Find tan A. If necessary, write your answer as a fraction.

Answer:

y = 10x - 82

Step-by-step explanation:

y - y = m(x - x)

Plug in the slope and given point and solve for y

y - (-2) = 10(x - 8)

y + 2 = 10x - 80

y = 10x - 82

The linear equation of the line is y + 2 = 10(x - 8) and y = 10x - 82

The slope is given as:

m = 10

The point is given as:

(x1, y1) = (8, -2)

The equation in point slope form is calculated as;

y -  y1 = m(x - x1)

So, we have:

y + 2 = 10(x - 8)

Expand

y + 2 = 10x - 80

Subtract 2 from both sides

y = 10x - 82 --- in slope intercept

Hence, the linear equation of the line is y + 2 = 10(x - 8) and y = 10x - 82

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The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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Answer:

Step-by-step explanation:

the x intercept takes coordinate (x,0)

the y intercept takes coordinate (0,y)

                                         x intercept                        y intercept

40: x+y=5                          (5,0)                                      (0,5)

x=0 , y=5, when y=0 x=5

41: x-y=5                            (5,0)                                      (0,-5)

x=0, -y=5 then y=-5, when y=0, x=5

42: 3x+4y=12                     (4,0)                                      (0,3)

x=0, 4y=12⇒y=12/4⇒y=3

y=0, 3x=12⇒x=12/3⇒x=4

43: 2x+3y=6                      (3,0)                                       (0,2)

x=0 , 3y=6⇒y=6/3=2

y=0 ,3y=6 ⇒ y=6/3 ⇒y=2

44: 3x+4y=-24                   (-8,0)                                      (0,-6)

x=0 , 4y=-24⇒y=-24/4 ⇒ y=-6

y=0 , 3x=-24⇒ x=-24/3⇒x=-8

45: 1/3x+2/3y=5/6            (5/2,0)                                    (0,5/4)

x=0 , 2/3 y=5/6 ⇒12y=15 ⇒ y=15/12 ⇒y=5/4

y=0 , 1/3 x=5/6 ⇒6x=15 ⇒x=15/6 ⇒x=5/2

46: x=-2                             (-2,0)                                   no y intercept

it is vertical line , there is no y intercept

47: y=15                    no x intercept                               (0,15)

horixzontal line, no x intercept

48: 3x-7y=8              (8/3,0)                                             (0,-8/7)

x=0 , -7y=8 ⇒y=-8/7

y=0 , 3x=8 ⇒x=8/3

The calculated value of the total interest is 12479.04

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

25998 x .08 x 6

In the above equation, we have

Principal = 25998

Rate of interest = 0.08

Time = 6

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

Total interest = 25998 x .08 x 6

Evaluate

Total interest = 12479.04

Hence, the total interest is 12479.04

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The public health official can estimate the vaccination rate in the community with a 95% confidence interval.

A public health official responding to an outbreak of measles needs to estimate the vaccination rate in the community. The official will use a confidence interval of 95%.
To estimate the vaccination rate with a 95% confidence interval, the official will need to collect a sample of individuals from the community and determine the proportion of vaccinated individuals in that sample. The confidence interval will then provide a range within which the true vaccination rate in the community is likely to fall.
Here are the steps to calculate the confidence interval:
1. Determine the sample size: The official needs to decide on the desired level of precision for the estimate. A larger sample size will provide a narrower confidence interval. The official may consult statistical tables or use a formula to determine the appropriate sample size.
2. Collect the sample: The official will need to randomly select individuals from the community to participate in the study. It is important to ensure that the sample is representative of the population.
3. Calculate the sample proportion: The official will calculate the proportion of vaccinated individuals in the sample. This is done by dividing the number of vaccinated individuals by the total sample size.
4. Determine the standard error: The standard error measures the uncertainty in the estimate of the sample proportion. It is calculated using the formula: sqrt((p * (1-p)) / n), where p is the sample proportion and n is the sample size.
5. Calculate the confidence interval: Using the sample proportion and the standard error, the official can calculate the confidence interval. The formula for the confidence interval is: sample proportion +/- (critical value * standard error). The critical value depends on the desired level of confidence. For a 95% confidence interval, the critical value is typically 1.96.
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The power of substitutes is one of the five forces in Porter's Five Forces framework and it is a measure of how easy it is for customers to switch to alternative products or services. The higher the power of substitutes, the more competitive the industry and the lower the profitability.

The power of substitutes is based on the premise that when there are readily available alternatives to a product or service, customers can easily switch to those alternatives if they offer better value or meet their needs more effectively. This poses a threat to the industry as it reduces customer loyalty and puts pressure on pricing and differentiation strategies.

The availability and quality of substitutes influence the degree to which customers are likely to switch. If substitutes are abundant and offer comparable or superior features, the power of substitutes is strong, increasing the competitive intensity within the industry. On the other hand, if substitutes are limited or inferior, the power of substitutes is weak, providing more stability and protection to the industry.

