Suppose you buy 3 shirts and 2 pairs of slacks on sale at a clothing store for 72. The next day, a friend buys 2 shirts and 4 pairs of slacks for 96. If the shirts you each bought were all the same price and the slacks were also all the same price, then what was the cost of each shirt and each pair of slacks?

Answer:

I have helped you on the other question you asked. It's the same question.

The volume of the container was V = l3n

The manager correctly found the volume of the container using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height. The employee double-checked the calculation by packing the container full of bento boxes, each of which has a volume of l3, where l is the length of each edge of the bento box. Both calculations yielded the same result, as the volume of the container was equal to the number of bento boxes it could hold, multiplied by the volume of each bento box. Thus, the volume of the container was V = l3n, where n is the number of boxes the container can hold. Both calculations resulted in the same answer, but with different methods.

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Monthly earning is $4139.25

Weekly earning is  $955.21

fortnightly earning is  $1910.423

What are mathematics operations?

A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.

• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.

Given :

peter earns a salary of $49671 per year,

There are 12 months in a year. For 12 months the salary is $ 49671

To find out monthly earning. we divide the yearly earning by 12 :

Monthly earning = 49671/12

                           = $4139.25

Monthly earning is $4139.25

In a year, there are 52 weeks . fortnightly we have 26 weeks

To find out fortnightly earning , we divide the salary by 26

fortnightly earning = 49671/26

                                = $1910.423

fortnightly earning is $1910.423

He earn fortnightly  $1910.423

In a year, there are 52 weeks , to find out weekly earning , we divide the salary by 52

weekly earning = 49671/52

                                = $955.21

weekly earning is $955.21

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Answer:

3, 1

Step-by-step explanation:

Slope is rise/run, with the rise being the y increase, and x being the x increase.

Since the run represented is 3, and the rise is 9:

9/3 = 3

The y-intercept is the value of f(x) (which is y) when x = 0

since the equation of the line is:

f(x) = 3x + b

we need to go down 3 units of x since x = 0

3 x 3 = 9

10 - 9 = 1

b = 1

The y-intercept is 1.

Answer:

slope = 2/5

y-intercept = (0, 14) or 14.

Step-by-step explanation:

We could use the given table of values to solve for the slope and the y-intercept of the line.

Choose two ordered pairs from the table: (5, 16) (10, 18)

Let (x1, y1) = (5, 16)

(x2, y2) = (10, 18)

Substitute these values into the following slope formula:

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

m = (18 - 16)/(10 - 5)

m = 2/5

Therefore, the slope of the line is 2/5.

The y-intercept is the y-coordinate of the point (0, b ) where the graph crosses the y-axis. The y-intercept is also the value of y when x = 0.

To find the y-intercept, we'll use the slope and one of the given ordered pairs (points) from the table (5, 16). Substitute these values into the slope-intercept form, y = mx + b, where m = slope, and b = y-intercept.

y = mx + b

16 = 2/5(5) + b

16 = 2 + b

Subtract 2 from both sides to isolate b:

16 - 2 = 2 - 2 + b

14 = b

The value of the y-intercept = 14  [this is the y-coordinate of the y-intercept, (0, 14)].

Therefore, the equation of the line is: y = 2/5x + 14.

The Laplace transform of f(t) is: L[f(t)] = e²¹s/(s^2+1)^2

the solutions to determine the Laplace transform of the following functions:

(i) f(t) = t sint cost

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The Laplace transform of t is 1/s^2, the Laplace transform of sint is 1/(s^2+1), and the Laplace transform of cost is 1/(s^2+1). Therefore, the Laplace transform of f(t) is: L[f(t)] = 1/s^4 + 1/(s^2+1)^2

(ii) f(t) = e²¹ (sint + cost)²

The Laplace transform of e²¹ is e²¹s, the Laplace transform of sint is 1/(s^2+1), and the Laplace transform of cost is 1/(s^2+1).

Therefore, the Laplace transform of f(t) is: L[f(t)] = e²¹s/(s^2+1)^2

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Using the properties of Laplace transformation;

a. The Laplace transform of f(t) = t * sin(t) * cos(t) is F(s) = 2s / (s² + 4)².

b. The Laplace transform of f(t) = e²¹ * (sin(t) + cos(t))² is F(s) = e²¹* (1/s + 2 / (s² + 4)).

(i) To find the Laplace transform of f(t) = t * sin(t) * cos(t), we can use the properties of the Laplace transform. The Laplace transform of f(t) is denoted as F(s).

Using the product rule property of the Laplace transform, we have:

L{t * sin(t) * cos(t)} = -d/ds [L{sin(t) * cos(t)}]

To find L{sin(t) * cos(t)}, we can use the formula for the Laplace transform of the product of two functions:

L{sin(t) * cos(t)} = (1/2) * [L{sin(2t)}]

The Laplace transform of sin(2t) can be calculated using the formula for the Laplace transform of sin(at):

L{sin(at)} = a / (s² + a²)

Substituting a = 2, we get:

L{sin(2t)} = 2 / (s² + 4)

Now, substituting this result into the expression for L{sin(t) * cos(t)}:

L{sin(t) * cos(t)} = (1/2) * [2 / (s² + 4)] = 1 / (s² + 4)

Finally, taking the derivative with respect to s:

L{t * sin(t) * cos(t)} = -d/ds [L{sin(t) * cos(t)}] = -d/ds [1 / (s² + 4)]

                      = -(-2s) / (s² + 4)²

                      = 2s / (s² + 4)²

Therefore, the Laplace transform of f(t) = t * sin(t) * cos(t) is F(s) = 2s / (s² + 4)².

(ii) To find the Laplace transform of f(t) = e²¹ * (sin(t) + cos(t))², we can again use the properties of the Laplace transform.

First, let's simplify the expression (sin(t) + cos(t))²:

(sin(t) + cos(t))² = sin^2(t) + 2sin(t)cos(t) + cos^2(t)

                    = 1 + sin(2t)

Now, the Laplace transform of e²¹ * (sin(t) + cos(t))² can be calculated as follows:

L{e²¹ * (sin(t) + cos(t))²} = e²¹ * L{1 + sin(2t)}

The Laplace transform of 1 is 1/s, and the Laplace transform of sin(2t) can be calculated as we did in part (i):

L{sin(2t)} = 2 / (s² + 4)

Now, substituting these results into the expression:

L{e²¹ * (sin(t) + cos(t))²} = e²¹ * (1/s + 2 / (s² + 4))

                              = e²¹ * (1/s + 2 / (s² + 4))

Therefore, the Laplace transform of f(t) = e²¹ * (sin(t) + cos(t))² is F(s) = e²¹* (1/s + 2 / (s² + 4)).

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Answer: -7

Step-by-step explanation:

-28=p+21

Move variables to the left- hand side and change its sign

-p-28=21

Move constant to the right hand side and change its sign

-p=21+28

Add the numbers

-p=49

Changes the sign on both sides of the equation

p=-49

Answer :p=-49

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Answer:

0.47..................

Step-by-step explanation:

..........

Answer:

x = -1 and y = 3

Step-by-step explanation:

Let's solve your system by elimination.

−2x−9y=−25;−4x−9y=−23

Multiply the second equation by -1, then add the equations together.

(−2x−9y=−25)

−1(−4x−9y=−23)

Becomes:

−2x−9y=−25

4x+9y=23

Add these equations to eliminate y:

2x=−2

x = -1

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

−2x−9y=−25

Substitute−1forxin−2x−9y=−25:

(−2)(−1)−9y=−25

−9y+2=−25(Simplify both sides of the equation)

−9y+2+−2=−25+−2(Add -2 to both sides)

−9y=−27

y = 3

Given that 2y = x + 2

To graph the following equation, we need two solutions

To find x, put y = 0

To find y, put x = 0

The two solutions to be graph is (-2, 0) and (0, 1)

Yes, it is valid to use the Central Limit Theorem (CLT) to describe the sampling distribution of the sample mean, even for a random sample of five households. Although a sample size of five is relatively small, the CLT still applies as long as the sample is random and independent.

  The Central Limit Theorem is a fundamental concept in statistics that states that, under certain conditions, the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

While a sample size of five may be considered small, the CLT still holds for this case. The key consideration is that the sample is selected randomly and each observation is independent of the others. As long as these conditions are met, the CLT can be applied, even for small sample sizes.

In practice, larger sample sizes are generally preferred to ensure better approximation to the normal distribution. However, the CLT provides a theoretical foundation for the validity of using the normal distribution as an approximation for the sampling distribution of the sample mean, even with relatively small sample sizes like five households.

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Answer:

Hope you understand it ^^.

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Answer:

2 and 2/3 for the first question

-1/8 for the second one

-1/5 for the third one

ive never done this type of question or maybe it was too long ago for me to remember but out of this answer choices i would guess that its the last one

this is 3

Step-by-step explanation:

you add the numerators which is the top number in order to get 2 and 2/3rds

you subtract 5 from 4 to get -1/8

same situation as the last one, subtract 15 from 11 to make it a negative 4/20 and then simplify that by dividing it by four to get 1/5th

this one i dont understand or remember how to do very well but if i had to guess its the last answer choice

this one you add 3/4 plus 1/4 in order to get 4/4 or rather 1, so basically its asking what 1+1+1 is which is 3

Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

Distance formula: d = √(x2-x1)^2 + (y2-y1)^2

d = √(5-2)^2 + (10-6)^2

d = √3^2 + 4^2

d = √9 + 16

d = √25

d = 5

The distance is 5 units.

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Ok, I'll try, the picture is below.

Answer:

true

false

true

false

true

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Answer:

Value of tan( π/3 ):

\({ \tt{ \frac{\pi}{3} = \frac{180}{3} = 60 \degree }}\)

60° lies within the first quadrant.

\({ \sf{ \tan( \frac{ \pi}{3} ) = ( \frac{1}{2} , \: \frac{ \sqrt{3} }{2}) }}\)

Since it's a half:

\({ \boxed{ \sf{ \tan( \frac{\pi}{3} ) = \sqrt{3} }}}\)

Length of hypotenuse:

\({ \bf{ \sin(31 \degree) = \frac{16.5}{h} }} \\ { \sf{h = 32.04}}\)

Hypotenuse = 32.0

Answer:

Yes, death opened the eyes of Ponyboy from the book 'The Outsiders' by S.E Hinton. The death of Johnny makes Ponyboy realize that death can happen to anyone at any time, and that he needs to live life while he can. When Johnny talks to Ponyboy at the hospital about how disappointed he was that he didn't have enough time to see everything he wanted to see, Ponyboy realizes he needs to live life to the fullest. Likewise, when Dally is shot by the police officers, Ponyboy realizes how precious and fragile life is. He feels sad about how Dally died, and how tragic it was. This is how death opened the eyes of Ponyboy in the book, The Outsiders by S.E. Hinton.

To determine the probability that Paul will not eat the pizza Chef Carl has made, we need to calculate the probability of Chef Carl selecting mushrooms as one of the toppings.

First, let's calculate the total number of possible combinations of two different toppings that Chef Carl can choose from the given options. Since order does not matter, we can use the combination formula:

C(n, r) = n! / (r! * (n-r)!),

where n is the total number of options and r is the number of choices. In this case, n = 5 (the number of toppings) and r = 2 (the number of choices).

C(5, 2) = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.

So there are a total of 10 possible combinations of two different toppings that Chef Carl can choose.

Next, we need to calculate the number of combinations that include mushrooms. Since Paul will not eat pizza with mushrooms, we want to exclude this option.

To choose one topping from the remaining four (excluding mushrooms), there are C(4, 1) = 4 possible choices.

Therefore, the probability that Chef Carl selects a combination with mushrooms is 4/10.

Finally, the probability that Paul will not eat the pizza Chef Carl has made is the complement of this probability, which is 1 - 4/10 = 6/10 = 3/5.

So, the probability that Paul will not eat the pizza is 3/5.

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The characteristic of the classical approach to probability is that the probabilities assume outcomes of an experiment are equally likely , the correct answer is (d) .

The Classical Approach to probability is also known as the "classical method" .

The classical approach is based on the assumption that all outcomes of an experiment are equally likely to occur.

The probability of an event is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

This classical approach is often used in situations where the outcomes of an experiment can be clearly defined and enumerated.

Therefore, the correct statement about Classical Approach is in Option(d).

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The given question is incomplete , the complete question is

Which one of the following is a characteristic of the classical approach to probability?

(a) Probabilities are based on outcomes observed from past experiments.

(b) None of the above.

(c) Probabilities are based on opinion.

(d) Probabilities assume outcomes of an experiment are equally likely.

The number of bacteria in a refrigerated food product is maximized when the temperature is T = 11/3. The number of bacteria in a refrigerated food product is given by the function N(T) = 30T^2 - 117T + 92.

We can find the maximum number of bacteria by finding the critical points of the function. A critical point of a function is a point in the domain of the function where the derivative is either equal to zero or undefined.

The derivative of N(T) is N'(T) = 60T - 117. N'(T) = 0 when T = 117/60 = 11/3. N'(T) is defined for all real numbers. Therefore, the only critical point of N(T) is T = 11/3.

To see if the critical point is a maximum point, we can evaluate N'(T) at T = 11/3. N'(11/3) = 60(11/3) - 117 = 15. Since N'(11/3) is positive, we can conclude that T = 11/3 is a maximum point of N(T).

Therefore, the number of bacteria in a refrigerated food product is maximized when the temperature is T = 11/3.

We can find the critical points of the function by setting the derivative equal to zero.

N'(T) = 60T - 117 = 0

T = 11/3

We can see that the critical point is a maximum point by evaluating the derivative at the critical point and seeing if it is positive or negative.

N'(11/3) = 60(11/3) - 117 = 15 > 0

Therefore, the critical point is a maximum point.

Therefore, the number of bacteria in a refrigerated food product is maximized when the temperature is T = 11/3.

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Simple interest is a method of calculating interest on an amount. The sum of the total balances of these accounts at the end of 7 years is $27,822.54.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

\(\rm Simple\ Interest=\dfrac{P\times R \times T}{100}\)

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

As it is given that the amount deposited by James is $12,000. While the interest earned on the first account is 2.2% compounded annually for a period of 7 years, therefore, the balance in the account will be,

\(\text{Account balance of first Account} = P(1+r)^t = 12,000(1.022)^7=\$13,974.54\)

In the second account, James deposited $12,000 at a rate of 2.2% annual simple interest. Therefore, the balance in the account will be,

\(\text{Account balance of second Account} = P+\dfrac{P\times R \times T}{100}\)

                                                        \(=12,000+\dfrac{12,000 \times 2.2 \times 7}{100} \\\\= \$13,848\)

Now, the balance of the account when combined together will be,

\(\rm Total\ Balance = \text{Account balance of first Account} +\text{Account balance of second Account} \\\\\rm Total\ Balance = \$13,974.54+\$13,848 = \$27,822.54\)

Hence,  the sum of the total balances of these accounts at the end of 7 years is $27,822.54.

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Answer:

3

Step-by-step explanation:

x =√9

x= 9½

Multiply both sides by the power of 2

x²=9½*²

x²= 9

x²=3²

x=3