Arya knows that if they need to add antifreeze to their car's radiator the mixture used must contain 50% antifreeze. How many gallons of a mixture containing 70% antifreeze must be added to a 3-gallon mixture containing 20% antifreeze to obtain the mixture they need?

Accοrding tο the given infοrmatiοn the measure οf arc PQR is 170 degrees.

A quadrilateral is a fοur-sided pοlygοn, which is a twο-dimensiοnal geοmetric figure with straight sides. Quadrilaterals can have a variety οf shapes, sizes, and angles, but they all have fοur sides and fοur vertices (cοrners).

Since the quadrilateral PQRS is inscribed in a circle, we knοw that angle PQR is an inscribed angle οf arc PR. By the Inscribed Angle Theοrem, the measure οf an inscribed angle is equal tο half the measure οf its intercepted arc. Therefοre, the measure οf arc PQR is twice the measure οf angle PQR, which is:

2 * 85 = 170 degrees.

Therefοre, accοrding tο the given infοrmatiοn the measure οf arc PQR is 170 degrees.

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Answer:

8 and 9

Step-by-step explanation:

Since 77 is between 64= 8² and 81= 9²

Answer:

y=1/3x+2

Step-by-step explanation:

(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

The probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

The symbol "∩" represents the intersection of two events.

For example, "a ∩ d" means the event where both "a" and "d" occur together.

The symbol "~" means "not" or "complement." So, "~ (a ∩ d)" means the event where "a ∩ d" does NOT occur, or in other words, where "a" OR "d" does not occur.

Now, onto the question.

We are given that p(a ∩ d) = 2/5, which means that the probability of both events "a" and "d" occurring together is 2/5.

We want to find the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur.

To find this probability, we need to use some basic probability rules.

One of these rules is that the probability of an event happening (let's call it "E") is equal to 1 minus the probability of the complement of that event not happening (~E).

In other words, p(E) = 1 - p(~E).

So, if we apply this rule to the event "~ (a ∩ d)", we get:
p(~ (a ∩ d)) = 1 - p(a ∩ d)

Now we can substitute in the value we were given for p(a ∩ d):
p(~ (a ∩ d)) = 1 - 2/5

Simplifying this gives:
p(~ (a ∩ d)) = 3/5

Therefore, the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

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\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

Answer:

The answer is 1x23

The other equal 24

Step-by-step explanation:

Answer:

y=12

Step-by-step explanation:

0=12-y+18x0

y=12

The expressions are solved below :

sinu = -3/5 3π/2 < u < 2π is [ 4th quadrant ]

Now we know that

By using trigonometric identities,

When there are trigonometric functions present in an expression or equation, trigonometric Identities come in handy. Every value of a variable appearing on both sides of an equation is valid in terms of trigonometric identities. These trigonometric functions of one or more angles, such sine, cosine, and tangent, are involved in these geometric identities.

sin²u + cos²u = 1

cos²u= 1-sin²u

cos²u = 1 -(-3/5)²

cos²u= 1 - 9/25

cosu = +4/5

:. u is in 4th quadrant

Now

1.  sin2u = 2 sinu cosu

= 2 (-3/5)(4/5) = -24/25

2. cos2u = 2cos²u- 1

       = 2(4/5)²- 1

       = 7/25

3. tan2u = sin2u /cos2u

              = -24/7

The exact values of the sine, cosine, and tangent of the angle are found.

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The cost of the fence used to make the rectangular sheep pen is £57.6. The result is obtained by multiplying the perimeter by the fencing price.

The cost for fencing a building can be calculated by multiplying the price of a certain size of fence by the perimeter or the length side to be fenced.

Bill builds a rectangular sheep pen.

Find the total cost of the fence!

The total cost of the fence will be

= P × fencing cost

= 24 m × £1.20 / ½ m

= 24 × £2.40

= £57.6

Hence, the fence to make the sheep pen will cost £57.6.

Your question is incomplete. But most probably your full question was

Bill needs to build a rectangular sheep pen. The pen must have a perimeter of 24 m. Every half meter of fencing costs him £1.20. Work out the cost of the fence used to make the sheep pen!

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The Laplace transform of the function f(t) =2t⁴ + 3t² + 5 is given by:

L[2t⁴ + 3t² + 5] = 2/s⁵ + 3/s³ + 5.

Here, we have,

To find the Laplace transform of the function f(t) = 2t⁴ + 3t² + 5,

we can apply the linearity property of the Laplace transform.

The Laplace transform of a constant is given by:

L[a] = a/s,

where 'a' is a constant and 's' is the complex variable.

Applying this property to each term in the function, we have:

L[2t⁴] = 2/s⁵,

L[3t²] = 3/s³,

L[5] = 5/s⁰.

Since s⁰ = 1, the Laplace transform of the constant term 5 is simply 5.

Combining these results using the linearity property, we get:

L[2t⁴ + 3t² + 5] = 2/s⁵ + 3/s³ + 5.

Therefore, the Laplace transform of the function f(t) =2t⁴ + 3t² + 5 is given by:

L[2t⁴ + 3t² + 5] = 2/s⁵ + 3/s³ + 5.

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D. \((6v, -3v)\)

Answer:

I think x might equal 25

Step-by-step explanation:

Answer:

Bro yours is correct but its just a little to complicated the answer is d

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

If Amy has 6 cakes and Barry has four times as many as she does then just do 6x4. After doing that you have 24. 24+6=30. Ok so you have 30 so far, Right? And Ceri bakes 12 more then Amy so what's 12+6? 18. 30+18=48.

