help prove they’re equal

First, assign variables to the given information:

We're given:

Plug the second equation into the first and solve using substitution:

[tex]x+y=709\\59+y+y=709\\59+2y=709\\2y=650\\y=325[/tex]

Therefore, 325 adult tickets were sold.

325 adult tickets were sold.

The area of an equilateral triangle having height 12 cm is 83.136 sq.cm.

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It is sometimes referred to as a regular triangle because it is a regular polygon.

if height h is given in equilateral triangle then first we have to find the length of side which can be solve by this formula like a right angle triangle where side of equilateral triangle is a and another side is a/2 and next is height which is given 12 cm.

[tex]a^{2} -(a/2)^{2} = 12^{2}[/tex]

[tex](3/4)a^{2} = 144[/tex]

[tex]a^{2} = 192\\a = \sqrt{192}[/tex]

a = 13.85

area of equilateral triangle = [tex]((\sqrt{3})/ 4 )a^{2}[/tex]

= 1.732*192/4

83.136 sq.cm

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The height of the portion AB of the lamppost is approximately 27.8 feet, as calculated using the tangent function with angle 55 degrees and length BC 20 feet.

Based on the given information, we can use trigonometry to find the height of the portion AB of the lamppost.

Let's call the height of AB "x". We can use the tangent function to solve for x:

tan(55) = x/20

Multiplying both sides by 20:

x = 20 tan(55)

Using a calculator, we get:

x ≈ 27.8 feet

Therefore,

The height of the portion AB of the lamppost is approximately 27.8 feet.

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Answer: 20 tan 55

Step-by-step explanation:

took test and got it right

its b is true I just took it

X = 2 (two) students study all three subjects (physics, geography, and economics). This can be found by adding the number of students who study only two subjects (6 + 4 + 5 = 15) and subtracting that from the total number of students who study at least one subject (55 - 20 = 35), since each of these 15 students who study two subjects is counted twice in the totals for each subject.

The number of students who study physics only is 10. This can be found by subtracting the number of students who study physics and at least one other subject (21 - 6 - 5 - 2 = 8) from the total number of students who study physics (21).

The number of students who study exactly one of the two subjects is 25. This can be found by adding the number of students who study each subject only (10 + 11 + 9) and subtracting that from the total number of students (55 - 20 = 35).

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The distance from the town to the North Pole is approximately 2290 miles.

To find the distance in miles from the town to the North Pole, we need to calculate the length of the meridian arc from the town to the North Pole. The meridian arc is a portion of a great circle passing through the town and the North Pole.

The length of the meridian arc can be calculated using the formula:

Length = (π/180) x radius of the Earth x angle in degrees

where π is approximately 3.14159, and the radius of the Earth is 3960 miles.

Since the town is located at latitude 32°N, the angle between the town and the North Pole is 90° - 32° = 58°.

Plugging in these values into the formula, we get:

Length = (π/180) x 3960 miles x 58°

Length = (3.14159/180) x 3960 miles x 58

Length ≈ 2290 miles

Therefore, the distance from the town to the North Pole is approximately 2290 miles.

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If the researcher divided subjects into three groups according to whether or not they have brown, blue or green eyes, then the researcher was using a stratified sampling method.

Here a researcher divided subjects into three groups according to whether or not they have brown, blue, or green eyes.

The selected members from each group for their sample

The stratified sampling method is defined as the sampling method that divides the total population into the smaller group

Here the total population is divided into three groups according to whether they have brown, blue or green eyes.

Therefore, researcher was using stratified sampling method

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See below for the description of the enlarged shapes when dilated

From the question, we have the following parameters that can be used in our computation:

Scale factor = 4

This means that if Mai enlarges the triangular sign by a multiple of 4,

Then the corresponding side in the enlarged sign to side EG is 4 times the length of side EG.

i.e Corresponding side = 4 * Original side

If Mai wanted to turn the sign so that side JK was on the bottom,

Then the corresponding side of the original sign would be the side that was previously opposite to JK.

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The probability of having more than the expected number of failures (i.e., at least five failures) in a set of nine Bernoulli trials is 0.2461, assuming that the probability of failure is 0.5.

In the field of probability, it is essential to understand the expected number of successes or failures in a given set of trials. However, what happens when we observe more or fewer outcomes than expected? In this scenario, we need to calculate the probability of observing a specific number of failures in a set of Bernoulli trials.

Let's assume that the probability of failure is denoted by "p," and the probability of success is denoted by "q." Thus, the expected number of failures in nine Bernoulli trials is given by:

E(X) = np

where n is the number of trials, and p is the probability of failure. In this case, n = 9, and we need to determine the probability of having more than the expected number of failures. This means we are interested in finding the probability of observing at least five failures since the expected number of failures is given by:

E(X) = 9p

If we assume that the probability of failure is 0.5 (i.e., p = 0.5), then the expected number of failures is 4.5 (i.e., E(X) = 9 * 0.5 = 4.5). Therefore, we are interested in finding the probability of observing at least five failures in nine Bernoulli trials.

