How many solutions to the equation: 3x + 5 = 3x - 7​

Answer:

Step-by-step explanation:

2(x+y)=60

2x+2y=60

The second is the same  as the 1st but with the distribution

                    perimeter formula: P=2(W+L)

 We can distribute .Then P =  2W+2L

Recall the following property of exponents:

[tex]a^b\cdot a^c=a^{b+c}[/tex]

[tex]\implies 216^{-3k}\cdot 216^{-2k}=216^{-3k-2k}=216^{-5k}[/tex]

Now, notice that 6² = 36 and 6³ = 216, which means that

[tex]216^{-5k}=36^{2k-1} \iff (6^3)^{-5k}=(6^2)^{2k-1}[/tex]

Recall another property of (real) exponents:

[tex](a^b)^c=a^{bc}[/tex]

[tex]\implies(6^3)^{-5k}=6^{3(-5k)}=6^{-15k}\text{ and }(6^2)^{2k-1}=6^{2(2k-1)}=6^{4k-2}[/tex]

So we have

[tex]216^{-5k}=36^{2k-1} \iff 6^{-15k}=6^{4k-2}[/tex]

Since both sides are equal powers of 6, that must mean that the exponents must be equal, so

[tex]-15k=4k-2[/tex]

Solve for k :

[tex]-15k-4k=(4k-4k)-2[/tex]

[tex]-19k=-2[/tex]

[tex]k=\dfrac{-2}{-19}=\boxed{\dfrac2{19}}[/tex]

Answer:

(a) [tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]

(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.

(c) The probability that n ≥ 4 is 0.018.

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.

Step-by-step explanation:

We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.

Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,

Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

So, the probability distribution of the geometric distribution is given by;

[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]

where, p = probability that the residents are of Hawaiian ancestry = 74%

(b) The probabilities that n = 1, n = 2, and n = 3 is given by;

[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}[/tex]

P(1) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{1-1}[/tex] = 0.74

P(2) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{2-1}[/tex] = 0.192

P(3) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{3-1}[/tex] = 0.050

(c) The probability that n ≥ 4 is given by = P(n ≥ 4)

     P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)

                   = 1 - 0.74 - 0.192 - 0.050

                   = 0.018

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)

We know that the mean of the geometric distribution is given by;

           Mean = [tex]\dfrac{p}{1-p}[/tex] = [tex]\dfrac{0.74}{1-0.74}[/tex]

                     = [tex]\dfrac{0.74}{0.26}[/tex] = 2.85 or 3 (approx).

Answer:

5 people will be left to play

Answer: Out of 10 to 15 people played,  5 people are left to play

Answer:

48

Step-by-step explanation:

12*4=48

substitute y for the given value

Answer:

48

Step-by-step explanation:

12y

Let y=4

12*4 = 48

Answer:

waala kang jowa sabi ko

Answer: the expression (120/100)*80 results in 80% of 120

Step-by-step explanation:

Answer:

5.73

Step-by-step explanation:

Answer:

He should have $5.73 as change

Step-by-step explanation:

First add 85.43 with 21 and 7.84 and then do 120 - 114.27.

Answer:

117

Step-by-step explanation:

The average of all 7 people is the total weight of the original 6 people, plus the weight of the 7th person, all divided by 7.

For problems like this involving an average of numbers that are "close" together, here is a different strategy for solving the problem that you might like to try.

The original 6 people have an average weight of 173, which is 8 pounds more than the average of all 7 people. So all together, the weight of those 6 people is 6*8=48 pounds over the 165 average. That means the 7th person's weight must be 48 pounds below the 165 average.

So the weight of the 7th person is 165-48 = 117 pounds.

Answer:

The 7th person weighted 117

Step-by-step explanation:

Average Value

The mean or average of a number n of measurements is defined as the sum of all values divided by n.

[tex]\displaystyle \bar x=\frac{\sum x_i}{n}\\[/tex]

The question gives us some input data. The average weight of n=6 people is [tex]\bar x=173[/tex]. With this information, we can set this relationship:

[tex]\displaystyle 173=\frac{\sum x_i}{6}[/tex]

From the above equation, we know the sum of the first 6 persons:

[tex]\sum x_i=6*173=1,038[/tex]

When a 7th person gets on, the new average gets down to 165 and n=7. The equation for the new average is:

[tex]\displaystyle 165=\frac{\sum x_i+X}{7}[/tex]

Note we have a new summand to the numerator. It's the weight of the 7th person. Let's solve for X:

[tex]\displaystyle 165=\frac{1,038+X}{7}[/tex]

Multiply by 7:

[tex]7*165=1,038+X[/tex]

Operate and swap sides:

[tex]1,038 +X=1,155[/tex]

[tex]X=1,155-1,038=117[/tex]

The 7th person weighted 117

====================================================

Explanation:

The left hand side of the first equation is x-3y

The left hand side of the second equation is 2x-6y = 2(x-3y). Note how it's simply double of the first expression x-3y

If we multiply both sides of the first equation by 2, we get

x-3y = 4

2(x-3y) = 2*4

2x-6y = 8

Meaning that 2x-6y = 8 is equivalent to x-3y = 4. Both produce the same line leading to infinitely many solutions. Each solution will lay along the line x-3y = 4.

We can say each solution is in the set {(x,y): x-3y = 4}

Which is the same as saying each solution is of the form (3y+4,y)

Answer:

About $2.85 per gallon

Step-by-step explanation:

We can set up a proportion [tex]\frac{45.3}{15.9}[/tex]=[tex]\frac{x}{1}[/tex] we can then cross multiply, getting 15.9x=45.3. When you divide you get about $2.85

Answer:

true

Step-by-step explanation:

Answer:

105 min

Step-by-step explanation:

60 minutes ÷ 4 miles= 15 minutes per mile

15min per mile x 7 miles = 105 minutes

Answer:

y = 1/3x + 2

Step-by-step explanation:

Rise over run + y intercept

Answer:

The answer is $5.99

Step-by-step explanation:

$23.96 divided by 4 is $5.99

Answer:

The answer is $5.99

Step-by-step explanation:

I just did the quiz.

Answer:

There are 14 horses and 21 chickens.

Step-by-step explanation:

First, you have to make expression for horse and chicken. So we can let x be the number of horses and y will be the number of chickens. Next, given that the total number of feet for both animals is 98 so you have to make simultaneous equation :

[tex]4x + 2y = 98[/tex]

( horse has 4 feet and chicken has 2 feet )

There are a total of 35 heads so the other equation will be :

[tex]x + y = 35[/tex]

Lastly, you have to solve it :

[tex]4x + 2y = 98[/tex]

[tex]2(2x + y) = 98[/tex]

[tex]2x + y = 49 - - - (1)[/tex]

[tex]x + y = 35 - - - (2)[/tex]

[tex](1) - (2)[/tex]

[tex]2x + y - x - y = 49 - 35[/tex]

[tex]x = 14[/tex]

[tex]substitute \: x = 14 \: into \: (2)[/tex]

[tex]14 + y = 35[/tex]

[tex]y = 35 - 14[/tex]

[tex]y = 21[/tex]

Answer:

A

Step-by-step explanation:

Tanmayi will need $30 more to reach her goal.

$120 + n = $150

$150 - $120 = 30

n = 30

Step-by-step explanation:

8(x + 9)

8x + 72 = 0

8x = -72

x = -72/8

x = -9

Answer:

Given : 8(x + 9)

Solution :

[tex]8(x + 9) = 0\\ [/tex]

Multiply 8 to both x and 9

[tex]8x + 72 = 0 \\ [/tex]

Now, Move 72 to RHS from LHS

[tex]8x = - 72 \\ [/tex]

[tex]x = \dfrac{ - 72}{8} \\ [/tex]

And the final ans we get is :

[tex]\boxed{x = - 9}[/tex]

Answer:

total of 482

Step-by-step explanation:

He sold 1940

20% on first 500  

500 *.20 = 100 commission

Then 25% on the next 1000

1940 -500 = 1440 left

He has 1000

1000 * 25%

1000*.25 = 250 commission

1440-1000 = 440 left

440 at 30%

440*.30 =132 commission

Add together

100+250+132 = 482

Answer:

D

Step-by-step explanation:

the answer is the graph on the bottom right corner, 400 pages on the y axis and 16 days on the x axis. 25 pages a day.

hope this helped!

Answer:

8=6 2/5

50=40

100=80

Step-by-step explanation:

8x4/5=6 2/5

4x10=40 so 5x10=50 (I got this from the second row)

5x20=100 so 4x20=80 (also from second row)

Answer:

7/2

Step-by-step explanation:

Answer:

Ok:

Step-by-step explanation:

So f°g . means f(g(x)). (The ° should be more center and bigger but I don't know to do that on a keyboard). f(g(x)) means that you replace the x in f(x) with the g(x) function. i.e:

if f(x) = 2x+2

and g(x) = [tex]x^2[/tex]

f(g(x)) = [tex]2x^2+2[/tex].

Similarly, in this case, we get f(x) = 2x-3 and g(x) = 3x-2.

Then, f(g(x)) or f°g(x) is 2(3x-2) - 3.

And we plug in -2 to solve:

2(3(-2)-2)-3.

and get -19.

Check if I am wrong because everyone makes mistakes but that is the way to solve this.

Answer:

150

Step-by-step explanation: one apple cost $0.50, so 75/ $0.50= 150

Answer: i believe the answer is B

Step-by-step explanation: because if p to q is true, then that means p and q are both true!

Answer:  Think about diagonal sides and horizontal bases.

Step-by-step explanation:  "Think outside of the box." as they say.

See the screenshot attached.

Answer: y=-3x+17

b = 17