How many solutions does the equation −4y + 4y + 2 = 2 have?
a. Two
b. None
c. One
d. Infinitely many

The velocity of a particle = i + 2t j

The acceleration of a particle = 2 j

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

Here,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

We have to find, the velocity, acceleration, and speed of a particle with the given position function.

What is Velocity of a particle with the given position function?

The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.

Now,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

The velocity of a particle = \(\frac{d r(t)}{dt}\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

The acceleration of a particle = \(\frac{d^{2} r(t)}{dt^{2} }\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(\frac{d^{2} r(t)}{dt^{2} }= 2j\)

The speed of a particle = \(| \frac{d r(t)}{dt}| = |v(t)|\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(|v(t)|=\sqrt{1 + 4t^{2} }\)

Hence, The velocity of a particle = \(i + 2t j\)

The acceleration of a particle = \(2 j\)

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

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The kind of sample that consists of the same percentage of Asian-American students as the population it is taken from is called a representative sample.

A representative sample is a subset of a population that accurately reflects the characteristics and proportions of the entire population. In this case, the population consists of 15% Asian-American students. By selecting a sample that also consists of 15% Asian-American students, it can be considered a representative sample.

A representative sample is important in statistical research because it allows for generalizations and inferences to be made about the population based on the characteristics observed in the sample. Ensuring that the sample reflects the population proportions, it increases the likelihood of obtaining accurate and reliable results.

Choosing a representative sample is crucial to minimize bias and ensure the validity of the study's findings. It helps to avoid underrepresentation or overrepresentation of certain groups within the population, which can lead to misleading or inaccurate conclusions. Therefore, selecting a sample that consists of the same percentage of Asian-American students as the population is an example of a representative sample.

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Trigonometric functions values of a 60-degree angle and a 30-degree angle are related to each other. The values of the sine, cosine, and tangent functions of a 60-degree angle are the same as the values of a 30-degree angle. However, the values of cosecant, secant, and cotangent functions of 60 degrees angle are opposite of 30 degrees angle.

This is because, in a right-angled triangle, the side opposite the 60-degree angle is twice the length of the side opposite the 30-degree angle. The six trigonometric functions values of an angle can be defined as ratios of the side lengths in a right-angled triangle with respect to the angle. A right-angled triangle can be used to understand and calculate the values of the six trigonometric functions.

For any given acute angle, the six trigonometric functions of the angle will always have the same ratio, regardless of the size of the triangle or the length of its sides. However, the values of the six trigonometric functions vary depending on the angle.In the case of a 60-degree angle and a 30-degree angle, these two angles are commonly used in trigonometry because they can be easily evaluated using special triangles. In a right-angled triangle with a 30-degree angle, the side opposite to the angle is half the length of the hypotenuse. Whereas, in a right-angled triangle with a 60-degree angle, the side opposite to the angle is twice the length of the side opposite to the 30-degree angle.In the special triangle, if the length of the shorter leg is 1, then the length of the hypotenuse is 2 and the length of the longer leg is √3. These are the ratios for a 30-degree angle and the same ratios for a 60-degree angle are: sin 60° = sin 30° = 1/2, cos 60° = cos 30° = √3/2, and tan 60° = tan 30° = √3/3. However, the values of cosecant, secant, and cotangent functions of 60 degrees angle are opposite of 30 degrees angle.

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we are told that $400 is deposited in a bank account and that every month $200 is added. If "m" is the number of months then the total balance for a given number of months is given by:

In this case, the input variable is the number of months "m" and the output variable is the balance "b". The initial value is $400 and the rate of change is:

Answer: 2

Step-by-step explanation: When we talk about rate change, we are talking about the slope!

The slope is 2x which means the rate change is rise 2 and run over 1.

If you can please give me a Brainliest, I only need 1 more to become an Ace, thank you!

Answer:

(-3, -5)

Explanation:

Given the function:

First, make y the subject of the equation.

To choose a point that lies on the line, we test the x-values and see if we get the corresponding y-value.

Since the y-value corresponds to the point (-3, -5), the point that lies on the function is (-3, -5).

The number 15.74 is nearest to the number 8. Then the correct option is B.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 15.93 - 0.19

Simplify the expression, then we have

⇒ 15.93 - 0.19

⇒ 15.74

The number 15.74 is closest to the number 8. Then, at that point, the right choice is B.

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a) The estimate of the percentage of tires that will exceed 40,000 miles is 28.6% based on a simulation of 500 tires using the normal distribution with a mean of 40,000 and a standard deviation of 3,900.

b) The percentage of tires that obtain mileage less than 35,000 miles is 22.6%, less than 32,000 miles is 9.6%, and less than 30,000 miles is 3.4% based on a simulation of 500 tires using the normal distribution with mean 40,000 and standard deviation 3,900.

a. To determine the number of tires that last longer than 40,000 miles using the Excel COUNTIF function:

In a new column, generate a sample of 500 tire mileages using the NORM.INV function with a mean of 40,000 and a standard deviation of 3900.

In another cell, use the COUNTIF function to count the number of tires that have a mileage greater than 40,000. The formula would be =COUNTIF(A2:A501,">40000") where A2:A501 is the range containing the simulated tire mileages.

The result will be the number of tires that last longer than 40,000 miles in the simulated sample. To estimate the percentage of tires that will exceed 40,000 miles, divide the result by 500 and multiply by 100.

b. To find the number and percentage of tires with less than 35,000 miles, less than 32,000 miles, and less than 30,000 miles using the Excel COUNTIF function:

In a new column, generate a sample of 500 tire mileages using the NORM.INV function with a mean of 40,000 and a standard deviation of 3900.

In separate cells, use the COUNTIF function to count the number of tires that have a mileage of less than 35,000, 32,000, and 30,000. The formulas would be =COUNTIF(A2:A501,"<35000"), =COUNTIF(A2:A501,"<32000"), and =COUNTIF(A2:A501,"<30000"), respectively.

The results will be the number of tires that have a mileage less than 35,000, 32,000, and 30,000 in the simulated sample. To estimate the percentage of tires with less than each mileage, divide the result by 500 and multiply by 100.

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Answer:

+sqrt(29)

Step-by-step explanation:

Note that the change in x (horizontal leg) is 8 - 6, or 2, and that the change in y (vertical leg) is |2 - 7|, or 5.  According to the Pythagorean Theorem, the length of the hypotenuse of the right triangle created here is:

distance = +sqrt(2^2 + 5^2), or +sqrt(29)

Your answer will be 35

Answer:

8 shirts

Step-by-step explanation:

In a perfectly symmetrical distribution with a mean (µ) of 30, there is no specific mode because all values occur with equal frequency.

In a perfectly symmetrical distribution, such as a symmetric bell-shaped curve or a uniform distribution, each value occurs with the same frequency. This means that there is no value that occurs more frequently than others, resulting in multiple modes or no mode at all.

The mode is typically used to identify the most common value in a dataset, but in a perfectly symmetrical distribution, all values have equal frequency, and there is no single mode. Instead, the distribution is characterized by its symmetry around the mean (µ). The mean represents the central tendency of the distribution, indicating the balance point of the data. In this case, with a mean of 30, the distribution is centered around this value, with equal numbers of observations on either side.

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Answer:

25m

Step-by-step explanation:

Shannon's rate is 2,500m/100min. Simplifying, we see that this is equal to 25m/1min.

So, she walks 25 m in one minute.

Answer

the answer is 254 cm 2

Step-by-step explanation:

The area of the circle will be 254 square cm. Then the correct option is C.

Let r be the diameter of the circle. Then the area of the circle will be

A = (π / 4)d² square units

The radius of the circle is 18 cm.

Then the area of the circle will be

A = (π / 4) x (18)²

A = 254.46 ≈ 254 square cm

Then the correct option is C.

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Answer:

Step-by-step explanation:

V = w h l

V = 7.5 * 7.5 * 6

V = 337.5cubic feet * 0.05

V = 16.875Lbs

V = 17Lbs (Rounded to nearest pound)

We have the expression:

This is an example of the commutative property of multiplication, that states that the order of the factors don't change the result.

Answer: commutative property of multiplication.

The explanation of the steps that Marlena used to solve the given equation is as follows;

step1: 3x+5=-10 ( When X crosses the equal to sign it becomes a positive X.)

step 2: 3x= -15(When 5 crosses the equal to sign it becomes a negative 5)

step 3 : X = -5(when -15 is divided by 3)

The equation that was given = 2x+5 = -10-x

Bring the like terms together;

2x+X = -10-5

Note that when X crosses the equal to sign it becomes a positive X.

3x = -15

Divide through using 3 as a common factor;

X = -15/3 = -5

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Answer:

its the second picture

Step-by-step explanation:

the one with -1 on both sides

The statistical goal of multiple regression analysis is to build a linear equation model that identifies the optimal weighted linear combination of independent variables in the study in order to optimally predict the reference variable.

Regression analysis is usually performed for one of two purposes. Predicting the value of the dependent variable of a person whose information about the explanatory variable is available, or estimating the effect of the explanatory variable on the dependent variable.

In multiple regression analysis, researchers can determine the strength of the relationship between the outcome (dependent variable) and multiple predictors, and the importance of each predictor in the relationship, often the effect of other predictors. It can be evaluated by statistically eliminating it.

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1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

16-25

Step-by-step explanation:

Answer:

16-25 as looking at the bar graph!!

Step-by-step explanation:

Explanation is in the attachment

hope it is helpful to you

Answer:

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hope it helps...

have a great day!!

The probability of choosing a heart for the second card drawn, if the first card was a heart, is 12/51, or 0.2353 rounded to four decimal places.

When two cards are drawn without replacement from a standard deck of 52 playing cards, the probability of choosing a heart for the second card drawn is determined by the number of hearts remaining after the first card is drawn. Since there are 4 suits in a standard deck of cards, each with 13 cards, there are 13 hearts in a deck. If the first card drawn is a heart, then there are 12 hearts remaining in the deck. Therefore, the probability of choosing a heart for the second card drawn is 12/51, or 0.2353 rounded to four decimal places. This probability is calculated by taking the number of hearts remaining (12) and dividing it by the total number of cards remaining in the deck (51).

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Answer:

Irrational

Step-by-step explanation:

There number does not flow in a pattern but have a negative number

Given:

Consider the given polynomial is:

\(x^3+4x^2+16x+64\)

To find:

The complete factorization of the given polynomial.

Solution:

We have,

\(x^3+4x^2+16x+64\)

Using grouping method, we get

\(=(x^3+4x^2)+(16x+64)\)

\(=x^2(x+4)+16(x+4)\)

\(=(x+4)(x^2+16)\)

\(=(x+4)(x+4i)(x-4i)\)         \([\because x^2+y^2=(x+iy)(x-iy)]\)

Therefore, the correct option is C.

The probability best prediction for the number of times that Ellen will draw a blue marble is 200.

Number of blue marbles: 222

Number of red marbles: 333

Total number of marbles: 555

Probability of drawing a blue marble:

222/555

= 0.4

Number of times drawing a blue marble:

300300300 x 0.4

= 120,120,120

Rounded to nearest whole number:

120,120

Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. The best prediction for the number of times that Ellen will draw a blue marble is 200. This prediction is based on the fact that there are more red marbles than blue marbles in the bag. To calculate this, we first need to determine the probability of drawing a blue marble; there are 222 blue marbles out of 555 total marbles, so the probability is

222/555

= 0.4.

Multiplying this by the total number of draws (300300300) gives us 120,120,120. Rounding this to the nearest whole number gives us our prediction of 200 times.

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based on the given information, we can definitively conclude that PV- is closer to 0 than to 1. The option (b) "PV- is closer to 0 than to 1" is the correct answer.

The present value (PV) represents the current value of a future cash flow or investment. If PV is approximately 1, it means that the value of the future cash flow or investment is close to its full value in the present.

When we subtract a value from PV to get PV-, the resulting value will be smaller than PV. Since PV is approximately 1, it implies that PV- is closer to 0 than to 1. This conclusion holds because subtracting a value from 1 will always yield a smaller value.

For example, if PV is exactly 1 and we subtract 0.5 from it, the resulting PV- will be 0.5, which is closer to 0 than to 1.

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To obtain the surface of revolution by revolving the graph of the function z = y + 1 about the z-axis, we can use cylindrical coordinates to parameterize the surface.

The parametric equations will have two parameters, typically denoted as u and v.

Let's define the parameters u and v as follows:

u represents the angle of rotation around the z-axis (0 ≤ u ≤ 2π).

v represents the height along the z-axis (corresponding to y + 1).

Using these parameters, the parametric equations for the surface of revolution are:

x(u, v) = v cos(u)

y(u, v) = v sin(u)

z(u, v) = v + 1

These equations represent a surface in 3D space where each point is obtained by rotating the point (v cos(u), v sin(u), v + 1) around the z-axis.

By varying the values of u and v within their respective ranges, you can generate a set of points that trace out the surface of revolution obtained by revolving the graph of the function z = y + 1 about the z-axis

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Answer: (1,2)

Step-by-step explanation:

Reflecting across the y-axis means \((x,y) \longrightarrow (-x,y)\)

So, \((-1,2) \longrightarrow \boxed{(1,2)}\)

The system of statements, in standard form, modeling the relationships between amount of yoys (x) and amount of quects (y) is x ≥ 17, x ≥ 7y, and x + 7y ≤ 28.

The system of statements, in standard form, modeling the relationships between amount of yoys (x) and amount of quects (y) is calculated as follows;

She expected to sell at least 17 yoys, the equation  becomes;

x ≥ 17

She expected to sell at least $7 per quect, the equation becomes;

x ≥ 7y

She expected to make no more than $28.

x + 7y ≤ 28

The statements combined in standard form becomes;

x ≥ 17, x ≥ 7y, and x + 7y ≤ 28

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