Write the set and set build a notation and an interval notation

Answer:

It is better to buy 8 eggs for 12 rupees.

Step-by-step explanation:

21/12 = 1.75

It cost 1.75 rupees per egg.

12/8 = 1.5

It costs 1.5 rupees per egg.

Answer:

John will run out of toner cartridges first

Step-by-step explanation:

First, find how many sheets he can print with the 3 toner cartridges:

3(2000)

= 6000 sheets of paper

Find how many sheets of paper he has:

15(500)

= 7500 sheets of paper

Since 6000 is less than 7500, John will run out of toner cartridges first.

Answer: Read the step by step explanation for the answer

Step-by-step explanation:

We can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the given point (4, 3) and the origin (0, 0):

r = √(4² + 3²) = 5

Then we can use the coordinates of the point (4, 3) to determine the values of the trigonometric functions:

sin(θ) = opposite/hypotenuse = 3/5

cos(θ) = adjacent/hypotenuse = 4/5

tan(θ) = opposite/adjacent = 3/4

csc(θ) = hypotenuse/opposite = 5/3

sec(θ) = hypotenuse/adjacent = 5/4

cot(θ) = adjacent/opposite = 4/3

Therefore, the values of the six trigonometric functions of θ are:

sin(θ) = 3/5

cos(θ) = 4/5

tan(θ) = 3/4

csc(θ) = 5/3

sec(θ) = 5/4

cot(θ) = 4/3

Answer:

Step-by-step explanation:

The term "for every" is a ratio indicator, meaning that every single time you use or do one thing then you must also do or use another thing. In this scenario, it is stating that every single time that you add a single cup of butter to the cookie recipe then you must also add three cups of flower to that recipe. This ratio always maintains its proportions meaning that if you add 2 cups of butter to the recipe you would need to add six cups of flower.

a. The mass remaining after t years, 130 is the initial mass, and 30 is the half-life of cesium-137.

b.  About 19.35 mg of the sample will remain after 100 years.

c.  After about 330 years, only 1 mg of the sample will remain

(a) The mass remaining after t years can be found using the formula:

\(y(t) = 130 * 2^(-t/30)\)

where y(t) represents the mass remaining after t years, 130 is the initial mass, and 30 is the half-life of cesium-137.

(b) To find how much of the sample remains after 100 years, we can substitute t = 100 into the formula:

\(y(100) = 130 * 2^(-100/30) = 19.35 mg\)

Therefore, about 19.35 mg of the sample will remain after 100 years.

(c) We need to solve the equation y(t) = 1 for t. Substituting y(t) and solving for t, we get:

\(1 = 130 * 2^(-t/30)\)

\(2^(-t/30) = 1/130\)

\(-t/30 = log2(1/130)\)

\(t = -30 * log2(1/130) = 330 years\)

Therefore, after about 330 years, only 1 mg of the sample will remain.

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a) The decay of cesium-137 can be modeled by the function \(y(t) = 130 * 2^{(-t/30)\)

b) after 100 years, only about 31.57 mg of the sample remains.

c) after about 207.1 years, only 1 mg of the sample will remain.

(a) The decay of cesium-137 can be modeled by the function \(y(t) = 130 * 2^{(-t/30)\), where t is the time in years and y(t) is the remaining mass of the sample in milligrams.

To find the mass that remains after t years, we simply plug in the value of t into the function:

\(y(t) = 130 * 2^{(-t/30)\)

(b) To find the amount of the sample that remains after 100 years, we plug in t = 100:

\(y(100) = 130 * 2^{(-100/30)\) ≈ 31.57 mg

So after 100 years, only about 31.57 mg of the sample remains.

(c) To find the time it takes for only 1 mg to remain, we set y(t) = 1 and solve for t:

\(1 = 130 * 2^{(-t/30)}\\\\2^{(-t/30)} = 1/130\)

Taking the natural logarithm of both sides, we get:

\(ln(2^{(-t/30)}) = ln(1/130)\)

Using the logarithmic identity \(ln(a^b) = b * ln(a)\), we can simplify the left side:

(-t/30) * ln(2) = ln(1/130)

Solving for t, we get:

t = -30 * ln(1/130) / ln(2) ≈ 207.1 years

So after about 207.1 years, only 1 mg of the sample will remain.

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The dimensions of the 12 by 12 yd office where the coverings is sold in square meters, will require 121 m^2 of coverings

The dimensions of the office is; A 12 yd by 12 yd.

Therefore, the area of the office, A is found as follows;

A = 12 yd × 12 yd = 144 yd^2

Using unit conversion factors, we have;

1 yd^2 = 0.836127 m^2

Therefore;

144 yd^2 = 144 × 0.836127 m^2 = 120.402 m^2

Given that the floor covering is sold in square meters, the number of square meters she will need is obtained by rounded to the next whole number, which is; 121 m^2.

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Answer:

I think is

2

-2(x +20x-100)

Answer:

53%

Step-by-step explanation:

Answer:

X = 6.

7 + X - 2 = 11

(9 + x) x 3 = 45

Answer:

Yes, a(b)+a(c) is the same as a(b+c)

Step-by-step explanation:

a(b)+a(c) is the same as a(b+c). We call it distributive property in math.

Answer:

1.5 x 10 ^4

Step-by-step explanation:

Answer:

1.5 x 10 ^4

Step-by-step explanation:

hello hope this helps

Answer:

x = 200

Step-by-step explanation:

substitute y = 15 into the equation

\(\frac{1}{5}\) x - (\(\frac{2}{3}\) × 15) = 30

\(\frac{1}{5}\) x - (2 × 5) = 30

\(\frac{1}{5}\) x - 10 = 30 ( add 10 to both sides )

\(\frac{1}{5}\) x = 40 ( multiply both sides by 5 to clear the fraction )

x = 5 × 40 = 200

Answer:

2j-20

Step-by-step explanation:

Multiply 2 into the parenthesis. So 2(j) -2(10).

This equals 2j-20.

Answer:

3. $3 + (5 * $3) = a, that is the answer

If an angle measures 90 degrees, it must be a right angle.

What is a right-angled triangle?

A right-angled triangle is a triangle that has one angle that measures exactly 90 degrees. This angle is called the right angle. The other two angles in the triangle are both acute angles, which are angles that measure less than 90 degrees.

In this case, the hypothesis is that the angle measures 90 degrees, and the conclusion is that the angle is a right angle. The conclusion follows logically from the hypothesis because, by definition, a right angle is an angle that measures exactly 90 degrees.

Hence, if an angle measures 90 degrees, it must be a right angle.

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Given:

The number of students vote is 10+15+10=35

Number of flavors are 3.

a) The probability that the student voted for chocolates.

Number of possibilities= 15.

Answer: 3/7

b) The probability that the student voted for vanilla.

Answer: 2/7

c) The probability that the student voted for chocolate or strawberry .

Answer: 5/7

d) The probability that the student voted for vanilla or chocolate .

Answer: 5/7

The series is given as

3,12,21..........

The first term is 3 .

To determine the common difference, subtract second term frim te

Answer:

$23.8 million

Step-by-step explanation:

w = previous weekends earnings

16.2 = .68w

x = 16.2/0.68

x = 23.8

Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

B

Step-by-step explanation:

We have to find which trinomial has:

1) two terms that are the perfect square of two numbers

2) a terms that is the double product of the two numbers

the first condition is satisfied by A and B, but only B satisfied the second., in fact the trinomial can be rewrite as: (2a-5)^2

Options C and D are traps because the square of a number can’t be negative

Answer:

       5/6 or 4/6

Step-by-step explanation:

6-2=

4/6 -with out two

5/6 -including two

The required general solution is:

y(x) = eˣ(C₁cos 3x + C₂sin 3x) - 1/8 sin(3x) + 3/8 cos(3x),

where C₁ and C₂ are constants.

The given differential equation is y'' - 2y' + 8y = 3 sin (3x)

The characteristic equation is obtained by assuming a solution of the form \(y = e^{(rt)\)

Let's solve the characteristic equation to get the homogeneous solution:

r² - 2r + 8 = 0

r = (-b ± √b² - 4ac) / 2a r

= (2 ± √(- 60)) / 2r

= 1 ± 3i

After solving the homogeneous equation, the roots of the characteristic equation are complex.

So the homogeneous solution is given by:

y(x) = eˣ(C₁cos 3x + C₂sin 3x)

The particular solution is obtained using the method of undetermined coefficients.

Let's assume that the particular solution is of the form:

Yp(x) = a sin(3x) + b cos(3x)

We get Yp(x) = - 1/8 sin(3x) + 3/8 cos(3x)

Therefore, the general solution is given by:

y(x) = eˣ(C₁cos 3x + C₂sin 3x) - 1/8 sin(3x) + 3/8 cos(3x)

Hence, the required general solution is:

y(x) = eˣ(C₁cos 3x + C₂sin 3x) - 1/8 sin(3x) + 3/8 cos(3x),

where C1 and C2 are constants.

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Answer:

91

Step-by-step explanation:

PEMDAS rules apply...so addition then subtraction

Using the Heaviside cover-up method, we can evaluate the integral of 12(x + 5) / (x - 21) with respect to x. The exact answer is -12ln|x - 21| + 12x + 60ln|x - 21| + C, where C represents the constant of integration.

To evaluate the integral using the Heaviside cover-up method, we first decompose the rational function into partial fractions. We can rewrite the given expression as follows:

12(x + 5) / (x - 21) = A/(x - 21) + B

To find the values of A and B, we multiply both sides of the equation by the denominator (x - 21):

12(x + 5) = A + B(x - 21)

Next, we substitute x = 21 into the equation to eliminate B:

12(21 + 5) = A

Simplifying, we find A = 312.

Now, substituting A back into the equation, we can solve for B:

12(x + 5) = 312/(x - 21) + B

To eliminate A, we multiply both sides by (x - 21):

12(x + 5)(x - 21) = 312 + B(x - 21)

Expanding and simplifying, we get:

12x^2 - 252x + 60x - 1260 = 312 + Bx - 21B

12x^2 - 192x - 972 = Bx - 21B

Matching the coefficients of x on both sides, we find B = -12.

With the partial fraction decomposition, we can rewrite the integral as:

∫ [A/(x - 21) + B] dx = ∫ (312/(x - 21) - 12) dx

Evaluating each term individually, we get:

∫ 312/(x - 21) dx - ∫ 12 dx = 312 ln|x - 21| - 12x + C

Simplifying further, the exact answer is -12ln|x - 21| + 12x + 60ln|x - 21| + C, where C represents the constant of integration.

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It can be seen that the mistake that was made by Marvin was on line 1.

2x² - 8x + 5.... move the 5 to the other side

2x² - 8x = -5

Now divide by 2

x² - 4x = -5/2

x² - 4x + 4 = -5/2 + 4

(x - 2)² = -5/2 + 8/2

(x - 2)² = 3/2

x - 2 = (+-)sqrt 3/2

x = 2 + sqrt 3/2 or x = 2 - sqrt 3/2

Therefore, he made his mistake on line 1.

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Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake. f(x) = 2x2 − 8x + 5. Line 1: f(x) = 2(x^2 − 8x) + 5 Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32 Line 3: f(x) = 2(x − 4)^2 − 27

The conclusion most likely supported by the data is that there is likely an association between the categorical variables because the relative frequencies are similar in value, with one being 0.48 and the other being 0.52.

The conclusion most likely supported by the data is:

There is likely an association between the categorical variables because the relative frequencies are both close to 0.50.

When the relative frequencies of two categorical variables are close in value, particularly around 0.50, it suggests that there might be an association between the variables. In this case, the relative frequencies are 0.48 and 0.52, which are relatively close and both near 0.50. This indicates that there may be a relationship or association between the two variables.

However, it's important to note that the conclusion is based on the similarity of relative frequencies alone, and further statistical analysis would be needed to establish a definitive association between the variables. Additional factors such as sample size, statistical tests, and domain knowledge would also contribute to a more comprehensive understanding of the relationship between the variables.

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Answer:

Step-by-step explanation:

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of 5 line pairs per millimeter (B).

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of B. 5 line pairs per millimeter.
Here's a step-by-step explanation:

1. The sampling frequency is given as 10 pixels per millimeter.
2. According to the Nyquist-Shannon sampling theorem, the maximum spatial frequency (in line pairs per millimeter) that can be accurately represented is half of the sampling frequency.
3. Divide the sampling frequency (10 pixels per millimeter) by 2: 10/2 = 5 line pairs per millimeter.

So, the answer is B. 5 line pairs per millimeter.

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