A credit card statement showed these transactions during October.

For ΔABC, which two relationships are true?

Phoenix [80]

The two correct relationships are:

$cos(\theta)=\frac{AB}{AC} = sin(90-\theta)\\\\sin(\theta)=\frac{BC}{AC} = cos(90-\theta)$

<h3>What is a right-angled triangle?</h3>

The triangle shown is a right-angled triangle

Considering < $(90-\theta)^o$

$cos(90-\theta)=\frac{BC}{AC} \\\\sin(90-\theta)=\frac{AB}{AC}\\\\tan(90-\theta)=\frac{AB}{BC}$

Considering < $\theta$

$cos(\theta)=\frac{AB}{AC} \\\\sin\theta)=\frac{BC}{AC}\\\\tan(\theta)=\frac{BC}{AB}$

Comparing < $\theta$ and < $(90-\theta)^o$ , the true statements are:

$cos(\theta)=\frac{AB}{AC} = sin(90-\theta)\\\\sin(\theta)=\frac{BC}{AC} = cos(90-\theta)$

Learn more on trigonometry here: brainly.com/question/20519838

6 0

2 years ago

Lucy reads 72 chapters of a book in 8 hours. What is her rate in chapters per hour?

Sophie [7]

She read nine chapters each hour

8 0

3 years ago

Read 2 more answers

In a study of the accuracy of fast food drive-through orders, one restaurant had orders that were not accurate among orders obs

Lesechka [4]

Complete Question

In a study of the accuracy of fast food drive-through orders, one restaurant had 32 orders that were not accurate among 367 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is equal to 10%. Does the accuracy rate appear to be acceptable?

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to show that the rate of inaccurate orders is equal to 10%

Step-by-step explanation:

Generally from the question we are told that

The sample size is n = 367

The number of orders that were not accurate is $k = 32$

The population proportion for rate of inaccurate orders is p = 0.10

The null hypothesis is $H_o : p = 0.10$

The alternative hypothesis is $H_a : p \ne 0.10$

Generally the sample proportion is mathematically represented as

$\^ p = \frac{k}{n}$

=> $\^ p = \frac{32}{367}$

=> $\^ p = 0.0872$

Generally the test statistics is mathematically represented as

$z= \frac{ \^ p - p }{ \sqrt{ \frac{ p(1 - p)}{ n} } }$

=> $z= \frac{ 0.0872 - 0.10 }{ \sqrt{ \frac{ 0.10 (1 - 0.10 )}{367} } }$

=> $z= -0.8174$

From the z table the area under the normal curve to the left corresponding to -0.8174 is

$P(z < -0.8173 ) = 0.20688$

Generally the p-value is mathematically represented as

$p- value = 2 * 0.20688$

=> $p- value = 0.4138$

From the value obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to show that the rate of inaccurate orders is equal to 10%

4 0

2 years ago

Solve 4(3x+3)=15x+7-3x+5

Flura [38]

Answer:

Infinite amount of solutions

Step-by-step explanation:

Step 1: Write equation

4(3x + 3) = 15x + 7 - 3x + 5

Step 2: Solve for <em>x</em>

Distribute 4: 12x + 12 = 15x + 7 - 3x + 5
Combine like terms: 12x + 12 = 12x + 12
Subtract 12 on both sides: 12x = 12x
Divide both sides by 12: x = x

Here, we can see that <em>x</em> would be infinite amount of solutions. We can plug in any number <em>x</em> and it would render the equation true.

4 0

3 years ago

It is a six-digit

KonstantinChe [14]

Ok, the first clue is it has six digit and the second clue is it’s a whole number!
So we know it lies between 99999 and 1000000
3rd clue tells it has only 3 different digits and 4th clue tells us each are used twice!
Moving on, 5th clue says none of its digits are even! 6th speaks none are divisible be 3
So the possibilities for digits are 1, 5, 7
And it’s greater than 600000, then the 1st digit must be 7! It is divisible be 5, so last digit must be 5!
7th clue states that It’s tenth digit is same as hundred-thousand! Means the tenth digit is 7
Let’s see what we got!
{7xxx75}
Clue no 8 as you can see says that it’s thousands digit is same as unit digit
So the number now is {7x5x75}
9th clue says it’s hundreds digit is different from tens digit meaning the hundreds digit is either 1 or 7 and we used 7 two times, so it’s 1 and clue 10 says it’s ten thousands digit is 1 so the number that’s playing hide ‘n seek or most probably riddle game is 715175!

8 0

2 years ago