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
Tpy6a [65]
3 years ago
13

What is the solution to this inequality: -4(3x-5)<2(3x+4)​

Mathematics
1 answer:
Delicious77 [7]3 years ago
7 0

Answer:

x > 2/3

Step-by-step explanation:

-4(3x - 5) < 2(3x + 4)​

Divide both sides by 2.

-2(3x - 5) < 3x + 4

Distribute on the left side.

-6x + 10 < 3x + 4

Subtract 3x from both sides.

-9x + 10 < 4

Subtract 10 from both sides.

-9x < - 6

Divide both sides by -9. Remember that when you divide both sides of an inequality by a negative number, the inequality sign changes direction.

x > (-6)/(-9)

x > 6/9

x > 2/3

You might be interested in
An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce p
ludmilkaskok [199]

Answer:

a) y=-0.317 x +46.02

b) Figure attached

c) S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03

Step-by-step explanation:

We assume that th data is this one:

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

a) Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720

\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324

\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200

\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540

\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900

And the slope would be:

m=-\frac{1900}{6000}=-0.317

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60

\bar y= \frac{\sum y_i}{n}=\frac{324}{12}=27

And we can find the intercept using this:

b=\bar y -m \bar x=27-(-0.317*60)=46.02

So the line would be given by:

y=-0.317 x +46.02

b) Plot the points and graph the line as a check on your calculations.

For this case we can use excel and we got the figure attached as the result.

c) Calculate S^2

In oder to calculate S^2 we need to calculate the MSE, or the mean square error. And is given by this formula:

MSE=\frac{SSE}{df_{E}}

The degred of freedom for the error are given by:

df_{E}=n-2=12-2=10

We can calculate:

S_{y}=\sum_{i=1}^n y^2_i -\frac{(\sum_{i=1}^n y_i)^2}{n}=9540-\frac{324^2}{12}=792

And now we can calculate the sum of squares for the regression given by:

SSR=\frac{S^2_{xy}}{S_{xx}}=\frac{(-1900)^2}{6000}=601.67

We have that SST= SSR+SSE, and then SSE=SST-SSR= 792-601.67=190.33[/tex]

So then :

S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03

5 0
3 years ago
Which of the following statement is false?​
emmainna [20.7K]

Answer:

D.) rational numbers are associative under subtraction

Step-by-step explanation:

rational numbers are closed under subtraction

↳ TRUE

zero is the identity for addition of rational numbers

↳ TRUE

subtraction is the inverse of the addition

↳ TRUE

rational numbers are associative under subtraction

↳ FALSE

5 0
2 years ago
In a school of 300 students, 110 offered French, 110 Hausa language, 180 history, 40 French and Hausa, 50 Hausa and history, 60,
Julli [10]

Answer:

Step-by-step explanation:

a

8 0
3 years ago
You have 60 waffles in all with a serving size of 2 waffles, there are 4 people, how many days will the waffles last. Show equat
Alja [10]
30÷2 =60
15 days 4×7=
5 0
3 years ago
Solve -14 +5x =-12 really need this answer
Paladinen [302]
Move the 14 over and get
5x = 2
divide by 5
x = 2/5
7 0
3 years ago
Read 2 more answers
Other questions:
  • What is scientific notation?
    13·2 answers
  • Please Help, WILL GIVE THANKS AND STARS
    13·1 answer
  • Can someone help me please? I don't know how to do this problem, could someone explain step by step? It would be greatly appreci
    5·2 answers
  • Davina selected 50 people at random and asked them whether they had watched the documentary on Antarctica on television the prev
    5·2 answers
  • A train is travelling from new orleans at a constant speed of 79 hours per hour. New Orleans and memphis are miles apart. How lo
    10·1 answer
  • Solve this equation with a variable term on both sides. 5.1y = –0.3y – 21.6 What is the solution? y =
    10·2 answers
  • Did you mean: a dolphin was swimming 28 meters below the ocean's surface it changed its depth to avoid a predator and ended up 2
    5·1 answer
  • 5. A jewelry store is having a 50% off sale
    10·1 answer
  • 7.) You and your friend go to a Mexican restaurant. You order 2 tacos and 2 enchiladas. Your friend
    8·1 answer
  • I've done the y = equations but I don't know how to do this one.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!