Abby has a collection of 61 dimes and nickels worth $4.40. How many nickels does she have? answer

Which statements are true regarding triangle LMN? Check all that apply.

dimaraw [331]

Answer:

$NM = x$

$LM = x\sqrt{2}$

$tan (45) = 1$

Step-by-step explanation:

Step 1: Pythagoras Theorem

Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:

$LM^{2} =LN^{2} +NM^{2}$

Step 2: Trigonometric Functions

Only for a right angle triangle following three trigonometric relations are valid

$sin (\theta) = \frac{opposite}{hypotenuse}$

$cos (\theta) = \frac{adjacent}{hypotenuse}$

$tan (\theta)=\frac{sin (\theta)}{cos (\theta)} = \frac{opposite}{adjacent}$

Step 3: Verifying all the possible answers

A: Since, LN = x and using $tan (45) =1$

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{NM}{x} =1$

therefore, NM = x (true)

B: As NM = x therefore it can not be equal to $x\sqrt{2\\}$ .

C: Using Pythagoras Theorem

$LM^{2} =LN^{2} +NM^{2}$

$LM^{2} =x^{2} +x^{2}$

$LM^{2} =2x^{2}$

$LM = \sqrt{2x^{2}} = x\sqrt{2}$

It can also be proved using trigonometric relation

$cos (45) = \frac{x}{LM}$

$LM = \frac{x}{cos (45)}$

As, $\frac{1}{cos (45)}= \sqrt{2}$

Therefore

$LM = x\sqrt{2}$

D and E:

Using same approach similar to part A

Since, LN = x and NM = x

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{x}{x} =1$

Therefore, $tan (45) = 1$ and not equal to $\frac{\sqrt{2} }{2}$

3 0

2 years ago

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In 2012, Gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that

nirvana33 [79]

Answer:

There is 95% confidence that the population proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is between 55.9% and 74.7%.

Step-by-step explanation:

We have to answer the population proportion for Vermont.

We can only do it by a confidence interval, as we only have information from a sample.

This sample, of size n=100, has a proportion p=0.653.

The degrees of freedom are:

$df=n-1=100-1=99$

We will calculate a 95% confidence interval, which for df=99 has a critical value of t of t=1.984.

The margin of error can be calculated as:

$E=t*\sigma_p=t\sqrt{\dfrac{p(1-p)}{n}}=1.984\sqrt{\dfrac{0.653*0.347}{100}}\\\\\\E=1.984*\sqrt{0.00226}=1.984*0.0476=0.094$

Then, the upper and lower bounds of the confidence interval are:

$LL=p-E=0.653-0.094=0.559\\\\UL=p+E=0.653+0.094=0.747$

Then, we can say that there is 95% confidence that the population proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is between 55.9% and 74.7%.

7 0

2 years ago

A 19% discount on a watch saved a shopper $76 . find the price of the watch before the discount

Alik [6]

The watch costed $400 before the discount.

76 * 100 = 7,600
7,600 / 19 = 400

3 0

2 years ago

A box of shredded wheat wheat weighs 0.35 .kg and a box of weetabix weighs 9/25 kg. Which box is heavier? Show your work.

MAXImum [283]

Answer:

weetablx is heavier

Step-by-step explanation:

lets simplify

wheat wheat - 0.35 kg

weetablx - 9/25

simplify into decimals

wheat wheat- 0.35 kg

weetablx- 0.36 kg

brainliest appreciated!

7 0

2 years ago

Brenna found 10% of 60. Her work is shown below. 10% of 60 = (60 ÷ 2) = 30 Is Brenna’s answer correct? No. Brenna should have di

Sav [38]

Answer:

The answer is No. She should have divided by 10 to find 10%.

Step-by-step explanation:

3 0

2 years ago

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