. Explain in your own words what is meant by the equation lim f(x) = 5 x 2 Is it possible for this statement to be true and yet f(2) = 3? Explain.

The percentage of students majoring in Business that plans to go to Graduate school is 27.78% (option d)

We are given a crosstabulation of 800 college seniors with their undergraduate major and whether or not they plan to go to graduate school. We need to find the percentage of business students who plan to go to graduate school.

From the table, we can see that:

Out of 252 business students, 70 plans to go to graduate school.

Therefore, the percentage of students majoring in Business that plans to go to Graduate school = (Number of business students who plans to go to graduate school / Total number of business students) × 100= (70 / 252) × 100= 0.2778 × 100= 27.78%

Hence, the answer is option d.

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Christine's grades for last semester were A, B, C, and C. An A is worth 4 points, a B is worth 3 points, a C is worth 2 points, and a D is worth 1 point. Her total grade points were 40 and her total credit hours were 14, resulting in a GPA of 2.86 if all courses were weighted the same.

Based on the information provided, the appropriate values in the Grade Value column for each grade are:

A: 4

B: 3

C: 2

D: 1

To calculate Christine's GPA if all courses were weighted the same, we need to first calculate her total grade points and divide by the total credit hours. The grade points for each course are calculated by multiplying the grade value by the credit hours. The table can be completed as follows

To calculate the GPA, we divide the total grade points (40) by the total credit hours (14):

GPA = 40/14 = 2.86

Therefore, if all courses were weighted the same, Christine's GPA would be 2.86.

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--The given question is incomplete, the complete question is given

" Name The goal of the first few questions will be to compute a grade point average, which is a good example of weighted grading Courses with more credit hours contribute more to the GPA than those with less Below are the grades that our friend Christine earned last semester. You'll he filling in the rest of the table as you work through Questions 14 Grade Grade Value Grade Points Course English Math Credit Hours 3.0 4.0 History Science 5.0 Totals: 1. In most GPA systems, an A is worth 4 points, a B is worth 3 points, a C2 points, and a D l point. Fill in the appropriate values in the Grade Value column. 4. What would her GPA have been if all courses were weighted the same? How did you decide"--

Answer:

It is 19

9+10=19

Answer:

19

Step-by-step explanation:

Simply put, 9 + 10 = 19.

Method 1

Distribute each number, then count individual numbers, take h's for example

hhhhhhhhh (9) + hhhhhhhhhh (10) = hhhhhhhhhhhhhhhhhhh (19)

Method 2

Plug this into a calculator, and get 19!

Answer:

4.189 radians

Step-by-step explanation:

Given data

θ=240 degrees

Let us convert from  degrees to radians

Angle in Radian= Angle in degree* π/180

Substitute

Angle in Radian= 240* π/180

Angle in Radian= 4* π/3

Angle in Radian= 4* 3.142/3

Angle in Radian=12.568/3

Angle in Radian=4.189 radians

For the two supplementary angles given, the value of x is 30. Two angles are called supplementary when their measures add up to 180 degrees.

If two angles are supplementary, their sum must equal 180 degrees. Supplementary angles are double of complementary angles.  So if m∠1=124° and

m∠2=(2x - 4)°, we can set up the equation:

124 + (2x - 4) = 180

Solving for x, we can isolate x by subtracting 124 from both sides:

2x - 4 = 56

Adding 4 to both sides:

2x = 60

Finally, dividing both sides by 2:

x = 30

So the value of x is 30

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The conditional PMF of Y=i given X=1 is 1 if i=1 and 0 otherwise and  X and Y are not independent because the value of X affects the possible range of values for Y.



a. To compute the conditional probability mass function (PMF) of Y=i given X=1, we need to find the probability of Y=i when X=1. Since X=1, the only possible outcome is (1,1), and Y can only be 1. Hence, the conditional PMF of Y=i given X=1 is:

P(Y=i | X=1) = 1, if i=1; 0, otherwise.

b. X and Y are not independent. If they were independent, the outcome of one die roll would not provide any information about the other die roll. However, given that X is the largest value and Y is the smallest value, we can see that X directly affects the possible range of values for Y. If X is 6, then Y cannot be greater than 6. Therefore, the values of X and Y are dependent on each other, and they are not independent.



Therefore, The conditional PMF of Y=i given X=1 is 1 if i=1 and 0 otherwise and  X and Y are not independent because the value of X affects the possible range of values for Y.

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Answer:

-8

Step-by-step explanation:

when there are two negetive numbers you add them not subtract

Answer:

C. 78

Step-by-step explanation:

Add all of them together, then divide by 5 because there are 5 different plants.

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

B

Step-by-step explanation:

Because its not A.

It will take approximately 7 years to accumulate $7000 or more in the account.

To find the number of years it will take to accumulate $7000 or more in the account, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount (7000 in this case),

P is the principal amount (4900),

r is the interest rate (5.5% or 0.055 as a decimal),

n is the number of times the interest is compounded per year (annually in this case), and

t is the number of years we need to find.

Let's substitute the given values into the formula and solve for t:

7000 = 4900(1 + 0.055/1)^(1*t)

Divide both sides by 4900:

7000/4900 = (1 + 0.055)^t

Simplify:

1.42857 = (1.055)^t

To solve for t, we can take the logarithm of both sides. Using the natural logarithm (ln):

ln(1.42857) = ln((1.055)^t)

Using the property of logarithms, we can bring down the exponent:

ln(1.42857) = t * ln(1.055)

Now, we can divide both sides by ln(1.055) to isolate t:

t = ln(1.42857) / ln(1.055)

Using a calculator, we can evaluate this expression:

t ≈ 6.81

Since the question asks for the smallest possible whole number answer, we round up to 7.

Therefore, it will take approximately 7 years to accumulate $7000 or more in the account.

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this the answer of . Factorise : 625y ^ 2 + 400y - 36 + 20z - z ^ 2

Answer:

y= 2/3x + 2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Using the rule of exponents/ radicals

\(a^{\frac{1}{2} }\) = \(\sqrt{a}\) , then

\(121^{\frac{1}{2} }\) = \(\sqrt{121}\) = 11 → C

Answer:  not sure. but as long as he saves his money wisely and doesn't spend frivilously

Step-by-step explanation:

The slope of the line perpendicular to the given line is calculated by taking the negative reciprocal of the given slope.The slope of the given line is 4/3. The slope of the line perpendicular to the given line is -3/4.

To find the slope of a line perpendicular to the given line, we need to take the negative reciprocal of the slope of the given line. The equation of the given line is y = 4/3x - 5/3. To calculate the slope, we need to rearrange the equation to the form y = mx + b, where m is the slope and b is the y-intercept. Rearranging the equation to the form y = mx + b, we get y = 4/3x - 5/3 which can be written as 4/3x - y = 5/3. The slope of the given line is 4/3. To find the slope of the line perpendicular to the given line, we take the negative reciprocal of 4/3 which is -3/4. Therefore, the slope of the line perpendicular to the given line is -3/4.

y = 4/3x - 5/3

4/3x - y = 5/3.

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Answer:90

Step-by-step explanation:

The distance between these cities on the map is 90 mm.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Cincinnati is about 225 miles from Cleveland and on scale 10 millimetres is equal to 25 miles.

The distance on the map will be calculated as,

25 miles = 10 mm

1 mile = 10 / 25 mm

225 miles = ( 225 x 10 ) / 25

225 miles = 90 mm

Therefore, the distance between these cities on the map is 90 mm.

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Answer:

X+6+2x=180

6+3x=180

3x=172

x=57 1/3

Paired data refers to observations that are matched or connected in some way. In this case, if we were comparing the rates of return for the two stocks on the same set of 50 days, then it would be considered paired data.

The data comparing the rates of return for the technology company Intel and the U.S. airline Southwest Airlines would not be considered paired data because the samples are not taken on the same days. Paired data refers to observations that are matched or connected in some way. In this case, if we were comparing the rates of return for the two stocks on the same set of 50 days, then it would be considered paired data.

However, in this scenario, two separate random samples of 50 days of stock returns are taken for each company. The days on which the stock returns are recorded are not necessarily the same for both Intel and Southwest Airlines. Therefore, there is no direct pairing or connection between the observations of the two stocks.

To illustrate this further, let's say we take a random sample of 50 days for Intel's stock returns, and another random sample of 50 days for Southwest's stock returns. The first day in the Intel sample may not correspond to the first day in the Southwest sample, and so on. Each sample represents independent observations for each stock, making the data unpaired.

It is important to recognize whether data is paired or unpaired as it can affect the statistical methods used for analysis. In this case, since the data is not paired, we would use different approaches to compare the rates of return for Intel and Southwest Airlines.

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Answer:

Step-by-step explanation:

There are 50-50 chances that you will get a head or a tail

When an arch is extended overhead into a half cylinder, it is known as a barrel vault.

A barrel vault is a curved architectural structure that resembles the shape of a half-cylinder. It is created by placing a series of arches side by side, forming a continuous and uninterrupted vaulted ceiling. The term "barrel" refers to the resemblance of the vault to the shape of a barrel or a tunnel.

Barrel vaults have been used in architecture for centuries and are often found in historical buildings and structures. They provide a sturdy and durable construction method, distributing the weight of the ceiling evenly along the arches. This allows for the creation of large and open interior spaces without the need for additional support columns.

Barrel vaults are commonly used in churches, cathedrals, and other monumental structures, where they serve both functional and aesthetic purposes. The sweeping and graceful curves of the barrel vaults add a sense of grandeur and elegance to architectural designs, making them a popular choice in various architectural styles throughout history.

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Answer:

-25

Step-by-step explanation:

Example 1: The coordinates of B are:

B = 2M - A = (2(7-Bx)/2-3, 2(-1+By)/2-4) = (11-Bx, -9/2+By)

Example 2:  The position vector of D is d = a + AD = i + 2j - k + (20i - 2j + k) = 21i + j.

Example 1:

Given that point P (7,-1) is the point of intersection of the diagonals of rectangle ABCD, and point A is (3,4), we can find the coordinates of point C as follows:

Since ABCD is a rectangle, we know that the diagonals bisect each other at their point of intersection. Therefore, the midpoint of diagonal AC is equal to the midpoint of diagonal BD. Let M be the midpoint of diagonal AC.

The coordinates of M are equal to the average of the coordinates of A and C:

M = (3+Cx)/2, (4+Cy)/2 = (7-By)/2, (-1+Bx)/2

Solving for Cx and Cy, we get:

Cx = 13 - Bx

Cy = -3 + By

Since ABCD is a rectangle, we know that the sides AB and CD are parallel and perpendicular to AC. Therefore, the vectors AB and CD are parallel and orthogonal to vector AC.

We can find the vector AC using the coordinates of A and P:

AC = <7-3, -1-4> = <4, -5>

To find the coordinates of C, we need to add vector AC to the coordinates of P:

C = A + AC = <3, 4> + <4, -5> = <7, -1>

Therefore, the coordinates of point C are (7, -1).

To describe the position of point B, note that B is the reflection of A across the midpoint of diagonal AC. Therefore, the coordinates of B are:

B = 2M - A = (2(7-Bx)/2-3, 2(-1+By)/2-4) = (11-Bx, -9/2+By)

Example 2:

Given the position vectors of points A, B, and C as a = i + 2j - k, b = 3i + j + 2k, and c = 21i, we can find:

a) The unit vector parallel to the vector AB is equal to the normalized vector in the direction of AB:

AB = b - a = (3-1)i + (1-2)j + (2+1)k = 2i - j + 3k

||AB|| = sqrt(2^2 + (-1)^2 + 3^2) = sqrt(14)

Unit vector AB = AB/||AB|| = (2/sqrt(14))i - (1/sqrt(14))j + (3/sqrt(14))k

b) To find the value of p such that A, B, and C are collinear, we can check if vector AC is a scalar multiple of vector AB. If AC = pAB, then the determinant of the matrix with rows AB, AC, and the zero vector is equal to zero:

|2 -21 0|

|-1 2p-2 -2|

|3 2p 1|

Expanding the determinant along the first row, we get:

2(-2(2p-2) + 2) - (-21(-3)(2p) + 21(2)) + 0 = 0

Simplifying, we get:

12p - 8 + 126p - 42 = 0

Solving for p, we get:

p = -2/13

Therefore, A, B, and C are collinear when p = -2/13.

c) To find the position vector of D so that ABCD is a parallelogram when p = -2, we need to find a vector AD that is parallel to BC. Since AB and CD are parallel, we can take AD = CD:

AD = c - a = 21i - (i + 2j - k) = 20i - 2j + k

Therefore, the position vector of D is d = a + AD = i + 2j - k + (20i - 2j + k) = 21i + j.

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Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

1. The given statement "A PQR has translated 12 units down" is True because translation maintains the size, shape, and orientation of the triangle. 2. The given statement "PQR is reflected across the x-axis" is True because a reflection preserves the size and shape of a triangle but changes its orientation. 3. The given statement "PQR is reflected across the y-axis" is True because reflecting Triangle PQR across the y-axis will create a congruent triangle to Triangle P'Q'R', as long as Triangle P'Q'R' is also a reflection of Triangle PQR across the y-axis.

1. If Triangle PQR has translated 12 units down, it will still be congruent to Triangle P'Q'R'.  Translations and reflections preserve the size and shape of triangles, making them congruent.

2. Reflecting Triangle PQR across the x-axis will create a congruent triangle to Triangle P'Q'R', provided that Triangle P'Q'R' is also a reflection of Triangle PQR across the x-axis.

3. The given statement "PQR is reflected across the y-axis" is True because Similar to the x-axis reflection, reflecting Triangle PQR across the y-axis will create a congruent triangle to Triangle P'Q'R', as long as Triangle P'Q'R' is also a reflection of Triangle PQR across the y-axis.

In summary, The congruence between Triangle PQR and Triangle P'Q'R' can be verified through a translation of 12 units down, reflection across the x-axis, or reflection across the y-axis, provided that the corresponding transformations apply to both triangles.

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Answer:

5*5*5*5

Step-by-step explanation:

5^4 means 5 times itself four times.

Answer:

625

Step-by-step explanation:

5 x 5 x 5 x 5

which is

625

45 billion Korean Won is equal to 45 million US Dollars.

The formula for  (USD) is USD = KRW / 1000. To calculate 45 billion won in USD, we must first convert KRW to USD. 45 billion KRW is equal to 45,000,000,000 KRW. Using the formula above, we can calculate the amount of USD:

USD = 45,000,000,000 KRW / 1000

USD = 45,000,000 USD

Therefore, 45 billion won is equal to 45 million US Dollars.

To better understand this conversion, it is important to remember that one US Dollar is equal to 1000 Korean Won. As an example, if you have 10,000 Korean Won, you can convert that to USD by dividing 10,000 by 1000, which equals 10 USD. The same concept applies when converting larger numbers. To convert 45 billion KRW to USD, we must divide 45,000,000,000 by 1000, which equals 45,000,000 USD.

In conclusion, 45 billion Korean Won is equal to 45 million US Dollars.

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Answer:

Step-by-step explanation:

The solutions are

x=2,x=3

Explanation:

x2−5x+6=0

Here we can first factorise the expression and then find the solution:

Factorising by splitting middle term

x2−2x−3x+6=0x(x−2)−3(x−2)=0(x−2)(x−3)=0

Equating the two factors with zero to obtain solutions:

x−2=0,x=2x−3=0,x=3

Answer:

x + 5x + 6

x + 3x + 2x +6

x(1 + 3) + 2(x + 3)

(x + 3) (x+2) = 0

x = -3 (or) x = -2