Ms. Regan is making a circular quilt and wants to include a lace pattern


around the outside of the quilt. If the area of the quilt is 28. 26 square feet, how many feet of lace does Ms. Regan need to purchase? (Use 3. 14 for pi. )

The length of rectangle is (x - 5).

We are given-

Area of rectangle = \(x^{3} - 5x^{2} + 3x - 15\)

Width of rectangle = \(x^{2} + 3\)

Using the formula, the length will be calculated by rewriting the formula as -

Length = Area/width

Keep the values in formula to find the length of rectangle.

Length = \(\frac{x^{3} - 5x^{2} + 3x - 15}{x^{2} + 3}\)

In numerator, separating the common values and rewriting the equation -

Length = \(\frac{x^{2} (x - 5) +3 (x - 5)}{x^{2} + 3}\)

Rewriting the equation to for ease of solving to find the length of rectangle -

Length = \(\frac{(x^{2} +3)(x - 5)}{(x^{2} +3)}\)

Cancelling \((x^{2} + 3)\) as it is common in both numerator and denominator. Now, we will get the value of length of rectangle.

Length = (x - 5)

Hence, the length of rectangle is (x - 5).

The complete question is -

The area of a rectangle is \(x^{3} - 5x^{2} + 3x - 15\), and the width of the rectangle is \(x^{2} + 3\). If area = length × width, what is the length of the rectangle? x + 5 x – 15 x + 15 x – 5

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The probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

The standard deviation of the age of people who suffered heart attacks soon after using cocaine was 10 years. In a random sample of size 49, what is the probability the mean age at heart attack after using cocaine is greater than 42?We are given the following details:

The mean age of people in the study who suffered heart attacks soon after using cocaine was only 44.

Standard deviation = 10

Sample size = 49

Now we need to find the z-score using the formula:

z = (x - μ) / (σ / √n)

wherez is the z-score

x is the value to be standardized

μ is the mean

σ is the standard deviation

n is the sample size.

Substitute the values in the formula as given,

z = (42 - 44) / (10 / √49)z = -2 / (10/7)

z = -1.4

Probability of z > -1.4 can be found using the standard normal distribution table or calculator.

P(z > -1.4) = 0.9192

Therefore, the probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

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The veterinarian should charge the patient's owner a total of $100.00 for administering four vaccines, as each vaccine is priced at $25.00.

The veterinarian charges a fixed price of $25.00 for each vaccination administered. In this case, since the veterinarian administered four vaccines to the patient, the total charge can be calculated by multiplying the cost of one vaccine ($25.00) by the number of vaccines administered (4). Therefore, the veterinarian should charge the patient's owner a total of $100.00 for the four vaccinations.

To break it down further, each vaccination carries an individual cost of $25.00. When the veterinarian administers the first vaccine, the owner is charged $25.00. Similarly, for the second, third, and fourth vaccines, the charges remain the same, totaling $75.00. Adding up all these charges, the total amount comes to $100.00. Hence, the veterinarian should charge the patient's owner $100.00 for administering four vaccines.

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Answer:

x = 4

Step-by-step explanation:

For this problem, we simply need to convert the words into the left hand side of the equation and solve for x:

The quantity of implies a grouping

x plus 20 is the quantity

And we want the quantity over 2 all equal to 3x:

( x + 20 ) / 2  = 3x

( x + 20 )  = 6x

20 = 5x

4 = x

And now we can check to see if x is correct by plugging back into the equation:

( x + 20 ) / 2 = 3x

( (4) + 20 ) / 2 ?= 3(4)

( 24 ) / 2 ?= 12

12 == 12

Therefore, we have shown the value of x to be equal to 4.

Cheers.

Answer:

x+20/2=3x.

6x=x+20.

6x-x=20.

5x=20.

x=4.

Using Pythagorean theorem, the side of the ladder will reach 22.45 ft far up now.

Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.

c² = a² + b²

If a 45 foot ladder is set up against the side of a house so that it reaches up 27 feet, then the distance between the base of the ladder and the base of the side of the house is the difference between the square of the two values.

c = 45 ft

a = 27 ft

b² = c² - a²

b² = (45 ft)² - (27 ft)²

b² = 2025 - 729

b² = = 1296

b = 36 ft

If Latanya grabs the ladder at its base and pulls it 3 feet farther from the house, then the distance becomes b + 3 = 39 ft.

Using Pythagorean theorem, determine how far up the ladder is on the side of the house.

c = 45 ft

b = 39 ft

a² = c² - b²

a² = (45 ft)² - (39 ft)²

a² = 2025 - 1521

a² = 504

a = 6√14

a = 22.45 ft

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Answer:

y = 8/3x + 4

Step-by-step explanation:

slope = m = rise/run = (4 - (-4))/(0-(-3)) = 8/3

y = 8/3x + 4

Answer:

3x+2

Step-by-step explanation:

i had a test with the same question, i promise its right :)

After expanding logarithm is \(\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}\)

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa.

The basic form of the logarithm function can be written as  .

    \(log_ax =N\)

where, a is the base of function or equation

          x define expression

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

\(log_b\frac{\sqrt{x} \sqrt{3} }{y^2 \sqrt{6z^2} } \\\\= log_b \sqrt{x} \sqrt{3} - log_b {y^2 \sqrt{6z^2} }\\\\= log_b\sqrt{x} + log_b\sqrt{3} - log_by^2 - log_b \sqrt{6z^2} \\\\= \frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - \frac{1}{2} log_b{(6z^2)} \\\\=\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}\)

Thus, after expanding logarithm is \(\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}\)

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The finite difference approximation for a Neumann boundary condition, \(\left(\frac{df}{dx}\right)\), at node \(n\) (right boundary) to \(O(h^2)\) is given by

\(\left(\frac{df}{dx}\right)_n \approx \frac{f_{n-2} - 4f_{n-1} + 3f_n}{2h}\),

where \(f_{n-2}\), \(f_{n-1}\), and \(f_n\) represent the function values at nodes \(n-2\), \(n-1\), and \(n\) respectively, and \(h\) represents the spacing between the nodes.

To derive this approximation, we start with the Taylor series expansion of \(f_{n-1}\) and \(f_n\) around \(x_n\):

\(f_{n-1} = f_n - hf'_n + \frac{h^2}{2}f''_n - \frac{h^3}{6}f'''_n + \mathcal{O}(h^4)\),

\(f_{n-2} = f_n - 2hf'_n + 2h^2f''_n - \frac{4h^3}{3}f'''_n + \mathcal{O}(h^4)\).

By subtracting \(4f_{n-1}\) and adding \(3f_n\) from the second equation, we eliminate the first-order derivative term and retain the second-order derivative term. Dividing the result by \(2h\) gives us the desired finite difference approximation to \(O(h^2)\).

In conclusion, the finite difference approximation for a Neumann boundary condition, \(\left(\frac{df}{dx}\right)\), at node \(n\) (right boundary) to \(O(h^2)\) is \(\left(\frac{df}{dx}\right)_n \approx \frac{f_{n-2} - 4f_{n-1} + 3f_n}{2h}\). This approximation is obtained by manipulating the Taylor series expansion of \(f_{n-1}\) and \(f_n\) to eliminate the first-order derivative term and retain the second-order derivative term, resulting in a second-order accurate approximation.

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The surface area of the desktop cube photo frame with an edge length of 3.1 inches is 57.66 square inches.

As per the given information,

The edge length of a cube = 3. 1 inches

As we know that the surface area of a cube is:

To get the cube's total surface area, multiply the length of each face by the number of faces.

∴ SA = \(6s^2\)

Where,

s = length of one edge.

SA = surface area of a cube

By substituting the given value s = 3.1 inches into the formula,

we get:

SA = \(6(3.1)^2\)

SA = 6(9.61)

SA = 57.66 square inches

Hence, the surface area of the desktop cube photo frame with an edge length of 3.1 inches is 57.66 square inches.

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There are 24 possible arrangements that begin with letter R

Combinations are used to determine the number of selections of an item within another while permutation is used for arrangements

The arrangements of the digits is an illustration of factorials

The word is given as: SHREK

If the first letter begins with the letter R, then we have the following possible arrangements

The number of arrangement is the product of the above values

So, we have

Arrangement = 1 * 4 * 3 * 2 * 1

Evaluate

Arrangement = 24

Hence. there are 24 possible arrangements that begin with letter R

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Answer:

45 & 47

Step-by-step explanation:

Forming the equation,

→ x + (x + 2) = 92

→ 2x + 2 = 92

Now the value of x will be,

→ 2x + 2 = 92

→ 2x = 92 - 2

→ x = 90/2

→ [ x = 45 ]

Then the required integers are,

→ x = 45

→ x + 2 = 45 + 2 = 47

Hence, the integers are 45, 47.

The probability that a randomly selected student in my class does not read either of them is 0.20.

We are given that;

- A: the event that a student reads WSJ

- B: the event that a student reads NYT

- P(A) = 0.60, the probability that a student reads WSJ

- P(B) = 0.50, the probability that a student reads NYT

- P(A \cap B) = 0.30, the probability that a student reads both WSJ and NYT

Now,

We can plug these values into the formula and calculate the probability that a student reads at least one of them:

\($$P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.60 + 0.50 - 0.30 = 0.80$$\)

Therefore, the probability that a randomly selected student in my class reads at least one of them is 0.80.

To find the probability that a randomly selected student in my class does not read either of them, we can use the fact that the sum of all probabilities in a sample space is 1. So, we can subtract the probability of reading at least one of them from:

\($$P(\text{neither}) = 1 - P(A \cup B) = 1 - 0.80 = 0.20$$\)

Therefore, by probability the answer will be 0.20.

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The translation here will be:

Translate the circle M onto point P & dilating the image with a scale factor of PQ/MN.

A change in size or transformation of an object is necessary during dilatation. The objects are shrunk or expanded using the specified scale factor in this operation.

Pre-image refers to the initial figure, whereas the image is the new figure that results after dilatation. Two different types of dilation exist:

The word "expansion" describes the growth in size of an object.

Size reduction is referred to as contraction.

Here in the question,

Circle M is having a radius MN.

Circle P is having a radius PQ.

Given scale factor is PQ/MN.

In the attached figure, you can see:

First translate point M onto the point P, we now have the blue circle.

Now, dilating the blue circle by PQ/MN, we have the red circle P.

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Answer:

1. f

2. n

3. n

4. f

5. f

6. f

7. n

8. f

Answer:

k = 56

Step-by-step explanation:

2k + 68 = 180

2k = 112

112 ÷ 2 = 56

k = 56

Answer:

x ∠ -3

Step-by-step explanation:

To solve this inequality, we have to follow the steps below

open the bracket

collect like term

subtract and then divide both sides so that we can be left with just the variable

9(2x +1) < 9x - 18

opening the bracket, the equation becomes;

18x + 9  < 9x - 18

collect like terms, numbers with x variables on the left-hand side, and numbers standing alone on the right-hand side of the inequality

18x - 9x < -18-9  

9x <  -27

Divide both sides of the equation by 9

9x/9 < -27/9

x  < -3

Given:

Consider the given equation is:

\(p\div \sqrt{2}=\sqrt{\dfrac{t}{r+q}}\)

To find:

The value of t in terms of p, q and r.

Solution:

We have,

\(p\div \sqrt{2}=\sqrt{\dfrac{t}{r+q}}\)

It can be written as:

\(\dfrac{p}{\sqrt{2}}=\sqrt{\dfrac{t}{r+q}}\)

Taking square on both sides, we get

\(\dfrac{p^2}{2}=\dfrac{t}{r+q}\)

Multiply both sides by (r+q).

\(\dfrac{p^2(r+q)}{2}=t\)

Therefore, the required solution is \(t=\dfrac{p^2(r+q)}{2}\).

The area principle is a fundamental concept in data visualization that states that the size of a graphical element (such as a bar, a pie slice, or a bubble) should be proportional to the quantity it represents.

In other words, the area of the graphical element should accurately reflect the magnitude of the data it is displaying. This principle is particularly important when comparing quantities, as it allows the viewer to quickly and accurately perceive the relative differences between them. For example, if two bars in a bar chart have the same width but different heights, the viewer may be misled into thinking that the two quantities are closer in magnitude than they actually are.

The area principle is often applied in conjunction with other principles of good data visualization, such as using clear and simple designs, avoiding clutter, and choosing appropriate scales and units. The goal is to create visualizations that are not only aesthetically pleasing but also informative and effective in communicating the underlying data.

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9514 1404 393

Answer:

  5187

Step-by-step explanation:

At the end of 1 hour, the count is 2.5% greater than at the beginning.

  5060 + 2.5% × 5060 = 5060 +126.5 = 5186.5

The count at the end of the hour was about 5187.

Answer:

what kind?

Step-by-step explanation:

Answer:55

Step-by-step explanation:

55

Answer:

17×10^8 is greater

Step-by-step explanation:

The expontent comes first which gives you

1000000000 then you multiply that with 17 to get

1700000000

The greater number in 17 × 10⁸ and 4 × 10⁸ is,

⇒ 17 × 10⁸

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The numbers are,

⇒ 17 × 10⁸ and 4 × 10⁸

Now, We can write the numbers as;

⇒ 17 × 10⁸

⇒ 17,00,000,000

⇒ 4 × 10⁸

⇒ 4,00,000,000

Thus, The greater number in 17 × 10⁸ and 4 × 10⁸ is,

⇒ 17 × 10⁸

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The lowest point should be used for measurement. To acquire a correct reading, students must read the meniscus at eye level. In order to read the meniscus at eye level, students need first set the graduated cylinder on the table and then stoop.

A measuring cylinder, often referred to as a graded cylinder, a cylinder measuring cylinder, or a mixing cylinder, is a piece of lab apparatus used to gauge the quantity of fluids, chemicals, or solutions used during a typical lab session. Compared to common laboratory flasks and beakers, graduated cylinders offer higher precision and accuracy. The graduated cylinder is a scientific tool that employs the metric system rather than the American standard system, so measurements are made in millilitres rather than ounces. The volume of an object or quantity of liquid is measured using a graduated cylinder, a common piece of laboratory glassware. It is a glass cylinder with side markings resembling those on a measuring cup, as its name suggests.

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No, 3(5a + 9) + 5a and 4(5a+6) are not equivalent

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

To know if 3(5a + 9) + 5a and 4(5a+6) are equivalent, we simplify both expressions and see if they will have result

simplifying 3(5a + 9) + 5a;

by opening the parentheses

15a+27+5a

collecting like terms

20a+27

simplifying 4(5a+6);

by opening the parentheses,

20a + 24

Therefore 20a + 27 is not thesame as 20a+24. This means 3(5a + 9) + 5a is not equal to 4(5a+6).

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The one example of absolute value function is x =|y| , and the graph is sketched below .

What is Absolut value Function ?

The absolute value function is defined as a function in algebra that consists of the variable in the absolute value bars. The general form of absolute value function is written as f(y) = a |y - h| + k .

let the absolute value function be : x = |y|  ;

we put y = -1 , we get ⇒ x = 1  ;

we put y = 1 , we get ⇒ x = 1 ;

we put y = 0 , we get ⇒ x = 0 ;

from the above points we observe that , what ever we put in the function , the result "x" is always positive .

Therefore , the graph of the function x = |y| , is a V shaped graph that faces Right .

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Atmosphere and temperatures of 273 Kelvin and 298 Kelvin, along with a pressure of 1 kilopascal and a temperature of 273 Kelvin.


Standard conditions refer to a specific set of conditions, usually including a pressure of 1 atmosphere and a temperature of 0 degrees Kelvin, that are used to measure enthalpy changes. Under these conditions, the enthalpy change of a given reaction is known as the standard enthalpy of reaction (ΔH°). Other standard conditions used to measure enthalpy changes include a pressure of 1 atmosphere and temperatures of 273 Kelvin and 298 Kelvin, along with a pressure of 1 kilopascal and a temperature of 273 Kelvin.

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By using the method of implicit differentiation, the value of dx/dt is 0 when xy = 5, dy/dt = 1, and x = 3.

Taking the derivative of both sides of the equation xy = 5 with respect to t, we get

d/dt(xy) = d/dt(5)

Using the product rule on the left-hand side, we have:

x(dy/dt) + y(dx/dt) = 0

Substituting the given value of dy/dt = 1 and the given value of xy = 5, we have

3(dx/dt) + y(dx/dt) = 0

Substituting y = 5/x, we get

3(dx/dt) + (5/x)(dx/dt) = 0

Factoring out dx/dt, we have

dx/dt(3 + 5/x) = 0

Solving for dx/dt, we get

dx/dt = 0 when x ≠ -5/3

Substituting the given value of x = 3, we have

dx/dt = 0 when x ≠ -5/3 = 0

Therefore, the value of dx/dt when x = 3 is 0.

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Answer:

∠ ABC ≈ 78°

Step-by-step explanation:

using the Cosine rule in Δ ABC

cos ABC = \(\frac{a^2+c^2-b^2}{2ac}\)

where a is the side opposite ∠ A , b is the side opposite ∠ B and c the side opposite ∠ C

here a = BC = 6 , b = AC = 7 and c = AB = 5 , then

cos ABC = \(\frac{6^2+5^2-7^2}{2(6)(5)}\) = \(\frac{36+25-49}{60}\) = \(\frac{12}{60}\) , then

∠ ABC = \(cos^{-1}\) ( \(\frac{12}{60}\) ) ≈ 78° ( to the nearest degree )

Answer:

Step-by-step explanation:

The angle and its supplementary angle have a difference of 15.8°. To find the measures, we need to solve an equation.

Let's assume the measure of the angle is x°. The measure of its supplementary angle would be (180° - x°). According to the given information, x° = (180° - x°) - 15.8°.

Simplifying the equation, we have:
x° = 180° - x° - 15.8°
2x° = 164.2°
x° = 82.1°

Therefore, the angle measures 82.1° and its supplementary angle measures (180° - 82.1°) = 97.9°. The difference between these angles is indeed 15.8°, as stated in the problem.

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