According to an architect's design, the new rectangle stables (housing for horses) will have total dimensions of 30 yards by 10 yards. The design includes a walkway between the stables where no horses can stay. The walkway will take up 45 yards ^ 2 Each horse requires a minimum of 12yards ^ 2. How many horses at most can live in the stables?

Answer:

[tex] a^\frac{5}{2} = \sqrt{a^5} = (\sqrt {a})^5 [/tex]

Step-by-step explanation:

A number raised to a fraction as an exponent means the number is raised to the numerator of the exponent, and then take the root shown by the denominator of the exponent.

For example, if the exponent is 2/3, raise the number to the 2nd power and take the third root.

Here is the definition:

[tex]a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m[/tex]

[tex] a^\frac{5}{2} = \sqrt{a^5} = (\sqrt {a})^5 [/tex]

Answer:

the value of M(2) would be 43

Step-by-step explanation:

M(2) mean y

y = 9t+25

= y=9(2) + 25

y = 18 + 25

y = 43

Answer:

Step-by-step explanation:

M(2) = 43; If Hazel mows 2 yards, she will earn $43.

Range of f(x)=[3,∞)

The range of a function in mathematics can refer to one of two ideas that are connected in some way:

1.Codomain for the function

2.an illustration of the action

Given two sets X and Y, a binary relation f between them is a (complete) function (from X to Y) if and only if there is precisely one y in Y such that f connects x and y. The terms "domain" and "codomain" of f, respectively, refer to the sets X and Y. The subset of Y made up only of those elements y of Y such that there is at least one x in X with f(x) = y is thus known as the image of f.

Given, f(x)= x²+3

Here x∈ R

x²+3≥3

Therefore, Range of f(x)=[3,∞)

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When an auditor uses monetary-unit sampling to examine the total value of invoices, each invoice has a probability proportional to its monetary value of being selected.

Monetary unit sampling (MUS) refers to a statistical sampling method utilized to determine if the account balances or monetary amounts in a population contain any misstatements in an account of transaction. Auditors use monetary unit sampling, which is also known as probability-proportional-to-size sampling or dollar-unit sampling, to establish the accuracy of financial accounts. With monetary unit sampling, each dollar in a transaction is a separate sampling unit. When an auditor uses monetary-unit sampling to examine the total value of invoices, each invoice has a probability proportional to its monetary value of being selected.

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Answer: 2 soulutions

Step-by-step explanation: Just factor them and solve the answer would be x = 4 √3 + 8 in its exact form and x = 14.92820323... in its decimal form

The value of f(0) is 2.

The y-intercept of a function is the value of the function when x=0.

Note that f(0) is the value of f when the graph of the function crosses the y-axis.

Note from the graph that the graph of the function crosses the y-axis at

x = 2.

Hence, the value of f(0) is 2.

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The measure of the angle ∠Z is 38°.

We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are Y, X, and Z. The angle ∠F is congruent to the angle ∠X. The angle ∠E is congruent to the angle ∠Y. The measures of the angles ∠E and ∠X are 62° and 80°, respectively. We need to find the measure of the angle ∠Z. The measure of the angle ∠Y must be equal to the measure of the angle ∠E.

∠Y = ∠E = 62°

Now, in the triangle ΔYXZ, we will use the angle sum property. The sum of all the angles in a triangle is equal to 180°.

∠Y + ∠X + ∠Z = 180°

62° + 80° + ∠Z = 180°

∠Z = 180° - (62° + 80°) = 180° - 142° = 38°

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The greatest number of cups of yogurt that Monica can buy is 14 cups

The amount that she has = $20

The cost of one gallon of milk = $2.50

The cost of one cup of yogurt = $1.20

Consider the number of cups of yogurt = x

Then the inequality will be

1.20x + 2 .50 ≤ 20

Solve the inequality and find the value of x

Subtract 2.50 from both side of the inequality

1.20 + 2.50 - 2.50 ≤ 20 - 2.50

1.20x ≤ 17.5

Divide both side of the equation by 1.20

1.20x / 1.20 ≤ 17.5 / 1.20

x ≤ 17.5 / 1.20

x ≤ 14.58

Hence, the greatest number of cups of yogurt that Monica can buy is 14 cups

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Answer:

22 degrees

Step-by-step explanation:

Sum of all three angles of a triangle equal 180 degrees so we can add these angles and set it equal to 18” degrees to find x

x+16+120+x=180

2x+136=180

    -136.  -136

2x=44

/2.  /2

x=22

So angle b is 22 degrees

Hopes this helps please mark brainliest

Justice is using a technique known as chunking.

Short-term memory can function more effectively thanks to chunking, however the quantity of chunks that can be stored efficiently declines as chunk size grows.

Large pieces of information may be divided into smaller bits and then grouped together using relevant information or attributes before being stored in order to improve retention of that information in the short term memory. To establish relational information or similarity between the information to be stored in order to improve retention and recall in the short term memory, information must be broken down before being regrouped. However, as chunk size grows, so does the efficiency of information chunking.

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Explanation:

5x+9y=41
(1,4)

Answer: 15 29/64

Step-by-step explanation: Convert the mixed numbers to fractions. 43/8 times 23/8. This would equal 989/64 and if you simplify that, it would be 15 29/64.

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The amount in the bank account at the end of 3 years will be; $5487.5

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

The amount deposited by Tyler's in the savings account is $5,000

Interest rate = 3.25% annually

Then Calculating the amount in the bank account after 3 years, using the formula;

Simple Interest = (Principal × Rate × Time) / 100

where P = principal invested

R = rate of interest annually

T = number of years amount is invested

So, Simple interest on the principal invested for 3 years=

5,000  x 3.25  x 3/100 = 487.5

The amount in the bank account at the end of 3 years will be;

= 487.5 + 5,000  

= $5487.5

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The total amount Bridget received from her mom will be $6 as she will get extra for cleaning before 6PM.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Here,

$5 for cleaning,

as she completed before 6 PM,

=5+20%*5

=5+1

=$6

Bridget's mother gave her $6 in total, with an additional $1 for cleaning before 6 o'clock.

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The height of the rectangular prism  is 4x+2 unit.

What is  rectangular prism?

A rectangular prism's volume is a measurement of the entire interior volume. Consider a rectangular water-filled container. In this instance, the container's capacity is equal to the maximum amount of water it can hold. A polyhedron known as a prism has the same cross-section along its entire length, equal bases, and flat rectangular side faces. Based on the design of their bases, prisms are categorised. A rectangular prism is within the category of three-dimensional shape. The prism has six faces, all of which are rectangles.

Here the given volume of rectangular prism is,

=> V= 4[tex]x^3+22x^2+10x[/tex] cubic unit

And area of base B = [tex]x^2+5x[/tex] square unit.

Now volume of rectangular prism

=> V= area of base × height

=> 4[tex]x^3+22x^2+10x[/tex]  = [tex]x^2+5x[/tex] × height

=> Height = [tex]\frac{4x^3+22x^2+19x}{x^2+5x}[/tex]

=> Height = [tex]\frac{2x(2x^2+11x+5)}{x(x+5)}[/tex]

=>Height = [tex]\frac{2(2x^2+x+10x+5)}{x+5}[/tex]

=> Height = [tex]\frac{2(x(2x+1)+5(2x+1))}{x+5}[/tex]

=> Height = [tex]\frac{2(2x+1)(x+5)}{x+5}[/tex]

=>Height = 2(2x+1)

=> Height = 4x+2 unit .

Hence height of the rectangular prism is 4x+2 unit.

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The value of 9−(−12) as an addition expression is 3.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, the expression given is illustrated as:

-9 - (-12)

It's important to note that (-) × (-) = +

Therefore, -9 - (-12)

= - 9 + 12

= 3

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Classification of the given numbers as terminating decimal or non-terminating recurring decimal or non-terminating non-recurring decimal:

a. 0.45  : terminating

b. 0.131313  : terminating

c. -12  : terminating

d. 0.09099099909999... : non-terminating non-recurring decimal

e. 3.143256143256... non-terminating recurring decimal

As given,

Classification of the given numbers in the following way :

a. 0.45 : terminating

b. 0.131313  : terminating

c. -12  : terminating

d. 0.09099099909999... : non-terminating non-recurring decimal

e. 3.143256143256... non-terminating recurring decimal

Therefore, classification of the numbers are given below:

b. 0.131313  : terminating decimal

c. -12  : terminating decimal

d. 0.09099099909999... : non-terminating non-recurring decimal

e. 3.143256143256... non-terminating recurring decimal

The complete question is:

Classify the following numbers as terminating decimal or non-terminating

recurring decimal or non-terminating non-recurring decimal.

a. 0.45

b. 0.131313

c. -12

d. 0.09099099909999...

e. 3.143256143256...

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20 m longer  to walk from A to B along the diagonal of the park than to walk along the edges of the park.

What is rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. It can alternatively be described as a parallelogram with a right angle, an equiangular quadrilateral, or a group of triangles with equal angles. A square is a rectangle that has four equal sides.

As given, a park is in the shape of a rectangle and measures length of

40 m and width of 30 m, ∠B = 90°.

So, by Pythagoras theorem,

[tex]AC^2 = AB^2 + BC^2\\AC^2 = (40)^2 + (30)^2\\AC^2 = 1600 + 900\\AC^2 = 2500\\AC = \sqrt{2500}\\ AC = 50[/tex]

So, the distance from A to B along the diagonal is,

AB = AC + BC = 50 + 40 = 90 m

The distance from A to B along with the edges is,

AB = AD + DC + CB = 40 + 30 + 40 = 110 m.

Therefore, 20 m longer  to walk from A to B along the diagonal of the park than to walk along the edges of the park.

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The total amount of the investment after 5 years is $15095

From the question, we have the following parameters:

Also from the question, the formula to determine the total amount  is given as

A = P(1 + r/n)^nt

Where the values of the variables have been stated above

Solving further, we replace the variables with their values in the above equation

So, we have the following representation

A = 13000 * (1 + 3%/4)^(5*4)

Evaluate the expressions in the brackets

A = 13000 * (1.0075)^(20)

Evaluate the product expression

A = 15095

Hence, the value of the amount after 5 years is $15095

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By using diagonal properties of square, we can prove the area of triangle as a².

A square is a flat object in geometry that has four equal sides and four right angles (90°). An equilateral rectangle is a specific sort of square, while a parallelogram is a special kind of square (an equilateral and equiangular one).

Prove: Area of square = a²

Suppose, there is a square of side length a.

Let, d be the length of each diagonal. We know, both diagonals of square have equal length.

So, d^2 = a^2 + a^2 = 2 * (a^2)

Or, d = a * (√2).

Also, we know that diagonals of a square are perpendicular bisectors.

So, we can consider that the square as four isosceles right angled triangles.

Length of each perpendicular side of every isosceles right angled triangle = (1 / 2) * d = (d / 2).

So, area of each isosceles right angled triangle = (1 / 2) * (d / 2) * (d / 2) = {(d^2) / 8}

Area of the square = 4 * {(d^2) / 8} = {(d^2) / 2}.

Since, d = a * √2; so we put in the above formula, the area becomes equal to that of (a^2).

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By solving the system graphically we get X=4 , Y=-5

What in mathematics is a linear equation?

Definitions: According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

The Answer to this question given in the Image

In this image we can see that line intersect at 1 point which is (4,-5)
Hence the ans is X=4 , Y=-5

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Two column proof is as follows

Statement                              Reason

AB ≅ CB                                Given                  

AD ≅ CD                               Given

< BAD ≅ < BCD                     Given

< ABD = < CBD                      Definition of angle bisection

AB = CB                                 Definition of equality

BD = BD                                 Reflexive property of congruence

AD = DC                                 Definition of bisection

Δ ABD = Δ CBD                     SSS postulate of congruence

This is a method of proof that consists of five parts which include

The postulate says that when the three sides of the triangles under comparison are equal then the triangles under comparison are said to be congruent.

In the figure,

AB =CB, from the given sides

BD = BD sharing common sides

AD = CD line AC was bisected by line BD

This completes the SSS proof of congruence

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Based on the image attached, The value of x = 26 and y = 60

Alternate interior angles are the angles formed on the opposite sides of the transversal. The angles that lie on the inner side of the parallel lines but on the opposite sides of the transversal.

And the alternative angle is equal to :

180°So, y° = y° at the alternative side

And so as (3x - 18)° = (3x - 18)° at the alternate side

The angle of a straight  line is  180°

The value of line m is a straight line so it is equal to 180°

So, y + (3x-18) = 180°

As also, the value of straight line (2x + 8)° + y° of the alternate side= 180°

So we have y° + (3x - 18)° = 180 and y° + (2x + 8)° = 180y + 3x = 180 + 18 and y + 2x = 180 - 8y + 3x = 198 and y + 2x = 172

By substituting method to get the value of x and y

when y = 172 - 2x

Substitute to equation 1172 - 2x + 3x = 198x = 198 - 172x = 26°

To find y = y + 2(26) = 172y +52 = 172y = 172 - 52y = 120°

Therefore the amount of x = 60 and y = 26

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Answer:

B) x = 11

Step-by-step explanation:

The three angles of a triangle always add up to 180°

3x+28+5x+52+2x-10

= 180

Combine like terms.

10x + 70 = 180

subtract 70

10x = 110

divide by 10

x = 11

The exponential function always exceeds the linear function

A mathematical function of form f (x) = an x is an exponential function. where x is a variable and an is the function's base constant The transcendental number e, which is approximately 2.71828, is the most commonly encountered exponential-function base.

An exponential function is distinguished from linear and quadratic functions in that the variable to be solved for is contained within the function's exponent rather than (necessarily) within the base of some exponential expression. Here are some examples:

Linear function: f(x) = 3x - 7: The exponents 1 and 0 are implied here, so f(x) is 3(x^1) - 7(x^0). It is worth noting that x is not a component of either exponent; rather, it is a component of the base of each exponent.

h(x) = 4^(3x + 7):This is an exponential function because the variable x is contained within the exponent in this expression.

As a result, the exponential function always outperforms the linear function.

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Answer:

-24/4 is yes

61.34 is no

Step-by-step explanation:

You have d dollars to buy fence to enclose a rectangular plot of land. the fence for the top and bottom costs $a per foot and for the sides it costs $b per foot.

To find the dimensions of the plot with the largest area.

Total Money = D dollars

Total cost for top and bottom fence = $4(2x)

Total cost for sides fence = $8(2y)

Hence total cost of fencing = 4(2x)+8(2y) = 8x+16y

C = 8x+16y

Given cost (c) = D dollars

D = 8x+16y

Now Area of the plot A = xy

A = xy is optimizing function and D = 8x+16y

= [tex](\frac{D-16y}{8})=x[/tex]

A = [tex]\frac{D-16y}{8}y[/tex]

For A to be maximum [tex]\frac{dA}{dy}=0[/tex]

A = [tex]\frac{D}{8}y-\frac{16}{8}y^{2}[/tex]

[tex]\frac{dA}{dy} = \frac{D}{8}-\frac{16}{8}(2y)[/tex]

[tex]\frac{dA}{dy} = \frac{D}{8}-4y[/tex]

[tex]\frac{dA}{dy} = 0 = \frac{D}{8}-4y=0[/tex]

[tex]\frac{D}{8} = 4y = y = \frac{D}{32}[/tex]

Now [tex]\frac{d^{2}A }{dy^{2}} = -4 = -ve number[/tex]

for y = [tex]\frac{D}{32}[/tex] area is maximum

[tex]x = \frac{D-16y}{8} = \frac{D-16 (\frac{D}{32} )}{8} = \frac{D}{16}[/tex]

Say the top and bottom dimensions are = [tex]\frac{D}{16}[/tex]

Sides dimensions are = [tex]\frac{D}{32}[/tex]

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The percentage of kids who were boys in the birthday party is 58.3%.

The percentage can be calculated by the relation-

Percentage = number of boys ÷ total number of kids × 100

Calculating each value before calculating the percentage.

Number of boys = 7

Total number of kids = number of boys + number of girls

Total number of kids = 7 + 5

Performing addition

Total number of kids = 12

Keep both the values in formula -

Percentage of boys = (7÷12)×100

Percentage of boys = 58.33%

Round the number of nearest tenth, we get percentage = 58.3%

Thus, there were 58.3% boys.

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Answer:

the two middle students are 63