A teacher gave his students the four graphs below. Which graph represents a geometric sequence?

Answer: B. Exponential decay

Step-by-step explanation:

An exponential function is a function of the form f(x) = ab^x where a and b are constants, x is the independent variable, and b is a positive number not equal to 1. In this case, f(x) = -3(4^x). The base of the exponential function is 4, and it is a common base of exponential decay, because the base is less than 1, and the exponent is positive, this means that the output of the function will decrease as the input increases. Therefore, the function represented by f(x) = -3(4^x) is an exponential decay function.

Answer:

Exponential Decay

Step-by-step explanation:

In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y=a(1-b)x wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed

Substitute the given value into the function and evaluate.

f(x)= -3⋅4^x/8

Answer:

hope this would help you!

The number of different schedules are possible is given by the permutation and the equation is P = 2,730 schedules

A permutation is an ordered arrangement.

The number of ordered arrangements of r objects taken from n unlike objects is:

Permutation ⁿPr = n! / ( n - r )!

Given data ,

Let the total number of schedules be P

Let the total number of European cities be n = 15

Let the number of cities Yolanda can visit in time r = 3 cities

So , the total number of different schedules is calculated by permutation and ,

The total number of different schedules = ⁿPr = n! / ( n - r )!

Substituting the values in the equation , we get

¹⁵P₃ = ( 15 ) ! / ( 15 - 3 ) !

¹⁵P₃ = ( 15 ) ! / ( 12 )!

¹⁵P₃ = 15 x 14 x 13

¹⁵P₃ = 2,730 schedules

Hence , the value of P is 2,730 schedules

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The value of f(-1) is either a³ - 31 or the absolute value of a³ - 31, depending on the value of a³ - 31.

It is not possible to find the exact value of f(-1) without knowing the value of a.

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Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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The line y = 3 is shown in the diagram of the graph of y = (x + 1)² for -4 ≤ x ≤ 2.

By using the graph, the solutions of (x + 1)² = 3 to 1 decimal place include the following:

x = -2.7 or x = 0.7.

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.

Next, we would use an online graphing calculator to plot the above quadratic equation with points of intersection at (-2.732, 3) and (0.732, 3) as shown in the graph attached below.

By critically observing graph of the given quadratic equation, we can logically deduce that the solutions of (x + 1)² = 3 on the x-coordinate are x is equal to -2.7 or x is equal to 0.7.

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Answer: a. The sum of two numbers is always greater than zero.

Step-by-step explanation:

A counterexample to this conjecture would be when the two numbers are both negative. For example, the sum of -5 and -3 is -8, which is less than zero.

b. The sum of a positive number and a negative number is always positive.

A counterexample to this conjecture would be when the negative number is greater than the positive number. For example, the sum of 5 and -6 is -1, which is less than zero.

c. If a figure has four sides, then it is a rectangle.

A counterexample to this conjecture would be a square. A square has four sides, but it is not a rectangle because all of its angles are 90 degrees while a rectangle has four right angles.

It's good to keep in mind that a conjecture is a statement that is made based on observations and that it hasn't been proven yet, therefore a counterexample can be used to show that the conjecture is false.

Answer:

a)  -5 + 1 = -4

b)  2 + (-10) = -8

c)  A scalene trapezium.

Step-by-step explanation:

A counterexample is proof that a conjecture is false.

Given conjecture:

If one of the numbers is negative, and its absolute value is equal to or greater than the value of the positive number, the result will always be equal to or less than zero.

Counterexample:

As -4 is less than zero, this proves that the conjecture is false.

Given conjecture:

If the absolute value of the negative number is greater than the value of the positive number, the result will always be negative.

Counterexample:

As -8 is negative, this proves that the conjecture is false.

Given conjecture:

Counterexample:

The interior angles of a rectangle are congruent (90°).

A scalene trapezium has four sides, but as its interior angles are all different, it is not a rectangle.  This proves that the conjecture is false.

The matrix products are given as follows:

a. AB = [58 -6 24]

        [18 63 45]

        [-22, -39, -33]

b. BA = [32 -26]

            [10 56]

The addition A + B is not possible to obtain, the matrices have different dimensions.

The dimensions of each matrix are given as follows:

Hence the dimensions of each product are given as follows:

To multiply matrices, the rows of the first are multiplied by the columns of the second, hence matrix AB is obtained as follows:

Hence the matrix AB is given as follows:

AB = [58 -6 24]

        [18 63 45]

        [-22, -39, -33]

Matrix BA is obtained as follows:

Hence the matrix BA is given as follows:

BA = [32 -26]

        [10 56]

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Answer:

To calculate the tip, we first need to find 24% of the total bill. To do this, we can multiply the bill amount by 24% (expressed as a decimal).

Tip = 0.24 * 73.25

= 17.58

Therefore, the tip should be $17.58 in dollars.

Answer:

[tex]\frac{1}{343}[/tex]

Step-by-step explanation:

[tex]7^{-3}[/tex] = [tex]\frac{1}{7^{3} }[/tex] = [tex]\frac{1}{7x7x7}[/tex] = [tex]\frac{1}{343}[/tex]

Marco pays $64  for credit card, $272 for Groceries and $672 for rent

percentage, a relative value indicating hundredth parts of any quantity.

Given that Marco budgets $1,600 a month for expenses.

According to the graph he pays 4% of credit card

Now let us find 4% of 1600

4/100×1600

0.04×1600

$64 Marco pays for credit card.

From graph, he pays 17% for groceries

17% of 1600

17/100×1600

0.17×1600=$272

$272 Marco pays for Groceries.

From graph, he pays 42% for rent

42/100×1600

0.42×1600=672

$672 Marco pays for Rent.

Hence, Marco pays $64  for credit card, $272 for Groceries and $672 for rent

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The simplified value for the function at g(0) and g(2) are 2 and -20 respectively.

To simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.

Given a function g(x) = -4x² - 3x + 2

to find the values of g(0)

and g(2)

for g(0)

substitute x = 0 in the equation,

g(x) = -4x² - 3x + 2

g(0) = -4(0)² - 3(0) + 2

g(0) = 2

for g(2), substitute x = 2 in the equation,

g(x) = -4x² - 3x + 2

g(2) = -4(2)² -3(2) + 2

g(2) = -4(4) - 6 + 2

g(2) = -16 - 6 +2

g(2) = -20

Hence the values for g(0) is 2 and for g(2) is -20.

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Answer: For converting Canadian Dollars to US Dollars divide 1 by 0.82 to give you an answer of around 1.2195(repeating). Then multiply that number by each of the Canadian Dollar amounts. US Dollars to Canadian Dollars is much simpler, as you just multiply the amount by 0.82 to find the answer.

$1.45 CAD x 1.2195 = $1.77 USD

$45.5 USD x 0.82 = $38.31 CAD

$2.50 CAD x 1.2195 = $3.05 USD

$1,500 CAD x 1.2195 = $1,829.27 USD

Hope this helped, and have a great day!

Answer:

9 students

Step-by-step explanation:

34 -25

well, there are 28 + 28 + 24 = 80 pieces total, or namely that's the 100%, and we know that 24 of those are chocolates

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 80 & 100\\ 24& x \end{array} \implies \cfrac{80}{24}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 10 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 10x=300\implies x=\cfrac{300}{10}\implies x=30[/tex]

To figure out what percentage of the trail mix is chocolate, we add up all the pieces, divide the number of chocolate pieces by the total and multiply by 100. In this case, we find that 35% of the trail mix is chocolate.

In order to figure out the percent of chocolate pieces in Caitlyn's trail mix, we first need to determine the total number of pieces. Caitlyn counts 28 raisins, 28 chocolate pieces, and 24 peanuts, which gives us a total of 80 pieces in the mix. Then, since there are 28 chocolate pieces, we divide 28 (chocolate pieces) by 80 (total pieces). This will give us the decimal representation of the portion of the mix that is chocolate. To convert this into a percentage, we multiply by 100. Hence, the calculation will be (28/80)*100 = 35%. So, 35% of the trail mix is chocolate.

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The year-end balance interest rate for a principal of $100.00 is $105.00, for a principal of $550.00 is $561.00, for a principal of $1,200.00 is $1,284.00.

Interest is the cost of borrowing money or the amount of money that is earned on an investment. It is the amount of money paid by a borrower to a lender or earned by an investment, in exchange for the use of the lender's or investor's money.

Here,

To calculate the year-end balance for each principal using the given annual interest rates, we can use the formula:

End of year balance = Principal + (Principal x Interest rate x Number of years)

For a principal of $100.00, the annual interest rate is 5%, and the number of years is 1. So, the end-of-year balance is:

End of year balance = $100.00 + ($100.00 x 0.05 x 1) = $100.00 + $5.00 = $105.00

For a principal of $550.00, the annual interest rate is 2%, and the number of years is 1. So, the end-of-year balance is:

End of year balance = $550.00 + ($550.00 x 0.02 x 1) = $550.00 + $11.00 = $561.00

For a principal of $1,200.00, the annual interest rate is 7%, and the number of years is 1. So, the end-of-year balance is:

End of year balance = $1,200.00 + ($1,200.00 x 0.07 x 1) = $1,200.00 + $84.00 = $1,284.00

For a principal of $5,000.00, the annual interest rate is 11%, and the number of years is 1. So, the end-of-year balance is:

End of year balance = $5,000.00 + ($5,000.00 x 0.11 x 1) = $5,000.00 + $550.00 = $5,550.00

Hence, the year-end balance for a principal of $100.00 is $105.00, for a principal of $550.00 is $561.00, for a principal of $1,200.00 is $1,284.00, and for a principal of $5,000.00 is $5,550.00

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The odds in favor of Amanda unlocking the treasure chest is 1/5.

We have to find the odds in favor of Amanda's character unlocking the treasure chest. Odds in favor is the ratio of the number of favorable outcomes to the number of unfavorable outcomes.

[tex]P (A) = \frac{no.of favorable outcomes}{no. of unfavorable oucomes}[/tex]

P(A), is used to denote the probability of the event A.

Before finding out the odds in favor, we need to find the probability of her unlocking the treasure chest {P(T)}

Total no. of outcomes = 6   (as a dice has 6 sides)

Number of outcomes desired = 1 (that unlocks the treasure chest)

Therefore, the probability of unlocking the treasure chest

P(T) = Number of outcomes desired/ Total no. of outcomes = 1/6

P(T) is our favorable outcome.

Any other outcome would be unfavorable,

Therefore, the number of unfavorable outcomes would be

= Total no. of outcomes - number of the desired outcomes = 6-1 = 5

Thus, applying the formula for P(A)

P(A) = no. of favorable outcomes/ no. of unfavorable outcomes

= 1 / 5 (Ans)

Thus, the odds in favor of Amanda unlocking the treasure chest is 1/5.

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Answer:

D) 7/12

Step-by-step explanation:

The first thing we want to do is find a like denominator for the fraction

Both 4 and 3 go into the multiple 12, so we'll use that

4x3=12

3x4=12

and what you do to one side, you must do to the other so we have

1/4x3= 3/12

2/3x4= 8/12

With that you get 2 3/12 and 1 8/12, which is subtractable

Take one from 2 so that you can make 3/12 15/12

15/12-8/12=7/12

This gives us our answer 7/12

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2 1/4 - 1 2/3

2 1/4 to an improper fraction is 9/4

1 2/3 to an improper fraction is 5/3

to get the same denominator multiply 9/4 by 3 and 5/3 by 4.

27/12 - 20/12

7/12 IS YOUR ANSWER.

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The boat and the whale are about 218.5 miles apart.

Using the Pythagorean theorem to calculate the distance between the boat and the whale.

Let's call the distance between the boat and the whale "d" and the time they moved apart "t".

1st movement:

d = 45t

2nd movement:

d = (45t + 25(t+35))²

To calculate the final distance, we need to square d from the second movement and add the result from the first movement.

d² = (45t)² + (25(t+35))²

We know that the boat and the whale were moving apart for 35 minutes and 25 minutes, so we can substitute t = 35 and t = 25 in the equation.

d² = (4535)² + (2560)²

Taking the square root of the result and get the final distance between the boat and the whale.

d =  ([tex]\sqrt{4535 ^{2} +2560^{2} }[/tex])

d ≈ 218.5 miles

Hence, the boat and the whale are about 218.5 miles apart.

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The given expression is equivalent to the expression -x² + x + 30.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Given expression,
= (5 + x)(6 - x)

Simplifying the expression using distributive property,
= 5 [6 - x] + x [6 - x]
= 30 - 5x + 6x - x²
= -x² + x + 30

Thus, the given expression is equivalent to the expression -x² + x + 30.

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Answer:

Step-by-step explanation:

When it comes to graphing a trigonometric function we use the amplitude, period, vertical shift and these values all help our graph come together to give us our final answer.

In this case,

The amplitude=2

period=1

and there is no phase / vertical shift.

The approximate distance around the outside of the circular field is B. 172.7 feet.

A circumference is the part of a circle which is referred to as the boundary. The length of the circumference of a circle is given as;

length of a circumference = 2πr

where r is the radius of the circle.

To determine the distance around the outside of the circular field, we have;

length of the distance around the outside of the circular field = 2πr

given that;

r = 27.5 feet

length of the distance around the outside of the circular field = 2πr

                                                            = 2*(22/ 7)*27.5

                                                            = 172.7

The length of the distance around the outside of the circular field is 172.7 feet.

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Answer:

Step-by-step explanation:

?

The car must travel a distance of 130.7 meters. This can be determined by using the equation for distance travelled with a constant acceleration:

Distance = Initial Velocity x Time + (1/2) x Acceleration x Time^2

In this case, the initial velocity is 18.1m/s, the acceleration is 3.7m/s^2, and the final velocity is 29.7m/s. We can set the final velocity equal to the initial velocity and solve for time:

29.7m/s = 18.1m/s + 3.7m/s^2 x Time

Time = 5.4 seconds

We can then plug this value for time into the equation for distance:

Distance = 18.1m/s x 5.4s + (1/2) x 3.7m/s^2 x 5.4s^2

Distance = 130.7 meters

Answer:

$180.00 sales price

$144.00 for a scratched one

Step-by-step explanation:

240 x .75 = 180

1/4 is 25%  (100% - 25% = 75% which is .75 as a decimal)

180 x .80 = 144

1/5 is 20% (100% -20% = 80% which is .8 as a decimal)

The constant of proportionality from the graph is 5.

Firstly, there is proportional relationship.

Two values x  and  y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called constant of proportionality.

The proportional relationship between x and y can be written symbolically as

[tex]x \propto y[/tex]

That middle sign is called sign of proportionality.

To find the constant of proportionality:

We can see that for every 1 unit we move to the right on the x- axis (positive), the line moves up 5 units.

Divide the change on y by that change on x:

5/1=5

For the next point;

10/2=5

Therefore, the proportionality constant will be 5

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Answer : Yes, it has rotational symmetry. The angle of rotation is, 60 degree.

It is a shape that has Rotational Symmetry when it still the same after the rotation.

here, we have,

The given figure is hexagon and it has rotational symmetry because it still the same after the rotation.

As there are 6 sides of hexagon geometry and the degree of rotation is, .

So, the angle of rotation = 360/60

                                        =60 degree

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Answer:

x<4

Step-by-step explanation:

_2*+13<_3 take-13 crossing the less sign acting same as equal then with number line, at point 13 go 3 steps to the left to get -16 then divide it by-2 to get x<4

Answer:

The total amount in your bank account per year is not a linear relationship, it's compound interest.

Step-by-step explanation:

The total amount in your bank account per year is not a linear relationship because it is not a straight line. Linear relationships are defined by an equation in the form of y = mx + b, where m is the slope of the line, x is the independent variable and y is the dependent variable, and b is the y-intercept.

In this case, the total amount in your bank account per year is not a straight line, it is a curve. The total amount in your bank account will increase as a function of time, but the rate of increase is not constant as it is with linear relationships.

The amount of money in your account will increase over time as the interest is compounded. The interest is calculated on the principal + accumulated interest, so the growth rate of the account is not constant, it increases as the balance grows.

For example, the first year you will earn $5000.03 = $15 in interest, and the second year you will earn $5150.03 = $15.45 in interest, the next year the interest will be $530.45*0.03 = $15.91 and so on.