GEOMETRY: TRIGONOMETRIC RATIOS

How tall is the tree?
A) 50 feet
B) 70 feet
C) 20 feet
D) 30 feet

Answer:

x = 9.0

Step-by-step explanation:

sin E = CD/EC = CD/x

<=>     sin 50 = 6.9/x     <=> x = 6.9/sin 50 ≅ 9.0

If Taylor is selected as one of the first two players out of ten players on the team, the probability of Jamie being selected as the third player is 4/9.

Using the multiplication rule of probability, the overall probability of both events happening is 8.9%

Assuming that there are only seniors and juniors on the team, the probability of Taylor being selected as one of the first two players is 2/10, since there are two juniors out of ten total players.

If Taylor is selected as one of the first two players, then there are nine players left, of which four are juniors, including Jamie.

Therefore, the probability of Jamie being selected as the third player, given that Taylor is already selected, is 4/9.

Using the multiplication rule of probability, the overall probability of both events happening is:

P(Taylor and Jamie) = P(Taylor) x P (Jamie | Taylor)

P(Taylor and Jamie) = 2/10 x 4/9

P(Taylor and Jamie) = 8/90

P(Taylor and Jamie) = 0.089 or 8.9% (rounded to the nearest tenth)

Therefore, the probability of Jamie being selected as the third player, given that Taylor is already selected as one of the first two players, is 8.9%.

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The area of Habib's diagram when s = 1/2 is 7.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point. The distance around the circle is called its circumference, and the distance across the circle passing through the center is called its diameter.

To find the area of Habib's diagram when s = 1/2, we just need to substitute s = 1/2 into the expression for the area:

Area = 6 + 4s²

Area = 6 + 4(1/2)²

Area = 6 + 4(1/4)

Area = 6 + 1

Area = 7

Therefore, the area of Habib's diagram when s = 1/2 is 7.

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Answer:

s = p - q - 1

Step-by-step explanation:

q + 1 + s = p  Subtract q and 1 from both sides

q -q +1 - 1 + s = p - q -1

s = p - q - 1

Helping in the name of Jesus.

Answer:

P54.75 per hour.

Step-by-step explanation:

If he earned 2190 pesos on working 8 hours each for 5 days then he earned 54.75

Equation: hours x days / earnings

Therefore, 8 hours x 5 days = 40

2190 / 40 = P54.75 / hour

Dianne and Tobi 14/9 hours to clean the house if they work together.

The total work required to clean the house is equivalent to 1 unit.

If Dianne can clean the house in 2 hours, she can clean 1/2 of the house in 1 hour (1/2 hour = 1 unit of work / 2 hours).

If Tobi can clean the house in 7 hours, he can clean 1/7 of the house in 1 hour (1/7 hour = 1 unit of work / 7 hours).

Working together, the two of them can clean 1/2 + 1/7 of the house in 1 hour.

[tex]1/2 + 1/7 = 7/14 + 2/14 = 9/14[/tex] of the house can be cleaned in 1 hour.

Dianne and Tobi 14/9 hours to clean the house if they work together.

Rounding off to the nearest tenth:

14/9 hours = 1.56 hours (approximately)

Dianne and Tobi approximately 1.56 hours (or 1 hour and 36 minutes) to clean the house if they work together.

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The set of constraints that represents all possible number of bracelets and necklaces is: 4b + 7n ≥ 150, b ≤ 36, and n ≤ 12.

Constraints are limitations and boundaries that must be applied to variables in equations used to simulate real-world scenarios.

It's possible that some answers, while theoretically proving an equation correct, may not make sense in the context of a real-world word problem. In order for the mathematical model to accurately depict the situation, constraints are then required.

An equation's related x-values (the independent variable) or y-values (the dependent variable) may be subject to restrictions.

Let us suppose number of bracelets = b.

Let us suppose the number of necklaces sold = n.

Thus, for profit we have:

4b + 7n ≥ 150

Also, according to the given constraints:

b ≤ 36

n ≤ 12

Hence, the set of constraints that represents all possible number of bracelets and necklaces is: 4b + 7n ≥ 150, b ≤ 36, and n ≤ 12.

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The correct answer is c, 4b+7n≥150 and b≤36, n≤12.

The total profit P made by selling b bracelets and n necklaces can be expressed as:

P = 4b + 7n

To make a profit of at least $150, we need:

4b + 7n ≥ 150

Also, we cannot sell a negative number of bracelets or necklaces, so we have the constraints:

b ≥ 0

n ≥ 0

And since they have already made 36 bracelets and 12 necklaces, we have:

b ≤ 36

n ≤ 12

So the correct set of constraints is:

4b + 7n ≥ 150

b ≥ 0

n ≥ 0

b ≤ 36

n ≤ 12

Therefore, option c is the correct answer.

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The value of p would be could be approximately -0.391 or  0.321.

Let's start by using the quadratic formula to find the roots of the polynomial [tex]px^2 + 5x + 8p[/tex]

[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]

Plugging in the coefficients, we get:

[tex]x = (-5 ± √(5^2 - 4p(8p))) / 2p[/tex]

Simplifying, we get:

[tex]x = (-5 ± √(25 - 32p^2)) / 2p[/tex]

Now, we know that the sum of the roots is equal to -b/a, and the product of the roots is equal to c/a. So:

Sum of roots = [tex](-5 + √(25 - 32p^2)) / 2p + (-5 - √(25 - 32p^2)) / 2p = -5/p[/tex]

Product of roots = [tex][(-5 + √(25 - 32p^2)) / 2p] * [(-5 - √(25 - 32p^2)) / 2p] = (25 - 32p^2) / 4p^2[/tex]

Since we're given that the sum of the roots is equal to the product of the roots, we can set these expressions equal to each other and solve for p:

[tex]-5/p = (25 - 32p^2) / 4p^2[/tex]

Multiplying both sides by 4p^2 gives:
[tex]-20p = 25 - 32p^2[/tex]

Adding [tex]32p^2[/tex] to both sides and rearranging, we get:
[tex]32p^2 + 20p - 25 = 0[/tex]

Now we can use the quadratic formula again to solve for p:

[tex]p = (-b ± √(b^2 - 4ac)) / 2a[/tex]

Plugging in the coefficients, we get:

[tex]p = (-20 ± √(20^2 - 4(32)(-25))) / 2(32)[/tex]

Simplifying, we get:

[tex]p = (-20 ± √1560) / 64[/tex]

p ≈ -0.391 or p ≈ 0.321

Therefore, the value of p could be approximately -0.391 or approximately 0.321.

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The first step in finding the distance between vertex P and vertex V is find the length of diagonal between vertex P and vertex R.

option A.

To find the distance between vertex P and vertex V, we need to draw a diagonal line from vertex P to vertex V.

After drawing the diagonal line, we will notice that we have a new right angle triangle.

So since we know the height of the right triangle, we need to find the base of the right triangle first, which is equal to length of diagonal length PR or TV

So the correct answer will be "find the length of diagonal PR first.".

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Answer:

7,000,000÷2000

= 3,500

Step-by-step explanation:

therefore, each worker makes 3500 bikes per year

The probability that the greater of the two random variables will surpass the population median is just 0.5 because both events are mutually exclusive.

The i.i.d means two random variable where there is an equal chance that one will be greater then the other.

So, it means there is 50% chances for both of them to be greater then the median.

The probability that the greater of the two random variables will surpass the population median is just 0.5 because both events are mutually exclusive. This conclusion is valid as long as the variable are given to be continuous and i.i.d.

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Answer:

The Answer is 40°

Step-by-step explanation:

Base angles of an isosceles triangle are equal

x+30=70

x=70-30

x=40°

so,

<C=70°

<A+<B+<C=180°

let <A be X

X+70+70=180°

X+140=180°

X=180-140

X=40°

X=2x-10

40°=2x-10

2x=40+10

2x=50°

divide both sides by 2

x=25°

Therefore , the solution of the given problem of equation comes out to be y = 1 is the equation for the horizontal line.

For one-variable problems, regression modelling employs the polynomial solution answers x = ax2 + b + c=0. There is only room for one solution, according to the Fundamental Principle of Algebra, because it has an additional order. Both straightforward and intricate solutions are accessible. A "non-linear algorithm" has four variables, as the name implies. This suggests that there might be a single squared word.

Here,

=> y = k, where k is the y-coordinate of any point on the horizontal line, is the equation of a horizontal line in the point-slope form.

