Convert 2 3/4 to a decimal number.

The value of z-score for James is 0.2

Step-by-step explanation:

From the formula of z-score we know that

z-score = individual score - mean / standard deviation

Given

James score = 40

Mean = 38

Standard deviation = 10 (missing in question)

To find

z-score =?

Let's put the values in the formula

z-score = 40-38/ 10

z-score = 0.2

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Answer:

x=7

Step-by-step explanation:

AC=3x+3  AB=-1+2x and BC=11

AC = AB + BC

ALL THE STEPS:

3 X + 3 = - 1 + 2 X + 11

3 X + 3 = 2 X + 10

3 X + ( - 2 X ) + 3 = 2 X + ( - 2 X ) + 10

X + 3 = 10

X + 3 + ( - 3 ) = 10 + ( - 3 )

X = 7

There are 28 ways to choose 6 teams for the playoffs if there are 8 college basketball teams in a certain sub-division.

To determine the number of ways to choose 6 teams for the playoffs out of the 8 college basketball teams in a certain Sub-Division, we can use the combination formula. The formula for combinations is given by

nCr = n! / (r! * (n-r)!),

where n represents the total number of teams and r represents the number of teams to be chosen.

In this case, n = 8 and r = 6.

Plugging in these values, we have

8C6 = 8! / (6! * (8-6)!) = 8! / (6! * 2!) = (8 * 7) / (2 * 1) = 28.

Therefore, there are total 28 ways to choose 6 teams.

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An equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4 is 3x - y + 3z = 0.

To find an equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4, we can use the fact that parallel planes have the same normal vector.

Step 1: Find the normal vector of the given plane.
The normal vector of a plane with equation Ax + By + Cz = D is . So, in this case, the normal vector of the given plane is <3, -1, 3>.

Step 2: Use the normal vector to find the equation of the parallel plane.
Since the parallel plane has the same normal vector, the equation of the parallel plane passing through the origin is of the form 3x - y + 3z = 0.

Therefore, an equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4 is 3x - y + 3z = 0.

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We need to divide the next rational expressions:

The first thing that we need to do is factorize the denominators and numerators, maybe we can cancel some terms.

The expression cant be factorized, now we are going to divide the terms:

Change the second fraction, now the denominator is the numerator:

Then change the division sign to the multiplication sing *

Multiply the expression and reduce the fraction if it is possible:

Factorize the expression:

Now, we have the expression like this:

Cancel the similar terms 6y-1:

Factorize 11y^2 + 46y + 48

=(11y^2+2y) + (44y+8)

Factorize y from (11y^2+2y)

=y(11y+2)

Factorize 4 from 44y+8

= 4(11y+2)

So the solution is:

=(11y+2)(y+4)

Cancel common terms 11y+2

Where 4y-1 is my numerator and y+4 my denominator.

David, Jeff, and Paula have (7d)/3 books.

To find out how many books David, Jeff, and Paula have altogether in terms of d, we can use the given information as follows:

1. David has d books.
2. David has 3 times as many books as Jeff, so Jeff has d/3 books.
3. David has the same number of books as Paula, so Paula also has d books.

Now, to find the total number of books for all three of them, we simply add the number of books each person has:

Total books = David's books + Jeff's books + Paula's books
Total books = d + d/3 + d

To combine these terms, we can find a common denominator (in this case, 3):
Total books = (3d + d + 3d) / 3

Now, we can simplify the expression:
Total books = (7d) / 3

So, altogether, David, Jeff, and Paula have (7d)/3 books in terms of d.

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The average value of f over the rectangle [0,6] x [0,1] is approximately 3.427.

The average value of a function f over a rectangle R is given by:

avg(f) = (1/Area(R)) * double integral of f over R

Here, f(x,y) = 5e^(yx) + e^y and R = [0,6] x [0,1]

The area of R is given by:

Area(R) = (6 - 0) * (1 - 0) = 6

So, the average value of f over R is:

avg(f) = (1/6) * double integral of f over R

We can evaluate the double integral using iterated integration. First, we integrate f with respect to y from 0 to 1, and then integrate the result with respect to x from 0 to 6:

integral of f(x,y) dy = integral of (5e^(yx) + e^y) dy

= (5x/2)e^(yx) + e^y + C

where C is the constant of integration.

Now, we integrate this result with respect to x from 0 to 6:

integral of [(5x/2)e^(yx) + e^y] dx = [(5/2) * integral of xe^(yx) dx] + integral of e^y dx

= [(5/2) * (1/y)e^(yx) - (5/2)(1/y^2)(e^(yx) - 1)] + ey + C

where C is another constant of integration.

Therefore, the average value of f over R is:

avg(f) = (1/6) * [(5/2) * (1/y)e^(yx) - (5/2)(1/y^2)(e^(yx) - 1) + ey] evaluated from y=0 to y=1 and x=0 to x=6

avg(f) = (1/6) * [(5/2) * (1/e^6 - 1) - (5/2)(1/e - 1/e^6) + e - 1]

avg(f) = (1/6) * [(5/2) * (1 - e^-6) - (5/2)(e^-1 - e^-6) + e - 1]

avg(f) = (1/6) * [(5/2) * (1 - e^-6 - e^-1 + e^-6) + e - 1]

avg(f) = (1/6) * [(5/2) * (1 - e^-1) + e - 1]

avg(f) ≈ 3.427

Therefore, the average value of f over the rectangle [0,6] x [0,1] is approximately 3.427.

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Answer:

x=8 and y=2

Step-by-step explanation:

x+y=10

x=4y

x+y=10

4y+y=10

5y=10(divide both sides by 5)

y=2

x=4y=4*2=8

Answer:

2 and 8.

Step-by-step explanation:

y = -x + 10

y = 4x

If we subtract we eliminate y:

0 = -x + 10 - 4x

0 = -5x + 10

5x = 10

x = 2.

and y = 4 * 2 = 8.

The substitution method proved that the solution to the recurrence equation T(n) = T(n/2) + n is T(n)

To show that the solution to the recurrence equation T(n) = T(n/2) + n is T(n) = O(n) using the substitution method,  to prove that T(n) is upper-bounded by a linear function of n.

We will use the substitution method to prove this by assuming that T(n) ≤ c × n for some constant c and for all n that are powers of 2.

Base case: Let's consider n = 1. The base case is given as T(1) = 1, which satisfies the inequality T(1) ≤ c × 1, where c can be chosen as any positive constant.

Inductive hypothesis: Assume that for all k < n, the inequality T(k) ≤ c × k holds.

Inductive step: We need to prove that T(n) ≤ c × n.

Using the recurrence equation, we have:

T(n) = T(n/2) + n

By the inductive hypothesis, we can substitute T(n/2) with c × (n/2):

T(n) ≤ c × (n/2) + n

Simplifying:

T(n) ≤ (c/2) × n + n

T(n) ≤ (c/2 + 1) × n

Let's choose c = 2 to ensure (c/2 + 1) = 2, resulting in:

T(n) ≤ 2 × n

Therefore, we have shown that T(n) is upper-bounded by a linear function of n, specifically T(n) = O(n).

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Using the Laplace transform, the solution to the given initial value problem y" - 4y - 60y = 0; y(0) = 12, y'(0) = 24 y(t) is "y(t) = 6e^(8t) + 6e^(-8t)."

To use the Laplace transform to solve the given initial value problem, we need to follow these steps:

1. Apply the Laplace transform to both sides of the equation. Recall that the Laplace transform of the derivative of a function is given by sF(s) - f(0), where F(s) is the Laplace transform of f(t). Similarly, the Laplace transform of the second derivative is s^2F(s) - sf(0) - f'(0).

Taking the Laplace transform of the given equation, we have:

s^2Y(s) - sy(0) - y'(0) - 4Y(s) - 60Y(s) = 0

Substituting the initial values y(0) = 12 and y'(0) = 24, we get:

s^2Y(s) - 12s - 24 - 4Y(s) - 60Y(s) = 0

2. Combine like terms and rearrange the equation to solve for Y(s):

(s^2 - 4 - 60)Y(s) = 12s + 24

Simplifying further, we have:

(s^2 - 64)Y(s) = 12s + 24

3. Solve for Y(s) by dividing both sides of the equation by (s^2 - 64):

Y(s) = (12s + 24) / (s^2 - 64)

4. Decompose the right side of the equation into partial fractions. Factor the denominator (s^2 - 64) as (s - 8)(s + 8):

Y(s) = (12s + 24) / ((s - 8)(s + 8))

Using partial fractions decomposition, we can write Y(s) as:

Y(s) = A / (s - 8) + B / (s + 8)

where A and B are constants to be determined.

5. Solve for A and B by equating numerators:

12s + 24 = A(s + 8) + B(s - 8)

Expanding and rearranging the equation, we get:

12s + 24 = (A + B)s + (8A - 8B)

Comparing the coefficients of s on both sides, we have:

12 = A + B        (equation 1)
0 = 8A - 8B       (equation 2)

From equation 2, we can simplify it to:

A = B

Substituting this result into equation 1, we get:

12 = 2A

Therefore, A = 6 and B = 6.

6. Substitute the values of A and B back into the partial fractions decomposition:

Y(s) = 6 / (s - 8) + 6 / (s + 8)

7. Take the inverse Laplace transform of Y(s) to find the solution y(t):

y(t) = 6e^(8t) + 6e^(-8t)

Therefore, the solution to the given initial value problem y" - 4y - 60y = 0; y(0) = 12, y'(0) = 24 y(t) is:

y(t) = 6e^(8t) + 6e^(-8t)

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Answer:

(0, 0), (4, 0), (4, -5)

Step-by-step explanation:

This one keeps the same lengths of the previous triangle. It also keeps the same proportions (or something) etc, etc. I solved this problem by graphing and seeing which one fit best.

Answer:

I think x is 60 and y is 50.

Step-by-step explanation:

70 + 50 = 120

180 - 120 = 60

x = 60

50 + 50 = 100

70 + 60 = 130

130 + 100 = 230

230 - 180 = 50

y = 50

I hope this helps u! :D

Answer:

x=60 y=50

Step-by-step explanation:

180 is equal to the whole triangle so 50+70=120 and 180-120= 60

the other triangle has a missing value by doing the same thing before we can figure out that the missing value is 70. 70+x which is 60 equals 130. A straight line is equal to 180 so 180-130= 50.

Hope I could help!

49.07 is the mean and standard deviation of the waiting time .

What is standard deviation in math?

Your dataset's average level of variability is represented by the standard deviation. It reveals, on average, how far away from the mean each value is.

                                A low standard deviation means that values are clustered close to the mean, whereas a high standard deviation means that values are typically far from the mean.

Let X shows the waiting time. So mean

μ = E(x) = a + b/2 =  30 + 200/2  = 115

Standard deviaiton

 σ = \(\sqrt{\frac{(b - a )^{2} }{12} }\)

     = \(\sqrt{\frac{(200 -30)^{2} }{12} }\)

     = 49.07

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Answer:

∠ MON = 15°

Step-by-step explanation:

∠ LOM + ∠ MON = ∠ LON, substitute values

9x + 44 + 6x + 3 = 77, that is

15x + 47 = 77 ( subtract 47 from both sides )

15x = 30 ( divide both sides by 15 )

x = 2

Thus

∠ MON = 6x + 3 = 6(2) + 3 = 12 + 3 = 15°

Answer:

Alternative exterior angles --> <1 and <7

Corresponding angles --> <2 and <6

Alternative Interior angles --> <3 and <5

Hope this helps and stay safe, happy, and healthy, thank you :) !!

Two rays with a common endpoint form an angle. An angle is defined as a geometric figure formed by two rays that share a common endpoint. In other words, an angle is formed when two rays emanating from a common point, and this common point is known as the vertex.

The rays are the sides of the angle, and the angle is measured in degrees. Angles have different measures, ranging from 0 degrees to 360 degrees. The two rays that make up an angle are also called the sides or arms of the angle. The angle is measured in degrees, and the size of the angle depends on the distance between the two sides of the angle that meet at the vertex.

In geometry, an angle can be named in different ways, depending on the context in which it is being used. Angles are essential in mathematics, physics, and other scientific fields, where they are used to measure the rotation of an object, determine the direction of an object, and in other applications involving rays and lines. Two rays with a common endpoint form an angle.

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Final Answer: \(x = 3 + \sqrt{2}, 3 - \sqrt{2}\)

Steps/Reasons/Explanation:

Question: Solve by using the quadratic formula:  \(x^{2} - 6x + 7 = 0\).

Step 1: Use the Quadratic Formula.

\(x = \frac{6 + \sqrt[2]{2} }{2}, \frac{6 - \sqrt[2]{2} }{2}\)

Step 2: Simplify solutions.

\(x = 3 + \sqrt{2}, 3 - \sqrt{2}\)

~I hope I helped you :)~ The quadratic formulaic is attached in an image.

The distance between the walkers will increase at the rate of 5mph.

According to the question,

Two people start walking in different direction from same point.

Speed on the person walking west = 3mph

Speed of the person walking south = 4mph

The angle formed by the point connecting two persons will be = 90 degree

Applying Pythagoreans  theorem,

\(p^{2} + b^{2} = h^{2}\)

\(4^{2} + 3^{2} = h^{2}\)

\(16 + 9 = h^{2}\)

\(h^{2} = 25\)

\(h = \sqrt{25}\)

h = 5mph.

Thus after two hours, the distance between same two persons will be 10m.

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The expression \(ln \sqrt[3]{\frac{A^2B}{C}}\) is equivalent to \(ln(\frac{B}{lnx})\).

The expression in a form with no logarithm of a product, quotient or power is;

\(ln \sqrt[3]{\frac{A^2B}{C}}\)

Using the laws of logarithms, we have;

\(\ln \sqrt[3]{\frac{A^2B}{C}} = \frac{1}{3}\ln(A^2B)-\ln(C)\)

Substituting A = B and C = ln x, we get;

\(\frac{1}{3}\ln(A^2B)-\ln(C) = \frac{1}{3}\ln(B^3)-\ln(lnx) = \ln(\sqrt[3]{B^3})-\ln(lnx) = \boxed{\ln(\frac{B}{lnx})}\)

Therefore, the expression \(ln \sqrt[3]{\frac{A^2B}{C}}\) is equivalent to \(ln(\frac{B}{lnx})\).

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The Niagara Falls incline railway rises vertically by approximately 98 feet.

The angle of elevation of 30° indicates the angle between the incline railway and the horizontal ground. The total length of the incline railway is given as 196 feet.

To find the vertical rise, we can use trigonometry. The vertical rise can be determined by calculating the sine of the angle of elevation and multiplying it by the total length of the incline railway:

Vertical rise = Total length × sine(angle of elevation)

Vertical rise = 196 ft × sin(30°)

Vertical rise ≈ 196 ft × 0.5

Vertical rise ≈ 98 ft

Therefore, the Niagara Falls incline railway rises vertically by approximately 98 feet.

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Answer:

The midpoint is (4, 3).

Step-by-step explanation:

to get the midpoint (x1+x2/2, y1+y2/2)

(0+8/2, 0+6/2)

(4, 3)

The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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Answer:

No, because the y-intercepts of lines g and h are different.

Step-by-step explanation:

The location of the given point F7 is: B(-9, -1)

There are different transformations such as:

Reflection

Translation

Rotation

Dilation

Since Point F' is the image when point F is reflected over the line x= -2 and then over the line y = 3. The location of F' is (5, 7).

So here we have to do graph the points, then connected the points i.e. 5 and 7. And, then reflect it over the line i.e. x = -2, and y = 3

So here the answer should be (-9,-1)

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Using a system of equations, the quantity of Type A coffee that Trey's Coffee Shop blended with Type B coffee was 78 pounds.

A system of equations or simultaneous equations is two or more equations solved concurrently, simultaneously, or at the same time.

Unit Cost Per Pound:

Type A coffee = $5.80

Type B coffee = $4.25

The total quantity of pounds of the blend = 142 pounds

The total cost of 142 pounds = $724.40

Let the number of Type A coffee = x

Let the number of Type B coffee = y

x + y = 142 ... Equation 1

5.8x + 4.25y = 724.40 ... Equation 2

Multiply Equation 1 by 4.25:

4.25x + 4.25y = 603.5 ... Equation 3

Subtract Equation 3 from Equation 2:

5.8x + 4.25y = 724.40

-

4.25x + 4.25y = 603.5

1.55x = 120.9

x = 78

Substitute x = 78 in either equation:

x + y = 142

78 + y = 142

y = 64

Thus, 78 pounds of Type A coffee was used for the mixture.

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The constant of proportionality of the relation between the height on set and the actual height is given as follows:

0.55.

A proportional relationship is defined according to the equation presented as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

The variables for this problem are given as follows:

Considering the values of these variables for the door, the constant is obtained as follows:

k = 44/80

k = 0.55.

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Answer:

f(1)=3×1^4- 1^2+4×1-2

f(1)=3-1+4-2

f(1)=7-3

f(1)=4

Ans:4

Answer:

8

Step-by-step explanation:

The measure of angle <3 is 105 degrees

The diagram that completes the question is added as an attachment

The angle is given as

<6 = 75

From the diagram, we have

<3 + <6 = 180 degrees

The above is true by the sum of internal angles between parallel lines

So, we have

<3 + 75 = 180

Subtract 75 from both sides of the equation

So, we have

<3 + 75 - 75 = 180 - 75

Evaluate the like terms

So, we have

<3 = 105

Hence, the measure of angle <3 is 105 degrees

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The population decreased by 5,400 people from 2015 to 2020.

Also known as population decline, means the reduction in a human population size

Population in 2015 = Population in 2010 + Growth from 2010 to 2015

Population in 2015 = 167,000 + (8% of 167,000)

Population in 2015 = 167,000 + 13,360

Population in 2015 = 180,360

Population in 2020 = Population in 2015 - Decrease from 2015 to 2020

Population in 2020 = 180,360 - (3% of 180,360)

Population in 2020 = 180,360 - 5,411.8

Population in 2020 = 174,948.2

The population decrease from 2015 to 2020 is:

= Population in 2015 - Population in 2020

= 180,360 - 174,948.2

= 5,411.8

= 5,400 to nearest 100 people.

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Answer:

No

Step-by-step explanation:

because if you use distribution on 2(x+3)+7x it gives you 2x+6=7x which does not equal 2x+3+7x