Find the sum of the first 6 terms of 3 - 6 + 12 + …

Answer:

x = -6

y = 4

Step-by-step explanation:

Rewriting the equations :

Now, solving the two equations using substitution method, we get :

x = -6

y = 4

Answer:

y = 4

x = -6

Step-by-step explanation:

1/2 x + 1/4 y= -2        first equation

-2/3 x + 1/2 y = 6      second equation

solution:

from the first equation:

8(1/2 x + 1/4 y) = -2*8

8x*1/2 + 8y*1/4 = -16

8x/2 + 8y/4 = -16

4x + 2y = -16        third equation

from the second equation

6(-2/3 x + 1/2 y) = 6*6

6x*-2/3 + 6y*1/2 = 36

-12x/3 + 6y/2 = 36

-4x + 3y = 36        fourth equation

from the third & fourth equation:

 4x + 2y  = -16

-4x + 3y  = 36

   0  + 5y = 20

5y = 20

y = 20/5

y = 4

from the fourth equation:

-4x + 3y = 36

-4x + 3*4 = 36

-4x + 12 = 36

-4x = 36 - 12

-4x = 24

x = 24/-4

x = -6

Check:

from the first equation:

1/2 x + 1/4 y = -2

1/2 *-6 + 1/4 * 4 = -2

-3 + 1 0 -2

from the second equation:

-2/3 x + 1/2 y = 6

-2/3 * -6  +  1/2 * 4 = 6

4 + 2 = 6

Answer:

Step-by-step explanation: Let all unknown no be x

Five more than the square of a number

= [tex]5 + x^2[/tex]

Five more than twice a number ;

[tex]5+2x\\= 2x+5[/tex]

Five less than the product of 3 and a number ;

[tex]5- 3x\\= 3x-5[/tex]

Twice the sum of a number and 5 ;

[tex]2(x+5)\\[/tex]

The sum of twice a number and 5 ;

[tex]2x+5[/tex]

The product of the cube of a number and 5;

[tex]x^3 \times 5\\=5x^3[/tex]

The cube of the product of 5 and a number ;

[tex](5\times x)^3\\(5x)^3[/tex]

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

[tex]5(2x + 4) = 15\\10x+20=15\\10x=-5\\x=-\dfrac{5}{10}=-0,5[/tex]

Answer:

[tex]\huge\boxed{x=-0.5}[/tex]

Step-by-step explanation:

[tex]5(2x+4)=15\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup(2x+4)}{5\!\!\!\!\diagup}=\dfrac{15\!\!\!\!\!\diagup}{5\!\!\!\!\diagup}\\\\2x+4=3\qquad\text{subtract 4 from both sides}\\\\2x+4-4=3-4\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-1}{2}\\\\\boxed{x=-0.5}[/tex]

Answer:

-3 is the answer.

Step-by-step explanation:

=2(-1+3)-7

=2(2)-7

=4-7

=-3

Hope it will help you :)

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:

p0 = 0.05

Step-by-step explanation:

Answer:

4.25, 4.5, 4.75, 5.00, 5.25, 5.5, 5.75, 6.00

Step-by-step explanation:

it is an arithmetic sequence with common difference 0.25

given: [tex] Ac=\frac{vt2}r \quad vt=2 \quad r=2[/tex]

$\therefore Ac=\frac{(2)2}{2}=2$

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:

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:

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:

[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:

Step-by-step explanation:

If I choose a number from the integers 1 to 25, the total number of integers I can pick is the total outcome which is 25. n(U) = 25

Let the probability that the number chosen at random is a multiple of  6 be P(A) and the probability that the number chosen at random is is larger than 18 be P(B)

P(A) = P(multiple of 6)

P(B) = P(number larger than 18)

A = {6, 12, 18, 24}

B = {19, 20, 21, 22, 23, 24, 25}

The conditional probability that the number is a multiple of 6 (including 6) given that it is larger than 18 is expressed as P(A|B).

P(A|B) = P(A∩B)/P(B)

Since probability = expected outcome/total outcome

A∩B = {24}

n(A∩B) = 1

P(A∩B) = n(A∩B)/n(U)

P(A∩B) = 1/25

Given B = {19, 20, 21, 22, 23, 24, 25}.

n(B) = 7

p(B) = n(B)/n(U)

p(B) = 7/25

Since P(A|B) = P(A∩B)/P(B)

P(A|B) = (1/25)/(7/24)

P(A|B) = 1/25*25/7

P(A|B) = 1/7

Hence the conditional probability that the number is a multiple of 6 (including 6) given that it is larger than 18 is 1/7

Answer:69

Step-by-step explanation:

Answer:

Inequality: 3 + 1.2c

What you'd put on graph: 1 ≥ 13.50

Answer:

No, each outcome is equally likely regardless of the previous outcome.

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:

We are asked to determine the correct factorization of the given trinomial which is 5x² - 5x -100. The solution to this problem is shown below:

5x² - 5x - 100 let the problem equal to zero such as:

5x² - 5x - 100 = 0 , factor out 5 from the given trinomial

5(x²-x-20) = 0

5 (x-5)(x+4) = 0

The correct factor is 5(x-5)(x+4).

Step-by-step explanation:

Answer:

  18√91 +54√3

Step-by-step explanation:

Name the point at the top of the pyramid "A", the point at the left front corner "B", and the one in the center of the hexagonal base "C". Then right triangle ABC is shown. The "base" BC of that triangle is the same measure as the front edge (6), because the diameter of a regular hexagon is equal to twice the side length.

Using the Pythagorean theorem, we can find the face edge length to be ...

  AB^2 = BC^2 +AC^2

  AB^2 = 6^2 +8^2 = 100

  AB = √100 = 10

If we call the midpoint of the front edge "D", then we need to find the length of AD in order to determine the face area. Again, we can use the Pythagorean theorem.

  AB^2 = BD^2 +AD^2

  AD^2 = AB^2 -BD^2 = 10^2 -3^2 = 91

  AD = √91

The area of one of the 6 lateral faces is ...

  A = (1/2)bh = (1/2)(6)√91 = 3√91

The area of one of the 6 equilateral triangles that make up the base is ...

  A = (√3)/4·s^2 = (√3)/4(6^2) = 9√3

Then the total area of the pyramid is ...

  total area = 6 × (face area + partial base area)

  = 6(3√91 +9√3)

  total area =  18√91 +54√3

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:

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:

−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:

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:

52.3555 north

1.1745 west

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.

Answer:

13 days

Step-by-step explanation:

Given that a one-way flight to europe will take 13 hours

A round trip will take = 13 hrs x 2 = 26 hours

Also given that we make one round trip per months for 12 months (1 year)

We will take a total of 12 round trips per year

Number of hours taken for 12 round trips

= 26 hours per round trip x 12 round trips

= 26 x 12

= 312 hours

Recall that there are 24 hours in a day, hence to convert 312 hours into days, we have to divide this by 24.

Number of days = number of hours ÷ 24

= 312 ÷ 24

= 13 days

Answer:

Well, let's assume that "cups" = 3 cups of flour.

Step-by-step explanation:

First, multiply 3x36.

If for some reason this is incorrect, try 2 cups instead of 3. Both are reasonable measurements when it comes to baking.

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:

[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