plss helppp mee! The corporate team-building event will cost $18 if it has 3 attendees. How many attendees can there be, at most, if the budget for the corporate team-building event is $42? Assume the relationship is directly proportional.

To find the value of x when sin(x) is equal to cos(30°), we can use the trigonometric identity:

sin(x) = cos(90° - x)

Using this identity, we can rewrite the equation as:

cos(90° - x) = cos(30°)

For two angles to be equal, their cosine values must also be equal. Therefore, we have:

90° - x = 30°

Subtracting 30° from both sides, we get

90° - 30° = x

To find the value of x, we need to determine the angle whose sine is equal to √3/2. This angle is 60 degrees, or π/3 radians. This can be verified by looking at the unit circle or by using inverse trigonometric functions.

Simplifying, we have:

60° = x

Therefore, the value of x that satisfies the equation sin(x) = cos(30°) is x = 60°.

Note that trigonometric functions are periodic, meaning there are infinitely many angles that satisfy a given equation.

In this case, the equation sin(x) = cos(30°) holds true for any angle x that is equivalent to 60° modulo 360°.

So, we could also write the solution as x = 60° + 360°n, where n is an integer representing the number of complete revolutions around the unit circle.

For more questions Trignometric:

https://brainly.com/question/13729598

#SPJ8

Answer:

1,792 c = 112 gal.

Step-by-step explanation:

Because their 16 cups in 1 gallon, we will divide 1,793 by 16 and we get 112.  Therefore, 112 is our answer.

Answer:

112 gallons

Step-by-step explanation:

there are 16 cups in 1 gallon

1=16

?=1792

to solve this, divide 1792 by 16 to get 112 gallons

112*16 is 1792

Answer:

a. -17 -9n

Step-by-step explanation:

Question written clearly below:

Which answer choice is equivalent to the expression below?

-7(2+n)+1/3(-9-6n)

a.-17 -9n

b, -14-12n

c. 11+5n

d. 14+2n

Solution

-7(2+n)+1/3(-9-6n)

Open parenthesis

(-14-7n)+(-9/3-6/3n)

= -14-7n+(-3-2n)

= -14-7n-3-2n

Collect like terms

= -14-3-7n-2n

= -17-9n

The answer is option a. -17 -9n

Answer:

-17 -9n

Step-by-step explanation:

i got it right on edge

The angle between the two vectors is approximately 125 degrees and 32 minutes.

(a) To find the dot product of the two vectors (5, -8) and (-3, 4), we use the formula for the dot product: Dot product = (5 * -3) + (-8 * 4), Dot product = -15 - 32, Dot product = -47. Therefore, the dot product of the two vectors is -47. (b) To find the angle between the two vectors, we can use the formula for the dot product and the magnitudes of the vectors: Dot product = ||a|| * ||b|| * cos(theta). In this case, vector a = (5, -8) and vector b = (-3, 4).

The magnitude of vector a (||a||) is calculated as: ||a|| = √(5^2 + (-8)^2) = √(25 + 64) = √89. The magnitude of vector b (||b||) is calculated as: ||b|| = √((-3)^2 + 4^2) = √(9 + 16) = √25 = 5. Substituting these values into the dot product formula, we have: -47 = √89 * 5 * cos(theta). To find the angle theta, we rearrange the equation: cos(theta) = -47 / (5 * √89). Using a calculator, we can evaluate this expression: cos(theta) ≈ -0.532

To find the angle theta, we take the inverse cosine (arccos) of this value: theta ≈ arccos(-0.532). Using a calculator, we find: theta ≈ 125.53 degrees. Rounding to the nearest minute, the angle between the two vectors is approximately 125 degrees and 32 minutes.

To learn more about vector, click here: brainly.com/question/29261830

#SPJ11

The altitude of the plane would be 7664 feet.

Given that Climb angle is 5°

Horizontal distance traveled is 20 miles.

To find the altitude, we need to determine the vertical component of the distance traveled.

The vertical distance (altitude) can be calculated using the formula:

Altitude = Horizontal distance× tan(angle)

First, we need to convert the angle from degrees to radians, as trigonometric functions typically operate in radians.

Angle in radians = Angle in degrees × π / 180

So, the angle in radians = 5° × π / 180

= 0.0873 radians

Now we can calculate the altitude:

Altitude = 20 miles × tan(0.0873 radians)

Altitude = 1.451 miles

To convert the altitude from miles to feet, we know that 1 mile is equal to 5280 feet.

Altitude in feet = 1.451 miles × 5280 feet/mile

=7664.08 feet

Hence, the altitude of the plane would be approximately 7664 feet.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ4

The altitude of the plane is 9219 feet.

We are given that;

The angle of elevation is 5° and the hypotenuse is 20 miles.

Now,

To find the opposite side, which is the altitude. We can use the sine function, which relates the opposite side and the hypotenuse of a right triangle:

\($$\sin 5° = \frac{\text{altitude}}{20}$$\)

Multiplying both sides by 20, we get:

\($$\text{altitude} = 20 \sin 5°$$\)

Using a calculator, we get:

\($$\text{altitude} \approx 1.7453 \text{ miles}$$\)

To convert miles to feet, we multiply by 5280, since there are 5280 feet in one mile. We get:

\($$\text{altitude} \approx 1.7453 \times 5280 \text{ feet}$$$$\text{altitude} \approx 9218.784 \text{ feet}$$\)

Rounding to the nearest foot, we get:

\($$\text{altitude} \approx 9219 \text{ feet}$$\)

Therefore, by trigonometric identities the answer will be 9219 feet.

Learn more about trigonometric identities here:

https://brainly.com/question/13094664

#SPJ2

The maximum probability that a photon with the polarization state will be transmitted through the A filter is 1/2

To solve this problem, we need to use Malus' law, which states that the intensity of light transmitted through a polarizer is proportional to the square of the cosine of the angle between the polarization direction of the incoming light and the axis of the polarizer.

To find the overall probability that a photon will be transmitted through all three filters, we need to multiply the probabilities of each filter

P = 1/2 × cos²(θ) × 1

We are not given the angle θ, so we cannot calculate the exact value of P. However, we can calculate the maximum value of P, which occurs when the rotated filter is aligned with the A filter (i.e., θ = 0). In this case, P = 1/2.

Learn more about probability here

brainly.com/question/11234923

#SPJ4

The given question is incomplete, the complete question is:

H filter Rotated filter Rotated filter followed by A filter An unpolarized photon beam is incident on a linear polarizing filter. The incoming photon flux is is 2.34 x 101 photons/m' /sec.  What is the probability that a photo with the polarization state be transmitted through a subsequent filter, that is aligned with the direction?

Answer: I think cash and checks??

Step-by-step explanation:

Sorry if I'm wrong

Answer: D

Step-by-step explanation:

The perimeter is all the sides added up

2.5x + 2.5x + 10 + 2 + 10 =>

5x + 22

It is also given that the perimeter is 10.5x

meaning that both these values are equal

5x + 22 = 10.5x

Answer: w=2

Step-by-step explanation:

5w+9=19

minis 9 on the 9 and 19

5w+10

divide 5 on the ten to get 2

w=2

The probability that both marbles are red is 2/14 or 1/7.

This is because there are only two red marbles in the box, so the probability of the first being drawn is 2/14 (or 1/7). Since the first marble is not replaced, the probability of the second being drawn is also 2/14 (or 1/7). Mathematically, this can be expressed as: P(Both Red) = P(Red 1) x P(Red 2) = (2/14) x (2/14) = 1/7

In general, when dealing with probability questions involving drawing multiple objects from a box, the probability of drawing one object followed by another is calculated by multiplying the probability of drawing each individual object.

In the case of two marbles being drawn without replacement, the probability of both marbles being the same color is calculated by multiplying the probability of the first marble being of that color by the probability of the second marble being of that color.

The probability of the second marble being of the same color is lower than the probability of the first marble being of that color since it is drawn from a reduced set (the original set minus the first marble).

In this case, the probability of the second marble being of the same color as the first is 2/14, or 1/7. In conclusion, the probability of both marbles being red is 2/14, or 1/7.

For more such questions on Probability.

https://brainly.com/question/20396773#

#SPJ11

Answer:

De acuerdo a la información proporcionada, dado que se van a repartir 5 barritas entre 8 niños, se tiene que dividir las barritas entre el número de niños y a partir de aquí, se construye la fracción 5/8. Esto lo que indica es que cada barrita se divide en ocho pedazos y cada niño recibiría 1/8 de cada barrita y para las 5 barritas sería:

1/8*5=5/8

After 30 years of 8.8% interest compounded monthly, an account has $4,000,000,he original deposit amount was $288,208.04

Compound Interest :

                          Compound interest is a form of interest calculated using the principal amount of a deposit  plus previously accrued interest.

  general formula for compound interest is

                             A = P (1 + r/n) ^ nt

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

According to question,

Given final amount is (A) =  $4,000,000

time (t) = 30 years

Rate of interest (r) = 8.8%

                                = 8.8/100

                                = 0.088  , Compounded monthly

Let P be the principal amount

    using the formula for compound interest compounded monthly,

         A = P (1 + r/12)^12*t

or,

         P = A/(1 + r/12)^12*t

             Substituting all values we get,

            P =   $4,000,000/ (1 + 0.088/12)^12 x 30

                = $4,000,000/13.8788

                = $288,209.35

                ≈ $288,208.04

To learn more about Compound Interest visit:https://brainly.com/question/14295570

#SPJ4

Answer:

x = 4

y = 28

Step-by-step explanation:

1) y = 7x

2) y = 2x + 20

substitute y = 7x into equation 2:

7x = 2x + 20   now you can solve for x:

7x - 2x = 20

5x = 20

x = 20/5 = 4

Plug x = 4 into either equation 1 or 2 to solve for y:

y = 7x = 7(4) = 28

Answer:

The answer is y squared over 12 minus x squared over 24 equals 1

Step-by-step explanation:

Answer:

-51706

Step-by-step explanation:

when working with negative numbers, the number of greater size will be smaller.

The IQ representing the 16th percentile is 80.4 (rounded to one decimal place). The IQR of the IQs is 18.4.

Given that the normal model N (99,14) represents the IQs of sample participants.

a) To find the IQ representing the 16th percentile:

As per the empirical rule: 68% of values lie within one standard deviation of the mean, 95% of values lie within two standard deviations of the mean, and 99.7% of values lie within three standard deviations of the mean.

Now we have to find the z-score for the 16th percentile.i.e.,

P(z < z-score) = 0.16

From the standard normal distribution table, the closest z-score is -0.99. Thus, we can say

-0.99 = (IQ - 99) / 14IQ = 80.44

So, the IQ representing the 16th percentile is 80.4 (rounded to one decimal place).

b) To find the IQ representing the 99th percentile: As per the empirical rule: 68% of values lie within one standard deviation of the mean, 95% of values lie within two standard deviations of the mean, and 99.7% of values lie within three standard deviations of the mean.

Now we have to find the z-score for the 99th percentile.i.e.,

P(z < z-score) = 0.99

From the standard normal distribution table, the closest z-score is 2.33. Thus, we can say

2.33 = (IQ - 99) / 14

IQ = 131.62

So, the IQ representing the 99th percentile is 131.6 (rounded to one decimal place).

c) The interquartile range (IQR) is the difference between the 75th percentile (Q3) and the 25th percentile (Q1).The 25th percentile can be calculated as follows:

P(z < z-score) = 0.25

From the standard normal distribution table, the closest z-score is

-0.67.-0.67 = (IQ - 99) / 14

IQ = 89.78

So, the 25th percentile (Q1) is 89.8 (rounded to one decimal place).

The 75th percentile can be calculated as follows: P(z < z-score) = 0.75

From the standard normal distribution table, the closest z-score is 0.67.

0.67 = (IQ - 99) / 14

IQ = 108.22

So, the 75th percentile (Q3) is 108.2 (rounded to one decimal place).

IQR = Q3 - Q1 = 108.2 - 89.8 = 18.4

Thus, the IQR of the IQs is 18.4.

Learn more about percentile visit:

brainly.com/question/1594020

#SPJ11

Answer:

The probability is 0.5 tiles will be green

Step-by-step explanation:

Hope this helps

well, the hexagonal pyramid is really just six triangles with a base of 24 and a height of 24 as well, and a hexagonal base with an apothem of 12√3 and sides of 24.

\(\textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap ~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=12\sqrt{3}\\ p=\stackrel{(24)(6)}{144} \end{cases}\implies A=\cfrac{1}{2}(12\sqrt{3})(144) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{\textit{six triangles}}{6\left[ \cfrac{1}{2}(\underset{b}{24})(\underset{h}{24}) \right]}~~ + ~~\stackrel{\textit{hexagonal base}}{\cfrac{1}{2}(12\sqrt{3})(144)}}\implies 1728+864\sqrt{3} ~~ \approx ~~ \text{\LARGE 3224}~m^2\)

The given initial value problem is a second-order linear homogeneous differential equation. To solve it, we first find the characteristic equation by substituting y = e^(rx) into the equation. This leads to the characteristic equation r^2 - 10r + 50 = 0.

The general solution of the differential equation is y(x) = e^(5x)(C₁cos(5x) + C₂sin(5x)), where C₁ and C₂ are constants determined by the initial conditions.

To determine the particular solution, we differentiate y(x) to find y'(x) = e^(5x)(5C₁cos(5x) + 5C₂sin(5x) - C₂cos(5x) + C₁sin(5x)), and then differentiate y'(x) to find y''(x) = e^(5x)(-20C₁sin(5x) - 20C₂cos(5x) - 10C₂cos(5x) + 10C₁sin(5x)).

Substituting the initial conditions y(0) = 1 and y'(0) = 5 into the general solution and its derivative, we obtain the following equations:

1 = C₁,

5 = 5C₁ - C₂.

Solving these equations, we find C₁ = 1 and C₂ = 4.

Therefore, the particular solution to the initial value problem is y(x) = e^(5x)(cos(5x) + 4sin(5x)).

To find the value of y when x = 1.52, we substitute x = 1.52 into the particular solution and evaluate it. The result will depend on the rounding instructions provided.

know more about characteristic equation :brainly.com/question/28709894

#SPJ11

The random variable x, which represents the amount of rain (in inches) that fell this spring, is a continuous random variable.

In this context, a continuous random variable is one that can take on any value within a certain range. The amount of rain can be measured with different levels of precision, such as 2.5 inches or 2.5342 inches, indicating that there is an infinite number of possible values between any two given points.

On the other hand, a discrete random variable would involve countable outcomes or a finite number of possible values. For example, if we were counting the number of rainy days during the spring, the random variable would be discrete since it can only take whole number values.

In the case of measuring the amount of rain, there can be infinitely many possible values within any given range, and therefore, it is considered a continuous random variable. So, the correct answer is option A.

Learn more about variable here:

https://brainly.com/question/28248724

#SPJ11

The complete question is:

Decide whether the random variable x is discrete or continuous. Explain your reasoning Let x represent the amount of rain (in inches) that fell this spring. Is the random variable x discrete or continuous? Choose the correct answer below.

A. Continuous, because x is a random variable that cannot be counted.

B. Discrete, because x is a random variable that can be counted.

Answer:

$493.75

Step-by-step explanation:

I hope this helps!

Answer:

B,D

Step-by-step explanation:

waiting for brainlist

Answer:

The correct answer here is B.

Step-by-step explanation:

Took the test

Answer:

They are congruent.

Step-by-step explanation:

Well, JK and GH segment ends are 8 "blocks" away from each other, so they are congruent.

Answer: 4:5

Step-by-step explanation: The lowest form

Answer:

Step-by-step explanation:

4:5

The value of the expression 7 - 9 using subtraction will be negative 2.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

7 and 9

Then the difference between the numbers 7 and 9 will be given by putting a minus sign between them. Then we have

⇒ 7 - 9

⇒ - 2

The value of the expression 7 - 9 using subtraction will be negative 2.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

Answer:

20

Step-by-step explanatio: because its adding 2 more spaces to the left

Please brainliest

Answer:

Step-by-step explanation:

Let A = 2×2×3×3×3×3×5×5×5×11

Let B = 2×2×2×2×2×3×3×5×7×13​

Highest Common factors = 2 x 2 x 3 x 3 x 5

                                            = 180

The perimeter of the egg comprising of arcs AB, AC, BD, and CD is π·(6-√2)/2 centimeters

The perimeter of a figure is the length of the boundary line of a plane occupied by the figure.

The perimeter of the egg can be found by finding the sum of the lengths of the arcs that together form a composite figure of the perimeter of the egg

The length of arc AC centered at point B is found as follows;

The angle at the center B is the base angle of the isosceles right triangle

The acute angle of an isosceles right triangle is 45°, therefore, the angle at B = 45°

The radius of the arc AC, AB = AO + OB = BC

AO and OB are the radii of the circle with center O

AO = OB = 1 cm

AB = 1 + 1 = 2 = BC

The length of AC = (45/360)× 2×π×2 = π/2

AC = π/2

The radii and angle at the center of arc BD are also 2 cm and 45°

The length of arc BD is therefore, (45/360) × 2 × π × 2 = π/2

BD = π/2

The angle at the center of arc CD = ∠CED

∠CED ≅ ∠AEB (Vertical angle postulate)

∠AEB = ∠AEO + ∠BEO = 45° + 45° = 90°

∠CED = ∠AEB (Definition of congruency)

∠CED = ∠AEB = 90°

The radius of the arc CD, CE = ED = BC - EB

EB = √(1² + 1²) = √2

CE = 2 - √2

Length of arc CD = (90°/360°) × 2 × π × (2 - √2)) = π × (2 - √2))/2

CD = π·(2 - √2)/2

The radius of the arc AB = 1 cm

Angle at the center of arc AB = 180°

Length of arc AB = π × 1 = π

AB = π

The perimeter of the egg = AC + CD + BC + AB

Therefore;

The perimeter of the egg = π/2 + π × (2 - √2))/2 + π/2 + π = π·(6 - √2)/2

The perimeter of the egg is π·(6 - √2)/2 cm

Learn more on the perimeter of a composite figure here: https://brainly.com/question/8971404

#SPJ1