A rancher needs to enclose two adjacent rectangular​ corrals, one for cattle and one for sheep. If the river forms one side of the corrals and 270 yd of fencing is​ available, find the largest total area that can be enclosed.

Ignore the negative sign, since that only affects the sign of the final product

3415₇ × 432₇

You can compute the product by considering the digit expansion, by which I mean first expanding each number as sums of powers of 7:

3415₇ = 3000₇ + 400₇ + 10₇ + 5₇

(It's the same thing as writing, for example, the decimal 3415 as 3000 + 400 + 10 + 5, just in a different base.)

Similarly,

432₇ = 400₇ + 30₇ + 2₇

Then apply the distributive property:

= (3000₇ + 400₇ + 10₇ + 5₇) × (400₇ + 30₇ + 2₇)

= 3000₇ × (400₇ + 30₇ + 2₇)

… + 400₇ × (400₇ + 30₇ + 2₇)

… + 10₇ × (400₇ + 30₇ + 2₇)

… + 5₇ × (400₇ + 30₇ + 2₇)

= {12}00000₇ + {9}0000₇ + 6000₇

… + {16}0000₇ + {12}000₇ + {8}00₇

… + 4000₇ + 300₇ + 20₇

… + {20}00₇ + {15}0₇ + {10}₇

where I use the curly braces to indicate products (written in base 10) of digits that exceed 6. Anything in these braces needs to be properly converted to base 7. For example,

{12}₇ = 7 + 5 = 15₇

So you would have

= 1500000₇ + 120000₇ + 6000₇

… + 220000₇ + 15000₇ + 1100₇

… + 4000₇ + 300₇ + 20₇

… + 2600₇ + 210₇ + 13₇

Add everything up:

• In the 7⁰ place,

3₇

• In the 7¹ place,

1₇ + 1₇ + 2₇ = 4₇

• In the 7² place,

2₇ + 6₇ + 3₇ + 1₇ = {12}₇ = 15₇

• Carry the 1 (underlined). In the 7³ place,

2₇ + 4₇ + 1₇ + 5₇ + 6₇ + 1₇ = {19}₇ = 25₇

• Carry the 2. In the 7⁴ place,

1₇ + 2₇ + 2₇ + 2₇ = {7}₇ = 10₇

• Carry the 1. In the 7⁵ place,

2₇ + 1₇ + 5₇ + 1₇ = {9}₇ = 12₇

• Carry the 1. In the 7⁶ place,

1₇ + 1₇ = 2₇

So, we end up with

3415₇ × 432₇ = 22045543₇

and thus

3415₇ × (-432₇) = -22045543₇

The sample size that will make the Alex's claim true is option E. 35.

Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.

This means that, if you do your experiment more than once and do resampling, then this is the percentage that the parameters falls within a range.

Sample size of Sasha = 30

She took a confidence interval of 95%.

Alex claims he can construct a confidence interval that is narrower by changing the sample size but keeping all other things the same.

The relation between the sample size and confidence interval is that when the size of sample increases, the confidence interval becomes narrower.

So if the Alex's claim has to be true, sample size must increase.

He can use sample size of 35.

Hence the correct option is E.

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Answer:

Since \(\overrightarrow{AB} = \overrightarrow{DC}\) and \(\overrightarrow{AD} = \overrightarrow{BC}\), then the quadrilateral ABCD is a parallelogram.

Step-by-step explanation:

First, we label each point of the quadrilateral with the help of a graphing tool. If the quadrilateral ABCD is a parallelogram, then \(\overrightarrow{AB} = \overrightarrow{DC}\) and \(\overrightarrow{AD} = \overrightarrow{BC}\). If we know that \(A(x,y) =(-1, 1)\), \(B(x,y) =(-3,4)\), \(C(x,y) = (1,5)\) and \(D(x,y) = (3,2)\), then the measure of each vector is, respectively:

\(\overrightarrow{AB} = (-3,4)-(-1,1)\)

\(\overrightarrow{AB} = (-2, 3)\)

\(\overrightarrow{DC} = (1,5)-(3,2)\)

\(\overrightarrow{DC} = ( -2,3)\)

\(\overrightarrow{AD} = (3,2)-(-1,1)\)

\(\overrightarrow{AD} = (4, 1)\)

\(\overrightarrow{BC} = (1,5)-(-3,4)\)

\(\overrightarrow{BC} = (4, 1)\)

Since \(\overrightarrow{AB} = \overrightarrow{DC}\) and \(\overrightarrow{AD} = \overrightarrow{BC}\), then the quadrilateral ABCD is a parallelogram.

The next 3 term of a sequence which is neither arithmetic nor geometric should be found

First term = 28

Second term = 14

difference = second term - first term

= 14 - 28

= -14

The next 3 terms will have a difference of -14 each

Third term = second term - 14

= 14 - 14

= 0

Third term = 0

Fourth term = Third term - 14

= 0 - 14

= -14

Fourth term = -14

Fifth term = Fourth term - 14

= -14 - 14

= -28

Fifth term = -28

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The height of the equilateral triangle is 41. 6 inches. Option C

The formula for finding the height of an equilateral triangle is given as;

h = (a√3)/2

we have a = 48 inches

Let's substitute the value

Height, h = \(\frac{48\sqrt{3} }{2}\)

Height = \(\frac{48 * 1. 732}{2}\)

Height = \(\frac{83. 14}{2}\)

Height = \(41. 6\) Inches

Thus, the height of the equilateral triangle is 41. 6 inches. Option C

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Answer:

2m-6

Step-by-step explanation:

M is the variable used for Mike's age

2m-6

2m is twice Mikes age

-6 is the 6 years younger

Hope this helps!

Step-by-step explanation:

6u+5v=-2 => ×1 => 6u + 5v = -2

2u+3v=6 => ×3 => 6u + 9v = 18

___________-

-4v = -20

=> v = -20/-4 = 5

2u +3v = 6

2u +3(5)=6

2u +15 = 6

2u = -9

u = -9/2 = -4.5

so, the solutions : {(-4.5 , 5)}

Answer:B

Step-by-step explanation:I’m not completely sure but y is going up twice as much as x.

Reason:

7 units to the left means x becomes x-7

2 units up means y becomes y+2

Therefore, the old preimage (x,y) translates or shifts to the new image (x-7, y+2)

Example:

\((\text{x},\text{y}) = (3,5)\\\\(\text{x},\text{y})\to(\text{x}-7,\text{y}+2)\\\\(3,5)\to(3-7,5+2)\\\\(3,5)\to(-4,7)\\\\\)

The preimage (3,5) moves to (-4,7) after shifting 7 units left and 2 units up.

According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer:

C

Step-by-step explanation:

Hamburger = Hotdog x 2

3(Hamburger) + 2(Hotdog) = 21

Now replace with x (Hotdog) and y (Hamburger)

y = 2x

3y + 2x = 21

Answer:

y > Two-thirds x + 1     /c

Answer:

2/15

Step-by-step explanation:

1/3 x 2/5

= ( 1 x 2 ) / ( 3 x 5 )

= 2/15

Answer:

2/15

Step-by-step explanation:

1/3*2/5

(1*2)/(3*5)

2/15

The quantity of candy that Eric ate would be = 14/15

The quantity of Candy Kim had = 2⅓ pounds.

The quantity of Kims candy that Eric ate = 2/5

That is 2/5 of 2⅓.

The actual quantity of candy that Eric ate = 2/5× 7/3 = 14/15

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Answer:

led the United States into the worst economic depression it had experienced up to that point in its history. Following the collapse of several Wall Street brokerage houses, over 600 banks and 16,000 businesses failed by the end of the year.

Answer:

Since, the baker use 5cups for 75cookies.Then for 30 cookies number of cups=

=75/5

=15.

Therefore no. 1cups for 15cookies.so,for 30 cookies=

=15*2

=30.

So, 2cups are needed for 30cookies

Answer:I think it would be 84 + 0.45m + 108.

Which simplified could be 0.45m + 192.

hope this helps!

Step-by-step explanation:

Answer:

There are 17.4 minutes of commercials are shown each hour.

Step-by-step explanation:

An hour has 60 minutes.

So in 3 hours, there are 3*60 = 180 minutes.

The commercials show 29% of the time.

So we have 0.29*180 = 52.2 minutes, in total, of commercial.

Per hour, we have 52.2/3 = 17.4 minutes of commercial.

Answer: 2a < 2b

Step-by-step explanation:

We are given a statement:

a < b and b < c, then 2a ____ 2b

We can use simple numbers that make the statement true.

Where,

a = 2

b = 3

c = 4

Now lets plug it in.

2 < 3 and 3 < 4, then 2(2) ____ 2(3)

and lets simplify:

2 < 3 and 3 < 4, then 4 ____ 6

We can see that 4 is less than 6,

so as a is less than b, 2a is less than 2b.

The only thing changing is the coefficient being multiplied by the variables a and b.

Step-by-step explanation:

Factors of 256: 1, 2, 4, 8, 16, 32, 64, 128 and 256.

Hope it will help :)❤

Here the answer hope this helps:

factors of 256 are.... 1, 2, 4, 8, 16, 32, 64, 128 and 256.

Step-by-step explanation:

hope this helps

The term variable implies that the rate is bound to change over time, in this context variable interest rate may double as an Advantage and also as a disadvantage.

D. increases when the market rate increases

Variable interest rate is advantageous because as the market rate increases, the rate at which the customer will receive his/her interest will increase too

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Answer: a

Step-by-step explanation:

Answer:

As = 256\(\pi\) or 804.25cm

Step-by-step explanation:

By formula As = \(4\pi r^{2}\)

As = 256\(\pi\) or 804.25cm

Answer:

Here you go, hope this helps

Step-by-step explanation:

Exact form: 13/12

Decimal form: 1.083 repeating

Mixed Number form: 1 1/12

Answer:

Exact Form:

13

12

Decimal Form:

1.083

Mixed Number Form:

1    1

    12

The theme is the underlying message, lesson, or central idea conveyed by the narrative or story.

Both a narrative and a story share several common elements that contribute to their structure and presentation. These elements include characters, setting, plot, conflict, and theme.

Characters are essential components of both narratives and stories. They are the individuals or entities that drive the events and experiences within the narrative or story. The setting is the time and place in which the events occur and provide the context for the story.

The plot refers to the sequence of events that unfold and create a structure for the narrative or story. Conflict represents the central problem or challenge faced by the characters and is often a driving force behind the plot's progression.

These shared elements create a framework for both narratives and stories, enabling the development and communication of experiences, ideas, and emotions to the audience. They contribute to the engagement, coherence, and impact of the narrative or story, regardless of the medium or genre in which they are presented.

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Answer:

you can make 12 cans of them