If A={1,2,3} and B={a,b}, write total number of functions from A to B.

The function describing the relationship of the given variables is a= 6r

The statement is givn as:

a varies directly with r

This means that

a= kr

Where k is the constant of variation

When r = 6 , a = 18, we have

18= 6k

Divide by 6

k = 3

Substitute k = 3 in a= kr

a= 6r

Hence, the function describing the relationship of the given variables is a= 6r

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Answer:

120

Step-by-step explanation:

We can do 90*(100/60) to figure out which number is 90 when it is only 60 percent.  This means the original number was 150.  Now we just do 150/5 which equals 30.  Then we can multiply 30*4 = 120.

Answer:

120

Step-by-step explanation:

60% of a number is 90.

Let the number be x.

60% of x = 90

0.6x = 90

x = 90/0.6

x = 150

The number is 150.

4/5 of 150 =

= 4/5 * 150

= 120

Answer:

y = 1/2x + 7

Step-by-step explanation:

This equation represents the rider's height above the ground as a function of time, taking into account the given conditions.

To determine the amplitude, period, axis of symmetry, and phase shift of the transformed sine function representing the rider's height above the ground versus time, we'll break down the problem step by step.

Step 1: Amplitude
The amplitude of a transformed sine function is equal to half the vertical distance between the maximum and minimum values.

In this case, the maximum and minimum heights occur when the rider is at the top and bottom of the Ferris wheel.

The maximum height occurs when the rider is at the top of the Ferris wheel, which is 3 m above the ground level.

The minimum height occurs when the rider is at the bottom of the Ferris wheel, which is 3 m below the ground level.

Therefore, the vertical distance between the maximum and minimum heights is 3 m + 3 m = 6 m.

The amplitude is half of this distance, so the amplitude of the transformed sine function is 6 m / 2 = 3 m.

Step 2: Period
The period of a transformed sine function is the time it takes to complete one full cycle. In this case, it takes 90 seconds to make one full revolution.

Since the rider enters a car from a platform that is located 30° around the rim before the car reaches its lowest point, we can consider this as the starting point of our function.

To complete one full cycle, the rider needs to travel an additional 360° - 30° = 330°.

The time it takes to complete one full cycle is 90 seconds. Therefore, the period is 90 seconds.

Step 3: Axis of Symmetry
The axis of symmetry represents the horizontal line that divides the graph into two symmetrical halves.

In this case, the axis of symmetry is the time at which the rider's height is equal to the average of the maximum and minimum heights.

Since the rider starts 30° before reaching the lowest point, the axis of symmetry is at the midpoint of this 30° interval.

Thus, the axis of symmetry occurs at 30° / 2 = 15°.

Step 4: Phase Shift
The phase shift represents the horizontal shift of the graph compared to the standard sine function.

In this case, the rider starts 30° before reaching the lowest point, which corresponds to a time shift.

To calculate the phase shift, we need to convert the angle to a time value based on the period.

The total angle for one period is 360°, and the time for one period is 90 seconds.

Therefore, the conversion factor is 90 seconds / 360° = 1/4 seconds/degree.

The phase shift is the product of the angle and the conversion factor:
Phase Shift = 30° × (1/4 seconds/degree)

= 30/4

= 7.5 seconds.

Step 5: Equation
With the given information, we can write the equation for the transformed sine function representing the rider's height above the ground versus time.

The general form of a transformed sine function is:
f(t) = A * sin(B * (t - C)) + D

Using the values we found:
Amplitude (A) = 3
Period (B) = 2π / period = 2π / 90 ≈ 0.06981317
Axis of Symmetry (C) = 15° × (1/4 seconds/degree) = 15/4 ≈ 3.75 seconds
Phase Shift (D) = 0 since the graph starts at the average height

Therefore, the equation is:
f(t) = 3 * sin(0.06981317 * (t - 3.75))

Note: Make sure to convert the angles to radians when using the sine function.
This equation represents the rider's height above the ground as a function of time, taking into account the given conditions.

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Answer:

scale factor of 1/3 from the big rectangle to the small rectangle

Step-by-step explanation:

Hope this helps! Please mark me as brainliest:)

The missing terms in the given factorized expression are:

3x²y + 12xy² + 9xy = 3xy ( x + 4y + 3 )

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

We have,

_ x²y + _ y² + 9 _ = 3x _ ( _ + 4y + _ )

We need to fill the boxes and make sure that both sides are equal.

We will remove the bracket on the right side.

i.e 3x _ _ + 12xy_ + 3x_ _

Now,

_ x²y + _ y² + 9 _ = 3x _ _ + 12xy_ + 3x_ _

We will make,

_ x²y  and 3x _ _ equal.

_ y²  and 12xy_ equal.

9 _  and + 3x_ _ equal.

So,

(3)x²y = 3x (x)(y)

(12x)y² = 12xy(y)

9 (xy) = 3x(y)(3)

Thus the missing terms in the given factorized expression are:

3x²y + 12xy² + 9xy = 3xy ( x + 4y + 3 )

3x²y + 12xy² + 9xy = 3x²y + 12xy² + 9xy

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Answer:

See Below

Step-by-step explanation:

Answer:

\(\textsf{b)}\quad \begin{array}{r|cccc}7&0&1&&\\6&1&5&7&\\5&0&2&4&5\\4&0&6&8&\\3&3&8&&\end{array}\)

Step-by-step explanation:

A stem and leaf plot is a type of data display that organizes data by showing the distribution of values along an axis. It provides a quick and easy way to see the distribution of the data.

In a stem and leaf plot, each value in the dataset is split into two parts: a stem and a leaf.

Each data point of the given data set has two-digits. Therefore, the value of the tens digit of each data point is the stem, and the value of the ones digit of each data point is the leaf.

Order the given set of data from smallest to largest:

The stem value is the tens digit of each data point. Therefore, the stem values are 3, 4, 5, 6, and 7.

Usually we would write the stem values in a column from smallest to largest, but as the given answer options show the stem values from largest to smallest, we will write the stem values in a column from largest to smallest:

\(\begin{array}{r|c}7&\\6&\\5&\\4&\\3&\end{array}\)

The leaf value is the ones digit of each data point.

Write the leaf values in a row next to each stem value in increasing order.

For example, the numbers 70 and 71 both have 7 as their stem value.  Their leaf values are 0 and 1, so write these in increasing order in the row next to the 7.

Therefore, the completed stem and leaf plot for the given data is:

\(\begin{array}{r|cccc}7&0&1&&\\6&1&5&7&\\5&0&2&4&5\\4&0&6&8&\\3&3&8&&\end{array}\)

The correct option is A, equilibrium price increases from $6 to $8.

In economics, equilibrium is a state in which the supply and demand for a product or service are balanced, resulting in a stable price. This can occur in a free market, where the price of a good or service is determined by the interaction of buyers and sellers.

Overall, equilibrium is a fundamental concept in many different fields, representing a state of balance or stability in a system or situation.

If the demand schedule changes from D2 to D1, then the demand curve shifts to the left. As a result, the new equilibrium point will be where the new demand curve (D1) intersects with the supply curve (S1).

From the table, we can see that the new equilibrium point is at a price of $8 and a quantity of 15. Therefore, the equilibrium price increases from $6 to $8, but the equilibrium quantity decreases from 15 to 13.

So the correct answer is: equilibrium price increases from $6 to $8.

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The correct answer to the given statistic question is (b) significant at α=0.05 but not at α=0.01. It is important to note that the significance level chosen for a test depends on the specific research question and the consequences of making a type I or type II error.

Based on the information provided, the value of the z statistic for Exercise 22.22 is 2.53. To determine the significance of this test, we need to compare it with the critical values of the standard normal distribution at the given significance levels. For α=0.05, the critical value is 1.96 and for α=0.01, the critical value is 2.58.

Since the value of the z statistic (2.53) is greater than the critical value at α=0.05 (1.96), we can say that the test is significant at α=0.05. However, the value of the z statistic is less than the critical value at α=0.01 (2.58), which means that the test is not significant at α=0.01.

Therefore, the correct answer to the given question is (b) significant at α=0.05 but not at α=0.01. It is important to note that the significance level chosen for a test depends on the specific research question and the consequences of making a type I or type II error.

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Answer:

x = -175

Step-by-step explanation:

Given:

⇒ \(-\frac{x}{7}-8=17\)

Solution:

Work:

\(-\frac{x}{7}-8=17\)

\(-\frac{x}{7}-8+8=17+8\)    ⇒ Add 8 to both sides

\(-\frac{x}{7}=25\)

\(7\left(-\frac{x}{7}\right)=25\cdot \:7\) ⇒ Multiply both sides by 7

-x = 175

\(\frac{-x}{-1}=\frac{175}{-1}\) ⇒ Divide both sides by -1

x = -175

Check:

Since, x = -175. We can substitute into the equation to check.

\(-\frac{-175}{7}-8=17\)

\(-\frac{-175}{7}=25\)

\(25-8=17\) ⇒ Statement = True (25 minus 8 is 17.

Hence, x = -175

Lenvy~

Answer:

$ 3,062.61

Step-by-step explanation:

Account Balance= 2,500(1+ .07/1)^3

Answer:

75 words

Step-by-step explanation:

take half of the 50 then add it to the 50

Answer:

\(\huge\boxed{\sf 75 \ words}\)

Step-by-step explanation:

Richard can type 50 words a minute.

1 minute = 50 words

Multiply both sides by 1.5

1 * 1.5 minutes = 50 * 1.5 words

1.5 minutes = 75 words

Richard can type 75 words in 1.5 minutes.

\(\rule[225]{225}{2}\)

Hope this helped!

Pull out a factor of 1/n from the summand and the result follows.

\(\displaystyle \lim_{n\to\infty} \sum_{i=1}^n \frac{i^4}{n^5} = \lim_{n\to\infty} \frac1n \sum_{i=1}^n \left(\frac in\right)^4 = \boxed{\int_0^1 x^4 \, dx}\)

Answer: 390

Step-by-step explanation:

65 x 6 = 390

78 x 5 = 390

It will take about 9.5 months (or 10 months rounded up) for the rabbit population to reach 5,800.

Let's use the formula for exponential growth to solve this problem:

N = N0 * 2^(t/k)

Where:

N0 = initial population (8 rabbits)

N = final population (5,800 rabbits)

k = doubling time (1 month)

t = time in months (what we're trying to find)

Substituting the values we have:

5,800 = 8 * 2^(t/1)

Dividing both sides by 8:

725 = 2^(t/1)

Taking the logarithm of both sides (base 2):

log2(725) = t/1

t = log2(725) ≈ 9.515

So it will take about 9.5 months (or 10 months rounded up) for the rabbit population to reach 5,800.

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Answer:

2 2/3

Step-by-step explanation:

Answer:

-7 1/3

Step-by-step explanation:

I already learned how to do that

Approximately 4680 minutes are required for 10.0% of a sample of cyclopropane to isomerize to propene at 700 K, based on the given rate constant of 6.2 × 10^(-4) min^(-1).

The isomerization of cyclopropane to propene follows first-order kinetics, which means that the rate of the reaction is directly proportional to the concentration of cyclopropane. The rate constant (k) is a proportionality constant that relates the rate of the reaction to the concentration of the reactant.

In this case, the rate constant for the reaction is given as 6.2 × 10^(-4) min^(-1), and we want to determine the time required for 10.0% of the cyclopropane to isomerize to propene. To solve this, we use the first-order kinetics equation:

ln(A/A₀) = -kt

Where ln is the natural logarithm, A₀ is the initial concentration of cyclopropane, A is the final concentration (10% of A₀), k is the rate constant, and t is the time.

By substituting the given values into the equation, we can isolate t and solve for it. The calculation yields approximately 4680 minutes as the time required for 10.0% of the cyclopropane sample to isomerize to propene at 700 K.

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Answer:

18 weeks

Step-by-step explanation:

So, Hugo received $100 for his birthday.

He saved $20 per week. Let x denote the weeks that passed. Therefore:

\(y=100+20x\)

This equation represents the total money y Hugo has after x weeks.

The printer cost $460. Thus, set y to $460:

\(460=100+20x\)

Solve for x.

Subtract 100 from both sides:

\(360=20x\)

Divide both sides by 20:

\(x=18\)

Therefore, it took Hugo 18 weeks to save up $460.

a. To calculate the expected value of the monthly demand, multiply each unit demand by its probability and then sum the results:

Expected value = (300 * 0.20) + (400 * 0.30) + (500 * 0.35) + (600 * 0.15) = 60 + 120 + 175 + 90 = 445 units

Carolina's monthly order quantity should be 445 units for this product.

b. If Carolina orders 445 units and the actual demand is 300 units, the revenue and cost can be calculated as follows:

Revenue: 300 units * $70 = $21,000
Cost: 445 units * $50 = $22,250

Gain/loss = Revenue - Cost = $21,000 - $22,250 = -$1,250

The company will lose $1,250 in a month if it places an order based on the expected value and the actual demand is 300 units.

c. To calculate the variance and standard deviation for the number of units demanded, first calculate the squared deviation of each demand value from the expected value (445):

(300 - 445)^2 = 21,025
(400 - 445)^2 = 2,025
(500 - 445)^2 = 3,025
(600 - 445)^2 = 24,025

Now, multiply the squared deviations by their respective probabilities and sum the results to obtain the variance:

Variance = (21,025 * 0.20) + (2,025 * 0.30) + (3,025 * 0.35) + (24,025 * 0.15) = 4,205 + 607.5 + 1,058.75 + 3,603.75 = 9,475

Standard deviation = √Variance = √9,475 ≈ 97.34 units

The variance and standard deviation for the number of units demanded are 9,475 and 97.34 units, respectively.

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Answer:15

Step-by-step explanation:

A ladder is resting against a wall.The top of the ladder touches the wall at a height of 9 feet.Find the length of the ladder if the length is 3 feet more than its distance from the wall.

Let the distance of the ladder from the wall be x

The length of the ladder = x+3

The ladder touches the wall at a vertical height of 9 feet.

(x+3)^2 = x^2 + 9^2 ( using the pythagoras theorem

x^2 + 6x+ 9 = x^2 + 81

x^2- x^2 +6x = 81-9

6x= 72

x= 12

Therefore the length of the ladder will be x+3 = 12 + 3 =15 Answer.

Answer:

0.8

Step-by-step explanation:

In order to find its decimal form, we first need to divide the fraction.

\(4\div 5=0.8\)

In decimal form, 4/5 = 0.8. The number is already rounded to the nearest tenth.

Answer:

C. Roanoke, Alexandria, Norfolk

Step-by-step explanation:

Lets expand all of the numbers

Alexandria 136,000

Norfolk 229,000

Roanoke 91,500

Using these number we can easily see that the order is "Roanoke, Alexandria, Norfolk"

I don't understand when you say "Please answer with two answers!" because only one answer is correct

Answer:

The hours are 5, 6,7, and 8.

The earnings are 60 for 5, 72 for 6, 84 for 7, and 96 for 8

Step-by-step explanation:

She earns 12 dollars a hour. So if you just multiply 12 times 5 and so on you get the answer for earnings and the hours.

Answer:

Hours:          Earnings:

5                   $60

6                   $72

7                   $ 84

8                   $96

Step-by-step explanation:

Because Brianna earns $12 per hour, find her earnings by multiplying the number of hours worked by 12:

To find the number hours she worked, given her earnings, divide her total earnings by 12:

Step-by-step explanation:

oh noo nothing can be seen properly..... °-°

but ik a math genius who can help u

If the algorithm has a constant number of steps independent of the input size, s(n) remains the same when n is doubled.

Then the effect on the number of steps required, denoted as s(n), when the number of items being processed (n) is doubled will depend on the specific algorithm and its complexity.

Here are a few possibilities:

1. Constant Time Complexity (O(1)): If the algorithm has a constant time complexity, it means that the number of steps required remains the same, regardless of the input size. In this case, doubling n would not have any impact on s(n).

2. Linear Time Complexity (O(n)): If the algorithm has a linear time complexity, it means that the number of steps required is directly proportional to the input size. Doubling n would approximately double the number of steps as well. Thus, s(n) would increase in a linear manner.

3. Quadratic Time Complexity (O(n^2)): If the algorithm has a quadratic time complexity, it means that the number of steps required grows quadratically with the input size. When n is doubled, the number of steps would be approximately four times the original amount. Thus, s(n) would increase significantly.

4. Logarithmic Time Complexity (O(log n)): If the algorithm has logarithmic time complexity, doubling n would not have a substantial impact on the number of steps required. The increase in s(n) would be relatively small compared to the increase in n.

These are just a few examples, and there are various other complexities that algorithms can exhibit.

Each algorithm has its own time complexity, which determines how the number of steps required changes as the input size is doubled.

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The given matrix is A = [1/2 1/4 1/2; -1/2 1/4 1/2; -1/2 1/4 -1/2]. An eigenvector of a square matrix A is a nonzero vector v such that the product Av is a scalar multiple of v.

That is, Av = λv, where λ is a scalar known as the eigenvalue of A corresponding to v. Therefore, the eigenvector of a matrix A is defined by the equation: A x = λx , where λ is a scalar and x is a vector. We solve the equation (A-λI) x = 0, where I is the identity matrix, in order to obtain the eigenvalues λ.

Then, we substitute each eigenvalue λ in (A-λI) x = 0 to get the eigenvectors x. To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0.

So, A - λI = [1/2 - λ, 1/4, 1/2; -1/2, 1/4 - λ, 1/2; -1/2, 1/4, -1/2 - λ].

Therefore, det(A - λI) = (1/2 - λ)[(1/4 - λ)(-1/2 - λ) - (1/2)(1/4)] - (1/4)(-1/2)(-1/2 - λ) - (1/2)[(-1/2)(-1/2 - λ) - (1/4)(-1/2)] + (1/2)[(-1/2)(1/4) - (1/2)(-1/2)]

det(A - λI) = (1/2 - λ)[λ³ - (3/4)λ - (1/4)] = 0

Hence, λ₁ = 1/2 and λ₂ = -1/2.

Now we find the eigenvectors corresponding to λ₁ = 1/2.

We need to solve the equation (A - λ₁I) x = 0.

So, A - λ₁I = [0 1/4 1/2; -1/2 -1/4 1/2; -1/2 1/4 -1] and

(A - λ₁I) x = [0 1/4 1/2; -1/2 -1/4 1/2; -1/2 1/4 -1] x = [0; 0; 0]

Multiplying (A - λ₁I) by x, we get the system of equations:

1/4 y + 1/2 z = 0-1/2 x - 1/4 y + 1/2 z

= 0-1/2 x + 1/4 y - z = 0

Multiplying the first equation by 2, we obtain: y + 2z = 0

Solving for y, we get: y = -2z

Substituting y = -2z in the second and third equations, we get: 1/2 x + 1/2 z = 0-1/2 x - 5/4 z = 0

Solving for x and z, we get: x = z and z = 0

Substituting z = 0 in y = -2z, we get y = 0.

So the eigenvector corresponding to λ₁ = 1/2 is x₁ = [0; 0; 0].

Now we find the eigenvectors corresponding to λ₂ = -1/2.

We need to solve the equation (A - λ₂I) x = 0.

So, A - λ₂I = [1 1/4 1/2; -1/2 3/4 1/2; -1/2 1/4 1/2] and

(A - λ₂I) x = [1 1/4 1/2; -1/2 3/4 1/2; -1/2 1/4 1/2]

x = [0; 0; 0]

Multiplying (A - λ₂I) by x, we get the system of equations:

x + 1/4 y + 1/2 z

= 0-1/2 x + 3/4 y + 1/2 z

= 0-1/2 x + 1/4 y + 1/2 z = 0

Multiplying the second equation by 2, we obtain:

-x + 3/2 y + z = 0

Multiplying the third equation by 2, we obtain: -x + 1/2 y + z = 0

Solving the system of equations, we get: x = y and y = -2z

The eigenvector corresponding to λ₂ = -1/2 is x₂ = [1; -2; 1].

Therefore, the answer is: (a) x₁ = [0; 0; 0] and (d) x₂ = [1; -2; 1].

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Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer:

0.15 = 3/20. 0.369= 369/1000.