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jok3333 [9.3K]
3 years ago
7

Given ABCE is a rectangle, D is the midpoint of CE Prove AD =~ BD

Mathematics
1 answer:
Bas_tet [7]3 years ago
5 0

Since the congruent operator is ≅ and since AD is congruent to BD, I'm going to assume that you want to prove that AD is congruent to BD.    
1. DE is equal to CD by definition since D is the midpoint of CE.  
2. AE is equal to BC since opposite sides of a rectangle are equal to each other.  
3. Angle AEC is equal to Angle BCE since all angles in a rectangle are right angles and all right angles are equal to each other.  
4. Triangles ADE and BDC are congruent to each other because we have SAS congruence for both triangles.  
5. AD is congruent to BC since they're corresponding sides of congruent triangles.
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Lifetime of $1 Bills The average lifetime of circulated $1 bills is 18 months. A researcher believes that the average lifetime i
OLEGan [10]
<h2>Answer with explanation:</h2>

Let \mu be the population mean lifetime of circulated $1 bills.

By considering the given information , we have :-

H_0:\mu=18\\\\H_a:\mu\neq18

Since the alternative hypotheses is two tailed so the test is a two tailed test.

We assume that the lifetime of circulated $1 bills is normally distributed.

Given : Sample size :  n=50 , which is greater than 30 .

It means the sample is large so we use z-test.

Sample mean : \overline{x}=18.8

Standard deviation : \sigma=2.8

Test statistic for population mean :-

z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

\Rightarrow\ z=\dfrac{18.8-18}{\dfrac{2.8}{\sqrt{50}}}\approx2.02

The p-value= 2P(z>2.02)=0.0433834

Since the p-value (0.0433834) is greater than the significance level (0.02) , so we do not reject the null hypothesis.

Hence, we conclude that we do not have enough evidence to support the alternative hypothesis that the average lifetime of a circulated $1 bill differs from 18 months.

6 0
3 years ago
A money bank has twice as many nickels as dimes. There is exactly $2.00 in the bank. How many nickels are there?
Makovka662 [10]
There is 16 nickels in 2 dollars
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−3(x−6)−3x⩾12equals ​
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The answer is X less than or equal to 1
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3 years ago
if a cylinder has a volume of approximately 125.6 cubic cm and has a height of 10cm what is the length of the radius
Elina [12.6K]

Answer:

radius = 4 cm

Step-by-step explanation:

To find the length of the radius, we will follow the step below;

First, write down the formula for finding the volume of a cylinder

v=πr²h

where v is the volume of a cylinder

r is the radius      and

h is the height of the cylinder

from the question given,

v=125.6    and h = 10 cm

we can now proceed to insert the values into the formula and solve for r

note that π is a constant which is equal to 3.14

v=πr²h

125.6 =3.14×r×10

125.6 =31.4 r

Divide both-side of the equation by 31.4

125.6/31.4 =31.4 r/31.4

4 = r

r =4 cm

The length of the radius = 4 cm

4 0
3 years ago
A movie rental store, Frank's Movies, offers customers two choices. Customers can pay a yearly membership of $45 and then rent e
STALIN [3.7K]

Answer:

13

Step-by-step explanation:

$45=3.50x

divide both sides by 3.50

13 movies (rounded to nearest whole number)

3 0
3 years ago
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