If F = xzi+y²z j + xyz k. a) Find div F. b) Find curl F.

The percentage of tires that will have a life of 45,000 to 55,000 miles is  68.27%. So the correct option is 68.27%.

To find the percentage of tires that will have a life of 45,000 to 55,000 miles, we can use the concept of the normal distribution.

First, we calculate the z-scores for both values using the formula:
z = (x - mean) / standard deviation

For 45,000 miles:
z1 = (45,000 - 50,000) / 5,000 = -1

For 55,000 miles:
z2 = (55,000 - 50,000) / 5,000 = 1

Next, we look up the corresponding values in the standard normal distribution table. The table will provide the proportion of data within a certain range of z-scores.

The percentage of tires with a life between 45,000 and 55,000 miles is the difference between the cumulative probabilities for z2 and z1.

Looking at the standard normal distribution table, the cumulative probability for z = -1 is 0.1587, and the cumulative probability for z = 1 is 0.8413.

Therefore, the percentage of tires that will have a life of 45,000 to 55,000 miles is:
0.8413 - 0.1587 = 0.6826

Converting this to a percentage, we get:
0.6826 * 100 = 68.26%

So the correct answer is 68.27%.

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Answer:

y=5x+21

Step-by-step explanation:

right now we know y=5x+b, so all we need is b.

graphing it on paper starting at (-4,1), you can go up 5, right 1 because your slope is 5.

you'll get (-4,1) (-3,6) (-2,11) (-1,16) (0,21)

Once you reach x=0, your intecept is 21, completing the slope intercept form, making it y=5x+21.

Answer:

I don't have a grid with me but look at it this way. if you look at the first set of points look at where they are starting. and. then look at the second set of points. see if the points plotted bend over the x axis or the y axis:)

Answer:

it is when it can make a mathematical statement

The probability of at least 10 cities out 45 have a commute time greater than 30 minutes is 0.893 or 89.3%

Apply the complement rule.

Probability that at least one of the 10 cities you select will have a commute time greater than 30 minutes,

The complement of the event is 'none of the 10 cities have a commute time greater than 30 minutes'.

The probability of the complement event can be calculated by ,

Multiplying probabilities of selecting a city with a commute time less than or equal to 30 minutes for each of 10 selections.

P(none of 10 cities have a commute time > 30 minutes) = (35/45) x (35/45) x ... x (35/45) (10 times)

Because there are 35 cities out of the total 45 that have a commute time less than or equal to 30 minutes.

So the probability that at least one of the 10 cities has a commute time greater than 30 minutes is,

1 - P(none of the 10 cities have a commute time greater than 30 minutes)

= 1 - (35/45) x (35/45) x ... x (35/45) (10 times)

= 1 - 0.1073

= 0.8926

Therefore, the probability that at least one of the 10 cities you select will have a commute time greater than 30 minutes is 0.893 or 89.3%.

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The above question is incomplete, the complete question is:

If i randomly sample two cities from this group (consider these 45 the 'population' if you will) then what is the probability that at least one of the 10 cities i select will have a commute time greater than 30 minutes?

The inequality according to the the cost of pack of paper can be written as x ≤ 14.28 and Mr. Valentino can purchase a maximum of 14 packs of paper.

What is inequality?

A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. The majority of the time, size comparisons between two numbers on the number line are made. The two most common notations for representing various forms of inequalities are as follows:

The symbol a < b indicates that a is smaller than b.

The symbol a > b indicates that a is bigger than b.

Let's assume he can buy x pack of paper.

Cost of x pack of paper will be equal to the x times cost of 1 pack of paper

i.e. Total cost =  1.75x

Now, Mr. Valentino has $25

Therefore,

1.75x ≤  25

Inequality is ⇒  x ≤ 14.28

It tells us that Mr. Valentino can purchase only 14 packs of paper.

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The area of a pool from the given situation is 816 ft².

Given that, the dimensions of plot is 50 ft and 40 ft.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Here, area of a plot = Length × Width

= 50 × 40

= 2000 ft²

Area of a pool = Area of a plot - Area of a grass

= 2000 - 1184

= 816 ft²

Therefore, the area of a pool from the given situation is 816 ft².

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Step-by-step explanation:

8^(-2) × 12⁴ ÷ 27²

1/8² × (2² × 3)⁴ ÷ (3³)²

1/(2³)² × 2⁸ × 3⁴ ÷ 3⁶

1/2⁶ × 2⁸ ÷ 3²

2⁸/2⁶ ÷ 3²

2² ÷ 3²

= 4/9

Step-by-step explanation:

Use the BODMAS rule multiply 8^-2 by 12^4 first then the answer you get divide by 27^2.

So it simplifies to give 1/64 ×207336=324

324÷27^2 which is

324÷729

the answer= 4/9

The Total surface of triangular prism  is 112 inches.

To calculate the surface area of a triangular prism, you need the measurements of the base and the height of the triangular faces, as well as the length of the prism.

The given measurements are;

Base ; 5 inches and  4 inches

height is 8 inches

Length of the prism is 2 inches.

To find the total surface area, we sum up the areas of all the faces:

Total surface area = area of triangular  faces + area of rectangular faces + area of lateral faces.

area of triangular faces = 5 inches × 4 inches = 20 inches.

area of the two faces = 20 ×2 =40

Area rectangular faces = 5 inches × 8 inches/ 2 = 40 inches.

Area of lateral faces = 8 inches ×2 = 16 square inches

for the two lateral faces is 16 × 2 = 32 square inches.

Total surface area = 40 square inches + 40 inches + 32 square inches = 112 square inches.

The Total surface of triangular prism  is 112 inches.

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Answer:

1.4, 1 1/8, 0.7

Step-by-step explanation:

1 1/8 is equal to 1.125 which it makes it less than 1.4 but more than 0.7.

Answer:

\(0.7, \frac{11}{8},1.4\)

Step-by-step explanation:

In order to understand what numbers are greater and what numbers are smaller, we need to make them have the same common denominator. So firstly, we turn all of these numbers into fractions, and we get...

\(0.7 = \frac{7}{10}\\\\1.4 = \frac{14}{10}\\\\\frac{11}{8 }= \frac{11}{8 }\)

Now we, need to find the least possible number divisible by 10 and 8, to find the least common denominator. And we get, that the least common denominator is 40, and knowing this, now we have to take each fraction and turn it into an equivalent fraction with the denominator of 40. So we do...

\(\frac{11}{8}= \frac{(11)(5)}{(8)(5)}= \frac{55}{40}\\\\\frac{7}{10} = \frac{(7)(4)}{(10)(4)} = \frac{28}{40} \\\\\frac{14}{10} = \frac{(14)(4)}{(10)(4)} = \frac{56}{40}\)

Now we can put these fractions in order from least to greatest...

\(\frac{28}{40} < \frac{55}{40}<\frac{56}{40}\)

Therefore, we know that...

\(0.7 < \frac{11}{8} < 1.4\)

Natiοnal Incοme statistics = Tοtal Rent + Tοtal Wages + Tοtal Interest + Tοtal Prοfit. gοοds and services prοduced in a cοuntry during a year is οbtained, which is called tοtal final prοduct. This represents Grοss Dοmestic Prοduct ( GDP ).

Natiοnal incοme is the tοtal incοme earned by all individuals and businesses in a cοuntry in a specific periοd οf time, usually a year. It includes all fοrms οf incοme such as wages, salaries, prοfits, rents, and interest earned. Natiοnal incοme is an impοrtant measure οf a cοuntry's ecοnοmic perfοrmance, as it reflects the tοtal οutput and incοme generated within the cοuntry's bοrders.

Natiοnal incοme statistics are calculated by measuring the tοtal value οf gοοds and services prοduced within a cοuntry during a given periοd οf time, typically οne year. The fοllοwing are sοme οf the key cοmpοnents οf natiοnal incοme statistics:

Grοss Dοmestic Prοduct (GDP): This is the tοtal value οf all gοοds and services prοduced within a cοuntry's bοrders in a given periοd οf time. It is calculated by adding up the value οf all final gοοds and services prοduced in a cοuntry during the year.

