The function [tex]\(f(x) = 7 \cdot 2^{-3x}\)[/tex] is a rewritten form using exponent properties.
To rewrite the function [tex]\( f(x) = 7 \left(\frac{1}{2}\right)^{3x} \) using the properties of exponents, we can first rewrite \( \frac{1}{2} \) as \( 2^{-1} \). Then, we can apply the property \( (a^m)^n = a^{mn} \)[/tex] to simplify the expression. Here's how it goes:
[tex]\[ f(x) = 7 \left(\frac{1}{2}\right)^{3x} \][/tex]
[tex]\[ = 7 \left(2^{-1}\right)^{3x} \][/tex]
[tex]\[ = 7 \cdot 2^{-3x} \][/tex]
So, [tex]\( f(x) = 7 \cdot 2^{-3x} \)[/tex] is the rewritten form of the function using the properties of exponents.
Bill is playing a game of chance with the following payout. 30% of the time you will lose 20 dollars, 20% of the time you will lose 40 dollars. 10% of the time you will win 50 dollars, 40% of the time you will win 5 dollars. Find the expected value of the event and explain if Bill should play this game based on the mathematical expectation.
please helpppop asappppp and show work so I understand please
Anybody know this??? please help
Answer:
The expected value of playing the game is -$7.
Bill should not play this game.
Step-by-step explanation:
The probability distribution of gain and loss is as follows:
X P (X)
-$20 0.30
-$40 0.20
$50 0.10
$5 0.40
Total 1.00
The expected value of a probability distribution is given by:
[tex]E(X)=\sum {X\times P(X)}[/tex]
Compute the expected value of playing the game of chance as follows:
[tex]E(X)=\sum {X\times P(X)}[/tex]
[tex]=(-\$20\times 0.30)+(-\$40\times 0.20)+(\$50\times 0.10)+($5\times 0.40)\\\\=-\$6-\$8+\$5+\$2\\\\=-\$7[/tex]
The expected value of playing the game is -$7.
The expected value of the game suggests that Bill will incur a loss of $7 if he plays.
So, it is safe not to play the game.
Drew’s dog weighs 24 lb 5 oz. How many ounces does drew’s dog weigh?
Answer:
Step-by-step explanation:
It weighs 389 pounds so the answer would be C.
Number eight, graph each question
Answer:
(1,3)
Step-by-step explanation:
x would be counted as (1,1) therefore, moving 1 number to the right, and 1 number up.
Connie collected 50 seashells during her 5-day vacation. Each day she collected 3 more than the previous day. How many seashells did she find each day? PLEASE HELP!
Answer:
The number of seashells collected on day 1 to day 5 is 4, 7, 10, 13 and 16 respectively
Step-by-step explanation:
This is a question that deals with consecutive numbers.
Let x represent the number of seashells collected on her first day.
Given that she collected 3 more each day, then
On day 2, she collected x + 3
On day 3, she collected x + 6
On day 4, she collected x + 9
On day 5, she collected x + 12
Adding up the above will give the number of sea shells collected on day 1;
i.e.
x + x + 3 + x + 6 + x + 9 + x + 12 = 50
Collect like terms
x + x + x + x + x + 3 + 6 + 9 + 12 = 50
5x + 30 = 50
5x = 50 - 30
5x = 20
Multiply ⅕ to both sides
⅕ * 5x = ⅕ * 20
x = 4.
This mean that she found 4 seashells on day 1;
Recall that day 2 = x + 3
So, day 2 = 4 + 3 = 7 seashells
day 3 = x + 6
day 3 = 4 + 6 = 10 seashells
day 4 = x + 9
day 4 = 4 + 9 = 13 seashells
day 5 = x + 12
day 5 = 4 + 13 = 16 seashells
Hence, the number of seashells collected on day 1 to day 5 is 4, 7, 10, 13 and 16 respectively
Write an equivalent
expression for
88 + 16x + 8
Answer:
16x + 96
Step-by-step explanation:
You can add 88 + 8 for and get the same answer
Answer: 16x+8+88
Step-by-step explanation:
All you need to do is move around the numbers and then you get the answer
Write the following equation in slope-intercept form: 4x – 5y = 15.
