A park ranger is interested in plant growth around the trails of the park. He finds the plants growth, G, is dependent on the number of sunny days that occur in three months, x, and can be modeled by the function G(x)=−8+3x.

Draw the graph of the growth function by plotting its G-intercept and another point

Answer:

x = 32

Step-by-step explanation:

Given

0.5x = 16 ( divide both sides by 0.5 )

x = \(\frac{16}{0.5}\) = 32

Answer:

x=32

Step-by-step explanation:

You have to isolate x, so do the opposite operation, which is division (because 0.5 is multiplying by x). So you divide both sides by 0.5, x is isolated because 0.5/0.5 is 1 and 16/0.5 is 32.

Answer:

Correct answer is option D. 96.4 yd.

Step-by-step explanation:

Please refer to the attached figure for labeling of the given diagram.

ABC is a triangle with the following labeling:

A is the hole, B is the Tee and C is the point where the ball is.

Sides are labeled as:

\(a =255\ yd\\c = 305\ yd\\\angle B =17^\circ\)

To find:

Side \(b = ?\)

Solution:

Here, we have one angle and two sides . Third side of the triangle is to be found opposite to the given angle.

We can use cosine formula here to find the value of the unknown side.

\(cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}\)

Putting all the values:

\(cos 17 = \dfrac{255^{2}+305^{2}-b^{2}}{2\times 255\times 305}\\\Rightarrow 0.956 = \dfrac{65025+93025-b^{2}}{155550}\\\Rightarrow 148753.2= 158050-b^{2}\\\Rightarrow b^{2}= 158050-148753.2\\\Rightarrow b^{2}= 9296.795\\\Rightarrow b= 96.42\ yd\)

So, the distance between the Ball and hole is 96.42 yd

Correct answer is option D. 96.4 yd.

Answer:

D.) 96.4 yd

Step-by-step explanation:

I got it correct on founders edtell

The sequence diagram provides a visual representation of the algorithm's execution, illustrating the interactions between objects and the flow of data during the computation of the vector norm.

The 'norm()' function's main sequence diagram can be summed up as follows:

1. The `norm()` function is called with an instance of the `Array` class as the input parameter.

2. The variable `the Norm` is initialized to 0.

3. A loop is executed from `index = 0` to `my Array. size()-1`.

4. In each iteration of the loop, the `get()` function of the `Array` class is called with the current `index` as the parameter to retrieve the value at that index.

5. The retrieved value is added to `the Norm`.

6. Once the loop is complete, the square root of `the Norm` is calculated and assigned back to `the Norm`.

7. The function ends, and the value of `the Norm` is returned as the result of the `norm()` function.

This diagram illustrates the interaction between the caller (which initiates the norm() function), the Array class, and the steps involved in computing the norm. The loop iterates over the indices of the array, retrieves the corresponding component using myArray.get(index), and accumulates the sum in theNorm.

Finally, the square root of theNorm is computed and returned as the result.

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Answer:3.6

Step-by-step explanation:

Answer:

3.6

Step-by-step explanation:

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

x + y = 420; y = 6x

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.

The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.

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Answer: 9 min

Step-by-step explanation:

Since team members: minutes are inversely proportional, you can use x = k/y to solve.

27 = k/5 (multiply by 5 for each side)

135 = k

Using this, you can see. that 135/15 = 9 minutes

If all the members pain at the same speed, then 15 members of the team will take 9 minutes to paint the wall.

The speed of all the members of the spray painting team is exactly the same.

5 members can paint a wall in 27 minutes.

Now, 15 members are painting the same wall.

Then the increase in man power is:

15 / 5 = 3 times more than before.

Since there is an increase in man power, therefore the time taken to paint the wall will also decrease by the same factor.

Therefore,

The time taken by 15 members to paint the wall will be:

Time = 27 / 3

Time = 9 minutes

Hence, 15 members will take 9 minutes to paint the wall.

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The value of 939 dx d939 d 939 (cos x) is cos x by computing first few derivatives and looking for a pattern.

To find 939 dx d939 d 939 (cos x), we need to compute the first few derivatives of cos x and look for a pattern.

The derivative is a key idea in calculus that gauges how quickly a function alters in relation to its input variable. In terms of geometry, the slope of the tangent line to the function graph at a particular location is represented by the derivative. The derivative has numerous crucial uses in mathematics, physics, engineering, and other disciplines, including optimisation, identifying extrema and inflection points, and simulating the rates of change of events that occur in the actual world. The derivative of various functions can be found using a variety of methods, including the power rule, product rule, chain rule, and quotient rule.

The first derivative of cos x is -sin x, the second derivative is -cos x, the third derivative is sin x, and the fourth derivative is cos x. We can notice that the pattern of the derivatives of cos x is that they cycle through the functions cos x, -sin x, -cos x, and sin x.

Since 939 is a multiple of 4 (939/4 = 234.75), we know that the 939th derivative of cos x will be the same as the fourth derivative of cos x, which is cos x.

Therefore, 939 dx d939 d 939 (cos x) = cos x.

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Answer:

−7.25x−10.4

Step-by-step explanation:

Let's simplify step-by-step.

−0.75x−5−(6.5x+5.4)

Distribute the Negative Sign:

=−0.75x−5+−1(6.5x+5.4)

=−0.75x+−5+−1(6.5x)+(−1)(5.4)

=−0.75x+−5+−6.5x+−5.4

Combine Like Terms:

=−0.75x+−5+−6.5x+−5.4

=(−0.75x+−6.5x)+(−5+−5.4)

=−7.25x+−10.4

The remaining side is 16.9 and remaining angles are 83.1 and 34.9.

The cosine formula to find the side of the triangle is given by:

c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.

Given:

m∠B = 62°, a = 11, and c = 19

Now, b² = a² + c² - 2ac cos B.

b = √ a² + c² - 2ac cos B

b = √ 11² + 19² - 2x 11  x 19 cos 62

b= 16.9

Now. a/ sin A = b/ sin B= c/ sin C

So, <C = arc sin ( c sin B /b)

<C = arc sin ( 19 sin 62 /16.9)

<C = 83.1

and, <A = arc sin ( a sin B /b)

<A = arc sin ( 11 sin 62 /16.9)

<A = 34.9

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The expression that shows the length of the adjacent side is 6cos(50)

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

Angle = 50 degrees

Hypotenuse = 6 meters

The length of the adjacent side is then calculated as

cos(angle) = adjacent/hypotenuse

substitute the known values in the above equation, so, we have the following representation

cos(50) = x/6

This gives

x = 6cos(50)

Hence, the expression is 6cos(50)

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The rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form. However, solving the resulting system of equations algebraically may be challenging. Alternatively, graphing the polar curves and visually identifying the points of intersection can provide an effective method.

To find the rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form, the rectangular coordinates of the above points are given below:

For the equation r = 2sin(2θ):

x = 2sin(2θ)cos(θ)

y = 2sin(2θ)sin(θ)

For the equation r = 2sin(θ):

x = 2sin(θ)cos(θ)

y = 2sin^2(θ)

The rectangular coordinates of the point(s) of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ) can be found by converting the polar equations to rectangular form and solving for the x and y coordinates.

To convert the polar equations to rectangular form, we can use the relationships x = rcos(θ) and y = rsin(θ). Substituting these expressions into the given polar equations, we get:

For the equation r = 2sin(2θ):

x = 2sin(2θ)cos(θ)

y = 2sin(2θ)sin(θ)

For the equation r = 2sin(θ):

x = 2sin(θ)cos(θ)

y = 2sin^2(θ)

To find the points of intersection, we need to set the x and y coordinates of both equations equal to each other and solve for θ. However, solving this system of equations algebraically can be complex due to the trigonometric functions involved.

Graphing the polar curves and visually inspecting the points of intersection may provide a more intuitive approach to finding the rectangular coordinates. By plotting both polar curves on a graph, the points where the curves intersect can be determined by their shared coordinates.

In summary, to find the rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form. However, solving the resulting system of equations algebraically may be challenging. Alternatively, graphing the polar curves and visually identifying the points of intersection can provide an effective method.

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Answer:

(6a-4)°=(2a+68)°

6a-2a=68+4

4a=72

a=72/4

a=18

Answer:

The answer is 18. (A)

Step-by-step explanation:

Let me know if this helps

Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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Given :

Price per folder = $2.15 .

Price per notebook = $4.60 .

The supply budget for this meeting is $150.

To Find :

Inequality represents the constraint on the number of folders f and notebooks n the office administrator can purchase.

Solution :

Let, number of folders and notebooks is f and n.

So, price of buying f and n number of folders and notebooks are :

P = 2.15f + 4.60n

Now, it is given that P ≤ $150 .

So,

2.15f + 4.60n ≤ 150

Hence, this is the required solution.

\(2.15f+2.5n\leq 150\) inequality will represent the constraint on the number of folders f and notebooks n the office administrator can purchase.

Given information:

An office administrator will be purchasing supplies for an upcoming meeting.

Staff will purchase folders, which are $2.15 each, and notebooks, which are $4.60 each.

The supply budget for this meeting is $150.

Let f be the number of folders purchased and n  be the number of notebooks purchased.

Now, the total amount spent on the whole purchase should not be greater than $150 which is the budget of the shopping.

In the form of inequality, the given condition can be written as,

\(2.15f+4.6n\leq 150\)

The total amount spent is less than equal to 150.

Therefore, \(2.15f+4.6n\leq 150\) inequality will represent the constraint on the number of folders f and notebooks n the office administrator can purchase.

For a graphical representation of the inequality, see the image attached.

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Step-by-step explanation:

at 3=3

at 0=9

at 4=1

\(y = ax + b\)

\(1 = 4a + b \\ 3 = 3a + b \\ 2 = - a \\ a = - 2 \\ 1 = - 4 \times 2 + b \\ b = 1 + 8 = 9 \\ y = - 2x + 9\)

Answer:

y=-2x+9

Step-by-step explanation:

From looking at the line you can already tell that the slope is going to be negative, and the y-intercept is going to be 9, since that's where y is when x is 0. You can see that when x is one, y is 7. When x is 2, y is 5. And when x is 3, y is 3.

So:

0: 9

1:7

2:5

3:3

And the difference of y over the difference of x is the slope

-2/1=-2

So the slope is -2

Therefore, putting the equation together makes:

y=-2x+9

Hope this helps!

Step-by-step explanation:

3. First, let's find the length of AB:

22²+14² = AB²

680 = AB²

AB = √680

AB ≈ 26.08

The sin of x° is equal to 14/2608

14/26.08 ≈ 0.54

Now you do the asin of 0.54:

asin(0.54) = 32.68°

4. The cos(41°) = x/34, and also the value of cos(41°) ≈ 0.75, so:

0.75 = x/34

x = 34•0.75

x = 25.5°

Answer:

he has 1/6 of a piza left

Step-by-step explanation:

becuase if you take the left over pizza, 3/4 it is bacially only a quarter of the piza gone, if image a pizza half of the circle is there, and half of the half circle is also there, and that is 3 sections, 6 d 3 get along, so ecaily each of the 3 section are wroth 2 slices and he ate 5, so 1 is left.

Answer:

G

Step-by-step explanation:

you have a 1 out of 6 chance of getting 11

Answer:

B

Step-by-step explanation:

There are 6 options to choose from.

11 is one of those 6 cards.

Therefore, the probability will be 1/6, or B

Hope that helps!

-scsb17hm

To complete the tables we need to evaluate both functions in the correspondent values.

For the first table the missing value is 6

For the second table, the missing value is 1.585

In the first table, we can see that:

f(x) = b^x

We can see that:

f(-1) = 0.5= b^-1 = 1/b

Now we can solve this for b.

b = 1/0.5 = 2

Then to complete the table, we need to evaluate this on x = 2.585

f(2.585) = 2^2.585 = 6

This is the value that goes on the first table.

For the second table, the function is:

g(x) = log_b(x) = ln(x)/ln(b)

We already know that b = 2, then:

g(x) = ln(x)/ln(2).

To complete the value, we need to evaluate in x = 3, then we have:

g(3) =  ln(3)/ln(2) = 1.585

This is the value that goes on the second table.

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Answer:

table l= 1.404

table ll= 1.661

Answer:

Here you go! :) (Its at (0,2/3)

\(\huge\boxed{\boxed{Hi\;there!}}\)

First of all, the slope of the line y=2/3 is 0, which means the line is horizontal.

Next, 2/3 is the y-intercept of the line (where the line touches the y-axis)

The line touches the y-axis at (0, 2/3) (or, 0.66667 in decimal form)

\(\huge\bold{Hope\;it\;helps\;you!\;Good\;luck!}}\)

\(\rule{250pt}}\)\(\huge\rm{StillEnjoyingLife :)\)

Answer: B

Explanation: Key word: Atleast. This shows that you can still get 16 but it's the lowest you can get. Meaning, if you were to say, atleast get a 16% done. It'll mean that getting 16% is good but also, you'll want to get a higher number of course.

The null hypothesis (H0) and alternative hypothesis (Ha) for each situation are a) H0: µ = 18 Ha: µ < 18 b) H0: µ = 50 Ha: µ > 50 c) H0: µ = 24 Ha: µ ≠ 24. Based on the given p-value of 0.02, the decision for each situation are a) Since p < 0.05, we reject the null hypothesis b) Since p < 0.05, we reject the null hypothesis c) Since p < 0.05, we reject the null hypothesis.

The null hypothesis (H0) and alternative hypothesis (Ha) for each situation are as follows:

a) H0: µ = 18 (the mean time for mice to complete the maze is equal to 18 seconds)
Ha: µ < 18 (the mean time for mice to complete the maze is less than 18 seconds)

b) H0: µ = 50 (the mean score for the teaching assistant's students is equal to 50)
Ha: µ > 50 (the mean score for the teaching assistant's students is greater than 50)

c) H0: µ = 24 (the mean score for students who passed the credit examination is equal to 24)
Ha: µ ≠ 24 (the mean score for students who passed the credit examination is not equal to 24)

Based on the given p-value of 0.02, the decision for each situation is as follows:
a) Since p < 0.05, we reject the null hypothesis and conclude that the loud noise does cause the mice to complete the maze faster.
b) Since p < 0.05, we reject the null hypothesis and conclude that the teaching assistant's students do have a higher mean score than the class as a whole.
c) Since p < 0.05, we reject the null hypothesis and conclude that the students who passed the credit examination do differ in their understanding of spoken French from students who actually take the French courses.

These decisions are justified because a p-value less than 0.05 indicates that there is a statistically significant difference between the sample mean and the population mean, and therefore we can reject the null hypothesis and accept the alternative hypothesis.

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Answer:

The answer is C i think  not that sure

Step-by-step explanation:

Divide the number of micrometers by 10,000 to get the equivalent number of centimeters.

To convert micrometers to centimeters, you need to use the conversion factor between the two units. There are 10,000 micrometers in a centimeter.

Here are the steps to convert micrometers to centimeters:

1. Start with the number of micrometers you want to convert.
2. Divide the number of micrometers by 10,000 to get the equivalent number of centimeters.
3. The result is the number of centimeters equivalent to the given number of micrometers.

For example, if you want to convert 50,000 micrometers to centimeters, you would divide 50,000 by 10,000 to get 5 centimeters.

So, the conversion formula is:

centimeters = micrometers ÷ 10,000

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Answer: third one

Step-by-step explanation: if you do the equation you will see the result and will be equivalents to numbers higher or exact to 0.

Answer:

5/72

Step-by-step explanation:

The runner's average speed between `t = 1` second and `t = 3` seconds is `8 feet/second.`

Given, the runner's position in feet is given by `s(t) = 10 + 2t²`.

The average speed is given by the formula:

Average speed = `(distance traveled) / (time taken)`

The distance traveled by the runner is equal to the displacement (change in position) between `t = 1` second and `t = 3` seconds.

The displacement between `t = 1` second and `t = 3` seconds is given by the difference between their positions:

Displacement = `s(3) - s(1)`

Putting `t = 3` in the given equation, we get:

s(3) = 10 + 2(3)² = 28Feet

Putting `t = 1` in the given equation, we get:s(1) = 10 + 2(1)² = 12Feet

Therefore, the displacement between `t = 1` second and `t = 3` seconds is:

Displacement = `s(3) - s(1)`

= 28 - 12

= 16 Feet

The time taken is

`t = 3 - 1

= 2` seconds

Therefore, the average speed is given by:

Average speed = `distance/time`

= `16 / 2`

= 8 feet/second

Hence, the runner's average speed between `t = 1` second and `t = 3` seconds is `8 feet/second.`

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The first two are functions the third one is not a function and the fourth one is a function

Answer:

302.3

Step-by-step explanation:

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86