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2 years ago

Write an inequality for the situation. all real numbers at most –9.5 or at least 5.5

Mathematics

2 answers:

Tomtit [17]2 years ago

8 0

Hello,

If b represents any real number,

b<=-9.5
or
5.5<=b

Answer C

dexar [7]2 years ago

3 0

Answer:

option (c) is correct.

The given expression all real numbers at most –9.5 or at least 5.5 is written as b ≤ –9.5 or b ≥ 5.5

Step-by-step explanation:

Given expression all real numbers at most –9.5 or at least 5.5

We have to represent the given expression mathematically and choose the correct from given options.

Consider the given expression all real numbers at most –9.5 or at least 5.5

Let the real number be represented by b

then the given expression contain two terms

1) all real numbers at most –9.5

Mathematically written as b ≤ –9.5 .....(1)

2) all real numbers at least 5.5

Mathematically written as b ≥ 5.5 ....(2)

Thus, the given expression all real numbers at most –9.5 or at least 5.5 is written as b ≤ –9.5 or b ≥ 5.5

Thus, option (c) is correct.

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Which equation can pair with x + 2y = 5 to create an inconsistent system?

Charra [1.4K]

X + 2y = 5
x = 5 - 2y

2x + 4y = 3
2(5-2y) + 4y = 3
10 - 4y + 4y = 3
10 ≠ 3

5x + 2y = 3
5(5-2y) + 2y = 3
25 - 10y + 2y = 3
-8y = 3 - 25
-8y = -22
y = -22/-8
y = 2.75

6x + 12y = 30
6(5-2y) + 12y = 30
30 -12y + 12y = 30
30 = 30

3x + 4y = 8
3(5-2y) + 4y = 8
15 - 6y + 4y = 8
-2y = 8 - 15
-2y = -7
y = -7/-2
y = 3.5

An inconsistent system is a system of equation that has NO SOLUTIONS.

2x + 4y = 3 is the equation to be paired with x + 2y = 50 to create an inconsistent system.

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2 years ago

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What is an equation for the linear function whose graph contains the points (9, 7) and (4, −8) ? Enter your answers in the boxes

Ahat [919]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~{{ 9}} &,&{{ 7}}~) 
% (c,d)
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\end{array}
\\\\\\
% slope = m
slope = {{ m}}\implies 
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{-8-7}{4-9}\implies \cfrac{-15}{-5}\implies \cfrac{3}{1}\implies 3$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-7=3(x-9)$

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2 years ago

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Dawn raises money for her school in a jog-a-thon. She will get three dollars for every lap she completes. If it takes 4 laps to

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If Dawn gets 3$ for every lap she completes and 1 mile is 4 laps, and it says she runs 11 miles you would do 4 multiplied by 3, which is 12, once you get that answer you would multiply 12 by 11 and your answer would be: 132$
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A batch of 445 containers for frozen orange juice contains 3 that are defective. Two are selected, at random, without replacemen

Elan Coil [88]

Answer:

When Two containers are selected

(a) Probability that the second one selected is defective given that the first one was defective = 0.00450

(b) Probability that both are defective = 0.0112461

(c) Probability that both are acceptable = 0.986

2. When Three containers are selected

(a) Probability that the third one selected is defective given that the first and second one selected were defective = 0.002.

(b) Probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay = 0.00451

(c) Probability that all three are defective = 6.855 x $10^{-8}$ .

Step-by-step explanation:

We are given that a batch of 445 containers for frozen orange juice contains 3 defective ones i.e.

Total containers = 445

Defective ones = 3

Non - Defective ones = 442 { Acceptable ones}

Two containers are selected, at random, without replacement from the batch.

(a) Probability that the second one selected is defective given that the first one was defective is given by;

Since we had selected one defective so for selecting second the available

containers are 444 and available defective ones are 2 because once

chosen they are not replaced.

Hence, Probability that the second one selected is defective given that the first one was defective = $\frac{2}{444}$ = 0.00450

(b) Probability that both are defective = P(first being defective) +

P(Second being defective)

= $\frac{3}{445} + \frac{2}{444}$ = 0.0112461

Since, total number of acceptable containers are 442 and total containers are 445.

So, Required Probability = $\frac{442}{445}*\frac{441}{444}$ = 0.986

Three containers are selected, at random, without replacement from the batch.

(a) Probability that the third one selected is defective given that the first and second one selected were defective is given by;

Since we had selected two defective containers so now for selecting third defective one, the available total containers are 443 and available defective container is 1 .

Therefore, Probability that the third one selected is defective given that the first and second one selected were defective = $\frac{1}{443}$ = 0.002.

(b) Probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay is given by;

Since we had selected two containers so for selecting third container to be defective, the total containers available are 443 and available defective containers are 2 as one had been selected.

Hence, Required probability = $\frac{2}{443}$ = 0.00451 .