What is the relationship between period and frequency? (both in words and mathematically)

Answer:

14/16, 21/24, and 28/32

Step-by-step explanation:

(7 x 4) (8 x 4) = 28/32

(7 x 3) (8 x 3) = 21/24

(7 x 2) (8 x 2) = 14/16

To save enough money to pay for one year of school, regardless of interest earned on the savings, Yasmine should choose a plan that allows her to save $9,000 annually. This means she should opt for a savings plan that offers a high-interest rate or a low-risk investment option.

Here are a few options that Yasmine can consider:

High-yield savings account: Yasmine can open a high-yield savings account that offers a competitive interest rate. By depositing $9,000 annually into the account, she can accumulate the required funds for one year of school.

Certificate of Deposit (CD): Yasmine can invest her money in a CD with a fixed interest rate and a specific maturity period, such as one year. This way, she can ensure that her savings are protected and will grow over time.

Money market account: Yasmine can open a money market account that typically offers higher interest rates than regular savings accounts. By consistently contributing $9,000 per year, she can build up the necessary funds for her education.

Remember, it is essential for Yasmine to research and compare different savings options, considering factors such as interest rates, fees, and any potential restrictions or penalties associated with the account. Consulting with a financial advisor can also provide valuable insights tailored to Yasmine's specific financial situation and goals.

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Since Callie cannot make a fraction of a necklace, she can make a maximum of 5 necklaces from the given length of leather cord.

To determine the number of necklaces Callie can make from the given length of leather cord, we need to convert the measurements to a consistent unit.

Given:

Length of leather cord = 4 yards

Length of each necklace = 28 inches

First, let's convert the length of the leather cord from yards to inches:

1 yard = 36 inches (since there are 3 feet in a yard and 1 foot = 12 inches)

4 yards = 4 * 36 = 144 inches

Now we can calculate the number of necklaces:

Number of necklaces = Length of leather cord / Length of each necklace

Number of necklaces = 144 inches / 28 inches ≈ 5.143

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Answer:

Both are correct

Step-by-step explanation:

Student A used the distributive property to multiply 17 and 4 and 17 and 15 and find the sum, which would give you:  17 * 4 + 17 * 15 = 68 + 255 = 323

Student A did the addition inside the parentheses first and then multiplied the 17 and 19, which gives us:  17(4 + 15) = 17 * 19 = 323

The requried another dose of Robitussin would need to be taken at least 5 hours after the initial dose in order for the body to maintain the minimum effective amount of 100 mg.

Let t be the number of hours that have passed since the dose was taken, and let A(t) be the amount of Robitussin in the body at time t. We know that A(0) = 1000 mg (the initial dose), and that A(t) = 0.55 A(t-1) (the rate of decay is 55% per hour).

We want to find the value of t such that A(t) = 100 mg. We can use recursive substitution to find A(t) in terms of A(0):

A(1) = 0.55 A(0) = 0.55 * 1000 = 550

A(2) = 0.55 A(1) = 0.55 * 550 = 302.5

A(3) = 0.55 A(2) = 0.55 * 302.5 = 166.375

A(4) = 0.55 A(3) = 0.55 * 166.375 = 91.50625

A(5) = 0.55 A(4) = 0.55 * 91.50625 = 50.3284375

So, after 5 hours, the amount of Robitussin in the body drops below 100 mg.

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6 is the maximum number of tickets he can buy with $50

To determine the maximum number of tickets Jordan can buy with $50, we need to divide the total amount of money by the cost of each ticket.

$50 / $7.75 per ticket = 6.45 tickets

However, since Jordan can only buy whole tickets,

the maximum number of tickets he can buy with $50 is 6.

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The least number of boxes the bakery can use is 4 boxes of 8-cupcake capacity (32 cupcakes) and 3 boxes of 5-cupcake capacity (15 cupcakes), totaling 47 cupcakes. In this arrangement, there are no empty spaces, and a total of 7 boxes are used.

To minimize the number of boxes used without empty spaces, the bakery needs to efficiently pack the 47 cupcakes into the 5-cupcake and 8-cupcake boxes.

To start, we can calculate how many 8-cupcake boxes can be filled by dividing the total cupcakes (47) by the capacity of the 8-cupcake box:

47 ÷ 8 = 5 (remainder 7).

This means that 5 boxes of 8-cupcake capacity can be filled, leaving us with 7 cupcakes.

Now we'll work with the remaining 7 cupcakes and the 5-cupcake boxes. Since one 5-cupcake box can fit 5 of the remaining cupcakes, we still have 2 cupcakes left. However, if we replace one 8-cupcake box with two 5-cupcake boxes, we can fit the remaining 2 cupcakes, effectively filling up all the boxes without empty spaces.

So, the least number of boxes the bakery can use is 4 boxes of 8-cupcake capacity (32 cupcakes) and 3 boxes of 5-cupcake capacity (15 cupcakes), totaling 47 cupcakes. In this arrangement, there are no empty spaces, and a total of 7 boxes are used.

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Answer: B. y = 3x - 5

Step-by-step explanation:

    First ,we know Option C will not be an option because of the y-intercept (the point at which the line intersects the y-axis) is -5. This is shown by the point (0, -5). Option C shows it as 1.

    We will substitute a point into the given equations and see if the simplified version remains true.

✗ A ➜ y = -3x - 5

  ➜ -2 = -3(1) - 5

  ➜ -2 ≠ -8

✓ B ➜ y = 3x - 5

  ➜ -2 = 3(1) - 5

  ➜ -2 = -2

✗ D ➜ y = -x - 5

  ➜ -2 = -1 - 5

  ➜ -2 ≠ -6

    Using this method of substitution, we can see the answer is B.

Answer:

$1.88

Step-by-step explanation:

We Know

7 packs of $13.18

What is the cost, in dollars, per pack?

We Take

13.18 ÷ 7 = $1.88

So, the cost per pack is $1.88

The solving of equation 3²x=4 in both the given cases gives the answer

x = 0.631.

We have,

A mathematical statement composed of two representations joined by an equal sign is known as an equation.

3x - 5 = 16 is an example of an equation.

We obtain the value for the variable x as x = 7 after solving this equation.

So,

(1) Common logarithm:

2x log 3 = log 4, or 2x(0.47712) = 0.60206

When we solve for x, we get 0.95424x = 0.60206, and x = 0.60206/0.95424.

x = 0.631

(2) Logarithm with base 3:

2x (log to the base 3 of 3) = (log to the base 3 of 4)

This can be reduced to 2x(1) = 2x = (log 4)/log 3 = 1.262.

Divide the result by 2 to get x = 0.631

Therefore, the solving of equation 3²x=4 in both the given cases gives the answer x = 0.631.

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complete question:

Show that solving the equation 3 ²x=4 by taking the common logarithm of each side is equivalent to solving it by taking the logarithm with base 3 of each side.

The list that contains three equivalent expressions is given as follows:

KT/KS, KN/KL, cos K.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For triangle KLN, we have that:

Hence:

cos(K) = KN/KL.

For triangle KTS, we have that:

Hence:

cos(K) = KT/KL.

As the two triangles are similar, they have the same trigonometric ratios.

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0.3514 * 380 ≈ 133.7 To find out how many students had scores between 35 and 61, we need to first calculate the interquartile range (IQR) which is the difference between the third quartile (Q3) and the first quartile (Q1).
Q1 is the median of the lower half of the data, which in this case is (11+35)/2 = 23.
Q3 is the median of the upper half of the data, which in this case is (70+79)/2 = 74.5.
So, IQR = Q3 - Q1 = 74.5 - 23 = 51.5.

Scores between 35 and 61 fall within one IQR from Q1. So, we need to find out what proportion of the scores fall within this range.
To do this, we need to calculate the z-scores for 35 and 61, using the formula z = (x - μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.
We don't have the mean and standard deviation, but we can estimate them using the five-number summary. The median (Q2) is (61+35)/2 = 48, and the mean is likely to be close to this value since the data is roughly symmetric. The range (max-min) is 79-11 = 68, so the standard deviation is roughly σ = range/4 = 17.
Using these estimates, we can calculate the z-scores as follows:
z1 = (35 - 48)/17 = -0.76
z2 = (61 - 48)/17 = 0.76

We can look up the proportion of scores between these two z-scores in a standard normal distribution table, or use a calculator or software to calculate it. It turns out to be about 0.3514, or 35.14%.
To find out how many students had scores between 35 and 61, we can multiply this proportion by the total number of students:
0.3514 * 380 ≈ 133.7
So, the answer is not one of the choices given.

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The answer is not one of the choices given.0.3514 * 380 ≈ 133.7 To find out how many students had scores between 35 and 61, we need to first calculate the interquartile range (IQR) which is the difference between the third quartile (Q3) and the first quartile (Q1).

Q1 is the median of the lower half of the data, which in this case is (11+35)/2 = 23.

Q3 is the median of the upper half of the data, which in this case is (70+79)/2 = 74.5.

So, IQR = Q3 - Q1 = 74.5 - 23 = 51.5.

Scores between 35 and 61 fall within one IQR from Q1. So, we need to find out what proportion of the scores fall within this range.

To do this, we need to calculate the z-scores for 35 and 61, using the formula z = (x - μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.

We don't have the mean and standard deviation, but we can estimate them using the five-number summary. The median (Q2) is (61+35)/2 = 48, and the mean is likely to be close to this value since the data is roughly symmetric. The range (max-min) is 79-11 = 68, so the standard deviation is roughly σ = range/4 = 17.

Using these estimates, we can calculate the z-scores as follows:

z1 = (35 - 48)/17 = -0.76

z2 = (61 - 48)/17 = 0.76

We can look up the proportion of scores between these two z-scores in a standard normal distribution table, or use a calculator or software to calculate it. It turns out to be about 0.3514, or 35.14%.

To find out how many students had scores between 35 and 61, we can multiply this proportion by the total number of students:

0.3514 * 380 ≈ 133.7

So, the answer is not one of the choices given.

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Thus, a decision to not reject the null hypothesis should be interpreted with caution and further investigation may be needed to fully understand the underlying factors affecting student study habits at the university.

The null hypothesis in this scenario would be that the mean number of hours students study at the university (per day) is equal to or greater than 4.4 hours.

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The sister who had less variation in her daily step count, given the box plots, would be Brenda.

To determine variation in a box plot, one can look at the length of the whiskers. Longer whiskers indicate greater variation in the data, while shorter whiskers indicate less variation.

A wider box indicates greater variation, while a narrower box indicates less variation.

We can also look at the range of the data.

Janet's range is:

= 9, 000 - 5, 000 steps

= 4, 000 steps

Brenda's range would be :

= 10, 000 - 7, 000

= 3, 000 steps

Brenda's range being lower means her variation is less.

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The correct expression to create a random number in the range of [-3,3) would be option A: r.nextDouble() * 6.0 - 3.0.

Explanation: The nextDouble() method of Random class returns a double in the range of [0,1), which means it can generate any random value between 0 (inclusive) and 1 (exclusive). To create a random number in the range of [-3,3), we need to scale and shift the output of the nextDouble() method.

Option A is the correct expression as it first scales the output by multiplying it by 3.0 (which will give a range of [0,3)) and then shifts it down by subtracting 3.0 (which will give a range of [-3,0)). Therefore, we need to modify the expression to r.nextDouble() * 6.0 - 3.0 to generate a random number in the range of [-3,3).

Option B multiplies the output of nextDouble() by 6.0, which gives a range of [0,6)) and then subtracts 0.5, which shifts the range to [-0.5,5.5). This is not the correct expression to generate a random number in the range of [-3,3).

Option C multiplies the output of nextDouble() by 6.0, which gives a range of [0,6)) and then adds 3.0, which shifts the range to [3,9). This is not the correct expression to generate a random number in the range of [-3,3).

Option D multiplies the output of nextDouble() by 6.0, which gives a range of [0,6)) and then adds 0.5, which shifts the range to [0.5,6.5). This is not the correct expression to generate a random number in the range of [-3,3).

Option E subtracts 3.0 from the output of nextDouble() and then multiplies it by 6.0, which gives a range of [-3,3). However, this expression is not the correct way to scale and shift the output of the nextDouble() method.

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Pat played a total of 11 + 7 = 18 games in the tournament.

Let's denote the number of games Pat lost as L and the number of games Pat won as W.

We are given the following information:
Pat started with 100 points.
In each game, Pat either loses 3 points (L games) or gains 2 points (W games).
We can set up the following equations based on this information:
Total points = Initial points + Gained points - Lost points
Total points = 100 + 2W - 3L
We need to find the total number of games Pat played, which is the sum of games won and lost (W + L).

To solve for W + L, we need to find a relationship between W and L.
We can rearrange the Total points equation to find such a relationship:
2W - 3L = Total points - 100
2W = 3L + (Total points - 100)
Now, we know that both W and L must be integers since Pat can't win or lose a fraction of a game.

As 2W and 3L are both integers, their sum (3L + (Total points - 100)) must be even.

Thus, the total points must be an even number.
We can try different even values for the total points and check if the corresponding W and L values are integers. After trying different values, we find that:
Total points = 122
W = 11
L = 7.

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Answer: 36

Step-by-step explanation: you would take 60-24 and that makes 36.

The solution of the equation is c= 2/5 and d= 3/2.

We have Equation.

5c + 4d = 8

-5c + 2d = 1

Solving above equation we get

5c + 4d = 8

-5c + 2d = 1

___________

         6d = 9

          d = 3/2

and, 5c + 4(3/2)= 8

5c = 8 - 6

5c = 2

c= 2/5

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The phrase that completes the sentence is "determined by."

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The IQ score that is higher than 90% of the population is 112.8.

We know that the IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 10.

Let X be the random variable representing the IQ scores. We want to find the value x such that 90% of the observations lie above x.

Using the standard normal distribution table or calculator, we can find the z-score corresponding to the 90th percentile as 1.28.

The z-score formula is z = (x - μ) / σ, where μ is the mean, σ is the standard deviation and x is the value we want to find.

Plugging in the values, we get 1.28 = (x - 100) / 10. Solving for x, we get x = 100 + 12.8 = 112.8.

Therefore, the IQ score that is higher than 90% of the population is 112.8.

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The first table with function y = 5+5x is completed as follows:

X = 0 1 2 3 4

Y = 5 10 15 20 25

The second table with function y= 5+5^x is completed as follows:

X= 0 1 2 3 4

y= 10 10 30 130 630

For the first table;

when X = 0 , y = 5+5(0) = 5

when X = 1, Y = 5+5(1) = 10

When X = 2, Y = 5+5(2) = 15

When X = 3, y = 5+5(3) = 20

When X = 4, y = 5+5(4) = 25

For the second table:

When X = 0, y = 5+5(^0) = 10

When X = 1, y = 5+5(^1) = 10

When X = 2, y = 5+5(^2) = 30

When X = 3, y = 5+5(^3) = 130

When X = 4, y = 5+5(^4) = 630

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Answer:

RT is perpendicular to WS because when parallel lines are cut by a transversal, the corresponding angles are equal.

Step-by-step explanation:

The correct option is: d. No. There are no free variables since the matrix must have 5 pivots

If the equation Ax=b is consistent for every b in R, it means that the matrix A is invertible, since the solutions to the equation can be expressed as x = [tex]A^(^-^1^)[/tex]b.

An invertible matrix has full rank, which means that it has 5 pivots in this case.

If Ax=b has more than one solution for some b, then there would be two different vectors x₁ and x₂ that satisfy the equation, which implies that A(x₁ - x₂) = 0.

This means that the matrix A has a nontrivial nullspace, which contradicts the fact that A has full rank. Therefore, it is not possible for Ax=b to have more than one solution for any b in R.

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A binomial tree with one-month time steps is used to value an index option. The interest rate is 3% per annum and the dividend yield is 1% per annum. The volatility of the index is 16%. The probability of an up movement is approximately 0.4704, which corresponds to answer choice A.

The probability of an up movement in a binomial tree is given by the formula:

[tex]p = (e^{r - q} * u - d) / (u - d)[/tex]

where r is the interest rate, q is the dividend yield, u and d are the up and down factors, respectively.

In this case, r = 0.03/12 = 0.0025 (monthly interest rate),

q = 0.01/12 = 0.000833 (monthly dividend yield), [tex]u = e^{\sigma * \sqrt{1/12}} = e^{0.16 * \sqrt{1/12}}[/tex] ≈ 1.0403, and

d = 1/u ≈ 0.9614.

Substituting these values into the formula, we get:

[tex]p = (e^{0.0025 - 0.000833} * 1.0403 - 0.9614) / (1.0403 - 0.9614)[/tex] ≈ 0.4704

Hence, the correct option is A) 0.4704.

The complete question is:

A binomial tree with one-month time steps is used to value an index option. The interest rate is 3% per annum and the dividend yield is 1% per annum. The volatility of the index is 16%. What is the probability of an up movement?

0.4704

0.5065

0.5592

0.5833

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The total number of hours Hong was driving is 34.5 hours, which is a mixed number in simplest form of 34 1/2 hours.

To find the total number of hours Hong was driving, we need to divide the total amount of gas used by the rate of gas consumption per hour.

Let's first convert the mixed number 3 5/6 to an improper fraction:

3 5/6 = (3 × 6 + 5) / 6 = 23/6

So, Hong used a total of 23/6 gallons of gas.

Now, we need to divide this by the rate of gas consumption per hour, which is 7/9 gallons:

(23/6) ÷ (7/9) = (23/6) × (9/7) = (23 × 3) / 2 = 34.5

Therefore, the total number of hours Hong was driving is 34.5 hours, which is a mixed number in simplest form of 34 1/2 hours.

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The solutions of the given equation in the interval [0, 2π) are:

x = π/4, 3π/4, 5π/4, 7π/4

Let's start by simplifying the given equation using the trigonometric identity:

sec²(x) - tan²(x) = 1

Rearranging, we get:

sec²(x) = tan²(x) + 1

Substituting this into the given equation, we get:

3sec²(x) - 2tan²(x) - 4 = 0

3(tan²(x) + 1) - 2tan²(x) - 4 = 0

tan²(x) = 1

Taking the square root of both sides, we get:

tan(x) = ±1

We need to solve for x in the interval [0, 2π), so we need to find all solutions of the equation tan(x) = ±1 within that interval.

When tan(x) = 1, we have x = π/4 and 5π/4, both of which are in the given interval.

When tan(x) = -1, we have x = 3π/4 and 7π/4, both of which are also in the given interval.

Therefore, the solutions of the given equation in the interval [0, 2π) are:

x = π/4, 3π/4, 5π/4, 7π/4

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The tangent to the circle is AP and the length of side AP = 24

Given data ,

Let the center of the circle be O

And , the length of the line segment OB = 7 units

The length of the line segment BP = 18 units

Now , the length of the line AP = √ ( OP )² - ( OB )²

On simplifying the equation , we get

AP = √ ( 25 )² - ( 7 )²

AP = √ ( 625 - 49 )

AP = √576 units

AP = 24 units

Hence , the length of the tangent AP = 24 units

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The fruit stand owner can make 23 complete orange baskets.

Division is a mathematical operation which involves the sharing of an amount into equal-sized groups. For example, “12 divided by 4” means “12 shared into 4 equal groups”, which would be 3.

To determine the number of complete orange baskets that can be made, divide the total number of oranges by the number of oranges per basket.

Total oranges: 185

Oranges per basket: 8

Divide 185 by 8 to find the number of complete baskets:

185 ÷ 8 = 23

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There are several types of values that individuals and societies hold. Here are the differences among global values, terminal values, instrumental values, and domain-specific values:

Global values are values that are considered important across cultures and societies. These values are often seen as universal and are not specific to any particular group or society.

Global values include traits such as honesty, integrity, and respect for others. These values are considered fundamental to human interaction and are often emphasized in ethical and moral teachings.

Terminal values are values that individuals or societies hold as ultimate goals or end states. These values are often seen as the most important goals that individuals or societies can strive for.

Examples of terminal values include happiness, freedom, and world peace. These values are often deeply rooted in culture and are influenced by factors such as religion, history, and political ideology.

Instrumental values are values that individuals or societies hold as means to achieve the terminal values. These values are seen as important because they help individuals or societies achieve their ultimate goals.

Examples of instrumental values include hard work, responsibility, and self-discipline. These values are often taught through socialization and are reinforced through the rewards and punishments for responsible.

Domain-specific values are values that are specific to a particular domain or area of life. These values are often shaped by the unique demands and characteristics of the domain.

For example, in the domain of business, values such as profitability, innovation, and customer satisfaction may be considered important.

These values are often influenced by the goals and objectives of the organization, as well as the needs and desires of stakeholders such as customers, employees, and shareholders.

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Solving the logarithm equation log4(x + 20) = 3 for x , the solution is 44

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

log4(x 20) = 3

Express properly

So, we have

log4(x + 20) = 3

Take the exponents of both sides

So, we have the following representation

x + 20 = 4^3

When the exponents are evaluated, we have

x + 20 = 64

Subtract 20 from both sides of the equation

This gives

x = 44

Hence, the value of x in the equation is 44

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