A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 10 centimeters to 40 centimeters?

Answer:

[tex]\huge\boxed{\sf r = 5}[/tex]

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

[tex]\rule[225]{225}{2}[/tex]

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

To determine the radius of each wheel, we can use the formula for the circumference of a circle:

Circumference = 2πr,

where "Circumference" represents the circumference of the wheel and "r" represents the radius of the wheel.

Given that the circumference of each wheel is 22 inches, we can set up the equation as follows:

22 = 2πr.

To solve for the radius, we'll isolate "r" by dividing both sides of the equation by 2π:

22 / (2π) = r.

Using a calculator for the approximation, we get:

r ≈ 3.5 inches.

Therefore, to the nearest length, the radius of each wheel is approximately 3.5 inches.

Answer:

C) 3.5 inch

Step-by-step explanation:

Answer:
To find the volume of a cone with radius 9 feet and height 4 feet, we can use the formula:

V = (1/3) * π * r^2 * h

Plugging in the values:

V = (1/3) * π * (9^2) * 4

Calculating:

V = (1/3) * π * 81 * 4

V ≈ 108.19 cubic feet

Therefore, the volume of the cone is approximately 108.19 cubic feet (rounded to two decimal places)

" Sum of area of Trapezoid and Semicircle "

its " 1/2 times (sum of parallel sides) times (perpendicular distance between them) "

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times ( 8+ 12) \times (5.5)[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times (20) \times (5.5)[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 10 \times 5.5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 55 \: \: cm {}^{2} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi {r}^{2} }{2} [/tex]

[tex] \textsf{[ diameter (d) = 8 cm, radius (r) = d/2 = 8/2 = 4 cm ]} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{3.14 \times ( {4)}^{2} }{2}[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 1.57 \times 16[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 25.12 \: \: cm {}^{2} [/tex]

- Area of Trapezoid + Area of Semicircle

[tex]\qquad\displaystyle \tt \dashrightarrow \: 55 + 25.12 = 80.12 \: cm²[/tex]

Traveling the world is a popular dream for many people, including students. While there is no way to know for sure what the probability is that a sophomore student will travel the world, there are some factors that may influence their likelihood of doing so.

For example, students who have access to financial resources and support from their families may be more likely to travel than those who don't. Additionally, students who are studying subjects that are related to travel, such as international relations, may be more interested in exploring the world.

There are also other factors that can influence a student's travel plans, such as personal preferences, cultural background, and availability of opportunities. Ultimately, the decision to travel the world is a personal one that depends on a wide range of factors.

In summary, there is no definitive answer to the question of what the probability is that a sophomore student will travel the world. However, there are many factors that can influence their likelihood of doing so.

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"dom(R) ⊂ UU R" means that the domain of relation R is a subset of the universal set associated with relation R

The notation "dom(R) ⊂ UU R" refers to the domain of a relation R being a subset of the universal set U.

Let me help you to break it down

1. dom(R): This represents the domain of the relation R. The domain of a relation is the set of all elements that appear as the first component in any ordered pair of the relation.

2. ⊂: This symbol indicates a subset relationship, meaning that the set on the left-hand side is a subset of the set on the right-hand side. In this case, "dom(R) ⊂ U" implies that the domain of relation R is a subset of the universal set U.

3. "UU R": The term "UU R" likely represents the universal set associated with relation R. It indicates the set that contains all possible elements that can be related by R.

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Using the proportion principle , Orange Juice has a greater percentage of water than Apple juice

To determine which juice has a greater percent of water, we need to calculate the percentage of water in each juice.

Percentage of water = (Water content / Total content) * 100

Water content = 32 ounces

Total content = 80 ounces

Percentage of water in apple juice = (32 / 80) * 100 = 40%

Water content = 48 ounces

Total content = 64 ounces

Percentage of water in orange juice = (48 / 64) * 100 = 75%

Comparing the percentages, we can conclude that orange juice has a greater percentage of water (75%) than the apple juice (40%).

Therefore, the orange juice contains a higher percentage of water.

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Complete question :

an 80 ounce bottle of apple juice contains 32 ounces of water a 64 ounce bottle of orange juice has 48 ounces of water which juice has a greater percent of water

Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

Let's denote the total number of books on the shelf as 'total_books', and the number of new books as 'new_books'.

The number of used books can be calculated as the difference between the total number of books and the number of new books:

used_books = total_books - new_books

To find the ratio of used books to all books on the shelf, we divide the number of used books by the total number of books:

Ratio of used books to all books = used_books / total_books

Substituting the expression for used_books, we have:

Ratio of used books to all books = (total_books - new_books) / total_books

Simplifying further:

Ratio of used books to all books = 1 - (new_books / total_books)

Therefore, the ratio of used books to all books on the shelf is equal to 1 minus the ratio of new books to total books.

