Rewrite each of the following expressions without using absolute value. |2b| if b<0

Mary baked a batch of three dozen cookies for 40 woman at the woman's club. Next month the woman's club is expecting 60 women to

blondinia [14]

Answer:

6 dozen

Step-by-step explanation:

8 0

3 years ago

The mean GPA for 127 residents of the local apartment complex is 1.6. What is the best point estimate for the mean GPA for all r

madam [21]

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

The Central Limit Theorem established that, for a normally distributed random variable X, with mean and standard deviation, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation ;

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

The sample of 112 residents has a mean GPA of 1.7.

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

Learn more about Mean:

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4 0

2 years ago

How does algebra affect how people can learn from each other?

pantera1 [17]

Algebra is Faster And Better Than “Basic” Math

Just as multiplying two by twelve is faster than counting to 24 or adding 2 twelve times, algebra helps us solve problems more quickly and easily than we could otherwise. Algebra also opens up whole new areas of life problems, such as graphing curves that cannot be solved with only foundational math skills.

3 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

Show that the following statement is an identity by transforming the left side into the right side. sin θ (sec θ + csc θ) = tan

ExtremeBDS [4]

Answer:

Step-by-step explanation:

Required to prove that:

Sin θ(Sec θ + Cosec θ)= tan θ+1

Steps:

Recall sec θ= 1/cos θ and cosec θ=1/sin θ

Substitution into the Left Hand Side gives:

Sin θ(Sec θ + Cosec θ)

= Sin θ(1/cos θ + 1/sinθ )

Expanding the Brackets

=sinθ/cos θ + sinθ/sinθ

=tanθ+1 which is the Right Hand Side as required.

Note that from trigonometry sinθ/cosθ = tan θ

8 0

4 years ago