I really need help understanding when/ what situations to use sine rule and cosine rule with triangles, plssss.
thank you :)))​

Answer:

x=6

Step-by-step explanation:

Since AD and BC are parallel lines:

Steps 1, 2, 3, and 4 are distributive prοperties, subtractiοn, additiοn, and divisiοn respectively.

The prοcess in mathematics tο οperate and interpret the functiοn tο make the functiοn οr expressiοn simple οr mοre understandable is called simplifying and the prοcess is called simplificatiοn.

Here,

-2(5x + 8) = 14 + 6x

Step 1  

-10x -16 = 14 + 6x

distributive prοperty

distribute -2 in the parenthesis tο 5x and 8

Step 2

-16x - 16 = 14

subtractiοn

subtractiοn οf -6x

Step 3

-16x = 30

Additiοn οf 16

Step 4

x = -30/16

divisiοn οf -16

x = -15 / 8

Thus, Steps 1, 2, 3, and 4 are distributive prοperties, subtractiοn, additiοn, and divisiοn respectively.

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

After 1 year = $2548

Step-by-step explanation:

The null hypothesis is that there is no significant difference between the mean blood pressure of rats with high capacity for exercise and rats with low capacity for exercise. The alternative hypothesis is that rats with low capacity for exercise tend to have a higher blood pressure than rats with high capacity for exercise.

This is the preferred alternative hypothesis for this kind of test because it is a one-tailed test with a directional hypothesis, indicating that we are specifically interested in whether the mean blood pressure of low-capacity rats is higher than that of high-capacity rats.

Therefore, the null hypothesis can be written as H0: μhc = μlc, and the alternative hypothesis can be written as Ha: μlc > μhc.

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The amount of candle burn after 6 hours is 4.95 inches.

What is the total amount?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total.

Here, we have

Given that the 9-inch candle burns in 6 hours.

We know that we first have to calculate how 1 hour how much candles will burn.

Candle burn in 1 hour is :

= 9 / 10

= 0.9 inch

Now,

To find out how far the candle burnt after 6 hours we need to multiply the part of the candle burned by one hour by 11/2 hours.

= 11/2 × 0.9

= 4.95 inches

Hence, the amount of candle burn after 6 hours is 4.95 inches.

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The probability of event A and event B is 6.

Given that, P(A)=6, P(B)=20 and P(A∩B)=6.

P(A/B) Formula is given as, P(A/B) = P(A∩B) / P(B), where, P(A) is probability of event A happening, P(B) is the probability of event B.

P(A/B) = P(A∩B) / P(B) = 6/20 = 3/10

We know that, P(A and B)=P(A/B)×P(B)

= 3/10 × 20

= 3×2

= 6

Therefore, the probability of event A and event B is 6.

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Answer:

Step-by-step explanation:

D

Answer:

Measure the time it takes for the dog to run a certain distance.

Speed= Distance/Time taken

Step-by-step explanation:

(a)  The cumulative distribution function F(t) = 0 for t<0, F(t) = t/a for 0<=t<=a, and F(t) = 1 for t>a.

(b)  The reliability function R(t) = 1 for t<0, R(t) = 1-t/a for 0<=t<=a, and R(t) = 0 for t>a.

(c) The hazard rate h(t) = 1/t for 0<t<=a, and the failure rate is decreasing.

(d)  The mean time to failure MTTF = a/2 and tmedian = a/2.

(e) p(T > a) = 0 and the uniform distribution does not have the memoryless property.

(a) The cumulative distribution function (CDF) for a uniform distribution over (0,a] is given by:

F(t) = P(T ≤ t) =

{ 0 if t < 0,

{ t/a if 0 ≤ t ≤ a,

{ 1 if t > a.

(b) The reliability function is defined as R(t) = 1 - F(t).

Therefore, for the uniform distribution over (0,a], we have:

R(t) =

{ 1 if t < 0,

{ 1 - t/a if 0 ≤ t ≤ a,

{ 0 if t > a.

(c) The hazard rate h(t) is defined as the instantaneous rate of failure at time t, given that the system has survived up to time t.

It is given by:

h(t) = f(t) / R(t),

where f(t) is the probability density function (PDF) of the distribution.

For the uniform distribution over (0,a], the PDF is constant over the interval (0,a], and zero elsewhere:

f(t) =

{ 1/a if 0 < t ≤ a,

{ 0 otherwise.

Therefore, we have:

h(t) =

{ 1/t if 0 < t ≤ a,

{ undefined if t ≤ 0 or t > a.

Since the hazard rate is decreasing with time, the failure rate is also decreasing.

This means that the system is more likely to fail early on than later on.

(d) The mean time to failure (MTTF) is given by:

MTTF = ∫₀ᵃ t f(t) dt = ∫₀ᵃ t/a dt = a/2.

The median time to failure (tmedian) is the time t such that F(t) = 0.5. Since F(t) is a linear function over the interval (0,a], we have:

tmedian = a/2.

(e) The probability that T > a is zero, since the uniform distribution is defined over the interval (0,a]. Therefore, p(T > a) = 0.

The uniform distribution does not have the memoryless property, which states that the probability of failure in the next time interval depends only on the length of the interval and not on how long the system has already been operating.

The uniform distribution is not memoryless because as time passes, the probability of failure increases, unlike in a memoryless distribution where the probability of failure remains constant over time.

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Answer:

\(x = y + 7 \\ \\ x = \frac{3 + y}{2} \: or \: y = 2x - 3\)

Step-by-step explanation:

\(1. \: 2x = 3 + y \\ 2. \: x = \frac{3 + y}{2} \: or \: y = 2x - 3 \\ \\ 1. \: y + 7 = x \\ 2. \: x = y + 7\)

Answer:

Bro this some alien hyroglyphics

Step-by-step explanation:

Answer:

m = - 27

Step-by-step explanation:

Given

3(m - 5) + 11 = - 85 ← distribute and simplify left side

3m - 15 + 11 = - 85

3m - 4 = - 85 ( add 4 to both sides )

3m = - 81 ( divide both sides by 3 )

m = - 27

The answer to all of them is in the picture. Let me know if you have any other question.

The probability that the student will fail, given that he guesses the answers, is 0.227.

Since there are only two possible outcomes for each question (true or false),

the probability of guessing a correct answer is 1/2 = 0.5.

Likewise, the probability of guessing a wrong answer is also 1/2 = 0.5.

To find the probability of failing the exam,

we need to find the probability of answering less than 11 questions correctly.

Using the binomial probability formula,

the probability of getting k successes (correct answers) in n trials (questions) is given by:

P(k) = (n C k) * p^k * q^(n-k)

where p is the probability of success (getting a correct answer),

q is the probability of failure (getting a wrong answer), and (n C k) is the number of combinations of n things taken k at a time.

In this case,

n = 17, p = 0.5, and

q = 0.5.

The number of ways to get less than 11 correct answers is:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)P(X = k) = (n C k) * p^k * q^(n-k)

Substituting the values:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)

P(X = 0) = (17 C 0) * (0.5)^0 * (0.5)^17 = 0.0015

P(X = 1) = (17 C 1) * (0.5)^1 * (0.5)^16 = 0.0146

P(X = 2) = (17 C 2) * (0.5)^2 * (0.5)^15 = 0.0586

P(X = 3) = (17 C 3) * (0.5)^3 * (0.5)^14 = 0.1558

P(X = 4) = (17 C 4) * (0.5)^4 * (0.5)^13 = 0.268

P(X = 5) = (17 C 5) * (0.5)^5 * (0.5)^12 = 0.327

P(X = 6) = (17 C 6) * (0.5)^6 * (0.5)^11 = 0.2732

P(X = 7) = (17 C 7) * (0.5)^7 * (0.5)^10 = 0.1537

P(X = 8) = (17 C 8) * (0.5)^8 * (0.5)^9 = 0.0573

P(X = 9) = (17 C 9) * (0.5)^9 * (0.5)^8 = 0.013

P(X = 10) = (17 C 10) * (0.5)^10 * (0.5)^7 = 0.0015

Therefore, P(X < 11) = 0.0015 + 0.0146 + 0.0586 + 0.1558 + 0.268 + 0.327 + 0.2732 + 0.1537 + 0.0573 + 0.013 + 0.0015P(X < 11) = 0.8857

Thus, the probability of failing is: P(fail) = P(X < 11) = 0.8857

The probability that the student will fail, given that he guesses the answers, is 0.227 (rounded to three decimal places).

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Answer

3π is the answer here is the steps I couldn't write it I'm busy so I just wanted to help I hope it helps

Answer:

difference between ratio and proportion.

Based on the line of best fit, the approximate maximum depth of a lake that has 31 miles of shoreline is; 142.968 ft

The line of best fit is defined as a straight line which is drawn to pass through a set of plotted data points to give the best and most approximate relationship that exists between such data points.

Now, we are given a table of values that shows the total shoreline in miles which will be represented on the x-axis and then the maximum depth of several area lakes which will be represented on the y-axis.

However, when the geologist found the graph, she arrived at an equation of best fit as;

y = 4.26x + 10.908.

Thus, for 31 miles of shoreline, the approximate maximum depth is;

Approximate maximum depth = 4.26(31) + 10.908.

Approximate maximum depth = 142.968 ft

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Answer:

143 feet

Step-by-step explanation:

its technically 142 and change but edmentum rounds up

Answer:

D

Step-by-step explanation:

Answer:

8.246 units long

2sqrt(17) units long in simplest radical form

Step-by-step explanation:

Use the Pythagorean Theorem to find the missing leg length:

a^2+b^2=c^2

4^2+b^2=sqrt(84)^2

16+b^2=84

b^2=68

b=sqrt(68)

b=2sqrt(17) <-- Simplest Radical Form

b=8.246

So the third side is approximately 8.246 units long

Answer:

480 in 5hrs

Rate is 96 per hour

Step-by-step explanation:

In 5 hours there are 300 minutes (5x60) and 300min/25min = 12. So 25 mins pass 12 times in 5 hours. Since each 25 mins its 40 ppl then 12x40 = 480.

480 in 5 hours so 480/5= 96 per hour

If the mean value of the data set is 509. Then the mean absolute deviation (MAD) for the data set will be 51.5.

It is the average distance between each data point and the mean.

The mean of the following data is 509.

{419, 450, 462, 499, 520, 521, 589, 612}

Then the mean absolute deviation (MAD) for the data set will be

\(\rm MAD =\dfrac{1}{n}\sum_{i=1}^{n}\left|x_i - \mu \right|\)

We have

μ = 509

n = 8

Then

\(\rm MAD =\dfrac{1}{8} \times (|419 - 509| + |450- 509| + ..... + |612 - 509|) \\\\MAD = 51.5\)

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Step-by-step explanation:

y = 3x

________

x y

-4 -12

-2 -6

0 0

2 6

4 12

________

Find some coordinates

Graph attached

To find the rectangular coordinates of a point whose cylindrical coordinates are given, we can use the following equations:

x = rcosθ

y = rsinθ

z = z

For part (a), where the cylindrical coordinates are (2, 6, 2), the rectangular coordinates are:

x = (2)cos(6) = -1.56

y = (2)sin(6) = 1.25

z = 2

Therefore, the rectangular coordinates of the point in part (a) are (-1.56, 1.25, 2).

For part (b), where the cylindrical coordinates are (4, -3, 2), the rectangular coordinates are:

x = (4)cos(-3) = -4.32

y = (4)sin(-3) = -3.14

z = 2

Therefore, the rectangular coordinates of the point in part (b) are (-4.32, -3.14, 2).

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Answer:

B

Step-by-step explanation:

\(\sqrt{9}\) = 3

3\(\pi\) = 9.42477

-2.4 = -2.4

-5 = -5

20% = 0.20

Answer:

y = 1/2x+2

Step-by-step explanation:

first find x intercepts : to find x intercept put 0 in y

1/2x+2 = 0

1/2x= -2

x = -4 the graph shows x intercept at 4

next find y intercept : to find y intercept put 0 into x

=1/2*0+2

=2

the graph shows y crosses at 2.

Answer:

y = 1/2x+2

The station of Point of Curvature (PC) is 319+50.

A horizontal curve on a 4-lane highway (i.e., 2-lanes in each direction) has a superelevation of 6% and central angle of 40 degrees. The pt and pi are located at stations 322 50 and 320 08, respectively. The roadway has 10 feet lanes and 8 feet shoulders on both sides with high retaining walls going up immediately next to shoulders.

What is the highest safe speed of this curve and at what station is the PC located? Solution:The following is a solution to the problem discussed above.

We know that, Maximum Safe Speed = Vmax = √Rf Where,Rf = G x f (Radius of Flair)G = 32.2 ft/s2 (Acceleration due to Gravity)

f = Superelevation of the RoadwayVmax = √RfG= √(160f) ft/s

Equation 1 Where

Now, Maximum Safe Speed = Vmax = 3.10 ft/s The Central Angle is given to be 40 degrees.

The Station of the PT and PI is given to be 322+50 and 320+08 respectively. Also, the roadway has 10 feet lanes and 8 feet shoulders on both sides with high retaining walls going up immediately next to shoulders.

To calculate the station of the Point of Curvature (PC), let's use the following formula:

PC = PI - (LC x sin ∆)

Where,

PC = 320+08 - (LC x sin 0.698)

Equation 2Let's calculate the Length of Curve (LC) for the curve.

LC = (Deg. of Curvature/ 360°) x 2πRWhere, 2L = Width of Pavement= 10 x 2 + 8 x 2= 36 feet

R = (2L/ sin ∆) + (2L/ tan 2∆)R = (18/ sin 0.698) + (18/ tan 1.397)R = 362.61 feet

LC = (40/ 360) x 2π x 362.61 feet= 80.14 feet

Now, substitute the value of LC and ∆ in Equation 2 and calculate the value of PC.

PC = 320+08 - (80.14 x sin 0.698)= 320+08 - 58.12= 319+50Hence, the station of Point of Curvature (PC) is 319+50.

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Answer:

650=65% of 1000

Step-by-step explanation:

650-600=65 or 65%

To estimate the regression in the given model Yi = B0 + B1Xi + B2Ziui, where the variance of Ui is Σi^2 = Σ(zi^2), you can use the method of weighted least squares (WLS). The weights for each observation can be determined by the inverse of the variance of Ui, that is, wi = 1/zi^2.

In the given model, Yi = B0 + B1Xi + B2Ziui, the error term Ui is assumed to have a constant variance, given by Σi^2 = Σ(zi^2), where zi represents the individual values of Z.

To estimate the regression coefficients B0, B1, and B2, you can use the weighted least squares (WLS) method. WLS is an extension of the ordinary least squares (OLS) method that accounts for heteroscedasticity in the error term.

In WLS, you assign weights to each observation based on the inverse of its variance. In this case, the weight for each observation i would be wi = 1/zi^2, where zi^2 represents the variance of Ui for that particular observation.

By assigning higher weights to observations with smaller variance, WLS gives more importance to those observations that are more precise and have smaller errors. This weighting scheme helps in obtaining more efficient and unbiased estimates of the regression coefficients.

Once you have calculated the weights for each observation, you can use the WLS method to estimate the regression coefficients B0, B1, and B2 by minimizing the weighted sum of squared residuals. This involves finding the values of B0, B1, and B2 that minimize the expression Σ[wi * (Yi - B0 - B1Xi - B2Ziui)^2].

By using the weights derived from the inverse of the variance of Ui, WLS allows you to estimate the regression in the presence of heteroscedasticity, leading to more accurate and robust results.

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Answer: I think is 3.5

Step-by-step explanation:

Answer:

D is the correct one: n=4p