If a car, with an initial velocity of 30 m/s, accelerates at a rate of 20 m/s2 for 5 seconds, what will its final velocity be?

Answer: 1287

Step-by-step explanation:

Complete Question:

g(x), represents transformations on the parent function of \(y = (\frac{1}{2})^x\).

Write the equation for g (x ) with the following transformations:

Reflect over y-axis, and shift right 7

Answer:

\(g(x) = (\frac{1}{2})^{-x-7}\)

Step-by-step explanation:

Given

\(y = (\frac{1}{2})^x\)

Represent the function as:

\(f(x) = (\frac{1}{2})^x\)

Taking the transformations, one after the other:

Reflect over the y-axis.

This is represented by the rule: (x,y) ==> (-x,y)

So, we have:

\(f'(x) = (\frac{1}{2})^{-x}\)

Shift right 7 units

This is represented by (x,y) = (x - b, y)

Where b represents the number of units

So, we have:

\(f'(x-7) = (\frac{1}{2})^{-x-7}\)

Hence:

\(g(x) = (\frac{1}{2})^{-x-7}\)

The score of the top 2.5% of the applicants would be at least 610.

To find the score of the top 2.5% of the applicants, we need to use the z-score formula:

z = (x - μ) / σ

where x is the score we want to find, μ is the mean (460), σ is the standard deviation (80), and z is the z-score corresponding to the area under the normal curve to the right of x.

We want to find the z-score such that the area to the right of z is 0.025 (since we're looking for the top 2.5%). Using a table or calculator, we find that the z-score corresponding to an area of 0.025 to the right is approximately 1.96.

So,

1.96 = (x - 460) / 80

Solving for x, we get:

x = 1.96 * 80 + 460 = 610.8

Rounding to the nearest integer, we get 610. Therefore, the score of the top 2.5% of the applicants would be at least 610.

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Answer:

9.4

Step-by-step explanation:

1+3+15+11+17=47

47/5=9.4

Answer:

i need answers

Step-by-step explanation:

The perfect square trinomial is 4x² - 4x + 1. The correct answer would be an option (A).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in option (A), as follows:

4x² - 4x + 1

(2x)² - 2 × 2x × 1 + 1²

Compare to the formula a² - 2 × a × b + b² = (a - b)², and we get

(2x - 1)²

Thus, this is a perfect square trinomial.

Hence, the correct answer would be an option (A).

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an inverted yield curve question content area bottom part is flat.

An inverted yield curve refers to a situation in which short-term interest rates are higher than long-term interest rates. This results in a flat or even downward-sloping curve when plotting the yields against the maturity dates of fixed-income securities, such as bonds. The term "inverted" signifies that the normal upward slope of the yield curve is reversed. Therefore, the correct answer is that an inverted yield curve is flat.

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The ratio of junior to adult = 6/5

What is proportion?

An equality between two ratios. According to proportion, if 2 sets of given numbers area unit increasing or decreasing within the same quantitative relation, then the ratios area unit aforesaid to be directly proportional to every different.

Main body:

Given - data in the question

To find answer the question

Solution - Let no of junior, children and adults be x, y, z respectively.

Now, ratio of junior to children = 1/3

So, x = 3y

Ratio of children to adult = 5/2

So, 5y = 2z

.(2)

So, from (1) we get, y = x / 3

So, 5x / 3 = 2z

⇒5x = 6z

⇒ x/z=6/5

Hence, the ratio of junior to adult = 6/5

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The 53586077 is composite, we can use Fermat's Little Theorem for primality testing. The theorem states that if p is a prime number and a is any positive integer less than p, then

\(a^(p-1) ≡ 1 (mod p).\)

Let's take a positive integer a = 2 as our witness. We need to calculate\( 2^(53586077-1) mod 53586077\) and check if it's equal to 1.

\(2^(53586076) mod 53586077 = 3639153\) (using a calculator or software)

Since 3639153 is not equal to 1, this shows that 53586077 is composite, and 2 is a valid witness.

For the Carmichael number 294409, we need to find a nontrivial square root of 1 modulo 294409. A nontrivial square root of 1 is an integer x such that x^2 ≡ 1 (mod 294409) and x ≠ 1 or x ≠ -1 (mod 294409).

Let's take a = 3 as our witness. We need to calculate 3^((294409-1)/2) mod 294409:

\(3^147204 mod 294409 = 1\) (using a calculator or software)

Now, we need to find 3^((294409+1)/2) mod 294409:

\(3^147205 mod 294409 = 294408 \)(using a calculator or software)

Since 1 and 294408 are the trivial square roots of 1 (mod 294409), 3 is not a valid witness for this Carmichael number. However, using trial and error with other witnesses, we can eventually find a nontrivial square root of 1, proving that 294409 is composite.

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Using proportions, it is found that:

42. x and y are not proportional.

43. The number 21 is 60% of 35.

44. The number 27 is 36% of the number 75.

Two variables, x and y, will represent a proportional relationship if the ratio between them is always the same.

From the table, the ratios are given as follows:

Different ratios, hence the variables x and y are not proportional.

To find the percentage of a number, the decimal equivalent of the percentage is multiplied by the number.

The decimal equivalent of a percentage of 60% is:

60/100 = 0.6.

Hence the percentage of 35 is calculated as follows:

0.6 x 35 = 21.

The percentage that the number 27 represents of the number 75 is given by the division of 27 by 75 multiplied by 100%, hence:

27/75 x 100% = 36%.

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The solution is: matching the left with its equivalent expression on the right, is: a - 3, b - 4 , c - 1 , d - 5, e - 2.

Given that,

a. ✓4x²y^4.     1. 2x✓y

b. ✓8x²y.        2. 2y✓2x

c. ✓4x²y.         3. 2xy²

d. ✓16xy².       4. 2x✓2y

e. ✓8xy².        5. 4y✓x

so, multiplying we get,

a. ✓4x²y^4 = ✓4 × ✓x² × ✓y^4

= 2 × x × y²

= 2xy²

Therefore, ✓4x²y^4 = 2xy²

b. ✓8x²y = ✓8 × ✓x² × ✓y

= ✓4 × ✓2 × ✓x² × ✓y

= 2 × ✓2 × x × ✓y

= 2x✓2y

Therefore, ✓8x²y = 2x✓2y

c. ✓4x²y = ✓4 × ✓x² × ✓y

= 2 × x × ✓y

= 2x✓y

Therefore, ✓4x²y = 2x✓y

d. ✓16xy² = ✓16 × ✓x × ✓y²

= 4 × ✓x × y

= 4y✓x

Therefore, ✓16xy² = 4y✓x

e. ✓8xy² = ✓8 × ✓x × ✓y²

= ✓4 × ✓2 × ✓x × ✓y²

= 2 × ✓2 × ✓x × y

= 2y✓2x

Therefore, ✓8xy² = 2y✓2x

Hence, The solution is: matching the left with its equivalent expression on the right, is: a - 3, b - 4 , c - 1 , d - 5, e - 2.

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complete question:

Match each expression on the left with an equivalent expression on the right

a. ✓4x²y^4.     1. 2x✓y

b. ✓8x²y.        2. 2y✓2x

c. ✓4x²y.         3. 2xy²

d. ✓16xy².       4. 2x✓2y

e. ✓8xy².        5. 4y✓x

The 18th term of the arithmetic sequence -13, -9, -5, -1, 3,... is 55. Thus, the right answer is option A. which is A(18) = 55

Arithmetic Progression is a sequence of numbers in which the difference between two numbers in the series is a fixed definite value.

The specific number in the arithmetic progression is calculated by

\(a_n=a_1+(n-1)d\)

where \(a_n\) is the term in arithmetic progression at the nth term

\(a_1\) is the initial term in the arithmetic progression

d is the difference between two consecutive terms

In the given question, \(a_1\) = -13

d = -9 - (-13) = 4

Therefore, to calculate the 18th term,

\(a_{13}=a_1+(18-1)d\)

= -13 + (17) 4

= -13 + 68

= 55

Hence, the 18th term of the above AP is 55

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To gather statistical data on various items of interest in your own statistics class, including height, age, gender, pulse, number of siblings, marital status, number of college credit hours completed, grade point average, major, number of credit hours enrolled in this term, number of scheduled hours working per week, distance from residence to first class, time it takes to travel from residence to first class, year, make, and color of car usually driven.

It is important to give clear directions for creating these questions. First, accuracy in measurements should be emphasized to ensure that the data collected is reliable. Age should be recorded as of last birthday to maintain consistency across the sample. Leading and biased questions should be avoided to prevent skewing the data in a particular direction. No questions should be misleading, and any open-ended questions should be clearly defined to avoid ambiguity.

Commonsense rules should be stated for any numerical answers to ensure that responses are consistent and accurate. Vague wording such as "often," "seldom," and "occasionally" should be avoided, and clear instructions should be provided for any questions that require interpretation. By following these guidelines, accurate statistical data can be collected to provide a better understanding of your own statistics class. A long answer would go into greater detail on each of these points, but the main takeaway is that clear and consistent directions are key to collecting accurate statistical data.

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No Solution.

Since, the x-axis (equation y=0) does not intersect y=-7 at any point. The given pair of equations has no solution

Consider the pair of linear equations in two variables x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.

2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables

3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.

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The mean of the following data 0,5,30,25,16,18,19,26,0,20,28 is 17.

Hence option D is the correct option.

Mean is the average value of a given set of data. It is calculated by the formula,

Mean =  {Summation of all the values in the data set} / {Number of observations is the data set}

That is, Mean = {Σ all values in the data set} / {number of observations}

The given data set is as follows,

0,5,30,25,16,18,19,26,0,20,28

The number of observations in the data set is 11.

