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3 years ago

Please find the value?

Mathematics

1 answer:

lesantik [10]3 years ago

8 0

Answer:

Step-by-step explanation:

By the marks on the angles of this triangle, it is isosceles. By the Isosceles Triangle Theorem, if 2 angles of a triangle have the exact same measure, then the sides across from those angles have the exact same measure as well. That means that, algebraically,

5x - 2 = 33 and

5x = 35 so

x = 7

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4 years ago

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ikadub [295]

Answer:

the complete graph is in the image

Step-by-step explanation:

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3 years ago

A thermometer is taken from a room where the temperature is 20◦C to the

lord [1]

Answer:

a) $T(2) = 8.265$ : at time t = 2 minutes the temperature will be 8.265 degress

b) $6 = T(3.55)$ : the temperature will be 6 degrees at time t = 3.55 minutes.

Step-by-step explanation:

When dealing with temperature changes, it's best to work with Newton's Law of Cooling.

$T(t) = T_s + Ce^{kt}$

here:

$T(t)$ : the temperature in the room.

$T_s$ : ambient (or outdoor) temperature (that always remains constant, in our case: $T_s = 5$ )

$C\,\text{and}\,k$ : are constants

Our conditions are provided:

1) $T(0) = 20$

2) $T(1) = 12$

using the first condition

$T(0) = 5 + Ce^{k(0)}\\20 = 5 + C(1)\\C = 15$

using the second condition:

$T(1) = 5 + Ce^{k(1)}\\12 = 5 + Ce^{k}\\e^k = \dfrac{7}{C}$

we can use our calculated value of C to find k

$e^k = \dfrac{7}{15}\\k = \ln{(\dfrac{7}{15})}\\k = -0.7621$

Finally we can put these constants back in the main equation:

$T(t) = T_s + Ce^{kt}$

$T(t) = 5 + 15e^{-0.7621t}$ or $T(t) = 5 + 15e^{\ln{(\frac{7}{15})t}$

a) Reading after one more minute?

so it's asking:

T(2) = ?

$T(2) = 5 + 15e^{\ln{(\frac{7}{15})(2)}}\\T(2) = \dfrac{124}{15} \approx 8.267$

Hence, after one more minute the temperature of the room will be 8.267 degrees

b) When will it be 6 degrees?

T(t) = 6?

$6 = 5 + 15e^{-0.7621t}\\\text{and solve for $t$}\\\\\dfrac{6-5}{15}=e^{\ln{(\frac{7}{15})}t}\\\ln{\left(\dfrac{1}{15}\right)} = \ln{\left(\dfrac{7}{15}\right)t}\\\ln{\left(\dfrac{1}{15}\right)} \div \ln{\left(\dfrac{7}{15}\right)} = t \approx 3.55\\$

Hence at t = 3.55 minutes the temperature of the room will be 6 degrees.

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3 years ago

The average score of all golfers for a particular course has a mean of 71 and a standard deviation of 3. Suppose 36 golfers play

Zielflug [23.3K]

Answer:

.0228

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .