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3 years ago

State what additional information is required in order to know that the triangles are congruent by SAS

Mathematics

1 answer:

zalisa [80]3 years ago

3 0

<h3>You are correct. The answer is the second choice.</h3>

BC = JC by the single tickmarks shown

CD = CD because of the reflexive property

The angles between these two pairs of sides, that you've marked in the second answer choice, are needed to use SAS (side angle side).

See the diagram below. In the diagram, angle BCD (green) is between segments BC and CD. Also, angle JCD (blue) is between JC and CD.

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A random sample of 64 students at a university showed an average age of 20 years and a sample standard deviation of 4 years. The

adelina 88 [10]

Answer:

The 90% confidence level is $19.15< L < 20.85$

Step-by-step explanation:

From the question we are told that

The sample size is $n = 64$

The mean age is $\= x = 20 \ years$

The standard deviation is $\sigma = 4 \ years$

Generally the degree of freedom for this data set is mathematically represented as

$df = n - 1$

substituting values

$df = 64 - 1$

$df = 63$

Given that the level of confidence is 90% the significance level is mathematically evaluated as

$\alpha = 100 - 90$

$\alpha =$ 10 %

$\alpha = 0.10$

Now $\frac{\alpha }{2} = \frac{0.10}{2} = 0.05$

Since we are considering a on tail experiment

The critical value for half of this significance level at the calculated degree of freedom is obtained from the critical value table as

$t_{df, \frac{ \alpha}{2} } = t_{63, 0.05 } = 1.669$

The margin for error is mathematically represented as

$MOE = t_{df , \frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

substituting values

$MOE = 1.699 * \frac{4 }{\sqrt{64} }$

$MOE = 0.85$

he 90% confidence interval for the true average age of all students in the university is evaluated as follows

$\= x - MOE < L < \= x + E$

substituting values

$20 - 0. 85 < L < 20 + 0.85$

$19.15< L < 20.85$

4 0

3 years ago

The cost for 75kg of soil is £375. Find the cost for 42kg of soil.

Natasha_Volkova [10]

Answer: The cost for 42kg is $210

Step-by-step explanation:

375/75=$5 for 1kg

$5*42=$210

3 0

2 years ago

Read 2 more answers

Assume the general population gets an average of 7 hours of sleep per night. You randomly select 45 college students and survey

tekilochka [14]

Answer:

a) ii. This is a left-tailed test.

b) -1.59

c) -1.301

d) i. reject null hypothesis

e) Option i) The data supports the claim that college students get less sleep than the general population.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 7 hours

Sample mean, $\bar{x}$ = 6.87 hours

Sample size, n = 45

Alpha, α = 0.10

Sample standard deviation, s = 0.55 hours

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 7\text{ hours}\\H_A: \mu < 7\text{ hours}$

a) We use one-tailed(left) t test to perform this hypothesis.

b) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{6.87 - 7}{\frac{0.55}{\sqrt{45}} } =-1.59$

c) Now,

$t_{critical} \text{ at 0.10 level of significance, 44 degree of freedom } = -1.301$

Since,

$t_{stat} < t_{critical}$

d) We fail to accept the null hypothesis and reject it.

We accept the alternate hypothesis and conclude that mean number of hours of sleep for all college students is less than 7 hours.

e) Option i) The data supports the claim that college students get less sleep than the general population.

8 0

3 years ago

Which situation can be modeled by the equation 705 – m= 430?<br> help !!!!

777dan777 [17]

Real world example could be:
Consider x is time in minutes
Consider y is the amount of fish food required in grams

The equation could then represent how much food (in grams) that a fish needs to be fed x minutes after it was previously fed.

6 0

3 years ago

Read 2 more answers

Can a -150/10 be classified as both a rational number and a integer

irakobra [83]

Yes! This is because -150/10 can be simplified to be -15, which is a rational number.

The word “rational” sounds like another math word you’ve heard of before. Do you know what it is?

Well, it’s “ratio”!! Ratios can be seen in the forms x:y and x/y.

ANY RATIONAL NUMBER HAS THE ABILITY TO BE WRITTEN AS A RATIO!! This will completely exclude numbers with super long decimal points (ex: 1.2345678809928374737272828...)

This number also meets the requirements of being an integer. An integer is any whole number (this excludes decimals and fractions)

I know it’s written as a fraction. However, the fraction could be simplified, making it -15, which means this is both a rational number and an integer!!

6 0

3 years ago