To calculate this probability, we need to use the binomial distribution formula, which is given by:

[tex]P(X = k) = (^n_k) \times p^k \times q^{n-k}[/tex]

where P(X = k) is the probability of observing k failures in n trials, (n choose k) is the binomial coefficient, which is calculated as n! / (k! (n-k)!), p is the probability of failure, q is the probability of success (i.e., q = 1 - p), and k is the number of failures we are interested in observing.

Using this formula, we can calculate the probability of observing at least five failures in nine Bernoulli trials as follows:

P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)

= (9 choose 5) x 0.5⁵ x 0.5⁴ + (9 choose 6) x 0.5⁶ x 0.5³ + (9 choose 7) x 0.5⁷ x 0.5² + (9 choose 8) x 0.5⁸ x 0.5¹ + (9 choose 9) x 0.5⁹ x 0.5⁰

= 0.2461

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Answer:       is 1 of them 31(2760)q -d)

Answer:

900

Step-by-step explanation:

5% of 18,000

The statement, coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. A definite occurrence has a chance of 1 while an impossible event has a probability of 0.

When a coin is flipped the probability of getting a heads and a tail is 50%.

Hence, without the consideration of the flips and the result the theoretical probability that the next coin flip will be heads is 50%.

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Answer:

49ft

Step-by-step explanation:

Sketching out the problem, we get something like the diagram below. Assuming the canyon makes a roughly 90° angle with the ground, we can see that we have two right-angled triangles formed.

Focusing on the first triangle: since we have the angle, and we know the height of the canyon is 230ft, we can also find the combined width of the ground and river (let's call this y) using cos:

cos38=230/y

0.7880107536=230/y

y=230/0.7880107536= 291.874189467ft

Focusing now on the first triangle: since we have the angle, and we know the height of the canyon is 230ft, we can find the width of the ground (let's call this x) using cos:

cos19=230/x

0.94551857559=230/x

x=230/0.94551857559= 243.252756673ft

Therefore, the width of the river must be the difference between the combined width of the ground and river, minus the width of the ground:

291.874189467ft - 243.252756673ft = 48.621432794ft ≈ 49ft

Answer:

[tex]10x^2+28x+15[/tex]

Step-by-step explanation:

[tex](2x^2+3)(4x+5)-8x(x^2-2)\\\\=(2x^2)(4x)+(2x^2)(5)+(3)(4x)+(3)(5)-8x^3+16x\\\\=8x^3+10x^2+12x+15-8x^3+16x\\\\=10x^2+28x+15[/tex]

The number of movies on the shelf is given as follows:

36 movies.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For this problem, the parameters are given as follows:

Hence the total number of outcomes, representing the number of movies on the shelf, is obtained as follows:

1/4 = 9/x

x = 9 x 4

x = 36 movies.

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Answer:

175m²

Step-by-step explanation:

Total area (of pool):

50 × 21 = 1050

Area of each lane:

1050 ÷ 6 = 175

Suppose x is the number of times a woman is selected when 3 people are randomly chosen from a group of 2 women and 2 men, the possible values of x are 0, 1, 2, and 3.

When 3 people are randomly chosen without replacement from a group of 2 women and 2 men, there are a total of 4C₃ = 4 possible outcomes, which we can list as follows:

WWx (two women and one of either gender)

WMx (one woman, one man, and one of either gender)

MWx (one man, one woman, and one of either gender)

MMx (two men and one of either gender)

In each of these outcomes, x represents the number of times a woman is selected. We can see that the possible values of x are 0, 1, 2, and 3, depending on which outcome occurs.

In outcome 1 (WWx), a woman is selected twice, so x = 2.

In outcomes 2 (WMx) and 3 (MWx), a woman is selected once, so x = 1.

In outcome 4 (MMx), no women are selected, so x = 0.

Therefore, the possible values of x are 0, 1, 2, and 3.

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The number of balls that he can make is given as follows:

249 balls.

The volume of a sphere of radius r is given by the equation presented as follows:

V = 4πr³/3.

Considering the radius of 3 inches, the volume of each ball is given as follows:

V = 4π x 3³/3

V = 113.1 in³.

He has a total of 28,260 in³ of material, hence the number of balls that he can make is given as follows:

28260/113.1 = 249 balls.

(rounding down, as there will not be enough material for the 250th ball).

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The expression for the number of paid vacation days for x years is

2 + 3x.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of paid vacation days = 2

Now,

She will receive an additional three days per year of paid vacation for each year she remains with the company.

This means,

For x years,

Number of paid vacation days = 2 + 3x

Now,

The expression for x years.

= 2 + 3x

Thus,

2 + 3x is the expression for the number of paid vacation days for x years.

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The complete question.

A)

Write an expression for the number of paid vacation days for x years.

Answer:

ST = 12 units

Step-by-step explanation:

Δ STE and Δ SRA are similar ( AA postulate ) , then the ratios of corresponding sides are in proportion, that is

[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{RA}[/tex] ( substitute values )

[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )

6 ST = 8(21 - ST)

6 ST = 168 - 8 ST ( add 8 ST to both sides )

14 ST = 168 ( divide both sides by 14 )

ST = 12 units

The coordinates of vertex D of the parallelogram is; (0, 1)

We are given the coordinates of the parallelogram as;

A(2,4), B(5,2) and C(3,-1)

Now, we know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the mid point of BD.

The formula for the midpoint between two coordinates is;

(x1 + x2)/2, (y1 + y2)/2

Thus;

Midpoint of AC = (2 + 3)/2, (4 - 1)/2 = 5/2, 3/2

Midpoint of BD = (5 + x)/2, (2 + y)/2

Thus;

(5 + x)/2 = 5/2

x = 0

(2 + y)/2 = 3/2

2 + y = 3

y = 1

Coordinate of D = (0, 1)

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The correct answer for each of the math expressions is given below:

The graph of a function f in mathematics is the collection of ordered pairs where displaystyle f(x)=y.

These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

Hence, given that in the graph,

f(x) = 4x + 3

g(x) = [tex]\frac{5}{3} ^x[/tex]

Over the interval (4,5), the average rate of change of g is greater than the average rate of change of f.

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The statement which is not true is a. Passive political risk management discourages managers from fully or partially hedging their bets against exposure to political hazards

Passive political risk management does not deter managers from fully or partially hedging their bets against political risk exposure. This management describes a strategy for controlling political risk that involves altering how a firm carries out a business to reduce political risk. This is generally performed without necessarily using financial instruments to safeguard against any degree of political risk.

It may entail taking necessary steps to spread the firm's operations across other geographies and regions, choosing joint venture partners with strong political influence, determining local contacts, and preserving strong ties with local individuals associated with politics. Even if a firm doesn't use active hedging tactics, these activities can efficiently assist it to lessen its exposure to political risk.

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The measured length of DE will be 4 cm.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

Given that AB is 5 cm, BC is 7 cm, and CA is 8 cm in the triangle ABC. The reep midpoints of AB and BC are Ids D and E.

The two triangles ABC and ADE will be similar to each other. The measure of the length DE will be calculated as:-

AC = DE = 7 / 3.5

DE = AC / 2

DE = 8 / 2

DE = 4 cm

Hence, the value of the side DE will be 4 cm.

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The total length of the two welded together is 26ft.

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. Division and multiplication are the other two fundamental mathematical operations. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).

Given that the length of the two pieces of the pipe is 23ft and 3ft.

The total length of the two welded together is:

23 + 3 = 26ft

Hence, the total length of the two welded together is 26ft.

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The time at which the rocket reaches its maximum height is 3.5 seconds. Therefore, b. is the correct answer.

An equation describing the relationship between the input (x) and the output (f(x)) is called the function f(x). Any equation that represents the connection between an input x and an output f is referred to as the function f(x) (x).

A function can be expressed as a graph or table in addition to the standard form of an equation. Functions can be stated using symbols and phrases in addition to equations. A function could be expressed, for instance, as "the square of x" or "f of x equals x squared."

Whatever form a function takes, it's critical to keep in mind that the input (x) always yields the same result (f(x)).

In the given question,

The maximum height of the rocket is achieved at the point when the velocity of the rocket is 112 feet. This can be determined by taking the derivative of the function S(t).

S'(t) = 112

Therefore, when S'(t) = 112, t = 3.5.

This means that the rocket reaches its maximum height at t = 3.5 seconds.

Therefore, the time at which the rocket reaches its maximum height is 3.5 seconds.

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Answer:  30% less than 40 is 28

Step-by-step explanation:

Answer:

The answer is 28.

Step-by-step explanation:

I'm bad at proving stuff but that's the answer I promise. (quick tip, you are more likely to get answers if you give more points. :D)

The weighted average grade of the student is 85.6% calculated by multiplying the weight of each category with the average score of that category, and summing up the results.

To find the weighted average grade of the student, we can use the following formula:

Weighted average = (weight of category 1 x average of category 1) + (weight of category 2 x average of category 2) + ... + (weight of category n x average of category n)

where n is the number of categories being considered.

Using this formula and the information given in the question, we can calculate the weighted average as follows:

Weighted average = (0.30 x 85%) + (0.40 x 83%) + (0.20 x 89%) + (0.10 x 91%)

= 25.5% + 33.2% + 17.8% + 9.1%

= 85.6%

Therefore,

The weighted average grade of the student is 85.6%.

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Answer:

7 traders sell oranges and mangoes alone.

Step-by-step explanation:

(21 + 4 + 5 + 10 + x + 35 – x + 32 – x = 100)

(107 – x = 100)

(x = 107 – 100 = 7)

Therefore, 7 traders sell oranges and mangoes alone.

(b) (312_{four} + 52_{x} = 96_{ten})

(312_{4} = 3 times 4^{2} + 1 times 4^{1} + 2 times 4^{0})

= (48 + 4 + 2 = 54_{10})

(52_{x} = 5 times x^{1} + 2 times x^{0})

= ((5x + 2)_{10})

(therefore 54 + (5x + 2) = 96)

(56 + 5x = 96 implies 5x = 96 – 56 = 40)

(x = 8)

(therefore 312_{4} + 52_{8} = 96_{10})