You and Chantal are in charge of designing a zip line.

There are two trees, both about 40 feet high and 130 feet apart.
There needs to be a 5% slack and follow the rule of 6-8 feet of horizontal change per 100 feet of vertical change. How long should the zip line be?

Please help me out with this…I’m totally stumped. Thank you!!

Answer:

(30-5n)

Step-by-step explanation:

The given sequence is :

25,20,15,10,5

Here,

First term, a = 25

Common difference = 20-25 = -5

We need to find the nth term of the given sequence. The formula for the nth term is given by :

\(a_n=a+(n-1)d\\\\a_n=25+(n-1)(-5)\\\\=25-5n+5\\\\=30-5n\)

So, the nth term of the above sequence is (30-5n).

Answer:

(A) No

(B) Yes

Step-by-step explanation:

(A) Using centimeters for example, it is not possible to create a closed or full triangle with side lengths 1cm, 5cm and 3cm. [See attachment for illustration]

(B) It is possible to create a triangle of side lengths 3cm, 4cm and 5cm. [See attachment also]

The Pythagoras Rule also applies in this case.

The sum of the squares of the lengths of the 2 shorter sides (the opposite side and the adjacent side) is equal to the square of the longest side (the hypotenuse).

(3×3) + (4×4) = (5×5)

9 + 16 = 25

Answer:

1) No

2) Yes

3) No

4) Yes

5) Yes

Step-by-step explanation:

edge 2020:)

All correct

The description corresponds to an observational study, which involves gathering data and information to draw conclusions without intervening in the process. Correct answer: letter D.

An experiment would involve manipulating the variables to see the effect of the manipulation. In this case, it would involve changing the caffeine consumption and observing the effect on heart arrhythmias.

In order to better understand the relationship between heart arrhythmias and caffeine consumption, researchers need to consider a variety of factors, including the amount of caffeine consumed, the timing of consumption, and any potential underlying medical conditions that could be influencing the results.

Furthermore, researchers need to ensure that the study population is large enough and diverse enough to accurately reflect the general population. Additionally, researchers need to consider potential confounding variables, such as lifestyle factors, medications, and other dietary components that could be influencing the results.

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Answer:

Step-by-step explanation:

80 / 12 = 6 2/3, so a twelfth of 80 is 6 2/3.

Cement:

6 2/3 * 1 = 6 2/3

Sand:

6 2/3 * 3 = 18 6/3 = 20

Gravel:

6 2/3 * 4 = 24 8/3 = 26 2/3

Answer:

Yep......a lot of notifications on my phone.....lol

thx for points!

Follow me! :)

Answer:

35.71%

Step-by-step explanation:

50:140*100 =

(50*100):140 =

5000:140 = 35.71

Yes , there can be a Right triangle with two side lengths as simple fraction and other side length as an integer .

In the question ,

we have to find , whether a Right Triangle can be made by two fractions and an integer length .

yes, we can make a Right Triangle with two lengths as fractions and other length as integer .

let us prove it with the help of an example .

Consider the triplet 7 , 24 , 25 .

let the two fractions side be 7/25 and 24/25 , and the hypotnuse of the right triangle be  1 .

We know that for the Right Triangle

(side1)² + (side2)² = hypotnuse²

(7/25)² + (24/25)² = 1²

49/625 + 576/625 = 1

(49+576) / 625 =1

625/625 = 1

1 = 1

hence ,it is a Right Triangle .

Therefore , Yes , there can be a Right triangle with two side lengths as simple fraction s and other side length as an integer .

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Answer:

10.3

Step-by-step explanation:

First, turn 5 1/2 to a decimal, and that is 5.5. Next subtract 15.8 to 5.5, and that is 10.3.

SAS Is the reason why these triangles are similar. If they are not, select "Not similar".

SAS (Side-Angle-Side) is a theorem in geometry that states that if two sides and the included angle of one triangle are equal to two sides and the included angle of a second triangle, then the two triangles are congruent. It is commonly used to prove the equality of two triangles and is one of the five postulates of Euclidean geometry.

The two triangles are similar because they both have two equal angles of 60°. This is known as the Side-Angle-Side (SAS) similarity criterion, which states that two triangles are similar if two angles of one triangle are equal to two angles of the other triangle and the sides including those angles are proportional.

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Answer:

some

some

some

some

no

Step-by-step explanation:

Answer:

1) no triangles

2)some triangles

3)no triangles

4)no triangles

5)all triangles

Step-by-step explanation:

i think that is right not sure tho

The image after the dilation is A' (-2,2) and (4,4)

Here, we have a pre-image with the endpoints A(-4,4) and B(8,8) and we want to find the image after dilation using the scale factor

To find its image after a dilation, we simply multiply the scale factor with each number on the coordinate

Thus, we have

A' as (-2,2) and B' as (4,4)

To plot the image, we can locate these coordinates and join them together and label them as A' and B'

\(x = 80\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\((x - 8)2 = 144 \\ ⇢ 2x - 16 = 144 \\ ⇢ 2x = 144 + 16 \\ ⇢ 2x = 160 \\ ⇢ x = \frac{160}{2} \\ ⇢ x = 80\)

\(\large\mathfrak{{\pmb{\underline{\orange{To\:verify }}{\orange{:}}}}}\)

\(2x - 16 = 144 \\ ➵ \: 2 \times 80 - 16 = 144 \\ ➵ \: 160 - 16 = 144 \\ ➵ \: 144 = 144 \\ ➵ \: L.H.S.=R. H. S\)

Hence verified.

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

9514 1404 393

Answer:

  sin(Z) = 3/5

  cos(Z) = 4/5

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you how to do this.

  Sin = Opposite/Hypotenuse

  sin(Z) = XY/XZ = 9/15

  sin(Z) = 3/5 . . . . . reduced fraction

__

  Cos = Adjacent/Hypotenuse

  cos(Z) = YZ/XZ = 12/15

  cos(Z) = 4/5 . . . . . reduced fraction

The number of times a 4 and an odd number are likely to be rolled will be 2. Then the correct option is A.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

Two fair six-sided number shapes, both numbered 1 through 6, are moved together multiple times.

The probability of getting 4 and an odd number will be given as,

p = 1/6 x 3/6

p = 3/36

p = 1/12

Then the expected value is calculated as,

E = 1/12 x 24

E = 2

The times a 4 and an odd number are probably going to be moved will be 2. Then the right choice is A.

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The statement that best explains whether or not a calculator is the most efficient way to simplify (0.68 – 0.38 – 0.2) × 2.3 is A. Multiplying the amount in the parentheses by 2.3 will be a time-consuming process, so using a calculator would most likely be more efficient.

In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product. In the multiplication problem 6 9 = 54, the numbers 6 and 9 are factors, and 54 is the product.

A product is the outcome of multiplication, or an expression that identifies the objects to be multiplied, known as factors.

Therefore, option A is the correct option as using the calculator is easier.

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Answer: Relation

Step-by-step explanation:

The graph fails the vertical line test.

Answer:

287

the original number is 286.526166

but i dk which way you want to round, so round whatever way you want to :)

Step-by-step explanation:

just ask

Answer:

It should cost you 5$

Step-by-step explanation:

10$ = 4 cans of soda

If we take half of 4 which equals 2

You should also take half of of 10$ which is 5$

So, 2 Cans= 5$

Answer:

A: 5

Step-by-step explanation:

So if a 4 pack is worth $10, then if you divide 4 in half to get 2, you also have to divide the $10 by 2. Then you have your answer! Good luck in your math career!

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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$1.50

I hope this helps!

Converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters. By definition conversion of units means the conversion between different units and measurements of the same quantity done by the process of multiplication or division. In maths, conversion is the process of changing the value of one form to another for example inches to millimeters, or liters to gallons. Units are used for measuring length, measuring weight, measuring capacity, measuring temperature, and measuring speed.

If we want to calculate how many Grams are 1000 Milligrams we have to multiply 1000 by 1 and divide the product by 1000. So for 1000, we have (1000 × 1) ÷ 1000 = 1000 ÷ 1000 = 1 Gram.

So finally 1000 mg = 1 g

Thus, converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.

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The measure of angle EDF is 140°, and the measure of angle HDE is 160°.

Given the parallel lines DF || EH, DR || ZEG, and alternate interior angles, we can determine some of the missing angles as explained below:When two parallel lines are intersected by a transversal line, they form eight angles, four on the top and four on the bottom. The four on top are the exterior angles, and the four on the bottom are the interior angles. Interior angles have two types; Alternate Interior Angles and Corresponding Angles.Alternate Interior Angles are opposite angles on opposite sides of the transversal, but on the inside of the parallel lines. They are equal in measure, as long as the parallel lines are cut by a transversal.

The alternate interior angles for the two parallel lines DF || EH and DR || ZEG are as shown in the diagram below:Parallel linesDF || EH and DR || ZEGAlternate interior anglesAs we can see in the diagram above, the alternate interior angles are congruent. Therefore, we can find the missing angle values by applying the alternate interior angles property. Let us consider the triangles below:triangleDEG and triangleDFHAngle EDF is the exterior angle of triangleDEG,Angle HDE is the exterior angle of triangleDFHBy applying the Exterior Angle Theorem, we know that the measure of an exterior angle of a triangle is equal to the sum of its remote interior angles.

in triangleDEG:Angle EDF = Angle EGD + Angle GDEAngle EDF = 80 + 60Angle EDF = 140°In triangleDFH:Angle HDE = Angle DHF + Angle DAFAngle HDE = 120 + 40Angle HDE = 160°

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The percentage of the sheets with no air bubbles is given as follows:

13.53%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are listed and explained as follows:

The mean for this problem is given as follows:

\(\mu = 2\)

The proportion of these sheets with no air bubbles is P(X = 0), hence it is given as follows:

P(X = 0) = e^-2 = 0.1353 = 13.53%.

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There is sufficient evidence for significance level 10%  to conclude students with study skills course have higher exam scores using hypothesis test.

To conduct a hypothesis test,

set up the null and alternative hypotheses and perform the necessary calculations.

Null Hypothesis (H₀),

The study skills course did not have a significant effect on the mean final exam scores. µ = 77.6.

Alternative Hypothesis (Hₐ),

The study skills course had a significant effect on the mean final exam scores. µ > 77.6.

To test this hypothesis, use a one-sample t-test since we have a sample mean and population standard deviation.

Sample mean (X) = 79.5

Population mean (µ) = 77.6

Population standard deviation (σ) = 7.2

Sample size (n) = 36

Significance level (α) = 0.10 (10%)

First, let's calculate the test statistic (t-value),

t

= (X - µ) / (σ / √n)

= (79.5 - 77.6) / (7.2 / √36)

= 1.9 / (7.2 / 6)

= 1.9 / 1

= 1.9

Next, determine the critical t-value from the t-distribution calculator.

Since the alternative hypothesis is one-sided (µ > 77.6), interested in the upper tail of the distribution.

At a significance level of 0.10 with 35 degrees of freedom (n - 1 = 36 - 1 = 35), the critical t-value is approximately 1.310.

Since the calculated t-value (1.9) is greater than the critical t-value (1.310), we have evidence to reject the null hypothesis.

Therefore, using hypothesis test there is sufficient evidence at 10% significance level to conclude that students who took study skills course had higher exam scores.

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The total number of permutations of the three tasks: 336 x 3! (3 factorial) = 40320

This question uses the combination and permutation theory. Combinations are used to calculate the total number of ways to assign the three tasks to the 8 people, and permutations are used to multiply the total number of ways to assign the three tasks by the total number of permutations of the three tasks.

given below :

1. Calculate the total number of ways to assign the three tasks to the 8 people: 8 x 7 x 6 = 336

2. Multiply the total number of ways to assign the three tasks by the total number of permutations of the three tasks: 336 x 3! (3 factorial) = 40320

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The domain and range of a given relation, we need to understand the nature of the relation and the restrictions it imposes on the variables involved.

Since you haven't provided a specific relation, I'll explain the general concepts of domain and range.

The domain of a relation refers to the set of all possible input values, or the values for which the relation is defined.

It represents the x-values that can be plugged into the relation to obtain a meaningful output.

The domain can be restricted due to various reasons, such as the presence of square roots, division by zero, or logarithms.

The range of a relation, on the other hand, refers to the set of all possible output values.

It represents the y-values that the relation can produce when given valid input values from the domain.

To determine the domain and range of a specific relation, you need to analyze the given relation for any restrictions on the variables involved.

If the relation contains a square root, the expression within the square root must be non-negative to avoid complex or imaginary numbers.

If there is a denominator, it should not be zero.

Without the specific relation, it's not possible to provide a detailed analysis.

Explanation helps you understand the general concept of domain and range.

If you provide the specific relation, I'll be glad to help you determine its domain and range.

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The domain of a relation is the set of all possible input values, or the x-values, of the ordered pairs. The range of a relation is the set of all possible output values, or the y-values, of the ordered pairs.

To find the domain and range of a given relation, we need to examine the x-values and y-values of the ordered pairs in the relation.

Let's consider the given relation:

First, we look at the x-values of the ordered pairs. The set of all x-values is the domain of the relation.

Next, we look at the y-values of the ordered pairs. The set of all y-values is the range of the relation.

By analyzing the given relation, we can determine the domain and range.

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The value of x in the triangle UVW is 45°.

A polygon which has three sides and three vertices is called as triangle.

The sum of all the angles of the triangle is 180°.

Given:

The measures of the angle of the triangle UVW are 24°, 30° and (3x - 9)°.

The sum of all the angles of the triangle is 180°.

24° + 30° + (3x - 9)° = 180°.

3x - 9 = 180 - 54

3x = 135

x = 45.

Therefore, the value of x is 45°.

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