The y-coordinate of the given point (2, 1) will be the same as the y-coordinate of any other point on the line because

the given line is horizontal and passes through that location.

Therefore, the equation of the horizontal line going through the point (2, 1) has the following point-slope form:

=> y - 1 = 0

or merely:

=> y = 1

Consequently, y = 1 is the equation for the horizontal line.

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It should be noted that to prove that arc AB is equal to arc CD, we can use the fact that vertical angles are equal. Specifically, the angles formed by radii OA and OB are vertical angles with angles formed by radii OC and OD.

Let's call the angle formed by radii OA and OB angle x, and the angle formed by radii OC and OD angle y. Since ZAOB is a central angle of circle O, we know that arc AB is equal to twice angle x. Similarly, since COD is a central angle of circle O, we know that arc CD is equal to twice angle y.

Now, since angles x and y are vertical angles, they are equal. Therefore, arc AB is equal to twice angle x, which is equal to twice angle y, which in turn is equal to arc CD.

Therefore, we have proven that arc AB is equal to arc CD.

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Assuming line ABCD is a diameter. The proof is not valid in general for any chord.

To prove AB = CD, we show triangles ABO and DCO are congruent.

1. OB=OC     radius of inner circle

2. OA=OD     radius of outer circle

3. angle ABO = angle DCO

4. SSA = SSA indicates congruent triangles

Therefore AB = CD

Angles ABC and DCB are straight angles.

Angles OBC and OCB are congruent triangle OBC is isosceles with OB=OC

Therefore angle ABO = ABC - OBC = DCB - OCB = DCO

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Answer:

$384

Step-by-step explanation:

$3,200 x 0.12 = $384

If the results are the same, then the numbers are associative under addition.
Venn diagram: integer: -2
rational number: 3/4

Diagrams are visual representations of concepts, ideas, or processes, using lines, shapes, and other visual elements. They are used to communicate information quickly and clearly, and can be used to explore complex topics. Diagrams can be used to show the relationships between different components of a system, to explain how a process works, or to illustrate the structure of an organization. Diagrams can also be used to show the flow of information, or to illustrate the stages of a project.

A1. The associative property of addition states that when three or more numbers are added together, the order in which they are added does not affect the result. To check whether the numbers (a, b, and c) are associative under addition, we can calculate (a + b) + c and a + (b + c) and compare the results. If the results are the same, then the numbers are associative under addition.

Venn diagram:

integer: -2
rational number: 3/4

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The solution to the system of inequalities is given by the image presented at the end of the answer.

One point on the solution set is given as follows:

(-9,3).

A system of inequalities is a set of two or more inequalities involving one or more variables. In a system of inequalities, the solution is a set of values for the variables that satisfy all of the given inequalities simultaneously.

The solution is the shaded region on the graph given by the image presented at the end of the answer.

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The aircraft carrier's average speed was 120 mph.

Answer:

b)

Step-by-step explanation:

If x - 2 is a factor polynomial f(x), then the polynomial can be expressed as f(x) = (x - 2) g(x), where g(x) is another polynomial.

Using this information, we can check each statement to see which one does NOT have to be true:

A) f(2) = 0:

If x - 2 is a factor of f(x), then plugging in x = 2 gives f(2) = (2 - 2) g(2) = 0. This statement has to be true.

B) f(-2) = 0:

If x - 2 is a factor of f(x), then plugging in x = -2 gives f(-2) = (-2 - 2) g(-2) = -4 g(-2). This statement does NOT have to be true. For example, if g(-2) = 1/(-4), then f(-2) would not equal 0.

C) 2 is a root of f(x):

If x - 2 is a factor of f(x), then 2 is a root of f(x), meaning f(2) = 0. This statement has to be true.

D) 2 is a zero of f(x):

The term "zero" can be interpreted in different ways, but if it means the same as a root or a solution, then this statement is the same as statement C and has to be true.

Therefore, the statement that does NOT have to be true is B) f(-2) = 0.

The scale factor used for the dilation of the triangle ABC to A'B'C' is 3.

To find the scale factor, we can compare the corresponding side lengths of the two triangles. Let's start by finding the length of side AB in both triangles.

Length of AB in the original triangle ABC:

AB = √[(3-(-3))² + (3-(-3))²]

= √[6² + 6²]

= 6√(2)

Length of A'B' in the dilated triangle A'B'C':

A'B' = √[(9-(-9))²+(9-(-9))²]

= √[18² + 18²]

= 18√(2)

Now we can find the scale factor by dividing the length of A'B' by the length of AB:

scale factor = A'B'/AB

= (18√(2))/(6√(2))

= 3

Therefore, the scale factor used is 3. The dilation has enlarged the triangle by a factor of 3.

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Answer:

Step-by-step explanation:

· Find the surface area of a cone with a slant height of 8 cm and a radius of 3 cm. SA = B + πrS = (πr2) + πrs = (π(32)) + π(3)(8) = 9π + 24π = 33πcm2 = 103.62cm2. Find the surface area of a rectangular pyramid with a slant height of 10 yards, a base width (b) of 8 yards and a base length (h) of 12 yards.

The surface area of the composite figure is 20048 sq. yd.

The formula SA = 2lw + 2lh + 2wh can be used to get the surface area (SA) of a rectangular prism, where l, w, and h are the length, width, and height of the prism, respectively. The formula determines the areas of the rectangular prism's six faces: the four sides, which are identical rectangles with areas of lh or wh, and the top and bottom, which are also identical rectangles with areas of lw each.

The composite figure can be divided into two parts one rectangular prism and a trapezium prism.

The surface area of the rectangular prism is given by:

2(lb + bh + hl)

Substituting the values we have:

SA = 2(62 yd x 55 yd + 55 x 25 + 25 x 62)

SA = 2(3410 + 1375 + 1550)

SA = 2(6335) = 12670 sq. yd.

Now, the area of the trapezoidal prism is:

SA = (b1 + b2)h + (b1 + b2 + a + b) l

Substituting the values b1 = 55 yd, b2 = 7 yd, h = 7 yd, a = b = 25 yd, l = 62 yd we have:

SA = (55 + 7)(7) + (55 + 7 + 25 + 25)62

SA = 434 + 6944

SA = 7378 sq. yd

Now, the surface area of the composite figure is:

SA =  12670 + 7378 = 20048 sq. yd.

Hence, the surface area of the composite figure is 20048 sq. yd.

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We need to deposit $326.56 into the savings account each month in order to reach your retirement goal at age 65, assuming an APR of 6% compounded monthly.

What is Compound interest?

Compound interest is a type of interest that is calculated not only on the principal amount of money borrowed or invested, but also on the accumulated interest from previous periods. In other words, it is interest calculated on both the initial principal and the interest earned in previous periods.

To determine how much money you need to deposit into the savings account each month in order to reach your retirement goal at age 65, you can use the formula for future value of an annuity:

FV = [tex]PMT * \frac{(1 + r/n)^{n*t} - 1 }{r/n}[/tex]

where:

FV is the future value, which is the amount of money you want to save for retirement ($900,000 in this case)

PMT is the payment you need to make each month

r is the annual interest rate (6% in this case)

n is the number of times the interest is compounded per year (12 in this case, since the interest is compounded monthly)

t is the number of years until retirement (45 in this case, since you are 20 years old and planning to retire at age 65)

Substituting these values into the formula, we get:

$900,000 =  [tex]PMT * \frac{(1 + 0.06/12)^{12*45} - 1 }{0.06/12}[/tex]

$900,000 = [tex]PMT * \frac{(1 + 0.005)^{540} - 1 }{0.005}[/tex]

$900,000 = [tex]PMT * \frac{(1.005)^{540} - 1 }{0.005}[/tex]

$900,000 = [tex]PMT * \frac{(14.78 - 1) }{0.005}[/tex]

$900,000 = PMT × 2756

   ∴ PMT = $326.56

Therefore, you need to deposit $326.56  into the savings account each month in order to reach your retirement goal at age 65, assuming an APR of 6% compounded monthly.

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The cone have measures for the base, lateral, and surface areas as 77.6 mm², 330 mm², and 408.6 mm² respectively.

The formula for the surface area of a cone is:

A = πr² + πrs

Where: A = surface area r = radius of the base s = slant height of the cone

Base area = 22/7 × 5 mm × 5 mm

Base area = 78.6 mm²

Lateral area = 22/7 × 5 mm × 21 mm

Lateral area = 330 mm³

Surface area = 78.6 mm + 339 mm²

Surface area = 408.6 mm²

Therefore, the cone have measures for the base, lateral, and surface areas as 77.6 mm², 330 mm², and 408.6 mm² respectively.

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All of these ratios are equal to b, and we have shown that there is a constant ratio between consecutive output values.

The common ratio is the ratio that remains constant between successive function output values. The behaviour of a geometric sequence, which is a series of numbers where each term is produced by multiplying the one before it by a set number (the common ratio), depends on the common ratio. The sequence is rising exponentially if the common ratio is bigger than 1. The sequence decreases exponentially if the common ratio is between 0 and 1.

To show that the function form shows a constant ratio we take:

[tex](x+1) / f(x) = (ab^{(x+1)}) / (ab^x) = b[/tex]

Similarly, we have:

[tex]f(x+2) / f(x+1) = (ab^{(x+2)}) / (ab^{(x+1)}) = b[/tex]

Hence, all of these ratios are equal to b, and we have shown that there is a constant ratio between consecutive output values.

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The formula for the volume of an sphere of radius r is given as follows:

V = (2/3)πr³  

The radius as a function of the volume is obtained as follows:

r³ = 3V/2π

[tex]r = \sqrt[3]{\frac{3V}{2\pi}}[/tex]

Hence the radius of a sphere of volume 25 in³ is given as follows:

[tex]r = \sqrt[3]{\frac{25}{2\pi}}[/tex]

r = 2.29 in.

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Answer: They both intersect once.

Step-by-step explanation: Solving for x, we get:

3x = 0

x = 0

Now we can substitute x = 0 into either equation to find the y-coordinate:

y = 2(0) + 4 = 4

So the two lines intersect at the point (0,4).

Therefore, the graphs of the equations y = 2x + 4 and y = −x + 4 intersect once.

Answer:

It intersects once.

Step-by-step explanation:

To plot y = 2x + 4, you start at the y-intercept which is 4. Then you go up 2 times, and to the right once.

To plot y = -x + 4, you start at the y-intercept which is also at 4. Then you go down once and to the right one time.

The graph will intersect at (0, 4).

Jose needs 61.23 square inches of paper to cover the stack of coins.

The total thickness of the stack of 100 coins is 100 x 0.18 = 18 inches. The diameter of each coin is 1 inch, so the radius of each coin is 0.5 inches.

To find the amount of paper needed to cover the stack of coins, we need to calculate the total surface area of the stack.

The area of each circle is given by:

πr^2 where r is the radius of the coin.

The area of the top and bottom circles is:

2 x π x (0.5)^2 = 0.5π

The circumference of the circle is given by:

2πr

So, the circumference of each coin is:

2π(0.5) = π

The height of the stack is 18 inches, so the area of the curved surface is:

π x 18 = 18π

Therefore, the total surface area of the stack is:

1.5π + 18π = 19.5π

To cover the stack of coins with paper, Jose will need 19.5π square inches of paper.

19.5π ≈ 19.5 x 3.14 ≈ 61.23 square inches.

Therefore, Jose will need approximately 61.23 square inches of paper to cover the stack of coins.

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The probability that at least one customer arrives at the shop during a one-minute interval is 0.632.

Since the arrival of customers at a Starbucks shop can be modeled as a Poisson process with an average rate of 1/min, the probability of exactly k customers arriving in a one-minute interval is given by the Poisson probability mass function:

P(k arrivals) = (λ^k * e^(-λ)) / k!

where λ is the average rate of arrivals (in this case, 1/min), e is the mathematical constant e, and k! is the factorial of k.

To find the probability that at least one customer arrives during a one-minute interval, we can use the complement of the probability that zero customers arrive (i.e., the probability of at least one arrival is 1 minus the probability of zero arrivals).

Thus, the probability of at least one customer arriving during a one-minute interval is:

P(at least one arrival) = 1 - P(0 arrivals)

P(at least one arrival) = 1 - [([tex]1^{0}[/tex] * [tex]e^{-1}[/tex]) / 0!] = 1 - [tex]e^{-1}[/tex] = 0.632

Therefore, the probability that at least one customer arrives at the shop during a one-minute interval is 0.632.

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