Which fraction has the greatest value? A number line going from negative 1 to positive 1 in increments of 1. StartFraction 5 Over 6 EndFraction StartFraction 1 Over 6 EndFraction Negative StartFraction 1 Over 6 EndFraction Negative StartFraction 5 Over 6 EndFraction

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: I think it’s the 4th one

Step-by-step explanation:

Answer:

2nd one

Step-by-step explanation:

Shaded below means less than

Answer:

3/5

Step-by-step explanation:

ir would be 6/10 but simplified it would be 3/5

The inequality expressions for the number of male and female sea turtles are given as 0 < x ≤ 8 and 0 < 2x ≤ 16 respectively.The correct option is (b).

A linear inequality is the equivalent expression for the range of the values of a variable. On the graph it represents the area either above or below a straight line.  

Suppose the number of male turtles be x and females be y.

Then, as per the question the inequality expression for the male population can be written as follows,

0 < x ≤ 8

But the equation for the female population is given as y = 2x.

Now, the inequality expression can be written as,

0 < x ≤ 8

Multiply 2 on all sides to get,

2 × 0 < 2x ≤ 8 × 2

⇒ 0 < 2x ≤ 16

The required expressions of inequality are 0 < x ≤ 8 and 0 < 2x ≤ 16 respectively.

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Answer:

25 : 1

Step-by-step explanation:

The diameter of the football is 5 times the diameter of the cricket ball. This means that the radius of the football is also 5 times the radius of the cricket ball.

Let the radius of the football be R.

Let the radius of the cricket ball be r.

This implies that:

R = 5r

Both balls are spherical.

The surface area of the cricket ball is given as:

\(a = 4\pi r^2\)

The surface area of the football is given as:

\(A = 4\pi R^2\)

\(=>A = 4\pi (5r)^2\\\\A = 100\pi r^2\)

Therefore, the ratio of their surface areas is:

A : a

\(100\pi r^2 : 4\pi r^2\)

= 100 : 4

25 : 1

Ratio of the surface area of football and cricket ball = 25 : 1

Recall:

Given:

By implication,

radius of football = 5 times radius of cricket ball

Let,

This means that:

R = 5r

Surface Area of Football:

A = 4 × π × (5r)²

A = 100πr²

Surface Area of Cricket ball:

a = 4 ×π × (r)²

a = 4πr²

Ratio of surface area of football and cricket ball = 100πr² : 4πr² = 25 : 1

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Speed can be defined as the distance covered per time.

The average speed formula is given as: Distance/Time

The average speed of Samuel's morning training is 7 2/3 miles/hour

We are to calculate the time in hours. Remember conversion rate :

60 minutes = 1 hour

He did 3 activities every morning

60 minutes = 1 hour

30 minutes = ?

Cross Multiply = 30 minutes x 1 hour / 60 minutes

= 0.5 hour

Hence: Speed = 4.5 miles/0.5 hour

=  9 miles/hour

60 minutes = 1 hour

20 minutes = ?

Cross Multiply = 20 minutes x 1 hour / 60 minutes

= 1/3 hour

Hence: Speed = 2/3 miles/ 1/3 hour

=  2/3 x 3/1 (miles/hour)

= 2 miles/hour

60 minutes = 1 hour

45 minutes = ?

Cross Multiply = 45 minutes x 1 hour / 60 minutes

= 3/4 hour

Hence: Speed = 9 miles/ 3/4 hour

=  9 x 4/3 (miles/hour)

= 12 miles/hour

(9 + 2 + 12) miles/hour / 3

= 23/3

= 7 2/3 miles/hour

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Answer: 3 meters

Step-by-step explanation:

Answer: 3 meters

Step-by-step explanation: A diving board being 3 cm would be too small so 3 meters is a better choice!

Answer:

C

Step-by-step explanation:

\((3x-2)(x^2-2x+3)\)

\(3x(x^2)-3x(2x)+3x(3)-2(x^2)-2(-2x)-2(3)\)

\(3x^3-6x^2+9x-2x^2+4x-6\\\)

Now, combine like terms

\(3x^3-6x^2-2x^2+9x+4x-6\)

\(-6x^2-2x^2=-8x^2\\\\9x+4x=13x\)

Thus, we have:

\(3x^3-8x^2+13x-6\)

So the answer is C. Hope this helps.

Answer:

3rd option

Step-by-step explanation:

(3x - 2)(x² - 2x + 3)

each term in the second factor is multiplied by each term in the first factor , that is

3x(x² - 2x + 3) - 2(x² - 2x + 3) ← distribute parenthesis

= 3x³ - 6x² + 9x - 2x² + 4x - 6 ← collect like terms

= 3x³ - 8x² + 13x - 6

Answer:

Step-by-step explanation:

Given:

Rule of transformation is rule R x-axis ∘ T⟨–5, 3⟩.

The point is (-3,-2).

To find:

The image of given point after the transformation.

Solution:

Consider the given point be P(-3,-2).

Rule of transformation is rule R x-axis ∘ T⟨–5, 3⟩. If means first we have apply translation T⟨–5, 3⟩ after that we have to apply reflection R x-axis.

If a figure translated by T⟨–5, 3⟩, then

\((x,y)\to (x-5,y+3)\)

\(P(-3,-2)\to P'(-3-5,-2+3)\)

\(P(-3,-2)\to P'(-8,1)\)

If a figure reflected by R x-axis, then

\((x,y)\to (x,-y)\)

\(P'(-8,1)\to P''(-8,-1)\)

Therefore, the image of given point after transformation is (-8,-1).

Answer:

N=6

Step-by-step explanation:

−3(

At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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Answer:

D

Step-by-step explanation:

View the process in the above picture.

Answer:

c.

Step-by-step explanation:

60= (4x - 20)

expl: vertically Opposite angles

Corrected Question

Sue travels by bus or walks when she visits the shops. The probability that she catches the bus to the shops is 0.4. The probability she catches the bus from the shops is 0.7. Show the probability that Sue walks at one way is 0.72

Answer:

\(P(A \cup B) =0.72\) (Proved)

Step-by-step explanation:

Sue travels by bus or walks when she visits the shops.

Let the event that she catches the bus to the shop=A

Let the event that she catches the bus from the shop=B

P(A)=0.4

P(B)=0.7

Both A and B are independent events.

Therefore,Probability that she catches the bus to and from the shop:

P(A∩B) = 0.4 X 0.7= 0.28

Probability Sue walks at least one way \(P(A \cup B) = 1 - P(A \cap B)\)

\(= 1 - 0.28\\= 0.72\)

Hence, the probability that Sue walks at least one way is 0.72.

The simplified expression is \((-2x^2 - 2 + 1)/(2x).\)

To simplify the expression (3/2x - 4) + (2/6 - 3x), we can first combine like terms. Let's work on each fraction separately:

For the first fraction, 3/2x - 4, we cannot directly combine the terms since the denominators are different. To add or subtract fractions, we need a common denominator. In this case, the least common denominator (LCD) is 2x. So, we multiply the numerator and denominator of the first fraction by x to obtain:

(3x)/(2x^2) - 4

Now, for the second fraction, 2/6 - 3x, the denominator is 6. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:

1/3 - 3x

Now, we can combine the two simplified fractions by finding a common denominator, which is 2x^2:

(3x)/(2x^2) - 4 + 1/3 - 3x

To add these fractions, we need to have the same denominator, so we multiply the second fraction by (2x^2)/(2x^2):

(3x)/(2x^2) - 4 + (2x^2)/(6x^2) - (6x^3)/(2x^2)

Combining the like terms:

(3x - 6x^3 + 2x^2 - 8x^2)/(6x^2)

Simplifying further:

(-6x^3 - 6x^2 + 3x)/(6x^2)

Finally, we can divide every term by the greatest common factor, which is 3x:

(-2x^2 - 2 + 1)/(2x)

The simplified expression is \((-2x^2 - 2 + 1)/(2x).\)

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The expression that is equivalent to (1 + (1/y))/(1 - (1/y)) is; (y + 1)/(y - 1)

We want to find the expression that is equivalent to;

(1 + (1/y))/(1 - (1/y))

Let us first simplify the numerator (1 + (1/y))

By using LCM method, we can express the numerator as;

(y + 1)/y

Similarly, for the denominator we have;

(1 - (1/y)) = (y - 1)/y

Thus the original expression is now;

((y + 1)/y)/((y - 1)/y)

y will cancel out to give us;

(y + 1)/(y - 1)

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Answer:

B. y+1/y-1

Step-by-step explanation:

edge 2022

The combined score for Jodi and Joe is 9-i

Two complex numbers, z₁ = a + bi and z₂ =c +di, can be added by adding the corresponding real and imaginary parts. That is:

z₁+z₂ = (a+c) + (b+d)i

Given: Jodi's score = 5−3i and Joe's score = 4 + 2i

Combined score = 5−3i + 4 + 2i

                           = (5+4) + (-3+2)i

                           = 9-i

Therefore, the combined score is 9-i

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Answer:

2.5 hours

Step-by-step explanation:

(380/50) x 20

7.6 x 20

152

The final answer wold be 152 minutes or 2.5 hours

To calculate the principal repaid by the 17th monthly payment of $750 on a $22,000 loan at 15% compounded monthly, we need to calculate the monthly interest rate, the remaining balance after 16 payments, and the interest portion of the 17th payment.

