A farmer wants to fence in a rectangular field of livestock. The boundary for one side of the field is a long, straight river. No fencing is needed on this side. For the remaining three sides, he has 400 meters of fencing available. What are the dimensions of the largest rectangular area that can be formed

Answer:

Step-by-step explanation:

Coordinates of the vertex A → (-4, -6)

Coordinates of the vertex A' → (6, 6)

Since, y-coordinates are same opposite in notation,

Therefore, by the rule of reflection, line of reflection will be a line parallel to y-axis.

And points A and A' will be equidistant from the line of reflection.

Midpoint between A and A' = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

                                              = [tex](\frac{-4+6}{2},\frac{-6+6}{2})[/tex]

                                              = (1, 0)

Therefore, x = 1 will be the line of reflection.

Answer:    y = 5x - 7

Step-by-step explanation:

y = mx + b, where m = slope

We plug in the point, where x = 2, and y = 3

y = 5x - b

3 = 5(2) - b

3 = 10 - b

b + 3 = 10

b = 7

y = 5x - 7

Answer:

636

8u2b4c9....°73vaultx8 3_2144,773,90=636

Step-by-step explanation:

993yuei92u83vaultx21564=636

Answer:

50

Step-by-step explanation:

Using proportions, it is found that the number of toys that is likely to be defective in a sample of 500 is given by:

C: 50

A proportion is a fraction of a total amount.

For the samples of 10, the mean number of errors is of:

( 0 + 2 + 1 + 1 + 2 + 0)/6 = 1

Hence, for samples of 500, the expected number of defective toys will be given by:

E = (500/10) x 1 = 50

Hence, option C is correct.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

The answer is 3,600,000,000

Step-by-step explanation:

Simply multiply 9,000,000 * 400 which equals 3,600,000,000.

Answer:

5.09 or 5.10(if u round up)

Step-by-step explanation:

When you convert √24 it will be 5.099

The decimal point must lie between 5 and 0

Hope this helps:)

Answer:

54 cm

Step-by-step explanation:

Perimeter = TZ + TX + RX + RY + SY + SZ

TZ = 5 cm

TX = 13 cm

RY = 9 cm

RX = TX = 13 cm (tangents drawn from and external point)

SY = RY = 9 cm (tangents drawn from and external point)

SZ = TZ = 5 cm (tangents drawn from and external point)

Plug in the values:

Perimeter = 5 + 13 + 13 + 9 + 9 + 5 = 54 cm

Answer:

0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they entered a profession closely related to their college major, or they did not. The probability of a graduate entering a profession closely related to their college major is independent of other graduates. This, coupled with the fact that they are chosen with replacement, means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

53% reported that they entered a profession closely related to their college major.

This means that [tex]p = 0.53[/tex]

9 of those survey subjects are randomly selected

This means that [tex]n = 9[/tex]

What is the probability that 3 of them entered a profession closely related to their college major?

This is P(X = 3).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 9) = C_{9,3}.(0.53)^{3}.(0.47)^{6} = 0.1348[/tex]

0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.

Answer:

Step-by-step explanation:

13). [tex]-\frac{q}{7}\geq -1[/tex]

     [tex]\frac{q}{7}\leq 1[/tex]

    [tex](\frac{q}{7}\times 7)\leq (1\times 7)[/tex]

      q ≤ 7

14). -12x < 60

      12x > -60

      [tex]\frac{12x}{12}>\frac{-60}{12}[/tex]

      x > -5

15). 5 > z - 3

     5 + 3 > z - 3 + 3

     8 > z

16). 0.5 ≤ [tex]\frac{y}{8}[/tex]

     0.5 × 8 ≤ [tex]\frac{y}{8}\times 8[/tex]

     4 ≤ y

Now we can draw these inequalities on a number line.

Vertical compression

Answer:

the answer is 69/100

Answer:

9.261 cm³

Step-by-step explanation:

2.1x2.1x2.1=9.261

Answer:

9.2

Step-by-step explanation:

the answer is 9.2 yo multiplu 2.1x2.1x2.1

Answer:

1/14

Step-by-step explanation:

Step-by-step explanation:

Due to the time it took to solve this question, I had little time to type the answers fully

The answers are contained fully in the attachment I have uploaded.

A. H0: u1 = u2

H1: u1 not equal to u2

The t statistics was solved to be 3.03

The degree of freedom was solved to be 26

Given this information, this is a 3 tailed test, critical value at 5% = +-2.056

T stat > critical value

We therefore reject the null hypothesis at 5% and conclude they have different mean wear

The p value is calculated using excel and the result is 0.00544

We reject null at 5% since p value is less than 0.05

B. H0: u1 = u2

H1: u1>u2

Alpha = 0.05

Following a,

Test stat = 3.03

Df = 26

Critical value for 1 tailed test = 1.706

Test stat > 1.706

We reject H0 and conclude company 1 has higher mean wear.

We find p value for a right tailed distribution using excel

Tdist(3.03,26,1)

= 0.002722

We reject h0

C. Confidence interval

1.610 < u < 8.390

Answer:

A. Homes using solar power always have lower utility bills than homes using only gas and electricity.

Step-by-step explanation:

Gas and Electricity

[tex]\bar x = 93[/tex]

[tex]\sigma = 11[/tex]

Solar

Bills: 56, 54 and 51

Required

Determine which of the statements is true

First, we calculate the mean of the given data

[tex]\bar x = \frac{\sum x}{n}[/tex]

[tex]\bar x = \frac{56 + 54 + 51}{3}[/tex]

[tex]\bar x = \frac{161}{3}[/tex]

[tex]\bar x = 53.67[/tex]

Then, the standard deviation

[tex]\sigma = \sqrt{\frac{\sum(x - x_i)^2}{n}}[/tex]

[tex]\sigma = \sqrt{\frac{(56 - 53.67)^2 + (54 - 53.67)^2 + (51 - 53.67)^2}{3}}[/tex]

[tex]\sigma = \sqrt{\frac{12.67}{3}}[/tex]

[tex]\sigma = \sqrt{4.223}[/tex]

[tex]\sigma = 2.05[/tex]

So, we have:

Gas or Electricity

[tex]\bar x = 93[/tex]

[tex]\sigma = 11[/tex]

Solar

[tex]\bar x = 53.67[/tex]

[tex]\sigma = 2.05[/tex]

By comparison.

The mean and standard deviation of homes using solar panel is less than home using gas and electricity.

This implies that: (a) is true.

Answer:

58.1

Step-by-step explanation:

9514 1404 393

Answer:

   3 ft square base, 7 feet high

Step-by-step explanation:

For minimum cost, each pair of opposite sides costs the same as any other pair of opposite sides.

If s is the edge length of the base, then the areas of the top and bottom are s² and their total cost is ...

  (s²)(0.22 +0.20) = 0.42s² . . . . cost of top and bottom

__

For a volume of 63 ft³, the height of the side of the box is ...

  63/s² = h

and the area of one side of the box is ...

  hs = 63/s

A pair of opposite sides will have a cost of ...

  (63/s)(0.09 +0.09) = 11.34/s . . . . cost of a pair of opposite sides

__

We want these two costs to be the same, so we have ...

  0.42s² = 11.34/s

  s³ = 11.34/0.42 = 27

  s = ∛27 = 3 . . . . feet

  h = 63/s² = 7 . . . . feet

__

The box dimensions are 3 feet square by 7 feet tall.

_____

Additional comment

Each pair of opposite sides will cost $3.78, so the total cost of the box is $11.34.

For the non-believers, we have shown a graph of the total cost of the box as a function of the base dimension (s). It has a minimum at $11.34 when s=3. You can find that by differentiating the cost function and and finding the zero(s) of that (or by reading the values from the graph).

Answer:

row 3

row 2

6 and 10

Answer:

The answers are 1( row 3 ) 2( row 2 ) 3( 6 and 10 )

Step-by-step explanation:

I got it right on edge and also the person above me is correct have a wonderful day. (✿◠‿◠)

Answer:

The last three,

2 cm, 5 cm, 6 cm

4 cm, 8 cm, 11 cm

10 in, 5 in, 13 in

As long as any two sides added together are long than the third side, it works as a triangle!

Answer:

x=8, y=10. (8, 10).

Step-by-step explanation:

-8x+7y=6

3x-2y=4

--------------

2(-8x+7y)=2(6)

7(3x-2y)=7(4)

-----------------------

-16x+14y=12

21x-14y=28

-------------------

5x=40

x=40/5

x=8

3(8)-2y=4

24-2y=4

2y=24-4

2y=20

y=20/2

y=10

Answer:

-9

Step-by-step explanation:

The city of Brussels will be the warmest. The difference in temperature between Oslo and London is -9°C and the temperature at 6:00 pm in Paris will be -2°C.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

(a)

A city which has the lowest temperature will be warmest since -1°C is the lowest so Brussels will have the warmest city.

(b)

The difference in temperature between Oslo and London will be as,

-12 °C - (-3 °C) = -9 °C.

(c)

At 6.:00 pm the temperature will be -5 °C + 3 °C = -2 °C.

Hence "The city of Brussels will be the warmest. The difference in temperature between Oslo and London is -9°C and the temperature at 6:00 pm in Paris will be -2°C".

To learn more about the arithmetic operators,

brainly.com/question/25834626

#SPJ2

Answer:

(a) Independent variable

(b) The constant factor is 12

Step-by-step explanation:

Given

[tex]m(c) = 12c + 80[/tex]

c = campers

m = total cost

Solving (a) What type of variable is the number of campers (c)

The total cost (m) is dependent on the number of campers (c) for its own value.

In other words, if c changes from 5 to say 7, the value of m will also change.

This implies that the number of campers is an Independent variable

Solving (b): Constant factor

This in other words means, rate of change (or slope)

A linear function is:

[tex]y = ax + b[/tex]

Where a represents the slope

By comparison with: [tex]m(c) = 12c + 80[/tex]

Hence, the constant factor is 12

Answer:

dependent, changes by a constant factor per camper.

Step-by-step explanation:

Answer:

Note that it is not a perfectly elastic result so it is irrational

Answer:

[tex]f^{-1}(x) = \sqrt[3]{\frac{x -4}{5}} +2[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5(x - 2)^3 + 4[/tex]

Required

Determine the inverse

[tex]f(x) = 5(x - 2)^3 + 4[/tex]

Replace f(x) with y

[tex]y = 5(x - 2)^3 + 4[/tex]

Swap the positions of x and y

[tex]x = 5(y - 2)^3 + 4[/tex]

Make y the subject

[tex]x -4= 5(y - 2)^3[/tex]

Divide by 5

[tex]\frac{x -4}{5}= (y - 2)^3[/tex]

Take cube roots of both sides

[tex]\sqrt[3]{\frac{x -4}{5}}= y - 2[/tex]

Add 2 to both sides

[tex]\sqrt[3]{\frac{x -4}{5}} +2 = y[/tex]

[tex]y = \sqrt[3]{\frac{x -4}{5}} +2[/tex]

Replace y with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x) = \sqrt[3]{\frac{x -4}{5}} +2[/tex]

Answer:

Mean: 4.71

Mode: 5

Median: 5

Step-by-step explanation:

Answer:

it's going to be negative