A helicopter hovering above a command post shines a spotlight on an object on the ground 250 feet away from the command post as shown in the diagram how far is the object from the helicopter to the nearest foot

After 5 and a half minutes, the temperature of the water will be 77°F.

In this scenario, we are given that the initial temperature of the water is 80°F. We also know that the temperature of the water decreases by 0.5°F every minute. We want to find out what the temperature of the water will be after 5 and a half minutes.

To solve this problem, we need to use a bit of math. We know that the temperature of the water is decreasing by 0.5°F every minute. So after 1 minute, the temperature of the water will be 80°F - 0.5°F = 79.5°F. After 2 minutes, the temperature will be 79.5°F - 0.5°F = 79°F. We can continue this pattern to find the temperature after 5 and a half minutes.

After 5 minutes, the temperature of the water will be 80°F - (0.5°F x 5) = 77.5°F. And after another half minute (or 0.5 minutes), the temperature will decrease by another 0.5°F, so the temperature will be 77.5°F - 0.5°F = 77°F.

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Answer:

[tex]h(x)=2x^2-12x+9[/tex],  [tex]p(x)=-5x^2-20x-5[/tex]

Step-by-step explanation:

To get to the standard form of a quadratic equation, we need to expand and simplify. Recall that standard form is written like so:

[tex]ax^2+bx+c[/tex]

Where a, b, and c are constants.

Let's expand and simplify h(x).

[tex]2(x-3)^2-9=\\2(x^2+9-6x)-9=\\2x^2+18-12x-9=\\2x^2+9-12x=\\2x^2-12x+9[/tex]

Thus, [tex]h(x)=2x^2-12x+9[/tex]

Let's do the same for p(x).

[tex]-5(x+2)^2+15=\\-5(x^2+4+4x)+15=\\-5x^2-20-20x+15=\\-5x^2-5-20x=\\-5x^2-20x-5[/tex]

Thus, [tex]p(x)=-5x^2-20x-5[/tex]

To compute the covariance matrix of the variables in the data, the "matrix-operation" which should be used is ([tex]X^{t}[/tex] × X)/n.

The "Covariance" matrix is defined as a symmetric and positive semi-definite, with the entries representing the covariance between pairs of variables in the data.

The "diagonal-entries" represent the variances of individual variables, and the off-diagonal entries represent the covariances between pairs of variables.

Step(1) : Compute the transpose of the centered data matrix X, denoted as [tex]X^{t}[/tex]. The "transpose" of a matrix is found by inter-changing its rows and columns.

Step(2) : Compute the "dot-product" of [tex]X^{t}[/tex] with itself, denoted as [tex]X^{t}[/tex] × X.

The dot product of two matrices is computed by multiplying corresponding entries of the matrices and summing them up.

Step(3) : Divide the result obtained in step(2) by the number of samples in the data, denoted as "n", to get the covariance matrix.

This step scales the sum of the products by 1/n, which is equivalent to taking the average.

So, the covariance matrix "C" of variables in "centered-data" matrix X can be expressed as: C = ([tex]X^{t}[/tex] × X)/n.

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The given question is incomplete, the complete question is

Let X be a matrix of centered data with a column for each field in the data and a row for each sample. Then, not including a scalar multiple, how can we use matrix operations to compute the covariance matrix of the variables in the data?

The probability of picking one bolt and one nut is 1/2 or 50%.

To find the probability that one is a bolt and one is a nut, we need to use the formula for calculating the probability of two independent events happening together: P(A and B) = P(A) × P(B)

Let's first calculate the probability of picking a bolt from the box:

P(bolt) = number of bolts / total number of parts = 3/6 = 1/2

Now, let's calculate the probability of picking a nut from the box:

P(nut) = number of nuts / total number of parts = 3/6 = 1/2

Since the events are independent, the probability of picking a bolt and a nut in any order is:

P(bolt and nut) = P(bolt) × P(nut) + P(nut) × P(bolt)

P(bolt and nut) = (1/2) × (1/2) + (1/2) × (1/2)

P(bolt and nut) = 1/2

Therefore, the probability of picking one bolt and one nut is 1/2 or 50%.

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the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.

To find the probability that one chosen part is a bolt and the other chosen part is a nut, we need to use the formula for probability:

Probability = (number of desired outcomes) / (total number of outcomes)

There are two ways we could choose one bolt and one nut: we could choose a bolt first and a nut second, or we could choose a nut first and a bolt second. Each of these choices corresponds to one desired outcome.

To find the number of ways to choose a bolt first and a nut second, we multiply the number of bolts (3) by the number of nuts (3), since there are 3 possible bolts and 3 possible nuts to choose from. This gives us 3 x 3 = 9 total outcomes.

Similarly, there are 3 x 3 = 9 total outcomes if we choose a nut first and a bolt second.

Therefore, the total number of desired outcomes is 9 + 9 = 18.

The total number of possible outcomes is the number of ways we could choose two parts from the box, which is the number of ways to choose 2 items from a set of 6 items. This is given by the formula:

Total outcomes = (6 choose 2) = (6! / (2! * 4!)) = 15

Putting it all together, we have:

Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 18 / 15
Probability = 1.2

However, this answer doesn't make sense because probabilities should always be between 0 and 1. So we made a mistake somewhere. The mistake is that we double-counted some outcomes. For example, if we choose a bolt first and a nut second, this is the same as choosing a nut first and a bolt second, so we shouldn't count it twice.

To correct for this, we need to subtract the number of outcomes we double-counted. There are 3 outcomes that we double-counted: choosing two bolts, choosing two nuts, and choosing the same part twice (e.g. choosing the same bolt twice). So we need to subtract 3 from the total number of desired outcomes:

Number of desired outcomes = 18 - 3 = 15

Now we can calculate the correct probability:

Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 15 / 15
Probability = 1

So the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.

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The estimated regression equation for the given data is y = -30.7 + 3.409x

To develop an estimated regression equation for the given data, we need to use the method of least squares.

The formula for the slope of the regression line is given by:

b = ∑(xi - x)(yi - y) / ∑(xi - x)²

where xi and yi are the individual values of the two variables, x and y are their respective means.

The formula for the intercept of the regression line is given by:

a = y - b × x

where a is the intercept and b is the slope.

Using the given data, we can calculate the values of x, y, b, and a as follows

x = (6 + 11 + 15 + 18 + 20) / 5 = 14

y = (7 + 9 + 12 + 21 + 30) / 5 = 15.8

∑(xi - x)(yi - y) = (6 - 14)(7 - 15.8) + (11 - 14)(9 - 15.8) + (15 - 14)(12 - 15.8) + (18 - 14)(21 - 15.8) + (20 - 14)(30 - 15.8) = 306.8

∑(xi - x)² = (6 - 14)² + (11 - 14)² + (15 - 14)² + (18 - 14)² + (20 - 14)² = 90

b = ∑(xi - x)(yi - y) / ∑(xi - x)² = 306.8 / 90 = 3.409

a = y - b × x = 15.8 - 3.409 × 14 = -30.7

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The given question is incomplete, the complete question is:

Given are data for two variables, x and y. Develop an estimated regression equation for these data.

The two null hypothesis that are correct answer are two-sample t-test and one-sample t-test.

Among the group of answer choices provided, the tests that require calculating degrees of freedom are the two-sample t-test and the one-sample t-test. Both of these tests belong to the t-test family and involve using degrees of freedom to determine the critical t-value.

In summary:
- Null hypothesis: The assumption that there is no significant difference between the sample and population or between two samples.
- T-test: A statistical test used to determine if there is a significant difference between the means of two groups or between a sample and population mean.
- Degrees of freedom: A value used in statistical tests that represents the number of independent values in a data set, which can affect the outcome of the test.

So answer is: two-sample t-test and one-sample t-test.

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The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-

sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also

requires degrees of freedom, but it is not a test for a null hypothesis.

The correct answer is: all of the above.

All these tests require calculating degrees of freedom:

1. Two-sample t-test:

Degrees of freedom are calculated using the formula (n1 + n2) - 2, where n1 and n2 are the sample sizes of the two

groups being compared.
2. Chi-squared test:

Degrees of freedom are calculated using the formula (rows - 1) * (columns - 1), where rows and columns represent the

number of categories in the data.
3. One-sample t-test:

Degrees of freedom are calculated using the formula n - 1, where n is the sample size.

The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-

sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also

requires degrees of freedom, but it is not a test for a null hypothesis.

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The main topic is the split-half reliability test used in psychological research to assess the internal consistency of a scale.

In psychological research, reliability is a crucial aspect of measuring constructs or attributes. One commonly used method for assessing the reliability of a scale is the split-half reliability test.

In this test, the scale questions are divided into two parts equally, and the resulting scores of both parts are correlated against one another.

For example, if a scale had 20 items, the items could be randomly split into two groups of 10 items each.

Scores are then calculated for each group, and the scores are correlated with each other to determine the degree of consistency between the two halves.

The correlation coefficient obtained from this analysis provides an estimate of the internal consistency of the scale.

A high correlation coefficient indicates a high level of internal consistency, indicating that the two halves of the scale are measuring the same construct or attribute.

Conversely, a low correlation coefficient suggests that the two halves of the scale are not measuring the same construct or attribute, and the scale may need to be revised or abandoned.

Overall, the split-half reliability test provides a quick and efficient method for evaluating the reliability of a scale.

However, it is important to note that this method does have some limitations, such as the possibility of unequal difficulty or discrimination of the items in each half of the scale.

Therefore, researchers often use other methods, such as Cronbach's alpha, in conjunction with the split-half reliability test to provide a more comprehensive assessment of the reliability of a scale

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The profit (p) is $7500 generated by selling 1500 units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x²

To maximize our profit, we must locate the vertex of the parabola represented by this function. The x-value of the vertex indicates the number of units that must be sold to maximize profit.

We may use the formula for the x-coordinate of a parabola's vertex:

x = -b/2a

where a and b represent the coefficients of the quadratic function ax² + bx + c. In this situation, a = -0.004 and b = 12, resulting in:

x = -12 / 2(-0.004) = 1500

This indicates that when 1,500 units are sold, the profit is maximized.

To calculate the greatest profit, enter x = 1500 into the profit function:

P(1500) = -1500 + 12(1500) - 0.004(1500)^2

P(1500) = -1500 + 18000 - 9000

P(1500) = $7500

Therefore, the maximum possible profit is $7,500 and it is generated when 1,500 units are sold.

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To achieve this maximum profit, exactly 1500 units must be sold.

To find the maximum profit and the number of units needed to generate it, we can use the given profit function p(x) = -1500 + 12x - 0.004x^2. We need to find the vertex of the parabola represented by this quadratic function, as the vertex will give us the maximum profit and the corresponding number of units.

Step 1: Identify the coefficients a, b, and c in the quadratic function.
In p(x) = -1500 + 12x - 0.004x^2, the coefficients are:
a = -0.004
b = 12
c = -1500

Step 2: Find the x-coordinate of the vertex using the formula x = -b / (2a).
x = -12 / (2 * -0.004) = -12 / -0.008 = 1500

Step 3: Find the maximum profit by substituting the x-coordinate into the profit function p(x).
p(1500) = -1500 + 12 * 1500 - 0.004 * 1500^2
p(1500) = -1500 + 18000 - 0.004 * 2250000
p(1500) = -1500 + 18000 - 9000
p(1500) = 7500

So, the maximum profit is $7,500, and 1,500 units must be sold to generate it.

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The current in the circuit when the resistance is 12 ohms is 40 amps.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.

We can use the inverse proportionality formula to solve this problem, which states that:

current (in amps) x resistance (in ohms) = constant

Let's call this constant "k". We can use the information given in the problem to find k:

24 amps x 20 ohms = k

k = 480

Now we can use this constant to find the current when the resistance is 12 ohms:

current x 12 ohms = 480

current = 480 / 12

current = 40 amps

Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.

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Answer:

see the images and explanation

Step-by-step explanation:

for the graph:

the domain 0 < x < 5

the range for each functions:

g(x) = 2x + 1

g(x) = y  ,   1 < y < 11

h(x) = 2x + 2 ,  2 < y < 12

Answer:

a 1053

b 250

multiply 650 by 1.62 for part a.

for part b divide by 1.62 since pound is less than dollar

hope this helps :)

The coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

The circumference of the coin can be calculated as follows to determine the number of turns it makes:

C = πd

where C is the circumference, d is the diameter, and π is the mathematical constant pi (approximately equal to 3.14159).

