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Blake wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Blake has 950 feet of fencing, you can find the dimensions that maximize the area of the enclosure.

a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write a function for the area A of the enclosure in terms of w . (HINT: First write one equation with w and l and one equation with w and l and A. Solve for l in the first equation and substitute for l in the other). A ( w ) = ____________

b) What width w would maximize the area? w = __________________ ft

c) What is the maximum area? A = ______________ square feet

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The coordinates are (0, 3) or (34/5, 3)

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

15x - 10y = -30 _____(1)

5x - 9y = 7 ______(2)

Multiply 3 on (2)

15x - 27y = 21 _____(3)

Using the elimination method we get,

From (1) and (3) we get,

 15x - 10y = -30

 15x - 27y = 21

(-)    (+)        (-)

      17y    = 51

This means,

y = 51/17

y = 3

Now,

Put y = 3 in (1) we get,

15x - 10y = -30

15x- 10 x 3 = -30

15x - 30 = -30

15x = 0

x = 0

Put y = 3 in (2) we get,

5x - 9y = 7

5x - 9 x 3 = 7

5x - 27 = 7

5x = 7 + 27

5x = 34

x = 34/5

Thus,

The coordinates are (0, 3) or (34/5, 3)

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Answer: a = 180 - 63 - 90

Step-by-step explanation:

180 degrees in a triangle

90 degrees in a right triangle

180 = 63 + 90 + a

move 63 and 90 to the other side

a = 180 - 63 - 90

Answer:

b

Step-by-step explanation:

The angle of elevation of the ramp to the nearest degree will be 5.71°.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that a ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The horizontal distance from the bottom of the ramp to the building is 10 feet.

The angle of elevation will be calculated as,

tanθ = ( 1 / 10)

θ = tan⁻¹(1/10)

θ  = 5.7°

Therefore, the angle of elevation of the ramp to the nearest degree will be 5.71°.

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The probability of the Komets losing their race and the Galaxy winning theirs is

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

The probability of the Galaxy team winning is 22%.

And, The probability of the Komets team winning is 47%.

Now,

Since, The probability of the Galaxy team winning is 22%.

And, The probability of the Komets team winning is 47%.

Hence, The probability of the Komets team losing = 100% - 47%

                                                                              = 53%

                                                                              = 0.53

Then, The probability of the Komets losing their race and the Galaxy winning theirs is = 0.53 × 0.22

                         = 0.1166

Thus, probability of the Komets losing their race and the Galaxy winning theirs is 0.1166.

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Answer:

11.66%

Explanation:

I put 12% as my answer, but I got it wrong. So I talked to my teacher and she said the CORRECT ANSWER WAS 11.66%!!

Answer:

3928.4087

Step-by-step explanation:

2441/0.6214

The width of Australia in kilometres will be equal to 3928.4087 km.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Australia is approximately 2441 miles in width. The width of Australia in kilometres will be calculated as,

1 km = 0.6214 miles

1 mile = 1 /0.624 kilometres

Width = 2441/0.6214

Width = 3928.4087 kilometres

Hence, the width of Australia in kilometres is 3928.4087.

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Answer:

Step-by-step explanation:

The number of bags he can make without having any cookies left over is 4 bags.

Number of chocolate chips = 48

Number of vanilla cookies = 64

Number of raisin cookies = 100

Answer:

Step-by-step explanation:

To find the number of four-letter words that can be formed using the letters in facetious, you can use the combination formula:

nCr = n! / (r! (n - r)!)

In this case, n is the total number of letters available (9) and r is the number of letters per word (4). Therefore, the number of four-letter words that can be formed is:

nCr = 9! / (4! (9 - 4)!) = 9! / (4! 5!) = (9 x 8 x 7 x 6) / (4 x 3 x 2 x 1) = 126

Therefore, there are 126 four-letter words that can be formed using the letters in facetious.

The true statement about J and K is - The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

The correct answer is option (c)

In this question, we have been given that a certain statistic will be used as an unbiased estimator of a parameter.

The sample size of J = 40.

and the sample size of K = 100.

We need to find the true statement about J and K.

By central limit theorem, both J and K will have same means.

An expression for standard deviation is:

s = σ/√n

From the above expression standard deviation is inversely proportional to the sample size n. This means, as the sample size increases, the standard deviation decreases.

Thus, the correct statement is - The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

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The complete question is:

A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.

Which of the following must be true about J and K ?

a. The expected values of J and K will be equal, and the variability of J will be less than the variability of K.

b. The expected values of J and K will be equal, and the variability of J will be equal to the variability of K.

c. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

d. The expected value of J will be greater than the expected value of K, and the variability of R will be greater than the variability of K.

e. The expected value of J will be greater than the expected value of K, and the variability of R will be less than the variability of K.

The number of alligators was there in Orange country, Florida in 2001 is equal to 43872.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other words, it is a relationship where the worth of the entire is always considered 100.

As per the given information provided in the question,

Total number of alligators 1992 = 285

Percent increase of alligators every year = 75%

Total number of years from 1992 to 2001,

2001 - 1992 = 9 years

The population of alligators in 2001,

= 285 × (175/100)⁹

= 285 × (7/4)⁹

= 43871.98 or,

= 43872 alligators.

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Answer:

x = -8

Step-by-step explanation:

Given equation,

→ (x/4) - 6 = -8

Now the value of x will be,

→ (x/4) - 6 = -8

→ x/4 = -8 + 6

→ x/4 = -2

→ x = -2 × 4

→ [ x = -8 ]

Hence, the value of x is -8.

Answer:

0.6 inches

Step-by-step explanation:

The equation to find the area of a circle is:

[tex]{a} = \pi {r}^{2} [/tex]

however the problem requires you replace π with 3.14.

Using inverse operations you can find the variable r.

Step 1:

Plug in variables.

[tex]0.2826 = 3.14{r}^{2} [/tex]

Step 2:

Solve for r.

[tex]0.2826 \div 3.14 = 3.14 \div 3.14 \times {r}^{2} \\ \sqrt{0.09} = \sqrt{ {r}^{2} } \\ r = 0.3[/tex]

Step 3:

Find diameter from radius.

[tex]0.3 \times 2 = 0.6[/tex]

The diameter of the circle is 0.6 inches.

The shortest side of a triangle is just opposite of the angle 47°.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

All the angle of a triangle are,

⇒ 63°, 47°, 70°

Now,

Since, All the angle of a triangle are,

⇒ 63°, 47°, 70°

We know that;

The smallest side of a triangle is just opposite of the smallest angle.

Thus, The shortest side of a triangle is just opposite of the angle 47°.

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Answer:

Attached

Step-by-step explanation:

Use the multinomial rule, the possible number of paths from A to B is m! n1! ×n2!

How do you find the number of paths on a grid?

To generalize our formula for any NxN grid, we can write: Incidentally, there is an easier way to write this: the number D = N! / (K! * (N-K)!) is also called the binomial coefficient and we can write (N choose K).

You may create a table by combining several question kinds using the grid question type. This implies that you could, for instance, create a grid that included both a multiple-choice question and a free-text inquiry.

A map's grid is a pattern made up of both horizontal and vertical straight lines. They cross one another to create a group of squares. On a map, grids aid in location finding. At the top, there are numbered gaps between the horizontal (side-to-side) lines.

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We have proved that ABCD is a rectangle.

What is the isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.

<EAD=<EDA  ------------------∆AED is isosceles triangle.

<EBC=<ECB    ------------------ ∆EBC is isosceles triangle.

AD= BC   -------------------------Given

<AED=<BEC       ------------------- Vertically opposite angle

<EAD=<ECB                              

2<EAD=180°- <AED

         = 180°-<BEC

            =2<ECB.

∆AED congruent to ∆BEC --------- By A-S-A Congruency.

AE=EC, DE=EB                   ----------Corresponding sides

ABCD is a parallelogram ----------- Diagonals bisect to each other.

AC=BD                                      

AE+EC=DE+EB.

ABCD is a rectangle.   ------------- Diagonals are equal.

Hence, we have proved that ABCD is a rectangle.

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By power algebra method,

a) [tex]\frac{16}{81}[/tex]

b) [tex]\frac{2xy}{3}[/tex]

c) [tex]\frac{16x^4}{y^8}[/tex]

d) [tex]\frac{3y^2}{x^3}[/tex]

According to the Quotient of Powers Property, you can maintain the base and subtract the exponents when dividing two exponents by the same base. Since you cannot divide by zero, this characteristic will always hold true as long as the base is not zero. For more information on this property, use the interactive below.

The Exponents Power Rule: am*n = (am)n. Multiply the exponent by the power to increase a number with an exponent to that power.

You divide them by the highest exponent in the numerator (the numerator) and the lowest exponent in the denominator (the bottom exponent).

a) [tex](\frac{2}{3})^4[/tex] = [tex]\frac{2*2*2*2}{3*3*3*3}[/tex] = [tex]\frac{16}{81}[/tex]

b) [tex]\frac{2x^2y}{3x}[/tex] = [tex]\frac{2*x*x*y}{3*x}[/tex] = [tex]\frac{2xy}{3}[/tex]

c) [tex](\frac{2x}{y^2})^4[/tex] = [tex]\frac{2x*2x*2x*2x}{y^2*y^2*y^2*y^2}[/tex] = [tex]\frac{16x^4}{y^8}[/tex]

d) [tex]\frac{3xy^4}{x^3}[/tex][tex].\frac{y}{xy^3}[/tex] = [tex]\frac{3x*y*y*y*y}{x*x*x} . \frac{y}{x*y*y*y}[/tex] = [tex]\frac{3y^2}{x^3}[/tex]

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Step-by-step explanation:

Just Substitute in place of X

Answer: Open

Step-by-step explanation: the dot is only filled in when the inequallity is "greater than or equal to" or "less than or equal to"

Answer:

The absolute value of a is equal to 3 * √(2), which is the simplest form of the surd.

Step-by-step explanation:

The absolute value of a number is the distance of the number from zero on the number line. To find the absolute value of a complex number, we take the square root of the sum of the squares of the real and imaginary parts.

In this case, the absolute value of a is given by:

|a| = √((-9)^2 + 9^2) = √(81 + 81) = √(162) = √(9 * 18) = 3 * √(2)

Therefore, the absolute value of a is equal to 3 * √(2), which is the simplest form of the surd.

this is ur answer

[tex]2y = - 9 \\ y = ( - 9) - 2 \\ y = - 11[/tex]

Answer:

3.714

Step-by-step explanation:

26 x ⅐ = 26 / 7

= 3.714 or [tex] 3 \frac{5}{7} [/tex]

The opportunity cost of mowing the lawn is The $15 he earns minus the enjoyment he would have received from watching the football game during that time.

Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them. Making smarter decisions requires an understanding of the possible opportunities lost when a company or person selects one investment over another.

Opportunity Cost =FO−CO where:

FO=Return on best-forgone option

CO=Return on the chosen option

​The formula for calculating an opportunity cost is simply the difference between the expected returns of each option.

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Answer:

you could sell is for $10,000

Step-by-step explanation:

because it increased in value you could sell it for more

Length of rectangle         Width of rectangle         Area of rectangle  

A. a + 5                                     3                                    3(a + 5) = 3a + 15

B. 6 + x                                     1/3                                  1/3(6 + x) = 2 + 1/3x

C. 3                                             r                                   r(1+1+1) = 3r

What is a rectangle?

An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

A.

There are 2 rectangles with side a and 5.

Therefore the length of the rectangle is (a + 5).

The width the rectangle is 3.

The area of rectangle is product of length and width.

The area of the rectangle is 3(a + 5)

Applying distributive property:

= 3a + 15

B.

There are 2 rectangles with side 6 and x.

Therefore the length of the rectangle is (6 + x).

The width the rectangle is 1/3.

The area of rectangle is product of length and width.

The area of the rectangle is 1/3(6 + x)

Applying distributive property:

= 2 + 1/3 x

C.

There are 3 rectangles with side 1, 1, and 1.

Therefore the length of the rectangle is (1 + 1 + 1).

The width the rectangle is r.

The area of rectangle is product of length and width.

The area of the rectangle is r(1 + 1 + 1)

Applying distributive property:

= r + r + r

= 3r

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Answer:

143

Step-by-step explanation:

35/55  = 91/x

7/11 = 91/x so 143

Answer:

DB = 143 units

Step-by-step explanation:

In similar triangles, corresponding sides are always in the same ratio.

If ΔDCB ~ ΔDRS then:

[tex]\implies \sf DC : DR = CB : RS = DB : DS[/tex]

From inspection of the given diagram:

Therefore:

[tex]\implies \sf 91 : 35 =DB : 55[/tex]

[tex]\implies \sf \dfrac{91}{35} =\dfrac{DB}{55}[/tex]

[tex]\implies \sf 55 \cdot \dfrac{91}{35} =55 \cdot \dfrac{DB}{55}[/tex]

[tex]\implies \sf 143=DB[/tex]

Answer: 37.5

Step-by-step explanation: 9 students didn't fw math, divide 9 by the total (24) n u get 37.5%

Answer:

Below

Step-by-step explanation:

9 out of 24 did NOT

9/24 = .375    =     37.5 %

The equation which have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 –p

Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.

Given that an expression;

2.3p – 10.1 = 6.5p – 4 – 0.01p

Firstly we will simplify the above expression by removing decimals.

For that,

(23 / 10)p – (101 / 10) = (65 / 10)p – 4 – (1 / 100)p

Now we will take LCM,

{ (23 - 101) / (10) }p = {650p - 400 - p} / 100

230p – 1010 = 650p – 400 –p

Therefore The equation which have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 –p.

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The percentage for blue balls will be 56% and the percentage for red balls will be 44%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

In this situation, there are 4000 balls and 2240 of then are blue while 1760 area red.

The percentage for blue balls will be:

= Number of blue balls / Total balls × 100

= 2240 / 4000 × 100

= 56%

The percentage for red balls will be:

= Number of red balls / Total balls × 100

= 1760 / 4000 × 100

= 44%

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After performing division on the given expression the quotient is x + 3 and the remainder is -16.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

x + 3) x² - 7 ( x + 3

         x² + 3x

       = 3x -7                

          3x + 9

        = -16 (Remainder)        

Hence, the quotient obtained after division is x+3.

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