Hector just acquired 200 acres of land for raising animals. He wants to have at least 50 horses and no more than 300 sheep. Horses require at least 2 acres each. A maximum of 6 sheep can share an acre. What are the inequalities for the system

The solution for the system of linear inequalities is y <-3 and x < 10.5

Linear inequalities are inequalities that have constant average rates of change.

A system of linear inequalities is a collection of at least two linear inequalities

In this case, the system of inequalities is given as

2x - 3y < 12

y < -3

Substitute y < -3  in 2x - 3y < 12

2x - 3(3) < 12

Evaluate the like terms

2x - 9 < 12

This gives

2x < 21

Divide by 2

x < 10.5

Hence, the solution is y <-3 and x < 10.5

See attachment for the graph where the green line represents y <-3 and the other represents 2x - 3y < 12

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The rules of Perfect Square Trinomial are, an expression obtained from the square of the binomial equation is a perfect square trinomial. If a trinomial is in the form [tex]ax^{2} +bx+c[/tex] is said to be a perfect square, if and only if it satisfies the condition [tex]b^{2} = 4ac[/tex].

Perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial. A perfect square is a number that is obtained by multiplying a number by itself. Binomials are algebraic expressions consisting of just two terms that are either separated by a positive (+) or a negative (-) sign. Similarly, trinomials are algebraic expressions consisting of three terms. When a binomial consisting of a variable and a constant is multiplied by itself, it results in a perfect square trinomial having three terms. The terms of a perfect square trinomial are separated by either a positive or a negative sign.

A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression. It is of the form [tex]ax^{2} +bx+c[/tex]. Here a, b, and c are real numbers and a ≠ 0. For example, let us take a binomial (x+4) and multiply it to (x+4). The result obtained is [tex]x^{2} +8x+16[/tex]. A perfect square trinomial can be decomposed into two binomials and the binomials when multiplied with each other gives the perfect square trinomial.

Therefore,

An expression obtained from the square of the binomial equation is a perfect square trinomial. If a trinomial is in the form [tex]ax^{2} +bx+c[/tex] is said to be a perfect square, if and only if it satisfies the condition [tex]b^{2} = 4ac[/tex].

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Using the angle theorems, the measure of angle 6, m ∠6, is 54°

From the question, we are to determine the measure of angle 6

From the given diagram, we can write that

(13x + 9)° = m ∠5 (Corresponding angles theorem)

and

m ∠5 + (5x + 9)° = 180° (Linear pair theorem)

Thus,

(13x + 9)°  + (5x + 9)° = 180°

Now, we will solve for x

13x + 9 + 5x + 9 = 180

18x + 18 = 180

Subtract 18 from both sides of the equation

18x + 18 - 18 = 180 - 18

18x = 162

x = 162/18

x = 9

Now, to determine the measure of angle 6

m ∠6 = (5x + 9)° (Vertical angles theorem)

Substitute the value of x

m ∠6 = (5(9) + 9)°

m ∠6 = (45 + 9)°

m ∠6 = 54°

Hence, measure of ∠6 is 54°

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The 10.78 watt–hour battery with a voltage rating of 3.85 V gives;

(a) The average current delivered in 3 hours is approximately 0.93 A

(b) The average power delivered at 0.93–A is approximately 3.593 watts

(c) The ampere hour rating of the battery is 2.8 Ah

Power is the rate at which energy is given out or expended.

Required;

(a) The amount of average current that can be delivered in 3 hours

Solution;

The power in the battery is given by the equation;

P = I²•R = I•V

10.78 watt–hour = 10.78 J/s × 60 × 60 s = 38,808 J

In 3 hours, the energy per second, which is the power is given by the equation;

P = 38,808 J/(3×60×60 s) ≈ 3.593 watts

I = P/V

Therefore;

I = 3.593 watts/(3.85 V) ≈ 0.93 A

(b) The average power delivered is given by the equation;

P = Energy/Time

Therefore;

(c) An equation that can be used to find the ampere hour, Ah is as follows;

Ah = Watt hour ÷ Voltage

The ampere hour rating of the battery is therefore;

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Answer:

m arcRP = 125°

m arcQS = 125°

m arcSP = 55°

m arcQR = 55°

Step-by-step explanation:

An arc is the curve between two points on the circumference of a circle.

An arc measure equals its corresponding central angle measure.

Vertical Angles Theorem:  When two straight lines intersect, the opposite vertical angles are congruent.

Angles on a Straight Line Theorem:  The sum of angles formed on a straight line is equal to 180°.

As m∠ROP = 125°

Therefore, m arcRP = 125°

Given the measure of angle ROP is 125°, and an arc measure equals its corresponding central angle measure, the measure of arc RP is 125°.

Using the Vertical Angles Theorem:

⇒ m∠QOS = 125°

Therefore, m arcQS = 125°

Using the Vertical Angles Theorem, the measure of angle QOS is equal to the measure of angle ROP, so the measure of angle QOS is 125°. As an arc measure equals its corresponding central angle measure, the measure of arc QS is 125°.

Using the Angles on a Straight Line Theorem:

⇒ m∠SOP = 180° - 125° = 55°

Therefore, m arcSP = 55°

Using the Angles on a Straight Line Theorem, the measure of angle SOP is 55°. As an arc measure equals its corresponding central angle measure, the measure of arc SP is 55°.

Using the Angles on a Straight Line Theorem:

⇒ m∠QOR = 180° - 125° = 55°

Therefore, m arcQR = 55°

Using the Angles on a Straight Line Theorem, the measure of angle QOR is 55°. As an arc measure equals its corresponding central angle measure, the measure of arc QR is 55°.

Property justifies the given statement 7(mn)= (7m)n is :

Associative property of multiplication.

As given in the question,

Given statement :

7(mn) = (7m)n

Property justifies the given statement 7(mn)= (7m)n is :

Therefore, property justifies the given statement 7(mn)= (7m)n is :

Associative property of multiplication.

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Answer:

6

Step-by-step explanation:

The body mass index of a person 65 inches tall with a weight of 175 pounds is 29.12

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The body mass index (BMI) is given by:

BMI = [mass in pounds / (height in inches)²] * 703

Given mass = 175 pounds, height = 65 in, hence:

BMI = [175/65²] * 703 = 29.12

BMI = 29.12

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Only height, because when you have an expression that relies only on multiplication (not addition or subtraction), we'll say:

cb = a

Tripling either c or b will also triple a. For example:

(8)(3) = 24

(8 + 8 + 8)(3) = 24(3)
(24)(3) = 24(3)

This will be true even if you multiply c by any other number.

So, in the expression v = πr²h, any term except r can be tripled with the result of tripling v. We exclude r because r has an exponent, which means tripling r will more than triple v.

Answer:

A

Step-by-step explanation:

[tex]m=2/5 \implies 10(2/5)=4 \\ \\ m=1/2 \implies 10(1/2)=5 \\ \\ m=1 \implies 10(1)=10 \\ \\ m=2 \implies 10(2)=20[/tex]

Of these, only 4 is a perfect square.

Construct a probability mass function (pmf) for x, the dollar amount won by a contestant in this game is 1/18.

What is a probability math example?

from above total number of chips =4+6+5+2+1 =18

hence Probabilty of win 0 P(0)=4/18

P(1) =6/18

P(5) =5/18

P(10) =2/18

P(100)=1/18

x     P(x)     xP(x)

0    0.22     0.00

1     0.33      0.33

5     0.28       1.39

10      0.11       1.11

100     0.06      5.56

                       8.39

therefore expeted value =8.39

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By using Binomial probability distribution, the mean number of adults who would have bank savings accounts is 32.

For every survey, there are only two possible outcomes.

First- they have bank savings accounts,

second- they do not.

So, by using the binomial probability distribution we can solve this problem.

Probability of exactly Y successes in ‘n’ repeated trials, with ‘p’ probability.

Probability = p

Successes repeated = n  times

The  value of the binomial distribution is:

E(Y) = n x p

In this problem, we have that:

p = 0.64

If we were to survey among 50 randomly selected adults, the mean number of adults who would have bank savings accounts is,

E(Y) when, n = 50

So,

E(Y)= n x p

= 50 x 0.64

= 32

Hence ,our required answer is 32 adults who would have bank savings accounts

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The percentage of decrease for the chemistry experiment is 25%.

The. percentage is defined as the number representing any number with respect to 100.

In this case, at the begining, the experiment was 4 millimeters and the end had an experiment of 3 millimeters.

The decrease in the percentage will be:

= Change in value /Original value × 100

= (4 - 3)/4 × 100

= 1/4 × 100

= 25%

The percentage is 25%.

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Answer:

What is this, give context and I'll help you.

Step-by-step explanation:

Need more context.

Step-by-step explanation:

you can ask questions for clarification

Answer:

3

Please refer to the photo below:

What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%

annual interest, compounded monthly?

Remember that

The compound interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

A=$120,000

t=12 years

r=14%=14/100=0.14

n=12

substitute in the given formula

Solve for P

The total price that Bryce got charged to his credit card is $120.54  .

In the question ,

it is given that the

price for Shorts = $14.00

price for Soccer Ball = $25.00

price for Shin guard = $10.00

price for Cleats = $60.00

the total price for all the items = 14+25+10+60 = $109  

Given that the sales tax is 6% of the total price .

So , the sales tax = 6% of 109 = 0.06×109 = $6.54

According to the question

total price = price + sales tax + shipping cost

= 109 + 6.54 + 5

= 120.54

Therefore , the total price that Bryce got charged to his credit card is $120.54  , the correct option is (D) $120.54   .

The given question is incomplete , the complete question is

Bryce orders the following items from a catalog. What is the total price he charges to his credit card if the sales tax is 6 percent and nontaxable shipping costs $5 for the order? Round to the nearest cent if necessary. Shorts=$14.00 ,Soccer ball=$25.00 ,Shin guards=$10.00 ,Cleats=$60.00 .

(A) $104.94

(B) $109.94

(C) $115.54

(D) $120.54

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

Explanation:

The car is initially worth 44000 pounds.

It loses 25% of its value after the first year, but keeps the remaining 75% of it.

75% of 44000 = 0.75*44000 = 33000

The car is worth 33000 pounds at the end of year 1. This is effectively the "starting" value when we change the rate of depreciation.

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

The new percentage of the depreciation rate is x%

The car loses x% of its value each year

But it keeps the remaining (100-x)% of the value from year to year. Refer to the previous section.

x% = x/100

(100-x)% = (100-x)/100 = 100/100 - x/100 = 1 - 0.01x

The 1 - 0.01x is the value of b in the exponential equation y = a*b^t

The value of 'a' is the "starting" value of 33000 pounds.

The t represents the number of years after that first year (so that means we have t+1 years total).

The equation we have is

y = a*b^t

y = 33000(1 - 0.01x)^t

The teacher mentions "after 3 years" which means we'll have t+1 = 3 solve to t = 2 which is what we'll plug in along with  y = 25555

Let's solve for x.

y = 33000(1 - 0.01x)^t

25555 = 33000(1 - 0.01x)^2

25555/33000 = (1 - 0.01x)^2

0.77439393939393 = (1 - 0.01x)^2

(1 - 0.01x)^2 = 0.77439393939393

1 - 0.01x = sqrt(0.77439393939393)

1 - 0.01x = 0.87999655646709

-0.01x = 0.87999655646709-1

-0.01x = -0.1200034435329

x = -0.1200034435329/(-0.01)

x = 12.00034435329

Due to rounding error, it appears that it should be x = 12 since your teacher mentions x is an integer.

Also, 12.00034435329 is pretty close to 12.

If it decays at 12% per year, then the car keeps the remaining 88% since 100-12 = 88

Therefore 0.88 is the base of the exponential, it's the value of b.

Computing 33000(0.88)^2 gets us 25,555.2 which isn't too far from the goal of 25,555 pounds.

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

We found the exponential decay equation to be

y = 33000(0.88)^t

where t is the number of years after that first year. We have t+1 years total.

Your teacher asks how much the car will be worth after 4 years, so we'll plug in t = 3 because it's the solution to t+1 = 4.

In other words, we're working 3 years after that first year is up, so 3+1 = 4 total years.

Plug in t = 3 to find the following

y = 33000(0.88)^t

y = 33000(0.88)^3

y = 22,488.576

Rounding to the nearest pence gets us 22,489.58 which is the value of the car after 4 years. You can verify this with a spreadsheet table as I have shown in the diagram below. The highlighted rows mention values on your screenshot.

I'll round to the nearest pound since the other car values mentioned were whole numbers rather than decimal ones.

The 22489.58 rounds to 22490

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

For the final part, we'll need logarithms to solve the equation. Logarithms are useful to isolate the exponent.

We'll plug in y = 14520 and solve for t

y = 33000(0.88)^t

14520 = 33000(0.88)^t

14520/33000 = (0.88)^t

0.44 = (0.88)^t

Log[ 0.88^t ] = Log[ 0.44 ]

t*Log[ 0.88 ] = Log[ 0.44 ]

t = Log[ 0.44 ]/Log[ 0.88 ]

t = 6.42227097958021

This rounds up to t = 7

Round up instead of down because we want to clear the hurdle of passing the 14520 marker.

Recall once again that t is the number of years after the first year.

So t = 7 represents t+1 = 7+1 = 8 years in total that have passed by. Therefore, after 8 years is when the car's value is below 14520 pounds. Refer to the table diagram below.

The length and width of the rectangular field is found as width x = 2.08 m and length = 5.16 m.

The given values in the question are-

The width of the field = w.

The length of the field = 2x+1

The area of the field =  600 m².

The formula of area of rectangular field;

A = length×width

Put the values;

600 = (2x+1)x

Simplifying the equation;

600 = 2x² + x

2x² + x - 600 = 0.

Find the factors of the above quadratic equation using quadratic formula.

x = 2.08, neglecting negative value.

Thus, the width is x = 2.08 m.

length = 2x + 1

length = 5.16 m.

Thus, the length and width of the rectangular field is found as width x = 2.08 m and length = 5.16 m.

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Medical insurance Jessica pays biweekly is $196.58 or 197 dollars.

Dental insurance Jessica pays biweekly is $22.3125 or 22 dollars.

Janice:

Medical insurance costs $6,740 annually

Dental costs $630

Solution:

Jessica:

70% of medical insurance = 70/100*6,740

= 674 * 7

=  $4,718/annum.

85% of dental insurance = 85/100 * 630

= 63 * 8.5

=  $535.5/annum

Medical insurance Jessica pays per month = 4,718/12 = $393.16

Medical insurance Jessica pays biweekly = 393.16/2 = $196.58 or $197

Dental insurance Jessica pays per month = 535.5/12= $44.625

Dental insurance Jessica pays biweekly = 44.625/2 = $22.3125 or $22.

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The image of (-8,6) after a reflection over the line y = -x is (-6, 8).

Given:

The image of (-8,6) after a reflection over the line y = -x.

The x-coordinate and y-coordinate of a point change positions and are negated when it is reflected across the line y = -x.

So, the reflection of the point (-8, 6) across the line y = -x is (-6, 8).

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It was 1.5 times the length of Noah's bike ride as Mai’s bike ride.

The problem we dealing with is related to mixed numbers which are referred to as mixed numbers and could be the whole number, and a proper division spoke together. It for the most part speaks to a number between any two whole numbers.

Since we are providing mai's rate which is  6 3/4  miles and Noah's  rate of 4 1/2 miles, So in  order to find the time the length of Noah's ride is compared to Mal's, we just need to divide the given rates by each other

=> 6 3/4 divided by 4 1/2,  

=> 27/4 divided by 9/2, (The result is an improper fractions)

=> 27/4 X 2/9

=>3/2

=> 1.5

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The value of the net force acting on the block will be equal to 79N.

Force may be defined as the product of mass and acceleration, and it acts on the body in order to move the body. Since, the external force is acting on the block there will be a frictional force which opposes the block to move. The frictional force may be represented by f(k) and is given by

f(k) = external force - (ma)

f(k) = 40N - (5×6)

f(k) = 40N - 30N

f(k) = 10N and since it opposes the external force then the sign will be negative that is f(k) = -10N.

Also, there is a force of gravity acting on the body which will be equal to mg where 'g' is the acceleration due to gravity.

Now, force of gravity = mg

= 5×9.8 = 49N

Now, net force acting on the block = 40N - 10N + 49N

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Answer:

211/4 is bigger number cause if you look at it right 52 4/9 is smaller than 211/4

Answer:

23.8/5.6=4.25

Step-by-step explanation:

Answer:

4.25

Step-by-step explanation:

[tex] \sf \: 23.8 / 5.6 =4.25[/tex]

[tex] \sf----------------------------------[/tex]

Metric measurement are given below:

The meter, liter, and gram are the corresponding base units for length (distance), capacity (volume), and weight (mass) in the metric system. To measure smaller or larger amounts, we use units that are derived from metric units.

The three most used base units in the metric system are the meter, gram, and liter. The liter is a unit of volume equal to 1.05 quarts, the meter is a unit of length equal to 3.28 feet, and the gram is a unit of mass about equivalent to 0.0022 pounds (or roughly the mass of a paper clip).

Given Data

a) 2.4 meters

b. 0.4 kilometers

c. 0.04 hectometers

d. 240 decimeters

_ 40 dekameters

_ 0.24 hectometers

_400 centimeters

_ 2400 millimeters

a) 2.4 meters = 2400 millimeters

b) 0.4 kilometers = 400 centimeters

c) 0.04 hectometers =  40 dekameters

d) 240 decimeters = 0.24 hectometers

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