Draw the reflection of quadrilateral ABCD over the x-axis. Name the coordinates of each vertex.

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Nonamiya [84]

Answer:

a. x = 180 - (j + k)

b.

j + k = (5x - 2) + (2x - 2) = 7x - 4

l = x

x = 180 - (7x - 4)

x = 180 - 7x + 4

8x = 184

x = 184/8

x = 23

l = 23°

j = 5x - 2

j = 5 × 23 - 2

j = 115 - 2

j = 113°

k = 2x - 2

k = 2 × 23 - 2

k = 46 - 2

k = 44°

or k = 180 - (23 + 113) = 180 - 136 = 44°

3 0

3 years ago

Area of isosceles triangle with side 13cm base 10cm

Greeley [361]

Answer:

A=60cm²

Step-by-step explanation:

3 0

3 years ago

Which number in the set {6, 12, 18, 36} satisfies the equation 3x - 9 = 27? Explain

PIT_PIT [208]

Answer:

12

Step-by-step explanation:

3 x 12= 36

36-9= 27

3 0

3 years ago

A bank offers all savings accounts 5% interest compounded annually. If one account has a principal of $100 and another

arsen [322]

Answer:

From the calculation for both the accounts, it is clear that both the account double in the same time period of 14 years 26 days .

Step-by-step explanation:

Given as :

The principal for the first account = p = $100

The rate of interest = r = 5% compounded annually

The account gets double , so, Amount = A = $200

Let the time after which account gets double = t years

So, From Compound Interest method

Amount = Principal × $(1+\dfrac{\trxtrm rate}{100})^{\textrm time}$

As amount is double its principal

So, A = 2 × $100 = $200

Or, A = p × $(1+\dfrac{\trxtrm r}{100})^{\textrm t}$

Or, $200 = $100 × $(1+\dfrac{\trxtrm 5}{100})^{\textrm t}$

Or, $\dfrac{200}{100}$ = $(1.05)^{\textrm t}$

Or, 2 = $(1.05)^{\textrm t}$

Taking Log both side

$Log_{10}2$ = $Log_{10}(1.05)^{t}$

Or, 0.3010 = t $Log_{10}1.05$

Or, 0.3010 = t × 0.0211

∴ t = $\dfrac{0.3010}{0.0211}$

I.e t = 14.26

So, The time period to get account double is 14 years 26 days

Again

Amount = Principal × $(1+\dfrac{\trxtrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\trxtrm r}{100})^{\textrm t}$

As amount is double its principal

So, A = 2 × $1000 = $2000

Or, $2000 = $1000 × $(1+\dfrac{\trxtrm 5}{100})^{\textrm t}$

Or, $\dfrac{2000}{1000}$ = $(1.05)^{\textrm t}$

Or, 2 = $(1.05)^{\textrm t}$

Taking Log both side

$Log_{10}2$ = $Log_{10}(1.05)^{t}$

Or, 0.3010 = t $Log_{10}1.05$

Or, 0.3010 = t × 0.0211

∴ t = $\dfrac{0.3010}{0.0211}$

I.e t = 14.26

So, The time period to get account double is 14 years 26 days

Hence From the calculation for both the accounts, it is clear that both the account double in the same time period of 14 years 26 days . Answer

7 0

3 years ago

If the actual distribution of tusk lengths does not match the ones predicted with the H-W equation, it may indicate that natural

Anna [14]

Answer:

See explanation below

Step-by-step explanation:

It depends on what null hypothesis is under consideration.

One of the most common null hypothesis that are subject of study in a given statistical model is the mean predicted by the model.

In this case, the scientist probably observed that the mean of tusk lengths she obtained in a sample did not match the one predicted with the H-W equation.

So, she decided to perform a statistical study by collecting random samples and measuring the tusk lengths to determine a new possible mean and contrast it against the one predicted by the H-W equation.

Let's call M the mean predicted by the H-W equation, and S the mean obtained by the scientist.

If M different of S and the p-value is 0.021, that means that there is at most 2.1% of probability that the difference between M and S could be due to a random sampling error.

It should be kept in mind that the p-value does not represent the probability that the scientist is wrong.

7 0

3 years ago