find the weighted average of the weighted points on the number line. a number line with four weighted points plotted. the point at negative 4 has weight three, the point at negative 2 has weight three, the point at one has weight one, and the point at five as weight three.

Answer:

27.5

Step-by-step explanation:

2x-6=49

2x=55

x=27.5

Using the concepts of area of rectangle, we got that  72 feet  is the the least amount of fencing he can use to create the area for his sheep.

Lets, suppose that the length of rectangle as x feet,

and width of rectangle as y feet.

So perimeter of rectangle as 2×( length + breadth)

We are given perimeter of rectangle as 72 feet

So, length of two sides of rectangle + width of rectangle=72feet.

=>2x+y=72 feet----------(eq1)

Now, we know that area of rectangle is given by =(length × breadth),or

=>(x × y)=20000

Putting values of y from eq1,we get

=>x × (72-2x)=20000

=>72x-2x²=20000

We need to find the least amount of fencing, so we find the local minima by using the differentiation

=>d(72x)/dx-d(2x²)/dx=d(20000)/dx

=>72-4x=0

=>x=18feet

Therefore, y=72-2×18=72-36=36feet

Hence, length of rectangle is 18 feet, and width is 36 feet

Therefore, length of fencing is =2x+y=2×18+36=72 feet.

Hence, if a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. he wants the area to be 20,000 square feet, then the least amount of fencing he can use to create the area for his sheep is 72 feet.

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(Complete question) is:

a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. Perimeter of rectangle is given as 72 feet. He wants the area to be 20,000 square feet. what is the least amount of fencing he can use to create the area for his sheep?

Parking 11,000 automobiles at the venue and 4,600 in satellites will bring in total $166,500.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.

Given,

If an arena charges $7. 50 to park in satellite parking and $12. 00 to park in an arena lot,

Multiplying:

$7.5 x 4,600 = satellite parking

$34,500 = satellite parking

The next step is to determine how much it will cost to park in the arena lot.

$11,000 ×12 = arena lot

$32,000 = arena lot

Let's now calculate the entire revenue from parking.

Total earnings equal $132,000 + $34,500.

Amount made in total is $166,500.

In conclusion Parking 11,000 automobiles at the venue and 4,600 in total satellites will bring in $166,500.

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The next two tems of the Fabonacci sequence are (a) 14, 23 (b) 23, 37 (c) 26, 42.

What is Fabonacci type sequence ?

The first two terms are already defined in the this sequence. The nth term of a Fabonacci type sequence is given by the following expression:

[tex]F_n=F_{n-1}+F_{n-2}[/tex]

(a)

In this case 5 terms are given hence, calculate the 6th term.

[tex]F_6=F_5+F_4\\F_6=9+5\\F_6=14[/tex]

Now, calculate the 7th term.

[tex]F_7=F_6+F_5\\F_7=14+9\\F_7=23[/tex]

(b)

Calculate the 4th term.

[tex]F_4=F_3+F_2\\F_4=14+9\\F_4=23\\[/tex]

Calculate the 5th term.

[tex]F_5=F_4+F_3\\F_5=23+14\\F_5=37[/tex]

(c)

The series is 4, 6, 10, 16, ...

[tex]F_5=F_4+F_3\\F_5=16+10\\F_5=26[/tex]

[tex]F_6=F_5+F_4\\F_6=26+16\\F_6=42[/tex]

Hence, the next two tems of the Fabonacci sequence are (a) 14, 23 (b) 23, 37 (c) 26, 42.

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The coordinates of point P that lies on the line segment MQ is P(-11/4 , 9/2).

Given:

M(-5, 3), Q(4, 9), and partition the segment at a ratio of 1 : 3.

(x1,y1) and (x2,y2) in the ratio m:n then,

(x,y) = (mx2+nx1 / m+n , my2+ny1 / m+n)

= (1*4+3*-5 / 1+3 , 1*9+3*3 / 1+3

= (4 - 15 / 4 , 9 + 9 / 4)

= (-11/4 , 18/4)

= (-11/4 , 9/2)

Therefore the coordinates of point P that lies on the line segment MQ is P(-11/4 , 9/2).

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Answer:

4/20=1/5 or 20% or 0.2

Step-by-step explanation:

if u write 4/20 simplify it which becomes 1/5

u can write in percentage or in decimal depending on what the question wants

If O is the midpoint of LM and N is the midpoint of KM  then the measure of NO is 10.

Linear equations are a combination of constants and variables where the value of the variable is calculated using mathematical operations.

We have given that Triangle KLM, N is the midpoint of KM and O is the midpoint of LM if NO equals 3+ 7X and KL equals 4X +16, we are supposed to find the measure of NO.

Using the Midpoint theorem, we can say that in Triangle KLM;

NO = KL / 2

Substituting values,

3+ 7X =  4X +16/ 2

3+ 7X =  2X + 8

7x - 2x = 8 - 3

5x = 5

x = 1

NO = 3+ 7X

NO = 3+ 7(1) = 10

NO equals 10

Hence the measure of NO is 10.

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Answer:

There are roughly 2,488,600 more people living in Chicago.

The equation of the number of pages is y = 40 + 10x and for 9 days, you read 130 pages

From the question, we have

Initial number of pages = 40

Rate per day = 10 pages per day

The equation of the number of pages is then represented as

y = Initial number of pages + Rate per day x Number of days

Substitute the known values in the above equation, so, we have the following representation

y = 40 +10 * x

Evaluate

y = 40 + 10x

For 9 days, we have

x = 10

This gives

y = 40 +10 * 9

Evaluate

y = 130

Hence, the number of pages is 130

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Answer:

Step-by-step explanation:

5.8, 5.8042, 5.84, 6.328

The sample size must be 543 so the sample proportion is will not differ by 5%

We are given the following in the question:

Margin of error = 5%

Confidence interval:

p ±z√(p'(1 - p')/n)

Margin of error =

p = ±z√(p'(1 - p')/n)

Since no particular proportion is given, we take

p' = 0.5

Z critical at α 0.02 is ± 2.33

Putting values, we get,

p = ±z√(p'(1 - p')/n)

2.33 x √(0.5(1 - 0.5)/n)

√n = 2.33x 0.5/0.05

n = 542.89 = 543

Thus, the sample size must be 543 so the sample proportion is will not differ by 5%

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According to the given voltage function, the value of the voltage for the power of 576 watts is 48 watts.

Function:

The relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Given,

The voltage V of an audio speaker can be represented by V=2√P, where P is the power of the speaker. An engineer wants to design a speaker with 576 watts of power.

Here we need to find the voltage of the given power.

In the given question we have the voltage function

v = 2√P

Where P refer the power of the speaker.

Here we have to find the voltage if engineer wants to design a speaker with 576 watts of power.

Which means the value of P is 576.

Then the value of V is calculated as,

v = 2 √576

We know that the value of √576 = 24,

So,

v = 2 x 24

v = 48.

Therefore, the voltage is 48 watts.

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Absolute value of Complex Number -2 + 3i is [tex]\sqrt{13}[/tex]

Absolute value of complex number:

                                                          z = x + iy is the general form of the complex number where x is real part and y is the imaginary part.

                 If we talk about absolute value of complex number z = x + iy then it is represented by |z| = |x + iy|.It is also rad as modulus of z.Absolute value is always going to be a positive value.

              and,

                       |z| = |x + iy|

                            = [tex]\sqrt{x^{2} + y^{2} }[/tex]

Now,

      We have to find the absolute value of complex number, 3i - 2

             z = 3i - 2

                = -2 + 3i

  Absolute value of z is,

                                     |z| = | -2 + 3i |

                                          = [tex]\sqrt{(-2)^{2} + 3^{2} }[/tex]

                                          = [tex]\sqrt{4 + 9}[/tex]

                                          = [tex]\sqrt{13}[/tex]

Thus,

       Absolute value of  Complex number  -2 + 3i is [tex]\sqrt{13}[/tex]

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The cost of one pound is $3.3 or the rate of per pound fruits is $3.3.

What is meaning of one pound?

Pound is an unit to measure mass of an object. The plural form of pound is pounds.

What is the unitary method?

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given that Miranda buys 5.1 pounds of avocados at the local store. The cost of the fruits is $16.83.

Apply unitary method to calculate the cost of 1 pound:

The cost 5.1 pounds fruit is $16.83.

The cost 1 pound fruit is $16.83/5.1 = $3.3.

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The algebraic expression is 2n - 3 if Julie runs three miles less than twice the number n that Hannah runs. So option (a) is correct

An algebraic expression is a mathematical expression made up of variables, constants, and algebraic operations.

It is assumed:

"Julie runs three miles less than twice as far as Hannah runs," the expression goes.

It states three miles less than a number, so you get a -3 and twice the number n, which is the same as 2n, and then you rearrange it to get 2n-3

The expression is 2n - 3

Thus, the algebraic expression is 2n - 3, if Julie runs three miles less than twice the number n that Hannah runs.

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Answer:

b

Step-by-step explanation:

it is the answer

Answer:

[tex]\textsf{B.} \quad g(x)=-x^2-2[/tex]

Step-by-step explanation:

Transformations

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.[/tex]

From inspection of the given graph, we can see that g(x) is function f(x) reflected in the x-axis and translated 2 units down.

Given function f(x):

[tex]f(x)=x^2[/tex]

Reflected in the x-axis:

[tex]-f(x) \implies g(x)= -x^2[/tex]

Translated 2 units down:

[tex]-f(x)-2 \implies g(x)=-x^2-2[/tex]

Therefore:

[tex]g(x)=-x^2-2[/tex]

Note:  

If the leading coefficient of a quadratic function is positive, the parabola opens upwards.

If the leading coefficient of a quadratic function is negative, the parabola opens downwards.

Therefore, as g(x) opens downwards, the term in x² will be negative.

Answer:

w = 6 units

Step-by-step explanation:

The perimeter is found by adding all the sides of a rectangle. The perimeter can be found using this equation:

[tex]P=2w+2l[/tex]

Where w represents width and l represents length.

To find the width, rearrange the equation so it is in terms of w:

[tex]P=2w+2l\\2w=P-2l\\w=\frac{P-2l}{2}[/tex]

Now, plug in the known values!

[tex]w=\frac{20-2(4)}{2}[/tex]

Simplify!

[tex]w=\frac{12}{2} \\w=6[/tex]

Answer:

  x < 0

Step-by-step explanation:

You want an inequality that represents the number line graph with an open circle at 0 and shading to the left.

The end point of an interval on a number line graph is indicated by either an open circle or a filled circle (dot). The circle is open if that end point is not included in the set being graphed. If the end point is included, then the circle is filled to become a solid dot.

The circle at x=0 on this graph is an open circle, so x=0 is not part of the solution set.

The shading on the number line indicates the values that are included in the solution set. Here, shading is to the left of x=0, so includes all values less than 0. This is written as the inequality ...

  x < 0

__

Additional comment

If you write number-line intervals using the left-pointing symbols < or ≤, then the location of x relative to the symbol is the same as the location of the shading relative to the end point.

Here, shading is to the left of 0, so we can write the inequality ...

  x < 0

where x is to the left of 0 in the inequality expression. (As we said above, we use < for the open circle. ≤ is used for a filled dot.)

Answer:

I would say answer D is correct since it is closest to 1,760 yards.

Step-by-step explanation:

;)

Answer:

  11 mi/h

Step-by-step explanation:

You want the speed of the boat when it travels 12 miles upstream against a current of 5 mph in the same time it travels 32 miles downstream with the current.

The relation between time, speed, and distance is ...

  time = distance/speed

If b represents the speed of the boat, the times upstream and downstream are the same, so we have ...

  (12 mi)/(b -5) = (32 mi)/(b+5)

Multiplying by the product of the denominators gives ...

  12(b+5) = 32(b-5) . . . . . . also divided by "mi"

  12b +60 = 32b -160 . . . . multiply by (b+5)(b-5)

  220 = 20b . . . . . . . . . . . . add 160 -12b

  11 = b . . . . . . . . . . . . . . . . . divide by 20

The speed of the boat in still water is 11 miles per hour.

__

Additional comment

Each trip took 2 hours.

Three betas will be in our model aside from the y-intercept.

In the given question, we have to find how many betas will be in your model aside from the y-intercept.

You operate a theme park and want to use the temperature outside and the day of the week to predict how many people will be in attendance each day.

While testing this model, you also want to see if the relationship between temperature and theme park visitors will be curvilinear.

You decide not to test for interactions.

From the given question,

We have y intercept that means our model well be

[tex]y=\beta_{0}+x_{1}\beta _{2}+x_{2}\beta _{2}+x_{1}x_{2}\beta _{12}[/tex]

where [tex]\beta _{1}[/tex] is for temperature and [tex]\beta _{2}[/tex] is day of the week.

3 betas are there aside intercept of y.

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Answer:

The is no number that I can substitue in for x to make the statement true.

Step-by-step explanation:

s + 3 = x -6  Subtract x from both sides

3 = -6  We get a false statement.

The two additional roots are:-0.17-7i and -2i

Given,

A polynomial function P(x) with rational coefficients has the given roots.

P(x) = 0.17+7i and 2i

we are asked to determine the two additional roots of the given P(x).

we know that a+bi is a root of P(x)=0, then a-bi is also a root of P(x)=0

we have:

0.17+7i and 2i are two roots pf P(x)

so, -0.17-7i and -2i are two additional roots of P(x).

Hence we get the required roots.

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Answer:

scalene acute

Step-by-step explanation:

scalene = 2 sides are the same and one is different

acute = all three angles are smaller than 90

Answer:

75%

Step-by-step explanation:

To solve this equation, we need to turn the fraction 72/96 into a percentage.

72 ÷ 96 = 0.75

0.75 as a percentage is 75%

Therefore, 75% of the coffees were regular.

Answer: y = 1/2x + 5

Step-by-step explanation:

3x-6y= -30

Step 1: Subtract 3x to cancel it out and put it on the other side.

3x-6y= -30 -3x

- 3x

After doing that, the equation should look like this: -6y = -3x - 30

Step 2: Divide by -6 to get y alone

-6y/-6= (-3x - 30)/-6

Step 3: Solve

After dividing everything by -6, we get our answer!!

y = 1/2x + 5

*Slope-Intercept form will always end up being in the same format as y=mx+b

I hope this helps :))

first off let's convert the mixed fractions to improper fractions and then divide.

[tex]\stackrel{mixed}{2\frac{4}{3}}\implies \cfrac{2\cdot 3+4}{3}\implies \stackrel{improper}{\cfrac{10}{3}} ~\hfill \stackrel{mixed}{1\frac{8}{7}}\implies \cfrac{1\cdot 7+8}{7}\implies \stackrel{improper}{\cfrac{15}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{10}{3}\div \cfrac{15}{7}\implies \cfrac{10}{3}\cdot \cfrac{7}{15}\implies \cfrac{10}{15}\cdot \cfrac{7}{3}\implies \cfrac{2}{3}\cdot \cfrac{7}{3}\implies \cfrac{14}{9}\implies 1\frac{5}{9}[/tex]

Answer: try a c and e

Step-by-step explanation: