This is 9th-grade math

The pattern in y = x² exhibits a nonlinear increase in y as x increases, forming a U-shaped curve, while the pattern in y = 15 + x shows a linear increase in y as x increases at a constant rate.

The patterns in the equations y = x² and y = 15 + x differ in terms of the direction of change. In the equation y = x², the pattern shows an increase in y as x increases.

As x increases from negative to positive values, the corresponding y values also increase, forming a symmetric U-shaped curve. The rate of increase for y becomes steeper as x moves further away from zero.

On the other hand, in the equation y = 15 + x, the pattern shows a linear increase in y as x increases. As x increases, the corresponding y values increase in a straight line.

The rate of increase for y remains constant at one unit per increase in x. This linear pattern reflects a constant upward shift of the graph as x increases.

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Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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The predictions of the 2.3 million people who responded to the questionnaire turned out to be wrong, and Roosevelt won in a landslide. This error in the prediction occurred due to undercoverage and non-response.

The problem that occurred during the poll conducted by the magazine called Literary Digest in 1936 was the undercoverage and non-response. The magazine mailed questionnaires to 10 million people, and they mailed questionnaires to people whose mailing addresses were selected from telephone directories, country club memberships, and automobile registrations. However, only 2.3 million people returned the questionnaires to the magazine, and they predicted that Landon would win with 57% of the vote. The predictions of the 2.3 million people who responded to the questionnaire turned out to be wrong, and Roosevelt won in a landslide. This error in the prediction occurred due to undercoverage and non-response.

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Answer:

6 and -2

Step-by-step explanation:

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

We can use the M/M/1 queuing model to solve this problem.

(a) The arrival rate of customers is λ = 10 per hour, and the service rate of the teller is μ = 15 per hour (since the average service time is 4 minutes or 0.067 hours). Using the formula for the utilization factor, we have:

ρ = λ/μ = 10/15 = 0.67

(b) Using the formula for the average number of customers in the system, we have:

L = λ/(μ-λ) = 10/(15-10) = 2

(c) Using the formula for the average time spent by a customer in the system, we have:

W = 1/(μ-λ) = 1/(15-10) = 0.2 hours or 12 minutes

In summary, the utilization factor of the teller is 0.67, the average number of customers in the system is 2, and the average time spent by a customer in the system is 12 minutes. These results indicate that the bank is operating at a relatively high level of congestion, with customers experiencing a significant amount of waiting time.

One possible solution to this problem is to add another teller to the bank to increase the service rate and reduce the average waiting time for customers. Alternatively, the bank could implement a system for scheduling appointments or prioritizing certain types of transactions to better manage the flow of customers.

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Analysis means examining the whole in order to learn about the individual elements. Correct option is b).

Analysis involves breaking down a complex system or situation into smaller parts in order to understand how they work together. This process allows for a more detailed examination of the individual components, which can then be studied in isolation or in relation to one another.

Analysis is a critical part of problem-solving and decision-making, as it enables us to identify patterns and relationships that might not be immediately apparent. By analyzing a situation or system, we can gain a deeper understanding of its strengths, weaknesses, opportunities, and threats, which can inform our strategic planning and risk management efforts. Correct option is b).

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Step-by-step explanation:

8+(-21)= -21+8

it is not associative property it is commutative property

Answer:

1. 0.37037037037

2. 0.88888888888

3. 1

4. 2.28571428571

Answer:

1) 10/27

2) 8/9

3) 2/2 or 1

4) 16/7 or 2 2/7

Step-by-step explanation:

Whenever fractions are to be be divided, it should first be rewritten with a multiplication sign with the second fraction's reciprocal.

Valerie needs to run \(8\frac{1}{8}\) laps.

What are mixed fractions?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

You can divide any fraction into two pieces. These are the denominator and numerator. A improper fraction is one in which the numerator is greater than the denominator. The numerator must then be multiplied by the denominator by the students. They will then receive a specific form of a fraction. That is referred to as a mixed fraction.

Given,

Number of laps valerie ran = \(3\frac{1}{4}\) laps

Number of times her coach wants her to run = \(2\frac{1}{2}\) times

Therefore,

total number of laps she needs to run = \(3\frac{1}{4} \times 2\frac{1}{2}\)

                                                               \(= \frac{13}{4} \times \frac{5}{2}\)

                                                               \(= \frac{65}{8}\) laps

                                                               \(=8\frac{1}{8}\) laps.

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Answer:

1330.5 cm³

Step-by-step explanation:

To find the volume you want to find the area of the circle and then times this  by 14 which is the length of the shape

Area of circle = πr²

11 = the diameter so 5.5 = radius

5.5² x π = 121/4 π

times this by 14 to get  1330.464489 cm³

to 1dp = 1330.5 cm³

Answer:

1330cm³ (rounded to 3 s.f.)

Step-by-step explanation:

The formula of finding the volume of a cylinder is: \(\pi\) × r² × h

r is the radius of the cylinder, which is also half of the diameter.

You know the diameter is 11cm and the height (h) is 14cm.

Volume of cylinder = \(\pi\) × (11÷2)² × 14

                                = \(\pi\) × 5.5² × 14

                                = \(\pi\) × 30.25 × 14

                                = 423.5\(\pi\)

                                = 1330cm³ (rounded to 3 s.f.)

Value of cot690° is -√3 .

Given,

The circular measure of the angle is given as 690° .

Thus according to trigonometric ratios ,

Cot (690)

Further simplifying cot (690) in the known range of angles .

Then,

cot(690) = cot(720 - 30)

cot (720 - 30) = cot (-30)

cot(-30) = -√3

Hence the value of cot 690 will be -1.73 .

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Answer:

After 10 years he will make 142 000$ more compared to what was earning without training

Answer:

B

Step-by-step explanation:

2 x 2.75 is for the pastries, and 1.45 for the tea.

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Answer:

7

Step-by-step explanation:

Answer:

You will have exact seven.

9514 1404 393

Answer:

  1.5 cm

Step-by-step explanation:

The midpoint of OB is 9/2 = 4.5 cm from O

The midpoint of OA is 12/2 = 6.0 cm from O

Since O is not on AB, we must have B on OA, so the distance between midpoints is ...

  6 cm -4.5 cm = 1.5 cm . . . . distance between midpoints

The function of the town's population is an exponential growth

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

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

Using the above as a guide, we have the following:

This means that the function is an exponential growth

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Answer:

5.6

Step-by-step explanation:

11*7=77

11.8*7= 82.6

82.6-77=5.6

In this scenario, we can expect most of the light bulbs to have lifetimes close to 10 months, with some variation due to the standard deviation of 2 months.

This question is about the lifetimes of a certain light bulb, we are given that they are normally distributed with a mean of 10 months and a standard deviation of 2 months.
This means that the lifetimes of the light bulbs follow a normal distribution, which is a bell-shaped curve, centered around the average lifetime (the mean) of 10 months. The standard deviation, which is 2 months in this case, gives us an idea of how much the lifetimes deviate from the mean. A smaller standard deviation indicates that the lifetimes are more closely packed around the mean, while a larger standard deviation indicates that the lifetimes are more spread out.

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Answer:

A=l×w×h

Step-by-step explanation:

5×5×6×7

1050. or if we add 4 in the solution part 2400

Answer:

8 tickets

Step-by-step explanation:

x = 10 in the given equation.

We have then:

C (x) = 17.5x - 10

C (10) = 17.5 * (10) - 10

C (10) = 165

Answer:

to buy 10 tickets cost:

$ 165

b. How many tickets can you buy with $ 130?  

For this case we must make the substitution: C (x) = 130

We have then:

C (x) = 17.5x - 10

130 = 17.5x - 10

Clearing x we have:

17.5x = 130 + 10

17.5x = 140

x = (140) / (17.5)

x = 8

Answer:

You can buy 8 tickets with $ 130

Answer:

1: C

2: D

3: A

4: B

5: C

Step-by-step explanation:

Answer:

Q1 - answer: D

Q2 - answer: D ( spelling mistake, I am going to assume that wases is washes)

Q3 -  19 ( is this really necessary?)

Step-by-step explanation:

Q1: can be answered by process of elimination. A, it consists of ONLY numbers i8s wrong! the expression contains 2 variables. then B is wrong once again. then C. now this one had me for a moment but if you look closer you will see the flaw. it says " it consists of numbers and A variable. In the equation there are 2. so C is also incorrect. so D is the correct answer. not only that everything it says applies to the expression.

Q2: for this one if you read the question carefully you will find out the answer. now, it says Chris earns 10 dollars EACH TIME he washes his neighbors car. so that means that, that the amount of times he washes the car is the variable. lets say or example, he washes the car 7 times. then the 10x becomes 10(7). which is 10 times 7.

I need to get to lunch i promise I will do 4 and 5 soon.

The domain of f′(x) is also x > 0 for the same reason.

Given, f(x) = 1/√x

We know that the derivative of a function is the slope of the tangent line at any point on the function.

It measures the rate at which the function is changing with respect to its variable.

We can find the derivative of the function f(x) using the power rule of differentiation which is given as follows,

Power rule of differentiation:

(d/dx)xn = nx^(n-1)

Here, f(x) = 1/√x = x^(-1/2)

Using the power rule of differentiation,(d/dx)f(x) = (d/dx)x^(-1/2)

= (-1/2)x^(-3/2)

= -1/(2x^(3/2))

Therefore, the derivative of the function f(x) = 1/√x is f′(x) = -1/(2x^(3/2)).

The domain of f(x) is x > 0 since the denominator of the function cannot be equal to zero or negative.

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A random sample variance is when a subset of individuals from a population is chosen using a random selection method, such as a random number generator, to ensure that each individual has an equal chance of being chosen.

A random sample is a type of sampling method used to select individuals from a population to form a sample. To generate a random sample, a list of all the individuals in the population must first be created. Each individual should be numbered consecutively. A random number generator, such as a computer or calculator, can then be used to generate a list of random numbers between 1 and the total number of individuals in the population. The individuals who correspond to the numbers generated by the random number generator form the sample. This ensures that each individual in the population has an equal chance of being chosen for the sample.

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The measure of the angles are 105 degrees

The sum of the angles is given as 210 degree

Alternate angles are equal.

So, we have:

x + x = 210

This gives

2x = 210

Divide by 2

x = 105

Hence, the measure of the angles are 105 degrees

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The general solution form for the recurrence tn = 120,-2 - 166n-3 + 2.

Given a recurrence relation tn = 120,-2 - 166n-3 + 2 we have to derive the general solution form for the recurrence sequence.

We have the recurrence relation tn = 120,-2 - 166n-3 + 2

We need to find the solution for the recurrence relation.

Associated Homogeneous Equation: First, we need to find the associated homogeneous equation.

                                     tn = -166n-3 …..(i)

The characteristic equation is given by the following:tn = arn. Where ‘a’ is a constant.

We have tn = -166n-3..... (from equation i)ar^n = -166n-3

                                Let's assume r³ = t.

Then equation i becomes ar^3 = -166(r³) - 3ar^3 + 166 = 0ar³ = 166

Hence r = ±31.10.3587Complex roots: α + iβ, α - iβ

Characteristics Polynomial:

                   So, the characteristic polynomial becomes(r - 31)(r + 31)(r - 10.3587 - 1.7503i)(r - 10.3587 + 1.7503i) = 0

The general solution of the Homogeneous equation:

Now we have to find the general solution of the homogeneous equation.

                  tn = C1(-31)n + C2(31)n + C3 (10.3587 + 1.7503i)n + C4(10.3587 - 1.7503i)

                        nWhere C1, C2, C3, C4 are constants.

Computing a Particular Solution:

                Now we have to compute the particular solution.

                                  tn = 120-2 - 166n-3 + 2

Here the constant term is (120-2) + 2 = 122.

The solution of the recurrence relation is:tn = A122Where A is the constant.

The General Solution of Non-Homogeneous Equation:

        The general solution of the non-homogeneous equation is given bytn = C1(-31)n + C2(31)n + C3 (10.3587 + 1.7503i)n + C4(10.3587 - 1.7503i)n + A122

Hence, we have derived the general solution form for the recurrence tn = 120,-2 - 166n-3 + 2.

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Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).