Answer:
1. $640
2. About 10.3 years later
Step-by-step explanation:
This is a compound decay problem. The formula is
[tex]F=P(1-r)^t[/tex]
Where
F is the future amount
P is the initial amount
r is the rate of decrease (in decimal), and
t is the time in years
Question 1:
We want to find F after 2 years of a phone initially costing 1000. So,
P = 1000
r = 20% or 0.2
t = 2
plugging into the formula, we solve for F:
[tex]F=P(1-r)^t\\F=1000(1-0.2)^2\\F=1000(0.8)^2\\F=640[/tex]
The phone is worth $640 after 2 years
Question 2:
We want to find when will the phone be worth 10% of original.
10% of 1000 is 0.1 * 1000 = 100
So, we want to figure this out for future value of 100, so F = 100
We know, P = 1000 r = 0.2 and t is unknown.
Let's plug in and solve for t (we need to use logarithms):
[tex]F=P(1-r)^t\\100=1000(1-0.2)^t\\100=1000(0.8)^t\\\frac{100}{1000}=0.8^t\\0.1=0.8^t\\ln(0.1)=ln(0.8^t)\\ln(0.1)=t*ln(0.8)\\t=\frac{ln(0.1)}{ln(0.8)}\\t=10.32[/tex]
So, after 10.32 years, the phone would be worth less than 10% of original value.
Which of the following elevations are deeper than -200 feet? Select all that apply.
-1,300 feet
sea level
300 feet
-250 feet
-400 feet
Answer:-250
Step-by-step explanation:
In the given right triangle, find the missing length to the nearest tenth.
13.3 ft
19.4 ft
2.8 ft
31.2 ft
Answer:
A)13.3
Step-by-step explanation:
20² + y² = 24²
400 + y² = 576
y² = 176
y=13.3
By Pythagoras theorem, in the given right triangle, the missing length to the nearest tenth is Option(A) 13.3 ft.
What is Pythagoras theorem?According to Pythagoras theorem, the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
Mathematically,
(Hypotenuse)² = (Base)² + (Height)² .
How to find the missing length of the given triangle ?For the given triangle, length of hypotenuse is 24ft., height is 20ft and base is y ft.
Using Pythagoras theorem,
⇒ (24)² = y² + (20)²
⇒ y² = 24² - 20²
⇒ y² = 176
∴ y = √176 = 13.2665 ≈ 13.3 ft.
Thus, by Pythagoras theorem, in the given right triangle, the missing length to the nearest tenth is Option(A) 13.3 ft.
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Jack owns a small restaurant called Best Burgers. For one week, he collected sales data on the type of side order served with each type of burger purchased. Jack serves a half pound of french fries with every kind of burger. If Jack sells 180 regular hamburgers how many pounds of french fries will he serve? (round to nearest whole number)
A) 35 pounds
B) 36 pounds
C) 54 pounds
D) 72 pounds
Answer:
The answer is C) 54 pounds
Step-by-step explanation:
because im batman
How many multiples of $8$ are between $100$ and $500$?
Answer:
There are 50 multiples of 8 between 100 and 500
Step-by-step explanation:
1. We need to find out the multiple of 8 closest and higher than 100.
......80, 88, 96, 104, 112, 120..... It's 104
2. We need to find out the multiple of 8 closest and lower than 500.
....480, 488, 496, 504, 512, 520......It's 496
3. Now, we use 104 and 496, this way:
(496 - 104)/8 + 1 =
392/8 + 1 =
49 + 1 = 50
There are 50 multiples of 8 between 100 and 500
Answer:
50
Step-by-step explanation:
The smallest multiple of 8 in this range is 13 ∙ 8 = 104, and the largest is 62 ∙ 8 = 496. The number of multiples of 8 in this range is the same as the number of numbers in the list
13, 14, 15, ...,60, 61, 62.
To count these, we subtract 12 from each, obtaining the new list
1, 2, 3, ..., 48, 49, 50,
which clearly contains 50 integers. There is one number in the original list for each number in the revised list, so the original list has 50 numbers in it, and there are 50 multiples of 8 between 100 and 500.
A box of pencils costs $10.The total cost (c) as a function of the number of boxes (b) is expressed as c = f(b) = 10b. What is the domain of this function?
A.
all positive integers and zero
B.
all real numbers
C.
all real numbers except 0
D.
all positive real numbers except 10
Answer:
All positive integers and zero
A is correct
Step-by-step explanation:
A box of pencils costs $10
The total cost (c) as a function of the number of boxes (b) is expressed as
c = f(b) = 10b
The function, f(b) = 10b
b is independent variable and c is dependent variable.
For any function find domain using independent variable.
b represents number of boxes.
Number of boxes neither be negative nor decimal.
Possible value of b: {0,1,2,3,4,5,.......}
All positive integers and zero.
Domain: All positive integers and zero
Complete the steps to find the difference
Answer:
3x² - 9x + 5
Step-by-step explanation:
Given
(5x² - 3x + 4) - (2x² + 6x - 1)
Distribute the first parenthesis by 1 and the second by - 1
= 5x² - 3x + 4 - 2x² - 6x + 1 ← collect like terms
= (5x² - 2x²) + (- 3x - 6x) + (4 + 1)
= 3x² - 9x + 5
What is the slope of the line that contains the points (4,8) and (9,8)? What type of line is it?
A. The line has no slope; it's a vertical line.
B. Slope = 0; horizontal line
C. The line has no slope; it's a horizontal line.
D. Slope = 0; vertical line
I believe the answer is B
Final answer:
The slope of the line containing the points (4,8) and (9,8) is 0, indicating that it is a horizontal line. The correct answer is B. Slope = 0; horizontal line.
Explanation:
The slope of a line is calculated by taking the difference in the y-values of two points on the line (rise) and dividing by the difference in the x-values (run). Using the points (4,8) and (9,8), we can calculate the slope as follows:
Change in y (rise) = 8 - 8 = 0Change in x (run) = 9 - 4 = 5Slope (m) = rise / run = 0 / 5 = 0.
Since there is no change in the y-value as we move from one point to the other, the line is horizontal. Thus, the line has a slope of 0. The correct answer to the student's question is B. Slope = 0; horizontal line.
a cylindrical container has a radius of 0.3 meter and a height of 0.75 meter the container is filled with kerosene. the density of kerosene is 815 kg/m^3
what is the mass of the kerosene in the container?
enter your answer in the box. use 3.14 for pi. round your final answer to the nearest whole number.
___kg
The volume of the cylinder is:
3.14 x 0.3^2 x 0.75 = 0.21 cubic meters.
Multiply the density of the kerosene by the volume of the cylinder:
0.21 x 815 = 17.85 kg.
Answer:
173
Step-by-step explanation:
A park ranger is looking out from their station at a 30 degree angle , angle of depression. The ranger is 80 feet above the ground.how far is it from the ranger up in the station down the fire?
Answer:
[tex]\boxed{\text{160 ft}}[/tex]
Step-by-step explanation:
The angle of depression from the ranger at point A and the angle of elevation from the fire on the ground at Point C are congruent (interior opposite angles).
The distance from the ranger up in the tower to the fire on the ground is the hypotenuse AC of the right triangle ABC.
sin 30 = 80/AC
AC = 80/sin30 = 80/0.5 = 160 ft
The distance is [tex]\boxed{\textbf{160 ft}}[/tex]
Two cars simultaneously left Points A and B and headed towards each other, and met after 2 hours and 45 minutes. The distance between points A and B is 264 miles. What is the speeds of the cars, if one of the cars travels 14 mph faster than the other?
The answer is:
[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]
Why?To calculate the speed of the cars, we need to write two equations in order to create a relation between the two speeds and be able to isolate one in function of the other.