Your welcome.

Answer:

Step-by-step explanation:

15+10y−4xy−66

Soustraire 66 de 15 pour obtenir −51.

−51+10y−4xy

Answer:

-4y

Step-by-step explanation:

15 + 10y - 4xy - 6=-4y

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer: 1; -5

Step-by-step explanation:

For this problem, we are asked to find the slope and y-intercept.

We see that this linear line goes through the y-axis at (0,-5). therefore, our y-intercept is -5.

To find the slope, we would use the formula \(m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }\). We can use the points (0,-5) and (5,0) since we can clearly see the line goes through these 2 points.

\(m=\frac{0-(-5)}{5-0} =\frac{5}{5} =1\)

From our formula, we found that the slope is 1.

For the first box, you would fill in 1, the slope. The second box would be -5, the y-intercept.

Answer:

y = x - 5

Step-by-step explanation:

One can immediately read off the slope, m, from the graph:  m = 5 / 5 = 1.

The y-intercept is (0, -5).

In slope-intercept form the equation of this graph is y = x - 5

Answer:

1 2/3

Step-by-step explanation:

To divide fractions you do the Keep Change Flip tactic, meaning keep the first fraction change the operation to multiplication and reverse the second fraction.

So with that being said, 5/6*2/1 would be the equation you need to solve. This would give you 10/6 and you have to change that into a mixed number, 1 4/6 and you can reduce that to SIMPLEST FORM by dividing by 2. 4/2=2 and 6/2=3 so in the end you get 1 2/3.

HOPE THIS HELPS!!!

Answer:

Hi there! Hope this helps!

Step-by-step explanation:

Since Jamie can types 1.5 times more than Iris, then it would be 60 x 1.5 = 90. Then, if Jamie can types 90 words in a minute, she can type 900 word in 10 minutes: 90 x 10 = 900.

First, calculate the difference in cost between buying 3 pounds of chicken across town and buying it in your neighborhood.

This is $0.90

Then, the distance between the two places is

The difference in distance is 5.2 miles.

Find the number of gallons needed to drive 5.2 miles,

Then, multiply the number of gallons by the cost per gallon of gas, as shown below

Then, the total savings are

The length of side PQ in the right-angled triangle is 2√3

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or anyone angle is a right angle.

Given is a triangle PQR,

To find the side PQ ; we need to first find the length of the given line segment which is perpendicular to side PR; let name it as QS.

Now, as Δ QSR is a right-angled triangle.

and the length of the side QR and SR is given, so using Pythagorean theorem we have

QR² = RS²+QS²

QS² = 5²-3²

QS² = 16

QS = 4

Now again Δ QSP is a right-angled triangle; so using Pythagorean theorem in Δ QSP we have

PQ² = QS²+PS²

PQ = 2√3

Hence, the length of side PQ is 2√3

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Answer: i think its B 14

Step-by-step explanation:

among the given numbers, i, iii, and iv are rational numbers, while ii is an irrational number

the numbers that are rational in the given list are i (0.25), iii (3), and iv (5/4).

i. The number 0.25 is a rational number because it can be expressed as a fraction, 1/4.

ii. The number √2 is an irrational number because it cannot be expressed as a fraction and its decimal representation goes on indefinitely without repeating.

iii. The number 3 is a rational number because it can be expressed as the fraction 3/1.

iv. The number 5/4 is a rational number because it can be expressed as a fraction, 5/4.

Therefore, among the given numbers, i, iii, and iv are rational numbers, while ii is an irrational number.

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Answer:

(x+2)^2 - 6

Step-by-step explanation:

The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

Given,The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam.

For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section.

The strength of an oak beam is 69, when the beam is 7 inches wide and 3 inches deep.Thus, we can conclude that k, a constant of proportionality exists, such that: S=k(W x D²), where W is the width, D is the depth of the rectangular cross-section and S is the strength of the beam.

Let's use this to calculate k: When the beam is 7 inches wide and 3 inches deep, S=69. Thus, we get:k = S/W x D²=69/(7 x 3²)=1.

Thus, the equation for S becomes:S = W x D²The radius of the oak tree is 28/2 = 14 inches and the beam must be 14 inches wide.

This implies that the rectangular cross-section of the beam must be square (or the largest rectangular cross-section is a square). Let the side of the square cross-section be x.

Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inchesWe need to determine the depth of the beam. The depth of the beam is half the height of the cylindrical log from which the beam is cut. The cylindrical log has a diameter of 28 inches. The beam has a width of 14 inches.

The largest rectangular cross-section is a square with sides of length x. This cross-section can be obtained by cutting the log at a height of x/2 from its center.Since the diameter is 28 inches, the radius is 14 inches. The height at which the beam is cut is h = 14 - x/2.

Thus, the depth of the rectangular beam cut from the cylindrical log is given by: D = 2(h) = 2(14 - x/2) = 28 - x.Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69Simplifying the above equation,x⁴ - 56x³ + 784x² - 69 = 0.

Using polynomial long division, we get:(x² + 16x - 69)(x² - 40x + 1) = 0The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.Therefore, the  answer is (b) S = 2231.

The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. Let the side of the square cross-section be x. Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inches. Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69.The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

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Answer:

to find the equation of the line you use y=mx+b

Step-by-step explanation:

m means the slope and the b is the y intercept of the line. so in this case the b is 5. the m is 6 so the answer is y=6x+5