In the given figure, l ∥ m and n are a transversal. If ∠1=80° and ∠5=100°,
find the measure of <2 , ∠3, ∠4.

Please give brief explanation

Answer:

20 - 20 =0 me trying to get the points lol edit : oh well I couldn't get the points:( lol

Given the mean length of metal strips produced by a machine process is 500mm and the standard deviation is 10mm.

The length of metal strips produced by the machine is normally distributed.

Mean, µ = 500mm, Standard deviation, σ = 10mm

(a) We need to find the probability that the length of a randomly selected strip is shorter than 490mm. Therefore, we need to find the value of the z-score in order to use the standard normal distribution tables.z = (x - µ)/σ = (490 - 500)/10 = -1P(Z < -1) = 0.1587 (from the standard normal distribution tables)Hence, the probability that the length of a randomly selected strip is shorter than 490mm is 0.1587 (approx) or 0.1587 to 4 decimal places.

(b) We need to find the probability that the length of a randomly selected strip is longer than 509mm. Therefore, we need to find the value of the z-score in order to use the standard normal distribution tables.z = (x - µ)/σ = (509 - 500)/10 = 0.9P(Z > 0.9) = 1 - P(Z < 0.9) = 1 - 0.8159 = 0.1841 (from the standard normal distribution tables).

Hence, the probability that the length of a randomly selected strip is longer than 509mm is 0.1841 (approx) or 0.1841 to 4 decimal places.

(c) We need to find the probability that the length of a randomly selected strip is between 479mm and 507mm.

Therefore, we need to find the value of z-scores for x1 and x2, respectively.z1 = (x1 - µ)/σ = (479 - 500)/10 = -2.1z2 = (x2 - µ)/σ = (507 - 500)/10 = 0.7P(479 < X < 507) = P(-2.1 < Z < 0.7) = P(Z < 0.7) - P(Z < -2.1) = 0.7580 - 0.0179 = 0.7401.

Hence, the probability that the length of a randomly selected strip is between 479mm and 507mm is 0.7401 (approx) or 0.7401 to 4 decimal places.

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Answer: 43.8cm

A marble has a diameter of 17in. What is the diameter of the marble?

Well, the answer is pretty much right there in the question, all we have to do is to convert inches to centimeters. To convert inches to centimeters, simply multiply the length by 2.54.

(17)(2.54)=43.18cm

The answer cannot be in cm^3. Diameter/Length is only in cm, cubed is for volume, and squared is for area.

Hope this helped!

Answer:

The angle SQR is half the intercepted arc SR which is 43°

The linear equation doesn't have a solution.

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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Answer:

nice

Step-by-step explanation:

Answer:

C.  2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units

Step-by-step explanation:

Answer:

The Answer is C.

Step-by-step explanation:

2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units

A confidence interval is made from a Sample statistic to estimate the truth for a Population parameter.

What do you mean by confidence interval?

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

The formula of the confidence interval,

\(CI = \bar{x} \pm z \frac{s}{\sqrt{n}}\)

According to the given question,

We have the statement on the confidence interval in given question in the form of fill ups as,

A confidence interval is made from a __________ to estimate the truth for a ______________.

Therefore, the correct fill in the blanks are:

A confidence interval is made from a Sample statistic to estimate the truth for a Population parameter.

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Answer:

Step-by-step explanation:

Mistake in step 3 the (2x+1) and the (x-1) both cancel out but the other binomials (x + 3) and (x - 3) are different so don't cancel out.

Step 3 should be 3(x-3) / 4(x+3)

3 should not be an excluded value.

The confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

In general, when dealing with inferences for two population proportions, the confidence interval method and the critical value method are equivalent. These two methods provide a range of plausible values (confidence interval) for the difference between two population proportions and involve the calculation of critical values to determine the margin of error.

On the other hand, the p-value method is not equivalent to the confidence interval and critical value methods. The p-value method involves calculating the probability of observing a test statistic as extreme as, or more extreme than, the one obtained from the sample data, assuming the null hypothesis is true. It is used in hypothesis testing to determine the statistical significance of the difference between two population proportions.

To summarize:

- Confidence interval method: Provides a range of plausible values for the difference between two population proportions.

- Critical value method: Uses critical values to determine the margin of error in estimating the difference between two population proportions.

- P-value method: Determines the statistical significance of the observed difference between two population proportions based on the calculated p-value.

Hence, the confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

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The equation of the line that passes through the points (7, 450) and (14, 401) is y + 7x = 499

The equation of a line  can be represented as follows:

y - y₁ = m(x - x₁)

where

Therefore, (7, 450)(14, 401)

m = 401 - 450 / 14 - 7 = -49 / 7 = -7

Therefore, using (7, 450)

y - 450 = -7(x - 7)

y - 450 = -7x + 49

y + 7x = 49 + 450

y + 7x = 499

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Answer:

387.4 is the answer

Step-by-step explanation:

hope this helps=)

Answer:

387.4 rounded to the nearest tenth is 387 because if it's 4 and below you'll get the ones place the same. And if it's 5 and over, the ones place will go up...

The surface area generated by rotating the given curve about the y-axis is approximately 5.37 square units.

For finding the surface area generated by rotating a curve around the y-axis, the formula is S=2π∫aᵇ y√(1+(dy/dx)²) dx. To apply this formula, we find dy/dx and integrate the given curve.

Similarly, for the curve x=9t², y=6t³, we use the formula for parametric equations, Surface Area = ∫[2πx * sqrt((dx/dt)² + (dy/dt)²)] dt, from t=0 to t=5, and integrate it.

To find the surface area generated by rotating the given curve about the y-axis, we need to use the formula:

S = 2π∫aᵇ y√(1+(dy/dx)²) dx

First, we need to find dy/dx:

dx/dt = 18t
dy/dt = 18t²

dy/dx = dy/dt ÷ dx/dt = 18t² ÷ 18t = t

Now, we can plug in y and dy/dx into the formula and integrate from 0 to 5:

S = 2π∫0⁵ 6t³ √(1+t²) dt
S = 2π∫0⁵ 6t³(1+t²)⁽¹/²⁾ dt

This integral is a bit tricky to solve, so we can use integration by substitution. Let u = 1+t², then du/dt = 2t and dt = du/2t. Substituting into the integral:

S = 2π∫1²⁶(u-1)⁽¹/²⁾ du/2
S = π∫1² (u-1)⁽¹/²⁾ du
S = π(2/3)(2⁽³/²⁾ - 1)

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Answer:

The slope is 5/8

Step-by-step explanation:

-5x+8y = 30

Add 5x to each side

8y = 5x+30

Divide by 8

8y/8 = 5/8x+30/8

y = 5/8x + 15/4

This is in slope intercept form y = mx+b where m is the slope and b is the y intercept

The slope is 5/8

Answer: 5/8

Step-by-step explanation:

You would first need to put the equation into standard form. so you add 5x on both sides

Then you divide 8 on both sides

that would give you y=5/8x+3.75

The slope is 5/8

Answer:

When you get your blood pressure numbers, there are two of them. The first, or “top” one, is your systolic blood pressure. The second, or “bottom,” one is diastolic blood pressure.

Step-by-step explanation:

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.

In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.

CV = (Standard Deviation / Mean) * 100

CV = (5.2 / 340) * 100

CV ≈ 1.53%

Therefore, the correct answer is option B: 1.53%.

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Yes, you can show significant differences using superscripts in an ANOVA (Analysis of Variance) single-factor test.

In an ANOVA test, superscripts are commonly used to indicate significant differences between the means of different groups or treatments.

Typically, letters or symbols are assigned as superscripts to denote which groups have significantly different means. These superscripts are usually presented adjacent to the mean values in tables or figures.

The specific superscripts assigned to the means depend on the statistical analysis software or convention being used. Each group or treatment with a different superscript is considered significantly different from groups with different superscripts. On the other hand, groups with the same superscript are not significantly different from each other.

By including superscripts, you can visually highlight and communicate the significant differences between groups or treatments in an ANOVA single-factor test, making it easier to interpret the results and identify which groups have statistically distinct means.

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Answer:

c.) 28

Step-by-step explanation:

I hope this helped. I know it probably doesn't. But I hope you get the question right. And I am sorry if you get it wrong.

Answer:

<70.71, -70.71>

Step-by-step explanation:

The vector has a module of 100 and a angle of -45° (negative because it is below the horizontal). So, to find its components, we need to use the sine and cosine relation of its angle:

horizontal component = module * cos(angle)

horizontal component = 100 * cos(-45)

horizontal component = 70.71

vertical component = module * sin(angle)

vertical component = 100 * sin(-45)

vertical component = -70.71

So the vector in the component form is <70.71, -70.71>

The negative sign of the vertical component means its direction is downwards.

The component form should be <70.71, -70.71>

horizontal component = module ( cos(angle))

= 100 (cos(-45))

= 70.71

And,

vertical component = module (sin(angle))

= 100 (sin(-45))

= -70.71

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The expected value E(X) of a random variable X is -1.04

The expected value of a random variable is a measure of its central tendency. It represents the average value that would be obtained if the experiment or process that generates the variable is repeated many times.

To find the expected value of a discrete random variable X with probability distribution P(X), we multiply each possible value of X by its corresponding probability and then sum these products. Symbolically, this can be written as:

E(X) = Σ[x * P(X)]

In words, this formula says that we take each possible value of X, multiply it by its probability, and then add up these products to get the expected value.

In the given problem, we are given the probability distribution of X and asked to find its expected value. We can use the formula above to do this, by plugging in the values of x and P(X):

E(X) = (-9 * 0.16) + (-7 * 0.11) + (-5 * 0.14) + (-3 * 0.17) + (-1 * 0.10) + (1 * 0.32)

E(X) = -1.04

Therefore, the expected value of X is -1.04.

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Step-by-step explanation:

the volume is 4/3 × pi × r^3

4/3 × 3 × 4^3

the volume is 256 cm cubed.

the radius is 4 cm.

Answer:

A. x = 1/4

Step-by-step explanation:

Simplify the equation:

(3x^2+1)/(x-1) + x = 4 + 4/(x-1)

(3x^2+1-4)/(x-1) = 4-x

(3x^2-3)/(x-1) = 4-x

Since (3x^2-3) = 3(x^2-1) and x^2-1 = (x+1)(x-1), substitute 3x^2-3 for 3(x+1)(x-1)

3(x+1)(x-1)/(x-1) = 4-x

Cancel (x-1) from the numerator and denominator:

3(x+1) = 4-x

Isolate x:

3(x+1) = 4-x

3x+3 = 4-x

4x = 1

x = 1/4.

x = 1/4 is the only valid solution unless both sides being undefined would count as a valid equation, then x = 1 would also be valid.

x-intercept of the linear equation that is parallel to y=-3x-5 and passes through (2, 6) is 4

What is the equation of the line?

The slope of the line and a point on the line can be used to create the equation of a line.

The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

Given equation of line is y = -3x - 5

Passing points (a,b) = (2,6)

As we know equation of the line is y = mx + c where m is the slope of the line and c is the y-intercept

On comparing the given equation of the line with y = mx + c , we have slope of the line is -3

Slope of two parallel lines is equal.

Equation of line having slope and passing point is given by y-b = m (x-a)

Therefore, equation of line having slope -3 and passing point (2,6) is y - 6 = -3(x - 2)

⇒ y - 6 = -3x + 6

⇒ y = -3x + 6 + 6

⇒ y = -3x + 12

Equation of line having slope and x-intercept is given by y = m(x - a) where m is the slope and a is the x- intercept

y = -3x + 12 can be written as y = -3(x-4)

On comparing this equation with y = m(x-a) we have x-intercept is 4

Therefore, x-intercept of the linear equation that is parallel to y=-3x-5 and passes through (2, 6) is 4

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Answer:

USE BODMAS

2^p+q

The statement is true. A put option is a financial contract that provides the holder with the right, but not the obligation, to sell an underlying asset, such as 100 shares of common stock, at a predetermined price, known as the strike price, before or at the expiration date of the option. If the price of the asset decreases below the strike price, the holder of the put option can sell the asset at the higher strike price and make a profit. However, if the price of the asset increases above the strike price, the holder can simply do nothing and let the option expire, without any obligation to sell the asset.

The price of a put option is influenced by various factors, such as the price of the underlying asset, the strike price, the time until expiration, and the volatility of the asset's price. Generally, the higher the volatility and the longer the time until expiration, the higher the price of the put option.

Selling a put option involves taking on the obligation to buy the underlying asset at the strike price, if the holder decides to exercise the option. Selling put options can be a strategy for generating income, but it also involves risks, such as potential losses if the price of the asset decreases significantly.

In summary, a put option is a security that provides the holder with the right to sell an underlying asset at a predetermined price, but not the obligation to do so. The price of a put option is influenced by various factors, and selling a put option involves taking on the obligation to buy the asset.

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The number of hours it would take Ganymede to complete a full rotation is 171.25 hours.

The first step is to convert days to hours. A day is equivalent to 24 hours. In order to convert days to hours, multiply 7 by 24.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

1 day = 24 hours

24 x 7 = 168 hours

The second step is to convert minutes to hours, In order to do this, divide 15 by 60. Division is the process that is used to determine the quotient of two or more numbers.

60 minutes = 1 hour

15 / 60 = 0.25 hours

Now, add all the converted hours together. Addition is the mathematical operation that is used to determine the sum of two or more numbers.

Total hours = 168 hours + 3 hours + 0.25 hours = 171.25 hours

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The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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The circumference of the tree trunk is approximately 25.13 inches.

We can calculate the circumference of the tree trunk using the formula:

C = πd

where C is the circumference and d is the diameter.

Assuming that you meant "tree trunk" instead of "tree wing":

Given that the diameter of the tree trunk is 8 inches, we can substitute this value into the formula to find the circumference:

C = π × 8 in

C = 25.13 in (rounded to two decimal places)

Therefore, the circumference of the tree trunk is approximately 25.13 inches.

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The value of the given expression is obtained using the property of composite function as g(f(2)) = 5.

For two functions f(x) and g(x), a composite function is defined as f(g(x)) or g(f(x)). The characteristics of this function can be described as,

The inverse of a composite function is equivalent to the composition of the inverse of both functions.

The composition of two one to one functions is always one to one.

The given table shows the values of two functions f(x) and g(x).

The given expression is equivalent to the value of g(f(x)) at x = 2.

Now, g(f(2)) can be obtained as follows,

The value of f(2) from the table is 1.

And, the value of g(1) is 5.

Thus, g(f(2)) = g(1) = 5

Hence, the value of the given expression is 5.

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