Mathematics College

Which of the following equations describes the nth term for the sequence

Answers

Answer 1

The nth term of the sequence 4/5, 1/5, 1/20. 1/80..... is an = 4/5(1/4)^(n - 1)

How to determine the value of tthe nth term of the sequence?

The definition of the function is given as

4/5, 1/5, 1/20. 1/80.....

The above definitions imply that we simply multiply 1/4 to the previous term to get the current term

Using the above as a guide, we have

First term, a = 4/5

Ratio, r = 1/4

So, we have the following equation

an = 4/5(1/4)^(n - 1)

Hence, the value of the nth term is an = 4/5(1/4)^(n - 1)

Related Questions

URGENT!!!

Find the value of n in the picture above. Leave your answer in simplest radical form.

Answers

The value of n in the given triangle is given as follows:

[tex]n = 4\sqrt{5}[/tex]

What is the geometric mean theorem?

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases of the triangle are given as follows:

8 and 10.

Hence the altitude n is given as follows:

n² = 8 x 10

n² = 80

[tex]n = \sqrt{80}[/tex]

[tex]n = \sqrt{16 \times 5}[/tex]

[tex]n = 4\sqrt{5}[/tex]

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What is the term-to-term rule for this sequence? 64, 32, 16, 8, 4

Answers

Answer:

Divide by two is the term-to-term rule.

Step-by-step explanation:

64/2=32

32/2=16

16/2=8

8/2=4

Given: Circle k(O) with OT ⊥ XY, OU ⊥ WZ, and ∠XOY ≅ ∠ZOW Prove: OT ≅ OU

50 points

Answers

Hopefully this help helps

The equation f(x) = (x - 1)²2 - 2 is being
moved 3 units to the right and 3 units up, write
the new equation

Answers

The new equation after moving 3 units to the right and 3 units up is

[tex]f(x) = (x - 4)^{2} 2 + 1.[/tex]

How to move the equation rights and up?

We need to change the equation to move the function [tex]f(x) = (x - 1)^{2} 2 - 2[/tex] three units to the right and three units up:

To shift the function three units to the right, replace x with (x - 3), which adjusts the graph three units to the right. [tex]f(x) = ((x - 3) - 1)^{2} 2 - 2[/tex], which simplifies to [tex]f(x) = (x - 4)^{2} 2- 2.[/tex]

To move the function three units up, multiply the equation by three.[tex]f(x) = (x - 4)^{2} 2 + 1[/tex] is the final equation.

The new equation is now [tex]f(x) = (x - 4)^{2} 2 + 1.[/tex]

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Irma has $41,000 in a savings account that earns 2% interest per year. The interest is not compounded.To the nearest cent, how much will she have in total in 4months?

Answers

The interest rate per year is 2%, which is equivalent to 0.02 in decimal form. Since the interest is not compounded, we can simply calculate the interest earned over 4 months as:

Interest = Principal x Rate x Time
Interest = $41,000 x 0.02 x (4/12) (4 months is one-third of a year)
Interest = $273.33

Therefore, the total amount Irma will have in 4 months is the sum of her initial savings and the interest earned:

Total = $41,000 + $273.33
Total = $41,273.33

Rounding to the nearest cent, Irma will have $41,273.33 in total in 4 months.

(If this doesn’t seem right to you make sure you comment below!)

The graph below
Which equation matches the graph?

Answers

Answer:

Step-by-step explanation:

Practice!
1.
In the diagram, JKLM~ EFGH.
C.
a.
b.
Find the scale factor of JKLM to EFGH.
k=
Find the values of x, y, and z.
x =
y =
Find the perimeter of each polygon.
4y + 4
H3G
11
zo
E 8 F
Z=
30
65°
M
20
D
K
L

Answers

Answer:

a. To find the scale factor of JKLM to EFGH, we can compare the corresponding sides:

JK/JH = KL/KG = LM/LF = x/x = 1

Therefore, the scale factor is 1.

b. Since JKLM~EFGH, the corresponding sides are proportional. We can set up the following ratios:

JK/EF = KL/FG = LM/FH = 1/1

JK/x = KL/20

LM/30 = 1/2

Solving for JK, KL, and LM:

JK = EF = x

KL = 20(1/2) = 10

LM = 30(1/2) = 15

c. To find the perimeter of JKLM, we add the lengths of its sides:

Perimeter of JKLM = JK + KL + LM + MJ

Perimeter of JKLM = x + 10 + 15 + x

Perimeter of JKLM = 2x + 25

To find the perimeter of EFGH, we can use the fact that corresponding sides are proportional:

FG = KL = 10

FH = LM = 15

EG = JK = x

EH = EF = x√2

Perimeter of EFGH = EF + FG + GH + EH

Perimeter of EFGH = x + 10 + 2z + x√2

We are not given a value for z, so we cannot calculate the perimeter of EFGH.

Note: The angle measures given in the diagram are not used in the calculations for this problem.

Statistics help!!!

I chose B and got it wrong, I still don’t understand how to get the correct answer or what that answer is, but I want to understand how to do it right !

What is the probability of rolling a single 6 sided dice three times and getting the following outcomes: 4, a number greater than two, and an
even number.

a) 4/9
b) 21/54 (wrong answer)
c) 1/27
d) 12/216

Answers

Answer:

I am not sure but I will say A I guess.

Choose the equation for the graph.
a) y = 2x - 3| +1
b) y = -2|x - 3| +1
c) y = 2x - 3| - 1
d) y = -2|x + 3| -1
e) y = 2x + 3| +1

Answers

The calculated equation for the graph is y = -2|x + 3| - 1

Choosing the equation for the graph.

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

The absolute value graph

An absolute value function is represented as

y = a|x - h| + k

Where

Vertex, (h, k) = (-3, -1)

So, we have

y = a|x + 3| - 1

The graph faces down

So, a is negative

Possible value is a = -2

So, we have

y = -2|x + 3| - 1

Hence, the function is y = -2|x + 3| - 1

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Identify all of the Independent Events

You randomly select and eat three chocolates out of the box

Drawing a marble out of a bag, replace it and draw another

Dominic picks an ice cream cone out of the freezer to eat, then Arianna picks one

Rolling a dice, then picking a block from a pile

Rolling a dice twice

Randomly picking a sock from a laundry basket to wear, then randomly picking a second one

Answers

Out of these events, the independent events are drawing a marble out of a bag, replacing it and drawing another and rolling a dice twice. So the correct option is 2 and 5.

Events that are independent are those in which the outcome of first event has no effect on the outcome of a second event. The independent event in each of the situations according to this definition are:

Drawing a marble out of a bag, replacing it, and drawing anotherRolling a dice twice

The outcome of the first event in either of these situations have no effect on the outcomes of the second event.

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A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $200.

If they offer a 2 year extended warranty for $30, what is the company's expected value of each warranty sold?

Answers

Step-by-step explanation:

The expected value of each warranty sold can be calculated using the following formula:

Expected Value = (Probability of Failure without warranty x Replacement Cost without warranty) + (Probability of Failure with warranty x Replacement Cost with warranty) - Cost of Warranty

Probability of Failure without warranty = 0.8% or 0.008 (given)

Replacement Cost without warranty = $200 (given)

Probability of Failure with warranty = 0% (since the product is covered under warranty)

Replacement Cost with warranty = $0 (since the cost of replacement is covered under warranty)

Cost of Warranty = $30 (given)

Expected Value = (0.008 x $200) + (0 x $0) - $30

Expected Value = $1.60 - $30

Expected Value = -$28.40

The company's expected value of each warranty sold is -$28.40, which means that on average, the company can expect to lose $28.40 for every warranty sold. This is because the cost of the warranty ($30) is greater than the expected cost of replacement without the warranty ($1.60). Therefore, it is not beneficial for the company to offer the extended warranty.

Carved into the desert are a number of drawings that can only be seen from a helicopter, See if you can see my dilation inspired drawings of the drawings! Fill in the missing four pieces (either the scale factor, (AB) or (A'B')) with correct values from the "Number Bank".

Answers

For the humming bird X = 130m

For the monkey r= 2

For the trapezoid X = 110m

For the whale r = 7/2

How to calculate the scale factor of a given model?

To calculate the scale factor of a given shape or model, the formula that should be used would be;

Scale factor = dimensions of bigger model/smaller model

For hummingbird:

X = 585/4.5

= 130m

For monkey ;

r= 440/220

= 2

For the trapezoid;

X= 165×2/3

= 330/3

= 110m

For the whale;

r= 420/120

= 7/2

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Your class is collecting bottled water for a service project. The goal is to collect 300
bottles of water. On the first day, Max brings in 3 packs of water with 6 bottles in each
pack. Sarah brings 6 packs with 6 bottles in each pack. How many bottles of water do
they still need to be brought?

Answers

Step-by-step explanation:

Goal: 300

Max brought: 3 × 6 = 18 bottles in total.Sarah brought: 6 × 6 = 36

36 + 18 = 54300 - 54 = 246

They still need 246 bottles.

There were 8 cows and 12 horses at a farm. 5 horses ran away. How many horses were left?

Answers

Answer:

Step-by-step explanation:

7 horses were left

Name the similar triangles. ΔBAC ~ ΔDEF , ΔBAC ~ ΔEDF, ΔBAC ~ ΔDFE, ΔBAC ~ ΔFED

Answers

Based on the angle-angle similarity theorem (AA), the similar triangles in the image given can be named as: ΔBAC ~ ΔEDF.

What are Similar Triangles?

When two triangles have the same shape but have different sizes, it means the triangles have corresponding pairs of congruent angles and corresponding pairs of sides that are proportional to each other. The triangles are said to be similar.

The image given show two set of triangles that have two corresponding pairs of congruent angles, based on the angle-angle similarity theorem, it means that they are similar to each other.

Therefore, the similar triangles are:

ΔBAC ~ ΔEDF.

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circumference of OC 7.5 m F G 76° C APARUMORISCHER

Answers

Answer: 570OC^2mFG

Step-by-step explanation: I did this in school! Trust Me! You can report if wrong!

23. As long as supplies last, the local animal shelter will give customers a free collar and name tag for each dog or cat
adopted this month. The shelter has the following collars: 5 blue, 8 green, 2 purple, and 5 brown. The name tags that
are available are 10 plastic, 4 leather, and 6 metal.
What is the probability that the first customer will randomly be given a brown collar?

Answers

The probability that the first customer will randomly be given a brown collar is given as follows:

0.25 = 25%.

How to calculate a probability?

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of collars is given as follows:

5 + 8 + 2 + 5 = 20 collars.

5 of these collars are brown, hence the probability that the first customer will randomly be given a brown collar is given as follows:

p = 5/20 = 1/4 = 0.25 = 25%.

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The Venn diagram below shows the number of items in sets A and B.

An item is chosen at random.

a) Explain how we can tell from the Venn diagram that P(A) ≤ P(B) without doing any calculations.

b) Calculate P(A) and P(B) as fractions in their simplest forms.
B4

A1

9
A is inside B and 9 is outside the venn diagram

Answers

The probability of A would be lesser than or equal to that of B because A is a subset of B

Explaining P(A) ≤ P(B) from the Venn diagram

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

The Venn diagram

On the Venn diagram, we have

A is inside B

This means that A is a subset of B

And as such the probability of A would be lesser than or equal to that of B

Calculating P(A) and P(B)

Here, we have

A = 1

B = 4

Outside = 9

So, we have

P(A) = 1/(1 + 4 + 9) = 1/14

P(B) = (1 + 4)/(1 + 4 + 9) = 5/14

Hence, the values of P(A) and P(B) are 1/4 and 5/14

Answers

Yes, your answer is correct.

The coordinates of the division point T are indeed (0, 5/3, -4/3).

We have,

To find the coordinates of the division point T, we use the formula:

T = A + r(B - A)

where r is the ratio in which AB is divided.

In this case, the ratio is 1:2, so r = 1/3 (since 1 + 2 = 3).

Substituting the given values.

T = (3, 2, -1) + (1/3)(-9, -1, -1)

T = (3, 2, -1) + (-3, -1/3, -1/3)

T = (0, 5/3, -4/3)

Thus,

The coordinates of the division point T are indeed (0, 5/3, -4/3).

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Find the reciprocal of the number. Check that the product of the number and its reciprocal is 1.
-7

Answers

The calculated value of the reciprocal of the number -7 is -1/7

Finding the reciprocal of a number

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

Number = -7

As a general rule, the reciprocal of a number x is 1/x

Using the above as a guide, we have the following:

Reciprocal = -1/7 given that Number = -7

To check, we have

-1/7 * -7

Evaluate

Result = 1

Hence, the reciprocal is 1

Answers

The figure that Kyle plans to estimate the area of is likely a series of squares, either full or partially shaded, that do not form a perfect square or rectangle.

The figure that Kyle plans to estimate the area of contains 40 full squares and 8 partial squares. Based on this information, we can assume that the figure is composed of a grid or a series of squares that are either full or partially shaded. Kyle plans to use the strategy of identifying the full and partial squares that make up the figure to estimate its area.

If the figure is a perfect square or rectangle, Kyle can use the formula A = l x w to find its exact area. However, since the figure is not described as a specific shape, Kyle will need to use estimation to find its area. By identifying the full and partial squares, he can estimate the total number of square units that the figure covers. Kyle can then multiply this estimate by the size of each square unit to find an approximate area.

In conclusion, Using his strategy, Kyle can estimate the total area of the figure by identifying the full and partial squares and multiplying his estimate by the size of each square unit.

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DO THE MATH: Dade buys a new patio bench in Wooster, Ohio for the price of
$266.20 which includes a sales tax of 6.5%. What is the price of the patio bench
without sales tax? Round your answer to the nearest penny.
$265.27
$248.90
$249.99
$249.95

Answers

Price without tax is $249.95.

What is patio bench ?

A patio bench is a common piece of outdoor furniture for a patio or deck. To fit varied outdoor locations and seating requirements, it can be produced in a number of forms and sizes and is often made of wood, metal.

We can multiply the total cost by (1 + tax rate) to get the cost of the patio bench sans sales tax.

(1 + 0.065) = 1.065

Price without tax = $266.20 / 1.065 = $249.9

Therefore, the correct answer is D) $249.95.

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Prove that ABC AADC.
51
51
2
B
Statement
D
1 m/BAC = m_DAC = 51
AB = AD=4
Pick statement
AABCEAADe
Reason
Pick statement
Given
Segments are the same length as themselves,
Pick congruence criterion
a hint
congruence

Answers

ΔABC and ΔADC are congruent by SAS

We have,

From the figure,

We have,

ΔABC and ΔADC

∠BAC = ∠DAC = 51 ( given )

AB = AD = 4 ( given )

AC = AC ( common length )

This means,

ΔABC and ΔADC are congruent by SAS

Thus,

ΔABC and ΔADC are congruent by SAS

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Line xy is parallel to line segment ac as shown in the figure below.

Answers

Yes, students are correct. By AA similarity criterion, triangle XBY and triangle ABC are similar.

Given that, line XY is parallel to line segment AC.

Consider triangle XBY and triangle ABC,

∠X=∠A (Corresponding angles are equal)

∠Y=∠C (Corresponding angles are equal)

By AA similarity, triangle XBY and triangle ABC are similar.

Yes, students are correct. By AA similarity criterion, triangle XBY and triangle ABC are similar.

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Is the answer 1479.20? Pic below

Answers

The expected profit for selling action movies is given as follows:

$15,583.20.

How to obtain the expected profit?

The expected profit for selling action movies is obtained applying the proportions in the context of the problem.

The proportion of action movies on the last month is given as follows:

2150/(2150 + 1721 + 829 + 300) = 0.43.

Hence, out of 8000 movies, the expected number of action movies is given as follows:

0.43 x 8000 = 3440.

The expected profit for each movie is of $4.53, hence the expected profit for action movies is given as follows:

4.53 x 3440 = $15,583.20.

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Question
Construct the exponential function that contains the points (0, 3) and (2, 75).
Provide your answer below:
f(x) = 0

Answers

The exponential function described is f(x) = 3*(5)^x

How to find the exponential function?

A general exponential function can be written as:

f(x)= A*(b)^x

Where A is the initial value and b is the base.

Here we know that the function contains the point (0, 3), then:

f(0) = 3 = A*(b)^0

3 = A

We also know that the function contains (2, 75), then:

f(2) = 75 = 3*(b)^2

75/3 = b^2

25 = b^2

√25 = b = 5

The exponential function is.

f(x) = 3*(5)^x

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Find the volume of figure two

Answers

Answer: 72

Step-by-step explanation:

V=lwh

=(3)(4)(6)

=72

Find the value of x for the following

Answers

The side has a length of 15 units.

Let us denote the length of the missing side by x. According to the Pythagorean theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse. In mathematical terms, this can be written as:

side² + side² = hypotenuse²

Substituting the given values, we get:

x² + 8² = 17²

Simplifying this equation, we get:

x² + 64 = 289

Subtracting 64 from both sides, we get:

x² = 225

Taking the square root of both sides, we get:

x = 15

Therefore, the missing side has a length of 15 units.

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A flower bed has the shape of a rectangle 5yards long 4 yards wide what is its area in square ft

Answers

The area of the flower bed is 180 square feet.

Area refers to the amount of space occupied by a two-dimensional shape or surface. It is measured in square units, such as square meters, square inches, or square centimeters. The area of a shape can be calculated by multiplying the length and width of the shape (in the case of a rectangle or square), or by using more complex formulas for other shapes, such as triangles or circles.

To convert yards to feet, we multiply by 3 since 1 yard = 3 feet.

The length of the rectangle in feet is 5 yards × 3 feet/yard = 15 feet.

The width of the rectangle in feet is 4 yards × 3 feet/yard = 12 feet.

The area of the rectangle in square feet is length × width = 15 feet × 12 feet = 180 square feet.

Therefore, the area is 180 square feet.

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Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1). Determine the image coordinates of M′ if the preimage is translated 4 units up.

M′(−4, −1)
M′(4, −1)
M′(0, −5)
M′(0, 3)

Answers

Answer: M′(−4, −1)

Step-by-step explanation: m=-2 j+-5+4=M′(−4, −1)

Answer:

Option D

Step-by-step explanation:

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