Fifty three million, eight hundred thousand and thirteen

Answer:

y = 2x + 12

Step-by-step explanation:

the formula for a line is typically

y = ax + b

a is the slope of the line (expressed as y/x ratio describing how many units y changes, when x changes a certain amount of units).

b is the offset of the line in y direction (for x=0).

we have the points (3, -4) and (-7, 1).

to get the slope of the line let's wander from left to right (x direction).

to go from -7 to 3 x changes by 10 units.

at the same time y changes from 1 to -4, so it decreases by 5 units.

so, the slope is -5/10 = -1/2

and the line equation looks like

y = -1/2 x + b

to get b we simply use a point like (3, -4)

-4 = -1/2 × 3 + b

-4 = -3/2 + b

-5/2 = b

so, the full line equation is

y = -1/2 x - 5/2

now, for a perpendicular line the slope exchanges x and y and flips the sign.

in our case this means +2/1 or simply 2.

so, the line equation for the perpendicular line looks like

y = 2x + b

and to get b we use the point we know (-2, 8)

8 = 2×-2 + b

8 = -4 +b

12 = b

so, the full equation for the line is

y = 2x + 12

Answer:

2x-y+12= 0 or y = 2x+12 is the answer

Step-by-step explanation:

slope of the line joining (3,-4) and (-7,1) is 1-(-4)/-7-3

= -5/10

= - 1/2

slope of the line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) = 2

Equation of the line line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) is y-8 = 2(x-(-2))

y-8 = 2(x+2)

y- 8 = 2x+4

y=2x+12 (slope- intercept form) or 2x-y+12= 0 (point slope form)

Answer:

The solutions for x are [tex]x = 4[/tex] and [tex]x = -1.5[/tex].

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

2x² - 5x - 12 = 0

This means that [tex]a = 2, b = -5, c = -12[/tex]

Solution:

[tex]\Delta = (-5)^2 - 4(2)(-12) = 121[/tex]

[tex]x_{1} = \frac{-(-5) + \sqrt{121}}{2*2} = 4[/tex]

[tex]x_{2} = \frac{-(-5) - \sqrt{121}}{2*2} = -1.5[/tex]

The solutions for x are [tex]x = 4[/tex] and [tex]x = -1.5[/tex].

Answer:

[tex]x=-\frac{15}{382}[/tex]

Step-by-step explanation:

32 × 12x + 1 = 2x - 14

384x + 1 = 2x - 14

384x + 1 - 1 = 2x - 14 - 1

384x = 2x - 15

384x - 2x = 2x - 2x - 15

382x = - 15

382x ÷ 382 = - 15 ÷ 382

[tex]x=-\frac{15}{382}[/tex]

Answer:

(i) The probability of at least 2 successes is 0.2093.

(ii) The probability of at least one but no more than 3 successes is 0.9548.

Step-by-step explanation:

Now the total number of cases = {1, 2, 3, 4, 5, 6} = 6.

Favourable cases = {1, 6} = 2.

[tex]p = \frac{2} {3} = \frac{1} {3} \\\\q = 1- p\\\\q = \frac{2}{3} \\\\n=5[/tex]

i) at least 2 successes,

[tex]P(X\geq 2) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\geq 2) = 0.2093[/tex]

ii) at least one but no more than 3 successes,

[tex]P(X\leq 3) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\leq 3)= 0.9548[/tex]

Answer:  

Step-by-step explanation:

[tex]\displaystyle\ \!\!6(x-2)>15 \\\\6x-12>15 \\\\6x>27\\\\ \boldsymbol{x>4,5 \ \ or \ \ x\in(4,5\ ; \infty)}[/tex]

Answer:

The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]

Step-by-step explanation:

Radius of the can:

The radius of the can is given by:

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

In which V is the volume and h is the height.

In this question:

[tex]V = 1280\pi, h = 16[/tex]

Thus

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

[tex]r^2 = \frac{1280\pi}{16\pi}[/tex]

[tex]r^2 = 80[/tex]

[tex]r = \sqrt{80}[/tex]

[tex]r = \sqrt{5*16}[/tex]

[tex]r = \sqrt{5}\sqrt{16}[/tex]

[tex]r = 4\sqrt{5}[/tex]

The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]

Answer:

D.

Step-by-step explanation:

cos is positive and sin is negative

=>

it must be in quadrant IV.

you remember, 1 = sin² + cos²

1 = sin² + (3/5)² = sin² + 9/25

25/25 = sin² + 9/25

16/25 = sin²

sin = 4/5 or -4/5

and as sin of this angle is < 0, our solution is -4/5

Answer:

Part A:

x + y = 50

y = x + 20

Part B:

Ted spends 35 minutes practicing the breaststroke every day.

Part C: It is not possible, as 45 + 65 isn't 50.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

1

2(3x + 1) = 4(x + 2) ← distribute parenthesis on both sides

6x + 2 = 4x + 8 ( subtract 4x from both sides )

2x + 2 = 8 ( subtract 2 from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

------------------------------------------------------------

2

6x = 4(x - 3) ← distribute parenthesis

6x = 4x - 12 ( subtract 4x from both sides )

2x = - 12 ( divide both sides by 2 )

x = - 6

-----------------------------------------------------------

3

2(4x + 7) = 4x + 30 ← distribute parenthesis on left side

8x + 14 = 4x + 30 (subtract 4x from both sides )

4x + 14 = 30 ( subtract 14 from both sides )

4x = 16 ( divide both sides by 4 )

x = 4

---------------------------------------------------------------------

4

50 = - (y + 22) ← distribute parenthesis by - 1

50 = - y - 22 ( add 22 to both sides )

72 = - y ( multiply both sides by - 1 )

- 72 = y , that is

y = - 72

Answer:

Step-by-step explanation:

Answer:

18.65

Step-by-step explanation:

1/4+2/5+18=18.65

18.65

hope it helps you good luck

Answer:

The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation.

This means that [tex]n = 3923, \pi = \frac{3196}{3923} = 0.8147[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 - 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.7987[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 + 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.8307[/tex]

The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).

8 < x < 8.5 is your answer

other sides has to always be less than the hypotenuse

9514 1404 393

Answer:

  0.5 < x < 16.5

Step-by-step explanation:

The sum of the two shortest sides of a triangle must always exceed the length of the longest side.

If x and 8.0 are the short sides, then ...

  x + 8.0 > 8.5

  x > 0.5

If 8.0 and 8.5 are the short sides, then ...

  8.0 +8.5 > x

  16.5 > x

So, for the given triangle to exist, we must have ...

  0.5 < x < 16.5

_____

Additional comment

You will notice that the value 0.5 is the difference of the given sides, and 16.5 is their sum. This will always be the case for a problem like this. The third side length always lies between the difference and the sum of the other two sides.

Answer:

0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.

Step-by-step explanation:

We have the mean during a time interval, which means that the Poisson distribution is used to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5.

This means that [tex]\mu = 5[/tex]

Calculate the probability of getting at least 4 calls between eight and nine in the morning.

This is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-5}*5^{0}}{(0)!} = 0.0067[/tex]

[tex]P(X = 1) = \frac{e^{-5}*5^{1}}{(1)!} = 0.0337[/tex]

[tex]P(X = 2) = \frac{e^{-5}*5^{2}}{(2)!} = 0.0842[/tex]

[tex]P(X = 3) = \frac{e^{-5}*5^{3}}{(3)!} = 0.1404[/tex]

Then

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0067 + 0.0337 + 0.0842 + 0.1404 = 0.265[/tex]

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.265 = 0.735[/tex]

0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.

Answer:

D: one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf

Step-by-step explanation:

A pair of 2 dependent events are simply those in which the choice of the second item depends on taking the first item such that the probability changes.

Because when the first item is taken without replacement, the sample size would have reduced and as such picking the exact same item will reduce the probability.

Now, what this means in relation to the question is that for 2 of the events to be independent, they must be on the same shelf and of same type of book such that the second book can't be selected until the first one has been selected.

The only option that fits this definition is option D where both books are on the same shelf and they are same type of books.

Answer:

one of the nonfiction books on the bottom shelf, and a second nonfiction book from the bottom shelf

Step-by-step explanation:

Answer:

Step-by-step explanation:

The idea here is to create lines according to the constraints we were given, graph the lines (which are actually inequalities), and then shade in the region that satisfies the inequality. Let's start at the beginning of the problem and we'll get our lines (inequalities) written.

The total number of boxes that can be produced according to the constraints is 800, so the inequality for that is

x + y ≤ 800 and solving for y:

y ≤ 800 - x

Another constraint on the white chocolate is that it has to be less than or equal to 200 boxes, so:

y ≤ 200

The max number of white chocolate boxes is half the number of milk chocolate, so:

y ≤ (1/2)x

The min number of milk chocolate boxes produced is:

x ≥ 0 and

The min number of white chocolate boxes produced is:

y ≥ 0 (This means that it is a possibility of making 0 milk chocolate boxes and all white chocolate boxes OR there is a possibility of making 0 white chocolate boxes and all milk chocolate boxes)

The production equation (which is used later) is:

2.25x + 2.50y (you make a profit of $2.25 on every milk chocolate box you sell and profit of $2.50 on every white chocolate box you sell).

The bold equations are the ones that need to be graphed (see graph below). Where those 3 lines intersect are the vertices of feasible region:

(0, 0), (400, 200), (600, 200), (800, 0).

Then take each x and y value from a coordinate and plug it into the profit equation (we don't need to use (0, 0)) starting with x = 400 and y = 200:

2.25(400) + 2.5(200) = $1400

Now using x = 600 and y = 200:

2.25(600) + 2.5(200) = $1850

Now using x = 800 and y = 0:

2.25(800) + 2.5(0) = $1800

So our max profit as seen by the evaluations is $1850, and that occurs when we sell 600 boxes of milk chocolate and 200 boxes of white chocolate.

9514 1404 393

Answer:

  0 = x⁴ -x³ -9x² -11x -4

Step-by-step explanation:

Each root r contributes a factor of (x-r). The factored form of the polynomial of interest is ...

  0 = (x +1)³(x -4)

  0 = (x³ +3x² +3x +1)(x -4)

  0 = x⁴ -x³ -9x² -11x -4

Answer:

17/15

Step-by-step explanation:

6/5 * 17/18

1/5 * 17/3

17/15

Answer:

2 1/6

Step-by-step explanation:

6.5x=2x+1.6=1/3

1/3*6.5=2 1/6

Answer:

x^2+y^2=1

Step-by-step explanation:

Since cos^2(x)+sin^2(x)=1, x^2+y^2=1

Answer:

Variance = 3.6 voteres

Step-by-step explanation:

Probability of favour voters, P = 0.22

Total number of voters, n = 21

The probability of voters who are in not favour of new hospital construction = 1  - P

The probability of voters who are in not favour of new hospital construction = 1  - 0.22

The probability of voters who are in not favour of new hospital construction, P* = 0.78

Variance = n x p* x (1 - p*)

Variance = 21 x 0.78 x 0.22

Variance = 3.6 voters

Answer:

4s-9t-7

Step-by-step explanation:

multiply the negative one with all terms inside the bracket, since they are all unlike terms the answer remains the same

9514 1404 393

Answer:

  Graph C: Daily High Temperatures and Bottled Water Sales

  On a graph, points are grouped together and form a line with positive slope.

Step-by-step explanation:

Apparently, Graph C shows data with the greatest degree of correlation. This suggests that any model of the data is likely to have less error than if the data were less well correlated.

Answer:

Graph C: Daily High Temperatures and Bottled Water Sales

On a graph, points are grouped together and form a line with positive slope.

Step-by-step explanation:

Answer:6^2

Step-by-step explanation:

Square has both sides with a length of 6 so 6x6 or 6^2

Answer:

A=36 ft²

Step-by-step explanation:

All sides of a square are the same, so when the length is 6 the width is also 6.

[tex]A=l*w\\A=6*6\\A=6^2[/tex]

then evaluate:

[tex]6^2=36[/tex]

hope this helps!

Answer:

Find the value of x if B is the midpoint of AC, AB = 2x + 9 and BC = 37

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

a) (– 3, –2) and (–3, 4)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(4 - (-2) / (-3 - (-3))

Simplify the parentheses.

= (4 + 2) / (-3 + 3)

Simplify the fraction.

(6) / (0)

= undefined

If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.

In this case, the x-coordinate for both points is -3.

Therefore, your equation is x = -3.

b) (3, 2) and (–4, –5)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-5 - 2) / (-4 - 3)

Simplify the parentheses.

= (-7) / (-7)

Simplify the fraction.

-7/-7

= 1

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.

2 = 1(3) + b

To find b, multiply the slope and the input of x(3)

2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-1 = b

Plug this into your standard equation.

y = x - 1

This is your equation.

Check this by plugging in the other point you have not checked yet (-4, -5).

y = 1x - 1

-5 = 1(-4) - 1

-5 = -4 - 1

-5 = -5

Your equation is correct.

Hope this helps!

Answer:

a and b are positive

Step-by-step explanation:

We are given that

[tex]a-3>b-3[/tex]

[tex]b>4[/tex]

We have to find that a and b are positive or negative.

We have

[tex]b>4[/tex]

It means b is positive and greater than 4.

[tex]a-3>b-3[/tex]

Adding 3 on both sides

[tex]a-3+3>b-3+3[/tex]

[tex]a>b>4[/tex]

[tex]\implies a>4[/tex]

Hence, a is positive and greater than 4.

Therefore, a and b are positive

Answer:

ok so they test 7 components so the probity of getting a bad one for each is 0.2 so we just multiply this 7 times

0.2*0.2*0.2*0.2*0.2*0.2*0.2=0.0000128

Hope This Helps!!!

The required probability will be 0.0000128 that the first defect is found in the seventh component tested.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

We have been given that a company ships computer components in boxes that contain 50 items.

Assume that the probability of a defective computer component is 0.2.

As per the given condition, the required solution would be as:

They test seven components, and the probability of obtaining a defective one for each is 0.2, so we just multiply this by seven.

⇒ 0.2×0.2×0.2×0.2×0.2×0.2×0.2

⇒ 0.0000128

Thus, the required probability will be 0.0000128 that the first defect is found in the seventh component tested.

Learn more about probability here:

brainly.com/question/11234923

#SPJ5

Answer:

-( cube root of 2x)-6(cube root of x)