a parking meter that is 1.6m tall costs a shadow of 3.6m long. at the same time, a tree costs a shadow 9m long. which proportion could be used to fin the height of the tree?

The corresponding equation is 4q + 3p = 22.

What is the slope of a line ?

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's b in mathematics.

Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. Locate two locations along the chosen line and find their coordinates.

Find the y-coordinate difference between these two places (rise). Find the difference between the x-coordinates of these two points (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).

The slope is defined as the relationship between the rise, or vertical change, between two points and the change, or horizontal change, between the same two points and can be represented as an equation.

Given that, coordinates are (p, 1/2) and (-8, q), slope is 3/4.

m = (y2 - y1)/(x2 - x1)

34 = (q - 1/2)/-8 - p

-24 - 3p = 4q - 2

4q + 3p = 22

The corresponding equation is 4q + 3p = 22.

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The area of the triangle is approximately 11.524 km²

What is an area?

We can find the area of the triangle using the formula:

Area = (1/2) * a * b * sin(C)

where a and b are the lengths of the two sides and C is the angle between them.

In this case, a = 5 km, b = 7 km, and C = 143°. However, before we can use this formula, we need to convert the angle to radians. We can do this by multiplying by pi/180:

C = 143 * pi/180

C ≈ 2.495 radians

Now we can substitute the values into the formula and calculate the area:

Area = (1/2) * 5 km * 7 km * sin(2.495)

Area ≈ 11.524 km²

Therefore, the area of the triangle is approximately 11.524 km².

What is triangle?

A triangle is a 2-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and is used in various fields such as mathematics, engineering, architecture, and art. Triangles can be classified into different types based on their sides and angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. The area of a triangle is calculated by using the formula A = 1/2 * base * height, where the base is the length of one of its sides and the height is the perpendicular distance between the base and the opposite vertex.

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Complete question is: The area of the triangle is approximately 11.524 km²

The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.

Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:

= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3

= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]

= (1/3) × [(9/2 + 6) - 0]

= (1/3) × (21/2)

= 7/2

Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

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To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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Answer: Perimeter of given square:40,Area of given square:100

Perimeter of Dilated square:200

Area of Dilated square: 2500

Step-by-step explanation:

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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The probability of choosing either "w" or "G" is 3/12.

Events that are mutually incompatible cannot take place at the same moment. The outcomes of receiving a head or a tail, for instance, are mutually incompatible when we toss a coin. You cannot have both at the same time.

On the other hand, independent occurrences are those that have no bearing on one another. For instance, if we flip a coin twice, receiving a head on one toss and a head on the other are separate occurrences. The result of the first toss has no bearing on the result of the second toss.

The probability of choosing either "w" or "G" is 3/12.

The probability of choosing "w" or "G" can be calculated as:

P(w or G) = P(w) + P(G) - P(w and G)

The probability of choosing "w" is 2/12.

The probability of choosing "G" is also 2/12.

The probability of choosing both "w" and "G" when the appear together is 1/12.

Substituting the values:

P(w or G) = P(w) + P(G) - P(w and G)

P(w or G) = 2/12 + 2/12 - 1/12

P(w or G) = 3/12

Hence, the probability of choosing either "w" or "G" is 3/12.

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There are 1089 in² in a square 11 yards on a side.

A square which is 11 yards on a side is 11 x 11 = 121 square yards. To convert square yards to square inches, multiply by the conversion factor of 9 square inches per square yard: 121 square yards x 9 square inches/square yard = 1089 square inches.

The area of a square is given by: A = l

Where,

Multiplication refers to binary operations in which different numerical sets are established. In mathematics the process of multiplication is elementary in several operations, it is also accompanied by addition, subtraction and division. Multiplication is the opposite of division.

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For dy/dt = (1 + t^2)/ (3y - y^2), the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point if y ≠ 0 and y ≠ 3.

The hypotheses of Theorem 2.4.2 state that for the initial value problem

dy/dt = f(t, y), y(t₀) = y₀

to have a unique solution in some interval t₀ - h < t < t₀ + h within α < t < β, provided that:

f and its partial derivative with respect to y, ∂f/∂y, are continuous in a rectangle α < t < β, γ < y < δ that contains (t₀, y₀).

To determine if the hypotheses are satisfied for the given differential equation we need to check if f and ∂f/∂y are continuous in a rectangle that contains the initial point (t₀, y₀). If they are, then the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point.

dy/dt = (1 + t^2)/ (3y - y^2)

dy/ dt = (1 + t^2)/ y(3 - y)

So dy/dt is not continuous at y = 0 and y = 3.

So the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point if y ≠ 0 and y ≠ 3.

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Answer:

it's a function

Step-by-step explanation:

the rule is you can repeat y values but not x values

this would be graphed as a horizontal line, which is still a function.

Euclid made significant contributions to our understanding and practice of geometry by compiling and organizing the principles of the subject into a systematic and logical framework known as Euclidean geometry. His work, "Elements," became the cornerstone of mathematical education for over two thousand years, shaping the way we approach geometry.

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Researcher can use factor analysis to cluster such traits as being talkative, social, and adventurous with extroversion.

Given is that a researcher wants to cluster such traits as being talkative, social, and adventurous with extroversion.

Therefore, Researcher can use factor analysis to cluster such traits as being talkative, social, and adventurous with extroversion.

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Answer:

After 6 months, Casey would pay $360 to join either gym.

Step-by-step explanation:

At the first gym, the cost is $35 per month in addition to a $150 joining fee.  So, the equation based on 'x' number of months and a total cost of 'c' is:

c = 35x + 150

At the second gym, the cost is just $60 per month.  So, the equation based on 'x' number of months and a total cost of 'c' is:

c = 60x

Since you want to find the number of months 'x' it would take until Casey would pay the same amount to be a member of either gym, you can take the two equations and set them equal to each other:

35x + 150 = 60x

Subtract 35x from both sides: 35x - 35x + 150 = 60x - 35x or 150 = 25x

Divide both sides by 25: 150/25 = 25x/25 or x = 6

So, after 6 months, the cost would be same.  The find the cost, replace 'x' with 6 in one of the equations:  c = 60(6) = $360.

If he is planning on canceling in 5 months, the better option would be the second gym that costs $60 per month

I hope this helps!!!

The area enclosed by the curve r = 9 + 2cos(θ) is 45π square units.

To find the area enclosed by the curve r = 9 + 2cos(θ), we can use the formula for the area enclosed by a polar curve, which is given by:

A = (1/2) \(\int\limits^a_b\) r(θ)^2 dθ

where a and b are the values of θ that correspond to the starting and ending points of the area we want to calculate.

In this case, since the curve r = 9 + 2cos(θ) describes a closed loop, we can choose a range of θ that covers the entire loop, for example, [0, 2π]. Therefore, the area enclosed by the curve is

A = (1/2)\(\int\limits^{2\pi }_0\) (9 + 2cos(θ))^2 dθ

Expanding the square and using the trigonometric identity cos^2(θ) = (1/2)(1 + cos(2θ)), we get

A = (1/2) \(\int\limits^{2\pi }_0\) (81 + 36cos(θ) + 4cos^2(θ)) dθ

= (1/2) \(\int\limits^{2\pi }_0\) (81 + 36cos(θ) + 2 + 2cos(2θ)) dθ

= (1/2) (81(2π) + 36sin(θ)|[0,2π] + 2θ|0,2π + sin(2θ)|[0,2π])

= 45π square units

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The given question is incomplete, the complete question is:

Find the area enclosed by the curve r = 9 + 2cos(θ)

Answer:

11/5 = 11 ÷ 5

Step-by-step explanation:

11/5 is a fraction, and every fraction is just a division problem.

Answer:

11/5=11÷5.

You just take the numbers from the fraction and put them into a division equation.

Answer:

y = 3x + 4

Step-by-step explanation:

slope is 9/3 simplified to 3

y intercept is 4

Answer:

A

Step-by-step explanation:

The other values are lesser than 5.63

Answer:

5.658-A

Step-by-step explanation:

Therefore, the limit of the sequence as n approaches infinity is 0.

To find the limit of the sequence {-sin(n)/(6n)}, we can analyze the behavior of the sequence as n approaches infinity. As n gets larger and larger, the numerator, -sin(n), oscillates between -1 and 1. However, the denominator, 6n, grows without bound.

Since the numerator remains bounded while the denominator grows, the value of the sequence {-sin(n)/(6n)} becomes increasingly small as n approaches infinity.

Therefore, the limit of the sequence as n approaches infinity is 0.

So, the correct choice is:

B. The limit of the sequence is 0.

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The price of the watch before the discount is calculated to be £24.44.

As the total price of the watch and a pair of trainers is £53. 55 and the price of the trainer before the discount was £38, we first calculate the price of the trainers after the discount as follows;

discount on a pair of trainers = 15/100 × 38 =  £5.7

cost of trainers after discount =  £38 - 5.7 =  £32.3

Now the price of the watch after the discount can be calculated by subtraction as follows;

price of watch after discount = total price - price of trainers after discount

price of watch after discount =  £53. 55 - £32.3

price of watch after discount = £21.25

Now the price of the watch before the discount can be calculated as follows;

price of watch before discount = £21.25 × 15/100

price of watch before discount = £21.25 + £3.1875

price of watch before discount = £24.44

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Answer:

Step-by-step explanation:

All square angles are 90° exactly 90° so we can use that to your advantage. since "7x + 3" is one of the square's angles, that means 7x + 3 must equal 90°. (7x + 3)° = 90°.

7x + 3 = 90

7x = 90 - 3

7x = 87

7x/7 = 87/7

x = 87/7

Answer:

Therefore, the surface area of the pyramid is 168 m2.

Step-by-step explanation:

To calculate the surface area of the rectangular pyramid, we need to find the area of each face and add them together.

The area of the base is:

6 meters x 6 meters = 36 square meters

There are four triangular faces of the pyramid. To find the area of each triangular face, we need to first find the area of the base of the triangle (which is half of the base of the rectangular pyramid) and then multiply by the height of the triangle.

The area of the base of each triangular face is:

(1/2) x 6 meters = 3 meters

The area of each triangular face is:

3 meters x 11 meters = 33 square meters

The total surface area of the pyramid is:

36 square meters (area of the base) + 4 x 33 square meters (area of each triangular face) = 168 square meters

Here are threeo examples t support the answer:1. 6 < x < 10If we add -5 to both sides, we get: 1 < x - 5 < 5So, the sign between 6 and 10 remains the same.2. 6 > y > 10If we add -3 to both sides, we get: 3 > y - 3 > 7So, the sign between 6 and 10 remains the same.3. 6 ≤ z ≤ 10If we add -2 to both sides, we get: 4 ≤ z - 2 ≤ 8So, the sign between 6 and 10 remains the same.

When a negative number is added to both sides of an inequality, the sign between the original numbers will not change. This can be demonstrated with the following examples:

If we have the inequality 6 < x < 10 and we add -5 to both sides, we get 1 < x - 5 < 5. The sign between 6 and 10 remains the same.

If we have the inequality 6 > y > 10 and we add -3 to both sides, we get 3 > y - 3 > 7. Again, the sign between 6 and 10 remains the same.

If we have the inequality 6 ≤ z ≤ 10 and we add -2 to both sides, we get 4 ≤ z - 2 ≤ 8. Once again, the sign between 6 and 10 remains unchanged.

Therefore, adding a negative number to both sides of the inequality does not alter the sign between the given numbers.

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Answer: its the first 3 i think

Step-by-step explanation:

Answer:they are not congruent

Step-by-step explanation:

The population of bacteria 1 minute ago was 25 million.

If the population of bacteria is increasing at the rate of 100% every minute, this means that the population is doubling every minute. So, if the population is currently at 50 million, then 1 minute ago it was half that amount.

To find out the population of bacteria 1 minute ago, we can divide the current population by 2:

50 million / 2 = 25 million

This is because if the population is increasing at 100% every minute, this means that every minute the population is doubling. So, if the current population is 50 million, then it must have been half that amount 1 minute ago, since it would have only undergone one doubling period in that time.

It is important to note that this assumption of exponential growth may not hold true for all populations, and that there may be other factors that affect the growth rate of bacteria in real-world scenarios.

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Complete Question : in an experiment, the population of bacteria is increasing at the rate of 100 % every minute. the population is currently at 50 million. how much was the population of bacteria 1 minute ago?

Answer:

471

Step-by-step explanation:

741-270=471

Answer:

Their stomach is upset. they eat the grass to calm their stomach. Don't worry it is good if your dog eats grass because that helps the dog's health out. Grass gives them vitamins and nutrients that helps their bowel system. seriously let you dog eat the grass, they will be okay. my four dogs do it as well and they feel better after. hope this helps

Answer:

\(\huge\boxed{\sf Star = 14}\)

Step-by-step explanation:

Let snowman be x , star be y and shopping bag be z.

So, the given equations are:

1) x + y = 20                 (Eq. 1)

2) z = x + x      

 z = 2x                         (Eq. 2)

3) z + x = 18                   (Eq. 3)

Put Eq. (2) in Eq. (3)

2x + x = 18

3x = 18

Divide both sides by 3

x = 18 / 3

x = snowman = 6

Now, Put x in (Eq. 1)

6 + y = 20

Subtract 6 to both sides

y = 20 - 6

y = 14

So,

Star = 14

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

nbsb.......uehsnsnsk:(bahs

Answer:

the y value is 83.99 dollars

Step-by-step explanation:

y=34.99x+49

x=1

y= (34.99*1) +49

y=34.99+49

y= 83.99

Answer:

-12  ??

Step-by-step explanation:

12-5x2+6-4x2

12-10+6-8

12-16-8

-12

Not really sure if that is correct, since the symbols look a little confusing with my glasses but ya.

Also, just in case yall forget:

P - parenthesis

E - exponents

M- multiply

D - divide

A - add

S - subtract