Suppose a farmer wants to create a four-sided rectangular pen with an area of 144 square feet. what is the length and width of the rectangular pen that uses the smallest perimeter possible to enclose this area? what is the perimeter of this pen?

pls help asap

Answer:

7 ≤ x ≤ 25

Step-by-step explanation:

Triangle Inequality Theorem

The sum of any two sides of a triangle is greater than or equal to the third side:

Therefore, the longest side of the triangle is "c".

Let the longest side be "x":

Therefore:

Let the longest side be 16:

Therefore:

As 9 < 16, the longest side cannot be 9.

Therefore, the length of the third side of the triangle, given that the other two sides are 9 ft and 16 ft is greater than or equal to 7, and less than or equal to 25:

By distributive property for real numbers, the expression (- 4 + v + 4 · x) · (- 6) is equivalent to the expression 24 - 6 · v - 24 · x.

In real algebra, distributive property is an algebraic property where a real number is "distributed" on every term of a sum of real numbers. This property is described below:

c · (a + b) = a · c + b · c

Where a, b, c are real numbers.

Now we proceed to use distributive property in the following case. First, write the entire expression:

(- 4 + v + 4 · x) · (- 6)

Second, apply distributive property:

(- 6) · (- 4) + (- 6) · v + (- 6) · (4 · x)

Third, use associative property:

(- 6) · (- 4) + (- 6) · v + [(- 6) · (4)] · x

Fourth, use sign laws and multiply on each term:

24 - 6 · v - 24 · x

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The possible number of handshakes in a group of 10 people, where each person shakes hands with everyone else once are equal to 45.

Number of people in the group = 10

Each person shakes hands with everyone else once. When n people shake hands with each other, the total number of handshakes = ⁿC₂

where C denotes the combination , is represent an arrangement of objects in different ways without care of order.

Total number of handshakes = ¹⁰C₂

= 10!/2!(10 - 2)! = 10!/2!×8!

= 10×9×8!/(2×1)8!

= (10×9)/2

= 45 handshakes.

In other words, when 10 people are shaking hands, each one will shake hands with 9 others. Then, the total possible number of handshakes in a group = 10 × 9 = 90

(but remember the point that , when A shakes hands with B, B is also shaking hands with A, i.e., we are counting one handshake twice, one from A's side and the other from B's side).

The total number of handshakes in actual way = 90/2 = 45 handshakes. Hence, the total number of handshakes in a group is 45.

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Stratified sampling is used when the population is heterogeneous.

What is Stratified sampling?

A method of probability sampling (where all members of the population have an equal chance of being included) Population is divided into 'strata' (sub-populations) and random samples are drawn from each. This increases representativeness as a proportion of each population is represented.

The sampling method described in the study is a stratified sampling method.

In stratified sampling, the population is first divided into subgroups or strata based on some relevant characteristic, such as size in this case.

Then, a simple random sample is taken from each stratum.

In this study, the sample is chosen by separating all cars by size and selecting 10 of each size grouping, this is the definition of stratified sampling.

Stratified sampling is useful when the population is heterogeneous and you want to ensure that the sample is representative of specific subgroups within the population.

This method allows for a more precise estimation of population characteristics and can reduce sampling error.

Hence, Stratified sampling is used when the population is heterogeneous.

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The provided integral may be expressed as follows using the following statement as a guide: 128/3 - 31 [tex]\sqrt{17}[/tex] /3

An integral in mathematics is either a number that depicts the area underneath the graph of a function over a specific period of time or a about before, the reversed of which includes the initial result (indefinite integral). To complete the whole, an essential component is required. The term crucial is a close synonym in this context. Integrals of functional and equations are a concept in mathematics. The word "aal" is derived from Middle English, which is derived from Latin Word integralis "thinking up unity," from Latin "with, entire."

To find [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex]

Put [tex]$16+r^2=t^2$[/tex]

[tex]$2 r d r=2 t d t$[/tex]

[tex]$r d r=d t$[/tex]

[tex]$r=0 \Rightarrow t=4$[/tex]

[tex]$r=1 \Rightarrow t=\sqrt{17}$[/tex]

[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\int_4^{\sqrt{17}} \frac{t^2-16}{t} t d t$[/tex]

[tex]$=\left[\frac{t^3}{3}-16 t\right]_4^{\sqrt{7}}$[/tex]

[tex]$=\frac{(\sqrt{17})^3}{3}-16(\sqrt{17})-\frac{(4)^3}{3}+64$[/tex]

[tex]$=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

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Answer:

Step-by-step explanation:

Use the formula for circles.

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

Since we already have the values of x and y in the given problem (-2,3), substitute the values in the fomula.

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

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

[tex]4 + 9 = r^{2}[/tex]

[tex]13 = r^{2}[/tex] (square both sides to get the radius)

[tex]\sqrt{13} = \sqrt{r^{2} }[/tex]

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

Answer:

(motorboat speed is 40 km/h)

(current speed) = 10 km/h

Step-by-step explanation:

Ok, let the speed of the water current be x and the speed of the motorboat be y. Then, the speed of the motorboat upstream

against the current is (x - y)

Putting it into the equation, we get,

5h (x - y) = 150 km or

(x - y) = 30 km/h -  1

Now, downstream speed is (x + y).

Again, forming it into equation, we get,

3(x + y) = 150

x + y = 50 km/h  -   2

Adding both equations, we get,

2x = 80 km/h

x (motorboat speed is 40 km/h)

40 - y = 30 km/h

y(current speed) = 10 km/h

Answer:

still water (s): 40 mph

current rate (c): 10 mph

Step-by-step explanation:

We are given two things:

1) 5 hours to travel 150 mi upstream

2) return trip 3 hours downstream

Note that when the boat goes upstream, it must push against the current, versus when it goes downstream, the current helps the boat to move. Also keep in mind the trip is always 150 mi both ways.

With that said, lets set up the problem. First, let s be the rate of the boat in still water, and let c be the rate of the current. We must keep in mind that when the boat goes upstream, it impedes its overall speed. So our equation for that looks like:

5(s-c)=150 (use for upstream)

And downstream would look like:

3(s+c)=150 (use for downstream)

Now that we have both equations, the next step is to expand them. You should get the two following equations:

5s-5c=150 AND 3s+3c=150.

Essentially, we are going to need to solve a system of equations here. You must add them to solve. First, multiply the first equation above by 3 and get 15s-15c=450 and multiply the second one by 5 and get 15s+15c=750.

When we add them we will get the following equation as a result: 30s=1200. Now divide both sides by 30 revelaing s to be 40. Now substiute in:

3(40)+3c=150

120+3c=150

-120      -120

3c=30

c=10

The system of equations is now solved revelaing the speed of the boat in still water to be 40 and the current speed to be 10.

In this scenario, the number of winning tickets follows a binomial distribution, since each ticket has a fixed probability of winning (1/4) and the trials (purchasing a ticket) are independent.

The probability that k out of n trials will be successful is given by the binomial probability mass function:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

Where n is the number of trials (100 tickets), k is the number of successful trials (winning tickets), p is the probability of success (1/4), and (n choose k) is the binomial coefficient.

To find the probability that fewer than 20 tickets are winners we have to calculate the probability of getting 0 to 19 winning tickets.

P(x<20) = P(0) + P(1) + P(2) +...+ P(19)

using the above formula we can find the probability of getting k winning tickets

P(x<20) = P(0) + P(1) + P(2) +...+ P(19)

= (100 choose 0) * (1/4)^0 * (3/4)^100 + (100 choose 1) * (1/4)^1 * (3/4)^99 +.... + (100 choose 19) * (1/4)^19 * (3/4)^81

This can be calculated using a calculator or spreadsheet software, however, it's not possible for me to provide you with the exact answer as it involves multiple complex calculations.

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Answer:

32

Step-by-step explanation:

[tex]8\sqrt{3}[/tex] is opposite to the 60 degree angle

The side opposite to the 60 degree angle = [tex]\sqrt{3}[/tex] times the side opposite to the 30 degree angle.

Side opposite to the 30 degree angle = 8

Leg opposite to the 30 degree angle theorem states that the side opposite to the 30 degree angle is half of the hypotenuse.

Hypotenuse = 16

In the big triangle, 16 is the side opposite to the 30 degree angle, which means it is half of the hypotenuse (big triangle).

Hypotenuse of the big triangle = x = 32

Hope this helps :)

Have a great day!

Answer:

Equation is 14h = 91

It solves to  h = 6.5

===========================================

Work Shown:

h = number of hours worked

14h = amount earned at $14 per hour

14h = 91 is the equation

To solve this equation, divide both sides by 14.

14h = 91

14h/14 = 91/14

h = 6.5

She worked 6.5 hours last week.

Answer: Root 16 = 4, 4*1/2= 2

5/9*1/2= 5/18

Root 3 = 1.73205...*1/2= 0.866025...

Root 3 is the answer

Answer:

Jeffrey drove a total of 303.43 miles on Monday, Tuesday, and Wednesday.

Step-by-step explanation:

To find the total miles driven by Jeffrey on Monday, Tuesday, and Wednesday, we need to add up the total miles. The total miles driven are 146.3 + 84.13 + 73.02 = 303.43 miles.

I would recommend taking this bet, as the expected value of the bet is Positive.

The expected value of a bet is the sum of the product of each possible outcome and its corresponding probability. In this case, the probability of getting two heads is 0.25, and the payout for that outcome is $10. The probability of not getting two heads is 0.75, and the payout for that outcome is -$2. When you multiply each outcome by its corresponding probability and sum them together, the expected value of the bet is $1.0. Because the expected value of the bet is positive, it is  a good bet to take. It is more likely that you will gain money .

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Answer:

4x+5 = 13

Step-by-step explanation:

2x-7= 5

The required number of ways to write 9 as sum of 1, 2, 4 is 96 ways.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1.

Two fours and one one Three numbers must be added up. Any one of the three spaces will accept a one before fours are used to fill the remaining slots. There are thus 3 possible arrangements for these. Thus, there are

1 + 8 + 21 + 6 + 20 + 20 + 5 + 12 + 3 = 96 ways

Thus, there are 96 ways to write 9 as sum of 1, 2, 4.

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The solution to the equations are

The number of blocks walked in 5 minutes = 4 blocks

The number of blocks walked in 30 minutes = 24 blocks

The time taken to walk 4 blocks = 5 minutes

The time taken to walk 12 blocks = 15 minutes

The time taken to walk 16 blocks = 20 minutes

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The time taken for the Scott family to walk 4 blocks = 5 minutes

So , time taken for the Scott family to walk 12 blocks = 3 x time taken for the Scott family to walk 4 blocks

Substituting the values in the equation , we get

Time taken for the Scott family to walk 12 blocks = 3 x 5 = 15 minutes

And ,

Time taken for the Scott family to walk 16 blocks = 4 x time taken for the Scott family to walk 4 blocks

Substituting the values in the equation , we get

Time taken for the Scott family to walk 16 blocks = 4 x 5 = 20 minutes

Now ,

Number of blocks walked in 5 minutes = 4 blocks

So , the number of blocks walked in 30 minutes = 6 x Number of blocks walked in 5 minutes

Substituting the values in the equation , we get

The number of blocks walked in 30 minutes = 6 x 4 = 24 blocks

Hence , the equations are solved

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Answer:

We can set up a system of equations using the information given:

x + 2y = 2830 (equation 1)

2x + y = 2540 (equation 2)

where x is the number of calories in one shake and y is the number of calories in one taco supreme.

We can use either equation to solve for one of the variables and then substitute that into the other equation.

From equation (1), x = 2830 - 2y

And substituting this into equation (2) we get

2(2830-2y) + y = 2540

Now we can solve for y.

5,660 - 4y + y = 2540

-3y = -3120

y = 1040

So, one taco supreme contains 1040 calories.

And substituting this value of y back into equation (1) we can find the number of calories in one shake:

x + 2(1040) = 2830

x = 550

So, one shake contains 550 calories.

The p-value is a probability and it should be between 0 and 1.

The p-value of a hypothesis test is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

In this case, the null hypothesis is that the population proportion of students who went to the movie theatre last weekend is equal to 0.2 and the alternative hypothesis is that the population proportion is greater than 0.2.

Given that the test statistic is 2.25, the p-value would be the probability of getting a test statistic as extreme or more extreme than 2.25 assuming the null hypothesis is true. Without more information, we can't give you an exact p-value, but you can use a one-sided test and find the p-value using a z-table or using software that can calculate the p-value.

It is also important to note that the p-value is a probability and it should be between 0 and 1.

Therefore,  The p-value is a probability and it should be between 0 and 1.

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Zach is trying to find out the hypotenuse value of the right-angle triangle.

What is the right triangle?

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The Pythagorean theorem states that "in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides".

Zach is most likely trying to find the length of the hypotenuse of a right triangle, which is the side opposite the right angle, given the lengths of the other two sides.

In this case, given 32 inches, 20 inches, and 20 inches values, he's trying to find out the hypotenuse value of the right-angle triangle.

Hence, Zach is trying to find out the hypotenuse value of the right-angle triangle.

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The length of each diagonal is of: 11 units.

The diagonal lengths are defined as follows:

As the figure is a rectangle, the diagonal lengths are the same, and thus the value of x is obtained as follows:

WY = XZ

6x - 7 = 3x + 2

3x = 9

x = 9/3

x = 3.

Hence the diagonal length is given as follows:

XZ = 3(3) + 2 = 9 + 2 = 11 units.

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the probability that none of the student's purchases arrive the next day

P( STUDENT) = 0.99 - 0.97 = 0.002

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

here,

the probabilities of next day orders arriving on time for each retailer are 0.99, 0.97, and 0.96,

the probability that none of the student's purchases arrive the next day

P( STUDENT) = 0.99 - 0.97 = 0.002

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Answer:

2023

Step-by-step explanation:

3 + 4x = y

y = 3 + 4(505)

y = 3 + 2020

y = 2023

An absolute value equation may have one solution, two solutions, or no solutions.

Absolute value means "distance from zero" on a number line. To represent the absolute value of a number, we use a vertical bar on either side of the number.

The absolute value is the distance from zero, It is the non-negative quantity, which defines the number as the distance of the number from zero on the number line.

The absolute value has only one solution when it is compared to 0.

When the absolute value equation is compared with any positive number, then the number of solutions is two.

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The correct term for each term is -

Federal Fund Rate

Bank holding company

Check clearing

Net worth

Discount rate

What is an account?

A certain kind of financial asset or debt that is kept and owned in your name.

When a bank borrows money from another bank, the interest rate it pays is called the Federal Fund Rate.

Ownership of more than one bank constitutes a bank holding company.

When a bank customer writes a check, the check will go through the process of check clearing.

A bank's total assets minus its total liabilities make up its net worth.

Banks repay loans from the Federal Reserve at a rate of interest called the discount rate.

Therefore, these are the key terms used in banking.

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Answer:

true

Step-by-step explanation:

i had the same question on a quiz.

The value of x for the equation 34+x4=1 is [tex]\frac{-33}{ 4}[/tex]

As we have [tex]34+4x=1[/tex]

Subtracting [tex]34[/tex] from both sides we get

[tex]4x=1-34[/tex]

[tex]4x=-33[/tex]

Dividing with [tex]4[/tex] both sides

we get the answer [tex]x=\frac{-33}{4}[/tex]

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Answer:$10

Step-by-step explanation:

Assume 20% = 0.20

50 x 0.20 = 10

OR

Move the decimal one place to the left for 10 percent, and double it to get 20 percent.

Answer:

Suppose 20% Equals 0.20.

50 x 0.20 = 10

To acquire 10%, move the decimal one position to the left, and to reach 20%, double it.

Step-by-step explanation:

Answer:

Step-by-step explanation:

all internal angles in a triangle add to 180 degrees.

77+36=113

180-113=67

we know that the final angle in the triangle is 67 degrees

the left parallel line makes another triangle in the bottom left. we know that one angle is 41 and we just calculated that the other is 67.

41+67=108

180-108=72

so now we know that the small triangle in the bottom left has angles of 41,67 and 72.

all straight lines are 180 degrees, and we just figures out that the left side of the left parallel line is 72 degrees. therefore the other side is 108 degrees.

since they are parallel lines, the left angle of both of them on the bottom line is 72, while the right angle is 108.

this means that x=108 degrees

i hope this is right and it helps if it is correct. really sorry if it is wrong. have a good day :)

In given triangle ABC the length if BC is 7.1 .

What is trigonometric functions?

A subfield of mathematics called trigonometry is concerned with the study of triangles. It is frequently referred to as "trig" casually. In trigonometry, mathematicians look at how triangles' sides and angles relate to one another.

Here in given triangle contains 90°, So it is right triangle.

Now using tangent function then

=> tan B = [tex]\frac{opposite}{adjacent}[/tex] then

=> tan 38° = [tex]\frac{AC}{BC}[/tex]

=> BC = tan 38° × AC

=> BC = tan 38° × 9.1

=> BC = 7.1

Hence the length of the side BC is 7.1.

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The length of BC in the triangle ABC is 7.109.

Trigonometry is a branch of mathematics concerned with the study of triangles. It is commonly referred to as "trig" in a casual manner. Trigonometry examines how the sides and angles of triangles relate to one another.

Because the given triangle contains 90°, it is a right triangle.

Now, using the tangent function,

The tangent function is one of trigonometry's six primary functions.

Tan A = Opposite Side/Adjacent Side is the Tangent Formula. In terms of sine and cosine, tangent may be represented as: Tan A = Sin

then,

= tan B = opposite side / adjacent side

= tan 38° = AC/BC

= BC = 38° tan x AC

= BC = tan 38° × 9.1

= BC = 7.109

As a result, the length of the side BC is 7.109.

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On solving the provided question, we can say that unlike other shapes, which all have parallel lines, only has one parallel side.

Parallel lines in geometry are coplanar infinite lines that don't intersect anywhere. In a given three-dimensional space, parallel planes are those that never cross. Curves with a constant minimum distance between them and no points of contact or intersection are said to be parallel. Two lines that are in the same plane, equally spaced apart, and never intersect are referred to as parallel lines in geometry. Either horizontal or vertical can apply. Parallel lines can be noticed in everyday objects like railroad tracks, rows of notebooks, and pedestrian crossings.

unlike other shapes, which all have parallel sides, only has one parallel side.

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Answer:

14.8%

Step-by-step explanation:

decrease = -100 * ((final - initial) / initial)

Answer:

14.8%

Step-by-step explanation:

Original fishing pole cost: $54

New fishing pole cost: $46

Using the percentage decrease formula:

[tex]\frac{Original Value - Final Value}{|Original Value|}[/tex]  ×100%

Substitute

[tex]\frac{54-46}{|46|}[/tex] ×100%

From this, you should get 14.814814814814814...

Round to nearest tenths.

Final answer: 14.8%