What are m∠1 and m∠2?

Two triangles intersect at a single vertex. The left triangle has an interior angle measuring 80 degrees and another interior angle labeled 1. The interior angle of the vertices that intersect are unlabeled on both triangles, but the upper exterior angle measures 115 degrees. The other two interior angles in the right triangle are labeled 85 degrees and 2.
1. m∠1 = 30°, m∠2 = 35°
2. m∠1 = 35°, m∠2 = 30°
3. m∠1 = 65°, m∠2 = 60°
4. m∠1 = 85°, m∠2 = 80°

To implement the distributing principle to the phrase 7(2x+5) - 4(2x+5), we must first divide the 7 and 4 within the parenthesis to their respective terms:

7(2x+5) - 4(2x+5) = (72x + 75) - (42x + 45)

Within the parenthesis, each term is simplified:

= (14x + 35) - (8x + 20)

We may now reduce the phrase by grouping similar terms:

= 14x - 8x + 35 - 20

= 6x + 15

As a consequence, using the distributive property on 7(2x+5) - 4(2x+5) yields 6x + 15.

By expansion or multiplying, the distribution principle is frequently employed to compress statements and solve problems. It enables us to translate complicated statements into shorter language and conversely. The distributive principle is commonly utilized in mathematics, mathematics, as well as other mathematical subjects.

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The distance between the two points (-8,-1) and (-8,4) is 5 units.

The distance formula is a mathematical formula used to find the distance between two points in a two-dimensional or three-dimensional coordinate system.

The distance between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be found using the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, the two points are (-8, -1) and (-8, 4). Therefore, we can substitute the values into the formula:

d = √((-8 - (-8))² + (4 - (-1))²)

= √(0² + 5²)

= √(25)

= 5

Therefore, the distance between the two points is 5 units, so the answer is (B) 5.

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The ship is about 65.6 meters away from the base of the lighthouse.

What is tangent function ?

Tangent is one of the three primary trigonometric functions, along with sine and cosine. In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

The tangent function is denoted by "tan" and is defined mathematically as:

tan(theta) = opposite / adjacent

where theta is the angle, opposite is the length of the side opposite the angle, and adjacent is the length of the side adjacent to the angle.

According to the question:
We can use trigonometry to solve this problem. Let's draw a right triangle with the lighthouse at the top, the ship at the bottom, and the line connecting them as the hypotenuse. The angle of depression of 26° is the angle between the hypotenuse and the horizontal line passing through the lighthouse. We know the height of the lighthouse is 32 meters.

Let x be the distance between the ship and the base of the lighthouse, which is the adjacent side of the angle of depression. Then we can use the tangent function:

tan(26°) = opposite / adjacent

We know the opposite side is the height of the lighthouse, which is 32 meters. Solving for x:

x = opposite / tan(26°)

x = 32 / tan(26°)

x ≈ 65.6 meters

Therefore, the ship is about 65.6 meters away from the base of the lighthouse.

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Answer:

x = 79

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ BHC = x is an exterior angle of Δ BHD , then

x = 33 + 46 = 79

Answer: A and C

Step-by-step explanation:

angles in a triangle add up to 180

180 - 30 = 150

other two angles must add up to 150 and two of the angles have to be the same.

Since one is already 30, one of the others have to also be 30 or both of the others have to be the same.

A and C both add up to 150 and both of them have one angle repeating

The total number of units produced in an 8-hour day is approximately 22.86 units.

There are different ways to approach this problem, but one possible method is to use the concept of cycle time and the total available production time to determine the number of units produced in a day.

An operation is performed on a batch of 100 units.

Setup time is 20 minutes and run time is 1 minute.

The total number of units produced in an 8-hour day is:

Step 1: Find the cycle time per unitThe cycle time per unit is the sum of the setup time and the run time:

Cycle time = setup time + run time = 20 minutes + 1 minute = 21 minutes.

Step 2: Find the total available production time in a day

One day has 24 hours, but 8 hours are not available for production due to breaks, maintenance, and other factors. Therefore, the total available production time is:

Total available production time = 8 hours × (60 minutes per hour) = 480 minutes.

Step 3: Calculate the number of units produced in a day

The number of units produced in a day is the total available production time divided by the cycle time per unit:

Units produced = total available production time ÷ cycle time= 480 minutes ÷ 21 minutes≈ 22.86 units (rounded to two decimal places)

Therefore, the total number of units produced in an 8-hour day is approximately 22.86 units.

This assumes that there is no variability in the process, and that all units are of good quality.

If there are any defects, rework, or other disruptions, the actual production may be lower.

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Answer:

The answer to your problem is:

The sum of those given numbers in the simplest form is written as 11

The result is rational.

Difference between irrational and rational:

Irrational: Those numbers that cannot be written as a ratio of integers.

Rational: Those numbers that can be written as a ratio of integers.

[tex]\sqrt[]{4} = \sqrt{2^{2} } = 2[/tex] ( We know that )

[tex]3\sqrt{9} = 3 * \sqrt{3^{2} } = 3*3 = 9[/tex] ( Ok )

Thus: \/

[tex]\sqrt[]{4} + 3\sqrt{9} = 2+9 = 11[/tex]

Thus, the answer to your problem is,

The sum of those given numbers in the simplest form is written as 11

The result is rational.

Answer:

  4 pieces each

Step-by-step explanation:

You want to know the number of $0.10 candies each brother can buy with his equal share of Karla's $1.44.

Each column of the diagram represents $0.10, the cost of one piece of candy. Then 3 columns represent 3 pieces, or one for each brother.

We can divide the shaded area into four (4) groups of 3 columns, representing 4 pieces of candy that each brother can buy. The remaining $0.24 will be divided so that each brother will have $0.08 left over after buying 4 pieces of candy.

A sample point refers to an option (c)  individual outcome of an experiment

In probability, a sample point is a specific outcome or event that can occur in an experiment or study. It represents a single instance or realization of the random process being studied. For example, if the experiment is flipping a coin, a sample point could be "heads" or "tails". The set of all possible sample points is called the sample space.

Sample points are important in probability theory because they help determine the probability of a particular event occurring. By calculating the number of sample points that satisfy a given condition, we can determine the likelihood of that condition being met, and make predictions about the behavior of random processes.

Therefore, the correct option is (c) individual outcome of an experiment

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11x + 7y ≤ 251 this is the inequality's standard form, where the constant is on the right and the variables are on the left.

A group of two or more inequalities that must be met concurrently constitute a system of inequalities. A collection of values for the variables that simultaneously fulfil all of the inequalities is the solution to the system. The variables in the inequalities indicate quantities that are connected to one another. Systems of inequalities are used to simulate real-world circumstances when a given task is subject to a number of restrictions or limits.

Let us suppose the number of regular cups = x.

The number of small cups = y.

Thus, the total for lemonades is:

11x + 7y ≤ 251

This is the inequality's standard form, where the constant is on the right and the variables are on the left.

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The probability of making a Type I error is represented by alpha (α), which is typically set to 0.05 in hypothesis testing. Therefore, if α = .05, the likelihood of making a Type I error is 5% at most.

What is hypothesis testing? Hypothesis testing, also known as statistical hypothesis testing, is a technique used to evaluate two hypotheses about a population using sample data. One hypothesis, known as the null hypothesis (H0), proposes that there is no significant difference between a population parameter and a sample parameter, whereas the other hypothesis, known as the alternative hypothesis (H1), suggests that there is a significant difference between a population parameter and a sample parameter.You might have made a Type I error, but the probability is only 5% at most is true if you complete a hypothesis test using α = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis, but the treatment actually has no effect. In the given situation, if the treatment actually has no effect, you might have made a Type I error, but the probability is only 5% at most. When the null hypothesis is rejected when it should not be, a Type I error occurs. The probability of making a Type I error is represented by alpha (α), which is typically set to 0.05 in hypothesis testing. Therefore, if α = .05, the likelihood of making a Type I error is 5% at most.

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The probability that the series lasts exactly five games is 2p raise to the power 4(1-p).

