On a scale drawing with a scale of 3 cm : 2 m, the height of a tree is 6 cm. How tall is the actual tree?

(i) 3 csc²(x) - 4 = 0

3 csc²(x) = 4

csc²(x) = 4/3

sin²(x) = 3/4

sin(x) = ± √3/2

x = arcsin(√3/2) + 2nπ  or   x = arcsin(-√3/2) + 2nπ

x = π/3 + 2nπ   or   x = -π/3 + 2nπ

where n is any integer. The general result follows from the fact that sin(x) is 2π-periodic.

In the interval 0 ≤ x ≤ 2π, the first family of solutions gives x = π/3 and x = 4π/3 for n = 0 and n = 1, respectively; the second family gives x = 2π/3 and x = 5π/3 for n = 1 and n = 2.

(ii) 4 cos²(x) + 2 cos(x) - 2 = 0

2 cos²(x) + cos(x) - 1 = 0

(2 cos(x) - 1) (cos(x) + 1) = 0

2 cos(x) - 1 = 0   or   cos(x) + 1 = 0

2 cos(x) = 1   or   cos(x) = -1

cos(x) = 1/2   or   cos(x) = -1

[x = arccos(1/2) + 2nπ   or   x = 2π - arccos(1/2) + 2nπ]   or   x = arccos(-1) + 2nπ

[x = π/3 + 2nπ   or   x = 5π/3 + 2nπ]   or   x = π + 2nπ

For 0 ≤ x ≤ 2π, the solutions are x = π/3, x = 5π/3, and x = π.

Answer:

The are vertical angles.

Step-by-step explanation:

So as you can see in my picture i drew those lines, they are vertically opposite from each other.

Hope this helps!

Good Luck!

Please mark me bralinest if you can :)

Answer:

Vertical

Step-by-step explanation:

<AGB and <EGD are vertical angles because they are vertically opposite from each other since they were created from two lines crossing.

-You know that they aren't adjacent because they aren't next to each other and don't share a side or a vertex.

-They can't be supplementary because they don't add up to 180 degrees

-They can't be complementary because they don't make up 90 degrees

Answer: c

Hope I helped

Answer:

Only Felpie is right because it asks the function of 24, 16, 8, 0

Not 32, 24, 16, 8, 0

Step-by-step explanation:

Answer:

"a Sample Statistic"

Step-by-step explanation:

A sampling distribution is defined as the probability distribution of "a statistic" drawn from a large number of samples gotten from a specific population. In order words, it is a sample statistic.

Thus, the correct answer is "a Sample Statistic"

The sampling distribution is the probability of a particular report based on random sampling; it displays the most likely values of various sample means

It is a probability distribution of data mining, which is the process of analyzing larger samples gathered from a given population.  

In this, a particular population is the distribution of frequencies of a variety of possible outcomes for a population statistic.

It is the distribution of the probability for a statistic is generated from a large number of samples gathered from a certain population.

Therefore, "The sampling distribution is the probability of a particular report based on random sampling; it displays the most likely values of various sample means".

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Answer:

Step-by-step explanation:

40/32 ?=? (40 + 12.5) / (32 + 10)

  1.25  ?=? 52.5 / 42

   1.25   =  1.25

similar via SAS

The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.

The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.

When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.

To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.

For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.

In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.

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Answer:

Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

Step-by-step explanation:

hourly pay: $5/hour

number of hours: 24 hours

total pay = hourly pay × number of hours

total pay = $5/hour × 24 hours

total pay = $120

MP3 player costs $100.

Total pay is $120.

Answer: Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

The correct statement regarding the function g(x), considering it's domain and range, is given as follows:

D. g(3) = 18.

Before knowing the definition of the domain and the range of a function, the input and the output of a function must be identified. In this function, they are given as follows:

The domain of a function is composed by all the values assumed by the input of the function. Hence, in this problem, g(x) can only be calculated for values of x that are between -1 and 4, inclusive. g(-5) and g(5), for example, cannot be calculated.

The range of a function is composed by all the values assumed by the output of the function. Hence, in this problem, the values assumed by g(x) must be between 0 and 18, inclusive, thus values such as g(x) = -1 or g(x) = 19 are not valid.

Thus the correct statement is given as follows:

As:

The options are given as follows:

A. g(5) = 12.

B. g(1) = -2.

C. g(2) = 4.

D. g(3) = 8.

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Answer: the present age of son is 15 years, and the present age of father is 45 years.

Step-by-step explanation:

Let the age of son be 'x' and that of his father be 'y'.

So according to the question, the 1st equation that can be formed will be:

y = 3(x) ->(1)

[as father's age is 3 times the age of son]

Now after 5 years:

Age of son = (x+5)

Age of father = (y+5)

So according to the question, the 2nd equation that can be formed will be:

(y+5) = 2.5×(x+5) ->(2)

[as father is now two and half times old as his son]

Substituting the value of equation (1) in (2), we get:

(3x+5) = 2.5×(x+5)

=> 3x + 5 = 2.5x + 12.5

=> 3x - 2.5x = 12.5 - 5

=> 0.5x = 7.5

=> x = 7.5/0.5 = 15

Thus, the present age of son is 15 years.

Note : we can calculate the age of father by putting the value of x in equation (1) or (2):

y = 3(x) = 3 × 15 = 45 (putting x in equation 1)

Thus, the present age of father is 45 years.

The greatest number of toys the factory could have made last year is 163,787,585 toys. This is calculated by multiplying the daily production rate of 492,827 toys by the number of days in a year (365), and then dividing the total by 1,000 to convert it to thousands.

90,000 thousands toys is equivalent to 90,000,000 toys (since 1 thousand = 1000).

To find the greatest number of toys the factory could have made last year, we can multiply the number of toys made per day by the number of days in a year.

Since there are 365 days in a year, the factory could have made

492,827 toys/day x 365 days = 179,847,755 toys

However, since the question asks for the greatest number of toys the factory could have made, we need to take into account any possible missed production days (e.g. holidays, maintenance, etc.).

Assuming the factory operated at full capacity for 90% of the year, the greatest number of toys they could have made would be fin my multiplying,

492,827 toys/day x 365 days x 0.9 = 163,787,584.5 or approximately 163,787,585 toys.

Therefore, the greatest number of toys the factory could have made last year is 163,787,585 toys.

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--The given question is incomplete, the complete question is given

"A toy factory makes 492,827 toys each day. a factory made about 90,000 thousands toys last year. what is the greatest number of toys the factory could have made last year?'--

Answer:

its 31.75

Step-by-step explanation:

12.5 inch = 31.75 cm

Answer: 11 hours

Step-by-step explanation:

22/2 = 11

Subtracting 3 at the end of the equation shifts the graph down 3 units

The percentage of drivers who are at least 45 is 62%

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

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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Answer: 1 pound

Step-by-step explanation:

-2 + 3 = 1

The probability that a person who tests positive actually has the disease is approximately 0.194.

What exactly is probability?

Probability is a measure of an event's possibility or chance of occurring. It is stated as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. Probabilities ranging from 0 to 1 reflect occurrences that are probable but not guaranteed.

P(A) denotes the probability of an event A as the ratio of the number of possibilities that favour event A to the total number of potential outcomes. In other words, it is the number of possible outcomes for event A divided by the total number of possible outcomes.

Now,

To compute the probability that a person who tests positive actually has the disease, we can use Bayes' theorem, which states that:

P(A|B)=P(B|A)*P(A)/P(B)

where A and B are events, P(A | B) is the probability of event A when event B has occurred, P(B | A) is the probability of event B when event A has occurred, P(A)= prior probability of event A, and P(B) = prior probability of event B.

In this case, let A be the event of having the disease and B be the event of testing positive.

The incidence rate of the disease is 0.8%, which means that P(A) = 0.008.

The false negative rate is 6%, which means that P(B' | A) = 0.06 (where B' is the complement of event B, i.e., testing negative given that the person has the disease).

The false positive rate is 3%, which means that P(B | A') = 0.03 (where A' is the complement of event A, i.e., not having the disease).

We can compute P(B) using the law of total probability:

P(B) = P(B|A)*P(A) + P(B|A')*P(A')

= (1-P(B'|A))*P(A)+P(B|A')*(1-P(A))

= (1 - 0.06) * 0.008 + 0.03 * (1 - 0.008)

= 0.0328

Now we can use Bayes' theorem to compute P(A | B):

P(A | B) = P(B | A) * P(A) / P(B)

= (1 - P(B' | A)) * P(A) / P(B)

= (1 - 0.06) * 0.008 / 0.0328

= 0.194

Therefore,

                 the probability will be 0.194.

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I would need to know the specific polynomial function to determine its end behavior. However, in general, the end behavior of a polynomial function can be determined by looking at the degree and leading coefficient of the polynomial.

If the degree of the polynomial is even and the leading coefficient is positive, then the end behavior will be the same on both ends and the function will approach positive infinity as x goes to negative infinity and positive infinity as x goes to positive infinity.

If the degree of the polynomial is even and the leading coefficient is negative, then the end behavior will be the same on both ends and the function will approach negative infinity as x goes to negative infinity and positive infinity as x goes to positive infinity.

If the degree of the polynomial is odd and the leading coefficient is positive, then the end behavior will be different on the left and right ends. As x goes to negative infinity, the function will approach negative infinity, and as x goes to positive infinity, the function will approach positive infinity.

If the degree of the polynomial is odd and the leading coefficient is negative, then the end behavior will be different on the left and right ends. As x goes to negative infinity, the function will approach positive infinity, and as x goes to positive infinity, the function will approach negative infinity.

Step-by-step explanation:

To determine the end behavior of a polynomial function, you need to look at the degree (highest power of x) and the leading coefficient (the coefficient of the term with the highest power of x).

If the degree of the polynomial is even and the leading coefficient is positive, then the end behavior is that the function approaches positive infinity as x approaches both positive and negative infinity.

If the degree of the polynomial is even and the leading coefficient is negative, then the end behavior is that the function approaches negative infinity as x approaches both positive and negative infinity.

If the degree of the polynomial is odd and the leading coefficient is positive, then the end behavior is that the function approaches positive infinity as x approaches both positive infinity and negative infinity, but approaches negative infinity as x approaches negative infinity.

If the degree of the polynomial is odd and the leading coefficient is negative, then the end behavior is that the function approaches negative infinity as x approaches both positive infinity and negative infinity, but approaches positive infinity as x approaches negative infinity.

Here's an example:

Let's consider the polynomial function f(x) = 2x^4 - 3x^3 + 5x - 1.

The degree of this polynomial is 4, which is even, and the leading coefficient is even, and the leading coefficient is positive, which means that as x approaches both positive and negative infinity, the function approaches positive infinity.

Therefore, we can say that the end behavior of the polynomial function f(x) is that f(x) → ∞ as x → ±∞.

If the third term is 31, then let's get the second term. We have to use the rule we were given and work backwards. So, we will add three and then divide by 2.

31 + 3 = 34

34 / 2 = 17

17 is the second term. Let's do the same thing we just did to find the first term: add three, divide by 2.

17 + 3 = 20

20 / 2 = 10

Answer: the first term is 10

Hope this helps!

Answer:

A

Step-by-step explanation:

Answer:

try looking it up on socratic

Answer:

-5

Step-by-step explanation:

The common ratio is what you have to multiply one term by to get the next term.

so:

\(18 \times r = -90\\-90 \times r = 450\)

where r is the common ratio

We can solve these equations:

-90 / 18 = -5

450/-90 = -5

therefore the common ratio is -5

Answer: (x+y)-6

Step-by-step explanation:

i think lol

The points that will lie on the line will be (0, 0) , (1, - 25) , (- 1, 25).

The general equation of a straight line is : y = mx + c.

[m] is called slope and it tells the unit rate of change in [y] with respect to [x].

[c] is called the [y] - intercept.

We have some points that lie on a line that passes through the origin with a slope of −25.

The equation of a straight line that passes through the origin and has slope of -25 will be -

y = - 25x

The points that will lie on the line will be -

(0, 0) , (1, - 25) , (- 1, 25)

Therefore, the points that will lie on the line will be (0, 0) , (1, - 25) , (- 1, 25).

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At least 3 decimal places, the probability that a person who tests positive actually has the disease is approximately 0.002482.

Bayes' relates the conditional probabilities of two events A and B as follows:

P(A | B) = P(B | A) × P(A) / P(B)

P(A) is the prior probability of A, P(B | A) is the conditional probability of B given A, P(B) is the marginal probability of B and P(A | B) is the conditional probability of A given B.

Let's define the following events:

D: the person has the disease

T: the person tests positive

We are interested in finding P(D | T) the probability that a person who tests positive actually has the disease.

We are given that:

P(D) = 0.009 (the incidence rate of the disease)

P(T | D') = 0.03 (the false positive rate, i.e., the probability of testing positive given that the person does not have the disease)

P(T' | D) = 0.06 (the false negative rate, i.e., the probability of testing negative given that the person has the disease)

We can compute the marginal probability of testing positive as follows:

P(T) = P(T | D) × P(D) + P(T | D') × P(D')

= (1 - P(T' | D)) × P(D) + P(T | D') × (1 - P(D))

Plugging in the given values, we get:

P(T) = (1 - 0.06) × 0.009 + 0.03 × (1 - 0.009)

≈ 0.0325

Now we can use Bayes' to compute P(D | T):

P(D | T) = P(T | D) × P(D) / P(T)

Plugging in the given values and the computed value of P(T), we get:

P(D | T) = (1 - P(T' | D)) × P(D) / P(T)

≈ (1 - 0.06) × 0.009 / 0.0325

≈ 0.002482

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Answer:

0.1666 cups vanilla or 8 teaspoons

Step-by-step explanation:

5 cups flour = 2 tsp vanilla

multiply each side by 4

20 cups flour = 8 tsp vanilla

there are 48 tsp in a cup, so divide 8 by 48

20 cups flour = 0.1666(repeating decimal) cups vanilla

Answer:

If you have 20 cups of flour you should use 8 teaspoons of vanilla

if you use 6 teaspoons of vanilla you should use 15 cups of flour.

Step-by-step explanation:

The solution to the given inequality is b ≤ 1.

Inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥.

Given inequality expression is,

7 (b - 1) / b ≤ 0

(7b - 7) / b ≤ 0

(7b / b) - (7 / b) ≤ 0

7 - 7/b ≤ 0

Adding 7/b on both sides,

7 ≤ 7/b

Multiplying b on both sides,

7b ≤ 7

b ≤ 1

Hence the value of b is b ≤ 1.

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Answer:

m= -1/7

b=2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.

Answer:

Ln x as opposed to log x

Step-by-step explanation: