Determine by inspection (that is, with only minimal calculations) if the given vectors form a linearly dependent or linearly independent set. Justify your answer u = [3]
[-1]
v=[6]
[-4]
w=[1]
[7]
a. Linearly dependent. Notice that u V 3w b. Linearly independent. If {u1, u2, . . ., um} is a set of vectors in Rn and n < m, then the set is linearly independent. c. Linearly dependent. Notice that v - 2u, so 2u- d. Linearly independent. The vectors are not scalar multiples of each other. e. Linearly dependent. If (ui, u2, ..., um) is a set of vectors in R" and n< m, then the set is linearly dependent.

[tex]f(x) = 2x is linear.f(x) = 4^x is exponential.[/tex] This is where at each level, each branch extends into 4 branches.

In the first prompt, the number of boxes in each row is increasing by a constant amount, so the function is linear. In the second prompt, the number of branches is increasing by a factor of 4 with each level, so the function is exponential.

A linear function is defined as one where the output increases by a constant amount for each increase in the input. An exponential function is defined as one where the output increases by a constant factor for each increase in the input. The first prompt corresponds to a linear function, while the second prompt corresponds to an exponential function.

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The complete question is-

Is the function f(x) = 4^x, where x is the number of branches at level x in a tree diagram, linear or exponential? Explain your answer.

Answer:

59

Step-by-step explanation:

writing down a problem is a problem halved

472/8

The answer is 59

A vertical line can be written in the form x = a, where a is the x-coordinate of any point on the line.

In mathematics, an equation is a statement that asserts the equality of two expressions. It contains an equals sign (=) and one or more variables, which represent unknown values. Equations are often used to solve problems and find the values of the variables that make the equation true. There are many types of equations, including linear equations, quadratic equations, and systems of equations, among others.

Here,

1. To find the equation of a line in slope-intercept form, we need to use the formula y = mx + b, where m is the slope of the line and b is the y-intercept. We are given the x-intercept and y-intercept of the line, so we can use them to find the slope and y-intercept:

x-intercept = -2, y-intercept = -10

To find the slope, we can use the formula:

m = (y2 - y1)/(x2 - x1), where (x1, y1) = (-2, 0) and (x2, y2) = (0, -10)

m = (-10 - 0)/(0 - (-2)) = -10/2 = -5

So the slope of the line is -5.

Now we can use the slope-intercept form equation to find the equation of the line:

y = mx + b

Substituting the values of m and b, we get:

y = -5x - 10

Therefore, the equation of the line in slope-intercept form that passes through the x-intercept = -2 and y-intercept = -10 is y = -5x - 10.

2. We are given a point (0, -6) and the slope m = 8. We can use the slope-intercept form equation to find the equation of the line:

y = mx + b

Substituting the values of m and the point (0, -6), we get:

-6 = 8(0) + b

b = -6

Therefore, the equation of the line in slope-intercept form that passes through the point (0, -6) and has a slope of m = 8 is y = 8x - 6.

3. We are given that the line is parallel to y = 5 and passes through the point (4, 9). Since the line is parallel to y = 5, it has the same slope as y = 5, which is 0. We can use the point-slope form equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values of m, x1, and y1, we get:

y - 9 = 0(x - 4)

y - 9 = 0

y = 9

Therefore, the equation of the line in slope-intercept form that is parallel to y = 5 and passes through the point (4, 9) is y = 9.

4. We are given that the line is perpendicular to x = -4 and passes through the point (3, 7). Since the line is perpendicular to x = -4, it is a vertical line and its slope is undefined. We can use the equation x = 3 to represent the line.

5. To find the slope of a line, we can use the formula:

m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

6. If the slope of a line is undefined, it means that the line is vertical. This happens when the change in the x-coordinates between any two points on the line is zero, which makes the denominator in the slope formula zero. In this case, the line does not have a slope, since the slope is defined as the ratio of the change in y-coordinates to the change in x-coordinates.

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Answer:

$58.50

Step-by-step explanation:

5616/96

The decision to rent or purchase a home for the Bainters will depend on several factors, including their financial situation, personal preferences, and long-term plans.

If the Bainters only plan to live in the house for 1 year, it may make more sense for them to rent. Renting allows for greater flexibility and mobility, as well as reduced responsibility for maintenance and repairs. The upfront costs of purchasing a home, such as closing costs and a down payment, may not be worth it for such a short period of time. Additionally, the monthly costs of renting may be lower than the monthly mortgage payments and related expenses for owning a home.

If the Bainters plan to live in the house for 5 years, it may make more sense for them to purchase a home. Over a 5-year period, the costs of renting can add up, and may end up being higher than the cost of owning. Additionally, a portion of a homeowner's monthly mortgage payment can go towards building equity in the property, which can be beneficial if the home's value appreciates over time.

If the Bainters plan to live in the house for 10 years or more, purchasing a home may be the more cost-effective option. Over a longer period of time, the costs of renting can significantly exceed the costs of owning, as renters do not build equity in the property. Additionally, if the Bainters plan to live in the same location for a long time, purchasing a home can provide stability and a sense of community.

To support their decision, the Bainters should calculate the total costs of renting and owning over each respective time period, taking into consideration all expenses, such as rent or mortgage payments, insurance, taxes, maintenance, and repairs. They should also consider factors such as their ability to afford a down payment, their credit score, and their employment stability. It may also be helpful for the Bainters to consult with a financial advisor or real estate professional.

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a. T(n) = O(n^4) and Ω(n^4): For the upper bound, we can use the substitution method to prove that T(n) is O(n^4). Let S(n) = cn^4, where c is a constant. We can then substitute S(n) into the recurrence to prove that T(n) is O(n^4):

T(n) = 2T(n/2) + n^4 <= 2S(n/2) + n^4 <= 2cn^4/2 + n^4 <= cn^4 + n^4 = (c + 1)n^4

Since (c + 1) is a constant, this expression is equal to O(n^4).

For the lower bound, we can use the recurrence tree method to prove that T(n) is Ω(n^4). Let k be the number of levels in the tree. We can then calculate the total cost of the tree:

Total Cost = 2^k * n^4 = n^4 * (2^k/n^4) = n^4 * (2/n)^k

Since 2/n is a constant and k is a function of n, this expression is equal to Ω(n^4).

b. For the upper bound, we can use the substitution method to prove that T(n) is O(n log n). Let S(n) = cn log n, where c is a constant. We can then substitute S(n) into the recurrence to prove that T(n) is O(n log n):

T(n) = T(7n/10) + n <= S(7n/10) + n <= c(7n/10) log (7n/10) + n = c(7/10)n log n + n = (c(7/10) + 1)n log n

Since (c(7/10) + 1) is a constant, this expression is equal to O(n log n).

For the lower bound, we can use the recurrence tree method to prove that T(n) is Ω(n). Let k be the number of levels in the tree. We can then calculate the total cost of the tree:

Total Cost = 7^k * n = n * (7^k/n) = n * (7/n)^k

Since 7/n is a constant and k is a function of n, this expression is equal to Ω(n).

c. For the upper bound, we can use the substitution method to prove that T(n) is O(n^2). Let S(n) = cn^2, where c is a constant. We can then substitute S(n) into the recurrence to prove that T(n) is O(n^2):

T(n) = 16T(n/4) + n^2 <= 16S(n/4) + n^2 <= 16cn^2/4 + n^2 <= 4cn^2 + n^2 = (4c + 1)n^2

Since (4c + 1) is a constant, this expression is equal to O(n^2).

For the lower bound, we can use the recurrence tree method to prove that T(n) is Ω(n^2). Let k be the number of levels in the tree. We can then calculate the total cost of the tree:

Total Cost = 16^k * n^2 = n^2 * (16^k/n^2) = n^2 * (16/n^2)^k

Since 16/n^2 is a constant and k is a function of n, this expression is equal to Ω(n^2).

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Answer:

494ft^2

Step-by-step explanation:

Area of trapezoid = [ (20 + 32) / 2 ] * 3 = 78 ft^2

Area of square = 32 * 13 = 416 ft^2

Total area: 78ft^2 + 416ft^2 = 494ft^2

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The value of X is 22.

Value is regard that something is held to deserve,  the important worth or usefulness of something.

The calculation is as follows:

In the case of an isosceles trapezoid if there is any lower base angle is supplementary to any upper base angle.

So,  

6x + 2x + 4 = 180

8x + 4 = 180

8x = 176

x = 22

Therefore we can conclude that The value of X is 22.

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The graph of the function g(x) = f(2x) is given by the image presented at the end of the answer.

The asymptotes of f(x) are given as follows:

Hence the definition of the rational function f(x) is given as follows:

f(x) = 2/(x - 2) - 2.

The function g(x) is obtained replacing the lone instance of x on f(x) by 2x, hence:

g(x) = 2/(2x - 2) - 2

g(x) = 2/(2(x - 1)) - 2

g(x) = 1/(x - 1) - 2.

Hence the graph of the function g(x) = 1/(x - 1) is given by the image presented at the end of the answer.

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Answer: Let's call the number of species N. The total length of the beetles walking up the gangplank will be N * (1 cm + 7 cm) = N * 8 cm.

The total time it will take for all the beetles to walk up the gangplank is the total length of the beetles divided by the walking speed of each beetle, which is (N * 8 cm) / (10 cm/s) = 0.8 * N seconds.

Finally, to convert this to hours, we divide by 3600 seconds per hour: (0.8 * N) / 3600 s/hr = 0.0002 * N hours.

So, for 1/4 million species, N = 1/4 * 10^6, it will take 0.0002 * N = 0.0002 * 1/4 * 10^6 = 25 hours.

Step-by-step explanation:

The value of an F'(1) is 114.

If F(x) = f(x f(x f(x))),

where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and f '(6) = 6.

We will differentiate F and wade our way slowly and methodically through finding the derivative of the right. First with the outermost function and chain rule:

[tex]$$F^{\prime}(x)=f^{\prime}(x f(x f(x)))\+x\left(\frac{d}{d x} f(x f(x))\right)\right]$$[/tex]

Now applying the product rule:

[tex]$$F^{\prime}(x)=f^{\prime}(x f(x f(x)))\left[f(x f(x))+x\left(\frac{d}{d x} f(x f(x))\right)\right]$$[/tex]

Reapplying the chain rule:

[tex]$$\begin{aligned}& F^{\prime}(x)=f^{\prime}(x f(x f(x)))\left[f(x f(x))+x\left(f^{\prime}(x f(x))+\left(\frac{d}{d x} x f(x)\right)\right)\right] \\& F^{\prime}(x)=f^{\prime}(x f(x f(x)))\left[f(x f(x))+x f^{\prime}(x f(x))+x\left(\frac{d}{d x} x f(x)\right)\right]\end{aligned}$$[/tex]

Product rule once more:

[tex]$$F^{\prime}(x)=f^{\prime}(x f(x f(x)))\left[f(x f(x))+x f^{\prime}(x f(x))+x\left(f(x)+x f^{\prime}(x)\right)\right]$$[/tex]

We could simplify this a little more.

Evaluating at x=1 :

[tex]$$& F^{\prime}(1)=f^{\prime}(f(f(1)))\left[f(f(1))+f^{\prime}(f(1))+1\left(f(1)+f^{\prime}(1)\right)\right] \\$$[/tex]

[tex]F'(1)=f'(f(4))) [f(4))+f'(4)+1(4+4))]\\[/tex]

[tex]F'(1)=f'(6)[6+5+8]\\[/tex]

[tex]F'(1)=6[19]=114[/tex]

[tex]F'(1)=114[/tex]

Therefore, the value of F'(1)=114.

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Based on the information, it can be inferred that the total number of students surveyed is: 2,498.

To find the number of students surveyed we can perform the following operation.

1. Add all the results of each category

854 + 644 + 199 + 407 + 109 + 108 + 84 + 93 = 2,498

According to the above, the total number of students surveyed would be 2,498. Additionally, this information can be classified in a Venn diagram to identify students who belong to two or three categories at the same time.

Note: This question is incomplete because there is some information missing. Here is the complete information

tasks

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Answer:

Step-by-step explanation:

8

In word problem , the Total bill including tax = $34.78+$2.08 = $36.86

and  you have to give server one $20 bill , one $10 bill, one $5 bill and two $1 bill, so yo don't get any pennies back.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here the bill = $34.78

Sales tax= 6% of Bill

=> Sales tax = 6% of 34.78

=> Sales tax = [tex]\frac{6}{100}\times 34.78[/tex]

=> Sales tax = $2.08

Now the Total bill including tax = $34.78+$2.08 = $36.86

Hence you have to give server one $20 bill , one $10 bill, one $5 bill and two $1 bill, so yo don't get any pennies back.

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f(7) = -1.906 (rounded to the nearest hundredth.

To find f(7), we first need to substitute 7 for x in the expression for f(x). So, we have:

f(7) = (3/(7+2)) - √(7-2)

f(7) = (3/(9)) - √(5)

f(7) = (1/3) - 2.236

f(7) = 0.33 - 2.236

f(7) = -1.906

So, f(7) = -1.906 (rounded to the nearest hundredth).

An expression is a mathematical phrase that can contain numbers, variables, and operators. Expressions are used to represent values or computations in mathematics. For example, 2x + 3 is an expression that represents the sum of two times x and three. Expressions can be evaluated to obtain a numerical result by substituting numerical values for variables and performing the operations. For instance, if we substitute x=5 into the expression 2x + 3, we get 2(5) + 3 = 10 + 3 = 13.

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The mode of the data set of temperatures in various cities in San Diego County is 78°.

Mode is a measure of central tendency that represents the value that occurs most frequently in a data set. It gives an idea about which value is the most likely to appear in the data set. In a set of data, there can be one mode, more than one mode (referred to as bimodal or multimodal), or no mode at all (referred to as being non-modal).

In this case, the number 78 appears twice, while all the others appear only once.

Therefore, the mode is 78.

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One possible solution from the graph(attached at the end of the solution) is selling 9 bags of popcorn and 5 bags of candies.

As per the given data:

The number of popcorn bags is x

The number of candies is y

The cost of each popcorn bag is $7

The cost of each candy is $4

She has $80 to spend on them

Inequality is the nonequal comparison of two or more variables and numbers.

So the first inequality is

7 x + 4 y ≤ 80

Since she must buy no less than 16 bags of popcorn and candies

The second inequality is

x + y ≥ 16

The red area represents the 1st inequality

The blue area represents the 2nd inequality

The solutions lie in the common part of red and blue colors

One possible solution is ordered pair (9,5)

(Graph attached at the end of solution)

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A box that measures 2 meters × 2 meters × 6 meters. So the longest piece of rebar (inside diagonal) that could fit in this box is 2√11 cm.

These are the specified parameters:

Length of the box (l) = 2 m

Breadth of the box (b) = 2 m

Height of the box (h) = 6 m

The longest piece of rebar (inside diagonal)

For example, inside diagonal = x

x² = l² + b² + h²

   = 2² + 2² + 6²

   = 4 + 4 + 36

   = 44

x = √44

x = 2√11 cm

So the longest piece of rebar (inside diagonal) is 2√11 cm.

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Answer:

Step-by-step explanation:

x=0 and xyz=4 so that would equal 40 and 46.

The correct statement is about 95% of the shoppers have between a 23.6% and a 28.2% chance of purchasing cookies.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

95% confidence interval for the proportion of all shoppers at a large grocery store who purchase cookies here is given to be (0.236, 0.282).

As the minimum limit value here is 0.236 and max limit value is 0.282, therefore the inferences here are given as:

At least 23.6% of the shoppers purchase cookies.

At most 28.2% of the shoppers purchase cookies

Therefore, the correct answer is A.

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Answer:

C

Step-by-step explanation:

you open up the brackets and multiply 2 to whatever is inside and you'll get C

Let the width be [tex]w[/tex] inches and the length be [tex]w+15[/tex] inches.

So, the dimensions of the box are [tex]w-6[/tex], [tex]w+9[/tex], and [tex]3[/tex] inches.

[tex]3(w-6)(w+9)=1350 \\ \\ (w-6)(w+9)=450 \\ \\ w^2+3w-54=450 \\ \\ w^2+3w-504=0 \\ \\ (w+24)(w-21)=0 \\ \\ w=-24,21[/tex]

Rejecting the negative case, [tex]w=21[/tex].

So, the dimensions are 21 by 36 inches.

The actual distance between the two cities is 70 kilometers.

The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.

Given that;

The distance between 2 cities is 3.5 cemtimetes

the map uses a scale in which 1 centimeter represents 20 kilometers

Since, One centimeter represents 20 kilometers

3.5 x 20 = 70

Theefore, the actual distance between the two cities;

70 kilometers.

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The p-value of 0.0761 indicates that there is not sufficient evidence to reject the null hypothesis, which states that the survival rates for the two treatments are equal.

Therefore, based on this study, the use of CC alone does not produce a significantly higher survival rate than the use of both CC and standard MMR.

The test of significance used a significance level of α = 0.05. This means that in order for the null hypothesis to be rejected, the p-value must be less than 0.05. However, the p-value in this study is 0.0761, which is greater than 0.05.

Therefore, there is not sufficient evidence to reject the null hypothesis and we must accept it, meaning that the survival rates for the two treatments are not significantly different. In this case, a Type I error could have been made, where the null hypothesis is rejected when it should have been accepted.

The consequence of this would be that the treatment using CC alone would have been incorrectly identified as providing significantly higher survival rates, leading to a potential misallocation of resources.

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For the following triangle Joseph is incorrect and for rectangle Chad is incorrect.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. In geometry, object transformations constitute the foundation for the majority of proofs. The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

The coordinate of X is (x , y ) is (-1, 7), hence the value of X' when the coordinates are transformed would be:

(x,y) → (y, -x)

(-1, 7) → (7, -1)

Hence, Tara is correct in the first question.

The transformation corresponding to (x,y) → (-x, -y) is rotation of 180 degrees, Hence, Darla is correct.

Hence, for the following questions Joseph and Chad are incorrect.

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Answer:

here

Step-by-step explanation:

Call the two integers a and b . We are given that a+b=−3, and ab=−10. Simple plug and chug yields the answers −5 and 2.

Based on the given square of ABCD, the length of BD is proven to be V3a. The Perimeter of the square is a (2 + 2√2 + √(√3)). The value of a is a = √(3/2 - 3/4√3) so that the area of the square equals to √3.

First, we can divide the square ABCD into 2 triangles, DAB and BCD. To find the length of BD, we will focus on triangle DAB.

On  triangle DAB, we have 2 angles and 1 side known. We will use the sinus formula to find the length of DB.

sin B = sin A = sin D

 DA      DB        AB

sin 120°  =   sin 30°

 DB                 a

We need to find the value of sin 120 using the sinus formula:

Sin 2a = 2 sin a. cos a

sin 2(60°) = 2 sin 60° cos 60°

sin 120° = 2 (1/2) (1/2√3)

sin 120° = 1/2 √3

sin 120° = sin 30°

DB            a

1/2 √3  = 1/2

 DB          a

DB = √3 a --> Proven!

To determine the perimeter of the square, we need to know the length of all sides of the square.

In the triangle DAB, we have not know the length of DA. We need to find the length of DA by finding the angle ABD. Since a triangle must have a sum of angles equals to 180, then:

180° = BDA + DAB + ABD

180° = 30° + 120° + ABD

180° = 150° + ABD

ABD = 30°

Since the angle ABD equals to BDA, the length of DA should be equal to AB which is a.

Next, we focus on the second triangle, BCD. We have 2 sides and 1 angle known. We need to find the length of CD. To solve this, we need to use the cosinus formula:

a² = b² + c² - 2bc. cos A

CD² = BC² + DB² - 2 BC DB cos DBC

CD² = (√3 a)² + (V2a)² - 2 (√3a)(√2a) cos 75°

CD² = 3a² + 2a² - 2√6a² cos 75°

CD² = 5a² - 2√6a² co 75°

To find the value of cos 75, we will use the cos formula:

cos (A+B) = cos A cos B - sin A sin B

cos 75° = cos (30° + 45°)

cos (30° + 45°) = cos 30° . cos 45° - sin 30° . sin 45°

cos 75° = (1/2 √3) (1/2 √2) - (1/2) (1/2 √2)

cos 75° = (1/4 √6) - (1/4 √2)

cos 75° = 1/4 (√6 - √2)

CD² = 5a² - 2√6a² cos 75°

CD² = 5a² - (2√6a²)(1/4(√6 - √2)

CD² = 5a² - 1/2(6)a² + 1/2√12a²

CD² = 5a² - 3a² +√3a²

CD² = 2a² + √3a²

We can find the perimeter of the square is:

P = AB + BC + CD + DA

P = a + √2a + a (√(2+√3)) + a

P = a (2 + 2√2 +√(√3))

To find the area of the square, we can try to find the area of each triangle first.

A triangle DAB is:

A₁ = 1/2 . a . a. sin 120°

A₁ = 1/2 a² (1/2 √3)

A ₁= 1/4 √3 a²

Area of triangle BCD is:

A₂ = 1/2 (a√2) (a√3) sin 75°

A₂ = 1/2 √6 a² sin 75

Sin 75° = sin (30° + 45°)

sin 75° = sin 30° cos 45° + cos 30° sin 45°

sin 75° = 1/2 (1/2 √2) + 1/2√3 (1/2√2)

sin 75° = 1/4√2 + 1/4 √6

sin 75° = 1/4 (√2+ √6)

A₂ = 1/2√6 a² (1/4 (√2 + √6))

A₂ = 1/8 √12 a² + 1/8 (6) a²

A₂ = 2/8 √3 a² + 6/8 a²

A₂ = (1/4 √3 + 3/4) a²

Total area of both triangle equals to √3, then:

A₁ + A₂ = √3

1/4 √3 a² + (1/4 √3 + 3/4) a² = √3

(1/2 √3 + 3/4) a² = √3

a² = √3 / (1/2√3 + 3/4)

a² =         √3                  x   1/2√3 - 3/4

         1/2√3 + 3/4                1/2√3 - 3/4

a² = 3/2 - 3/4√3

       3/4 - 9/16

a² = 3/2 - 3/4 √3

       3/4  - 3/4

a = √(3/2 - 3/4√3)

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The rate of the area with the circle is increased after each of the following.

a. after 1s 15,707.963cm^2/s b. after 4s 62,800.889cm^2/s c. after 7 s 109,955.74 cm^2/s

50cm/s is the radius of the ripple per second, that is, radius(r) of the ripple after t seconds = speed * time(t)

Speed = 50cm/s

r = 50t

Area of a circle(A) = πr^2

The rate of change of area with radius is measured by:

dA/dt = π2r . dr/dt

Speed of ripple 50cm/s.

This can be the rate at which the radius changes with time (dr/dt)

dr/dt = 50cm/s

The rate at which the area is increased with time:

dA/dt = π2r . dr/dt

dA/dt = π2(50t).50

dA/dt = 5000πt

After 1 second:

dA/dt = 5000π(1)

= 15,707.963cm^2/s

After 4 seconds:

dA/dt = 5000π(4)

= 62,800.889cm^2/s

After 7 seconds:

dA/dt = 5000π(7)

= 109,955.74cm^2/s

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The difference between the maximum and the minimum values of the trigonometric function is 6.

We have to determine the difference between the maximum and the minimum values of the trigonometric function.

The function is y = -3cos(2x) + 8

The maximum and the minimum value of cos can be defined at the value of 0 and 1.

As we know that, the value of cos0 = 1 and the value of cos90 = 0

Now the value of the function at x = 0

y = -3cos(2×0) + 8

y = -3cos(0) + 8

y = -3×1 + 8

y = -3 + 8

y = 5

Now the value of the function at x = 90

y = -3cos(2×90) + 8

y = -3(-1) + 8

y = 3 + 8

y = 11

The difference between the maximum and the minimum values of the trigonometric function = 11 - 5

The difference between the maximum and the minimum values of the trigonometric function = 6

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The number of grasses is 17, the number of weeds is 3 × 17 - 7 = 42, and the number of trees is 3 × 17 + 3 = 56.

Pollen is a fine powdery substance consisting of microscopic grains that are produced by the male reproductive organs of seed plants.

Let's call the number of grasses "G".

The number of weeds is 3G - 7.

The number of trees is 3G + 3.

The total number of sources is G + (3G - 7) + (3G + 3) = 108.

Combining like terms, we get 7G = 118.

Dividing both sides by 7, we find G = 17.

Therefore, the number of grasses is 17, the number of weeds is 3 * 17 - 7 = 42, and the number of trees is 3 × 17 + 3 = 56.

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