Trig Ratios and Finding Missing Sides Notes
What are the sine, cosine, and tangent ratios for ZH?
H
15
G
F
12

Answer:

a

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = \(\frac{1}{3}\) , then

y = \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (6, 4 ) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = \(\frac{1}{3}\) x + 2 ← equation of line

a) To determine the value of k such that f(x₁, x₂) is a valid probability distribution, we need to ensure that the sum of f(x₁, x₂) over all possible values of x₁ and x₂ is equal to 1.

b) To find P(≤0.5), we need to calculate the probability that the joint random variable (X₁, X₂) takes on a value less than or equal to 0.5.

c) To find F(1,4), we need to calculate the cumulative distribution function (CDF) at the point (1,4), which represents the probability that (X₁, X₂) is less than or equal to (1,4).

d) To find P(X₂ ≤ 3-X₁), we need to calculate the probability that X₂ is less than or equal to 3 minus X₁.

e) To find P(X₁X₁ > 2), we need to calculate the probability that the product of X₁ and X₂ is greater than 2.

f) To find P(X₁ ≤ 1, 2X₂ = 4), we need to calculate the probability that X₁ is less than or equal to 1, given that 2X₂ is equal to 4.

a) We can determine the value of k by calculating the sum of f(x₁, x₂) over all possible values of x₁ and x₂ and setting it equal to 1. Since the given values of x₁ and x₂ are limited to 1, 2, and 3, we can calculate the sum and solve for k.

b) P(≤0.5) involves finding the probability that (X₁, X₂) takes on a value less than or equal to 0.5. This requires summing up the probabilities of all pairs (x₁, x₂) such that (x₁, x₂) ≤ 0.5.

c) F(1,4) represents the cumulative probability that (X₁, X₂) is less than or equal to (1,4). This involves summing up the probabilities of all pairs (x₁, x₂) such that (x₁, x₂) ≤ (1,4).

d) P(X₂ ≤ 3-X₁) requires calculating the probability that X₂ is less than or equal to 3 minus X₁. This involves summing up the probabilities of all pairs (x₁, x₂) such that x₂ ≤ 3 - x₁.

e) P(X₁X₂ > 2) involves finding the probability that the product of X₁ and X₂ is greater than 2. This requires summing up the probabilities of all pairs (x₁, x₂) such that x₁x₂ > 2.

f) P(X₁ ≤ 1, 2X₂ = 4) requires calculating the probability that X₁ is less than or equal to 1, given that 2X₂ is equal to 4. This involves summing up the probabilities of all pairs (x₁, x₂) such that x₁ ≤ 1 and 2x₂ = 4.

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Given the subtotal of $55.97, apply taxes as shown below (remember that 6.75%=6.75/100=0.0675)

Now, apply the discount (20%=20/100=0.20)

The answer is approximately $47.8 (taxes first, then discount)

Answer:

1. 9.8

2. 3.8

3. -19

Hope it helps :)

Answer:

1. The ball is thrown from a height of 2 ft

Step-by-step explanation:

Since 2 does not have a variable that would be the y-intercept; the y-intercept it where the ball is first getting thrown from.

The scalar product is very simple, if we have a 2 dimension vetorial space the inner product is

Therefore, we have

Therefore the correct answer is

Concatenation is both commutative and associative, meaning that the order in which sequences are combined and the grouping of sequences does not affect the result of the concatenation.

Concatenation is a term used in computer science and mathematics to describe the process of combining two or more strings, lists, or other sequences into a single, longer sequence.

The question of whether concatenation is commutative or associative refers to the order in which the elements are combined and whether the result is the same regardless of the order.

Commutativity refers to the property of an operation where changing the order of the operands does not change the result. In the case of concatenation, if A and B are two sequences, then the result of concatenating them (A followed by B) is the same as the result of concatenating them in the opposite order (B followed by A). This means that concatenation is commutative.

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There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

The argument is valid. It follows the form of modus ponens where the first premise establishes a conditional statement "if p, then q", and the second premise affirms the antecedent "p". Therefore, the conclusion "q" logically follows. There is no fallacy present in this argument.

The given argument is as follows:
1. If he rides bikes (p), he will be in the race (q).
2. He rides bikes (p).
3. He will be in the race (q).

Let's determine if the argument is valid or a fallacy, and identify the form that applies.

In this case, the argument is valid and follows the form of Modus Ponens. Modus Ponens is a valid argument form that has the structure:

1. If p, then q.
2. p.
3. Therefore, q.

Here, since the argument follows this structure (If he rides bikes, he will be in the race; he rides bikes; therefore, he will be in the race), it is a valid argument and not a fallacy.

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Answer:

7/13

Step-by-step explanation:

(0.538461538)

Answer:

Php 3,230

Step-by-step explanation:

1. calculate x= the number of days worked in a week (5days)

which is,

x= 5 (no of days) x 550 ( total amount of Php received in a day)

x= Php 2,750

2. calculate y= the number of extra hours ( 6 hours )

which is,

y= 6 ( total number of extra hours ) x 80 ( because extra hours is paid at the amount of Php 80 )

y= Php 480

3. Add x and y to get the final answer

which is,

Php 2,750 + Php 480 = Php 3,230

Answer:

Step-by-step explanation:

The temperature when the plane reaches an altitude of 5000 ft will be 47.2 F.

Temperature Drop per 1000 ft      :       1.6 F

Temperature Drop for 5000 ft       :       1.6 x (5000/1000)

      :       1.6 x 5 = 8.0

Temperature at 5000 ft                   :      55.2 – 8  = 47.2 F

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The temperature when the plane reaches an altitude of 5000 feet will be 47.2 Fahrenheit.

In the given case, there is a drop of 1.6 Fahrenheit in temperature for every thousand feet that an airplane climbs into the sky.

The temperature on the ground is 55.2 Fahrenheit.

Temperature Drop per 1000 feet = 1.6 Fahrenheit

Temperature Drop for 5000 feet = 1.6 x (5000/1000)

                                                       = 1.6 x 5

                                                       = 8.0 Fahrenheit

To get the temperature when the plane reaches an altitude of 5000 feet,

The temperature at 5000 feet = 55.2 – 8 = 47.2 Fahrenheit

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Answer:

144*

Step-by-step explanation:

decagon has 10 sides every side is 144* angles

Answer:

144

Step-by-step explanation:

The quotient between the fractions -1/10 and -2/3 is:

(-1/10)÷(-2/3) = 3/20

Here we want to take the quotient between the two fractions -1/10 and -2/3.

Remember that the quotient between two fractions a/b and c/d is given by:

(a/b)÷(c/d) = (a/b)*(d/c) = (a*d)/(b*c)

Here we can write:

(-1/10)÷(-2/3) = (-1/10)*(-3/2) = (-1*-3)/(10*2) = 3/20

That is the quotient.

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The similarity theorem that proves the two given triangles are similar is: B. AA similarity theorem.

Recall:

The angle-angle similarity theorem (AA) states that if two angles in one triangle are of the same measure with two corresponding angles in another triangle, both triangles are similar to each other.

In the image given:

\(\angle F\) in \(\triangle ETF\) is congruent to \(\angle U\) in \(\triangle VTU\) (\(\angle F = \angle U = 78\))

\(\angle ETF = \angle VTU\) (vertical angles are equal)

This implies that two angles in \(\triangle ETF\) are congruent to two corresponding angles in \(\triangle VTU\).

Therefore, both triangles can be proven to be similar by the angle-angle similarity theorem (AA).

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Answer:

blank 1-2x+y1=86

Blank 2- x+y=48

Step-by-step explanation:

EXPLANATION :

From the problem, we have an elevator that is 0.9m by 0.9m

If we draw a diagonal line, the length of a diagonal line of a square is :

where s is the side of the square.

That will be :

So you can apply the social distancing by standing at the opposite corners of the elevator.

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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Answer:

p = 131.25

Step-by-step explanation:

The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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Answer:

B. midpoint

Step-by-step explanation:

UT is located in the middle of UT as the lengths of ST and US are equal

Answer:

1 / 5

Step-by-step explanation:

a = 2 - 9a

a + 9a = 2

10a = 2

a = 2 / 10

a = 1 / 5

The total area of the regions between the curves is 0.17 square units

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

x = y² - 2 and x = y - 2

For the intervals, we have

x = -2 and x = -1

Make y the subjects

So, we have

y = √(x + 2) and y = x + 2

So, the area of the regions between the curves is

Area = ∫x + 2 - √(x + 2)

This gives

Area = ∫x + 2 - √(x + 2)

Integrate

Area =  -[4(x + 2)^3/2 - 3x(x + 4)]/6

Recall that x = -2 and x = -1

So, we have

Area = [4(-1 + 2)^3/2 - 3(-1)(-1 + 4)]/6 + [4(-2 + 2)^3/2 - 3(-2)(-2 + 4)]/6

Evaluate

Area =  0.17

Hence, the total area of the regions between the curves is 0.17 square units

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The arc BX, central angle BCX, and inscribed BNX are connected through different relationships. : Arc BX and central angle BCX:1. Arc BX is the length of the arc that joins B and X points.2. Central angle BCX is an angle with vertex C that has a side BC and the other side goes through the midpoint of the arc BX.

3. The length of the arc BX is directly proportional to the measure of the central angle BCX.4. The measure of the arc BX is equal to the measure of the central angle BCX multiplied by the radius of the circle. Inscribed BNX and central angle BCX:1. The inscribed angle BNX is an angle formed by two chords inside a circle.2. The chord BX is the base for both inscribed angle BNX and central angle BCX. 3. The measure of the inscribed angle BNX is half the measure of the central angle BCX. 4.

The vertex of the inscribed angle BNX lies on the circumference of the circle, while the vertex of the central angle BCX lies at the center of the circle. 5. The inscribed angle BNX and the central angle BCX are always supplementary, meaning that their measures add up to 180 degrees.

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Answer:

15

Step-by-step explanation:

Count the units in the green shape or 3 x 5 = 15

Answer:

25

Step-by-step explanation:

10+7+8=25 this is because her cat weighs 8 pounds and her dog weighs 10 pounds more so that's 18 lb. after words it says Cameron's dog weighs 7 pounds less than bills so you do 18+7 and that equals 25

Given that the mean and standard deviation of the sample of age data is mean = 33.2 and standard deviation = 9.41.

Now, we are supposed to find the standard error of the mean and how it would change if the sample size had been 225 instead of 25.

A) Standard Error of Mean (SEM): The formula to calculate the standard error of the mean (SEM) is given by SEM = \frac{s}{\sqrt{n}}.

Where s is the standard deviation, and n is the sample size. Substituting the given values in the formula, we get the standard error of the mean is 1.88 years.

B) Effect of Increase in Sample Size on SEM. From the above formula, we know that as the sample size (n) increases, the standard error of the mean decreases. As the sample size increases, the sample mean is more likely to be closer to the actual population mean. Thus, for a sample size of 225, the standard error of the mean would be,

SEM = 0.6267. Hence, the standard error of the mean would be 0.6267 years if the sample size were 225 instead of 25.

Given the mean and standard deviation of the sample of age data, the standard error of the mean is 1.88 years. The standard error of the norm would be 0.6267 years if the sample size were 225 instead of 25. With the increase in the sample size, the standard error of the mean (SEM) decreases, making the sample mean closer to the actual population mean.

As the sample size gets bigger, the standard error of the mean gets smaller, which means that the sample mean is more likely to be closer to the actual population mean.

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Answer:

Triangles

Step-by-step explanation:

By using triangles you should be able to construct a hexagon.

Answer:

a)  See attached diagram.  The figures formed inside the hexagon are equilateral triangles.

b) Create 6 congruent equilateral triangles and place together to form a hexagon.

One albino laboratory rat is an independent variable.

To investigate how alcohol affects reaction times, sixty participants were randomly split into two groups. Those in one group drank a certain amount of alcohol, while those in the other group drank non-alcoholic beverages. Both groups' reaction times were timed before and after the beverage.

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The question is incomplete and wrong:

Sixty albino laboratory rats were randomly divided into two groups as part of a study on the effects of alcohol on reaction time. Each member of one group consumed a specified amount of alcohol and members of the other group had a non-alcoholic beverage. The reaction time of both groups was measured before and after taking the beverage/alcoholic drink. What is the INDEPENDENT VARIABLE?

a. Amount of alcohol

b. Reaction time

c. One albino laboratory rat

d. Sixty albino laboratory rats​