The monthly interest rate is calculated by dividing the annual interest rate by the number of compounding periods per year. In this case, it would be 15% / 12 = 1.25%.

The remaining balance after 16 payments can be calculated using the loan balance formula:

\($$B = P(1 + r)^n - (PMT/r)[(1 + r)^n - 1]$$\)

Where B is the remaining balance, P is the initial principal, r is the monthly interest rate, n is the number of payments made, and PMT is the monthly payment amount.

Substituting the values into the formula, we get:

\($$B = 22000(1 + 0.0125)^{16} - (750/0.0125)[(1 + 0.0125)^{16} - 1]$$\)

After calculating this expression, we find that the remaining balance after 16 payments is approximately $17,135.73.

The interest portion of the 17th payment can be calculated by multiplying the remaining balance by the monthly interest rate: $17,135.73 * 0.0125 = $214.20.

Therefore, the principal repaid by the 17th payment is $750 - $214.20 = $535.80.

Answer:

a. already done

b. x=3, x=4, and x=5

c. x=2, x=3, x=4, and x=6

Step-by-step explanation:

The < symbol means less than, so all values of x less than what is stated are correct

The ≤ symbol means less than or equal to, so all values of x less than, and what is stated are correct

The answer is in the screenshot.
Let me know if it helps

Answer: 0.34439?

Happy To help :)

Step-by-step explanation:

Answer:

0.34439  or if you put it the other way its

344.39

Answer:

y = 3x - 9

Step-by-step explanation:

First, find the slope using y2 - y1 / x2 - x1

36 - 21 = 15

15 - 10 = 5

15/5 = 3, so the slope (m) is 3.

Now, plug into point-slope form: y - y1 = m (x - x1)

y - 21 = 3 (x - 10)

Simplify

y - 21 = 3x - 30

y = 3x - 9

I hope this helps!!

Answer:

y = 3/2x+5

Step-by-step explanation:

A polygon is a closed shape that is bounded by straight sides and vertices. Convex and reflex angles are angles inside a polygon. Convex angles are less than 180 degrees, while reflex angles are greater than 180 degrees.Design of 6-sided polygon with two reflex angles separated by one convex angle, such that no less than two guards would be needed to guard this polygon is impossible. The sum of all interior angles in a polygon with n sides is 180(n-2). This implies that the sum of the angles in a 6-sided polygon is 720°. The polygon can be divided into three convex angles, each of which measures 120°.Now, if the polygon had two reflex angles, each reflex angle would measure at least 180 degrees. This implies that the sum of the angles in the polygon would be greater than 720 degrees. As a result, the given polygon design is impossible.

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Answer:

D would be the wisest choice.

Step-by-step explanation:

Consider the taxes and extra expenses the purchase may have. They may raise the actual payment, plus if you don't pay the balance immediately it'll keep growing and growing until you're in deeper debt.

Hope this helped, have a nice day!

The power shown in Marbury v. Madison that established the right of the judiciary to review laws is an important part of the U.S. system of government.

The power shown in Marbury v. Madison, which established the right of the judiciary to review laws, is a crucial element of the U.S. system of government. This landmark Supreme Court case in 1803 solidified the concept of judicial review, allowing the Supreme Court to determine the constitutionality of laws passed by Congress and actions taken by the executive branch.

The significance of this power lies in the system of checks and balances that it helps maintain. By granting the judiciary the authority to interpret the Constitution and declare laws unconstitutional, it ensures that no single branch of government becomes too powerful. This principle safeguards individual rights and liberties, prevents potential abuses of power, and upholds the Constitution as the supreme law of the land.

The power of judicial review provides a vital mechanism for maintaining a balance of power within the U.S. government. It allows the judiciary to act as a check on both the legislative and executive branches, ensuring that laws and actions are consistent with the Constitution. As a result, it protects the rights of citizens and reinforces the principle of constitutional supremacy.

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The sum of the angles in triangle MNP is 180, and subtracting 135 from both sides gives 45 degrees. With the angle sum property of triangle, ∠MNP = 121°.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex.

The joint vertex is the common terminal of the two beams.

According to the given question,

45° + 90° + ∠MNP = 180°

135° + ∠MNP = 180°

∠MNP = 45°

Hence, With the angle sum property of triangle, ∠MNP = 121°.

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