A flagpole is 25 ft tall. The flagpole is casting a shadow that is 42 feetlong. What is the angle of depression?

Answer:

x = \(\frac{-5}{2}\) or  x = \(\frac{-1}{3}\)

Step-by-step explanation:

5 − 6 2 − 1 3 = 0

− 6 2 − 1 3 + 5 = 0 -6x^2-13x+5=0 −6x2−13x+5=0 − 1

( 6 2 + 1 3 − 5 ) = 0

Answer:

- 5/2, 1/3

Step-by-step explanation:

See image below:) I could only show half of the steps. But you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps.

The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;

5 a. The value of a is 3.5

b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel

A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential  function

The function is f(x) = a·log₃(x - 4),

x > 4 and a > 0

The coordinates of a point on the graph of the function, f is A(13, 7)

5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows

f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²

7 = a·log₃3²

7 = 2·a·log₃3 = 2·a·1 = 2·a

2·a = 7

a = 7 ÷ 2 = 3.5

a = 3.5

5 b. The coordinates of the x-intercept of the graph = (5, 0)

The equation of the function is;

f(x) = 3.5·log₃(x - 4)

A third point on the graph is given when f(x) = 14 as follows;

f(x) = 14 = 3.5·log₃(x - 4)

log₃(x - 4) = 14 ÷ 3.5 = 4

3⁴ = x - 4

x = 3⁴ + 4 = 85

Which gives the point, (85, 14)

Similarly, we have the point (31, 10.5), (7, 3.5)

Please find attached the graph of f(x) created with MS Excel

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Answer:

9.8

Step-by-step explanation:

Answer:

9.9

Step-by-step explanation:

The surface area of the wooden structure is approximately 1012 cm².

To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.

Surface Area of the Cone:

The surface area of a cone is given by the formula:

A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.

The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:

\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)

Using the given measurements:

\(s_{cone\) = √(7² + 24²) cm

\(s_{cone\) ≈ √(49 + 576) cm

\(s_{cone\) ≈ √625 cm

\(s_{cone\) ≈ 25 cm

Now, we can calculate the surface area of the cone:

\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)

\(A_{cone\) = (22/7) × 7 cm × 32 cm

\(A_{cone\) = 704 cm²

Surface Area of the Hemispherical Base:

The surface area of a hemisphere is given by the formula:

\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.

Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:

\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²

\(A_{hemisphere\) = (22/7) × 2 × 49 cm²

\(A_{hemisphere\) = 308 cm²

Total Surface Area:

To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:

Total Surface Area = \(A_{cone} + A_{hemisphere}\)

Total Surface Area = 704 cm² + 308 cm²

Total Surface Area = 1012 cm²

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The probability that you select a Jack given that it is a Club P(Jack∣Club) is 1/13.

The probability that you select a Club given that it is a Jack is P(Club∣Jack) is 1/4.

The probability that you select a card that is NOT a Jack given that it is NOT a Club,P(NotJack∣NotClub) is 47/38

The probability that you select a card that is NOT a Club given that is it NOT a Jack is 38/47

The probability that you select a Jack given that it is a Club P(Jack|Club):

There are 4 Jacks in a deck (one for each suit), and since we are given that the selected card is a Club, we only need to consider the 13 cards in the Club suit.

So, the number of favorable outcomes is 1 (the Jack of Clubs), and the total number of possible outcomes is 13 (the number of cards in the Club suit)

P(Jack|Club) = 1 / 13

The probability that you select a Club given that it is a Jack

P(Club|Jack):

P(Club|Jack) = Number of favorable outcomes / Total number of possible outcomes

P(Club|Jack) = 1 / 4

The probability that you select a card that is not a Jack given that it is not a Club

P(NotJack|NotClub):

The number of cards that are not Jacks is 52 - 4 = 48 (since there are 4 Jacks in the deck), and the number of cards that are not Clubs is 52 - 13 = 39 (since there are 13 cards in the Club suit).

P(NotJack|NotClub) = Number of favorable outcomes / Total number of possible outcomes

P(NotJack|NotClub) = (48 - 1) / (39 - 1)

=47/38

P(NotClub|NotJack) = (39 - 1) / (48 - 1)

=38/47

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Answer:

(B) v=p-10 1/10

Step-by-step explanation:

v does equal p if you take 10.1 away each time that's what the 1/10 is there for

If a constant is added to a variable then the graph gets shifted toward left and vice-versa. Then the graphs are shown below.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The parabola is given below.

f(x) = x²

Then the parabolas with respect to the position of their vertices from left to right will be

1: y = f(x) = x²

2: y = f(x - 4) = (x - 4)²

3: y = f(x + 3) = (x + 3)²

4: y = f(x - 7) = (x - 7)²

5: y = f(x + 2) = (x + 2)²

6: y = f(x - 1/2) = (x - 1/2)²

The graph of the parabola is given below.

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Answer:

lol I would think its some type of witchcraft. probably burn it!

Answer: around -$0.77

Step-by-step explanation:

To calculate the expected value of this lottery game, we need to find the probability of winning the game and the probability of losing the game.

Probability of winning:

There are a total of C(25, 6) possible combinations of choosing 6 numbers out of 25, where C(n, k) represents the number of combinations of choosing k items from a set of n items. The formula for combinations is:

C(n, k) = n! / (k!(n-k)!)

C(25, 6) = 25! / (6!19!) = 177100

So, there are 177,100 possible combinations. Since there's only 1 winning combination, the probability of winning is:

P(Winning) = 1 / 177,100

Probability of losing:

Since there's only 1 winning combination, the probability of losing is:

P(Losing) = 1 - P(Winning) = 1 - (1 / 177,100) = 177,099 / 177,100

Expected value:

Now, we can calculate the expected value (EV) by multiplying the probabilities of each outcome by their respective values and then summing up these products:

EV = P(Winning) * Value(Winning) + P(Losing) * Value(Losing)

EV = (1 / 177,100) * $40,000 + (177,099 / 177,100) * (-$1)

EV ≈ ($40,000 / 177,100) - ($177,099 / 177,100)

EV ≈ $0.2256 - $1

EV ≈ -$0.7744

The expected value of this lottery game is approximately -$0.7744. This means that, on average, a player would lose about 77.44 cents per game.

Answer:

25 tickets more

Step-by-step explanation:

I got x+y is (less than or equal to) 55 for the first inequality and 60x+40y>600 for the second one!

Step-by-step explanation:

Since Blaine can sell a maximum of 55 tickets, the first inequalitly is x+y is less than OR EQUAL TO 55. Since the tickets in the back section cost $40 each, 40y represents the money made from those tickets. Blaine needs to make 600 in sale so the inequality is 60x+40y>600.

Answer:

=∣∣−5∣∣=5

Step-by-step explanation:

∣∣x−y∣∣=5

Solution:

∣∣x−y∣∣

=∣∣2−7∣∣

=∣∣−5∣∣=5

Answer:

l2-7l

Step-by-step explanation:

The solution of the equation 3x(x - 3) = 12 will be 4 and negative 1.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

3x(x - 3) = 12

Simplify the equation, then we have

3x(x - 3) = 12

x(x - 3) = 4

x² - 3x - 4 = 0

Factorize the equation, then we have

x² - 3x - 4 = 0

x² - 4x + x - 4 = 0

x(x - 4) + 1(x - 4) = 0

(x - 4)(x + 1) = 0

x = 4, -1

The solution of the equation 3x(x - 3) = 12 will be 4 and negative 1.

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The distance between town A and town B is 93.5 km.

Solving for  the distance between town A and town B:

Let's first convert the 42 minutes delay of the car to hours:

42 minutes = 42/60 hours

                    = 0.7 hours

Now, let's assume that the time it took for the car to travel from A to B is t hours.

The distance between A and B is the same for both the lorry and the car, so we can set up an equation:

Distance = Speed x Time

For the lorry:

Distance = 50t

For the car:

Distance = 80 (t-0.7)

We know that when the car arrived at B, the lorry had 25km left to cover. So:

50t - Distance covered by lorry = 25

50t - (50t - 25) = 25

Simplifying:

25 = 25

This equation is always true, which means our assumptions are correct.

Therefore, we can equate the two distance equations:

50t = 80(t-0.7)

50t = 80t - 56

30t = 56

t = 1.87 hours

Finally, we can use the distance equation with either the lorry or the car to find the distance between A and B:

Distance = Speed x Time

Distance = 50 x 1.87

Distance = 93.5 km

So the distance between town A and town B is 93.5 km.

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Answer:

16

Step-by-step explanation:

Answer:

\(c = -3\)

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The 95% confidence interval for the poll is given as follows:

(0.3571, 0.4429).

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The sample proportion and the estimate for this problem are given as follows:

\(\pi = 0.4, n = 500\)

Then the lower bound of the interval is calculated as follows:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.96\sqrt{\frac{0.4(0.6)}{500}} = 0.3571\)

The upper bound of the interval is calculated as follows:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.96\sqrt{\frac{0.4(0.6)}{500}} = 0.4429\)

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The variable g has its value to be -4 on the given coordinate point

From the question, the points are given as

(g, -1) and (2, 5)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (g, -1) and (2, 5)

The slope of the line is given as

Slope = 3/2

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (g, -1) and (2, 5)

Substitute the known values in the above equation

So, we have the following equation

3/2 = (5 + 1)/(2 - g)

Evaluate the sum in the equation

This gives

3/2 = 6/2 - g

Cross multiply

So, we have

2(2 - g) = 12

Divide by 2

2 - g = 6

Make g the subject of the formula

g = 2 - 6

Evaluate the like terms

g = -4

Hence, the value of g of the line is -4

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Answer:

-2

Step-by-step explanation:

The product of the expression 7 x 63 is 441.

We have,

To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:

7 x 63 = 7 x (60 + 3)

Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:

7 x (60 + 3) = 7 x 60 + 7 x 3

Simplifying further:

7 x 60 + 7 x 3 = 420 + 21

Therefore,

The product of 7 x 63 is 441.

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One way to answer this is by plugging each point for x and y in the equation as follows:

Then:

For (-26, 8), we have:

3 * (-26) - 8 * (8) = -142 (No).

For (-6, -4), we have:

3 * (-6) - 8 * (-4) = 14 (Yes).

For (10, 2), we have:

3 * (10) - 8 * (2) = 14 (Yes).

For (18, 5), we have:

3 * (18) - 8 * (5) = 14 (Yes).

For (22, -10), we have:

3 * (22) - 8 * (-10) = 146 (No).

Then, the points that lie on the graph of the line 3x - 8y = 14 are: (-6, -4), (10, 2), and (18, 5).

Answer:

y = -x + 8

Step-by-step explanation:

m = -1  ; x1 = 3 ; y1 = 5

Slope point form: y - y1 = m(x -x1)

y - 5 = -1(x - 3)

y -  5 = -1x - 3 *(-1)

y - 5 =-x + 3

    y =  -x + 3 + 5

     y = -x + 8

Answer:

38 meters

Step-by-step explanation:

The equation of the parabola is\((y + 6)^2 = 4(x - 13)\), where the vertex is (13, -6) and the distance between the directrix and focus is 14.

To determine the equation of the parabola, we need to use the standard form for a parabola with a horizontal axis:

\((x - h)^2 = 4p(y - k)\)

Where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus (and also from the vertex to the directrix).

Given that the parabola opens to the right, the vertex will be on the left side. Let's assume the vertex is (h, k).

We know that the focus of the parabola is at (13, -6), so the distance from the vertex to the focus is p = 13 - h.

We are also given that the focal diameter is 28, which means the distance between the directrix and the focus is twice the distance from the vertex to the focus.

Therefore, the distance from the vertex to the directrix is d = 28/2 = 14.

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The statement about function g which is true is that: function g is exponential because g(x) changes by equal factors over equal intervals of x.

The slope of a line simply refers to the gradient of a line and it's typically used to describe both the ratio, direction and steepness of an equation of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

\(Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Slope = (40 - 10)/(2 - 1)

Slope = 30/1

Slope = 30

Slope = (160 - 40)/(3 - 2)

Slope = 120/1

Slope = 120.

Factor = 40/10 = 4

Factor = 160/40 = 4

Factor = 640/160 = 4.

Therefore, function g is exponential because g(x) changes by equal factors over equal intervals of x.

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Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.

When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.

Increased employment opportunities result in more individuals having access to income and improved standards of living.

Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.

Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.

Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.

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Answer:x-(2 7/8)=1/2

Step-by-step explanation:

Answer:

x = 10

m∠K = 90°

y = 15

JM = 65

Step-by-step explanation:

KJ = LM

⇒ x + 31 = 5x - 9

⇒ 40 = 4x

⇒ x = 10

From inspection of the diagram, m∠K = 90° (right angle)

KL = JM

⇒ 4y + 5 = 2y + 35

⇒ 2y = 30

⇒ y = 15

JM = 2y + 35

⇒ JM = 2(15) + 35

⇒ JM = 30 + 35

⇒ JM = 65

Opposite sides of rectangle are equal

\(\\ \rm\Rrightarrow x+31=5x-9\)

\(\\ \rm\Rrightarrow 4x=40\)

\(\\ \rm\Rrightarrow x=10\)

\(\\ \rm\Rrightarrow 4y+5=2y+35\)

\(\\ \rm\Rrightarrow 2y=30\)

\(\\ \rm\Rrightarrow y=15\)

Answer:

x = \(\frac{y}{7}\), y = 7x

Step-by-step explanation:

hope this helps