How to find probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The higher the probability, the more likely it is that the event will occur.

To find the probability that the series lasts exactly five games, we need to consider all possible ways in which a team can win four games in five games played.

One possible scenario is that team A wins the first four games and team B wins the fifth game. The probability of this happening is:

P(A wins the first four games and B wins the fifth game) = p⁴ * (1-p)

Another possible scenario is that team B wins the first game, team A wins the next four games. The probability of this happening is:

P(B wins the first game and A wins the next four games) = p⁴* (1-p)

Therefore, the probability that the series lasts exactly five games is the sum of these two probabilities:

P(series lasts exactly five games) = p⁴* (1-p) + p⁴ * (1-p)

Simplifying the expression, we get:

P(series lasts exactly five games) = 2p⁴(1-p)

Therefore, the probability that the series lasts exactly five games is 2p⁴(1-p).

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Answer:

f(x) = x ³ shifted 4 units to the right will be g(x) = f(x-4) = (x - 4)³

Step-by-step explanation:

If a function f(x) is shifted right 4 units every x coordinate will become x - 4

g(x)  = f(x - 4) = (x - 4)³

For the number of miles driven, Company A will charge less than Company B if x<y, where x is the number of miles driven for Company A and y is the number of miles driven for Company B. Therefore, the inequality is x<y.

When comparing two companies for their charges for a specific service, it is necessary to obtain a basic understanding of the charges for each company. You can make use of the inequality operator to check when one company will charge less than the other company.

To use the inequality operator, you'll need to calculate the differences between the two companies for the specific mileage. Let's assume that the mileage is represented by "m" and that the charge for company A is "cA" and the charge for company B is "cB".

If the question only provides specific numerical values for these variables, you can substitute them into the inequality formula. If you're given algebraic expressions, you'll need to simplify them before substituting them into the inequality formula.

The inequality formula for comparing the charges is as follows: cA < cB.

To use this formula, substitute the expression for each variable.

For example: 4m + 20 < 3.5m + 35 Now, you'll need to simplify the inequality by performing algebraic operations on both sides of the inequality. Begin by subtracting 3.5m from both sides of the inequality: 0.5m + 20 < 35.

Next, subtract 20 from both sides of the inequality: 0.5m < 15 Finally, divide both sides of the inequality by 0.5: m < 30

Therefore, Company A will charge less than Company B for any mileage less than 30.

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To use the normal approximation for the confidence interval in the sampling distribution of the population proportion, the following conditions must be met:

If these conditions are met, then the distribution of the sample proportion can be approximated by a normal distribution with a mean of p and a standard deviation of sqrt(p*(1-p)/n).

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Full Question ;

The sampling distribution of the population proportion is based on a binomial distribution. What condition must be met to use the normal approximation for the confidence interval?

The perimeter of the letter "T" is 22 inches.

Since the letter "T" is formed by placing two rectangles next to each other, its perimeter is the sum of the perimeters of the two rectangles minus the shared side.

The shared side will be the width of the rectangles, which is 2 inches.

The lengths of the rectangles are 4 inches each.

Let's calculate the perimeter:

Perimeter of the top rectangle = 2 * (length + width) = 2 * (4 + 2) = 12 inches

Perimeter of the bottom rectangle = 2 * (length + width) = 2 * (4 + 2) = 12 inches

Now, subtract the shared side (width) once:

Shared side = 2 inches

Total perimeter = (Perimeter of top rectangle + Perimeter of bottom rectangle) - Shared side

Total perimeter = (12 + 12) - 2 = 22 inches

So, the perimeter of the letter "T" is 22 inches.

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The approximate value of the maximum of the function is 2350. In terms of the problem scenario this means that the company will make a maximum daily profit of $2350.

Part A:

The y-intercept is the point where the graph intersects the y-axis, which is when x = 0. Therefore, we can find the y-intercept by substituting x = 0 into the equation:

P(0) = -[tex]6(0)^2[/tex] + 180(0) + 1000

P(0) = 1000

The approximate value of the y-intercept is 1000. In terms of the problem scenario, this means that when the company doesn't increase the price of the solar panels (x = 0), the daily profit is $1000.

Part B:

The x-intercept is the point where the graph intersects the x-axis, which is when P(x) = 0. Therefore, we can find the x-intercept by solving the equation:

-[tex]6x^2[/tex] + 180x + 1000 = 0

We can use the quadratic formula to solve for x:

x = (

where a = -6, b = 180, and c = 1000

x = (-180 ± sqrt([tex]180^2[/tex] - 4(-6)(1000))) / 2(-6)

x = (-180 ± sqrt(32400 + 24000)) / (-12)

x = (-180 ± sqrt(56400)) / (-12)

x ≈ 4.4 or x ≈ 29.4

The approximate value of the x-intercept is 4.4 (or 29.4). In terms of the problem scenario, this means that the company would need to increase the price of the solar panels by approximately $22 (or $147) in order to break even and not make a profit or loss for the day.

Part C:

The maximum of the function occurs at the vertex of the parabola, which is given by the formula:

x = -b / 2a

In this case, a = -6 and b = 180, so:

x = -180 / 2(-6) = 15

To find the maximum profit, we can substitute x = 15 into the equation:

P(15) = -[tex]6(15)^2[/tex] + 180(15) + 1000

P(15) = 2350

The approximate value of the maximum of the function is 2350. In terms of the problem scenario, this means that the company will make a maximum daily profit of $2350 when they increase the price of the solar panels by $75 (i.e., 15 increments of $5).

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Answer: x 3= 27/125

Step-by-step explanation:

Therefore, the mean salary paid to the office assistants in this company is $24,000.Answer: B. $24,000

A large company has offices in two locations, one in New Jersey and one in Utah. The mean salary of office assistants in the New Jersey office is $28,500. The mean salary of office assistants in the Utah office is $22,500. The New Jersey office has 128 office assistants and the Utah office has 32 office assistants. The mean salary paid to the office assistants in this company can be calculated by taking the weighted average of the mean salaries of the two offices.
Here's the formula to calculate the weighted average:
Weighted average = (weight1 × value1 + weight2 × value2) / (weight1 + weight2)
Where weight represents the number of data points, and value represents the mean salary of office assistants.
In this question, the weight of the New Jersey office is 128, and the weight of the Utah office is 32. The value of the New Jersey office is $28,500, and the value of the Utah office is $22,500.
Now let's plug in the values:
Weighted average = (128 × 28,500 + 32 × 22,500) / (128 + 32)
= (3,648,000 + 720,000) / 160
= 24,000

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Jason is correct when he says that a graph of the relationship includes the point (63, 140).

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The relationship is defined according to the equation presented as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one, which is also the constant ratio of the relationship.

From the table given at the end of the answer, when x = 54, y = 120, hence the constant is given as follows:

k = 120/54

k = 2.2222.

Hence the equation is:

y = 2.2222x.

When x = 63, the output of the function is given as follows:

y = 2.2222 x 63

y = 140.

Hence Jason is correct when he says that a graph of the relationship includes the point (63, 140), as when x = 63, the output of the function is of y = 140.

The table is given by the image presented at the end of the answer.

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The solution of the given problem of equation comes out to be the quadratic function's expression is  [tex]y = -2x² + 8x + 3[/tex]

Variable words are commonly used in complex algorithms to show uniformity between two incompatible claims.

Academic expressions called equations are used to show the equality of various academic numbers. Instead of a unique formula that splits 12 into two parts and can be used to analyse data received from [tex]y + 7[/tex]  , normalization in this case yields b + 7.

Here,

A quadratic function's curve is shown in the provided illustration. The quadratic function's expression is

=> [tex]y = -2x² + 8x + 3[/tex]

We can use the knowledge that a quadratic function's standard form is

=>  [tex]y = ax² + bx + c[/tex]  , where a, b, and c are constants, to see this.

When y =  [tex]-2x² + 8x + 3[/tex] is provided,

we can see that a = -2, b = 8, and c = 3 by comparing it to the standard form.

Therefore, the quadratic function's expression is [tex]y = -2x² + 8x + 3[/tex]

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Answer:

[tex]26 > n + 15[/tex]

[tex]11 > n[/tex]

[tex]n < 11[/tex]

The line of reflection is the y-axis

Reflection is a geometric transformation that involves flipping an object over a line or a plane, creating a mirror image of the original object.

When a figure or polygon is reflected over the y-axis, it means that each point in the original figure is moved to a new point with the same y-coordinate but a negated x-coordinate.

Here we have

Triangle DEF has vertices at D(−3, 5), E(−10, 4), and F(−11, 8).

Triangle D′E′F′ is the image of triangle DEF after a reflection.

After reflection, the vertice E′ is located at (10, 4).  

Here the x-coordinate of E, − 10 is changed to 10  

As we know when the figure is reflected over the y-axis the sign of the x coordinate will be changes  

Hence,

The line of reflection is the y-axis

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There are 4320 ways in which at least two pairs of people from the same country are seated together.

This is question of 'permutation and combination'.

The total number of ways in which all 8 people can be seated

= (8-1)! = 7! = 5040

Let's calculate the number of ways in which no two people from the same country are seated together.

First, we will fix the position of one of the Americans (let's call him A1) in the first seat. We can do this in one way.

In the next seat, we can seat any one of the six remaining people (2nd American, 1st Canadian, 2nd Canadian, 1st Mexican, 2nd Mexican, or 1st Jamaican).

Let's say we seat the 1st Canadian in the second seat. We can do this in six ways. The seventh seat can be occupied by the remaining person. We can do this in one way.So, the number of ways in which no two people from the same country are seated together is

6! = 720.

Now, let's calculate the number of ways in which at least two pairs of people from the same country are seated together.We can do this by finding the total number of ways in which all eight people can be seated and then subtracting the number of ways in which no two people from the same country are seated together.

So, the number of ways in which at least two pairs of people from the same country are seated together is:

5040 - 720 = 4320.

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Answer:

25%

Step-by-step explanation:

U flipped a coin 12 times, it lands on tail 9 times. Now the probability of landing on head = 12-9

= 3

In percentage= 12\3 *100

=25%

Answer:

0.25%

Step-by-step explanation:

approximately Normal.

In the given problem, suppose you are going to roll a 10-sided die 50 times and record p, the proportion of times that the roll is 3 or lower. The question is asking us to determine the sampling distribution of p.The mean of p is given by: [tex]μp = 50 × 0.3 = 15[/tex]And

the standard deviation of p is given by: σp = sqrt[tex](50 × 0.3 × 0.7) = 3.24[/tex]

Therefore, the correct option is: Mean = 0.3; Standard deviation = 3.24;

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Answer:

3(2c + d) - 4(c - d) + d² = 32

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

We have to use,

→ d = 3

→ c = 1

The given expression is,

→ 3(2c + d) - 4(c - d) + d²

Let's simplify the expression,

→ 3(2c + d) - 4(c - d) + d²

→ 3(2(1) + 3) - 4(1 - 3) + 3²

→ 3(2 + 3) - 4(-2) + 9

→ 3(5) + 8 + 9

→ 15 + 17

→ 32 => {final answer}

Therefore, the answer is 32.

Thus, the least number of times the button need to be pressed is: red- 4 times, green 3 times and blue button 6 times.

The technique of expressing all numbers as the product of primes is known as prime factorization. So, let's take something like the number 20 as an example. It can be divided into two components. "Well, that's 4 times 5," we can respond. Observe that 5 is a prime number.

Given data:

The number formed as:

(x²) .(y³).(z)  ...eq 1

Number appeared on screen - 2592

Find the prime factors of 2592.

2592 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3

This can be written as:

2592 = 4² x 3³ x 2 x 3

2592 = 4² x 3³ x 6¹  .....eq 2

comparing eq 1 and 2

(x²) .(y³).(z)  =  4² x 3³ x 6¹  

x = 4, y = 3 and z = 6

Thus, the least number of times the button need to be pressed is: red- 4 times, green 3 times and blue button 6 times.

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