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Alborosie
2 years ago
14

Zoe must draw a triangle with two 35° angles and an included side with a length of 50 cm. How many such triangles are possible?

Mathematics
1 answer:
Gennadij [26K]2 years ago
6 0
C is the correct answer!!
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Two workers finished a job in 12 days. How long would it take each worker to do the job by himself if one of the workers needs 1
Lorico [155]

Two workers finished a job in 7.5 days.

How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

let t = time required by one worker to complete the job alone

then

(t+8) = time required by the other worker (shirker)

let the completed job = 1

A typical shared work equation

7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1

multiply by t(t+8), cancel the denominators, and you have

7.5(t+8) + 7.5t = t(t+8)

7.5t + 60 + 7.5t = t^2 + 8t

15t + 60 = t^2 + 8t

form a quadratic equation on the right

0 = t^2 + 8t - 15t - 60

t^2 - 7t - 60 = 0

Factor easily to

(t-12) (t+5) = 0

the positive solution is all we want here

t = 12 days, the first guy working alone

then

the shirker would struggle thru the job in 20 days.

8 0
2 years ago
Read 2 more answers
A television station plans to ask a random sample of 400 city residents if they can name the news anchor on the evening news at
hodyreva [135]

Answer:

There is an 8.38% probability that the anchor will be fired.

Step-by-step explanation:

For each resident, there is only two possible outcomes. Either they can name the news anchor on the evening news at their station, or they cannot.

This means that the binomial probability distribution will be used in our solution.

However, we are working with samples that are considerably big. So i am going to aaproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

400 city residents are going to be asked. So n = 400.

Suppose that in fact 12% of city residents could name the anchor if asked. This means that p = 0.12.

So,

\mu = E(X) = 400*0.12 = 48

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.12*0.88} = 6.5.

They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so.

What is the approximate probability that the anchor will be fired?

10% of the residents is 0.10*400 = 40 residents.

Fewer than 10% is 39 residents. So the probability that the anchor will be fired is the pvalue of Z when X = 39.

So:

Z = \frac{X - \mu}{\sigma}

Z = \frac{39 - 48}{6.5}

Z = -1.38

Z = -1.38 has a pvalue of 0.0838. This means that there is an 8.38% probability that the anchor will be fired.

5 0
3 years ago
Rewrite the logarithm as a ratio of common logarithms and natural logarithms. log4 45
tiny-mole [99]

Answer:

Common logarithm

log_451= \frac{log_1_045}{log_1_08}

Natural logarithms

log_445= \frac{log_e45}{log_e4}

or

log_445= \frac{In45}{In4}

Step-by-step explanation:

From the question we are told that

Log_445

Generally converting log from base x to base 10 si mathematically represented as

log_xa=log_1_0a *log_x10

log_xa= \frac{log_1_0a}{log_1_0x}

Therefore

Common logarithm

log_451= \frac{log_1_045}{log_1_08}

Generally Natural logarithms log_ex\ or\ inx is mathematically represented as

log_xa= \frac{log_ea}{log_ex}

Therefore

Natural logarithms

log_445= \frac{log_e45}{log_e4}

or

log_445= \frac{In45}{In4}

6 0
3 years ago
Are the two expressions equivalent when x=5
adell [148]

Answer:

Yes

Step-by-step explanation:

The first one is 35+15 because 7*5 is 35 and 3*5 is 15

The second one is 45+5 because 9*5=45

35+15=50

45+5=50

Yes, they are equal.

7 0
3 years ago
Read 2 more answers
GCF of 35,5,70 is???
Vanyuwa [196]

Answer:

5

Because, five can go into 5, 35 and 70. Nothing else bigger can. If we went bigger we would be going over five.

Hope this helps :)

6 0
3 years ago
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