So, for the given $2 coin with a diameter of 25.75 mm, the circumference is:

C = πd = 3.14159 x 25.75 mm ≈ 80.926 mm

Divide the distance traveled by the coin's circumference to determine the number of turns it makes when rolled on its edge for 1.34 meter:

Number of turns = distance traveled / circumference of the coin

Number of turns = 1.34 m / 0.080926 m

Number of turns ≈ 16.53

Therefore, the coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

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"It can vary - it really depends on the distribution of the variable."

The number of intervals, or bins, to choose when creating a histogram can vary depending on the distribution of the variable.

Most often, about 8-10 intervals are used, but there is no set rule. It is generally recommended to have at least 5 intervals, but if the data is highly skewed or has outliers, more intervals may be needed to accurately represent the distribution.

Ultimately, the goal is to choose a number of intervals that provides a clear visual representation of the data without oversimplifying or overcomplicating the histogram.

The number of intervals or bins to be chosen when creating a histogram can vary and it really depends on the distribution of the variable.

While most often, about 8-10 bins are used, there is no hard and fast rule for the number of bins to be used in a histogram.

In general, the number of bins should be large enough to display the shape of the distribution clearly, but not so large that it obscures important features of the distribution or leads to overfitting.

A minimum of 5 bins is recommended to display the basic shape of the distribution, but more bins may be necessary for complex or multi-modal distributions.

Depending on the distribution of the variable, a histogram's number of intervals or bins can be altered.

There is no established guideline, however 8–10 intervals are typically utilized.

A minimum of five intervals are often advised, however if the data is extremely skewed or contains outliers, more intervals could be required to correctly depict the distribution.

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Answer:

f(x) is the blue graph, g(x) is the red graph.

x^2 - 3x + 17 - (2x^2 - 3x + 1) = 16 - x^2

16 - x^2 = 0 when x = -4, 4

So the area between these two graphs is (using the TI-83 graphing calculator):

fnInt (16 - x^2, x, -4, 4) = 85 1/3

Answer: there is only one number

Answer:

Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.

Espero haber ayudado :D

The correct statement regarding the null hypothesis is: the null hypothesis claims the opposite of what the researcher believes.

The null hypothesis is the claim that no relationship exists between two sets of data or variables being analyzed. The

null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative

relationship does not exist, hence the term "null".

In research, the null hypothesis is a statement of no effect or no relationship between variables, while the alternative

hypothesis represents the effect or relationship the researcher is interested in demonstrating.

The purpose of statistical testing is to determine whether there is enough evidence to reject the null hypothesis in

favor of the alternative hypothesis.

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The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.

The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.

Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.

For the given problem, Transformation to get the desired result can be carried out as:

Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.

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The two column proof is written as follows

Statement                                                           Reason

MA = XR                                           given (opposite sides of rectangle)

MK = AR                                           given (opposite sides of rectangle)

arc MA = arc RK                               Equal chords have equal arcs

arc MK = arc AK                               Equal chords have equal arcs

An arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.

If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.

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Answer:

The correct answer is:

10√2

Explanation:

In a right triangle, the hypotenuse is the side opposite the right angle and is also the longest side. The other two sides are called the legs.

In this problem, the hypotenuse of the resulting triangles is given as 20 inches. Since the quilt squares are cut on the diagonal to form triangular quilt pieces, the hypotenuse of each triangle is formed by the diagonal cut of a square.

Let's denote the side length of each square as "s" inches.

According to the Pythagorean Theorem, which relates the sides of a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

In this case, the hypotenuse is 20 inches, so we have:

20^2 = s^2 + s^2 (since the two legs of the right triangle are the sides of the square)

400 = 2s^2

Dividing both sides by 2, we get:

200 = s^2

Taking the square root of both sides, we get:

s = √200

Since we are looking for the side length of each piece in simplified radical form, we can further simplify √200 as follows:

√200 = √(100 x 2) = 10√2

So, the side length of each quilt piece is 10√

The side length of each piece of the triangular pieces of quilt cut from squares will be 10√2 inches.

This is a simple mathematics problem that can be solved using the Pythagoras theorem. This theorem states that in a right-angled triangle, the square root of the sum of the two perpendicular sides (p,b) is equal to the longest side, called the hypotenuse (h).

[tex]h = \sqrt{p^2 + b^2}[/tex]

Since the triangle pieces have been cut from a square, they will be right-angled triangles, and the two perpendicular sides will be equal, i.e., p = b.

20 = √2p²  (since p and b are equal, b can be taken as p)

On squaring both sides,

400 = 2p²

p² = 400/2

p² = 200

p = √200

p = 10√2 = b

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The leg measurement will make a right triangle is 21 cm.

The longest side of a right-angled triangle, i.e. the side opposite the right angle, is called the hypotenuse in geometry.

Pythagorean theorem :

If p be the length of the hypotenuse of a right-angled triangle, q and r be the lengths of the other two sides, then

p² = q² + r²

The lengths of the other two sides of the given right-angled triangle are 20 cm and 21 cm. Put these values in the above theorem to get the desired result.

Now, p² = (20)² + (21)²

= 400 + 441 = 841

i.e. p = √(841) = 29

Therefore the length of the hypotenuse is 29 cm. The right angle traingle is 21 cm.

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It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.

The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.

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Step-by-step explanation:

Again, using similar triangle ratios

7.2 m  is to 2.4 m  

     as   AB is to  12.0 m

7.2 / 2.4  = AB/12.0    Multiply both sides of the equation by 12

12 *   7.2 / 2.4   = AB = 36.0 meters

Step-by-step explanation:

hope this will help you Thanks

For a percentage data of students who play the different game and win the prize, the expected amount to pay for prizes for that booth by the carnival committee is equals to the $218.70.

We have a booth of school carnival in past years, The percentage of students win a stuffed toy = 22%

The percentage of students win a jump rope = 16%

The percentage of students win a t-shirt

= 6%

The winning amount for stuffed toy game = $ 3.60

The winning amount for jump rope game = $1.20

The winning amount for t-shirt game

= $7.90

The remaining students do not win a prize. Now, total number of students play the game at the booth = 150

So, number of students who win stuffed toy = 22% of 150 = 33

Number of students who win jump rope = 16% of 150 = 24

Number of students who win stuffed toy

= 6% of 150 = 9

For determining the expected pay using the simple multiplication formula. Total expected pay for prizes for that booth is equals to the sum of resultant of multiplcation of number of students who play a particular game into pay amount for that game. That is total excepted pay in dollars = 3.60 × 33 + 1.20 × 24 +7.90 × 6

= 218.7

Hence required value is $218.70.

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Answer: 6 3/7

Step-by-step explanation:

9/1 x 5/7

If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.

Answer:

[tex]\frac{45}{7}[/tex] or 6.4285

Step-by-step explanation:

First, multiply 9 and 5, which gives you 45.

9(5)=45

Then, divide 45 by 7.

45/7=6.4285

That gives  you  [tex]\frac{45}{7}[/tex] or 6.4285

Hope this helps!

Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.

To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.

Here,

By dividing the overall elevation change (12 metres) by the total time required (4 seconds),

it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.

=> Elevation change equals 12 metres

=> Total duration: 4 seconds

=>  12 meters / 4 seconds

=> 3 meters/second

As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.

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Answer:

1

Step-by-step explanation:

First of all we use the "law of sines"

to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x

and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°

180°=70°+51°+ x

x = 180°-121°

=59°

Using law of sines:

(sides are represented by small letters/capital letters are the angles)

a/sinA= b/sinB= c/sinC

We have one given side which is "9"

so,

9/sin70= x/sin59

doing the criss-cross method,

9×sin59=sin70×x

9×sin59/sin70=x

x=8.2 (answer 1)

I hope this was helpful <3

Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:

sin^2(a) + cos^2(a) = 1

sin^2(a) + (-5/9)^2 = 1

sin^2(a) = 1 - (-5/9)^2

sin^2(a) = 1 - 25/81

sin^2(a) = 56/81

Taking the square root of both sides:

sin(a) = ±sqrt(56/81)

Since a is in quadrant III, sin(a) is positive. Therefore:

sin(a) = sqrt(56/81) = (2/3)sqrt(14)