MATHEMATICS COLLEGE

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 9 hours of burning, a candle has a height of 25.4 centimeters. After 23 hours of burning, its height is 19.8 centimeters. What is the height of the candle after 22 hours?

Answers

Answer 1

Answer:

Answer:

Suppose that the height (in centimeters) of a candle is a linear function of

the amount of time (in hours) it has been burning.

After 11 hours of burning, a candle has a height of 23.4 centimeters.

After 30 hours of burning, its height is 12 centimeters.

What is the height of the candle after 13 hours?

Assign the given values as follows:

x1 = 11; y1 = 23.4

x2 = 30; y2 = 12

Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29

m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19

Find the equation using the point/slope formula: y - y1 = m(x - x1)

y - 23.4 = -11.4%2F19(x - 11)

y - 23.4 = -11.4%2F19x + 125.4%2F19

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19

y = -11.4%2F19x + 570%2F19

y = -11.4%2F19x + 30, is the equation

What is the height of the candle after 13 hours?

x = 13

y = -11.4%2F19(13) + 30

y = -148.2%2F19 + 30

y = -7.8 + 30

y = 22.2 cm after 13 hrs

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You are given that angle RST and angle TUR are right angles. What additional piece of info allows you to prove they are congruent

Answers

Answer:

the additional info required is - the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle.

Step-by-step explanation:

As given , RST and angle TUR are right angles.

So the triangles are right angle triangles.

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

So, the additional info required is - the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle.

Final answer:

To prove that angle RST and angle TUR are congruent, we need the additional information that the length of the sides RS and TU are equal.

Explanation:

In order to prove that angle RST and angle TUR are congruent, we need the additional piece of information that the length of the sides RS and TU are equal. This is because congruent right angles must have congruent sides.

Learn more about Congruent Angles here:

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Find tan x if sec x = sort 37/6 and sin x <0

Answers

Answer:

tan(x) = -1/6

Step-by-step explanation:

We can use the relation between tan and sec:

$\displaystyletan(x)=\pm\sqrt{\sec^2{x}-1}\n\ntan(x)=-\sqrt{\left((√(37))/(6)\right)^2-1}\quad\text{negative because sine is negative}\n\n=-\sqrt{(37-36)/(36)}=\boxed{-(1)/(6)}$

The tangent of x is -1/6.

Point G(−7, 4) is translated using the rule (x+10, y−6). What is the x-coordinate of G′ ?

Answers

Answer:

x = 3

Step-by-step explanation:

The translation rule (x + 10, y - 6) means add 10 to the original x- coordinate and subtract 6 from the original y- coordinate, that is

G(- 7, 4) → G'(- 7 + 10, 4 - 6) → G'(3, - 2)

Suppose that the sitting back-to-knee length for a group of adults has a normal distribution with a mean of μ=22.5 in. and a standard deviation of σ=1.1 in. These data are often used in the design of different seats, including aircraft seats, train seats, theater seats, and classroom seats. Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater) ≤0.01 and a value is significantly low if P(x or less) ≤0.01.Find the back-to-knee lengths separating significant values from those that are not significant.

Answers

Answer:

Measures equal or lower than 19.94 inches are significantly low.

Measures equal or higher than 25.06 inches are significantly high.

Step-by-step explanation:

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:

$Z = (X - \mu)/(\sigma)$

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.

In this problem, we have that:

$\mu = 22.5, \sigma = 1.1$

Find the back-to-knee lengths separating significant values from those that are not significant.

Significantly low

In this exercise, a value is going to be to significantly low if it has a pvalue of 0.01 or less. So we have to find X when Z has a pvalue of 0.01. This is between $Z = -2.32$ and $Z = -2.33$ , so we use $Z = -2.325$

$Z = (X - \mu)/(\sigma)$

$-2.325 = (X - 22.5)/(1.1)$

$X - 22.5 = -2.325*1.1$

$X = 19.94$

Measures equal or lower than 19.94 inches are significantly low.

Significantly high

In this exercise, a value is going to be to significantly high if it has a pvalue of 0.99 or more. So we have to find X when Z has a pvalue of 0.99. This is $Z = 2.325$ . So:

$Z = (X - \mu)/(\sigma)$

$2.325 = (X - 22.5)/(1.1)$

$X - 22.5 = 2.325*1.1$

$X = 25.06$

Measures equal or higher than 25.06 inches are significantly high.

Final answer:

To find the separating back-to-knee lengths, we calculate the corresponding z-scores for the given probabilities. Using the standard normal distribution table, we find that the separating values are 24.78 inches for significantly high lengths and 20.22 inches for significantly low lengths.

Explanation:

To find the back-to-knee lengths separating significant values from those that are not significant, we need to calculate the z-scores corresponding to the given probabilities. For a value to be significantly high, we look for a z-score such that the area to its right is 0.01. Using the standard normal distribution table, we find that z = 2.33. Similarly, for a value to be significantly low, we look for a z-score such that the area to its left is 0.01. Again using the table, we find that z = -2.33. Converting these z-scores back to actual back-to-knee lengths, we can calculate the separating values as: 22.5 + (2.33 * 1.1) = 24.78 inches for significantly high lengths, and 22.5 - (2.33 * 1.1) = 20.22 inches for significantly low lengths.

Learn more about Back-to-knee lengths here:

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Recent statistics show that 62% of people wash their hands after using the restroom.If you shake hands with three random people, what is the probability that all of them washed their hands after previously using the restroom?

Answers

Answer:

p = 0.62

Step-by-step explanation:

Probability that all three has washed their hands after previously using the restroom = 0.2383 approx. The probability that all of the 3 washed their hands after previously using the restroom is 0.2383. Explanation: It is given that, 62% of people wash their hands after using the restroom that is p = 0.62.

2. Half of the pieces of fruit in the bowl are apples. There arealso 3 oranges, 2 pears, and a banana.
How many apples are there in the bowl? Show your work!

Answers

Answer:

6 apples

Step-by-step explanation:

3+2+1 = 6 and 6 × 2 is 12 therefore half of the fruit is 6 so six apples (if that makes sense HAHA)

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