Allen is showing his work in simplifying -8.3 + 9.2 - 4.4 + 3.7. Identify and explain any errors in his work or in his reasoning. Write feedback to Allen explaining the mistake he made and how to correct his work.
Step Work Reasoning
−8.3 + 9.2 − 4.4 + 3.7 Original problem
1 −8.3 + 9.2 + 4.4 + 3.7 Additive inverse
2 −8.3 + 4.4 + 9.2 + 3.7 Commutative property
3 −8.3 + (4.4 + 9.2 + 3.7) Associative property
4 −8.3 + 17.3 Simplify
5 9 Simplify

The value of Cosine of C is 8/10. So the option d is correct.

In the given question, we have to find which of the following is showing the correct ratio for Cosine of C.

The given options are:

(a) 6/10

(b) 10/8

(c) 6/8

(d) 8/10

As we know that cosine is the ration of adjacent side and hypotenuse.

From the given diagram we can see that;

Adjacent Side = 8

Hypotenuse = 10

Opposite Side = 6

Now the;

CosC = Adjacent Side/Opposite Side

CosC = 8/10

Hence, the value of CosC is 8/10. So the option d is correct.

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Answer:

[tex]\boxed{\bf{\underline{ y\le -\cfrac{3}{2}x-2}}}[/tex]

Step-by-step explanation:

From the given graph,

[tex]\bf y-intercept :\boxed{\tt -2}[/tex]

[tex]\bf Slope:\tt \cfrac{\Delta y}{\Delta x} =\cfrac{-3}{2} =\boxed{-\cfrac{3}{2} }[/tex]

Notice that graph is shaded below (not above), so y is less than the other side of the inequality. the graph elso has a solid line (not dashed), so we are dealing with an "or equal to" inequality.

Therefore, we should use the less than or equal to symbol.

[tex]\boxed{\bf{ y\le -\cfrac{3}{2}x-2}}[/tex]

_____________________

Hope this helps!

Have a great day!

Answer:

Step-by-step explanation:

3.) Slope: 15x

Y-int: 120

Y=15x+120

4.) For this one i'm not sure maybe..

5.) Slope: 5x

Y-int: 250

Y=5x+250

The simplification of the expressions in the question using the rules of indices are as follows;

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2. (3⁻⁴ + 5⁻³)⁻¹ = [tex]49\frac{31}{206}[/tex]

3. (3⁻⁴ + 5⁻³)⁻² = [tex]2415\frac{32685}{42436}[/tex]

4.) [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{10\cdot c^{-5} \cdot d^6 \cdot e^{-8}}[/tex] = [tex]\dfrac{c^5\cdot e^8}{2\cdot d^5}[/tex]

5.)  [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5}\right)^{-3 }}{7\cdot \left(p^{-6} \cdot q^8\right)^{-4}} =\dfrac{-5\cdot m^{12}\cdot n^{15}\cdot q^{32}}{7\cdot p^{24}}[/tex]

An index or indices is the power by which a number or variable or expression raised.

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰

6·e⁰ + (11·f)⁰ - 5/g⁰ = 6 × 1 + 1 - 5/1

6 × 1 + 1 - 5/1 = 6 + 1 - 5 = 2

Therefore;

6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2.) (3⁻⁴ + 5⁻³)⁻¹

(3⁻⁴ + 5⁻³)⁻¹ = (1/(3⁴) + 1/(5³))⁻¹ = 1/(1/(3⁴) + 1/(5³))

1/(1/(3⁴) + 1/(5³)) = 1/(1/81 + 1/125) = 1/((125 + 81)/(81×125))

1/((125 + 81)/(81×125)) = (81 × 125)/(125+81) = 10125/209

10125/206 = 49 + 31/206

(3⁻⁴ + 5⁻³)⁻¹ = [tex]49 \frac{31}{206}[/tex]

3.) (3⁻⁴ + 5⁻³)⁻²

(3⁻⁴ + 5⁻³)⁻² = 1/((1/3⁴ + 1/5³)²)

1/((1/3⁴ + 1/5³)²) = 1/((1/81 + 1/125)²)

1/((1/81 + 1/125)²) = 1/(((125 + 81)/(81 × 125))²)

1/(((125 + 81)/(81 × 125))²) = 1/((206/10125)²)

1/((206/10125)²) = (10125)²/(206)² = 102515625/42436

102515625/42436 = 2415 32685/42436

(3⁻⁴ + 5⁻³)⁻² = [tex]2415\frac{32685}{42436}[/tex]

4.)  [tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}[/tex]

[tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}} = \dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) }[/tex]

[tex]\dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) } = \dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) }[/tex]

[tex]\dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) }[/tex]

[tex]\dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{c^5\times e^8}{2\cdot d^6}[/tex]

[tex]\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}= \dfrac{c^5\times e^8}{2\cdot d^6}[/tex]

5.) [tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\rright)^{-4}}[/tex]

[tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} =\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} }[/tex]

[tex]\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} }[/tex]

[tex]\dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 }[/tex]

[tex]\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) }[/tex]

[tex]\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) } = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}[/tex]

[tex]\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}[/tex]

6.) (3·x⁻⁴·y⁻⁵·z⁻²)⁻²

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = [tex]3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right)[/tex]

[tex]3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right) = 3\cdot \left(x^4\cdot y^5\cdot x^2\right)^2[/tex]

3·(x⁴·y⁵·x²)² = 3·x⁸·y¹⁰·x⁴

Therefore;

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = 3·x⁸·y¹⁰·x⁴

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Hello, I'm pretty sure this answer is D

Answer: D) BC/EF=CA/FD

Step-by-step explanation:

Answer:

The anwser is 1.769

Step-by-step explanation:

I did this on a calculator

To solve this problem, we need to use the formula for the area of a rectangle, which is length times width. We can set up the formula as follows:

Area = length * width

Since we know that the width is 7 greater than ⅔ the length, we can represent the width as follows:

width = ⅔ * length + 7

We can substitute this expression for the width in the area formula to get the following:

Area = length * (⅔ * length + 7)

We are given that the area of the rectangle must be 172, so we can set up the following equation:

172 = length * (⅔ * length + 7)

To solve for the length of the rectangle, we can first distribute the length on the right-hand side of the equation, like this:

172 = length * ⅔ * length + 7 * length

We can then combine like terms on the right-hand side of the equation to get the following:

172 = ⅔ * length^2 + 7 * length

To solve for the length, we can use the quadratic formula, which is as follows:

length = (-b +/- sqrt(b^2 - 4ac)) / 2a

In this case, a = ⅔, b = 7, and c = -172. Plugging these values into the quadratic formula, we get the following:

length = (-7 +/- sqrt(49 - 4 * ⅔ * -172)) / 2 * ⅔

Simplifying this expression, we get the following:

length = (-7 +/- sqrt(49 + 576)) / ⅓

We can further simplify this expression by calculating the value of the square root, like this:

length = (-7 +/- sqrt(625)) / ⅓

Simplifying again, we get the following:

length = (-7 +/- 25) / ⅓

To find the final value of the length, we need to calculate the two possible values of the square root, which are 25 and -25. Plugging these values into the equation for the length, we get the following:

length = (-7 + 25) / ⅓ = 18 / ⅓ = 6

length = (-7 - 25) / ⅓ = -32 / ⅓ = -10

Since the length of a rectangle must be positive, we can discard the negative value and only consider the value of 6. This means that the length of the rectangle is 6, and the width is ⅔ * 6 + 7 = 11. Therefore, the dimensions of the rectangle are 6 by 11.

Triangle ΔPMO and  ΔNMO are congruent, therefore  ΔPMO ≅ ΔNMO.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

MO bisects ∠PMN and OM bisects ∠PON.

1.

MO bisects ∠PMN,

Reason : It is given condition.

2.

∠PMO ≅ ∠NMO

Reason : The image is symmetrical, therefore ∠PMO ≅ ∠NMO.

3.

MO = MO

Reason : In triangle, PMO and NMO the side MO is common,

Therefore, MO = MO

4.

OM bisects ∠PON.

Reason : It is given condition.

5.

∠POM =  ∠NOM

Reason : The image is symmetrical, therefore  ∠POM =  ∠NOM.

6.

ΔPMO ≅ ΔNMO

Reason : The figure is symmetric, and triangle ΔPMO and  ΔNMO are congurent.

Therefore, ΔPMO ≅ ΔNMO.

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Answer:

19.048%

Step-by-step explanation:

The formula for the increase in cost will be :

[(New cost - Original Cost)÷Original Cost] × 100

So let's substitute values in from the question :

[(50-42)÷42] × 100

[8÷42] × 100

0.19048 × 100

19.048%

Hope this helped and have a good day

Answer:

angle b

Step-by-step explanation:

let's assume the triangle is a right angle triangle . either angle a or c can be equal to 60 degree

Answer:

100000000000000000000000000000000000000000000000000

Step-by-step explanation:

The length of the arc is = [tex]\frac{2}{27}22^{\frac{3}{2} }[/tex]m

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.

According to the given information

We can find the length of the arc by

L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt} ^{2}+\frac{dy}{dt} ^{2} } } \, dt[/tex]

Find the derivative of x w.r.t to t

dx/dt = [tex]3t^{\frac{1}{2} }[/tex]

Find the derivative of y w.r.t to t

dy/dt = 2

Putting the values in above equation

We get

L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt} ^{2}+\frac{dy}{dt} ^{2} } } \, dt[/tex]

L= [tex]\int\limits^2_0 {\sqrt{9t+4} } \, dt[/tex]

L = [tex]\frac{2}{27}(9t+4)^{\frac{3}{2} }[/tex]

limit approaches from 0 → 2

Hence

The length of the arc is = [tex]\frac{2}{27}22^{\frac{3}{2} }[/tex]m

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a) The total number of books in Tim's collection is; 300 books

b) If Tim adds 20 more nonfiction books to his collection, the new percentage of nonfiction books is; 17.5%

We are given;

Number of Non fiction books Tim has = 36

Percentage of non-fiction books = 12%

a) Let the total number of books in his collection be x. Thus;

(12/100) * x = 36

x = 3600/12

x = 300 books

b) He adds 20 more non fiction books to his collection. Thus;

New total non fiction books = 36 + 20 = 56

New total number of all books = 300 + 20 = 320

Thus;

New percentage of non fiction books = 56/320 * 100%

New percentage of non fiction books = 17.5%

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the probability that the first song played is a folk song is 9.1%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

Carter has 153 songs on a playlist. He's categorized them in the following manner:

20 country, 31 blues, 8 Latin American, 17 jazz, 26 rap, 14 folk, and 37 hip hop.

The number of folk songs is 14

P(folk) = number of folk songs/ total

= 14/ 153

=0.091

Hence the probability that the first song played is a folk song is 9.1%.

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The expression representing the situation is (r+6).

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given that, Conrad has 6 more marbles than Rory and r represents the number of marbles that Rory has,

We see, Conrad has more marble than Rory and Rory has r marbles,

Mathematical can be represented as,

c = r+6

Hence, The expression representing the situation is (r+6).

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Answer:

part A: The appropriate design for the study includes;Treatment used; Chamomile oil treatment

Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves

Treatment assignment; Treatment should be assigned to patients with pinched nerves

Variables that should be measured; Reduction or relief of pain as reported by the patients

Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female

Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.

Step-by-step explanation:

Gavin already had 12 rolls of towels, and he is buying 3 rolls per week.

Slope tells us the change between two points given, and is shown by  the change in the y coordinate divided by the corresponding change in the x coordinate.

Given that, Gavin is stocking up on paper towel rolls. He already has some at his house, and begins buying more every week at a constant rate. The line y = 3x + 12 represents this scenario.

Here the equation is y = 3x+12

When comparing with standard equation of the line, y = mx+c where m is slope, we get,

m = 3 and c = 12

Therefore, the change is 3, that means, he is buying 3 rolls per week,

and the constant is 12 that tells that he already have 12 rolls in stock.

Hence, a) he is buying 3 rolls every week, b) he has 12 rolls in stock.

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Here is the two column proof:

    Statement                                        Reason                                              

===================================================

    Statement                                        Reason                                              

Answer:

[0, 799.95]

Step-by-step explanation:

First, we need to isolate the variable by subtracting 9 from both sides of the inequality:

20t + 9 - 9 ≤ 16,000 - 9

This gives us:

20t ≤ 16,000 - 9

Next, we can divide both sides of the inequality by 20 to isolate the variable:

20t / 20 ≤ (16,000 - 9) / 20

This simplifies to:

t ≤ 799.95

Finally, we need to express the solution in interval notation. Since the value of t cannot be negative, the solution is:

[0, 799.95]

Therefore, the solution to the inequality in interval notation is [0, 799.95].

The value of θ is 60°.

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin, cos , tan , cosec , sec and cot

Let the angle be θ , that is;

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

Thus, tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data that the angle be represented as θ

Now , we are given that the angle θ is acute

Since Acute angles measure less than 90 degrees

So , the value of θ < 90°

when the value of sec θ = 2

cos θ = 1/sec θ

, cos θ = 1/2

The value of θ when cos θ is 1/2.

when the angle θ is 60°

Therefore ,

the value of θ is 60°

sec 60° = 2

Hence , The value of θ is 60°

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We follow the inclusive rule, The answer to the question is (A) that is

if y>=10 and y <=50

In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number you may imagine is a real number.

The intervals used are:

(a , b) , All the numbers between a & b without including them.

[a, b] , All the numbers between a & b including them.

y lies in [10,50].

And since it means that it includes 10 and 50 and all the numbers between them.

The final answer is (A) that is if y>1=10 and y <=50.

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Answer: c = 7

Step-by-step explanation:

180 = 86 + 31 + 9c
180 = 117 + 9c
63 = 9c
7 = c

Answer:

  c = 7°

Step-by-step explanation:

You want the value of c given that angles in a triangle are marked 86°, 31°, and 9c.

The angle sum theorem tells you the sum of angles in a triangle is 180°. Using given angle values, this means ...

  86° +31° +9c = 180°

  117° +9c = 180° . . . . collect terms

  9c = 63° . . . . . . . subtract 117°

  c = 7° . . . . . . . . divide by 9

The value of c is 7°.

The slope of the equations is equal. Then the lines are parallel to each other.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y = 2x + 1        ....1

2x - y = 3

y = 2x - 3         ....2

The slope of both equations is 2.

The slope of the equations is equal. Then the lines are parallel to each other.

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There are 100 students and 400 adults.

The 480 tickets sold had a $10 fall in ticket sales.

What is system of equations?

A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.

Let d be the number of adults and y be the number of students.

⇒ d + s = 500                   ..(1)

The number of adult tickets sold at $6.50 and the number of student tickets sold at $3.50 each.

⇒ 6.5d + 3.5s = 2050         ..(2)

From equation (1) d = 500 - s

Plug the value of d in equation (2)

6.5(500 - s) + 3.5s = 2050

3250 - 6.5s + 3.5s = 2050

3250 - 3s = 2050

3s = 3250 - 2050

3s = 1200

s = 400

Plug s = 400 in d = 500 - s

⇒  d = 500 - 400 = 100

Hence, there are 100 students and 400 adults.

Now,  at one performance there were three times as many student tickets sold as adult tickets.

⇒ s = 3d

3d - s = 0          ..(3)

d + s = 480       ..(4)

⇒ 4d = 480

     d = 120  Adults

Plug d = 120 in equation (4)

120 + s = 480

         s = 480 - 120

         s = 360 Students

The money earned from these 480 people is

120 * 6.5 + 360 * 3.5 = 780 + 1260 = $2040.

$2040 - $2040 = $10

Hence, the 480 tickets sold had a $10 fall in ticket sales.

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The equations for parallel lines:

y = -1/2 x - 2  ----- y = -1/2 x + 6

y = 1/2 x + 4   ----- y = 1/2 x - 4

y = 2x -4       -----  y =2/1x + 2

y = 5x + 2     -----  y = 5x - 1

y = 1/5 x + 10 ----   y = 1/5 x + 3

What is slope of line?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

If an equation in the form y = mx + c then m is the slope of the line.

Equation of line               slope          Slope parallel line

y = -1/2 x - 2                        -1/2                        -1/2

y = 1/2 x + 4                          1/2                           1/2

y = 2x -4                                2                            2

y = 5x + 2                               5                           5

y = 1/5 x + 10                          1/5                         1/5

Now identify the lines from the option whose slope are  -1/2,  1/2, 2, 5,  1/5.

The slope of the line y = -1/2 x + 6 is  -1/2.

The slope of the line y = 1/2 x - 4 is  1/2.

The slope of the line y = 2x -4 is 2.

The slope of the line y = 5x + 2  is 5.

The slope of the line y = 1/5 x + 10 is 1/5.

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Answer:

To simplify the given equation, we can start by using the rules of algebra to rearrange the terms and combine like terms on both sides of the equation. This gives us:

-x - (-4x - 6) = 6

We can then distribute the negative sign on the left side of the equation to get:

-x + 4x + 6 = 6

We can then combine like terms on the left side of the equation to get:

3x + 6 = 6

We can then subtract 6 from both sides of the equation to get:

3x = 0

We can then divide both sides of the equation by 3 to get the final result:

x = 0

Therefore, the simplified form of the given equation is x = 0.

Step-by-step explanation:

The area of the figure is 84.139 square ft

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

Shapes = Rectangle and Semicircle

For the rectangle, we have

Length = 5 ft and Width = 14 feet

For the circle, we have

Diameter = 14 ft - 4 ft - 4 ft

Evaluate

Diameter = 6 feet

Start by calculating the radius of the semicircle

So, we have the following representation

radius = Diameter/2

This gives

radius = 6/2

Evaluate

radius = 3

The area of the shape is then calculated as

Area = Length * WIdth + πr²/2

So, we have

Area = 5 * 14 + 3.142 * 3²/2

Evaluate

Area = 84.139

Hence, the area is 84.139 square ft

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Answer:

Step-by-step explanation:

we are allowed to change the vertical axis on a line chart.

suppose we have a large range of value needed to plot along the vertical and horizontal axis, but the current line chart cannot meet this demand. in such cases, we can customize the scales to provide more vertical and horizontal spaces.

dramatic slopes are the steep slopes of a straight line calculated by vertical and horizontal coordinate of two points laying on it. By changing the vertical axis as well as the horizontal axis we can plot a graph of a straight line more properly and finally more dramatic slope is visible there.

hence, we can change the scale values on a line chart to meet the requirement of the plot.

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https://brainly.com/question/29833410

Answer:

No, there is not sufficient evidence that the scores improved.

Step-by-step explanation:

Just because these people were given a six-page review handout doesn't mean that:

a. They actually did any of it

b. They learned anything

c. Since the kids have other experiences in class, the scores might not have necessarily improved that much, if at all

d. They had enough time to study

e. They cared enough in the first place

Generally, there is no rock-solid evidence at all pointing to the fact that their test scores improved. While you could make the assumption assuming every kid did what they were supposed to do, there isn't enough evidence to say that the scores improved.