find two positive numbers that satisfy that the product is 147 and the sum of the first number plus three times the second number is a minimum.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

In this problem, the function is:

H(x) = 6x + 90.

Hence the slope and the intercept are given as follows:

m = 6, b = 90.

The domain and the range of the function are given as follows:

The problem is given by the image shown at the end of the answer.

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the closest estimate of the words he would type in that hour is 3180 at this rate.

Given,

rate of 742/14 units

The unit rate will come out to be 53,

then multiply by 60 since there are often 60 minutes in an hour. So the answer is 3180

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Examples of linear equations are 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. Above is sometimes referred to as a "linear equation of two variables," where variables y and x are.

The three primary forms of linear equations are point-slope, standard, and slope-intercept.

Linear equations are a key tool in science that have several real-world applications. They enable researchers to compute rates, define relationships between two variables in the physical world, and make predictions. Linear equations are frequently graphed to identify patterns.

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The green ornaments that Peter remove from the box will be; 30

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

We are given that box of 120 holiday ornaments, 75% are green and the rest are red.

Therefore, 120 ornaments = 100%

75% are green = 75% of 120

0.75 x 120 = 90

And the rest are red means

120 - 90 = 30

Peter removes green ornaments from the box until only 60% of the ornaments in the box are green that means;

60% of 90

0.60 x 90 = 54

Then the green ornaments that Peter remove from the box will be; 30

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Answer:

1176 oz of drink

Step-by-step explanation:

112 * 4 = 448

112 * 3 = 336

112 * 2.5 = 280

112 * 1 = 112

The third side of the triangle whose two sides are 11 cm and 19 cm can be between 9 and 29.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

The sides of triangles are 11 cm and 19 cm,

Let the third side of the triangle is x,

Since, a side of a triangle is greater than the difference of two sides and less than the sum of two sides,

implies that,

19-11<x<19+11

8 < x < 30

The possible range of third side is (9,29).  

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Answer:

8cm < x < 30cm

Step-by-step explanation:

To find the range of lengths for the third side of a triangle when two side lengths are known, first, assign a variable for the length of the third side.

Let x be the length of the unknown side.

Use the Triangle Inequality Theorem to write the three inequalities.

x + 11x > 19

x + 19 > 11

11 + 19 > x

Solve each inequality.

x > 8

x > -8

30 > x

Now find the range of values that satisfies all three inequalities.

The range between 8 and 30 satisfies all 3 inequalities. Therefore, this triangle's third side lengths range is 8cm < x < 30cm.

The acute triangle can not measure 90 degrees because the criteria requires angles to be less than 90 degrees.

Acute triangle is the triangle with all the angles less than 90 degrees. However, the acute angles should always add up to 90 degrees. There are different types of acute triangles such as scalene, isosceles and equilateral triangle.

Acute Equilateral triangle has all the equal sides, acute isosceles triangle has two equal sides and acute scalene triangle has three different sides with different lengths.

Apart from acute angles, there are many other types of angles like obtuse angle and right angle. Right triangle has a 90 degree angle and obtuse triangle has more than 90 degrees angle.

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The equation of the line having equal intercepts on the axes is:

13x+13y=6.

Given:

the straight lines are:

4x-7y-3 and 2x-3y+1

we are asked to determine the equation of the straight line passing through the point of intersection of the lines 4x-7y-3 and 2x-3y+1 and cut with the equal intercept on the axes.

Let the equation of the line having equal intercepts on the axes be

x/a + y/a =1

x + y = a ... eq(1)

On solving equation 4x-7y-3 and 2x-3y+1 we obtain x = 1/13 and y = 5/13.

{1/13,5/13} is the point of intersection of the two given lines.

Since equation (1) passes through point {1/13,5/13}

{1/13+5/13} = a

⇒ a = 6/13

∴ Equation (1) becomes x+y=6/13

⇒ 13x+13y=6

Thus the required equation of the line is 13x+13y=6.

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Your question is incomplete. Please find the missing content here.

Find the equation of the line passing through the point of intersection of the lines 4x-7y-3 and 2x-3y+1  that has equal intercepts on the axes.

The differential equation that satisfies the given amount of investment is A'(t) = rA(t)

Let the rate of investment = r

The amount of investment must satisfy the differential equation

A'(t) = r A(t)

Initial condition is the value of A(t) at t = 0

No compounding will be applied at t = 0 and the amount is equal to the original amount invested, known as principal.

If the Principal amount is P, then the initial condition is A(0) = P

Hence, the differential equation is A'(t) = rA(t)

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The total number of ways to line up 12 people are 479,001,600.  

We have 12 members of wedding party. We need to make arrangements for 12 people to line up for a photograph.

If we have total n objects and we need to arrange r objects then it can be done in [tex]^nP_r[/tex] ways which is equivalent to =(n!/(n-r)!)

Now, here we have 12 members for photograph, we are free to choose any of members from 12 members.

So, this can be done in [tex]^1^2P_1_2[/tex] ways which is equivalent to =(12!/(12-12)!)=12!/0!

We know that 0!=1

Therefore,12!/0!=12!=479,001,600

Hence, total number of ways are 479,001,600.

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Thus, the minimum time taken for a car from start to end of the assembly unit is 14.

Algorithm for assembly line scheduling using dynamic programming:-

1. We need following parameter:

· S[i,j]: The jth station on ith assembly line

· a[i,j]: Time required at station S[i,j], because every station has some dedicated job that needs to done. · e[i]: Entry time of product on assembly line i [here i= 1,2] · x[i]: Exit time from assembly line i· t[i,j]: Time required to transit from station S[i,j] to the other assembly line.

2. Further in dynamic programming we have to ways to do so:

· Reach station S1j from S1,j-1 (same assembly line).

· Reach station S1j from S2,j-1 (switch from second assembly line).

3. Calculate minimum time to leave.

4. After that find the minimum time to leave the previous two stations.

5. Then combining it with the time spent on station.

6. calculate the leaving time of previous stations.

7. Finally, we need two tables to store the partial results that are calculated for each station in an assembly line.

Example:- a = [[5,4,3], [2,3,7]], t = [[0,2,2], [0,1,1]]

e1 = 3, e2 = 2

x1 = 3, x2 = 4

T1[0] = e1 + a[0][0] = 3+5 = 8

T2[0] = e2 + a[0][1] = 2+2 = 4

T1 = [8, 0, 0]

T2 = [4, 0, 0]

i = 1

T1[1] = min(T1[1-1] + a[0][1], T2[1-1] + t[1][1] + a[0][1])

= min(8+4, 4+1+4) = min(12,9)

T1[1] = 9

T2[1] = min(T2[1-1] + a[1][1], T1[1-1] + t[0][1] + a[1][1])

= min(4+3, 8+2+3) = min(7,13)

T2[1] = 7

T1 = [8, 9, 0] T

2 = [4, 7, 0]

i = 2

T1[2] = min(T1[2-1] + a[0][2], T2[2-1] + t[1][2] + a[0][2])

= min(9+3, 7+1+3) = min(12,11)

T1[2] = 11

T2[2] = min(T2[2-1] + a[1][2], T1[2-1] + t[0][2] + a[1][2])

= min(7+7, 9+2+4) = min(14,15)

T2[2] = 14​

T1 = [8, 9, 11]

T2 = [4, 7, 14]

ans = min(T1[n-1]+x1, T2[n-1]+x2)

= min(11+3, 14+4) = min(14, 18)

ans = 14

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Answer:

18.75

Step-by-step explanation:

"Of", in math, typically denotes multiplication, which means we multiply 75% and 25 to find "75% of 25":

75% = 0.75

0.75 * 25 = 18.75

Sand is leaving at the rate of 3528 cm³/s when Sand collects in a conical pile with a radius that is always three times.

Given that,

Sand collects in a conical pile with a radius that is always three times its height as it falls from an overhead container. When the pile is 14 cm high, assume that the height of the pile is growing at a rate of 2 cm/s.

We have to find how quickly is the sand currently leaving the bin. Let V and h represent the cone's volume and height, respectively. Create an equation that connects V and h but leaves out the cone's radius.

We know that,

From given  r = 3 × h

Get an equation for the cone's volume in terms of height first.

v = 1/3 × π × r² × h

v = 1/3 × π × (3 × h)² × h

v = 1/3 × π × 9 × h³

Take derivative of both sides

d/dt { v = 3 × π × h }

dv/dt = 9 × pi × h² × dh/dt

In your problem,

dh/dt =2cm/sd

h = 14 cm

Plug in and solve for dh/dt

dv/dt = 9× π × 196 m² × 2

dv/dt = 3528 π cm³/s

Therefore, Sand is leaving at the rate of 3528 cm³/s when Sand collects in a conical pile with a radius that is always three times.

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Amount invested at rate 8% is, $5060.

Amount invested at rate 2% is, $4260.

What is addition method?

Using the Addition Method to Solve Systems of Equations in Two Variables. The addition approach, often known as the elimination method, is a third strategy for resolving linear equation systems. With this approach, we combine two components that share the same variable but have opposing coefficients, resulting in a sum of zero.

Let,  money is invested at two rates of interest.

One rate is 8% and the other is 2%.

There is $800 more invested at 8 % than at 2 %.

Total annual interest received is $490.

Let x = amount invested at 8 % and

y = amount invested at 2 %.

So,

x - y = 800                    ..(1)

0.08x + 0.02y = 490        ..(2)

Multiply equation (1) by -8 and equation (2) by 100

-8x + 8y = -6400            ..(3)

8x + 2y = 49000           ..(4)

Adding equation (3) and (4)

(-8x + 8y) + (8x + 2y) = -6400 + 49000

                           10y = 42600

                               y = 4260

Plug y = 4260 in equation (1)

x - 4260 = 800

           x = 800 + 4260

           x = 5060

Hence, amount invested at 8% = $5060.

amount invested at 2% = $4260.

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The common ratio is 1/3.

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

The common ratio is expressed as the value r. It can be calculated by taking any term in the sequence and dividing it by the term before it.

Here, 108/324 = 1/3 ( it is a constant ratio )

Hence it is a geometric sequence and common ratio is 1/3.

Next terms can be found by multiplying the common ratio with the previous term.

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As per the given probability, the estimated number of tosses in a single trial of the game is 7/11

Probability:

Basically, the term Probability refers the possibility of happening the particular event.

Given,

Here we have to simulate a toss of a coin we let the digits 0, 1, 2, 3, and 4 correspond to a head and the digits 5, 6, 7, 8, and 9 correspond to a tail. And consider the following game: We are going to toss the coin until we either get a head or we get two tails in a row, whichever comes first. If it takes us one toss to get the head we win $2, if it takes us two tosses we win $1, and if we get two tails in a row we win nothing.

While we looking into the given question we have identified that, the total number possible events is 11.

And we have to find the single trial of the game that is 7.

So, the estimated number of tosses in a single trial of the game is written as,

=> 7/11

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Using Combination formula,

Total 5,110 ways are possible that the coin land tails either exactly 9 times or exactly 2 times

Combinations:

If the order of events is not important, the concept of combination determines the number of ways in which a sequence of events can be obtained. I need to find the total number of expected events and the total number of possible events.

We have given that,

A unbiased or fair coin is tossed 15 times.

let us consider two events

A : the coin land tails exactly 9 times

B : the coin land tails exactly 2 times

Now, for calculating the required result we use

Combination formula,

ⁿCₓ= n! /x! (n-x)!

here, n= 15

the number of ways that exactly 9 times coin land as tails (n(A))= ¹⁵C₉ = 15! /9!× 6!

= 15×14×13×12×11×10×9!/ 9!(6×5×4×3×2×1)

= (15×14×13×12×11×10)/( 6×5×4×3×2×1 )

= (15×14×13×11)/6 = 7× 5× 13×11 = 5005

the number of ways that exactly 2 times coin land as tails (n(B))= ¹⁵C₂= 15! /2!× 13!

= 15×14×13!/13!(2)

= 15×14/2 = 15×7 = 105

Now, the number of ways that the coin land tails either exactly 9 times or exactly 2 times

= n(A) + n(B) = 5005 + 105

= 5110

Hence , total required ways are 5,110.

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The probability that the mean time for the sample of 150 returns for this year is greater than 92 is 0.95907

Given,

Mean, [tex]\overline x[/tex] = 90 minutes

standard deviation, [tex]\sigma[/tex] = 14 minutes

to find probability that mean for sample 150 returns is greater than 92, [tex]P(\overline x > 92)[/tex]

This means we need to find probability the related z-value of expected mean

where, [tex]z=\frac{\overline x-\mu_x}{\sigma_x}[/tex]

Here,

[tex]\mu_x[/tex]= expected mean =92

[tex]\sigma_x[/tex]=standard deviation for new sample i.e. 150

[tex]\sigma_x[/tex] can be calculated by formula,

[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\\sigma_x=\frac{14}{\sqrt{150}}\\\\\sigma_x=1.143[/tex]

Now,

[tex]z=\frac{90-92}{1.143}\\\\z=-1.749[/tex]

Now,

[tex]P(\overline x > 92)\\\\=P(z > -1.749)\\\\=1-P(z < -1.749)\\\\=1-0.04093\\\\=0.95907[/tex]

In above calculation, the z-value is  determined from the z-table.

Thus, the probability that mean is greater than 92 is 0.95907

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Your question is incomplete, please complete the question.

Answer:

36 different salads can be ordered

Step-by-step explanation:

The two facts that might be multiplied by two to get the result of eight and four are (4 and 4)

Given,

The two facts of a doubled number can be written as: 2 b = c.

Here,

The value of c is (84) = 32.

After entering the values into the equation, find b.

2 × b = c

2 × b = 32

Divide through by 2

b = 32 / 2

b = 16

Therefore, (4 4) is a pair of facts that can be doubled.

2(4 × 4) = 2(16) = 32

That is,

The two facts that might be multiplied by two to get the result of eight and four are (4 and 4)

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Answer:

94°

Step-by-step explanation:

Interior angles:

m<C = 49°

m<D = ?

Angles CBD and CBY are supplementary.

m<CBD = 180° - 143° = 37°

m<C + m<D + m<CBD = 180°

49° + m<D + 37° = 180°

m<D = 94°

Sketch is attached in the graphical form to illustrate the linear relationship with slope of 3 that is not the proportional relationship.

A statistical word is used to express the straight-line relationship between two variables which is a linear relationship (or linear association). A straight line connecting the variable and the constant can be used to represent a linear relationship graphically, or the dependent variable can be determined by multiplying the independent variable by the slope coefficient and a constant.

A linear non - proportional relationship could be written with as a slope - intercept with a non - zero intercept value. One such relationship with a slope of 3 can be expressed thus :

   y = 3x + 5

Here, the linear relationship, has a slope value of 3 and an intercept value of 5. The function cannot be proportional due to the presence of a non-zero constant

Hence, Using a graph plotter, the sketch of the given linear relationship is attached.

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The points have two coordinates, (x, y)

To plot a point, mark x coordinate on the x-axis, y-coordinate on the y-axis, then add imaginary lines parallel to x- and y-axis, the intersection of those lines is the point to be plotted.

The points we have:

See attached, it should be clear visually.

Standard Deviation statistic of the sampling distribution is used in calculating the margin of error for a confidence interval of the population mean.

Basically, the margin of error is stated as follows:

Error margin, E = Z* (Standard deviation)

Therefore, the calculation of the margin of error does not employ the mean at all.

The margin of error is computed using the standard deviation.

The term "standard deviation" reveals that a measurement of the data's dispersion from the mean. While a high standard deviation indicates that the data are more spread or dispersed, a low standard deviation suggests that the data are clustered or gathered around the mean.

It depicts the average deviation of each score from the mean. A high standard deviation in a normal distribution denotes that values are often far from the mean, while a low standard deviation denotes that values are grouped together around the mean.

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The difference between 2X₁ and  X₁+X₂ is N(0,6σ²)

According to the Central Limit Theorem, any large sum of the independent, identically distributed(iid) random variables is approximately Normal.

We know very well that the Normal distribution is defined by two parameters, the mean is μ , and the variance is σ²  and written as X=N(μ,σ²).

Using the  properties of normal random variables, we get

if  X=N(μ₁,σ₁²)and Y=N(μ₁,σ₁²) are two independent identically distributed random variables then

the sum of normal random variables is represented by

=>X+Y=N(μ₁+u₂,σ₁²+σ₂²)

and the difference of normal random variables is represented by

=>X-Y =N( μ₁-u₂,σ₁²+σ₂²)  

When  Z=aX+bY, the linear combination of X and Y is given by

=>Z=N(aμ₁+bu₂,a²σ₁²+b²σ₂²)

Similarly, When Z=aX , the product of X is given by

=>Z=  N(aμ₁,a²σ₁²)

We need to find 2X₁

Thus, following the property of multiplication, we get

=>2X₁=N(2μ,2²σ²)

=>2X₁=N(2μ,4σ²)

and following the property of addition,

X₁+X₂=N(μ+μ,σ²+σ²)

And the difference between the two is given by

2X₁-(X₁+X₂)=N(2μ-2μ,2σ₁²+4σ₂²)

=>2X₁-(X₁+X₂)=N(0,6σ²)

Hence, the required difference is N(0,6σ²).

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(Complete question) is:

consider two random variable X₁, X₂, which are uniformly distributed in the triangle. now suppose that Y₁ ,Y₂ are two random variables and If X₁ = N(μ, σ₂) and X₂ =N(μ, σ₂) are iid normal random variables, then what is the difference between 2 X₁ and X₁ + X₂?    

Answer:

6 + [tex]\frac{3}{y}[/tex]

Step-by-step explanation:

"Sum of" means "this number plus whatever follows." In other words: 6 + ?.

"The quotient of 3 and a number" means 3 divided by said number, so:

6 + 3/x

Answer:

No. It is not possible to construct a triangle with lengths of its sides 4cm, 5cm and 9cm because the sum of two sides is not greater than the third side:

5 + 4 is not greater than 9.

Step-by-step explanation:

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The equation of the line that passes through the point (8,0) and is parallel to the line x + y = 5 is x + y = 8.

Two lines are parallel with each other if they do not intersect no matter how much you extend both lines. Parallel lines have equal slopes.

Get the slope of the given line x + y = 5.

y = -x + 5

m = -1

Hence, the equation of the line should also be equal to -1.

Using the point slope form, plug in the values of the slope and the point to set up the equation.

(y - y₁) = m(x - x₁)

(y - 0) = -1(x - 8)

y = -x + 8

Rearranging, x + y = 8.

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The sum of integers is: S = n(a + l)/2

Integer numbers are those without fractional or decimal parts. When there are fewer numbers to add, it is possible to determine the sum of integers using basic mathematics. However, we employ the sum of integers formula if we need to add multiple consecutive integers at once. Our computations are made easier, and the amount of time we spend adding is reduced.

The sum of an arithmetic sequence's n terms is what is meant by the sum of integers formula. The formula for the sum of integers is:

S = n(a + l)/2

where,

S = sum of the consecutive integers

n= number of integers

a= first term

l = last term

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The solution to the system of linear equation is (x, y) = (6, 2)

What in mathematics is a linear equation?

3x - 2y = 14 (1)

3x - 2y = 14 (1)5x + y = 32 (2)

From (2)

y = 32 - 5x

Substitute y = 32 - 5x into (1)

3x - 2y = 14 (1)

3x - 2(32 - 5x) = 14

3x - 64 + 10x = 14

13x = 14 + 64

13x = 78

x = 78/13

x = 6

Substitute x = 6 into (2)

5x + y = 32 (2)

5(6) + y = 32

30 + y = 32

y = 32 - 30

y = 2

(x, y) = (6, 2)

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The complete question is -

What is the solution to this system of linear equations? 3x – 2y = 14 5x + y = 32 (3, 5) (6, 2) (8, –1) (14, –18)

Answer:

(6,2)

Step-by-step explanation:

i just did the