Jake forgot to replace the cap on a bottle of deodorant. The deodorant began to evaporate at the rate of 12% per day. If the original amount of deodorant in the bottle was 30 grams, which of the following graphs best represents the amount of deodorant f(x) that would remain in the bottle after x days?
graph of function f of x equals 30 multiplied by 0.88 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis
graph of function f of x equals 50 multiplied by 0.82 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis
Answer:
1. Graph of function f of x equals 30 multiplied by 0.88 to the power of x
Step-by-step explanation:
We are given that,
Original amount of deodorant in the bottle = 30 grams
The rate of evaporation = 12% = 0.12
That is, we see that the deodorant is decreasing as the number of days increases.
So, the function form of the decrease in the amount of deodorant is given by,
[tex]f(x)=30(1-0.12)^x[/tex], where x is the number of days.
i.e. [tex]f(x)=30(0.88)^x[/tex], where x is the number of days.
Hence, the graph representing the amount of deodorant after x number of days is,
1. Graph of function f of x equals 30 multiplied by 0.88 to the power of x
A student solved this problem and said the answer was hour 3/4. Cindy rode her bike for 1/2 hour and ran for 1/4 hour. What was the total length of time that Cindy exercised? Is the student's answer reasonable?
A. Yes, the answer is reasonable.
B. No, the answer is not reasonable. It should be about 2 hours.
C. No, the answer is not reasonable. It should be about 1/4 hour.
D. No, the answer is not reasonable. It should be about 6 hours.
ABC is an isosceles right triangle in which AB has a slope of -1 and angle ABC = 90 degrees. Triangle ABC is dilated by a scale factor of 1.8 with the origin as the center of dilation, resulting in the image A'B'C'. What is the slope of B'C'?
Answer:
Slope of 1
Step-by-step explanation:
C. 1
Tickets to a movie cost $7.25 for adults and $5.50 for students. a group of friends purchased 8 tickets for $52.75. how many adult tickets did they purchase?
How many triangles are formed by dawing all the diagonals from a single vertex of a convex polygon
(n-2) triangles can be formed by drawing all the diagonals from a single vertex.
What is Polygon?a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
Given a convex polygon with n vertices, the number of triangles that can be formed by drawing all the diagonals from a single vertex can be calculated.
a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge
Let's consider a convex polygon with 4 vertices.
(n-2) triangles can be formed by drawing all the diagonals from a single vertex.
Hence, (n-2) triangles can be formed by drawing all the diagonals from a single vertex.
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The difference of two numbers is 44 1 /2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.
Required numbers as per the given condition are [tex]50\frac{3}{14}[/tex] and [tex]5\frac{5}{7}[/tex].
What is a number?" A number is defined as the count of any given quantity."
According to the question,
[tex]'x'[/tex] represents the greater number
[tex]'y'[/tex] represents the smaller number
As per the given condition equation we have,
[tex]x- y = 44\frac{1}{2} \\\\\implies x-y = \frac{89}{2}[/tex] ______[tex](1)[/tex]
[tex]x-7y =10 \frac{3}{14} \\\\\implies x-7y = \frac{143}{14}[/tex] ______[tex](2)[/tex]
Subtract equation [tex](2)[/tex] from [tex](1)[/tex] to get the required numbers,
[tex]6y = \frac{89}{2} -\frac{143}{14} \\\\\implies 6y = \frac{623-143}{14}\\ \\\implies 6y = \frac{480}{14}\\ \\\implies y = \frac{40}{7}\\ \\\implies y = 5\frac{5}{7}[/tex]
Substitute the value of [tex]'y'[/tex] in [tex](1)[/tex] we get,
[tex]x= \frac{89}{2}+ \frac{40}{7} \\\\\implies x = \frac{623+80}{14} \\\\\implies x= \frac{703}{14}\\ \\\implies x= 50\frac{3}{14}[/tex]
Hence, required numbers as per the given condition are [tex]50\frac{3}{14}[/tex] and [tex]5\frac{5}{7}[/tex].
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Jason's current yearly income is $13,000...If Jason’s training will allow him to get a job making $34,000 a year, how long will it take him to recover his initial investment of $35,200?
The product of two consecutive even integers is 528. find the integers
Heron’s formula: Area = Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.
A line has a slope of - 3/5. Which ordered pairs could be points on a parallel line? Check all that apply.
A). (–8, 8) and (2, 2)
B). (–5, –1) and (0, 2)
C). (–3, 6) and (6, –9)
D). (–2, 1) and (3, –2)
E). (0, 2) and (5, 5)
I think it's A, but I'm not sure. Please help, I'll pick Brainliest! :-P
The ordered pairs will be the points on the parallel line are
(-8, 8) and (2, 2)
(-2, 1) and (3, -2)
What is the slope of a line?A slope of a line is the change in y coordinate with respect to the change in x coordinate.
How to find the slope of line from the two points?If [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] be the two points then the slope of the line is given by
[tex]slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
According to the given question.
We have slope of a line is [tex]\frac{-3}{5}[/tex].
As, we know that the two parallel lines have the same slope.
Now according to the given ordered pairs
A). (-8, 8) and (2, 2)
[tex]slope = \frac{2-8}{2+8} = \frac{-6}{10} =\frac{-3}{5}[/tex]
Therefore, (-8, 8) and (2, 2) are the ordered pairs could be the points on the parallel line.
B) (-5, -1) and (0, 2)
[tex]slope = \frac{2+1}{0+5} =\frac{3}{5} \neq \frac{-3}{5}[/tex]
Hence, the ordered pair (-5, -1) and (0, 2) will never be the points on the parallel line.
C) (-3, 6) and (6, -9)
[tex]slope = \frac{-9-6}{6+3} =\frac{-15}{9} =\frac{-5}{3}\neq \frac{-3}{5}[/tex]
The ordered pair (-3, 6) and (6, -9) will never be the points on the parallel line.
D). (-2, 1) and (3, -2)
[tex]slope = \frac{-2-1}{3+2} =\frac{-3}{5}[/tex]
Therefore, (-2, 1) and (3, -2) are the ordered pairs could be the points on the parallel line.
E). (0, 2) and (5, 5)
[tex]slope = \frac{5-2}{5-0} =\frac{3}{5} \neq \frac{-3}{5}[/tex]
Therefore, (0, 2) and (5, 5) are the ordered pairs could not be the points on the parallel line.
Hence, the ordered pairs will be the points on the parallel line are
(-8, 8) and (2, 2)
(-2, 1) and (3, -2)
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To determine if the given ordered pairs could be points on a parallel line with a slope of -3/5, we can calculate the slope of each line and compare it to the original slope. The pairs (D) (-2, 1) and (3, -2) have a slope of -3/5, making them parallel.
Explanation:A line with a slope of -3/5 is a line that slopes downwards from left to right. In order for a line to be parallel to this line, it must have the same slope. To determine if the given ordered pairs could be points on a parallel line, we can calculate the slope of each line and compare it to the slope of the original line.
B) (-5, -1) and (0, 2): The slope of this line is (2 - (-1))/(0 - (-5)) = 3/5, which is different from the original slope of -3/5. Therefore, this line is not parallel.
D) (-2, 1) and (3, -2): The slope of this line is (-2-(-2))/(3-(-2)) = -3/5, which is equal to the original slope of -3/5. Therefore, this line is parallel.
E) (0, 2) and (5, 5): The slope of this line is (5 - 2)/(5 - 0) = 3/5, which is different from the original slope of -3/5. Therefore, this line is not parallel.
So, the parallel lines are (D) (-2, 1) and (3, -2).
A television production company charges a basic fee of $4000 and then $2000 per hour when filming a commercial.
A. Write an equation in slope-intercept form relating the basic fee and per-hour charge.
B. Graph your equation
C. Use your graph to find the production costs if 4 hours of filming were needed.
Please help me! I don't understand anything that i am learning right now and its all just confusing
The equation in slope - intercept form is as - y[h] = 2000h + 4000 and for 4 hours of filming, the production cost would be $12000.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a television production company charges a basic fee of $4000 and then $2000 per hour when filming a commercial.
Assume that the number of hours required for filming the commercial be [h]. Then, we can write, the equation as follows -
y[h] = 2000h + 4000
The graph of the equation is attached with the answer.
For 4 hours of filming, the production cost would be -
y[4] = 2000 x 4 + 4000 = 8000 + 4000 = 12000
Therefore, the equation in slope - intercept form is as - y[h] = 2000h + 4000 and for 4 hours of filming, the production cost would be $12000.
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1 .
Factor 13x⋅(x−3)+10⋅(x−3)
2.
Factor 17t⋅(17t−9)−12⋅(17t−9)
Determine if the properties define a Ray or a line segment
A ray in geometric optics represents the path of light as a straight line originating from a point, while a line segment is a part of a line with two endpoints and a measurable length. The properties mentioned can be used to determine if they define a ray or a line segment.
Explanation:A ray in geometric optics is a straight line that originates at some point. In the context of light, a ray represents the path of light as it travels. When light encounters objects or changes media, it may change direction but it continues to travel in a straight line or as a ray. We can think of a ray of light as a straight line or a laser ray.
A line segment, on the other hand, is a part of a line with two endpoints. It has a definite length and can be measured. In the context of light, a line segment would indicate a finite path of light.
Given the properties mentioned, we can determine if they define a ray or a line segment. If the properties describe a straight line with no defined endpoints, it is a ray. If the properties suggest a line with two endpoints and a measurable length, it is a line segment.
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Investments are different from savings accounts in that they _____.
A. guarantee never to lose money
B. are FDIC-insured
C. can only be accessed online
D. offer high profit potential
@Loveiskey18
4400 dollars is placed ina an account with an annual interest rate of %8.25. How much will be in the account after 29 years
Answer: 43839.13
Step-by-step explanation:
Final answer:
To calculate the amount in the account after 29 years, use the formula for compound interest. The amount in the account will be approximately $40,882.53.
Explanation:
To calculate the amount in the account after 29 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal is $4400, the annual interest rate is 8.25%, and since it is not specified, we'll assume interest is compounded annually. So, the formula becomes:
A = 4400(1 + 0.0825/1)^(1*29)
To calculate this, we can enter the expression into a calculator or spreadsheet:
A = 4400(1 + 0.0825)^(29)
After evaluating this expression, we find that the amount in the account after 29 years will be approximately $40,882.53.
A patient needs 0.024grams of a sulfa drug. There are 8-mg tablets in stock. how many tablet should be given?,
A line that is parallel to y=12 has slope m=
The sculpture consists of five identical prisms. JD says the surface area of the sculpture is 44 times the surface area of one prism. Which statement about JD's method is true?
Sean has 3 times as many vegetable plants as Liz and Sejuan combined. Liz has 3 vegetable plants, and Sejuan has 2 vegetable plants. How many vegetable plants does Sean have?
Which statements about this word problem are true? Check all that apply.
This is an example of a part-whole problem.
This is an example of a comparison problem.
Addition then multiplication can be used to solve the problem.
Subtraction then division can be used to solve the problem.
Division then multiplication can be used to solve the problem.
This is a comparison problem in mathematics where addition and multiplication are used. Liz and Sejuan together have 5 vegetable plants and since Sean has 3 times what both of them have combined, Sean has 15 vegetable plants.
Explanation:The problem at hand is about a comparison of the number of vegetable plants between Sean, Liz and Sejuan. It's an example of a comparison problem where addition and multiplication are used to find the solution. First, you need to find the total number of plants that Liz and Sejuan have by adding their plants together (3 + 2). We get a result of 5. Then, we know that Sean has 3 times as many plants as Liz and Sejuan together, so you multiply the combined total by 3 (5 * 3). The result is 15, so Sean has 15 vegetable plants.
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Quadrilateral RSTU is a rectangle with diagonal RT. If 8x + 4 and = 3x – 2, find x
Answer:
did u ever find the asnwer? cuz I need it rn
Step-by-step explanation:
Help me
Show all your work
help, please show how to find x, thank you
Write each of the following expressions without using the absolute value sign. |x−4| if x>4. PLEASE INCLUDE EXPLANATION!!!
1. picture
2.picture
3.which graph represents f(x)=4sin(2πx)?
4. A cosine function has a period of 3, a maximum value of 20, and a minimum value of 0. The function is a reflection of its parent function over the x-axis.
Which function could be the function described?
5. A sinusoidal function whose frequency is 3, maximum value is 15, minimum value is −3 has a y-intercept of 6.
Which function could be the function described?
f(x)=9sin(6πx)+3
f(x)=9sin(3x)+3
f(x)=9sin(x3)+6
f(x)=9sin(6πx)+6
The graph is shown in the figures.
Sinusoidal functionIt is a function that repeats itself after a regular interval of time.
How to calculate?1. Graph of g(t) = 4sin(3t) + 2 is shown below.
2. Graph of f(x) = 3cos(2x) - 1 is shown below.
3. Graph D represents the f(x) = 4sin(2[tex]\rm \pi[/tex]x) because the value of sine maximum and the minimum are 1 and -1 so the value of f(x) is maximum and the minimum is 4 and -4.
4. The maximum and minimum value of f(x) 20 and 0. and period is 3. then our f(x) will be
[tex]f(x) = 10\ cos(\dfrac{2\pi }{3}x ) +10[/tex]
5. For this D is the correct option. because maximum and minimum values, as well as frequency, satisfy the equation.
Thus, the graph is shown in figures.
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Simplify each expression. Use positive exponents.
(x–2y–4x3) –2,
Vesna vulovic survived the longest fall on record without a parachute when her plane exploded and she fell 6 miles and 551 yards. how many feet is this?
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work. Sn: 12 + 42 + 72 + . . . + (3n - 2)2 = n(6n^2-3n-1)/2
Paige bought 34 yards of yarn at the store and 2⁄9 of the yarn was blue. How many yards of blue yarn did Paige buy?
Answer:
the right answer is 7 5/9 yards.
Step-by-step explanation:
For f(x)=2x+1 and g(x)=x+14 , find (g o f) (x).
Answer:
(g o f) (x) = 2x + 16
Step-by-step explanation:
" (g o f) (x) )" is called "the composition of f and g."
Evaluating this involves substituting the function f(x) = 2x + 1 for x in g(x) = x+14:
(g o f) (x) = 2(x+1) + 14, or
(g o f) (x) = 2x + 2 + 14, or
(g o f) (x) = 2x + 16
Answer:
2x+29
Step-by-step explanation:
a p e x
PLEASE HELP ME
If strictly practiced, which of the following methods of birth control is 100 percent effective?
abstinence
condoms
withdrawal
diaphragm with spermicide