The initial value is 6.787
The growth factor is 1.25
Growth
The growth rate of the function is 25%
Determining the characteristics of an exponential functionFrom the question, we are to determine the characteristics of the given exponential function
The given exponential function is
y = 6.787(1.25)ˣ
The initial value of the function is value of the function when x = 0 \
y = 6.787(1.25)⁰
y = 6.787
Therefore,
The initial value is 6.787
In an exponential function, the growth or decay factor is determined by the value of the base.
For example,
Given an exponential function of the form
y = a(b)^x
The base is b.
Thus,
In y = 6.787(1.25)ˣ
The base is 1.25.
Since the base is greater than 1, it is a growth factor.
Therefore,
The growth factor is 1.25
Growth or Decay?
Growth (Since the growth factor is greater than 1)
Growth or Decay rate
The growth or decay rate can be determined from the growth or decay factor. In this case, we have a growth factor of 1.25. This means the function y increases by a factor of 1.25. The is equivalent to a growth rate of 25%.
Hence,
The growth rate of the function is 25%
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Emily is working with rolling a standard number cube (die) and flipping a quarter.
Which experiment can yield a 50% probability?
Answer:
flipping a quarter
Step-by-step explanation:
a quarter has two sides so the chance of getting one is 1/2
a dice has 6 sides so the chance of getting a certain number is 1/6
Adition and subtraction of functions
f(x) = x^2 + 1. g(x)=5-x
(f + g)(x) =
x^2 + x -4
x^2+x+4
x^2-X+6
x^2 + x + 6
Answer:
(f + g)(x) = x² - x + 6
Step-by-step explanation:
Step 1: Define
f(x) = x² + 1
g(x) = 5 - x
Step 2: Find (f + g)(x)
(f + g)(x) = x² + 1 + 5 - x
(f + g)(x) = x² - x + 6
Answer:
(f + g)(x) = x² - x + 6
Step-by-step explanation:
In a circle, an angle measuring 8.7 radians intercepts an arc of length 3.9. Find the radius of the circle to the nearest 10th.
Answer:
r = .5 units
Step-by-step explanation:
8.7 R is an improper FRACTION of the 2 pi R of the entire circle ....set up a ratio:
8.7 / (2 pi) = 3.9 / x where x is the entire circumference measurement
x = 3.9 / (8.7 / (2 pi) ) = 2.82 units
To find the radius circumf = 2 pi r
2.82 = 2 pi r shows r = .5 units
A school club wants to collect at least 500 canned goods for a school food drive. The club has already collected 30 canned goods
Part A
If 10 club members each collect the same number of canned goods, which inequality represents the minimum number of canned goods, n, each club
member must select for the club to meet the goals?
Answer:
The correct answer is 10n ≥ 470.
Step-by-step explanation:
Since, the school club wants to collect at least 500 canned goods, then we know that they don't want to collect any less: they must collet 500 or more canned goods.
They already collected 30 canned goods, therefore we can subtract this quantity from out goal.
500 - 30 = 470
Since there are 10 club members, the number of members multiplied by "n" the minimum amount of canned goods that they can collect, will equal the total amount of canned goods that they need.
Hope this helps! :D
Find the discount of a jacket priced at $50 with 30% off.
Answer:
15.00% savings
Step-by-step explanation:
50 - more than half % off 50
Find the value of X.
Answer:
x=2
Step-by-step explanation:
\(2^{3x+1}+52=180^o\)
\(2^{3x+1}+52-52=180-52\)
\(2^{3x+1}=128\)
\(3x+1=7\)
\(x=2\)
Which diagram represents the factors of m^2-10+16?
Answer:
LAST TABLLEE
Step-by-step explanation:
We are given a equation m²-10m+16
We have to find which diagram represents the factor of m²-10m+16 we will use splitting the middle term method:
m²-10m+16 can also be written as
m²-8m-2m+16
= m(m-8)-2(m-8)
=(m-2)(m-8)
so, Last Table represents the factors of m²-10m+16
Determine whether the functions y₁ and y₂ are linearly dependent on the interval (0,1).
y₁ = sint cost, y₂ = 6 sin 2t
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. Since y₁ = (__)y₂ on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.)
B. Since y₁ = (__)y₂ on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer.)
C. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly independent on (0,1).
D. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly dependent on (0,1).
Option (B) Since y₁ = (__)y₂ on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer.) is the correct answer
We have two functions which are y₁ = sin(t)cos(t)y₂ = 6sin(2t)
We need to determine whether the given functions are linearly dependent or linearly independent on the interval (0, 1).
To check whether y₁ and y₂ are linearly dependent or not, we must check if one of them can be represented as a linear combination of the other:
That is, we need to check whether there exist constants a and b, not both zero, such that: a y₁ + b y₂ = 0
On substituting the given values, we get: asin(t)cos(t) + b6sin(2t) = 0
We need to show that there exists non-zero values for 'a' and 'b' such that the above equation holds true. So we need to manipulate the above equation and try to solve for a variable.
6sin(2t) = -asin(t)cos(t)/b ⇒ 6sin(2t)/sin(t)cos(t) = -a/b
We can use the identity sin(2θ) = 2 sin(θ)cos(θ) to rewrite the left-hand side of the equation above:6sin(2t)/sin(t)cos(t) = 6(2sin(t)cos(t))/(sin(t)cos(t)) = 12
So, we have:12 = -a/b
Therefore, we can say that there exist non-zero values of 'a' and 'b' such that the linear combination a y₁ + b y₂ = 0. Thus, the given functions are linearly dependent on the interval (0, 1).Option (B) Since y₁ = (__)y₂ on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer.) is the correct answer.
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A computer downloads a movie at a constant rate. What does the slope represent?
Answer:
hope it helps you
Step-by-step explanation:
A computer downloads a movie at a constant rate. What does the slope represent? 2000
Download (megabytes)
000-
400
Time (min)
CLEAR
CHECK
Number of minutes for download completion
Downloading speed in megabytes per minute
Unit rate of minutes per megabyte
Unit rate of megabytes per movie
Answer:
Downloading speed in megabytes per minute
Step-by-step explanation:
did on ttm
Which expressions are equal to 105?
(10'4)1
10'3.10'2
1/10'5
(10'3)2
10.10.10.10.10
Answer:
103 and 102
Step-by-step explanation:
u add them together
Name all things on the list that are renewable or nonrenewable
A coal
B natural gas
C oil
D sunlight
E water
F wood
Answer:
yes
Step-by-step explanation:
Answer:
Coal is nonrenewable
Natural gas is renewable
oil is nonrenewable
sunlight is renewable
water is renewable
wood is renewable
Finn read 43 pages of his book in an hour
and a half. How many minutes would it take
to read 135 pages?
135 /43 = 3.14
60 * 3.14 = 188.4 minutes
Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like to buy souvenir bracelets, which are $3.25 each. All prices include taxes.
Answer:
3.25 <26.50 (put a line under the < sign please Ok)
0mar can buy 8 bracelets
Step-by-step explanation:
40.00 -13.50 (for hat)
=26.50 remaining
each bracelet cost 3.25
let x be the bracelets
3.25x < 26.50 (put a line under the < sign ok )
divide both sides by 3,25
3.25x /3.25 < 26.50 /3.25 (put line under the < sign)
x = 8.15 Bracelets cant be in decimal form so round to the nearest whole number x < 8 (put a line under the < sign)
Therefor Omar can buy 8 bracelets
A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n)
Answer:
A normal distribution.
Step-by-step explanation:
hope this helps
How can I find X and Y for these
Answer:
1) x=7 and y=9
3) x=3 and y=2
Sorry i don’t know the others
1. evaluate the line integralſ, yềz ds , where c is the line segment from (3, 3, 2) to (1, 2, 5).
The value of the line integral is 2sqrt(14) - 5.
To evaluate the line integral, we need a vector function r(t) that traces out the curve C as t goes from a to b.
We can find a vector function r(t) for the line segment from (3, 3, 2) to (1, 2, 5) as follows:
r(t) = <3, 3, 2> + t<-2, -1, 3> for 0 ≤ t ≤ 1
We can then compute the differential ds as:
ds = |r'(t)| dt = sqrt(14) dt
Substituting y = 3-t, z = 2+3t, and ds = sqrt(14) dt in the given line integral:
∫C (-y)dx + xdy + zds
= ∫[0,1] [(3-t)(-2dt) + (3+3t)(-dt) + (2+3t)(sqrt(14) dt)]
= ∫[0,1] [-2t - 3 + 3t - sqrt(14)t + 2sqrt(14) + 3sqrt(14)t] dt
= ∫[0,1] [(6sqrt(14) - 2 - sqrt(14))t - 3] dt
= [(6sqrt(14) - 2 - sqrt(14))(1/2) - 3(1-0)]
= 2sqrt(14) - 5
Therefore, the value of the line integral is 2sqrt(14) - 5.
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Find the abscissa on the curve x2=2y which is nearest
to a
point (4, 1).
The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).
Given the equation x^2 = 2y.
The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:
To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].
Now we need to find the value of x that will minimize this expression.
We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.
Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T
he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).
The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).
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isaiah is a high school basketball player. in a particular game, he made some free throws (worth one point each) and some two point shots. isaiah scored a total of 12 points and made 4 times as many free throws as two point shots. write a system of equations that could be used to determine the number of free throws isaiah made and the number of two point shots he made. define the variables that you use to write the system.
The system of linear equations which could be used to determine the number of free throws isaiah made and the number of two point shots he made is;
x + 2y = 12.x = 4y.Which system of.linear equations can be used to determine the number of each kind of shots he made?Let the number of free throws isaiah made be; x.
Let the number of two point shots he made be; y.
On this note, since the individual, isaiah scored a total of 12 points. The algebraic equations which represents the word phrase is;
x + 2y = 12.
Also, it follows from the task content that;
Isaiah made 4 times as many free throws as two point shots. The equation which represents the situation as described is;
x = 4y.
Consequently, the system of linear equations which correctly could be used to determine the number of free throws and two point shots isaiah made is;
x + 2y = 12.x = 4y.Read more on system of linear equations;
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Answer:
zczczczczczcz
Step-by-step explanation:
1, I cannot fail this if I do I have a F in math!! Please make sure u know it’s correct I can’t do it alone.
Answer:One way of knowing the correct answers, we substitute the ordered pairs to the function and see whether it would make the function true.
3x – 4y = 21
A. (−3, 3)
3(-3) – 4(3) = 21
-21 = 21 ---------------> not equal
B. (−1, −6)
3(-1) – 4(-6) = 21
21 = 21 ---------------> equal
C. (7, 0)
3(7) – 4(0) = 21
21 = 21 ---------------> equal
D. (11, 3)
3(11) – 4(3) = 21
21 = 21 ---------------> equal
which of the following expressions is equivalent to -10?
a.-7 3
b.-3 - 7
c.3 - 7
d.7 - 3
The expression which is equivalent to -10 is the option b, -3 - 7.
Explanation:
We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;
-3 - 7 = -10 (-3 - 7)
The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.
If we add -3 and -7 we will get -10. This makes the option b the correct answer.
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Part A. If F(2, 2) = 5x^3y^3+ 9x, what is f(3,1)? Part B. Find the percent change in the function f(x, y)= 1.3^x/y from (5,1)(8,4)
Part A:
To find f(3,1), we simply substitute x = 3 and y = 1 into the function f(x,y) = 5x^3y^3 + 9x.
f(3,1) = 5(3)^3(1)^3 + 9(3) = 135 + 27 = 162.
Therefore, f(3,1) = 162.
Part B:
To find the percent change in the function f(x,y) = 1.3^(x/y) from (5,1) to (8,4), we need to use the formula for percent change:
Percent Change = (New Value - Old Value)/Old Value x 100%
Let's first find the value of f(5,1) and f(8,4) using the given function:
f(5,1) = 1.3^(5/1) = 7.211
f(8,4) = 1.3^(8/4) = 4.746
Now we can substitute these values into the formula for percent change:
Percent Change = (4.746 - 7.211)/7.211 x 100%
Percent Change = -34.21%
Therefore, the percent change in the function f(x,y) = 1.3^(x/y) from (5,1) to (8,4) is -34.21%.
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Please help me in this question.I need it right now!!!
Answer:
X=102 y=288 =390
Step-by-step explanation:
X=50+32=82=180-82=102
Y= 50+32=82=360-82=288
Total answer is =390
Help please
6÷2(1+2)=?
8÷2(2+2)=?
Answer:
6÷2(1+2)=9
8÷2(2+2)=16
Step-by-step explanation:
Help please
6÷2(1+2)=?
8÷2(2+2)=?
Remember PEMDAS
6 : 2 * (1 + 2) =
3 * 3 =
9
----------------
8 : 2 * (2 + 2) =
4 * 4 =
16
1. In a karate class there are 22 students. 15 of the students are male. What is the ratio of females to the total number of students?
22:15
7:22
7:15
Answer:
239392iq5858558586867685858484939939
e
Step-by-step explanation:
abcdefghijklmnopqrstuvwxyz
please use the following scores to answer questions 2a and 2b: x y 1 6 4 1 1 4 1 3 3 1
The correlation coefficient between the x and y scores is -2.167.
I will use the provided scores to answer questions 2a and 2b.
2a) Calculate the mean of the x scores.
To calculate the mean of the x scores, we add up all the x scores and divide by the total number of scores:
mean = (1 + 4 + 1 + 1 + 3)/5 = 2
Therefore, the mean of the x scores is 2.
2b) Calculate the correlation coefficient between the x and y scores.
To calculate the correlation coefficient between the x and y scores, we first need to calculate the covariance between the x and y scores:
cov(x,y) = (1-2)(6-2) + (4-2)(1-2) + (1-2)(4-2) + (1-2)(3-2) + (3-2)*(1-2) = -10
Next, we need to calculate the standard deviations of the x and y scores:
s_x = sqrt([(1-2)^2 + (4-2)^2 + (1-2)^2 + (1-2)^2 + (3-2)^2]/4) = 1.247
s_y = sqrt([(6-2)^2 + (1-2)^2 + (4-2)^2 + (3-2)^2]/4) = 2.309
Finally, we can calculate the correlation coefficient:
r = cov(x,y)/(s_x * s_y) = -10/(1.247 * 2.309) = -2.167 (rounded to three decimal places)
Therefore, the correlation coefficient between the x and y scores is -2.167.
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Use the image to answer the question.
An illustration of a scatterplot graph is titled Animal Longevity. It shows x-axis, labeled as average, ranging from 0 to 45 in increments of 5 and y-axis, labeled as maximum, ranging from 0 to 80 in increments of 10. Multiple points are plotted around a line that points upward to the right with an arrowhead on the top. The line passes approximately through left parenthesis 0 comma 20 right parenthesis, left parenthesis 15 comma 40 right parenthesis, left parenthesis 30 comma 60 right parenthesis, and left parenthesis 40 comma 78 right parenthesis. Two dotted lines are drawn forming a triangle under the line with the line being the hypotenuse. The dotted lines are drawn from left parenthesis 15 comma 40 right parenthesis to left parenthesis 30 comma 40 right parenthesis and from left parenthesis 30 comma 60 right parenthesis to left parenthesis 30 comma 40 right parenthesis. 8 points are plotted close to the line.
Write an equation in slope-intercept form of the trend line.
(1 point)
y=
The equation of the trend line is given as follows:
y = 1.33x + 20.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:
m represents the slope of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.Two points on the line in this problem are given as follows:
(0, 20) and (15, 40).
When x = 0, y = 20, hence the intercept b is given as follows:
b = 20.
When x increases by 15, y increases by 20, hence the slope m is given as follows:
m = 20/15
m = 1.33.
Hence the function is given as follows:
y = 1.33x + 20.
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For an independent-measures t statistic, the estimated standard error measures how much difference is reasonable to expect between the sample means for two samples selected from the same population.
For an independent-measures t statistic, the estimated standard error measures how much difference is reasonable to expect between the sample means for two samples selected from the same population.
True
What is standard error measures?The reliability of a measure is determined by the standard error of measurement. It is frequently mentioned in standardized testing and it describes how variable a test's measurement error is. A confidence interval for the true score of an element or an individual can be generated using the standard error of measurement.
What is independent-measures t statistic?To ascertain whether there is statistical support that the linked population means are statistically substantially different, the Independent Samples t Test compares the means of two independent groups. An example of a parametric test is the Independent Samples t Test. Additionally called the Independent t Test.
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A sign is being made from a rectangular board of wood that originally measures 36 inches by
18 inches. Triangles are to be cut from the board along the dotted lines so that the remaining
shape is an isosceles trapezoid whose shorter parallel side is 24 inches long as shown.
Since the two triangles are equal (as said in the question):
=> Area of triangles: 2(1/2 x 6 x 18)=> Area of triangles: 6 x 18=> Area of triangles: 108 in²Solution (c):Subtract the area of the triangles from the area of the rectangle.
648 - 108 = Area of trapezoid=> 540 in² = Area of trapezoidSolve for the right triangle.A=56° 41’, c= 253m, C=90°Draw the right triangle.Round side lengths to two decimal places if necessary.I believe they are looking for angle a, B and b since they have B, C and c.
Given the right triangle:
First, we know that ∡A and ∡B are complementary angles
\(\begin{gathered} \measuredangle B=90\degree-\measuredangle A \\ \Rightarrow\measuredangle B=90\degree-56\degree41^{\prime} \\ \Rightarrow\measuredangle B=33\degree19^{\prime} \end{gathered}\)Now, using the trigonometric functions:
\(\begin{gathered} \sin A=\frac{a}{c} \\ \sin B=\frac{b}{c} \end{gathered}\)Finally, using the values of A, B, and c to find a and b:
\(\begin{gathered} \sin 56\degree41^{\prime}=\frac{a}{253}\Rightarrow a=211.42\text{ m} \\ \sin 33\degree19^{\prime}=\frac{b}{253}\Rightarrow b=138.96\text{ m} \end{gathered}\)Summarizing:
\(\begin{gathered} \measuredangle A=33\degree19^{\prime} \\ a=211.42\text{ m} \\ b=138.96\text{ m} \end{gathered}\):
Ahmed must pay off his car by paying BD 5700 at the beginning of each year for 12 years and is charged an interest of 8%. What is the present value of Ahmed's payments? BD 46392.10 OBD 42955.64 OBD 116823.19 OBD 108169.62
To calculate the present value of Ahmed's payments, we need to discount each annual payment back to the present using the appropriate discount rate. In this case, the discount rate is the interest rate of 8%. The formula to calculate the present value of an annuity is:
PV = Payment × [(1 - \((1 + r)^{(-n)\)) / r],
where PV is the present value, Payment is the annual payment, r is the interest rate, and n is the number of periods.
Plugging in the values from the given information:
Payment = BD 5700
Interest rate (r) = 8% or 0.08
Number of periods (n) = 12
Using the formula, we can calculate the present value:
PV = BD 5700 × [(1 - \((1 + 0.08)^{(-12)\)) / 0.08]
Calculating this equation, the present value of Ahmed's payments is approximately BD 46,392.10. Therefore, the correct answer is BD 46,392.10.
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