Function and Reasoning:

There are 60 calories in 5 ounces of a certain brand of soda.

Part A: Represent the relationship between the number of calories and the number of ounces of soda as a line in the coordinate plane below.

Part B: What is the number of calories per ounce of soda?

Part C: How does the unit rate relate to the slope of the line in the graph above? Explain your answer.

Answer: 17/25

Step-by-step explanation:

This equals 68%, which equals 68/100.

Let's divide both sides by 2.

68/2 = 34

100/2 = 50

This gives us 34/50.

We can simplify even more!

34/2 = 17

50/2 = 25.

This gives us 17/25.

We can no longer simplify, which means 17/25 is our final answer.

Answer:

4x+8=54 this is the correct answer

Answer:

Infinitely many solutions

Step-by-step explanation:

Solve: 4(x-1)-x=3(x+5)-11

First distribute.

4x-4-x=3x+15-11

Comvine like terms.

3x=4=3x-4

Infinitely many solutions.

Hope this helps plz hit the crown :D

3²+2 = 11

hope it helps

Answer:

11

Step-by-step explanation:

3 squared is 9

squared just means multiplied by itself

which would be 3×3

and then add 2

which is 11

The equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is its radius.

We have given that circle having radius of 8 units. Thus, r = 8.

Since we know that circle having the center (10,−7).

Thus, the equation of the circle, with a radius of 8 units is;

(x - h)² + (y - k)² = r²

(x - 10)² + (y + 7)² = 8²

Thus, the equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

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After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.

When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.

The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.

Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.

The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.

It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.

The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.

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Answer:

(7;1)

Step-by-step explanation:

The abscissa of B' is going to be the same as abscissa of B , becuse the points are simmetrical over axis x.

However the ordinate of the point B'  will have the opposite sign as ardinate  B. However the module of ordinate B'  is going to be the same as module of orrdinate B.

Answer:

v = 23.370 mph

Step-by-step explanation:

It is given that,

The world record for the 100 meter dash is finished in 9.572 seconds in Berlin. We need to find the Bolt’s average race speed in miles per hour.

We know that,

1 mile = 1.609 km

or

1 mile = 1609.34 m

⇒ 100 m = 0.0621 miles

1 hour = 3600 seconds

⇒ 1 second = (1/3600) hour

Average speed = distance/time

So,

\(v=\dfrac{\dfrac{100}{1609.34 }\text{miles}}{\dfrac{9.572}{3600}\ \text{hour}}\\\\v=23.36963\ \text{mph}\)

or

v = 23.370 mph

Hence, Bolt’s average race speed is 23.370 mph.

To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:

Monthly basic salary: Rs 48,000

Social security tax rate: 1%

Income tax rate on income up to Rs 5,00,000: 0% (no tax)

Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%

Dashain allowance: 1 month's salary

Deposit in Citizen Investment Trust (CIT): 10%

Rebate on income tax: 10%

(i) Annual Income:

Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:

Annual Basic Salary = Monthly Basic Salary x 12

= Rs 48,000 x 12

= Rs 5,76,000

Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:

Annual Income = Annual Basic Salary + Dashain Allowance

= Rs 5,76,000 + Rs 48,000

= Rs 6,24,000

Swornima's annual income is Rs 6,24,000.

(ii) Tax Rebate:

Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.

(iii) Annual Income Tax:

First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.

Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000

= Rs 1,24,000

Income Tax in this range = Taxable Income x Tax Rate

= Rs 1,24,000 x 0.1

= Rs 12,400

Now, let's calculate the total annual income tax:

Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000

= Rs 12,400

Next, we calculate the rebate on income tax:

Tax Rebate = Total Annual Income Tax x Rebate Rate

= Rs 12,400 x 0.1

= Rs 1,240

Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.

To summarize:

(i) Swornima's annual income is Rs 6,24,000.

(ii) Swornima's tax rebate is Rs 1,240.

(iii) Swornima should pay an annual income tax of R

The exact value of sin(5π/12) is (√6 + √2)/4

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

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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Answer:

Step-by-step explanation:

1 )

\(\frac{2}{5}( \frac{5x}{4} - \frac{10}{3})-\frac{4x}{3} \\\frac{x}{2} - \frac{4}{3} - \frac{4x}{3}\\ \frac{-5x}{6}-\frac{4}{3}\)

2 )

\(\frac{17x}{8}+\frac{3x}{4}+\frac{1}{6}-\frac{7x}{12}+\frac{17}{3}\\ \frac{51x}{24}+\frac{18x}{24}-\frac{14x}{24}+\frac{35}{6}\\\frac{55x}{24}+\frac{35}{6}\)

Answer: NO

Step-by-step explanation:

This is not a function, since there are multiple outputs for ONE input.

Answer:

no

Step-by-step explanation:

to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.

Answer:

y = \(-\frac{5}{2}\)x - 1

Step-by-step explanation:

5x + 2y = 12

2y = -5x + 12

y = \(-\frac{5}{2}\)x + 6

y = mx + b

4 = \(-\frac{5}{2}\) ( -2 ) + b

4 = 5 + b

b = -1

y = \(-\frac{5}{2}\)x - 1

The most likely to be discussed in a feminist criticism of Chinua Achebe's work is his portrayal of gender roles and  Ina is a typical woman . The correct option is 2.

What is a novelist person?

A novelist is a person who writes novels. The key to success as a romantic novelist is absolute belief in your story. Synonyms: author, writer More Synonyms of novelist

Who is Chinua Achebe?

Chinua Achebe is a novelist and poet. He  is famous for his pivotal direction in literature of Africa. His first novel was Things fall apart.

The options are attached here:

his life story and literary achievements

his portrayal of gender roles

his descriptions of the landscape

his literary influences and preferences

Thus, the correct option is 2. his portrayal of gender roles.

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Answer:

4,-2 1/2 is the coordinates of point F.as it

lies in 4 th quadrant where x is positive and y is negative.

Answer:

35.71%

Step-by-step explanation:

So, let's determine the number of jobs the industry will have in 2030.

So, in 2020, the industry has 123,200 jobs.

Each year, the industry loses 4,400 jobs.

Thus, by 10 years in (2030), the industry would have lost (4,400)(10) or 44,000 jobs.

This means that in 2030, there will only be 123,200-79200 jobs left.

Now, percentage change is given by:

\(PC=\frac{New-Old}{Old}\cdot100\%\)

The new value is 79200 and the old value is 123,200. Substitute them:

\(PC=\frac{(79200)-(123200)}{123200}\cdot100\%\\\)

Use a calculator. Simplify:

\(PC=\frac{-44000}{123200}\cdot100\%\\ PC\approx-0.3571\cdot100\%\\PC\approx-35.71\%\)

If the result is negative, then it's a decrease. Therefore, the percentage change from 2020 to 2030 is approximately 35.71%

Answer:

The answer is 35.71%

Step by step explanation

In 2020 the industry has 123,200 jobs.

Each year, the industry loses 4,400 jobs.

Thus, by 10 years in (2030), the industry would have lost (4,400)(10) or 44,000 jobs.

This means that in 2030, there will only be 123,200-79200 jobs left.

Now, percentage change is given by:

New−Old

⋅100%

The new value is 79200 and the old value is 123,200. Substitute

123200

(79200)−(123200)

⋅100%

Simplify:

PC≈−0.3571⋅100%

PC≈−35.71%

the percentage change from 2020 to 2030 is 35.71%

Phil would need to save for at least 6 weeks to have enough money to buy the bike.

Phil saves one-quarter of his pay each week, which is:

1/4 x £240 = £60

Let's assume it takes him n weeks to save enough to buy the bike. Then, the amount he saves in n weeks is:

n x £60 = £349

We can solve for n by dividing both sides by £60:

n = £349 / £60

n ≈ 5.82

Since we can't have a fraction of a week, Phil would need to save for 6 weeks to have enough money to buy the bike.

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Answer:

The nth term is Tn = 2[T(n- 1) -2]

The next term is 356

Step-by-step explanation:

Given

Terms: 15,26,48,92,180

Solving (a) : The recursive n term

We have:

T1 = 15

T2 = 26 = 13 * 2 = (15 - 2) * 2

T3 = 48 = 24 * 2 = (26 - 2) * 2

T4 = 92 = 46 * 2 = (48 - 2) * 2

T5 = 180 = 90 * 2 = (92 - 2) * 2

So, the nth term can be represented as:

Tn = [T(n-1) - 2] * 2

Tn = 2[T(n-1) - 2]

The next term is the 6th term.

So, substitute 6 for n in the above formula.

T6 = 2 * [T(6 - 1) - 2]

T6 = 2 * [T5 - 2]

Substitute 180 for T5

T6 = 2 * (180 - 2)

T6 = 2 * 178

T6 = 356

Answer:

24 sq inches. Hope this helps :)

Step-by-step explanation:

Check the picture below.

\(\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{7\times 7}{49}\\ V=82 \end{cases}\implies \begin{array}{llll} 82=\cfrac{49h}{3}\implies 246=49h\implies \cfrac{246}{49}=h \\\\\\ 5.02\approx h \end{array}\)

Without seeing the graph of the linear function, it is impossible to determine if Tom's answer of 12 is correct or incorrect. However, it is important to understand the concept of slope and how it is calculated for a linear function.

The slope of a linear function represents the rate at which the y-coordinate changes for each unit increase in the x-coordinate. In other words, it measures the steepness of the line. Mathematically, the slope of a line is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line.

To calculate the slope of a line given its graph, one can choose any two points on the line and find the difference in their y-coordinates and x-coordinates. The slope is then the ratio of the change in y-coordinates to the change in x-coordinates. This can be expressed as:

slope = (change in y-coordinate) / (change in x-coordinate)

Now, if Tom has correctly identified two points on the line and calculated the difference in their y-coordinates and x-coordinates, and if he has obtained a ratio of 12 for the change in y-coordinate to the change in x-coordinate, then his answer of 12 for the slope would be correct.

However, it is also possible that Tom made an error in his calculation, or that he misread the graph, and obtained an incorrect answer. Therefore, it would be necessary to verify his calculations by checking the points he used and the formula he applied.

In conclusion, without further information about the graph of the linear function and the points chosen by Tom to calculate the slope, it is impossible to determine if his answer of 12 is correct or incorrect.

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Answer:

I can tell you that #7 is 86.

Can’t help with 6

Step-by-step explanation:

Answer:

6. the answer is 2

7. the answer is 86

Step-by-step explanation:

6. 3/4+3/4= 6/4

6/4+1/4+1/4=8/4

Simplify that to 2

7. search on the calculator it's really simple math

The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV is the future value of the annuity,

P is the yearly payment,

r is the interest rate per compounding period, and

n is the number of compounding periods.

In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.

Let's substitute these values into the formula and calculate the total value of the annuity:

FV = 693 * ((1 + 0.053)^16 - 1) / 0.053

FV = 693 * (1.053^16 - 1) / 0.053

Using a calculator, we can evaluate the expression inside the parentheses:

1.053^16 ≈ 1.9738

Substituting this value back into the formula:

FV = 693 * (1.9738 - 1) / 0.053

FV = 693 * 0.9738 / 0.053

FV ≈ 12739.62

Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

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While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.

Here's a three-column table evaluating how learning takes place according to Piaget, Vygotsky, and Bruner:

Theorist Approach to Learning Key Concepts

Piaget Constructivism 1. Schema: Individuals actively construct their knowledge through assimilation and accommodation, organizing information into mental structures called schemas. 2. Stages of Development: Learning occurs through cognitive development stages, from sensorimotor to formal operational, where individuals progressively acquire more complex mental abilities. 3. Active Exploration: Children learn best through hands-on exploration and interactions with the physical world.

Vygotsky Sociocultural Theory 1. Zone of Proximal Development (ZPD): Learning takes place within the gap between a learner's actual developmental level and their potential level with guidance from a more knowledgeable other. 2. Social Interaction: Learning is facilitated through social interactions with peers and adults, such as cooperative learning and scaffolding. 3. Cultural Tools: The use of language, symbols, and cultural artifacts plays a central role in cognitive development and learning.

Bruner Constructivism 1. Scaffolding: Instruction should provide support and guidance tailored to the learner's current abilities to help them progress to higher levels of understanding. 2. Discovery Learning: Learners construct knowledge by actively exploring and discovering concepts and relationships on their own. 3. Spiral Curriculum: Learning is organized in a spiral manner, revisiting key concepts and building upon previous knowledge in a progressive and interconnected way.

While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.

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Answer:

the answer is D I hope this helps

Answer:

Yes, if 2 is a factor of Y and 3 is a factor of Y, 6 will be a factor of Y.

Step-by-step explanation:

I will be giving 3 examples.

Example #1: Let's say Y is 18.

2 is a factor of 18, 3 is a factor of 18, and 6 is also a factor of 18.

18 = 2 * 9

18 = 3 * 6

18 = 6 * 3

Example #2: Let's say Y is 6.

2 is a factor of 6, 3 is a factor of 6, and any positive integer (such as 1, 2, 3, 4, 5, etc...) is a factor of itself, so 6 is a factor of 6.

Example #3: Let's say Y is 40.

2 is a factor of 40, 3 is NOT a factor of 4, and 6 is also NOT a factor of 40. Any number that can be factored by 2 and 3 can also get factored by 6, no matter what.

Answer:

1024/3

Step-by-step explanation:

First we want to do 8^4 which is 4096/12. Now, we can factor this equation by factoring out 4: 4(1024)/12. Cancel the common factors to get 1024/3. This can also be written as 341. 3 (the decimal 3 has a line over it) or 341 1/3

Answer:

1024/3

Step-by-step explanation:

Answer:

y = 64

Step-by-step explanation:

log y of base 4 = log y / log 4 = log y / log (2^2) = log y / ( 2 * log 2)

log y of base 2 = log y / log 2

So, log y base 4 + log y base 2 = [log y / ( 2 * log 2)] + [log y / log 2] = 3/2 log y base 2

So, 3/2 log y base 2 = 9

=> log y base 2 = 6

=> y = 2^6 = 64

The value of y, given that Log ₄ Y + Log ₂ Y = 9, can be found to be 64.

We are given the equation:

Log ₄ Y + Log ₂ Y = 9

This can also be written as:

Log ₂ Y / Log ₂ 4  + Log ₂ Y = 9

Simplifying further we have :

Log ₂ Y / 2 + Log ₂ Y = 9
3 / 2 Log ₂ Y = 9

Given this relationship, we can finally solve for Y to be :

Log ₂ y = 6

y = 2 ⁶

y = 64

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Answer:

21

Step-by-step explanation:

PEMDAS : Parenthesis, Exponent, Multiplication/Division, Addition/Subtraction.

First, we want to deal with the parenthesis within the parenthesis.

(4.6/2) = 2.3

Rewrite it into the equation.

[3 * 2.3] + 14.1 = ?

Now, do the work in the parenthesis again.

[6.9] + 14.1 = ?

There isn't anymore parenthesis, exponents, or multiplication/division, so we move onto addition now and add both terms.

6.9 + 14.1 = 21

? = 21

The answer is 21.