Answer: The Mode

Step-by-step explanation:

The mode is the data value that occurs the most often in a data set

The required reverse Euclidean algorithm is the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Given that (5*x) mod 91 =32.

To solve the modular equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular inverse of 5 modulo 91.

Consider  (5*x) mod 91 =32.

5x = 32(mod 91)

Apply the Euclidean algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in congruence form,

1 = 91 - 18 *5

On simplifying the equation,

1 = 91 (mod 5)

The modular inverse of 5 modulo 91 is 18.

Multiply equation by 18 on both sides,

90x = 576 (mod91)

To obtain the smallest positive  solution,

91:576 = 6 (mod 91)

Divide both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the Euclidean algorithm,

91 = 1*90 + 1.

Simplify the equation,

1 + 1 mod (90)

The modular inverse of 90 modulo 91 is 1.

Substitute the modular inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

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As per the given data, the area of the rectangular field is approximately 204 square meters.

To find the area of the rectangular field, we need to multiply its length by its width.

Given that the length is 18 2/5 m and the width is 11 2/23 m, we need to convert these mixed fractions into improper fractions for easier calculation.

Length: 18 2/5 m = (5 * 18 + 2)/5 = 92/5 m

Width: 11 2/23 m = (23 * 11 + 2)/23 = 255/23 m

Now, we can calculate the area of the rectangular field:

Area = Length * Width

     = (92/5) m * (255/23) m

     = (92 * 255)/(5 * 23) m^2

     = 23460/115 m^2

     = 204 m^2 (rounded to the nearest whole number)

Therefore, the area of the rectangular field is approximately 204 square meters.

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Your question seems incomplete, the probable complete question is:

A rectangular field is 18 2/5 m long and 11 2/23 m wide. Find its area. ​

Answer: C

Step-by-step explanation:

|-8| = 8

We can deduce here that in the diagram the ratios  AD : DB  and  AE : EC  are equal.

Triangles that resemble one another but may differ in size are said to be similar triangles. They have equal corresponding angles and proportional corresponding sides, in other words.

Two triangles are similar if and only if the following conditions are met:

The corresponding sides of two triangles that are comparable are proportionate. The length of the comparable side in the other triangle can be obtained by multiplying the length of a side in one triangle by the same factor.

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The answer to this question: B

The solution to the given differential equation is y(x) = (C1 + C2x) * e^(3x), where C1 and C2 are arbitrary constants.

To solve the given differential equation, we need to find the function y(x) that satisfies the equation:

(D^2 - 6D + 9)y(x) = 0,

where D represents the differentiation operator.

Let's break down the solution process step by step:

Characteristic Equation

First, we'll find the characteristic equation associated with the given differential equation. For a second-order linear homogeneous differential equation of the form aD^2y + bDy + cy = 0, the characteristic equation is obtained by replacing D with λ:

λ^2 - 6λ + 9 = 0.

Solving the Characteristic Equation

Now, we solve the characteristic equation to find the values of λ. Factoring the equation, we get:

(λ - 3)^2 = 0.

From this, we see that λ = 3 (with a multiplicity of 2).

General Solution

The general solution of the differential equation is given by:

y(x) = C1e^(λ1x) + C2xe^(λ2*x),

where C1 and C2 are arbitrary constants, and λ1, λ2 are the distinct roots of the characteristic equation.

In our case, since we have repeated roots, the general solution simplifies to:

y(x) = C1e^(3x) + C2xe^(3*x).

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The average fourth grader is about three times as tall as the average newborn baby. If babies are on average 45 cm 7 mm when they are born,  137 cm 1 mm is the height of the average fourth grader.

Given information,

Baby height is typically 45 cm. 7 mm 45 cm Since there are 10 millimeters in a centimeter, 7 mm is equal to 45.7 cm.

Assume that a fourth-grader is x inches tall.

The average height of a newborn baby (x) = 3 times the height of a fourth-grader.

A fourth-grader's height (x) is equal to 3 x 45.7.

A fourth-grader's height is equal to (x)=137.

Fourth-grader height (x) = 137 cm 1 millimeter

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Using the compound interest formula,  the interest after one month is $1300

The compound interest formula is given by A = P(1 + r)ⁿ where

Now, since y borrow $25,000 at an interest rate of 5.2% compounded monthly and your monthly payment is $231.49. To find  the interest accrued in the first month, we proceed as follows.

So, in the compound interest formula, we have that

So, to find the amount after one month, we substitute the values of the variables into the equation. So, we have that

A = P(1 + r)ⁿ

A = 25000(1 + 0.052)¹

A = 25000(1.052)

A = 26300

So, the interest after one month is I = A - P

= $26300 - $25,000

= $ 1300

So, the interest is $1300

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In the excerpt, Li's crush gave his girl   friend a rose. The text states: Li's crush gave his girl   friend a rose. She was so happy!

Li's mother was upset about the gift later because she thought it was too expensive.

The text states: Li's mother was upset when she found out how much the rose cost. She thought it was too much money to spend on a gift.

Li's mother's reaction is understandable. Roses are expensive flowers, and it is possible that Li's mother did not have the money to spend on such a gift. However, it is also important to remember that Li's crush was trying to do something nice for his girl friend, and the rose was a symbol of his love for her. In the end, it is up to Li and his girl friend to decide whether or not the rose was worth the money.

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This is not a question. Next time, please add a question so that others might be able to help you with it

The best representation of the number of tiles that will be needed to cover the Floor is 80 tiles.

The number of tiles needed to cover the floor, we can calculate the total area of the floor and divide it by the area of each tile.

The area of the floor is given by the product of its length and width: 15 feet * 12 feet = 180 square feet.

The area of each tile is given by the product of its length and width: 1.5 feet * 1.5 feet = 2.25 square feet.

To find the number of tiles needed, we divide the total area of the floor by the area of each tile:

Number of tiles = (Total area of the floor) / (Area of each tile) = 180 square feet / 2.25 square feet = 80 tiles.

therefore, the best representation of the number of tiles that will be needed to cover the floor is 80 tiles.

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Answer:

Step-by-step explanation:

To find the measure of angle A

a = 30°

b = 180-135 = 45°

total angle inside triangle = 180°

x = 180-(30+45) = 105°

The values of the variables are y = 102° and z = 23°.

Given that are two parallel lines j and m we need to find the measures of the variables y and z,

So,

Since, j║m, therefore, y and 78° are supplementary because they are exterior consecutive angles between two parallel lines,

So,

y + 78° = 180°

y = 180° - 78°

y = 102°

Now,

y and (4z-14) are linear pair angles, which means they are also supplementary.

Therefore,

y + (4z-14) = 180°

102° + 4z - 14 = 180°

4z + 88 = 180°

4z = 92°

z = 23°

Hence the values of the variables are y = 102° and z = 23°.

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The regression equation is: y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

To compute the regression equation based on the given data, we can use the formulas for slope (b1) and y-intercept (bo):

b1 = (NΣXY - ΣXΣY) / [tex](N\sum X^2 - (\sum X)^2)[/tex]

bo = (ΣY - b1ΣX) / N

Where:

N = Number of data points (in this case, 11)

ΣX = Sum of all X values (prices)

ΣY = Sum of all Y values (average number of pounds sold per day)

ΣXY = Sum of the product of X and Y values

[tex]\sum X^2[/tex] = Sum of the squares of X values

Using the provided data:

Ex = 210

Xy = 450

Zcy = 10387

Zz = 7275

Xy = 42471

Let's calculate the required values:

N = 11

ΣX = Ex + Zcy + Zz = 210 + 10387 + 7275 = 17872

ΣY = Xy = 450

ΣXY = Xy = 450

[tex]\sum X^2 = (Ex)^2 + (Zcy)^2 + (Zz)^2 = (210)^2 + (10387)^2 + (7275)^2 = 239208144[/tex]

Now, substitute these values into the formulas to find b1 and bo:

[tex]b1 = (11 \times450 - 17872 \times 450) / (11 \times239208144 - (17872)^2)[/tex]

= -14112250 / 2050445128

≈ -0.0068824

bo = (450 - (-0.0068824 [tex]\times[/tex] 17872)) / 11

= (450 + 122.7790368) / 11

≈ 36.8881

Therefore, the regression equation is:

y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

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The complete question may be like:

Over a period of one year, retailer sells widgets at 11 different prices. He Calculates the average number of oiunds sold per day at each different price. From theese data, the following are calculated. Ex = 210, Xy = 450, Zcy = 10387, Zz? 7275 Xy? 42471 Compute the regression equation , SELEC A) y 0.20261x + 0.549951 B) y = 0.549951x + 30.410021 C) y = 0.20261. + 30.410021 D) none of these =b1x + bo.

The function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.

The given table is

Days After                        Number of

Release Date                   Games sold

       0                                   1024

       1                                     512

       2                                     256

       3                                     128

Here, the common ratio = 512/1024

= 1/2

The formula to find nth term of the geometric sequence is aₙ=arⁿ⁻¹. Where, a = first term of the sequence, r= common ratio and n = number of terms.

Here, [tex]G(t)= 1024(0.5)^{t-1[/tex]

Therefore, the function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.

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