So, let be the first car speed "x" and the second car speed "y", writing the equations we have:
For the first car:
[tex]x_{FirstCar}=x_o+v*t[/tex]
For the second car:
We know that the speed of the second car is the speed of the first car plus 14 mph, so:
[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]
Now, we already know that both cars met after 2 hours and 45 minutes, meaning that positions will be the same at that moment, and the distance between A and B is 264 miles, so, we can calculate the relative speed between them:
If the cars are moving towards each other the relative speed will be:
[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]
Then, since we know that they covered a combined distance which is equal to 264 miles of distance in 2 hours + 45 minutes, we have:
[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]
Writing the equation, we have:
[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]
We have that the speed of the first car is equal to 41 mph.
Now, for the second car we have that:
[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]
Hence, we have that:
[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]
Have a nice day!
Answer:
55 miles per hour and 41 miles per hour.
Step-by-step explanation:
Enjoy...It is correct because RSM told me so.
Need Help Please, This One Is A Bit Difficult.
Answer: 432 units²
Step-by-step explanation:
The figure is composed by two trapezoids.
The formula for calculate the area of a trapezoid is:
[tex]A=\frac{h}{2}(B+b)[/tex]
Where "B" is the larger base, "b" is the smaller base and "h" is the height.
Let be [tex]A_f[/tex] the area of the figure, [tex]A_1[/tex] the area of the trapezoid on the left and [tex]A_2[/tex] the area of the trapezoid of the right. Then the area of the figure will be:
[tex]A_f=A_1+A_2[/tex]
[tex]A_f=\frac{h_1}{2}(B_1+b_1)+\frac{h_2}{2}(B_2+b_2)[/tex]
Substituting values, you get:
[tex]A_f=\frac{16units}{2}(25units+4units)+\frac{10units}{2}(25units+15units)=432units^2[/tex]
Answer:
Area of given figure = 432 unit ²
Step-by-step explanation:
Points to remember
Area of trapezoid = h(a + b)/2
Where h - height and a and b are two parallel sides
To find the area of given figure
It is given two trapezoid
Area of 1st trapezoid
h = 16, a = 25 and b = 4
Area = h(a+ b)/2
= 16(25 + 4)/2
= 232 units ²
Area of 2nd trapezoid
h = 10, a = 25 and b = 15
Area = h(a+ b)/2
= 10(25 + 15)/2
= 200 units ²
Total area = 232 + 200 = 432 units²
In 1990, the rate of change of the world population was approximately 0.09125 billion per year (or approximately 1 million people every four days). The world population was estimated to be 5.3 billion in 1990.
Write an equation to model the population, P (in billions), in terms of t, where t is the number of years since 1990 (t = 0 corresponds to 1990)
A. P= 5.3 + 0.09125t
B. P= 5.3t + 0.09125
C. P= -5.3 + 0.09125t
D.P= -5.3t + 0.09125
Answer: Option A
[tex]P = 5.3 + 0.09125t[/tex]
Step-by-step explanation:
Note that for the initial year, 1990, the population was 5.3 billion.
The exchange rate is 0.09125 billion per year. In other words, each year there are 0.09125 billion more people.
In year 2 there will be 0.09125 * 2 billion people
In year 3 there will be 0.09125 * 3 billion people
In year 4 there will be 0.09125 * 4 billion people
In year t there will be 0.09125 * t billion of people
So the equation that models the number of people that there will be as a function of time is:
[tex]P = P_0 + rt[/tex]
Where [tex]P_0[/tex] is the initial population
[tex]P_0 = 5.3[/tex] billion
r is the rate of increase
[tex]r = 0.09125[/tex] billion per year
finally the equation is:
[tex]P = 5.3 + 0.09125t[/tex]
The correct answer is option A.
Find the length of the hypothesis of a 45degree -45 -90 triangle with leg length 13 square root of 2
Check the picture below.
Jerome is a co-owner of a small company and received 1/3 of the company’s profits this year. What were the company’s overall profits if Jerome made $150,000? Type an equation and solve..
Answer: $450,000
Step-by-step explanation:
Answer: $450,000
Step-by-step explanation:
We know that Jerome's earnings were from $150,000
And we know that this was 1/3 of the company's overall earnings.
Then let's call "x" to the company's general earnings
So a third multiplied by x must equal Jerome's earnings
[tex]\frac{1}{3}x=150,000[/tex]
Now we solve the equation for the variable x
[tex]x=150,000*3\\\\x= \$450,000[/tex]
Finally, the general earnings of the company were $450,000
Elizabeth is getting ready to run a marathon why is her thinking incorrect
I believe we would need some more information to help you answer
Answer:
ATP is an unstable molecule
Explanation:
Recall that ATP and ADP are too unstable to serve as long-term energy storage units. In contrast, glucose has a stable molecular structure, so it stores energy more efficiently than ATP.
#pennfosternotes
See page Biology (v2): Lesson 2: Page 65 in Biology_Lesson 2.pdf
Thanks so much! I hope this helps! =)
Use the graph , Help needed 10 points.
The answer is:
The function is greater or equal to 0 at the points (-3,6), (-2,0), (0,6) and (4,0).
Why?To find where the function is greater or equal to 0, we need to look (using the graph) where the function is above the x-axis
So, we can see that the function is above the x-axis from the point (-3,6) to the point (4,0), for these points, the function is greater or equal to 0.
Hence, the function is greater or equal to 0 at the points (-3,6), (-2,0), (0,6) and (4,0), or the function is greater or equal to 0, from -3 to 4 (x-axis values or input).
We have that:
[tex]f(-3)=6\\6\geq 0\\\\f(-2)=0\\0=0\\\\f(0)=6\\6\geq 0\\\\f(4)=0\\0=0[/tex]
Have a nice day!
determine the missing number in the equation 13-2=12-?
For the equation to work, you have to have the same number on both sides of the equal sign
so to find ?, you can do:
13 - 2 = 12 - ? Simplify
11 = 12 - ? Subtract 12 on both sides
-1 = - ? Multiply -1 on both sides
1 = ?
To find the missing number in the equation 13-2=12-?, we subtract the known numbers on both sides of the equation.
Explanation:To find the missing number in the equation 13-2=12-?, we subtract the known numbers on both sides of the equation.
In the equation 13-2=12-x, we need to find the missing number x.
We can solve this equation by subtracting the known numbers on both sides.
Subtract 2 from 13 to get 11.Subtract x from 12 to get 12-x.Using the concept of simple mathematics, we found the subtraction of the given number.
So the missing number in the equation 13-2=12-x is 11.
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A text message plan costs $3 per month plus $0.37 per text. Find the monthly cost for x text messages
The monthly cost of x messages is
dollars.
Answer:
y= (.37)x + 3
Step-by-step explanation:
1. Best thing to use would be y=mx + b.
2. Flat fee is $3 so that is your b.
y=mx+ 33. Every additional message is $0.37, that is your slope(m)
y=(.37)x + 34. That is your answer, x represents the number of text messages
Answer:
The monthly cost for x messages is (3 + 0.37x)$.
Step-by-step explanation:
We are given the following information in the question:
Monthly cost for text message = $3 per month
Cost of each text message = $0.37
Let x be the number of total text messages.
Monthly cost for x messages =
Formula:
[tex]\text{Monthly charges} + (\text{Text messages}\times \text{Cost of each message})\\\text{Putting the values, we get}\\= 3 + (0.37\times x)\\=3 + 0.37x[/tex]
Hence, the monthly cost for x messages is (3 + 0.37x)$.
Find the sum of the first 10
terms.
8,20,32,44,...
The sum of first 10 terms is 620.
What is arithmatic progression?Arithmetic Progression (AP) is a numerical series in which the difference between any two subsequent numbers is always the same.
How to find the sum?Here a1= 8,a2 = 20,a3 = 32 and a4= 44
Find the difference between two terms
a2 - a1 = 20 - 8 = 12
a3 - a2 = 32 - 20 = 12
a4 - a3 = 44 - 32 = 12 sum of n terms is = n/2[2a1 + (n-1)d]
For the given sequence we have n = 10, a1= 8 and d = 12
substituting values of a1 and n in S = 10/2[2x8 + (10-1)x12]
S = 5[16+9x12]
S = 5[16+108]
S = 5[124]
S = 5x124
S = 620
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Please help me with these 2 questions thank you so much #17 and #18
#17: Domain: [−4,∞),{x|x≥−4}
Range: [−2,∞),{y|y≥−2}
#18 g(2)=4(2)+2
g(2)=10
f(10)=3(10)^2-2
f(10)=298
For this case we have:
Question 1:
We have the following functions:
[tex]f (x) = 2x-1\\g (x) = x ^ 2-2[/tex]
We must find (g_ {0} f) (x).
By definition of composition of fusions we have to:
[tex](g_ {0} f) (x) = g [f (x)]\\(g_ {0} f) (x) = g [2x-1]\\(g_ {0} f) (x) = (2x-1) ^ 2-2\\(g_ {0} f) (x) = 4x ^ 2-2 (2x) + 1-2\\(g_ {0} f) (x) = 4x ^ 2-4x-1[/tex]
Answer:
[tex](g_ {0} f) (x) = 4x ^ 2-4x-1[/tex]
Question 2:
For this case we have a function of the form[tex]y = f (x)[/tex], where: [tex]f (x) = \sqrt {x + 4} -2[/tex]
We must graph the given function.
By definition, the domain of the function will be given by the values for which the function is defined. The function is not defined when the root is negative, that is to say for values of "x" less than -4. Then, the domain is:
[-4, ∞)
For its part, the range is the set of values that correspond to the domain. When replacing the values from -4 to infinity we have the following range:
[-2, ∞)
Answer:
See attached image
Domain: [-4, ∞)
Range: [-2, ∞)
Question 3:
For this case we have the following functions:
[tex]f (x) = 3x ^ 2-2\\g (x) = 4x + 2[/tex]
We must find, (f + g) (x):
By definition, we have to:
[tex](f + g) (x) = f (x) + g (x)\\(f + g) (x) = 3x ^ 2-2 + (4x + 2)\\(f + g) (x) = 3x ^ 2-2 + 4x + 2\\(f + g) (x) = 3x ^ 2 + 4x[/tex]
Now, we must find [tex](f + g) (2):[/tex]
[tex](f + g) (2) = 3 (2) ^ 2 + 4 (2)\\(f + g) (2) = 3 (4) +4 (2)\\(f + g) (2) = 12 + 8\\(f + g) (2) = 20[/tex]
Answer:
[tex](f + g) (2) = 20[/tex]
Write a quadratic function in the standard form who’s graph satisfies the given conditions
1. Passes through (-5,0), (1,0), and (4,0)
Answer:
This is frankly impossible.
Step-by-step explanation:
What you have given me are three x-intercepts. And it is impossible for a quadratic function to have more than two roots. However, if this was an cubic function, we could multiply (x+5)(x-1)(x-4) which results in the equation which simplifies into x^3 -21x + 20. However, this is a cubic function, not a quadratic function, so something must be wrong with this problem all together.
Need Help!!!!!!!!!!!!!!!
Add by positive 3 for each of the numbers
-6+3=-3
-3+3=0
0+3= 3
3+3= 6
Answer is 6
ANSWER
The next term is 6.
EXPLANATION
The given arithmetic sequence is -6,-3,0,3,
There is a constant difference of 3.
That is,
-3--6=-3+6=3
This means that, we need to add 3 to the previous terms to get the subsequent terms.
To get the next term after 3, we add 3 to obtain 3+3=6
Therefore the next term of the sequence is 6.
You decide to throw a guacamole party at your house. You have a mixing bowl that is 12 inches in diameters if one Tostito scoop chip and hold 1.125 cubic inches, which of the following is closest to the maximum number of scoops the mixing bowl can hold.
A. 804 scoops
B. 201 scoops
C. 402 scoops
D. 18 scoops
Answer: d
Step-by-step explanation:
What is the coefficient in the expression 4x^2+3x-3
Answer:
The coefficients would be 4 and/or 3.
Step-by-step explanation:
The coefficient is always the number before the variable.
Answer:
a = 4, b = 3, and c = -3
Step-by-step explanation:
A quadratic equation of a variable is an equation that has the general form of:
[tex]ax^{2}+bx+c=0[/tex], [tex]a\neq 0[/tex]
Where x is the variable, and a, b and c constants; a is the quadratic coefficient (other than 0), b the linear coefficient and c is the independent term. This polynomial can be interpreted by means of the graph of a quadratic function, that is, by a parabola. This graphical representation is useful, because the abscissas of the intersections or point of tangency of this graph, in the case of existing, with the X axis are the real roots of the equation. If the parabola does not cut the X axis the roots are complex numbers, they correspond to a negative discriminant.
So, the coefficients are a = 4, b = 3, and c = -3
Solve the following system by the elimination method.1/3x+y=0/3 and 1/6x+1/5y=9/10
Answer:
x = 9 and y = -3 → (9, -3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}\dfrac{1}{3}x+y=\dfrac{0}{3}&\text{multiply both sides by 3}\\\\\dfrac{1}{6}x+\dfrac{1}{5}y=\dfrac{9}{10}&\text{multiply both sides by 30}\end{array}\right\\[tex]\left\{\begin{array}{ccc}x+3y=0&\text{multiply both sides by (-2)}\\5x+6y=27\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-2x-6y=0\\5x+6y=27\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad3x=27\qquad\text{divide both sides by 3}\\.\qquad\boxed{x=9}\\\\\text{Put the value of x to the first equation:}\\\\9+3y=0\qquad\text{subtract 9 from both sides}\\3y=-9\qquad\text{divide both sides by 3}\\\boxed{y=-3}[/tex][/tex]
Rob ran 27.2 miles less than Jasmine last week. Rob ran 10 miles. How many miles did Jasmine run?
Answer:
Jasmine ran last week 37.2 miles
Step-by-step explanation:
Let
x ----> number of miles Rob ran last week
y ----> number of miles Jasmine ran last week
we know that
x=y-27.2 ----> equation A
x=10 ----> equation B
Substitute equation B in equation A and solve for y
10=y-27.2
y=10+27.2
y=37.2 miles
what is the answer to this problem
3= 1/5 k-2
Answer:
k = 25
Step-by-step explanation:
Step 1: Isolate k by adding 2 on both sides.
1/5k = 5
Step 2: Simplify by multiplying 5 on both sides.
k = 25
If a+b = 11 and a−b = 7, then ab
Answer is..
ab= 18
Explanation..
a + b = 11...---> a= 11-b
a -b = 7
11 - b - b = 7
11 - 2b = 7
2b = 18
b = 9
and a = 11 - 7
a = 2
So
ab = 2 * 9 =18
Kayla scored 110 in the first game she bowled but she can’t remember her score from the second game. The average of the two scores is 116. Help Kayla figure out what her second score was
Answer:
122
Step-by-step explanation:
The average of her two scores is calculated by the sum of her two scores divided by 2.
[tex]\boxed{\text{Average}=\frac{\text{sum of data}}{\text{number of data sets}} }[/tex]
Total score= 116(2)
Total score= 232
Total score= score of 1st game +score of 2nd game
Substituting value of first score and total score:
110 +score of 2nd game= 232
Subtract 110 from both sides:
score of 2nd game
= 232 -110
= 122
Additional:
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https://brainly.com/question/7471517David earns $12.00/hour and works 36 hours
Answer:
$432.00
Step-by-step explanation:
$12.00x36= $432.00