a box has width $m$, where $m$ is a prime number. if the box has height $m 2$, length $m-1$, and a volume of 140, what is $m$?

Answer:

2,3 is the paired fraction

Step-by-step explanation:

Answer:

the answer is to this question is f(x)=46

To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

where:

Q is the discharge (flow rate)

n is Manning's coefficient (0.014 in this case)

A is the cross-sectional area of the channel

R is the hydraulic radius of the channel

S is the slope of the channel bed

First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:

A = π * r^2 = π * (3m)^2 = 9π m^2

Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:

R = r = 3m

Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:

S = 1/600

Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):

Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)

Using a calculator, the discharge can be evaluated to get the final result.

To learn more about coefficient : brainly.com/question/1594145

#SPJ11

The equation of the tangent plane to the surface x = h(y, z) at the point (-3, 1, -2) is: -3(x + 3) - 5(y - 1) + (z + 2) = 0.

To find the equation of the tangent plane to the parametrized surface x = h(y, z) at the point (x₀, y₀, z₀) = (-3, 1, -2) with the given partial derivatives, follow these steps:
Step 1: Calculate the gradient vector
Given that ∂h/∂y(1, -2) = -3 and ∂h/∂z(1, -2) = -5, the gradient vector of h at (1, -2) is:
∇h(1, -2) = <-3, -5>.

Step 2: Use the gradient vector to find the normal vector
The gradient vector represents the normal vector of the tangent plane:
Normal vector = <-3, -5, 1> (with the coefficient of x being 1, as required).

Step 3: Write the equation of the tangent plane using the point-normal form
The equation of the tangent plane in point-normal form is:
A(x - x₀) + B(y - y₀) + C(z - z₀) = 0,
where (A, B, C) is the normal vector and (x₀, y₀, z₀) is the point on the plane.

Plugging in the values, we get:
-3(x - (-3)) - 5(y - 1) + 1(z - (-2)) = 0.

So, the equation of the tangent plane to the surface x = h(y, z) at the point (-3, 1, -2) is:
-3(x + 3) - 5(y - 1) + (z + 2) = 0.

To know more about  tangent plane visit:-

https://brainly.com/question/29730345

#SPJ11

Answer:

Given a triangle ABC, Pythagoras' Theorem shows that:

\(c^2=a^2+b^2\)

Thus,

\(c = \sqrt{a^2+b^2}\)

The distance formula, gives an equivalent expression based on two points at the end of the hypotenuse for a triangle.

\(d^2 = (x_{2} -x_{1})^2 + (y_{2} -y_{1})^2\)

\(d = \sqrt{(x_{2}-x_{1})^2 + (y_{2} -y_{1})^2 }\)

Therefore when given the hypotenuse with endpoints at

\((x_{1}, y_{1}) and {(x_{2}, y_{2})\)

We know that the third point of the right triangle will be at

\((x_{2}, y_{1})\)

and that the two side lengths will be defined by the absolute values of:

\((x_{2} - x_{1}) = a\)

\((y_{2} - y_{1}) = b\)

λn = (nπ)^2 - 1, and the corresponding eigenfunction is y_n(x) = B sin(nπ x).

The general solution of the differential equation is of the form

y(x) = A sin(√(λ+1) x) + B cos(√(λ+1) x).

Applying the boundary condition y'(0) = 0, we have:

y'(x) = A√(λ+1) cos(√(λ+1) x) - B√(λ+1) sin(√(λ+1) x)

y'(0) = A√(λ+1) cos(0) - B√(λ+1) sin(0) = 0

Here  A = 0.

Applying  the boundary condition y'(1) = 0, we have:

y'(x) = - B√(λ+1) sin(√(λ+1) x)

y'(1) = - B√(λ+1) sin(√(λ+1)) = 0

Which means that √(λ+1) = nπ for n = 1, 2, 3, ...

In conclusiuon,  λn = (nπ)^2 - 1, and the corresponding eigenfunction is y_n(x) = B sin(nπ x).

Learn more about eigenfunction at: https://brainly.com/question/2289152

#SPJ1

The sum of angle in a triangle is 180°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

The sum of angle A, B and C is 180 i.e A+B +C = 180°

Also a triangle is a 3 sided polygon. The sum of of angle in a polygon is( n-2)180

How do we prove that the sum of angle in a triangle is 180°?

Since triangle is 3 sided, n= 3, because n denote the number if sides

therefore the sum of angle = (n-2) 180 = (3-2)×180

= 180°

therefore the sum of angle In a triangle is 180°

learn more about sum of angle In a triangle from

https://brainly.com/question/25215131

#SPJ1

Answer: The answer is y=3.

Step-by-step explanation: Write in slope-intercept form, y=mx+b. Please mark me as brainliest.

The total number of ways for the men and women to sit on the round table is d) 7!

Since the table is round, we can fix the position of any one person, say a man, without loss of generality. Then there are 7! ways to arrange the 7 men in the remaining positions around the table.

Now, we need to place the 7 women in such a way that no two of them sit together. This can be done as follows: We first place the 7 men in a row. Then, we place the 7 women in the 7 spaces between the men, such that no two women sit together.

The number of ways to do this is the same as the number of ways to arrange the 7 women in a line such that no two of them are consecutive. This is a classic example of a permutation problem with constraints, and the number of such arrangements is given by the formula:

P(7,7) - 7! = 7! - 7! = 6! x 7

Therefore, the total number of ways for the men and women to sit on the round table is:

7! x 6! x 7 = (7!)

For more questions like Permutation click the link below:

https://brainly.com/question/30649574

#SPJ11

To show that {Y(t), t ≥ 0} is a Martingale, we need to prove that E[Y(t)|F(s)] = Y(s) for all s ≤ t, where F(s) is the sigma-algebra generated by B(u), 0 ≤ u ≤ s.

Using the hint, we can compute E[Y(t)|F(s)] as follows:
E[Y(t)|F(s)] = E[B2(t) - t |F(s)]
             = E[B2(t)|F(s)] - t   (by linearity of conditional expectation)
             = B2(s) - t  (since B2(t) - t is a Martingale)
Therefore, we have shown that E[Y(t)|F(s)] = Y(s) for all s ≤ t, and thus {Y(t), t ≥ 0} is a Martingale.
To compute E[Y(t)], we can use the definition of a Martingale: E[Y(t)] = E[Y(0)] = E[B2(0)] - 0 = 0.

Learn more about Martingale here:

https://brainly.com/question/13679553

#SPJ11

We will show that {Y(t), t≥0} is a Martingale by computing its conditional expectation. The expected value of Y(t) is zero.

To show that {Y(t), t≥0} is a Martingale, we need to compute its conditional expectation given the information available up to time s, E[Y(t)|B(u), 0≤u≤s]. By the Martingale property, this conditional expectation should be equal to Y(s).

Using the fact that B2(t) - t is a Gaussian process with mean 0 and variance t3/3, we can compute the conditional expectation as follows:

E[Y(t)|B(u), 0≤u≤s] = E[B2(t) - t | B(u), 0≤u≤s]

= E[B2(s) + (B2(t) - B2(s)) - t | B(u), 0≤u≤s]

= B2(s) + E[B2(t) - B2(s) | B(u), 0≤u≤s] - t

= B2(s) + E[(B2(t) - B2(s))2 | B(u), 0≤u≤s] / (B2(t) - B2(s)) - t

= B2(s) + (t - s) - t

= B2(s) - s

Therefore, we have shown that E[Y(t)|B(u), 0≤u≤s] = Y(s), which implies that {Y(t), t≥0} is a Martingale.

Finally, we can compute the expected value of Y(t) as E[Y(t)] = E[B2(t) - t] = E[B2(t)] - t = t - t = 0, where we have used the fact that B2(t) is a Gaussian process with mean 0 and variance t2/2.

Learn more about variance here:

https://brainly.com/question/31432390

#SPJ11

The number of unemployed in the given economy can be calculated as follows:

Unemployed = Number of Labour force - Number of Employed Unemployed = 625 million - 480 million Unemployed = 145 million

The unemployment rate can be calculated by dividing the number of unemployed individuals by the number of individuals in the labour force and then multiplying the quotient by 100.

Unemployment Rate = (Unemployed/Labour force) × 100 Unemployment Rate = (145 million/625 million) × 100 Unemployment Rate = 23.2%

The population of the given economy can be calculated as follows:

Population = Number of Employed + Number of Individuals not in Labour ForcePopulation = 480 million + 125 millionPopulation = 605 million

Therefore, the number of unemployed in the given economy is 145 million, the unemployment rate is 23.2%, and the population is 605 million.

To know more about hypothetical economy visit:
https://brainly.com/question/30889430

#SPJ11

The directed line segment for all the given transformations to match the transformed line segment from translation 1 to translation 4.

In this question, the translations are defined by a line segment.

Such that in each translation, we can easily find the segment PQ (the measure and the direction).

And all the points in the Polygon P will be connected by that same segment PQ to the equivalent point in the Polygon Q. (where you only move the segment to the correct location, but the length and direction remains constant)

Thus, to find the line segment for each transformation, you need to correctly measure the length of the segment PQ, and also the direction (that can be defined by an angle).

With the above, we can find the directed line segment for all the given transformations to match the transformed line segment from translation 1 to translation 4.

Read more about line segments translation at; https://brainly.com/question/17370215

#SPJ1

Answer:

c

Step-by-step explanation:

1. The number of visitors attending the park when the admission fee is $20.00 is 8,000.

2. The equilibrium price (P*) is $5 and the equilibrium quantity (Q*) is 15.

1. To find the number of visitors attending the park when the admission fee is $20.00, we substitute P = $20.00 into the demand equation Q = 10,000 - 100P:

Q = 10,000 - 100(20)

Q = 10,000 - 2,000

Q = 8,000

Therefore, the number of visitors attending the park when the admission fee is $20.00 is 8,000. The correct answer is option D.

2. To find the equilibrium price (P*) and quantity (Q*) for vanilla ice cream, we set the demand equation equal to the supply equation and solve for P:

20 - p = 10 + p

Combine like terms:

2p = 10

Divide both sides by 2:

p = 5

To find the equilibrium quantity, substitute the value of p into either the demand or supply equation:

Q = 20 - p

Q = 20 - 5

Q = 15

Therefore, the equilibrium price (P*) is $5 and the equilibrium quantity (Q*) is 15. The correct answer is option B.

To learn more about equilibrium price

https://brainly.com/question/22569960

#SPJ11

Answer:

B?

Step-by-step explanation:

Answer:

Step-by-step explanation:

6.56

a) To find the expected value (mean) of the amount of gravel sold in a week, we need to calculate the integral of x times the probability density function (PDF) over the interval [0, 1].

The expected value is given by:

E[X] = ∫x * f(x) dx

Integrating the given PDF over the interval [0, 1]:

E[X] = ∫x * 3(1 - x^2) dx

= 3∫(x - x^3) dx

= 3[(x^2/2) - (x^4/4)] evaluated from 0 to 1

= 3[(1/2) - (1/4) - (0 - 0)]

= 3(1/4)

= 3/4

= 0.75

Therefore, the expected value of the amount of gravel sold in a week is 0.75 tons.

To find the standard deviation, we need to calculate the variance first.

The variance is given by:

Var(X) = E[X^2] - (E[X])^2

To calculate E[X^2], we integrate x^2 times the PDF over the interval [0, 1]:

E[X^2] = ∫x^2 * 3(1 - x^2) dx

= 3∫(x^2 - x^4) dx

= 3[(x^3/3) - (x^5/5)] evaluated from 0 to 1

= 3[(1/3) - (1/5) - (0 - 0)]

= 3(8/15)

= 8/5

= 1.6

Substituting the values into the variance formula:

Var(X) = 1.6 - (0.75)^2

= 1.6 - 0.5625

= 1.0375

Finally, the standard deviation is the square root of the variance:

σ = √(Var(X))

= √(1.0375)

≈ 1.018

Therefore, the standard deviation of the amount of gravel sold in a week is approximately 1.018 tons.

b) To find P(90 ≤ X ≤ 100) for a normally distributed random variable X with a mean (μ) of 85 and a standard deviation (σ) of 10, we need to calculate the probability using the standard normal distribution.

First, we standardize the values:

z1 = (90 - 85) / 10

= 0.5

z2 = (100 - 85) / 10

= 1.5

Next, we look up the corresponding probabilities from the standard normal distribution table:

P(0 ≤ Z ≤ 0.5) = 0.3085

P(0 ≤ Z ≤ 1.5) = 0.4332

Finally, we calculate the desired probability using the properties of the standard normal distribution:

P(90 ≤ X ≤ 100) = P(0 ≤ Z ≤ 1.5) - P(0 ≤ Z ≤ 0.5)

= 0.4332 - 0.3085

= 0.1247

Therefore, the probability of 90 ≤ X ≤ 100 for a normally distributed random variable X with a mean of 85 and a standard deviation of 10 is approximately 0.1247.

Learn more about integral here

https://brainly.com/question/22008756

#SPJ11

Answer:

x = x, y = −5 −3x

Step-by-step explanation:

hope this helps

Correlation is a bi-variate analysis that measures the strength of association between two variables and the direction of the relationship.

What is bi-variate analysis?

Bivariate analysis is one in every of the only kinds of quantitative (statistical) analysis. It involves the analysis of 2 variables (often denoted as X, Y), for the aim of deciding the empirical relationship between them.

Main Body:

The correlation coefficient's value ranges from +1 to -1. the entire degree of correlation between the 2 variables is indicated by a worth of one. The association between the 2 variables are weaker because the parametric statistic price approaches zero.

Hence correlation investigate linear association between two variables.

To know more about bi-variate analysis click on the link below

https://brainly.com/question/16795255

#SPJ4

Answer:

1. To solve a one-variable equation, it may be necessary to first multiply by using the Distributive Property

2. The next step is to combine like terms as needed.

3. Then solve for the variable by applying inverse operations.

4. If solving lead to a true equation, then the equation has infinitely many solutions.

5. if solving leads to an untrue equation, then the equation has no solution.

Answer:

0.07–

Step-by-step explanation:

The answer is above :)

Answer:

to express in decimal form , we have to join convert the mixed fraction into a improper fraction.

8 7/90 = d * w + n

          =  90 * 8 + 7

        =    720 + 7

          = 727 / 90

 now you have to make the denominator into a mutiple of 10

         = 727 / 90  divided by 9

        =  80 / 10

       = 0.80

Step-by-step explanation:

hope it helps .

Answer:

the answer is d

Step-by-step explanation:

hope this helps

The minimum number of neckless needed to sell to make a profit is 18 thus option (A) is correct.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

12n > 135 + 4.50n

In order to make a profit and solve inequality,

12n - 4.50n > 135

7.5n > 135

n > 18

Thus, it needed to sell more than 18 to make a profit.

Hence "The bare minimum of necklaces that must be sold in order to turn a profit is 18".

For more about inequality,

brainly.com/question/20383699

#SPJ1

The scores of both groups are skewed, so the median and standard deviation are the best measures for comparison. Option D is correct.

In comparing the test scores of two groups, it is important to choose appropriate measures of center and variation to accurately represent the data. If both distributions are nearly symmetric, the mean and standard deviation are commonly used.

However, if the distributions are skewed, it is better to use the median and standard deviation as measures. In this particular case, the scores of Group B are skewed right, which means that the mean may not be a reliable measure of center. Instead, the median should be used. The range is not a good measure of variation for skewed data because it is sensitive to extreme values, so the standard deviation is more appropriate. Hence, option D is answer.

To know more about distributions, here

brainly.com/question/13955188

#SPJ4

--The complete question is, The table shows the test scores of students who studied for a test as a group (Group A) and students who studied individually (Group B).

Which would be the best measures of center and variation to use to compare the data?

The scores of Group B are skewed right, so the mean and range are the best measures for comparison.

Both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison.

Both distributions are nearly symmetric, so the median and the interquartile range are the best measures for comparison.

The scores of both groups are skewed, so the median and standard deviation are the best measures for comparison.--

Answer:

135

Step-by-step explanation:

Ratio = 3 : 9

Angles are : 3x , 9x

3x + 9x = 180         {supplementary angles}

   12x   = 180  {divide both side by 12}

       x = 180/12

x = 15

Larger angle = 9x = 9*15 = 135

If a merchant bought an item for $50.00 and sold it for 30% more (markup), the item's selling price was $65.00.

The markup is the percentage or amount by which an item is sold.

The markup is based on the cost price.  After adding the markup amount, the selling price is determined to generate some profits for the seller.

The purchase price of an item = $50.00

The markup = 30%

Markup factor = 1.3 (1 + 0.3)

The selling price of the item = $65.00 ($50.00 x 1.3)

Thus, for adding 30% more (markup) on the cost of the item, the selling price is determined as $65.00.

Learn more about markups at https://brainly.com/question/1445853.

#SPJ1

Answer: (5p^2+3)(p-2)

Step-by-step explanation:

In this problem, we need to write the factor form of expression .

5p^3-10p^2+3p-6

It can be done as follows :

5p^3-10p^2+3p-6=(5p^3+3p)+(-10p^2-6)

Taking common form the terms as follows :

=p(5p^2+3)-2(5p^2+3)

It can be also written as :

=(5p^2 +3)(p-2)

Hence, the factored form of  is

Answer:

(p-2)(5p^2+3)

Step-by-step explanation:

see the image

Answer: multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14)

Step-by-step explanation:

becaue... multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14)