You have a coupon for your favorite clothing store for $20 off any purchase of more than $75. The store is
also running a 15%-off sale on its entire inventory. Let x be the original price,
f x( )
be the price with the $20
coupon applied, and
g x( )
be the price with the 15% discount applied.
(a) Write an expression for
f x( ) . (3 points)
(b) Write an expression for
g x( ) . (3 points)
(c) Write the expression
(f g x )( )
and explain what it represents? (3 points)
(d) Write the expression
(g f x )( )
and explain what it represents? (3 points)
(e) If the store allows you to apply both the 15% discount and the $20-off coupon, does it matter which
you apply first? How do you know? (3 points

A petri dish is a shallow cylindrical glass or plastic lidded dish that biologists use to culture cell cultures or small mosses. The petri dish can be used to grow a range of bacteria, fungi, and algae, as well as small mosses.

Because the amount of nutrients is finite, it will be exhausted at a specific time point. When the nutrients are depleted, the bacteria will stop growing and begin to die.

The bacterial population grows exponentially until the nutrient supply is exhausted. The time it takes for the bacteria to reach half of the population is the doubling time. To calculate the doubling time, the formula is t= ln(2)/r. This can be derived from the formula P=P0e^(rt), where P is the final population, P0 is the initial population, e is the exponential constant, r is the growth rate, and t is time. Where P=2P0, the time to double the population is t= ln(2)/r.

In conclusion, the time for a bacterial population to reach half its population is equal to the time it takes for it to double its population. The time it takes for bacteria to double its population can be calculated using the formula t= ln(2)/r. Therefore, in this case, it will be half full in 14.5/ln(2) days.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

A) M =5

B= $2

hope it helped!

Step-by-step explanation:

I think.

Answer:

Step-by-step explanation

Kf i help u wojld u help me

Answer: your answer will be 72 divided by 8

Step-by-step explanation: because they wanna know how many pages she put stickers on in if you divide it will tell you how many pages she put stickers on witch is 9

We need to find the function f(n) whose terms are the same as the series in question. We can then integrate this function from n=1 to infinity and determine if the integral is convergent or divergent. If it is convergent, then the series is convergent. If it is divergent, then the series is also divergent.

To determine whether a series is convergent or divergent using the integral test, we need to first check if the series satisfies three conditions:

1) The terms of the series are positive.

2) The terms of the series are decreasing.

3) The series has an infinite number of terms.

Assuming these conditions are satisfied, we can use the integral test which states that if the integral of the function f(x) from n=1 to infinity is convergent, then the series with terms a_n = f(n) is also convergent. Conversely, if the integral is divergent, then the series is also divergent.

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Answer:

(1,5)

Step-by-step explanation:

x = 1

y = 8

If you move down 3 units, it means the y would be lower. This is because y is the vertical value in a pair of coordinates.

8-3 = 5

Answer:

(1, 5)

Step-by-step explanation:

A coordinate defined as point (x, y) is called Cartesian Coordinate. The x-coordinate represents right-left direction while the y-coordinate represents up-down direction.

Its transformation depends on how would you move the coordinate point. An example is if you start with (x, y) point and move to right 3 units, our new position will be at (x + 3, y).

Properties

Suppose we have point (x, y), if we move to right “a” units then the new point will be (x + a, y)

If we move (x, y) to left “a” units, our new point will be (x - a, y)

If we shift (x, y) up “a units”, you’ll get (x, y + a)

If we shift (x, y) down “a units”, we’ll have (x, y - a)

Suppose you start at (1, 8) and you move down 3 units, you can apply the transformation property to find your new position.

Since you move down, this means you are dealing with y-coordinate only so you’ll apply property of (x, y - a)

You’ll have (1, 8 - 3) which equals to (1, 5).

Hence, you’ll end at (1, 5).

The probability that both Event A (the first die is 4 or less) and Event B (the second die is even) will occur is 1/3.

To find the probability that both Event A and Event B will occur, we need to calculate the individual probabilities of each event and then multiply them together.

Event A: The first die is 4 or less.

There are 6 possible outcomes for the first die (numbers 1 to 6), and out of those, 4 outcomes (numbers 1, 2, 3, and 4) satisfy the condition. Therefore, the probability of Event A is 4/6, which simplifies to 2/3.

Event B: The second die is even.

For a fair six-sided die, there are 3 even numbers (2, 4, and 6) out of a total of 6 possible outcomes. Therefore, the probability of Event B is 3/6, which simplifies to 1/2.

To find the probability that both events will occur, we multiply the probabilities of Event A and Event B:

Probability of both events occurring = Probability of Event A * Probability of Event B

P = (2/3) * (1/2)

P = 2/6

P = 1/3

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a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.

b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.

a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

- n is the total number of trials (number of people selected)

- k is the number of successful trials (number of males selected)

- p is the probability of success in a single trial (probability of selecting a male)

- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)

In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:

P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)

b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.

P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).

Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.

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Answer:

The answer is C

Step-by-step explanation:

Both A and B.

The functions are matched with their periods as follows:

The period of a trigonometric function is the smallest positive value of "T" for which the function repeats itself.

Note that to determine the period of a function, we need to identify how the function changes over one cycle. The period can then be obtained by dividing the length of the cycle by the number of complete cycles in the full range of the function.

1) y = - 3 ⁢ tan ⁡ 3 ⁢ x: The period of the tangent function is π/b, where b is the coefficient of x. So, the period of y = - 3 ⁢ tan ⁡ 3 ⁢ x is π/3.

2) y = 6 ⁢ sin ⁡ 3 ⁢ x: The period of the sine function is 2π/b, where b is the coefficient of x. So, the period of y = 6 ⁢ sin ⁡ 3 ⁢ x is 2π/3.

3 )y = - 4 ⁢ cot ⁡ x 4: The period of the cotangent function is π/b, where b is the coefficient of x. So, the period of y = - 4 ⁢ cot ⁡ x 4 is π.

4) y = 2 ⁢ cos ⁡ 2 ⁢ x 3: The period of the cosine function is 2π/b, where b is the coefficient of x. So, the period of y = 2 ⁢ cos ⁡ 2 ⁢ x 3 is 3π.

5 )y = - 2 3 ⁢ sec ⁡ x 5: The period of the secant function is 2π/b, where b is the coefficient of x. So, the period of y = - 2 3 ⁢ sec ⁡ x 5 is 2π/5.

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So, the cost of either option for 8 rides is $39.

Let's start by setting up an equation to represent the cost of each option in terms of the number of rides Clare goes on. Let x be the number of rides Clare goes on. Then:

Cost of option 1 (unlimited rides) = $39

Cost of option 2 (admission plus $3 per ride) = $15 + $3x

We want to find the value of x that makes these two costs equal. So we can set up the following equation:

$39 = $15 + $3x

Solving for x, we get:

$3x = $39 - $15

$3x = $24

x = 8

So if Clare goes on 8 rides, the two options will cost the same amount. To find that cost, we can substitute x=8 into either equation:

Cost = $15 + $3x

Cost = $15 + $3(8)

Cost = $15 + $24

Cost = $39

So, the cost of either option for 8 rides is $39.

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The square root function involves the square root symbol √ which is  mostly read as "square root of", the rule says that the square root of a number 'x' is a number 'y' such that y² = x.

We know that the square root of a number can be either positive or negative, but while defining the square root function, we restrict its range to be the set of all positive real numbers and hence making all square roots possible to be positive.

If the range for the square root of a number is set to be positive as well as negative it wont be a function that is why there is a restriction to the range of this set allowing only positive real numbers.

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The simplified expression is 7x- 2.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

−4x−2y+6 from 3x−2y+4.

So, subtraction will be as follows

3x - 2y + 4-( -4x  -2y + 6 )

or, 3x - 2y + 4  + 4x + 2y -6

or, 7x - 2

Hence, the simplified expression is 7x- 2.

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The approximate size of the cover that Maria will need to buy is 45. 84 square feet

The formula for calculating the circumference of a circle is expressed as;

Circumference = πr²

Where 'r' is the radius of the circle

Now, let's substitute the value of the circumference

24 = 2 × 3. 14 × r

r = 24/6. 28

r = 3. 82 feet

Formula for area = πr²

Substitute value of r

Area = 3. 14 × (3. 82)²

Area = 3. 14 × 14. 59

Area = 45. 84 square feet

Hence, the value is  45. 84 square feet

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Answer:

b) 2 Km para o leste

Step-by-step explanation:

1. 2 km N

2. 2 km W

3. 1 km S

4. 4 km E

5. 2 km S

Sul e Norte:

(1.) 2 km N + (3.) 1 km S + (5.) 2 km S = 2 km - 1 km - 2 km = 0

Este e Oeste:

(2.) 2 km W + (4.) 4 km E = -2 km + 4 km = 2 km E

Veja imagem abaixo.

Answer:

3.2t - 2.4

Step-by-step explanation:

Given

- 3.6 - 1.9t + 1.2 + 5.1t ← collect like terms

= (- 1.9t + 5.1t) + (- 3.6 + 1.2)

= 3.2t + (- 2.4)

= 3.2t - 2.4

The basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.

In the provided figure.

∠1 + ∠2 = 180 degrees ( linear pair of angles)...(i)

∠ 1 + ∠4 = 180 degrees ( linear pair of angles)...(ii)

According to transitive property, if a = b and b = c then a = c

Therefore,

∠1 + ∠2 = ∠1 + ∠4...(iii)

⇒∠2 = ∠4

Similarly, we can prove that

∠1 = ∠3

Therefore, we conclude that vertically opposite angles are always equal.

Hence, the basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".

Thus, statement c is correct.

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\(5.50p + 3.25\)

\(41.75 = 5.50p + 3.25\)

\(41.75 - 3.25 = 5.50p + 3.25 - 3.25\)

\(38.5 = 5.50p\)

\( \frac{38.5}{5.50} = \frac{5.50p}{5.50} \)

\(7 = p\)

Allison ordered 7 pictures.

The difference in the two polynomials as described in the task content is; 7y² + 8xy -3.

The polynomial given in the task content is;

(7y² + 6xy) – (–2xy + 3)

Hence, upon evaluation, the expression is

7y² + 6xy +2xy -3

7y² + 8xy -3

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Answer:

9+10 is 21

Step-by-step explanation:

Answer:

b. the triangle is not a right triangle

Step-by-step explanation:

Answer:

The triangle in this particular question may or may not be a right angled triangle

Step-by-step explanation:

~basically triangle are known to have 3 sides otherwise we would not call it a triangle...however in this particular question they may be no definite answer and triangle with 3 sides can be any sort of triangle:

-isosceles triangle with 3 uneven sides

-right angled triangle like stated with an hypotenuse

or

-scalene triangle with simply to equal sides...

glad I could help thumbs

disclaimer this answer may not be accurate and I do not take any responsibility if this answer is wrong thank you

Answer:

B.

Step-by-step explanation:

f(x) = 2^0 + 4 = 0 + 4 = 4

f(x) = 2^3 + 4 = 8 + 4 = 12

f(x) = 2^7 + 4 = 128 + 4 = 132

Answer:

The value of the experimental probability is greater

Step-by-step explanation:

For the theoretical probability;

the probability that a card with the number 3 is selected is 1/5

We consider that the probabilities of each selection are equal, for the theoretical probability

For the experimental, we simply place the frequency of the selection 3 over the total

that will be 128/400 = 8/25

As we know that 8/25 is greater than 1/5

We can conclude that the value of the experimental probability is greater than that of the theoretical

Answer:

I hate math

Step-by-step explanation:

The solutions for the given congruence equations are:

i) x ≡ 1 (mod 43)

ii) x ≡ 1 (mod 35)

To solve the given congruence equations, we'll use the Chinese Remainder Theorem (CRT). The CRT states that if we have a system of congruences of the form:

x ≡ a (mod m)

x ≡ b (mod n)

where m and n are coprime (i.e., they have no common factors), we can find a unique solution for x modulo mn.

Let's solve the congruence equations step by step:

i) x⁵ ≡ 21 (mod 43)

First, we need to find the prime factorization of 43 - 1 = 42:

42 = 2 × 3 × 7

To solve the congruence, we'll calculate the residues of 21 raised to the powers of 42 divided by the prime factors:

\(21^{42/2}\) ≡ 1 (mod 43)

\(21^{42/3}\)≡ 1 (mod 43)

\(21^{42/7}\) ≡ 1 (mod 43)

Now, we'll find the values of x⁵ modulo 43 for these residues:

x⁵ ≡ \(21^{(42/2 * 2)}\) ≡ 21⁴² ≡ 1² ≡ 1 (mod 43)

x⁵ ≡ \(21^{(42/3 *3) }\) ≡ 21⁴² ≡ 1³ ≡ 1 (mod 43)

x⁵ ≡ \(21^{(42/7 * 7)}\) ≡ 21⁴² ≡ 1⁶ ≡ 1 (mod 43)

Since all three residues are congruent to 1 modulo 43, there is only one solution for x modulo 43, which is x ≡ 1 (mod 43).

ii) x⁷ ≡ 2 (mod 35)

First, we need to find the prime factorization of 35 - 1 = 34:

34 = 2 ×17

To solve the congruence, we'll calculate the residues of 2 raised to the powers of 34 divided by the prime factors:

\(2^{34/2}\) ≡ 1 (mod 35)

\(2^{34/17}\) ≡ 1 (mod 35)

Now, we'll find the values of x⁷ modulo 35 for these residues:

x⁷ ≡\(2^{34/2*2}\) ≡ 2³⁴ ≡ 1² ≡ 1 (mod 35)

x⁷≡ \(2^{34/17*17}\) ≡ 2³⁴ ≡ 1² ≡ 1 (mod 35)

Since both residues are congruent to 1 modulo 35, there is only one solution for x modulo 35, which is x ≡ 1 (mod 35).

Therefore, the solutions for the given congruence equations are:

i) x ≡ 1 (mod 43)

ii) x ≡ 1 (mod 35)

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Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

As per given condition of completing a job in 3 hours when working together, then time taken by  Shoab to complete a job alone is equal to  12 hours.

As given in the question,

Time taken by Tharthat and Shoab to complete a job when working together = 3 hours

Let us consider time taken by Tharthat to complete a job when he works alone = x hours

And as per given condition Shoab takes 3 times more than Tharthat to complete a job when he works alone = 3x

Required equation is :

( 1 / x ) + ( 1 / 3x ) = ( 1 / 3 )

Simplify it by taking least common multiple we get,

⇒ ( 3 + 1 ) / 3x = ( 1 / 3 )

⇒ 4 / 3x = 1 / 3

⇒ 3x  = 4 × 3

⇒ 3x = 12 hours

⇒ x = 4 hours

Time taken by Shoab is 3x = 12 hours.

Therefore, completing a job in 3 hours when working together then time taken by  Shoab to complete a job alone is equal to  12 hours.

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Answer:

Step-by-step explanation:

answer B

since for all real positive r,  r^x >0

The unique function who give a negative answer is f(x)=-3* 2^x

Susie needs to select minimum 14 to be sure to get 6 marbles of the same color.

With replacement

(3R, 7G, 10B)

P(at least 1 red marble) = 1- p(no red marbles) = 0.5563

P(2R, 2G, 2B) = 0.0827

P(4B, 4G) = 0.0657

Without replacement

P(at least 1 red marble) = 1- p(no red marbles) = 0.6009

P(2R, 2G, 2B) = 0.0731

P(4B, 4G) = 0.0583

if we select 3+5+5=13 marbles then there is only one way that we won't have at least 6 marbles of the same color when 3R, 5G and 5B are selected, so to get 6 marbles of the same color, we need to select minimum 14, then we will be 100% sure.

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