Answer:
y = (4/5)x - 3
Step-by-step explanation:
slope intercept form: y = mx + b
Note the equal sign, what you do to one side, you do to the other. First, subtract 4x from both sides:
4x - 5y = 15
4x (-4x) - 5y = 15 (-4x)
-5y = -4x + 15
Next, divide -5 from both sides:
(-5y)/-5 = (-4x + 15)/-5
y = (-4x + 15)/-5
Simplify Divide -5 from all terms within the parenthesis:
y = (4/5)x - 3
y = (4/5)x - 3 is your answer.
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i really need help! can someone help me
Answer:
M + $13.72 = $58.22
Step-by-step explanation:
Manny and Sam combined (+) have a total (=) of $58.22
M + S = $58.22
M + $13.72 = $58.22
Answer:
m + $13.72 = $58.22
Step-by-step explanation:
Together they have $58.22.
We know one of them has $13.72, so if we add that to (m) we should get $58.22.
which function will add the same number each time
A linear function adds the same number each time. It has a constant rate of change which means it adds or subtracts a certain amount at each step. An example of this would be the equation y = 3x + 2.
Explanation:The function described in the question which will add the same number each time is called a linear function. In mathematics, a linear function is a function that has a constant rate of change. This means that it adds or subtracts the same amount each time. For example, the equation y = 3x + 2 is a linear function. Every time you increase x by 1, y will increase by 3. Similarly, each time you decrease x by 1, y will decrease by 3. This is because the slope of a linear function is constant, indicating a consistent rate of change.
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Please help!! :) Cant solve it on paper currently since its late and just doing it online.
Answer:
14.4 in
Step-by-step explanation:
Using the formula of the Pythagorean theorem, a² + b² = c², we can find the length of the missing side.
a = 8
b = 12
c = ?
8² + 12² = 208
To get your answer, you must take the square root of 208.
√208 = 14.4222051
What is the volume of the rectangular prism? show all work please
Answer:
V= Ab x h
= l x w x h
= 10.4mm × 5mm × 8mm
= 416 mm³
Answer:
416mm
Step-by-step explanation:
V=Bh
B=10.4*5=52
h=8
52*8=416
Which of these polygons is not formed by the cross-section created when a plane intersects a cube? Select all that are possible.
square
circle
pentagon
octagon
triangle
rectangle
Answer:
Circle
Octagon
Step-by-step explanation:
There are no curves in a cube to make a circular cross section, and there aren't enough edges to make an octagon (just visualize)
Answer:
A circle is not possible. Neither is a square or a rectangle.
Step-by-step explanation:
COMPLETE
log798= ? ________________________
Answer:
2.90200289135
Step-by-step explanation:
i used a calculator and it gave me 2.90200289135 round it if you need.
Write 6,020,300 in expanded form.
Answer:
6,000,000 + 20,000 + 300
Step-by-step explanation:
A town with a population of approximately 20,530 people is planning to build a new park. The town government is trying to find out what entertainment options citizens would prefer the park to include and plans to survey people running the trail in the existing park over a period of a month.
Answer:
Step-by-step explanation:
Which equation BEST represents the line of best fit for the scatterplot?
A) y = 3x
B) y = x - 2
C) y = x - 3
D) y = x + 3
Which value is equivalent to 2 x 3 + 4 -
6^2?
A. -26
B. -22
C. -2
D. 10
- Electricity City increases the price of televisions by 25%. If a television now sells for
$425, what was the original price?
Answer:
340
Step-by-step explanation:
Let x = original price
We increase by 25%
x+x*25% = new price
Change to decimal form
x+.25x = new price
Factor out the x
x(1+.25) = new price
x(1.25) = new price
x(1.25) = 425
Divide each side by 1.25
x = 425/1.25
x =340
The original price is 340
-10° i need help pleaseeee
Help me please
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Answer:
2
Step-by-step explanation:
The Fundamental theorem of algebra states that a polynomial of degree n has n roots. These can be real or complex.
A quadratic is of degree 2 and has 2 roots.
18/x=-2
what number does x represent
Answer:
9
Step-by-step explanation:
18/x = 2
or, 18 = 2x
or, 18/2 = x
or, 9 = x
ans ; x = 9
Point A is at (-2,-7) and point B is at (7,4).
What is the midpoint of line segment AB?
The coordinates of the midpoint would be (5/2, -3/2) of line segment AB.
What is Midpoint?A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.
Let two points A (x₁, y₁) and B (x₂, y₂), the midpoint between A and B is given by,
M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Coordinates of A are (-2,-7),
Coordinates of B are (7, 4),
M is the midpoint of AB which is given in the question
So the coordinates of M as:
⇒ M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Substitute the values, and we get
⇒ M = ((-2 + 7)/2, ( -7 + 4)/2)
⇒ M = ((5)/2, ( -3)/2)
⇒ M = (5/2, -3/2)
Therefore, the coordinates of the midpoint would be (5/2, -3/2) of line segment AB.
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Which mathematical symbol would best fill in the blank to compare the two real numbers? (4 points) square root of 7 blank 14 over 5 Group of answer choices < > = ≈
Answer is <
Step-by-step explanation:
To compare the square root of 7 and 14 over 5, we find their approximate values. Since 2.65 (root 7) is less than 2.8 (14/5), the correct mathematical symbol to use is <.
Explanation:The question asks us to compare two real numbers: the square root of 7 and 14 over 5. First, we need to estimate these numbers. The square root of 7 is approximately 2.65. 14 divided by 5 equals 2.8. Therefore, we can say that 2.65 is less than 2.8. As such, the mathematical symbol that should be used is < which means 'less than'.
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What is the simplified expression for the expression below
On a coordinate plane, parallelogram A B C D is shown. Point A is at (negative 3, negative 1), point B is at (7, 9), point C is at (8, negative 1), and point D is at (negative 2, negative 11). Create a rectangle around the parallelogram. The dimensions of this rectangle are ____(1). Find the area of the four right triangles surrounding the parallelogram. The total area of the triangles is _____(2) square units. Subtract the triangle areas from the area of the rectangle to obtain the area of the parallelogram. The area of parallelogram ABCD is ______(3) square units.
Answer: HOPE THIS HELPSS!!! please mark me brainliestt
11 by 20
110
110
Answer:
just wanted to say hi
Step-by-step explanation:
Plz give 5 star
At a certain time of day, the angle of elevation of the sun is 40°. To the nearest foot,find the height of a tree whose shadow is 35 feet long.
Multiply.
Your answer should be a monomial in standard form.
(Y^8)(-2y²) =
[tex]( {y}^{8} )( - 2 {y}^{2} ) = - 2 {y}^{10} [/tex]
To multiply the monomials (Y⁸)(-2y²), add the exponents and multiply the coefficients resulting in -2y¹⁰.
To multiply the given monomials (Y⁸)(-2y²), we use the laws of exponents which state that when multiplying like bases, we add the exponents. The coefficient -2 multiplies by 1 (the implied coefficient of Y⁸) to remain -2. The new exponent for 'y' is the sum of 8 and 2, which is 10. So, the product in standard form is -2y¹⁰.
Step by step solution:
Identify like bases, which in this case is 'y'.Add the exponents of 'y' (8 from Y^8 and 2 from y²) to get a new exponent of 10.Multiply the coefficients (1 and -2) to get -2.Write the final answer combining the new coefficient and the new exponent of 'y': -2y¹⁰.A sphere has a radius of 3 ft. What is the volume of the sphere? Give the exact value in terms of Pi.
Answer: 36π
Step-by-step explanation:
equation
V= 4/3(pi)r^3
Plz help don’t have enough time
Answer: The first answer is the right one (1.25 + 0.75g is less than or equal to 20)
Step-by-step explanation:
He can’t spend more than 20 right, so his full cost of the shoes and game has to be less than (or equal to) the amount he has, which is 20.
Answer:
i say A
Step-by-step explanation:
because he has $20 and it has to be either less than or equal to 20 in order to play games
The low temperature in Chicago was -3 °F. The low temperature in Milwaukee was -11 °F. Which statement is true?
-3 is greater than -11, so it was colder in Milwaukee.
-11 is greater than -3, so it was colder in Milwaukee.
-3 is greater than -11, so it was colder in Chicago.
-11 is greater than -3, so it was colder in Chicago.
Answer:
-11 is greater than -3, so it was colder in Milwaukee.
Step-by-step explanation:
-11 is greater than -3, so it was colder in Milwaukee. because -11 is less than -3 because it is more to the left which makes it less
Solve 2x² -9x-5=0 by factoring. what is the
Solution?
Answer:
0
Step-by-step explanation: