find the area of an equilateral triangle ABC, whose sides are 7cm each and the height 4.2cm​

The answer to the following questions is: (a) So, the expected number of defects = 1000 × 0.3174 ≈ 317, rounded to the nearest integer. (b) expected number of defects = 1000 × 0.0456 ≈ 46, rounded to the nearest integer. (c) So, the option (a) is correct.

(a) The probability of a defect is 0.1587.  The z-values for 9.84 and 10.16 are -1.00 and 1.00 respectively. Therefore, P( -1.00 < z < 1.00) = P(z < 1.00) - P(z < -1.00) = 0.8413 - 0.1587 = 0.6826. Hence, the probability of a defect is 1- 0.6826 = 0.3174, rounded to four decimal places.
The expected number of defects for a 1,000-unit production run can be calculated by multiplying the number of units produced by the probability of defects. So, the expected number of defects = 1000 × 0.3174 ≈ 317, rounded to the nearest integer.

(b) The probability of a defect is 0.0228.  The z-values for 9.84 and 10.16 are -1.00 and 1.00 respectively. Therefore, P(-1.00 < z < 1.00) = P(z < 1.00) - P(z < -1.00) = 0.9772 - 0.0228 = 0.9544. Hence, the probability of a defect is 1 - 0.9544 = 0.0456, rounded to four decimal places.
The expected number of defects for a 1,000-unit production run can be calculated by multiplying the number of units produced by the probability of defects. So, the expected number of defects = 1000 × 0.0456 ≈ 46, rounded to the nearest integer.

(c) Reducing the process variation has an advantage in terms of quality control. If the process variation is decreased, the control limits are placed at a greater number of standard deviations from the mean. In order to detect changes in the process more quickly, the control limits must be placed at a greater distance from the mean.

By reducing process variation, the number of defective items produced can be minimized. Hence, the advantage of reducing process variation is reducing the process standard deviation causes a substantial reduction in the number of defects. Therefore, the option (a) is correct.

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The value of tan(60°) is √3, and option C is correct.

In order to find the value of tan(60°) using the given diagram, we need to use the tangent formula which is:tan(x) = opposite / adjacentIn the case of the given diagram, we can see that the angle we're interested in is 60°, and the side opposite the angle is the length of the line marked "√3" and the side adjacent to the angle is the length of the line marked "1".Thus, we can plug in these values into the formula:tan(60°) = opposite / adjacenttan(60°) = √3 / 1tan(60°) = √3.

The value of tan(60°) is √3, and option C is correct.

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Answer:

.20x = 72, so x = 360

.30(360) = 108

The mathematical term 'i' is the imaginary unit which is defined by its property i²=-1. The powers of 'i' follow a pattern that repeats every 4 numbers, so i¹⁰ is the same as i², which is -1.

In mathematics, i is the imaginary unit, which is defined by the property that i2 = -1. When raising i to a power, there's a pattern that repeats every 4 numbers. Specifically, i1 = i, i2 = -1, i3 = -i, and i4 = 1. This pattern starts over with i5 = i, i6 = -1, etc.

Given this, to find i10, you can realize that 10 is a multiple of 4 (2*4) plus 2. So i10 is same as i2, which is -1.

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Paul performed an enlargement or dilation Transformation on the original segment to obtain the image segment.

To determine the type of transformation Paul performed, we can analyze how the coordinates of the points changed from the original segment to the image segment.

The original segment has two points: (3, 6) and (-4, 8). The image segment as two points: (9, 18) and (-12, 24).

Let's calculate the changes in the x-coordinates and y-coordinates separately:

For the x-coordinates:

- The x-coordinate of the first point changed from 3 to 9. This is an increase of 6.

- The x-coordinate of the second point changed from -4 to -12. This is also an increase of 8.

For the y-coordinates:

- The y-coordinate of the first point changed from 6 to 18. This is an increase of 12.

- The y-coordinate of the second point changed from 8 to 24. This is also an increase of 16.

From the changes observed, we can conclude that both the x-coordinates and y-coordinates increased by the same scale factor. This indicates a dilation or enlargement transformation.

Additionally, since the scale factor is greater than 1 (the coordinates increased), it suggests that the dilation was an enlargement.

Therefore, Paul performed an enlargement or dilation transformation on the original segment to obtain the image segment.

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The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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The inequality "x ≤ 1" has infinitely many negative integer solutions as any negative integer value for x satisfies this condition.

The inequality that has infinitely many negative integer solutions is "x ≤ 1".

To understand why this is the case, let's break down the inequality and consider its implications. The inequality x ≤ 1 means that x is less than or equal to 1. In other words, any value of x that is smaller than or equal to 1 satisfies this inequality.

Now, when it comes to negative integers, they are numbers less than zero. Since negative integers are smaller than 1, any negative integer value for x will fulfill the condition x ≤ 1. For example, if we take x = -1, -2, -3, and so on, they are all less than or equal to 1, thereby satisfying the inequality.

Moreover, there are infinitely many negative integers (-1, -2, -3, and so on), meaning that there is no limit to the number of negative integer solutions that satisfy x ≤ 1. Hence, the inequality has infinitely many negative integer solutions.

On the other hand, the inequalities "x > 5" and "0 < x" do not have infinitely many negative integer solutions. "x > 5" implies that x must be greater than 5, excluding negative integers. "0 < x" states that x must be greater than zero, also excluding negative integers. Finally, "x ≥ 8" requires x to be greater than or equal to 8, which again does not include negative integers.

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Step-by-step explanation:

SIn      S-O-H

sin is   opposite leg / hypotenuse

sin Φ = 20/29 =.69

Answer:

y = 2x + 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 0) and (x₂, y₂ ) = (0, 8) ← 2 points on the line

m = [tex]\frac{8-0}{0-(-4)}[/tex] = [tex]\frac{8}{0+4}[/tex] = [tex]\frac{8}{4}[/tex] = 2

the line crosses the y- axis at (0, 8 ) ⇒ c = 8

y = 2x + 8 ← equation of line

Answer:

a) .38 × 2,450 = 931 people buy the local newspaper.

b) 2,450 - 931 = 1,519 people do not buy the local newspaper.

Answer:

All Real Number

Step-by-step explanation:

5x + 3(x - 5) = 6x + 2x - 15

5x + 3x - 15 = 8x - 15

8x - 15 = 8x - 15

-15 = -15

Since the -15 = -15, the equation will always be true for any value of x.

So, the answer is All Real Number.

The side length of the cube is [tex]s = \sqrt[3]{V}[/tex]

From the question, we have the following parameters that can be used in our computation:

V = s³

Where

Using the above as a guide, we have the following:

V = s³

Take the cube root of both sides

[tex]s = \sqrt[3]{V}[/tex]

Hence, the side length of the cube is [tex]s = \sqrt[3]{V}[/tex]

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The probability that 80 customers will arrive during tomorrow's morning rush is approximately 0.0629, rounded to 4 decimal places.

To find the probability that 80 customers will arrive during tomorrow's morning rush, we can use the Poisson distribution. The Poisson distribution is commonly used to model the number of events that occur in a fixed interval of time or space.

In this case, the average number of customers per hour is given as 75. The Poisson distribution is defined by a single parameter, λ (lambda), which represents the average rate of the event occurring in the given interval.

To calculate the probability, we can use the formula:

P(x; λ) = (e^(-λ) * λ^x) / x!

where P(x; λ) represents the probability of x events occurring given the average rate λ.

In this case, x = 80 and λ = 75. Plugging these values into the formula, we get:

P(80; 75) = (e^(-75) * 75^80) / 80!

Calculating this expression using a calculator or software, we find that P(80; 75) ≈ 0.0629.

The probability that 80 customers will arrive during tomorrow's morning rush is approximately 0.0629, rounded to 4 decimal places.

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Let's break down the calculation into several steps.

1. First, we will calculate the amount of interest that accrued over the 3 years that Boris was in school. This will be calculated using the formula for simple interest, which is:

   I = PRT,

   where:

   I is the interest,

   P is the principal amount (the initial amount of money),

   R is the rate of interest per period, and

   T is the time the money is invested for.

2. Next, we will add this accrued interest to the initial loan amount to find out how much Boris owes when he starts repaying the loan.

3. Finally, we will calculate the monthly payments Boris has to make. This will be calculated using the formula for an amortizing loan, which takes into account both the principal and the interest on the loan. The formula for the monthly payment of an amortizing loan is:

   M = P[r(1 + r)^n] / [(1 + r)^n – 1],

   where:

   M is your monthly payment,

   P is the principal loan amount,

   r is your monthly interest rate (annual interest rate divided by 12),

   n is the number of payments (the number of months you will be paying the loan).

Let's do these calculations.

1. Calculate the accrued interest over the 3 years in school:

   I = PRT

   I = $15,485 * 6.6/100 * 3

   I = $3060.57

2. Calculate the total amount owed at the start of repayment:

   Total = Principal + Interest

   Total = $15,485 + $3060.57

   Total = $18,545.57

3. Calculate the monthly payments:

   First, convert the annual interest rate to a monthly rate:

   r = 6.6% / 12 / 100 = 0.0055 per month

   Then, use the formula for the monthly payment of an amortizing loan:

   M = $18,545.57 * [0.0055(1 + 0.0055)^120] / [(1 + 0.0055)^120 – 1]

   M = $210.83

So, Boris will have to make monthly payments of approximately $210.83 for 10 years after he graduates.

Answer: The formula in factored form is h(t) = (t - 5)(t - 11). The true statements are B and D.

Step-by-step explanation: To rewrite the formula in factored form, we need to find two numbers that multiply to 55 and add to -16. These numbers are -5 and -11. So, we can write:

h(t) = t^2 - 16t + 55 h(t) = (t - 5)(t - 11)

This means that the swimmer’s depth is zero when t = 5 or t = 11. These are the times when the swimmer dives into the water and comes back up, respectively. So statement B and D are true.

To find the maximum depth of the swimmer, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:

x = -b/2a x = -(-16)/2(1) x = 8

The y-coordinate of the vertex is given by:

y = h(8) y = (8 - 5)(8 - 11) y = (-3)(-3) y = 9

So the maximum depth of the swimmer is 9 feet, not 16 feet. Therefore, statement A is false.

Statement C is also false because the swimmer comes back up at t = 11, not t = 16.

Statement E is also false because the function shows that the swimmer dives into the water only once, not twice. The function has only two zeros, which correspond to the times when the swimmer enters and exits the water.

Hope this helps, and have a great day! =)

There are 14,000 different ways for Diane to choose the squares for her quilt.

we want to find the number of ways Diane can choose the squares for her quilt, we can use the concept of combinations.

Diane needs to choose three squares with a yellow undertone, two squares with a blue undertone, and four squares with a white undertone. She has six squares with a yellow undertone, five squares with a blue undertone, and eight squares with a white undertone to choose from.

The number of ways to choose the squares for each color can be calculated using combinations:

To calculate the total number of ways to choose the squares for the quilt, we multiply the number of ways for each color together:

Total number of ways = 20 * 10 * 70 = 14,000

there are 14,000 ways for Diane to choose the squares for her quilt.

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Miguel originally put $728 into his bank account at a rate of 4% annually

An equation is an expression that shows how numbers and variables are related to each other.

Let r represent the interest rate. Between successive years, Miguel money increased from $757.12 to $787.40. Hence:

Interest rate = $787.40 / $757.12 = 1.04

The interest rate = 4% annually.

Let x represent the money Miguel had initially, hence:

x * 1.04 = $757.12

x = $728

Miguel originally put $728 into his bank account

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Answer: 43

Step-by-step explanation:

Look at the graph when 0 coupons are sold - the line is at about 45. The closest answer to that is 43.

Answer:

f(g(x)) = x + 11

g(f(x)) = √(x² + 11)

Step-by-step explanation:

f(x) = x² + 5

g(x) = √(x + 6)

f(g(x)) = f(√(x + 6))

= (√(x + 6))² + 5

= x + 6 + 5

f(g(x)) = x + 11

g(f(x)) = g(x² + 5)

= √(x² + 5 + 6)

g(f(x)) = √(x² + 11)

9. How does g(x) differ from the graph of f(x): A. the graph translates to the right 1 unit.

10. How does g(x) differ from the graph of f(x): A. the graph translates up 1 unit.

In Mathematics and Geometry, the translation of a graph to the right adds a number to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph up adds a number to the numerical value on the y-coordinate of the pre-image:

g(x) = f(x) + N

Question 9.

The graph of the parent exponential function [tex]f(x) = 6^x[/tex] is shifted to the right by 1 unit, in order to produce the graph of this transformed exponential function [tex]g(x) = 6^{x-1}[/tex].

Question 9.

The graph of the parent exponential function [tex]f(x) = 2^x[/tex] is shifted to the up by 1 unit, in order to produce the graph of this transformed exponential function [tex]g(x) = 2^{x}+1[/tex].

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Step-by-step explanation:

Slope intercept form is

[tex]y = mx + b[/tex]

So you need to isolate the y variable

For the first equation

[tex]2x + y = - 3[/tex]

[tex]y = - 2x - 3[/tex]

For the second equation,

[tex]y = - 3 - 2x[/tex]

Notice that this system will have infinite solutions

Answer:

P(8) = 1/9

Step-by-step explanation:

There are 9 balls, 1,2,3,4,5,6,7,8,9

We want to get ball 8

P(8) = number of balls marked 8/ total number of balls

       = 1/9

Answer:

P = 1/9

Step-by-step explanation:

Probability of selecting the ball marked with 8

[tex]\sf Probability = \dfrac{Number\: of \:favorable\: outcomes }{ Total \:number\: of\: possible\: outcomes}\\\\\sf Probability = \dfrac{1 }{9}[/tex]

It will take Sarah approximately 15.9 years to pay off the loan.

To determine how long it will take Sarah to pay off the loan, we can use the formula for the number of periods required to pay off a loan:

[tex]\(n = \frac{{\log\left(\frac{{P \cdot r}}{{P - M \cdot r}}\right)}}{{\log(1 + r)}}\)[/tex]

Where:

n is the number of periods (in this case, the number of months)

P is the principal amount (loan amount), which is $300,000

r is the monthly interest rate, which is 0.525% or 0.00525 (expressed as a decimal)

M is the monthly payment, which is $1,925

Substituting the values into the formula, we have:

[tex]\(n = \frac{{\log\left(\frac{{300,000 \cdot 0.00525}}{{300,000 - 1,925 \cdot 0.00525}}\right)}}{{\log(1 + 0.00525)}}\)[/tex]

Using a calculator to evaluate the logarithms and perform the division, we find that [tex]\(n \approx 190.6\)[/tex] months.

Since we are asked to determine the time to the nearest tenth of a year, we divide 190.6 by 12 to convert it into years:

[tex]\(\frac{{190.6}}{{12}} \approx 15.9\) years[/tex]

Therefore, it will take Sarah approximately 15.9 years to pay off the loan.

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Title: The Number of Coins That Teachers Carry with Them

Research Report

1. Research Question: What is the average number of coins carried by teachers?

2. Data Source: The data will be collected directly from teachers in a sample group.

3. Data Collection Instrument: A survey questionnaire will be used to collect the necessary data. The questionnaire will contain questions about the number of coins carried by teachers on a regular basis.

4. Data Type: Numerical data will be obtained, specifically discrete data.

5. Instrument Questions:

a) How many coins do you carry with you on a daily basis?

b) What is the highest number of coins you have carried with you?

6. Completed Instrument: Please find the attached completed survey questionnaire.

7. Data Collection: Data will be gathered from a sample of 20-25 respondents using the survey questionnaire.

8. Tally Marks and Data Table:

Number of Coins Tally

1

2

3

4

5

6

7

8

9

10

Step 2: Representing Data

9. The graph that best represents the data collected would be a bar graph. A bar graph is suitable for displaying discrete numerical data, such as the number of coins carried by teachers. It allows for easy visualization and comparison of the frequencies of different coin quantities.

Graph:

 |          

 |  |        

 |  ||    |  

 |  |||   |  

 |  ||||  |  

 |  ||||  |  

 |  ||||  |  

 |  ||||  |  

 |  ||||  |  

-----+--------+-----

1 5 10 15 20

10. Questions for Interpreting the Graph:

a) What is the most common number of coins carried by teachers?

b) How many teachers carry more than five coins with them?

11. Interpretation:

Based on the bar graph, it can be observed that the most common number of coins carried by teachers is around 4. Additionally, approximately 10 teachers carry more than five coins with them. This information provides insights into the typical coin-carrying habits of teachers within the sample group.

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The expression that represents the total amount of change Alexis should receive is:

20 - 3x

Cereals are the grains belonging to the grain family. Wheat, rice, corn, millet, rye, and many others. These are rich in carbohydrates.

The cereals most commonly cultivated are wheat, rice, rye, oats, barley, corn (maize), and sorghum.

The expression that represents the total amount of change Alexis should receive is:

20 - 3x

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Answer:

A. 20 – 3x

Step-by-step explanation:

To solve for s in P = b + 2s, we need to isolate s on one side of the equation.

We can do this by subtracting b from both sides of the equation:

P - b = 2s

Then, we can divide both sides by 2:

(P - b) / 2 = s

Therefore, s = (P - b) / 2.

Answer: x^4 - 2x^2 - 24

Answer:

y = 16

Step-by-step explanation:

y = 3x - 2 ← substitute x = 6

y = 3(6) - 2 = 18 - 2 = 16

The simplified equation 1,0008 = 10w can be represented as 1024 = 10w, and we can determine that w is equivalent to 24 by comparing the exponents. This implies that the value of w required to make the equation true is 24.

To simplify the equation[tex]1,000^{8}[/tex]= [tex]10^{w}[/tex], we need to recognize that 1,000 is equal to [tex]10^{3}[/tex]. Therefore, we can rewrite the equation as [tex](10^{3})^{8}[/tex] = [tex]10^{w}[/tex]

Using the property of exponents, when raising a power to another power, we multiply the exponents. Applying this property, we get [tex]10^{3*8}[/tex] = [tex]10^{w}[/tex].

Simplifying further, we have [tex]10^{24}[/tex] = [tex]10^{w}[/tex].

In order for two exponential expressions to be equal, their bases must be the same. In this case, both bases are 10. Therefore, we can conclude that the exponents must also be equal.

Hence, w = 24.

The simplified equation 1,000^8 =[tex]10^{w}[/tex]can be expressed as [tex]10^{24}[/tex] = [tex]10^{w}[/tex], and by comparing the exponents, we find that w is equal to 24. This means that the value of w that makes the equation true is 24.

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