Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.

The total area of the two non-shaded crescent-shaped regions =25π ^2

The length of hypotenuse = 10

(6^2 + 8^2 = 10^2 )

Therefore, the radius of the large semicircle equals 5.            
area of large semi-circle = 25π

As a result, the total area of the two non-shaded regions is 25π^ 2

A semicircle is formed when a circle is divided in half along its diameter

The circumference of a semicircle is curved, and the diameter is straight.
A semicircle has a right angle of 90.


For example PR is a diameter and (angle PRQ=25.  The size of (angle QPR) is  (angle PQR=90circ) because it is the angle in a semicircle. The sum of  triangle's three angles is 180.    
   
     
To learn more about a semicircle                
https://brainly.com/question/30023569
#SPJ4                                                  

3.31 it will take her to complete the triathlon.

To find this, we can apply the equation distance = rate x time.

We are aware of the length and pace of each triathlon leg. Let's name them, respectively, d and r. We must locate the time, which we shall designate as t.

d = r x t    or

t = d/r

The distance is 0.93, or 93/100, and the rate is 1.2, or 12/10 when swimming. As a result of our formula, we have:

12/10 divided by 93/100 yields the same result as

93/100 * 10/12

time to swim = 93/120 = 31/40

We have a distance of 24.8 miles, or 248/10, and a speed of 18.8 miles, or 188/10, for biking. Using the same formula, we obtain:

248/10 divided by 188/10 or

248/10 * 10/188 = 248/188 = 62/47 = time to bike

Finally, for the run, the distance is 6.2 = 62/10 and the rate is 5.1 or 51/10. Plugging this into the formula gives:

62/10 divided by 51/10 or

62/10 * 10/51 = 62/51 = time to run

= 31/40 + 62/47 + 62/51

=3.31

Know more about distance

https://brainly.com/question/26046491

#SPJ4

Answer:

20/9 laps

Step-by-step explanation:

convert everything to minutes to make things a little easier

3/10 of an hour = 1/10 of an hour (6 minutes) * 3 = 18 minutes

2/3 of an hour = 1/3 of an hour (20 minutes) * 2 = 40 minutes

18 minutes = 1 lap

40 minutes = ? laps

multiply the first equation by 40/18 to get 40 minutes on the left sides

40 minutes = 40/18 laps = 20/9 laps

The answer to the simplification is 56.

The order of precedence is the hierarchical order in which calculations are conducted. The simplest example of this is the way you always multiply before you add numbers.

In mathematics, you have BODMAS

B = Bracket

O = of

D = Division

M = Multiplication

A = Addition

S = Subtraction

From the equation;

7 x (-7 +15)

Removing the bracket

7 x (8)

Multiplying

56

Learn more about order of precedence here:https://brainly.com/question/1599125

#SPJ1

both the equation both equations are similar and they may or may not be equivalent.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Given equation (2d) / (d/r1) + (d/r2)

and (r1t1 + r2t2) / (t1 +t2)

Taking LCM: 2d/(dr2) (dr1) / r1r2

The product 2r1r2/ r1+r2

So both the equation equations are similar and they may or may not be equivalent.

Learn more about equations, by the following link

brainly.com/question/2972832

#SPJ1

840  ways can we form a subcommittee with 3 republicans and 2 democrats

Given that

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical. (It is not important how each set's members are arranged.) If there are n elements in the set, then C kn is the number of k-combinations.

a senate committee has 8 republicans and 6 democrats.

now, we need to find how many ways can we form a subcommittee with 3 republicans and 2 democrats

= 8[tex]C_{3}[/tex] × 6[tex]C_{2}[/tex]

=[tex]\frac{8!}{5!3!}[/tex] × [tex]\frac{6!}{4!2!}[/tex]

=56 × 15

=840

840  ways can we form a subcommittee with 3 republicans and 2 democrats

To learn more about combinations:

https://brainly.com/question/20211959

#SPJ4

Answer:

9 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{4}{1}[/tex] x [tex]\frac{7}{3}[/tex] = [tex]\frac{28}{3}[/tex] = 9 [tex]\frac{1}{3}[/tex]

Answer:

It can't be (-2,8)  as u can't join (2,1) and (8,1) with (-2,8) without it ruining the rectangle.

Therefore , the solution of GCD problem comes out to be the greatest common factor of 252 and 60 is 223 = 12.

The number that divides two or more numbers most precisely by itself is said to be the largest common denominator (GCD) of those numbers. It is also known as the highest common denominator (HCF). Since both 15 and 10 can be divided by 5, for instance, the highest common factor of these two numbers is 5.

Here,

The highest common factor (hcf), greatest common factor, and the greatest common divisor (gcd) are other names for it (gcf).

The highest integer which divides both numbers is known as the largest common series of 2 numbers.

We must choose the number that divides 252 and 60 most equally.

252's prime factorization is as follows:

252 = 2×2×3×3×7

the prime factors that make up 60 are.

60 = 2×2×3×5

These common elements are: 2 2 3

Therefore, the greatest common factor of 252 and 60 is 223 = 12.

Therefore , the solution of GCD problem comes out to be the greatest common factor of 252 and 60 is 223 = 12.

To know more about GCD , visit

https://brainly.com/question/2292401

#SPJ4

The explanation of each of the term are defined below.

The order of each reactant is known as the reaction orders in a rate law describe the mathematical dependence of the rate on reactant concentrations.

The term rate law expression in math is defined as the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power in which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.

The term overall order of the reaction is known as  the sum of orders for each reactant.

Finally value of the rate constant means the rate constant is temperature dependent.

To know more about expression here.

https://brainly.com/question/14083225

#SPJ4

Based on mathematical operations, Emmet's score at the end of Level 1 of the Digging Up Dinos video game was -3.

The basic mathematical operations include addition, subtraction, division, and multiplication.

These mathematical operations manipulate variables, values, numbers, and constants, including mathematical operands and the equal symbol, to solve mathematical problems.

In this situation, the 17 points Emmet lost are subtracted from the 14 points that he gained to arrive at the final score at Level 1.

The number of points earned in Level 1 = 14

The number of points lost in Level 1 = 17

The net points at the end of Level 1 = -3 (14 - 17)

Thus, the subtraction operation shows that Emmet lost 3 more scores than he gained during Level 1.

Learn more about mathematical operations at https://brainly.com/question/4721701

#SPJ1

Answer:

Step-by-step explanation:

Answer:

5x = y

10x= 5y

20x= 15y

50x= 45y

Check the picture below.

so, let's notice the angle made by the hand from 2pm to 4:45pm, well, it goes around twice, 2 revolutiions, then it goes 270° more after that, and we know the "radius" is 10.5"

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =\stackrel{360+360+270}{990~\hfill }\\ r=10.5 \end{cases}\implies s=\cfrac{(990)\pi (10.5)}{180} \\\\\\ s=\cfrac{231\pi }{4}\implies s\approx 181.43~in[/tex]

Answer:

4am, it's 4 am.

The number of years after which the population is less than 6000 is 5 years.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation

We have,

The rate at which the population is decreasing per year = 7%.

The equation for the number of population after t years.

P = C [tex](1 - 0.07)^t[/tex]

Now,

After 5 years,

P = 8500 [tex](1 - 0.07)^5[/tex]

P = 8500 x [tex]0.93^5[/tex]

P = 8500 x 0.69

P = 5865

The population after 5 years is 5865 which is less than 6000.

Thus,

After 5 years the population will be less than 6000.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

As per the unitary method, the length of his shadow changing is 30 feet.

The term unitary method is known as a process of finding the value of a single unit, and based on this value.

Here we have given that a 6-foot man is running away from the base of a streetlight that is feet high.

Then let us consider that the man be x feet away from the street light and his shadow length be y,

Here we have also consider that let the tip of the shadow be l feet away from the light is written as

=> l = x + y

Here we are given that,

=> dx/dt=2

Then as per the concept of similar triangles, we can write it as,

=> x/5 = 6x+6/31

=> 31x = 30x + 30

=> x = 30

To know more about unitary method here.

https://brainly.com/question/28276953

#SPJ4

The sum of the numbers written on the faces of the cube is 333.

A vertex, also known as a point, is a fundamental part of a shape or an object. It is the point at which two or more lines, edges, or faces meet. Vertex can also refer to the corner of a polygon, where multiple lines meet. In 3D geometry, a vertex is a point where three or more edges meet. In a 3D object, each vertex is considered to be a corner of the object. Vertices are a crucial part of the structure and design of shapes, and can be used to define a shape's size, shape and dimension.

The sum of the numbers written on the faces of the cube is equal to the sum of the products of the numbers assigned to the vertices of the cube divided by three. Since the sum of the numbers assigned to all the vertices is equal to 1001, the sum of the numbers written on the faces of the cube is equal to 1001/3, which is equal to 333. Therefore, the sum of the numbers written on the faces of the cube is 333.

To know more about vertex click-
https://brainly.com/question/21191648
#SPJ4

The correct statement regarding the two functions in this problem is given as follows:

f(2) = g(2).

The graphic solution of a system of equations is given by the point of intersection of all the equations that compose the system.

The points through which each function passes in this problem are given as follows:

The point that is common to both function is given as follows:

(2,0).

Meaning that the two functions intersect at x = 2, which is the solution to the system of equations, also meaning that they have the same numeric value at x = 2.

The fact that the two functions have the same numeric value at x = 2 means that the correct statement is given as follows:

f(2) = g(2).

Which is the first statement.

A similar problem, also featuring a system of equations, is presented at brainly.com/question/24342899

#SPJ1

Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.

A linear regression model is one that conforms to the algebraic equation y=mx+b. The slope is B, and the y-intercept is m. The previous clause is usually referred to as an "mathematical equation having two variables because both y and x are unique parameters. Two variables make up bivariate linear equations. Linear equations have a variety of applications, all of which have a zero outcome. Y=mx+b, where m stands for the gradient and b for the y-intercept, is the formula for a linear equation.

Here,

Given : 55=0.1(m-500)+50

where m is the number of minute

=> 55=0.1(m-500)+50

=> 55=0.1m-50+50

=>55=0.1m-0

=>55-0=0.1

=>55=0.1

=>0.1=0.1

=>550=m

Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ4

Answer:

The amount of phones that were not defective is 98% or 49/50 as a fraction in simplest form

Step-by-step explanation:

Steps to solve "what percent is 100 of 5000?"

100 of 5000 can be written as:

100/5000

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

100

5000

×

100

100

= (

100 × 100

5000

) ×

1

100

=

2

100

Therefore, the answer is 2%

If you are using a calculator, simply enter 100÷5000×100 which will give you 2 as the answer. That lets you know how many were defective

If only 2% were defective, then 98% were not

the expression StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot is equivalent to 25x9y3 / 64x6y11.

StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot

= 25x9y3 / 64x6y11

StartRoot is the beginning of the root expression and StartFraction is the beginning of the fraction within the root expression. 25x9y3 is the numerator of the fraction and 64x6y11 is the denominator of the fraction. Superscript is used to raise the numbers to the power indicated. Baseline is the number which the Superscript is raised to. EndFraction indicates the end of the fraction and EndRoot indicates the end of the root expression.

Therefore, the expression StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot is equivalent to 25x9y3 / 64x6y11.

Learn more about expression here

https://brainly.com/question/14083225

#SPJ4

Answer:

The rate of change from year 1 to year 2 is - 2%.

The rate of change from year 9 to year 10 is -0.02%

The rate of change will be the same for all years.

Step-by-step explanation:

While this seems an unlikely answer (why would the rate reamin the same every year?), it is the correct answer since we are told that one equation is valid for t years.  With no other information, we must conclude the rate of change remains the same every year.  The actual number by which the population shrinks is changing, but the rate remains the same.

The function P(t) = 227,000(.98)^t says that the initial population in year 0 is 227,000 [227,000(0.98)^0 = 227,000].  The factor (0.98) is the result of the expression (1-(0.02)^t).  The 1 is the factor for the initial population and the -0.02 is the fraction of 1 by which the population declines each year (2%).

Initial population = 227,000 [227,000(0.98)^0 = 227,000

Year 1 population would be (227,000)*(1-0.02)^1 or (227,000)*(0.98)

Year 2 population would be (227,000)*(1-0.02)^2 or (227,000)*(0.98)^2

Year 9 population would be (227,000)*(1-0.02)^9 or (227,000)*(0.98)^9

Year 10 population would be (227,000)*(1-0.02)^10 or (227,000)*(0.98)^10

The change is the same every year (0.98).

The equation and the accompanying justification that describes a line that is parallel to EF is: C. Y = -1/3x + 5 1/3 the slopes are equal.

If two lines are said to be parallel to each other, their equations that is expressed as y = mx + b, will have the same slope value of m. Y = mx + b is the slope-intercept form of any equation that represents a line.

Given that the equation y = -1/3x + 4 represents the line EF, its slope is -1/3. This means the slope of any line that is parallel to y = -1/3x + 4 will be the same as -1/3.

Therefore, the correct justification is: C. Y = -1/3x + 5 1/3 the slopes are equal.

Learn more about the slope of parallel lines on:

https://brainly.com/question/10790818

#SPJ1

Answer:C

Step-by-step explanation:

x is [tex]\sqrt{7} \\[/tex]=2.645

which means 2.645²=7

The value of the size of angle PSQ of the given triangle is; 61°

From the given triangle ΔPQR, we see that;

m∠QPS = 65°

m∠PRQ = 43°

Now, it is clear that Line PSR is a straight line divided in the ratio;

size of angle PQS : size of angle SQR = 3:1

m∠PQS : m∠SQR = 3:1

Thus, since sum of angles in a triangle is 180°, then we say that;

∠PQR = 180° - (∠QPS + ∠PRQ)

Plugging in the relevant values;

∠PQR = 180° - (65° + 43°)

∠PQR = 72°

Using the concept of angle addition postulate, we have that;

∠PQR = m∠PQS + m∠SQR

Since m∠PQS : m∠SQR = 3:1, then we have;

m∠PQS = 3 × m∠SQR

Thus;

∠PQR =  (3 × m∠SQR) + m∠SQR

∠PQR = 4 × m∠SQR

4 × m∠SQR = ∠PQR

4 × m∠SQR  = 72°

m∠SQR = 72°/4

m∠SQR  = 18°

m∠PQS = 3 × m∠SQR

m∠PQS = 3 × 18°

m∠PQS  = 54°

Finally;

∠PSQ = 180° - (65° + 54°)

∠PSQ  = 61°

Read more about missing angle of triangle at; https://brainly.com/question/23327304

#SPJ1

Answer:

  see attached for a graph

  a. BA≅BC (the compass told me so)

  c. AD≅CD

Step-by-step explanation:

You want a graph of ∆ABC, with A(4, 7), B(0, 0), and C(8, 1). You want to identify the congruent sides, construct an angle bisector, and comment on how it divides the opposite side.

The graph of the points, and the construction of the angle bisector are shown in the attachment.

Since you have your compass available for construction, you can use set it to the measure of one side and compare that to the other two sides. It does not take long to identify AB ≅ BC. (A compass setting shows they are the same length.)

As you know, an angle bisector is constructed by first identifying two points on the sides of the angle that are the same distance from the vertex of the angle. Then two intersecting arcs are drawn with the same radius using those points as their centers. The vertex and the intersection of the arcs defines the ray that is the angle bisector. This is shown in the attachment.

You can count grid squares (or use the compass) to determine that AD and CD are the same length: D is the midpoint of AC.

This reinforces your knowledge that the angle bisector of the a.pex angle of an isosceles triangle is also an altitude and a median.

[tex] \frac{5a}{r} \: - 2 = y[/tex]

Step-by-step explanation:

A = r(y +2) /5

A×5 = r(y+2)

(5A)/r = y+2

(5A)/r - 2 = y

•: y = (5A)/r - 2

(only applicable when

[tex]a = \frac{ry + 2r}{5} [/tex]

expand)

The power of two by which the height was divided is given as follows:

Tenth power of 2.

The power of two by which the height was divided is obtained applying the proportions in the context of this problem.

The equation that relates the heights and the scale factor is given as follows:

New height = Old height / Scale factor.

The parameters for this problem are given as follows:

Then the scale factor is obtained as follows:

Scale factor = 324/0.3

Scale factor = 1080.

The tenth power of 10 is given as follows:

2^10 = 1024.

Which is close to 1080, and hence the height was divided by the tenth power of 2.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Therefore , area and capacity of volume values equal f2 f 2 and f3 f 3, respectively, if the curve is f, f, and also the rim step size is f, f.

When we enlarge a shape by a scale factor, we multiply the area of the shape by the square of the scale factor. When we enlarge a shape by a scale factor, we multiply the volume of the shape by the cube of the scale factor. The scale factor is the proportional relationship that exists between the sides of similar figures.

Here,

Similar geometric shapes' edges, areas, and volumes are also connected to the scale factor.

The peripheral scale factor is f, f if the curve is f, f, and the surface and volume ratios are f2 f 2 but also

f3, f 3, respectively, if the correction factor is f, f.

Therefore , area and capacity values equal f2 f 2 and f3 f 3, respectively, if the curve is f, f, and also the rim step size is f, f.

To know more about volume visit:-

brainly.com/question/1578538

#SPJ1