Write whether each is an example of commutative, associative, or distributive properties.

The measurement of the length of two sides and the included angle are given. Hence, using law of cosines, the approximate length of the lake is found to be 296.1 yards.

Given : b = 245 yards, c= 270 yards,

To find: The length of the lake which is the value of x

To find [tex]\angle A[/tex], we know that [tex]110^o\, and\, \angle A[/tex] lie on straight line. So

[tex]110^o + \angle A = 180^o\\\\\angle A = 180^o - 110^o = 70^o[/tex]

Using law of cosines

[tex]a^2 = b^2 +c^2 - 2bc\cdot cosA[/tex]

Plugging the values of b , c and A into the equation, we get

 [tex]a^2 =245 ^2 +270^2 - 2\times 245 \times 270 \times \cos 70^o \\[/tex]

The value of [tex]\cos 70^o[/tex] is 0.342 approximately

On substituting this in the equation, we get

a = 296.1 yards

Every triangle has three vertices and three sides. If in a triangle, the three vertices are A, B, and C, then, the sides opposite these vertices are a, b, and c, respectively. The angle at each vertex is given the same name as the vertex. Therefore, the three angles are also named A, B, and C. To solve such a  triangle is to find the lengths of each of its sides and all its angles.

The sine rule  or law of sines is used when we are given either

a) two angles and one side

or

b) two sides and the angle that is not included between these two sides.

[tex]\frac{\sin A}{a} =\frac{\sin B}{b} =\frac{\sin C}{c}[/tex]

The cosine rule or law of cosines is used when we are given either

a) three sides (SSS)

or

b) two sides and the included angle (SAS)

[tex]c^2=a^2+b^2-2ab\cdot\ cosC \\ b^2=a^2+c^2-2ac\cdot\ cosB\\ a^2=b^2+c^2-2bc\cdot\ cosA\\[/tex]

The measurement of the length of two sides and the included angle are given. Hence, using law of cosines, the approximate length of the lake is found to be 296.1 yards.

To know more about law of cosines, check out: https://brainly.com/question/4372174

#SPJ1

Answer: $350 = t

Step-by-step explanation:

might help);   600-250 = t

t + 250 ≤ 600  INEQUALITY

Answer: $350.

Explanation: if you do  [tex]600 -250[/tex] you will end up with $350

Answer:

They would have sold 8.2 eggs

Step-by-step explanation:

^

The reaction described by 2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of oxidation - reduction reaction

Any chemical process in which a participating chemical species' oxidation number changes is known as an oxidation-reduction reaction, often known as a redox reaction. The phrase refers to a broad range of procedures.

The equation of the reaction is written as

2H₂O + 2K → 2KOH + 2H₂

The reducing agent here is Potassium which is K it transformed from Potassium to Potassium Hydroxide. Potassium is electron donor

The oxidizing agent is water which ended up as Hydrogen molecule

Learn more about redox reaction at:

https://brainly.com/question/26263317

#SPJ1

Answer:

Hi again, use the sine rule for length. answer: 82.42

Step-by-step explanation:

Answer:   [tex]\frac{\sqrt{55}}{8}[/tex]

This is the same as writing sqrt(55)/8 where the 8 is not inside the square root.

=====================================================

Explanation:

Draw a right triangle in the quadrant Q1, which is in the northeast corner.

We're given [tex]\cos(\theta) = 3/8[/tex]. Recall that cosine is the ratio of adjacent over hypotenuse.

[tex]\cos(\text{angle}) = \text{adjacent/hypotenuse}[/tex]

This right triangle will have an adjacent side of 3 and hypotenuse of 8.

Refer to the diagram below.

Use the pythagorean theorem [tex]a^2+b^2 = c^2[/tex] to find the missing side is exactly [tex]\sqrt{55}[/tex], which is the opposite side of angle theta.

Then as one last step, we would say:

[tex]\sin(\text{angle}) = \text{opposite/hypotenuse}\\\\\\\sin(\theta) = \frac{\sqrt{55}}{8}[/tex]

--------------

A very similar approach is to use the pythagorean trig identity

[tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex]

Solving for sine gets us

[tex]\sin(\theta)=\sqrt{1-\cos^2(\theta) }[/tex]

Sine is positive in Q1.

Then plug in [tex]\cos(\theta) = 3/8[/tex] and simplify. You should get the answer mentioned above.

Answer:

8x + 9

Step-by-step explanation:

5x + 3x + 6 + 3

8x + 9

Answer:

Step-by-step explanation:

17-8=9 but if 18-7=11 then 19-8=7

The amount invested at 8% and 6% is 1000 and 1900 respectively.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, The person invested $2900 in two mutual funds and the total profit is $194.

Let the amount invested at 8% is x, then the amount invested at 6% is:

2900-x

Since the total profit is $194, it follows:
8% of x + 6% of (2900 - x) = 194

8x/100 + 6(2900 - x)/100 = 194

8x + 17400 - 6x = 19400

2x = 19400 - 17400

2x = 2000

x = 1000

The amount invested at 6% is:
2900 - 1000

= 1900

Hence, the amount invested at 8% and 6% is 1000 and 1900 respectively.

Learn more on percentages here:

https://brainly.com/question/14979505

#SPJ1

Sine and cosine are the fundamental trigonometric functions associated to the sides of a right triangle and tangent is a derivate trigonometric function.

Let be a right triangle, whose features are introduced in the figure attached below. The side with measure y is the side opposite to the angle θ, whereas the side with measure x is the side adjacent to the angle θ. The side with measure r represents the hypotenuse of the right triangle, which can be found by means of Pythagorean theorem:

r = √(x² + y²)

Trigonometric functions are trascendent functions that relates two sides of the right triangle. There are two fundamental trigonometric functions and four derivate trigonometric functions:

Fundamental

sin θ = y / r = (Opposite side) / (Hypotenuse)

cos θ = x / r = (Adjacent side) / (Hypotenuse)

Derivate

tan θ = sin θ / cos θ = y / x = (Opposite side) / (Adjacent side)

cot θ = 1 / tan θ = cos θ / sin θ = x / y = (Adjacent side) / (Opposite side)

sec θ = 1 / cos θ = r / x = (Hypotenuse) / (Adjacent side)

csc θ = 1 / sin θ = r / y = (Hypotenuse) / (Opposite side)

To learn more on trigonometric functions: https://brainly.com/question/14746686

#SPJ1

In a residual plot if the linearity assumption is the points are scattered and there is no obvious pattern.

Residual plot:

in statistics, residual value is a measure of how much a regression line vertically misses a data point.

Given,

Here we need to find what would you expect to see in a residual plot if the linearity assumption is correct.

As per the definition of residual plot, there is no obvious pattern for this plot and the positive and negative values are evenly spread across the whole range.

Therefore, in the regression line there are some points are misses the line on the vertical base.

To know more about Residual point here.

https://brainly.com/question/27864993

#SPJ4

Answer: 166

Step-by-step explanation:

The sum of two odd numbers is an even number.

85 is odd, and so is the sum of an odd number and an even number.

2×83=166

The question is an illustration of equation of circles.

The equation of the dartboard circle is:  [tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]

Brian's dart lands on the dartboard because D = 11.5 feet , 5 feet is within the circumference of the dartboard.

Given that,

h = 5 feet 8 inches ---- the height at which the dartboard was hung

d = 18 inches in diameter ---- the diameter of the dartboard

B = 12 feet --- the bull's eye

D = 11.5 feet , 5 feet --- Brian's dart

Equation of the circle

First, we convert all units to feet

This is done by dividing inches units by 12

h = 5 feet 8 inches

h = 5 ft + 8/12 ft

h = 5 ft + 2/3 ft

Take LCM

h = [tex]\frac{15+2}{3}[/tex] ft

h = [tex]\frac{17}{3}[/tex] ft

d = 18 inches

d = [tex]\frac{18}{12}[/tex] ft

d = [tex]\frac{3}{2}[/tex] ft

Divide by 2 to calculate radius

r = [tex]\frac{3}{2*2}[/tex] ft

r = [tex]\frac{3}{4}[/tex] ft

To find the equation of a circle when you know the radius and centre, use the formula as [tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex] , where represents the centre of the circle, and is the radius.

The equation of the circle is represented as:

[tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex]

In this case:

a = B = 12 feet -- the distance between the bull's eye and the wall

b = h = [tex]\frac{17}{3}[/tex] ft  ---- the height at which the dartboard was hung

So, we have:

[tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex]

[tex](x-12)^{2} +(y-\frac{17}{3}) ^{2} = (\frac{3}{4}) ^{2}[/tex]

Evaluate the exponents

[tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]

Hence, the equation of the circle is:

[tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]

Does Brian’s dart land on the dartboard?

Yes her dart lands on the dartboard because

D = 11.5 feet , 5 feet is within the circumference of the dartboard

Therefore,

The question is an illustration of equation of circles.

The equation of the dartboard circle is:  [tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]

Brian's dart lands on the dartboard because D = 11.5 feet , 5 feet is within the circumference of the dartboard.

To learn more about Equation of circles visit :

brainly.com/question/28948111

#SPJ4

The system of equations is  y = 50 + 3x; y = 34 + 4x. The number of cups that Aunt Emily orders is 16. The cost of either shop for 16 cupcakes is $98.

What is substitution method?

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

Assume that x number of cups that ordered by Aunt Emily.

Given that, Clarksville Bakery charges $3 for each cupcake, plus $50 for the large cake.

Therefore, the cost of x cupcake is 50 + 3x.

y = 50 + 3x

Also, Sebastian's Sweet Shoppe charges $34 for the large cake and $4 for each cupcake.

Therefore, the cost of x cupcake is 34 + 4x.

y = 34 + 4x

The system of equations is

y = 50 + 3x  ....(i)

y = 34 + 4x  ...(ii)

To find the number of cupcakes that Aunt Emily orders, use substitution method to solve the system of equation.

Substitute y = 50 + 3x in equation (ii)

50 + 3x = 34 + 4x

Subtract 3x from both sides:

50 = 34 + x

x = 16

Putting x = 16 in equation (i)

y = 50 + (3 × 16) = 98

To learn more about system of equation, click on below link:

https://brainly.com/question/21603338

#SPJ1

Answer:  12

Step-by-step explanation:

hope this helps

The values of x and w on the triangle are given as follows:

w = 14.4, x = 11.2.

The values of x and w are obtained applying the trigonometric ratios, as the triangle is a right triangle.

The three trigonometric ratios are given as follows:

For the angle of 48º, we have that:

Hence:

tan(48º) = 16/w

w = 16/tan(48º)

w = 14.4.

For the angle of 32º, we have that:

Hence:

tan(32º) = 16/(14.4 + x)

tan(32º)(14.4 + x) = 16

x = (16 - 14.4tan(32º))/tan(32º)

x = 11.2.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

Heather worked 5 hours every evening during each dinner shift.

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.

A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.

Let morning shift = m

evening shift = e

Representing the word problem in an equation;

4(m + e) = 28

Diving both sides by 4

m + e = 7

but she always works 2 hours in th morning shift

2 + e = 7

e = 7 - 2

e = 5

Therefore she worked 5 hours in the evening shift for 4 days.

Learn more about linear equations here: https://brainly.com/question/2030026

#SPJ1

Two more adults can board the elevator if there are 17 children present inside.

The number of adults who can still enter will be determined by the linear equation solution.

let

20c = 15a ; 5 divided by both sides

4c = 3a

Another 3 kids can enter the elevator if there are already 17 in it.

The fact that;

3c =  9/4 a

3c =  9/4 a

3c = 2.25 a

3c = 2 a (no fraction)

Thus, two more adults can board the elevator if there are 17 children present inside.

To know more about the linear equation, here

https://brainly.com/question/2030026

#SPJ4

For the given number line the inequality equation would be -10 < x ≤ 20.

What is inequality?

In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

In the given number line, a hollow circle represents that the number is excluded and solid circle represents that the number is included in the range

and the range lies between -10 to 2.

Let's take a variable to describe the relationship,

By using inequality we can prepare the inequality equation as

                -10 < x ≤ 20

Hence, for the given number line the inequality equation would be -10 < x ≤ 20.

To learn more about inequalities, visit:

https://brainly.com/question/21103162

#SPJ1

Answer: 1452 units^3

The required volume of the cylinder with a height of 12 units and radius of 11 units is 1452π cubic units.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

The formula for the volume of a cylinder is given as:

V = πr²h

Where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the cylinder.

Substituting the given values, we get:

V = π(11)²(12)

= π(121)(12)

= 1452π cubic units

Therefore, the volume of the cylinder with a height of 12 units and radius of 11 units is 1452π cubic units.

Learn more about Volume here:
https://brainly.com/question/1578538

#SPJ5

Answer:

√53 or 7.28

Step-by-step explanation:

To find the length of the line segment from the point (4, 2) to the point (-3, 4), you can use the distance formula, which is:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates of the two points, you get:

distance = √((-3 - 4)^2 + (4 - 2)^2)

Simplifying this expression gives:

distance = √((-7)^2 + (2)^2)

Which simplifies to:

distance = √(49 + 4)

Which simplifies to:

distance = √53

So the length of the line segment from the point (4, 2) to the point (-3, 4) is approximately 7.28.

Answer: It is correct.

Step-by-step explanation:

Answer: 11 / 20

Step-by-step explanation:

Answer:

There are 9 small $5 bags and 6 large $8 bags

Step-by-step explanation:

9 x 5 = 45

6 x 8 = 48

45 + 48 = 93

The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to 54.52 , 1.808, 3.2712 respectively.

As given in the question,

Let success be defined by health department inspection is passed by restaurant

Probability of success rate 'p' = 0.94

Value of ' 1 - p ' = 1 - 0.94

                        = 0.06

Number of owners of restaurant which are surveyed 'n' = 58

For the given binomial experiments calculation of the following distributions are:

Mean 'μ' = np

             = 58 × 0.94

             = 54.52

Standard deviation 'σ' = √ np (1 - p)

                                   = √ 58 × 0.94 × 0.06

                                   = √3.2712

                                   = 1.808

Variance 'σ²' =  np( 1 - p )

                    = 58 × 0.94 × 0.06

                   = 3.2712

Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.

Learn more about probability visit:

brainly.com/question/11234923

#SPJ4