A sequence $\{a_n\}$ satisfies $a_1 = 1$ and
\[a_n = \frac{a_{n - 1}}{1 + a_{n - 1}}\]for all $n \ge 2.$ Find $a_{10}.$

Answer:

x ≈ 2.7 m

Step-by-step explanation:

since the 2 triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{x}{1.6}[/tex] = [tex]\frac{4}{2.4}[/tex] ( cross- multiply )

2.4x = 4 × 1.6 = 6.4 ( divide both sides by 2.4 )

x = [tex]\frac{6.4}{2.4}[/tex] = 2.6666...

height of statue x ≈ 2.7 m ( to 1 decimal place )

Answer:

I ammm really sorry for the question

i don't know sorry

The value of "a" will be 30 for the given Algebraic expression.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, a algebraic expression 6a -4a +5a = 210

Simplifying the equation in terms of a

6a -4a +5a = 210

adding or subtracting the terms with the same variables

7a = 210

divide by 7 on both sides

a = 30

Therefore, the value of "a" will be 30 for the given Algebraic expression.

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In the parallelogram ABCD the measure of ∠BEC is obtained as 113°.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

It is given that ABCD is a parallelogram.

The measure of ∠EAD = 30°.

The measure of ∠EDA = 37°.

In the parallelogram ∠EBC = ∠EDA as they form alternate interior angles pair.

Similarly, ∠ECB = ∠EAD as they form alternate interior angles pair.

The measure of ∠ECB = 30°.

The measure of ∠EBC = 37°.

Since EBC forms a triangle, so the sum of the angles of a triangle is 180°.

The equation is -

∠ECB + ∠EBC + ∠BEC = 180°

Substitute the values into the equation -

30° + 37° + ∠BEC = 180°

67° + ∠BEC = 180°

∠BEC = 180° - 67°

∠BEC = 113°

Therefore, the measure of ∠BEC = 113°.

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Answer:

16Ft

Step-by-step explanation:

We can use proportions to solve this problem.

Let's let "x" be the height of the flagpole. We know that the sign is 4 feet high, and it casts a shadow of 1 1/4 feet. So we can set up the proportion:

4/1.25 = x/5

Simplifying the left side of the equation, we get:

4/1.25 = 16/5

Substituting into the original equation, we have:

16/5 = x/5

Multiplying both sides by 5, we get:

16 = x

Therefore, the height of the flagpole is 16 feet.

Answer:

To calculate the periodic interest rate for an account billed monthly with an APR of 21.99%, we need to divide the APR by the number of billing periods in a year.

Since there are 12 months in a year for a monthly billing cycle, we can divide 21.99% by 12 to get the monthly periodic interest rate.

Periodic Interest Rate = APR / Number of Billing Periods in a Year

Periodic Interest Rate = 21.99% / 12

Periodic Interest Rate = 1.8325%

Rounding this answer to the nearest hundredth, we get a periodic interest rate of 1.83%.

The dimension of the square metal sheet is x = 4 ft

Dimensions are the measure of a physical property of an object such as length, width or height.

Since an open box is to be constructed from a square sheet of metal with dimensions x feet by x feet by removing a square of side 1 foot from each corner and turning up the edges.

The volume V of the box is V(x) = (x - 2)².

To find the dimensions of the sheet metal needed to make a box that will hold 4 cubic feet by solving the equation V(x) = 4, we make V(x) = 4 and solve the equation.

So,  V(x) = (x - 2)².

(x - 2)² = 4

Taking square roots of both sides, we have that

√(x - 2)² = ±√4

x - 2 = ±2

x = 2 ± 2

x = 2 - 2 or x = 2 + 2

x = 0 or x = 4

Since the dimension cannot be 0, x = 4

So, the dimension of the sheet is x = 4 ft

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The equation that shows  the damping ratio for a mass-spring-damper system which is defined in terms of the mass, m, stiffness, k, and damping, b is  ζ = b / (2sqrt(mk)).

The damping ratio ζ is defined as the ratio of the damping coefficient b to the critical damping coefficient b_c, which is the minimum damping required to prevent the system from oscillating.

The damping ratio is a dimensionless quantity that represents the amount of damping in the system relative to the critical damping needed to prevent oscillations. A higher damping ratio indicates a more heavily damped system, while a lower damping ratio indicates a less damped system that may oscillate more.

The motion of a mass-spring-damper system can be described by a second-order linear ordinary differential equation (ODE) of the form:

md²x/dt² + bdx/dt + kx = F(t)

where m is the mass of the system, b is the damping coefficient, k is the spring constant, x is the displacement of the mass from its equilibrium position, and  the external force applied to the system is F(t).

The critical equation will be -

b_c = 2√(mk)

Therefore, the damping ratio can be expressed as:

ζ = b / b_c

Substituting the expression for b_c into the above equation, we get:

ζ = b / (2√(mk))

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Answer:

I agree with Sharon's teacher and I believe that the factoring of x^2 + 81 as (x+9)(x-9) is incorrect because the difference of two squares method can only be used to factor polynomials of the form x^2 - a^2, and not x^2 + a^2.

Step-by-step explanation:

The correct answer is x^2 + 81 can be factored as (x + 9)(x + 9) using the trinomial method.

Answer:

3

Step-by-step explanation:

Amplitude is the absolute value of the number in front

3cos(2x) + 5

The value of the expression 3 (x - y) is 12

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

x - y = 4

Multiply both sides of the equation by 3

So, we have the following representation

3 * (x - y) = 4 * 3

Evaluate the products

This gives

3 (x - y) = 12

Hence, the soluton of 3 (x - y) is 12

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Answer: 186 cubic in

Step-by-step explanation:

The mathematical model that can be used to express the verbal statement of the proportional relationships are;

10. y = k/x²

11. P = k/V

12. P = k·V·I

A proportional relationship is one in which the output variable is a multiple of the input variable and a constant (the constant of proportionality).

10. The verbal statement is; y varies inversely as the square of x

The inverse relationship indicates that a variable is related to the reciprocal of the other variable, therefore;

The mathematical model for the statement can be presented as follows;

y ∝ 1/x²

The constant of proportionality k can therefore be applied as follows;

11. The verbal statement is; For a constant temperature, the pressure P of a gas is inversely proportional to the volume V of the gas

The mathematical model of the proportional relationship is; P ∝ 1/V

Therefore;

12. The verbal statement is; The electric power P of a direct current circuit is jointly proportional to the voltage V and the electric current I

The mathematical model is therefore;

P ∝ V·I

Therefore;

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Answer:

Step-by-step explanation:

o divide 6029 by 28, we can use long division:

             215

          ---------

28 |    6029

             56

             ---

            182

           168

             ---

           144

          140

           ---

            4

So 6029 divided by 28 is 215 with a remainder of 4. Therefore, the answer to the problem is:

6029/28 = 215 R 4

A. The height of the cuboid is 2.5 cm.

B. The suggested dimensions of the cuboid is 25 x 5 x 1.

The volume of a given three dimensional figure is the total quantity of matter that it can contained. Thus various figures has different methods of determining their volume.

volume of a cube = length x length x length

                             = (length)^3

volume of a cuboid = length x width x height

Considering the given question, since the volumes of the cube and cuboid are the same, then we have:

volume of a cube = volume of a cuboid

(length)^3 = length x width x height

5^3 = 10 x 5 x height

125 = 50 x height

height = 125/ 50

           = 2.5

The height of the cuboid is 2.5 cm.

B. volume of the cuboid = length x width x height

                          = 10 x 5 x 2.5

                          = 125 cm^3

Thus possible dimensions for the cuboid 25 x 5 x 1.

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Answer:

Question 19: The person who traveled the farthest lives 12 miles from the restaurant, which is the same distance as Kellan.

Question 20: Kellan would have left his house at 8:10 AM in order to arrive at Andrea's house at 8:30 AM and then walk to the restaurant with Andrea at a rate of 2.5 miles per hour, arriving at the restaurant at 8:50 AM, five minutes early. So the answer is 810.

The placebo effect refers to an experiment where neither the participants nor the experimenters know who belongs to the treatment group and who belongs to the control group. As a​ result, it is impossible for the experiments to link certain effects to certain​ patients, which make the results difficult to interpret.

What is the placebo effect is an experimental study refers to the?

The placebo effect is a phenomenon where people report real improvement after taking a fake or nonexistent treatment, called a placebo. Because the placebo can't actually cure any condition, any beneficial effects reported are due to a person's belief or expectation that their condition is being treated.

Hence , The placebo effect refers to an experiment where neither the participants nor the experimenters know who belongs to the treatment group and who belongs to the control group. As a​ result, it is impossible for the experiments to link certain effects to certain​ patients, which make the results difficult to interpret.

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C. A placebo refers to a situation in which a patient improves simply because they believe they are receiving a useful treatment.

1.) Skewed left

2.) a. z-score = 0.54
    b. z-score = 0.77

    c. z-score = -0.77
3.) a. z-score = 1.24

    b. Large Chain

    c. Local Brewery

4.) a. The middle 95% of six-packs at the local brewery will have an average fill between 327.50 ml and 329.70 ml.

     b. The middle 95% of six-packs at the large chain will have an average fill between 327.75 ml and 328.25 ml.

What is the z-score?

In statistics, the z-score, also known as the standard score, is a measure of how many standard deviations an observation or data point is above or below the mean of the data set.

1.)

Skewed Left, since the possible values are clustered towards the upper limit of 330 ml, and it is impossible to fill the bottle with more than 330 ml.

2.)

a. z-score = (328.6 - 328.3) / 0.9 * √6 = 0.54

b. z-score = (328.6 - 328.3) / 0.9 * √12 = 0.77

c. z-score = (327.9 - 328.3) / 0.9 * √1 = -0.77

3.)

a. z-score = (328.6 - 328) / 0.7 * √6 = 1.24

b. Large Chain, since the z-score for the large chain is higher, indicating a larger average fill for the bottles in the six-pack.

c. Local Brewery, since the z-score for the local brewery is lower, indicating a smaller average fill for the bottles in the twelve-pack.

4.)

a. The middle 95% of six-packs at the local brewery will have an average fill between 327.50 ml and 329.70 ml.

b. The middle 95% of six-packs at the large chain will have an average fill between 327.75 ml and 328.25 ml.

Hence,

1.) Skewed left

2.) a. z-score = 0.54
    b. z-score = 0.77

    c. z-score = -0.77
3.) a. z-score = 1.24

    b. Large Chain

    c. Local Brewery

4.) a. The middle 95% of six-packs at the local brewery will have an average fill between 327.50 ml and 329.70 ml.

     b. The middle 95% of six-packs at the large chain will have an average fill between 327.75 ml and 328.25 ml.

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The two solutions are (1, 1/7) and (3.36, 1)

Assume that you spend some time walking (t_w) and some time canoeing (t_c) to cover a 30-mile trip. We can use the following formula to relate the time spent walking and canoeing:

distance = speed × time

For the walking part of the trip, the distance covered is (30 - d), where d is the distance covered by canoeing. We know that the walking speed is 4 mph, so we can write:

(30 - d) = 4t_w

For the canoeing part of the trip, the distance covered is d. We know that the canoeing speed is 7 mph, so we can write:

d = 7t_c

We also know that the total time spent on the trip is:

t_w + t_c

So, the constraint equation is:

t_w + t_c = 30/4 + 30/7

Simplifying this equation, we get:

11t_w - 7t_c = 30

Now, to determine two solutions, we can arbitrarily assign a value to one of the variables and then solve for the other. Let's assume t_w = 1, then we get:

11(1) - 7t_c = 30

7t_c = 1

t_c = 1/7

So, one solution is t_w = 1 and t_c = 1/7.

Similarly, assuming t_c = 1, we get:

11t_w - 7(1) = 30

11t_w = 37

t_w = 3.36

So, another solution is t_w = 3.36 and t_c = 1.

To graph the equation, we can plot t_w on the x-axis and t_c on the y-axis, and then plot the line 11t_w - 7t_c = 30. The two solutions will be the points of intersection of the line with the axes.

The two solutions are (1, 1/7) and (3.36, 1).

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The solution for the table has been provided below. It has been obtained by using arithmetic operations.

What are arithmetic operations?

Mathematicians claim that all real numbers may be described using the four basic operations, also referred to as "arithmetic operations." The four mathematical operations that produce quotient, product, sum, and difference, respectively, are divide, multiply, add, and subtract.

We are given a table of the number of crafts x and the number of ounces y.

x        4          9         7            6            5           5            4           8

y        19        46       30          31          23         28          21         42

xy     76       414      210        186        115         140        84         336

x²       16       81         49         36         25          25         16          64

y²       361     2116     900      961        529        784       441        1764

Hence, the table has been completed.

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Answer:

When cash is received, it should be entered as a debit to the cash account, as the cash account is an asset account that reflects an increase in the company's assets. Therefore, the journal entry would be:

Date: Oct - 1

Account: Cash

Account Number: 1000

Debit: $8000

Credit: $0

Answer:

Step-by-step explanation:

The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products. In each of the given expressions, we can use the Distributive Property to expand the expression by multiplying the coefficient outside the parentheses to each term inside the parentheses, and then adding the resulting products. This results in an equivalent expression that is simplified but has the same value as the original expression.

Answer:

Step-by-step explanation:

6(x+4)

Distribute 6 between the terms x and 4 as:

6(x)+6(4)

=6x+24

2(5+r)

Distribute 2 between the terms 5 and r as:

2(5)+2(r)

=10+2r

11(n+3)

Distribute 11 between the terms n and 3 as:

11(n)+11(3)

=11n+33

The equation is true for all real numbers, and therefore the solution set is (C) all real numbers.

In arithmetic, a solution to the equation expresses can be replaced for the variable to provide a piece of real number information.

We can start simplifying the equation using the distributive property:

4(6x - 4) = 8(3x - 2)

24x - 16 = 24x - 16

We can see that both sides of the equation are identical, so the equation is an identity. This means that the equation is true for all real numbers, and therefore the solution set is all real numbers.

In other words, any value we choose for x will make the equation true.

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The complete question would be as:

How many solutions have the below equation?

4(6x - 4) = 8(3x - 2)

A. one solution.

B. no solution.

C. all real numbers.

Using arithmetic operations it is obtained that there were approximately 76 female animals in the herd.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

If 32% of the animals were males, then 100% - 32% = 68% of the animals were female.

To find the number of female animals in the herd of 112 animals, multiply the total number of animals by the percentage that were female -

68% = 68/100 = 0.68

Number of female animals = 0.68 x 112

Number of female animals = 76.16

Rounding this to the closest whole number gives -

Number of female animals ≈ 76

Therefore, the number of female animals is 76.

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The balance at the end of a year is $1051.56.

To find the balance at the end of a year, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the balance after t years

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $1000, r = 0.05, n = 2 (since the interest is compounded semi-annually), and t = 1. Plugging these values into the formula, we get:

A = $1000(1 + 0.05/2)^(2*1)

= $1000(1.025)^2

= $1051.56

Therefore, the balance at the end of a year is $1051.56.

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Answer:

B

HOPE THIS HELPS

Answer:

5:1

Step-by-step explanation:

d_a = 20

d_b = 5

Equation for the circumference of a circle:

C = pi*d

C_a = pi * d_a

C_a = pi*20

C_b = pi * d_b

C_b = pi * 5

Ratio of C_a to C_b = C_a/C_b

C_a/C_b = (pi * 20)/(pi * 4) = 5:1

The interest to pay at the end of the first month C. $18.71.

To calculate the monthly interest rate, divide the annual percentage rate by 12. For excellent credit, the monthly rate is 4.75% / 12 = 0.3958%, and for good credit, the monthly rate is 5.00% / 12 = 0.4167%.

The total cost of the mobile home including sales tax is $92,738 ($89,000 x 4.2% sales tax). With a $3,000 down payment, the amount financed is $89,738.

For excellent credit, the monthly interest rate :

= 4.75% / 12

So, the interest charged in the first month is $89,738 x  4.75% / 12 = $355.21

For good credit, the monthly interest rate is 0.4167%. So, the interest charged in the first month is $89,738 x 0.004167 = $33.91.

The difference in interest charged between good and excellent credit is $373.91 - $355.21 = $18.71.

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The complete question is:

Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment. How much more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent?

Secured Unsecured

Credit APR (%) APR (%)

Excellent 4.75 5.50

Good 5.00 5.90

Average 5.85 6.75

Fair 6.40 7.25

Poor 7.50 8.40

Options:

$29.39

$21.10

$18.71

$19.02