The yield in bushels from a grove of orange trees is given by
Y = x(600 − x),
where x is the number of orange trees per acre. How many trees will maximize the yield?
_________ trees

Answer:

initial velocity = 64 m/s

Step-by-step explanation:

Differentiate H = 64t - 16t² to find an equation for velocity:

Velocity = \(\frac{dH}{dt}\) = 64 - 32t

Initial velocity (u) is when t = 0:

   u = 64 - 32(0)

⇒ u = 64 - 0

⇒ u = 64 m/s

Answer:

x = 12

Step-by-step explanation:

The midsegment VY is half the sum of the parallel bases , that is

VY = \(\frac{EF+CD}{2}\) , then

3x + 18 = \(\frac{1}{2}\) (x + 96) ← multiply both sides by 2 to clear the fraction

6x + 36 = x + 96 ( subtract x from both sides )

5x + 36 = 96 ( subtract 36 from both sides )

5x = 60 ( divide both sides by 5 )

x = 12

Answer: 600

Step-by-step explanation:

I just took the test

The average weekly sales for the first 2 weeks after online sales began is approximately $1.72 (rounded to the nearest cent).

The average weekly sales for the first 2 weeks after online sales began can be found by calculating the average value of the sales function S(t) = 2e^t over the interval [0, 2]. To find the average, we need to integrate the function over the interval and divide the result by the length of the interval.

The average weekly sales can be calculated as follows:

Average weekly sales = (1/(b-a)) * ∫[a,b] S(t) dt,

where [a, b] represents the interval of interest. In this case, a = 0 (since it is the start of online sales) and b = 2 (representing the first 2 weeks).

Substituting the given sales function S(t) = 2e^t into the formula, we have:

Average weekly sales = (1/(2-0)) * ∫[0,2] 2e^t dt.

Simplifying, we have:

Average weekly sales = (1/2) * ∫[0,2] 2e^t dt.

Integrating 2e^t with respect to t gives us 2e^t evaluated from 0 to 2:

Average weekly sales = (1/2) * [2e^2 - 2e^0].

Simplifying further, we have:

Average weekly sales = (1/2) * [2e^2 - 2].

Evaluating this expression, we get:

Average weekly sales ≈ 1.7183.

Therefore, the average weekly sales for the first 2 weeks after online sales began is approximately $1.72 (rounded to the nearest cent).

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Answer:

I am pretty sure the answer would be 51 feet

The standard deviation is best described as a measure of the spread of a distribution around its mean or expected value.

What is standard deviation?

Standard deviation (SD) is a numerical measurement of how spread out or dispersed a set of data is. It can be expressed as the square root of variance (s²), which is the average deviation of a data point from the mean.

What is the formula for standard deviation?

The formula for standard deviation can be written as:

s = √(Σ (Xi - µ)² / (n - 1))

where:s = standard deviation

           Σ = sum

           Xi = each data point

           µ = the mean of the data points

           n = number of data points

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Answer of each statement is described below.

In the given figure,

We can see that,

In the graph X- axis represents the time

And Y- axis represents the height gain by rock.

The curve is passing through (0, 53), (4, 85) and (10.5, 0)

Now from figure we can observe that,

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Answer: The sum of two prime numbers is always even (which is composite).

Hope this helped :)

The graph as an inequality expression is y < -2x - 3

From the question, we have the following parameters that can be used in our computation:

The graph of the inequality

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

c = -3 from the graph

The equation becomes

y = mx - 3

Using the other points, we have

-3m - 3 = 3

So, we have

-3m = 6

This gives

m = -2

Recall that

y = mx - 3

So, we have

y = -2x - 3

The bottom part is the shaded region

So, we have

y < -2x - 3

Hence, the graph as an inequality is y < -2x - 3

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Given:

The combination is:

\(^{34}C_{21}\)

To find:

The \(^{34}C_{21}\) as the sum of two terms from pascals triangle.

Solution:

According to the pascals triangle:

\(^{n+1}C_{r+1}=^nC_r+^nC_{r+1}\)

We have,

\(^{34}C_{21}\)

Using the pascals triangle formula, we get

\(^{34}C_{21}=^{33}C_{20}+^{33}C_{21}\)

Therefore, \(^{34}C_{21}=^{33}C_{20}+^{33}C_{21}\).

Note: Your equation expression seems a little unclear. So, I am assuming that your expression is

y = x - 4

The solution steps would anyway still clear your concept so that no matter what you can solve whatever the expression it is because the procedure remains the same.

Answer:

The value of y = -7 if x = -3

Step-by-step explanation:

Assuming the given the expression

\(y = x - 4\)

Given that we have to find the value of y if x = -3.

so substituting x = -3 in the equation

\(y = x - 4\)

\(y = (-3) - 4\)

\(y = -3-4\)

\(y = -7\)

Therefore, the value of y = -7 if x = -3

The graph of the equation y = x- 4 is also attached below.

Answer:

A=130

B=15

C=35

The exponential equation that describes the monster's growth, in meters, is given as follows:

y = 0.02(5)^x.

The height of the monster after 3.7 days is given as follows:

19.3 meters.

An exponential function is defined as follows:

y = ab^x.

For which the parameters are given as follows:

Considering the initial height of the monster and the fact that the height is multiplied by five each day, the function is given as follows:

y = 0.02(5)^x.

Hence the height after 3.7 days is given as follows:

y = 0.05(5)^3.7

y = 19.3 meters.

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Answer: 144 dresses in 1440 minutes.

Step-by-step explanation:

Divide 144 and 12 you get 12. So you multiply 12 and 120 and you get 1440.

The rate is 120min/12dresses. Let's simplify it.

12/120 = 10min/1dress (or just 10)

Lets use this rate for 144 dresses

10 x 144 = 1140

It will take 1440 minutes to sell 144 dresses.

Maria spends $22 on lottery tickets every week and $133 every month on food yearly

This means that in a year

there are 52 weeks and she spends 22 x 52 = $1,144 on Lottery tickets

and there are 12 months in a year, so she spends 133 x 12 = $1,596 on food

The money spent to buy lottery tickets in relation to the money spent on food yearly in percentage is

The correct option- The perpendicular bisector of AB has the slope -1/3.

The difference between the change in y-values and the change in x-values is known as the slope of a line. This figure represents the slope of a line.

Formula for slope m = (y2 - y1)/(x2 - x1)

Line segment AB coordinates :

A (1,5) and B (9,17).

Slope m1 = (17 - 5)/(9 - 5)

m1 = 12/4

m1 = 3

The line perpendicular to AB.

Let the slope of m2.

The relation between the slopes of perpendicular lines:

m1 x m2 = -1

3 x m2 = -1

m2 = -1/3.

Thus, the slope of the line perpendicular to the given line AB is found as:  -1/3.

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Complete question:

AB in the coordinate plane has endpoints with coordinates A (1,5) and B (9,17). Which of the following is true?

The perpendicular bisector of  AB has slope 3/2.

The perpendicular bisector of AB has slope -2/3.

The perpendicular bisector of AB  has slope -2/3.

The perpendicular bisector of AB has slope -1/3.

Answer: you will meet in two hours.

Step-by-step explanation:

\(50h=190-45h\\50h+45h=190-45h+45h\\95h=190\\\)

Divide both parts of the equation by 95:

\(h=2\ hours\)

Answer:

x = 24

y = 19

Step-by-step explanation:

From the picture attached,

m(∠CAB) = (5y - 23)° [Vertically opposite angles]

By applying triangle sum theorem in ΔABC,

(5y - 23)° + (2x + 13)° + 47° = 180°

2x + 5y = 143 -----(1)

(3x)° = (5y - 23)° [Corresponding angles]

3x - 5y = -23 -----(2)

By adding equation (1) and (2)

(2x + 5y) + (3x - 5y) = 143 - 23

5x = 120

x = 24

From equation (2)

3(24) - 5y = -23

72 - 5y = -23

5y = 95

y = 19

Answer:100/400

Step-by-step explanation:

The answer is 10 calories per minute, will tai burn in 1 minute while biking.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

We do not have much information to go on such as the speed that Tai is biking or his/her weight.

Regardless we can use the data gathered by the University of Harvard which after a study came up with the following results.

Their results showed that if an individual bikes at a speed of 13 mph and are around 155 pounds they will burn calories at a rate of 10 calories per minute.

Therefore we can assume that Tai is burning roughly 10 calories per minute.

his rate increases if the person bikes at a faster speed or weighs more as they are exerting more energy.

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complete question:

How many calories will tai burn in 1 minute while biking? Enter the answer in the box.

The System Effectiveness is approximately 0.763.

To calculate the System Effectiveness, we need to multiply the values of Operational Readiness, Design Adequacy, Availability, Maintainability, and Mission Reliability.

System Effectiveness = Operational Readiness * Design Adequacy * Availability * Maintainability * Mission Reliability

Plugging in the given values:

System Effectiveness = 0.89 * 0.95 * 0.98 * 0.93 * 0.99

System Effectiveness ≈ 0.763

Therefore, the System Effectiveness is approximately 0.763.

The correct answer is a. 0.763.

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Answer:

Here,

JM=MK

so,

7x+5 = 8x

\(7x + 5 = 8x \\ ⇒ 5 = 8x - 7x \\ ⇒5 = x\)

. ° . JM = 7x+5 = 7×5+5 = 40

. ° . MK = 8x = 8×5 = 40

Hence,

The measure of angle 1 is 67.4°. The measure of angle 2 is 104.5°.

An angle is the measure of the amount of rotation between two lines or two planes that meet at a point. It is typically measured in degrees or radians. An angle can be acute, meaning it is less than 90 degrees, right, meaning it is exactly 90 degrees, obtuse, meaning it is greater than 90 degrees but less than 180 degrees, or straight, meaning it is exactly 180 degrees. An angle can also be positive or negative, depending on the direction of rotation between the lines or planes. Angles are used in various fields such as mathematics, engineering, physics, and geometry.

Here,

180-121.8=58.2°

180-(58.2+17.3)=104.5°

180-104.5=75.5°

180-(75.5+37.1)=67.4°

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Answer: 2

Step-by-step explanation:

By the geometric mean theorem,

\(\sqrt{8k}=4\\\\8k=16\\\\k=\boxed{2}\)

The relationships which describe angles 1 and 2 is the adjacent angles as they have in common side.

Angles formed by the transverse line cut by the transversal-

The angles 1 and 2 shown below in the attached image.  In the image, the angle 1 and 2 have the common side which cut them from between with the common vertex.

The relationships which describe angles 1 and 2 is the adjacent angles as they have in common side.

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Answer: A. 0

Step-by-step explanation: To determine the number of solutions for the system of equations x - y = 7 and y = sqrt(3x + 3) - 2, we can substitute y in the first equation with the expression for y in the second equation, giving us x - (sqrt(3x + 3) - 2) = 7. Simplifying this equation, we get sqrt(3x + 3) = -x + 9.

Since the square root of a number is always non-negative, we can conclude that there are no solutions to this system of equations. Therefore, the answer is A. 0.

- Lizzy ˚ʚ♡ɞ˚

There are two ways to color a cube with two colors so that no two adjacent vertices are the same color. A cube has 8 vertices, and each vertex can be colored either black or white.Therefore, the first vertex can be colored in two ways.

After coloring the first vertex, there are two vertices adjacent to the first vertex. Each of these vertices can be colored in only one way since they cannot be the same color as the first vertex. After coloring the first vertex and the two vertices adjacent to it, there are two pairs of adjacent vertices left.

The second vertex of the first pair can be colored in one way only (since it cannot be the same color as the first vertex or the vertex adjacent to it). The second vertex of the second pair can be colored in one way only, and this will also determine the color of the fourth vertex (since it cannot be the same color as the second vertex of the second pair).

This completes the coloring of the cube. Therefore, there are two ways to color a cube with two colors so that no two adjacent vertices are the same color.  

There are two ways to color a cube with two colors so that no two adjacent vertices are the same color.

We have to paint a cube with two colors so that no two adjacent vertices are of the same color. A cube has 8 vertices, each of which can be painted black or white. Consider the cube with one of its vertices painted black. Then there are three vertices that are adjacent to it, each of which must be painted white.

We have now fixed 4 vertices: one black and three white. There are now two cases to consider. Either the two remaining vertices are opposite each other, in which case they must be painted black, or they are adjacent to one another, in which case they can each be painted black or white. Therefore, we can paint the cube in 2 ways.

Therefore, there are two ways to paint a cube with two colors so that no two adjacent vertices are the same color.

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Answer:

option c

Step-by-step explanation:

because the y intercept is -3