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3 years ago

If a system of two inequalities has a solution, then their two half planes intersect , true or false ?

Mathematics

1 answer:

Nana76 [90]3 years ago

7 0

Answer: The answer is true.

Step-by-step explanation: The given statement is

'If a system of two inequalities has a solution, then their two half planes intersect'.

We are to check whether the statement is true or false.

Let a system of two inequalities be

$x+y\geq 3,\\\\2x+5y\leq 10.$

These inequalities has a solution, for example, x = 2, y = 1.

Plotting these inequalities on a graph paper (please see the attached graph), we see that the two half planes intersect, which is represented by the double shaded region in the graph.

Thus, the given statement is TRUE.

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Complete the proof in picture

BARSIC [14]

it won't let me type the answer I may be missing something but it says I am using rude words so sorry if I am

5 0

3 years ago

Two surfers and statistics students collected data on the number of days on which surfers surfed in the last month for 30 longbo

Alisiya [41]

Answer:

Do not reject H0. The mean days surfed for longboarders is significantly larger than the mean days surfed for all shortboarders

Step-by-step explanation:

The null hypothesis is that the mean days surfed for all long boarders is larger than the mean days surfed for all short boarders

H0: μL > μs against the claim Ha: μL≤ μs

the alternate hypothesis is the mean days surfed for all long boarders isless or equal to the mean days surfed for all short boarders (because long boards can go out in many different surfing conditions)

The test statistic is

t= x1- x2/ √s1/n1+ s2/n2

1) Calculations

Longboards

Mean

ˉx=∑x/n=4+8+9+4+9+7+9+6+6+11+15+13+16+12+10+12+18+20+15+10+15+19+21+9+22+19+23+13+12+10/30

=377/30

=12.5667

Longboard Variance S2=[∑dx²-(∑dx)²/n]/n-1

=[831-(-13)²/30]/29

=831-5.6333/29

=825.3667/29

=28.4609

Shortboard Mean

ˉx=∑x/n=6+4+6+6+7+7+7+10+4+6+7+5+8+9+4+15+13+9+12+11+12+13+9+11+13+15+9+19+20+11/30

=288/30

=9.6

Shortboard Variance S2=[∑x²-(∑x)²/n]/n-1

=[ 3270-(288)2/30]/29

=3270-2764.8/29

=505.2/29

=17.4207

2) Putting values in the test statistic

t=|x1-x2|/√S²1/n1+S²2/n2

t =|12.5667-9.6|/√28.4609/30+17.4207/30

t =|2.9667|/√0.9487+0.5807

t=|2.9667|/√1.5294

t=|2.9667|/1.2367

t=2.3989

3) Degree of freedom =n1+n2-2=30+30-2=58

4) The critical region is t ≤ t(0.05) (58) =1.6716

5) Since the calculated t= 2.4 does not fall in the critical region t(0.05) (58) ≤ 1.6716 we do not reject H0.

The p-value is 0.008969. The result is significant at p <0 .05.

6 0

3 years ago

Help me with question 7 pls

Marrrta [24]

If the coefficient of x^2 is negative, the graph will be n shaped and curve down instead of like a u shape if it was positive. If the vertex is below the x axis and curves down, it won’t pass the x axis, Tia is right.

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2 years ago

Marco needs 2 gal of paint, he has 10 qts is that enough, explain

DiKsa [7]

Yes it is. A gallon is 4 quarts, so he has more than enough. He has 2 quarts extra.

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3 years ago

Please help!!!!!!!!!!

lapo4ka [179]

Answer: 18.7

Step-by-step explanation:

Find the lengths of AB, BC, and CA