Answer:
Both models are exponential
A: $21,573.58
B: $21,589.58
Step-by-step explanation:
A
f(x) = 16,000[tex](1 + .03/4)^{4(10)}[/tex]
f(x) = (16000)[tex]1.0075^{40}[/tex]
f(x) = $21,573.58 Rounded to the nearest cent.
B
f(x) = 16000[tex](1+ .03/12)^{12(10)}[/tex]
f(x) = (16000)[tex]1.0025^{120}[/tex]
f(x) = $21,589.66 Rounded to the nearest cent
In a bag of 10 marbles, there are 4 blue, 3 red, 2 green, and 1 yellow. What is the probability that you draw one marble that is blue, replace it, and draw another marble that is green? Enter your answer as a fraction in lowest terms. Do not add spaces to your answer. (EX: 1/2)
Work Shown:
A = the 1st marble is blue
B = the 2nd marble is green
Replacement is applied. This makes A and B independent.
P(A) = (4 blue)/(10 total) = 4/10 = 2/5
P(B) = (2 green)/(10 total) = 2/10 = 1/5
P(A and B) = P(A)*P(B) ... see note below
P(A and B) = (2/5)*(1/5)
P(A and B) = 2/25
Note: The equation is valid because events A and B are independent.
If Tristan's pay was $1600 for the week, he sold ? vacuums
Answer: $3,000
(There are 7 days in a week) I don't know if i'm correct or not but it should be the answer.
In a survey of 500 tourists, 350 like Pokhara, 200 like Chitwan and number of tourist who like both is half of who like Chitwan and 20 like neither of two, using Venn-diagram find how many like only one place.
Answer:
160 tourists like only one place. This can be determined by using a Venn diagram. Of the 500 tourists surveyed, 350 like Pokhara, 200 like Chitwan, and 50 like both places. That leaves 20 who like neither of the two places. To get the number of tourists that like only one place, subtract the number of tourists who like both (50) and the number of tourists who like neither (20) from the total number of tourists surveyed (500), resulting in a total of 160 tourists who like only one place.
The area of the triangle is less than 18 square inches. Find the possible
values of a by writing and solving an inequality.
Area of a triangle = (base height)
a
6 in
⚠️HELP IM FAILING MATH⚠️
Answer:
0 < a < 6
or
(0, 6) in interval notation
Step-by-step explanation:
The area of the triangle is
[tex]Area \;A = \dfrac{1}{2}(base \cdot height)\\[/tex]
We are given base = 6 in, height = a and area A < 18 in²
Using the formula for area we get
[tex]A = (1/2)(6 \cdot a) = 3a[/tex]
We know this area is < 18
So 3a < 18
Dividing both sides by 3 gives us
3a/3 < 18/3
a < 6
So height a must be less than 6 inches.
Height cannot be 0 so the lower bound on height is
a > 0
Putting these together we get the rang of a as
0 < a < 6
In Interval notation this is written as (0, 6)
Hope that helps you. Have confidence in yourself and seek help for your doubts here or elsewhere on the net. You will succeed
Given the point g' at (4,6) and the rule (x,y) > > > (x-7,y+3). Find the coordinates of g.
The new co-ordinates of the point after transformation is (-3,9)
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,
Given here: The point g'(4,6)
The point transforms to (x-7,y+3)
Thus the new points are 4⇒4-7=-3
6⇒6+3=9
Thus, The new co-ordinates of the point after transformation is (-3,9)
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A fitness center has several rectangular rooms where exercise classes are held. The area of Room A is 27x−18 square units. What are possible dimensions of Room A?
The possible dimensions of rectangular room A are 9 and 3x - 2.
What is rectangular shape?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.
Given:
A fitness center has several rectangular rooms where exercise classes are held.
The area of Room A is 27x − 18 square units.
The area of the rectangle = length x width
27x − 18 = length x width
9 (3x - 2) = length x width.
Therefore, 9 and 3x - 2 are the dimensions.
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Choose whether the representation is or is not a function for the problem and select the
reasoning for the answer.
30
8
18
28
38
Y
77
77
77
- 77
To verify if the representation is a function for this problem, we should verify if each input is mapped to a single output. If there is an input that is mapped to more than one output, then the relation is not a function.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.
With arrows, only one arrow can depart from each value of x, or more than one arrow departing from the same value of x but necessarily arriving at the same value of y.
Missing InformationThe problem is incomplete, hence the general procedure to verify if a relation represents a function was presented.
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Geraldine is 4 years younger than Tom. If Tom is t years old, how old is
Geraldine? Also, if Steven is twice as old as Geraldine, how old is he?
Using equations, we know that the age of Geraldine and Steven is t - 4 and 2t - 8 respectively.
What are equations?It basically consists of a variable, perhaps with an additional numerical constant.
To easily understand this concept, consider the example below. 3x – 4 = 5. It is a straightforward class 7 equation.
The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
So, we have the following algebraic expression after converting the word problem:
To Geraldine:
g = t - 4
To Steven:
s = 2g
Inputting Tom's age into equation 1 results in:
g = t - 4
To determine Steven's age:
s = 2(t-4)
s = 2t - 8
Therefore, using equations, we know that the age of Geraldine and Steven is t - 4 and 2t - 8 respectively.
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8) The graph shows the total cost C of making x photocopies at a copy shop.
Making Photocopies
Total cost (dollars)
40
35
30
25
00
0
100 200 300 400 500
Number of copies
X
a) Does it cost more money to make 100 photocopies or
101 photocopies? Explain.
b) You have $40 to make photocopies. Can you buy more
than 500 photocopies? Explain.
Answer: a) It costs more money to make 101 photocopies than 100 photocopies. This can be seen from the graph as the cost increases as the number of photocopies increases.
b) You cannot buy more than 500 photocopies with $40. This can be seen from the graph as the cost of making photocopies exceeds $40 when the number of photocopies is more than 500.
Step-by-step explanation:
The solution is,
a) it costs more money to make 100 photocopies
b) you can buy more than 500 photocopies for $40
Here, we have,
we know that,
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
a) In the graph , 100 photocopies cost $10,
For 101 photocopies, the point on the line comes below of 10 on y axis
So, it costs more money to make 100 photocopies
b) graph arrow shows line moves on...
so, you can buy more than 500 photocopies for $40
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**I WILL GIVE 50 POINTS, A HINT TO THE ANSWER, AND BRAINLIEST**
A cone has a volume of 392π cubic centimeters and a radius of 7 centimeters. What is the height of the cone? Be sure to show all work again (HINT: instead of solving for the radius, you will be solving for the height since you know what the radius measurement already is)!
The height of the cone is 24 centimetres.
How to find the height of the cone?A cone has a volume of 392π cubic centimetres and a radius of 7 centimetres. Therefore, the height of the cone can be found as follows;
Hence,
volume of a cone = 1 / 3 πr²h
where
h -= height of the coner = radius of the coneTherefore,
volume = 392π
r = 7 cm
392π = 1 / 3 × π × 7² × h
392π = 49 / 3 πh
cross multiply
1176π = 49πh
divide both sides by 49π
h = 1176π / 49π
h = 24 cm
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solve the system of equations below
The solution of the system of equations is:
x = 3
y = 2
How to solve the system of equations?Here we want to solve the system of equations below:
2x + y = 8
x - 3y = -3
First, let's isolate one variable in one of the equations, I will isolate y on the first one.
y = 8 - 2x
Now we can replace that in the other one to get:
x - 3*(8 - 2x) = - 3
x - 24 + 6x = -3
7x = -3 + 24
7x = 21
x = 21/7 = 3
And the value of y is:
y = 8 - 2x = 8 - 2*3 = 2
The solution is x = 3 and y = 2.
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Tito purchased 11 tickets to a baseball game for $374. About how much did one ticket cost?
Answer: It is 34$ per one ticket
Step-by-step explanation:
$374 divided by 11 is 34
Answer:
$34 per ticket
Step-by-step explanation:
We were told $374/11tickets.
We are looking for how much per 1 ticket.
Divide to find the per-ticket cost.
Use either 374÷11
374/11 .
374÷11 = 34
This means $34 per ticket.
forty two out of fifty six students voted Michael for president. What fraction of the workers did not vote for him?
Answer: [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
1) Subtract Michael's voters from all the voters 56/56 - 42/56. When you have the same denominator, subtract the numerator and keep the denominator the same to get 14/56.
2) Simplify, both the numerator and denominator is divisible by 14, so divide 14/14 to get 1 as our new numerator and divide 56/14 to get 4 as our denominator leading us to our answer of 1/4
Find a solution to this system of equations:
5x-3y=20
15x+6y=60
Write your solution in (x,y) form.
Please help!!!!!
Answer:
(x, y) = (4, 0)
Step-by-step explanation:
You want the solution to the system of equations ...
5x -3y = 2015x +6y = 60Standard formIt often works well to start the solution process by putting both equations into standard form. We do that by removing any common factors from the coefficients. Here, we see that the second equation's coefficients each have a factor of 3, so we can remove that and rewrite the system as ...
5x -3y = 205x +2y = 20ObservationChanging the coefficient of the y-term has no effect, telling us that y=0, and the equation reduces to ...
5x = 20
x = 4
More formally, if we subtract the first equation from the second, we get ...
(5x +2y) -(5x -3y) = (20) -(20)
5y = 0 . . . . . . simplify
y = 0 . . . . . . . divide by 5
The solution is (x, y) = (4, 0).
Answer. please.........
The area of the given parallelogram is 6.6 square units.
What is the area of the parallelogram?The region or space occupied by a parallelogram in a two-dimensional plane is referred to as the area of a parallelogram. A unique category of a quadrilateral is a parallelogram.
A quadrilateral is referred to as a parallelogram if it has two sets of parallel opposite sides. A parallelogram can be anything from a rectangle to a square to a rhombus.
The area of the partogram is calculated as:-
Area = Base x Height
Area = 2.2 x 3
Area = 6.6 square units
Therefore, the parallelogram will have an area of 6.6 square units.
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What is equation of the line graphed below. Y= - 5/2 x-2 -this question was accidentally cut out
Answer:
y = - [tex]\frac{5}{2}[/tex] x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line
m = [tex]\frac{-2-3}{0-(-2)}[/tex] = [tex]\frac{-5}{0+2}[/tex] = - [tex]\frac{5}{2}[/tex]
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = - [tex]\frac{5}{2}[/tex] x - 2 ← equation of line
A ball is thrown from the top of a building with an initial velocity of 10 m/s and a height of 100 m. The ball makes an angle of 30 degrees with the horizontal and reaches a maximum height of 80 m. Calculate the potential energy of the ball at its highest point.
Step-by-step explanation:
To calculate the potential energy of the ball at its highest point, we first need to find the gravitational potential energy of the ball. Gravitational potential energy is given by the equation:
PE = mgh
where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s^2 on the surface of the earth), and h is the height of the ball above the ground.
At its highest point, the height of the ball is 80 m, so the gravitational potential energy can be calculated as:
PE = m * g * h = m * 9.8 * 80
where m is the mass of the ball.
Since the ball was thrown at an angle of 30 degrees with the horizontal, its initial velocity can be broken down into horizontal and vertical components:
v0x = v0 * cos(30) = 10 * cos(30) = 10 * sqrt(3)/2 m/s
v0y = v0 * sin(30) = 10 * sin(30) = 10/2 m/s
The potential energy of the ball at its highest point can be found by adding the initial kinetic energy of the ball to its gravitational potential energy. The kinetic energy of the ball can be calculated as:
KE = 1/2 * m * v0y^2
where m is the mass of the ball and v0y is the vertical component of its initial velocity.
The total potential energy of the ball at its highest point is given by:
PE = KE + mgh = 1/2 * m * v0y^2 + m * g * h
Substituting in the given values, we find:
PE = 1/2 * m * (10/2)^2 + m * 9.8 * 80
Note: The mass of the ball (m) is not given, so the answer is given in terms of m.
Answer:
Step-by-step explanation:
PE = 1/2 * m * (10/2)^2 + m * 9.8 * 80
6. Find the measure of an angle if five times the measure of its complement is 24° less than
twice the measure of its supplement.
Equation:
Measure:
Answer: Let's call the measure of the angle x.
The complement of the angle is (90 - x) degrees, and the supplement is (180 - x) degrees.
So, using the information given in the problem, we can set up an equation:
5 * (90 - x) = 2 * (180 - x) - 24
Expanding both sides and simplifying, we get:
450 - 5x = 360 - 2x - 24
Solving for x, we get:
6x = 294
x = 49
Therefore, the measure of the angle is 49 degrees.
Step-by-step explanation:
Find 2 numbers whose product is 57, and one of the numbers is 5 less than eight times the other number
One of the numbers is 21, and the other number is 2.5
What is an algebraic expression?
An algebraic expression is when we combine numbers and words to solve a mathematical problem.
Let's call one of the numbers "x". We know that x is 8 times greater than the other number, which we'll call "y". So we have:
y = x / 8
The product of x and y is 57, so:
x * y = 57
Substituting y = x / 8 into the equation above:
x * (x / 8) = 57
Expanding the right side of the equation:
[tex]x^2 / 8 = 57[/tex]
Multiplying both sides by 8:
[tex]x^2 = 8 * 57[/tex]
Solving for [tex]x^2[/tex]:
[tex]x^2 = 456[/tex]
Taking the square root of both sides:
[tex]x =\sqrt{456}[/tex]
x = 21
So, One of the numbers is 21, and the other number is 21 / 8 = 2.5.
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Which other expression has the same value as (-14)-8
Answer: The expression (-14) - 8 has the same value as -22.
Which number has a digit that is 10x greater
than 70?
a) 3,607
b) 7,391
c) 1,738
d) 7,246
Answer:
C
Step-by-step explanation:
Look at 70. What digit is it in? The tens.x10 moves our digit once to the left (70 => 700) AKA 7 hundreds!Look at the answers.3607 ( "7" ones)
7391 ( "7" thousands)
1738 ( "7" hundreds)
7246 ( "7" thousands)
Find the roots of the function f(x)=x^2+15x-16
Answer:
x = -16 and x = 1
Step-by-step explanation:
"Finding the roots" means solving the equation. We'll set the equation equal to 0 (replace f(x) with zero) and factor.
0 = x^2 + 15x - 16
0 = (x + 16)(x - 1)
This is factored.
Using the Zero Product Property, we separate this into two small equations.
x+16 = 0 and x-1 = 0
Solve these one-step equations.
x = -16 and x = 1
These are the roots (and roots are solutions, are zeros, are x-intercepts) If the question ask for zeros, roots, solutions or x-intercepts, set it equal to 0, factor and solve.
Find the geometric mean between 4 and 5.
Answer:
1.106209714987%
Step-by-step explanation:
Negative values detected. All input values threated as percentages (e.g. an input of 0.1 is threated as 0.1%, -10 is threated as -10%).
Which expressions are equivalent to 7^{-2} times 7^{6}
Answer:
(7^2)^2
Step-by-step explanation:
(7^-2)*(7^6)=7^-2+6
......since the base 7 is the same, when u multiply them, you should add the exponents and keep 7 as it is. That will be 7^4, which in equivalent to ans D(7^2)^2
does anybody know the answer to this?
Step-by-step explanation:
x=97+40 degree (being sum of two interior angle is equal to one exterior angle)
HELP!!!!!!!ASAP!!! I NEED TO SUBMIT! WILL GIVE 100 POINTS AND BRAINLIEST!!!!!!!!!!
A group of students was asked about the number of flights they have taken. The data is shown in the line plot. Which of the following best describes the spread of the data? Explain its meaning in this situation. The data has a range of 5, which is a wide spread. This means the greatest number of flights was 5. The data has a range of 15, which is a narrow spread. This means that there is not a large difference in the number of flights taken by the students. The data has a range of 5, which is a narrow spread. This means that most of the students have taken a similar number of flights. The data has a range of 15, which is a wide spread. This means that there is a difference of 15 flights between each of the students.
Answer:
In the case presented, the range is the difference between the maximum value and the minimum value of the data. The range describes the breadth of the data and how much they vary from the minimum value to the maximum value. Therefore, the range indicates the dispersion of the data.
The statement indicates that the range is 5, which means that the most flights made by students is 5. Since the data has a narrow dispersion, we can conclude that most students have taken a similar number of flights, implying that most students have flown an amount close to the maximum number observed.
Therefore, the option that best describes the dispersion of the data is: "The data has a range of 5, which is a narrow dispersion. This means that most students have taken a similar number of flights."
Step-by-step explanation:
**I WILL GIVE 50 POINTS AND BRAINLIEST**
A cone has a volume of 192π cubic inches. Its height is 9 inches, what it's radius? Show all your work.
Answer:
4.5 inches
Step-by-step explanation:
The bookstore had 56 copies of magazine yesterday and sold 1/4 of them today sold 4/7 of what remain how many copies does the book store have 
Step-by-step explanation:
Find 1/4 of 56
56 / 4 = 14
Now
56-14=42
Now
42/7=6
6x4=24
42-24=18
18 copies left
"20 decreased by the sum of 6 and b."
Responses
A 20 + (6 – b)20 + (6 – b)
B 20 – (6 + b)20 – (6 + b)
C (20 + 6) – b(20 + 6) – b
D (20 – 6) + b
The expression for the statement is 20 - (6 + b).
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given statement is 20 decreased by the sum of 6 and b.
Sum means adding two or more numbers or expressions.
Sum of 6 and b means 6 + b.
Decreased means some number is subtracted.
The expression is 20 - (6 + b).
Hence the expression for the phrase is 20 - (6 + b).
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Your options for the question seems a little confusing. Probably the options for the question is given below :
In exercise 11-14 find the value of x for each one thank you whoever gets all of it right gets brainliest photo is below please help I have one day to turn this in or I fail
Answer:
For exercise 11: x = 64
For exercise 12: x = 66
For exercise 13: x = 89
For exercise 14: x = 99
Step-by-step explanation:
The sum of interior angles of an n-sided polygon = [tex](n- 2 )[/tex] x [tex]180^{o}[/tex]
where n = number of sides
For all the four figures in this exercise, n = 4
Therefore, Sum of interior angles = [tex](4 - 2)[/tex] x [tex]180^{o}[/tex]
= 2 x [tex]180^{o}[/tex]
= [tex]360^{o}[/tex]
For Exercise 11:
[tex]x^{o} + 100^{o} + 130^{o} + 66^{o} = 360^{o}[/tex]
[tex]x^{o} + 296^{o} = 360^{o}[/tex]
[tex]x = 360 - 296[/tex]
x = [tex]64^{o}[/tex]
Apply the above stated concept in the other three exercises