1. The retail price of grapes is $2.17 per pound. if a customer paid $8.68 for grapes, how many pounds did she buy?

The system of equations best represented by the graph are 4x + y = 6 and −2x + y = −5

The solution of the equations plotted in the graph can be found by checking the point of intersection of the lines

By examining the given graph we can guess the x and y values of the point of intersection. We need to guess because we do not have a means of getting the exact value from the graph. I guess x = 1.9 and y = -1.4

In order to find the system of equations represented by the graph, we need to solve the equations given in the option and check which one gives us  x and y values close to what we guessed from the graph

By Solving 4x + y = 6 and −2x + y = −5:

4x + y = 6          (1)

−2x + y = −5      (2)

Using elimination, subtract (2) from (1), this gives:

6x = 11            

x = 11/6 = 1.83

Put x = 11/6 into (1):

4(11/6) + y = 6

y = 6 - 4(11/6)

y = 6 -44/6 = -4/3 = -1.33

Since these calculated values are very close to the guessed values

Therefore, 4x + y = 6 and −2x + y = −5 are the system of equations best

represented by the graph. So option A is the answer

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Answer:

45.47

Step-by-step explanation:

The cost of covering the field with grass pallets is $40996.58.

Given that the rectangular field measures 90 m and 162 m.

Hence, the area of the field is 90 X 162 m²

The grass pallets are sure in shape with an area covering 90 square yards.

1 m = 1.09 yards

Hence,

1 m² = 1.09² square yards

Hence,

90 X 162 m² = 90 X 162 X 1.09² square yards

Hence the number of pallets to be used is

(90 X 162 X 1.09²) / 90

= 162 X 1.09² pallets.

= 192.4722 pallets.

1 pallet costs $213

Hence,

192.4722 pallets cost

192.4722 X 213

= $40996.58

Therefore we get the cost of covering the field with grass is  $40996.58.

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The standard form of 5.2E11 using the set scientific notation and rules is 311345.5369.

The standards for putting mathematical elements in standard form make it easier for anyone to read, write, and interact with them. The standard form is the most popular approach to representing a mathematical element.

In mathematics, the standard form is the most prevalent way of describing a specific element. Every element in arithmetic is represented in a standard form, from enormous numbers to little integers, or equations to lines.

A standard form is a method of writing a particular mathematical notion, such as an equation, or expression, in a way that adheres to specified criteria. The standard form is used to portray very big or very small numbers in a succinct manner.

The standard form of 5.2E11 using the set scientific notation and rules is:

311345.5369.

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The number of liters of fuel required for the vehicle to travel 1, 428 kilometers is 5. 67

Inverse variation can be defined as the relationship between two variables, so that if the value of one of the variable increases the value of the other variable decreases.

Example: If a varies inversely as b

This can be represented as;

a ∝ 1/b

Then,

ab = k

Where k is the proportionality constant

From the information given, we have that;

x ∝ 1/ y

Then,

xy = k

Substitute the values

476 (17) = k

k = 8092

If x = 1428 and k = 8092

Let's determine the value of y

y = k/x

y = 8092/1428

y = 5. 67 liters

Hence, the value is 5. 67 liters

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The area of the  triangle to the nearest hundredth of a square meter is 0.217m²

A right triangle has a hypotenuse of 1 meter and a leg of 1/2 meter

Hypotenuse = 1

base = 0.5

We need to calculate the perpendicular

h² = b² + p²

1² = 0.5² + p²

p² = 1 - 0.25

p = √0.75

p = 0.866

area of the triangle = 1/2 base x height

area = 1/2 (0.5 x 0.866)

area = 0.2165m²

Therefore the area of the  triangle to the nearest hundredth of a square meter is 0.217m²

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Answer:

0

Step-by-step explanation:

[tex]m=\frac{-21-(-21)}{-14-36}[/tex]

Answer: slope = 0  

Step-by-step explanation:

slope = Δy ÷ Δx = (-21 - (-21)) / (-14 -36) = 0 / -5 = 0

It's a horizontal line

Deep foundations are recommended for larger or hillside developments , or those on poor soil .

Foundation Systems in Building

There are two classifications of foundations in building shallow foundations and deep foundations . These categories refer to the depth of soil in which the foundation is formed .

Shallow Foundations : Shallow foundations are usually located less than six feet below the lowest finished floor of a structure.

Deep Foundations : Deep foundations are structural elements that are used to transfer loads from weak and compressible soils to a stronger layer, usually located at a significant depth below the ground.

Recommendation

A shallow foundation can be constructed in as little as a one-foot depth , whereas a deep foundation is formed at a depth of 10 - 300 feet . Deep foundations are recommended for larger or hillside developments , or those on poor soil .

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Answer:

Step-by-step explanation: A shallow foundation distributes loads from the building into the upper layers of the ground.

Shallow foundations perform very well on sites with strong soils, sufficiently thick natural gravel rafts overlying weaker soils or where robust, engineered ground improvement is carried out.

Deep foundations can provide a good foundation for houses on sites with poor soil conditions near the surface,

Answer:

The rocket reaches its maximum height at 2.25 seconds.

It’s maximum height is 88 feet.

This can be found by finding the derivative of the function and setting it to zero.

-16x² +72x + 7

Taking first derivative and setting to zero:

-32x + 72 = 0

x = -72/-32=2.25

Find the height when x is 2 seconds by substituting this value into the original function:

-16 * (2.25)² + 72 * 2.25 + 7 = 88

Therefore the maximum turning point of the parabola will be (2.25, 88)

The original number from the given decimal number is  0.02.

For the given question;

Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.

This results in:

10000x = 4.(1/x)

Simplifying.

x² = 4/10000

x > 0.

Taking square root of the number.

x = 2/100

x = 0.02

Thus, the original number from the given decimal number is  0.02.

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Option B is the correct choice.

Based on the findings, the following list compares the portfolios' overall performances, ranking them from best to worst:

Portfolios 2, 3, and 1, respectively.

The weighted average ROR is calculated by adding the rates of return on the portfolio's assets and the percentage of the portfolio that is invested in each investment.

For Portfolio 1:

Total Investment= $700 + $2575 + $220 + $1000 + $1430 = $5925

Therefore, total investment = $5,925

Weighted Average ROR= (-3.8% * $700) / $5925 + (2.1% * $2575) / $5925 + (11.3% * $220) / $5925 + (5.8% * $1000) / $5925 + (1.6% * $1430) / $5925

WAROR = (-0.0045) + 0.0091 + 0.0042 + 0.0098 + 0.0039 = 0.0225

Therefore, the Weighted Average ROR= 2.25% (third)

For Portfolio 2:

Total Investment = $1250 + $1700 + $1515 + $1345 + $1,675 = $7485

Therefore, Total Investment = $7,485

Weighted Average ROR = (-3.8% * $1250) / $7485 + (2.1% * $1700) / $7485 + (11.3% * $1515) / $7485 + (5.8% * $1345) / $7485 + (1.6% * $1,675) / $7485

= (-0.0063) + 0.0048 + 0.0229 + 0.0104 + 0.0036 = 0.0354

Therefore, the Weighted Average ROR = 3.54% (first)

For Portfolio 3:

Total Investment = $1025 + $500 + $790 + $250 + $2500 = $5065

Therefore, Total Investment = $5,065

Weighted Average ROR = (-3.8% * $1025) / $5065 + (2.1% * $500) / $5065 + (11.3% * $790) / $5065 + (5.8% * $250) / $5065 + (1.6% * $2,500) / $5065

= (-0.0077) + 0.0021 + 0.0176 + 0.0029 + 0.0079 = 0.0228

Therefore, Weighted Average ROR = 2.28% (second)

Therefore, the correct order of portfolios based on the performance from best to worst will be:

Portfolio 2, Portfolio 3, and Portfolio 1. (Option B)

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COMPLETE QUESTION:

ROR Portfolio 1 Portfolio 2 Portfolio 3 −3.8% $700 $1,250 $1,025 2.1% $2,575 $1,700 $500 11.3% $220 $1,515 $790 5.8% $1,000 $1,345 $250 1.6% $1,430 $1,675 $2,500 Using technology, calculate the weighted average of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?

A) Portfolio 1, Portfolio 3, Portfolio 2

B) Portfolio 2, Portfolio 3, Portfolio 1

C) Portfolio 1, Portfolio 2, Portfolio 3

D) Portfolio 3, Portfolio 2, Portfolio 1

Answer:

$24,067.32

Step-by-step explanation:

If you look up a compound interest calculator and put in the data correctly you should get $24,067.32

The value of the three consecutive integers will be 10, 11, and 12.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Three consecutive integers are such that three times the smallest is 18 more than the largest.

Let the three consecutive number be x, x + 1, and x + 2. Then the equation will be:

3x = (x + 2) + 18

Simplify the equation, then the value of the variable x will be:

3x = x + 2 + 182x = 20x = 20 / 2x = 10

Then the value of the integers will be:

x + 1 = 10 + 1 = 11x + 2 = 10 + 2 = 12

The value of the three consecutive integers will be 10, 11, and 12

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Answer: D

Step-by-step explanation:

-7(-4-(4)(-6))

-7(-4-(4)(-6))

=140

If k and n are non-negative integers and n is the greater of the two, then the ordered list of k of the n things without repetition is the k-permutation of the n separate objects.

The total number of ways to select k objects from a set of n elements is n(n1), with (nk+1) alternatives being available for the kth place.when ordering matters and repetition is not permitted. A k-permutation of the elements in set A is any of the chosen lists in the previous configuration (choose k elements, in any order, with no repetition). Pnk=0 if k is greater than n. This makes sense because it is impossible to select k unique elements from an n-element collection if k>n.

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Answer:

y + 1 = 1/2 (x - 3)

Step-by-step explanation:

Point-slope form of an equation is a shortcut, fill-in-the-blank way to write the equation of a line. All you need is slope (usually symbolized with an m) and a point (any point on the line)

Here's Point-slope:

y - Y = m (x - X)

The slope they gave you is 1/2, put that in for the m.

And also fill in 3 for the X and -1 for the Y. Because a point is (X,Y)

Just leave the first y as a y, right there. And leave the first x in the parentheses as an x. They are variables in the equation. They stay letters.

y - -1 = 1/2 (x - 3)

Simplify.

y + 1 = 1/2 (x - 3)

Minus a negative is the same as plus a positive, that's what happened there on the left. Also, when you write it, make sure the 1/2 is beside the parentheses on the right. The parentheses should not be on the bottom with the 2, but just beside the fraction.

The given inequality solved for y is y > 4

From the question, we are to solve the given linear inequality.

To solve an inequality, we will solve for the variable in the inequality.

The given inequality is

-16 > -4y

The variable in the inequality is y.

Now, we will solve for y

-16 > -4y

Divide both sides by -4

-16/-4 > -4y/-4

4 < y

Thus,
y > 4

Hence, the solution is y > 4

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That is one way to find out the answer

Answer:

2.43

Step-by-step explanation:

The quotient is the answer to a division problem.

67.98/28 = ~2.42785714286

To round to the nearest hundredth, leave 2 decimal digits remaining. If the thousandth place (3rd decimal digit) is greater they or equal to 5, add 1 to the hundredths digits.

