Using this plot of annual peak discharge, what is the probability each year that a flood of 1,000 cubic meters per second will occur

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

Hi! So I saw your question and decided to answer it as soon as I can. Please check the file I uploaded to this question to guide you to get the right answer <3

Answer:

the answer is 36 inches

Step-by-step explanation:

divide the circumference by pi to get the answer

113.04 / 3.14 = 36

Answer:

36

Step-by-step explanation:

circumference = diameter x pi

circ / pi = diameter

113.04 / 3.14 = 36

If the average square footage in an apartment in a town is 1,800 square feet with a standard deviation of 120 square feet, the square footage is normally distributed and if you randomly select 10 apartments in the town, then the probability that the mean will be more that 1900 square feet is 0.46%

To find the probability, follow these steps:

Therefore, the probability that the mean will be more than 1900 square feet is approximately 0.0046, or 0.46%.

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Answer:

Step-by-step explanation:

1. Subtract 200 from 180

200 - 180 = 20

2. Divide the difference of the number of bookmarks by last years

20 / 200 = 0.1

3. Multiply 0.1 by 100 to get the percentage

0.1 x 100 = 10 %

4. Since this is a reduction in number of bookmarks sold, then it would be a -10% change in the number of bookmarks sold.

Answer:

Chemical Change-

Answer:

the right side of the image is truncated,

but "A" seems to be the answer....

take (2,3) and (3,4)

#1) y2-y2/x2-x1 ... 4-3/3-2 = 1 ... slope = 1

#2 ) y = 1x + b

#3 plug in (2,3) ... 3 = 1(2) + b ... B=1

#4 Y= 1 x + 1

Step-by-step explanation:

For the given real number, the correct answer is b. Assumed: 0 < x or x < 3, Proven: \(15 - 8x + x^2 > 0.\)

What is real number?

In mathematics, real numbers are a set of numbers that includes both rational numbers (such as integers and fractions) and irrational numbers. Real numbers can be represented on the number line, extending infinitely in both the positive and negative directions.

In a proof by contrapositive, the original statement is logically equivalent to its contrapositive. The contrapositive of the theorem is formed by negating both the hypothesis and the conclusion of the original statement.

The original statement is:

"For any real number x, if 0 < x < 3, then \(15 - 8x + x^2 > 0.\)"

The contrapositive of the theorem is:

"For any real number x, if 15 - 8x + x^2 ≤ 0, then x ≤ 0 or x ≥ 3."

Now, let's examine the facts assumed and proven in each of the given options:

a. Assumed: \(15 - 8x + x^2 < 0\)

Proven: 0 < x and x > 3

This does not match the contrapositive. It assumes that the expression is negative and concludes that 0 < x and x > 3, which is not the same as the contrapositive.

b. Assumed: 0 < x or x < 3

Proven: \(15 - 8x + x^2 > 0\)

This matches the contrapositive. It assumes either 0 < x or x < 3 and concludes that the expression \(15 - 8x + x^2\) is greater than 0.

Therefore, the correct answer is b. Assumed: 0 < x or x < 3, Proven: \(15 - 8x + x^2 > 0.\)

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The probability of all 4 computers being good was 45.62%, the probability of 3 being good and 1 being defective was 4.58%, and the probability of 2 being good and 2 being defective was 2.29%.

1. The probability that all 4 are good is 90/100 x 89/99 x 88/98 x 87/97 = 0.4562, or 45.62%.

2. The probability that 3 are good and 1 is defective is 90/100 x 89/99 x 88/98 x 10/97 = 0.0458, or 4.58%.

3. The probability that 2 are good and 2 are defective is 90/100 x 89/99 x 10/98 x 10/97 = 0.0229, or 2.29%.

For the first problem, we can use the formula P(A) = n(A)/n(T), which is the probability of an event A occurring. In this case, P(A) = n(A)/n(T) = 4/100 = 0.04. This gives us the result of 0.4562, or 45.62%.

For the second problem, we use the same formula P(A) = n(A)/n(T), which is the probability of an event A occurring. In this case, P(A) = n(A)/n(T) = 3/100 = 0.03. This gives us the result of 0.0458, or 4.58%.

For the third problem, we use the same formula P(A) = n(A)/n(T), which is the probability of an event A occurring. In this case, P(A) = n(A)/n(T) = 2/100 = 0.02 ,then the probability of the next event, which is 89/99, then the probability of the next event, which is 10/98, then the probability of the last event, which is 10/97. This gives us the result of 0.0229, or 2.29%.

