From the given information, Therefore, the function [tex]= > y = 4(\frac{5}{6} )^x[/tex] is an exponential decay.
What is exponential decay?The process of decreasing a sum at a constant percentage rate over time is referred to in mathematics as exponential decay. It may be written as the formula y=a(1-b)x, where y represents the final amount and a, b, and x, respectively, represent the initial amount and the decay factor.
The formula for an exponential function is where b is a positive integer that is not equal to 1.
Whether a function is an exponential growth or a decay depends on the value of b. If b > 1 or if b< 1, an exponential function exhibits exponential growth and exponential decline, respectively.
given,
[tex]= > y = 4(\frac{5}{6} )^x[/tex]
[tex]= > b = \frac{5}{6} < 1[/tex]
Therefore, the function [tex]= > y = 4(\frac{5}{6} )^x[/tex] is an exponential decay.
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See attached for the question
Check the picture below.
Answer:
∠ U = 12°
Step-by-step explanation:
the inscribed angle RST is half the measure of its intercepted arc RT , then
arc RT = 2 × ∠ RST = 2 × 30° = 60°
the secant- tangent angle U is equal to half the difference of its intercepted arcs, that is
∠ U = [tex]\frac{1}{2}[/tex] ( RS - RT ) = [tex]\frac{1}{2}[/tex] × (84 - 60)° = [tex]\frac{1}{2}[/tex] × 24° = 12°
A karaoke machine regularly costs $163 and is on sale for 25% off. How much is the discount?
$20.38
$40.75
$114.10
$122.25
Use the diagram to answer the both questions.
What is the value of x?
x =
What is the measure of the unknown angle?
Angle =
The value of x is 56 and the value if the unknown angle is 106°
What are angles on a straight line?Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line. The law of angle on a straight line states that the sum of angle on a straight line is 180°
This means that (2x-6)°+74= 180
(2x-6)°= 180-74
(2x-6)° = 106
add 6 to both sides
2x= 106+6
2x= 112
x= 112/2
x= 56
therefore the unknown angle = 2(56)-6 = 112-6= 106°
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An accountant used to charge $91.50 per hour, but recently decided to charge 10% less. Now how much does she charge per hour?
Answer:
82.35
Step-by-step explanation:
91.5-(91.5*0.1)=
91.5-9.15=82.35
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 36 minutes of calls is
$24.24, and the remaining credit after 55 minutes of calls is $21.20. What is the remaining credit after 63 minutes of calls?
The remaining credit after 63 minutes of calls is $19.92.
What is the remaining credit after 63 minutes of calls?From the information illustrated, the remaining credit after 36 minutes of calls is $24.24, and the remaining credit after 55 minutes of calls is $21.20.
The rate will be:
= (24.24 - 21.20) / (55 - 36)
= 3.04 / 19
= 0.16
The remaining credit after 63 minutes of calls will be:
= $21.20 - ((63 - 55) × $0.16)
= $21.20 - $1.28
= $19.92
The credit is $19.92.
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PLEASE HELP ME!! I WILL GIVE YOU BRAINLIST!!!!
Answer: it should be C.
Step-by-step explanation: because its ascking to describe the formation.
There are 10 fewer Robins than Cardinals. There are 3 time as many bluebirds than robins. There are 16 cardinals. How many bluebirds there are?
The number of bluebirds is 18.
How many are bluebirds?The following equations can be determined from the question:
10 = c - r equation 1
b = 3r equation 2
Where:
c = number of Cardinals b = number of bluebirds r = number of robinsSubstitute for c in the first equation :
10 = 16 - r
r = 16 - 10
r = 6
Substitute for r in the second equation:
b = 6 x 3
b = 18
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Which is equivalent to ³√8^x?
O ^x√8^3
O 8^3/x
O8^x/3
O8^3x
After solving the given expression it will be equivalent to [tex]8^\frac{x}{3}[/tex]. Hence, option C is correct.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the given expression in the question,
[tex]\sqrt[3]{8}^x[/tex]
So, this form is written as power/root
Then, then it can be written as [tex]8^\frac{x}{3}[/tex].
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If f(x)=5x³-2 and g(x)=x+1, find (f - g)(x).
Answer:
5x³ - x - 3
Step-by-step explanation:
(f - g)(x) =
f(x) - g(x) =
5x³-2 - (x+1) = ==> plug in known values
5x³-2 - x - 1 = ==> simplify
5x³ - x - 2 - 1 = 5x³ - x - 3
f(x) = 5x³ - 2
g(x) = x + 1
Therefore, (f - g)(x) = (5x³ - 2) - (x + 1) = 5x³ - x - 3
So, (f - g)(x) = 5x³ - x - 3.
Identify the equation of a line in point slope from that passes through the points (5,-4) and (-3,2)
Slope: −34
y-intercept: (0,−14)
[IF ITS WRONG TELL ME]
Question 61 A recipe calls for 1 cup of milk for every 2 ...
To make the similar cake for 8 persons , the number of cups of both flour and milk will be needed is [tex]4\frac{2}{3}[/tex] cups .
In the question ,
it is given that ,
number of cups of milk needed to make the cake is = 1 cup
number of cups of flour needed to make the cake is = [tex]2\frac{1}{2}[/tex] = 5/2 cups .
So , the total is = cups of milk + flour
= 1 + 5/2 = 7/2
So , for 6 persons , 7/2 cups of milk and flour is needed .
for 1 person 7/12 cups of milk and flour is needed .
and for 8 persons = 8×7/12 cups of milk and flour is needed .
= 14/3
= [tex]4\frac{2}{3}[/tex] cups .
Therefore , the number of cups of milk and flour needed is [tex]4\frac{2}{3}[/tex] cups .
The given question is incomplete , the complete question is
A recipe calls for 1 cup of milk for every [tex]2\frac{1}{2}[/tex] cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 persons ?
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suppose that as a follow up question you asked all the students who were graduating with stem degrees if they planned on working in academia. out of the 95 students graduating with stem degrees, 9 report they plan on working in academia. build a 95% confidence interval for the true percentage of students graduating with stem degrees that plan on working in academia. make sure to interpret your interval and check any necessary conditions. (hint: make sure to use an appropriate method to do this)
The sample size must be more than 30 and the sample must be chosen at random for this confidence interval to hold true. The sample size in this example is 95, and the students were chosen at random, thus both of these requirements are satisfied.
How do percentages work?Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. (Value/Total Value)100% is the formula for calculating percentages.
How do you find the percentage?We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
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Find the perimeter in centimeters.
Answer: 210
Step-by-step explanation:
Answer: 210cm
Step-by-step explanation:
This is a parallelogram, the sides opposite of each other are congruent. So we can just add up all the sides 50+50+55+55=210cm.
In the following question, we will count distinct integer solutions to the equation X_1 + X_2 + X_3 + X_4 = 35. How many solutions are there if all the variables must be non-negative? How many solutions are there if all the variables must be positive? How many solutions are there if X_1 greaterthanorequalto 2, X_2 greaterthanorequalto 4, X_3 greaterthanorequalto 0, and X_4 greaterthanorequalto 0? How many solutions are there to the equation X_1 + X_2 + X_3 + X_4 lessthanorequalto 35 in which all the X_i are non-negative?
There are 364 positive variables and 5984 non - negative integers.
An integer is zero (0), a positive integer (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). [1] A negative number is the additive reciprocal of the corresponding positive number. [2] In mathematics languages, sets of integers are often represented by a bold Z or blackboard bold . The integers form the smallest group and smallest ring containing the natural numbers. In algebraic number theory, integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, (rational) integers are algebraic integers that are also rational numbers.
Let us take each xi = a₁+1
x₁+x₂+x₃+x₄ = 35
∴a₁+a₂+a₃+a₄ = 31 ,where each ai is non-negative.
Now using the stars and bars method the answer is -
([tex]\left \{ {{31 + 4 - 1} \atop {4 - 1}} \right.[/tex] = [tex]\left \{ {{34} \atop {3}} \right.[/tex]}
= [tex]\frac{34!}{3! * (34 - 3)!}[/tex]
= 5984
A particular solution of this equation corresponds to the placement of 3 addition signs in the 14 spaces between successive ones in a row of 15 ones.
Since, a particular solution of the equation corresponds to the placement of k−1 addition signs in the n−1 spaces between successive ones in a row of n ones, the number of solutions of the equation x₁ + x₂ + x₃ +⋯+xₐ=n in the positive integers is
[tex]\left \{ {{n - 1} \atop {k - 1}} \right.[/tex]}
For instance, placing an addition sign in the fourth, seventh, and twelfth spaces gives
1111+111+11111+111
which corresponds to the solution x₁ = 4, x₂ = 3, x₃ = 5, x₄ = 3.
Hence, the number of such solutions is the number of ways we can select which three of the 14 spaces between successive ones in a row of 15 ones will be filled with addition signs, which is
[tex]\left \{ {{14} \atop {3}} \right.[/tex]}
= [tex]\frac{14!}{3! * (14 - 3)!}[/tex]
= 364
Therefore, there are 364 positive variables and 5984 non - negative integers.
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Question
Write a linear function f with f(5)=7 and f(2)=0
f(5) = 7 is another to say a point at (5 , 7)
f(2) = 0 is another to say a point of (2 , 0)
to get the equation of any straight line, we simply need two points off of it, let's use those two above
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{5}}} \implies \cfrac{ -7 }{ -3 } \implies \cfrac{ 7 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{ 7 }{ 3 }}(x-\stackrel{x_1}{5}) \\\\\\ y-7=\cfrac{ 7 }{ 3 }x-\cfrac{ 35 }{ 3 }\implies y=\cfrac{ 7 }{ 3 }x-\cfrac{ 35 }{ 3 }+7\implies {\Large \begin{array}{llll} y=\cfrac{ 7 }{ 3 }x-\cfrac{14}{3} \end{array}}[/tex]
1. Helen took four tests, for which her mean score was 26. Later on, it was found that her score in the English test was wrongly recorded as 51 instead of 15. What was the corrected mean score?
The corrected mean will be 17.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Helen took four tests, for which her mean score was 26.
Later on, it was found that her score in the English test was wrongly recorded as 51 instead of 15.
Now,
Since, Later on, it was found that her score in the English test was wrongly recorded as 51 instead of 15.
Hence, The correct mean = 26 - (51 - 15)/4
= 26 - 36/4
= 26 - 9
= 17
Thus, The corrected mean will be 17.
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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washery=2−1/2x, y = 0, x 1, x = 2; about the x-axis
The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.
Volume of a solid plain:
The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.
Given in the question:
y = 2 - 1/2x
y = 0 , x = 1 and x = 2
As we know that:
[tex]\int\limits^2_1 {\pi (2 - \frac{1}{2}x - 0 })^2 \, dx[/tex] ------------------------------ (1)
Simplifying,
[tex]\pi \int\limits^2_1 {(2 - \frac{x}{2} )}^2 \, dx[/tex][tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]
⇒ [tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]
⇒ [tex]\pi [ 4x - x^2 + \frac{x^3}{12}]_1^2[/tex]
⇒ [tex]\pi [(8 - 4+ \frac{8}{12} ) - ( 4 - 1 + \frac{1}{12} )[/tex]
⇒ [tex]\pi (1 + \frac{7}{12})[/tex]
⇒ [tex]\frac{19\pi }{12}[/tex]
We can write 19π / 12 as
(19× 22/7 )÷ 12
= 209/ 42
= 4.97 ≈ 5 cm³
Therefore, the volume is 5 cm³
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A manufacturing company finds that they can sell 275 items at $2.50 per item and 350 items at $2.00 per item. If the relationship between the number of items sold i and the price per item p is a linear one: Find a formula that gives x in terms of p, 2 = Preview Now use the formula to find the number of items they will sell if the price per item is $3.50. They will sell items if the price is $3.50.
The number of items 125 they will sell if the price per item is $3.50. They will sell 125 items if the price is $3.50.
In the given question, a manufacturing company finds that they can sell 275 items at $2.50 per item and 350 items at $2.00 per item.
If the relationship between the number of items sold i and the price per item p is a linear one then we have to find a formula that gives x in terms of p, x =
Now we have to use the formula to find the number of items they will sell if the price per item is $3.50. They will sell items if the price is $3.50.
Let’s find the slope using
m = {y(2)-y(1)}/{x(2)-x(1),
where
x(1) = 2.5 y(1)=275
x(2) = 2 y(2)=350
m = (350-275)/(2-2.5)
m = 75/(-0.5)
m = -150 is the slope
Point slope form to find the equation:
y - y1 = m(x-x1)
y - 275 = -150(x - 2.5)
y - 275 = -150x + 375
y = -150x + 275 + 375
y = -150x + 650,
But they want to have x = items sold and p = the price
So we have to write the equation where x is in terms of p
x = -150p + 650:
then use the formula to find the number of items they will sell if the price per item is $3.00.
x = -150(3.5) + 650
x = -525 + 650
x = 125 items sold when the price is $3.5
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Translate the following into a formula:
The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.
The value of the formula will be;
⇒ S = 180 (n - 2)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.''
Now,
Since, The algebraic expression is,
''The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.''
Hence, We can formulate the expression as;
⇒ S = 180 (n - 2)
Thus, The value of the formula is,
⇒ S = 180 (n - 2)
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. A cartographer creates a map using the function
d = 250n where n is the number of inches on the
map and d is the actual distance between the
locations in miles. If the actual distance between
two cities is 1,125 miles, how far apart on the ma
should the cities be?
(A) 0.5 inches
(B) 1.5 inches
(C) 2.5 inches
(D) 4.5 inches
To find the distance between two cities on the map, we can use the formula provided in the question:
d = 250n
where d is the actual distance between the cities in miles, and n is the number of inches on the map. Since we are given that the actual distance between the two cities is 1,125 miles, we can substitute this value for d in the formula above to find the number of inches on the map:
1,125 = 250n
Solving for n, we get:
n = 1,125 / 250 = 4.5 inches
This means that the distance between the two cities on the map should be 4.5 inches, so the correct answer is (D) 4.5 inches.
Josh wants to determine the number of loaves of bread he can bake using the 13 and one-third cups of flour he has. If each loaf requires 3 and four-fifths cups of flour, how many loaves can Josh bake?
3 loaves of bread
4 loaves of bread
50 loaves of bread
51 loaves of bread
(4 loaves of bread is wrong)
On solving the provided question, we got to know that he can bake 200/57 loaves or 3 29/57 loafs.
what is fraction?Mathematically speaking, fractions are represented by integers that indicate a portion of a whole. In the same way that a whole can be any quantity, value, or object, a fraction can be a portion or subset of any quantity of a whole. As an example, let's try to comprehend this idea. The pizza in the picture below is cut into 8 equally sized pieces. The chosen slice of pizza might now be expressed as 1/8 if we wanted to. This indicates that we are talking about one of eight equally sized sections. It denotes a ratio of 1/8. Reading options include: One-eighth, or
1 by 8
13 1/3 divided by 3 4/5
Let's first convert these mixed numbers to incorrect fractions.
13 1/3 = 13(3) + 1 = 39 + 1 = 40/3
3 4/5 = 3(5) + 4= 19/5
Now that we have divided 40/3 by 19/5, we can just switch the operation to multiplication and flip the second fraction because we know how to divide fractions.
40/3 x 5/19 = 200/57
he can bake 200/57 loaves or 3 29/57 loafs.
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Evaluate for d = 10, u = 7, e = 3. 2 de
i think its 28 but im not sure
Answer:
32
Step-by-step explanation:
Just plug in the numbers for [ d times e ]
The equation is then [ 10 x 3.2 = ? ]
The answer is 32
Need to help my sister with these problems
Answer:
have her do the number times each number every time so if the number is seven and there is a four on top, add or multiply or subtract 7 by 4
Step-by-step explanation:
Need some help pls. Amanda needs 3 quarters for the washing machine and 2 quarters for the dryer for a complete load at the laundromat. Which function shows the relationship between the number of complete loads of laundry (x) and the total number of quarters needed (y)?
1 .y= x + 5
2.y= 3/2x
3.y= 3x + w
4 y= 5x
Answer:
y=5x
Step-by-step explanation:
Because we already know we need atleast 5 quarters to complete a full load (Wash and dry) so we would multiply that number by how many loads were doing (x) and y is the amount we need. For example five loads is y=5x5 and then we can find y which would be y=25
what is 58388383-776463783
Answer:
Subtract 58388383 - 776463783
4. Which equation describes the line that
passes through (2, 1) and (0, -5)?
A. Y=1/3x-5
B. Y=3x-5
C. Y=-1/3x-5
D. Y=-3x-5
The equation that describes the line that passes through (2, 1) and (0, -5) is: B. y = 3x - 5.
How to Write the Equation of a Line?To find the equation of a line, find the value of the slope (m) and the y-intercept (b), and plug in the values into y = mx + b.
Given the points:
(2, 1) and (0, -5)
Slope (m) of the line = change in y / change in x = (-5 - 1) / (0 - 2)
Slope (m) = -6/-2
Slope (m) = 3
The y-intercept (b) = -5 (this is because it is the value of y when x = 0).
To write the equation, substitute m = 3 and b = -5 into y = mx + b:
y = 3x - 5
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The standard deviation of returns averages28 percent. The options mature in 5 years and the risk-freerate is 2.36 percent. What is the value of e−Rt?
The value of e⁻ᴿᵗ is 0.8886 for the given the standard deviation of returns averages 28 percent with the options mature in 5 years and the risk-free rate is 2.36 percent.
So, the correct option is option ( C).
Exponential function is characterized by rapid increase (as in size or extent) and an exponential growth rate.
We have given that,
standard deviation of returns averages = 28%
options mature, t = 5 years and
Risk-free rate , R = 2.36 percent.
we have to calculate the value of e−Rt.
Exp(-Rt) = e⁻⁽²·³⁶⁾⁵
use exp(value) function to find the value :
=exp(-5 × 2.36%)
= exp(- 0.118 )
=0.8886
Hence, the the value of e⁻ᴿᵗ is 0.8886.
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Complete question:
I. M. Greedy has been granted options on 500,000 shares. The stock is currently trading at $48 a share and the options are at the money. The standard deviation of returns averages 28 percent. The options mature in 5 years and the risk-free rate is 2.36 percent. What is the value of e-rt?
a) .7087
b) .8476
c) .8886
d) .6087
e) .7952
in fair bankes alaska the tempreture the tempreture on that one day was -18f. on that same day the tempreture was 83 degrees higher than honolulu hawaii what was the temperature in honolulu hawaii on that day
Answer:
The answer is 65 degrees fahrenheit.
Step-by-step explanation:
Jeff Ryan bought 200 shares of BUI for $19.50. Eight weeks later he sold the stock for $20.75. Assuming a 3% commission, his bottom line was a gain of:
Multiple Choice
$250.00
$374.50
$8.50
$257.50
His bottom line was a gain from selling and 3% commission is $257.50.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
The cost price of 200 shares of BUI is (19.50×200) = $3900.
The selling price of 200 shares of BUI is (20.75×200) = $4150.
The net gain is (4150 - 3900) = $250 and with 3% commission it is,
= (103/100)×250.
= $257.50.
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______ results from the exclusion of certain groups of subject from a population frame. coverage error measurement error sampling error non-response error
Coverage Error results from the exclusion of certain groups of subjects from a population frame. The answer for the given statement is Coverage Error.
What is Coverage Error?Coverage errors come from failure to cover sufficiently all components of the population being studied. Incomplete sampling frames usually result in coverage errors. Coverage errors happen because of the divergences between the target population and the frame.
Coverage error also may happen when not all members of the population of interest have an equal chance of being selected for the survey. For example, if we use e-mail lists or phone lists to build the sample and not all potential respondents are on those e-mail or phone lists.
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