7 [tex]\geq[/tex] 5

2.42+0.01

2.43

Answer: 82 is the answer

Step-by-step explanation: I just did this question and worked it out and it said it was right

Answer:

ii think that the figure will be determined by 13#

Step-by-step explanation:

you have to round up to the nearest meter

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal ≤

Greater than and equal ≥

The inequality that correctly orders the numbers is

-3.67 < -2.5 < -0.4

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

-2/5 = -0.4

-11/3 = -3.67

-2.5

Now,

We see that,

-0.4 is greater than -2.5 and -2.5 is greater than -3.67.

This can be represented as an inequality:

-3.67 < -2.5 < -0.4

Thus,

The inequality that correctly orders the numbers is

-3.67 < -2.5 < -0.4

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Answer: n=1/27=0.037

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3*n-(1/9)=0

Simplify 1/9

3n -  1/9  = 0

Rewrite the whole as a fraction using  9  as the denominator :

          3n     3n • 9

    3n =  ——  =  ——————

          1        9  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3n • 9 - (1)     27n - 1

————————————  =  ———————

     9              9  

End of step 2  

27n - 1

 ———————  = 0

    9  

Start of step 3

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 27n-1

 ————— • 9 = 0 • 9

   9  

Now, on the left hand side, the  9  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  27n-1  = 0

Solving a Single Variable Equation:

3.2      Solve:    27n-1 = 0

Add  1  to both sides of the equation :

                     27n = 1

Divide both sides of the equation by 27:

                    n = 1/27 = 0.037

The area of the figure is 21. 25 m². Option D

It is important to note that the figure is a kite.

The formula for calculating the area of a kite is expressed as;

A= pq/2

Where;

Using tangent identity

tan 45 = x/ 2. 5

1(2. 5) = x

x = 2. 5

p = 2. 5 + 2. 5 = 5

q = 2. 5 + 6 = 8. 5

Now, substitute the values into the formula

Area = 5(8. 5)/ 2

Area = 42. 5/ 2

divide the values

Area = 21. 25 m²

Hence, the value is 21. 25m²

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Step-by-step explanation:

Simplify Calculator. Step 1: Enter the expression you want to simplify into the editor. The simplification calculator allows you to take a simple or complex expression and see fro googlle bro

Answer:

16 - 11i

Step-by-step explanation:

When Adding or Subtracting any Complex Number

we Add or Subtract the Real Parts together and Add or Subtract the Imaginary Parts together

So for our Question

( 9 - 9i ) - ( -7 + 2i ) = ( 9 - (-7) ) + ( -9 - 2 )i = 16 - 11i

Expression x is equivalent to [tex]x^{1}[/tex] by using the exponent rule.

What do you mean by algebraic expression?

A mathematical expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

There are three primary categories of algebraic expressions, including:

Monomial expression

Binomial expression

Polynomial expression

An algebraic expression can be divided into two additional types in addition to the monomial, binomial, and polynomial types. These are:

Numeric Expression

Variable Expression

Numeric expression - A numeric expression consists of numbers and operations, but never include any variable.

Variable expression - A variable expression is an expression that contains variables along with numbers and operation to define an expression.

As we know, exponent form [tex]x^{n}[/tex] can be simplified as [tex]x \times x\times x\times ........n~ times[/tex]

In this way ,  [tex]x^{1}[/tex]can be written as x multiplied by 1 time which is equal to x

Therefore, expression x is equivalent to [tex]x^{1}[/tex].

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The probability that their mean length is greater than 20.1 inches is 0.32.

Standard deviation:

The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The given value are:

Mean = 18.8 inches

Standard deviation = 6.2 inches

We have to find the probability that their mean length is greater than 20.1 inches.

Variance of sample mean = 6.2 / 48

                                           = 0.13

S.D of sample mean=   [tex]\sqrt{0.13}[/tex]

                                 = 0.36

Z score for the length of 20.1 is ( 20.1 - 18.8) / 0.36 = 0.468

The p-value for 0.468 in the standard normal table is 0.32.

Therefore 0.32 chance of the sample means is greater than 20.1 inches.

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