Select the correct answer.
Which expression is equivalent to the given expression?


45
A.

9
⁢
5
B.

3
⁢
5
C.

5
⁢
3
D.

5
⁢
9

The change of 74.375 bushels is seen with around 86 bushels remaining with farmer for further sale.

We are given the total number of bushels as 160. Now, the average sale on each day is [tex]14\frac{7}{8}[/tex] bushels.

Converting this mixed fraction into fraction -

Average bushels sold everyday = ((8×14)+7)÷8

Performing multiplication and addition to find average bushels sold each day

Average bushels sold everyday = 119÷8

So, at this rate the total number of bushels sold in five days will be = (119÷8)×5

Performing multiplication and division on Right Hand Side of the equation to find the number of bushels

Total number of bushels sold in five days will be = 74.375

So, after five days of sale, the available number of bushels are 160 - 74.375

Change in number of bushels = 85.62

Rounding off to find the exact number of bushels = 86

Hence, the change of 74.375 bushels is seen with around 86 bushels remaining with farmer for further sale.

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Answer:

150pi

Step-by-step explanation:

The formula for the volume of a cone is one-third the volume of a cylinder.

It is   [tex]V=\frac{1}{3} Bh[/tex]   where B is the area of the circle base and h is the height of the cone.

To find the base of the cone, use the formula for the area of a circle. So, the radius is 5. So, the area of the base is pi × radius².

[tex]5^{2} =25[/tex]

[tex]\frac{1}{3}[/tex] × 25pi × 18 = 150pi

The probability that three of the children have sickle cell anemia and three of the children are healthy 13.2%.

Sickle cell anemia is an autosomal recessive condition, the trait is only visible in the homozygous state.

The parents are heterozygous( Aa × Aa), and the progeny (AA, Aa, Aa, and aa) have a normal probability of 3/4 and an affected probability of 1/4.

The binomial theorem can be used to calculate the probability of a normal and affected child:

Probability =  n! / x! ( n! - x!) × pˣqⁿ⁻ˣ.

Here, n is the total children 6,

Let 'x' be the normal child

Then, n! - x! is the affected child.

Let 'p' is the normal child probability (= 3/4) and

Then, 'q' is affected child probability (= 1/4).

Substituting the values in the formula;

probability = (6!/3!×3!)×(3/4)³×(1/4)³

on solving

probability = 0.1318

probability = 13.18%

probability = 13.2% (approximately)

Therefore,  the binomial theorem to determine the probability that three of the children have sickle cell anemia and three of the children are healthy is 13.2%.

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(x+3i)(x-3i)

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, I = √-1 and both a and b are real numbers.

Consequently, a complex number is a straightforward illustration of the addition of two integers, specifically a real number and an imaginary number. It consists of two parts: one that is entirely real, the other entirely fantastical.

Using complex numbers,

x²+81 = x² - (-9i)²

           = (x²- 9²i²)

           = (x+3i)(x-3i)

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The specified value of n for trapezoidal rule, the midpoint rule, and simpson's rule is 10.36 , 10.72 and 10.52.

Trapezoidal Rule: In Calculus, “Trapezoidal Rule” is one of the important integration rules. The name trapezoidal is because when the area under the curve is evaluated, then the total area is divided into small trapezoids instead of rectangles. This rule is used for approximating the definite integrals where it uses the linear approximations of the functions.

The trapezoidal rule is mostly used in the numerical analysis process. To evaluate the definite integrals, we can also use Riemann Sums, where we use small rectangles to evaluate the area under the curve.

Midpoint rule : In mathematics, the midpoint rule, also known as the midpoint Riemann sum or midpoint method, is a method of estimating the integral of a function or the area under a curve by dividing the area into rectangles of equal width. The midpoint rule formula is. The midpoint method formula works by summing the areas of each of the rectangles to produce an estimate for the area under a curve.

Simpson's Rule: Simpson's rule is used to find the value of a definite integral (that is of the form b∫ₐ f(x) dx) by approximating the area under the graph of the function f(x). While using the Riemann sum, we calculate the area under a curve (a definite integral) by dividing the area under the curve into rectangles whereas while using Simpson's rule, we evaluate the area under a curve is by dividing the total area into parabolas. Simpson's rule is also known as Simpson's 1/3 rule (which is pronounced as Simpson's one-third rule).

Now,

a=1,b=4,Δx =(b-a)/n =3/6 =1/2

f(x)=4√(ln(x))

trapezoidal rule:

∫4√(ln(x)) dx =(Δx /2)[f(1)+2*[f(1.5)+f(2)+f(2.5)+f(3)+f(3.5)]+f(4)]

∫4√(ln(x)) dx =((1/2) /2)[4√(ln(1))  +2*[4√(ln(1.5)) +4√(ln(2)) +4√(ln(2.5)) +4√(ln(3)) +4√(ln(3.5))] +4√(ln(4))]

∫4√(ln(x)) dx =10.365336

midpoint rule :

∫4√(ln(x)) dx =(Δx)[f(1.25)+f(1.75)+f(2.25)+f(2.75)+f(3.25)+f(3.75)]]

∫4√(ln(x)) dx =(1/2)[4√(ln(1.25))  +4√(ln(1.75)) +4√(ln(2.25)) +4√(ln(2.75)) +4√(ln(3.25)) +4√(ln(3.75)) ]

∫4√(ln(x)) dx =10.724182

simpsons rule:

∫4√(ln(x)) dx =(Δx /3)[f(1)+4*f(1.5)+ 2*f(2)+ 4*f(2.5)+  2*f(3)+  4*f(3.5)]+f(4)]

∫4√(ln(x)) dx =((1/2) /3)[4√(ln(1))  +4*4√(ln(1.5)) +  2*4√(ln(2))  +4*4√(ln(2.5))  +2*4√(ln(3)) + 4*4√(ln(3.5)) +4√(ln(4))]

∫4√(ln(x)) dx =10.527905

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Answer:

1.72m is height of man

Step-by-step explanation:

since we know tan60°=[tex]\sqrt{3}[/tex];

then here tan60°=height/base;

height =64-height of man (let be x)

base=36;

now

[tex]\sqrt{3}[/tex]=[tex]\frac{64-x}{36\\}[/tex]

x=64-36[tex]\sqrt{3}[/tex]

x=1.72 m

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Answer: Answer is 4(16 - 9[tex]\sqrt{3}[/tex])

Step-by-step explanation: Concept:

The term angle of elevation denotes the angle from the horizontal upward to an object. An observer’s line of sight would be above the horizontal.

tan θ = [tex]\frac{opposite}{adjacent}[/tex]

tan 60 =[tex]\sqrt{3}[/tex]

Given:

It is given that AB is the height of the man, the angle of elevation is 60°, the distance from the man to the tower BC is 36 m and the height of the tower is 64 m.

The height of the man AB.

In ΔADE

tan 60 = [tex]\frac{ED}{AD}[/tex]

[tex]\sqrt{3}[/tex] = [tex]\frac{ED}{36}[/tex]

36 [tex]\sqrt{3}[/tex] = ED

Now,

DC=CE-CD

CD = 64 -36  [tex]\sqrt{3}[/tex]

CD = 4(16 - 9  [tex]\sqrt{3}[/tex])

Now, given that  AB=CD

Therefore, The height of the man is 4(16 - 9[tex]\sqrt{3}[/tex])

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Answer:

Step-by-step explanation:

Y-3x=13+3x

Using a system of equations, it is found that there are 204 boys at the school.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

The average of the number of boys, girls, male teachers, and female teachers is 117, hence:

(x + y + z + w)/4 = 117

x + y + z + w = 468.

The average of the number of boys, girls, and male teachers is 151, hence:

(x + y + z)/3 = 151

x + y + z = 453.

Then:

x + y + z + w = 468.

453 + w = 468

w = 15.

There are 6 fewer male teachers than there are female teachers, hence:

z = w - 6 = 15 - 6 = 9.

So:

x + y + z = 453.

x + y = 444.

The number of female teachers is 1/16 the number of girls, hence:

There are 204 boys at the school.

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The expression becomes 4 + 2*(14-3) to get the answer value of the 26.

According to the statement

We have to find that the parentheses of the given expression.

So, For this purpose, we know that the

Algebraic expression definition, a symbol or a combination of symbols used in algebra, containing one or more numbers, variables, and arithmetic operations.

From the given information:

The expression is :

4 + 2 * 14 – 3

Then rearrange it to get the answer value of 26.

For this use associative property

then

it will become and Written like this    

4 + 2*(14-3)

4 + 2*(14-3)  = 4 + 2*11

4 + 2*(14-3)  = 4 + 22

4 + 2*(14-3) = 26

So, The expression becomes 4 + 2*(14-3) to get the answer value of the 26.

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The number of tickets that she buys will be 14 tickets.

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.

Marianne owes $56 for tickets to the school play. If each ticket cost $4. Then the number of tickets that she buys will be given as,

⇒ 56 / 4

⇒ 14 tickets

The number of tickets that she buys will be 14 tickets.

Your question was incomplete, but the complete question was given below.

Marianne owes $56 for tickets to the school play. If each ticket cost $4, how many tickets did she buy?

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Answer:

c between 30 and 40 mins

Step-by-step explanation:

if you look at the graph that's the only line going down.

The value of the variable x is found to be x = 9.

A bisected angle divides the two sides in equals.

JKM = LKM

As, both are equal.

Then, each of these angles are 1/2 the angle JKL.

1/2 JKL = MKL

1/2 ×( 92) = 5x + 1

Further simplifying;

46 = 5x+1

Subtract 1 from each side

46-1 = 5x

45 = 5x

Divide each side by 5

45/5 = 5x/5

x = 9

Thus, the value of the unknown variable is found to be x = 9 units.

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The sum of the whole numbers from 1 to 680 is 231540.

Arithmetic sequence is a list of numbers where each number is equal to the previous number, plus a constant called the common difference.

The formula for sum of first n numbers can be expressed as;

Sₙ = (n/2)( a₁ + aₙ )

Where n is the number of terms, a₁ is the first term and aₙ is the nth term.

Given that,

The numbers are whole numbers from 1 to 680

Plug the given values into the equation above.

Sₙ = (n/2)( a₁ + aₙ )

S₆₈₀ = (680/2)( 1 + 680 )

S₆₈₀ = 340( 681 )

S₆₈₀ = 231540

Therefore, the sum of the whole numbers from 1 to 680 is 231540.

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Answer:

When expenses are greater than revenue (first choice)

Step-by-step explanation:

Answer:

When expenses are greater than our revenue

Answer:

See explanation

Step-by-step explanation:

p=1 pie

p divided by 7 is p/7 ==> 1/7

Each friend get 1/7 of the pie.

Since Omar only has half of the pie left and needs to share it equally among his 7 friends, we'll need to divide.

So, a pie has 6 pieces and Omar has only 3 pieces left.

Then, we divide 3 by 7. This gives us a REALLY long decimal so we would have to round.

The rounded answer would be 0.43.

Finally, each friend will get forty-three hundredths of the pie that is left.

Answer:

$14.67

Step-by-step explanation:

The value of the discount is,

→ (10/100) × 16.30

→ 0.1 × 16.30

→ $1.630

Then the amount he should pay is,

→ 16.30 - 1.630

→ $14.67

Hence, he must pay $14.67.

Answer:

=14.67

Step-by-step explanation:

0.10×16.30=1.63 or

16.30-1.63=14.67 or[tex]\frac{1467}{100}[/tex]

i

Answer:

V≈743.25

Step-by-step explanation:

V=5

12tan(54°)ha2=5

12·tan(54°)·4·182≈743.24624

In  linear equation, the distance of the flowerbed from the hive is 2250 feet.

What in mathematics is a linear equation?

Let , the distance of the flowerbed from the hive is  feet.

The bee flies 20 feet per second directly to a flowerbed from its hive and flies directly back to the hive at 12 feet per second.

      time =   distance / speed

So, the time taken by the bee to reach the flowerbed x/20 seconds and the time taken to fly back to the hive = x/12  seconds.

The bee stays at the flowerbed for 15 minutes or (15×60)seconds or 900 seconds and it is away from the hive for a total of 20 minutes or (20×60)seconds or 1200 seconds.

So, the equation will be

 x/20 + x/12 + 900 = 1200

3x + 5x / 60 = 300

8x  = 300 * 60

x = 2250

Thus, the distance of the flowerbed from the hive is 2250 feet.

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The dimension of the base of the rectangular building is 340 x 135ft.

Perimeter of Rectangle:

The definition of perimeter of the rectangle is the total length or distance of its boundary on all sides.

The general formula to calculate the Perimeter of a rectangle is,

P = 2(l + w)

Where,

l represents the length of the rectangle

w represents the width of the rectangle.

Given,

The building in a city has a rectangular base. the length of the base measures 65ft less than three times the width.

The perimeter of this base is 910ft.

Now, we need to find the dimensions of the rectangular base.

According to the given details, the values of

L = 3W - 65

W = W

P = 910

Apply the values on the formula, then we get,

=> 910 = 2 * (L + W)

=> 910/2 = (L + W)

=> 455 = L + W

Apply the value of L,

=> 475 = 3W - 65 + W

=> 475 + 65 = 4W

=> 540 = 4W

=> 540/4 = W

=> W = 135

Apply the value of W as 135, in order to get the value of L,

=> L = 3*135 - 65

=> L = 405

=> L = 340

Therefore, the dimension of the rectangular base is 340 x 135 ft.

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Answer:

12/15

Step-by-step explanation:

Answer:

-6r+5

Step-by-step explanation:

Combining the like terms

⇒-4r-2r+5

⇒-6r+5

Answer:

The Recursive formula for the given condition is f(n-1) . 1/2 and the Explicit formula for the same situation is f(n) = 300 . (1/2)^x

Step-by-step explanation:

It is given that Claire has $300 in an account and she decides that she is going to take out half of the amount left in there in the account at the end of each month.

For such a situation, first of all let's take a look at the graph given below;

Now, let us understand what is recursive and explicit;

Recursive: A recursive formula bases its value on the preceding term whereas,

Explicit: An explicit formula offers the value of a given phrase depending on the location.

Furthermore, by looking at the graph attached herewith, it can be figured out that,

Recursive formula for the above mentioned condition will be;

=> f(0) = 300, f(n)

=> f(n-1) . 1/2

and the Explicit formula for the above mentioned situation will be;

=> f(n) = 300 . (1/2)^x

Therefore, the Recursive formula for the above mentioned condition is f(n-1) . 1/2 and the Explicit formula for the above mentioned situation is f(n) = 300 . (1/2)^x

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8x+y=31

perpendicular means the slopes are opposite reciprocals of each other.  perpendicular to: y +5= 8(x +4)   →   m = 8   m⊥ = -8

Input the slope (m⊥ = -8) and the point (x₁, y₁) = (4, -1) into the Point-Slope formula: y - y₁ = m(x - x₁)

y - (-1) = -8(x -4)

y + 1 = -8 x + 32      simplified

8x+y =31      

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The actual mean weight of the infants when they were 1 month old is 4.297

The residual plot doesn't show any obvious leftover pattern, confirming that a linear model is appropriate.

the equation of this line as ˆy=12x−1 with an accent on the y to indicate that the y-values computed using this equation

y = 4.88 + 0.267(1)

y = 5.147

residual = -0.85 = A - 5.147 + 5.147

residual = 4.297

the actual mean weight of the infants when they were 1 month old is 4.297

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The expression for the area of a triangle with a height of n and a base of 6 is 6n/2

The formula for calculating the area of a triangle is expressed as:

A = 1/2 bh

where

b is the base of the triangle

h is the height of the triangle

Given the following parameters

base = 6

height = n

Substitute

A = 1/2 × 6 × n

A = 6n/2

Hence the expression for the area of a triangle with a height of n and a base of 6 is 6n/2

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The algebraic expression is,

⇒ 10 + c/3 = 12

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

''ten more than the quotient of c and three is 12.''

Now, We can formulate;

⇒ ten more than the quotient of c and three is 12

⇒ 10 + c/3 = 12

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Complete question is this,

Ten more than the quotient of c and three is 12.

Using algebraic expressions and equations, Carol should buy 2 t-shirts and 9 sweatshirts.

We can set up an algebraic expressions and equations to determine how many of each type of gift should Carol buy.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

1. Write an equation for the total number of members.

x + y = 11   (equation 1)

where x is the number of members who will get t-shirt

y is the number of members who will get sweatshirt

2. If each t-shirt costs $5 and each sweatshirt costs $12, write an equation for the total amount spent buying the gift.

$5(x) + $12(y) = $118     (equation 2)

where x is the number of members who will get t-shirt

y is the number of members who will get sweatshirt

3. Rewrite equation 1 as an equation of y in terms of x.

x + y = 11   (equation 1)

y = 11 - x

4 . Plug in the expression for y in equation 2 and solve for x.

$5(x) + $12(y) = $118     (equation 2)

5x + 12(11 - x) = 118

5x + 132 - 12x = 118

-7x = -14

x = 2

5. Substitute the value of x in either equation 1 or 2 and solve for x.

x + y = 11   (equation 1)

2 + y = 11

y = 11 - 2

y = 9

Hence, Carol should buy 2 t-shirts and 9 sweatshirts.

Checking,

2 + 9 = 11

Each member will receive a gift.

2($5) + 9($12) =$118

Carol will be spending $118 for the gifts.

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Answer:

The 2 is placed in the Hundredths place

Step-by-step explanation:

Hope it helps! =D

The dimensions of the rectangular base of the building with the given perimeter are 120ft and 285ft.

The perimeter of rectangle is expressed as;

P = 2( l + w )

Given the data in the question;

Let x represent the width of the rectangular base.

Plug these values into the equation above.

P = 2( l + w )

810 = 2( (3x-75) + x )

810 = 6x - 150 + 2x

810 = 8x - 150

8x = 810 + 150

8x = 960

x = 960/8

x = 120

Hence,

Width of the rectangle = x = 120ft

Length of the rectangle = 3x-75 = 3(120) - 75 = 285ft

Therefore, the dimensions of the rectangular base of the building with the given perimeter are 120ft and 285ft.

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