Alberto bought his bicycle for$275. He sold for $350. What was the amount of his Percentage profit?

The required relative frequency based on the frequency distribution of the students is 8.33%

The relative frequency is the frequency fraction of the number of observations the events occur to the total number of observations. The relative frequency provides a clear understanding of the distribution. This also helped to make a histogram and chart.

The number of times a value appears in a dataset is its frequency. The pattern of frequencies for a variable is known as a frequency distribution. The frequency with which each potential value of a variable appears in a dataset.

The frequency distribution is given.

Total number of student=36

The relative frequency for the class with lower-class limit 31 is calculated as;

R.F=No. of students in class interval/Total no.of students

=3/36

=0.0833

=8.33%

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HOPE IT HELP (≧▽≦)(≧▽≦)(≧▽≦)

Answer:

Step-by-step explanation:

the answer is wrong its  34.3

Answer: Let's call the time it takes for Mrs. Cunningham to overtake Mr. Cunningham "t".

In that time, Mr. Cunningham will have traveled for 4 more hours than Mrs. Cunningham, so he will have traveled 4 + t hours.

We can set up an equation to represent the distance each person traveled:

distance = rate x time

For Mr. Cunningham:

distance = 46 mph x (4 + t) hours

For Mrs. Cunningham:

distance = 62 mph x t hours

Since they end up at the same place, their distances must be equal:

46 mph x (4 + t) = 62 mph x t

Simplifying this equation:

184 + 46t = 62t

16t = 184

t = 11.5

Therefore, it will take Mrs. Cunningham 11.5 hours to overtake Mr. Cunningham.

Step-by-step explanation:

Answer:

The bus traveled 143 km. The car traveled 159 km.

Step-by-step explanation:

Basically, you just have to go to the 3 miles mark and approximate the x value.

Answer:

The car covered 160km. The bus covered 145 km.

Step-by-step explanation:

Answer:

D 63

Step-by-step explanation:

First convert 3 1/2 to a decimal. Then multiply 3.5 by 18.

The number of subjects that Paige would study D. 2 subjects.

It should be noted that Paige would study for one hour. She spends 1/2 an hour, or 30 minutes, on a subject.

An hour is 60 minutes. If Paige studied 2 subjects, then she would of studied for 60 minutes.

30 + 30 = 60

So, if Paige spends 1/2 hour on Spanish, she would study 2 subjects to reach an hour.

Therefore, the correct option is D.

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Complete question

Paige spends 1 hour on her homework. She spends equal amounts of time on all subjects. If Paige spends 1/2 hour on Spanish, how many subjects does she study?

3 subjects

1 subject

4 subjects

2 subjects

True. Both impulse and momentum are vector quantities.

In physics, a vector quantity has both magnitude and direction. Impulse and momentum are both examples of vector quantities. Impulse is defined as the change in an object's momentum over time, while momentum is the product of an object's mass and velocity. Both impulse and momentum are crucial concepts in understanding the motion of objects in physics. Since they are vector quantities, their direction matters, as well as their magnitude. Understanding the direction of the vector is essential in solving problems related to impulse and momentum. It is also important to note that, in a closed system, the total momentum is conserved, meaning that the initial momentum of the system is equal to the final momentum of the system. Therefore, understanding the vector nature of impulse and momentum is fundamental in analyzing physical systems.

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\(f(x)=-\cfrac{1}{2}x^2 + 5x\hspace{13em}g(x)=x^2+2 \\\\[-0.35em] ~\dotfill\\\\ g(-2)=(-2)^2+2\implies g(-2)=4+2\implies g(-2)=6 \\\\[-0.35em] ~\dotfill\\\\ f(~~g(-2)~~)\implies f(6)\implies f(6)=-\cfrac{1}{2}(6)^2+5(6) \\\\\\ f(6)=-\cfrac{36}{2}+30\implies f(6)=-18+30\implies \stackrel{f(~~g(-2)~~)}{f(6)}=12\)

Answer:

Sam average speed for the whole journey =  \(3\frac{3}{11} mph\)

Step-by-step explanation:

Formula: Speed = \(\frac{Distance}{Time}\)

i.e. Time = \(\frac{Distance}{Speed}\)

If Sam walked x miles at 4 mph, then time taken by him = \(\frac{x}{4}\) hours

If he then walked 2x miles at 3 mph, then time for this period =  \(\frac{2x}{3}\)hours

Average speed = \(\frac{Total Distance}{Total Time}\)

=\(\frac{x+2x}{\frac{x}{4} \frac{2x}{3} }\)

=\(\frac{3x}{\frac{x1}{4} \frac{2}{3} }\)

=\(\frac{3}{\frac{3+8}{12} }\)

=\(\frac{3 x 12}{11}\)

=\(\frac{36}{11}\)

=\(3\frac{3}{11} mph\)

Hence, Same's average speed for the whole journey =  \(3\frac{3}{11} mph\)

The correct statement is option a: If the marginal investor becomes more risk averse, the required return on Stock B will increase by more than the required return on Stock A.

The beta of a stock measures its sensitivity to market movements. A beta greater than 1 indicates that the stock tends to move more than the market, while a beta less than 1 suggests that the stock moves less than the market.

In this case, Stock A has a beta of 0.8, which means it is less volatile than the overall market. Stock B, on the other hand, has a beta of 1.6, indicating it is more volatile than the market.

When the marginal investor becomes more risk averse, they are less willing to take on risk. As a result, they will require a higher return for taking on additional risk.

Since Stock B is riskier than Stock A due to its higher beta, the required return on Stock B will increase by a greater magnitude than the required return on Stock A when the marginal investor becomes more risk averse. This is because the investor needs to be compensated more for taking on the higher risk associated with Stock B.

Therefore, option a is the correct statement in this case.

Regarding the other options:
- Option b states that Stock B's required return is double that of Stock A's. However, without specific information on the required returns or risk-free rate, we cannot determine the exact relationship between the required returns of Stock A and Stock B.
- Option c states that if the risk-free rate increases but the market risk premium remains constant, the required return on Stock A will increase by more than that on Stock B. Without further information, we cannot determine the effect of changes in the risk-free rate on the required returns of Stock A and Stock B.
- Option d states that an equally weighted portfolio of Stocks A and B will have a beta lower than 1.2. However, without specific information on the weights assigned to each stock in the portfolio, we cannot determine the exact beta of the portfolio.

In summary, option a is the correct statement based on the given information.

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Answer:

-12

Step-by-step explanation:

When you say it will drop which means it will get less in this case since -2 is a negative we need to add 10 which will make it -12. Hope this helps and makes it clear for you

a. ln 7 = y in exponential equation is e^y = 7

b. e² = x in logarithm function is log x base e = 2

What is exponential and logarithmic function?

An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.

The logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as. For x > 0 , a > 0, and a ≠1, y= loga x if and only if x = a^y

Therefore,

ln 7 = y

using inverse of ln

7 = e^y

and;

e² = x

using logarithm function as inverse

log x base e = 2.

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The solution of the system of equations graphed is (0, 3)

When we have the graph of a system of equations, to find the solution we need to find the point where the graphs intercept. That point will be the solution.

In this case, we can see that the two lines intercept at (0, 3), so that is the solution of the system of linear equations.

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Answer:

z≥-10

Step-by-step explanation

it just is, trust.

P(B∣A) is approximately 0.310, rounded to three decimal places.

To find the probability P(B∣A), we can use Bayes' theorem:

P(B∣A)= P(A) / P(A∣B)⋅P(B)

Given information:

P(B)=0.2

P(A∣B)=0.9

P(B')=0.8 (probability of not B)

P(A∣B′)=0.5 (probability of A given not B)

First, we need to calculate

P(A), the probability of event A. We can use the law of total probability to express P(A) in terms of the probabilities related to B and not B:

P(A)=P(A∣B)⋅P(B)+P(A∣B′)⋅P(B′)

Substituting the given values:

P(A)=0.9⋅0.2+0.5⋅0.8=0.18+0.4=0.58

Now, we can substitute the known values into Bayes' theorem:

P(B∣A)= P(A)/ P(A∣B)⋅P(B)

= 0. 9.0.2 / 0.58

Calculating this expression:

P(B∣A)≈ 0.5 80.18 ≈0.310

Therefore, P(B∣A) is approximately 0.310, rounded to three decimal places.

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The 8-point Discrete Fourier Transform (DFT) of x[n] = 2cos²(nπ/4) is given by X[k] = [4, 0, 0, 0, 0, 0, 0, 0] for k = 0, 1, 2, 3, 4, 5, 6, 7.

The Discrete Fourier Transform (DFT) is used to transform a discrete-time sequence from the time domain to the frequency domain. To find the DFT of x[n] = 2cos²(nπ/4), we need to evaluate its spectrum at different frequencies.

The DFT formula for an N-point sequence x[n] is given by:

X[k] = Σ(x[n] * exp(-j2πkn/N)), for n = 0 to N-1

Here, N represents the number of points in the DFT and k is the frequency index.

Using the double-angle formula for cosine, we can express cos²(nπ/4) as (1 + cos(2nπ/4))/2.

Substituting this expression into the DFT formula, we have:

X[k] = Σ((2 * (1 + cos(2nπ/4))/2) * exp(-j2πkn/8)), for n = 0 to 7

Simplifying, we get:

X[k] = Σ((1 + cos(2nπ/4)) * exp(-j2πkn/8)), for n = 0 to 7

Using the identity exp(-j2πkn/8) = exp(-jπkn/4) for k = 0, 1, ..., 7, we can further simplify:

X[k] = Σ((1 + cos(2nπ/4)) * exp(-jπkn/4)), for n = 0 to 7

Notice that cos(2nπ/4) = cos(nπ/2), which takes on the values of 1, 0, -1, 0 for n = 0, 1, 2, 3, respectively.

Substituting these values, we find that X[k] = [4, 0, 0, 0, 0, 0, 0, 0] for k = 0, 1, 2, 3, 4, 5, 6, 7.

This means that the 8-point DFT of x[n] = 2cos²(nπ/4) has non-zero values only at the 0th frequency component (k = 0), while all other frequency components have zero amplitude.

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The number of cups of vinegar that Mike used lies between the whole numbers 2 and 4

If Mike used one cup of vinegar for each salad dressing recipe, then he used a total of 3 cups of vinegar (1 cup x 3 recipes = 3 cups).

However, the question states that he used "a cup of vinegar" in each recipe, which could mean that he used slightly less than one cup, exactly one cup, or slightly more than one cup.

Assuming that Mike used at least 3/4 cup of vinegar in each recipe (which is still close to "a cup"), then he used a minimum of 2 and 1/4 cups of vinegar in total (3/4 cup x 3 recipes = 2 and 1/4 cups).

Assuming that Mike used at most 1 and 1/4 cups of vinegar in each recipe (which is still close to "a cup"), then he used a maximum of 3 and 3/4 cups of vinegar in total (1 and 1/4 cups x 3 recipes = 3 and 3/4 cups).

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Answer: (2, 6)

Step-by-step explanation:

We know that \(\overrightarrow{UM}=\overrightarrow{MT}\). From the given coordinates, \(\overrightarrow{UM}=(-1, -2)\). Therefore, the coordinates of \(T\) are \((3,8)+(-1,-2)=(2,6)\).

The gravitational potential energy of the vacationers will decrease as they approach the end of the pier.

As the vacationers approach the end of the pier, their gravitational potential energy will decrease.

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It depends on the height of the object and the acceleration due to gravity.

In this scenario, as the vacationers walk out on the horizontal pier, their height above the ground remains constant. Since the height does not change, the gravitational potential energy also remains constant.

However, as they approach the end of the pier, their distance from the center of the Earth decreases. As a result, the gravitational potential energy decreases because it is directly proportional to the distance from the center of the Earth.

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Answer:divideing by the whole number

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Given:

\(i^{50}\)

Rewrite 50 as the product of 2 and 25:

\(\implies i^{(2 \cdot 25)}\)

\(\textsf{Apply the exponent rule} \quad a^{bc}=(a^b)^c:\)

\(\implies \left(i^2\right)^{25}\)

Apply the imaginary number rule  i² = -1 :

\(\implies \left(-1\right)^{25}\)

\(\textsf{Apply the exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}:\)

\(\implies -1^{25}\)

As 1²⁵ = 1 then:

\(\implies -1\)

Answer:

(i)⁵⁰ = -1

Step-by-step explanation:

The problem is,

→ (i)⁵⁰

Formula we use,

→ i² = -1

Let's solve the problem,

→ (i)⁵⁰

→ (i²)²⁵

→ (-1)²⁵

→ -1

Hence, the answer is -1.

Natalie bought pistachios at a lower price per pound compared to Nicholas.

To compare the prices of pistachios at store A and store B, we need to calculate the price per pound for each store based on the given information.

Natalie's purchase at store A:

Weight of pistachios = 3 4/5 pounds

Cost of pistachios = $17.75

To calculate the price per pound at store A, we divide the total cost by the weight:

Price per pound at store A = $17.75 / (3 4/5) pounds.

To simplify the calculation, we can convert the mixed fraction 3 4/5 to an improper fraction:

3 4/5 = (3 \(\times\) 5 + 4) / 5 = 19/5

Substituting the values, we have:

Price per pound at store A = $17.75 / (19/5) pounds

Price per pound at store A = $17.75 \(\times\) (5/19) per pound

Price per pound at store A = $3.947 per pound (rounded to three decimal places).

Nicholas's purchase at store B:

Weight of pistachios = 4 7/10 pounds

Cost of pistachios = $19.50

To calculate the price per pound at store B, we divide the total cost by the weight:

Price per pound at store B = $19.50 / (4 7/10) pounds

Converting the mixed fraction 4 7/10 to an improper fraction:

4 7/10 = (4 \(\times\) 10 + 7) / 10 = 47/10

Substituting the values, we have:

Price per pound at store B = $19.50 / (47/10) pounds

Price per pound at store B = $19.50 \(\times\) (10/47) per pound

Price per pound at store B = $4.149 per pound (rounded to three decimal places).

Comparing the prices per pound, we find that the price per pound at store A ($3.947) is lower than the price per pound at store B ($4.149).

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Yes, The entry in the 4th row and 5th column of A4 is 1, which means there is a walk of length 4 from vertex 4 to vertex 5 in graph G.

The given adjacency matrix A has 5 rows and 5 columns. The entry in row i and column j represents the edge between vertices i and j. For example, A[1][2] = 1, which means there is an edge from vertex 1 to vertex 2.

To find whether there is a walk of length 4 from vertex 4 to vertex 5 in graph G, we need to examine the entry in the 4th row and 5th column of the matrix A4.

However, we are only given the matrices A, A2, and A3, but not A4. We can calculate A4 using matrix multiplication, specifically by multiplying A3 and A:

A4 = A3 x A

Multiplying A2 by A, we get A3:

A3 = A2 x A

Substituting A3 in the formula for A4, we get:

A4 = (A2 x A) x A

To find the entry in the 4th row and 5th column of A4, we calculate the dot product of the 4th row of A2 and the 5th column of A:\

A2[3][0] x A[0][4] + A2[3][1] x A[1][4] + A2[3][2] x A[2][4] + A2[3][3] x A[3][4] + A2[3][4] x A[4][4]

Simplifying this expression, we get:

1 x 0 + 0 x 0 + 0 x 0 + 1 x 1 + 0 x 0 = 1

Therefore, the answer to the question is yes.

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Complete Question:

A directed graph G has 5 vertices, numbered 1 through 5. The 5 x 5 matrix A is the adjacency matrix for G. The matrices AP and As are given below.

0 1 0 0 0 0 0 0 0 A2 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0

Use the information given to answer the questions about graph G.

(a) Is there a walk of length 4 from vertex 4 to vertex 5 in G?

Answer:

anung itsura ng sand pit?

Answer:

GCF= 11

Step-by-step explanation: