Calcula el area y perímetro de un triángulo equilátero de 5.9 cm de lado

Answer:

c = -1/4

e = 1 2/5

Step-by-step explanation:

4c - 5 = -6

add 5 to both sides

4c = -1

divide each side by 4

c = -1/4

5e + 2 = 9

subtract 2 from both sides

5e = 7

divide both sides by 5

e = 1 2/5

-Chetan K

Answer:

c = -1/4

e = 7/5

Step-by-step explanation:

1. 4c - 5 = -6, 4c = -1, c = -1/4

2. 5e + 2 = 9, 5e = 7, e = 7/5

9514 1404 393

Answer:

  50.3 inches

Step-by-step explanation:

720 degrees is 2 full turns, or twice the circumference of the pulley. The circumference is given by ...

  C = 2πr

  C = 2π(4 in) = 8π in

Then 2 times that is ...

  height lifted = 2(8π in) = 16π in ≈ 50.3 in

The object was lifted about 50.3 inches.

The equation formed using the given data is 195 = x + 12 and your final score is 183 points.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say your final score is x

Given that,

Your final score x is 12 points less than your friend's final score.

So,

x = friend final score - 12

Now,

Friend final score = 195

So,

x = 195 - 12

x + 12 = 195

195 = x + 12

Now,

x = 195 - 12 = 183

Hence "The equation formed using the given data is 195 = x + 12 and your final score is 183 points".

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Answer:

16+1/2x-4

Step-by-step explanation:

Answer:

14 is the answer if you mean 3 by that e

Answer:

(-1,2)

Step-by-step explanation:

90 degree rotation from (a,b) is (-a,b)

The speed of the faster cyclist is 14\ miles/hr.

What is speed?

It is the average distance coverd in unit time. It is also defined as the rate of change of distance with respect to time.

Since the speed of the first cyclist is double than the second cyclist hence, the first cyclist will cover the double distance than the second cyclist. Consider the first cyclist covers 2s distance and first cyclist covers s distance. The sum of these two distances should be 42 miles. Hence,

\(2s+s=42\\3s=42\\s=14\)

Now, distance coverd by the first cyclist is \(2s=2\times 14\\=28 \ $miles\).

Now, both the cyclists meet after 2 hr hence, time taken by the first cyclist is 2 hr.

\(Speed=\frac{Total\ distance}{Total\ time}\\=28\ miles/2 \ hr\\=14\ miles/hr\)

Hence, the speed of the faster cyclist is 14\ miles/hr.

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Answer:

Step-by-step explanation:

7x-11=4x+4(being vertically opposite abgles)

7x-4x=4+11

3x=15

x=15/3

x=5

angle 2+angle1=180 degree(being straight line)

7x-11+angle 1=180

7*5-11+angle 1=180

35-11+angle1=180

24+angle 1=180

angle 1=180-24

angle 1=156 degree

Using the cosine ratio formula, the length of RQ to the nearest tenth is: 13.2.

The cosine ratio formula is given as, cos ∅ = length of adjacent side / length of hypotenuse.

Find m∠PRT in ΔPRT using the cosine ratio formula:

cos(m∠PRT) = 15/17

m∠PRT = cos^(-1)(15/17)

m∠PRT ≈ 28.07°

Find RQ in ΔPRQ using the cosine ratio formula:

cos(28.07) = RQ/15

RQ = cos(28.07) × 15

RQ ≈ 13.2

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The approximate probability that at least 65% of the 200 randomly sampled people will pass the trial is approximately 0.9251 or 92.51%

To calculate the approximate probability that at least 65% of the 200 randomly sampled people will pass the trial, we can use the binomial distribution and the cumulative distribution function (CDF).

In this case, the probability of success (passing the trial) is p = 0.6, and the sample size is n = 200.

We want to calculate P(X ≥ 0.65n), where X follows a binomial distribution with parameters n and p.

To approximate this probability, we can use a normal distribution approximation to the binomial distribution when both np and n(1-p) are greater than 5. In this case, np = 200 * 0.6 = 120 and n(1-p) = 200 * (1 - 0.6) = 80, so the conditions are satisfied.

We can use the z-score formula to standardize the value and then use the standard normal distribution table or a calculator to find the probability.

The z-score for 65% of 200 is:

z = (0.65n - np) / √np(1-p))

z = (0.65 * 200 - 120) /√(120 * 0.4)

z = 1.44

Looking up the probability corresponding to a z-score of 1.44in the standard normal distribution table, we find that the probability is approximately 0.0749.

However, we want the probability of at least 65% passing, so we need to subtract the probability of less than 65% passing from 1.

P(X ≥ 0.65n) = 1 - P(X < 0.65n)

P(X ≥ 0.65)  =1 - 0.0749

P(X ≥ 0.65) = 0.9251

P = 0.9251 or 92.51%

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Answer:

6) a

7) c

Step-by-step explanation:

question 6 is incorrect because you have to find the distance between the two points. for question 6, you are finding the distance between -2 and 1. that is three!

On solving the provided question, we got to know that side length of the square is 8 units.

Four sides that are equally spaced apart make up a square. Around us, a lot of things are rectangular. Equal sides and a 90° interior angle serve as a visual cue to identify a square. A closed square has four sides and exists in two dimensions (2D). A square has an equal number and parallel alignment of its four sides.

A four-sided shape known as a square has sides that are all the same length and angles that are all right angles with a 90 degree angle.

Here,

Area of square = \((side)^2\)

64 =  \((side)^2\)

\(Side = \sqrt{64}\)

Side = 8 units

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Let X be the number of fixed points of a random permutation of n elements. A fixed point is an element that remains in the same position after the permutation. Thus, the probability that an element is fixed is 1/n, and the probability that it is not fixed is (n-1)/n.

Using the linearity of the expected value, we can calculate the expected value of X as:

E(X) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn)

where Xi is the indicator random variable that is equal to 1 if the i-th element is fixed and 0 otherwise. Since the probability of an element being fixed is 1/n, we have E(Xi) = 1/n. Therefore,

E(X) = n * (1/n) = 1

To find the variance of X, we need to compute E(X^2) - E(X)^2. We can use the fact that X^2 = X1 + X2 + ... + Xn, where Xi is the indicator random variable that is equal to 1 if the i-th and j-th elements are both fixed and 0 otherwise. Then,

E(X^2) = E(X1 + X2 + ... + Xn)^2 = E(X1^2 + X2^2 + ... + Xn^2) + 2 E(X1X2 + X1X3 + ... + X(n-1)n)

Since there is only one way to fix two elements out of n, we have E(XiXj) = 1/(n(n-1)). Therefore,

E(X^2) = n * (1/n) + n(n-1) * (1/(n(n-1))) = 1 + 1/n

Finally, the variance of X is

Var(X) = E(X^2) - E(X)^2 = 1 + 1/n - 1^2 = 1/n

Therefore, the variance of the number of fixed elements of a randomly selected permutation of n elements is 1/n.

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Answer:

The first thing that you would need to do is slove for your parentheses.

Step-by-step explanation:

PEMDAS

Answer:

Parentheses

Step-by-step explanation:

PEMDAS

To find the equation for the osculating plane of the curve at t = 6, we first need to calculate the position vector r(6) and the velocity vector v(6) at that specific value of t.

Given r(t) = (t^2 - 8)i + (2t - 5)j + 8k, we substitute t = 6 into the equation:

r(6) = (6^2 - 8)i + (2(6) - 5)j + 8k

= 28i + 7j + 8k

The position vector r(6) is equal to 28i + 7j + 8k.

Next, we calculate the velocity vector at t = 6:

v(6) = d(r(t))/dt = (2t)i + 2j

v(6) = (2(6))i + 2j

= 12i + 2j

Now, we can write the equation for the osculating plane using the position vector r(6) and the velocity vector v(6):

(x - 28)i + (y - 7)j + (z - 8)k • (12i + 2j) = 0

Simplifying this equation gives:

x - 28 + y - 7 + 12z - 96 + 2z - 16 = 0

x + y + 14z - 147 = 0

Therefore, the equation of the osculating plane at t = 6 is x + y + 14z - 147 = 0.

The correct answer is not listed among the options provided.

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The probability of selecting a piece of pottery is 7/26, and when converted to a percentage and rounded to the nearest whole percent, it is approximately 27%.

An archaeologist uncovers 26 artifacts from a site. The types of artifacts are shown below. The horizontal axis represents tools, pottery, and coins. The vertical axis represents the number of artifacts and ranges from 0 to 16, in increments of 2. The number of artifacts of tools is 14. The number of artifacts of pottery is 7. The number of artifacts of coins is 5.

The total number of artifacts at the site = 26

Number of pottery artifacts = 7

Probability of selecting a piece of pottery = Number of pottery artifacts/Total number of artifacts

Probability of selecting a piece of pottery = 7/26

If we want to express this probability in a percentage, we can convert it by multiplying it by 100.

Thus,Probability of selecting a piece of pottery = 7/26 = 0.269 = 26.9% (rounded to the nearest whole percent)

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From the question, the order of reaction is second order for A

The rate of a second-order reaction is exactly proportional to the product of the concentrations of the two reactants or to the square of the concentration of a single reactant. Depending on the particular reaction and its stoichiometry, the rate equation for a second-order reaction can take on several shapes.

Studying reaction kinetics, figuring out reaction processes, and planning and optimizing chemical reactions all depend on understanding the order of events.

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

The area under the graph of the function f(x) = e^x over the interval [-2, 2] is approximately 13.77 square units.

To calculate the area under the graph of the function, we can use integration. In this case, we need to integrate the function f(x) = e^x with respect to x over the interval [-2, 2].

The definite integral represents the area under the curve between the given limits.

∫[a,b] e^x dx

Applying the integral, we have: ∫[-2,2] e^x dx

Using the rules of integration, we can evaluate this integral to find the area under the curve.

The antiderivative of e^x is e^x itself. Evaluating the integral at the upper and lower limits, we get: [e^x] from -2 to 2

Plugging in the values, we have: e^2 - e^(-2)

This is the exact answer in terms of e. To get the numerical approximation, you can substitute the value of e into the expression to get the approximate area.

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Answer:

6

Step-by-step explanation:

If you push two triangle tables together you just multiply 3*2

The road was 9.62 miles long after rebuilding.

The road was initially 3.7 miles long

After a rebuild it was 2.6 miles as long

The new length can be calculated by multiplying the initial length which is  3.7 by 2.6

= 3.7 × 2.6

= 9.62

Hence, after the rebuild the road was  9.62 miles long

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To find the spherical coordinate limits for the integral, we first need to determine the bounds for ρ, θ, and ϕ.

Since the sphere and hemisphere intersect at ρ=4cos(ϕ), we can set these two equations equal to each other to find the limits for ϕ:

4cos(ϕ) = 6

ϕ = arccos(3/2)

For the limits of θ, we note that the solid is symmetric about the z-axis, so we can integrate from 0 to 2π.

Finally, for the limits of ρ, we need to find the limits for z. Since the hemisphere has equation ρ=6 and z≥0, we know that the top of the solid is at z=6. To find the bottom of the solid, we need to solve for z in the equation for the sphere:

ρ = 4cos(ϕ)

z = 4cos(ϕ)cos(θ)sin(ϕ)

Substituting ρ=4cos(ϕ) and simplifying, we get:

z = 2cos^2(ϕ)sin(θ)

Since z≥0, we have:

0 ≤ 2cos^2(ϕ)sin(θ) ≤ 6

0 ≤ sin(θ) ≤ 3/(2cos^2(ϕ))

So the limits for ρ are 4cos(ϕ) ≤ ρ ≤ 6, the limits for θ are 0 ≤ θ ≤ 2π, and the limits for ϕ are arccos(3/2) ≤ ϕ ≤ π/2.

