let x1 and x2 be independent random variables with uniform distribution on [0, 1]. a stick of unit length is broken at points with distance x1 and x2 from one of the ends. what is the probability that the three pieces may be used to make a triangle?

9514 1404 393

Answer:

  b.  11 years

Step-by-step explanation:

Since we're interested in the time going forward, we can write the expnential function for Rosa's balance as ...

  y = 4500(4500/2000)^(x/6)

where x is the number of years from now, and y is the balance at that time.

  20,000 = 4,500(2.25^(x/6))

Dividing by 4500, we get ...

  40/9 = 2.25^(x/6)

  log(40/9) = (x/6)log(2.25) . . . . take logs

  x = 6·log(40/9)/log(2.25) ≈ 11.037 . . . . divide by the coefficient of x

It will take 11 more years for Rosa to have $20,000 in the bank.

_____

Comment on the exponential function

You can generally write an exponential function for a question of this sort pretty easily. The form of it is ...

  f(t) = (initial value)×(growth factor)^(t/(growth period))

Here, we're given a growth factor of 4500/2000 = 2.25 corresponding to a period of 6 years. This tells us t is in years, and the exponential term will be ...

  2.25^(t/6)

The "initial value" we choose corresponds to t=0. Since we want 'years from now', the "initial value" will be the value in the account now, 4500.

Answer:

B 11 years

Step-by-step explanation:

Using the given information, the mean number of books read is 3.41

From the question, we are to calculate the mean number of books read

From the given information, we have the table

Number of students             Number of books

        2                                               1

        11                                              3

        16                                             4

Then,

Mean number of books read = [(2×1) +(11×3) + (16×4)]/(2+ 11+ 16)

Mean number of books read = (2 + 33+ 64)/29

Mean number of books read = 99/29

Mean number of books read = 3.41

Hence, the mean number of books read is 3.41

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Answer:

-4

Step-by-step explanation:

→Distribute the -1 to (x - 1):

(x - 5) - (x - 1)

x - 5 - x + 1

→Add like terms (x and -x, -5 and 1):

-4

Answer:

-4

Step-by-step explanation:

(x-5)-(x-1)

x-5-x+1

x-x-5+1 = -4

Answer:

> twelve divided by open bracket four subtract by two multiple by three close bracket.

The required form of expression 12 ÷ (4 - 2.3) is a division of 12 by a difference of 4 and 2.3.

Given that,
To write the expression  12 ÷ (4-2.3) in word form.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.

Here,
In the expression, 12 ÷ (4-2.3)
12 is getting divided by the subtraction 2.3 from 4, this implies the division of 12 by a difference of 4 and 2.3.

Thus, the required form of expression 12 ÷ (4 - 2.3) is a division of 12 by a difference of 4 and 2.3.

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The third side of the triangle is 12 units and the measure of the angle θ is 37°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The third side of the triangle 'a' is calculated by Pythagoras' theorem. Then we have

c² = a² + b²

20² = a² + 16²

400 = a² + 256

a² = 400 - 256

a² = 144

a = 12

Then the value of the angle θ is calculated as,

sin θ = 12 / 20

sin θ = 3 / 5

sin θ = sin 37°

θ = 37°

The third side of the triangle is 12 units and the measure of the angle θ is 37°.

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Answer: KVL

Step-by-step explanation:

This would be the correct name for the angle since the V needs to be in the middle of the answer. In the angle you can see L V and K all pass 5 making it the correct name for the angle

Answer:

He bough 1.25 lbs of shrimp and 3.75 lbs of potato.

Step-by-step explanation:

Since the stew is composed of shrimps and potatoes, then the sum of the weighs of these ingredients must be equal to the weigh of the stew, so we have:

\(shrimp + potato = 5\)

We also know that he bought three times more potatoes than shrimps, therefore:

\(potato = 3*shrimp\)

Using the second equation on the first one, we have:

\(shrimp + 3*shrimp = 5\\4*shrimp = 5\\shrimp = \frac{5}{4} = 1.25\)

\(potato = 3*shrimp = 3*1.25 = 3.75\)

He bough 1.25 lbs of shrimp and 3.75 lbs of potato.

Answer:

Let S = starting point

Let ST = length of tunnel

SR = 1414 m

RT = 2236 m

Set up:

ST^2 + SR^2 = RT^2

ST^2 + (1414)^2 = (2236)

Solve for RT to find your answer.

Step-by-step explanation:

The prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4  is 1/2.

In science, the prοbability οf an event is a number that indicates hοw likely the event is tο οccur. It is expressed as a number in the range frοm 0 and 1, οr, using percentage nοtatiοn, in the range frοm 0% tο 100%. The mοre likely it is that the event will οccur, the higher its prοbability.

space οf twο-digit numbers that can be created using the digits 7,1 ,9 and 4. What is the prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4 ?

here are a tοtal οf 16 pοssible οutcοmes in the sample space, as shοwn in the tree diagram. Out οf these 16 pοssible οutcοmes, 8 οf them cοntain the digit 1 οr 4 (i.e., 14, 17, 19, 41, 44, 71, 74, 91).

Therefοre, the prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4 is:

P(1 οr 4) = 8/16 = 1/2

Sο the prοbability is 1/2.

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The value of StartFraction P (t) Over A EndFraction for this problem will be 20

Take the value of x that they provide you and plug it into the problem for these kinds of difficulties.

The fraction's numerator is the highest number. It stands in for the entire thing that must be divided.

A fraction's denominator is the value at the bottom. It shows how many equally sized pieces are divided up in the object.

adding 3 to the formula:

6/(3) + 2(3)^2 —> use PEMDAS. Apply the 32 exponents first, followed by left-to-right multiplication and division, and finally addition.

6/x + 2x^2,

when x = 3

=20

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The question the incomplete the full question:

What is the value of StartFraction 6 Over x EndFraction + 2x2, when x = 3?

Answer:

The second part is 0.8 and B. About 1,845 years.

Step-by-step explanation:

:)

Answer:

x = 16

Step-by-step explanation:

8x - 8 = 7x + 8

Angles are vertical angles so they will be equal to each other.

x = 16

On solving the provided question, we can say that Probability ( At least one of the students is a senior) = 0.4632 approx

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

P(All four players are senior) = 0.00033 approx

P(There is one each: freshman, sophomore, junior and senior) = 0.0944 approx.

P(There are 2 sophomores and 2 freshman) = 0.0568  approx

P( At least one of the students is a senior) = 0.4632 approx

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Answer:

\(\frac{30x+30}{x+7}\) is the simplified radical expression.

Step-by-step explanation:

For this one, we have fractions in the bottom of a fraction (denominator).

So, we would multiply by \(\frac{1}{x+1}\).

\(\frac{5x+5}{\frac{1}{6}x+\frac{7}{6} }\)

Then Multiply by 6.

\(\frac{30x+30}{x+7}\) is the simplified radical expression.

Answer:

y = -5/4x +1

Step-by-step explanation:

The slope-intercept form of a line is given by

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

We are given the slope and a point on the line

y = -5/4 x + b

We can substitute the point for x and y and solve for b

-9 = -5/4(8)+b

-9 = -10+b

Add 10 to each side

-9+10=-10+10+b

1 = b

The slope intercept form of the equation is

y = -5/4x +1

Answer:

3/5???

Step-by-step explanation:

we graph from 1/4 < x < 2

hope this help, comment is any doubt

The high-tech sector employees were less likely to lose their jobs option fourth is correct.

It is given that the estimated employment change by sector 2004–2020 a bar graph titled estimated employment change by sector from 2004 to 2020 has the year on the x-axis and the percentage of change in employment on the y-axis.

It is required to find the correct statement.

It is defined as the visual way to show the data a systematically with rectangle box on the x-axis and y-axis. The height and vertical lines show the proportional data.

From the given data many businesses stagnated and had to fire employees, but these were primarily people who could be quickly replaced by someone willing to work for a lower wage.

Employees in the high-tech sector are frequently too valuable to the company to be laid off, therefore their job security was strong because no one could replace them.

Thus, the high-tech sector employees were less likely to lose their jobs option fourth is correct.

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Answer:

D- High-tech sector employees were less likely to lose their jobs.

Step-by-step explanation:

edge economics 22

If testing shows that there is less than a 5% chance the results were random, the study is considered statistically significant.

In statistical hypothesis testing, researchers often set a significance level, denoted as α (alpha), which is typically 0.05 or 5%. This significance level represents the threshold below which the researchers consider the results to be statistically significant. If the p-value, which is a measure of the evidence against the null hypothesis, is less than the chosen significance level, it indicates that the results are unlikely to have occurred by chance alone.

When testing shows that there is less than a 5% chance (or any chosen significance level) that the results were random, the study is considered statistically significant. This means that the observed data provides evidence to reject the null hypothesis in favor of the alternative hypothesis. The results are deemed significant because the probability of obtaining such extreme or more extreme results under the assumption of randomness is very low.

Statistical significance is an important criterion in research as it helps researchers draw valid conclusions and make inferences from their data. However, it is essential to note that statistical significance does not imply practical significance or the magnitude of the effect observed. Additional considerations, such as effect size and contextual relevance, are necessary to fully interpret the implications of a statistically significant result in practical terms.

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Answer:

look below

Step-by-step explanation:

I think the answer is for A 12mm because there is a -3 in the spot and you have 15 mm and for B 17mm because you still have that 15mm but this time you have a +2  

I think this might be the answer I am kind of good at math but I don't really know this one sorry if I get it wrong

9514 1404 393

Answer:

  True

Step-by-step explanation:

We assume your equation is intended to be ...

  \(\sqrt{x+56} =x\)

The usual method of solution squares both sides, then solves the resulting quadratic.

  \(x+56=x^2\\\\x^2-x-56=0\\\\(x-8)(x+7)=0\longrightarrow x=\{-7,+8\}\)

Considering the initial problem, we require x ≥ 0, so the x=-7 solution is extraneous.

__

A graphical solution shows there is only one value of x that satisfies the equation. The other "solution" arises from considering the negative square root. It is introduced when the equation is squared.

Answer:

13mn

Step-by-step explanation:

(10mn-5m+3n)+(mn-5m-3n)+(mn+9m+4n)

8mn+(-8mn)+13mn

=13mn

that's the answer I think

SOLUTION:

Step 1:

we are to find the measure of minor arc cut off by one of the diagonals;

The sum of interior angles in a pentagon is:

Each interior angle of a regular pentagon is

So the size of the major arc can be gotten by the circle theorem; the angle at the centre is twice the angle at the circumference.

Then recall,

Step 2:

We are to find the length of the same minor arc in problem;

Where our angle (titan) is 144 and radius is 10

So the length of the minor arc, given that the radius is 10 cm is 8 pi

Answer:

B) 146 ≥ 9c+10

Step-by-step explanation:

$9 per yoga class can be represented with 9c, and then we have 9c+10 to represent the additional $10 yoga mat bought.

Since she can't use more than $146, then we have the inequality 9c+10≤146, which is the same as 146≥9c+10, so option B is correct.

Step-by-step explanation:

(x + 2)(x + 3) = 12

x² + 5x + 6 = 12

x² + 5x - 6 = 0

(x + 6)(x - 1) = 0

By zero product rule, we have (x + 6) = 0 or (x - 1) = 0.

=> x = -6 or x = 1. (A)

To show that Γ(1) = 1, we substitute z = 1 into the integral representation of the gamma function. Using integration by parts, we can evaluate Γ(2) = 0 + 1 = 1. Using recursive formula for Γ(n), Γ(n) = (n-1)Γ(n-1).

(a) To show that Γ(1) = 1, we substitute z = 1 into the integral representation of the gamma function:

Γ(1) = ∫₀^∞ x^(1−1)e^(−x) dx = ∫₀^∞ e^(−x) dx.

Integrating the exponential function e^(-x) from 0 to infinity gives us the limit as x approaches infinity, which is 0. Therefore, Γ(1) = 0 - 1 = 1.

(b) Using integration by parts, we can evaluate Γ(2):

Γ(2) = ∫₀^∞ x^(2−1)e^(−x) dx.

Let u = x, dv = e^(-x) dx. Then du = dx and v = -e^(-x).

Applying the integration by parts formula: ∫ u dv = uv - ∫ v du, we have:

Γ(2) = [-xe^(-x)]₀^∞ + ∫₀^∞ e^(-x) dx.

The first term on the right-hand side evaluates to 0 - 0 = 0. The second term is the same as the integral in part (a), which we previously determined to be 1.

Therefore, Γ(2) = 0 + 1 = 1.

(c) Using integration by parts again, we can derive the recursive formula for Γ(n):

Γ(n) = ∫₀^∞ x^(n−1)e^(−x) dx.

Let u = x^(n-1), dv = e^(-x) dx. Then du = (n-1)x^(n-2) dx and v = -e^(-x).

Applying the integration by parts formula, we have:

Γ(n) = [-x^(n-1)e^(-x)]₀^∞ + ∫₀^∞ (n-1)x^(n-2) e^(-x) dx.

The first term evaluates to 0 - 0 = 0. The remaining integral is (n-1) times the integral of x^(n-2)e^(-x), which is Γ(n-1).

Therefore, Γ(n) = (n-1)Γ(n-1).

By repeatedly applying this recursive formula, we can express Γ(n) in terms of Γ(n-1), Γ(n-2), and so on, until we reach Γ(1) = 1. This leads to the conclusion that Γ(n) = (n-1)!, demonstrating the connection between the gamma function and the factorial function for counting numbers n.

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Answer:

\(y=2x+4\)

Step-by-step explanation:

The slope of the given line is \(\frac{-2-4}{-2-1}=2\).

Parallel lines have the same slope, so the equation is:

\(y-6=2(x-1) \\ \\ y-6=2x-2 \\ \\ y=2x+4\)