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1 year ago

ΔABC has three sides with these lengths: AB = 9, BC = 40, and CA = 41. What is the value of cos C?

Mathematics

1 answer:

Effectus [21]1 year ago

6 0

From the Law of Cosines
Cos (C) = (a^2 + b^2 -c^2) / 2 * a * b
Cos (C) =(40^2 + 41^2 -9^2) / 2 * 40 * 41
Cos (C) = 1,600 + 1,681 - 81 / 3,280
Cos (C) = 3,200 / 3,280
Cos (C) = 0.9756097561 
Incidentally, Angle C = 12.68 Degrees

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Is 52L greater than 5,200mL?

Vesnalui [34]

5200mL → 520 cL → 52dL → 5.2L

Example:

If

1L ------ 1000mL
x -------- 5200mL

1000x = 5200
 $x = \frac{5200}{1000}$
x = 5,2

Therefore:
52L > 5200mL or 5.2L (True)

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2 years ago

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Customers can pick their own apples at the happy apple farm. they pay $6 to enter the farm and $3.50 per pound for the apples th

Amanda [17]

Y = 3.5x + 6

Shows the 6 inital fee plus the 3.50 for each pound

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2 years ago

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You save $5,000.00 and invest 60% of it in stocks while leaving the rest in a savings account earning a 4.9% APR. The stock incr

Angelina_Jolie [31]

Answer:

5,340

Step-by-step explanation:

Hi there:)

Amount invested in stock

=5000×0.6=3000

Amount invested in a saving account

5000-3000=2000

The stock increases 9% in the first year

3,000×(1+0.09)=3,270

and loses 4% of its value the second year

3,270×(1−0.04)=3,139.2

Amount of a saving account after two years

2,000×(1+0.049)^(2)=2,200.8

the total amount gained during the 2 years

3,139.2+2,200.8=5,340...answer

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2 years ago

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In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in t

victus00 [196]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The probability that he or she would choose the pair of socks in the center position is $p =\frac{1}{5}$

The correct answer choice is

X has a binomial distribution with parameters n=100 and p=1/5

The mean is $\mu = 20$

The standard deviation is $\sigma=4$

The probability, $P =0.0002$

The correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.

Using the R the probability $Pe = 0.0003$

The probabilities $P \approx Pe$

Step-by-step explanation:

Since the person selects his or her desired pair of socks at random , then the probability that the person would choose the pair of socks in the center position from all the five identical pair is mathematically evaluated as

$p =\frac{1}{5}$

$=0.2$

The mean of this distribution is mathematical represented as

$\mu = np$

substituting the value

$\mu = 100 * 0.2$

$\mu = 20$

The standard deviation is mathematically represented as

$\sigma = \sqrt{np (1-p)}$

substituting the value

$= \sqrt{100 * 0,2 (1-0.2)}$

$\sigma=4$

Applying normal approximation the probability that 34 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random would be mathematically represented as

$P=P(X \ge 34 )$

By standardizing the normal approximation we have that

$P(X \ge 34) \approx P(Z \ge z)$

Now z is mathematically evaluated as

$z = \frac{x-\mu}{\sigma }$

Substituting values

$z = \frac{34-20}{4}$

$=3.5$

So using the z table the $P(Z \ge 3.5)$ is 0.0002

The probability P and Pe that 34 or more subject would choose the center pair is very small So

The correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.

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2 years ago

PLEASE HELP, I’ve been stuck on this question for a whileIn the diagram, AB is divided into equal parts. The coordinates of poin

castortr0y [4]

AB is divided into 8 equal parts and point C is 1 part FROM A TO B, so the ratio is 1:7, with C being 1/7 of the way. The ratio is k, found by writing the numerator of the ratio (1) over the sum of the numerator and denominator (1+7). So our k value is 1/8. Now we need to find the rise and the run (slope) of the points A and B. $m= \frac{5-9}{9-(-3)}$ . That gives us a rise of -4 and a run of 12. The coordinates of C are found in this formula: $C(x,y)=[ x_{1} +k(run), y_{1} +k(rise)]$ . Filling in accordingly, we have $C(x,y)=[-3+ \frac{1}{8}(12),9+ \frac{1}{8}(-4)]$ which simplifies a bit to $C(x,y)=(-3+ \frac{3}{2},9- \frac{1}{2})$ . Finding common denominators and doing the math gives us that the coordinates of point C are $(- \frac{3}{2}, \frac{17}{2})$ . There you go!

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2 years ago

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