To evaluate the integral, we use the formula for a volume in spherical coordinates:

V = ∫∫∫ ρ^2sin(ϕ) dρdθdϕ

Applying the limits we found above, we get:

V = ∫ from arccos(3/2) to π/2 ∫ from 0 to 2π ∫ from 4cos(ϕ) to 6 (ρ^2sin(ϕ)) dρdθdϕ

Evaluating the integral, we get:

V = 256π/15 - 8/3

Therefore, the volume of the solid is 256π/15 - 8/3 cubic units.

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If the total degrees of freedom (dftotal) in an analysis of variance comparing three treatment conditions is 32, the group size for each condition needs to be determined.



To determine the number of individuals in each group, we need to divide the total number of individuals (dftotal) by the number of treatment conditions (groups).

Given that dftotal = 32 and there are three treatment conditions (groups), we can divide dftotal by the number of treatment conditions to find the number of individuals in each group.

Number of individuals in each group = dftotal / number of treatment conditions

Number of individuals in each group = 32 / 3

Number of individuals in each group ≈ 10.67

Since the groups must have the same size, we need to round the result to the nearest whole number. Therefore, there are approximately 11 individuals in each group.

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Answer:

123 degrees

Step-by-step explanation:

Angles in a quadrilateral add up to 360 degrees

so we add all the angles

114 + 80 + 43 which is 237

360 - 237 is 123

so angle x is 123 degrees

The initial number of dice rolled = 1000

What is exponential modeling?

Based on an equation like where Y = deterioration, T = time, and A and B = parameters to be calculated by the regression approach based on historical data, the exponential model represents the degradation failure process.

Here,

Linear models are used when a phenomenon is changing at a constant rate whereas exponential models are used when a phenomenon is changing in a way that is quick at first, then more slowly, or slow at first and then more quickly. This is the defining characteristic of the exponential model.

(a)

dice(n) = 1000 × (−0.138629436ln)........... (1)

The initial number of dice rolled when n=0

Putting n=0 in (1),

dice(0) = 1000e(0) = 1000

Hence, the initial number of dice rolled = 1000

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The solutions are x = 1/9, x = 25/8, and x = 1. Substituting these values back into either equation will give the corresponding values of y.

We can solve this system of equations by using elimination or substitution method.

Elimination Method:

From the second equation, we can isolate x or y in terms of the other variable:

5xy - 2(x + y) = 20

5xy - 2x - 2y = 20

5xy - 2x - 2y + 4 = 24

5xy - 2(x + 2y) + 4 = 24

5xy - 2(2 - y + 2y) + 4 = 24 (using x + y = a)

5xy - 2(2 + y) + 4 = 24

5xy - 2y = 22

y(5x - 2) = 22

y = 22/(5x - 2)

Substituting this expression for y into the first equation, we get:

2(x² + (22/(5x-2))²) - 5(x + 22/(5x-2)) = 1

Multiplying through by (5x - 2)², we get:

2(5x - 2)²(x² + 22²) - 5(5x - 2)(x(5x - 2) + 22) = (5x - 2)²

Simplifying and rearranging, we get:

9x⁴ - 100x³ + 328x² - 100x + 4 = 0

This is a quartic equation which can be solved using various methods, such as factoring, graphing, or numerical methods.

Substitution Method:

From the first equation, we can solve for y in terms of x:

2(x²+y²)-5(x+y)=1

2x² + 2y² - 5x - 5y = 1

2y² - 5y = 1 - 2x² + 5x

Using the quadratic formula, we get:

y = (5 ± sqrt(25 - 8(1-2x²+5x)))/4

y = (5 ± sqrt(8x² - 25x + 24))/4

Substituting this expression for y into the second equation, we get:

5x(5 ± sqrt(8x² - 25x + 24))/4 - 2(x + (5 ± sqrt(8x² - 25x + 24))/4) = 20

Simplifying and rearranging, we get:

(9x - 4)(8x - 25)(x - 1) = 0

Thus, the solutions are x = 1/9, x = 25/8, and x = 1. Substituting these values back into either equation will give the corresponding values of y.

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Answer:

Step-by-step explanation:            

let angles be 3x, 5x, 10x

3x+5x+10x=180(angle sum property)

18x=180

x=180/18

x=10

therefore, angles are 3*10=30

5*10=50

10*10=100..

a.The probability that a randomly selected watch will be in working condition for more than five years is approximately 6.68%. b.Approximately 93.32% of the watches will be in operating condition after the warranty period. c. The maximum life expectancy of the middle 95% of the watches is approxiamately 63.68 months. d.The range of the middle 95% of the watches is from 32.32 months to 63.68 months. The range represents 95% of the watches, it means that 5%.

a. To find the probability that a randomly selected watch will be in working condition for more than five years, we need to convert the time to the same unit as the distribution. Since the mean is given in years and the standard deviation is given in months,

we need to convert five years to months.

Mean = 4 years = 4 x 12 months = 48 months

Standard deviation = 8 months

To calculate the probability, we need to find the area under the normal distribution curve to the right of 60 months (5 years).

Using a standard normal distribution table or a calculator, we can find the z-score corresponding to 60 months:

z = (x - μ) / σ

z = (60 - 48) / 8 = 12 / 8 = 1.5

The probability can be found by looking up the z-score in the standard normal distribution table or using a calculator. From the table or calculator, we find that the probability is approximately 0.0668, or 6.68%.

b. The warranty period for Timely brand watches is three years. To find the percentage of watches that will be in operating condition after the warranty period, we need to find the probability that a randomly selected watch will last longer than three years.

We need to convert three years to months:

Warranty period = 3 years = 3 x 12 months = 36 months

We calculate the z-score:

z = (x - μ) / σ

z = (36 - 48) / 8 = -12 / 8 = -1.5

Using the standard normal distribution table or a calculator, we find the area to the left of -1.5 is approximately 0.0668. The probability that a randomly selected watch will not last longer than three years is approximately 0.0668.

To find the percentage of watches that will be in operating condition after the warranty period, we subtract this probability from 1 (since we want the complementary probability):

Percentage = 1 - 0.0668 = 0.9332 = 93.32%

c. The middle 95% of the watches represents the range within which 95% of the watches' life expectancy falls. To find the minimum and maximum life expectancy of this range, we need to determine the z-scores that correspond to the cumulative probability of 0.025 and 0.975.

For the minimum life expectancy (lower bound), we look up the z-score that corresponds to a cumulative probability of 0.025. This z-score is approximately -1.96.

z = -1.96

Using the z-score formula, we can find the corresponding value in months:

x = μ + (z x σ)

x = 48 + (-1.96 * 8) = 48 - 15.68 = 32.32

The minimum life expectancy of the middle 95% of the watches is approximately 32.32 months.

For the maximum life expectancy (upper bound), we look up the z-score that corresponds to a cumulative probability of 0.975. This z-score is also approximately 1.96.

z = 1.96

Using the z-score formula, we can find the corresponding value in months:

x = μ + (z x σ)

x = 48 + (1.96 x 8) = 48 + 15.68 = 63.68

d. Ninety-five percent of the watches refer to the range between the 2.5th and 97.5th percentiles. We already calculated the z-scores corresponding to these percentiles in part c: -1.96 and 1.96.

To find the range in months,

we convert the z-scores back:

\(x_{1}\)= μ +\(z_{1}\) x σ = 48 + (-1.96) x 8 = 32.32 months,

and \(x_{2}\)= μ + \(z_{2}\) x σ

= 48 + 1.96 x 8

= 63.68 months.

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