which point represents the vertex of the marked angle

a. a

b. e

c. c

d. b

Answer:

112

Step-by-step explanation:

the formula for area is length times width,so in this case 14×8 = the area

Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

The smallest power of 2 greater than 29.2 is 32, obtained by increasing the exponent by 1 from the largest power of 2 less than 29.2, which is 16.

A power of 2 is a number that can be expressed as 2 raised to some non-negative integer exponent. To find the smallest power of 2 greater than 29.2, we can start by finding the closest power of 2 that is less than or equal to 29.2. The largest power of 2 that is less than 29.2 is \(2^4\), which equals 16.

To find the smallest power of 2 greater than 29.2, we need to increase the exponent by 1. Therefore, the smallest power of 2 greater than 29.2 is \(2^5\), which equals 32. Since 32 is the smallest power of 2 greater than 29.2, it satisfies the given conditions.

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The section of the bar labeled x must be less than 117 for the inequality to be true.

so x < 117.

We can find the solution with linear inequalities with one unknown.

x + 9 < 126

Group all constants on the RHS of the equation

so we need to subtract the 9 from both sides of the equation.

x + 9 - 9 < 126 -9

x < 117

We can also plot the solution on a coordinate plane for this we have coordinates like (-∞, 117)

The bar graph of the inequality is shown in below here dotted line represents 126.

As in inequality show < the sign, which means the box is drawn on the left of the 126.

The bar represents x + 9. Label the bar diagram.

The section of the bar labeled x must be less than 117 for the inequality to be true.

so x < 117.

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Answer:

0

Step-by-step explanation:

5a-3=5a-3

or, 5a-5a=-3+3

or, 0=0 answer

Answer: 40 bales of hay

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

Only 4 and 5 can be considered because 6 is not included, so the probability would be 2/4, or 50%.

Answer: 50%

Step-by-step explanation: It says if you pick a random card that is less than 6 or 4. That means that 4 and 5 are the ones you hope to get. 2/4 = 50%.

1) The probability that the random variable will assume a value between 42.5 and 57.5 is 0.8664, rounded up to 4 decimals.

2) The probability that the random variable will assume a value more than 65 is 0.0013, rounded up to 4 decimals.

Using the standard normal distribution table, we need to convert the values of interest into z-scores, which represent the number of standard deviations away from the mean. The formula to calculate the z-score is:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

For the lower limit of 42.5, the z-score is:

z = (42.5 - 50) / 5 = -1.5

For the upper limit of 57.5, the z-score is:

z = (57.5 - 50) / 5 = 1.5

Using the standard normal distribution table, we can find the area under the curve between the z-scores of -1.5 and 1.5, which is 0.8664.

To answer this question, we need to find the area under the normal distribution curve to the right of the value of interest, which represents the probability of the random variable assuming a value greater than 65.

Using the z-score formula, the z-score for 65 is:

z = (65 - 50) / 5 = 3

Using the standard normal distribution table, we can find the area under the curve to the right of the z-score of 3, which is 0.0013.

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Answer:

3, 2, 2

Step-by-step explanation:

Answer:

2×2×3

Step-by-step explanation:

prime factor is a number that is a prime number. A prime number has only 2 factors, 1 and the number itself.

The prime factors of 12=2×2×3

12=2²×3

because 2×2 gives 4 and 4×3 gives 12.

and the factors are prime numbers

The flag pole is 6.8 meters tall.

Trigonometric functions are mathematical formulas that connect the angles and side lengths of a right triangle. The six trigonometric functions are sin, cos, tangent, cosec, sec, and cotangent.

Height,p of the flagpole should be calculated.

Given;

base,b=2.9m

Angle subtended=67

Using trigonomteric identity

tan67=Height/base

Tan67=h/b

Tan67=h/2.9

h=2.9tan67

h=6.8m

Height pf the flag pole is 6.8m.

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The complete question is attached below:

Using the cosine rule, the distance the plane has flown during Jack's phone call can be calculated by taking the square root of the sum of the squares of the initial and final distances, minus twice their product, multiplied by the cosine of the angle difference.

To determine the distance the plane has flown during Jack's phone call, we can use the cosine rule in trigonometry.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the initial distance from Jack to the plane as d1 and the final distance as d2.

We know that the altitude of the plane remains constant at 2400 meters.

According to the cosine rule:

\(d^2 = a^2 + b^2 - 2ab \times cos(C)\)

Where d is the side opposite to the angle C, and a and b are the other two sides of the triangle.

For the initial angle of elevation (70°), we have the equation:

\(d1^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \timescos(70)\)

Similarly, for the final angle of elevation (50°), we have:

\(d2^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \times cos(50)\)

To find the distance the plane has flown, we subtract the two equations:

\(d2^2 - d1^2 = 2 \times 2400 \times a \times (cos(70) - cos(50))\)

Now we can solve this equation to find the value of a, which represents the distance the plane has flown.

Finally, we calculate the square root of \(a^2\) to find the distance in meters.

It's important to note that the angle of elevation assumes a straight-line path for the plane's movement and does not account for any changes in altitude or course adjustments that might occur during the phone call.

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Answer:

Please check the explanation.

Step-by-step explanation:

Completing table 1)

Given the function

y = -3x+2

put x = 3

y = -3(3)+2 = -9+2 = -7

so (x, y) = (3, -7)

Given the function

y = -3x+2

put x = 1

y = -3(1)+2 = -3+2 = -1

so (x, y) = (1, -1)

Given the function

y = -3x+2

put x = 0

y = -3(0)+2 = 0+2 = 2

so (x, y) = (0, 2)

Given the function

y = -3x+2

put x = -1

y = -3(-1)+2 = 3+2 = 5

so (x, y) = (-1, 5)

So the table becomes

x            y = -3x+2          y              (x, y)

3             y = -3(3)+2        -7            (3, -7)

1             y = -3(1)+2         -1             (1, -1)

0             y = -3(0)+2        2             (0, 2)

-1           y = -3(-1)+2          5            (-1, 5)

The graph of the equation y = -3x+2 is also attached below.

On the diagram, the red line represents the y = -3x+2 line.

Similarly,

Completing table 2)

Given the function

y = 2x+4

put x = 0

y = 2(0)+4=0+4 = 4

so (x, y) = (0, 4)

Given the function

y = 2x+4

put x = 1

y = 2(1)+4=2+4 = 6

so (x, y) = (1, 6)

Given the function

y = 2x+4

put x = 2

y = 2(2)+4=4+4 = 8

so (x, y) = (2, 8)

Given the function

y = 2x+4

put x = -1

y = 2(-1)+4=-2+4 = 2

so (x, y) = (-1, 2)

So the table becomes

x            y = 2x+4           y              (x, y)

0            y = 2(0)+4        4            (0, 4)

1             y = 2(1)+4         6            (1, 6)

2             y = 2(2)+4       8            (2, 8)

-1           y = 2(-1)+4         2            (-1, 2)

The graph of the equation y = 2x+4 is also attached below.

On the diagram, the blue line represents the y=2x+4 line.

The correct logic translation of "some people are afraid of some animals" is:

∃x∃y, Person(x) ∧ Animal(y) ∧ Afraid(x, y)

This translates to "There exist some person x and some animal y such that x is afraid of y, and x is a person, and y is an animal." This statement asserts the existence of at least one person who is afraid of at least one animal.

To break down the statement, the quantifier ∃x asserts that there is at least one person x who is afraid of some animal, and the quantifier ∃y asserts that there is at least one animal y that some person is afraid of. The predicates Person(x), Animal(y), and Afraid(x, y) specify the properties of x and y, where Person(x) means x is a person, Animal(y) means y is an animal, and Afraid(x, y) means x is afraid of y. The ∧ symbol represents the logical operator "and," which combines the predicates to form a single statement.

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Step-by-step explanation:

It's a system of equations.

From the first one we isolate x:

x = 9-y

And we substitute in the second one:

(9-y)y = 14

-y^2 + 9y - 14 = 0

y^2 - 9y + 14 = 0

D = 25

y1/2 = (9 +- 5)/2 = 2 or 7

y = 2 => x = 7

y = 7 => x = 2

x^2 + y^2 = 7^2 + 2^2 = 53

There are 10 numbers less than 100 but larger than 30 that, when divided by 5 and 6, yield the same remainder. This can be determined by finding the least common multiple (LCM) of 5 and 6, which is 30.

Then, we identify the numbers in the range (30, 100) that have the same remainder when divided by 30, which is 0.

To find the numbers that satisfy the given condition, we need to consider the common multiples of 5 and 6. The LCM of 5 and 6 is 30. Any number that leaves the same remainder when divided by 5 and 6 will also leave the same remainder when divided by their LCM, which is 30.

In the given range, (30, 100), we can find the numbers that yield a remainder of 0 when divided by 30. Starting from 30 itself, we can increment by multiples of 30 to find other such numbers. The numbers that satisfy the condition are: 30, 60, 90, and so on.

To determine the total count of these numbers, we need to consider how many multiples of 30 fall within the range of (30, 100). We can divide the range width, which is 100 - 30 = 70, by the increment, which is 30. The result is (70 ÷ 30 = 2 remainder 10), meaning there are two complete sets of multiples of 30, plus an additional 10 numbers.

Therefore, there are 2 sets of numbers (30, 60, 90) and an additional 10 numbers (40, 50, 70, 80, 100) that satisfy the condition. The total count is 2 + 10 = 12.

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The decision between the two cities involves tradeoffs: the first city offers a wide range of class sizes but a smaller sample, while the second city has a larger sample but a narrower class size range.

The decision of which city to choose for the study involves tradeoffs. The first city allows for a wide range of class sizes, providing a comprehensive analysis of the relationship between class size and academic performance. However, the smaller sample size limits generalizability.



The second city offers a larger sample size, increasing generalizability, but with a narrower range of class sizes. Researchers should consider their specific research objectives, available resources, and constraints. If the goal is to assess the impact of extreme variations in class size, the first city is suitable. If obtaining highly generalizable results is paramount, the second city, despite the narrower range, should be chosen.



Therefore, The decision between the two cities involves tradeoffs: the first city offers a wide range of class sizes but a smaller sample, while the second city has a larger sample but a narrower class size range.

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Answer:

24 and 36

Step-by-step explanation:

2x + 3x = 60

5x = 60

x = 12

Dawn has 2(12) = 24

Jackson has 3(12) = 36

Step-by-step explanation:

To find the number of baseball cards each person received we must first find the total parts

That's

2 + 3 = 5

For Dawn

Dawn's part is 2

We have

2/5 × 60

For Jackson

Jackson's part is 3

That's

3/5 × 60

Hope this helps you

Based on the context of the problem, the range of the exponential function y = \(45,529(0.78)^x\) is y > 0.

The exponential function for depreciation given in the problem is:

y = 45,529(0.78)^x

This function gives us the value of Sharlene's truck in dollars after x months of ownership, assuming that the depreciation follows a constant rate and is modeled by an exponential function.

To find the range of the function, we need to consider the minimum value that y can take. Since depreciation leads to a decrease in value over time, y should always be greater than zero. In other words, the range of the function is:

y > 0

In practical terms, this means that Sharlene's truck will always have some positive value, even if its market value has decreased due to depreciation. In other words, a truck is never worth zero or less than zero (unless it has additional debts associated with it), and Sharlene's truck will always have some resale or scrap value even if it has depreciated significantly.

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Answer:

1. a = 68°

  b = 112°

  c = 68°

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

2. a = 127°

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

3. a = 35°

   b = 40°

   c = 35°

   d = 70°

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

4. a = 20°

   b = 70°

   c = 20°

   d = 70°

   e = 110°

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

5. a = 90°

   b = 90°

   c = 42°

   d = 48°

   e = 132°

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

6. a = 70°

   b = 55°

   c = 25°

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

Step-by-step explanation:

Answer:

P = 16w - 4

Step-by-step explanation:

P = (5w-2 + 3w)2

P = (8w-2)2

P = 16w - 4

The Phillips curve describes the relationship between the unemployment rate and the rate of change of wages. Option C is the correct option.

What is  Phillips curve?

The relationship between the rate of inflation and the unemployment rate is represented by the Phillips curve. The analysis of wage inflation and unemployment in the United Kingdom from 1861 to 1957 by A. W. H. Phillips, despite having forerunners, is a significant development in the field of macroeconomics. When unemployment was high, wages rose slowly; when unemployment was low, wages rose quickly, according to Phillips' research.

According to Phillips' hypothesis, as the unemployment rate declines, the labor market becomes more competitive and firms are forced to raise wages more quickly in order to recruit qualified workers. The pressure decreased as unemployment rates rose. The average relationship between wage behavior and unemployment over the course of the business cycle was represented by Phillips' "curve."

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Research has shown that competent communicators achieve effectiveness by adjusting their behaviors to the person and situation (option e).

Effective communication involves being adaptable and responsive to the specific context, individual preferences, and the needs of the situation.

Competent communicators recognize that different people have different communication styles, preferences, and expectations. They understand the importance of tailoring their communication approach to effectively connect and engage with others.

This may involve using appropriate language, tone, non-verbal cues, and listening actively to understand the needs and perspectives of others.

By adapting their behaviors, competent communicators can build rapport, foster understanding, and promote effective communication exchanges. They are mindful of the social and cultural dynamics at play, and they strive to communicate in a way that is respectful, inclusive, and conducive to achieving mutual goals.

In summary, competent communicators understand that effective communication is not a one-size-fits-all approach. They adjust their behaviors to the person and situation, demonstrating flexibility and adaptability in order to enhance communication effectiveness.

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Competent communicators achieve effectiveness mostly by adjusting their behaviors to suit the person they are communicating with and the situation they find themselves in. While other factors, like having a broad vocabulary or giving feedback, play a part in effective communication, the former is considered the most crucial.

Research suggests that competent communicators achieve effectiveness mostly through adjusting their behaviors depending on the person they are communicating with and the situation they are in. This is option e. of your question. Communicating effectively involves behaviors like active listening, understanding the other person's point of view, being able to express thoughts and ideas clearly, and being polite and respectful. While a broad vocabulary (option b.) can be useful, it is not as crucial as adapting your behavior to fit the situation. Moreover, giving feedback (option d.) is a part of effective communication but not the sole defining factor. Apologizing when offending others (option c.) is also important but it doesn't necessarily make one a competent communicator. Using the same type of behavior in various situations (option a.) might not always work, as different situations and individuals require different communication styles.

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Solving a linear equation with 2 variables

First isolate y term

10 y = -6x - 80

Now divide by 10

y = (-6/10)x -(80/10)

y = (-3/5)x - 8

Answer:

y = 7/4x - 3

Step-by-step explanation:

y = mx + b

y = 7/4x - 3

Answer:

See Below

Step-by-step explanation:

First off lets Let x = quiz score on Friday

We are given that Lula's mean for quiz marks is 58

We also know that her quiz marks were 67, 45, 55, and 60 for the first four days.

Given this we must create an equation so we can solve for her quiz mark on Friday.

First off,  Mean = average, more specifically

Mean = sum of numbers / # of numbers

In this case, mean = sum of quiz marks for each day  / number of days

If x = quiz mark on Friday than sum of quiz marks is 67 + 45 + 55 + 60 + x

If Lulu took her quiz marks from 5 days than the mean of her quiz marks is

(67 + 45 + 55 + 60 + x) / 5

We know that the mean of her quiz marks is 58

Therefore (67 + 45 + 55 + 60 + x) / 5  must equal 58

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

Note that we've just created an equation that we can use to solve for x ( or quiz mark on Friday )

We now solve for x using the equation we created

(67 + 45 + 55 + 60 + x) / 5 = 58

* combine like terms *

( 227 + x ) / 5 = 58

* multiply both sides by 5

227 + x = 290

* subtract both sides by 227

x = 63

Thus, we can conclude that her quiz mark on Friday was 63

Given:

A rectangle with sides 40 and 25.

A circle with radius 8 inside the rectangle.

The area of circle is unshaded.

To find:

The probability that a point (randomly selected) will lie in the unshaded region.

Solution:

The area of the rectangle is:

\(A_1=Length\times Width\)

\(A_1=40\times 25\)

\(A_1=1000\)

The area of the circle is:

\(A_2=\pi r^2\)

Where, r is the radius.

\(A_2=\pi (8)^2\)

\(A_2=\pi (64)\)

\(A_2=64\pi\)

\(A_2\approx 201.06\)

The probability that a point (randomly selected) will lie in the unshaded region is:

\(\text{Probability}=\dfrac{\text{Unshaded region}}{\text{Total region}}\)

\(\text{Probability}=\dfrac{A_2}{A_1}\)

\(\text{Probability}=\dfrac{201.06}{1000}\)

\(\text{Probability}=0.20106\)

Therefore, the required probability is 0.20106.

Answer:

b = -14

Step-by-step explanation:

Step  1  : B/14 Simplify

Step  2  :

Rewriting the whole as an Equivalent Fraction

Adding fractions that have a common denominator

Step  3  :

Rewriting the whole as an Equivalent Fraction

Adding fractions that have a common denominator

Step  4  :

Pulling out like terms

Step  5  :

When a fraction equals zero

Answer:    b = -14

Hope this helps.

Answer:

b= -50

Step-by-step explanation:

-10= b/14-9

Switch sides

b/14-9 = -10

Multiply both sides by 5

5b/14-9= 5(-10)

Simplify

b= -50

HOPE THIS HELPS :)

Answer: the probability is 1/221

The probability that a girl will win two weeks in a row is 24%.

Probability tells how many times something will happen or be present.

The probability of a girl winning in a given week is 17/35 since there are 17 girls and 35 students total. Assuming each week's selection is independent of previous selections, the probability of a girl winning two weeks in a row is (17/35) x (17/35) = 289/1225.

Rounding this to the nearest percent gives a probability of 24%.

Therefore, the probability is 24%.

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