A company manufactures a wash-down motor that is used in the food processing industry. The motor is marketed with a warranty that guarantees it will be replaced free of charge if it fails within the first 12,000 hours of operation. On average, the wash-down motors operate for 14,000 hours with a standard deviation of 1, 050 hours before failing. The number of operating hours before failure is approximately normally distributed.


a. What is the probability that a wash-down motor will have to be replaced free of charge?

b. What percentage of wash-down motors can be expected to operate for more than 16,100 hours?

c. If the company wants to design a wash-down motor so that no more than 1% are replaced free of charge, what would the average hours of operation before failure have to be if the standard deviation remains at 1,050 hours?

It will take Chantel approximately 2.028 hours or 122.68 minutes to complete the triathlon.

What is average ?

An average, also known as a mean, is a measure of central tendency that represents the typical value of a set of data. To calculate the average of a set of numbers, you add them up and then divide by the number of items in the set.

Time = Distance / Speed

For the swimming segment, the distance is 0.93 miles and the speed is 2.1 mph. So the time it will take Chantel to swim the 0.93 miles is:

Time = 0.93 / 2.1 = 0.445 hours or 26.7 minutes

For the biking segment, the distance is 24.8 miles and the speed is 18.2 mph. So the time it will take Chantel to bike the 24.8 miles is:

Time = 24.8 / 18.2 = 1.367 hours or 81.02 minutes

For the running segment, the distance is 6.2 miles and the speed is 5.1 mph. So the time it will take Chantel to run the 6.2 miles is:

Time = 6.2 / 5.1 = 1.216 hours or 72.96 minutes

To get the total time, you have to add the time for each segment:

Total time = 0.445 + 1.367 + 1.216 = 2.028 hours or 122.68 minutes

So , It will take Chantel approximately 2.028 hours or 122.68 minutes to complete the triathlon.

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The correct result for the expression 3x + 10/2 + 4(x + 3/2) is solved to be

The math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

applying the sequence the problem is solved as follows

= 3x + 10/2 + 4(x + 3/2)

parenthesis

= 3x + 10/2 + 4x + 6

division

= 3x + 5 + 4x + 6

addition

= 3x + 4x + 6 + 5

= 7x + 11

solving for x

7x = -11

x = -11/7

x = -1 4/7

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By plotting the given points (0,0) , (1,10 ) for y=5x and the points for y=45-10x are (0,45) , (1,35) and (2,25) we get the required graph.

What is linear equation ?

Linear equation can be defined as the equation in which highest degree is one.

Given Equation,

y = 5x and y = 45 - 10x

So,

use the slope form is

y= mx+b , where m is slope and b is the y-intercept.

find the valued of m an b using the form y = mx+b

m = 10 and b=0

The slope of line is the value of m and y-intercept the value of b

slope = 10

y-intercept = (0,0)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding 2y values.

create a table for x and y values.

x    y

0    0

1      10

and soon

Similarly for y = 45-10x

x    y

0   45

1     35

2    25

and soon

And Hence plot the points in the graph.

Therefore, By plotting the given points (0,0) , (1,10 ) for y=5x and the points for y=45-10x are (0,45) , (1,35) and (2,25) we get the required graph.

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The roots of the quadratic function f(b) = b² - 75 are Ob=5√3 and Ob=-5√3.

A quadratic function is a polynomial function of degree two, which means it is a function that can be expressed as an equation with the second-degree degree of the highest exponent of the unknown variable. It is typically expressed as ax^2 + bx + c, where a, b and c are constants, and x is an unknown variable. Quadratic functions can be used to model many real-world situations, such as the height of a projectile in motion or the area of a circle.

The Quadratic Formula can be used to solve for the roots of a quadratic function. The Quadratic Formula states that for a quadratic equation of the form ax² + bx + c = 0, the two roots are given by x = [-b ± √(b² - 4ac)]/2a.

In this case, a = 1, b = 0, and c = -75. Therefore, the two roots are given by x = [-0 ± √(0² - 4(1)(-75)]/2(1). This simplifies to x = [0 ± √(75)]/2, or x = ±5√3/2. The two roots are thus Ob=5√3 and Ob=-5√3.

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The value of the equation A = 154,504 / 28 = 5518

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Let the dividend be p = 154,504

Let the divisor be q = 28

Substituting the values in the equation , we get

A = p / q

A = 5,518

     5518

28 | 154504

1 4 0      

 1 4 5    

 1 4 0    

     5 0  

     2 8  

     2 2 4

     2 2 4

         0

So , the remainder of the equation is 0 and the quotient is 5518

Hence , the equation is A = 5518

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Kallie and Jeie sold 4 regular lemonade for $1.50 amount each, and 16 strawberry lemonade for $2 each, and made a total of $45.

Regular Lemonade: 9

Strawberry Lemonade: 21

Regular Lemonade:

Price of Regular Lemonade = 1.50

Total earnings from Regular Lemonade = 9 x 1.50 = 13.50

Strawberry Lemonade:

Price of Strawberry Lemonade = 2

Total earnings from Strawberry Lemonade = 45 - 13.50 = 31.50

Number of Strawberry Lemonade sold = 31.50 / 2 = 15.75

Number of Regular Lemonade sold = 15.75 - 12 = 3.75

Rounded to nearest whole number,

Number of Regular Lemonade sold = 4

Number of Strawberry Lemonade sold = 16

Kallie and Jeie sold 4 regular lemonade for $1.50 amount each, and 16 strawberry lemonade for $2 each, and made a total of $45.

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Sample proportion of 0.585, p-value of 0.0491, not strong evidence of more than 50% support.

What is null hypothesis ?

The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

The null hypothesis is that the proportion of Americans supporting the new health policy is less than or equal to 0.5 (p <= 0.5). The alternative hypothesis is that the proportion of Americans supporting the new health policy is greater than 0.5 (p > 0.5).

The test statistic for a one-sample proportion test is:

z = (p^ - p) / sqrt((p * (1-p)) / n)

where p^ is the sample proportion (117/200 = 0.585), p is the hypothesized proportion of Americans supporting the new health policy (0.5), and n is the sample size (200).

Sample proportion of 0.585, p-value of 0.0491, not strong evidence of more than 50% support.

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The amount of each item, pizza and chicken wings that should be bought are 7 and 4 respectively. For an additional member the additional number of pizzas is 0 and chicken wings are 10.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

A: X is the quantity of pizzas, while Y is the quantity of bags of chicken wings.

1 pizza cost x, thus 6 cost = 6 x

1 bag of chicken wings costs y dollars, thus 7 cost = 7 y.

Given: Total cost = 6x + 7y = 70

Total servings are now equal to (24)(2) for a total of 48.

One pizza includes four portions, thus 1 x 4 = 4

Servings in a bag of chicken wings are 5y.

Servings total: 4x + 5y = 48

The set of linear equations is hence 1.

6x + 7y = 70 .....(I)

4x + 5y = 48 ......(II)

Having solved (I) and (II), we obtain x = 7 and y = 4.

B:

One more guest brings the total to 25.

Total portions are therefore 4x + 5y = 2.25 = 50.

The total cost of 6x + 7y stays at 70.

The set of linear equations is hence 1.

6x + 7y = 70 .....(I)

4x + 5y = 50 ......(II)

We obtain x = 0 and y = 10 by solving for (I) and (II).

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The constant of proportionality of the proportional relationship, given the values of x and y is D.  5 / 12

The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship.

The Constant of proportionality can therefore be found by picking a random point on the graph which is ( 2, 5 / 6 )

The constant of proportionality is:

= 5 / 6 ÷ 2

= 5 / 6 x 1 / 2

= 5 / 12

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The number line which shows all the values of x that make the provided inequality -3x+1<7 true is shown in number line D.

Now, According to the question:

The number line is the way of representation of number and digits in a arranged form to understand the data batter.

The inequality is :

- 3x + 1 < 7

Subtract 1 both side of the equation and solve it further,

-3x + 1 - 1 < 7 - 1

-3x < 6

Divide with number 3,on both sides

-x < 6/3

-x < 2

Change the sign of the inequality by filliping the inequality sign,

x > -2

Here, the inequality is greater than the number negative 2. The value of x is greater than, thus, the arrow will point towards left and there will be open circle. This is shown in the option D.

Thus, the number line which shows all the values of x that make the provided inequality -3x+1<7 true is shown in number line D.

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20-s is the number of pages written by Leo this week.

An expression is combination of variables, numbers and operators.

Given that Leo wrote s of his 20-page paper last week.

In last week she wrote s pages.

Leo completed his writing the paper this week.

20-s

Twenty minus s is the expression which gives the pages Leo write this week

Hence, 20-s is the number of pages written by Leo this week.

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Answer:

To find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8), we can use the formula:

P = (1 - t)A + tB

where t is a scalar value that represents the position of P on the segment AB, and A and B are the coordinates of the two endpoints of the segment.

In this case, we know that the part-to-whole ratio is 1:5, so t = 1/6.

So we substitute the values for A, B and t into the formula:

P = (1 - 1/6)A + (1/6)B

P = (5/6)A + (1/6)B

P = (-95/6, 35/6) + (1/6, 8/6)

P = (-15/2, 5/2) + (1/6, 4/3)

P = (-15/2 + 1/6, 5/2 + 4/3)

P = (-30/3, 23/6)

The coordinates of P are (-10,3.83)

For the second problem,

To find the coordinates of P so that P partitions the segment AB in the ratio 3 to 1 if A(7, -4) and B(-5, 4), we can use the same formula as above:

P = (1 - t)A + tB

In this case, we know that the part-to-whole ratio is 3:1, so t = 3/4.

So we substitute the values for A, B and t into the formula:

P = (1 - 3/4)A + (3/4)B

P = (1/4)A + (3/4)B

P = (7/4, -4/4) + (-53/4, 43/4)

P = (7/4 + -15/4, -4/4 + 3)

P = (-8/4, -1/4)

The coordinates of P are (-2,-0.25)

So in the first problem point P is (-10,3.83) and in the second problem point P is (-2,-0.25)

Given the above function:

a) Note that the number of people that need to sign up for a tour in order for the profit to be at least $108 is:

b) The number of people that need to sign up for a tour in order for the profit to be more than $144 is:

c) Yes, it is possible to make a negative profit on the tour in which case they would have made a loss.

a) To find out the number of people that need to sign up for the profit to be at least $108 where the function y = - x7 + 24x, models profit in y,

we must equate the function to $108 and solve for x.

Thus:

- x7 + 24x = 108

resolve like terms

17x = 108

x = 108/17

x = 6.35294117647

x [tex]\approx[/tex] 6. 4

Plug x back into the formula, and we have:

-(6.4) * 7 + 24 (6.4) = 108.8 this shows that our calculation is correct. Since you can have 6.4 persons, the best number to aim for is 7.

b) The number of people that need to sign up for the project to turn a profit of $144 is:

- x7 + 24x = 144

resolve like terms

17x = 144

x = 144/17

x = 8.4705882353

Let's impute back 8.5 into the equation:

-(8.5)7 + 24(8.5)

= 144.5.

This shows that our calculation is correct. However since you cannot have 8.5 persons, the number to budget for would be 9 persons.

c) for the tour guide to lose money, the amount made, that is revenue, would have to be less than the amount invested.

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The probability that two random people being born on the same day is thus 1/365 or about 0.3%

We apply our probability model above to the task at hand.

First, we suppose Person 1. This person is born on a certain date of the year.

Since this is a random person, we can fix this person's birthday to a specific date (a number between 1 and 365) without loss of generality for the problem.

Let's say this person is born on 10. (i.e. January 10th)

Now, we take Person 2. In order to achieve the event that Person 2 is born on the same date as Person 1,

we need them to be born on 10. In other words, we seek the probability of Person 2 being born on 10.

Based on our model, we have that this probability is 1/365.

The probability that two random people being born on the same day is thus 1/365 or about 0.3%

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Answer:

see below

Step-by-step explanation:

make x = 7

Answer:

Subtract 5 from both sides

x = 7

Step-by-step explanation:

x + 5 = 12  Subtract 5 from both sides

x + 5 - 5 = 12 - 5

x = 7

If horse's body temperature T is considered to be normal if it is within at least 0.9 °F of 99.9 °F , then normal range of body temperature of a horse as an inequality 99 ≤ T ≤ 100.8  .

If the temperature of the horse denoted by "T" , is within at least 0.9 °F of 99.9 °F , then it is considered as Normal ;

To express this as an inequality, we can use the following:

⇒ 99.9 - 0.9 ≤ T ≤ 99.9 + 0.9  ;

Simplifying further , this inequality can also be written as:

⇒ 99 ≤ T ≤ 100.8

Therefore , the normal range of body temperature of a horse is 99 ≤ T ≤ 100.8 .

The given question is incomplete , the complete question is

A horse's body temperature T is considered to be normal if it is within at least 0.9 °F of 99.9 °F. Write the normal range of body temperature of a horse as an inequality .

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Answer:

100%

Step-by-step explanation:

The mark-up percentage is the amount by which the cost price of a product is increased to arrive at the selling price. To calculate the mark-up percentage, you can use the formula:

Mark-up percentage = (selling price - cost price) / cost price x 100

In this case:

Cost price = $450

Selling price = $900

Mark-up percentage = ($900 - $450) / $450 x 100 = 100%

So the specialty shop has a mark-up of 100% on each painting.

It means that the shop is charging twice as much as the price they procured the paintings.

The simplified exponential expression for this problem is given as follows:

(3² x 5)³ = 3^6 x 5³.

The exponential expression for this problem is defined as follows:

(3² x 5)³.

As we have a product applied to the exponent, the exponent can be applied to each factor of the exponent, as follows:

(3²)³ x 5³.

Applying the power of power rule, we have that:

(3²)³ = 3^(2 x 3) = 3^6.

Hence the simplified exponential expression for this problem is given as follows:

(3² x 5)³ = 3^6 x 5³.

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The number of miles that a person walks at this speed to use at least 250 ​calories will be 2.49 miles.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

A​ 150-pound person uses 6.7 calories per minute when walking at a speed of 4 mph.  If the number of calories burnt is 250. Then the number of minutes the person is given as,

T = 250 / 6.7

T = 37.313 minutes

T = 0.62 hours

Then the distance is given as,

D = 4 x 0.62

D = 2.49 miles

The number of miles that a person walks at this speed to use at least 250 ​calories will be 2.49 miles.

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The equation that accurately represents the statement "negative 3 less than 4.9 times a number, x, is the same as 12.8" is:

4.9 x - 3 = 12.8

This equation can be gotten by replacing "negative 3 less than 4.9 times a number, x" with "4.9 x - 3" and "is the same as" with "=". The correct form of the equation is gotten by using the correct order of operations:

negative 3 less than 4.9 x

= 4.9 x - 3

= 12.8

The other equations listed do not accurately represent the statement. For example, the equation "Negative 3 minus 4.9 x = 12.8" would be incorrect because it does not use the correct order of operations. The correct order of operations would be to subtract 4.9 x from negative 3, which would give us 4.9 x - 3 = 12.8.

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The scatter plot shows data points that do not follow a trend, thus it shows a: nonlinear association.

A nonlinear association is a relationship between two variables, whereby a change in one does not correspond to a change in another.

Thus, on a scatter plot showing a nonlinear association, the data points do not follow a trend line and are scattered, therefore, predictions cannot be made using the scatter plot.

Thus, the scatter plot that is given shows: nonlinear association.

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If you invested $10000 in a stock with 5% compounded monthly you will have $16470 in 10 years.

Compound interest is simply interest that is earned over prior interest. You receive interest on the initial principal as well as the interest that builds up over time when you open a savings account that pays compound interest.

When you deposit funds into a savings account or other type of account, you will earn interest on the amount you deposited. For instance, after a year, if you deposited $1,000 in an account with 1% annual interest, you would have received $10 in interest.

Compound interest formula is

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Here,

P = $10000

r = 5%

n = 12

t = 10

A = to find

Lets solve,

[tex]$\text A = 10000(1 + \frac{0.05}{12})^{12\times 10}[/tex]

A = 16470

Thus, If you invested $10000 in a stock with 5% compounded monthly you will have $16470 in 10 years.

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An equation in slope intercept form passing through the point (-10,1) and parallel to the line 10x+5y=15 is y=-2x+19.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = mx +c

To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

Given;

Line is  passing through the point (-10,1)

Parallel to the line 10x+5y=15.

So, the slope of the line is equal to the line parallel to it

Slope of given line

5y=-10x+15

y=-10x/5+15

m=-2

Equation; 1=-2x+c

c=-2*-10-1

c=19

Therefore, the equation will be y=-2x+19.

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Answer: Let "t" be the fare of the train.

The fare of the bus is "b".

We know that t + b = 4000 (the total fare of the journey)

On the return trip, the fare of the bus was hiked by half of what was paid, so b*1.5 = b + (b/2) = new fare of the bus.

The total fare of the return journey is 4800, so t + (b + (b/2)) = 4800

Now we have two equations:

t + b = 4000

t + b + (b/2) = 4800

We can substitute the first equation into the second equation:

t + b + (b/2) = 4800

t + (4000 - t) + (b/2) = 4800

t + (b/2) = 800

t = 800 - (b/2)

Now we have an equation that only involves one variable "t" (the fare of the train)

We can substitute the first equation back in:

t + b = 4000

800 - (b/2) + b = 4000

800 = (3/2)b

b = 1200

So the fare of the bus is 1200 and the fare of the train is 800

Step-by-step explanation:

Answer:

Step-by-step explanation:Seriously you probably going to need a ruler because you don't like you can't just remember measurement inside your head you have to really like a ruler so actually go get a ruler and then take a picture of it doing with the ruler and then you might like get it.

Answer:

There are only 6 factors of the number 44 which are 1, 2, 4, 11, 22 and 44.

From this list, the factors of 44 are:

1) 22

2) 44

3) 1

4) 4

5) 11

6) 2

Answer:

1,2,4,11,22,44

Step-by-step explanation:

Let's work our way up.

You can start with 1, cause every number has a factor of 1. Then you can find that 44, cause every number is divisible by itself. and 1 × 44 = 44. Since 44 ends with a 4, it has to be divisible by 2. So to find the number that multiplies with 2 to get 44, divide 44 by 2 which equals 22. So 2×22=44. 44 is not divisible by 3. But it is divisible by 4. 4×11=44. No other number is a factor of 44. Therefore; 1,2,4,11,22,44

Hope that helps. Let me know if you have any further questions!

The example for the y-intercept, slope, two points, and the ordered pair

are given below.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

Let a line in the slope-intercept form,

y = x + 1.

And the line passes through the two ordered pairs (3, 4) and (5, 6).

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

m = 1

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

y - 4 = x -3

y = x+1

Substitute x = 0,

then y = 1

the y-intercept is 1.

Therefore, all the required values are given above.

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The domain and the range of the relation shown to the right are given as follows:

The graph is not a function, as a vertical line for x > -5 would cross a function in multiple points.

The domain of a function is the set that contains all the input values of the function, hence on the graph it is the values of x, thus the domain is of:

x >= -5.

The range of a function is the set that contains all the output values of the function, hence on the graph it is the values of y, thus the domain is of:

All real values.

As there are inputs that are mapped to multiple outputs, the graph does not represent a function.

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Answer:

Step-by-step explanation:

The transformation of triangle QRS that results in an image triangle DEF where angle Q is congruent to angle D, angle R is congruent to angle E, and angle S is congruent to angle F, and QR/DE = QS/DF = RS/EF ≠ 1 is a similarity transformation.

A similarity transformation is a type of transformation that preserves the angles between the corresponding sides of the original and the image figures. It means that the corresponding angles of the two figures are congruent, and the ratios of the corresponding sides are equal. In the case of a triangle, it preserves the angles and the ratios of the sides.

So, if a transformation of triangle QRS results in an image triangle DEF where angle Q is congruent to angle D, angle R is congruent to angle E, and angle S is congruent to angle F, and QR/DE = QS/DF = RS/EF ≠ 1, it is a similarity transformation.

The transformation is similarity transformation.

Similarity transformations are transformations where there occurs a dilation with one or more transformations like rotation, reflection or translation.

This is called so because the triangles so formed will be similar triangles.

We need two triangles QRS and DEF to be similar triangles.

Similar triangles are those triangles which has the same shape but different size and the length of sides are proportional.

This is the required transformation here.

Similar triangles can be formed by transforming a triangle first with dilation.

Then you can do any of the other rigid transformations.

The triangles will be similar.

Hence the transformation here is similarity transformation.

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