Marcus is buying a pair of running shoes that are discounted 20% from the original price
of $100. The store is also having a holiday sale, so they will take an additional 20% off the
sale price. How much will Marcus pay for his shoes?​

Using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

To approximate the integral [sin(x²+1) dx] using the trapezoidal rule with 5 ordinates, we can use the following formula:

∫[a,b]f(x)dx ≈ [(b-a)/2n][f(a) + 2f(a+h) + 2f(a+2h) + 2f(a+3h) + 2f(a+4h) + f(b)]

where n is the number of ordinates (in this case, n = 5), h = (b-a)/n is the interval width, and f(x) = sin(x²+1).

First, we need to find the interval [a,b] over which we want to integrate. Since no interval is given in the problem statement, we'll assume that we want to integrate over the interval [0,1].

Therefore, a = 0 and b = 1.

Next, we need to find h:

h = (b-a)/n = (1-0)/5 = 0.2

Now, we can apply the trapezoidal rule formula:

∫[0,1]sin(x²+1)dx ≈ [(1-0)/(2*5)][sin(0²+1) + 2sin(0.2²+1) + 2sin(0.4²+1) +             2sin(0.6²+1) + 2sin(0.8²+1) + sin(1²+1)]

≈ (1/10)[sin(1) + 2sin(0.05²+1) + 2sin(0.15²+1) + 2sin(0.35²+1) + 2sin(0.65²+1) + sin(2)]

≈ (1/10)[0.8415 + 2sin(1.0025) + 2sin(1.0225) + 2sin(1.1225) + 2sin(1.4225) + 1.5794]

≈ 0.5047

Therefore, using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

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The range of the graph of the exponential function is (b) {y | y > 0}

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

The graph of the exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

From the graph, the constant term is 0

So, the range is y > 0

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Answer:  a+b+c/3

Step-by-step explanation:

mean= sum of all values/number of values

Answer:

200 lbs.

Step-by-step explanation:

Divide mass value by 16 to convert oz to lbs.

3,200/16=200

Answer:

5.33333333333

CAN I HAVE BRAINLIEST?

a. The marginal profit function Py is Py = -30x + 47y - 915 and

b. Change in profit if price increase by 1 cent is 831 cents.

To find the marginal profit functions Px and Py, we need to find the partial derivatives of the profit function P(x, y) with respect to x and y, respectively.

Given:

P(x, y) = (x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)

a. Marginal profit function Px:

To find Px, we differentiate P(x, y) with respect to x while treating y as a constant:

Px = ∂P/∂x = (∂/∂x) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]

Expanding the terms and simplifying:

Px = (55 - 4x + 5y) + (x - 40)(-4) + (70 + 5x - 7y)(5)

Simplifying further:

Px = 55 - 4x + 5y - 4x + 40 + 350 + 5x - 7y

Combining like terms:

Px = 355 - 3x - 2y

b. Marginal profit function Py:

Similarly, to find Py, we differentiate P(x, y) with respect to y while treating x as a constant:

Py = ∂P/∂y = (∂/∂y) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]

Expanding the terms and simplifying:

Py = (x - 40)(5) + (70 + 5x - 7y)(-7) + (y - 45)(5)

Simplifying further:

Py = 5x - 200 - 7y - 490 - 35x + 49y + 5y - 225

Combining like terms:

Py = -30x + 47y - 915

This is the profit function Py.

b. Estimating the daily change in profit:

To estimate the daily change in profit, we need to evaluate Px and Py at the given prices and calculate the change in profit when the prices are increased as specified.

Given initial prices:

First brand price (x) = 70 cents

Second brand price (y) = 73 cents

To estimate the change in profit, we substitute the initial prices into Px and Py and calculate the results:

Px(70, 73) = 355 - 3(70) - 2(73)

          = 355 - 210 - 146

          = -1

Py(70, 73) = -30(70) + 47(73) - 915

          = -2100 + 3431 - 915

          = 416

The daily change in profit can be estimated by multiplying the changes in price (1 cent for the first brand and 2 cents for the second brand) with the respective marginal profit functions:

Change in profit = ΔP ≈ Px(70, 73) * 1 + Py(70, 73) * 2

               ≈ -1 * 1 + 416 * 2

               ≈ -1 + 832

               ≈ 831 cents

Therefore, the estimated daily change in profit when the salesperson increases the price of the first label by 1 cent and the price of the second label by 2 cents is 831 cents.

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Answer:

The answer is A, 3.50w.

Step-by-step explanation:

When there is 1 pound, it is 3.50. 2 pounds it's 7.00 which is 3.50 times 2.

If this helped I would appreciate it if you marked me Brainliest. thank you and have a nice day!

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Here we go ~

\(\qquad \sf  \dashrightarrow \: f(x)= {6}^{x} \)

we need to find f'(2) = ??

\(\qquad \sf  \dashrightarrow \: f {}^{ \prime} (x) = \displaystyle \sf \lim_{h \to0} \: \: \dfrac{f(x + h) - f(x)}{h} \)

\(\qquad \sf  \dashrightarrow \: f {}^{ \prime} (x) = \displaystyle \sf \lim_{h \to0} \: \: \dfrac{6 {}^{x + h} - 6 {}^{x} }{h} \)

\(\qquad \sf  \dashrightarrow \: f {}^{ \prime} (x) = \displaystyle \sf \lim_{h \to0} \: \: \dfrac{6 {}^{x + h} - 6 {}^{x} }{h} \)

\(\qquad \sf  \dashrightarrow \: f {}^{ \prime} (x) = \displaystyle \sf \lim_{h \to0} \: \: \dfrac{6 {}^{x }( 6 {}^{h} - 1)}{h} \)

\(\qquad \sf  \dashrightarrow \: f {}^{ \prime} (x) =\: 6 {}^{x} \: log_{e}(6) \)

Now, plug in 2 for x ~

\(\qquad \sf  \dashrightarrow \: f {}^{ \prime} (2) =\: 6 {}^{2} \sdot log_{e}(6) \)

\(\qquad \sf  \dashrightarrow \: f {}^{ \prime} (2) =\: 36 \sdot (1.79)\)

\(\qquad \sf  \dashrightarrow \: f {}^{ \prime} (2) =64.44\)

Using the subtraction operation, the number of flowers with 10 petals that Mrs. Moth picked was 6.

A subtraction operation is one of the four basic mathematical operations, including addition, division, and multiplication.

The subtraction operation involves the minuend, the subtrahend, and the difference.

The minuend is the number or value being subtracted from by the subtrahend.  The result of a subtraction operation is known as the difference.

The total number of picked flowers = 24

The number of flowers with 9 petals = 6

The number of flowers with 8 petals = 7

The number of flowers with 3 petals = 5

The total number of flowers identified = 18 (6 + 7 + 5)

The number of flowers with 10 petals = x

x = 24 - 18

= 6

Thus, 6 flowers had 10 petals out of the 24 Mrs. Moth picked.

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Answer:

A'(4,-4)

B'(6,2)

C'(8,8)

Step-by-step explanation:

we have to change the sign of y in reflection on x-axis and the sign of X in reflection on y-axis

Ab=3.14xRadious to the power of 2

then to the area of the rectange you do B x H = YOUR ANSWER

Bruce and Felicia would have a unique solution to the given equation. The value of x that satisfies the equation is 15.

To determine if the equation 6x + 2 = 5x + 17 has a unique solution, we need to check if the variable x has a consistent value that satisfies the equation.

By simplifying the equation, we can see that the equation becomes:

6x - 5x = 17 - 2

Simplifying further, we have:

x = 15

Since the variable x has a specific value, in this case, x = 15, the equation does have a unique solution. When x is substituted with 15 in the equation, both sides are equal.

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The sum of the geometric sequence in this problem is given as follows:

5.77.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.

The first term, the common ratio and the number of terms for this problem are given as follows:

\(a_1 = 10, q = -\frac{2}{3}, k = 8\)

The formula for the sum of the first n terms is given as follows:

\(S_n = a_1\frac{1 - r^n}{1 - r}\)

Hence the sum for this problem is given as follows:

\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)

\(S_8 = 5.77\)

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Answer:

Ratio is 1:5

Step-by-step explanation:

There is no table btw

Answer:

B $104.50

Step-by-step explanation:

3 + 9 + 7 = 19

19 x 5.50 = 104.50

Answer:

B. $104.50

Step-by-step explanation:

hi there!

friday: $16.50 (5.50x3)

saturday: $49.50, (5.50x9)

sunday: $38.50 (5.50x7)

add them all up and altogether, she makes $104.50 dollars :)

I hope this helps! comment if you need further explanation :D

Julio will be 30 years old when his father is twice his age.

To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.

Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.

For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.

Setting up an equation to solve for x:

x + 30 = 2x

Simplifying the equation, we subtract x from both sides:

30 = x

Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.

Therefore, Julio will be 30 years old when his father is twice his age.

Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?

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Answer:

First, we know that the function IxI works as follows:

IxI = x   if x ≥ 0

IxI = -x  if x < 0

So IxI is always positive.

then:

a) f(x) = Ix - 2I

this is:

f(x) = (x - 2)           if   (x - 2) ≥ 0

       -(x - 2)          if    (x - 2) < 0

Then the graph of this function will be two lines (where the separation of the lines depends on the vale of x)

For the case of b we have

g(x) = -IxI + 1

then we have:

g(x) = -x + 1          if   x ≥ 0

g(x) = -(-x) + 1       if   x < 0

To graph the functions, you need to graph these lines for the given values of x. You also can see the graphs below. Where the red graph is the one for the point 4a, and the blue graph is the one for point 4b.

Now, let's find the domain and range:

4a) f(x) = Ix  - 2I

The domain is the set of the possible values of x that we can input in that function. For this case, we do not have any value of x that generates a problem (like a zero in a denominator, for example) then the domain is the set of all real numbers:  x ∈ R

The range is the set of the possible values of y.

f(x) = Ix - 2I is always equal or greater than zero (as you can also see in the graph) then the range will be:

R: y ∈ R, such that y ≥ 0.

4b) g(x) = -IxI + 1

Similar as the prior case, here the domain is the set of all real numbers:

D: x ∈ R

For the range, now we have:

y = -IxI + 1

if IxI is always equal or larger than zero, then -IxI is always equal or smaller than zero. If we add a + 1 to that, then the function will be always equal or smaller than 1.

Then the range is:

R: y ∈ R, such that y ≤ 1

If two angles are cut by a transversal so that the "alternate interior angles are congruent, then the lines are parallel.

The correct answer is option E.

To reflect a point over the y-axis, we negate the x-coordinate of the point. To reflect the resulting point over the x-axis, we negate the y-coordinate of the point. So, to find the new point A'', we can perform these operations on the original point A:

1. Reflect A over the y-axis to get A': (-2, 2)

2. Reflect A' over the x-axis to get A'': (-2, -2)

Therefore, the new point A'' is (-2, -2).

Answer:

option D

Step-by-step explanation:

Exterior angle = sum of interior

               105 = 50 + x

               105 - 50 = x

                      55° = x

Answer:

hope it helps

Step-by-step explanation:

We may infer from comparing the medians of the two data sets that Bus 14 normally travels at a higher rate because its median is greater than Bus 18's median, which is greater than its median. Bus 14 is the appropriate response, with a median of 14.

In mathematics, the mean is the average of a set of data, which is calculated by adding all the numbers together and then dividing the result by the total number of numbers.

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

We must compare the central tendency of the two data sets in order to ascertain which bus normally has a shorter trip duration. The median is a suitable centre measurement because the data in each graph are not symmetrically distributed.

Looking at the Bus 14 graph, the median travel time is the value that separates the top half of the data from the bottom half, which is the middle value of the ordered data set. In this case, the median is 14, which means that half of the 15 students take 14 minutes or less to travel to school on Bus 14, and the other half take 14 minutes or more.

When examining the Bus 18 graph, the median trip time is also 12, the middle value in the sorted data set. This indicates that half of the 15 kids take Bus 18 to school in 12 minutes or less, while the other half take 12 minutes or longer.

We may infer from comparing the medians of the two data sets that Bus 14 normally travels at a higher rate because its median is greater than Bus 18's median, which is greater than its median. Bus 14 is the appropriate response, with a median of 14.

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Answer:

(100/500) *200 =40%

Step-by-step explanation:

Among the given, only 0.5 can be exactly represented in binary notation with a finite number of bits

Hence, option (d) is the correct choice.

Binary is a base-2 number system in which a number is represented by two states: 0 and 1. We can also refer to it as a true and false condition. A binary number is constructed in the same manner as a decimal number.

Binary data is information expressed or displayed using the binary number system. Binary data is the only type of data that a computer can directly understand and execute. It is represented numerically as a series of zeros and ones.

The binary representation of 0.5 is 0.1_2, and it is the only terminating fraction among the available possibilities.

As a result, it is the only fraction that can be expressed precisely.

All of the other possibilities have a non-terminating fraction portion and hence cannot be expressed accurately with a limited amount of bits.

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The complete question may be:

Which of the following decimal numbers can be exactly represented in binary notation with a finite number of bits?

(a) 0.1

(b) 0.2

(c) 0.4

(d) 0.5

(e) All the above

Answer:

The Break-in by: Jimmy D Lock

Origin of Man by: Evan Lu Shun

Making Soap by: Phil T Hans

All vectors of the form(a, b, a - 2b) is a subspace of R³. So, the correct option is option(D).

If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if

Now, check the options and find out the option which satisfy the subspace conditions.

A) All the vectors are of form (0, a,a²)

let (0,1,1) = u and v=(0,2,4) and both are belongs to { 0, a,a² : a∈R }, (0,0,0)∈ {0, a,a² : a∈R }.

u + v = (0,1,1) + (0,2,4) = (0,3, 5) not belongs to

{ 0, a,a² : a∈R }. So, this is not correct option.

B) Here, (0,0,0) does not belongs to

{0, a, a+2 : a∈R } because if a= 0 then a+2 =/ 0 .

So, it is also not subspace.

C) All vectors of the form (a, b, 2)

The third tuple is 2 which never be equal to zero. Hence, (0,0,0) does not belongs to (a, b, 2) and it is not form subspace.

D) All vectors of the form (a, b, a - 2b)

When a = 0 , b = 0 => (0,0,0) ∈(a, b, a - 2b)

let u = ( a1, b1 , a1- 2b1) and v = ( a₂, b₂ , a₂ - 2b₂)

and α∈R

u + v = ( a₁, b₁ , a₁- 2b₁ ) + ( a₂, b₂ , a₂ - 2b₂)

= ( a₁ +a₂ , b₁+b₂ , a₁+a₂ -2(b₁ - b₂)) €(a, b, a - 2b)

αu = α(a₁ , b₁ , a₁- 2b₁)

=( αa₁ , αb₁ , α(a₁ - 2b₁))∈(a, b, a - 2b)

both the conditions are satisfied, so it is Subspace of R³.

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The difference between the selling price and the cost price is the profit he earned.

Profit = Selling Price - Cost Price

Profit = $216 - $180

Profit = $36

To find the percentage profit, we need to calculate what proportion of the cost price the profit represents, and express that as a percentage :

Percentage Profit = (Profit : Cost Price) * 100%

Percentage Profit = ($36 : $180) * 100%

Percentage Profit = 0.2 * 100%

Percentage Profit = 20%

Therefore, his percentage profit is 20%.

Answer:

Ameliorate retort, pertaining to preceding albeit contingent interrogate proximates subject to x = 12.

Step-by-step explanation:

Availing, exploiting, albeit maneuvering the Mathematic convention, Order of Operations (OO), the contiguous albeit proximate equation may ascertain as the preeminent imminent:

Groups: Not identified.

Exponents: Not identified, disparaging ₁.

Multiplication: Derived, pertaining to subtraction, 4 · (7/4x) = 4 · 21  7x = 84

Division: Derived, pertaining to multiplication, 7x = 84 ⇒ x = 12

Addition: Aggregate constants ⇒ 5/2x = 3/4x +21

Subtraction: Abate algebraic groups ⇒ 7/4x = 21