I need help with trigonometry
Again..

(a) The radius of the small sphere is 2 centimeters.

(b) The measure of the angle XAB is approximately 36.870°.

(c) The area of the shaded region is approximately 3.107 square centimeters.

Herein we have a geometric system formed by three big semicircles and a small circle, whose geometric diagram is attached below. (a) The relationship between the semicircles and the circle is represented by two formulae:

8² + h² = (8 + r)²     (1)

h + r = 8                  (2)

Where r is the radius of the small circle.

Then, we solve the system:

8² + (8 - r)² = (8 + r)²

64 + 64 - 16 · r + r² = 64 + 16 · r + r²

32 · r = 64

r = 2

The radius of the small sphere is 2 centimeters.

(b) The measure of the angle XAB is found by trigonometric relations:

cos m ∠ XAB = OA / AX

cos m ∠ XAB = 8 / 10

m ∠ XAB ≈ 36.870°

The measure of the angle XAB is approximately 36.870°.

(c) The area of the shaded region is the area of the triangle minus the area of the three circular sections:

A = 0.5 · (16 cm) · (10 cm) · sin 36.870° - (36.870° /180) · π · (8 cm)² - 0.5 · (106.260° / 180) · π · (2 cm)²

A ≈ 3.107 cm²

The area of the shaded region is approximately 3.107 square centimeters.

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1. Independent Variable (x) is the number of toys.

Dependent Variable (y) is the amount.

2. Graph A - Income Graph.

Graph B - Expense Graph.

3. Zandi won't make a profit while selling 5 toys.

4. Zandi must sell 10 toys to reach break-even.

5. Zandi's variable cost per toy is $15.

6. The total cost function is, total cost = 100 + 15x.

1. The independent variable will be the number number of toys marked on the x-axis, whereas the dependent variable will be the amount on the y-axis, as the cost and revenue both depend on the units.

2. Graph A will be Zandi's income as when the unit is 0, the income is 0, whereas graph B is the expense graph as when the unit is 0, still some fixed expenses are generated for example rent.

3. Zandi will make a loss while making and selling 5 toys as the amount on graph B corresponding to 5 toys, that is, the expenses, are greater than the amount on graph A corresponding to 5 toys, that is, the income.

4. The break-even is the point where the income = expense, which on the graph is at the point where the number of toys is 10.

Thus, Zandi must sell 10 boys to reach break even.

5. The variable cost per toy can be found as the slope of the expense graph, m = (400 - 100)/(20 - 0) = 300/20 = 15.

Thus, Zandi's variable cost is $15.

6. Total cost = Fixed cost + a number of units*variable costs.

Thus, the total cost = 100 + 15x.

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The correct equation that shows the area of painted area is

A=[tex]x^{2} -8x-16[/tex].

Given that the length of the  floor,x,is atleast 12 feet.The width of the floor is 4 feet less than the length.There is a right angle of height x-4 and base 8 feet. The rectangle inside has length of 8 feet and width be 4 feet.

We are required to find the painted area of the theater room in square feet.

To find the painted area of the theater the following steps must be followed:

1) Find the area of the theater room.

length =x

Breadth=x-4

Area=x(x-4)

=[tex]x^{2} -4x[/tex]

2) Area of the right triangle.

Height=x-4

Base=8

Area=1/2 *8*(x-4)

=4(x-4)

=4x-16

3) Find the area of the rectangle inside labeled closet.

Length=8

Width=4

Area=8*4

=32

Area=Area of theater room-Area of of right triangle-Area of closet.

=[tex]x^{2} -4x[/tex]-4x+16-32

=[tex]x^{2} -8x-16[/tex]

Hence the correct equation that shows the area of painted area is

A=[tex]x^{2} -8x-16[/tex].

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Answer:

A = x(x − 4) − 0.5(8)(x − 4) − 3(7)

Work:

x = length, making the width (x-4)

The stage closet will be (x-4)(8)(1/2)

The rectangle is 7(3)

which makes the painted area x(x-4) - 4(x-4)

thus giving us

x(x − 4) − 0.5(8)(x − 4) − 3(7)

Step-by-step explanation:

hope this helps :)

Answer:

Speed of the plane in still air: [tex]779\; {\rm km \cdot h^{-1}}[/tex].

Windspeed: [tex]100\; {\rm km \cdot h^{-1}}[/tex].

Step-by-step explanation:

Assume that [tex]x\; {\rm km \cdot h^{-1}}[/tex] is the speed of the plane in still air, and that [tex]y\; {\rm km \cdot h^{-1}}[/tex] is the speed of the wind.

The question states that when going against the wind ([tex]v = (x - y)\; {\rm km \cdot h^{-1}}[/tex],) the plane travels [tex]6111\; {\rm km}[/tex] in [tex]9\; {\rm h}[/tex]. Hence, [tex]9\, (x - y) = 6111[/tex].

Similarly, since the plane travels [tex]7911\; {\rm km}[/tex] in [tex]9\; {\rm h}[/tex] when travelling in the same direction as the wind ([tex]v = (x + y)\; {\rm km \cdot h^{-1}}[/tex],) [tex]9\, (x + y) = 7911[/tex].

Add the two equations to eliminate [tex]y[/tex]. Subtract the second equation from the first to eliminate [tex]x[/tex]. Solve this system of equations for [tex]x[/tex] and [tex]y[/tex]: [tex]x = 779[/tex] and [tex]y = 100[/tex].

Hence, the speed of this plane in still air would be [tex]779\; {\rm km \cdot h^{-1}}[/tex], whereas the speed of the wind would be [tex]100\; {\rm km \cdot h^{-1}}[/tex].

Using a system of equations, it is found that one large jar holds 6 ounces and one small jar holds 4 ounces.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

One large jar and five small jars can hold 26 ounces of jam, hence:

l + 5s = 26, which is the first equation in matrix form.

Then:

l = 26 - 5s.

One large jar minus one small jar can hold 2 ounces of jam, hence:

l - s = 2, which is the second equation in matrix form:

Then:

l = 2 + s = 26 - 5s

2 + s = 26 - 5s

6s = 24

s = 4.

l = 26 - 5s = 6.

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Answer:

  456 kg

Step-by-step explanation:

Mass is the product of volume and density.

The product of volume and density is ...

  M = Vρ

  M = (2600 m³)(0.1755 kg/m³) ≈ 456 kg

The balloon contains about 456 kg of He.

The concept exhibited by the thirteen year old who was unsure of one of her responses. she decided to go with the answer that felt the ""most right."" is an example of; Intuitive thought.

It follows from the task content that the thirteen year old was unsure of one of her responses. she decided to go with the answer that felt the ""most right."".

Such concept may be attributed to Intuitive thought.

This follows from the fact that the internal impulse which prompts individuals to make decisions is termed; Intuition.

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Answer:

7.

Step-by-step explanation:

Calculate the means for each group:

mean of 0-4 is 2

mean of 5-9 is 7

mean of 10-14 is 12

Mean = (Sum of frequencies * mean) / sum of frequencies

= required mean = [ (2(2) + 1(7) + 2(12)] / (2+1+2)

=  35/ 5

= 7.

[tex]\boldsymbol{\sf{\dfrac{4}{5}+\dfrac{9}{10} } }[/tex]

The least common multiple of 5 and 10 is 10. Convert 4/5 and 9/10 to fractions with denominators of 10.

[tex]\boldsymbol{\sf{\dfrac{4\times2}{5\times2}+\dfrac{9}{10} \ \ \to \ \ Simplify }}[/tex]

[tex]\boldsymbol{\sf{ \dfrac{8}{10}+\dfrac{9}{10} }}[/tex]

Since 8/10 and 9/10 have the same denominator, join their numerators to add them.

[tex]\boldsymbol{ \sf{\dfrac{8+9}{10} \ \to \ \ Add }}[/tex]

Simplify

[tex]\boldsymbol{\sf{ \dfrac{17}{10}= }}\boxed{\boldsymbol{\sf{1\frac{7}{10} }}}[/tex]

Step-by-step explanation:

the highest or greatest or largest common factor is the product of the prime factors the numbers have in common :

540 ÷ 2 = 270

270 ÷ 2 = 135

135 ÷ 2 no

135 ÷ 3 = 45

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 3 no

5 ÷ 5 = 1

540 = 2² × 3³ × 5¹

360 ÷ 2 = 180

180 ÷ 2 = 90

90 ÷ 2 = 45

45 ÷ 2 no

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 3 no

5 ÷ 5 = 1

360 = 2³ × 3² × 5¹

so, the HCF = 2² × 3² × 5¹ = 4×9×5 = 180

(1)

to satisfy the condition max. 180 visitors can be invited.

(2)

540 / 180 = 3

so, every visitor can receive 3 pieces of chicken.

and 360 / 180 = 2 cups of drink.

Based on the given graphs and their equations, the solutions will be located at points (-2, 7) and (0, 1).

To find the solution to y = -2x+ 3, assume that x is a certain number then solve for y.

Given the options, we can assume that x = -2. Solution is:

= -2(-2) + 3

= 4 + 3

y = 7

Solution point is (-2, 7)

The second equation can be solved by equating x to 0:
y = 0² - 0 + 1

y = 1

Solution point is:

= (0, 1)

In conclusion, the solution points are (-2, 7) and (0,1).

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Answer:

5040 ways

Step-by-step explanation:

7! = 5040

7 choices on day 1

6 choices on day 2

5 choices on day 3

4 choices  on day 4

3

2

1                                 7 x 6 x 5 x 4 x 3 x 2 x1 = 5040

Answer:

HL

Step-by-step explanation:

The hypotenuses and the long legs of the right triangles are congruent, therefore using the rule HL, the triangles are congruent.

Answer:

The cost of one pass is 25$

Step-by-step explanation:

Call the cost of one of the passes, P.   So we have

63 =  13 + 2P - subtract 13 from both sides

50 = 2P - divide both sides by 2

25 = P

So the cost of one pass = $25

Answer:

  m∠B ≈ 70.8°

Step-by-step explanation:

The Law of Cosines relates three sides of a triangle and the angle opposite one of them.

The law of cosines tells you ...

  b² = a² +c² -2ac·cos(B)

Solving for angle B, we get ...

  B = arccos((a² +c² -b²)/(2ac))

where 'a' and 'c' are the sides adjacent to the angle of interest. We want angle B, so we can fill this formula as follows:

  B = arccos((13² +11² -14²)/(2·13·11))

  B = arccos(94/286)

  B ≈ 70.812°

__

Additional comment

Another angle can be found using the Law of Sines.

  A = arcsin(sin(70.812°)×13/14) ≈ 61.281°

Then angle C is ...

  C = 180° -70.812° -61.281° = 47.907°

Total number of men and women wearing sunglasses = 290

According to the question,

Total number of men and women = 2000

half of the adults were women = 1/2 × 2000

Number of women = 1000

Number of men = (Total adults) - (Number of women )

Number of men = 2000 - 1000

= 1000

given,

20% of women were wearing sunglasses = 20/100 × 1000

= 200

9% of men were wearing sunglasses = 9/100 × 1000

= 90

Total number of adults wearing glasses = 200 + 90

= 290

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

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A simultaneous equation refers to two or more equations that are solved at the same time.

A simultaneous equation refers to two or more equations that are solved at the same time. Now we shall solve each of the equations;

a. 2x + y = 3 ------(1)

   x - y = 4 ------ (2)

x = 4 + y  ----- (3)

Substituting (3) into (1)

2(4 + y) + y = 3

8 + 2y + y = 3

8 + 3y = 3

3y = 3 - 8

3y = -5

y = -5/3

Hence;

 x - y = 4

x - (-5/3) = 4

x = 4 + 5/3

x = 17/3

b. 2x + 6y =9 -----(1)

x + 3y = 2 ------ (2)

x = 2 - 3y ------ (3)

Substitute (3) into (1)

2( 2 - 3y)  + 6y =9

4 - 6y + 6y = 9 (From this stage we can see that it is not possible to solve the quadratic)

c. 6x - 3y = 12 -----(1)

4x + 2y = 10 ---- (2)

12x - 6y = 24 ---- (3)

12x + 6y = 30 --- (4)

Add (3) to (4)

24x = 54

x= 54/24 = 9/4

Hence;

4(9/4) + 2y = 10

9 + 2y = 10

2y = 10 - 9

y = 1/2

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The equation of the given parabola is y2=−20(x+3)

A parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

In general in a parabola, if we have

(y−n)2=4p(x−m),

then the vertex is (m,n)

The axis of symmetry is y=m

The focus is (p+m,n)

The directrix is x=m−p.

Hence, for the given case

p+m=−8

n=0

m−p=2

⇒n=0

m=−3

p=−5

So, the answer will be y2=−20(x+3)

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By finding some points on the curve and then connecting them.

Here we have the rational function:

t = d/s

Where t represents time, d distance, and s speed.

We assume that d is a fixed value, then our variables are time and speed.

On the examples, you can see that the value of d is:

d = 616.5km, then we just need to graph the equation:

t = (616.5km)/s

To do so, you can evaluate the function in different values of s, like the points the problem asks to graph, and then connect all these points with a curve.

Doing that, you should get a graph like the one below:

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Answer: I believe the answer would be as follows:

8.431 grams

5.46 seconds

980 meters

900 miles

Step-by-step explanation:

it would first be which has the largest number after the decimal point, so if there’s three it goes first (0.12*3*). Then you would pick the one that is the smallest form of measurement, which would be meters in this case.

Hope this helped!

102 degrees

Step-by-step explanation:

Angles in a quadrilateral add to 360 degrees.

y = 360 - (120 + 85 + 53)

y = 360 - 258

y = 102 degrees

3.35 feet have a maximum inaccuracy of 0.005 feet.

The correct option is C.

When students consistently commit mistakes, an approach known as error analysis is frequently employed to determine the root of the problem. Reviewing student work is the first step in the process, after which misunderstood patterns are sought out. Mathematics mistakes can be conceptual, procedural, or factual, and they can happen for a variety of reasons.

The window is 3.35 feet long.

Find the biggest error you can

Half of the measuring unit is considered to be the maximum amount of measurement error.

3.35 feet are calculated to the nearest centimeter, or 0.01 feet

Consequently, the largest conceivable error is equal to half of the measurement unit.

= .01/2

= .005

Therefore, the maximum inaccuracy for 3.35 feet is 0.005 feet.

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If the probability of obtaining success is 0.3 and the value of n is 9 then the probability at the value of x be 3 is 0.3811.

Given that the value of n is 9 and the value of p is 0.3.

We are required to find the probability when the value of x is equal to 3.

Probability is the calculation of chance of happening an event among all the events possible.It lies between 0 and 1.

Probability=Number of items/total items.

Binomial probability is basically the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes.

[tex](a+b)^{n}[/tex]=[tex]nC_{0}a^{0} b^{n-0} +nC_{1}a^{1} b^{n-1} +................nC_{n}a^{n} b^{0}[/tex]

We have to find the value when n=9, p is 0.3 and r=3.

=[tex]9C_{3} (0.3)^{3} (1-0.3)^{6}[/tex]

=9!/3!6!*0.027*0.16807

=84*0.00453789

=0.381182

Hence if the probability of obtaining success is 0.3 and the value of n is 9 then the probability at the value of x be 3 is 0.3811.

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Answer: y=-3m+13

Step-by-step explanation:

y=mx+c

m is the gradient

y=-3x+c

We know one point

-2=3(-5)+c

Solve for c

-2=-15+c

13=c

y=-3m+13

Modern numbers are the ten numerical digits used in constructing other numbers.

Modern numbers are also called Arabic numerals. They are the ten numerical digits:

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Uses of modern numbers;

Hence, modern numbers are the ten numerical digits used in constructing other numbers.

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f(x) = 2 * (1/2)^x

f(3) = 2 * (1/2)^3

f(3) = 2 * (1/2 * 1/2 * 1/2)

f(3) = 2 * 1/8

f(3) = 2/8

f(3) = 1/4

Hope this helps!

Answer:

[tex]f(x) = 2 \times ( { \frac{1}{2} })^{x} \\ \\ f(3) = 2 \times ({ \frac{1}{2}})^{3} \\ \\ = 2 \times \frac{1}{8} \\ \\ f(3) = \frac{1}{4} = 0.25[/tex]

Answer:

c

Step-by-step explanation:

In geometry, an equilateral triangle is a triangle in which all three sides have the same length.

Answer:

the top 2 and the left bottom corner

Step-by-step explanation:

the first one in the first row is a reflection

the second one in the first row is a rotation

the one on the left bottom corner just moved a unit

Answer:

Option 3

Step-by-step explanation:

The first answer is a reflection across the y-axis, the second is a rotation, and the last one is two translations. So, the third one is correct because it's the only single translation.

Answer:

B

Step-by-step explanation:

If x and y vary inversely, then as x increases, y decreases. That eliminates answers A, C, and D.

Answer: B

The pencil is longer than the pair of scissors by  [tex]2\frac{7}{8}[/tex] inches.

A pencil measures  [tex]8\frac{3}{8}[/tex]  inches.

A pair of scissors measures  [tex]5\frac{1}{2}[/tex]  inches.

We need to find the difference between the measures of a pencil and the scissors.

We see that the pencil measure is greater than the pair of scissors.

A fraction is a part of a whole number. It has two parts - numerator and denominator.

Example: If you cut a cake into three slices each slice is 1/3.

Where 1 = numerator and 3 = denominator.

Four types of fractions:

Unit fraction - when the numerator is 1.

Proper fraction - When the numerator is less than the denominator.

Improper fraction - When the numerator is greater than the denominator.

Mixed fraction - When the fraction contains a whole number with a proper fraction.

Example:  [tex]3\frac{1}{3}[/tex]

The given measure of the pen and the pair of scissors is in mix fraction.

The pencil measure is longer than the pair of scissors measure so,

We will subtract the measure of the pair of scissors from the measure of the pen.

We have,

       =  [tex]8\frac{3}{8} - 5\frac{1}{2}[/tex]

We can write the mix fraction into an improper fraction.

We multiply the denominator with the whole number and add this product with the numerator to get our numerator of the improper fraction. The denominator will remain the same as the mix fraction in the improper fraction.

So,

[tex]8\frac{3}{8}=\frac{(8\times8)+3}{8}=\frac{64 + 3}{8} = \frac{67}{8}\\ 5\frac{1}{2} =\frac{(5\times2)+1}{2}= \frac{(10+1)}{2} = \frac{11}{2}[/tex]

= 67/8 - 11/2

= (67-44) / 8

= 23 / 8

Writing in mix fraction.

=  [tex]2\frac{7}{8}[/tex]

Thus the pencil is longer than the pair of scissors by  [tex]2\frac{7}{8}[/tex] inches.

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