Grοss Natiοnal Prοduct (GNP): This is similar tο GDP, but alsο includes the value οf gοοds and services prοduced by a cοuntry's citizens and cοmpanies abrοad.

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The surface area of the given prism is 484 cm². A prism is a three-dimensional object that has two parallel congruent bases and rectangular sides connecting these bases.

To find the surface area of a prism, we need to add up the areas of all its faces.

In this case, we are given the dimensions of the prism as follows:
- The length of one base is 12 cm
- The width of one base is 5 cm
- The height of the prism (distance between the bases) is 13 cm
- The length of each rectangular side is 7 cm

To start finding the surface area, we can begin by calculating the area of each face of the prism. The two bases are congruent rectangles, so each has an area of:

Area of one base = length x width
Area of one base = 12 cm x 5 cm
Area of one base = 60 cm²

Since there are two bases, we can multiply this by 2 to get the total area of both bases:

Total area of both bases = 2 x 60 cm²
Total area of both bases = 120 cm²

Next, we need to calculate the area of each of the four rectangular sides of the prism. Each of these is a rectangle with length 7 cm and height 13 cm. So, the area of one side is:

Area of one side = length x height
Area of one side = 7 cm x 13 cm
Area of one side = 91 cm²

Since there are four sides, we can multiply this by 4 to get the total area of all four sides:

Total area of all four sides = 4 x 91 cm²
Total area of all four sides = 364 cm²

Finally, to get the total surface area of the prism, we need to add together the areas of both bases and all four sides:

Total surface area of the prism = area of both bases + area of all four sides
Total surface area of the prism = 120 cm² + 364 cm²
Total surface area of the prism = 484 cm²

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Answer:

x = 20

Step-by-step explanation:

The triangles are similar

3          (3+5)

----- = ----------

12        (12+x)

Using cross products

3(12+x) = 12*(3+5)

3(12+x) = 12*8

3(12+x) = 96

Divide by 3

3(12+x)/3 = 96/3

12+x = 32

Subtract 12

12+x-12 =32-12

x = 32-12

x =20

Answer: 72

Step-by-step explanation:

25:18 - 25 total : 18 made

25:18 x 4 = 100:72

100:72- 100 total : 72 made

Answer:

we should expect him to make 72 shots

Step-by-step explanation:

25x4=100

so if we multiply 18 by 4 we get 72

From SOHCAHTOA

Sin0=Opp/HYP

Sin0 = 9/15

Step-by-step explanation:

sinβ=p/h

sinβ=12/15

sinβ=4/5

The p-value of this test is 0.0294.

a) The absolute value of the critical value of this test is "1.645".

The critical value for the given test can be calculated using the following formula;`

Critical value =

± z_(α/2)`

Where,`α` is the level of significance of the test.

`z_(α/2)`

is the critical value from the standard normal distribution table.

Since, the significance level of the test is 20%,

α = 0.2 or 0.20

Level of Significance = 0.20α/2 = 0.20/2α/2 = 0.10

Now, the critical value of the test can be found from the standard normal distribution table at 0.10 level of significance.

It comes out to be 1.645.

So, the absolute value of the critical value of this test is 1.645.

b) The absolute value of the calculated test statistic is "2.23".

The test statistic for the given test is the t-value calculated using the sample data.

It can be calculated using the following formula;

`t = (x¯1 - x¯2) / [ s_p * √(1/n1 + 1/n2) ]`

Where,`x¯1 and x¯2` are the sample means.

`s_p` is the pooled standard deviation.

`n1 and n2` are the sample sizes.

So, the test statistic of the given test comes out to be 2.23.So, the absolute value of the calculated test statistic is 2.23.

c) The p-value of this test is "0.0294".

The p-value for the given test is the probability of getting a t-value more extreme than the calculated t-value, assuming the null hypothesis is true.

The p-value can be calculated using the t-distribution table.

The degrees of freedom for the given test is

`df = n1 + n2 - 2`.

Substituting the values in the formula, the p-value for the given test comes out to be 0.0294.

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Let:

From that equation:

If two lines are perpendicular, then:

Given an arbitraty point:

Using the point slope equation:

Answer:

9.94

Step-by-step explanation:

y = \(\frac{1}{4}\) x - 9

y - 2 = - 4(x - 3)

y = - 4x + 14

- 4x + 14 = \(\frac{1}{4}\) x - 9

16x - 56 = - x + 36

17x = 92

x = \(\frac{92}{17}\)

y = (-4) \(\frac{92}{17}\) + 14 = - \(\frac{368}{17}\) + \(\frac{238}{17}\) = - \(\frac{130}{17}\)

(3, 2) , ( \(\frac{92}{17}\) , - \(\frac{130}{17}\) )

d ≈ 9.94396

27/4 , -3.2, -∛60 ,√48, 7.05 when arranged in ascending order we get:

-3.2 , -∛60 , 27/4 , √48, 7.05

Given list of numbers,

27/4 , -3.2 , -∛60 , √48 , 7.05.

simplifying each numbers ,

=> 27 / 4 = 6.75

=> -∛60 = - ∛(2 × 2 × 3 × 5)

= -3.9149.

=> √48  = √(2 × 2 × 2 × 2 × 2)

= 4√3

= 6.928  

So the list after simplification is ,

6.75 , -3.2 , -3.9149 , 6.928 , 7.05

Now arrange the numbers from least to greatest,

-3.2 , -3.91 , 6.75 , 6.928 , 7.05  

= -3.2 , -∛60 , 27/4 , √48, 7.05.

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Answer: => 56.52 cm²

Step-by-step explanation:

Answer:

ggabdfsa

Step-by-step explanation:

The z-score for the second group is negative, which means that the score of 34.1 is 2.4 standard deviations below the mean of the second group

To compare the scores of the two groups, we can use the concept of z-scores. The z-score represents the number of standard deviations a data point is from the mean.

For the first group, the z-score for a score of 35.3 is:

z = (35.3 - 35.3) / 3.6 = 0

For the second group, the z-score for a score of 34.1 is:

z = (34.1 - 35.3) / 0.5 = -2.4

Mean: The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Standard deviation: The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a database is in relation to its mean.

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The mean exam score for the first group of twenty examinees applying for a security job is 35.3 with a standard deviation of 3.6.

The mean exam score for the second group of twenty examinees is 34.1 with a standard deviation of 0.5. Both distributions are close to symmetric in shape.

Use the mean and standard deviation to compare the scores of the two groups.

Answer:

A

Step-by-step explanation:

Based on the given statement, the correct answer would be:

option A. The statement makes sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must be depressed.

The given statement is discussing a potential relationship between Sally's emotional state of being depressed and her behavior of listening to music. The question asks whether the statement makes sense, is clearly true, or does not make sense, and provides four options to choose from.

Option A states that the statement makes sense and suggests that if Sally is listening to music, then she must be depressed. This option is reasonable because the statement establishes a connection between Sally's depression and her behavior of listening to music. It implies that listening to music is a coping mechanism or an activity she engages in when she experiences depressive feelings.

Therefore, if someone observes Sally listening to music, it can be inferred that she might be in a depressed state at that moment.

On the other hand, options B and C can be eliminated because they make extreme and unsupported claims. Option B suggests that Sally only listens to music when she is depressed, which is not explicitly stated in the given statement. Option C states that if Sally is listening to music, then she must not be depressed, which contradicts the initial connection established between depression and listening to music in the statement.

Option D highlights the incomplete nature of the statement but does not render it entirely senseless. It acknowledges that the statement mentions Sally's behavior of listening to music when she is depressed but does not provide information about other potential reasons she might listen to music.

In summary, option A is the most appropriate choice as it aligns with the established correlation between Sally's depression and her listening to music, while considering the possibility of other reasons for her music listening behavior.

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Answer:the legth is 40

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

1.)A   2.)B.  3.)C.  4.)C.   5.)B

I think the only one i might of gotten wrong is 4. if any are wrong. please let me know for future reference.

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Hope this helps! If so please ,mark brainliest!

Answer:

1. A

2. A

3. C

4. C

5. B

Step-by-step explanation:

i do beleive these are the correct answers