In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
A(t) = 800e^(-0.86t)
Step 02:
Rate of change
t1 = 0
A(t) = 800e^(-0.86t)
A(t) = 800e^(-0.86*0)
A(0) = 800
t2 = 5
A(t) = 800e^(-0.86t)
A(t) = 800e^(-0.86*5)
A (t) = 800e^(-4.3)
A(5) = 10.85
Step 03:
[tex]\frac{\Delta y}{\Delta x}=\frac{A(5)\text{ - A(0)}}{5-0}[/tex][tex]\frac{\Delta y}{\Delta x}=\frac{10.85-800}{5-0}=\frac{-789.15}{5}=-157.83[/tex]Find ( f+g ) (x) for each of the following functions
Answer:
(f + g)(x) = 2x³ + 3x² + x + 2
Explanation:
If f(x) = 2x³ - 5x² + x - 3 and g(x) = 8x² + 5, we can calculate (f + g)(x) as follows
(f + g)(x) = f(x) + g(x)
(f + g)(x) = (2x³ - 5x² + x - 3) + (8x² + 5)
Then, we can simplify the expression adding the like terms, so
(f + g)(x) = 2x³ - 5x² + x - 3 + 8x² + 5
(f + g)(x) = 2x³ + (-5x² + 8x²) + x + (-3 + 5)
(f + g)(x) = 2x³ + 3x² + x + 2
Therefore, the answer is:
(f + g)(x) = 2x³ + 3x² + x + 2
Answer this, please
Zachariah and Khai collect stamps. Zachariah has 7 American stamps out of 12 stamps. Khai has 15 American stamps out of 24 stamps. Which statement is correct?
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is greater than 15 over 24.
Khai has a higher ratio of American stamps than Zachariah because 7 over 12 is less than 15 over 24.
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24.
Zachariah and Khai have the same ratio of American stamps.
The last statement would be true, because you would convert 7/12 into a fraction and 15/24 into a fraction. From their fraction eyes to State you would turn them into decimals and then percentiles.
Answer:
D: They are both the same
Step-by-step explanation:
I took the test
11. The table lists postage for letters weighing as much as 3 oz. You want to mail a letter that weighs 1.7 oz.Graph the step function. How much will you pay in postage?Weight Less ThanPrice1 oz422 oz66903 Oz
In the table says that every letter that weighs less that 1 oz. have a price of 42, in the graphic we represented that in this part:
Following the data in the table as above we got the final graphic.
And for the question:
If you have a letter that weighs 1.7 oz. it will be more than 1 oz. but less than 2 oz. so you will pay 66, as we can see in the following graphic:
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Answer:
translated 8 units down and then reflected across the y-axis
are these places correctly.and yes it is math. pls answer fast
we have that
Costs that stay the same from week to week or month to month
-savings for college
-Rent
Costs that cannot be adjusted within a budget
-Car insurance
-Health care
Costs that can be adjusted within a budget
-cell phone
-gasoline
-hair cut
-Groceries
solve for x and y (2x+7)(x+1)(y+5)(x-4)
Answer:
I am assuming you are looking for the x-intercepts and y-intercepts...here they are.
x-intercepts: (-7/2,0) , (-1,0) , (4,0)
y-intercepts: (0,-5)
Hope this helps...if not, please expound your question more.
O GRAPHS AND FUNCTIONSDomain and range from the graph of a piecewise function
ANSWER:
[tex]Domain:(-5,-4]\cup[-1,2][/tex][tex]Range:[-3,0)\cup[1,4][/tex]EXPLANATION:
Given:
To find:
The domain and the range
Recall that the domain of a function is the set of possible input values for which the function is defined.
To determine the domain of a function from a graph, we consider the possible x-values from left to right.
So the domain of the given function can be written as;
[tex]Domain:(-5,-4]\cup[-1,2][/tex]The range of a function is the set of possible output values.
To determine the range of a function from a graph, we consider the possible y-values from the bottom to the top.
So the range of the given function can be written as;
[tex]Range:[-3,0)\cup[1,4][/tex]26.219 Miles in 128 minutes. what is speed in km per minute?
26.219 Miles in 128 minutes.
First we have to convert miles to km:
Since 1 mile = 1,609 km
26.219 x 1,609 = 42,041.561 km
Then divide the distance by the time:
42,041.561/ 128 = 192.85 km per minute
Find the length and width of a rectangle with the following information belowArea = 2x^2 + 3x Perimeter = 6x + 6
Length: L
Width: W
The area of a rectangle is:
[tex]A=L\cdot W[/tex]The perimeter of a rectangle is:
[tex]P=2W+2L[/tex]Given information:
[tex]\begin{gathered} A=2x^2+3x \\ \\ P=6x+6 \end{gathered}[/tex][tex]\begin{gathered} L\cdot W=2x^2+3x \\ 2W+2L=6x+6 \end{gathered}[/tex]Solve L in the second equation (Perimeter):
[tex]undefined[/tex]I think is the average of the highest point and the lowest one, what's the midline of the graph?
The Midline of a Sinusoid
A sinusoid is a periodic function which parent expression is:
f(x) = A. sin (wt)
Where A is the amplitude and w is the angular frequency
The sine function has a maximum value of A and a minimum value of -A.
The midline can be found as the average value of the maximum and the minimum value.
For the parent function explained above, the midline is:
[tex]M=\frac{\text{Mx}+Mn}{2}[/tex]Since Mx and Mn are, respectively A and -A, the midline is zero.
The graph shown in the image has a maximum of Mx=1 and a minimum of Mn=-5.
Thus, the midline is:
[tex]M=\frac{\text{1}-5}{2}=-\frac{4}{2}=-2[/tex]The midline of the graph is y=-2
Find the simple interest. Principal Time in Months Rate 1 $11.800 21% 4 The simple interest is $ (Round to the nearest cent.)
we use the formula
Where Cn is the final amount= co the initial amount, n the number of months and i the rate dividing between 100
transform the mixed number
[tex]2\frac{1}{4}=2.25[/tex]now, replace
[tex]\begin{gathered} Cn=11,800(1+(4)\times(\frac{2.25}{100})) \\ \\ Cn=11,800(1.09) \\ \\ Cn=12862 \end{gathered}[/tex]the solution is 12,862
What are the slope and the y-intercept of the linear function that is represented by the table? -- Nicol у 3 2 1 0 -2 / 0 Nlw 3 1 2 -1 The slope is -3, and the y-intercept is 3 The slope is -3, and the y-intercept is z. 1 The slope is 3, and the v-intercept is -
We will assume the next table to answer this question (a linear function) (since the data in the question is not clear):
Having this information, we can find the slope using the formula for it:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]If we pick up from the table the next points:
x1 = 1, y1 =6
x2 = 2, y2 = 8
Then
[tex]m=\frac{8-6}{2-1}=\frac{2}{1}\Rightarrow m=2[/tex]We can use the slope-point formula to find the y-intercept. We can use the point (3, 10). Then, we have:
[tex]y-y_1=m\cdot(x-x_1)\Rightarrow y-10=2\cdot(x-3)\Rightarrow y-10=2x-6[/tex][tex]y=2x-6+10\Rightarrow y=2x+4[/tex]We end up with the slope-intercept formula for the line. Then the y-intercept is 4. In other words, if we have x = 0, then y = 4.
Then the slope for the values represented in the proposed table is m = 2, and the y-intercept is y = 4.
A school debate team has 4 girls and 6 boys. A total of 4 of the team members will be chosen top participate in the district debate. What is the probaility that 2 girland 2 boys will be selected?
The probability that 2 girls and 2 boys are selected is given by:
[tex]P(\text{ 2 boys, 2 girls })=\frac{4C2\times6C2}{10C4}=\frac{6\times15}{210}=\frac{3}{7}[/tex]Therefore, the correct choice is option D) 3/7.
10. Find the area of ABC. (A) 84 (B) 168 (C) 170 (D) 48 (E) 56A: 10B: 17C: 21Right angle: 8
we know that
the area of triangle ABC is equal to the area of two right triangles
so
triangle ABD and triangle BDC
D is a point between point A and point C
step 1
Find the length of segment AD
Applying Pythagorean Theorem in the right triangle ABD
10^2=AD^2+8^2
100=AD^2+64
AD^2=100-64
AD^2=36
AD=6
Find teh area of triangle ABD
A=AD*BD/2
A=6*8/2
A=24 units^2
step 2
Find the area of triangle BDC
A=DC*DB/2
DC=21-6=15 units
A=15*8/2
A=60 units^2
step 3
Find teh area of triangle ABC
Adds the areas
A=24+60=84 units^2
therefore
the answer is the option A 84 units^2Tommy paid $8.25 for three pounds of gummy candy.Tommy created a graph from the data on his chart. Is his graph correct? Why or Why not?
Notice that the relationship between the number of pounds of gummy candy and the number of dollars that that number of pounds costs is a function because there cannot be two prices for the same number of pounds.
Now, notice that the graph that Tommy creates does not represent a function because it fails the vertical line test at x=3.
Also, from the given table we get that (4,11) is a point of the graph.
Then the graph that Tommy creates is not correct.
Answer: No, because the graph does not represent a function and the point (4,11) is not part of the graph.
Triangle RST has the coordinates R(0 , 2), S(2 , 9), and T(4 , 2). Which of the following sets of points represents a dilation from the origin of triangle RST? A. R'(0 , 2), S'(8 , 9), T'(16 , 2) B. R'(0 , 2), S'(2 , 36), T'(16 , 2) C. R'(4 , 6), S'(6 , 13), T'(8 , 6) D. R'(0 , 8), S'(8 , 36), T'(16, 8)
The set of points that represents a dilation from the origin of triangle RST are: D. R'(0 , 8), S'(8 , 36), T'(16, 8).
What is dilation?In Mathematics, dilation is a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
For the given coordinates of triangle RST, the dilation with a scale factor of 4 from the origin (0, 0) or center of dilation should be calculated as follows:
Point R (0, 2) → Point R' (0 × 4, 2 × 4) = Point R' (0, 8).
Point S (2, 9) → Point S' (2 × 4, 9 × 4) = Point S' (8, 36).
Point T (4, 2) → Point T' (4 × 4, 2 × 4) = Point T' (16, 8).
In conclusion, the other sets of points do not represents a dilation from the origin of triangle RST.
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As of the given condition ordered pair in the option D R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.
Given that,
Coordinates of the triangle, R(0 , 2), S(2 , 9), and T(4 , 2).
The scale factor for the dilation = 4
The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
According to the question,
The dilated coordinate is given as,
R' = (0×4 , 2×4) = (0, 8)
S' = (2×4, 9×4) = (8, 36)
T' = (4×4, 2×2) = (16, 8)
Thus, As of the given condition ordered pair in the option D R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.
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Dejah is comparing two numbers shown in scientific notation on her calculator. The first number was displayed as 7.156E25 and the second number was displayed as 3.498E-10. How can Dejah compare the two numbers?
Answers
The first number is about
2 x 10¹⁵
2 x 10³⁵
2 x 10‐¹⁵
2 X 10‐³⁵
times bigger than the second number.
Answer:
2 x [tex]10^{35}[/tex]
Step-by-step explanation:
7 ÷ 3 is about 2
[tex]\frac{10^{25} }{10^{-10} }[/tex] = [tex]10^{35}[/tex] When you are dividing powers with the same bases, you subtract the exponents
25 - -10 = 25 + 10 = 35
Suppose a charity received a donation of $19.4 million. If this represents 43% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Given :
a charity received a donation of $19.4 million
Which represents 43% of the charity funds
Let the total funds = x
So,
43% of x = 19.4 million
So,
[tex]\begin{gathered} 43\%\cdot x=19.4 \\ \\ 0.43\cdot x=19.4 \\ \\ x=\frac{19.4}{0.43}\approx45.12 \end{gathered}[/tex]Rounding to the nearest million ,
The answer is : total donated funds = 45 million
Solve for the Limit of Function by applying appropriate Limit Theorems
Answer:
Given to solve,
[tex]\lim _{x\to-1}(2x+2)(x+2)[/tex]From the rules for limits, we can see that for any polynomial, the limit of the polynomial when x approaches a point k is equal to the value of the polynomial at k.
The given function of the limit is a quadratic function, the limit of the quadratic equation when x approaches a point -1 is equal to the value of the quadratic equation at -1.
we get,
[tex]\lim _{x\to-1}(2x+2)(x+2)=(2(-1)+2)((-1)+2)[/tex][tex]=(-2+2)(1)=0[/tex][tex]\lim _{x\to-1}(2x+2)(x+2)=0[/tex]
Answer is : 0
Imagine you are four years old. A rich aunt wants to provide for your future. She hasoffered to do one of two things.Option 1: She would give you $1000.50 a year until you are twenty-one.Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amounteach year until you were 21.If you only received money for ten years, which option would give you the most money?
Given the situation to model the arithmetic and the geometric sequences.
Imagine you are four years old. A rich aunt wants to provide for your future. She has offered to do one of two things.
Option 1: She would give you $1000.50 a year until you are twenty-one.
This option represents the arithmetic sequence
The first term = a = 1000.50
The common difference = d = 1000.50
The general formula will be as follows:
[tex]\begin{gathered} a_n=a+d(n-1) \\ a_n=1000.50+1000.50(n-1) \\ \end{gathered}[/tex]Simplify the expression:
[tex]a_n=1000.50n[/tex]Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amount each year until you were 21.
This option represents the geometric sequence
The first term = a = 1
The common ratio = r = 2/1 = 2
The general formula will be as follows:
[tex]\begin{gathered} a_n=a\cdot r^{n-1} \\ a_n=1\cdot2^{n-1} \end{gathered}[/tex]Now, we will compare the options:
The first term of both options is when you are four years old that n = 1
you only received money for ten years so, n = 10
So, substitute with n = 10 into both formulas:
[tex]\begin{gathered} Option1\rightarrow a_{10}=1000.50(10)=10005 \\ Option2\rightarrow a_{10}=1\cdot2^{10-1}=2^9=512 \end{gathered}[/tex]So, the answer will be:
For ten years, the option that gives the most money = Option 1
Point S is on line segment \overline{RT} RT . Given RT=3x,RT=3x, RS=3x-5,RS=3x−5, and ST=3x-1,ST=3x−1, determine the numerical length of \overline{RT}. RT .
The numerical length of the line segment RT is 6.
Length:
Length is the measuring unit used to identifying the size of an object or distance from one point to the other.
Given,
There is a point on the line segment RT.
And the values of the pots are,
RT = 3x, RS = 3x - 5 and ST = 3x - 1.
Now we need to find the length of the line segment RT.
To find the line of the line segment RT,
We have to add the length of the segments,
That can be written as,
=> RT = RS + ST
Now, we have to apply the values of the point to the equation, then we get,
=> 3x = 3x - 5 + 3x - 1
=> 3x = 6x - 6
=> 6x - 3x - 6
=> 3x - 6
=> 3x = 6
=> x = 2
If the value of x is 2, then the length of the line segment RT is,
RT = 3x => 3 x 2 = 6
Therefore, the length of the line segment RT is 6.
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quick!! will give brainliest!! Given g(x) = -x + 3, solve for a when g(2) = -1
We have the following:
[tex]g(x)=-x+3[/tex]replacing when x is 2:
[tex]g(2)=-2+3=1[/tex]Use the following function rule to find f(48).
f(x) = 12 + x/4
Answer:
See image
depending on what is in the numerator of your question:
24 OR 15 SEE IMAGE!
Step-by-step explanation:
f(48) just means to use 48 in place of x in your work.
f(x) = 12 + x/4
f(48) = 12 + 48/4
Hopefully, your text/worksheet/screen is clear on which problem you are doing.
A box contains 4 red balls and 6 green balls. If a ball is drawn at random, then find the probability that the ball is red.1/102/104/106/10
To calculate the probability of event A, divide the number of outcomes favorable to A by the total number of possible outcomes.
[tex]P(A)=\frac{favourable\text{ outcomes}}{total\text{ outcomes}}[/tex]so
Step 1
a)let
[tex]\begin{gathered} favourable\text{ outcomes=red balls = 4 \lparen there are 4 red balls\rparen=4} \\ total\text{ outcomes= total balls= 4 red+6 green=10 balls=10} \end{gathered}[/tex]b) now, replace in the formula and simplify
.
[tex]P(A)=\frac{4}{10}=\frac{2}{5}[/tex]therefore, the answer is
[tex]\frac{4}{10}[/tex]I hope this helps you
find distance between 2 points A(-1,-7), B(-8,7)
To calculate the length between A and B you have to draw them in the cartesian system and link them with a line, then using that line as hypothenuse, draw a right triangle, whose base will be paralel to the x-axis and its height will be paralel to the y-axis.
Using the coordinates calculate the length of the base and height of the triangle:
Base= XA-XB= (-1)-(-8)=7
Height= YB-YA=7-(-7)=14
Now you have to apply pythagoras theorem you can calculate the length of the hypotenuse:
[tex]\begin{gathered} a^2+b^2=c^2 \\ c^2=7^2+14^2 \\ c^2=245 \\ c=\sqrt{245}=15.65 \end{gathered}[/tex]The distance between poins A and B is 15.65
5. Which of the following expressions isequivalent to the expression below?2 394Х4AC29;woltON Alw94B+D1M
A) 9 cups of berries to 12 cups of juice
Explanation
to figure out this, we need to find the original ratio and then compare
Step 1
find the ratio:
ratio cups of berries to cups of juices
[tex]\text{ratio}=\frac{3\text{ cups of berries}}{4\text{ cups of juices}}=\frac{3}{4}[/tex]hence, the rario is 3/4
Step 2
now, check the ratio of every option
a)9 cups of berries to 12 cups of juice
[tex]\begin{gathered} \text{ratio}_a=\frac{9\text{ cups of berries}}{12\text{ cups of juice}}=\frac{3}{4} \\ \text{ratio}_a=\frac{3}{4} \end{gathered}[/tex]b) 12 cups of berries to 9 cups of juice
[tex]\text{ratio}_b=\frac{12\text{ cups of berries}}{9\text{ cups of juice}}=\frac{4}{3}[/tex]c) 6 cups of berries to 15 cups of juice
[tex]\text{ratio}_c=\frac{6\text{ cups of berries }}{15\text{ cups of juice}}=\frac{6}{15}=\frac{2}{5}[/tex]d) 15 cups of berries to 10 cups of juice
[tex]\text{ratio}_d=\frac{15\text{ cups of berries }}{10\text{ cups of juice}}=\frac{15}{10}=\frac{3}{2}[/tex]therefore, the option that haas the same ratio is a) 3/4
I hope this helps you
A pile of cards contains eight cards, numbered 1 through 8. What is the probability of NOT choosing the 6?
The probability of NOT choosing the 6 is 7/8.
What is the probability?Probability is used to calculate the likelihood that a random event would happen. The chances that the random event happens is a probability value that lies between 0 and 1. The more likely it is that the event occurs, the closer the probability value would be to 1. If it is equally likely for the event to occur or not to occur, the probability value would be 0.50.
The probability of NOT choosing the 6 = number of cards that are not 6 / total number of card
Cards that do not have a value of 6 = 1, 2, 3, 4, 5, 7, 8
Total is 7
The probability of NOT choosing the 6 = 7 / 8
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how do you find the exponential equation for growth? or what is the exponential equation for growth?
Answer:
The equation f(x) = a(1 + r)x can also be used to compute exponential growth, where:
The function is represented by the word f(x).
The initial value of your data is represented by the a variable.
The growth rate is represented by the r variable.
Time is represented by the variable x.
there are twelve inches in one foot,creating the equation y=12x. if a door frame is 6.5 feet tall,how many inches tall is it
Let's begin by listing out the information given to us:
[tex]\begin{gathered} 12in=1ft \\ y=12x \end{gathered}[/tex]The height of the door frame is 6.5 feet. To convert to inches, we have:
[tex]\begin{gathered} y=12(6.5)=78inches \\ y=78inches \end{gathered}[/tex]In 2011, the average daily temperature in Darrtown was 65°F. In 2012, the average daily temperature increased by 3% but then decreased by 4.5% in 2013.What was the daily average temperature in Darrtown in 2013?A.62°FB.64°FC.68°FD.74°F (thank you in advanced for who helps i was having trouble with this question)
Solution
In 2011 The temperature in Darrtown is
[tex]65^{\circ}F[/tex]The temperature increased by 3% in 2012
The temperature will be
[tex](1+\frac{3}{100})\times65=(1.03)(65)=66.95^{\circ}F[/tex]The temperature decreased by 4.5% in 2013
The temperature will be
[tex]\begin{gathered} (1-\frac{4.5}{100})\times66.95=0.955\times66.95=63.93725 \\ \\ (1-\frac{4.5}{100})\times66.95=64^{\circ}F\text{ (to the nearest whole number)} \end{gathered}[/tex]Therefore, the temperature in 2013 is 64 degrees Fareheint
Option B