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Harrizon [31]
3 years ago
14

Which value is included in the solution set for the inequality graphed one the number line?

Mathematics
1 answer:
Soloha48 [4]3 years ago
6 0

<em>We can also graph inequalities on the number line. The following graph represents the inequality x≤2 . The dark line represents all the numbers that satisfy x≤2 . If we pick any number on the dark line and plug it in for x, the inequality will be true.</em>

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Square ABCD and isosceles triangle BUC are drawn to create trapezoid AUCD. Square A B C D and triangle B U C are attached at sid
Art [367]

Answer:

d) 135º

Step-by-step explanation:

Note that the angle DCU is the sum of the angles DCB and BCU. The angle DCB is 90º because A B C D is a square, then all its angles are equal to 90º.

After attaching B U C to A B C D, we obtain a trapezoid A U C D. Since A U C D has at least one pair of parallel sides, then AU should be parallel to CD, thus the angle CBU must be 90º.

B U C is isoceles, so we conclude that other two angles must have the same size, and due to the sum of the angles of a triangle being 180º, then both BUC and BCU are equal to 45º

As a result, the angle DCU is equal to 90º+45º = 135º. Option d is the correct one.

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3 years ago
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3 years ago
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Please procedure and solution <br><br>2 x |-6|-3 x |2|+|-14|=​
lora16 [44]

Applying the rule of modulus for given values, the expression will result to 20.

<h3>What is Modulus or Absolute Values</h3>

The modulus of a value for example |a|=a if a is greater than or equal to zero

and also

|a|=-a if a is less than zero

In the expression given; the modulus of -6 written as

|-6|=-(-6) this is because the value is less than zero

The modulus of 2 written as; |2|=2 this is because the value is greater than zero. and;

|The modulus of -14 written as; |-14|= -(-14) since the value is less than zero.

Hence, we can rewrite the expression as;

we deal with multiplication first following the rules of BODMAS

2×-(-6)-3×2+[-(-14)]

2×6-6+14

and thus adding values

12+14-6

and finally we subtract;

26-6

which will results to the solution of 20.

5 0
2 years ago
Last year 64 new houses were built in a neighborhood so far this year 7/8 of them have been sold how many new houses have been s
laiz [17]

Answer:

56

Step-by-step explanation:

for this problem you would first figure out what 1/8 of 64 is. 1/8 of 64 is 8.so we do 7*8 to get 56 so 56 of the 64 houses have been sold

6 0
2 years ago
Consider a system with one component that is subject to failure, and suppose that we have 115 copies of the component. Suppose f
castortr0y [4]

Answer:

Step-by-step explanation:

From the given information:

the mean (\mu) = 115 \times 20

= 2300

Standard deviation = 20 \times \sqrt{115}

Standard deviation (SD) = 214.4761

TO find:

a) P(x > 3500)= P(Z > \dfrac{3500-\mu}{214.4761})

P(x > 3500)= P(Z > \dfrac{3500-2300}{214.4761})

P(x > 3500)= P(Z > \dfrac{1200}{214.4761})

P(x > 3500)= P(Z >5.595)

From the Z-table, since 5.595 is > 3.999

P(x > 3500)=1-0.9999

P(x > 3500) = 0.0001

b)

Here, the replacement time for the mean (\mu) = \dfrac{0+0.5}{2}

= 0.25

Replacement time for the Standard deviation \sigma = \dfrac{0.5-0}{\sqrt{12}}

\sigma = 0.1443

For 115 component, the mean time = (115 × 20)+(114×0.25)

= 2300 + 28.5

= 2328.5

Standard deviation = \sqrt{(115\times 20^2) +(114\times (0.1443)^2)}

= \sqrt{(115\times 400) +(114\times 0.02082249}

= \sqrt{(46000) +2.37376386}

= \sqrt{(46000) +(2.37376386)}

= \sqrt{46002.374}

= 214.482

Now; the required probability:

P(x > 4125) = P(Z > \dfrac{4125- 2328.5}{214.482})

P(x > 4125) = P(Z > \dfrac{1796.5}{214.482})

P(x > 4125) = P(Z >8.376)

P(x > 4125) =1-  P(Z

From the Z-table, since 8.376 is > 3.999

P(x > 4125) = 1 - 0.9999

P(x > 4125) = 0.0001

7 0
2 years ago
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