Simplify the radical expression and shows steps

Answer:

Option 2: [tex]\sin(30)=\frac{1}{2}[/tex]

Step-by-step explanation:

Given:

From the triangle shown below;

A triangle QRS with angle QRS = 90°, ∠QSR = 30°.

Side QR = 5, SQ = 10 and RS = 5√3

Now, we know from trigonometric ratio that,

[tex]\sin (A) = \frac{Opposite\ side}{Hypotenuse}[/tex]

Here, opposite side of angle QSR is QR and Hypotenuse is the side opposite angle QRS which is SQ. Therefore,

[tex]\sin(\angle QSR)=\dfrac{QR}{SQ}\\\\\\\sin(30)=\dfrac{5}{10}\\\\\\\sin(30)=\dfrac{5}{2\times 5}=\dfrac{1}{2}[/tex]

Therefore, the value of sine of 30° is one-half. So, second option is correct.

Answer:

B

Step-by-step explanation:

Answer:

The answer to your question is letter E. cos²α

Step-by-step explanation:

                            cot²Ф  - cot²Фcos²Ф

Remember that    cot = [tex]\frac{cos \alpha}{sin \alpha }[/tex] ; substitute in the previous equation

                            [tex]\frac{cos^{2}\alpha }{sin^{2} \alpha} - \frac{cos^{2}\alpha }{sin^{2}\alpha } cos^{2}\alpha[/tex]

                                 [tex]\frac{cos^{2}\alpha - cos^{4}\alpha }{sin^{2}\alpha }[/tex]                     Factor  cos²α

                                [tex]\frac{cos^{2}\alpha(1 - cos^{2}\alpha }{sin^{2}\alpha }[/tex]

Remember that   sin²α = 1 - cos²α

                                [tex]\frac{cos^{2}\alpha sin^{2}\alpha}{sin^{2} \alpha}[/tex]

Simplify

                              cos²α

Answer:

Step-by-step explanation:

The graph is sketched in the attachment. It's easy to sketch the same graph using the given information. Let's say h is the height. For time t=0 you put a dot on 3 feet since it's the lowest point of the ferris wheel (you get that by substracting the diameter of 40 feet from the highest point given (43 feet).

Second dot is your highest point 43 feet at t=4 sec since it is the half of the circle.

The third dot is your lowest point again at t=8 sec. If you connect the dots like a sine you get the sketched graph.

To find out what is the equation for the graph you need to look at the amplitude which in this case is 20 feet. Then you need to find out the frequency at which the wheel is turning. Since you are given the period (8 sec for a full cycle) you get the frequency:

[tex]f=\frac{1}{T}=\frac{1}{8}[/tex]

Now you need to find out the phase of the wave. Since we want to be at 0 feet at t=0 you need to shift the wave 90° degrees forward or [tex]\frac{\pi}{2}[/tex] in radians.

Finally it's important to shift the whole wave up. You do that by adding the appropriate amount that is in this case the half of the diameter plus the 3 feet to the ground.

The equation you get is:

[tex]h(t)=23+A\sin(2\pi f t-\phi)=23+20\sin(0.25\pi t-\frac{\pi}{2})[/tex]

where A is amplitude, [tex]\phi[/tex] is the phase shift and [tex]f[/tex] is the frequency.

Finally you can get the height at [tex]t=4.5[/tex] sec:

[tex]h(t=4.5)=23+20\sin\left(0.25\pi4.5-\frac{\pi}{2}\right)=41.478\ \text{ft}[/tex]

Answer:$2430

Step-by-step explanation:

6x45=270

270x9=2430

Answer:

There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.

Step-by-step explanation:

Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.

 The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is [tex] {11 \choose 3} = 165 . [/tex] As a result, we have 165 ways to distribute the blackboards.

If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is [tex] {7 \choose 3} = 35 [/tex]. Thus, there are only 35 ways to distribute the blackboards in this case.

If 8 identical blackboards are to be divided among 4 schools, there are 70 possible divisions. If each school must receive at least 1 blackboard, there are 56 possible divisions.

If 8 identical blackboards are to be divided among 4 schools, the number of ways this can be done is 8C4, which is equal to 70.

If each school must receive at least 1 blackboard, then we need to subtract the cases where one or more schools do not receive a blackboard.

