner from Gaston) * P(second winner from Pike, given that first winner is from Gaston)

P(Gaston first and Pike second) = (2/9) * (1/4)

P(Gaston first and Pike second) = 2/36

Therefore, the probability that the first winner lives in Gaston and the second winner lives in Pike is 2/36, which simplifies to 1/18.

The volume of the box is 72 cubic feet.

We have,

To find the volume of the box, we need to multiply its length, width, and height.

Given:

Length = 4 ft

Breadth = 6 ft

Height = 3 ft

The volume of the box is:

Volume = Length x Breadth x Height

Volume = 4 ft x 6 ft x 3 ft

Volume = 72 cubic feet

Therefore,

The volume of the box is 72 cubic feet.

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Answer:1/4

Step-by-step explanation:3*2/(2*12)=1/4 so our answer is 1/4.

The type of error occurs when certain sample elements are excluded is sample frame error. Then the required answer for the given question is Option B.

The type of error that takes place when a particular sample elements are eliminated or when the whole population is not accurately projected in the sampling frame is called sample frame error.

There are 4 types of sampling error

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Answer:

Step-by-step explanation:

2,3,1

The null hypothesis that the population mean is equal to 60 seconds cannot be rejected at a 0.01 significance level based on the available sample data, indicating that the students are reasonably good at estimating one minute.

To test the claim that the population mean is equal to 60 seconds, we can use a one-sample t-test. The null hypothesis is that the population mean is equal to 60 seconds, and the alternative hypothesis is that it is not equal to 60 seconds.

We can first calculate the sample mean and standard deviation:

sample mean (x') = (68 + 81 + 39 + 64 + 40 + 22 + 62 + 61 + 67 + 48 + 64 + 69 + 94 + 91) / 14 = 63.57

sample standard deviation (s) = 20.11

The test statistic can be calculated as:

t = (x' - μ) / (s / √n)

where μ is the hypothesized population mean (60 seconds), n is the sample size (14), and x' and s are the sample mean and standard deviation, respectively.

Substituting the values, we get:

t = (63.57 - 60) / (20.11 / √14) = 1.74

The degrees of freedom for the t-distribution is n - 1 = 13. Using a t-table or calculator, the p-value associated with a two-tailed test with 13 degrees of freedom and t = 1.74 is approximately 0.106.

Since the p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis. Therefore, we do not have enough evidence to suggest that the students are not good at estimating one minute. We can conclude that it is plausible that the population mean is equal to 60 seconds, based on the available sample data.

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The correct statement regarding whether the events are independent is given as follows:

No, P(carry cash) ≠ P(carry cash|have children).

Conditional probability is the probability of one event happening, considering the result of a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

An event B is classified as independent if:

P(B|A) = P(B).

According to a recent survey of adults, approximately 62% carry cash on a regular basis, hence:

P(carry cash) = 0.62.

The adults were also asked if they have children. Of the 46% who have children, 85% carry cash on a regular basis, hence the conditional probability is given as follows:

P(carry cash|children) = 0.85.

As the probabilities are different, the events are not independent.

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The estimated number of sophomores is between 1,380 and 1,620. Then the correct option is C.

Given that:

The sample proportion is 12.5% or 0.125, and the population size is 12,000.

We can use the following formula to calculate the estimated number of sophomores who shop online at least once per month:

Estimated number = sample proportion x population size

The estimated number using this lower bound (i.e., 12.5% - 1%):

Estimated number = 0.115 x 12,000 = 1,380

Similarly, the estimated number using this upper bound (i.e., 12.5% + 1%):

Estimated number = 0.135 x 12,000 = 1,620

Therefore, the estimated number of sophomores who shop online, at least once per month, is between 1,380 and 1,620, which means that the answer is "Between 1,380 and 1,620".

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The number of cubes that can be fitted in the crate is 22

To solve this problem, first calculated the volume of the crate and the volume of one cube, both of which are measured in cubic units (cubic centimeters, in this case).

We then divided the volume of the crate by the volume of one cube to find the number of cubes that can fit inside the crate.

Here we have

The dimensions of the crate are 2.4m × 1.8 m ×  1.1 m

The volume of the crate

= 2.4m × 1.8 m ×  1.1 m

=  4.752 m³

Given that side of the cube = 60 cm = 0.6 m

Hence, Volume of the cube = (0.6 m)³ = 0.216 m³  

Using the formula,

Number of boxes = Volume of box/ Volume of the cube

= 4.752 m³/0.216 m³ = 22

Therefore,

The number of cubes that can be fitted in the crate is 22

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Isolate the variable term on one side of the equation by using equality's multiplication property. Then the correct option is A.

Given information:

[tex]\dfrac{2}{5} \left ( \dfrac{1}{2} y + 20 \right) - \dfrac{4}{5} = \dfrac{9}{20} \left ( 2y-1 \right)[/tex]

The distributive property is often expressed as:

a(b + c) = ab + ac

a(b - c) = ab - ac

Where "a" is a coefficient (or factor) and "b" and "c" are terms.

The equation is simplified as,

[tex]\dfrac{1}{5} y + 8 - \dfrac{4}{5} = \dfrac{9}{10} y- \dfrac{9}{20}[/tex]

Isolate the variable term on one side of the equation by using equality's multiplication property. Then the correct option is A.

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If you're hoping to land a job, carry out your research and compile a list of potential questions to inquire. Doing this will communicate that you are seriously interested in the position and significantly increase your chances of being chosen.

It should be noted that to master something, practise is key. If I had an interview coming up, I'd practice my answers prior to entering the room.

If you long to receive money for your efforts, get active by filing for a job. During the interviewing process, it may be nerve-racking but with the right preparation, nothing should obstruct you from showing the interviewer why you're suited for the role. Here are some helpful tips:

When you are ready to attend an interview, jot down a list of queries to ask the recruiter. This will indicate that you have investigated the company and undeniably demonstrate a passionate interest in the occupation.

If they question if you comprehend anything regarding the corporation, you need to respond with assurance. Doing so implies that you are well informed on the business and have done your research beforehand.

Always don your professional attire when participating in an interview; slipping into casual garments against the recruiter in smart-looking attire could cause discomfort or result in failure at garnering the job.

If during the interview, you happen to feel uneasy, breathe deeply and take some time to chill out. This way, conducting oneself calmly, any queries answered will make more sense.

In respect of disclosing personal weaknesses, truthfully give an account but without overly criticising yourself. Exhibiting self-comprehension as well as striving towards improving these areas will reflect self-awareness and commitment to development.

Finally, thank the interviewer for their time once the interview reaches its conclusion. Doing so displays politeness and appreciation.

Up to this point, solely exhibiting positive impressions, even after affirmative results, extend gratitude with a follow-up note. Doing this illustrates excitement for the job whilst displaying admiration for the opportunity.

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The number of voters that should be sampled for a confidence interval depends on the desired level of confidence and the margin of error.

A larger sample size generally leads to a smaller margin of error and a higher level of confidence in the accuracy of the results. However, the relationship between sample size and margin of error is not linear, meaning that doubling the sample size will not necessarily halve the margin of error.
To calculate the required sample size, a formula can be used that takes into account the margin of error, level of confidence, and population size.
the number of voters that should be sampled for a confidence interval depends on several factors and cannot be determined without more information.
To determine the required sample size, you can use the following formula:
n = (Z^2 * p * (1-p)) / E^2

Where:
- n is the sample size
- Z is the Z-score (usually 1.96 for a 95% confidence interval)
- p is the estimated proportion of the population (usually 0.5 for the worst-case scenario)
- E is the margin of error (in decimal form)

Hence, without the specific margin of error, we cannot provide the exact sample size needed.

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If a card is drawn from a pack of playing cards, then the probability that card is "red-king" or "4-of-diamonds" is 3/52.

There are 2 card of "red-kings" and 1 card of "4-of-diamonds" in a deck of cards. There are 52 cards in total.

So, probability of drawing a "red-king" is "2/52", because there are two "red-kings" out of 52 cards, and

The probability of drawing 1-card of "4-of-diamonds" is "1/52", because there is only 1 "4-of-diamonds" out of 52 cards,

To find probability of drawing a "red-king" or "4-of-diamonds", we add the probabilities of these two events and subtract the probability of drawing both of them, because they are not mutually exclusive,

⇒ P(red-king or 4-of-diamonds) = P(red king) + P(4 of diamonds) - P(red king and 4 of diamonds),

⇒ P(red-king or 4-of-diamonds) = 2/52 + 1/52 - 0,

⇒ P(red-king or 4-of-diamonds) = 3/52,

Therefore, the required probability is 3/52.

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Answer:

Using the Pythagorean Theorem to find the height of this right triangle:

[tex] {h}^{2} + {8}^{2} = {(2 \sqrt{19} )}^{2} [/tex]

[tex] {h}^{2} + 64 = 76[/tex]

[tex] {h}^{2} = 12[/tex]

[tex]h = 2 \sqrt{3} [/tex]

From this, the area of this right triangle is:

[tex] \frac{1}{2} (8)(2 \sqrt{3} ) = 8 \sqrt{3} [/tex]

A is the correct answer.

Answer:

Step-by-step explanation

Use Pythagorean Theorem:

8² + b² = (2√19)²

64 + b² = 4 × 19

64 + b² = 76

64 -64 + b² = 76 -64

b² = 12

√b² = √12

b = √4 · 3

b = 2√3

This is the height - use in the area formula:

1/2(8)(2√3)

4(2√3)

8√3

Answer:

Step-by-step explanation:

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Answer: $92.75

Step-by-step explanation:

I think this is the answer, sorry if incorrect. When finding the total area of the wall you split the shape in 2. You would get 175 + 1150 inches squared. You then get the total of 1,325 inches squared as the total area of the wall. You divide that number by the number of inches of each tile, which would get you 53 tiles that will be on the wall. Times 53 by the price of each tile, $1.75, and get the answer of $92.75. Hope this helps!

Answer: Crosses the x-axis at 3

touches the x-axis at -2

has a vertical asymptote at x=1

has a horizontal asymptote at y=2

Step-by-step explanation:

Using the unitary method, the cost of 3 meters, 6 meters, and 9 meters of cloth with a cost of 320 for 5 meters is 192, 384, and 576 respectively

To use the unitary method, we need to find the cost per unit length of the cloth first.

Cost per unit length = Cost of 5m of cloth / Length of cloth = 320 / 5 = 64 per meter

Now, we can use this cost per meter to find the cost of different lengths of cloth

Cost of 3 meters of cloth = 64 x 3 = 192

Cost of 6 meters of cloth = 64 x 6 = 384

Cost of 9 meters of cloth = 64 x 9 = 576

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Answer:

Step-by-step explanation:

First of all 3^2 is equal to 3*3 NOT 3*3*3

3^2 means "3 raised to the power of 2," which is equal to 3 multiplied by itself 2 times:

3^2 = 3 x 3 = 9

Therefore, 3^2 is equal to 9.

Your welcome

Answer:We can estimate that 900 people in attendance would prefer mustard on a hot dog.

Step-by-step explanation:What is proportion?

Proportion is a mathematical concept that refers to the relationship between two quantities, expressed as a ratio or a fraction. It represents the size of one quantity relative to another quantity, typically within a larger population or sample.

To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.

The proportion of people in the sample who prefer mustard is:

27/150 = 0.18

To estimate the number of people who prefer mustard in the entire population of 5,000 attendees, we can multiply this proportion by the total number of attendees:

0.18 x 5,000 = 900

Therefore, we can estimate that 900 people in attendance would prefer mustard on a hot dog.

Answer:

The answer to your problem is, A. [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

We would need to count the entire shaded area both green and blue for the numerator. Which shown the denominator will be all the colors yellow, blue and green squares.

Total Green and blue 24, numerator

Total Green, blue Yellow 30, denominator

Which then divide 24 ÷ 30.

Simplify: divide numerator and denominator by 6

= [tex]\frac{4}{5}[/tex]

Thus the answer to your problem is, A. [tex]\frac{4}{5}[/tex]

Answer: it is only a mind set

Step-by-step explanation: when you are in a good mindset you will do well but when you are in a negative mindset it will be hard.

Answer:

It depends if its like 1st grade then you might have to get that checked out but if its 12th grade probally to make kids question life :)

Step-by-step explanation:

PLS GIVE BRAINLIST

HAVE A GOOOOODY DAY!!!

The total cost of the carpeting for the room is [tex]$283.50[/tex].

To calculate the cost of carpeting a room, we need to find the total area of the room and multiply it by the cost per square foot of the carpet. In this case, the room measures 9 feet by 6 feet, so its area is 9 x 6 = 54 square feet.

The carpet is sold at [tex]$5.25[/tex] per square foot, the cost of the carpeting for the room can be calculated by multiplying the total area of the room (54 square feet) by the cost per square foot ([tex]$5.25[/tex]). The cost of the carpet for the room is therefore:[tex]54[/tex] sq ft x[tex]$5.25[/tex] /sq ft = [tex]$283.50[/tex].

This cost only covers the carpeting itself, and does not include any additional expenses such as padding or installation. It's always a good idea to get a detailed estimate from a professional carpet installer to ensure that you have a clear understanding of the total cost of the project.

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Answer: C (-0.6)

Step-by-step explanation:

-2.1--0.6=-1.5

-1.5 as fraction = -1 1/2