A cable company must provide service for 6 houses in a particular neighborhood. They would like to wire the neighborhood in a way to minimize the wiring costs (or distance). What is the minimal length of the network required to span the entire neighborhood? House Distances (yards) 1 to 2 250 1 to 3 400 1 to 4 300 2 to 3 400 2 to 4 400 2 to 5 400 3 to 5 350 3 to 6 450 4 to 5 300 4 to 6 350

Answer:

a=90 degrees

b=90 degrees

x=22 degrees

Step-by-step explanation:

3x+22+(5x-18)=180

8x=176

x=22

Answer:

x = 22°, ∠a = 88°, ∠b = 92°.

Step-by-step explanation:

Angle b has the same measurement as the angle of 5x - 18, since the two angles are corresponding angles.

Angle a has the same measurement as the angle of 3x + 22, since the two angles are alternate interior angles.

Since angle a and the angle of 5x - 18 form a straight line, the two angles add up to be 180 degrees. Since angle a is the same as the angle of 3x + 22, we can substitute the angle for angle a.

(5x - 18) + (3x + 22) = 180

5x + 3x - 18 + 22 = 180

8x + 4 = 180

8x = 176

x = 22°.

3(22) + 22 = 66 + 22 = 88 degrees.

That means that ∠a = 88°.

5(22) - 18 = 110 - 18 = 92 degrees.

That means that ∠b = 92°.

Hope this helps!

Answer:

[tex]\boxed{\sf 2737.5 \ hours}[/tex]

Step-by-step explanation:

The average is 7.5 hours of sleep each night.

There are 365 nights in 1 year.

[tex]\sf Multiply \ the \ value \ by \ 365.[/tex]

[tex]7.5 \times 365[/tex]

[tex]2737.5[/tex]

Answer:

2,737 hours for a normal year, 2,745 if it is a leap year.

Step-by-step explanation:

Because there 365 days in a year, you should multiply the amount you sleep every day (7.5) by the number of days in a year (365)

[tex]7.5*365[/tex]

Multiply 7.5 by 365 to get

[tex]2,737.5[/tex]

Every year you will sleep 2,737 hours if you sleep 7.5 hours each day.

(If it is a leap year, just change 365 to 366 which will give you 2,745 hours)

I hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day! :)

Answer:

The cost to rent each chair is $2.75 and the cost to rent each table is $8.50

Step-by-step explanation:

Let the:

Cost to rent a chair = x

Cost to rent a table = y

We would form an algebraic equation.

The total cost to rent 2 chairs and 3 tables is $31

2x + 3y = 31 ...... Equation 1

The total cost to rent 6 chairs and 5 tables is $59

6x + 5y = 59 ......... Equation 2

We solve the above equation above using elimination method

Multiply Equation 1 all through by the coefficient of x = 6 in Equation 2

Multiply Equation 2 all through by the coefficient of x = 2 in Equation 1

Hence, we have:

2x + 3y = 31 ...... Equation 1 × 6

6x + 5y = 59 ......... Equation 2 × 2

12x + 18y = 186........ Equation 3

12x + 10y = 118 .…...... Equation 4

Subtracting Equation 4 from Equation 3

= 8y = 68

y = 68/8

y = 8.5

Therefore, the cost to rent a table = $8.50

Substituting 8.5 for y in Equation 1 to get the value of x

2x + 3y = 31 ...... Equation 1

2x + 3(8.5) = 31

2x = 31 - 3(8.5)

2x = 31 - 25.5

2x = 5.5

x = 5.5/2

x = 2.75

The cost to rent a chair = $2.75

Therefore, the cost to rent each chair is $2.75 and the cost to rent each table is $8.50

Answer:

0.5216

Step-by-step explanation:

Given the function  y =kx(1-x), the pattern of attractors are the value(s) of y at the initial value of k and x. Given the value of k = 3.26 and x = 0.8, to get the pattern of attractors, we will substitute the given initial value into the function as shown;

[tex]y =kx(1-x)\\\\y = 3.26(0.8)(1-0.8)\\\\y = 3.26*0.8*0.2\\\\y = 0.5216\\\\[/tex]

Hence, the pattern of attractor for the equation y is 0.5216

Answer:

Step-by-step explanation:

Part A

(m + n)x = 4x + 5 + 8x - 5

(m + n)x = 12x   The fives cancel

Part B

(m - n)x = 4x + 5 - 8x + 5

(m - n)x = -4x + 10

Part C

The trick here is to put n(x) into m(x) wherever m(x) has an x.

m[n(x)] = 5(n(x)) + 5

m[n(x)] = 5(8x - 5) + 5

m[n(x)] = 40x - 20 + 5

m[n(x)] = 40x - 15

Answer:

1510 h, or 3:10 PM.

Step-by-step explanation:

The next time they meet at the bus terminal will be a multiple of 50, 80, and 100.

A common factor among the three numbers is 10. If we divide all three by 10, we will get 5, 8, and 10. 5 is a factor of 10, so as long as 5 is multiplied by an even number, 10 will be a multiple.

Since the number will have to be divisible by both 5 and 8, the smallest possible number would be 5 * 8 = 40. So, the next time they meet at the bus terminal will be 40 * 10 = 400 minutes after 8:30.

400 minutes in hours is 400 / 60 = 40 / 6 = 20 / 3 = 6 hours and 2/3.

2/3 of an hour in minutes is (2/3) * 60 = 2 * 20 = 40.

So, they will meet again in 6 hours and 40 minutes.

8:30 plus 6 hours and 40 minutes is 14:70. 70 minutes translates into an hour and 10 minutes. So, the time will be 15:10, or 3:10 PM.

Hope this helps!

Answer:

105°

Step-by-step explanation:

Supplementary angle of 75° = 180° - 75° = 105°

Answer:

105°

Step-by-step explanation:

angle given is 75°

= 180° - 75°

= 105°

Answer:

  [tex]\boxed{2144}[/tex]

Step-by-step explanation:

The sum can be found by adding the parts:

  [tex]\sum\limits_{n=1}^{32}{(4n+1)}=4\sum\limits_{n=1}^{32}{n}+\sum\limits_{n=1}^{32}{1}=4\cdot\dfrac{32\cdot 33}{2}+32\\\\= 2112+32=\boxed{2144}[/tex]

__

The sum of numbers 1 to n is n(n+1)/2.

Step-by-step explanation:

Using trigonometrical functions we can obtain the required side lengths.

[tex] \sin 45\degree = \frac{a}{16\sqrt 2}\\\\

\therefore \frac{1}{\sqrt 2}= \frac{a}{16\sqrt 2}\\\\

\therefore a = \frac{16\sqrt 2}{\sqrt 2}\\\\

\huge\red {\boxed {\therefore a = 16}} \\\\

\cos 45\degree = \frac{c}{16\sqrt 2}\\\\

\therefore \frac{1}{\sqrt 2}= \frac{c}{16\sqrt 2}\\\\

\therefore c = \frac{16\sqrt 2}{\sqrt 2}\\\\

\huge\purple {\boxed {\therefore c = 16}} \\\\

\sin 30\degree = \frac{a}{b}\\\\

\therefore \frac{1}{2}= \frac{16}{b}\\\\

\therefore b = {16\times2}\\\\

\huge\orange{\boxed {\therefore b = 32}} \\\\

\tan 30\degree = \frac{a}{d}\\\\

\therefore \frac{1}{\sqrt 3}= \frac{16}{d}\\\\

\therefore d = {16\times\sqrt 3}\\\\

\huge\pink {\boxed {\therefore d = 16\sqrt 3}} \\\\

[/tex]

Answer:

False

Step-by-step explanation:

To find <A, we can do 5x - 80 = 3x + 20.

As we simplify, we will get 2x = 100, which is x = 50

Therefore, <A will be 50 degrees and not 45 degrees.

Also, if you need y, you can do:

3y - 7 = y + 7

2y = 14

y = 7

Answer:

Sample size 'n' = 384

Step-by-step explanation:

Explanation:-

Given margin of error = 0.04

The sample proportion 'p'= 0.80

The margin of error is determined by

                               [tex]M.E = \frac{Z_{\alpha } \sqrt{p(1-p)} }{\sqrt{n} }[/tex]

                             [tex]0.04 = \frac{1.96 \sqrt{0.80(1-0.80)} }{\sqrt{n} }[/tex]

Cross multiplication, we get

                             [tex]\sqrt{n} = \frac{1.96 \sqrt{0.80(1-0.80)} }{0.04 }[/tex]

                             √n = 19.6

Squaring on both sides , we get

                            n = 384.16≅384

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 13/3, 4 1/3, or 4.3

▹ Step-by-Step Explanation

x + 7 - 4(x + 1) = -10

x + 7 - 4x - 4 = -10

-3x + 7 - 4 = -10

-3x + 3 = -10

-3x = -10 - 3

-3x = -13

x = 13/3, 4 1/3, or 4.3

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

x = 13/3

Step-by-step explanation:

x + 7 - 4(x + 1) = -10

x + 7 - 4x - 4 = -10

-3x + 3 = -10

-3x = -13

x = -13/(-3)

x = 13/3

Answer:

Yes the sample data   indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years

Step-by-step explanation:

From the question we are told that

   The sample size is  [tex]n = 51[/tex]

    The sample mean is  [tex]\= x = 2.03[/tex]

    The sample standard deviation is  [tex]\sigma = 0.82[/tex]

    The population mean is  [tex]\mu = 1.75[/tex]

    The level of significance is  [tex]\alpha = 0.01[/tex]

The null hypothesis  is  

      [tex]H_o : \mu = 0.82[/tex]

The alternative hypothesis is

     [tex]H_a : \mu >1.75[/tex]

The critical value of the the level significance [tex]\alpha[/tex] obtained from the critical value table for z-value is [tex]z_\alpha = 2.33[/tex]

 Now the test statistic is mathematically evaluated as

          [tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]

substituting values  

           [tex]t = \frac{ 2.03 - 1.75 }{\frac{0.82}{\sqrt{51} } }[/tex]

           [tex]t = 2.44[/tex]

From that calculated and obtained value we see that the critical value of the level of significance is less than the test statistics so we  reject the null hypothesis

Hence there sufficient evidence to proof that the sample data indicates that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years

Answer:

Step-by-step explanation:

[tex]60\% =\\\\\frac{60}{100} \\=0.6[/tex]

Answer:

3/5

Step-by-step explanation:

60% as a fraction is 3/5 :)

Answer: 8.5 sq. units.

Step-by-step explanation:

Formula:

Area of triangle : [tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

Given: Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2)

Then, Area of triangle  IJK = [tex]\dfrac{1}{2}|3(-4-(-2))+7(-2-(-7))+4(-7-(-4))|[/tex]

[tex]\dfrac{1}{2}|3(-2)+7(5)+4(-3)|\\\\=\dfrac{1}{2}|-6+35-12|\\\\=\dfrac{1}{2}(17)\\\\=8.5\text{ sq. units}[/tex]

Hence, the area of this triangle  IJK on a Coordinate Grid = 8.5 sq. units.

Answer:

7(m-8)

Step-by-step explanation:

We are given: 7 times the difference between m and 8

We want to write an expression. Let’s begin with “the difference between m and 8”.

Difference means subtraction. Therefore, we must subtract m and 8.

(m-8)

Now, let’s add on “7 times”

Times means multiply. Therefore, we must multiply 7 and the expression we just wrote.

7(m-8)

Therefore, 7 times the difference between m and 8 can be written as: 7(m-8)

Answer:

7(m-8)

Step-by-step explanation

7 times the difference between m and 8​ = 7*(m-8)

First, we know that difference, in a mathematical term, means subtraction, and “times” Means multiplication.

But, since it says,” difference between m and 8”, we must put those in parentheses, so we know that it is m-8, not 7*m.

so, therefore you have 7*(m-8), or 7(m-8)

Answer:

18 is a composite number. 18 = 1 x 18, 2 x 9, or 3 x 6. Factors of 18: 1, 2, 3, 6, 9, 18. Prime factorization: 18 = 2 x 3 x 3, which can also be written 18 = 2 x 3².

All the prime factorization of 18 are,

⇒ 2, 3, 3

Because 2×3×3 = 18

We have to given that,

To find all the prime factorization of number 18.

Now, We need to find all the factors of 18.

Hence,

18 = 2 x 9

   = 2 x 3 x 3

Therefore, All the prime factorization of 18 are,

⇒ 2, 3, 3

Because 2×3×3 = 18

Learn more about the Greatest common factors visit:

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Answer:

x^2 + 6x - 16

=x^2 + ( 8-2 )x -16

=x^2 + 8x - 2x -16

= X(X+8) -2(X+8). ( Taking common from term 1 and 2 and then from 3 and 4)

= ( X+8 ) ( x-2 ) ( Taking common from term 1 and 2).

so, this is the factored form of the expression x^2 + 6x - 16.

Answer:

1.(x-2)(x+8)

Step-by-step explanation:

1.x2+8x-2x-16

=×(x+8)-2(x+8)

=(x-2)(x+8)

Answer:

Step-by-step explanation:

We assume you are not interested in five infinite sets of translations. Rather, we assume you want to pick 5 translations from the infinite set of possibilities.

The attached graph shows f(x), g(x), and 5 lines (dashed or dotted) that represent possible reflections and shifts of the function f(x).

The function f1 represents a reflection of f(x) about the x-axis, followed by a left-shift of 6 units. To make it match g(x), we need to shift it upward 4 units. Then the set if translations is ...

  g(x) = f(x) ... {reflected over the x-axis, shifted left 6, shifted up 4}

Along the same lines, other possibilities are ...

  g(x) = f(x) ... {reflected over the x-axis, shifted left 3, shifted up 3}

  g(x) = f(x) ... {reflected over the x-axis, shifted left 0, shifted up 2}

  g(x) = f(x) ... {reflected over the x-axis, shifted right 3, shifted up 1}

  g(x) = f(x) ... {reflected over the x-axis, shifted right 9, shifted down 1}

___

Additional comment

All of the transformations listed above use reflection in the x-axis. Reflection could use the y-axis, as well. Reflection of the basic function f(x) in the y-axis will have the identical effect as reflection in the x-axis. The listed translations would apply unchanged.

Answer:

2m - 9

Step-by-step explanation:

To simplify this, we need to combine like terms. m + m = 2m and -4 - 5 = -9 so the simplified version would be 2m - 9.

Answer: see below

Step-by-step explanation:

[tex]f(x)=-x^2\qquad g(x)=\dfrac{1}{\sqrt x}[/tex]

[tex]f og(x)=f\bigg(\dfrac{1}{\sqrt x}\bigg)\\\\.\qquad =-\bigg(\dfrac{1}{\sqrt x}\bigg)^2\quad \\\\.\qquad =-\dfrac{1}{x}\\\\\text{Domain:}\ x>0[/tex]

[tex]gof(x)=g(-x^2)\\\\.\qquad =\dfrac{1}{\sqrt{-x^2}}\\\\.\qquad =\dfrac{1}{xi}\\\\\text{Domain: Does Not Exist since result is an imaginary number}[/tex]

Hey there! I'm happy to help!

Let's set this up as a system of equations, where x is equal to the number of 10 dollar bills and y is equal to the number of 50 dollar bills.

10x+50y=1080

x+y=28

We want to solve for x or y. We can rearrange the second equation to find the value of one of the variables.

x+y=28

Subtract x from both sides.

y=28-x

Now, we have a value for y. So, we could replace the y in the first equation with 28-x and the solve for x.

10x+50(28-x)=1080

We use distributive property to undo the parentheses.

10x+1400-50x=1080

We combine like terms.

-40x+1400=1080

We subtract 1400 from both sides.

-40x=-320

We divide both sides by -40.

x=8

Since there are 28 total bills, this means that there must be 20 50 dollar ones because there are 8 10 dollar bills.

Have a wonderful day! :D

Answer:

72

Step-by-step explanation:

There are 12 inches in a foot.

Therefore in 8 feet there are 96 inches

Therefore the square floor is 96 * 96.

Therefore the area of the square floor is 9216 inches squared.

Each tile is 8 inches by 8 inches meaning it has an area of 64 inches squared.

9216 / 64 = 144.

Therefore 144 tiles are needed to tile the floor

Since each tile is 50 cents, 144 * 0.5 = 72

Therefore it costs 72 dollars to tile the floor.

Answer:

f(0) = 0

Step-by-step explanation:

f(x) = -sqrt(x)

Let x= 0

f(0) = -sqrt(0)

f(0) = 0

Value of the given function [tex]f(x) = -\sqrt{x}[/tex] for [tex]f(0) = 0.[/tex]

" A function is defined as the relation between the given variable represents set of all input value should have one output each."

According to the question,

Given function,

[tex]f(x) = -\sqrt{x}[/tex]

Substitute the different values for 'x' for the given function we get,

[tex]x=1 , f(1) = -\sqrt{1}[/tex]

                 [tex]=-1[/tex]

[tex]x=4 , f(4) = -\sqrt{4}[/tex]

                 [tex]=-2[/tex]

[tex]x=0, f(0) = -\sqrt{0}[/tex]

                 [tex]=0[/tex]

Therefore, given relation is a function.

Hence, value of the given function [tex]f(x) = -\sqrt{x}[/tex] for [tex]f(0) = 0.[/tex]

Learn more about function here

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Answer:

4, 3, 5, 8, 7, 6, 1, 2

Step-by-step explanation:

Let’s label the options with numbers.

Solve the percentages:

1) 442/(442+267) = 62.4%

2) 701/(701+187) = 78.9%

3) 267/(267+442)= 37.7%

4) 187/(187+701) = 21.1%

5) 442/(442+701) = 39.4%

6) 701/(442+701) = 61.3%

7) 267/(187+267) = 58.8%

8) 187/(187+267) = 41.2%

Arrange from least to greatest.

4, 3, 5, 8, 7, 6, 1, 2

Answer:

The last set.

Step-by-step explanation:

The first 3 sets  contain  'one-to-many' relations , for example (1, 3) and (1, 5) in set 1 and (0, 0) and (0, 2) in set  3 , so they are not functions.

The last set does not have any of these and is a function.

Answer:

576"

Step-by-step explanation:

AL=ph

AL= (4*12)12

AL= 48*12

AL=576"

Answer: lower bound = 0.7404; upper bound = 0.8596

Step-by-step explanation:

The proportion p for this population:

p = [tex]\frac{240}{300}[/tex]

p = 0.8

Confidence interval for proportion is calculated as:

p ± z-score.[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

Z-score for a 99% confidence interval is: z = 2.58

Calculating:

0.8 ± 2.58.[tex]\sqrt{\frac{0.8(0.2)}{300} }[/tex]

0.8 ± 2.58.[tex]\sqrt{0.00053}[/tex]

0.8 ± 2.58(0.0231)

0.8 ± 0.0596

This means that the lower limit of this interval is 0.7404 and upper bound is 0.8596

Answer:

Step-by-step explanation:

The line passes through points ( - 1 , 2 ) and ( 3 , 1 )

Let there points be A and B

A ( -1 , 2 ) -----> ( x1 , y1 )

B ( 3 , 1 ) -------> ( x2 , y2 )

Now, Let's find the gradient ( slope)

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

plug the values

[tex] = \frac{1 - 2}{3 - ( - 1)} [/tex]

Calculate the difference

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

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression

[tex] = \frac{ - 1}{3 + 1} [/tex]

Add the numbers

[tex] = \frac{ - 1}{4} [/tex]

Use [tex] \frac{ - a}{b} = \frac{a}{ - b} = - \frac{a}{b} [/tex] , to rewrite the fraction

[tex] = - \frac{1}{4} [/tex]

Hope this helps...

Best regards!!

Answer:

Step-by-step explanation:

The best first step to solve this is to just subtract 5/3 from both sides so it is easier to simplify.

Answer:

Subtract 5/3 to the other side

Step-by-step explanation:

Hey there!

Well the best first step is to -5/3 to both sides and move it to the right side.

-4x + 5/3 > 5/10

-5/3 to both sides

-4x > -7/6

Hope this helps :)