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3 years ago

Can someone help me with this problem please?

Mathematics

1 answer:

MrRissso [65]3 years ago

6 0

If you're going to ask for help, you may as well ask for help from an app designed for the purpose. This app is available for both Android and iOS devices. My TI-83/84 calculator also has a triangle solver app.

(A) There is only one possible solution

b = 16.3
C = 26°
B = 87°

_____
If you want to do this yourself, you can use the Law of Sines to find angle C.
.. C = arcsin(7.1/15*sin(67°)) ≈ 25.8302° . . . . don't round intermediate values
Then angle B is 180° -67° -angle C = 87.1698°
and side b is found from the Law of Sines:
.. b = 15*sin(C)/sin(A) ≈ 16.2755

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Find the two square roots of 144.

spin [16.1K]

Answer:

The square root function

sqrt(144) or √144 produces a single positive value, 12.

However if you have an equation

x² = 144, then you have two possible values for x, 12 and -12.

Two ways to look at it.

x² - 144 = 0

Difference of two squares

(x+12)(x-12) = 0

x = -12, 12

x² = 144

x = ±√144

x = ±12

x = -12, 12

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3 years ago

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The sum of a rational number and an irrational number produces an irrational number.

sashaice [31]

Answer:

True

Step-by-step explanation:

Example: sqrt(5) (which decimals continue forever) will mean that if you did 5+sqrt(5) it would still have those decimals.

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3 years ago

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Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

4 0

4 years ago

Which property allows you to write the expression

umka2103 [35]

Answer:

the associative property

Step-by-step explanation:

the associative property allows the numbers to add regardless of how you group the numbers

8 0

3 years ago

A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average

marysya [2.9K]

Answer:

a) player’s expected payoff is $ 240

b) probability the player loses $1000 or more is 0.1788

c) probability the player wins is 0.3557

d) probability of going broke is 0.0594

Step-by-step explanation:

Given:

Since there are 60 hands per hour and the player plays for four hours then the sample size is:

n = 60 * 4 = 240

The player’s strategy provides a probability of .49 of winning on any one hand so the probability of success is:

p = 0.49

Solution:

Expected payoff is basically the expected mean

Since the bet is $50 so $50 is gained when the player wins a hand and $50 is lost when the player loses a hand. So

Expected loss = μ

= ∑ x P(x)

= 50 * P(win) - 50 * P(lose)

= 50 * P(win) + (-50) * (1 - P(win))

= 50 * 0.49 - 50 * (1 - 0.49)

= 24.5 - 50 ( 0.51 )

= 24.5 - 25.5

= -1

Since n=240 and expected loss is $1 per hand then the expected loss in four hours is:

240 * 1 = $ 240

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

= 110.5 - 117.6 / √117.6(1-0.49)

= −7.1/√117.6(0.51)

= −7.1/√59.976

= −7.1/7.744417

=−0.916789

Here the player loses 1000 or more when he loses at least 130 of 240 hands so the wins is 240-130 = 110

Using normal probability table:

P(X≤110) = P(X<110.5)

= P(Z<-0.916)

= 0.1788

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

= 120.5 - 117.6 / √117.6(1-0.49)

= 2.9/√117.6(0.51)

= 2.9/√59.976

= 2.9/7.744417

=0.374463

Here the player wins when he wins at least 120 of 240 hands

Using normal probability table:

P(X>120) = P(X>120.5)

= P(Z>0.3744)

= 1 - P(Z<0.3744)

= 1 - 0.6443

= 0.3557

Player goes broke when he loses $1500

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

= 105.5 - 117.6 / √117.6(1-0.49)

= -12.1/√117.6(0.51)

= -12.1/√59.976

= -12.1/7.744417

=−1.562416

Here the player loses 1500 or more when he loses at least 135 of 240 hands so the wins is 240-135 = 105

Using normal probability table:

P(X≤105) = P(X<105.5)

= P(Z<-1.562)

= 0.0594

7 0

3 years ago