For which situation does one quantity change at a constant rate per unit interval relative to another quantity?

Responses

For every day that passes, a person drives 54 miles.
.
For every month that passes, a savings account earns interest at a rate of 1.5%


For every week that passes, a vine doubles in length 2 times a week.

.

For every year that passes, a population of insects increases by 6%

The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:

D. x³ + 2x² - 21x + 18.

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros of the polynomial are given as follows:

x = 3, x = -6, x = 1.

Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:

(x - 3)(x + 6)(x - 1)

(x² + 3x - 18)(x - 1)

x³ + 2x² - 21x + 18.

Meaning that option D is correct.

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The only two options with equations that are true for x = –2 and x = 2 are;

Option A: x² - 4 = 0

Option D: 4x² = 16

The domain of a function is the set of all input values  for which the function is possible.

Now, we are given the domain values as  x = –2 and x = 2.

a) x² - 4

f(-2) = (-2)² - 4

= 0

f(2) = (2)² - 2

= 0

b) x² = -4

f(-2) = (-2)²

= 4

f(2) = (2)²

= 4

c) 3x² + 12

f(-2) = 3(-2)²  + 12

= 24

f(-2) = 3(2)²  + 12

= 24

d) 4x²

f(-2) = 4(-2)²

= 16

f(2) = 4(2)²

= 16

e) 2(x - 2)²

f(-2) = 2(-2 - 2)²

= 32

f(2) = 2(2 - 2)²

= 0

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Answer:

it's c trust me I had the same problem

The given exponential function represents the growth in the function. The percentage of growth (increase) is 1%.

An exponential growth function is a function where the quantity increases slowly and after some time, it increases rapidly.

It is represented by the formula,

y = a(1 + r)ˣ

Here the term 'a' is the initial amount of the quantity, the term 'r' is the rate of increase and the term 'x' is the period.

The given exponential function is y = 10(1.01)ˣ

Here we can write the function as

y = 10(1.01)ˣ

⇒ y = 10(1 + 0.01)ˣ

Since 1.01 > 1, it is an exponential growth function.

So, when comparing with the formula, we get the rate of increase,

r = 0.01

Converting it into fractions, we get 1/100

Then, the percentage rate of increase is 1%.

Therefore, the given exponential function grows with a rate of 1% increase.

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i) The random variable is the number of suspicious transmissions reviewed until finding the first blocked one and the random variable is distributed usinng geometric distribution

ii) The expected value of the random variable: 2.5 which means the specialist will review 2.5 suspicious transactions on average before finding the first transmission that will be blocked.

In this question we have been given a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history.

Based on past history, the specialist blocks 40 percent of the suspicious transactions.

so, p = 0.40

i. Let X represent the number of suspicious transmissions reviewed until finding the first blocked one.

We will use a geometric distribution to model the first transmission.

ii. We know that according to the geometric model the expected value of the random variable would be.

E(X) = 1/p ,

       = 1/0.4

       = 2.5

This means, the specialist will review 2.5 suspicious transactions on average before finding the first transmission that will be blocked.

Therefore,  i) the random variable: the number of suspicious transmissions reviewed until finding the first blocked one.

ii) the expected value of the random variable: 2.5

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The complete question is:

At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is sufficient evidence of fraud, the transaction is blocked. Based on past history, the specialist blocks 40 percent of the suspicious transactions. Assume a suspicious transaction is independent of other suspicious transactions.

Suppose the specialist wants to know the number of suspicious transactions that will need to be reviewed until reaching the first transaction that will be blocked.

(i) Define the random variable of interest and state how the variable is distributed.

(ii) Determine the expected value of the random variable and interpret the expected value in context.

The average rate of change of the function at the interval 0 ≤ x ≤ 4 is 11.25

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

x  0   1   2   3  4   5

y 3   6  12   24 48 96

The interval is given as

0 ≤ x ≤ 4

On the table, we have

x = 0 and y = 3

x = 4 and y = 48

This means that

f(0) = 3 and f(4) = 48

The average rate of change is then calculated as

Average rate of change = [f(4) - f(0)]/[4 - 0]

Substitute the known values in the above equation, so, we have the following representation

Average rate of change = [48 - 3]/[4 - 0]

Evaluate

Average rate of change = 11.25

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The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0).

Does the order of transformations matter in functions?

Order is not important. According to algebra, y=12f (x3). Our four transformations are (1), (3), (2), and (4); all four are in the x direction. When we combine a stretch and a translation in the same direction, the sequence counts.

The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.

ABCD can be transformed to A'B'C'D' by ...

rotation 90° CCW about the point (-1, -1)

Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...

reflection across the line y=x

reflection across the line x=-1

Complete question: A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.

b.) There is more than one way to transform quadrilateral ABCD into quadrilateral A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.

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Answer: The answer is $s$ > 7, which represents the number of seconds that can pass for the temperature in the cryotherapy chamber to drop below -20°F.

Step-by-step explanation: The temperature in the chamber will drop below -20°F when it reaches -20°F + 2.5°F = -17.5°F.

The temperature in the chamber is currently 0°F, so we can represent this situation with the inequality 0 - (2.5 * $s$) < -17.5, where $s$ is the number of seconds that can pass.

We can simplify this inequality by multiplying both sides by -1 to get the following: 2.5 * $s$ > 17.5.

Dividing both sides by 2.5, we get the final inequality: $s$ > 7.

Therefore, the number of seconds $s$ that can pass for the temperature in the cryotherapy chamber to drop below -20°F is greater than 7 seconds.

The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;

⇒ 0.9375

The term probability refers to the likelihood of an event occurring

Given that;

The probability that a visitor is offered a coupon (p) = 50%

Now,

Since, The probability that a visitor is offered a coupon (p) = 50%

Hence, The probability that he gets coupon all 4 days is,

⇒ p (4) = p⁴

⇒ p (4) = (50%)⁴

⇒ p (4) = 0.0625

Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,

⇒ p' = 1 - 0.0625

⇒ p' = 0.9375

Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375

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The operations between functions are:

a) h(f(3)) = 5

b) (f×g)(4) = -8

c) f(  g(h(0))) -1

The first thing we want to find is a composition, we want to find:

h(f(3))

That means that we need to evaluate h(x) in f(3), look at the graph and you can see that f(3) = -4

Replacing that we get:

h(f(3)) = h(-4)

And on the graph, we can see that h(-4) = 5

then h(f(3)) = 5

b) Now we have the product:

(f×g)(4) = f(4)*g(4)

Again, looking at the graph:

f(4) = -4

g(4) = 2

Then:

(f×g)(4) = f(4)*f(4)

(f×g)(4) = -4*2

(f×g)(4) = -8

c) Finally we have other composition:

f(  g(h(0)))

So we have 2 compositions, first we find:

h(0) = 5

f(  g(h(0))) = f(g(5))

Then:

g(5) = 0

f(  g(5)) = f(0)

Finally, look at the graph and you can see that f(0) = -1

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The complete equation in the slope-intercept form is y = 4x-1.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

So, the equation is,

y - y₁ = m (x - x₁)

And the standard form of the slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

From the question, we have

m = 4 and coordinates of b is (0, -1).

So, the equation is,

y + 1 = 4 (x - 0)

y +1 = 4x

y = 4x-1

Therefore, the equation is y = 4x-1.

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Answer:

[tex]\displaystyle \frac{9}{4}[/tex]

Step-by-step explanation:

[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} )[/tex]

The second term of this sum is an Infinite Geometric Progression
To find the sum of an Infinite Geometric Progression,

- Find the first term ( 1/5 ) of the progression and call it a
- Find the common ratio, (divide any term by it's predecessor. i.e [tex]\displaystyle \frac{\frac{1}{5^2} }{\frac{1}{5} } = \frac{5}{5^2} = \frac{1}{5}[/tex]) and call it r

Finding the sum of given Geometric Progression:
Sum of Infinite GP: [tex]\displaystyle \frac{a}{1-r}[/tex]

Plugging our values in this equation, we get:
Sum of Geometric Progression = [tex]\displaystyle \frac{\frac{1}{5} }{1 - \frac{1}{5} } = \frac{\frac{1}{5} }{\frac{5 - 1}{5} } = \frac{1}{4}[/tex]

Adding to find the actual answer:
[tex]\displaystyle (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = 2 + \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{9}{4}[/tex]

A triangle with coordinates (1,1) (4,2) (3,5) is translated three units down and five units to the left. New coordinates will be (-4,-2), (-1,-1),(-2, 2).

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Given

A triangle with coordinates (1,1) (4,2) (3,5)

The value of a coordinate is impacted by translations left or right but not by translations up or down or left or right.

We multiply all of the numbers by 3 since we are translating the entire triangle down three units.

Additionally, we are converting the entire triangle to left-to-right units of five, thus we will multiply all values by 5.

A = (1 - 5, 1 - 3)

B = (4 - 5, 2 -3)

C = (3 - 5, 5 - 3)

New coordinates will be:

A = (-4,-2)

B = (-1,-1)

C = (-2, 2)

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The conclusion is that the angle which measures 120° is not Acute angle.

The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the form of the angle can alternatively be used to symbolise the angle, with the middle letter indicating the location of the angle (i.e.its vertex). Greek characters such θ, α, β, etc. are frequently used to denote angles.

In geometry, there are mainly six different kinds of angles. All angles have the following names and characteristics:

Angle B measures 120°.

Here the angle is more than 90° so the angle is not acute.

The conclusion is that the angle which measures 120° is not Acute angle.

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Answer:

Solve the equation for [tex]{y}[/tex].

[tex]y=\frac{5x}{2}[/tex]

Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.

Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(0,0)}[/tex]

Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex](1,\frac{5}{2})[/tex]

Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(2,5)}[/tex]

These are three possible solutions to the equation.

[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]

The solution of the equation is x = 6±2√11.

What is a quadratic equation?

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

Here, we have

Given: x² - 12x = 8

Now, we factorize the given equation and find the solution.

x² - 12x = 8

x² - 12x - 8 = 0

We apply here the quadratic formula.

= (-b ±√b²-4ac)/2

= (12 ±√12²-4×1×(-8))/2

= (12±√144+32)/2

= (12±√176)/2

= (12±4√11)/2

= 6±2√11

Hence, the solution of the equation x² - 12x = 8 is 6±2√11.

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Answer: Tiffany

Step-by-step explanation: Ramon Ratio 8:2 can be reduced to 1 cup of sugar every 4 cups of water. Tiffany Ration is 9:3 which is reduced to 1 cup of sugar every 3 cups of water.

The inequality that can be used to represent this situation is 2x + 1.50y ≤ 20.

The maximum number of apples she can buy is 7 apples.

Mia went into a grocery store and where they sell apples for $2 each and mangos $1.50 each.

where

Therefore, let's represent the inequality when Mia has to spend 20 dollars.

2x + 1.50y ≤ 20

If Mia decide to buy 3 mangoes , the maximum number of apples she can buy can be calculated as follows:

2x + 1.50y ≤ 20

2x + 1.50(3) ≤ 20

2x + 4.5 ≤ 20

2x ≤ 20 - 4.5

2x ≤ 15.5

x ≤ 15.5 / 2

x ≤ 7.75

Therefore, the maximum she can buy is 7 apples.

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We can conclude that the number of possible schedules for next semester could she make is 7920.

In more mathematical terms, the factorial of a number (n!) is equal to

n(n-1). For example, if you want to calculate the factorial for four, you would write: 4! = 4 x 3 x 2 x 1 = 24.

Given that,

The student needs 11 more classes to graduate.

And, possible schedules for next semester could she make if she plans to take 4 classes

Based on the given expression, the calculation is as follows:

The combination formula is given to be:

[tex]n_{C} _{r} =\frac{n!}{r!(n-r)!}[/tex]

= [tex]11_{C} _{4}[/tex] ! * 4 !

= [tex]\frac{11 !}{4!(11-4)!}[/tex]  * 4 !

= [tex]\frac{11!}{4!7!}[/tex] * 4 !

= [tex]\frac{11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1*7*6*5*4*3*2*1}[/tex] * 4 !

We can cancel the coefficients,

= [tex]\frac{11*10*9*8}{4*3*2*1}[/tex] * 4 !

= [tex]\frac{7920}{24}[/tex] * 4 !

= 330* 4 !

= 330 * 4*3*2*1

= 7920

Therefore,

We can conclude that the number of possible schedules for next semester could she make is 7920.

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The surface area of the triangular prism is 136 square units

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

The surface area of the triangular prism is the sum of the areas of the above shapes

So, we have

Surface area = 2 * area of rectangle 1 + 1 * area of rectangle 2 + 2 * area of triangle 1

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2 * 7 * 5 + 1 * 7 * 6 + 2 * 0.5 * 4 * 6

Evaluate

Surface area = 136

Hence, the surface area is 136 square units

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This mean there are infinite solutions.

Each side is equally satisfied in an endless solution. Infinite is a symbol for boundlessness or limitlessness. Typically, the sign "" is used to denote it.

Solving an equation, Henry gets to the last line of his work and is left with “3 = 3”.

Any value for the Variable would make the equation true, according to infinite solutions.

We can tell which instance it is by examining our findings. If both sides of the equal sign end up having the same word,

such as

3=3 or 3x=3x, then. Finite solutions exist.

This mean there are infinite solutions.

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44 is the proportion of the botched dressing will be olive oil.

Given, Miguel is mixing up a salad dressing. regardless of the number of servings,

the recipe requires that 58 of the finished dressing mix be olive oil, 14 vinegar, and the remainder an even mixture of salt, pepper and sugar. if he accidentally doubles the vinegar and forgets the sugar altogether,

we have to find the proportion of the botched dressing that will be olive oil.

first we will find the amount of the even mixture of salt, pepper and sugar.

as, olive oil + vinegar + even mixture of salt, pepper and sugar = 100

58 + 14 + mixture of salt, pepper and sugar = 100

mixture of salt, pepper and sugar = 100 - 72

mixture of salt, pepper and sugar = 28

if he mixed doubles of the vinegar i.e. 28 then olive oil be,

x + 28 + 28 = 100

x = 100 - 56

x = 44

Hence, 44 is the proportion of the botched dressing will be olive oil.

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Answer:

To determine how many miles Naomi's car can go on one gallon of gas, we first need to determine how many gallons of gas the car used to travel 15\tfrac{1}{2}15 2 1 ​ miles. We are told that the car used \frac{2}{5} 5 2 ​ of a gallon to travel this distance, so we can multiply this value by 15\tfrac{1}{2}15 2 1 ​ to get the total number of gallons used:

\frac{2}{5} \cdot 15\tfrac{1}{2} = 9

Therefore, the car used 9 gallons of gas to travel 15\tfrac{1}{2}15 2 1 ​ miles. To determine how many miles the car can go on one gallon of gas, we need to divide the total number of miles traveled by the number of gallons used:

15\tfrac{1}{2} \div 9 = \frac{31}{18}

This means that the car can go 31/18 miles on one gallon of gas. Since this fraction is not in simplest form, we can further simplify it by dividing the numerator and denominator by the greatest common factor, which is 3:

\frac{31}{18} \div \frac{3}{3} = \frac{31}{18} \cdot \frac{3}{3} = \frac{31 \cdot 3}{18 \cdot 3} = \frac{93}{54}

Therefore, the car can go 93/54 miles on one gallon of gas. This fraction can be further simplified by dividing the numerator and denominator by the greatest common factor, which is 1:

\frac{93}{54} \div \frac{1}{1} = \frac{93}{54} \cdot \frac{1}{1} = \frac{93 \cdot 1}{54 \cdot 1} = \frac{93}{54}

Therefore, the final answer is that the car can go 93/54 miles on one gallon of gas.

Answer:

Step-by-step explanation:

it is c

If ABCD is a parallelogram, then the measure of D is 68

        9x + 5 + 16x(<DAB) = 180 ....... because it is straight line.

        25x + 5 = 180

        25x = 180 - 5

        25x = 175

            x = 7

          <ADC+ <DAB= 180

          <ADC+ 112 = 180

          < ADC= 180 - 112

          < ADC = 68

Therefore, the measure of D is 68

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Answer:

look at the explanation below

Step-by-step explanation:

The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:

Step 1: Start with the prime factorization of the given number.

Step 2: Then, divide the factors obtained into groups containing the same factors.

Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number not a perfect cube and we cannot find the cube root of that number

i hope this helps

Answer:

  parallel

Step-by-step explanation:

You want to know the parallel/perpendicular status of the lines described by the equations ...

Parallel lines have the same slope. The slope is the coefficient of x when the equation is written in the form ...

  y = mx +b

as is the second equation.

The first equation can be put in that form by solving for y.

  2x -5y = 25 . . . . . . given equation

  2x -25 = 5y . . . . . . add 5y -25

  2/5x -5 = y . . . . . . divide by 5

The coefficient of x (slope) is 2/5, same as the second equation.

The lines are parallel.

__

Additional comment

Your graphing calculator can help you figure this out, too. The graphed lines are parallel.

Answer:

170 is the smallest

745 is the largest

Step-by-step explanation:

It is what it is

The significant figure by multiplying 101 with 52 is 5000.

Here given,

101 x 52

Round 101 to 100 and 52 to 50, then multiply together to get 5000.

Significant Figures: 1

Decimals: 0

The significant notation: 5e+3

Therefore the significant notation is 5000.

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