the lifetime of a certain electronic component is a random variable with the expectation of 5000 hours and a standard deviation of 200 hours. using central limit theorem, find the probability that the average lifetime of 100 components is less than 4650 hours?

The measure of the angles are 27 and 63 degrees. The angles are adjacent.

The two angles are said to be adjacent angles when they share the common vertex and side. In other words, adjacent angles have common side and vertex but do not overlap.

Therefore, the angles are adjacent angles.

The sum of the angles is 90 degrees. This means the angle is a right angle.

Therefore,

3x + 7x = 90

10x = 90

x = 90 / 10

x = 9

Therefore, the angles are as follows:

3(9) = 27 degrees

7(9) = 63 degrees

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Here, we will use the method of steepest descent to find the minimiser of the function f(x1, x2, x3). The steepest descent method is an iterative optimization algorithm used to find the local minimum of a function.

Step 1: Initialize the starting point (x1, x2, x3) and set the initial values.
Step 2: Compute the gradient of the function f(x1, x2, x3) with respect to each variable (x1, x2, x3). The gradient is a vector that points in the direction of the steepest increase of the function.
Step 3: Calculate the step size, which determines how far along the descent direction we move. This can be done using various techniques, such as line search or a constant step size.
Step 4: Update the current point by moving in the direction of the negative gradient (steepest descent direction) with the computed step size. The new point will be (x1_new, x2_new, x3_new).
Step 5: Check the convergence criteria. If the change in the function value or the variables is below a certain threshold, stop the iteration process. Otherwise, return to Step 2 with the updated point.
By following these steps, the method of steepest descent will help us find the minimizer of the function f(x1, x2, x3).

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From the given information provided, emily and john should drink 56.7 cups of water for 42 hours hiking.

If hikers should drink 2.7 cups of water for every 2 hours of hiking, then we can use a proportion to find how much water Emily and John should drink over their 42-hour hike:

2.7 cups / 2 hours = x cups / 42 hours

To solve for x, we can cross-multiply:

2.7 cups × 42 hours = 2 hours × x cups

113.4 cups = 2x

Finally, we can divide both sides of the equation by 2 to solve for x:

x = 56.7 cups

Therefore, Emily and John should drink a total of 56.7 cups of water during their 42-hour hike.

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Answer:2

Step-by-step explanation:

1+1=2

Answer:

[tex]\frac{\sqrt{202} }{9}[/tex] OR ≈ 1.57919

Step-by-step explanation:

tanθ = opp/adj

opp/adj = 11/9

hyp = [tex]\sqrt{202}[/tex]

secθ = 1/cosθ

cosθ = [tex]\frac{9}{\sqrt{202} }[/tex]

1/cosθ = [tex]\frac{1}{\frac{9}{\sqrt{202} } }[/tex]

= [tex]\frac{\sqrt{202} }{9}[/tex] or ≈ 1.57919

The value of x is 7, and NM and OL are both equal to 37.

Since LMNO is a parallelogram, its opposite sides must be parallel and equal in length. Therefore, we have,

NM = OL

We also have the following information:

NM = x + 30

OL = 4x + 9

Substituting the first equation into the second equation, we get:

x + 30 = 4x + 9

Simplifying this equation, we get:

3x = 21

Therefore, x = 7.

Substituting this value back into the original equations, we get:

NM = x + 30 = 7 + 30 = 37

OL = 4x + 9 = 4(7) + 9 = 37

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Answer:

There are 13 hearts in a deck of cards, so the probability of drawing a heart on the first draw is 13/52. After the first heart is drawn, there are 12 hearts left in the deck out of a total of 51 cards, so the probability of drawing another heart is 12/51. This process continues until we have drawn 4 hearts and 1 spade. Therefore, the total number of ways to draw 5 cards with 4 hearts and 1 spade is:

(13/52) x (12/51) x (11/50) x (10/49) x (13/48) x 5!

The factor of 5! accounts for the fact that the 5 cards can be drawn in any order. Simplifying the expression above, we get:

(13/52) x (12/51) x (11/50) x (10/49) x (13/48) x 120 = 0.000495 or approximately 1 in 2,020 ways.

Therefore, there are approximately 2020 ways to draw 5 cards from a regular deck of cards and get 4 hearts and 1 spade.

There are 54,145,200 ways to draw 5 cards and get 4 hearts and 1 spade from a regular deck of cards.

There are 13 hearts in a deck of cards, so the probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing another heart on the second draw, given that one heart has already been drawn, is 12/51. The same goes for the third and fourth draws. The probability of drawing a spade on the fifth draw is 13/50.

To calculate the number of ways to draw 4 hearts and 1 spade, we need to multiply the number of ways to choose 4 hearts from 13 (13 choose 4 or 715) by the number of ways to choose 1 spade from 13 (13 choose 1 or 13) and then multiply that by the number of ways to arrange those 5 cards (5!). So, the total number of ways is:

715 * 13 * 5! = 54,145,200

Therefore, there are 54,145,200 ways to draw 5 cards and get 4 hearts and 1 spade from a regular deck of cards.

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Answer:

The answer should be 20,365.714 but I am not sure

Step-by-step explanation:

Variable b represents the number of hours Kevin spends watching television each week.

A statement proving the equality of two mathematical expressions is known as an equation.

Given equation a + b = 15 relates the number of hours.

If here Kevin spends doing homework each week (represented by the variable "a") and the number of hours he spends watching television each week (represented by the variable "b").

Since the total number of hours Kevin spends doing homework and watching television each week is 15, we can write:

homework + watching television = 15 hours

a + b = 15

To find out what b represents, we can rearrange the equation to solve for b:

b = 15 - a

This means that b represents the number of hours Kevin spends watching television each week, given that he spends a hours doing homework each week and the total number of hours spent on both activities is 15.

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Complete question-

The equation is a + b = 15

The probability of drawing the first yellow ball on the eighth draw is 1/2772.

The probability of drawing a yellow ball on the eighth draw is the probability of drawing 7 non-yellow balls followed by a yellow ball.

The probability of drawing a non-yellow ball on the first draw is 7/12 since there are 7 non-yellow balls out of a total of 12 balls in the bag. After the first non-yellow ball is drawn, there will be 6 non-yellow balls left out of a total of 11 balls. So the probability of drawing a non-yellow ball on the second draw is 6/11. Continuing in this manner, the probability of drawing 7 non-yellow balls in a row is

(7/12) × (6/11) × (5/10) × (4/9) × (3/8) × (2/7) × (1/6)

Now, there are 5 yellow balls left out of a total of 5 + 7 + 3 = 15 balls. So the probability of drawing a yellow ball on the eighth draw is 5/15.

Therefore, the probability of drawing the first yellow ball on the eighth draw is

(7/12) × (6/11) × (5/10) × (4/9) × (3/8) × (2/7) × (1/6) × (5/15)

Simplifying this expression, we get

(7 × 6 × 5 × 4 × 3 × 2 × 1 × 5) / (12 × 11 × 10 × 9 × 8 × 7 × 6 × 15)

which simplifies to:

1/2772

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The given question is incomplete, the complete question is:

A bag contains 3 red balls, 4 green balls, and 5 yellow balls. If balls are drawn one at a time without replacement, what is the probability that the first yellow ball is drawn on the eighth draw?

Answer: y=4

Step-by-step explanation:

you would plug in 10 wherever x would be so your new equation would be 10-7y=-18.

subtract 10 from both sides.

-7y=-28

then divide by -7

y=4

As a result, the app stοre's οwner prοjects that in its third year οf οperatiοn, there will be rοughly 2.197 milliοn app dοwnlοads.

A mathematical functiοn with the fοllοwing fοrmula is an expοnential functiοn: f(x) = [tex]a^x[/tex] where x is the expοnent and an is a cοnstant knοwn as the base. Expοnential functiοns have a distinctive structure where the value οf the functiοn rapidly rises (οr falls) as the expοnent x value rises. The rate οf increase οr decline is determined by the expοnential functiοn's base. If a > 1, the functiοn will quickly increase as x rises, and if 0 a 1, the functiοn will quickly decrease as x rises.

We can use the fοrmula: tο create an expοnential grοwth functiοn f(x) that prοvides the number οf app dοwnlοads (in milliοns) in year x.

[tex]f(x) = f(0) * (1 + r)^x[/tex]

where x is the number οf years since the app stοre first launched, r is the grοwth rate, and f(0) is the οriginal number οf dοwnlοads.

In this instance, there were 1 milliοn initial dοwnlοads, and the grοwth rate was 30%, οr 0.30. Thus, the fοllοwing is the expοnential grοwth equatiοn fοr the milliοns οf app dοwnlοads in year x:

[tex]f(x) = 1 * (1 + 0.30)^x[/tex]

[tex]f(x) = 1.3^x[/tex]

Therefοre, fοr instance, entering x=3 intο the functiοn will return the amοunt οf app dοwnlοads (in milliοns) fοr the third year.

[tex]f(3) = 1.3^3[/tex]

[tex]f(3) = 2.197[/tex]

As a result, the app stοre's οwner prοjects that in its third year οf οperatiοn, there will be rοughly 2.197 milliοn app dοwnlοads.

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The length of the reflected line segment is approximately 11.66 units.

The endpoints of the line segment mentioned in the question are (0,5) and (6,5). After the line segment is reflected across the x-axis, the endpoints of the reflected line segment are (0, -5) and (6, -5).To find the length of the reflected line segment, we will use the distance formula.

Using the distance formula:d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (5 - 5)²]d = √[36 + 0]d = √36d = 6 units. So the length of the original line segment is 6 units.Now, let's find the length of the reflected line segment.Using the distance formula :d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (-5 - 5)²]d = √[36 + 100]d = √136d = 11.66 (approx) units. So the length of the reflected line segment is approximately 11.66 units.

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Joelle has a total of 32 yards of ribbon in all, the correct option is A.

Let's use x to represent Joelle's total amount of ribbon. We know that 24 yards of the ribbon represent 86% of her total amount of ribbon, which can be expressed as:

24 = 0.86x

We can solve for x by dividing both sides by 0.86:

x = 27.91

The response options are all integers, thus we must round to the closest whole number because of this. Since 0.91 is greater than or equal to 0.5, we round up to 28.

Therefore, Joelle has a total of

x = 27.91 / 0.86

= 32.44 yards of ribbon.

Once again, we round to the nearest whole number, which is 32.

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The complete question is:

To wrap gift boxes, Joelle uses 24 yards of ribbon, which is 86 of her total amount of ribbon. How many yards of ribbon does she have in all?

A 32

B 192

C 300

D 1920​

The area of the given shape is 22 square tiles. The given shape consists of two rectangles and a square.

To find the area of the shape, we need to find the area of each of these three shapes and then add them up.

First, we can see that the length of the longer rectangle is 6 tiles and the width is 2 tiles. Therefore, the area of this rectangle is 6 × 2 = 12 tiles.

Next, the length of the shorter rectangle is 3 tiles and the width is 2 tiles. Thus, the area of this rectangle is 3 × 2 = 6 tiles.

Finally, the square has a side length of 2 tiles, so its area is 2 × 2 = 4 tiles.

Adding up the areas of the three shapes, we get 12 + 6 + 4 = 22 tiles.

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Answer:

$118

Step-by-step explanation:

If there are 59 students going on the field trip, and the cost is $2 per student, then the total cost for all the students to go on the field trip would be:

Total cost = Number of students × Cost per student

Total cost = 59 × $2

Total cost = $118

It would cost $118 in total for all 59 students to go on the field trip, assuming there are no taxes or additional fees involved.

Answer:

Step-by-step explanation:

no because 6 , 7 and 10 doesn't add up to 180 so it is not

A triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers is not a right triangle.

To determine if a triangle is a right triangle, you can use the Pythagorean Theorem. The Pythagorean Theorem states that "In a right-angled triangle, the sum of the square of the two shorter sides is equal to the square of the longest side." It can be written as:

a² + b² = c², where 'a' and 'b' are the lengths of the two legs of a right triangle, and 'c' is the length of the hypotenuse.

In this triangle, the two shorter sides have lengths of 6 kilometers and 7 kilometers and the longest side is 10 kilometers.

The square of 6 kilometers is 36 kilometers and the square of 7 kilometers is 49 kilometers.

The sum of 36 kilometers and 49 kilometers is 85 kilometers.

The longest side of the triangle has a length of 10 kilometers, and the square of 10 kilometers is 100 kilometers.

Since 85 kilometers is not equal to 100 kilometers, this triangle is not a right triangle.

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In two successive years, the population of the town increased by 12% and 25%. So the percentage of the population increased after two years is 40%

   The population growth rate of the town can be calculated as follows:

   The population of the town increased by 12% in the first year.

             Hence, the population of the town after one year becomes 1.12x where x is the initial population of the town. In the second year, the population of the town increased by 25%.

   Therefore, the population of the town after two years becomes  

               1.25(1.12x) = 1.4x.

Now, the percentage increase in the population of the town after two years can be calculated as follows:

    Total percentage increase = ((New population - Old population) / Old population) x 100%

   Total percentage increase = ((1.4x - x) / x) x 100%Total percentage increase = (0.4x / x) x 100%

     Total percentage increase = 40 %

Therefore, the percentage increase in the population of the town after two years is 40%.

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Answer:

The answer is six eighths

There's 8 letters in all and 6 of them are consonants (M, T, H, C, L, B)

Step-by-step explanation:

so all you have to do is take out all the vowel and count the letters that are consonant then you make that your top number than you put that over the amount of numbers in total

Since Latasha looked at 3 websites every 15 hours, at that rate, it will take Latasha 25 hours to look at 5 websites.

The unit rate shows the ratio between two values.

The unit rate is the quotient of two numbers, computed using the division and multiplication operations.

The number of websites Latasha looked in 15 hours = 3

The time it will take Latasha to look at 5 websites = 25 (15/3 x 5)

Thus, based on the rate, we can conclude that Latasha uses 5 hours to look at one website.

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The year that saw 164 billion dollars being spent on advertising, given the function for the advertising would be c. 1994

The dimensions of the rectangle, given the area of the rectangle would be:

The function is given by y = 0.93x² + 2.2x + 130, where y is the amount of money spent (in billions of dollars) and x is the number of years since 1990. We need to find the value of x when y = 164.

164 = 0.93x² + 2.2x + 130

0.93x² + 2.2x + 130 - 164 = 0

0.93x² + 2.2x - 34 = 0

x = 2.5

Now, we'll find the year by adding the value of x to 1990:

Year = 1990 + 2.5 = 1992.5

= 1994 which is the closest year in options

The area of the rectangle is given by:

Area = width × length

91 = (x + 2)(2x + 3)

91 = 2x² + 3x + 4x + 6

91 = 2x² + 7x + 6

2x² + 7x - 85 = 0

When solved differently:
x = 4.9

x = -3.5

Using the positive values:

Width = x + 2 ≈ 4.9 + 2 = 6.9 meters

Length = 2x + 3 ≈ 2(4.9) + 3 ≈ 9.8 + 3 = 12.8 meters

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Triangle ABC will be dilated with a scale factor of 2, centered at the origin. What will be the resulting coordinate of B' will be (4,12).

A polygon with three sides and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with points A, B, and C. In Euclidean mathematics, any three points that are not collinear produce a distinct triangle and a distinct plane.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more integers, or coordinates. The order of the coordinates is important, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". In elementary mathematics, the coordinates are assumed to be real numbers. Analytic geometry is based on the use of a coordinate system, which enables issues with geometry to be converted into problems with numbers and vice versa.

Triangle ABC will be dilated with a scale factor of 2, centered at the origin.

Coordinates of B are (2,6).

When the triangle is dilated, we multiply the coordinates by 2.

hence, B'(4,12)

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Since sample proportion is a mean, one can find the z-value and an acceptance interval is true statement about sample proportion. (A)

The sample proportion is the ratio of the number of items in the sample having a given attribute (the numerator) to the total number of items in the sample (the denominator).

By taking a sample of data and calculating the sample proportion, one can use the z-score to find the acceptance interval and estimate the true population proportion.

For example, if the sample size is 100, and the number of items with a given attribute is 35, then the sample proportion would be 35/100 = 0.35. Using the z-score, one can then calculate the acceptance interval, which is the range of values in which the true population proportion is likely to fall.

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Answer: It should be -1,7

Step-by-step explanation: x=1-2=-1

y=8-1=7

Answer:

(-1, 7)

Step-by-step explanation:

A left translation is a negative number affecting the x-coordinate.

1 - 2 = -1

A down translation is a negative number affecting the y-coordinate.

8 - 1 = 7

(1, 8) --------> (-1, 7)

Hence, after investing $3,350 for 8 years at a 6.2% interest rate, compounded 365 times a year, the total amount is roughly $4,865.25.

In mathematics, the term "amount" typically refers to a number or a thing's numerical value. It can stand in for anything that can be counted or measured, such as the amount of money in a checking account, the time needed to finish a task, or the concentration of a specific item in a solution. Several branches of mathematics, such as arithmetic, algebra, and calculus, all depend on the idea of amount.

given

With a principal of P and an interest rate of r compounded k times annually, the amount amassed after t years is calculated as follows:

[tex]A = P(1 + r/k)^(kt) (kt)[/tex]

Putting in the specified values

P = $3,350

r = 6.2%

t = 8

k = 365

[tex]A = $3,350(1 + 0.062/365)^(365*8)[/tex]

A ≈ $4,865.25 (rounded to the nearest cent) (rounded to the nearest cent)

Hence, after investing $3,350 for 8 years at a 6.2% interest rate, compounded 365 times a year, the total amount is roughly $4,865.25.

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Answer:

length = 42 in , width = 14 in

Step-by-step explanation:

given the width is [tex]\frac{1}{3}[/tex] of the length , then

y - 4 = [tex]\frac{1}{3}[/tex] (2y + 6) ← multiply both sides by 3 to clear the fraction

3y - 12 = 2y + 6 ( subtract 2y from both sides )

y - 12 = 6 ( add 12 to both sides )

y = 18

then

length = 2y + 6 = 2(18) + 6 = 36 + 6 = 42 in

width = y - 4 = 18 - 4 = 14 in

Therefore , the solution of the given problem of equation comes out to be the equation has a slope of 1/2 and a y-intercept of -1, and is written as y = 1/2x - 1.

In intricate algorithms, variable words are frequently used to demonstrate consistency between two incompatible assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this instance, normalization results in c + 7 rather than a singular formula that divides 12 into two components and can be applied to data obtained from y + 9.

Here,

We must isolate y on the left side of the equation in order to convert the provided equations to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

=> y = -x - 4:

=> x + y = -4

=> y = -x - 4

As a result, the equation has a slope of -1 and a y-intercept of -4, and is written as y = -x - 4.

=> y = 1/2x - 1:

=> y - 1/2x = -1

=> y - 1/2x + 1 = 0

The words with y and the constant term must be combined in order to represent this equation in slope-intercept form:

=> y + 1 = 1/2x

By taking away 1 from both edges, we obtain:

=> y = 1/2x - 1

As a result, the equation has a slope of 1/2 and a y-intercept of -1, and is written as y = 1/2x - 1.

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Answer:

Perimeter of semi-circle = 16.5 cm.

Step-by-step explanation:

Given that,

Diameter of the semi-circle, [tex]\text{d} = 10.5 \ \text{cm}[/tex]

So, Radius of the semi-circle, [tex]\text{r} = 10.5\div2 \ \text{cm}[/tex]

We know that,

Perimeter of a Circle [tex]= 2\pi r[/tex]

So, Perimeter of a semi-circle [tex]= \dfrac{1}{2} \times 2\pi r[/tex]

[tex]= \pi r[/tex]

[tex]= \dfrac{22}{7} \times 10.5\div2[/tex]

[tex]= 16.5 \ \text{cm}[/tex]

Hence, Perimeter of the semi-circle with diameter 10.5 cm is 16.5 cm.

The probability of drawing a diamond from a deck of cards is 1/4. So, the odds in favor of drawing a diamond from an ordinary deck of cards are 1/3.

A deck of cards has 52 cards in it, and there are 13 cards of diamonds in it. So, the probability of drawing a diamond is 13/52. Simplifying 13/52, we get 1/4. The odds of an event happening are the ratio of the probability of an event happening to the probability of an event not happening. It's expressed in the form of x:y.

The probability of an event happening is the probability of success. The probability of an event not happening is the probability of failure. In the current scenario, the probability of drawing a diamond is 1/4. So, the probability of not drawing a diamond is 3/4. Therefore, the odds in favor of drawing a diamond are:

=1/3

The odds in favor of drawing a diamond from an ordinary deck of cards are 1/3.

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