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3 years ago

The triangles shown are congruent. Which of the following statements must be true? A. YZ = JG

Mathematics

1 answer:

BaLLatris [955]3 years ago

8 0

D. m < Y = m < H

It is because they both are adjacent angles to perpendicular. and opposite sites are equal to their magnitude is same

Hope this helps!

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Construct a 99% confidence interval for the population mean, mu. Assume the population has a normal distribution. A group of 1

Zarrin [17]

Answer:

99% confidence interval for the population mean is [19.891 , 24.909].

Step-by-step explanation:

We are given that a group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

Assuming the population has a normal distribution.

Firstly, the pivotal quantity for 99% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean age of selected students = 22.4 years

s = sample standard deviation = 3.8 years

n = sample of students = 19

$\mu$ = population mean

Here for constructing 99% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.878 < $t_1_8$ < 2.878) = 0.99 {As the critical value of t at 18 degree of

freedom are -2.878 & 2.878 with P = 0.5%}

P(-2.878 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.878) = 0.99

P( $-2.878 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.878 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ , $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ]

= [ $22.4 -2.878 \times {\frac{3.8}{\sqrt{19} }$ , $22.4 +2.878 \times {\frac{3.8}{\sqrt{19} }$ ]

= [19.891 , 24.909]

Therefore, 99% confidence interval for the population mean is [19.891 , 24.909].

6 0

3 years ago

On a school trip to a theme park, 4 busses each carry 70 students.

DanielleElmas [232]

Answer:

165 Students Have No Made Plans For Lunch.

Step-by-step explanation:

According To the Question,

Given,On a school trip to a theme park, 4 busses each carry 70 students Then Total Number Of Students on a trip is 70×4=280 Students.

And,35% of the students are bringing their own lunch. Thus,35% Of 280 Students is 98 Students. Then Remaining 182 Students not bring their own lunch.

Now, 17 of the students are buying lunch when they get to the theme park. Thus students Who have not made plans for lunch is 182-17⇒165Students

7 0

3 years ago

D Question 5 5. Given A is between Y and Z and YA = 14x, AZ = 10x and YZ = 12x + 48, find AZ

Anna007 [38]

Answer:

Step-by-step explanation:

If A is in between Y and Z, then;

YA+AZ = YZ

Given.

YA = 14x,

AZ = 10x and

YZ = 12x + 48

Substitute into the formula

14x+10x = 12x+48

Find x;

24x = 12x+48

24x-12x = 48

12x = 48

x = 48/12

x = 4

Get AZ

AZ = 10x

AZ =10(4)

AZ = 40

3 0

3 years ago

How are radicals and rational exponents related?

icang [17]

Answer:

Any radical in the form can be written using a fractional exponent in the form . The relationship between and works for rational exponents that have a numerator of 1 as well. For example, the radical can also be written as , since any number remains the same value if it is raised to the first power.

Step-by-step explanation:

8 0

3 years ago

What time and day will it be 154hr 36 mins after Thursday 1:26pm?

loris [4]

Answer:

12:02 AM on the next Thursday

Step-by-step explanation:

First we wanna find how many days that is. 154/24. that is 6 and 5/12 days.

5/12 of a day is equal to 10/24, so 10 hours, sice there are 24 hours in a day.

so that's 10 hours and 36 minutes which equals 2:02 pm + 10 hours 12:02 AM on Friday

Now just add the 6 days so 12:02 AM on the next Thursday

5 0

3 years ago