The main bearing clearance (in mm) in a certain type of engine is a random variable with probability density function

Answer:

Step-by-step explanation:

\(a_1=-28\\a_2=-13\\\\d=a_2-a_1=-13-(-28)=-13+28=15\\\\a_n=a_1+d(n-1)\\\\a_{58}=-28+15(58-1)=-28+15\cdot27=-28+405=377\)

Given the midpoint M(3, 1) and point A(4, 3),then the coordinates of point B are (2, -1).

To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M(x, y) between two points A(x1, y1) and B(x2, y2) are given by:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

Given that the midpoint M is (3, 1) and the coordinates of point A are (4, 3), we can substitute these values into the midpoint formula and solve for the coordinates of point B.

Let's calculate it step by step:

Step 1: Identify the known values

Coordinates of point A: (x1, y1) = (4, 3)

Midpoint coordinates: (x, y) = (3, 1)

Step 2: Apply the midpoint formula

x = (x1 + x2) / 2

3 = (4 + x2) / 2

Multiply both sides by 2:

6 = 4 + x2

Subtract 4 from both sides:

x2 = 6 - 4

x2 = 2

y = (y1 + y2) / 2

1 = (3 + y2) / 2

Multiply both sides by 2:

2 = 3 + y2

Subtract 3 from both sides:

y2 = 2 - 3

y2 = -1

Step 3: Determine the coordinates of point B

The coordinates of point B are (x2, y2) = (2, -1)

Therefore, the coordinates of point B are (2, -1).

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Answer:

x = 2

Step-by-step explanation:

-8(x-6) = 32 (distribute)

-8x+48 = 32 (subtract 48 from both sides)

-8x = -16 (divide)

x = 2

Answer:

x = 2

Step-by-step explanation:

Divide both sides :

−8(x−6)=32

Divide both sides of the eqaution by -8 :

x - 6 = -4

Move the constant to the right :

x - 6 = -4

Move the constant to the right - hand side and change its sign :

x = -4 + 6

Calculate :

x = -4 + 6

Calculate the sum :

x = 2

Therefore, the answer is x = 2

The general convention is to reject a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect. This is False.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

After a performing a test, scientists can reject the null hypothesis meaning there is a definite, consequential relationship between the two phenomena

In this case, the convention is to accept a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect.

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Answer:

$18.71

Step-by-step explanation:

7.\° Of 15.55=2.22

15.55+2.22=17.77

18.\° Of 17.77=0.94

17.77+0.94=18.71

With a smaller error bound, the confidence interval narrows, increasing confidence in the estimated mean age with a more precise range of values.

To construct a 95% confidence interval for the true mean age of Winter Foothill College students, we need to calculate the margin of error and then determine the interval.

First, let's calculate the standard error, which is the standard deviation divided by the square root of the sample size:

Standard Error = (Population Standard Deviation) / sqrt(sample size)

Standard Error = 15 / sqrt(25)

Standard Error = 15 / 5

Standard Error = 3

The margin of error is then calculated by multiplying the standard error by the appropriate critical value from the t-distribution. For a 95% confidence level, the critical value is 2.063 (assuming a sample size of 25 and using a t-distribution).

Margin of Error = (Critical Value) * (Standard Error)

Margin of Error = 2.063 * 3

Margin of Error = 6.189 (rounded to three decimal places)

To calculate the confidence interval, we subtract and add the margin of error to the sample mean:

Confidence Interval = Sample Mean ± Margin of Error

Confidence Interval = 30.4 ± 6.189

Confidence Interval = (24.211, 36.589)

The area in each tail is determined by the confidence level. In this case, it's a 95% confidence interval, so there is 2.5% of the total area in each tail.

In one complete sentence, the 95% confidence interval means that we are 95% confident that the true mean age of Winter Foothill College students falls within the interval of (24.211, 36.589).

