What is the sum of the geometric sequence?

Answer:

2hrs 24mins

Step-by-step explanation:

Very simple the time they will meet again at the point will be the LCM of their various time taken to complete a cycle.

Ans LCM(24, 36, 48) = 144 mins

= 2hrs 24mins

Answer:

The answer is 2 hours and 24 minutes

Step-by-step explanation:

Hope you get this right:)

Answer:

[tex]71,100[/tex]

Step-by-step explanation:

If you are trying to find a number that is written in word form, we can just use place values to find what goes where.

A number is broken down into this:

Ten thousands, thousands, hundreds, tens, ones.

If they have 7 ten thousands, the first digit will be a 7.

If they have 1 thousand, the second digit will be a 1.

If they have 1 hundred, the third digit will be a 1.

Since nothing is stated about tens, we assume it's value is 0.

And since there are no ones, it's value is 0.

So:

71,100.

Hope this helped!

Answer:

0.70319018

Step-by-step explanation:

Given the following:

Number of students surveyed (n) = 15

Probability of attending tet festival (p) = 24% =0.24

Therefore,

Probability of not attending (1 - p) = (1 - 0.24) = 0.76.

The probability that at most 4 students will attend can be obtained using the binomial probability relation:

p(x) = nCx * p^x * (1 - p)^(n-x)

At most 4 students means:

p(x=0) + p(x=1) + p(x=2) + p(x=3) + p(x=4)

p(x=0) = 15C0 * 0.24^0 * 0.76^(15 - 0)

p(x=0) = 1 * 1 * 0.0004701 = 0.00047018

p(x=1) = 15C1 * 0.24^1 * 0.76^(14)

p(x=1) = 15 * 0.24 * 0.021448 = 0.07721

p(x=2) = 15C2 * 0.24^2 * 0.76^(13) =

p(x=2) = 105 * 0.0576 * 0.02822 = 0.17068

p(x=3) = 15C3 * 0.24^3 * 0.76^(12)

p(x=3) = 455 * 0.013824 * 0.037133 = 0.23356

p(x=4) = 15C4 * 0.24^4 * 0.76^(11) =

p(x=4) = 1365 * 0.0033177 * 0.048859 = 0.22127

0.00047018 + 0.07721 + 0.17068 + 0.23356 + 0.22127 = 0.70319018

Answer:

the answer is 4

Step-by-step explanation:

so 1 rotation is like a circle 1 unit circle requires 4 quadrant to be in this is the most simplified i can get

Answer:

Solution : 4

Step-by-step explanation:

The question asks us how many polar coordinates are possible for one rotation. For one rotation there will be 4 polar coordinates, one present in each quadrant such that,

( r, theta ), ( r, theta ), ( - r, theta ), ( - r, theta )

Respectively if theta was q say,

( r, q ), ( r, - q ), ( - r, q ), ( - r, -q )

Therefore there are 4 sets of polar coordinates for one rotation, in each of the 4 quadrants.

Answer:

C

Step-by-step explanation:

A sequence is defined as a list of numbers or objects in a special order.

They may be arithmetic or geometric or neither.

For example

0, 1, 4, 9, 16, 25, ..... ← is the sequence of square numbers.

Note it is neither arithmetic or geometric.

Answer:

5/12

Step-by-step explanation:

(5 * 2^1/4)/4 * 162^1/4) = (5 * 2^1/4)/4 * 3 *2^1/4)

multiply top and bottom by 2^3/4

(5 * 2)/4 * 3 * 2) = 10/24 = 5/12

Answer:

a. Mean = 20

Sd = 4

b. Probability of X = 20 = 0.1960

Step-by-step explanation:

we have

n = 25

p = 80% = 0.8

mean = np

= 0.8 * 25

= 20

standard deviation = √np(1-p)

= √25*0.8(1-0.8)

=√4

= 2

probability that exactly 20 favours ban

it follows a binomial distribution

= 25C20 × 0.8²⁰ × 0.2⁵

= 53130 × 0.01153 × 0.00032

= 0.1960

Probability of X = 20 = 0.1960

Answer:

1 year

Step-by-step explanation:

Hello,

Continuously compounding with an annual interest rate of 4.5% means multiplying the initial investment by (for t tears).

[tex]\displaystyle e^{(1+4.5\%)t}=e^{\left( 1.045\cdot t \right) }[/tex]

So we need to find t so that:

[tex]\displaystyle e^{\left( 1.045\cdot t \right) }=3\\\\1.0.45t=ln(3)\\\\t=\dfrac{ln(3)}{1.045}=1.051304...[/tex]

Rounding to the nearest whole number gives 1 year.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

25

Step-by-step explanation:

Trust me

Answer:

A. A data set is a collection of similar data.

D. A data set contains data all of which have some common characteristic.

Answer:

Inequality: 3 + 1.2c

What you'd put on graph: 1 ≥ 13.50

Answer:

  -4

Step-by-step explanation:

(f+g)(1) = f(1) +g(1)

In each case, you need to locate the ordered pair with 1 as the first element.

  (1, f(1)) = (1, -2) . . . . f(1) = -2

  (1, g(1)) = (1, -2) . . . . g(1) = -2

  f(1) +g(1) = (-2) +(-2) = -4

(f+g)(1) = -4

Answer:

Step-by-step explanation:

Let the number to be found be x

The product of a number and 3 is written as

15 minus twice the number is written as

Now equate the two statements

That's

3x = 15 - 2x

Group like terms

3x + 2x = 15

5x = 15

Divide both sides by 5

the final answer is

Hope this helps you

Answer:

The probability that the assembly line will be shut down is 0.00617.

Step-by-step explanation:

We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.

Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.

Let X = Number of bottles in the sample that are not within specification.

The above situation can be represented through binomial distribution;

[tex]P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.....[/tex]

where, n = number of trials (samples) taken = 12 bottles

             x = number of success  = 2 or more bottles

            p = probabilitiy of success which in our question is probability that  

                 bottles are not within specification, i.e. p = 0.01

So, X ~ Binom (n = 12, p = 0.01)

Now, the probability that the assembly line will be shut down is given by = P(X [tex]\geq[/tex] 2)

  P(X [tex]\geq[/tex] 2) = 1 - P(X = 0) - P(X = 1)

                 = [tex]1-\binom{12}{0} \times 0.01^{0}\times (1-0.01)^{12-0}-\binom{12}{1} \times 0.01^{1}\times (1-0.01)^{12-1}[/tex]

                 = [tex]1-(1 \times 1\times 0.99^{12})-(12 \times 0.01^{1}\times 0.99^{11})[/tex]

                 = 0.00617

Answer:

He should find 24 defective lightbulbs.

Step-by-step explanation:

1. Divide the number of defective bulbs by the total number of bulbs for each section.

2. Make sure the number you get is the same each time.

3. Divide the guessed number of bulbs (24) by the total number of bulbs (336)

4. If the number you got for step 4 matches the number you got for step 3, then he is right

Answer:

The answer is A

Step-by-step explanation:

on NCCA

Answer: The slope of the line that passes through (2, 12) and (4, 20) is 4.

The value of the y-intercept is 9.

Step-by-step explanation:

Slope of line passing through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

Then, the slope of the line that passes through (2, 12) and (4, 20) = [tex]\dfrac{20-12}{4-2}[/tex]

[tex]=\dfrac{8}{2}=4[/tex]

So, the slope of the line that passes through (2, 12) and (4, 20) is 4.

To find the y-intercept of 3x + 2y = 18, first write in slope intercept form y=mx+c ( where c= y-intercept ).

[tex]2y=-3x+18\\\\\Rightarrow\ y=-\dfrac{3}{2}x+9[/tex]

By comparison,  c= 9

Hence, the value of the y-intercept is 9.

Answer:

D. [tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]

Step-by-step explanation:

Given

[tex]y = \frac{2}{5}x - 5[/tex]

Required

Determine its equivalent

From the list of given options, the correct answer is

[tex]x - \frac{5}{2}y = \frac{25}{2}[/tex]

This is shown as follows;

[tex]y = \frac{2}{5}x - 5[/tex]

Multiply both sides by [tex]\frac{5}{2}[/tex]

[tex]\frac{5}{2} * y = \frac{5}{2} * (\frac{2}{5}x - 5)[/tex]

Open Bracket

[tex]\frac{5}{2} * y = \frac{5}{2} * \frac{2}{5}x - \frac{5}{2} *5[/tex]

[tex]\frac{5}{2}y = x - \frac{25}{2}[/tex]

Subtract x from both sides

[tex]\frac{5}{2}y - x = x -x - \frac{25}{2}[/tex]

[tex]\frac{5}{2}y - x = - \frac{25}{2}[/tex]

Multiply both sides by -1

[tex]-1 * \frac{5}{2}y - x * -1 = - \frac{25}{2} * -1[/tex]

[tex]-\frac{5}{2}y + x = \frac{25}{2}[/tex]

Reorder

[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]

Hence, the correct option is D

[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]

Answer:

The 4th option

Step-by-step explanation:

Answer:

Decision Rule:  To reject the null hypothesis if t > 1.328

t = 3.913

Step-by-step explanation:

The summary of the given statistics include:

sample size n = 21

the correlation between the number of passengers and total fuel cost r = 0.668

(1) We are tasked to state the decision rule for 0.10 significance level

The degree of freedom df = n - 1

degree of freedom df = 21 - 1

degree of freedom df = 19

The  null and the alternative hypothesis can be computed as:

[tex]H_o : \rho < 0\\ \\ Ha : \rho > 0[/tex]

The critical value for [tex]t_{\alpha, df}[/tex]  is  [tex]t_{010, 19}[/tex] = 1.328

Decision Rule:  To reject the null hypothesis if t > 1.328

The test statistics can be computed as follows by using the formula for t-test for Pearson Correlation:

[tex]t = r*\sqrt{ \dfrac{(n-2)}{(1-r^2)}[/tex]

[tex]t = 0.668*\sqrt{ \dfrac{(21-2)}{(1-0.668^2)}[/tex]

[tex]t = 0.668*\sqrt{ \dfrac{(19)}{(1-0.446224)}[/tex]

[tex]t = 0.668*\sqrt{ \dfrac{(19)}{(0.553776)}[/tex]

[tex]t = 0.668*5.858[/tex]

t = 3.913144

t = 3.913    to 3 decimal places

Answer:

L = 13.3649

Step-by-step explanation:

We are given;

x = t − 2 sin(t)

dx/dt = 1 - 2 cos(t)

Also, y = 1 − 2 cos(t)

dy/dt = 2 sin(t)

0 ≤ t ≤ 2π

The arc length formula is;

L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt

Where α and β are the boundary points. Thus, applying this to our question, we have;

L = (0,2π)∫√((1 - 2 cos(t))² + (2 sin(t))²)dt

L = (0,2π)∫√(1 - 4cos(t) + 4cos²(t) + 4sin²(t))dt

L = (0,2π)∫√(1 - 4cos(t) + 4(cos²(t) + sin²(t)))dt

From trigonometry, we know that;

cos²t + sin²t = 1.

Thus;

L = (0,2π)∫√(1 - 4cos(t) + 4)dt

L = (0,2π)∫√(5 - 4cos(t))dt

Using online integral calculator, we have;

L = 13.3649

Answer: 20 sq. units .

Step-by-step explanation:

Let A(0, -2), B(3,2), C(8,2), and D(5, -2) are the points for the parallelogram.

First we plot these points on coordinate plane, we get parallelogram ABCD.

By comparing the y-coordinate of B and C with A and D , we get

height = 2+2 = 4 units

Also by comparing the x coordinates of A and D, we get base = 5-0= 5 units  

Area of parallelogram = Base x height

= 5 x 4 = 20 sq. units

Hence, the area of a parallelogram ABCD is 20 sq. units .

Answer:

Step-by-step explanation:

Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.

Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229

Also, the ratio of the sample students with math score below grade level to sample population will be 163:452

On equating both ratios, we will have;

x:2229 =  163:452

[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]

Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804

Answer:

−4<x<−2

Step-by-step explanation:

8 > 4 − x > 6

8 > −x + 4 > 6

8 + −4 > −x + 4 + −4 > 6 + −4

4 > −x > 2

Since x is negative we need to divide everything by -1 which gives us...

−4 < x < −2

Answer:

[tex]\{P^2: P\ E\ Z\ and\ 1\leq p\leq 10\}[/tex]

Step-by-step explanation:

Given

Range: = 1 to 100 (Inclusive)

Required

Determine the notation that represents the perfect square in the given range

Represent the range with P

P = 1 to 100

Such that the perfect squares will be P² and integers

In set notation, integers are represented with Z

The set notation becomes

[tex]\{P^2: P\ E\ Z\ and\ 1\leq p\leq 10\}[/tex]

The [tex]\leq[/tex] shows that 1 and 100 are inclusive of the set

Answer:

x(x + 11)

Step-by-step explanation:

x^2 + 11x when factored gives a result of x(x + 11)

Answer:

x(x+11)

Step-by-step explanation:

We are given the expression:

[tex]x^2+11x[/tex]

This can be factored using the Greatest Common Factor (GCF).

The GCF of x^2 and 11x is x.

Factor out an x.

[tex]x(x+11)[/tex]

x^2+11x factored is: x(x+11).

Answer:

A. There is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.

D. Fail to reject H0.

Step-by-step explanation:

From the summary of the given test statistics.

The null and the alternative hypothesis are:

[tex]H_0:\mu_1=\mu_2 \\ \\ Ha:\mu_1 \neq \mu_2[/tex]

This test is also a two tailed test.

Similarly, the t value for the test statistics = 1.44

The p- value - 0.167

The level of significance ∝ = 0.05

The objective we are meant to achieve here is to determine which of the following from the given options are appropriate conclusions for this hypothesis test.

From what we have above:

Decision Rule: We fail to reject the null hypothesis since the p-value is greater than the level of significance at 0.05

CONCLUSION: Therefore, we can conclude that  there is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag as we fail to reject H0.

Answer:

Step-by-step explanation:

Given

Garden: [tex]x^2+18x+81[/tex]

One Bag: [tex]x^2 - 81[/tex]

Requires

Determine the number of bags to cover the whole garden

This is calculated as thus;

[tex]Bags = \frac{x^2+18x+81}{x^2 - 81}[/tex]

Expand the numerator

[tex]Bags = \frac{x^2+9x+9x+81}{x^2 - 81}[/tex]

[tex]Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}[/tex]

[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 81}[/tex]

Express 81 as 9²

[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}[/tex]

Evaluate as difference of two squares

[tex]Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}[/tex]

[tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]

Hence, the number of bags is [tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]

Answer:

p(n) = -1/100 n  40

Step-by-step explanation:

Use the two points (n, p): (1000, 30) and (3000, 10).

Now we find the equation of the line that passes through these two points.

m = (10 - 30)/(3000 - 1000)

m = -20/2000

m = -1/100

p(n) = mn + b

30 = -1/100 * 1000 + b

30 = -10 + b

b = 40

The equation is:

p(n) = -1/100 n  40

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.