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A, B & C form the vertices of a triangle.CAB = 90°, ABC = 60° and AB = 8.6.

Calculate the length of BC rounded to 3 SF.

BC =

Answers

Answer 1
Answer:

Answer:

BC = 17.2.

Step-by-step explanation:

Since CAB = 90º, this is a right triangle.

The triangle format is given below:

C

A           B

We have that AB = 8.6, and angle B measures 60º.

Length of BC:

BC is the hypotenyse.

Side AB is adjacent to angle B = 60º.

In a right triangle, angle \alpha, it's adjacent side with length s and the hypotenuse h are related by the cosine of the angle, that is:

cos(\alpha) = (s)/(h)

In this question, we have an angle of 60º, with has cosine 0.5. We also have that side AB = s = 8.6, and the hypotenuse h is side BC. So

cos(\alpha) = (s)/(h)

0.5 = (8.6)/(h)

0.5h = 8.6

h = (8.6)/(0.5)

h = 17.2

BC = 17.2.

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Veronica is making emergency- preparedness kits to share with friends. She has 20 bottles of water and 12 cans of food, which she would like to distribute equally among to kits, with nothing left over. What is the greatest number of kits Veronica can make ?

Answers

Answer:

she could only make 4

Step-by-step explanation:

Deanna and Lise are playing game at the arcade. Deanna started with $20 and the the game she is playing costs $0.25 each game. Lise started with $40, and her machine costs $0.75 per game. How many games will it be before they both have the same amount of money left? Make an expression the solves the problem.

Answers

Deanna 78 games 19.50

Lisa 26 games 19.50

Hope that helps..

Final answer:

To determine how many games it will take for Deanna and Lise to have the same amount of money left, set up an equation using their net losses per game and solve for 'g'. It will take 40 games for them to have the same amount of money left.

Explanation:

To determine how many games it will take for Deanna and Lise to have the same amount of money left, we need to set up an equation. Let's start by determining their net loss per game by subtracting the cost of each game from their initial amount of money. For Deanna, her net loss per game is $0.25. For Lise, her net loss per game is $0.75.

Let's represent the number of games they play with the variable 'g'. To find the number of games it will take for them to have the same amount of money left, we need to set up an equation. Deanna's remaining money after 'g' games can be represented as $20 - $0.25g. Lise's remaining money after 'g' games can be represented as $40 - $0.75g.

Setting the two expressions equal to each other, we can solve for 'g':

$20 - $0.25g = $40 - $0.75g

$20 = $40 - $0.5g

$0.5g = $20

g = $20 / $0.5 = 40

Therefore, it will take 40 games before Deanna and Lise have the same amount of money left.

Will give brainleast What number is the opposite of -2 1/8

Answers

2 1/8 is the opposite

-17 irrational number

Answers

Answer:

both rational and irational

Step-by-step explanation:

The time needed for all college students to complete a certain paper-and-pencil maze follows a normal distribution with a population mean of 30 seconds and a population standard deviation of 3 seconds. You wish to see if the mean time μ (where μ stands for population mean) is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. It takes them an sample average of 31.2 seconds to complete the maze. Use this information to test the hypotheses:

H0: μ = 30,

Ha: ≠30

at the significance level of 0.01.

You conclude:


a) There is not enough evidence to support the claim.

b) There is enough evidence to support the claim.

Answers

Answer:

The correct option is a

Step-by-step explanation:

From the question we are told that

   The population mean is  \mu = 30\ seconds

    The standard deviation is  \sigma = 3 \ seconds

     The sample size is  n  = 9

    The null hypothesis is H_o: \mu = 30

     The alternative hypothesis is  H_a : \mu \ne 30

    The level of significance is  \alpha = 0.01

    The sample mean is  \= x = 31.2

Generally the test statistics is mathematically represented as

      z = ( \= x - \mu )/( (\sigma)/(√(n) ) )

=>   z = ( 31.2 - 30)/( (3)/(√(9) ) )

=>   z = 1.2

From the z table  the area under the normal curve to the right corresponding to  1.2  is    

         P(Z > 1.2) = 0.11507

Generally the p-value is mathematically represented as

         p-value = 2 * P(Z > 1.2)

=>       p-value = 2 *0.11507

=>       p-value = 0.230

From the value obtained w can see that

         p-value > \alpha hence

The decision rule is  

Fail to reject the null hypothesis

The conclusion is there is not enough evidence to support the claim

Final answer:

To test the hypotheses, use a one-sample t-test to compare the sample mean to the population mean. Calculate the t-value and compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Explanation:

To test the hypotheses, we can use a one-sample t-test since we know the population standard deviation and the sample size is small. The null hypothesis (H0) is that the population mean (μ) is equal to 30 seconds, while the alternative hypothesis (Ha) is that the population mean is not equal to 30 seconds.

Using the given information, we can calculate the t-value by using the formula:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Once we have the t-value, we can compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, we reject the null hypothesis. If not, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.

Learn more about Hypothesis testing here:

brainly.com/question/31665727

#SPJ11

WILL GIVE BRANLIEST!!!! URGENT!!!HELP!!!!! . Find x. A) 3.36 B) 3.3 C) 35.98 D) 38.43

Answers

Answer:

C) 35.98

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 17 = 11/x

x tan 17 = 11

x = 11/ tan 17

x =35.9793788

Answer:

Tjhe final answer I came apon was  35.98  for this problem.

"C) 35.98"

Here why :

First of all it is an

right triangle,

so we can use trigonometry. functions

oppration : tan theta = opp /adj

Step 1 tan 17 = 11/x

Step 2  x tan 17 = 11

Step 3  x = 11/ tan 17

Step 4 x =35.98 (when roundened)

Hope this helps

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