A grading machine can grade 96 multiple choice tests in 2 minutes. If a teacher has 300 multiple choice tests to grade, predict the number of minutes it will take the machine to grade the tests.​

The formula of the sequence is aₙ = 13.5 - 3.5n

The sequence is as follows:

10, 6.5, 3, −0.5, −4...

Studying the sequence, it's an arithmetic sequence.

Therefore, using arithmetic formula,

aₙ = a + (n - 1)d

where

Therefore,

common difference = d = 6.5 - 10 = -3.5

a = first term = 10

Therefore, the formula of the sequence is as follows:

aₙ = 10 + (n - 1)-3.5

aₙ = 10 - 3.5n + 3.5

aₙ = 13.5 - 3.5n

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[tex]\bf \longrightarrow{f(x) = \frac{1}{x - 7} \: \: \: \: , \: \: \: g(x) = \frac{1}{x - 5} }[/tex]

[tex]\bf \longrightarrow{f \circ g = \frac{1}{ \frac{1}{x - 5} - 7} }[/tex]

[tex] \bf \longrightarrow{so \: \: x - 5 \neq0 \: \: , \: \: \frac{1}{x - 5} \neq7} \\ \\ \bf \longrightarrow{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x \neq0 \: \: , \: \: \frac{1}{x - 5} \neq0 }\\ \\\bf \longrightarrow{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 5 \frac{1}{7} } \\ \\ \bf \longrightarrow{and \: a < b }\\ \bf \longrightarrow{so \: a = 5 \: , \: b = 5\frac{1}{7} }[/tex]

Answer:

-152

Step-by-step explanation:

-156 - (-4)

-156+4

= -152

you could also just go into a normal chrome browser at the top and type in -156-(-4) it will give you -152.

Answer:

13

Step-by-step explanation:

9 - 3 = 6

5 - 12 = -7

6 - ( -7 ) = 13

Answer:

-1

Step-by-step explanation:

Absolute value means distance from zero.

9-3 is 6 so nothing special there. 5-12, though is negative 7, but since we need the absolute value of that it is just 7.  So our math problem becomes 6 - 7, which is -1.

Answer:

x=70°

x=109°

Step-by-step explanation:

x+30+80=180

x=180-30-80=70

16.

x=64+45=109°

According to the linear equation, The number of adults tickets are 44  and number of Student tickets are 10.

According to the statement

We have to find that the Linear equation and solve it.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

A charity-event manager counted 54 ticket receipts the day after an event. The price for an adult ticket was $21, and the price for a student ticket was $5. The register confirms that $974.

Then

Let number of adult tickets = x

Let number of student tickets = y

And charity-event manager counted 54 ticket receipts

=> x + y = 54 -(1)

The price for an adult ticket was $21

price for a student ticket was $5

Total Amount = 21x + 5y

The register confirms that $974 was taken in.

=> 21x + 5y = 974 -(2)

The system of equations represents matters :

x + y = 54

21x + 5y = 974

Eq2 - 5 * Eq1

=> 21x - 5x = 974 - 270

=> 16x = 704

=> x = 44

And

44 + y = 54

=> y = 10

The number of tickets are 44 Adults & 10 Student tickets.

So, According to the linear equation, The number of adults tickets are 44  and number of Student tickets are 10.

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Answer:

50.2655

Step-by-step explanation:

Answer:

[tex]60cm {}^{2} [/tex]

Step-by-step explanation:

Area for triangle is equal to half base time perpendicular height.

[tex] \frac{1}{2} (10 \times 12)[/tex]

[tex] \frac{1}{2} (120)[/tex]

[tex]60cm ^{2} [/tex]

note that it's 10cm X 12 cm that's how you get cm²

Answer:

the answer is 3.6 ft

Step-by-step explanation:

I didn't know how to do it so I looked it up

Answer: 4.5 x 10^-11

Step-by-step explanation:

4.5E-11 = 4.5 x 10^-11      ==> 4.5e-11 is basically 10^-11 multiplied by 4.5

√3 is an irrational number as it is non terminating and non repeating number.

Irrational number - In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.

They are non terminating and non repeating in nature.

For example 22 / 7 , √ 5 , √ 7 and many more.

Here, √3 is an irrational number as it is non terminating and non repeating number.

Therefore, √3 is an irrational number as it is non terminating and non repeating number.

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All steps to prove for the value of x are given below.

What is meant by Angle bisector?

Angle bisector is refer to a line that split an angle into two equal angles.

Given that;

Measure of ∠DEH = (10x - 2)°

Measure of ∠HEF = (6x + 10)°

Ray EH is angle bisector of ∠DEF.

Now, Ray EH is angle bisector of ∠DEF.

Hence,

1. Measure of ∠DEH = Measure of ∠HEF

Reason = Ray EH is angle bisector of ∠DEF.

2. (10x - 2)° =  (6x + 10)°

Reason = Measure of ∠DEH = (10x - 2)° and Measure of ∠HEF = (6x + 10)°

3. 10x - 2 - 6x = 6x + 10 - 6x

Reason = Subtract 6 both side.

4. 4x - 2 = 10

Reason = Apply sum or difference rule.

5. 4x - 2 + 2 = 10 + 2

Reason = Add 2 both side.

6. 4x = 12

Reason = Apply sum or difference rule.

7. x = 3

Reason = Divide 4 both side.

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Answer:

x = -13

Step-by-step explanation:

-2 (x + 4) = 18

distributive property  -2x + (-8) = 18

simplify   -2x - 8 = 18

cancel out 8 by addition  -2x = 26

cancel out -2 by division  x = -13

The Function that has a range of {y|y ≤ 5} is  mathematically given as

f(x) = –(x – 4)2 + 5

This is further explained below.

Generally, the equation for the function is  mathematically given as

f(x)=-(x-4)^2+5

Where

f(x)=-(x-4)^2+5 is a quadratic function. Its graph looks like a parabola. One of the vertices in the graph is (4,5) and opens in a downward direction.

Proving that f(x)=-(x-4)^2+5≤  5 for all x

[tex]x^2 \geq 0 \Rightarrow(x-4)^2 \geq 0 \\\\-(x-4)^2 \leq 0 \\\\-(x-4)^2+5 \leq 5 \text {. }[/tex]

In conclusion, The Function that has a range of {y|y ≤ 5} is  mathematically given as

f(x) = –(x – 4)2 + 5

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The diagram could be used to prove △ABC ~ △EDC using similarity transformations is (a) Triangle ABC is rotated about point C and then dilated to form triangle CED.

From the question, we have the following highlights

Similar triangles do not have to be congruent triangles

This means that if two triangles are similar, then one triangle  has been dilated to form the other triangle

This also means that

The corresponding angles of the triangles are equal while the corresponding sides of the triangles are not equal

The transformation that supports the above highlights is (a) Triangle ABC is rotated about point C and then dilated to form triangle CED.

Hence, the diagram could be used to prove △ABC ~ △EDC using similarity transformations is (a) Triangle ABC is rotated about point C and then dilated to form triangle CED.

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Answer: A. or the first one.

Step-by-step explanation: TRUST ME!  Answer correct on Edge.

My first attempt was wrong but my second attempt was correct.

It should be noted that the product of 61.18 and 82 will be 5016.76.

It should be noted that a product of a given set of numbers simply means the multiplication of the numbers that are given.

In this case, we want to get the product of 61.18 and 82. This will be:

= 61.18 × 82

= 5016.76

In conclusion, the product of 61.18 and 82 will be 5016.76.

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What is the product of 61.18 and 82?

The result of the arithmetic expression as given in the task content is; 112.

It follows from the task content that the given expression is; 38 - (-74).

Hence, in a bid to solve the parentheses, the two negative signs are multiplied to yield a positive sign.

Ultimately, we have the result of the indicated operation as; 38 + 74 = 112.

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Answer: 471.9 miles

Step-by-step explanation:

This is a right triangle so a^2+b^2=c^2

205^2=42025

425^2=180625

=222650

sqrt222650 =471.9

The dimensions of the original shapes are 15 and 25 inches respectively

The formula for volume of a rectangle is expressed as;

Volume = length × width × height

From the information given, we have;

Substitute the values

1875 = 5 × y × y + 10

Divide both sides 5

1875 / 5 = y(y + 10)

expand the bracket

375 = y² + 10y

y² +10y - 375 = 0

y² + 25y - 15y - 375 = 0

y(y + 25) - 15( y + 25) = 0

y= 15 or y = -25

If y = 15 Inches

Width = 15 + 10 = 25 Inches

Thus, the dimensions of the original shapes are 15 and 25 inches respectively

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Answer:76 copies

Step-by-step explanation:

hope this helps

Answer:

312 in total.

Step-by-step explanation:

if 1 type of cookie is 24 cookies. so 13 types of cookies are 312 cookies.l. because 13×24=312

The figure with these coordinates are G'(3, -5), H'(2, 0), I'(0, -1) and J'(-1, -4)  given below. Therefore, option C is the correct answer.

Given that the shape is reflected across the y-axis.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

The coordinates of the given figure are G(-3, -5), H(-2, 0), I(0, -1) and J(1, -4)

When the coordinates of the figure GHIJ are reflected across the y-axis we get G(-(-3), -5), H(-(-2), 0), I(0, -1) and J(-(1), -4)

So, the coordinates are G'(3, -5), H'(2, 0), I'(0, -1) and J'(-1, -4)

The figure with these coordinates are G'(3, -5), H'(2, 0), I'(0, -1) and J'(-1, -4)  given below. Therefore, option C is the correct answer.

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(a) The HCF of ( 9y + x ) and ( 3y + 4x ) is 11x

b) The LCM of ( 9y + x ) and ( 3y + 4x ) is 22x.

The ratio of x and y is given as:

x : y = 3 : 7

Then,

(x / y) = ( 3 / 7)

7x = 3y

(a) HCF of ( 9y + x) and ( 3y + 4x)

Now,

9y + x = 3(3y) + x

9y + x = 3(7x) + x

9y + x = 22x

And;

3y + 4x = 7x + 4x

3y + 4x = 11x

Now, the HCF of 22 and 11 is 11 because 22 = 2 × 11 and 11 = 11 × 1.

Therefore,

HCF of ( 9y + x ) and ( 3y + 4x ) is 11x.

(b) The LCM of (9y+x) and (3y+4x)

We know,

9y + x = 22x and 3y + 4x = 11x

So, LCM of ( 9y + x ) and ( 3y + 4x ) is 22x.

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The required angle measure for the condition of the proportion of angles m∠RPS is 212.35°.

Given that,
m∠QPS = 88
m∠RPS = 5x+34
m∠QPR=8x+15
The measure of the angle m∠RPS is to be determined.

The angle can be defined as the one line inclined over another line. the measure of an angle is measured in two units of degrees and in radiants.

Here,
m∠QPR = m∠QPS + m∠RPS
8x + 15 = 88 +  5x + 34
8x  - 5x = 88 + 34 - 15
3x = 107
x = 107 / 3
x = 35.67
Now,
m∠RPS = 5x+34 = 5 * 35.67 + 34 = 212.35°

Thus, the required angle measure for the condition of the proportion of angles m∠RPS is 212.35°.

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The percentage is 50%

From the question we are told that  

The  mean is μ= 14 hours

The  standard deviation is σ=1 hour

Generally on the normal distribution curve the mean divides the curve into  two. with the half to the left of the mean (50% to the left )representing the percentage of the batteries that will last less than 14 hours and  the area under the curve to the right (50% to the right)representing the percentage of batteries that will last longer than mean (14 hours )

Hence the percentage of the cell phone batteries that will be expected to last longer than 14 hours is 50%

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the probability that the sample contains two white balls and one green ball is 21/40.

In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the probability of drawing one color or another, or some other properties.

Total number of balls: 7 White and 3 Green = 10 balls

Cases for three balls are drawn at random:

Selection of 3 balls from 10 balls = [tex]^1^0C_3[/tex]

Case A: 1 White and 2 Green = [tex]\frac{^7C_1 * ^3C_2}{^1^0C_3} = \frac{7*3}{120} = \frac{21}{120} \\[/tex]

Case B: 2 White and 1 Green = [tex]\frac{^7C_2 * ^3C_1}{^1^0C_3} = \frac{21*3}{120} = \frac{63}{120}[/tex]

Case C: 3 White and 0 Green = [tex]\frac{^7C_3 * ^3C_0}{^1^0C_3} = \frac{28*1}{120} = \frac{28}{120}[/tex]

Case D : 0 White and 3 Green = [tex]\frac{^7C_0 * ^3C_3}{^1^0C_3} = \frac{1*1}{120} = \frac{1}{120}[/tex]

The probability that the sample contains two white balls and one green ball = Case B

So, the probability that the sample contains two white balls and one green ball = 63/120 = 21/40

Therefore, the probability that the sample contains two white balls and one green ball is 21/40.

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the probability that the sample contains two white balls and one green ball is 21/40.

In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the probability of drawing one color or another, or some other properties.

Total number of balls: 7 White and 3 Green = 10 balls

Cases for three balls are drawn at random:

Selection of 3 balls from 10 balls = [tex]^1^0C_3[/tex]

Case A: 1 White and 2 Green = [tex]\frac{^7C_1*^3C_2}{^1^0C_3} =\frac{7*3}{120}= \frac{21}{120}[/tex]

Case B: 2 White and 1 Green = [tex]\frac{^7C_2*^3C_1}{^1^0C_3} =\frac{21*3}{120}= \frac{63}{120}[/tex]

Case C: 3 White and 0 Green = [tex]\frac{^7C_3*^3C_0}{^1^0C_3} =\frac{35*1}{120}= \frac{35}{120}[/tex]

Case D : 0 White and 3 Green = [tex]\frac{^7C_0*^3C_3}{^1^0C_3} =\frac{1*1}{120}= \frac{1}{120}[/tex]

The probability that the sample contains two white balls and one green ball = Case B

So, the probability that the sample contains two white balls and one green ball = 63/120 = 21/40

Therefore, the probability that the sample contains two white balls and one green ball is 21/40.

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Answer: (3+3*5):6

Step-by-step explanation:

[tex](3+3*5):6=\\(3+15):6=\\18:6=\\3[/tex]

Answer:

12

Step-by-step explanation:

1. \: 3 + 15 - 6 \\ 2. \: 18 - 6 \\ 3. \: 12

Answer:

See below

Step-by-step explanation:

Area * thickness = volume

540 m^2  * .5 m = 270 m^3

15 trucks  ===>     270 m^3 / 15 trucks = 18 m^3 per truck

Answer:

24x^4+32x^3+32x^2+16x+10

Step-by-step explanation:

Using distributive property,

1. multiple 4x^2 times (6x^2+8x+5)

2. multiple 2 times (6x^2+8x+5)

3. add them together

24x^4+32x^3+20x^2

+ 12x^2+16x+10

______________________

24x^4+32x^3+32x^2+16x+10