Calc 2
Suppose that 5 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 49 cm.
a) How much work (in J) is needed to stretch the spring from 40 cm to 44 cm? (Round your answer to two decimal places.)
------J
b) How far beyond its natural length (in cm) will a force of 20 N keep the spring stretched? (Round your answer one decimal place.)
------cm

Option A. The percentage of items that can be recycled is 35%

We are first to determine the objects that can be recycled and those that cannot be recycled.

The recyclable objects that we have here are:

milk bottles = 2

soda cans = 2

newspapers = 3

The total number of recyclables = 7

The items that can not be recycled are:

1 banana peel

12 apple cores

The total number of recyclables = 13

The total number of objects = 7 + 13 = 20

The percentage of recyclables would be 7 / 20 * 100

= 35%

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Answer:

[tex]2\frac{2}{3}[/tex] cups of milk

Step-by-step explanation:

The problem is [tex]\frac{2}{3}[/tex] of a cup per milkshake times 4 milkshakes.  Keeping in mind that we can write any number over 1 without changing its value, our math problem is:

[tex]\frac{2}{3}[/tex] × [tex]\frac{4}{1}[/tex]

We multiply numerator times numerator and denominator times denominator to get [tex]\frac{8}{3}[/tex].  If we convert that improper fraction to a mixed number fraction we get [tex]2\frac{2}{3}[/tex].

The number of cups of milk would be 2 2/3 needed in the four milkshakes.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other

We have been given that martin is making four milkshakes. The recipe calls for 2/3 cup of milk.

We have to determine the number of cups of milk he needs

Let the number of cups of milk would be x in the four milkshakes.

As per the given situation, we can write the ratio would be as:

1 milkshakes : 2/3 cup of milk = 4 milkshakes : x cup of milk

⇒ 1 / (2/3) = 4/x

Reciprocal the term in the numerator,

⇒ 3/2 = 4/x

Apply the cross-multiplication operation,

⇒ 3x = 8

⇒ x = 8/3

⇒ x = 2 2/3

Thus, the number of cups of milk would be 2 2/3 in the four milkshakes.

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The area of the glass inside the 10 inches metal rim is 25/π square inches

The area of a geometric shape or figure is a measure of the flat surface the shape occupies.

The dimension in the question, obtained from a similar question online are;

The length of the metal rim around the magnifying glass = 10 inches around

Required; The surface area of the glass inside the rim

The metal rim around the magnifying glass indicates the circumference of the glass inside;

Therefore;

The circumference of the glass inside the rim = 10 inches

The formula for the circumference of a circle = 2·π·r

Where;

r  = The radius of the circle;

Therefore;

r = Circumference ÷ (2×π)

The radius of the glass inside is therefore;

r = 10 inches/(2·π) = 5/π inches

The area of a circle = π × r²

The area of the glass, A = π × (5/π)² = 25/π

The area of the glass inside is A = 25/π square inches

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According to the Pythagoras theorem, the exact value of tan A is 3/4 and the value of tan B is 15/8

Pythagoras Theorem

Pythagoras theorem defines that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“

Given,

Here we have the value of sin A = 3/5, cos B = 8/17 and A and B are acute angles.

And we need to find the value of tan A and tan B.

According to the Pythagoras theorem,

If the value of sin A = 3/5, then we have the value of the right angle triangle of hypotenuse and the opposite.

So, the adjacent value is calculated based on the theorem is,

=> 5² = ad² + 3²

=> 25 = ad² + 9

=> ad² = 25 - 9

=>  ad = √16

=> ad = 4

Therefore, the value of tan A is written as,

=> tan A = opposite/ adjacent

=> tan A = 3/4

Similarly, the value of tan B is calculated as,

If the value of cos B = 8/17, then we have the value of the right angle triangle of hypotenuse and the adjacent.

So, the opposite value is calculated based on the theorem is,

=> 17² = 8² + op²

=> 289 = 64 + op²

=> op² = 289 - 64

=> op = √225

=> op = 15

Therefore, the value of tan B is written as,

=> tan B = opposite/ adjacent

=> tan B = 15/8

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Slope intercept form of (-2,-1) and (0,1) is y = 3/2x +1.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.

Given,

Coordinates = (-2,-1) and (0,1)

For slope:

m = y₂ - y₁/ x₂ - x₁

m = 1 + 2/0 + 2

m = 3/2

Slope intercept form:

y = mx + b

y = 3/2x +1

Slope intercept form of (-2,-1) and (0,1) is y = 3/2x +1.

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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).

The equation of a line is given by the expression:

(y-y1)=m(x-x1)

in the given problem the slope is m=1 and the point (x1, y1) is (5, 3), so substituting those values we have:

(y-3)=1(x-5)

simplifying:

y-3=x-5

isolating "y":

y=x-5+3

y=x-2

The complete questions is,

Which is the equation of a line that has a slope of 1 and passes through point (5, 3)? A.y = x – 2

B.y = x + 2 C.y = x + 3

D.y = x – 5

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Answer: 5 5/6

Step-by-step explanation: make them both into fractions so 7/1 and 5/6 multiply across 7*5=35 and 1*6=6 simplify that down into a mixed number gives you 5 5/6

Reason:

We have 50 mint condition coins out of 250 total

This forms the ratio 50:250, in which we divide both parts by the GCF 50 to end up with 1:5

The ratio 1:5 tells us that the total is 5 times that of the number of mint condition.

Size of sample needed to determine the percentage of people with give margin of error is equal to 1691.

As given in the question,

Margin of error = 2%

                          = 0.02

Sample proportion 'p' = 0.5

⇒ (1 - p) = 1 - 0.5

             = 0.5

Let 'n' represents the sample size

Z- value at confidence interval 90% = 1.645

Formula used

Margin of error = z-value √ [p( 1-p)/n]

Substitute the value we get,

0.02 = 1.645 √ (0.5)(0.5)/n

Squaring on both the side

0.0004 = 2.706025 ( 0.25/n)

⇒ n = ( 2.706025 × 0.25 )/ 0.0004

⇒ n = 1691.26

⇒ n ≈ 1691

Therefore, size of sample needed with given margin of error is equal to 1691.

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Using the sample space, the probability of rolling an even number with a six-sided dice is 3/6 or 1/2.

In the given question we have to find the probability of rolling an even number with a six-sided dice.

The sample space of dice through the experiment is

{1,2,3,4,5,6}

The even numbers is {2,4,6}.

The probability of rolling an even number with a six-sided dice is

P(E)=Total number of even outcome/Total number of outcome

P(E)=3/6

P(E)=1/2

Hence, the probability of rolling an even number with a six-sided dice is 3/6 or 1/2.

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Answer:

x = 9

Step-by-step explanation:

Triangles are similar due to AAA (all angles are congruent due to shared angle and corresponding angles). Thus, the sides are proportional, and we can set up a proportion with corresponding sides:

9/(72 + 9) = (3x - 20)/(3x - 20 + 56)

9/81 = (3x - 20)/(3x + 36)

(1/9) * (3x + 36) = 3x - 20

(3x + 36)/9 = 3x - 20

3x + 36 = (3x - 20)*9

3x + 36 = 27x - 180

36 + 180 = 27x - 3x

216 = 24x

x = 9

Answer: its 12 and 8 10 12 14 16 either of those

Step-by-step explanation:

Answer:

?jsp?3×4=5/6(9÷43)=2×3=45/_<7<78>(56)

Step-by-step explanation:

(2x - 5)(x-3)

FOIL method: multiply first, outer, inner, and last of the pairs

[tex]2x^2-6x-5x+15\\\\2x^2-11x+15[/tex]

Answer:

Step-by-step explanation:

The statistical procedure that would be best to use for this study is the two-sample t test.

We were interested in determining if there were differences in the average prices of items at two local supermarkets. We randomly picked six items to compare at both supermarkets. We need to identify the statistical procedure that would be best to use for this study.

Statistics is the study of data gathering, organization, analysis, interpretation, and presentation. It is customary to begin with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.

The statistical procedure that would be best to use for this study is the two-sample t test because determining if there were differences in the average prices among two local supermarkets.

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The percent that Marie will earn during her training is 66.67%.

What is percentage?

Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given,

She earns working in new job = $15

She earns while training = $10

percentage she will earn during her training

= earing during training/earning during job multiplied by 100.

= 10/15(100)

=66.67%

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First three terms of sequence are 25,22,19 and first negative term of the sequence is -2.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The nth term of a sequence is 25 - 3n

Twenty five minus three times of n.

25 - 3n

the first three terms are

the first term is 25

25-3=22

25-6=19

25-9=16

The first three terms are 25,22,19.

25-3(9)=25-27=-2

The first negative term of the sequence is -2.

Hence, first three terms of sequence are 25,22,19 and first negative term of the sequence is -2.

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The cartons hold 1305 blocks.

What are Comparing quantities?

- Finding an unknown quantity that has a relationship with a certain condition associated to it is the process of comparing quantities.

- One or more quantities with their units will be provided to us, and we will   be required to determine the value of the same quantity in other units (i.e.  in higher values or in lower values).

We given that,

A carton holds 87 blocks.

It means, 1 carton holds = 87 blocks

So find 15 cartons holds how much of blocks.

15 cartons holds = 15 * 87

                            = 1305 blocks

Hence, we can say that the cartons hold 1305 blocks.

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The table of solutions to the given Linear Equation, be

x     0     1     2     3     4

y     1      7    13    19    25

Given, a linear equation

y = 6x + 1

the table of solutions to the given equation, be

x     0     1     2     3     4

y     1      7    13    19    25

as, when x = 0,

y = 6(0) + 1

y = 1

when x = 1,

y = 6(1) + 1

y = 7

when x = 2,

y = 6(2) + 1

y = 13

when x = 3,

y = 6(3) + 1

y = 19

when x = 4,

y = 6(4) + 1

y = 25

Hence, the table of solutions to the given Linear Equation, be

x     0     1     2     3     4

y     1      7    13    19    25

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If the given net was folded into a cube, the number that would be opposite of 1 would be number 6.

If the net was folded into a cube, it would be done such that 1 would be at the bottom of the cube. 4 and 3 would raised to be on the sides of the cube. 2 and 5 would also be raised as well. This would then put 6 on the top of the dice.

With 6 being on top of the dice, this means that it would be the opposite of 1 which is at the bottom. 3 and 4 would be opposites and 5 and 2 would be opposites.

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Yes, the LCM changed for the two terms. Because there is no common term in the 3 and 8.

It is defined as the common number of two integers, which is the lowest number that is a multiple of two or more numbers. The full name of LCM is the least common multiple.

It is given that Pedro finds applesauce that comes in packages of 8, but now he finds juice bottles only in packages of 3.

The factor of 8,

8=2×2×2×1

The factor of 3,

3=3×1

There are no common terms in both the given integers as a result the LCM changes.

Thus, the LCM changed for the two terms. Because there is no common term in the 3 and 8.

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Answer:

Step-by-step explanation:

Based on the information, the two integers are 30 and 31.

Let the first integer be x. The second consecutive integer will be (x + 1).

So, the smaller integer = 2x

The larger integer = 3(x + 1)

Their sum = 153

Forming the equation now -

2x + 3(x + 1) = 153

Performing multiplication on Left Hand Side of the equation

2x + 3x + 3 = 153

Performing addition on Left Hand Side of the equation

5x = 153 - 3

Performing subtraction on Right Hand Side of the equation

5x = 150

x = 150/5

Performing division on Right and Side of the equation

x = 30

Smaller integer = 30

Large integer = 30 + 1

Large integer = 31

Thus, the two integers are 30 and 31.

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The center of the circle is (6,7) and the radius of the circle is 1.414 units

The diameter with endpoints = (5, 8) and (7, 6)

The mid point of the diameter = The center of the circle

The center of the circle = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Substitute the values in the equation

The center of the circle = ( (5+7)/2 , (6+8)/2 )

= (12/2 , 14/2)

= (6, 7)

The radius of the circle = The distance between (6, 7) and (7, 6)

The distance between two points = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The distance between (6, 7) and (7, 6) = [tex]\sqrt{(7-6)^2+(6-7)^2}[/tex]

= [tex]\sqrt{1^2+(-1)^2}[/tex]

= [tex]\sqrt{1+1}[/tex]

= [tex]\sqrt{2}[/tex]

= 1.414 units

Hence, the center of the circle is (6,7) and the radius of the circle is 1.414 units

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The number of waffles can be made from 15 eggs are, 20 waffles.

the waffles can be calculates as follows

4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles

we need 6 eggs to make 8 waffles

So, the waffles can we make from 15 eggs = [tex]\frac{8}{6} X 15 = 20[/tex] waffles

Hence, the number of waffles can be made from 15 eggs are 20 waffles.

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Answer:

I think C is correct

Step-by-step explanation:

I am not really sure

The greatest number of 150-kilogram crates that can be loaded into the shipping container are 138

Greatest weight that can be loaded = 27500 kilograms

Weight of each crate = 150 kilogram

Weight of other shipments = 6800 kilograms

Let c be the greatest number of 150 kilogram crates that can be loaded.

The required inequality

27500 ≥ 6800 + 150c

27500 - 6800 ≥ 150c

20700 ≥ 150c

c ≥ 20700/150

c ≥ 138

Hence, the maximum number of crates are 138.

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The simplified form of given radical expression :

1) √216k⁴ = 6√6k²

2) √28x³y³ = 2xy√(7xy)

3) √192n³ = 8n√(3n)

4)∛40n² = 2∛n²n^(2/3)

5) ∛216x³ = 6x

6) ⁴√128x⁶y⁸ =  2xy8^(1/4)√(yx)

7) √252a³b^4 = 6ab²√(7a)

We need to solve given radical expressions.

1) √216k⁴

= √216 × √k⁴

= √(6 × 36) × √(k²)²

= 6√6 × k²

= 6√6k²

2) √28x³y³

= √(7 * 4) × √x³ × √y³

= 2√7 * x√x * y√y

= 2√7 * xy√(xy)

3) √192n³

= √(64 × 3) * √n³

= 8√3 * n√n

= 8n√(3n)

4)∛40n²

= ∛(8 × 5) * ∛n²

= ∛2³ * ∛5 * ∛n²

= 2∛n²n^(2/3)

5) ∛216x³

= ∛216 * ∛x³

= ∛6³ * ∛x³

= 6 * x

= 6x

6) ⁴√128x⁶y⁸

=  ⁴√128 *  ⁴√x⁶ *  ⁴√y⁸

= ⁴√(16 × 8) *  x(⁴√x²) *  y(⁴√y²)

= 2 * 8^(1/4) * xy (x²y²)^(1/4)

=  2xy8^(1/4)√xy

7) √252a³b^4

= √(36 × 7) * √a³ * √b^4

= 6√7 * a√a * b²

= 6ab²√(7a)

Therefore, the simplified form of given radical expression :

1) √216k⁴ = 6√6k²

2) √28x³y³ = 2xy√(7xy)

3) √192n³ = 8n√(3n)

4)∛40n² = 2∛n²n^(2/3)

5) ∛216x³ = 6x

6) ⁴√128x⁶y⁸ =  2xy8^(1/4)√(yx)

7) √252a³b^4 = 6ab²√(7a)

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Answer:

A. x = 13

B. x = 1

And the next equation answers are:

C. x = 1-5√2

D. x = 1+5√2

Step-by-step explanation:

Just took it. Edg 2020. Hope this helps :)

Answer:

brand b is the better buy, brand a unit price is 0.0427, and brand b is 0.0346

Step-by-step explanation:

hope it helped :)