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miv72 [106K]
2 years ago
12

Using a number line, find both the intersection and the union of the following intervals: (−3, +∞) and (4, +∞)

Mathematics
1 answer:
sammy [17]2 years ago
3 0

Answer:

The intersection of the two intervals = 4, 5, 6,.......+∞ = (4, +∞)

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞ = (-3, +∞)

Step-by-step explanation:

The given intervals are;

First interval  = (-3, +∞)

Second interval  = (4, +∞)

Using the number line, we therefore, the first interval includes, -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞

The second interval includes, 4, 5,.....,+∞

Which gives the intersection as 4, 5, 6,.......+∞

The union is the interval that combines the two sets of intervals which is given as follows;

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞

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he Statue of Liberty is approximately 305 feet tall. If the angle of elevation of a ship to the top of the statue is 22.9 degree
Andru [333]

Answer:

is at a distance of 722 feet

Step-by-step explanation:

we have the angle that forms between the water and the imaginary line between the ship and the tip of the statue

we have the statue height that would be the opposite leg to our angle and we want to know the distance of the ship to the statue that would be the adjacent leg

we see that it has (angle, adjacent, opposite)

well to start we have to know the relationship between angles, legas and the hypotenuse

a: adjacent

o: opposite

h: hypotenuse

sin α = o/h

cos α= a/h

tan α = o/a

it's the tangent

tan α = o/a

we replace the values ​​and solve

tan α = o/a

tan 22.9 = 305/a

a = 305/tan22.9

a = 305/0.4224

a = 722

is at a distance of 722 feet

7 0
2 years ago
Read 2 more answers
From 99° to 70°f what is the percent decrease
SSSSS [86.1K]

Answer:

should be -29.29 %

Step-by-step explanation:

8 0
2 years ago
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Write fifty two and 40 hundredths in the standard form decimal ​
Mashutka [201]

Answer:

52.4

Step-by-step explanation:

40 hundredths as a decimal is 40/100 which is .40.

The "fifty two" is a whole number which is in front of the ".40" which makes 52.4 or 52.40.

5 0
3 years ago
The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches.
Mama L [17]

Answer:

a) P(Y > 76) = 0.0122

b) i) P(both of them will be more than 76 inches tall) = 0.00015

   ii) P(Y > 76) = 0.0007

Step-by-step explanation:

Given - The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches.

To find - (a) If a man is chosen at random from the population, find

                    the probability that he will be more than 76 inches tall.

              (b) If two men are chosen at random from the population, find

                    the probability that

                    (i) both of them will be more than 76 inches tall;

                    (ii) their mean height will be more than 76 inches.

Proof -

a)

P(Y > 76) = P(Y - mean > 76 - mean)

                 = P( \frac{( Y- mean)}{S.D}) > \frac{( 76- mean)}{S.D})

                 = P(Z >  \frac{( 76- mean)}{S.D})

                 = P(Z > \frac{76 - 69.7}{2.8})

                 = P(Z > 2.25)

                 = 1 - P(Z  ≤ 2.25)

                 = 0.0122

⇒P(Y > 76) = 0.0122

b)

(i)

P(both of them will be more than 76 inches tall) = (0.0122)²

                                                                           = 0.00015

⇒P(both of them will be more than 76 inches tall) = 0.00015

(ii)

Given that,

Mean = 69.7,

\frac{S.D}{\sqrt{N} } = 1.979899,

Now,

P(Y > 76) = P(Y - mean > 76 - mean)

                 = P( \frac{( Y- mean)}{\frac{S.D}{\sqrt{N} } })) > \frac{( 76- mean)}{\frac{S.D}{\sqrt{N} } })

                 = P(Z > \frac{( 76- mean)}{\frac{S.D}{\sqrt{N} } })

                 = P(Z > \frac{( 76- 69.7)}{1.979899 }))

                 = P(Z > 3.182)

                 = 1 - P(Z ≤ 3.182)

                 = 0.0007

⇒P(Y > 76) = 0.0007

6 0
3 years ago
9328553.99 multiply by 10 the decimal will move one place to the left or two places to the left or one place to the right or two
VARVARA [1.3K]
93285539.900000000000
7 0
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