A set of 5 numbers has an average of 50. The largest element in the set is 5 greater than 3 times the smallest element in the set. If the median of the set equals the mean, what is the largest possible value in the set

The expanded form of the given expression is 2 × w × z × z

From the question, we are to determine the expanded form of the given expression

The given expression is

2wz²

To write an expression in an expanded form, we will write the expression as a repeated multiplication in the simplest way possible.

To do this, we will first expand the index in the given expression.

The index in the given expression is z²

Thus, we get

z² = z × z

Now, we will include the remaining individual terms in the expression and write them as product.

That is,

2wz² = 2 × w × z × z

Hence, the expanded form of the given expression is 2 × w × z × z

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Answer: (0, 3)

Step-by-step explanation:

     The y-intercept of the line is where the line intercepts the y-axis. In other words, the coordinate value of the line when x is 0.

Answer: (3, 0)

Step-by-step explanation:

y-intercept = y=a number and x=0

So, y=3, x=0.

(3, 0)

Answer:

y = 3x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 3x + 3 ← equation of line

Answer:

y = 3x + 3

Step-by-step explanation:

See attached image.

Answer: [tex]\triangle RQP \sim \triangle VPW[/tex]

Step-by-step explanation:

By the corresponding angles theorem, [tex]\angle RPQ \cong \angle VWP[/tex] and [tex]\angle RQP \cong \angle VPW[/tex].

Therefore, [tex]\triangle RQP \sim \triangle VPW[/tex] by AA.

Answer:

answer is the third choice : 104

Step-by-step explanation:

Inscribed Angle Theorem

If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.

so the intercepted arc is TWICE the measure of an angle inscribed in a circle

1. A central angle is an angle with endpoints located on a circle's circumference and vertex located at the circle's center. A central angle in a circle determines an arc.

2. An inscribed angle is an angle formed by three points on the circle's circumference.

Angle at the Center Theorem: An inscribed angle is half of the central angle (if they determine the same arc).

In your case angles:

1. ∠QSR is insribed (determines the arc QR);

2. ∠QTR is central (determines the arc QR).

Then by Angle at the Center Theorem, m∠QTR=2m∠QSR=2·52°=104°. Arc QR has the same measure as central angle QSR.

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Now you can equate it with second one to get x

Answer:

Substitute y = 3x + 2 into x² - 3x + 2y = -4

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}x^2-3x+2y=-4\\y=3x+2\end{cases}[/tex]

Since y is already isolated in the second equation, the best first step would be to substitute the second equation into the first equation, then solve for x.

Substitute equation 2 into equation 1:

[tex]\implies x^2-3x+2(3x+2)=-4[/tex]

Expand the brackets and simplify so that the equation equals zero:

[tex]\implies x^2-3x+6x+4=-4[/tex]

[tex]\implies x^2+3x+4+4=0[/tex]

[tex]\implies x^2+3x+8=0[/tex]

Now use the Quadratic Formula to solve for x.

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Define the variables:

[tex]\implies a=1, \quad b=3, \quad c=8[/tex]

Substitute the values into the formula and solve for x:

[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(8)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-23}}{2}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-1 \cdot 23}}{2}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-1}\sqrt{23}}{2}[/tex]

Remember that [tex]i^2=-1[/tex]

[tex]\implies x=\dfrac{-3 \pm i\sqrt{23}}{2}[/tex]

Therefore, the solutions to the system of equations are:

[tex]x=\dfrac{-3 + i\sqrt{23}}{2}, \quad \dfrac{-3 - i\sqrt{23}}{2}[/tex]

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Answer:

940

Step-by-step explanation:

Since there is a 5 in the ones spot we round the number is the tens spot up by 1: 935 --> 940

The area of the rectangle is 105 square cm

Represent the dimensions of the rectangle with x and y

So, the length of the square would be:

Length = x - 2

Width = y + 6

The areas are then calculated as:

Rectangle = xy

Square = (x -2)(y + 6)

The relationship between the areas is:

(x -2)(y + 6) = 64 + xy

Expand

xy + 6x - 2y - 12 = 64 + xy

This gives

6x - 2y - 12 = 64

Add 12 to both sides

6x - 2y= 76

Divide through by 2

3x - y = 38

By trial by error, we have:

x = 15 and y = 7

The rectangle area is then calculated as:

Rectangle = xy

This gives

Rectangle = 15 * 7

Evaluate

Rectangle = 105

Hence, the area of the rectangle is 105 square cm

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Answer: 8.2 cm

Step-by-step explanation:

Area of a rectangle = l x w

[tex]A= 25 cm^{2}[/tex]

[tex]l= ?[/tex]

[tex]w= 2.5 cm[/tex]

[tex]25cm^{2} = l(2.5cm)[/tex]

[tex]\frac{25cm^{2} }{2.5cm}= l[/tex]

[tex]8.2 cm=l[/tex]

The change in the scale factor from the old scale to the new scale is 3.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension.

The change in the scale factor = larger scale / smaller scale

3.3 / 1.1 = 3

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There are 120 ways in which 5  riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

Now,

We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

i.e.

The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],

Now,

Substituting values,

We get,

[tex]^5N_5 = \frac{5!}{(5-5)!}[/tex]

We get,

The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

So,

There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5  riders and 5 horses can be arranged.

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Answer: (0, -7.2)

Step-by-step explanation:

Substituting into point-slope form, the equation is

[tex]y+6=4(x-0.3)[/tex]

The y-intercept is when x=0, so substituting in x=0,

[tex]y+6=4(-0.3)\\\\y+6=-1.2\\\\y=-7.2[/tex]

So, the y-intercept is (0, -7.2).

None of the points could be added to the graph f(x)=-|x+3| to keep the graph a function

The equation of the function is given as:

f(x) = - |x + 3|

The points are given as:

(0, 3) and (-3, -6)

When x = 0, we have:

f(0) = - |0 + 3|

f(0) = -3 --- different y value from (0, 3)

When x = -3, we have:

f(-3) = - |-3 + 3|

f(-3) = 0 --- different y value from (-3, -6)

This means that the x values point to different y values (this does not represent a function)

Hence, none of the points could be added to the graph f(x)=-|x+3| to keep the graph a function

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Answer: 3x - 6 (in^2)

Step-by-step explanation:

base * height / 2

=

3 ( 2x - 4) / 2 (in^2)

= 3x - 6 (in^2)

Answer: 3x-6 in^2

Step-by-step explanation:

There is no way to figure out what x is without additional information, so you have to leave the answer in this form

The probability of at least one of them being a physics instructor is 120 ways to form the committee.

Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.

There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.

Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.

6 select 2; 8 select 3

15×56 =840

We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.

(9) = 20 options for selecting the professors. 3

(3) = 6 options for selecting the professors.

(9) (¹) = 20 × 6 = 120 ways.

Therefore, 120 ways to form the committee.

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Complete question:

There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?

The standard error of the estimate of average height in the city is 0.25.

Given average height 64 inches, sample mean and sample standard deviation of 4 inches.

We have to determine the standard error of the estimate of the average height in the city.

Standard error is the error which is predicted before research to happen in research. It is calculated by dividing the standard deviation of the sample by the square root of the sample size.

n=256

μ=mean

s = sample standard deviation

Standard error=s/[tex]\sqrt{n}[/tex]

=4/[tex]\sqrt{256}[/tex]

=4/16

=0.25

Hence the standard error of the estimate of the average height is 0.25.

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The equation which represents exponential decay is y=[tex]6(1/3)^{x}[/tex]

Given four equations : 1)y=[tex]3^{x} -4[/tex], 2) y=[tex]2(4)^{x}[/tex], 3) y=[tex]3^{x}/2[/tex], 4) y=[tex]6(1/3)^{x}[/tex].

Equation is relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Exponential equation look like [tex]a^{x}[/tex].

Decay means when x value increases ,the y value decreases.

We haveto put 3 values for x in the equations to check.

1)y=[tex]3^{x} -4[/tex]

put x=0,y=-3

put x=1, y=-1

put x=2, y=5

No,itdoes not represents exponential decay.

2) y=2[tex]4^{x}[/tex]

put x=0,y=2

put x=1, y=8

put x=2, y=32

No,it does not represents exponential decay.

3) y=[tex]3^{x}/2[/tex]

put x=0,y=0.5

put x=1, y=1.5

put x=2, y=4.5

No,it does not represents exponential decay.

4)y=6[tex](1/3)^{x}[/tex]

put x=0,y=6

put x=1, y=2

put x=2, y=0.67

Yes ,it represents exponential decay.

Hence the equation which represents exponential decay is y=6[tex](1/3)^{x}[/tex].

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44% is the answer

6 Article price at buying =5 Rs

1 Article price at buying = 5/6...(i)

5 Articles sold at Rs. 6

1 Articles cost at sold = 6/5 ....(ii)

% Gain=((6/5 - 5/6)/ 5/6) * 100

= 11/25 * 100 = 44%

Profit is a general increase in an asset or the value of an asset. If the item's current price is higher than the original purchase price, you will make a profit. For accounting and tax purposes, profits can be categorized in several ways: B. Gross profit and net profit, or realized profit and unrealized (paper) profit.

The definition of victory is profit, benefit, or increase. An example of profit is a 5% increase in income over the past year. An example of a win is a 5 point lead over another team.

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Answer:

okay so I think its, horizontal shift right 2 and a vertical shift down 1

Step-by-step explanation:

so x says + 2 so right 2 and y says -y so down 1..?

I'm kinda rusty tho so yeah

The volume of the cylinder is approximately, 1,539.4 cubic meters.

Volume of a cylinder = πr²h

Given the following:

Diameter of cylinder = 14 m

Radius (r) = 14/2 = 7 m

Height of cylinder = 10 m

Volume of cylinder = πr²h = π(7²)(10)

Volume of cylinder ≈ 1,539.4 cubic meters.

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The equivalent equation of the given equation is 39x - 45 = 15x - 24.

Hence, option C) is the correct answer.

Given the equation; 3[x + 3(4x – 5)] = 15x – 24

We expand and collect like terms

3[x + 3(4x – 5)] = 15x – 24

3( x + 12x - 15 ) = 15x - 24

3x + 36x - 45 = 15x - 24

We add the like terms on both sides

39x - 45 = 15x - 24

Therefore the equivalent equation of the given equation is 39x - 45 = 15x - 24.

Hence, option C) is the correct answer.

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Answer:

Its A or B

Step-by-step explanation:

Answer:

M: 74.579° = 74°34'43" = 1.30164

O: 49.421° = 49°25'17" = 0.86256 rad

Answer:

D

Step-by-step explanation:

You are looking for what you would need to cancel the yards in 800 yards.

800 yards (1 mile/ 1760 yards).  You have yards in the numerator of your original measurement.  You will cross cancel out the yard on the the top and the yards on the bottom.

Answer:

Step-by-step explanation:

The necessary units conversion can be accomplished by multiplying by appropriate conversion factors. Quantity can be found by multiplying rate by time.

The number of gallons of water produced by melting 1.9 m³ of ice is ...

  [tex]1.9\text{ m$^3$ (ice)}\times\left(\dfrac{100\text{ cm}}{1\text{ m}}\right)^3\times\dfrac{0.92\text{ cm$^3$ (water)}}{1\text{ cm$^3$ (ice)}}\times\dfrac{1\text{ gal}}{3800\text{ cm$^3$}}\\\\=\dfrac{1.9\times10^6\times0.92}{3800}\text{ gal}=\boxed{460\text{ gal}}[/tex]

Multiplying the melting rate by time and converting to height, we have ...

  [tex]\dfrac{179.4\text{ km$^3$}}{1\text{ yr}}\times\dfrac{364\text{ cm}}{1000\text{ km$^3$}}\times6\text{ yr}\approx\boxed{392\text{ cm}}[/tex]

__

Additional comment

The area of the world's oceans is about 361e6 km², so addition of 1000 km³ of water might be expected to increase the water level by (1000/361)e-6 ≈ 2.77e-6 km = 0.277 cm. Something seems a little off in this problem statement.

The correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.

The square inches of paper needed A = surface area of cone +  area of overlap

The surface area of the cone is given by A = πr[r + √(h² + r²)] where

So, A = πr[r + √(h² + r²)]

A = π × 2 × [2 + √(6² + 2²)]

A = π × 2 × [2 + √(36 + 4)]

A = π × 2 × [2 + √40]

A = π × 2 × [2 + 2√10]

A = 2π[2 + 2√10]

A = 4π + 4π√10

The area of overlap A' = wL where

So, A' = wL

A' = w[√(h² + r²)]

A' =  1/2[√(6² + 2²)]

A' =  1/2[√(36 + 4)]

A' =  1/2[√40]

A' =  1/2 × 2√10

A' = √10

So, the number of square inches of paper needed is A" = A + A'

=  4π + 8π√10 + √10

Since the number of square inches of paper needed is 4π + 4π√10 + √10

So, the correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.

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Answer:

2 hours 46 minutes and 40 seconds

Step-by-step explanation:

First we divide by 60 to find how many minutes are in 10000 seconds :

10000÷60 = 166 minutes with remainder 40 seconds

If 166 minutes and 40 seconds is 100000 seconds then we change 166 minutes into hours and minutes :

We do this by dividing 166 by 60 :

166 ÷ 60 :

2 hours Remainder 46 minutes

So our final answer is :

2 hours 46 minutes and 40 seconds

Hope this helped and have a good day

Answer: [tex]\frac{12}{x}[/tex] is an asymptote

Step-by-step explanation:

Apply a table, and plug in values of x into the equation.  For example f(2)=[tex]\frac{12}{2} =6[/tex]. That's one of the points on the graph that we just found (2,6)

Answer:

c 1:4

Step-by-step explanation: