Every year since 1548, the average height of a human male has increased slightly. The new height is 100.05% of what it was the previous year. If the average male's height was 54 inches in 1548, what was the average height of a male in 2008?

Answer:

a) Common ratio r = [tex]\boxed{2}[/tex]

b) Formula for common ratio:
[tex]\dfrac{a_{n+1}}{a_n} , n = 1, 2, 3, 4....\\[/tex]

Formula for nth term:
[tex]a_n = a_1r^{n-1}[/tex]

(see explanation below for part b)

c) [tex]a_{10} = \boxed{1024}[/tex]

d) Recursive formula: [tex]\boxed{a_{n+1} = 2a_n}[/tex]

Step-by-step explanation:

a) The common ratio r for a geometric sequence is the ratio of any term(except the first) to the previous term. And this is a constant for that sequence

If we have a sequence [tex]a_1, a_2, a_3, a_4, a_5,....\\[/tex]

[tex]r = \dfrac{a_2}{a_1} = \dfrac{a_3}{a_2} = \dfrac{a_4}{a_3} = \dfrac{a_5}{a_4}[/tex]

Here [tex]a_1[/tex] is the first term in the sequence

The sequence we have here is
2, 4, 8, 16

So
[tex]r = \dfrac{4}{2} = \dfrac{8}{4} = \dfrac{16}{8} = 2\\[/tex]
Answer to a)

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b) This part is confusing. Are they asking for a formula for the common ratio or a formula for the nth term? You can write both or check with your teacher

The explicit formula for the common ratio is

[tex]\dfrac{a_{n+1}}{a_n} , n = 1, 2, 3, 4....\\[/tex]

The explicit formula for the nth term, [tex]a_n[/tex] of a geometric sequence is
[tex]a_n = a_1r^{n-1}[/tex]

where [tex]a_1[/tex] is the first term of the sequence and r is the common ratio
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c)
The formula for finding the nth term of a geometric sequence is
[tex]a_n = a_1r^{n-1}\\\\[/tex]

Therefore

[tex]a_{10} = a_1 r^{(10-1)} = a_1 \times r^9\\\\[/tex]

[tex]a_1 = 2, r = 2\\\\[/tex]

So
[tex]a_{10} = 2 \cdot 2^9 \\\\= 2 \cdot 512\\\\= 1024\\[/tex]ANSWER c)

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d)

A recursive formula is just an expression that denotes the relationship between one term and the next

We know that
[tex]r= \dfrac{a_{n+1}}{a_n} \\\\[/tex]

Multiplying both sides by [tex]a_n[/tex],

[tex]ra_n = a_{n+1}[/tex]

Or

[tex]a_{n+1} = ra_n\\\\[/tex]

For the specific case of r = 2 we get the recursive formula as

[tex]a_{n+1} = 2a_n[/tex]

ANSWER d)

The overlapping triangles which are congruent by ASA are ΔEBC and ΔADC which is therefore denoted as option C.

This is a scenario in which all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Taking ΔEBC and ΔADC, we have the following below:

∠B=∠D (90°)

CB= CD (Given)

∠BCE=∠ACD( Common)

Therefore, by ASA we can deduce that,

Δ EBC ≅ΔADC.

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The value of log10 5 as required to be determined using the given information is; 0.3979 + P..

It follows from the task content that; the value of log10 5 is to be determined based on the given information.

Since the given expression is; log10 2 = P;

The expression which can be inferred from the equation above is;

10^P = 2..............(i)

However, let; log10 5 = x

Therefore; 10^x = 5..........(ii)

By dividing the equation (ii) by (i); we have that;

10^(x - P) = 2.5

Therefore, from the converse of logarithmic law;

x - P = log10 2.5

x = P + log10 2.5

where, log10 2.5 = 0.3979

x = 0.3979 + P

Ultimately, the value of log10 5 as required is; 0.3979 + P.

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The solution for the absolute value equation is:

|7 - 11| = 4

Here we want to solve an absolute value equation:

|7 - 11| = ?

First, remember how the absolute value works, it is:

|x| = x  if x  ≥ 0

|x| = -x  if x < 0.

Now let's return to our equation:

|7 - 11|

If we simplify the left side, we will get:

|-4|

Notice that it is a negative number, so we just need to change the sign:

|-4| = 4

Then the equation is:

|7 - 11| = 4

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Answer:

[tex] \sf \: ∣7-11∣ = 4[/tex]

Step-by-step explanation:

Given problem,

→ ∣7 - 11∣

Let's solve the problem,

→ ∣7 - 11∣

→ ∣-4∣ = 4

=> Absolute value

=> It is always positive

Hence, the answer is 4.

Answer: a) To compute the mean of these data, we need to add up all of the ratios and divide by the total number of ratios.

(94+112+78+68+46+111+66+140+428+190+118)/11 = 101.36

The mean is 101.36

b) To compute the median of these data, we need to arrange the data in increasing order and find the middle value.

46, 66, 68, 78, 94, 111, 112, 118, 140, 190, 428

The median is 111

c) The measure that describes the center of this distribution the most accurately is the mean, because it takes into account all of the values in the data set and provides an overall measure of central tendency. The median is also a measure of central tendency but it is affected by the outliers present in the dataset and doesn't provide a good representation of the central value.

Step-by-step explanation:

Answer:

A and B

Step-by-step explanation:

You draw the points on the Cartesian plane and draw a straight line that passes through two of the drawn points, if ALL the drawn points are ON the drawn line, then it is a linear function,

If only ONE point lies outside the line, then it is NOT a linear function

The maximum score that can be in the bottom 5% of scores is 2.64

The middle 90% of scores lie between 2.88 and 4.56.

(a) We must determine the score that corresponds to the 5th percentile of the normal distribution in order to determine the highest score that may fall inside the lowest 5% of scores.

We may use the standard normal table to determine that the 5th percentile corresponds to a standard normal score of -1.28 using the mean and standard deviation supplied (3.6 and 0.75, respectively). We may use the following formula to return to the original scale:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

x= 2.64

(b)

We must determine the 5th and 95th percentiles of the normal distribution in order to determine the range of scores that the middle 90% of scores fall inside.

The standard normal table may be used to determine that the 5th percentile corresponds to a normally distributed score of -1.28 and the 95th percentile corresponds to a standard normal rating of 1.28 using the mean and standard deviation supplied (3.6 and 0.75, respectively). We may use the following formula to return them to their original scale:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

= 2.88 for the 5th percentile

x = 3.6 + 1.28 * 0.75

= 4.56 for the 95th percentile

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Answer:

Step-by-step explanation:

let   5x - 2y = 10             ........... (1)

and 7x - 3y = 13             ............(2)

now multiply equation (1) by 3 and equation (2) by 2, we get,

 15x - 6y = 30             ............(3)

 14x - 6y = 26             ............(4)

after substracting  equation (3) and (4) we get,

  x = 4

after putting the value of x in eq (3) we get,

    15 * 4 - 6y = 30

=> 60 - 6y =30

=>     y =  -30/ -6

=>     y = 5

so, the vale of x and y is 4 and 5 respectively.

Answer:

If you want an answer I would suggest you to put the whole question up ty

Step-by-step explanation:

Answer:

3.75 days

Step-by-step explanation:

To find out how long it takes to consume 13500 watt hours, you would divide 13500 by the number of watt hours consumed per day, which is 3600.

13500 / 3600 = 3.75

So it takes 3.75 days for the light bulb to consume 13500 watt hours.

2 × 10³ is an exponential expression, which has a standard form as 2000.

Exponential expressions are just a way to write powers in short form. The exponent

indicates the number of times the base is used as a factor. So in the case of 32 it can

be written as 2 × 2 × 2 × 2 × 2 = 25, where 2 is the “base” and 5 is the “exponent”.

The expanded form comes in a variety of forms. Exponents are employed. The expanded form of that expression is what is stated above.

One more makes use of multipliers like 1, 10, 100, 1000, and so forth. The expression broadens in that form as...

10^2 = 1×100

Another expanded form uses the expanded form's individual digits, setting the others to zero.

10^2 = 100

The standard format is...

10^2 = 100.

Thus, 2 × 10³ is an exponential expression, which has a standard form as 2000.

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Answer:The price of a bond can be calculated using the formula:

Price = Maturity Value / (1 + r)^n

Where:

Maturity Value = $12,000

r = the annual interest rate as a decimal (7.25% / 100 = 0.0725)

n = the number of years to maturity (11 years)

So the price of the bond is:

Price = $12,000 / (1 + 0.0725)^11

By solving this equation we get the price of bond is $7,065.87 approximately.

Note: The bond price is the amount you pay to buy the bond and receive the maturity value at the end of the bond term.

Step-by-step explanation:

Answer:false

Step-by-step explanation:

[tex]\overline{A}[/tex]  = {0, 1, 4, 5, 6, 7, 8}, [tex]\overline{B}[/tex] =  {2, 4, 7, 9}, A ∪ B =  {0, 1, 2, 3, 4, 5, 6, 8, 9} and

A ∩ B = {3}.

A set is a collection of well-defined objects.

A subset contains all the elements or few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Given,

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is a universal set.

A = {2, 3, 9} and B = {0, 1, 3, 5, 6, 8}.

[tex]\overline{A}[/tex] = (U - A) = {0, 1, 4, 5, 6, 7, 8}.

[tex]\overline{B}[/tex]= (U - B) = {2, 4, 7, 9}.

A ∪ B = U - {7}.

A ∪ B =  {0, 1, 2, 3, 4, 5, 6, 8, 9}.

A ∩ B = {3}

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The formula for t in terms of P, I and r is t=I/Pr.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, the formula form simple interest is I=Prt, where I is the interest, P is the principal, r is the interest rate and t is the number of years.

Now, I=Prt

t=I/Pr

Therefore, the formula for t is t=I/Pr.

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Answer:

In an absolute value graph, the slope of one side of the graph is the opposite of the other side.

For example, if the slope of one side of an absolute value function is positive, then the other side of the equation has a slope of negative.

The value of the summation expression given in the task content is; 16.

It follows from the task content that the value of the summation expression given is to be determined.

Since the given expression is; 2x - 3,

On this note;

On this note, the sum of all of the results above is the correct Evaluation of the given expression; 1 + 3 + 5 + 7 = 16.

On this note, the result of the evaluation is; 16.

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The ordered pairs that satisfies the linear inequality x < - 3 are (-4, -3) and (-3, -3)

A linear inequality is a mathematical statement that describes a relationship between two or more variables that are not necessarily equal. It is similar to a linear equation, but instead of an equal sign, it uses one of the inequality signs: <, >, ≤, or ≥.

A linear inequality can also be represented graphically on a coordinate plane, by shading the region of the plane that satisfies the inequality. The solution set of a linear inequality is the set of all points that make the inequality true.

A linear inequality can also have infinitely many solutions, no solution or a unique solution. The solution set will be a region in a coordinate plane which is a half-plane, a line or a point depending on the inequality.

In the problem, the inequality x < -3 will have an ordered pair of solution of

(-∞, -3).

This implies that all values of x must lies from negative till infinity while y lies up to - 3.

In the options given, only (-4, -3) and (-3, -3) satisfies this criteria.

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F(x) = x³ on the interval [-2, 1], x = -2 and x = 1, the absolute maximum value is 1 and the absolute minimum value is -8.

A function's critical numbers are the independent variable values at which the function is not continuous, or when the derivatives are equal to 0 or undefined.

1. For the function f(x) = x³ on the interval [-2, 1], the critical numbers are x = -2 and x = 1. The absolute maximum value is 1 and the absolute minimum value is -8.

2. For the function f(x) = x² - 2x² + 3 on the interval [-1, 2], the critical numbers are x = -1 and x = 2. The absolute maximum value is 5 and the absolute minimum value is -2.

3. For the function f(x) = 5 - 2x on the interval [-1,2], the critical numbers are x = -1 and x = 2. The absolute maximum value is 5 and the absolute minimum value is -3.

4. For the function f(x) = x² - 3x² on the interval [-1, 3], the critical numbers are x = -1, x = 0, and x = 3. The absolute maximum value is 0 and the absolute minimum value is -3.

5. For the function f(x) = 2cosx + x on the interval [0,2], the critical numbers are x = 0 and x = 2. The absolute maximum value is 3 and the absolute minimum value is -1.

6. For the function f(x) = 3x³ - 20x³ on the interval [-2, 2], the critical numbers are x = -2 and x = 2. The absolute maximum value is -4 and the absolute minimum value is -32.

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Answer:

3.8729

Step-by-step explanation:

6.28 cubic centimeters is the volume of the gap in the jar.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that cylindrical jar contains three glass balls each has a diameter of 2cm

Let us find the volume of each sphere.

Volume of sphere=4/3×πr³

As diameter is 2 then radius is 1.

Volume of each sphere=4.186

Volume of three spheres=3×4.186=12.56

Now let us find the volume of cylinder.

The diameter of cylinder will be 2 and height is 6 cmas there are 3 spheres of diameter 2cm.

Volume of cylinder=πr²h

=3.14×1×6

=18.84 cubic centimeters.

So the volume of the gap in the jar = 18.84-12.56

=6.28 cubic centimeters.

Hence, 6.28 cubic centimeters is the volume of the gap in the jar.

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The quadrilateral's new coordinates will be J(4, 4), K(3, 4), L(1, 1), and M (4,1) when the procedure is applied.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given coordinates of a quadrilateral J(-4, 4), K(-3, 4), L(-1, 1), M(-4,1)

Reflect in the x-axis

Since,

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

thus new coordinates will be,

J(-4, -4), K(-3, -4), L(-1, -1), M(-4,-1)

Rotate 180 degrees about the origin

Since,

When we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.

Thus new coordinates will be

J(4, 4), K(3, 4), L(1, 1), M(4,1)

Therefore, After applying the given operation the new coordinates of the quadrilateral will be  J(4, 4), K(3, 4), L(1, 1), and M(4,1).

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Answer: 90

Step-by-step explanation:

If you're looking for the number of times she has to visit the movie theater in order to have 310 points for the free movie ticket then;

310-85 = 225

225/2.5 = 90

Eva needs 90 visits before she can get a free movie ticket.

Answer: 1 + 2x

Step-by-step explanation:

To solve this problem, it's helpful to understand "order of operations." The order is: parentheses, exponents, multiplication, division, addition, and lastly, subtraction.

A helpful mnemonic is PEMDAS. I was taught "Parachute Expert My Dear Aunt Sally" to help remember the order.

We must work with the numbers inside the parantheses, since "parantheses" is the first operation. We'll start with the first paranthesis: (-5x2 + 10x - 12).

Since there are no exponents in this equation, we can go to the third operation: multiplication. (I like to use the "·" symbol to show that two numbers are multiplied because it's easy for me to confuse the letter X with "x" when it is used as a multiplication symbol).

-5 · 2 = -10

Two negative numbers are added, so -10 and -12 = -22

This leaves (-22 + 10x)

The -22 and 10x are not added together because numbers without a letter cannot be added to numbers with letters.

Now we'll work with the second paranthesis: (-4 · 2 + 8x - 15)

-4 · 2 = -8

-8 and -15 is added to make -23

The paranthesis now looks like:

(-23 + 8x)

Notice that there is a negative sign outside of the second paranthesis in the equation.

(-22 + 10x) − (-23 + 8x)

When a number or symbol is outside of a paranthesis, that number or symbol is multiplied across everything within the parantheses.

Now, it is:

(23 - 8x)

All of the numbers can be taken out of the parantheses now:

-22 + 10x + 23 - 8x

-22 + 23 = 1

10x - 8x = 2x

The final answer:

1 + 2x

Hope this helps!

Answer:

0.124176

Step-by-step explanation:

.06 x .995 x 1.3 x 1.6= 0.124176

You change a percent into a decimal by dividing it by 100%

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$200\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (200)(0.10)(1) \implies I = 20~\hfill \underset{total~amount~in~savings}{\stackrel{200~~ + ~~20}{\text{\LARGE 220}}}[/tex]

Answer:

$ 220

Step-by-step explanation:

i = prt = 200 * .1 * 1  = 20  dollars interest

  add in her original deposit of 200 for a total of 220 dollars

The inequality that represents the interval shown on the number line is:

5 ≤ x ≤ 9

We want to use inequality notation to define the interval shown on the number line.

We can see that the first point is marked with a closed circle, at x = 5.

And then we have another closed circle at x = 9

The closed circles means that these points are solutions to the inequality, so we need to use the symbols:

≤ and ≥

Then we can write the inequality:

5 ≤ x ≤ 9

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Answer:

1,000 was the interest charge which leaves you with 24000 as the regular vaule

Step-by-step explanation:

Answer:The function is linear because we are dealing with a straight line.

Step-by-step explanation:

Answer: the probability that a student chosen at random plays the bass is 1/3 in simplest form.

Step-by-step explanation:

The probability of an event can be found by taking the number of favorable outcomes and dividing it by the total number of outcomes. In this case, we are looking for the probability that a student chosen at random plays the bass.

We know that there are a total of 6 + 4 + 7 + 2 = 19 seventh grade students and 4 + 15 + 13 + 6 = 38 eighth grade students. So there are a total of 19 + 38 = 57 students.

We also know that there are 4 seventh grade bass players and 15 eighth grade bass players, for a total of 4 + 15 = 19 bass players.

So, the probability that a student chosen at random plays the bass is 19/57. This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor which is 19/57 = 1/3.

So, the probability that a student chosen at random plays the bass is 1/3 in simplest form.