If (k+1), 3k, (4k+2) are three consecutive terms of an AP then k = ?​

Answer:

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Step-by-step explanation:

There's a handy formula we can use to find the sum of a geometric sequence, and here it is

[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]

The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.

First lets visualize this sequence

[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]

Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.

[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]

Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.

[tex]S_n = \sum{a*r^{n-1}}[/tex]

To finish up lets plug these coefficients in and get our sum after 10 terms.

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Answer:

width = 7, length = 11

Step-by-step explanation:

area = 77

length = 3w - 10

width = w

w(3w - 10) = 77

3w^2 - 10w - 77 = 0

(3w + 11)(w - 7) = 0

we rule out 3w + 11 = 0 because w would be negative

so we use w - 7 = 0

so the width = 7

length = 3w - 10

length = 21 - 10

length = 11

I believe the answer is B!

Hope this helped you! Please follow my account, thanks!

Answer: y = x - 7

Slope intercept form: y = mx + b

[tex]2x-2y=14\\\\-2y=-2x+14\\\\y=\frac{-2x+14}{-2} =\frac{-2(x-7)}{-2} =x-7[/tex]

Answer:

Step-by-step explanation:

To find the times that the height is 26 feet, we set the position equation equal to 26 and solve for t:

[tex]26=-16t^2+40t+4[/tex] and

[tex]0=-16t^2+40t-22[/tex] and factor that however you are factoring in class to solve a problem like this. When you do that you get

t = .86 seconds and t = 1.68 seconds. That means that .86 seconds after the ball is thrown into the air, it reaches a height of 26 feet; it goes up to its max height and then gravity takes over and pulls it back down. When this happens, it will pass 26 feet again on its way back down. This second time is after 1.68 seconds.

Answer:

x = 8

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

6x - 6 = 42

Step 2: Solve for x

Answer: -6

Step-by-step explanation:

We can create an equation based on the info given.

6-6x=42 Now you solve for x, the unknown number.

-6      -6      Subtract 6 on both sides

-6x=36

/-6   /-6       Divide by -6 on both sides

x=-6

The number is -6.

Answer:

-2

Step-by-step explanation:

5 + (-7)

Since the 7 is larger than 5, the 7 will overpower the 5 in a way. So, all you do is subtract 7 and 5.

7 - 5 = 2

But the 7 has a negative with it (since it's larger), so you add the negative to the 2.

7 - 5 = -2

The answer will be -2.

Answer:

The correct answer is - $720 or 20%.

Step-by-step explanation:

Given:

Total expense = 3600

Electric=30%

Heating and gas=50%

Water and sewer=X%

Solution:

For electric: 3600*30/100 = 1080

for heating and gas: 3600*50/100 = 1800

Left money for expense of water and shower = total - (electric and heating)

= 3600-1880

= 720

Percentage of water and shower = 720*100/3600

= 20%

Answer:

Correct!

Step-by-step explanation:

Thank you this is correct :) I took the test

Answer:

The answer is "Option D"

Step-by-step explanation:

In a rotation, an item is rotated around with a known location. Clockwise or anticlockwise spinning is possible. Rotation centers are spherical geometry in space where rotation occurs. The direction of inclination is the indicator of the total rotation made. Rotary point refers to that part point of a figure around which it is revolved.

9514 1404 393

Answer:

  m = n = 5

Step-by-step explanation:

The side ratios in a 45°-45°-90° triangle are 1 : 1 : √2. That is, the hypotenuse is √2 times the side length. Here, the hypotenuse is 5√2, so the side length must be 5.

  m = n = 5

9514 1404 393

Answer:

  (b) ∠STU

Step-by-step explanation:

Transversal UT between parallel sides RU and ST creates alternate interior angles RUT and STU. These are congruent.

  ∠STU has the same measure as ∠RUT

_____

The figure shown is a trapezoid, not a parallelogram.

Answer:

95%

Step-by-step explanation:

Mean , xbar = 64.3; standard deviation, s= 2.4

Using the empirical formula where ;

68% of the distribution is within 1 standard deviation from the mean ;

95% of the distribution is within 2 standard deviation from the mean

percent of heights that lie between 59.5 inches and 69.1 inches.

Number of standard deviations from the mean /

Z = (x - μ) / σ

(x - μ) / σ < Z < (x - μ) / σ

(59.5 - 64.3) / 2.4 < Z < (69.1 - 64.3) / 2.4

-2 < Z < 2

Thia is within 2 standard deviations of the means :

2 standard deviation form the mean = 95% according to the empirical rule.

Answer:

C

Step-by-step explanation:

The slope of the line will be (2) and the equation will be C

Solution :

Given information :

A sample of n = 10 adults

The mean failure was 24 and the standard deviation was 3.2

a). The formula to calculate the 95% confidence interval is given by :

[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]

Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]

                       = 2.145

Substitute the values

[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]

(26.17, 21.83)

When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]

b). The formula to calculate 95% prediction interval is given by :

    [tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]

   [tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]

   (31.13, 16.87)

Answer:

$32

Step-by-step explanation:

Multiply $40*3000 students. Subtract 2 students that might receive a $12000 policy each. Divide by 3000 students to find average payout.

I don't know sorry I am weak in math

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{x}{3}[/tex] < 5 ( multiply both sides by 3 to clear the fraction )

x < 15 → C

Answer:

Accuracy = Tape measurement.

Precision = Laser measurement

Step-by-step explanation:

Given that :

True height, = 70.2 inches

Laser measured height = 71.05 (nearest hundredth)

Tape measured height = 69.5 - nearest half inch.

Accuracy simply means how close a measured value is to the true value of the measurement. ;

True height - tape measurement

70.2 - 69.5 = 0.7

True measurement - laser measurement :

|70.2 - 71.05| = 0.85

Fron the difference in the values, the measurement which is closer to the true height is the tape measurement.

However, in terms of detail in the measured value, the laser measure value is expressed to the nearest hundredth, hence giving it more precision over the tape measured value.

Answer:

7/10 or 0.7

Step-by-step explanation:

a probability is always the ratio of possible cases over all cases.

"all cases" here is 100.

possible cases are all iPads not cracked in the inventory = 70 (because 30 are cracked, that leaves 100-30=70 not cracked).

so, the probability to select a non-cracked unit is

70/100 or simplified 7/10 (or 0.7)

Answer:

Indication of Actual Quantity and Estimated Quantity

Actual Quantity:

Registered students in the university = 25,000

Sample of students = 400

Students living at home = 317

Estimated Quantity:

317 out of 400 students

79%

Step-by-step explanation:

An actual quantity does not require to be estimated.  It is usually given in the question or scenario.  For example, the number of registered students in the university is an actual quantity.  The percentage of students who live at home from the simple random sample of 400 is an estimated quantity.

The pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.

To determine if two functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's analyze the given options:

A. f(x) = 5 + x and g(x) = 5 - x

To check if they are inverses, we compute f(g(x)) = f(5 - x) = 5 + (5 - x) = 10 - x, which is not equal to x. Similarly, g(f(x)) = g(5 + x) = 5 - (5 + x) = -x, which is also not equal to x. Therefore, these functions are not inverses.

B. f(x) = 2x - 9 and g(x) = x + 9/2

By calculating f(g(x)) and g(f(x)), we find that f(g(x)) = x and g(f(x)) = x, which means these functions are inverses of each other.

C. f(x) = 3 - 6 and g(x) = x + 6/2

Similar to option A, we compute f(g(x)) and g(f(x)), and find that they are not equal to x. Hence, these functions are not inverses.

D. f(x) = x/3 + 4 and g(x) = 3x - 4

After evaluating f(g(x)) and g(f(x)), we see that f(g(x)) = x and g(f(x)) = x. Therefore, these functions are inverses of each other.

In summary, the pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.

Learn more about function here:

https://brainly.com/question/782311

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Answer:

An expression is shown below:

10n³− 15n² + 20xn² − 30xn

Part A: Rewrite the expression so the GCF is factored completely. (4 points)

10n³− 15n² + 20xn² − 30xn

2*5*n*n*n-5*3*n*n+2*5*2*x*n*n-2*5*3*x*n

Greatest common factor=5*n=5n

Part B: Rewrite the expression completely factored. Show the steps of your work.

Solution given;

10n³− 15n² + 20xn² − 30xn

5n(2n²-3n+4xn-6x)

5n(2n²+4xn-3n-6x)

5n(2n(n+2x)-3(n+2x))

5n(n+2x)(2n-3)

Answer:

[tex]5n(2n-3)(n+2x)[/tex]

Step-by-step explanation:

Step 1:   Rewrite the expression so the GCF is factored completely

[tex]10n^{3} - 15n^{2} + 20xn^{2} - 30xn[/tex]

The GCF is 5n so factor it out

[tex]5n(2n^{2} - 3n + 4xn - 6x)[/tex]

Step 2:  Rewrite the expression completely factored

[tex]5n(2n^{2} - 3n + 4xn - 6x)[/tex]

[tex]5n(2n(n+2x)-3(n+2x))[/tex]

[tex]5n(2n-3)(n+2x)[/tex]

Answer:  [tex]5n(2n-3)(n+2x)[/tex]

Answer:

x = 3

Step-by-step explanation:

First, use trigonometric function to find RT.

θ = 60°

Opposite = 2√3

Hypotenuse = RT

Apply SOH:

Sin θ = Opp/Hyp

Plug in the values

Sin 60° = 2√3/RT

RT*Sin 60° = 2√3

Divide both sides by Sin 60°

RT = 2√3/sin 60°

RT = 2√3 × √3/2 (sin 60° = √3/2)

RT = (2√3 × √3)/2

RT = (2 × 3)/2

RT = 3

✔️Find x

θ = 45°

Opposite = x

Adjacent = 3

Apply TOA:

Tan θ = Opp/Adj

Substitute

Tan 45° = x/3

3 × Tan 45° = x

3 × 1 = x (tan 45° = 1)

3 = x

x = 3

Vertex is the point where the function is at its maximum/ minimum.

Answer:

Pretty sure it's 0.528

The partial fraction expansion takes the form

-6x/((x + 2) (x + 8)) = a/(x + 2) + b/(x + 8)

Both factors in the denominator are linear, so the numerators in the corresponding partial fractions have degree 1 - 1 = 0 and are thus constants.

Combine the fractions on the right side into one with a common denominator, then set the numerators on both sides of the equation equal to each other:

-6x = a (x + 8) + b (x + 2)

Expand the right side and collect terms by powers of x :

-6x = (a + b) x + (8a + 2b)

It follows that

a + b = -6   and   8a + 2b = 0

==>   a = -2   and   b = 8

So we end up with

-6x/((x + 2) (x + 8)) = -2/(x + 2) + 8/(x + 8)

Answer:

15.4 degrees

Step-by-step explanation:

b= 53

h = 55

cos -¹( 53/53)= 15.4

Let x(t) denote the amount of salt (in kg) in the tank at time t. The tank starts with 18 kg of salt, so x (0) = 18.

The solution is drained from the tank at a rate of 90 L/min, so that the amount of salt in the tank changes according to the differential equation

dx(t)/dt = - (x(t) kg)/(9000 L) × (90 L/min) = -1/100 x(t) kg/min

or, more succintly,

x' = -1/100 x

This equation is separable as

dx/x = -1/100 dt

Integrating both sides gives

∫ dx/x = -1/100 ∫ dt

ln|x| = -1/100 t + C

x = exp(-1/100 t + C )

x = C exp(-t/100)

(a) Using the initial condition x (0) = 18, we find

18 = C exp(0)   ==>   C = 18

so that

x(t) = 18 exp(-t/100)

(b) After 20 minutes, we have

x (20) = 18 exp(-20/100) = 18 exp(-1/5) ≈ 14.74

so the tank contains approximately 14.74 kg of salt after this time.