If the confidence level were reduced to 90%, the critical value from the t-distribution would change. With a smaller critical value, the margin of error would decrease.

Therefore, the error bound would become smaller, resulting in a narrower confidence interval. This means that we would have a higher level of confidence in the estimated mean age, but the interval would be less wide, providing a more precise range of potential values for the true mean age.

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The equivalent expression of (5 ^3/4)^2/3 is √5

Expressions are mathematical statements that are represented by variables, coefficients and operators

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The expression is given as

(5 ^3/4)^2/3

Evaluate the product of the exponents

So, we have

(5 ^3/4)^2/3 = 5^(3/4 x 2/3)

Evaluate the product of the exponents

So, we have

(5 ^3/4)^2/3 = 5^(2/4)

Evaluate the quotient

So, we have

(5 ^3/4)^2/3 = 5^(1/2)

Express as square roots

So, we have

(5 ^3/4)^2/3 = √5

Hence, the equivalent expression of (5 ^3/4)^2/3 is √5

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Work Shown:

A = 1110 = final amount

r = 0.037 = decimal form of the interest rate

n = 1 = compounding frequency (annual)

t = 13 = time in years

----------

A = P(1+r/n)^(n*t)

1110 = P(1+0.037/1)^(1*13)

1110 = P(1.60370259909214)

1.60370259909214P = 1110

P = 1110/1.60370259909214

P = 692.14828274792

P = 692.15 ....... rounding to the nearest cent

P = 700 .... rounding to the nearest hundred dollars

Answer:

P≈ 700

Step-by-step explanation:

There are many types of functions and each type of function has its own characteristics. This implies that their graph has also its own characteristics.

Based on the graph, the absolute value function has a "V-Shaped" graph.

Every absolute value graph makes a “V”-shaped figure. It consists of two parts: one with a negative slope and one with a positive slope. The point of their intersection is called the vertex. An absolute value graph is symmetrical, meaning that it can be folded in half on its line of symmetry.

An absolute value graph has a distinct V-shape. It is symmetric about the vertical line which passes through its vertex. The vertex of an absolute value function is the point at which the graph changes direction. Since the graph of y=|x-1|+1 changes direction at (1,1), this point is the vertex.

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Answer:

34

Step-by-step explanation:

I really don't know I just wanted to answer for points

As per the volume of the rectangular tank, the dimensions are 13.78 x 379.82 x 13.78

Volume of rectangle:

The general formula to calculate the volume of the rectangle is

V = length x width x height.

Given,

A rectangular tank that is 5234 ft^3 with a square base and open top is to be constructed of sheet steel of a given thickness.

Here we need to find the dimensions of the rectangular tank,

As per the given volume of rectangular tank, when we equate this with the formula, then we get,

=> 5234 = length x width x height.

Let us consider the length and the width are equal then we get the value of height as.

=> height = 5234/length

So, the value is calculated by using the surface area formula,

=> A = length² + 5234/length

When we differentiate the surface area with respect to

=> dA/dl = 2l - 5234/l²

To minimize the surface area, so dA/dl = 0,

=> 2l = 5324/l²

=> 2l³ = 5234

=> l³ = 2617

=> l = ∛2617

Therefore, the value of length is 13.78

Then the height is calculated as.

=> h = 5234/13.78 = 379.82

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Answer:

Step-by-step explanation:

425 - 59 is 366

:)

Answer:

366.

Step-by-step explanation:

Answer:

Point C

Step-by-step explanation:

The correct answer would be about 2.2 so C is the closest.

Answer:

6

Step-by-step explanation:

mark me brainliesst please

Fallis has 2000 square centimeters (cm²) tiles, she does not have enough tiles to cover the entire counter.

To find out if Ms. Fallis has enough tiles to cover the counter, we need to calculate how many tiles are required to cover an area of 2 square meters.

Since the tiles have a side length of 3 centimeters, we need to convert the area of the counter to square centimeters.

1 square meter = 10000 square centimeters (cm²)

So, 2 square meters = 20000 square centimeters (cm²)

Now, we need to calculate the area of each tile:

Side length of each tile = 3 centimeters (cm)

Area of each tile = \((side length)^2\) = \((3 cm)^2\) = 9 square centimeters (cm²)

To cover the counter, we need to divide the total area of the counter by the area of each tile:

Number of tiles required = (Total area of counter) / (Area of each tile)

= 20000 cm² / 9 cm²

= 2222.22

Since we cannot have a fraction of a tile, we need to round up to the nearest whole number of tiles. So, Ms. Fallis needs at least 2223 tiles to cover the counter.

Since she has 2000 square centimeters (cm²) tiles, she does not have enough tiles to cover the entire counter.

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In the story "Three's A Crowd" by Kimbra Gish, two important themes that emerge are friendship and the challenges of navigating love triangles.

Friendship is a significant theme throughout the story. The bond between the three main characters is explored, emphasizing the depth of their connection and the support they provide for one another.

The theme of friendship highlights the importance of trust, loyalty, and understanding in maintaining strong relationships. It also delves into the complexities of friendship when conflicts and personal desires arise, forcing the characters to confront difficult choices.

The second theme revolves around the challenges of navigating a love triangle. The story explores the intricate dynamics that emerge when three individuals find themselves entangled romantically.

The theme examines jealousy, competition, and the emotional turmoil that accompanies such situations. It delves into the conflicting feelings of love, desire, and guilt that the characters experience as they navigate their relationships.

Through this theme, the story raises questions about the nature of love, loyalty, and the sacrifices that may need to be made when multiple people are vying for affection.

Overall, "Three's A Crowd" explores the complexities of human relationships, delving into the intricacies of friendship and the challenges of navigating love triangles. It offers insights into the delicate balance between loyalty, personal desires, and the emotional complexities that arise when three hearts become entwined.

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Among the provided functions, the ones that approach positive infinity as x approaches negative infinity are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

To determine which functions approach positive infinity as x approaches negative infinity, we need to analyze the leading terms of the functions. The leading term dominates the behavior of the function as x becomes very large or very small.

Let's examine each function and identify their leading terms:

1. f(x) = 2x^5

The leading term is 2x^5, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

2. f(x) = 9x + 100

The leading term is 9x, which has a positive coefficient but a lower power of x compared to the constant term 100.

As x approaches negative infinity, the leading term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

3. f(x) = 6x^8 + 9x^6 + 32

The leading term is 6x^8, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

4. f(x) = -8x^3 + 11

The leading term is -8x^3, which has a negative coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and negative, indicating that f(x) approaches negative infinity, not positive infinity.

5. f(x) = -10x + 5x + 26

Combining like terms, we have f(x) = -5x + 26.

The leading term is -5x, which has a negative coefficient but a lower power of x compared to the constant term 26.

As x approaches negative infinity, the leading term becomes very large and positive, indicating that f(x) approaches negative infinity, not positive infinity.

6. f(x) = -x + 8x^4 + 248

The leading term is 8x^4, which has a positive coefficient and the highest power of x.

As x approaches negative infinity, this term becomes very large and positive, indicating that f(x) approaches positive infinity.

Therefore, the correct choices are:

- f(x) = 2x^5

- f(x) = 6x^8 + 9x^6 + 32

- f(x) = -x + 8x^4 + 248

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Answer:

22/9

Step-by-step explanation:

Answer:

She missed 6 questions.

Step-by-step explanation:

88% can be written as (88/100) or as 0.88.

You can set this as a ratio problem which is,  

88/100 = correct/50

correct = (88/100)*50       (multiply both sides by 50)

correct = 44

So, 50 (total questions) - 44 = 6 incorrect questions

Answer:

\( {eb}^{2} = {ab}^{2} + {ea}^{2} \\ {ab}^{2} = {eb}^{2} - {ea}^{2} \\ {ab}^{2} = {20}^{2} - {12}^{2} \\ ab = 16 \\ \\ {db}^{2} = {bc}^{2} + {dc}^{2} \\ {bc}^{2} = {db}^{2} - {dc}^{2} \\ {bc}^{2} = {20}^{2} - {16}^{2} \\ bc = 12 \\ \\ so \: ac = ab + bc \\ ac = 28\)

The probability of washing dishes by me tonight will take between 15 and 16 minutes is 14.29%.

The term "uniform distribution" refers to a type of probability distribution in which the likelihood of each potential result is equal.

Let's consider, the lower limit for this distribution as a and the upper limit for this distribution as b.

The following formula gives the likelihood that we will discover a value for X between c and d,

\(P(c\leq X\leq d)=\frac{d-c}{b-a}\)

Given the time it takes me to wash the dishes is 11 minutes and 18 minutes. From this, a = 11 and b = 18.

Then,

\(P(15\leq X\leq 16)=\frac{16-15}{18-11}=0.1429=14.29\%\)

The answer is 14.29%.

The complete question is -

The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 18 minutes. What is the probability that washing dishes tonight will take me between 15 and 16 minutes?

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The following system of equations models this scenario;

A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system consists of two equations & two variables.

Linear equations (those that graph like straight lines) are easier to understand than non-linear ones.

According to the question,

The art museum had a total of 224 visitors on Tuesday.

Let 'x' be the visitors who are older than 18 years.

Let 'y' be the visitors who are younger than 18 years.

Then, total visitors are;

x + y = 224

Now,

Visitors older than 18 paid $12 for admission.

Total money collected by the older visitors are 12x.

Visitors 18 years or younger paid $8 for admission.

Total money collected by younger visitors are 8y.

Thus, total money collected by all visitors are-

12x + 8y = 2,520.

Therefore, the two set of linear equations are-

x + y = 224 and 12x + 8y = 2,520.

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The ordered pair that is in the solution set of the inequality is (-1, 6). So, the correct option is (a).

The inequality given is y≥1/3+4.

We have to find the ordered pair that is in the solution set of this inequality.

To find the ordered pair, we need to substitute the values of x and y from the options given and then check whether it satisfies the inequality or not.

a)

(-1, 6) => y=6 which is greater than (1/3+4).

Hence, (-1, 6) is in the solution set of the inequality.

b)

(1, -6) => y=-6 which is not greater than (1/3+4).

Hence, (1, -6) is not in the solution set of the inequality.

c)

6, -1) => Here, y=-1 which is not greater than (1/3+4).

Hence, (6, -1) is not in the solution set of the inequality.

d)

(-6, 1) => Here, y=1 which is not greater than (1/3+4).

Hence, (-6, 1) is not in the solution set of the inequality.

Therefore, the ordered pair that is in the solution set of the inequality is (-1, 6). So, the correct option is (a). We can conclude that (-1, 6) is the only solution of the inequality y≥1/3+4.

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The length of the minor axis of the ellipse described by the equation in the task content is; 6.

It follows from the task content that the length of the minor axis of the ellipse is to be determined.

Since the equation given in the task content is;

x² + 4y² = 36.

By dividing both sides by 36; we have;

(x²/36) + (y²/9) = 1

By expressing the denominators as squares; we have;

x²/6² + y²/3² = 1

By comparison of the equation above with the standard equation of an ellipse; x²/a² + y²/b² = 1 where; a = major axis and b = minor axis.

a = 6 and b = 3.

Ultimately, the length of the minor axis is given by; 2b = 2 × 3 = 6.

The length of the minor axis is therefore; 6.

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Answer:

14.7 feet and 20.2 feet

Step-by-step explanation:

sin 36(25)=14.7

cos 36(25)=20.2

Answer:

2 x 20^2

Step-by-step explanation:

I did it on paper and looked it up to make sure