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Answer:

\(x=\boxed{6.6}\)

\(\overline{\sf DE}=\boxed{13.2}\:\:\sf units\)

Step-by-step explanation:

Geometric Mean Theorem - Altitude Rule

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments.  The ratio of one segment to the altitude is equal to the ratio of the altitude to the other segment:

\(\sf \dfrac{segment\:1}{altitude}=\dfrac{altitude}{segment\:2}\)

From inspection of the given diagram:

\(\begin{aligned}\sf \dfrac{segment\:1}{altitude} & = \sf \dfrac{altitude}{segment\:2}\\\\\implies \dfrac{5}{9} & = \dfrac{9}{2x+3}\\\\5(2x+3) & = 81\\\\10x+15 & = 81\\\\10x & = 66\\\\ \implies x & = 6.6\end{aligned}\)

Substitute the found value of x into the expression for DE:

\(\begin{aligned}\sf \overline{DE} & = 2x+3\\\implies \sf \overline{DE} & = 2(6.6)+3\\& = 13.2+3\\& =16.2\:\: \sf units\end{aligned}\)

The first 3 terms of the sequence are 21, 24 and 29

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

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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Answer:

am not sure of my answer ohhh

Answer:

19.95

Step-by-step explanation:

The calculated vertex of the graph represented in the figure is (-3, -3)

Given that we have the graph

The curve on the graph is a quadratic function

As a general rule, the vertex of a graph is the minimum or the maximum point on a graph

From the graph, we have the minimum point to be

Minimum = (-3, -3)

This means that

Vertex = (-3, -3)

Hence, the vertex is (-3, -3)

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The airplane is flying 94.8 feet above the farmhouse.

The formula for finding the height of an object from a given angle of elevation is:

Height = tan(angle of elevation) * Distance

In this case, we have two angles of elevation and two distances. We can solve for the height of the airplane by first calculating the distance from the observer to the top of the farmhouse. We can do this by using the same formula, but substituting in the angle of elevation of the farmhouse and the known distance between the observer and the farmhouse:

Distance to farmhouse = tan(24°) * 50 feet

Distance to farmhouse = 43.6 feet

Once we have the distance to the farmhouse, we can use the same formula to calculate the height of the airplane above the farmhouse. This time, we substitute in the angle of elevation of the airplane and the distance to the farmhouse:

Height of airplane = tan(70°) * 43.6 feet

Height of airplane = 94.8 feet

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Answer:

-4/9

Step-by-step explanation:

I used a calculator.

5/6(−8/15) in simplest form is -4/9.

A fraction is written in the form of a numerator and a denominator.There are two types of fractions. One is proper fraction in which numerator is less than the denominator and another one is improper fraction in which denominator is less than the numerator.All fractions can be written in the form of p/q, where q ≠ 0 cause anything divided by 0 is undefined.

According to the given questions we have to multiply two fractions        (5/6)(-8/15) which is

= -40/90.

= -4/9.

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Answer:

KM=LM+KL.  If KM is 9 and LM is 5, then KM-LM=KL. So 9-5=4.  KL is 4.

Step-by-step explanation:

The value of KL will be equal to 4 in the line segment KM.

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that point, L is on line segment KM. Given LM = 5 and KM=9. The value of the line segment KL will be calculated as below:-

KM = LM + KL.  

If KM is 9 and LM is 5, then,

KM-LM=KL.

KL =  9-5=4.  

KL = 4

Therefore, the value of KL will be equal to 4 in the line segment KM.

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The efficiency of the power screw in raising the load is approximately 6976%.

The efficiency of a power screw can be calculated using the formula: Efficiency = (Ideal Mechanical Advantage / Actual Mechanical Advantage) x 100% To find the Ideal Mechanical Advantage (IMA) of the screw, we can use the formula:

IMA = (π / tan(α)) x (π / 2) x (D / P)

Where: π is the mathematical constant pi (approximately 3.14159) tan(α) is the coefficient of friction (given as 0.20) D is the major diameter of the screw (given as 19 mm) P is the pitch of the screw, which can be calculated as (25.4 mm / number of threads per inch) First, let's calculate the pitch: Number of threads per inch = 6

Pitch = 25.4 mm / 6 = 4.23 mm (approximately)

Now, we can substitute the values into the formula to find IMA:

IMA = (π / tan(α)) x (π / 2) x (19 mm / 4.23 mm)

Using the given coefficient of friction, we have:

IMA = (π / 0.20) x (π / 2) x (19 mm / 4.23 mm)

Simplifying the equation, we get:

IMA = 9.87 x 1.57 x 4.49

Calculating IMA, we find:

IMA ≈ 69.76

Now, we need to find the Actual Mechanical Advantage (AMA), which can be calculated using the formula:

AMA = Load / Effort

Where:

Load is the weight being lifted (given as 17.80 kN)

Effort is the force applied to turn the screw

Since the screw is being used to lift the load, the Effort is equal to the load.

AMA = 17.80 kin / 17.80 kin

AMA = 1

Now, we can calculate the efficiency using the formula:

Efficiency = (IMA / AMA) x 100%

Efficiency = (69.76 / 1) x 100%

Efficiency ≈ 6976%

The efficiency of the power screw in raising the load is approximately 6976%.

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Answer:

1Step-by-step explanation:

1 + IS 1 AND ITS 1

Answer:

See below

Step-by-step explanation:

E means exponent of 10

8.50246E6   means   8.50246 x 10^6   = 8502460

The number that will complete the square to solve equation is 1/36.

What is completing the square?

For some values of h and k, completing the square is an elementary algebraic method for changing a quadratic polynomial of the form

ax^2 + bx + c to the form a^2 + k. In other words, the quadratic expression is completed by inserting a perfect square trinomial.

Consider, the given polynomial

3w^2 - w - 24 = 0

Rewrite the polynomial in the form ax^2 + bx = c

Add 24 on both sides,

3w^2 - w - 24 + 24 = 24

⇒ 3w^2 - w = 24

Divide both sides by 3,

\(w^2-\frac{1}{3}w = 8\)

To complete the square x^2 + bx, we add \((\frac{b}{2} )^2\)

Here, b = -1/3

So, \((\frac{b}{2})^2 = (\frac{-1/3}{2})^2 = (-\frac{1}{6})^2 = \frac{1}{36}\)

Adding to both sides of the equation, we have

\(w^2-\frac{1}{3}w+\frac{1}{36} = 8+\frac{1}{36}\)

Hence, the number that will complete the square to solve an equation is 1/36.

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Answer:

Step-by-step explanation: Answer c the -1 is equivalent to the -0 and -* to the third power equaled the equation mathematics of it being c

Thus, the answer c

To prove that if F2 is integrable on R, then |f| is integrable on R, we can use the triangle inequality.

1. Recall that the triangle inequality states that for any two real numbers a and b, |a + b| ≤ |a| + |b|.

2. Let's consider the function f: R ⊂ R^n → R, which is bounded.

3. Since F2 is integrable on R, we can express it as F2 = g + h, where g and h are integrable functions on R.

4. Applying the triangle inequality, we have |f(x)| = |g(x) + h(x)| ≤ |g(x)| + |h(x)| for any x in R.

5. By the properties of integrable functions, |g(x)| and |h(x)| are integrable on R.

6. Therefore, by the linearity of integrability, |f(x)| = |g(x)| + |h(x)| is also integrable on R.

In conclusion, if F2 is integrable on R, then |f| is integrable on R.

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We are going to find the coordinates of the points A'B', which are given by the dilation of AB about the point (5,5) with a scale factor of 2.

For doing so, we will determine the distance between the points A and (5,5), and we will multiply it by 2 (the scale factor). This will be the distance between A' and (5,5). We will do the same between the point B and (5,5).

As the lines x=5 and y=5 are perpendicular, the angle BPA is right (where P is the point (5,5)), we can find the distance of the point A'B' using the Pythagorean Theorem.

Now, we find the distance between A and P:

And the distance between B and P:

Multiplying by the scale factor we obtain:

And using the Pythagorean Theorem we obtain:

This means that the length of the dilation of AB will be 10.

The probability that the team will win at most 4 out of 5 games is 8/9.

To calculate the probability of winning at most 4 out of 5 games, we need to find the probability of winning 0, 1, 2, 3, or 4 games.

The probability of winning exactly k games out of 5 is given by the binomial distribution formula:

P(X = k) = (5 choose k) * (2/3)^k * (1/3)^(5-k)

Where "n choose k" is the binomial coefficient, representing the number of ways to choose k items from a set of n items. In this case, it represents the number of ways to win k games out of 5.

Using this formula, we can calculate the individual probabilities:

P(X = 0) = (5 choose 0) * (2/3)^0 * (1/3)^5 = (1) * (1) * (1/243) = 1/243

P(X = 1) = (5 choose 1) * (2/3)^1 * (1/3)^4 = (5) * (2/3) * (1/81) = 10/243

P(X = 2) = (5 choose 2) * (2/3)^2 * (1/3)^3 = (10) * (4/9) * (1/27) = 40/243

P(X = 3) = (5 choose 3) * (2/3)^3 * (1/3)^2 = (10) * (8/27) * (1/9) = 80/243

P(X = 4) = (5 choose 4) * (2/3)^4 * (1/3)^1 = (5) * (16/81) * (1/3) = 80/243

To find the probability of winning at most 4 out of 5 games, we sum up these probabilities:

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = (1/243) + (10/243) + (40/243) + (80/243) + (80/243) = 8/9.

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In unit-vector notation, the sum of a= \(5.2 \ \boldsymbol{\hat{i}}+1.4\ \boldsymbol{\hat{j}}\) and b= \(-12.0\ \boldsymbol{\hat{i}}+6.8\ \boldsymbol{\hat{j}}\) is \(-6.8\ \boldsymbol{\hat{i}}+8.2\ \boldsymbol{\hat{j}}\), the magnitude of a+b is 10.65m and the direction of a+b relative to \(\hat{i}\) is \(-50^\circ\).

a) To find the sum of a+b, follow these steps:

b) To find the magnitude of a+b, follow these steps:

c) To find the direction of a+b relative to \(\boldsymbol{\hat{i}}\), follow these steps:

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According to the given data 47% of the fans that attend the event, purchase the peanuts.

The sample collected was among 200 fans which means total fans = 200

out of which 94 fans purchased peanuts which means

Percentage of Fans purchased Peanuts  = \(\frac{94}{200}\)  X 100

                                                                     = 47 %

Not exactly the half of the fans purchased the peanuts but approximately half that is 3% less than 50 % fans puchased the peanuts which implies => 47 % fans purchased peanuts.                

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Average rate of growth over this period is 0.4%.

Average rate of growth over a period is given by:

A=P\(e^{rT}\) where,

A- Population at time T

P- Initial population

r-average rate of growth

T-Time period

Now, P=250,000, A=310,000 and T=21 (2000-1980+1)

therefore, putting values in the equation, we get:

310,000=250,000\(e^{21r}\)

⇒ \(e^{21r}\) = 1.24

⇒ 21r = log(1.24)

⇒ r = 0.0044 or 0.4%.

so, the average rate of growth over this time period is 0.4%.

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Answer:

10. 89

11. 36

12. $29.95

13. 700

14. 14.23 ( may be wrong )

15. 129

16. $22.97

Step-by-step explanation:

My single braincell worked.

The amount of heat released when 12.0g of helium gas condense at 2.17 K is; -250 J

The latent heat of vapourization of a substance is the amount of heat required to effect a change of state of the substance from liquid to gaseous state.

However, since we are required to determine heat released when the helium gas condenses.

The heat of condensation per gram is; -21 J/g.

Therefore, for 12grams, the heat of condensation released is; 12 × -21 = -252 J.

Approximately, -250J.

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Answer:

its a

Step-by-step explanation:

Option (A). 2 is the correct option that will claim the student statement "The value of the expression 3x+3 is always greater than the value of the expression 2x+6." as false.

Expression:

Expression means the sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Given,

A student evaluates the expressions 3x+3 and 2x+6 at several different values of .

The student claims, "The value of the expression 3x+3 is always greater than the value of the expression 2x+6."

Here we need to find value of x can be used to show that the student's claim is false.

For that, we have to verify each value in order to find the correct one,

Then,

Let option (A) x = 2

=> 3(2) + 3 = 2(2) + 6

=> 6 + 3 = 4 + 6

=> 9 < 10

Now we have to apply the other option (B),

Let x = 4, then

=> 3(4) + 3 = 2(4) + 6

=> 12 + 3 = 8 + 6

=> 15 > 14

Now we have to apply the other option (C),

Let x = 6, then

=> 3(6) + 3 = 2(6) + 6

=> 18 + 3 = 12 + 6

=> 21 > 18

Now we have to apply the other option (D),

Let x = 6, then

=> 3(8) + 3 = 2(8) + 6

=> 24 + 3 = 16 + 6

=> 27 > 22

So, the correct option is (A) x = 2.

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Answer:

816.67

Step-by-step explanation:

The equation of the line that satisfies the given condition is:

y = mx + b

In the equation y = mx + b, 'y' represents the dependent variable (usually the output or the value we want to find), 'x' represents the independent variable (usually the input or the value we can control), 'm' represents the slope of the line (indicating the rate of change of y with respect to x), and 'b' represents the y-intercept (the value of y when x is equal to zero).

To find the equation of a line that satisfies a given condition, we need to determine the values of 'm' and 'b' based on the information provided. The condition could be in the form of coordinates of a point on the line, the slope of the line, or any other relevant information.

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Answer:

A = 540 m²

Step-by-step explanation:

consider the shape split into 3 rectangles

the length is divided into 3 congruent sections

single dash = 30 m ÷ 3 = 10 m

the width is divided into 3 congruent sections

double dash = 27 m ÷ 3 = 9 m

then area (A) is the total of the 3 rectangular areas

A of left rectangle = 10 × 9 = 90 m²

A of middle rectangle = 10 × (9 + 9) = 10 × 18 = 180 m²

A of right rectangle = 10 × 27 = 270 m²

total area = 90 + 180 + 270 = 540 m²