1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nadezda [96]
3 years ago
6

How do you solve -2(6x+3)=-27–5x ?

Mathematics
1 answer:
kvasek [131]3 years ago
8 0
Hi!

Our goal is to isolate x on one side by doing the same operation on both sides.

First let's use the distribution property.
-2 x 6 = -12
-2 x 3 = -6
-12x - 6 = -27 - 5x

Add 6 to both sides
-12x - 6 + 6 = -27 + 6 - 5x
-12x = -21 - 5x

Add 5x to both sides
-12x + 5x = -21 - 5x + 5x
-7x = -21

Divide by -7 on both sides
-7x/-7 = -21/-7
x = 3

The answer is x = 3

Hope this helps! :)
You might be interested in
This graph shows the water level as a bathtub is filled. How many inches does the water level in the bathtub increase by every 1
I am Lyosha [343]
3 inches of water when the tub is filled for a minute
7 0
3 years ago
Read 2 more answers
83333333333/10000000000 simplified answer
makkiz [27]
8.33333333. You know you can use a calculator.
6 0
3 years ago
A food-packaging apparatus underfills 10% of the containers. Find the probability that for any particular 10 containers the numb
Maksim231197 [3]

Answer:

a) P(X = 1) = 0.38742

b) P(X = 3) = 0.05740

c) P(X = 9) = 0.00000

d) P(X \geq 5) = 0.00163

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem

There are 10 containers, so n = 10.

A food-packaging apparatus underfills 10% of the containers, so p = 0.1.

a) This is P(X = 1)

P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742

b) This is P(X = 3)

P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740

c) This is P(X = 9)

P(X = 9) = C_{10,9}.(0.1)^{9}.(0.9)^{1} = 0.00000

d) This is P(X \geq 5).

Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:

P(X < 5) + P(X \geq 5) = 1

P(X \geq 5) = 1 - P(X < 5)

In which

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.1)^{0}.(0.9)^{10} = 0.34868

P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742

P(X = 2) = C_{10,2}.(0.1)^{2}.(0.9)^{8} = 0.1937

P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740

P(X = 4) = C_{10,4}.(0.1)^{1}.(0.9)^{9} = 0.38742

So

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.34868 + 0.38742 + 0.19371 + 0.05740 + 0.01116 = 0.99837

Finally

P(X \geq 5) = 1 - P(X < 5) = 1 - 0.99837 = 0.00163

3 0
3 years ago
The state of New Jersey makes approximately $1.55 billion annually from tolls of the $1.55 billion about 3/4 comes from tolls on
Rama09 [41]

Percent of turn pike is 75% and percent of parkway is 25%.

<u>Solution:</u>

Given, The state of New Jersey makes approximately $1.55 billion annually from tolls of the $1.55 billion

About \frac{3}{4} comes from tolls on the turnpike

Remaining \frac{1}{4} comes from tolls on the parkway  

<em><u>To find the percent of the total revenue from turnpike:</u></em>

\begin{array}{l}{\text { Percent of turnpike }=\frac{\text { amount from parkway }}{\text { total revenue }} \times 100} \\\\ {=\frac{\frac{3}{4} \text { of total revenue }}{\text { tot al revenue }} \times 100} \\\\ {=\frac{\frac{3}{4} \times \text { total revenue }}{\text { total revenue }} \times 100} \\\\ {=\frac{3}{4} \times 100=3 \times 25=75 \%}\end{array}

<em><u>To find the percent of the total revenue from parkway:</u></em>

\begin{array}{l}{\text { Percent of parkway }=\frac{\text { amount from parkway }}{\text { total revenue }} \times 100} \\\\ {=\frac{\frac{1}{4} \text { of total revenue }}{\text { total revenue }} \times 100} \\\\ {=\frac{\frac{1}{4} \times \text { total revenue}}{\text { total revenue }} \times 100} \\\\ {=\frac{1}{4} \times 100=25 \%}\end{array}

<em><u>Summarizing the results:</u></em>

Percent of turn pike is 75%

Percent of parkway is 25%

3 0
3 years ago
What is the vertex of this equation y = -x^2+ 3
Svetach [21]

Answer: (0,3)

Step-by-step explanation: To find the x-value of the vertex for any quadratic, you can use the formula -b/2a. In this case, there is no clear b, but you can think of it like y=-x^2 +0x+3 so in the form ax^2 + bx +c, b=0. Therefore the x-value is 0/ -2, or 0. So we know the vertex is (0, y). To find y, just plug 0 into the original equation for x, getting you y=0+3, so y=3, so the vertex is (0,3)

4 0
3 years ago
Other questions:
  • a paramedic stocks ambulance with 4 boxes of gauze. , each box contains 12 gauze pads. they use 28 pafs. what fraction represent
    11·1 answer
  • 108/40 in its simplest form
    13·1 answer
  • A company sold equipment that originally cost $290000 for $203000 cash. The accumulated departing the equipment was $87000.The c
    10·1 answer
  • Add 4.136+29.95 and show all your work!<br><br> *please don't go on the internet and copy and paste*
    13·1 answer
  • Estimate the product of 54 x 68
    13·1 answer
  • Express the number in scientific notation. 63,600,000
    11·2 answers
  • Please help!<br> A- answer as a percent rounded to nearest tenth<br> B- answer as a fraction
    13·1 answer
  • Help please!!!!!!!!!!!!!!!!!!
    12·2 answers
  • After a robot vacuum is fully charged, it can run for 15 minutes. It can vacuum 1/2 square foot every second. Can a fully charge
    14·1 answer
  • A) Show that 4x² -6x+9 is positive for all values real numbers x.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!