To calculate this, we can subtract the number of ways that three schools do not receive a blackboard (4C1 = 4), the number of ways that two schools do not receive a blackboard (4C2 = 6), and the number of ways that only one school does not receive a blackboard (4C3 = 4).

So, the number of divisions where each school receives at least 1 blackboard is 70 - 4 - 6 - 4 = 56 ways.

Answer:

What is the figure you are talking about?

In order to find 30% of 75, we simply calculate 75 x 0.3.

75 x 0.3 amounts to 22.5, which is the amount we deduct.

This leaves a final price of $52.50.

A 30% discount on an item priced at $75 results in a deduction of $22.5.

The student's question is about calculating a discount on an item. Here, the discount is a 30% decrease or reduction off the original price of the item, which is $75. To calculate the discount, you multiply the original price by the percentage discount. Remember, since percentage is a proportion, you'll need to convert the percentage to a decimal first by dividing it by 100. Therefore, the formula will be:

Discount = Original Price x Percentage Discount

Substituting in the given values:

Discount = $75 x 30/100 = $22.5

So, with the 30% discount, you can deduct $22.5 from the original price of the item.

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Final answer:

To find out how many liters of paint are needed for one door, when 3 liters were used for 1 4/5 doors, divide the total amount of paint by the number of doors. The calculation is 3 liters divided by 9/5, which results in 1.67 liters of paint for one door.

Explanation:

Maren used 3 liters of paint to cover 1 4/5 doors which implies that the amount of paint needed for 1 door can be found by dividing the total amount of paint by the number of doors painted. To calculate this:

Therefore, 1.67 liters of paint are needed for 1 door.

Answer:

4 hrs 48 min

Step-by-step explanation:

It takes 6 presses 4 * 3/5 = 12/5 hours to print 3000 newspapers.

It takes 3 presses 2 * 12/5 = 24/5 hours = 4h48min to print 3000 newpapers

Answer:

6

Step-by-step explanation:

jus did it

Answer:

  2 1/4 gallons

Step-by-step explanation:

We assume your problem is intended to say there are five tanks, each having a volume of 1/2 gallon, and that 4.5 of these have been filled so far.

The volume of water used is ...

  (4.5 tanks)(0.5 gal/tank) = 2.25 gal

2.25 gallons of water have been used.

Answer: the speed of the commercial jet is 540 mph

the speed of the private airplane is 330 mph

Step-by-step explanation:

Let x represent the speed of the commercial jet and

Let y represent the speed of the private airplane.

It takes the commercial jet 1.1 hours for the flight from Denver to Phoenix.

Distance = speed × time

Therefore, distance covered by the commercial jet from Denver to Phoenix would be

1.1 × x = 1.1x

it takes the private airplane 1.8 hours to cover the same distance. The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane. It means that

y = x - 210

Distance covered by the private airplane would be

1.8(x - 210) = 1.8x - 378

Since the distance is the same, then

1.8x - 378 = 1.1x

1.8x - 1.1x = 378

0.7x = 378

x = 378/0.7 = 540

y = x - 210 = 540 - 210

y = 330

To find the speeds of a commercial jet and a private airplane, we can set up and solve an equation using the distance and time information provided in the question.

The question is about the speeds of a commercial jet and a private airplane flying from Denver to Phoenix. Let's assume the speed of the private airplane is 'x' miles per hour. According to the question, the commercial jet is 210 miles per hour faster than the private airplane. So, the speed of the commercial jet is 'x + 210' miles per hour.

Now, we have the speeds of both planes. We can use the formula 'speed = distance / time' to calculate the distance. Since the time for the commercial jet is 1.1 hours and the time for the private airplane is 1.8 hours, the distances traveled by the commercial jet and the private airplane are '1.1(x + 210)' and '1.8x' miles, respectively.

Since both planes are traveling the same distance, we can set up the equation '1.1(x + 210) = 1.8x' to find the value of 'x'. Solving this equation will give us the speed of the private airplane. Once we have the speed of the private airplane, we can calculate the speed of the commercial jet by adding 210 to it.

Answer:

Angular speed of the towers top about its base is [tex]6.91\times 10^{-13}[/tex] rad per sec.

Step-by-step explanation:

Linear velocity of leaning bell tower 'v' = 1.2 mm per year

v = [tex]\frac{1.2\times 10^{-3}}{365\times 24\times 60\times 60}[/tex]

v = 3.8 × [tex]10^{-11}[/tex] meter per second

Height of the tower = 55 meter

From the formula of angular velocity,

v = rω

ω = [tex]\frac{v}{r}[/tex]

ω = [tex]\frac{3.8\times 10^{-11}}{55}[/tex]

ω = [tex]6.91\times 10^{-13}[/tex] rad per second.

Therefore, top of the tower is moving with an angular speed of [tex]6.91\times 10^{-13}[/tex] rad per second.

Final answer:

To rewrite a conditional statement in if-then form, use the example given. The converse, inverse, contrapositive, and biconditional can be formed by changing the order and negating the original statement in different ways.

Explanation:

To rewrite the conditional statement 'Right angles are 90°' in if-then form, we can state: 'If an angle is a right angle, then it measures 90°.'

The converse of the conditional statement is: 'If an angle measures 90°, then it is a right angle.'

The inverse of the conditional statement is: 'If an angle is not a right angle, then it does not measure 90°.'

The contrapositive of the conditional statement is: 'If an angle does not measure 90°, then it is not a right angle.'

The biconditional statement is: 'An angle is a right angle if and only if it measures 90°.'

Answer:

Molarity is the concentration of x moles of solute in 1 L of solution. ... have different properties i.e., a low molarity acid and high molarity acid can ... For example, a 0.25 mol/L NaOH solution contains 0.25 mol of sodium hydroxide in every litre of solution ... 15.0 g of NaOH in enough water to make a total of 225 mL of solution

Step-by-step explanation:

Answer:the time for processing the payment took 58 seconds.

Step-by-step explanation:

An experienced cashier at a grocery store takes 2 seconds to scan each item and 40 seconds to process the customer's payment. If Anna bought 31 items at the grocery store, the total time for Anna's transaction would be

(31 × 2) + 40 = 62 + 40 = 102 seconds.

The time to to process the Anna's payment took longer due to glitches. If the total time for Anna's transaction took 2 minutes = 120 seconds, then the amount of time it took to process the payment (p) would be

p = 120 - 62 = 58 seconds

Answer:

[tex]q=4p-14[/tex]

Step-by-step explanation:

The first step in solving

[tex]5q-4p+6=4q-8[/tex]

is to bring [tex]4q[/tex] on the right the left side to the right side by subtracting it from both sides:

[tex](5q-4p+6)-4q=(4q-8)-4q\\\\(5q-4q)-4p+6=-8\\q-4p+6=-8[/tex]

and we subtract 6 from both sides and get:

[tex]q-4p=-14[/tex]

finally we add [tex]4p[/tex] to both sides and get:

[tex]q-4p+4p=-14+4p[/tex]

[tex]\boxed{q=4p-14}[/tex]

Answer:

Number of gallons of 4% salt solution in the mixture = 20.08

Number of gallons of 30% salt solution in the mixture = 24.92

Step-by-step explanation:

Given:

There are two bottles of brine solution:

1 has 4% salt

2 has 30% salt

The chemist mixes some gallons of each bottle to get a 45 gallons solution containing 18.4% salt.

To find the gallons of each solution taken to make the mixture.

Solution:

Let the number of gallons of 4% salt solution mixed be  = [tex]x[/tex]

So, number of gallons of 30% salt solution mixed will be = [tex]45-x[/tex]

Amount of salt in [tex]x[/tex] gallons of 4% salt solution will be :

⇒ Percentage concentration x Gallons of solution

⇒ [tex]0.04\times x[/tex]

⇒ [tex]0.04x[/tex]

Amount of salt in [tex](45-x)[/tex] gallons of 30%% salt solution will be :

⇒ Percentage concentration x Gallons of solution

⇒ [tex]0.3\times (45-x)[/tex]

Using distribution

⇒ [tex]13.5-0.3x[/tex]

Total amount of salt in 45 gallons of solution can be given as:

⇒ [tex]0.04x+13.5-0.3x[/tex]

Combining like terms

⇒ [tex]-0.26x+13.5[/tex]

Amount of salt in 45 gallons of 18.4% solution:

⇒ [tex]0.184\times 45[/tex]

⇒ [tex]8.28[/tex]

Thus, we have:

[tex]-0.26x+13.5=8.28[/tex]

Subtracting both sides by 13.5

[tex]-0.26x+13.5-13.5=8.28-13.5[/tex]

[tex]-0.26x=-5.22[/tex]

Dividing both sides by -0.26.

[tex]\frac{-0.26x}{-0.26}=\frac{-5.22}{-0.26}[/tex]

∴ [tex]x=20.08[/tex]

Number of gallons of 4% salt solution in the mixture = 20.08

Number of gallons of 30% salt solution in the mixture = [tex]45-20.08[/tex] = 24.92

Answer:they would meet after 4.5 hours

Step-by-step explanation:

At the point where they will both meet, they would have covered a total distance of 540 miles.

Let t represent the time it will take the car and the truck to meet.

Distance = speed × time

The car drives at a speed of 65 miles per hour. Distance covered by the car in t hours would be

65 × t = 65t

The truck travels at a speed of 55 miles per hour.

Distance covered by the truck in t hours would be

55 × t = 55t

Therefore,. 65t + 55t = 540

120t = 540

t = 540/120 = 4.5 hours

Answer:

[tex]Depth = x= 4 units[/tex]

[tex]length = 5x= 5(4)= 20 \ units[/tex]

[tex]height = 2x-2= 2(4)-2= 6 \ units[/tex]

Step-by-step explanation:

You have a block of wood with a depth of x units, a length of 5x units, and a height of 2x units.

height is decreased by 2 units , so height becomes 2x-2

Volume of a block is length times width time height

[tex]volume = x \cdot 5x \cdot (2x-2)[/tex]

[tex]480 = 10x^3-10x^2[/tex]

divide whole equation by 10

[tex]48= x^3-x^2[/tex]

Subtract 48 from both sides

[tex]x^3-x^2-48=0[/tex]

[tex]\left(x-4\right)\left(x^2+3x+12\right)=0[/tex]

[tex]x-4=0[/tex], x=4

[tex]Depth = x= 4 units[/tex]

[tex]length = 5x= 5(4)= 20 \ units[/tex]

[tex]height = 2x-2= 2(4)-2= 6 \ units[/tex]

Answer:

-7

Step-by-step explanation:

From the graph (see attached), we can read off the values of f(-8) and f(4)

when x = -8, y = f(-8) = -5

when x = 4, y = g(4) = 3

hence, substituting the above values into the given equation:

-1 * f(-8) - 4 * g(4)

= -1 * (-5) - 4 * 3

= 5 - 12

= -7

Answer:

i dont understand

Step-by-step explanation:

Answer:

x= 8

Step-by-step explanation:

60/48=1.25

15/1.25= 12

12-4=8

Answer:

A

Step-by-step explanation:

Answer:

ima need that brainliest dawg the answer a

Step-by-step explanation:

Answer:

Bob now has 53 candy bars.

Step-by-step explanation:

: )

Answer:

53 bars

Step-by-step explanation:

100-47=53

Answer: 16

Step-by-step explanation:

Answer:

The height of each pyramid is 1/2 h units.

Step-by-step explanation:

did it on edg 2020

Answer:

  {-4.6, -4.2, -3.8, -3.4}

Step-by-step explanation:

The length of the space Karlie is dividing is -3-(-5) = 2 units. Then the length of each of those equal 5 spaces will be 2/5 units = 0.4 units.

Each mark on the number line is 0.4 units to the right of the previous one. The first (left-most) mark is 0.4 units to the right of -5, so is at -5+0.4 = -4.6.

The marks have to be placed at -4.6, -4.2, -3.8, and -3.4.

Answer:

The probability that they sit next to each other is 50%.

Step-by-step explanation:

Consider the provided information.

It is given that there are four seats within the row are first come, first served during boarding.

There are 4 seats and 2 customers (Karen and Georgia)

The total number of ways in which Karen and Georgia can sit is: [tex]^4C_2[/tex]

Now if they will sit together, then consider  Karen and Georgia as a single unit.

Thus, the number of ways in which they can sit together is: [tex]^3C_1[/tex]

The required probability is:

[tex]P=\frac{^3C_1}{^4C_2} \\\\P=\frac{3}{6}\\\\P=\frac{1}{2}[/tex]

Hence, the probability that they sit next to each other is 50%.