MATHEMATICS HIGH SCHOOL

An investment counselor calls with a hot stock tip. he believes that if the economy remains strong, the investment will result in a profit of $50 comma 000. if the economy grows at a moderate pace, the investment will result in a profit of $10 comma 000. however, if the economy goes into recession, the investment will result in a loss of $50 comma 000. you contact an economist who believes there is a 30% probability the economy will remain strong, a 60% probability the economy will grow at a moderate pace, and a 10% probability the economy will slip into recession. what is the expected profit from this investment?

Answers

Answer 1

Answer:

Answer: $ 16,000 profit

Step-by-step explanation:

Given the following :

Profit when economy is strong = 50,000

Profit when economy is moderate = 10,000

Loss when economy goes into recession = 50000

Resulting probabilities of the three probable occurrences are:

Probability of strong economy; p(strong) = 30/100 = 0.3

Probability of moderate; P(moderate) = 60/100 = 0.6

Probability of recession; P(recession) = 10/100 = 0.1

Expected profit :

Summation of the product of each probability and its accompanying profit or loss.

P(strong) × profit of strong = 0.3 × 50000 = 15000

P(moderate) × profit of moderate = 0.6 × 10000 = 6000

P(recession) × loss on recession = 0.1 × 50000 = 5000 = - 5000 ( loss)

Expected profit :

$(15,000 + 6000 - 5000) = $16,000 profit

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Subtract: 3x^2 - 7x + 4 from 5x^2 - 3x + 8.

Answers

subtrace x from y means y-x so
subtract 3x^2-7x+4 from 5x^2-3x+8 means
5x^2-3x+8-(3x^2-7x+4)=
5x^2-3x+8-1(3x^2-7x+4)
5x^2-3x+8-3x^2+7x-4=
5x^2-3x^2-3x+7x+8-4=
2x^2+4x+4

The circumference of a circle measures the distance around the circle.

True or False

Answers

Answer:

True

Step-by-step explanation:

Answer: True

Step-by-step explanation:

Which graph shows the end behavior of the graph of f(x) = 2x^6 – 2x^2 – 5?

Answers

For the given function, f(x) = 2x^6 - 2x^2 - 5, as x becomes extremely large in either the positive or negative direction, the function value grows without bound, heading towards positive infinity. This behavior is a characteristic of functions with even degrees and positive leading coefficients.

Analyzing the end behavior of a function is a valuable tool in understanding how the function behaves as the input, denoted by 'x', approaches positive or negative infinity. In this case, we are given the function f(x) = 2x^6 - 2x^2 - 5 and tasked with determining its end behavior.

Degree of the Function: The degree of a function is the highest power of the variable it contains. In our function, the highest power of the variable 'x' is 6, as it appears in the term 2x^6.

Leading Coefficient: The leading coefficient is the coefficient of the term with the highest power. In our function, the leading coefficient is 2, associated with the term 2x^6.

With these pieces of information, we can deduce the end behavior of the function:

The degree of the function is 6, which is an even degree.

The leading coefficient is 2, and it's positive.

For a function with an even degree and a positive leading coefficient, the end behavior is as follows:

As x approaches positive infinity (+∞), the function value f(x) also approaches positive infinity (+∞).

As x approaches negative infinity (-∞), the function value f(x) also approaches positive infinity (+∞).

For more such information on: function

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Tan154-tan49/1+tan154tan49

*all are in degrees.
What does sin, cos, and tan equal?

Answers

tan(154)-tan(49)=-1.638...
Ans/(1+(tan(154)tan(49))
=-3.73205

Given the equation Square root of 8x plus 1 = 5, solve for x and identify if it is an extraneous solution.

Answers

It depends if you mean $√(8x) +1=5$ or $√(8x+1) = 5$

$√(8x) +1=5$

Subtract 1 from both sides.

$√(8x) =4$

Take the square root of both sides.

8x = sqrt(4)
8x = 2
x = 1/4.

Plugging it back in:
sqrt(8*0.25) + 1 = 5
sqrt(2) = 4

This is not true because the square root of 2 is about 1.41, which does not equal 4.
So it is an extraneous solution.
__________________________________________
$√(8x+1) = 5$
Square both sides.
8x + 1 = 25
8x = 24
x = 3

Not extraneous because equation works out when you plug x back in.

Choose the equation that could be used to find three consecutive integers whose sum is 36.n + (n + 2) + (n + 4) = 36

n + (n + 1) + (n + 3) = 36

n + (n + 1) + (n + 2) = 36

n + (n − 1) + (n − 3) = 36