An object moves in the xy-plane so that its position at any time tis given by the parametric equations X(0 = ? _ 3/2+2andy (t) = Vt? + 16.What is the rate of change of ywith respect t0 when t = 3 1/90 1/15 3/5 5/2'

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles. That means that the measure of angle DEF is equal to the sum of measure of angle C and measure of angle D. Substituting known values gives you 2y + 9 + 6y + 10 = 115, then you can solve

8y + 19 = 115

8y = 96

y = 12

The measure of angle C is 33 degrees, the measure of angle D is 82 degrees, and because the measure of angle DEF is 115 degrees, its supplement angle (DEC) measures 65 degrees.

It is important to know that a decreasing line has a negative slope, as the image shows.

The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

13

Step-by-step explanation:

6.5/3=13/6

6(13/6)=13

Answer:

142 cm squared

Step-by-step explanation:

the formula used was 2(lw + wh +lh)

where l is length

w is width

and h is height

Answer:

142

Step-by-step explanation:

5 x 3 = 15 Times by 2 = 30

7 x 5 = 35 Times by 2 = 70

7 x 3 = 21 Times by 2 = 42

Answer:

100=29+71

46= 63-17

63

To convert 72 feet per day to a different unit, we can use unit conversion factors:

1 day = 24 hours

1 hour = 60 minutes

1 foot = 12 inches

So, we can set up the following calculation:

72 feet/day × (1 day/24 hours) × (1 hour/60 minutes) × (12 inches/1 foot) = 0.1 inches/minute

Therefore, the converted rate is in units of inches per minute.

Answer: (4) inches/minute

The correct formula for the revenue generated by the item is Revenue = 200p - 5p^2.

The revenue generated by the item can be calculated by multiplying the price (p) by the unit sales (200 - 5p). Therefore, the correct formula for the revenue generated by the item is:

Revenue = Price x Unit Sales
Revenue = p(200 - 5p)
Revenue = 200p - 5p^2

The revenue generated by the item is a quadratic function of the price (p). To find the maximum revenue, we need to differentiate the function with respect to p and set it equal to zero:

dRevenue/dp = 200 - 10p = 0
10p = 200
p = 20

Therefore, the maximum revenue is generated when the price of the item is $20. Substituting p = 20 in the revenue formula, we get:

Revenue = 200(20) - 5(20^2) = $2000

Hence, the correct formula for the revenue generated by the item is Revenue = 200p - 5p^2, and the maximum revenue is achieved when the price of the item is $20, generating a revenue of $2000.

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Answer:

when the water has a height of 120 cm, or 1.2 meters, the rate at which the height of the water is changing is 2.4 m/s.

Step-by-step explanation:

To find the rate at which the height of the water is changing, we need to use calculus.

We can define the height of the water at any given time as a function h(t). The rate at which the water is being pumped into the trough can be represented as a constant function f(t) = 6 m/s. The rate at which the water's height is changing at any given time is equal to the derivative of the height function with respect to time, or h'(t).

The volume of water in the trough is equal to the area of the base of the trough (which is in the shape of an isoceles triangle) times the height of the water. The volume of the water in the trough can also be represented as a function V(h).

We can set up the following equation to represent the relationship between the volume of water in the trough and the height of the water:

V(h) = (1/2) * b * h * h

where b is the base of the isoceles triangle (5 meters).

We can also set up the following equation to represent the relationship between the volume of water being pumped into the trough and the rate at which the water's height is changing:

V'(h) = f(t)

We can substitute the expression for V(h) into the equation for V'(t) and solve for h'(t):

h'(t) = f(t) / [(1/2) * b]

= (6 m/s) / [(1/2) * 5 m]

= 6 m/s / (1/2) * (5 m)

= 6 m/s / (2.5 m)

= 2.4 m/s

So when the water has a height of 120 cm, or 1.2 meters, the rate at which the height of the water is changing is 2.4 m/s.

Answer:

4.9

Step-by-step explanation:

Plug in 13 and 2 for each variable separately to get 0.7(13) - 2.1(2).  0.7 multiplied by 13 equals to 9.1 and 2.1 multiplied by 2 equals 4.2.  Subtract 4.2 from 9.1 to get your final answer which is 4.9.

From the given information, total surplus in a market is equal to the sum of consumer surplus and producer surplus.

Consumer surplus is the difference between the highest price a consumer is willing to pay for a good or service (the "reservation price") and the actual price they pay. Producer surplus is the difference between the lowest price a producer is willing to accept for goods or services and the actual price they receive.

When a market is in equilibrium, the price and quantity are such that the quantity demanded equals the quantity supplied. At this point, total surplus is maximized, since all trades that benefit both consumers and producers have taken place. The total surplus represents the net benefit to society from the production and consumption of the good or service in the market.

In other words, total surplus is the sum of the gains from trade that accrue to consumers and producers in the market, and it represents the difference between the value that buyers and sellers place on the good or service and the resources that were actually used to produce it.

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a. the probability that less than 5 customers will arrive in a 5-minute period is approximately 0.0292 or 2.92%. b. The probability that the time between two consecutive arrivals will be more than 1 minute is approximately 0.1353 or 13.53%.

a. To calculate the probability that less than 5 customers will arrive in a 5-minute period, we can use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space when the average rate of occurrence is known.

Given that the average number of customers arriving per hour is 120, we need to adjust this rate to the 5-minute period. Since there are 60 minutes in an hour, the average rate for a 5-minute period is 120/12 = 10 customers.

To calculate the probability of less than 5 customers arriving in a 5-minute period, we can sum the probabilities of 0, 1, 2, 3, and 4 customers using the Poisson distribution formula. The formula is as follows:

P(X = k) = (e^(-λ) * λ^k) / k!,

where λ is the average rate and k is the number of events.

Using this formula, we can calculate the individual probabilities and sum them up:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4),

P(X = 0) = (e^(-10) * 10^0) / 0! = e^(-10) ≈ 0.0000454,

P(X = 1) = (e^(-10) * 10^1) / 1! = 10e^(-10) ≈ 0.000454,

P(X = 2) = (e^(-10) * 10^2) / 2! = 50e^(-10) ≈ 0.00227,

P(X = 3) = (e^(-10) * 10^3) / 3! = 500e^(-10) ≈ 0.00757,

P(X = 4) = (e^(-10) * 10^4) / 4! = 2500e^(-10) ≈ 0.01892.

Summing these probabilities:

P(X < 5) ≈ 0.0000454 + 0.000454 + 0.00227 + 0.00757 + 0.01892 ≈ 0.0292.

Therefore, the probability that less than 5 customers will arrive in a 5-minute period is approximately 0.0292 or 2.92%.

b. To find the probability that the time between two consecutive arrivals will be more than 1 minute, we need to consider the exponential distribution. The exponential distribution models the time between events in a Poisson process.

The average rate of customer arrivals per minute can be calculated by dividing the average rate per hour by 60:

λ = 120 / 60 = 2 customers per minute.

Let T represent the time between two consecutive arrivals. The exponential distribution is defined as:

P(T > t) = e^(-λt),

where λ is the average rate and t is the time interval.

Substituting the values:

P(T > 1) = e^(-2 * 1) = e^(-2) ≈ 0.1353.

Therefore, the probability that the time between two consecutive arrivals will be more than 1 minute is approximately 0.1353 or 13.53%.

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(a)If log₄​x = 5, the base is 4 and the logarithm is 5 , then x = 1024. (b) If log₆​x = 8 the base is 6 and the logarithm is 8  then x = 1679616.

(a) In the equation log₄​x = 5, the base is 4 and the logarithm is 5. To solve for x, we need to rewrite the equation in exponential form. In exponential form, 4 raised to the power of 5 is equal to x. Therefore, x = 4^5 = 1024.

(b) In the equation log₆​x = 8, the base is 6 and the logarithm is 8. Rewriting the equation in exponential form, 6 raised to the power of 8 is equal to x. Hence, x = 6^8 = 1679616.

In both cases, we used the property of logarithms that states: if logₐ​x = y, then a raised to the power of y equals x. By applying this property, we can convert the logarithmic equations into exponential form and find the values of x.

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Answer:2.54

Step-by-step explanation:

1x2.54

1 inch is equal to 2.54 cm in conversion of units.

What are units?

Units are the tools to measure and compare different things. Comparison becomes easy when all the units for the measurement are the same.  Different units can be classified depending on their use.

There are two type of units

1. Fundamental Units: Fundamental units are all those units that do not depend on any other unit (including themselves). These units cannot be further reduced to the elementary level. In fact, these are elementary units. Only seven fundamental units exist in Metric System or SI system which are

Length (meter, m)

Mass (kilogram, kg)

Time (second, s)

Temperature (kelvin, K)

Amount of substance (mole, mole)

Electric current (ampere, A)

Luminous intensity (candela, cd)

2. Derived units: These units are all those units that are obtained by multiplying and/or dividing one or more fundamental units with or without introducing any other numerical factor. These units can be reduced to their elementary level, which is composed of fundamental units. There exist a large number of derived units in the Metric System.

Examples:

Velocity (m/s)

Acceleration (m/s2)

Momentum (kg-m/s)

Force (N)

Density (kg/m3)

Heat (J)

Energy (J)

Power (W), etc.

Now,

To convert Inch into cm we multiply inch with 2.54.

e.g. 7inch=7*2.54 cm=17.78 cm

Hence,

           1 inch is equal to 2.54 cm.

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The coordinates of point A is(-1,5) of coordinate  plane.

What is the short definition of a coordinate plane?

For point (x1,y1) and (x2,y2) on coordinate plane if m is the midpoint of these points, then coordinate of mid point  is given by

(x1+x2)/2,  (y1+y2)/ 2

Given point

B= (-5,1)

M = (-3,3)

we have to find point A, let it be (x,y)

using the above formula , midpoint m is

-3= (-5+x)/ 2                    3=  (1+y)/ 2

-3*2= -5+x                           6= 1 +y

-6 +5 = x                             6-1 =y

x = -1                                    y = 5

Thus, the coordinates of point A is(-1,5).

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The circumference of the circle in terms of π is 8π yards.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

the diameter of the circle = 8yrd

the circumference of the circle in terms of π

=π  * 8

= π8 yrd.

Hence, The circumference of the circle in terms of π is 8π yards.

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Answer:

62

Step-by-step explanation:

inverse tangent of 43/23 is 62

The constant of proportionality between the number of miles driven and the number of gallons used is 28.2

What is Constant of Proportionality?

When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used. The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship.

As we know higher gallons of fuel will take us much far

that means  fuel used is directly proportional to miles driven

therefore,

930.6 = K*33

1212.6 = K*43

1297.2 = K*46

from the above equation

we get

K=28.2

The constant of proportionality is 28.2

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Answer:

perimeter: 29 cm

Area: 49.5 cm^2

Step-by-step explanation:

perimeter is 9.5 + 6 + 7 + 6.5 = 29

Area: 7 * 6 = 42

9.5 - 7 = 2.5

2.5 * 6 = 15

15/2 = 7.5

42 + 7.5 = 49.5

The number of cubic centimeters of paint that will fit in the cylindrical container is:

66.36 cm³

The volume of a cylinder can be determined by multiplying the area of the base by the height. It may be expressed using the formula:

V = πr²h

where π (pi) is approximately equal to 3.14, r is the radius, and h is the height.

You should also note that the radius of the cylinder is one-half of the diameter.

V = πr²h

Since the cylindrical container of paint has a diameter of 3 cm, its radius would be 1.5 cm. Furthermore, its height is around 7 cm. As a result, by substituting the given values into the formula, we may get the following result:

V = πr²hV = π(1.5)²(7)

V = 66.36 cm³

Therefore, the cylindrical container of paint can hold approximately 66.36 cubic centimeters of paint.

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Answer:

The answer would be A) 4

Answer:

Step-by-step explanation:

Slope-intercept form: y = mx + b

Isolate the y. Note the equal sign, what you do to one side, you do to the other.

First, subtract 4x from both sides:

4x (-4x) - 5y = 2 (-4x)

-5y = -4x + 2

Next, divide -5 from both sides:

(-5y)/-5 = (-4x + 2)/-5

y = (4/5)x - (2/5)

\(y = \frac{4}{5}x - \frac{2}{5}\) is your answer.

~

Answer:

8x + 20 ≥ 25

Step-by-step explanation:

Well 8 times the sum of a number "x" plus 20,

So we can write the following,

8x + 20

and that should be greater than or equal to 25

8x + 20 ≥ 25

Thus,

as an inequality it is 8x + 20 ≥ 25.

Hope this helps :)

Player 1's expected value (E(X)) is lower than Player 2's expected value (E(Y)) in the snake-picking game due to the higher probability of Player 1 picking a venomous snake. Therefore, statement A is correct, stating that E(Y) is greater than E(X) because there is a greater possibility of Player picking up a venomous snake.

The expected value of Player 1's pick (E(X)) in the snake-picking game can be calculated, and the expected value of Player 2's pick (E(Y)) can also be determined. The relationship between E(X) and E(Y) depends on the probabilities associated with picking a venomous or non-venomous snake.

In this scenario, Player 1 has the advantage of picking first. To calculate E(X), we need to consider the probabilities of picking a venomous snake (earning zero points) or a non-venomous snake (earning one point). Since there are 2 venomous snakes and 1 non-venomous snake, the probability of Player 1 picking a venomous snake is higher. Therefore, E(X) will be less than E(Y).

The correct answer is A. E(Y) is greater than E(X) as there is a greater possibility that Player 1 picks up a venomous snake. The order in which the players pick the snakes affects the probabilities and, consequently, the expected values. Player 2 has a better chance of picking a non-venomous snake since Player 1 might have already picked a venomous snake, increasing the likelihood of E(Y) being higher than E(X).

Thus, the relationship between E(X) and E(Y) in this example is that E(Y) is greater than E(X) due to the higher possibility of Player 2 picking a non-venomous snake after Player 1's turn.

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Step-by-step explanation:

-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4

Answer:

32 mm²

Step-by-step explanation:

perimeter of left rectangle = 2(9 mm + 3 mm) = 24 mm

length of right rectangle = L

perimeter of right rectangle = 2(L + 4 mm) = 2L + 8

perimeter of right rectangle = 24 mm

The perimeter of the right triangle is 2L + 8 and also 24, so 2L + 8 must equal 24. We can solve for L and find the length of the right rectangle.

2L + 8 = 24

2L = 16

L = 8

area of right triangle = length × width

area = 8 mm × 4 mm

area = 32 mm²

**Disclaimer** Hi there! I assumed the purple triangle to be the one on the right. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.

Answer: \(\Large\boxed{Area=32~mm^2}\)

Step-by-step explanation:

Given information

Rectangle A:

Rectangle B:

Both rectangles have the same perimeter

Given formula

1) P = 2 (b + h)

2) A = b × h

Substitute values into 1) formula to find the perimeter of rectangle A

P = 2 (b + h)

P = 2 (3 + 9)

Simplify by addition

P = 2 × 12

Simplify by multiplication

P = 24 mm

Substitute values into 1) formula to find the perimeter of rectangle B

P = 2 (b + h)

24 = 2 (4 + h)

Divide 2 on both sides

24 / 2 = 2 (4 + h) / 2

12 = 4 + h

Subtract 4 on both sides

12 - 4 = 4 + h - 4

h = 8 mm

Substitute values into 2) formula

A = b × h

A = 4 × 8

Simplify by multiplication

\(\Large\boxed{Area=32~mm^2}\)

Hope this helps!! :)

Please let me know if you have any questions

Let:

x = Amount invested at 3%

y = Amount invested at 9%

Joy invests a total of $8,500, so:

after one year, the total interest was $705.00. so:

From (1) solve for x:

Replace (3) into (2):

Replace y into (3):

Answer:

$1000 were invested at 3%

$7500 were invested at 9%