Answers
The correct location of exponential expression on the table is
2 1 1/2
((3 ×2)⁴ × 3⁻³)/ 2³ × 3 (3⁻³ × 2⁻³ × 6³)/ (4⁰)² (2⁴ × 3⁵)/ (2 × 3)⁵
(3² × 4³ × 2⁻¹)/(3 × 4)²
What are exponential expression and how do we solve for them?
Exponential expressions have a base raised to a power, whre the power it has been raise to tells us how many times the base should be multiplied by itself.
Lets simplify each exponential expression
1. ((3 ×2)⁴ × 3⁻³)/ 2³ × 3
= 6⁴ × 3⁻³/ 2³ × 3
= 1296 × 1/27 / 8 × 3
= 48 / 24
= 2
2. (2⁴ × 3⁵)/ (2 × 3)⁵
= 16 × 243 / 6⁵
= 3888 / 7776
= 1/2
3. (3² × 4³ × 2⁻¹)/(3 × 4)²
= (9 × 64 × 1/2) / 12²
= 288 / 144
= 2
4. (3⁻³ × 2⁻³ × 6³)/ (4⁰)²
= 1/27 × 1/8 × 216 / 1²
= 1
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Related Questions
Danielle ordered $118.75 worth of food for a party and had it delivered. She gave the delivery person a 25% tip. What is the total cost of the food with delivery, to the nearest cent?
Answers
Total cost of the food with delivery for Danielle is given by approximately $ 29.69.
Danielle ordered food for a party which costs = $118.75
Now she also gave the delivery person a 25% tip.
So the amount of tip which she paid to the delivery person is given by
= 25 percent of the amount $118.75
= 25% of the amount $118.75
= $(118.75*(25/100))
= $(118.75*(1/4)) [eliminating the similar terms from the numerator and denominator of the fraction 25/100]
= $ 29.6875
= $ 29.69 [Rounding off to the nearest cent]
Hence the total cost of food with the delivery is $ 29.69.
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reflected over y-axis, x-axis, or neither
1. B (-3,-7) B' (-7,-3)
2. D (5,-8) D' (5,8)
3. F (10,0) F' (-10,0)
pls hurry
Answers
Answer:
1. neither
2. x axis
3. y axis
Step-by-step explanation:
1. Neither
2. reflection over the x -axis
3. reflection over the y -axis
Explanation
The rule for a reflection over the x -axis is (x,y)→(x,−y)
The rule for a reflection over the y -axis is (x,y)→(−x,y)
1. B (-3,-7) B' (-7,-3) neither, this does not fit either rule
2. D (5,-8) D' (5,8) the y changes from -8 to + 8 so reflection over the x -axis
3. F (10,0) F' (-10,0) the x changes from +10 to -10 so reflection over the y -axis
Use the t-formulas to prove the following:
tan(1/2 x + pi/4) + tan(1/2 x - pi/4) = 2tanx
Answers
Answer:
m
Step-by-step explanation:
Chen is building a ramp for his remote control car. He wants the end of the ramp to extend 4 feet from the base of the ramp. The base of the ramp is 18 inches high. How long should the piece of wood for the ramp be?
Answers
The piece of wood for the ramp should be about 4.27 feet long using Pythagorean theorem.
Define Pythagorean theorem ?
The Pythagorean theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right-angled triangle. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the adjacent and opposite sides).
We can use the Pythagorean theorem to find the length of the ramp.
First, we need to convert the height of the ramp from inches to feet:
18 inches = 1.5 feet
Let x be the length of the ramp in feet. Then, according to the Pythagorean theorem:
[tex]x^2 = 4^2 + 1.5^2[/tex]
[tex]x^2 = 16 + 2.25[/tex]
[tex]x^2 = 18.25[/tex]
x ≈ 4.27
Therefore, the piece of wood for the ramp should be about 4.27 feet long.
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9 + n = -2?
A. -11 B. -7 C. 2 D. 7
Answers
Answer: Answer is A. -11
Step-by-step explanation:
Try doing all the numbers ( The answer choices) minus 9.
-11 - 9 = -2
If a < 0 and b > 0, then the point (a, b) is in Quadrant...
A. I
B. II
C. III
D. IV
Answers
Answer:
The point (a, b) would be in Quadrant III, where both the x-coordinate and y-coordinate are negative.
Select the correct answer. A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius? A. (-7, -1), 36 units B. (7, 1), 36 units C. (7, 1), 6 units D. (-7, -1), 6 units
Answers
The center of the circle is (-7, -1) and the radius is the square root of 36, which is 6. So, correct option is D.
To find the center and radius of a circle given by its equation in the form of (x-a)² + (y-b)² = r², we need to convert the given equation to this standard form by completing the square for both x and y terms.
x² + y² + 14x + 2y + 14 = 0
(x² + 14x) + (y² + 2y) = -14
(x² + 14x + 49) + (y² + 2y + 1) = -14 + 49 + 1 // add and subtract the square of half the coefficient of x and y terms respectively
(x + 7)² + (y + 1)² = 36
Comparing with the standard form (x-a)² + (y-b)² = r², we can see that the center of the circle is (-7, -1) and the radius is the square root of 36, which is 6.
Therefore, the correct answer is option D, (-7, -1), 6 units.
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Questions from Page 47 in Dale Seymour Publications' Developing Skills in Algebra Book B (adding all of this info in case someone needs to keyword it at some point)
3.] The length of one rectangle is 7 m more than the width. The width of a smaller rectangle is 4 m less than and the length is 3m more than the width of the larger rectangle. The difference in the areas of the two rectangles is 108 m^2. Find the length of the smaller rectangle.
5.] A rectangular swimming pool with uniform depth is 12 ft wider than twice the depth and 10 ft longer than five times the depth. The volume of the pool is 5640 ft^3 less than the sum of ten times the cube of the depth and eight times the product of the length and width. Find the length of the pool.
6.] The longer base of a trapezoid is 12 cm more than the height, and the shorter base is 6 cm less than the longer base. The area of the trapezoid is 167 cm^2 less than the product of the bases. Find the height of the trapezoid.
7.] The width of a rectangular gravel pit is 1 m less than 4 times its depth, and the length is 3 m more than 16 times the depth. The volume is 45 m^3 less than the difference between 64 times the cube of the depth and 4 times the square of the depth. Find the length of the gravel pit.
Answers
For the 5th question, the length of the pool based on the information given will be 70ft.
How to calculate the lengthThe length of the pool can be described by the equation: length = 5x + 10, while the width of the pool can be portrayed through the equation: width = 2x + 12.
After weighing out the rationale for both sides of the expression, simplify it down to: x^3 + 12x^2 - 528x - 564 = 0. This can be broken up with synthetic division or a calculator and a possible solution to this problem is x = 12.
Further compounding the two equations, length = 70 ft and width = 36 ft emerge; presenting length being 70 ft and width claimed at 36 ft.
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Kara's teacher divides her class of 20 students into 4 equally sized teams: the red team, the yellow team, the green team, and the blue team. She assigns each student to a team. What is the probability that Kara is on the red team?
Answers
The probability of Kara is on the red team among all four equally sized team is given by 0.03%.
Total number of students in class = 20
Number of equally sized team = 4
Since there are 4 equally sized teams and 20 students,
There are 20/4 = 5 students on each team.
Since each student is equally likely to be assigned to any of the four teams.
The probability of Kara being on the red team is ,
= Ratio of number of ways she can be assigned to red team to total number of possible assignments.
The number of ways Kara can be assigned to the red team is 5 since there are 5 students on the red team.
Total number of possible assignments is the number of ways to choose 5 students out of 20.
= ²⁰C₅
= 20! / (5! × 15!)
= 15,504
The probability that Kara is on the red team is,
⇒ P(Kara is on the red team) = 5/15,504
⇒ P(Kara is on the red team) ≈ 0.0003225
⇒ P(Kara is on the red team) ≈ 0.03%.
Therefore, the probability of the Kara is on the red team is equal to 0.03%.
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Graph the inequality y is greater than or equal to one third times x plus one.
The graph shows a solid line that passes through negative 3 comma 0 and 0 comma 1, with shading above the line.
The graph shows a solid line that passes through negative 3 comma 0 and 0 comma 1, with shading below the line.
The graph shows a dashed line that passes through negative 3 comma 0 and 0 comma 1, with shading above the line.
The graph shows a dashed line that passes through negative 3 comma 0 and 0 comma 1, with shading below the line.
Answers
Answer:
Step-by-step explanation:
The inequality y ≥ (1/3)x + 1 represents all the points that lie on or above the line y = (1/3)x + 1.
To graph this line, we can first plot the y-intercept at (0, 1). From there, we can use the slope of (1/3) to find additional points on the line.
For example, if we move one unit to the right (x = 1), we would move up one-third units (y = 1 + 1/3), giving us the point (1, 4/3). Similarly, if we move two units to the right (x = 2), we would move up two-thirds units (y = 1 + 2/3), giving us the point (2, 5/3).
To indicate that the inequality includes points on the line, we use a solid line.
Finally, to determine which region to shade, we can test a point not on the line. For example, the point (0, 0) is below the line, so we shade the region above the line.
Therefore, the correct answer is: The graph shows a solid line that passes through negative 3 comma 0 and 0 comma 1, with shading above the line.
Dessie has 2 hours of free time. She spent 20 minutes completing her reading assignment, 25 minutes working on a craft, and the remaining amount of time playing outside. What percent of her time was spent playing outside?
Answers
Answer:
Step-by-step explanation:
solve the simultaneous equation:
2x+3y=13
4x-y=-2
Answers
Answer:
x=1/2, y=4
Step-by-step explanation:
2x+3y=13
or,y=(13-2x)/3 ........eq(i)
4x-y=-2
or,y=4x+2 ..............eq(ii)
From eq(i) and (ii),
(13-2x)/3=4x+2
or,13-2x=12x+6
or,13-6=12x+2x
or,7=14x
or,x= 7/14
x=1/2
y=4×(1/2)+2
y=4
Jenise wants to find out if the students at her school
would support using money to buy new band uniforms.
Which survey will result in a random sample?
A. She asks each student on her bus.
B. She asks all brand members in the school.
C. She picks every fourth student that leaves the school on
Tuesday.
D. She picks 75 names at random, sends emails, and records
those that return.
Answers
If Jenise wants to find out if the students at her school would support using money to buy new band uniforms, the survey that will result in a random sample is D. She picks 75 names at random, sends emails, and records those that return.
What is a random sample?A random sample is a sample that gives each unit in the population an equal chance of participation or being selected.
A random sample involves selecting a subset of the population. The result of the sample survey is generalized on the population to each some conclusions about the population parameters.
Thus, the correct option is D because it involves a random selection.
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The diameter of Earth is about 7,920 miles. A satellite orbits 200 miles above Earth’s surface. Calculate the circumference of Earth and the distance the satellite travels in one orbit around Earth.
Answers
Circumference = π x Diameter
where π (Pi) is a mathematical constant approximately equal to 3.14.
Circumference = 3.14 x 7,920 miles
Circumference = 24,876.8 miles
So the circumference of Earth is approximately 24,876.8 miles.
The distance traveled by the satellite during one orbit around Earth is equal to the circumference of the orbit, which is the sum of the distance traveled horizontally (the circumference of Earth) and the distance traveled vertically (the altitude of the satellite).
The altitude of the satellite is given as 200 miles, so the radius of the orbit is 7,920 + 200 = 8,120 miles. The circumference of the orbit can be calculated using the formula:
Circumference of orbit = 2 x π x radius
Circumference of orbit = 2 x 3.14 x 8,120 miles
Circumference of orbit = 51,139.2 miles
So the distance traveled by the satellite during one orbit around Earth is approximately 51,139.2 miles.
7,920 × 3.14 = 24,868.8, not the answer above. How is this right?
Amelia is going to invest $47,000 and leave it in an account for 5 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Amelia to end up with $64,000?
Answers
The interest rate required in order for Amelia to end up with $64,000 assuming the interest is compounded continuously is 6.2%.
Given that,
Amelia is going to invest $47,000 and leave it in an account for 5 years.
Principal amount, P = $47,000
Time, t = 5 years
Final amount, A = $64,000
Interest is compounded continuously.
Final amount, A, can be calculated as,
A = P e^(rt)
64,000 = 47,000 e^(5r)
e^(5r) = 1.3617
Taking natural logarithms on both sides,
5r = ㏑ (1.3617)
r = 0.0617 ≈ 6.2%
Hence the interest rate is 6.2%.
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The square shown is dilated by a factor of 2. What is the area, in square units, of the dilated square?
Answers
Answer:
18
Step-by-step explanation:
To solve this problem, you could either do this two ways: solve for x immediately and then multiply it by 2, or you could multiply the equation by two and solve for x.
I will be using the first option.
Step 1: Solve for x
[tex]-2x+7=-4x+11\\\\[/tex] - We can set these equal to each other because a square has all sides congruent, which means that this side and all the others are equal to each other
[tex]-2x+2x+7=-4x+2x+11\\\\7=-2x+11[/tex]- We add 2x to both sides so we can isolate all the variables on one side and all the constants on one
[tex]7-11=-2x+11-11\\\\-4=-2x[/tex]- We do this so all the constants are on one side
[tex]\frac{-4}{-2}=\frac{-2x}{-2} \\\\2=x[/tex]- We divide by the coefficient of x so that we can fully isolate it
So now we have what x is, so we have to reinsert x into the equations and multiply it by itself to find the original area, after that we multiply it by 2.
[tex]-2x+7\\\\-2(2)+7\\\\-4+7\\\\3*3=9\\\\9*2=18[/tex]
how the value of x is applied ?
justify your answer
Answers
a state accounting process in brief
The transformation from green triangle to red triangle can be described as "a 9 unit slide to the right." It can also be written mathematically as `\left(x,\ y\right)`--> `\left(x+9,\ y\right)`. (Note: I used the minus sign twice and a greater than to make an arrow. Describe in words and in symbols the transformation from green triangle to blue triangle.
Answers
The transformation from green triangle to blue triangle is translation moved down by 6 units.
Given that,
Vertices of green triangle are (-3, 9), (-5, 4) and (2, 6)
Vertices of blue triangle are (-3, 3), (-5, -2) and (2, 0)
We can see that, x-coordinates of all the ordered pairs are same.
y-coordinates of all the ordered pairs are changed that is
(9-3)=6, (4-(-2))=6 and (6-0)=6
So, the triangles are slide down by 6 units.
Mathematically it is represented as (x, y-6)
Therefore, the transformation from green triangle to blue triangle is translation moved down by 6 units.
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PLEASE HELP!!!!
Complete the frequency table:
Method of Travel to School
Walk/Bike | Bus | Car | Row totals
Under age 15 | 0 | 0| 18| 165
Age 15 and above | 65 | 0 | 0| 195
Column totals | 152 | 110 | 98 |360
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
A. 36%
B. 26%
C. 45%
D. 50%
Answers
Walk/Bike | Bus | Car | Row totals
---|---|---|---
65 | 0 | 0 | 195
The table tells us that 0 students age 15 and above travel to school by bus, out of a total of 195 students in that age group. To find the percentage, we can use the formula:
percentage = (part/whole) x 100
where "part" is the number of students age 15 and above who travel to school by bus, and "whole" is the total number of students age 15 and above.
So, the percentage of students age 15 and above who travel to school by bus is:
(0/195) x 100 = 0%
Rounding to the nearest whole percent, the answer is (A) 0%, since there are no students age 15 and above who travel to school by bus according to the table.
At a high school football game, Mike bought 4 soft pretzels and 4 bottles of water for $15. Ling bought 3 soft pretzels and 2 bottles of water for $10. What is the cost of each item?
Answers
If Mike bought 4 "soft-pretzels" and 4 bottles of water for $15, Ling purchased 3 "soft-pretzels" and 2 bottles of water for $10, the each "soft-pretzels" cost $2.5 and each "water-bottle" cost 1.25.
Let the cost of a "soft-pretzel" be = $x and
Let the cost of a bottle of water be = $y,
We know that, Mike purchased 4 "soft-pretzels" and 4 bottles of water for $15,
Ling purchased 3 "soft-pretzels" and 2 bottles of water for $10,
So, the equations are :
⇒ 4x + 4y = 15 ...(1)
⇒ 3x + 2y = 10 ...(2)
We solve this by using substitution method:
Solving equation (2),
We get,
⇒ 3x + 2y = 10,
⇒ x = (10 - 2y)/3,
Now we substitute this expression for "x" in equation(1),
⇒ 4x + 4y = 15,
⇒ 4[(10 - 2y)/3] + 4y = 15,
⇒ y = 5/4,
Substituting this "y" into equation(2),
We get,
⇒ 3x + 2y = 10,
⇒ 3x + 2(5/4) = 10,
⇒ x = 5/2 = 2.5,
Therefore, cost of a soft pretzel is $2.5 and cost of a bottle of water is $1.25.
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You will turn in the results of this activity for your assessment for this lesson.
Create a wrapping paper design that includes at least four of the following constructions:
a bisected angle
a perpendicular line drawn from a point not on a line to a line
a perpendicular line drawn through a given point on a given line
a quadrilateral with at least one pair of parallel lines
a segment bisected by a perpendicular line
two congruent angles
two congruent segments
two parallel lines, one of which is drawn through a given point
Your design should be8 and one-half inches by 11 inches (the size of a standard sheet of computer paper).
Number each element and create a key that names each element in your design. For example: Element 1: Two congruent segments. If several elements are combined in one figure, then number each element in that figure and describe each element on the key.
Create instructions, in your own words, describing how to create each element using only a compass and a straightedge.
Give your key and your instructions to a friend and see if they can recreate your wrapping paper design. If she can’t, then revise your key and instructions so that there is no room for confusion.
You will turn in the following:
a key describing each element
a wrapping paper design with the elements numbered
instructions for creating each element, written in your own words
Answers
The wrapping paper design could consist of a repeating pattern of quadrilaterals with at least one pair of parallel lines.
How to explain the quadrilateralInside each quadrilateral, there could be two congruent angles and two congruent segments. The segments could be bisected by perpendicular lines, creating a bisected angle within the quadrilateral.
In addition, there could be perpendicular lines drawn from a point not on a line to a line and perpendicular lines drawn through given points on given lines. These lines could intersect with the quadrilaterals in various ways, creating a dynamic and visually interesting design.
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Algebrai expression (1+2)1-4)
Answers
Answer:
-9
Step-by-step explanation:
(1+2)1-4)
(3) - 3
-9
The point B lies on the segment AC.
Find the coordinates of B so that AB is 5/9 of AC
Answers
The coordinates of B so that AB is 5/9 of AC is (51/14, -10/7).
What is a coordinate?Coordinates are a pair of numbers which are used to determine the position of a point or a shape in a 2-dimensional plane.
To calculate the coordinates of B (x,y), so that AB is 5/9 of AC, we use the formula below
Formula:
For y coordinate = (my₂+ny₁)/(m+n)................... Equation 1Ferom the question,
Given:
m = 5n = 9y₁ = 5y₂ = -13Substitute these value into equation 1
y = [5(-13)+9(5)]/(9+5)y = -20/14y = -10/7Similarly for coordinate x we use the formula below
x = (mx₂+nx₁)/(m+n)............. Equation 2Where:
x₁ = -6x₂ = 21Substitute into equation 2
x = [5(21)+9(-6)]/(5+9)x = 51/14Hence, the coordinates of B is (51/14, -10/7).
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Convert 0.009m to milli meters
Answers
Answer:
0.009 meters is equal to 9 millimeters.
Please solve this as soon as possible!
Answers
The values of the trigonometric identities are;
sin θ = 4/5 = 0. 800
cos θ = 3/5 = 0. 600
tan θ = 4/3 = 1. 333
How to determine the valuesThere are six trigonometric identities;
sinecosinetangentcotangentsecant cosecantFor the secant identity, we have the ratio;
sec θ = hypotenuse/adjacent
Then, using the Pythagorean theorem, we have the the square of the hypotenuse is equal to the sum of the squares of the other two sides, then
5² = 3² + x²
x² = 25 - 9
x²= 16
find square root
x = 4
For the value of sin θ
sin θ = 4/5 = 0. 8000
For cosine ratio
cos θ = 3/5 = 0. 6000
for tangent ratio
tan θ = 4/3 = 1. 333
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Amanda's office has 40 employees.
The employees want to have a catered
dinner. They have found a company
that will provide what they need for $25
per person. Amanda knows that some
people will bring a guest. The company
has budgeted $1500 for this event. How
many guests can they invite? Assume the
price of $25 includes all taxes.
Write an equation for this problem.
Answers
Answer:
[tex]25x+1000=1500[/tex] which means [tex]x=20[/tex] guests
Step-by-step explanation:
The initial 40 employees cost 40*25 = $1000
So, we can set up the equation:
[tex]25x + 1000=1500[/tex] where x is the number of guests.
This means [tex]25x=500[/tex].
[tex]x=20[/tex]
a coin is to be tossed 1000 times. what is the probability that the 785th toss is heads? group of answer choices 0 1/4 1/2 3/4 1
Answers
A coin is to be tossed 1000 times, the probability that the 785th toss is heads is 1/2.
Hence option c is the correct answer.
A coin is to be tossed 1000 times and the probability of the outcome to be Heads oor Tails is recorded accordingly.
Probability of an event refers to the possibility of the event to occur or in other words, how likely is tthe event to occur. Probability ranges from 0 to 1 as number and 0% to 100% as percentage.
Probability can be calculated with the formula as,
Probability of an event to occur = (Nmber of favourable outcomes) / (Total number of outcomes possible)
Here, when tossing a coin we have two outcomes, Heads and Tails
The number of favourable outcome, that is the outcome is Heads is 1.
Thus the probability that the outcome is a Head = 1/2
When a coin is tossed for 785th time the probability that the head will come up = 1/2 (assuming that the coin is unbiased).
The probability remains unchanged for tossing the coin for the first time and for the 785th time since no number of times the coin is tossed the number of favourable outcome is 1 and total outcomes is 2.
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What is the approximate circumference of a circle that has a radius of 90? Use 3.14 for π and express your answer to the tenths place. fill in the blank
__
Answers
Answer:
565.2
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi * r
C = 2 * (3.14) * 90
C =565.2
Answer:
565.2
Step-by-step explanation:
Given,
Radius ( r ) = 90
π = 3.14
To find : Circumference of a circle
Formula
Circumference of a circle = 2πr
Circumference of a circle
= 2 x 3.14 x 90
= 6.28 x 90
= 565.2
An actor invested some money at 9% simple interest, and $49,000 more than three times the amount at 10%. The total annual interest earned from the investment was $38,440. How much did he invest at each amount?
Answers
An actor invested some money at 9% simple interest, and $49,000 more than three times the amount at 10%. The total annual interest earned from the investment was $38,440. Then, the actor invested $307,000 at 10% simple interest.
Let's use the following variables to represent the amounts invested;
x; amount invested at 9% simple interest
3x + 49000: amount invested at 10% simple interest (as it is $49,000 more than three times the amount invested at 9%)
We know that the total annual interest earned from the investment was $38,440, so we can set up the following equation;
0.09x + 0.1(3x + 49000)
= 38440
Simplifying and solving for x, we get;
0.09x + 0.3x + 4900 = 38440
0.39x = 33540
x = 86000
So the actor invested $86,000 at 9% simple interest. Using this value, we can calculate the amount invested at 10%;
3x + 49000 = 3(86000) + 49000
= 307000
Therefore, the actor invested $307,000 amount.
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on an american roulette table, there are 38 squares that correspond to 38 slots in the roulette wheel. you can bet on single squares or combinations of squares. each square has a number and a color. eighteen of the squares are red, 18 are black, and 2 are green. one thing you can do is bet red (or black), and it pays even money. (you risk $1, but if the roulette lands on any red space, you get back your $1 plus $1 in winnings.) if you play 30 times, betting $1 on red each time, what is the probability you will come out ahead? 0.64 0.36 0.50 none of the above.
Answers
The probability of coming out ahead after 30 spins is about 0.0732
The probability of winning on a single spin by betting on red (or black) is 18/38, which is approximately 0.4737.
Assuming each spin is independent of the others, the probability of winning exactly 15 times out of 30 is given by the binomial distribution with n=30 and p=0.4737. This can be calculated using the formula
P(X = k) = (n choose k) × [tex]p^k[/tex] × [tex](1-p)^{n-k}[/tex]
where X is the random variable representing the number of times we win in 30 spins, k is the number of times we win, "choose" denotes the binomial coefficient, and ^ denotes exponentiation.
Using a calculator or software that can calculate binomial probabilities, we find that
P(X = 15) = (30 choose 15) × 0.4737¹⁵ × 0.5263¹⁵ ≈ 0.0971
This means that the probability of winning exactly 15 times out of 30 is about 0.0971, or approximately 9.71%.
To find the probability of coming out ahead (winning more than you bet) after 30 spins, we need to consider all the possible outcomes. If we win exactly 15 times, we break even (winning 15 dollars and losing 15 dollars). If we win more than 15 times, we come out ahead. If we win less than 15 times, we come out behind.
The probability of winning more than 15 times can be calculated by adding up the probabilities of winning 16 times, 17 times, and so on, up to 30 times. This can be expressed as
P(X > 15) = P(X = 16) + P(X = 17) + ... + P(X = 30)
Using the same binomial distribution formula as before, we can calculate each term in this sum and add them up:
P(X > 15) ≈ 0.0732
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The give question is incomplete, the complete question is:
On an American roulette table, there are 38 squares that correspond to 38 slots in the roulette wheel. you can bet on single squares or combinations of squares. each square has a number and a color. eighteen of the squares are red, 18 are black, and 2 are green. one thing you can do is bet red (or black), and it pays even money. (you risk $1, but if the roulette lands on any red space, you get back your $1 plus $1 in winnings.) if you play 30 times, betting $1 on red each time, what is the probability you will come out ahead?
