An instructor gives four 1-hour exams and one final exam, which counts as two 1-hour exams. Find a student's grade if she received 63, 78, 95, and 90 on the 1-hour exams and 85 on the final exam. Round your answer to one decimal place if necessary.

The scale factor for the given quadrilateral would be 1.5.

A scale factor is a numerical value that is used to represent an object's enlarged or shrunk shape. It is a number that can be used to alter the size of any geometric figure or shape in relation to its original size. It aids in altering the figure's size but not its shape.

Given that the two quadrilaterals are similar to each other and are dilated by some scale factor.

The scale factor will be calculated as:-

Scale factor = 15 / 10

Scale factor = 1.5

Hence, the scale factor will be 1.5.

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Answer:

x = - 3.5 , y = - 5.5

Step-by-step explanation:

y = x - 2 → (1)

y = 3x + 5 → (2)

substitute y = 3x + 5 into (1)

3x + 5 = x - 2 ( subtract x from both sides )

2x + 5 = - 2 ( subtract 5 from both sides )

2x = - 7 ( divide both sides by 2 )

x = - 3.5

substitute x = - 3.5 into either of the 2 equations for y

substituting into (1)

y = x - 2 = - 3.5 - 2 = - 5.5

then x = - 3.5 and y = - 5.5

The cost of the book in Naira is N 24.99  

Mr. Awolowo needs to pay N 4165 at the post office.  

An exchange rate determines the value of one unit of currency in relation to another type of money. Which means exchanging the price from one currency to another currency.

People use the exchange rates when they want to travel abroad and It is necessary to convert cash into local currency in order to do purchases locally.

Here we have

The book costs £3. If the rate of exchange is £ 1 = N 8.33  

Cost of the book in Naira = 3 × N 8.33  

= N 24.99  

Mr Awolowo wants to send £500 to his brother in the United Kingdom  

As we know the rate of exchange, is £ 1 = N 8.33    

=>  £500 = 500 × 8.33  = N 4165  

Therefore,

The cost of the book in Naira is N 24.99  

Mr. Awolowo needs to pay N 4165 at the post office.  

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The expression without absolute value bars is 3.84.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

|√10 - 7 |

= | 3.16 - 7 |

= | -3.84 |

= 3.84

Thus,

The value of the expression is 3.84.

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The value of the given expression, -50 + 5/13p, when p = -26 is -60

From the question, we are to evaluate the given expression for the given value of p

The given expression is

-50 + 5/13p

and

The given value of p is p = - 26

Substitute the given value of p into the given expression

That is,

-50 + 5/13p

When p = -26, the expression becomes

-50 + 5/13(-26)

Simplify

-50 + 5(-2)

-50 - 10

= - 60

Hence, the value of the expression is -60

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Answer:

see below

Step-by-step explanation:

60+75=135

BOC =180 -135 =45

DOE = BOA =60

AOE =180-DOE =120

From the audio, what is inferred from the fairy's action is that she was appreciative. The Option A is correct.

A fairy tale is a story, typically intended for children, that features fantastic and wondrous characters such as elves, goblins, wizards, and even, but not always, fairies. The term "fairy" tale appears to refer to a story's fantastic and magical setting or magical influences, rather than the presence of a fairy character within that story.

Fairy tales are frequently traditional; many were passed down from storyteller to storyteller before being written down in books. Examples of Fairy Tale includes Snow White, Cinderella, Rip Van Winkle, The Twelve Dancing Princesses, Rumpelstiltskin, Thumbelina

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Answer: She was vengeful

Step-by-step explanation:

The audio states that the other fairies were giving the princess positive spells while a fairy that wasn't invited to the party casted an evil spell on the princess, making her sleep for a 100 years. (It's based on the sleeping beauty story)

Answer:

3 millimeters

Step-by-step explanation:

The formula for finding perimeter: 2W+2L=P

W= width

L= length

P= Permiter

So just substitute the numbers in the equation

4 millimeters is the width

14 millimeters is the perimeter

So this is your equation

2*4+2L=14

8+2L=14

Subtract 8 from both sides

2L=6

Divide both sides by 2

L=3

So your length is 3 millimeters

To check:

(2*4)+(2*3)=14

8+6=14

14=14

The value of the expression is q^6 + q^4r^2 + q^2r^4s^2 - q^4r^2s - q^2r^4s + r^6s^3

From the question, we have the following parameters that can be used in our computation:

(blankq^2-r^2s)(blankq^4+blankq^2r^2+blankr^4s^2)

Express properly

So, we have

(q^2-r^2s)(q^4+ q^2r^2 + r^4s^2)

Open the brackets

q^6 + q^4r^2 + q^2r^4s^2 - q^4r^2s - q^2r^4s + r^6s^3

There are no like terms in the expression

So, the solution is q^6 + q^4r^2 + q^2r^4s^2 - q^4r^2s - q^2r^4s + r^6s^3

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The required number of Barnes & Noble stores in 2009 is 725.28.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

To determine the number of Barnes & Noble stores in 2009, we need to evaluate the piecewise function for t = 2009.

Since 2009 is between the interval 6 ≤ t < 12, the number of stores is given by the first piece of the function:

y = -3.692 × x² + 65.28 × x + 437.30

put x = 9 for the year 2009

y = -3.692 × 9² + 65.28 × 9 + 437.30 = 725.28

So, there were 725.28 Barnes & Noble stores in 2009.

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Answer: a) To make apple crumble for 16 people, Farid will need to double the ingredients as compared to serving 8 people. Hence, he will need:

700g * 2 = 1400g of apples

240g * 2 = 480g of sugar

180g * 2 = 360g of flour

So, Farid needs 360g of flour to make apple crumble for 16 people.

b) To make apple crumble for 2 people, Amal will need to use 1/8 of the ingredients as compared to serving 8 people. Hence, she will need:

700g / 8 = 87.5g of apples

240g / 8 = 30g of sugar

So, Amal needs 30g of sugar to make apple crumble for 2 people.

c) To make apple crumble for 6 people, Shahina will need to adjust the ingredients based on the apples she has available. To calculate the amount of sugar and flour required, she can use the ratio of sugar and flour to apples as follows:

Sugar: 700g / 8 = 87.5g per serving * 6 people = 525g

Flour: 700g / 8 = 87.5g per serving * 6 people = 525g

Since Shahina has plenty of the other ingredients, including butter, she can make apple crumble for 6 people with the amount of apples she has available. So, the answer is Yes, Shahina can make apple crumble for 6 people.

Step-by-step explanation:

The answers to all parts shown below.

A set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.

Given:

a) The system of linear equations

3A + 2B + 6C = 71, 000

3A + 2B +4C = 81, 000

5A + 7B + 0C= 92, 000

B) The equation for the system of linear equations

Y = [tex]\left[\begin{array}{ccc}3&2&6\\3&2&4\\5&7&0\end{array}\right][/tex] , Z = [tex]\left[\begin{array}{ccc}71000\\81000\\92000\end{array}\right][/tex]

So, YX = Z

X = Z[tex]Y^{-1[/tex]

C) The inverse matrix method

               14/11  21/11   -2/11

= 1/22    10/11  -15/11   3/11

        1/2   -1/2      0

= 7/ 121   21/ 242   -1/121

  5/121    -15/242    3/242

  1/44        -1/44         0

and, X = Z[tex]Y^{-1[/tex]

X  =  [tex]\left[\begin{array}{ccc}71000\\81000\\92000\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}7/ 121 &21/ 242& -1/121\\ 5/121&-15/242&3/242\\1/44&-1/44&0\end{array}\right] \\[/tex]

A= 10,376.03

B = 946.28

C= 227.72

d) The production for A = RM 7,263.221

The production for B = RM 473.14

The production for C = RM 204.948

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The required, 180 items rentals were tubes or rafts of 300 items.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

The circle graph shows that tubes and rafts made up 60% of the total rentals. If there were 300 items rented in June, then 60% of those rentals were tubes or rafts:

300 items × 60% = 180 items

So the answer is A. 180.

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The domain is the second option:

(2, 8]

For a function y = f(x), we define the domain as the set of the possible inputs for the function.

Here we have a piecewise function that is defined in the 3 regions:

2 < x  ≤ 4

4 < x < 8

x ≥ 8

So the domain is the set of any value larger than 2, and we can write that as:

(2, 8]

We end it at "8" becase is the last defined value and that is the only option that makes sense.

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The system of equations are solved and the number of performers for the show A is 10,034

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as T

Now , the value of T is

The total number of performers in the two shows T = 16,756

A + B = 16,756

The number of performers in show A = 3312 + number of performers in show B

Substituting the values in the equation , we get

A = B + 3,312

On simplifying the equation , we get

A + A - 3,312 = 16,756

Subtracting 3,312 on both sides of the equation , we get

2A = 16,756 + 3,312

2A = 20,068

A = 10,034

Hence , the equation is A = 10,034

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The equation which models the product is, A = 6 x 8

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

Given that,

A area model,

which has 6  box in column arrangement and 8  box in row arrangement,

Suppose, each box has 1 unit square area

Now, area of a model can be written as,

Area = Number of box in column x Number of box in row

Number of box in column  = 6

Number of box in row = 8

Each box has 1 unit square area,

So,

A = 6 x 8

   = 48 unit square

Hence, it can be represented as, A = 6 x 8

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Answer:

Step-by-step explanation:  https://flexbooks.ck12.org/cbook/ck-12-middle-school-math-concepts-grade-6/section/6.15/primary/lesson/elapsed-time-msm6/

The solution is Option D.

The derivative of the function is given by the equation f' ( x ) = -x / ( √5-x² )

In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately

Given data ,

Let the function be represented as f ( x )

Substituting the values in the equation , we get

f ( x ) = √ ( 5 - x² )

Now , the derivative of the function is f' ( x )

f' ( x ) = ( 1/2 ) 1 / √( 5 - x² ) ( d/dx ) ( -x² )

On simplifying the equation , we get

f' ( x ) = ( 1/2 ) 1 / √( 5 - x² ) ( -2x )

On further simplification , we get

f' ( x ) = ( -2x/2 ) 1 / √( 5 - x² )

f' ( x ) = -x / ( √5-x² )

Hence , the derivative of the function is f' ( x ) = -x / ( √5-x² )

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Answer:

68

Step-by-step explanation:

170/5=34 34*2=68

Answer:

There are two solutions:

[tex]\boxed{v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}}\\\\or\\\\\boxed{v = 1.3333.... \text{ and }v= 1.5}\\[/tex]

Step-by-step explanation:

The given equation is  :

[tex]\dfrac{2}{v-2}=-6\:+\:\dfrac {1}{v-1}\\\\[/tex]

Find the LCM of the denominators:

LCM = [tex]\left(v-2\right)\left(v-1\right)[/tex]

Multiply by LCM:
[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right)[/tex]

Simplify

[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right):\quad 2\left(v-1\right)[/tex]

[tex]\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right):\quad v-2[/tex]

So the equality becomes
[tex]2\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+v-2[/tex]

Expand the brackets:
[tex]2\left(v-1\right):\quad 2v-2[/tex]

[tex]\text {Right side becomes: }\\-6\left(v-2\right)\left(v-1\right)+v-2\\Expand \; \left(v-2\right)\left(v-1\right):\quad v^2-3v+2\\\\\text {Right side becomes}\\-6\left(v^2-3v+2\right) + v -2\\= -6v^2+6\cdot \:3v-6\cdot \:2 + v - 2\\\\\\= -6v^2+18v-12+v-2\\\\\text{Simplify}\\= -6v^2+19v-14\\\\\text{Left side}2(v-1= 2v-2\\\\\text{Finally we get}\\2v - 2 = 6v^2+19v-14\\\\[/tex]

Switch sides:
[tex]-6v^2+19v-14=2v-2[/tex]

Move 2 from right to left(sign changes)
[tex]-6v^2+19v-14 + 2 =2v\\\rightarrow -6v^2+19v-12=2v\\\\[/tex]

Move 2v to left side(sign changes)

[tex]-6v^2+19v-12-2v = 0\\\\\rightarrow -6v^2+17v-12=0\\\\[/tex]

This is a quadratic equation which can be solved with a quadratic equation calculator. I used a calculator to solve this:

The solutions are:
[tex]v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}\\\\\\\text{In decimal these would be}\\\\v = 1.3333.... \text{ and v}= 1.5\\[/tex]

The solution to the system of equations is ( 1 , -1 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

y = -6x + 5   be equation (1)

Let the second equation be represented as B

Now , the value of B is

y = x - 2   be equation (2)

On simplifying the equations , we get

Substitute the value of y from equation (2) in equation (1) , we get

x - 2 = -6x + 5

Adding 6x on both sides of the equation , we get

7x - 2 = 5

Adding 2 on both sides of the equation , we get

7x = 7

Divide by 7 on both sides of the equation , we get

x = 1

Substitute the value of x in equation (2) , we get

y = 1 - 2

y = -1

Hence , the value of x and y is 1 and -1 respectively

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Answer: D

Step-by-step explanation:

Think about it this way, 3 squared is 3x3 correct? that equals 9. 4 squared is 16 so there you go. Sorry if this isn't answered clearly.I'm trying my best to help

Answer: It's the fourth option; f^-1(x)=x^3/125 -7

The length of segment AB is determined as 13 units.

The distance between two points is the length of the line segment that connects the two points in a plane.

here, we have,

The length of segment AB is the distance between point A and point B, which is calculated as follows;

|AB| = √[(x₂ - x₁)² + (y₂ - y₁)²]

where;

x₁ is the x - component of point A

x₂ is the x - component of point B

y₁ is the y - component of point A

y₂ is the y- component of the point B

|AB| = √[(x₂ - x₁)² + (y₂ - y₁)²]

|AB| = √[(-5 - 7)² + (5 - 10)²]

|AB| = √[144+25]

|AB| = 13 units

Thus, the length of segment AB is the distance between point A and B.

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The linear function for the population in t years after 2000 is given as follows:

P(t) = 2200t + 44000.

The estimate for the population in 2010 is given as follows:

66,000.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Two points for the function are given as follows:

(5, 55000) and (8, 61600).

Dividing the change in the output by the change in the input, the slope m is given as follows:

m = (61600 - 55000)/(8 - 5)

m = 2200.

Hence:

P(t) = 2200t + b.

When x = 5, y = 55000, hence the intercept b is given as follows:

55000 = 2200(5) + b

b = 55000 - 2200(5)

b = 44000.

Hence the function is:

P(t) = 2200t + 44000.

2010 is 10 years after 2000, hence the estimate is given as follows:

P(10) = 2200(10) + 40000

P(10) = 66,000.

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The set {10,17,27} does not represent the three sides of a triangle,

Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given  the sets for the triangles,

property of triangles says that,

The length of a triangle's two longest sides added together is longer than the third side.

Similarly to this, the length of the third side of a triangle third side is shorter than the difference between its two sides.

1: given sides are 10, 17, 27

according to the property sum of 10 and 17 should be greater than  27 but sum  is equal to 27,

10 + 17 = 27,

so the sides do not represent the triangle

2: sides are 9, 22, 30

here 9 + 22 > 30

the set represents the triangle.

3: sides 6, 16, 19

6 + 16 > 19

the set represents the triangle.

4: sides 4, 7, 9

4 + 7 > 9

set represents the triangle.

Hence option A is correct.

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Answer:

Step-by-step explanation: A rectangle's perimeter formula is P=2(l+w), therefore,

P=2(21.9+18.3)

P=2(40,2)

P=80,4

You will need 80,4 inches of fondant to cover all the edges of the cake