Write the geometric sequence in function notation.
4,2,1,1/2,1/4,...
A) AX) = (2) - (1/4)x - 1
OB) Ax) = (2) - (1/2)x - 1
C) Ax) = (4) · (/4)x - 1
D AX) = (4) · (1/2)x - 1

Answer:

(a) Residents

(b) [tex]Median = 0.13[/tex]

(c)  [tex]\bar x = 0.14[/tex]

(d) Right skewed

Step-by-step explanation:

Given

The data of residents without health insurance

Solving (a): The variable

The variable is the residents

Solving (b): The median

First, we sort the data

[tex]Sorted: 0.09, 0.10, 0.11, 0.13, 0.13, 0.14, 0.16, 0.19, 0.25[/tex]

So, the median position is:

[tex]Median = \frac{n + 1}{2}[/tex]

[tex]Median = \frac{9 + 1}{2}[/tex]

[tex]Median = \frac{10}{2}[/tex]

[tex]Median = 5th[/tex]

The 5th element of the dataset is: 0.13

So:

[tex]Median = 0.13[/tex]

Solving (c): The mean

This is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

[tex]\bar x = \frac{0.09+ 0.10+ 0.11+ 0.13+ 0.13+ 0.14+ 0.16+ 0.19+ 0.25}{9}[/tex]

[tex]\bar x = \frac{1.3}{9}[/tex]

[tex]\bar x = 0.14[/tex]

Solving (d): The shape of the distribution

In (b) and (c), we have:

[tex]Median = 0.13[/tex]

[tex]\bar x = 0.14[/tex]

By comparison, the mean is greater than the median.

Hence, the shape is: right skewed.

Answer:

D. <S, <R, <T

Step-by-step explanation:

Recall: On a triangle, the bigger an angle measure the longer the side opposite it and vice versa.

In ∆RST,

The longest side, SR = 22, is opposite to <T

Therefore, <T is the biggest angle.

Medium side, ST = 21, is opposite to <R, therefore,

<R is the medium angle measure

The smallest angle measure <S is opposite to the shortest side, RT.

Angels I'm order form the smallest to largest will be:

<S, <R, <T

Answer:

D) x = e - 1

General Formulas and Concepts:

Pre-Algebra

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle ln(x + 1) = 1[/tex]

Step 2: Solve for x

Answer:

Point C represents the unit rate

Step-by-step explanation:

Answer:

The volume is increasing at a rate of 27093 cubic inches per second.

Step-by-step explanation:

Volume of a cone:

THe volume of a cone, with radius r and height h, is given by:

[tex]V = \frac{1}{3} \pi r^2h[/tex]

In this question:

We have to differentiate implictly is function of t, so the three variables, V, r and h, are differenciated. So

[tex]\frac{dV}{dt} = \frac{\pi r^2}{3}\frac{dh}{dt} + \frac{2\pi rh}{3}\frac{dr}{dt}[/tex]

The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.4 in/s.

This means that [tex]\frac{dr}{dt} = 1.4, \frac{dh}{dt} = -2.4[/tex]

Radius is 140 in. and the height is 186 in.

This means that [tex]r = 140, h = 186[/tex]

At what rate is the volume of the cone changing?

[tex]\frac{dV}{dt} = \frac{\pi r^2}{3}\frac{dh}{dt} + \frac{2\pi rh}{3}\frac{dr}{dt}[/tex]

[tex]\frac{dV}{dt} = \frac{\pi (140)^2}{3}(-2.4) + \frac{2\pi 140*186}{3}1.4[/tex]

[tex]\frac{dV}{dt} = -0.8\pi(140)^2 + 62*2\pi*1.4*140[/tex]

[tex]\frac{dV}{dt} = 27093[/tex]

Positive, so increasing.

The volume is increasing at a rate of 27093 cubic inches per second.

Answer:

5 + c > -22

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Sum of 5 and c is greater than -22

↓ Identify

Sum = addition

Is greater than = inequality

Add them all together:

5 + c > -22

Answer:

c. 5.5 years, 0.51 years

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Mean of 5.5 years and a standard deviation of 2.1 years.

This means that, for the population, [tex]\mu = 5.5, \sigma = 2.1[/tex]

Random samples of size 17.

This means that [tex]n = 17[/tex]

Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.

The mean is the same as the mean for the population, that is, 5.5 years.

The standard deviation is:

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{2.1}{\sqrt{17}} = 0.51[/tex]

This means that the correct answer is given by option c.

Answer:

The length is of 59 cm.

Step-by-step explanation:

Perimeter of a rectangle:

The perimeter of a rectangle with width w and length l is given by:

[tex]P = 2(w + l)[/tex]

Width of 49 centimeters and a perimeter of 216 centimeters:

This means that [tex]w = 49, P = 216[/tex]

The length is cm.

We have to solve the equation for l. So

[tex]P = 2(w + l)[/tex]

[tex]216 = 2(49 + l)[/tex]

[tex]216 = 98 + 2l[/tex]

[tex]2l = 118[/tex]

[tex]l = \frac{118}{2}[/tex]

[tex]l = 59[/tex]

The length is of 59 cm.

If we simplify, both Joe and Hope factored the polynomial correctly but Joe didn't complete it fully.

The first binomial can be further factored:

The quadratic expression needs to have two roots in order to be factored as two binomials.

The discriminant must be positive or zero:

We have a = 3, b = k, c = -8

So we get following inequality:

Since k² is positive for any value of k, the solution is any value of k:

Hope this attachment helps you.

Answer:

I got u, it is litearly 16540/83.8 = $19737.5

Step-by-step explanation:

its very simple sincen 100-16.2=83.8

Answer:

65 students.

Step-by-step explanation:

Given that :

Every student planted as many plant as their number ;

Then let the number of student = x

Then the number of plant planted by each student will also = x

The total number of plants planted by all the students = 4225

The Number of students can be obtained thus ;

Total number of plants = Number of plants * number of plants per student

4225 = x * x

4225 = x²

√4225 = x

65 = x

Hence, there are 65 students

This question is incomplete, the complete question is;

We know that the remainder R[tex]_n[/tex] will satisfy | R[tex]_n[/tex] | ≤ b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex].

We must make n large enough so that this is less than 0.0001.

Rounding to five decimal places,

we have b₂ = _________ , b₃ =_________and b₄ =__________

Answer:

b₂ = 0.00617, b = 0.00046 and  b₄ = 0.00004

Step-by-step explanation:

Given the data in the question;

| R[tex]_n[/tex] | ≤ b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex]

Now,

b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex]

b₂ = b[tex]_{ 1 + 1[/tex] = 1 / ( 1 + 1 )9[tex]^{ 1 + 1[/tex] = 1 / (2)9² = 1 / 162 = 0.00617   { 5 decimal places }

b₃ = b[tex]_{ 2 + 1[/tex] = 1 / ( 2 + 1 )9[tex]^{ 2 + 1[/tex] = 1 / (3)9³ = 1 / 2187 = 0.00046 { 5 decimal places }

b₄ = b[tex]_{ 3 + 1[/tex] = 1 / ( 3 + 1 )9[tex]^{ 3 + 1[/tex] = 1 / (4)9⁴ = 1 / 19683 = 0.00004 { 5 decimal places }

Therefore, b₂ = 0.00062, b = 0.00046 and  b₄ = 0.00004

The perimeter of the whole garden would be 66m.

Hope this helps! :)

Answer:

The area of the shed=[tex]64m^2[/tex]

Step-by-step explanation:

We are given that

Side of square =8m

We have to find the area of the shed.

To find the area of shed we will find the area of square.

We know that

Area of square=[tex]side\times side[/tex]

Using the formula

Area of square=[tex]8\times 8[/tex]

Area of square=[tex]64m^2[/tex]

Area of shed=Area of square

Area of shed=64 square m

Hence, the area of the shed=[tex]64m^2[/tex]

Answer:

x = 80

Step-by-step explanation:

3x/2=120°

3x=240°

x=80°

Answered by GAUTHMATH

Answer:

x<-12

Step-by-step explanation: hope this helps!

Answer:

the probability that I chose red or blue is 75%

75%

Answer:

There is not enough info to tell

Step-by-step explanation:

Khan acadamey

Answer:

Factors of number 52

Factors of 52: 1, 2, 4, 13, 26 and 52.

Negative Factors of 52: -1, -2, -4, -13, -26 and -52.

Prime Factors of 52: 2, 13.

Prime Factorization of 52: 2 × 2 × 13 = 22 × 13.

Sum of Factors of 52: 98.

Answer:

Option B, 29°

Step-by-step explanation:

The diagram is a angle bisecting diagram which divides the 58° angle into two 29° angles.

Answered by GAUTHMATH

Answer:

y = 75.5

Step-by-step explanation:

Reference angle (θ) = 49°

Hypotenuse = 100

Opposite = y

Apply trigonometric function, SOH. Which is:

Sin θ = Opp/Hyp

Plug in the values

Sin 49 = y/100

100*Sin 49 = y

y = 75.5 (nearest tenth)

Hey there!

We are given two functions - one is Exponential while the another one is Linear.

[tex] \large{ \begin{cases} f(x) = {4}^{x} - 8 \\ g(x) = 5x + 6 \end{cases}}[/tex]

1. Operation of Function

[tex] \large{(f + g)(x) = f(x) + g(x)}[/tex]

2. Substitution

[tex] \large{(f + g)(x) = ( {4}^{x} - 8) + (5x + 6)}[/tex]

3. Evaluate/Simplify

[tex] \large{(f + g)(x) = {4}^{x} - 8 + 5x + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 8 + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 2}[/tex]

4. Final Answer

Answer:

A. false B. true C. false D. true

Whope you all like this answer

Answer:

This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]

Step-by-step explanation:

We are given the following functions:

[tex]f(x) = 1[/tex]

[tex]g(x) = x - 4[/tex]

Can you evaluate (g•f)(0)?

This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]

Answer:

To evaluate the composition, you need to find the value of function f first. But, f(0) is 1 over 0, and division by 0 is undefined. Therefore, you cannot find the value of the composition.

You must evaluate the function f first.

Division by 0 is undefined.

The composition cannot be evaluated.

Step-by-step explanation:

we know that 1m=100cm

so 1m:5m(final)

1:5

Answer:

1/5

Step-by-step explanation:

Since 100cm = 1m

then

100cm:5m becomes 1m:5m

which in fraction is 1/5

Answer:

It will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.

Step-by-step explanation:

Given that a crew clears brush from 1/3 acre of land in 2 days, to determine how long will it take the same crew to clear the entire plot of 2 1/2 acres, the following calculation must be performed:

1/3 = 0.333

1/2 = 0.5

0.333 = 2

2.5 = X

2.5 x 2 / 0.333 = X

15 = X

Therefore, it will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.

[tex] {64}^{ \frac{2}{3} } \div {27}^{ \frac{5}{3} } \times 54 \\ = > \: {({2}^{3} )}^{ \frac{2}{3} } \div ({{3}^{3}})^{ \frac{5}{3} } \times 54 \\ = > \: {2}^{2} \div {3}^{5} \times 54 \\ = > \: 4 \div 243 \times 54 \\ = > \: 4 \div 13122 \\ = > \: \frac{4}{13122} \\ = > \: \frac{2}{6561} [/tex]

Hope it helps!!!!!!!!!!

9514 1404 393

Answer:

  1604 m

Step-by-step explanation:

The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

Here, the "opposite" is the elevation of point B above point A, and the "hypotenuse" is the length of the railway. Then the total height of point B is ...

  B = 856 + 864·sin(120°)

  B = 856 +864(√3)/2 = 856 +432√3 ≈ 1604.246

The height of the train at point B is about 1604 m above sea level.

Step-by-step explanation:

total number of students are :4x 3 = 12

Fraction that's boys are : 3÷12