the amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 110 minutes and a standard deviation of 11 minutes. what is the probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes?

Answer:A

Step-by-step explanation:

The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:

θ = 7π/6

We can start by manipulating the given equation to express cscθ in terms of cscx:

2 csc x = 3 csc θ − csc θ sin θ

2/cscθ = 3 - sinθ

cscθ/2 = 1/(3 - sinθ)

cscθ = 2/(3 - sinθ)

Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:

1/cosθ = 2/(3 - sinθ)

cosθ = (3 - sinθ)/2

Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:

sin²θ + cos²θ = 1

sin²θ + [(3 - sinθ)/2]² = 1

Multiplying both sides by 4, we get:

4sin²θ + (3 - sinθ)² = 4

Expanding and simplifying, we get:

8sin²θ - 6sinθ - 8 = 0

Dividing both sides by 2, we get:

4sin²θ - 3sinθ - 4 = 0

Using the quadratic formula with a = 4, b = -3, and c = -4, we get:

sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))

sinθ = [3 ± √49]/8

sinθ = (3 ± 7)/8

Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8

= -1/2 corresponds to an angle of 7π/6 in the third quadrant.

To find cosθ, we can use the identity sin²θ + cos²θ = 1:

cosθ = ±√(1 - sin²θ)

Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:

cosθ = -√(1 - (-1/2)²)

cosθ = -√(3/4)

cosθ = -√3/2

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The rearranged expression will be equal to y = (-5/4)x + 2.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given expression will be rearranged as below:-

−5x−4y=−8

Solve the above expression for the value of y and the x variable will become independent.

−5x−4y=−8

Take -5x to the right side of the equation.

-4y = 5x - 8

Divide the equation by -4.

y = ( -5 / 4 )x + 2

Therefore, the rearranged expression will be equal to y = (-5/4)x + 2.

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Answer:

\(\frac{n}{6}\) - 1

Step-by-step explanation:

whenever the word than is there (less than, greater than) you have to switch the order so it the words 1 was first or in the beginning of the sentence but since the words less than are there, 1 goes toward the end or after the quotient of a number n and 6.

Answer:

1/4 of the way

(a quarter of the way)

Answer:

1=original image before transformation

2=shape or object that has been transformed

3=change made to shape or object

4=the mirror line

5=transformation in which figure flipped over line

Step-by-step explanation:

Answer:

1. pre-image the original shape or object that is being transformed

2. image is a shape or object that has been transformed

3. transformation is a change made to a shape or object.

4. line of reflection is the mirror line; the line across where a figure is flipped

5. reflection is a transformation in which the figure is flipped  over a line to give a mirror image of the original figure

Step-by-step explanation:

The probability of the arrow landing on an odd number is the number of odd numbers divided by the total number of possible outcomes. Therefore, the probability of the arrow landing on an odd number is  0.5 or 50%.


To find the probability that the arrow will point at an odd number on a circular board with 8 equal parts, we'll first determine the total number of odd numbers present and then divide that by the total number of possible outcomes.

Step 1: Identify the odd numbers on the board. They are 1, 3, 5, and 7. The game consists of spinning the arrow on a circular board with 8 equal parts, which means there are 8 possible outcomes or numbers. Since we want to know the probability of landing on an odd number, we need to count how many odd numbers are on the board. In this case, there are four odd numbers: 1, 3, 5, and 7.

Step 2: Count the total number of odd numbers. There are 4 odd numbers.

Step 3: Count the total number of possible outcomes. Since the board is divided into 8 equal parts, there are 8 possible outcomes.

Step 4: Calculate the probability. The probability of the arrow pointing at an odd number is the number of odd numbers divided by the total number of possible outcomes.

Probability = (Number of odd numbers) / (Total number of possible outcomes)
Probability of landing on an odd number = Number of odd numbers / Total number of possible outcomes
Probability of landing on an odd number = 4 / 8

Step 5: Simplify the fraction. The probability of the arrow pointing at an odd number is 1/2 or 50%.

So, the probability that the arrow will point at an odd number is 1/2 or 50%.

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Answer:

Waves superimpose upon each other when they collide, while objects do not

Step-by-step explanation:

The main difference between the collision of waves and the collision of objects is simply the superposition principle.

When waves collide, they do not do so in the same way objects do. The superposition principle explains that waves can either collide in a constructive or destructive manner.

Case A: Waves colliding in a constructive manner

When waves collide in a constructive manner, this means that they are in phase, in simpler terms, it means that they have the same shape as they move through space-time. Constructive collision leads to a formation of a bigger wave with a higher amplitude. This is how stereo speakers operate. They produce louder sounds by releasing the same audio waves, causing them to superimpose upon each other.

Case B: Waves colliding in a destructive manner:

When waves are out of phase(i.e do not have the same shape as they move through space-time) and they collide, they try to cancel each other out, leading to a new wave with a weaker amplitude. This is how noise-cancelling headphones work. They emit an equal and opposite wave sound to the noise around your ears, thus cancelling it out.

Let the common root is ‘x’

Let the common root is ‘x’x2 + ax + b = 0 ……(1)

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1⇒ x = 1

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1⇒ x = 1⇒ {1 + a + b = 0} (From equation (1))

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1⇒ x = 1⇒ {1 + a + b = 0} (From equation (1))⇒ a + b = –1

Cevap:

450 kilogram

Adım adım açıklama:

Verilen:

Toplam ton elma = 3/5 ton

Totka tonundan satılan elma oranı = 1/4

Bu nedenle, satılan ton cinsinden elma miktarı:

(1/4) * toplam elma tonu

(1/4) * (3/5)

= 3/20 ton

Bu nedenle, kalan elma miktarı şöyle olacaktır:

Toplam elma tonu - satılan elma tonu

3/5 - 3/20

(12 - 3) / 20 = 9/20 ton

Dolayısıyla kalan elma sayısı = 9/20 ton

Tonları kg'a çevirmek:

9/20 ton * 1000 = 9 * 50 = 450 kilogram

Answer:

Step-by-step explanation:

2115

Answer:

456 is the answer

Step-by-step explanation:

(4y(5))^2+9z(7)-7

Answer:

0.052589 day

Step-by-step explanation:

Step 1: Find conversion

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

Step 2: Use Dimensional Analysis

\(4567 \hspace{2} s(\frac{1 \hspace{2} min}{60 \hspace{2} sec} )(\frac{1 \hspace{2} hr}{60 \hspace{2} min} )(\frac{1 \hspace{2} day}{24 \hspace{2} hr} )\) = 0.052589 day

1. The scale factor is 2

2. angle C is 67.47 degrees

3. angle Z is 75.56 degrees

4. 6 units

The scale factor is calculated used reference points and comparing the points

Using WZ  = 3 units and AD = 6 units, let the scale factor be k

WZ * k = AD

3 * k = 6

k = 2

Angle C corresponds to angle XYZ = 67.47 degrees

Angle Z corresponds to angle CDA = 75.56 degrees

Side AD is gotten by counting the number of units in the x direction and this is 6 units

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Measures of central tendency, measures of variation, and crosstabulation are all types of descriptive statistics.

Descriptive statistics summarize and describe the main features of a data set, including the typical or central values (measures of central tendency) and the spread or variability of the data (measures of variation). Crosstabulation, also known as contingency tables, is a way to summarize the relationship between two variables by displaying their frequency distributions in a table format.
Measures of central tendency, measures of variation, and crosstabulation are types of descriptive statistics. Descriptive statistics are used to summarize and describe the main features of a dataset in a simple and meaningful way.

Central tendency refers to the measures that help identify the center or typical value of a dataset, such as mean, median, and mode. Variation measures describe the spread or dispersion of data, including range, variance, and standard deviation. Crosstabulation is a method of organizing data into a table format to show the relationship between two categorical variables.

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The dimensions of the box that will have the greatest volume are:

Length and width of the base: 2√3 feet

Height: h = (36 - x^2) / 8x = (√3)/2 feet

Let the length and width of the base be x, and let the height be h.

The surface area of the top is x^2, and the surface area of the remaining four sides is \(2(xh + xh) = 4xh\).

The cost of the top is \(x^2\), and the cost of the remaining four sides is \(2(4xh) = 8xh\). Therefore, the total cost is:

\(C(x,h) = x^2 + 8xh\)

We know that the total cost is $36, so we have:

\(x^2 + 8xh = 36\)

Solving for h, we get:

\(h = (36 - x^2) / 8x\)

The volume of the box is given by:

\(V(x,h) = x^2h\)

Substituting h in terms of x, we get:

\(V(x) = x^2 ((36 - x^2) / 8x)\)

Simplifying, we get:

\(V(x) = (1/8) x (36x - x^3)\)

To find the dimensions of the box that will have the greatest volume, we need to find the value of x that maximizes V(x). We can do this by taking the derivative of V(x) with respect to x, setting it equal to 0, and solving for x:

\(V'(x) = (1/8) (36 - 3x^2) = 0\)

Solving for x, we get:

x = 2√3

Therefore, the dimensions of the box that will have the greatest volume are:

Length and width of the base: 2√3 feet

Height: \(h = (36 - x^2) / 8x\) = (√3)/2 feet

The volume of the box is:

\(V = x^2h\)= (2√3)^2 ((√3)/2) = 9√3 cubic feet

Note: To confirm that this value represents the maximum volume, we can check that V''(x) < 0, which indicates a maximum point. We have:

\(V''(x) = (1/8) (-6x) = -3x/4\)

At x = 2√3, V''(x) = -3(2√3)/4 = -3√3/2 < 0, so this is indeed a maximum point.

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The answer is O 0.260.

To find the probability of rolling two 5's when 8 fair six-sided dice are thrown, we can use the binomial probability formula. The probability of rolling a 5 on one die is 1/6, and the probability of not rolling a 5 on one die is 5/6. We want to find the probability of getting exactly two 5's, which can happen in different ways. We can roll a 5 on the first die and another 5 on the second die, or we can roll a 5 on the second die and another 5 on the third die, and so on. Therefore, the probability of getting exactly two 5's is:

P(X = 2) = (8 choose 2) * (1/6)^2 * (5/6)^6

where (8 choose 2) is the number of ways to choose 2 dice out of 8, which is equal to 28. Using a calculator, we get:

P(X = 2) ≈ 0.260

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Answer:

The best answer would actually be C

:According to the question:You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium.

During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population.

According to the Hardy-Weinberg equilibrium equation p² + 2pq + q² = 1, the frequency of D (p) and d (q) alleles are:p + q = 1Thus, the frequency of q is 0.4. Here are the calculations for the Hardy-Weinberg equilibrium:p² + 2pq + q² = 1(0.6)² + 2(0.6)(0.4) + (0.4)² = 1After simplifying, it becomes:0.36 + 0.48 + 0.16 = 1This means that the population is in Hardy-Weinberg equilibrium. This is confirmed as the frequencies of DD, Dd, and dd genotypes

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a. This gives the general solution to the given equation. Note that the constant of integration D can be determined by applying initial conditions if they are given. b. This gives the general solution to the given equation. The constant of integration C can be determined by applying initial conditions if they are given.

a) To solve the equation (3x^2y + 2xy + y^3) + (x^2 + y^2)y' = 0, we can use an integrating factor to simplify the equation and make it easier to solve.

The integrating factor is given by the exponential of the integral of the coefficient of y', which in this case is (x^2 + y^2). So, the integrating factor is e^(∫(x^2 + y^2) dx).

Integrating (x^2 + y^2) with respect to x, we get (1/3)x^3 + xy^2 + C(y), where C(y) is an arbitrary function of y.

Therefore, the integrating factor is e^((1/3)x^3 + xy^2 + C(y)).

Multiplying the given equation by the integrating factor, we obtain:

e^((1/3)x^3 + xy^2 + C(y)) * [(3x^2y + 2xy + y^3) + (x^2 + y^2)y'] = 0.

By simplifying and rearranging the terms, we get:

(3x^2y + 2xy + y^3)e^((1/3)x^3 + xy^2 + C(y)) + (x^2 + y^2)y'e^((1/3)x^3 + xy^2 + C(y)) = 0.

Now, we can recognize the left side of the equation as the derivative of a product. Applying the product rule, we have:

d/dx [y^3e^((1/3)x^3 + xy^2 + C(y))] = 0.

Integrating both sides with respect to x, we obtain:

y^3e^((1/3)x^3 + xy^2 + C(y)) = D,

where D is a constant of integration.

Finally, we can solve for y:

y = [D / e^((1/3)x^3 + xy^2 + C(y))]^(1/3).

This gives the general solution to the given equation. Note that the constant of integration D can be determined by applying initial conditions if they are given.

b) The equation y'e^(2x) + y - 1 can be solved using separation of variables.

First, let's rearrange the equation to isolate the terms involving y and y':

y' = (1 - y)e^(-2x).

Now, we can separate the variables and integrate both sides:

∫(1 - y) dy = ∫e^(-2x) dx.

Integrating, we get:

-y + (1/2)e^(-2x) = C,

where C is a constant of integration.

Finally, we can solve for y:

y = 1 - (1/2)e^(-2x) + C.

This gives the general solution to the given equation. The constant of integration C can be determined by applying initial conditions if they are given.

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The probability of event E, which represents the sum of the numbers showing face up on the blue and gray dice being at least 9, can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, event E consists of the outcomes {24, 36, 53, 66}, which means there are 4 favorable outcomes. The total number of possible outcomes is 36 since there are six possible outcomes for each die roll. Therefore, the probability of event E is 4/36 or 1/9.

To calculate the probability of event E, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, the event E represents the sum of the numbers on the blue and gray dice being at least 9. The favorable outcomes are the outcomes in the sample space S that satisfy this condition, namely {24, 36, 53, 66}. There are four favorable outcomes in this case.

The total number of possible outcomes can be found by counting all the elements in the sample space S. Since each die has six sides and can show numbers from 1 to 6, there are 6 possible outcomes for each die roll. As there are two dice being rolled together, the total number of possible outcomes is 6 * 6 = 36.

To calculate the probability, we divide the number of favorable outcomes (4) by the total number of possible outcomes (36). Therefore, the probability of event E is 4/36, which can be simplified to 1/9.

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Answer:

Two times two minus eight

Answer:

C, f(x) = 3(2)^x

Step-by-step explanation:

Since the y-intercept is 3, the function will have 3 multiplying by some number to the power of x.

As x increases by 1, we notice that y multiplies by 2 every time.

This leads us to believe that the equation is 3 * 2^x

The exponential function represented by the graph is:

\(f(x) = 3(2)^x\)

It is modeled by:

\(y = ab^x\)

In which:

In the graph, there is point (0,3), hence a = 3, and it also has point (1,6), hence:

\(6 = 3b\)

\(b = 2\)

Thus, the equation is:

\(f(x) = 3(2)^x\)

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Answer:

600000

Step-by-step explanation:

Answer:

600000

Step-by-step explanation:

10000×60

10000

×     60

---------------

1

× 6

----------------  (Eliminate all the zeros and than add them to the end of 1 × 6)                                                          

   600000

-------------------

Hope this was helpful!!!!

Answer:

y=3

Step-by-step explanation:

Answer:

  2.6

Step-by-step explanation:

A is after the 6th of 10 spaces between 2 and 3. It has the value 2 +6/10 = 2.6.

Answer: The polygon has 18 sides.

Answer:

False

Step-by-step explanation:

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Answer:

number 1 is 5x 1/2 the others I'd not know