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Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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Answer:

64% of the movies he watched were rated as very good

Step-by-step explanation:

\(\frac{16}{25} = \frac{x}{100}\)

16*100 = 1600

1600/25 = 64

\( \huge \underline{ \boxed{ \color{cyan}\tt \dag \: Answer}}\)

\(\tt : \implies percentage = \dfrac{16}{25} \times 100\% \\ \\ \tt : \implies percentage = 16 \times 4 \% \\ \tt : \implies percentage = 64\% \\ \)

\( \color{fuchsia} \tt Hence, \: Answer \: is \: 64 \%.\)

It is proved that 1) AB = AC, 2) angle B = angle C fo the given triangles.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Here in Delta ADB and Delta ADC.

i) Three pair of equal parts are:

AD = AD ( common side )

BD = CD ( as d is the mid point of BC)

AB = AC (given in the question)

ii) Now,

by SSS Concurrency rule,

Delta ADB\cong \Delta ADC

iii) As both triangles are congruent to each other we can compare them and say

angle B = angle C.

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Complete question:

In figure AB=AC and D is the mid point of BC state the 3 pairs of equal parts in

Triangle ADB and triangle ADC

is ADB= ADC? give reason

is <B = <C? why?

PLEASE ANSWERRR ASAP​

Answer:

Perimeter of ABCD = 2(24 + 26 + 28 + 25) = 206 mm.

Step-by-step explanation:

Perimeter of ABCD = 2(24 + 26 + 28 + 25) = 206 mm.

Answer:

$5

Step-by-step explanation:

15x18=270

1170-270=900

900/18=50

Answer:

$60

Step-by-step explanation: This helpful but I can not step by step

(3a) The 95% confidence interval of σ\(_{1}^{2}\)/σ\(_{2}^{2}\) is: [0.1932 , 1.2032].

Variance is the anticipated squared deviation of a random variable from its population mean or sample mean in probability theory and statistics.

F test for variances, using F distribution (\(df_{num}\)=19,\(df_{denom}\)=20) (two-tailed) (validation).

Hypotheses

\(H_{0}:sigma_{1} = sigma_{2}\\\\H_{1}:sigma_{1}\neq sigma_{2}\)

1. H0 hypothesis

Since p-value > α, H0 is accepted.

The sample standard deviation (S) of LaJolla.res' population is considered to be equal to the sample standard deviation (S) of Pt.Loma.ke's population.

In other words, the difference between the sample standard deviation (S) of the LaJolla.res and Pt.Loma.ke populations is not big enough to be statistically significant.

2. P-value

The p-value equals 0.1152, ( p(x≤F) = 0.05759 ). It means that the chance of type I error, rejecting a correct \(H_{0}\), is too high: 0.1152 (11.52%).

The larger the p-value the more it supports \(H_{0}\).

3. The statistics

The test statistic F equals 0.4796, which is in the 95% region of acceptance: [0.3986 : 2.4821].

S1/S2=0.69, is in the 95% region of acceptance: [0.6313 : 1.5755].

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Answer:

B

Step-by-step explanation:

\(\sqrt{x}\) + 6 = x ( subtract 6 from both sides )

\(\sqrt{x}\) = x - 6 ( square both sides )

x = (x - 6)² ← expand using FOIL

x = x² - 12x + 36 ( subtract x from both sides )

0 = x² - 13x + 36 , that is

x² - 13x + 36 = 0 ← in standard form

(x - 4)(x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 9 = 0 ⇒ x = 9

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = 4

left side = \(\sqrt{4}\) + 6 = 2 + 6 = 8

right side = x = 4

Since 8 ≠ 4 then x = 4 is an extraneous solution

x = 9

left side = \(\sqrt{9}\) + 6 = 3 + 6 = 9

right side = x = 9

Thus the solution is x = 9 → B

The quotient of the given expression is (X - 4) / 2X(X + 4).

What is quotient ?

In mathematics, the quotient refers to the result of dividing one number by another. It represents the answer to a division problem, and is commonly expressed in the form of a fraction or decimal. For example, the quotient of 10 divided by 2 is 5, and can be expressed as the fraction 5/1 or the decimal 5.0.

Where as, the remainder is the amount left over after one number is divided by another. When one integer is divided by another integer, the remainder is the integer that is left over and does not divide evenly into the quotient.

To simplify the expression, we can start by factoring the denominator of the second fraction:

2X / (X² - 16) = 2X / (X + 4)(X - 4)

Then, we can rewrite the entire expression using the division by fraction rule, which states that division by a fraction is the same as multiplication by its reciprocal:

X / (X + 4) ÷ 2X / (X + 4)(X - 4)

= X / (X + 4) x (X - 4) / 2X

Next, we can simplify by canceling out common factors:

X / (X + 4) x (X - 4) / 2X

= (X / X) x (X - 4) / (X + 4) x (2 x X)

= (X - 4) / (2X² + 8X)

= (X - 4) / 2X(X + 4)

Therefore, the quotient of the given expression is (X - 4) / 2X(X + 4).

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The problem involves finding the distance from a given point (12, 14, 1) to the y-z plane. The distance can be determined by finding the perpendicular distance from the point to the plane.

The equation of the y-z plane is x = 0, as it does not depend on the x-coordinate. We need to calculate the perpendicular distance between the point and the plane.

To find the distance from the point (12, 14, 1) to the y-z plane, we can use the formula for the distance between a point and a plane. The formula states that the distance d from a point (x₀, y₀, z₀) to a plane Ax + By + Cz + D = 0 is given by the formula:

d = |Ax₀ + By₀ + Cz₀ + D| / √(A² + B² + C²)

In this case, since the equation of the y-z plane is x = 0, the values of A, B, C, and D are 1, 0, 0, and 0 respectively. Substituting these values into the formula, we can calculate the distance from the point to the y-z plane.

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I have attached the image.

a. The upper bound on the probability that the center will recycle more than 55,000 cans on a particular day is 90.9%.

b. Chebyshev’s inequality does not provide a useful lower bound on the probability that the center will recycle 40,000 to 60,000 cans on a certain day

a) Markov’s inequality states that for a non-negative random variable X and any constant c > 0, the probability that X is greater than or equal to c is at most the expected value of X divided by c. Mathematically, we have:

P(X >= c) <= E(X) / c

In this case, X is the number of tin cans recycled in a day, and c = 55,000. The expected value of X is 50,000 cans, so we can apply Markov’s inequality:

P(X >= 55,000) <= E(X) / 55,000 = 50,000 / 55,000 = 0.909 or 90.9%

b) Chebyshev’s inequality states that for any random variable X with finite mean mu and variance sigma^2, the probability that X deviates from its mean by some number k standard deviations is at most 1/k^2. Mathematically, we have:

P(|X - mu| >= k sigma) <= 1 / k^2

In this case, mu = 50,000 and sigma^2 = 10,000, so sigma = sqrt(10,000) = 100. We want to find a lower bound on the probability that the center will recycle between 40,000 and 60,000 cans, which is the same as finding an upper bound on the probability that X deviates from its mean by more than 1 standard deviation. Therefore, we set k = 1 in Chebyshev’s inequality:

P(|X - 50,000| >= 100) <= 1 / 1^2 = 1

Therefore, the probability that X deviates from its mean by more than 1 standard deviation is at most 1. This means that the probability that the center will recycle between 40,000 and 60,000 cans is at least:

1 - P(|X - 50,000| >= 100) >= 1 - 1 = 0 or 0%

since it only guarantees that the probability is not zero, but gives us no information about how close to zero it actually is.

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Using the definition of covariance, Cov(Y(1)Y(2))= 0. From the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2)). So, it can be concluded that Uncorrelated variables need not be independent.

Given joint probability function of Y(1) and Y(2), is

p(Y(1)*Y(2)) = 1/3, for (y(1)*y(2)) = (- 1, 0), (0, 1), (1, 0)

So Y(1), takes random variable -1,0,1.

And Y(2) takes random variable 0,1.

Y(2)|Y(1)      -1               0             1

0                  1/3            0             1/3

1                   0               1/3           0

From the table:

The marginal probability function of Y(1) is;

P(Y(1)=y(1)) = ∑P(Y(1)=y(1)), y(1)= -1,0,1. That is;

Y(1)=y(1)                      -1                   0               1

P(Y(1)=y(1))                  1/3                 1/3             1/3

From the definition of expectation,

E[y(1)]= \(\Sigma_{y_{1}}\) y(1)P(Y(1)=y(1))

E[y(1)]= -1(1/3)+0(1/3)+1(1/3)

E[y(1)]= -1/3+0+1/3

E[y(1)]= 0

The marginal probability mass function of y(2) is

P(Y(2)=y(2)) = ∑P(y(1)y(2)), y(2)= 0,1. That is;

Y(2)=y(2)                    0               1

\(P_{Y(2)}\)(y(2))                  2/3             1/3

Now E[y(2)]= \(\Sigma_{y_{2}}\) y(2)P(Y(2)=y(2))

E[y(2)]= 0(2/3)+1(1/3)

E[y(2)]= 1/3

And

E[y(1)y(2)]= \(\Sigma_{y_{1}}\Sigma_{y_{2}}\) y(1)y(2)P(y(1)y(2))

E[y(1)y(2)]= -1(0)(1/3)+0(1)(1/3)+1(0)(1/3)

E[y(1)y(2)]= 0

From the definition of covariance.

The Cov(Y(1)Y(2))= E[Y(1)Y(2)]-E[Y(1)E[Y(2)]

Cov(Y(1)Y(2))= 0-1/3 (0)

Cov(Y(1)Y(2))= 0

The Cov(Y(1)Y(2))=0, implies that the two variables are uncorrelated. But from the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2))

Hence, it can be concluded that Uncorrelated variables need not be independent.

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Answer:

78

Step-by-step explanation:

1 metre of plastic sheet= 25 1/2

3 1/17 plastic sheet = x

Cross multiply

x = 3 1/17 × 25 1/2

x = 52/17 × 51/2

x = 2652/34

x = 78

Hence the price of 3 1/17 metre of plastic is ¥78

Answer:

\((6x-5)(x^2+2)\)

Step-by-step explanation:

\(~~~6x^3 -5x^2 +12x -10\\\\=6x^3-5x^2+12x-10\\\\=x^2(6x-5) +2(6x-5)\\\\=(6x-5)(x^2+2)\)

Answer:

$4050

Step-by-step explanation:

16% of 7500 is 1200

30% of 7500 is 2250

A very simple way of figuring that out is moving the decimal place two to the left (7500 is now 75.00) and multiplying it by the percent (75*16=1200)

Just subtract the percentage numbers and you're done

7500-1200=6300

6300-2250=4050

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To solve the given problem, we can use the simplex method to maximize the objective function Z = 5x₁ + 8x₂, subject to the following constraints:

4x₁ + 2x₂ ≤ 80

-3x₁ + x₂ ≤ 4

-x₁ + 2x₂ ≤ 20

x₁ ≥ 0, x₂ ≥ 0

(a) To set up the initial tableau for the simplex method, we introduce slack variables s₁, s₂, and s₃ to convert the inequalities into equations:

4x₁ + 2x₂ + s₁ = 80

-3x₁ + x₂ + s₂ = 4

-x₁ + 2x₂ + s₃ = 20

The initial tableau is as follows:

   BV     x₁    x₂    s₁    s₂    s₃    RHS

  ------------------------------------------

   Z      -5    -8     0     0     0      0

  ------------------------------------------

   s₁      4     2     1     0     0     80

   s₂     -3     1     0     1     0      4

   s₃     -1     2     0     0     1     20

(b) By performing the simplex method iterations, we find that the optimal solution is achieved at the corner point (8, 36), with Z = 380. The table of CPF solutions, defining equations, BF solution, nonbasic variables, and Z values is as follows:

 Iteration    CPF Solution    Defining Equations    BF Solution    Nonbasic Variables    Z Value

 -------------------------------------------------------------------------------------------

     1          (8, 0)        s₁ = 0, s₂ = 12, s₃ = 4     (8, 0)          x₁, x₂            40

     2         (8, 36)        s₂ = 0, s₁ = 44, s₃ = 4    (8, 36)             -              380 (Optimal)

(c) Since all the constraints are satisfied at the corner-point feasible solutions, there are no infeasible solutions in this problem.

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The standard unemployment rate can be calculated based on the labor force and the number of unemployed individuals. In this case, with a labor force of 152 million and 13 million unemployed, we can determine the standard unemployment rate.

The standard unemployment rate is a widely used measure to assess the health of an economy's labor market. It is calculated by dividing the number of unemployed individuals by the labor force and multiplying by 100 to express it as a percentage.

The labor force is given as 152 million and the number of unemployed individuals is 13 million. To calculate the standard unemployment rate, we divide the number of unemployed by the labor force and multiply by 100:

Standard Unemployment Rate = (Number of Unemployed / Labor Force) * 100

Plugging in the given values:

Standard Unemployment Rate = (13 million / 152 million) * 100

Calculating this expression, we find that the standard unemployment rate is approximately 8.55%. This means that 8.55% of the labor force is currently unemployed. It is important to note that the standard unemployment rate provides an overview of the current unemployment situation but may not capture the full complexity of the labor market dynamics.

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Answer:

X>3

Step-by-step explanation:

X+9<4X

x-x+9<4x-x

9<3x

3<x

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

In geometry, triangular polygons are ones that have three vertices and a right side. This object in two dimensions has three straight sides. Triangles are examples of three-sided polygons. The sum of a triangle's three angles is 180 degrees. The triangle lies on one plane.

Here,

Given : side = 12cm

Area of an equilateral triangle

=> √3/4 * side²

Side of triangle =12 cm

Area of an equilateral triangle

= >  √3/4 * 12²

=>√3/4 * 12*12

=> 62.28 cm²

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

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The 2-D shape used here is a right triangle. When rotated about the axis, this becomes a cone which is 3-D. See the attached.

In mathematics, rotation is a notion that originated in geometry. Any rotation is a movement of a specific space that retains at least one point.

A rotation differs from the following motions: translations, which have no fixed points, and (hyperplane) reflections, which each have a full (n 1)-dimensional flat of fixed points in an n-dimensional space.

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Answer:

2 miles i think

Answer:

In 1 hour, he'll walk 4/3 miles

Step-by-step explanation:

Ratios:

\(\frac{1/3}{1/4} =\frac{x}{1} \\\\\frac{1}{4} x=\frac{1}{3} \\\\x=\frac{4}{3}\)