a company produces steel rods. the lengths of the steel rods are normally distributed with a mean of 107.7-cm and a standard deviation of 0.7-cm. find the probability that the length of a randomly selected steel rod is less than 107.7-cm. p(x < 107.7-cm)

The range of possible box heights, h, is from 0 to 1.4 ft.

Let's assume that the height of the box is h feet, then the volume of the box can be given as V = 2.5h. Since the maximum volume is restricted to 3.5 ft^3, we can write:

2.5h ≤ 3.5

h ≤ 1.4

Therefore, the maximum height of the box is 1.4 ft.

To find the minimum height, we need to consider the base area of the box, which is 2.5 ft^2. Let's assume the base has a length l and width w. Since the area is fixed at 2.5 ft^2, we can write:

l × w = 2.5

We need to minimize the height of the box, so we need to maximize the length and width of the base. Since the base area is fixed, the maximum length and width will occur when l = w = √2.5 ft (square root of 2.5).

Therefore, the minimum height of the box can be found as:

h = V/(lw) = 2.5/(√2.5)^2 = 2.5/2.5 = 1 ft.

Thus, the range of possible box heights, h, is from 0 to 1.4 ft.

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Answer: least to greatest

-13, -9, -8.1, -8, -7.9, -7, -3, 0, 3, 7, 7.9

Answer:

$500

Step-by-step explanation:

100-12=88

88/100=440/x

88x=100(440)

88x=44000

/88.  /88

x=500

hopes this helps

Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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Answer:

Solving for x

5x - 9 = 3x + 7

subtract 3x from both sides

-3x          -3x

2x - 9 = 7

get rid of constants by adding 9 on both sides since addition is the inverse operation of subtraction

+9      +9

2x = 16

divide by 2 since that is the inverse operation of multiplication

/2    /2

x = 8

The solution for ''x'' for the expression ( 5x – 9 = 3x + 7

Expressions can be evaluated, meaning that they can be simplified to a single value. The value of an expression depends on the values of any variables or numbers within the expression.

To solve for x in equation 5x - 9 = 3x + 7, we want to isolate x on one side of the equation. We can do this by performing the same operation on both sides of the equation, in order to keep the equation balanced.

First, we can simplify both sides of the equation by combining like terms:

5x - 9 = 3x + 7

2x - 9 = 7

Next, we can add 9 to both sides of the equation to isolate the variable term:

2x = 16

Finally, we can divide both sides of the equation by 2 to get the value of x:

x = 8

Therefore, the solution to the equation 5x - 9 = 3x + 7 is x = 8.

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J = (3,0)

K = (3,negative two)

L = [ 0, negative two]

I apologise for the way this is set out, half of the keys on my laptop do not work

Answer:

J- (3,0)

K- (3,-2)

L- (1,-2)

Reasoning- Just move the points to where it's asking.

Answer:

The perimeter of QRST is 20 ft.

Step-by-step explanation:

Trapizeod EFGH is equal to QRST so that means their permiters are the same.

If the perimeter for EFGH is 20 ft (5 + 4 + 3 +8) so then QRST is 20 ft too. Hope this helps. :)

The temperature at which ΔrG° = 0.00 kJ is 1,596 K.


We know that:

ΔrG° = ΔrH° - TΔrS°

where ΔrG° is the standard free energy change of the reaction, ΔrH° is the standard enthalpy change of the reaction, ΔrS° is the standard entropy change of the reaction, and T is the temperature.

For ΔrG° to equal 0.00 kJ, we can rearrange the equation to solve for T:

T = ΔrH°/ΔrS°

Plugging in the values we have:

T = (2112 kJ)/(132.9 J/K)
T = 1,596 K

Therefore, the temperature at which ΔrG° = 0.00 kJ is 1,596 K.

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Answer: 4

Step-by-step explanation: If Caleb starts with 4 and subtracts 6, he'll get -2. -2 times 2, equals -4. If he starts with 4 and subtracts 8, he'll again end up with -4, meaning the original number is 4!

4-6= (-2)

-2*2= (-4)

4-8= (-4)

Answer:

Step-by-step explanation:

i can't solve without seeing the prism

Answer:

-4,747

Step-by-step explanation:

PEMDAS (1. parentheses, 2. exponents, 3. multiplication, 4. division, 5. addition, and 6. subtraction)

Parentheses: NONE

Exponents: NONE

Multiplication: 5446 x 435 = 2,369,010

Division: 2,369,010 / 890 = 2661.80899 (rounding too 2662)

Addition: 2662 + 246 = 2908

Subtraction: 2908 - 7655 = -4,747

To measure the volume of an irregular-shaped object, you can use the water displacement method, geometric approximation, or advanced techniques like 3D scanning technology.

To measure the volume of an irregular-shaped object, you can use one of several methods depending on the object's characteristics. Here are a few common approaches:

1. Water Displacement Method:

  - Fill a container with water and measure the initial volume (V1) of the water.

  - Carefully place the irregular object into the container, ensuring it is fully submerged.

  - The object will displace a volume of water equal to its own volume.

  - Measure the final volume (V2) of the water and subtract the initial volume (V1) to determine the volume of the object.

  Volume of the object = V2 - V1

2. Graduated Cylinder Method:

  - If the irregular object is small enough, you can use a graduated cylinder filled with a liquid (such as water) instead of a large container.

  - Carefully lower the object into the graduated cylinder, ensuring it is fully submerged.

  - Read the initial volume of the liquid in the graduated cylinder.

  - Measure the final volume of the liquid after adding the object.

  - The difference between the initial and final volume indicates the volume of the object.

3. Geometric Approximation:

  - If the irregular object has a shape that closely resembles a known geometric shape (e.g., a cone, cylinder, or box), you can approximate its volume using the appropriate formula for that shape.

  - Measure the relevant dimensions of the object, such as height, base radius, or length, depending on the shape.

  - Calculate the volume using the appropriate formula for the geometric shape.

4. 3D Scanning Technology:

  - Advanced techniques involve using 3D scanning technology to create a digital model of the irregular object.

  - Specialized software can then calculate the volume based on the digital model.

It's important to note that the accuracy of these methods depends on the precision of the measurements and any assumptions made in the process. Select the method that suits your object and available resources best, considering factors such as size, material, and the desired level of accuracy.

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From the graph, we can see that the graph crosses the y-axis at (0,-3) Hence, the correct answer is A (0,3).

The intersection of the graph of the function with the y-axis gives the y-intercept of that function.

The y-intercept is the value of y on the y-axis at which the considered function intersects it.

Assume that we've got: y = f(x)

At y-axis, we've got x = 0, so putting it will give us the y-intercept.

Thus, y-intercept of y = f(x) is y = f(0)

The y-intercept is where a line crosses the y-axis, so this is the point where x = 0.

From the graph, we can see that the graph crosses the y-axis at (0,-3)

Hence, the correct answer is A (0,3).

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Answer:

x=-6

Step-by-step explanation:

6(x+3)+8=-10

6x +18+8=-10

6x+26=-10

-26 -26

6x= -36

÷6 ÷6

x=-6

Answer:

The answer is 2

Step-by-step explanation:

just subtract the powers of 10 and 8.

Answer:

Factors of 105 are the list of integers that can be evenly divided into 105. There are overall 8 factors of 105 among which 105 is the biggest factor and 1, 3, 5, 7, 15, 21, 35, and 105 are positive factors. The sum of all factors of 105 is 192 and its factors in Pairs are (1, 105), (3, 35), (5, 21), and (7, 15).

Factors of 105: 1, 3, 5, 7, 15, 21, 35 and 105

Negative Factors of 105: -1, -3, -5, -7, -15, -21, -35 and -105

Prime Factors of 105: 3, 5, 7

Prime Factorization of 105: 3 × 5 × 7 = 3 × 5 × 7

Sum of Factors of 105: 192

Step-by-step explanation:

To calculate the factors of 105, we can use the division method. Let's start with 1.

105 ÷ 1 leaves remainder 0.

Since 105 is not an even number, 2 does not divide 105 completely. Thus, it leaves a remainder.

105 ÷ 3 leaves remainder 0.

105 ÷ 5 leaves remainder 0.

105 ÷ 7 leaves remainder 0.

105 ÷ 15 leaves remainder 0.

105 ÷ 21 leaves remainder 0.

105÷ 35 leaves remainder 0.

105 ÷ 105 leaves remainder 0.

Thus, the factors of 105 that we have obtained are 1, 3, 5, 7, 15, 21, 35, and 105.

Explore factors using illustrations and interactive examples

Factors of 75: The factors of 75 are 1, 3, 5, 15, 25 and 75

Factors of 175: The factors of 15 are 1, 3, 5, and 15.

Factors of 35:  The factors of 35 are 1, 5, 7, and 35.

Factors of 70: The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

Factors of 42: The factors of 1, 2, 3, 6, 7, 14, 21, and 42.

It (B) cannot be determined that there is a statistically significant difference between Mr. Goodman's ratings and those of the History Department in the context of Mr. Goodmain and with all the material provided.

In statistics, a simple random sample (or SRS) is a subset of people (a sample) picked at random from a larger group of people (a population), all with the same probability.

It is a method of choosing a sample at random. Each subset of k people in SRS has the same chance of getting selected for the sample as any other subset of k people.  

An objective sampling strategy is a straightforward random sample. Simple random sampling is a fundamental kind of sampling that can be used in combination with other, more sophisticated sampling techniques.

So, in the given situation of Mr. Goodmain and with all the information given we can conclude that it cannot be concluded that there is a statistically significant difference in Mr. Goodman’s evaluations and the History Department’s.

Therefore, it (B) cannot be determined that there is a statistically significant difference between Mr. Goodman's ratings and those of the History Department in the context of Mr. Goodmain and with all the material provided.

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Complete question:

Students at a high school are asked to evaluate their experience in the class at the end of each school year. The courses are evaluated on a 1-4 scale – with 4 being the best experience possible. In the History Department, the courses typically are evaluated at 10% 1’s, 15% 2’s, 34% 3’s, and 41% 4’s. Mr. Goodman sets a goal to outscore these numbers. At the end of the year, he takes a random sample of his evaluations and finds 11 1’s, 14 2’s, 47 3’s, and 53 4’s. At the 0.05 level of significance, can Mr. Goodman claim that his evaluations are significantly different than the History Departments?

Hypotheses:

H0: There is (no difference /difference) in Mr. Goodman’s evaluations and the History Department’s.

H1: There is (no difference /difference) in Mr. Goodman’s evaluations and the History Department’s.

Enter the test statistic - round to 4 decimal places.

Enter the p-value - round to 4 decimal places.

Can it be concluded that there is a statistically significant difference between Mr. Goodman’s evaluations and the History Department’s?

a. Yes

b. No

Answer:

66

Step-by-step explanation:

Answer: x= -1

Step-by-step explanation:

\(3\left|2x+2\right|-2x=x+3\\\)

Next, we find Positive and Negative Intervals!

\(x < -1,\:\:x\ge \:-1\)

Then Last we Solve The inequality for each interval.

No Solution or x= -1

Based on the given conditions, Jane has $31, Kevin has $25, and Hans has $50 in their wallets.

Let's solve the problem step by step.

First, let's assume that Jane has X dollars in her wallet. Since Kevin has $6 less than Jane, Kevin would have X - $6 dollars in his wallet.

Next, we're given that Hans has 2 times what Kevin has. So, Hans would have 2 * (X - $6) dollars in his wallet.

According to the information given, the total amount of money they have in their wallets is $106. We can write this as an equation:

X + (X - $6) + 2 * (X - $6) = $106

Simplifying the equation:

4X - $18 = $106

4X = $124

X = $31

Now we know that Jane has $31 in her wallet.

Substituting this value into the previous calculations, we find that Kevin has $31 - $6 = $25 and Hans has 2 * ($25) = $50.

To find the total amount they have, we sum up their individual amounts:

Jane: $31

Kevin: $25

Hans: $50

Adding these amounts together, we get $31 + $25 + $50 = $106, which matches the total amount stated in the problem.

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The complete question is:

Jane, kevin and hans have a total of $106 in their wallets. kevin has $6 less than Jane. hans has 2 times what kevin has. how much do they have in their wallets?

The slope of the line is 0.393.

Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").

Given,

A data set has an r- value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772.

We'll use the following formula for slope if the r- value (or Pearson's coefficient) and the standard deviations of the x and y coordinates are provided:

m = 8ₓ/8ₐ

where m is the slope of the best-fit line.

8ₓ = Standard deviation of the x-coordinates is 5.591,

8ₐ =  the standard deviation of the y-coordinates is 2.772.

Slope is:

m = 8ₐ/8ₓ

m = (0.793)(2.772)/5.591

m = 0.393

The slope of the line is 0.393.

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The fraction of the cabins that have windows is 29 / 80.

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a portion or section taken from a whole, which can be any number, a certain amount, or an object.

Given that there are 80 cabins on a ship. 29 of the cabins have windows. The ratios of the cabins that have windows will be calculated below.

Fraction = ( Number of windows) / ( Number of the cabins)

Fraction = 29 / 80

Hence, the proportion of cabins with windows is 29/80.

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The estimated probability that all four randomly selected young American men are 68 inches or shorter is approximately 0.004 or 0.4%.

To calculate the probability that all four randomly selected young American men are 68 inches or shorter, we need to consider the probability for each individual man and multiply them together.

Let's assume that the probability of an individual young American man being 68 inches or shorter is p. Since we are selecting four men at random, the probability of each man being 68 inches or shorter is the same, and we can multiply their probabilities together.

The probability of one man being 68 inches or shorter is p. Therefore, the probability of all four men being 68 inches or shorter is p × p × p × p = p^4.

However, we are not given the specific value of p in the problem statement. If we assume that the height of young American men follows a normal distribution, we can look up the corresponding z-score for a height of 68 inches or shorter and use the standard normal distribution to estimate the probability.

For example, if we find that a height of 68 inches corresponds to a z-score of -1.0, we can use a standard normal distribution table or a calculator to determine the probability of a z-score less than or equal to -1.0. Let's say this probability is approximately 0.1587.

Therefore, the estimated probability that all four randomly selected young American men are 68 inches or shorter would be (0.1587)^4 = 0.004.

Thus, the probability is approximately 0.004 or 0.4% rounded to three decimal places.

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The probability that a woman was wearing a belt given that she was also carrying a purse is 0.333 or 33.3%.

To find the probability that a woman was wearing a belt given that she was also carrying a purse, we need to use conditional probability.

We know that out of the 30 women observed, 18 were carrying purses and 6 were both carrying purses and wearing belts.

This means that the number of women carrying purses who were also wearing belts is 6.
Therefore, the probability that a woman was wearing a belt given that she was also carrying a purse is:
P(wearing a belt | carrying a purse) = number of women wearing a belt and carrying a purse / number of women carrying a purse
P(wearing a belt | carrying a purse) = 6 / 18
P(wearing a belt | carrying a purse) = 0.333
Given the information provided, we can determine the probability of a woman wearing a belt, given that she is also carrying a purse.

First, we need to find the number of women carrying a purse and wearing a belt, which is 6. There are 18 women carrying purses in total.
So, to find the probability, we will use the formula:
P(Belt | Purse) = (Number of women wearing belts and carrying purses) / (Number of women carrying purses)
P(Belt | Purse) = 6 / 18
P(Belt | Purse) = 1/3 or approximately 0.33
Therefore, the probability that a woman was wearing a belt, given that she was also carrying a purse, is 1/3 or approximately 0.33.

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Answer:

Possible - 1 and 0

.....

The candle burns at a rate of 1.25 inches per hour. This means that every hour, the length of the candle decreases by 1.25 inches until it burns down completely after 10 hours.

The rate at which the candle burns down can be calculated as the ratio of the length of the candle to the time it takes to burn down completely. In this case, the candle is 12 1/2 inches long and burns down in 10 hours.

To find the rate, we divide the length of the candle (in inches) by the time it takes to burn down (in hours):

Rate = Length / Time

Rate = 12.5 inches / 10 hours

Rate = 1.25 inches per hour

Therefore, the candle burns at a rate of 1.25 inches per hour. This means that every hour, the length of the candle decreases by 1.25 inches until it burns down completely after 10 hours.

It's important to note that the rate of burning may not be constant throughout the life of the candle, as the wax may melt more quickly towards the end when the flame is larger. However, this calculation assumes a constant rate of burning over the entire 10 hours.

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Answer:

x =  9(a+g)

Step-by-step explanation:

x/9 - g = a

Add g to each side

x/9 - g+g = a+g

x/9 = a+g

Multiply each side by 9

x/9 * 9 = 9(a+g)

x =  9(a+g)

The probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons, is approximately 0.54.

(a) The probability that the person is traveling on business is 0.7(0.5) + 0.3(0.7) = 0.56.

(b) The probability that the person is traveling for business on a privately owned plane is 0.3(0.7) = 0.21.

(c) The probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons, is given by Bayes' theorem as:

P(private plane | business) = P(business | private plane) * P(private plane) / P(business)

= (0.7 * 0.3) / (0.7 * 0.5 + 0.3 * 0.7) = 0.3 / 0.56 ≈ 0.54.

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