2. Which of the following numbers are prime? a) 53 b) 12 c) 18 d) 28​

The average cost in dollars per pound of the steaks sold on Tuesday is 9.17 per pound.

First step is to calculate the total cost for steaks

Total cost=400×$9.98 + 120×$6.49

Total cost=$4770.8

Second step is to calculate the total pound

Total pound=400 + 120

Total pound= 520

Third step is to calculate the average cost in dollars

Average cost=$4770.8 / 520

Average cost= 9.174615385

Average cost=9.17 per pound (Approximately)

Inconclusion the average cost in dollars per pound of the steaks sold on Tuesday is 9.17 per pound.

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The general solution of the differential equation is: y = c1 e^(3t) cos(t) + c2 e^(3t) sin(t), where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.

The given differential equation is a second-order homogeneous linear differential equation with constant coefficients. Its characteristic equation is obtained by assuming a solution of the form y = e^(rt), where r is a constant. Substituting this into the differential equation, we get:

r^2 e^(rt) - 6r e^(rt) + 10 e^(rt) = 0

Dividing both sides by e^(rt) (which is non-zero), we get:

r^2 - 6r + 10 = 0

Solving for r using the quadratic formula, we get:

r = (6 ± sqrt(6^2 - 4(1)(10))) / 2

r = 3 ± i

Therefore, the general solution of the differential equation is:

y = c1 e^(3t) cos(t) + c2 e^(3t) sin(t)

where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.

This solution consists of a linear combination of two functions: the exponential function e^(3t) and the periodic function cos(t) or sin(t), which oscillates between -1 and 1. The exponential function represents the growth or decay of the system, while the periodic function represents the oscillations or vibrations of the system. The constants c1 and c2 determine the amplitude and phase of the oscillations, respectively. The behavior of the system depends on the signs and magnitudes of the real and imaginary parts of the roots, which determine whether the solutions are overdamped, critically damped, or underdamped.

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Answer:

1.   ( 5 , 0)

2.   ( 0 , -3)

Step-by-step explanation:

Answer:

Okay so to find the y intercept on a graph you have to see where the line intersects on the y-axis. And for the x- intercept basically the exact same thing you need to see where it intersects on the x-axis.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We need to transform the given x^2 - 19x + c into the form

                                                      (x - a)^2 + d

by completing the square:

1.  Take half of the coefficient (-19) of x, obtaining -19/2.

2.  Square this result, obtaining 361/4.

3.  Add this to x^2 - 19x, and then immediately subtract it:

    x^2 - 19x + c becomes x^2 - 19x + 361/4 - 361/4+ c

4.  Replace the first three terms with (x - 19/2)^2:

     x^2 - 19x + 361/4 - 361/4+ c  =>  (x - 19/2)^2 - 361/4 + c

5.  Put this into final form: (x - 19/2)^2 - (361/4 - c)

f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

Answer:

4

Step-by-step explanation:

Divide each value of y by the corresponding value of x.

20/5 = 4

40/10 = 4

80/20 = 4

200/50 = 4

All quotients are 4.

Answer: 4

The statement “for all functions f and g, f(g(x)) = g(f(x))” is false.

Here's an explanation why: There are a few ways to disprove a statement like this, but one simple method is to find a counter example - that is, a pair of functions f and g that don't satisfy the equation.

Let's try f(x) = x + 1 and g(x) = x - 1. Then we have:

f(g(x)) = f(x - 1) = (x - 1) + 1 = x and g(f(x)) = g(x + 1) = (x + 1) - 1 = x

So we have shown that f(g(x)) = x and g(f(x)) = x are not always equal, which means the statement is false.

In general, it is not safe to assume that function composition is commutative - that is, that f(g(x)) = g(f(x)) for all functions f and g.

There may be some specific cases where this is true, but it is not true in general.

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In other words, there are 24 different ways to get a full house of kings and fives when dealing 5 cards from a standard 52-card deck.

To calculate the number of hands with a full house of kings and fives, you need to consider the number of ways to choose 3 kings and 2 fives from a standard 52-card deck. There are 4 kings and 4 fives in the deck.

To choose 3 kings, use the combination formula: C(4,3) = 4! / (3!(4-3)!) = 4.
To choose 2 fives, use the combination formula: C(4,2) = 4! / (2!(4-2)!) = 6.

Now, multiply these results together to find the total number of hands with a full house of kings and fives: 4 * 6 = 24.

So, there are 24 possible hands with a full house of kings and fives when dealt from a standard 52-card deck.

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Answer:

x = - 3

Step-by-step explanation:

Since the x- coordinates of both points are equal, both - 3

This indicates the line is vertical with equation

x = c ( c is the value of the x- coordinates the line passes through )

The line passes through (- 3, 9) and (- 3, - 5) with x- coordinates - 3 , then

x = - 3 ← equation of line

Answer:

the equation of line is

y=-14x-33

Answer:

this is the answer Hope's it helps

Answer:

9x8=72      72-8=64  64x9=576

Step-by-step explanation:

Answer:

Nine times the difference of 8 and a number = 9(x-8)

Answer:

4 cm

Step-by-step explanation:

The Volume of a Come formula =

πr²h/3 or 1/3 πr²h

We are asked to find the height of the cone

r= 5cm

Volume = 110 cm³

The formula for height of a cone =

3V/πr²

= 3 × 110/π × 5²

h = 4.20169 cm

Approximately to the nearest whole number = 4 cm

Answer:

3

Step-by-step explanation:

1 1/2 + 1 1/2

1 + 1 = 2

1/2 + 1/2 = 1

2 + 1 = 3

Or

1 1/2 times 2

Answer:

3 gallons

Step-by-step explanation:

1.5 x 2 = 3

Answer:

3/2

Step-by-step explanation:

Answer:

249.88

Step-by-step explanation:

415-82.13-9.74-31.75-41.50

For the statement "No major roads connecting the city to its bus stations were open. "The correct option is B. No major roads connecting the city to its bus stations were open. For the statement :All integers are not numbers. The correct option is D. All integers are not numbers. For the part C  :The correct option is A. A∪U={1,2,3,4,5,6,7}.

Part A:The given statement is "No major roads connecting the city to its bus stations were open."A. At least one major road connecting the city to its bus stations was openB. No major roads connecting the city to its bus stations were open.C. The bus stations were forced to closeD. At least one major road connecting the city to its bus stations was not open.The correct option is B. No major roads connecting the city to its bus stations were open.

Part B:All integers are not numbers. We need to express the quantified statement in an equivalent way and then write the negation of the quantified statement. The equivalent statement of the quantified statement is "Not all integers are numbers". A. No integer is a number. B. All integers are not numbers. C. Not all integers are numbers. D. At least one integer is a number. The correct option is C. Not all integers are numbers. The negation of the quantified statement is "All integers are numbers". A. Some integers are not numbers. B. Some integers are numbers. C. No integers are numbers. D. All integers are not numbers. The correct option is D. All integers are not numbers.

Part C:U={1,2,3,4,5,6,7,} and A={5,6,7,6}.We need to find union A∪U.A∪U = {1,2,3,4,5,6,7}The correct option is A. A∪U={1,2,3,4,5,6,7}.

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Answers in bold

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \boldsymbol{0.5}\\\cline{1-2}6 &3\\\cline{1-2}10 & \boldsymbol{5}\\\cline{1-2}16 & \boldsymbol{8}\\\cline{1-2}25 & \boldsymbol{12.5}\\\cline{1-2}n & \boldsymbol{0.5n}\\\cline{1-2}\end{array}\)

========================================================

Explanation:

The given table looks like this

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \\\cline{1-2}6 & 3\\\cline{1-2}10 & \\\cline{1-2}16 & \\\cline{1-2}25 & \\\cline{1-2}n & \\\cline{1-2}\end{array}\)

Focus on the row that has two values in it.

x = number of rolls = 6

y = number of people 3

k = constant of proportionality

y = kx

k = y/x = 3/6 = 0.5

The constant of proportionality is k = 0.5 which gives the direct variation equation of y = 0.5x

If x = 1, then y = 0.5*1 = 0.5 meaning that 1 roll feeds 0.5 people. This means we need 2 rolls to feed one person.

If x = 10, then y = 0.5x = 0.5*10 = 5 people can be fed with those 10 rolls. This process is continued until we finish filling out the table.

What paper are you talking about?

The amount in the account after the given time if compounded semiannually is $1104.2

Interest is any amount added on a sum of money over a period of time. The formula for calculating the compound interest is:

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

Given

P = $1000

rate r = 0.05

time =3years

n = 2

Substitute

A = 1000(1 + 0.05/3)^3(2)
A= 1000(1.1042)
A = $1104.2

Hence the amount in the account after the given time if compounded semianually is $1104.2

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The standard deviation for this Gaussian random variable is approximately 5.09.

Standard deviations are a measure of the spread of data around the mean. The standard deviation is the square root of the variance of a dataset. It is the most commonly used measure of spread and is a measure of how the individual data points deviate from the mean. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.

This is calculated by finding the square root of the variance of the random variable, which is the difference between the mean and the probability given:

Variance = (60 - 0.382)2 = 35.22

Standard deviation = √35.22 = 5.09

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Answer:

y' = 2x + 1

y'' = 2

Step-by-step explanation:

y = x² + x + 8

y' = 2x + 1

y'' = 2

Answer:

20

Step-by-step explanation:

I did this test is 20

60 percent of 20 is 12 dollars

The original price of a pair of jeans would be; 30 dollar.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b% Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Given that a pair of jeans is only $12 after a 60% discount.

The original price in percentage terms = 100%

After the first discount, the price is : 100- 60% = 40%

The equation can be used to represent the price;

40% x original price = $12

0.40 x p = 12

where p = original price

Divide both sides of the equation by 0.40;

p= $30

Hence, The original price of a pair of jeans would be; 30 dollar.

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Answer:

4i

Step-by-step explanation:

Distribute the 2, you get 4i.

It's imaginary because it has an i with it

Answer:

-4, real

Step-by-step explanation:

Hi there!

‘i’ is characterized as the sqrt of -1 or, alternatively, i^2= -1

If the problem is asking us to square i, then we know that it is going to equal -1. If we distribute the exponent, we would also square the 2, making it become 4. Now that we have done that, we multiply -1 and 4 to get a final answer of -4. This would be a real number as it is not imaginary.

I hope this can help!

Answer:

undefined

Step-by-step explanation:

To find the slope

m = ( y2-y1)/(x2-x1)

   = ( 6-5)/( -2 - -2)

   = (6-5) /(-2+2)

    = 1/0

We cannot divide by zero, so the slope is undefined

Simplification of the expression gives 2a + c = -24

4+4-3-4-2-5-1-8-9-0=a +c + a

First, let's add

\(8 -3 -4-2-5-1-8-9-0 = a+ c + a\)

Then, let's substract

\(-24 = a + c + a\)

\(-24 = 2a + c\)

We then have,

\(2a + c = -24\)

Thus, simplification of the expression gives 2a + c = -24

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Answer:

12

Step-by-step explanation:

PEMDAS

FILLER FILLER FILLER

Answer:

15

Step-by-step explanation:

2x2x2=8

8x2=16

16/16=1

8+8=16

16-1=15

Answer:

See below.

Step-by-step explanation:

They invested in a ratio of Julie:Kristen of 5:12.

5 + 12 = 17

Julie invested 5/17 of the amount, and Kristen invested 12/17 of the mount.

a.

Julie: 5/17 * $51,000 = $15,000

Kristen: 12/17 * $51,000 = $36,000

b.

Kristen owns 12/17 of the business.

As a percent, 12/17 = 12/17 * 100% = 70.6%

c.

The percent of the business each owns does not change with the amount the company is worth.

Kristen owns 70.6%, so Julie owns 100% - 70.6% = 29.4%

The length of the flag measure in meters is,

⇒ 1.52 meters

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

We have to given that;

A flag is 152 centimeters long.

Now,

We know that;

1 centimeters = 1/100 meters

Hence, We get;

The length of the flag measure in meters is,

⇒ 152 centimeters

⇒ 152/100 meters

⇒ 1.52 meters

Thus, The length of the flag measure in meters is,

⇒ 1.52 meters

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Answer:

As per the moment I cannot answer this due to know screenshot and lack of informatio

Step-by-step explanation: