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(2^4x+4) / (2^x+1)

The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.

Given:

The volume of closed right circular cylindrical cans = 128π cm³

As we know the volume of a cylinder = πr²h

By equating;

πr²h = 128π

h = 128/r²

To get the dimensions of a can with minimum surface area;

S = 2πrh + 2πr

Put h = 128/r²;

Therefore, S(r) = 256π/r + 2πr²

                 S'(r) =  -256π/r² + 4πr

                S''(r) = -(2*256π)/r³ + 4π

Now, for S(r) = 0;

               r = 4cm

         for S''(4) > 0 at r = 4 is minimum point.

Hence,

h = 128π/(π*4*4)

h = 8cm

Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.

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Answer:

  (-1, -8)

Step-by-step explanation:

You want the image of P(-8, 1) after rotation 90° counterclockwise about the origin.

The transformation for 90° CCW is ...

  (x, y) ⇒ (-y, x)

Then

  P(-8, 1) ⇒ P'(-1, -8)

__

Additional comment

We observe that this answer is not among the choices listed in this problem statement. We suspect a typo somewhere. The transformations represented by the given choices are ...

  A: reflection across the x-axis and rotation 90° CCW

  B: reflection across the x-axis

  C: reflection across the x-axis and rotation 90° CW

  D: reflection across the origin

These are shown in the second attachment.

Answer:

The slope is -3/5=-0.6

Step-by-step explanation:

Slope: (5-8)/(8-3)= -3/5=-0.6

Answer:

[tex]m=-\frac{3}{5}[/tex]

Step-by-step explanation:

Step 1: Slope

Step 2: Set up equation and solve for m

The inequality is x ≤ 39.2. The actual number of items that can be bought is 39.

There is a set budget of $145 to buy some items. The price of each item is $3.70. We need to form an inequality for the given information and solve it.

Let the number of items be denoted by the variable "x". Then we can say that :

3.70*x ≤ 145

x ≤ 145/3.70

x ≤ 39.2

The actual number of items that can be bought must be a whole number. We will take the greatest integer less than or equal to the solution.

The actual number of items that can be bought is 39.

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Answer: 7. 0 cause there is  not a number next to the 3

-2 is the slope you distribute the -2 by the parenthese

Step-by-step explanation:

Answer:

-5.2,-4.75,-9/2

Step-by-step explanation:

Answer:-5.2 -4.75 -9/2

Step-by-step explanation:

Answer:

ñ/3 and 3√25

Step-by-step explanation:

pi is irrational and the cube root of 25 is irrational :)

Answer:

Step-by-step explanation:

1 ) + 9 = 13

+ 9 ≠ 13

False

2 ) 3 = 12

3 ≠ 12

False

3 ) + 5 − 9 = 0

-4 ≠ 0

False

4 ) 2 + 5 = 17

7 ≠ 17

False

5 ) 5 − 3 = 17

2 ≠ 17

False

6 ) − 3 = 1

− 3 ≠ 1

False

7 ) 7x = 35

  a ) Divide both sides by 7...

    [tex]\frac{7x}{7} = \frac{7}{35}[/tex]

     [tex]x = 5[/tex]

8 ) [tex]\frac{4x}{4}=\ 4[/tex]

      a ) Multiply both sides by 4...

        [tex]\frac{4x}{4}=\ 4[/tex]

        [tex]\frac{4x}{4}[/tex] × [tex](4)=(4)[/tex] × [tex](4)[/tex]

        [tex]4x=16[/tex]

       b ) Divide both sides by 4...

        [tex]\frac{4x}{4}= \frac{16}{4}[/tex]

         [tex]x=4[/tex]

9 ) 3 + 4 = 15

7 ≠ 15

False

10 ) 8 + − 5 = 7

3 ≠ 7

False

Hope this helps! :)

Answer:   700x+1700

This represents the total amount spent over the x weeks that have gone by.

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

Explanation:

x = number of weeks

700x = amount spent over those x weeks ($700 per week)

700x+1700 = total amount spent when adding on the $1700 tv.

------

An example:

Let's say x = 10 weeks have elapsed. He spends $700 a week, so 700x = 700*10 = 7000 dollars have been spent so far if we ignore the tv. Then add on the $1700 tv cost to get 7000+1700 = 8700 dollars total spent.

Then note how 700x+1700 = 700*10+1700 = 8700 matches what we got earlier.

I recommend trying out other values of x to get a better idea of what's going on.

For breakfast, you have had 1/2 a serving of cereal and 1/4 cup of raisins, which count as one serving of fruit.

For breakfast, you have had one serving of cereal and one serving of fruit. In general, one serving of cereal is considered to be one cup, while one serving of fruit is considered to be one half cup. Therefore, in your bowl of oatmeal, you would have had two servings of cereal, and in your quarter cup of raisins, you would have had one serving of fruit. For lunch, you have had one serving of fruit in your glass of orange juice.

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She bought 13 books in $58.

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. LHS = RHS is a common mathematical formula.

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:

Let b represent the number of books.

So, the equation will be

5b - 7 = 58

Now, add 7 to both sides of the equation

5b = 65.

b = 13.

Thus, she bought 13 books at 5 dollars a piece.

After she gets a 7 dollar discount off of 65 dollars, so she paid a total of 58 dollars after the discount.

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Answer:

C

Step-by-step explanation:

(h - g)(2)

= h(2) - g(2)

= 2² + 1 - 2(2) = 4 + 1 - 4 = 1

The amounts, using proportions, are given as follows:

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem from which the fraction was built.

The tip is of 20% of the total bill of $54.65, hence it's value is given as follows:

Tip = 0.2 x 54.65 = $10.93.

(because 0.2 is the decimal equivalent to the percentage of 20%, then it is multiplied by the total amount to find the desired amount).

The total cost of the meal is given by the sum of the bill of the meal plus the tip, hence:

Total Cost = 54.65 + 10.93 = $65.58.

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The sides of DEF in order from least to greatest will be x + 6, (5x - 8) and (9x + 2).

The total angles that can be found in a triangle is 180°.

Therefore, the angles will be illustrated thus:

x + 6 + (5x - 8) + (9x + 2) = 180°

x + 6 + 5x - 8 + 9x + 2 = 180°

15x = 180°

Divide

x = 180° / 15.

x = 12°

Therefore,

x + 6 = 12 + 6 = 18°

(5x - 8) = 5(12) + 8

= 60 + 8

= 68°

(9x + 2) = 9(12) + 2

= 108 + 2

= 110°

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The amount of gallons of oil that are in the gun when it is full is 6 gallons , the correct option is (c) .

In the question ,

it is given that

A lube gun dispenses the same amount of oil each time , and

the equation is y = (-0.03125)x + 6

where , x is the number of times the oil is dispensed and

y is the number of gallons of oil remaining in the gun ,

when the gun is full , the number of times oil dispensed will be zero .

that is x = 0  ,

Substituting x = 0 in the given equation ,

we get ,

y = (-0.03125)(0) + 6

y = 0 + 6

y = 6

Therefore , The amount of gallons of oil that are in the gun when it is full is 6 gallons .

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The statement 'If an integer is negative, its absolute value is also its additive inverse.' is True.

In this question, we have been given a statement 'If an integer is negative, its absolute value is also its additive inverse.'

We know that for any non zero real number 'm', the additive inverse is '-m'

as m + (-m) = 0

We know that the absolute value of any non-zero real number is always positive.

Consider a negative integer -p.

The absolute value of -p is |-p| = p

We can observe that -p + p = 0

-p + |-p| = 0

Therefore, the statement 'If an integer is negative, its absolute value is also its additive inverse.' is True.

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The required value of the variable x is - 4

A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilised. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.

The given equation is :

10-6x + 9x = x+2

On solving this equation we get :

10 + 3x = x + 2

Subtract - 3x on both sides and we will get

10 = - 2 x + 2

Subtract 2 on both sides

we get

8 = -2x

On dividing both sides of the equation by 2 we get

x = - 4

Thus the required value of the variable x is - 4

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The time that it will take Joe to catch up with Mary is; 8 hours

We are told that;

Time Mary leaves the house = 12 pm

Time that Joe leaves the house = 2 pm

Speed of Mary = 45 mi/hr

Speed of Joe = 60 mi/hr

This means that Mary had a 2 hour time lead over Joe.

Thus;

Distance is calculated from the formula;

Distance = Speed * time

Thus;

Distance covered by Mary in the 2 hours lead is;

Distance = 45 * 2 = 90 miles

Thus, time that it will take Joe to catch up with mary is;

t = 2 + (90/(60 - 45))

t = 2 + 6

t = 8 hours

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Answer:

a) 0.566 b)8.62

Step-by-step explanation:

0.56565656...

4th number after decimal is 6, which is greater than 5. the value of 3rd number after dp goes up by 1

therefore 0.566

7×12%=0.84

7+0.84=7.84

7.84×10%=0.784

7.84+0.784=8.62

Answer: 290

Step-by-step explanation:

58 x 5 = 290

Margo jumps 290 times in five minutes

The solution to the given system of linear equations is x = -2 and y = -8. That is, (-2, -8).

From the question, we are to determine the solution to the given system of linear equations.

The given system of linear equations is

y = 5x + 2         ---------- (1)

4x - y = 0          ---------- (2)

Substitute equation (1) into equation (2)

4x - y = 0

4x - (5x + 2) = 0

4x - 5x -2 = 0

-x -2 = 0

-2 = x

x = -2

Substitute the value of x into equation (1)

y = 5x+ 2

y = 5(-2) + 2

y = -10 + 2

y = -8

Hence, the solution is x = -2 and y = -8

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The expression is -10 > 2x+ 14.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

Negative ten is no less than two times a number plus 14

let the number x

so, two times a number plus 14

= 2x+ 14

and, Negative ten is no less than two times a number plus 14

-10 > 2x+ 14

hence, the expression is -10 > 2x+ 14.

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92% = 69 questions

100% = 75 questions

The total number of questions on the test is 75 questions.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Total number of answers answered correctly = 69

The percentage of the test questions answered correctly = 92%

This means,

92% = 69

The total number of questions in percentage = 100%

Now,

92% = 69

Multiplying 100/92 on both sides.

100% = 100/92 x 69

100% = 75

Thus,

The total number of questions on the test is 75 questions.

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Answer: -64 and 64

Step-by-step explanation:

Option (A) is the correct answer: Panel a illustrate Increasing Return to Scale and panel b illustrate Constant Return to Scale.

Return to Scale:

It is the Variation or change in productivity that is the outcome from a proportionate increase of all the input.

Increasing Return to Scale:

An increasing return to scale occurs when the output increase by a larger proportion than the increase in inputs during the production process. For Example: if input is increased by 3 times but output increases by 3.75 times, then the firm or economy has experienced an increasing return to scale. This increase is due to many reasons like division external economies of scale.

Constant Return of Scale:

Constant Return of Scale refers to the production situation in which output increases exactly in the same proportion in which factors of production are increased. In simple words, if factors of production are doubled output will also be doubled. In this case, internal and external economies are exactly equal to internal and external diseconomies. This situation arises when after reaching a certain level of production, economies of scale are balanced by diseconomies of scale. For Example:  A car wash in which one car wash takes 30 minutes. If there is one wash space and two workers running two 8 hours shifts total product would be 32.

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The line of best fit for the data presented in the scatterplot is y = 0.5x. (Option B)

A line of best fit represents a straight line that is the best approximation of the given set of data used to examine the nature of the relation between two variables. It is an educated guess about where a linear equation might fall in a set of data plotted on a scatter plot. The slope-intercept form of a linear equation is given by y = mx + b where m is the slope of the line and b is the y intercept of the graph. For any two points (x1, y1) and (x2, y2), the slope is given by:

m = (y2-y1)/(x2-x1)

Choosing two points from the line say (180, 90) and (220,110),

m = (110 – 90)/(220 – 180) = 20/40 = 0.5

Hence, y = 0.5x + b

Substituting a point from the graph into the equation say (240, 120)

120 = 0.5(240) + b

120 = 120 + b

b = 0

Hence, the equation is y = 0.5x

Note: The question is missing the scatterplot (which is attached) and options which are A. y = -0.5x, B. y = 0.5x, C. y = -2x, D. y = 2x.

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The y-intercept is y = 10, and that is the initial height of the flower in inches.

And the rate of change between n = 1 and n = 5 is:

R = 0.21

For any function y = f(x), the y-intercept is the value that y takes when we evaluate in x = 0.

In this case, we have the exponential function:

g(n) = 10*(1.02)^n

Evaluating in n = 0 we get:

g(0) = 10*(1.02)^0 = 10*1 = 10

The y-intercept is y = 10, and it means that the initial height of the flower is 10 inches.

Now we want to get the average rate of change on the interval [1, 5].

Remember that for a function f(x) the average rate of change on an interval [a, b] is:

R= [ f(b) - f(a)]/(b - a)

In this case we will have:

R = [ g(5) - g(1)]/(5 - 1) = [g(5) - g(1)]/4

Where:

g(5) = 10*(1.02)^5  =11.041

g(1) = 10*(1.02) = 10.200

Replacing that:

R = [11.041 - 10.200]/4 = 0.21

This means that the plant increases about 0.21 inches per day on these 4 days.

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