The summation of all the values in the data set is = {0 + 5 + 30 + 25 +
16 + 18 + 19 +26 + 0 + 20 + 28} = 187

Therefore, by applying  the formula of Mean we get

Mean = 187/ 11 = 17

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Answer:

2/5

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Out of these four card choices, for the first pick there are two even cards and four cards in total. This means that on the first pick there is a 2/4=1/2 chance that you pick an even card. On the second pick, if you do not replace the card, then there is 1 even card remaining, and 3 cards in total, leaving a probability of 1/3. Multiplying these two probabilities together, you get an overall chance of 1/6. Hope this helps!

The solution to the equation ln(2x) = 3 is x ≈ 7.389. By substituting this value back into the equation, we can verify that ln(2 ×  7.389) does indeed equal 3.


To solve the equation ln(2x) = 3, we need to isolate x. Firstly, we can rewrite the equation in exponential form as e 3 = 2x. Next, we divide both sides by 2 to solve for x, giving us x = e 3/2 ≈ 7.389.
To verify our solution, we substitute x = 7.389 back into the original equation: ln(2 ×  7.389). Using a calculator, we find that ln(2 × 7.389) is indeed approximately equal to 3. Thus, x ≈ 7.389 is the correct solution.

It’s important to note that when working with logarithmic equations, we should always check the solution by substituting it back into the original equation to ensure it satisfies the given equation.

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If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:

\(\boxed{8-2=6}\\\boxed{6/2=3}\)

We are going to take that 25% and multiply it with 3 to get are final answer.

\(\boxed{25*3=75}\\\boxed{So,2=75}\)

Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

There are 26^7 * 21 number of ways to create an 8-letter word using the 26-letter alphabet that begins or ends with a vowel, where 26 is the number of letters in the alphabet, and 21 is the number of consonants.

To find the number of 8-letter words that either begin or end with a vowel, we need to consider two cases: words that begin with a vowel and words that end with a vowel.

For words that begin with a vowel, we have one vowel as the first letter and any of the 26 letters of the alphabet for the remaining 7 letters. Hence, there are 26^7 ways to create an 8-letter word that begins with a vowel.

For words that end with a vowel, we have 21 consonants for the first letter and any of the 26 letters of the alphabet for the remaining 7 letters, followed by one of the five vowels. Hence, there are 21 * 26^7 * 5 ways to create an 8-letter word that ends with a vowel.

Therefore, the total number of 8-letter words that either begin or end with a vowel is the sum of the two cases: 26^7 + 21 * 26^7 * 5, which simplifies to 26^7 * 21.

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Answer:

x = -5/6

Step-by-step explanation:

Since it is on the unit circle  

  x^2   +  ( -sqrt(11)/6)^2    = 1 ^2     (pythagorean theorem)

x^2 = 1 - 11/36

x^2  = 25 /36

x =   +-5/6       since x is in Q III  it is the negative

The solution to the system of equations that are represented by the table given is: (-1, 6).

Recall:

Solution to a system of equations that is represented by a table is the value of x that will give the same value of y for each linear equation.

Thus, from the table given, when x = -1, the values of y1 and y2 equals 6. This represents the solution of the system of equations.

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The best definition of decision variables in an optimization model is they are unknown values that the model seeks to determine. Option C

Decision variables are simply unknowns in an optimization problem and are has a domain.

This domain is a compact representation of all possible values  in the set for the variable.

These are also seen as references to objects whose nature solely depends on the underlying optimizer of the model.

The values of these decision variables are values which can vary over a feasible set of alternatives to either increase or decrease the value of the objective function.

They could be linear or continuous.

Hence, the decision variable has an unknown value.

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Answer:

the length of cube

is 2 mm

Answer:

2m

Step-by-step explanation:

A cube is a 3-dimensional object with all sides of equal length. So, length = breadth = height

Let the side of cube be x.  

Then Volume of cube = x * x * x

So, length (side) of cube is 2m

Answer:

the first one

Step-by-step explanation:

i think that's the correct answer

The distance between points A and B is 14 units.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.

According to the number line,

Point A lie at - 2 on the number line and point B lie at 12 on the number line.

Now from 0 to point B,

The distance between point 0 and B is 12 units.

And from point A to 0 the distance is 2 units.

Therefore,

The total distance between points A and B will be:

AB = AO + OB

AB = 2 units + 12 units

AB = 14 units

Hence, the correct option is (D) 14 units.

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Answer:

1. y=2x^2-8X-1

2. y=-6x^2+36x-63

3. y=-3x^2+18x-34

4. y=9x^2+54x+76

5. y=-x^2+8x-22

6. y=6x^2-48x+90

7. y=8x^2+16x+5

8. y=2x^2-8x+1

Have a great day :)

Answer:

x = 30

Step-by-step explanation:

110 and 3x - 20 are supplementary angles, sum to 180° , then

110 + 3x - 20 = 180

90 + 3x = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Answer:

x = 30

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the terrible drawing.)

For this question, you must be clear of the angle properties.

z + 110 = 180 (Sum of Angles on a straight line)

z = 180 - 110 = 70

z = 3x - 20 (Corresponding Angles)

3x - 20 = z

3x - 20 = 70

3x = 70 + 20

3x = 90

x = 90 / 3 = 30