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3 years ago

In 2017, there were about 21 million teenagers (aged 13-17) in the United States. They each

Mathematics

1 answer:

vivado [14]3 years ago

5 0

The Number of text messages sent in a month is 1.68 × $10^{(-8)}$

Step-by-step explanation:

Step 1 :

Total number of teenagers in United States = 21 million

Average text messages sent per month = 800

We need to find the number of text messages sent each month

Step 2 :

The number of text messages in a month can be computed by taking the product of the total number of teenagers and average messages sent per month

Therefore

Number of text messages that is sent in a month = 21 million × 800

= 21 × $10^{6}$ × 800

= 168 × $10^{6}$ = 1.68 × $10^{(-8)}$

Step 3 :

Answer :

The Number of text messages that is sent in a month is 1.68 × $10^{(-8)}$

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Georgianna claims that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

Allisa [31]

Answer:

The condition are

The Null hypothesis is $H_o : \mu = 5$

The Alternative hypothesis is $H_a : \mu < 5$

The check revealed that

There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 5 \ year$

The sample size is n = 20

The sample mean is $\= x = 4.6 \ years$

The standard deviation is $\sigma = 2.2 \ years$

The Null hypothesis is $H_o : \mu = 5$

The Alternative hypothesis is $H_a : \mu < 5$

So i will be making use of $\alpha = 0.05$ level of significance to test this claim

The critical value of $\alpha$ from the normal distribution table is $Z_\alpha = 1.645$

Generally the test statistics is mathematically evaluated as

$t = \frac{\= x - \mu}{ \frac{\sigma }{\sqrt{n} } }$

substituting values

$t = \frac{ 4.6 - 5}{ \frac{2.2}{\sqrt{20} } }$

$t = -0.8131$

Looking at the value of t and $Z_{\alpha }$ we see that $t < Z_{\alpha }$ so we fail to reject the null hypothesis

This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

4 0

2 years ago

Which biconditional is not a good definition?

Xelga [282]

The correct answers are:

A ray is a bisector of an angle if and only if it splits the angle into two angles; and
A) I can afford to buy a ticket.

Explanation:

For the first question, the first three answers are very specific and true:

A whole number is odd if it is not divisible by 2, and a number is not divisible by 2 if it is odd;
an angle is straight if its measure is 180 degrees, and the measure of an angle is 180 degrees if it is a straight angle;
a whole number is even if it is divisible by 2, and a number is divisible by 2 if it is even.

However, with the fourth choice, we are missing a key word in the definition. A ray is a bisector of an angle if and only if it splits the angle into two CONGRUENT angles. It is not just a ray that cuts an angle into two pieces, the pieces must be equal.

For the second question, the Law of Detachment says if our conditional "if p, then q" is true and p is true, then q must also be true.

For this question, "I can go to the concert if I can afford to buy a ticket" is true as well as "I can go to the concert." This means "I can afford to buy a ticket" must be true as well.

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3 years ago

Which expression is equivalent to 7a^3(6a^2+a^2)-4a^6?

Thepotemich [5.8K]

Simply simplify:

7a³(7a²)-4a^6 ⇒ 49a^6 - 4a^6 ⇒ 45a^6

Hope that helps!

3 0

3 years ago

1. Point C lies on BD. Draw a diagram and label the parts. If BC = 52.39 mm and CD = 21.83 mm, what is

kondaur [170]

Answer:

74.32

Step-by-step explanation: