which pair of numbers shows an integer and its opposite?
1 point
A.7 , -7
B.7 , 1/7
C.-7 , 1/7
D.1/7 , 1/7

For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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Yes, because\(np0 > 10\)and \(n(1-p0) > 10\).

Thus, the sampling distribution of p-hat is approximately normal, given the conditions of \(np0 > 10 and n(1-p0) > 10.\)

This is because the sampling distribution of p-hat follows the Central Limit Theorem, which states that when sample sizes are greater than 30,

the sampling distribution of the sample proportion will be approximately normal. The Central Limit Theorem is used in this example because the number of BYU students from Texas (n) is greater than 30, so the sample proportion (p-hat) is normally distributed.

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Answer:

(2x−3z)(3y−1)

Step-by-step explanation:
6xy-2x+3z-9zy
2x(2xy-1)+3z-9zy
2x(-1+3y)+3z(1-3y)

(2x−3z)(3y−1)

The probability that your survey will provide a sample proportion within 0.05 of the population proportion = 0.8818

Here,  people end up tossing 10% of what they buy at the grocery store

So, the probability of occurance P = 0.1

q = 1 - p

q = 1 - 0.1

q = 0.9

Also, the sample size (n) = 90

Now the standard error of the distribution of sample means would be,

s = \(\sqrt{\frac{p\times q}{n} }\)

s = 0.032

We need to calculate the probability that your survey will provide a sample proportion within 0.05 of the population proportion.

z₁ = (-0.05)/(0.032)

z₁ = -1.5625

z₂ = (+0.05)/(0.032)

z₂ = +1.5625

p(z-score between -1.5625 and +1.5625) = 0.8818

Therefore the required probability is 0.8818

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Answer:

The real numbers include natural numbers or counting numbers, whole numbers, integers, rational numbers (fractions and repeating or terminating decimals), and irrational numbers. The set of real numbers is all the numbers that have a location on the number line.

Step-by-step explanation:

The number k is equal to 60 when the top right angle at the intersection of the lines y and x is (2 k + 11) degrees and the bottom left angle is 131 degrees.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A mathematical expression is a sentence that includes numbers, variables, or both. The equal sign is never used in expressions. A mathematical statement stating the equality of two expressions is known as an equation.

Here,

Those two angles have the same measure. so you have,

2k+11=131

22k=120

k=60

The value of k where at the intersection of lines y and x, the top right angle is (2 k + 11) degrees and at the intersection of lines z and x, the bottom left angle is 131 degrees is 60.

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A quadratic equation is a polynomial equation of degree 2, which means the highest power of the variable is 2. It is generally written in the form: ax^2 + bx + c = 0. Option (d) x = -8, x = 8 is the correct answer.

The given equation is 15x^2 - 56 = 88 - 6x^2.

We need to find the values of x that are solutions to the given equation.

Solution: We are given an equation 15x² - 56 = 88 - 6x².

Rearrange the equation to form a quadratic equation in standard form as follows: 15x² + 6x² = 88 + 56  21x² = 144  

x² = 144/21 = 48/7

Therefore x = ±sqrt(48/7) = ±(4/7)*sqrt(21).

The values of x that are solutions to the given equation are x = -4/7 sqrt(21) and x = 4/7 sqrt(21).

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The given equation is 15x² - 56 = 88 - 6x². Values of x are solutions to the equation below 15x² - 56 = 88 - 6x² are x = -2.62, 2.62 or x ≈ -2.62, 2.62.

Firstly, let's add 6x² to both sides of the equation as shown below.

15x² - 56 + 6x² = 88

15x² + 6x² - 56 = 88

Simplify as shown below.

21x² = 88 + 56

21x² = 144

Now let's divide both sides by 21 as shown below.

x² = 144/21

x² = 6.86

Now we need to solve for x.

To solve for x we need to take the square root of both sides.

Therefore, x = ±√(6.86).

Therefore, the values of x are solutions to the equation below are x = -2.62, 2.62 or x ≈ -2.62, 2.62.

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True. Line graphs are not suitable for representing central tendencies and variation between categorical data.They are effective in showing changes and patterns in numerical data.

Line graphs are typically used to display trends over time or the relationship between two continuous variables. However, when it comes to categorical data, which consists of distinct categories or groups, line graphs are not appropriate for representing central tendencies and variation.

Central tendencies, such as the mean or median, are measures that describe the average or typical value within a set of data. Variation refers to the spread or dispersion of the data points. Categorical data does not have a natural numerical scale or order, making it difficult to determine central tendencies and variation using line graphs.

For categorical data, alternative graphical representations like bar charts, pie charts, or stacked column charts are more suitable. These graphs provide a visual representation of the frequencies or proportions of different categories, allowing for a better understanding of the distribution and comparison between categories. Such graphs are effective in capturing the central tendencies and variation in categorical data.

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Answer:

Step-by-step explanation:

7 - 3(-3) - 3(7) = 7 + 9 - 21 = 16 - 21 = -5

Answer:

-5

Step-by-step explanation:

(Refer to image)

Plug in the y and z and use order of operations to simplify!

Answer:

delaneys lunch is cheaper

Step-by-step explanation:

The acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

To find the acceleration of the particle at \(t = 2\) seconds, we need to differentiate the position function twice with respect to time. First, let's differentiate the position function \(s(t)\) once to find the velocity function \(v(t)\). Using the chain rule, we have:

\(\(v(t) = \frac{d}{dt}[(4t+1)^{3/2}]\)\)

To simplify the differentiation, we can rewrite the function as\(\(v(t) = (4t+1)^{3/2}\)\) . Applying the power rule, the derivative becomes:

\(\(v(t) = \frac{3}{2}(4t+1)^{1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(v(t) = 6(4t+1)^{1/2}\)\)

Next, we differentiate the velocity function \(v(t)\) to find the acceleration function \(a(t)\):

\(\(a(t) = \frac{d}{dt}[6(4t+1)^{1/2}]\)\)

Using the power rule again, we get:

\(\(a(t) = 6 \cdot \frac{1}{2}(4t+1)^{-1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(a(t) = 12(4t+1)^{-1/2}\)\)

Now we can find the acceleration at \(t = 2\) seconds by substituting \(t = 2\) into the acceleration function:

\(\(a(2) = 12(4 \cdot 2 + 1)^{-1/2}\)\)

\(\(a(2) = 12(9)^{-1/2}\)\)

Simplifying the expression, we have:

\(\(a(2) = \frac{12}{3} = 4\) cm/s²\)

Therefore, the acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

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Answer:

x=1.45

Step-by-step explanation:

4x+10+6x+13+2=180

10x+25=180

     -25    -25

10x=145

10x/10=145/10

x=14.5

The product of (6x+5)(6x-5) is 36x^2 - 25.

To find the product of (6x+5)(6x-5), we can use the rule for the product of the sum and difference of two terms, which states that the product of (a+b)(a-b) is equal to a^2 - b^2.

In this case, the terms are (6x+5) and (6x-5), where a = 6x and b = 5. Applying the rule, we have:

(6x+5)(6x-5) = (6x)^2 - 5^2

Simplifying further:

(6x)^2 - 5^2 = 36x^2 - 25

Therefore, the product of (6x+5)(6x-5) is 36x^2 - 25.

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The value of \(b=6\)

It is given that \(a\) varies directly to \(b\)

So, we can write \(a=kb\)  (\(k\) = constant)

We know that \(a=7\) when \(b=2\)

that is \(7= 2k\)

          \(k=\frac{7}{2}\)

so when \(a=21\)

                    \(a=kb\)

substitute the value of \(a\) and \(k\)

 that is     \(21=\frac{7}{2} b\)

                    \(b=6\)

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Answer:

Milk: \(4\frac{1}{2}\)

Flour: \(6\frac{3}{4}\)

Other ingredients: 4

Step-by-step explanation:

36 is 3 times as much as 12. To find how many cups of each ingredient are needed for 36 waffles, we can multiply each cup amount needed to make 12 waffles by 3.

---------------------------------------

\(1\frac{1}{2}\) × 3 = \(4\frac{1}{2}\)

\(2\frac{1}{4}\) × 3 = \(6\frac{3}{4}\)

\(1\frac{1}{3}\) × 3 = 4

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Raw data can be calculated by using mathematical operations such as addition, subtraction, multiplication, and division.

This can be done manually or by using a calculator or a computer program .Additionally, statistical methods such as mean, median, mode, and standard deviation can be used to calculate raw data.Raw data can also be manipulated in various ways. For example, data can be sorted, filtered, and organized into categories or hierarchies. Data can also be visualized in graphs, charts, and diagrams to make patterns and trends easier to identify. Statistical methods such as correlation and regression can also be used to analyze and interpret raw data. Additionally, data can be combined with other data sets to create new insights and relationships. Finally, machine learning and predictive analytics can be used to make predictions about future outcomes based on existing data.

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Answer:

\(\mathbf{6xe^xy+y^2e^x = C}\) which implies that C is the integrating factor

Step-by-step explanation:

The correct format for the equation given is:

\(y(6x+y +6)dx +(6x +2y)dy=0\)

By the application of the general differential equation:

⇒ Mdx + Ndy = 0

where:

M = 6xy+y²+6y

\(\dfrac{\partial M}{\partial y}= 6x+2y+6\)

and

N = 6x +2y

\(\dfrac{\partial N}{\partial x}= 6\)

∴

\(f(x) = \dfrac{1}{N}\Big(\dfrac{\partial M}{\partial y}- \dfrac{\partial N}{\partial x} \Big)\)

\(f(x) = \dfrac{1}{6x+2y}(6x+2y+6-6)\)

\(f(x) = \dfrac{1}{6x+2y}(6x+2y)\)

f(x) = 1

Now, the integrating factor can be computed as:

\(\implies e^{\int fxdx}\)

\(\implies e^{\int (1)dx}\)

the integrating factor = \(e^x\)

From the given equation:

\(y(6x+y +6)dx +(6x +2y)dy=0\)

Let us multiply the above given equation by the integrating factor:

i.e.

\((6xy+y^2 +6y)dx +(6x +2y)dy=0\)

\((6xe^xy+y^2 +6e^xy)dx +(6xe^x +2e^xy)dy=0\)

\(6xe^xydx+6e^xydx+y^2e^xdx +6xe^xdy +2ye^xdy=0\)

By rearrangement:

\(6xe^xydx+6e^xydx+6xe^xdy +y^2e^xdx +2ye^xdy=0\)

Let assume that:

\(6xe^xydx+6e^xydx+6xe^xdy = d(6xe^xy)\)

and:

\(y^2e^xdx +e^x2ydy=d(y^2e^x)\)

Then:

\(d(6xe^xy)+d(y^2e^x) = 0\)

\(6d (xe^xy) + d(y^2e^x) = 0\)

By integration:

\(\mathbf{6xe^xy+y^2e^x = C}\) which implies that C is the integrating factor

9514 1404 393

Answer:

  $2.563

Step-by-step explanation:

To find dollars per gallon, divide dollars by gallons.

  $34.60/(13.5 gal) ≈ $2.563 /gal

Michelle paid about $2.563 per gallon.

__

Additional comment

We have reported the price to the nearest 1/10th cent, as that is the way gas prices are usually posted.

Answer: 243

Step-by-step explanation: The length of a rectangle is three times its width. If the perimeter is 72cm, then the answer is 243  is the width of the rectangle?

Answer:

360

Step-by-step explanation:

120 = 1/3 x

120 x 3 = x

360 = x

The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3

from the question, we have the following parameters that can be used in our computation:

The pair of equations

By definition;

The slopes of perpendicular lines are opposite reciporcals

So, we have

(a) -1/3 and -3 false

(b) -3 and -6 false

(c) 3 and 3 false

(d) 1/6 and -6 true

Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3

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Answer:

It is D

Step-by-step explanation:

It is the only reasonable answer

Answer:

Step-by-step explanation:

-2x + 9 < x - 9                     Add 9 to both sides

-2x + 9 + 9 < x - 9 + 9        Combine

-2x + 18 < x                         Add 2x to both sides

-2x+2x + 18 < x + 2x           Combine

18 < 3x                                 Divide by 3

18/3 < 3x/3

6 < x

The relationship between the sides MN, MS, and MQ in the given regular heptagon is \(\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}\)

The area to be planted with flowers is approximately 923.558 m²

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

\(A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )\)

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

\(\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}\)

\(s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69\)

\(The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52\)

The area of the heptagon MNSRQPO is therefore;

\(A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94\)

\(MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08\)

By sine rule, we have

\(\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}\)

\(sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})\)

\(\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}\)

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

\(Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}\)

The area of the of the garden plated with flowers, \(A_{req}\), is given as follows;

\(A_{req}\) = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

\(A_{req}\)= 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, \(A_{req}\) ≈ 923.558 m²

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When an algorithm necessitates extensive sharing of instantaneous results, parallelism slows it down. Because there are multiple independent parallel processes and the right number of threads, parallelism will speed up an algorithm.

The ones with data dependencies are the most challenging. It will be exceedingly challenging, for instance, if you are dealing with a vector and the input for the computation at point n depends on the output at position n-1.

When this occurs, you must comprehend what the original algorithm is doing and take an alternative approach. For the aforementioned case, it might be a difficulty with digital signal processing including a feedback-containing digital filter. These are challenging to parallelize, but that is not the sole solution. Instead, you might use the filter and signal's fast Fourier transforms, multiply them, and then perform the inverse transform. All of these operations can be partially parallelized.

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\(f^2(3) = 576\)

Given:

\(f(x) = (x +2)^2 -1\)

Solving for \(f^2(3)\):

\(f^2(3) = (f(3))^2 \\ f^2(3) = (((3) +2)^2 -1)^2 \\ f^2(3) = ((3 +2)^2 -1)^2 \\ f^2(3) = ((5)^2 -1)^2 \\ f^2(3) = (25 -1)^2 \\ f^2(3) = 24^2 \\ f^2(3) = 576\)

To be 200% higher means, 200% higher is 3 times as strong.

In the given question, we have to explain what does it mean to be 150% of something.

A figure or ratio stated as a fraction of 100 is called a percentage. It is frequently indicated by the percent sign, "%."

When something gets 200% higher, you must also factor in its original 100% strength, which is expressed as follows:

200% + 100% = 300%

Additionally, keep in mind that "percent" refers to anything relative to 100, therefore we can rephrase the percentage as a number:

300% = 300/100 = 3

Therefore, something that is 200% higher is 3 times as strong.

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Answer:

4

Step-by-step explanation: