Sort each equation according to whether it has one solution, infinitely many solutions, or no solution.
5(x - 2) = 5x - 7
One Solution
Infinitely Many Solutions
No Solution
-3(x-4) =-3x + 12
4(x + 1) = 3x + 4
-2(x - 3) = 2x - 6
6(x+5) = 6x +11

Answer:

the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166

Step-by-step explanation:

The summary of the given statistical data set are:

Sample Mean = 186

Standard deviation = 29

Maximum capacity 3,417 pounds or 17 persons.

sample size = 17

population mean =3417

The objective is to determine the probability  that a random sample of 17 persons will exceed the weight limit of 3,417 pounds

In order to do that;

Let assume X to be the random variable that follows the normal distribution;

where;

Mean [tex]\mu[/tex] = 186 × 17 = 3162

Standard deviation = [tex]29* \sqrt{17}[/tex]

Standard deviation = 119.57

[tex]P(X>3417) = P(\dfrac{X - \mu}{\sigma}>\dfrac{X - \mu}{\sigma})[/tex]

[tex]P(X>3417) = P(\dfrac{3417 - \mu}{\sigma}>\dfrac{3417 - 3162}{119.57})[/tex]

[tex]P(X>3417) = P(Z>\dfrac{255}{119.57})[/tex]

[tex]P(X>3417) = P(Z>2.133)[/tex]

[tex]P(X>3417) =1- 0.9834[/tex]

[tex]P(X>3417) =0.0166[/tex]

Therefore; the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166

Answer:

Speed of current is 3 miles per hour.

Step-by-step explanation:

Speed of boat without current, u = 13 miles/hr

Let speed of current = v miles/hr

Speed upstream = (13 - v) miles/hr

Speed downstream = (13 + v) miles/hr

Distance traveled upstream, [tex]D_1[/tex] = 80 miles

Distance traveled downstream, [tex]D_2[/tex] = 80 miles

Total time taken, T ([tex]T_1+T_2[/tex]) = 13 hours

Formula for Total Time taken:

[tex]Time= \dfrac{Distance}{Speed}[/tex]

Time taken in Upstream:

[tex]T_1 = \dfrac{80}{13-v}\ hours[/tex]

Time taken in Downstream:

[tex]T_2 = \dfrac{80}{13+v}\ hours[/tex]

[tex]T = T_1+T_2 = 13\ hours\\\Rightarrow 13 = \dfrac{80}{13-v}+\dfrac{80}{13+v}\\\Rightarrow 13 = 80(\dfrac{13+v+13-v}{13^2-v^2})\\\Rightarrow 13^2-v^2 = \dfrac{80(26)}{13}\\\Rightarrow 169-v^2 = 80\times 2\\\Rightarrow v^2 = 169-160 = 9\\\Rightarrow v = 3\ miles/hr[/tex]

So, speed of current is 3 miles/hr

Answer:

the answer is A

Step-by-step explanation:

Answer:

  (f+g)(x) = 5x^2 -4

Step-by-step explanation:

  [tex](f+g)(x)=f(x)+g(x)\\\\=(4x^2+1)+(x^2-5)=(4+1)x^2+(1-5)\\\\\boxed{(f+g)(x)=5x^2-4}[/tex]

Answer:

about 10

Step-by-step explanation:

62.8 = 2 pi r/2

62.8/2 = pi r

31.4/pi = pi r/pi

about 10 = r

Answer:

s=5

Step-by-step explanation:

This triangle is right and with two equal sides since it has two congruent angle so we will use the pythagorian theorem:

Answer:

Smart TV, Smart Navigation in cars

Step-by-step explanation:

Smart TV :

Smart navigation in cars:

Answer:

b median

Step-by-step explanation:

Answer:

  orthocenter

Step-by-step explanation:

The red segment is an altitude of the triangle, as are the two legs. The intersection point of the altitudes is the orthocenter.

__

This is basically a vocabulary question.

Answer:

A. 7.88*10^(-16)

B. 1.0000000 (almost certainty)

Step-by-step explanation:

United Airlines flight 1832 from chicago to orlando is on time 80% of the time, according to united states airlines. Suppose 65 flights are randomly selected.

Binomial distribution will be required for the discrete case where there can be only two outcomes for each trial, success or failure, and where the number of experiments is known, and the probability of success is known and remains constant.

P(x) = n* (C(n,x)*p^x*(1-p)^(n-x)

where

n = size of experiment in number of trials

p = probability of success of one individual trial

x = number of successes

C(n,x) = number of combinations when x objects are taken out of n

         = n!/(x!*(n-x)!)

P(x) = probability of success out of n experiments.

A) find the probability that exactly 22 flights are on time.

n = 65

x = 22

p = 0.80

P(22) = C(65,22) (0.80^22 * 0.20^(65-22))

= 65!/(22!(65-22)!) * (0.80^22 * 0.20^(65-22))

= 7.88*10^(-16)

B) Find the probability that at least 2 flights are on time.

We find the probabilities of 0 and 1 flight on time, and subtract from 1 to get probability of at least 2 on time.

P(0) = C(65,0)*0.8^0*0.2^65 = 3.689*10^(-46)

P(1) = C(65,1)*0.8^1*0.2^64 = 9.59*10^(-44)

Therefore probability of having at least 2 flights on time equals

1-P(0)-P(1) = 1-3.689*10^(-46)-9.59*10^(-44) = 1.0  (almost certainty)

Answer:

4380 ways

Step-by-step explanation:

We have to form 3 project of 16 employees, they tell us that the first project must have 5 employees, therefore we must find the number of combinations to choose 5 of 16 (16C5)

We have nCr = n! / (R! * (N-r)!)

replacing we have:

1st project:

16C5 = 16! / (5! * (16-5)!) = 4368 combinations

Now in the second project we must choose 1 employee, but not 16 but 11 available, therefore it would be to find the number of combinations to choose 1 of 11 (11C1)

2nd project:

11C1 = 11! / (1! * (11-1)!) = 11 combinations

For the third project we must choose 10 employees, but since we only have 10 available, we can only do a combination of this, since 10C10 = 1, therefore:

3rd project: 1 combination

The total number of combinations fro selecting 16 employees for each project would be:

4368 + 11 + 1 = 4380 combinations, that is, there are 4380 different ways of forming projects with the given conditions.

Answer:

Suppose that the first die we roll comes up as a 1. The other die roll could be a 1, 2, 3, 4, 5, or 6. Now suppose that the first die is a 2. The other die roll again could be a 1, 2, 3, 4, 5, or 6. We have already found 12 potential outcomes, and have yet to exhaust all of the possibilities of the first die. But with a second dice, there will be 24 different possibilities.

Step-by-step explanation:

   1     2        3 4   5     6

1 (1, 1)   (1, 2)   (1, 3)   (1, 4)  (1, 5)   (1, 6)

2 (2, 1)   (2, 2)  (2, 3)  (2, 4) (2, 5)  (2, 6)

3 (3, 1)   (3, 2)  (3, 3)  (3, 4)  (3, 5)  (3, 6)

4 (4, 1)   (4, 2)  (4, 3)  (4, 4)  (4, 5)  (4, 6)

5 (5, 1)   (5, 2)  (5, 3)  (5, 4)  (5, 5)  (5, 6)

6 (6, 1)   (6, 2)  (6, 3)  (6, 4)  (6, 5)  (6, 6)

Answer:

15.87%

Step-by-step explanation:

We have to calculate the value of z:

z = (x - m) / (sd / n ^ (1/2))

where x is the value to evaluate, m is the mean, n is the sample size and sd is the standard deviation, we replace:

p (x <60,527) = z = (x - m) / (sd / n ^ (1/2))

p (x <60,527) = z = (60,527 - 60) / (5/90 ^ (1/2))

z = 1

if we look in the attached table, for z = 1 it is 0.8413

p (x> 60,527) = 1 - 0.8413

 p (x> 60,527) = 0.1587

Therefore the probability is 15.87%

Answer:

y = [tex]\frac{1}{2}[/tex] x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

Parallel lines have equal slopes

line M crosses the y- axis at (0, 3) ⇒ c = 3

y = [tex]\frac{1}{2}[/tex] x + 3 ← equation of line M

Answer: 11 ft × 6 ft

Step-by-step explanation: l = w+5. Substitute that value in A = lw and rewrite the equation.

w(w + 5) = 66

w^2 + 5w - 66 = 0 Factor that.

(w -6)(w + 11) =0. Solve for w.

w -6= 0, w = 6 but discard the other -11 as dimensions of real polygons can't be negative

L = w + 5 so L = 6+5

So L=11

Answer:

324000000000000000000000

Answer:

His monthly income is 9000 Rs

Answer:

Step-by-step explanation:

Reflecting on the x-axis is multiplying the formula by a -1. That is, the resulting form is pointing up. When translated to the left 3 units, the tip of the graph is at the point (-3,0). Then when shifted 4 units up the tip is at (-3,4). Dilated by a factor of 4 will affect the values in x, but not the values in y. So the tip remains at the point (-3,4) which corresponds to the second graph

The second graph is the right one.

Answer:

a = ±4√5

Step-by-step explanation:

Solve for c.

3√c = 9

√c = 9/3

√c = 3

c = 3²

c = 9

Put b=2√2 and c=9, solve for a.

a² + (2√2)² + 9² = 169

a² + 8 + 81 = 169

a² = 169 - 81 - 8

a² = 80

a = ±√80

a = ±4√5

Answer:

Length =  502 ft

Width = 212 ft

Step-by-step explanation:

Recall the formula for the perimeter of a rectangle of length "L" and width "W":

Perimeter = 2 L + 2 W = 1428  ft

Now, since the length is 78 ft more than twice the width, then we can write this in mathematical form as:

L = 2 W +78

so, 2 W = L -7 8

and now replace "2 W" with it equivalent  "L - 78"  in the first perimeter equation and solve for "L":

2 L + L - 78 = 1428

3 L = 1428 + 78

3 L = 1506

L = 1506/3

L = 502 ft

Then the width W can be obtained via:

2 W = L - 78

2 w = 502 -78

2 W = 424

w = 212 ft

Answer:

(x, y) = (-8/3, -60)

Step-by-step explanation:

y = 30x + 20

y = 10 * 2 - 80 → y = 20 - 80

y = 30x + 20

y = -60

30x + 20 = -60

x = -8/3

(x, y) = (-8/3, -60)

Hope this helps! :)

Answer:

3.15 dollars

Step-by-step explanation:

The sales tax rate is 7% = 0.07

So, we need to multiply the listed price and the sales tax rate.

= 45 * 0.07 = 3.150 (3.15)

Hope this helps and please mark as the brainliest

Answer:

Two events are said to be dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.

Also, Two events are said to be independent if the outcome or occurrence of the first does not affects the outcome or occurrence of the second so that the probability is not changed.

Read more on Brainly.com

Answer:E. P(B\A)≠P(B)

Step-by-step explanation:

Answer:

  50.18°

Step-by-step explanation:

  ∠BAD = ∠BAC +∠CAD

  102° = (8x+17)° +(9x+11)° . . . . . substitute given values

  102 = 17x +28 . . . . . . . . . . simplify, divide by degrees

  x = (102 -28)/17 = 74/17 . . . . . solve for x

Then the angle of interest is ...

  ∠CAD = (9x +11)° = (9(74/17) +11)° = 50 3/17°

  ∠CAD ≈ 50.18°

Answer:

Step-by-step explanation:

If, for example, we translate the graph of f(x) = |x| 3 spaces to the right, then the equation becomes g(x) = |x - 3|

Answer:

40°

Step-by-step explanation:

The reference angle is the positive acute angle created by the terminal arm and the x-axis.

The highlighted red in the picture below shows what we're looking for.

The arm rotated 220° (but 'backwards' so the value given is negative).

|-220°| - 2(90°)          <= Subtract two right angles for two quadrants

= 220° - 2(90°)

= 220° - 180°

= 40°

Therefore, the reference angle is 40°.

If you got 50°, you probably calculated the angle with the terminal arm and the y-axis. Remember to always use the nearest side of the x-axis!

Answer:  c) SAS Postulate

Step-by-step explanation:

DP = PC              Sides are congruent

∠ADP ≡ ∠BCP    Angles are congruent (angles are between the sides)

AD = BC             Sides are congruent

To finish the proof, we can state that ΔADP ≡ ΔBCP by the Side-Angle-Side (SAS) Postulate

Answer:

y= 3x+2

Step-by-step explanation:

i think im sorry if its wrong

Organic chemistry is the study of molecules that contain carbon ("organic molecules").

Answer: x=-3/4

Step-by-step explanation:

Since we know f(x)=6, we can set it equal to the equation.

6=9+4x           [subtract 9 on both sides]

-3=4x              [divide both sides by 4]

x=-3/4

Answer:

m∠1 = 43°27'

m∠2 = 136°73'

m∠4 = 136°73'

Step-by-step explanation:

∠1 = ∠3 because of Vertical Angles Theorem

180 - ∠1 = ∠2 because of Supplementary angles

∠2 = ∠4 because of Vertical Angles Theorem

Answer:

0.9056

Step-by-step explanation:

We are given;

Number of students enrolled in both General Chemistry and Calculus I = 540 students

Number of students who received an A in general chemistry = 51 students

Number of students who received an A in calculus = 59 students

Number of students who received an A in both general chemistry and calculus = 30 students

Now, we want to find the probability that a randomly chosen student did not receive an A in general chemistry.

So, first of all let's calculate number of students who didn't receive an A in chemistry.

So,

No without A in chemistry = 540 - 51 = 489 students

So, probability that a randomly chosen student did not receive an A in general chemistry = 489/540 = 0.9056