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2 years ago

Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply.

Mathematics

2 answers:

HACTEHA [7]2 years ago

7 0

Answer:

$x=0$ and $x=10$

Step-by-step explanation:

The inequality is given as: $4(2-x)>-2x-3(4x+1)$

Using distributive property [ $a(b+c)=ab+ac$ ] and a little algebra, we have:

$4(2-x)>-2x-3(4x+1)\\8-4x>-2x-12x-3\\$

Taking all the x's to one side and number to another:

$-4x+2x+12x>-3-8\\10x>-11\\x>\frac{-11}{10}\\x>-1.1$

Now, of the 5 numbers shown, which of them are GREATER THAN $-1.1$ ?

They are 0 and 10.

steposvetlana [31]2 years ago

4 0

4(2 - x) > -2x - 3(4x + 1)
8 - 4x > -2x - 12x - 3
-4x + 2x + 12x > -3 - 8
10x > -11
x > -11/10
x > -1.1

Therefore, x = 0 and x = 10 zre solutions to the inequality.

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Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty perso

Step2247 [10]

Answer:

the probability is 0.1143

Step-by-step explanation:

here are the details from the question you asked

number of people = 6

nuber of weapons = 6

number of rooms = 9

after narrowing it down to

3 people,3 weapons, and 6 rooms

= ⁶C₃ * ⁶C₃ *⁹C₆ / ²¹C₁₂

= 20 * 20 * 84 / 293930

= 33600/293930

= 0.1143

The probability of making a random guess of the person who is guilty, weapon and location from this choices that have been narrowed down and the guess being correct is 0.1143

7 0

2 years ago

Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of

Strike441 [17]

Answer:

Step-by-step explanation:

The two force F1 and F2 are represented by vectors with initial points that are at the origin.

the terminal point of the vector is point P(1, 1, 0)

Therefore, the direction of the vector force is

$v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j$

The unit vector in the direction of force will be

$\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}$

The magnitude of the force is 40lb, so the force will be

$F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)$

The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

$v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k$

$\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}$

The magnitude of the force is 60lb, so the force will be

$F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)$

The resultant of the two forces is

$F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k$

The magnitude force will be

$|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68$

to (1 decimal place)=55.7lb

b) The direction angle of force F

The angle formed by F and x axis

$\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469$

The angle formed by F and y axis

$\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=$

The angle formed by F and z axis

$\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359$

8 0

2 years ago

Which describes money that is received from sales of goods or services?

Lana71 [14]

the answer would be revenue

7 0

2 years ago

Sue wants to paint the longest wall in her bedroom pink. she measured the wall and found that it is 10 feet long and 8 feet tall

jekas [21]

Answer:

Sue should buy 1.6 quart of paint.

Step-by-step explanation:

First we need to find out the area of longest wall

Area =length × breadth

Area= 10 × 8 = 80 square feet

To cover 50 square feet we have required 1 quart of paint

So for covering 1 square feet we have required 1/50 quart of paint

So for covering 80 square feet we have required ( 1×80 ) / 50 quart

= 1.6 quart of paint

6 0

2 years ago

A study was conducted to determine if there was a difference in the driving ability of students from West University and East Un

Sholpan [36]

Answer:

There is no significant evidence which shows that there is a difference in the driving ability of students from West University and East University, assuming a significance level 0.1

Step-by-step explanation:

Let p1 be the proportion of West University students who involved in a car accident within the past year

Let p2 be the proportion of East University students who involved in a car accident within the past year

Then

$H_{0}:$ p1=p2

$H_{a}:$ p1≠p2

The formula for the test statistic is given as:

z= $\frac{p1-p2}{\sqrt{\frac{p*(1-p)*(n1+n2)}{n1*n2} } }$ where

p1 is the sample proportion of West University students who involved in a car accident within the past year (0.15)
p2 is the sample proportion of East University students who involved in a car accident within the past year (0.12)

p is the pool proportion of p1 and p2 ( $\frac{15+12}{100+100}=0.135$ )
n1 is the sample size of the students from West University (100)
n2 is the sample size ofthe students from East University (100)

Then we have z= $\frac{0.03}{\sqrt{\frac{0.135*0.865*(100+100)}{100*100} } }$ ≈ 0.6208

Since this is a two tailed test, corresponding p-value for the test statistic is ≈ 0.5347.

Assuming significance level 0.1, The result is not significant since 0.5347>0.1. Therefore we fail to reject the null hypothesis at 0.1 significance

6 0

2 years ago