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3 years ago

Half a number is at least 2 units from 20. write the sentence as an absolute value inequality

Mathematics

2 answers:

Anuta_ua [19.1K]3 years ago

8 0

Answer:

|1/2x - 20| ≥ 2

Step-by-step explanation:

The number is half of two and at least two units away.

sammy [17]3 years ago

6 0

Answer:

$|20-\dfrac{x}{2}|\geq 2$

Step-by-step explanation:

Half a number is at least 2 units from 20.

Let number be x

Write phrase as inequality.

"Half a number" $\Rightarrow \dfrac{x}{2}$

"From 20" $\Rightarrow 20-\dfrac{x}{2}$

"at least 2" $\Rightarrow \geq2$

Absolute inequality:

$|20-\dfrac{x}{2}|\geq 2$

Hence, The absolute value inequality is $|20-\dfrac{x}{2}|\geq 2$

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Wendy is standing 60 feet away from a tree. Her eyes are 5 feet above the ground. She sees a bird hovering above a tree. The ang

Gennadij [26K]

The bird is 17 feet above the tree.

Explanation:

We need to think of this in terms of right triangles. If Wendy is 60 feet from a tree, the base of the right triangle is 60 feet. The height of the tree is the height of the right triangle. The angle of elevation is the one from the ground at her feet to the top of the tree and then to the bird. Let's start with the top of the tree first.

She's 60 feet away, we have the angle of elevation as 25 degrees, and we are looking for the height of the tree. In regards to the angle, the base of 60 is adjacent, and the height of the tree is opposite. The tangent ratio is height / base.

Let x be the height of the tree.

So,

$tan (25) = \frac{x}{60}$

$60 tan(25) = x\\\\x = 27.9 feet$

x is approximately 28 feet

Since, Wendy's eyes are 5 feet above the ground, the height of the tree becomes

28 + 5 = 33 feet

For bird

Let y be the height of the bird in the air

$tan(37) = \frac{y}{60} \\\\60 tan(37) = y\\\\y = 45.2 feet$

y is approximately 45 feet

Since, Wendy's eyes are 5 feet above the ground, the height of the tree becomes

45 + 5 = 50 feet

To know how far above the tree that bird is

50 - 33 = 17 feet

Therefore, the bird is 17 feet above the tree.

3 0

3 years ago

g A fair coin is tossed 20 times. The number of heads observed is the count X of successes. Give the distribution of X . Choose

Nuetrik [128]

Answer:

We assume that we have a fair coin that is $p(Head)=p(Tails)=0.5$

For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:

$X \sim Binom(n=20, p=0.5)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

We assume that we have a fair coin that is $p(Head)=p(Tails)=0.5$

For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:

$X \sim Binom(n=20, p=0.5)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

3 0

3 years ago

Choose the quadrilateral that is not a rhombus of congruent sides and two angle that each measure 120 degrees

Amanda [17]

Answer for the above question is option C

Step-by-step explanation:

Option C - It's a quadrilateral but not a rhombus . As we know rhombus has congruent sides while its two angle can't be measured 120 degrees but in option C it seems two vertically opposite angles of to be 120 degrees. In rhombus opposite angles are same while adjacent angles are supplementary. All options except C are the rhombus of congruent sides.

5 0

3 years ago

Divide

mote1985 [20]

Answer:

0.014767

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

WILL GIVE BRAINLIEST ANSWER! A circular flower bed is 21 m in diameter and has a circular sidewalk around it that is 33m wide. F

Alina [70]

Answer:

The area of the sidewalk is 144.44 m².

The 2-m wide walk adds 4 m to the diameter, making it 21+4=25.

Since the radius is half the diameter, r = 25/2 = 12.5.

The area of the entire bed with walkway is 3.14(12.5)² = 490.625 m².

The diameter of the bed is 21, so the radius is 21/2 = 10.5.

The area of just the flower bed is 3.14(10.5)² = 346.185.

The difference between the two is 490.625-346.185 = 144.44 m². This is the area of the walkway.

Have a Great Day!

5 0

3 years ago