The function y = 18(0.914)^m is having exponential decay. The decay percent of this function is 8.6%
What is exponential growth or decay function?Consider the function:
[tex]y = a(1\pm r)^m[/tex]
where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is plus sign, then there is exponential growth happening by r fraction or 100r %
If there is negative sign, then there is exponential decay happening by r fraction or 100r %
For this case, the exponential growth/decay function given is:
[tex]y = 18(0.914)^m[/tex]
That means, there is multiplication of (0.914) for each growth/decay.
We can rewrite 0.914 as:
0.914 = 1 - 0.086
This shows decay as multiplication with 0 < quantity < 1 makes the number less in magnitude.
A quantity times (1 - 0.086) = that quantity - that quantity times 0.086
and we can write 0.086 = 8.6/100 = 8.6%
Thus, we're decreasing 8.6% each time from a quantity when we multiply that quantity with (1-0.086)
Thus, there is exponential(exponential because of the presence of variable 'm' as exponent in the given function) decay of 8.6%.
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Find the area and the circumference of a circle with radius .
Use the value for , and do not round your answers. Be sure to include the correct units in your answers.
Answer: 25.12
Step-by-step explanation:
Circumference = πd or 2πr
Since the radius is given (which is 4) we will use 2πr
2× 3.14×4=
8 × 3.14 =
25.12
Three companies offer swim lessons by the hour. Their information is shown in the tables below.
Which company has a signup fee of $11 and a cost per hour of $6
The answer is B because 6*2 = 12 + 11 = 23 !
the least common multiple of 9 and 6 is 54
Answer:
18
Step-by-step explanation:
The multiples of 9 are 9,18,27,36,45,54,63,...
The multiples of 6 are 6,12,18,24,30,36,42,...
which compound inequality is equivalent to the absolute value inequality |b|>6?
The compound inequality equivalent to the absolute value inequality |b|>6 is b > 6, and b < -6
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequality:
|b| > 6
Hence:
b > 6 and -b > 6
b > 6, and b < -6
The compound inequality equivalent to the absolute value inequality |b|>6 is b > 6, and b < -6
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Answer:
Answer is A
Step-by-step explanation:
Got it right on the quiz
A line has a slope of min Which ordered pairs could be
points on a parallel line? Select two options.
D (-8, 8) and (2, 2)
0 (-5, -1) and (0, 2)
(-3, 6) and (6, -9)
D (-2,1) and (3, -2)
D (0, 2) and (5, 5)
Answer:
-2,1 and 3,-2 also -5,-1 and 0,2
Step-by-step explanation:
solve only number 6
To find the tangent line of the graph:
⇒ must find:
point at which the tangent line touches the graphslope of the tangent lineLet's find the point at which the tangent line touches the graph:
At x = -1,
[tex]y = ((-1)^3+2)^5=(-1+2)^5=1^5=1[/tex]
Point: (-1,1)
Let's find the slope of the tangent line
⇒ get the derivation of function than plug (-1) in the x-position to get
the exact slope
[tex]\frac{d}{dx}(x^3+2)^5=5(x^3+2)^4*\frac{d}{dx}(x^3+2)=5(x^3+2)^4*3x^2\\ \\ 5((-1)^3)+2)^4*3(-1)^2=5(-1+2)^4*3*1=5*(1)^4*3=5*1*3=15[/tex]
Slope of tangent line: 15
Now put all the calculated value into the point-slope form:
[tex](y-y_{0})=m(x-x_{0} )[/tex]
[tex](x_{0} ,y_{0} )[/tex] --> point on the tangent linem --> tangent slope's valueSo:
[tex](y-1)=15(x+1)\\y - 1= 15x + 15\\y = 15x + 15 + 1\\y = 15x + 16[/tex]
Thus the tangent line's equation is y = 15x + 16
Answer: y = 15x + 16
Hope that helps!
The table shows the weights (in pounds) and the prescribed dosages (in milligrams) of medicine for six patients.
Weight (lb), x Dosage (mg), y
94 72
119 90
135 103
150 115
185 140
202 156
a. Find an equation of the line of best fit. Round the slope and the y -intercept to the nearest tenth, if necessary.
y=
Question 2
Identify the correlation coefficient. Round your answer to the nearest thousandths.
Question 3
Interpret the correlation coefficient.
0 / 10000 Word Limit
Question 4
b. Interpret the slope of the line of best fit.
Question 5
c. A patient who weighs 140 pounds is prescribed 135 milligrams of medicine. How does this affect the line of best fit? Explain.
(A) Using calculator, the equation of the line of best fit is y=0.77x-1.1y=0.77x−1.1 and correlation coefficient is 0.9990.999
The relationship is strongly positive as correlation coefficient is very close to +1.
Step 2
(B) The slope of best fit gives the change in dosage for a unit (lb) increase in weight of patient. We find that the dosage increases by about 0.77 mg for a unit increase in weight of patient.
Step 3
(C) Adding observation (140, 135)(140,135) to the data set. the regression line changes to y=6.12+0.75xy=6.12+0.75x. It increases the intercept but decreases slope.
But the correlation falls to 0.9340.934, weakening the relationship. This happens as the observation is an outlier.
Result
a. y=0.77x-1.1y=0.77x−1.1, strong positive relationship
b. represents change in dosage for a unit increase in weight
c. regression line changes to y=6.12+0.75xy=6.12+0.75x.
(A) The line of best fit's equation is y=0.77x-1.1y=0.77x1.1, and the correlation coefficient is 0.9990.999. The correlation coefficient is near +1, indicating that the link is positive.
What is the equation?The definition of an equation in algebra is a mathematical statement demonstrating the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Step 2
(B) The change in dosage for a unit (lb) increase in patient weight is indicated by the best-fit slope. We discover that for every unit increase in patient weight, the dosage rises by around 0.77 mg.
Step 3
(C) Including observation (140, 135) in the data set. y=6.12+0.75xy=6.12+0.75x is the new value of the regression line. Although the slope is reduced, the intercept is increased.
However, the link is weakened when the correlation drops to 0.9340.934. This occurs because the observation is an anomaly.
Result
a. Strong positive association, y=0.77x-1.1y=0.77x1.1
B. indicates a dose modification for a unit weight increase
C. y=6.12+0.75xy=6.12+0.75x is the new value of the regression line.
Therefore, y=0.77x-1.1y=0.77x1.1 is the equation for the line of best fit, and the correlation coefficient is 0.9990.999.
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"Place a number in each box so that each equation is true and each equation has at least one negative number."
Answer:
x=1, y=-1
Step-by-step explanation:
Given the equation:
where x and y are the blank boxes.
We want to find
A positive value of x
A negative value of y
That makes the equation true.
If x=1, y=-1
This can be confirmed using addition law of indices()
In general, any pair of a number and its negative value will satisfy the equality.
Step-by-step explanation:
DE joins the midpoints of AB and AC. Find the value of x
and y.
Answer:
x = 6
y = 4
Step-by-step explanation:
2(4x + 1) = 11x - 16
8x + 2 = 11x - 16
8x + 2 + 16 = 11x - 16 + 16
8x + 18 = 11x
8x + 18 - 8x = 11x - 8x
18 = 3x
6 = x
5y + 4 = 8(y - 1)
5y + 4 = 8y - 8
5y + 4 + 8 = 8y - 8 + 8
5y + 12 = 8y
5y + 12 - 5y = 8y - 5y
12 = 3y
4 = y
I need help with this please.
Answer:
1782 cm²
Step-by-step explanation:
the required surface area =1782
units= cm²
Find the value of x. Round to the nearest degree.
Answer:
x = 39°Step-by-step explanation:
The opposing side and the hypotenuse for the angle are given.
Remember, when the opposing side and the hypotenuse are given, take the cos ratio.
cosx = 7/9x = cos⁻¹ (7/9)x = 38.9424413°x = 39°The equation y - 1 =-7(x-3) is written in point-slope form. What is the y-intercept of the line?
O -4
O-2
O 20
O 22
Find the area of the shaded shape. Write the area in square units
help please I realy nead help
Answer:
B) 77.5 square feet
Step-by-step explanation:
cut shape into rectangle and triangle
area of rectangle = x*y
area of rectangle = 5*13
area of rectangle = 65
area of triangle = (z-x)*(y-w)/2
area of triangle = 5*3/2
area of triangle = 7.5
Total area = 65 + 7.5
Total area = 77.5, B)
Answer:
77.5
Step-by-step explanation:
Cut the figure into a triangle and a rectangle
XxY=65
Z-x=5
Y-W=5
5x5=25
25/2=13.5
65+35.5=77.5
When randomly choosing two coins from a cup of coins that contains a penny, nickel, a dime, and a quarter, what is the probability of choosing a penny and a nickel?
Which distribution has the greatest spread?
A. Mean: 13.7 & Standard Deviation: 3.1
B. Mean: 423.6 & Standard Deviation: 1.3
C. Mean: 38.4 & Standard Deviation: 7.2
D. Mean: 231.4 & Standard Deviation: 5.5
Answer:
C. Distribution 3
Step-by-step explanation:
The more spread out a data distribution is, the greater its standard deviation.
4) Louise stops at the gift store to buy a souvenir of the Statue of Liberty. THe original
height of the statue is 151 ft. If a scale factor of 1in = 20 ft is used to design the
souvenir, what is the height of the replica?
Pls I need help ASAP
To find the height of Replica,
we'll divide the original height by the given scale factor ⇢151/20 inches⇢7.55 inchesDialted scale factor=1in=20ft
So height of replica
151/207.557.6inSolve using the elimination method -4x-2y=-18
Step-by-step explanation:
-4x – 2y= -18
Add 2y to both sides
-4x- 2y+ 2y = -18 + 2y
Simplify
-4x = -18 + 2y
Divide both sides by -4
-4x/-4= -18/-4+ 2y/-4
simplify
x= - -9+y/2
tan(x)+cot(x)= sec(x)*csc(x)
show me all of the steps, labeled. I would really appreciate it!
hence proved
hope it helps...!!!
A bucket of water was 1/2 full, but it still had 3 and 3/5 gallons of water in it. How much water would be in one fully filled bucket?
Question:
A bucket of water was 1/2 full, but it still had 3 and 3/5 gallons of water in it. How much water would be in one fully filled bucket?
Answer:
7 1/5
Step-by-step explanation:
The bucket was halfway full. It still had 3 3/5 gallons in it. So all you'd have to do is multiply 3 3/5 by 2. Here is the actual work for proof:
3 3/5 × 2 =
18/5 × 2 =
18 × 2
5 × 1 =
36/5 = 7 1/5.
x+3=y
what is y?
GIVING BRANLIEST
Answer:
There isn't a way to solve for y but I can give you this
Step-by-step explanation:
Slope=1
x-intercept is -3/1
y-intercept is 3/1
HELPPP Pleaseeee
Last year, Dan opened an investment account with $6600. At the end of the year, the amount in the account had increased by 26.5%. How much is this increase
in dollars? How much money was in his account at the end of last year?
Answer:
1,749
8,349
Step-by-step explanation:
We can multiply 6,600 by 1.265 to get 8,349. To get the percentage all we have to do is multiply 6,600 by .265 and get 1,749.
Hope this helps
HELPPP PLS IM GIVING 60 POINTSSSSS IT'S EASYYYYYY 6TH GRADE MATHH
solve for the value of k
pls help me asap
Answer:
k=13
Step-by-step explanation:
We know that
straight angle is equal to 180⁰
(4k-7)⁰+90⁰+(3k+6)⁰=180⁰
4k-7+3k+6=90
7k=91
k=13
I hope it helped you
A random survey found that 6
prefer blueberry candies from
of the 27 people surveyed prefer blueberry candies. Based on those results, about how many people
a population of 108 people?
A. 24
B. 18
C. 30
D. 12
Answer:
A
Step-by-step explanation:
108/24 finds you the ratio from people surveyed to population
gets you 1:4
so for the 6 who prefer candies you sub it it
6:(4*6)
6:24
so its 24 = A :)
What is the value of log5 125?
The log base value is three.
Oil leaks from a tank. At hour t = 0 there are 360 gallons of oil in the tank. Each hour after that, 3% of the oil leaks out.
(a) What percent of the original 360 gallons has leaked out after 8 hours?
%
(b) if Q(t) = Q0e^kt the quantity of oil remaining after t hours, find the value of k.
k=
(c) What does k tell you about the leaking oil? Select all that apply if more than one statement is true
A. It tells what percent of oil remains after each hour.
B. It is the amount that the oil that leaks out each second.
C. Because it is less than one, we know the amount of oil in the tank is decreasing,
D. It tells by what percent of oil decays each hour.
E. Because it is negative, we know the amount of oil in the tank is decreasing.
F. It gives the continuous hourly rate at which oil is leaking.
G. None of the above
Find the value of x.
Explain your answer.
Answer:
Step-by-step explanation:
The hypotenuse is 16 and the adjacent angle is x.
So using SohCahToh
O is opposite, H is the hypotenuse, and A is adjacent.
Soh: sin(theta)= O/H
Cah: cos(theta)= A/H
Toh: tan(theta)= O/A
Any side length that is next to degree 60° is adjacent so x is adjecent.
Using Cah.
cos(theta)= A/H
cos(60°)= x/16
x=16*cos(60°)
x=16*1/2
x=8
How do you know if a net will fold into a pyramid?
Step-by-step explanation:
A pyramid is made when 4 triangle meet on square then mate on each together .
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.
8 divided by the sum of 2 and a number
Answer:
8/x+2 or [tex]\frac{8}{2+x}[/tex]
Step-by-step explanation:
To answer, carefully read the question and pick up on key words like "sum." To begin, we know that "sum" means addition, therefore the sum of 2 and a number (which will be replaced by the variable x) is equivilent to 2 + x. Furthermore, we know that 8 is being divided by the sum. So, the final expression should be [tex]\frac{8}{2+x}[/tex] . Good luck!