Instructions:
• View the video found on page 1 of this journal activity.
. Using the information provided in the video, answer the questions below.
. Show your work for all calculations.
The Student's Conjecture: What are you trying to determine? (1 point)
Conjecture

Since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

Similar triangles are triangles with corresponding sides that have the same ratio.

Thus:

AD is parallel to BC (bases of a trapezoid are parallel)

Therefore:

∠ACB = ∠CAD (alternate interior angles)

This implies that, ΔABC ~ ΔACD by AA similarity theorem.

Thus:

AC/DA = CB/AC

Substitute

AC² = 12 × 27

AC = √324

AC = 18 m

Therefore, since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

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14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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Step-by-step explanation:

The way you can think about volume is that we have some cross sectional area times the height of the solid.

27.

The volume of a square based pyramid is

\(v = {s}^{2} ( \frac{h}{3} )\)

where h is the height of the pyramid

s is the side length of the square base.

S=7

h=12

\(v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196\)

28. The volume of a rectangular prism

\(v = l \times w \times h\)

where l is length

w is width

h is height

\(v = 11 \times 11 \times 8 = 968\)

29.

Use the same formula in 27

\(v = 100(3) = 300\)

30.

Volume of a Cylinder is

\(v = \pi {r}^{2} h\)

where r is the radius of the circle

where h is the height

r is half of the diameter

The diameter is 22, thus the radius is 11.

\(v = {11}^{2} (8)(\pi)\)

\(v = 968\pi\)

pi is approximately 3.14

\(v = 3041.06\)

31. Volume of A Sphere

\( \frac{4}{3} \pi {r}^{3} = v\)

The radius is half of diamter, thus r=7

\( \frac{4}{3} \pi( {7}^{3} ) = 1436.76\)

Answer:

188

Step-by-step explanation:

Ive attached my work

Hope it helps, Let me know if you have any questions !

Answer: I don't think so

Step-by-step explanation:

Answer:

3 dollars

Step-by-step explanation:

Khan academy said so

We can claim that after answering the above question, the So, logarithm \(log4 (0.5^(1/2)) =-0.0752\)

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

Using the following property of logarithms:

\(log_a (b^c) = c * log_a (b)\\log4 (0.5^(1/2))\\(1/2) * log4 (0.5)\\log4 (0.5) = log (0.5) / log (4)\\log (0.5) ≈ -0.3010\\log (4) = 2\)

Therefore,

\(log4 (0.5) ≈ -0.3010 / 2 ≈ -0.1505\\(1/2) * log4 (0.5) ≈ (1/2) * (-0.1505) ≈ -0.0752\\\)

So, \(log4 (0.5^(1/2)) =-0.0752\)

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The copy machine make 44 copies per minute.

The unitary method is the method of solving a problem by the first value of a single unit and than finding the value of single unit by multiplying. Unitary method is a technique by which we can find the value of a single unit from the value of multiple data and also the value of more than one unit from the value of single unit. This is a method that we use for most of the calculations in mathematics;

We are given that Time copy machine take= 4min 15sec

Number of copies=187

Now, 1min=60sec

4min=240sec

Total time=240+15 =255sec

Therefore, 255sec=187copies

60sec= 187 x 60/255

=44

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The probability that their mean length is less than 17.4 inches is 28.26%

Given :

A manufacturer knows that their items have a normally distributed length, with a mean of 19.7 inches, and standard deviation of 4 inches , If 25 items are chosen at random .

z = ( X - μ ) / σ, where X = date , μ = mean , σ = standard deviation .

substitute the values

z = 17.4 - 19.7 / 4

= -2.3 / 4

= -0.575

P - value at z = -0.575 is 0.2826

Converting into percentage :

= 0.2826 * 100%

= 28.26 %

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In order to show that △ ABC ≅ △ DEF by SAS congruence, we need the sides of triangles ABC and DEF with the angle between the respective sides.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "" is the congruence symbol. When two figures are comparable to one another in terms of their size and shape, this is what mathematicians mean by congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables.

Congruency Requirements:

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

RHS (Right angle-Hypotenuse-Side) 

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Answer:

first term is 3.................

Answer:

17

Step-by-step explanation:

We will use angle A as theta in our trigonometric function equation.

We are dealing with hypotenuse and opposite, so the trig ratio is sine.

\(sin(39) = x/27\)

\(27sin(39)=x\)

\(27(0.6293) = x\)

\(x=16.992\)

When rounded to the nearest tenth, \(x=17\)

Answer:

x =79.6

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hypotenuse

sin 31 = 41/ x

x = 41/ sin 31

x = 79.60576508

To the nearest tenth

x =79.6

Heracio used the computer 4 more hours to do homework than shop online.

To find out how many more hours Heracio used the computer to do homework than shop online, we first need to calculate the number of hours he spent on each activity.

Let's start by calculating the number of hours Heracio spent on each activity:

Shopping: 10% of 40 hours = 4 hours

Videos: 15% of 40 hours = 6 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Now, to find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 4 hours (shopping) = 4 hours

Therefore, Heracio used the computer 4 more hours to do homework than shop online.

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Answer: B- Mutual Savings Bank

Step-by-step explanation:

Answer: If you divide a trinomial by a monomial the result is a bionomial

A. True

B. False

Step-by-step explanation: tell me the correct answer and I'll tell you

Answer:

The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).

Example

Find the distance between (-1, 1) and (3, 4).

This problem is solved simply by plugging our x- and y-values into the distance formula:

Sometimes you need to find the point that is exactly between two other points. This middle point is called the "midpoint". By definition, a midpoint of a line segment is the point on that line segment that divides the segment in two congruent segments.

If the end points of a line segment is (x1, y1) and (x2, y2) then the midpoint of the line segment has the coordinates: HOPES THIS HELPS

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

4*2*3 for the 4 flaps

2*4*3 for the 2 tops

(4*2*3) + (2*4*3) = 48

Answer:

52 square inches

Step-by-step explanation:

to find the surface area of a rectangular prism the formula is

S.A.=2(l*w+l*h+w*h)

2(4*3+4*2+3*2)

=52 square inches

here l is length w is width and h is height

Answer:

1/16

Step-by-step explanation:

you have a 1/2 chance to get the answer right. Each time you add a new answer, you multiply the current chance by the chance of getting the new answer correct. So, the chance of getting 4 answers correct is 1/2^4, or 1/16

It is recommended that you visit your courses on D2L frequently, ideally at least once a day, to stay up-to-date with any new announcements or assignments posted by your instructor. This will help you stay on track with your coursework and prevent you from falling behind. Additionally, regular visits to your courses can help you participate in discussions with your peers and ask questions if you are unsure about any of the material. It's important to remember that online learning requires a high level of self-discipline and responsibility, so making a habit of checking in on your courses regularly can contribute to your overall success in the class.

Answer:

The new standard deviation will be greater than $26

Step-by-step explanation:

The new bicycle has a price much larger than the price of the others. In fact it is almost double the price of the other bicycles. It causes a large increase as a result. Also, I took the quiz.

Answer:

10 calories per minute

Step-by-step explanation:

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

10. im adding this last part because it needs 20 letters k bye

Step-by-step explanation:

la respuesta está en la imagen de arriba



Answer:

Not independent

Step-by-step explanation:

Given

See attachment for two way table

Required

Are male and favor independent?

From the table, we have:

\(Male = 20+15+17\)

\(Male = 52\)

\(Favor = 20 + 18\)

\(Favor = 38\)

\(Total = 20+15+17+18+12+7\)

\(Total = 89\)

Calculate P(Male)

\(P(Male) = \frac{Male}{Total}\)

\(P(Male) = \frac{52}{89}\)

Calculate P(Favor)

\(P(Favor) = \frac{Favor}{Total}\)

\(P(Favor) = \frac{38}{89}\)

Calculate P(Male and Favor)

\(P(Male\ and\ Favor) = \frac{Male\ and\ Favor}{Total}\)

\(P(Male\ and\ Favor) = \frac{20}{89}\)

\(P(Male\ and\ Favor) = 0.2247\)

The events are independent is:

\(P(Male\ and\ Favor) =P(Male) * P(Favor)\)

So, we have:

\(P(Male\ and\ Favor) =\frac{52}{89} * \frac{38}{89}\)

\(P(Male\ and\ Favor) =\frac{52*38}{89*89}\)

\(P(Male\ and\ Favor) =\frac{1976}{7921}\)

\(P(Male\ and\ Favor) =0.2495\)

By comparison:

\(P(Male\ and\ Favor) =0.2495\) and \(P(Male\ and\ Favor) = 0.2247\) are not equal

Hence, the events are not independent

Answer:

42

Step-by-step explanation:

in a parallelogram, opposite sides have equal lengths.

FM=HJ=42

Answer:

6.0

6.25

0.123

59

Step-by-step explanation:

replace the formula with numbers

Julian uses ordered pairs to record the temperature variations over time during a chemistry experiment (time in minutes, temperature in °C). (0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100) (25, 100).

It is the cause that is the independent variable. Its worth is unrelated to other study variables. The effect serves as the dependent variable. The independent variable's modifications determine its value. It is a thing that is dependent on other things. The amount of study you did, how much sleep you had the night before the test, or even how hungry you were when you took it.

Could all affect your test result, which makes it a dependent variable. The dependent variable is impacted by the independent variable. For instance, your exam results are influenced by how much sleep you get (an independent variable) (dependent variable). This is understandable, but Ex. How much sleep you get depends on your test results.

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Answer: Let's call the angles of the parallelogram A and B.

From the given information, we know that the diagonal of the parallelogram forms 25° and 35° angles with the sides of the parallelogram.

Using the fact that the opposite angles of a parallelogram are equal, we can say that angles A and B are also 25° and 35°, respectively.

So the angles of the parallelogram are 25° and 35°.

Step-by-step explanation: