It will take t=18 months to take for the account to have $5000 in it.
What is meant by interest rate?The proportion charged for borrowing money by the lender is known as the interest rate. An actual cost of borrowing should be reflected by the APR, or annual percentage rate. Along with interest rate, the APR calculation also accounts for fees and discount points. In relation to the amount lent, deposited, or borrowed, the amount of interest due each period is expressed as an interest rate (called the principal sum).
An annual interest rate is a rate that is calculated over a year. Over different time frames, such a month, other interest rates are in effect.
FV=PV[tex](1+r)^{t}[/tex]
Given,
FV=5000
PV=3000
r=5%
r=5/100
r=0.05
5000=3000[tex](1+0.05)^{t}[/tex]
[tex](1+0.05)^{t}[/tex]=1.667
t log(1.05)=log(1.667)
t=log(1.667)-log(0.05)
t=1.5 years
t=1.5×12
t=18 months
Therefore, It will take t=18 months to take for the account to have $5000 in it.
To know more about interest rate, visit:
https://brainly.com/question/13324776
#SPJ1
Enter the value of n so that the expression (-y + 3) + (2y - 4) is equivalent to (ny - 1).
Answer:
n=1
Step-by-step explanation:
(-y + 3) + (2y - 4) = (ny - 1)
-y + 3 + 2y - 4 = ny - 1
-y + 2y + 3 - 4 = ny - 1 -> combine like terms on the left side of the equation
y - 1 = ny - 1 ==> simplify
y - 1 + 1 = ny - 1 + 1
y = ny ==> solve for n
y/y = ny/y
1 = n ==> n=1
These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Perimeter= 20m
Area=19.6m^2
Perimeter=34m
What is the Area=
The area of the larger figure that is similar to the smaller one is: 28.2 m².
How to Find the Area of Similar Figures?Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:
Area of figure A / Area of figure B = a²/b².
Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:
Perimeter of smaller figure = 20 m
Area of smaller figure = 19.6 m²
Perimeter of larger figure = 34m
Area of larger figure = x
Therefore:
20/34 = a/b
Simplify:
10/17 = a/b.
Find the area (x) of the larger figure using the formula given above:
10²/12² = 19.6/x
100/144 = 19.6/x
100x = 2,822.4
x = 2,822.4/100
x ≈ 28.2 m²
Learn more about area of similar figures on:
https://brainly.com/question/17132861
#SPJ1
A student rewrites the expression 12⋅16−s as another equivalent expression. Which expression could the student write?
The equivalent expression could be 4×3·4×4−s
What is a equivalent expressions?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
Think about the numbers 3²+1 and 5×2. They both add up to 10. These two expressions are equivalent, so to speak.
Let's now have a look at some expressions with variables, such 5x+2.
It is possible to rewrite the expression as 5x+2=x+x+x+x+x+1+1.
The right side of the equation can be regrouped to 2x+3x+1+1, x+4x+2, or another combination. When the same value is used as x, all of these equations have the same result. These two expressions are equivalent, so to speak.
When two expressions have the same value regardless of the value of the variable(s) they contain, they are said to be equivalent.
Here, 4×3=12 and 4×4=16
therefore, 4×3·4×4−s is equal to the expression 12⋅16−s
4×3·4×4−s and 12⋅16−s are equivalent expressions.
Hence, The equivalent expression could be 4×3·4×4−s
To learn more about equivalent expression refer to:
https://brainly.com/question/24734894
#SPJ1
The equivalent expression could be 4×3·4×4−s.
What is a equivalent expressions?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.Think about the numbers 3²+1 and 5×2. They both add up to 10. These two expressions are equivalent, so to speak.Let's now have a look at some expressions with variables, such 5x+2.It is possible to rewrite the expression as 5x+2=x+x+x+x+x+1+1.The right side of the equation can be regrouped to 2x+3x+1+1, x+4x+2, or another combination. When the same value is used as x, all of these equations have the same result. These two expressions are equivalent, so to speak.When two expressions have the same value regardless of the value of the variable(s) they contain, they are said to be equivalent.Here, 4×3=12 and 4×4=16
therefore, 4×3·4×4−s is equal to the expression 12⋅16−s
4×3·4×4−s and 12⋅16−s are equivalent expressions.
Hence, The equivalent expression could be 4×3·4×4−s
To learn more about equivalent expression refer to:
https://brainly.com/question/24734894
#SPJ1
Aniyah invests $2300 in one account and $1400 in an account paying 4 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest
She invested $2300 at 2% and $1400 at 6% interest.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P₁ = $2300, P₂ = $1400, t₁ = t₂ = 1 and r₂ = r₁ + 4.
The sum of the simple interests from both these accounts is $130.
Therefore, (2300×r₁×1)/100 + (1400×(r₁ + 4)×1)/100 = 130
2300r₁/100 + 1400r₁/100 + 5600/100 = 130.
2300r₁ + 1400r₁ + 5600 = 13000.
3700r₁ = 7400.
37r₁ = 74.
r₁ = 2% and hence r₂ = 6%.
learn more about simple interests here :
https://brainly.com/question/11564235
#SPJ1
Rewrite 20x4y3 − 30x3y4 using a common factor. 2x4y4(10 − 15x) 2x3y3(10y − 15x) 5x4y3(4 − 6y) 5x3y3(4x − 6y)
The expression which represents the correctly rewritten form of the given expression; 20x⁴y³ - 30x³y⁴ is; 5x³y³ ( 4x - 6y ).
Which expression correctly represents the rewritten form of the expression 20x⁴y³ - 30x³y⁴?It follows from the task content that the expression which correctly represents the rewritten form of the given expression be determined.
On this note, since the given expression is;
20x⁴y³ - 30x³y⁴
The greatest common factor of both terms in the expression is; 10x³y³ .
On this note, the expression can be factorised completely as follows;
10x³y³ ( 2x - 3y )
However, the expression which is equivalent to the expression above among the answer choices is;
5x³y³ ( 4x - 6y )
Read more on factorisation;
https://brainly.com/question/22048677
#SPJ1
one of the 4 choices
The translation from the parent function is defined according to the following option:
A translation of 5 units to the right.
How to define the translation?The four possible translations are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function in this problem is defined as follows:
f(x) = x².
The translated function is given as follows:
g(x) = (x - 5)².
Meaning that the translated function can be written as follows:
g(x) = f(x - 5).
Thus the transformation to the parent function is given as follows:
x -> x - 5.
Thus it was a translation right of five units, and the third option is the correct option.
More can be learned about translations at brainly.com/question/29211183
#SPJ1
a car manufacturer wants to learn more about the brand preferences of electric car owners. there are millions of electric car owners in the world. who should the company survey? 1 point the entire population of electric car owners a sample of car owners who have owned more than one electric car a sample of all electric car owners a sample of car owners who most recently bought an electric car
A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.
What is Survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.
Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.
As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.
To know more about Survey:
https://brainly.com/question/17373064
#SPJ1
Use factoring and the zero-product property to find the zeros of:
f(x) = 2x² + 3x-2
Answer:
Step-by-step explanation:To find the zeros of the quadratic function f(x) = 2x² + 3x - 2, we can use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
We can write the function as follows:
f(x) = 2x² + 3x - 2 = 0
We can then factor the quadratic as follows:
f(x) = 2(x-1)(x+1) = 0
Since the product of the factors is zero, at least one of the factors must be zero. Therefore, the zeros of the quadratic are x = 1 and x = -1.
1,000 individuals total: 900 are fully susceptible (fs) to methicillin, meaning they die early in the course of treatment. 90 are somewhat susceptible (ss) to methicillin, meaning they have some resistance to methilicillin. 10 are killed only by a full treatment with methicillin (ft), meaning they have the greatest degree of resistance. what is the percentage of each type of s. aureus?
The percentage of each types of s. aureus
Fully susceptible (fs) to methicillin = 90% Somewhat susceptible (ss) to methicillin = 9% Killed only by a full treatment with methicillin = 1%Total number of individuals = 1000
Number of individuals susceptible (fs) to methicillin = 900
The percentage = (Number of individuals susceptible (fs) to methicillin / Total number of individuals) × 100
= (900/1000) × 100
= 90%
90 are somewhat susceptible (ss) to methicillin
The percentage = (90 /1000) × 100
= 9%
10 are killed only by a full treatment with methicillin (ft)
The percentage = (10/1000) × 100
= 1%
Therefore, the percentage of each types of s. aureus are 90%, 9% and 1%
Learn more about percentage here
brainly.com/question/12715980
#SPJ4
Two angles form complements. One angle measure is eight more than twice the other. Find both angles measures.
Answer:
41° and 49°
Step-by-step explanation:
Two angles are said to be complements if the sum of their measures is 90 degrees. Since one angle is eight more than twice the other, we can set up the following equation to represent the situation:
2x + 8 = 90
Solving for x, we get:
2x = 82
x = 41
Since the two angles are complements, their measures must add up to 90 degrees. Therefore, the measure of the other angle is 90 - 41 = 49 degrees.
Therefore, the two angles have measures of 41 and 49 degrees.
find the domain of the function
The domain of the function is { (x, y) ∈ R² | x² + y² ≥ 1 }
What is Domain of function?
A function's domain is the collection of all potential inputs. For instance, all real numbers are in the domain of f(x)=x², and all real numbers are in the domain of g(x)=1/x, with the exception of x=0. Special functions with more constrained domains can also be defined.
According to question
⇒ [tex]z = e^{\sqrt{x^{2}+ y^{2} -1 } }[/tex]
⇒ x² + y² - 1 ≥ 0
⇒ x² + y² ≥ 1
Hence, the Domain of f(x, y) is { (x, y) ∈ R² | x² + y² ≥ 1 }
To learn more about Domain , check out
https://brainly.com/question/28135761
#SPJ1
The expression - 270 +18.3y represents a submarine that began at a depth of 270 feet below sea level and ascended at a rate of 18.3 féet par minute. What was the depth
of the submarine after 8 minutes?
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A. The submarine ___ was feet below sea level after 8 minutes.
(Type an integer or a decimal:)
B. The submarine will have reached sea level after 8 minutes.
The depth of the submarine after 8 minutes is -123.6 feet below sea level.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Depth of the submarine after y minutes.
= -270 + 18.3y
The depth of the submarine after 8 minutes.
= -270 + 18.3 x 8
= -270 + 146.4
= -123.6
Thus,
The submarine is at -123.6 feet below sea level.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
For a sample size of 85 and a population parameter of 0.2, what is the standard error of the sampling distribution?
Answer:
0.043
Step-by-step explanation:
I hope this helps you! Let me know if you have any questions! :)
Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of f(x)=x^2-5x+1 . Write a rule for g .
Answer:We may rewrite f(x) = (x-1)^2
We stretch by having 3(x-1)^2
We reflect about the y axis by changing x to -x: 3(-x-1)^2 = 3(x+1)^2
We move to the left by adding 2 to x: 3(x+2+1)^2 = 3(x+3)^2
Step-by-step explanation:A way to verify this: Consider y = x^2 to be the unit parabola. f(x) = (x-1)^2 moves the unit parabola one to the right, so it is symmetric about x = 1; We then vertically stretch it by a factor of 3; reflection about the y-axis moves the parabola to be symmetric about x = -1; moving to the left by 2 means the parabola is now symmetric about x = -3; thus, we have a stretched unit parabola symmetric about x = -3, so g(x) = 3(x+3)^2
We may write g(x) = 3x^2 + 18x + 27, also.
Please help! I will give brainlist
Answer:
3. 32, 28, 30
4. 38, 142
Step-by-step explanation:
3. (x + 3) + (x - 1) + (x + 1) = 90
3x + 3 = 90
3x = 87
x = 29
angle 1: x + 3 = 29 + 3 = 32
angle 2: x - 1 = 29 - 1 = 28
angle 3: x + 1 = 29 + 1 = 30
4. x + (x + 104) = 180
2x + 104 = 180
2x = 76
x = 38
angle 1: x = 38
angle 2: x + 104 = 38 + 104 = 142
Mr.green Is putting lights around 8 windows; each window is 3 and 1/2 feet wide and 5 feet long. How many feet of light does he need?
Answer:
The answer is 140
Step-by-step explanation:
The first step is simple L x W which will give us.
L being 5 and W being 3.5 The equation is 5 × 3.5 = 17.5.
With that being said I just need to multiply that answer by 8 which gives us 140.
This means that he will need 140 ft of light in order to put light around each window.
Hope this helped :)
Given: segment BD bisects angle ABC and segment BD bisects angle ADC. Prove: segment AD is congruent to segment CD
If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.
What is bisector of an angle?
In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..
Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.
Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.
AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.
Consider △ABD and △DBC:
∠ABD = ∠DBC
∠ADB = ∠BDC
Therefore, △ABD ≅ △DBC
According to CPCT, AD ≅ CD.
To learn more about congruent triangle, click on below link:
https://brainly.com/question/15064982
#SPJ1
Graph this line using the slope and y-intercept: y=–19x+10
The graph of the equation, y = -19x + 10 is shown below.
How to Graph the Line of an Equation Using the Slope and Y-intercept?If the equation of a line is expressed in slope-intercept form as y = mx + b, it means that:
the slope of the line is m, which is the rise over the run of the line.the y-intercept of the line is b, which means the line will intercept the y-axis at y = b.Given a line has the equation, y = -19x + 10, therefore;
the slope (m) = -19.
the y-intercept (b) = 10.
Therefore, the graph of the line is shown in the attachment below and it cuts the y-axis at 10.
Learn more about the graph of a line on:
https://brainly.com/question/29752649
#SPJ1
Which one. Multiple choice.
In the given relation, 1 is not a domain.
What is domain?The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.
All the values that go into a function. The output values are called the range.
The domain of a function is the set of all possible inputs for the function.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.
Given that, a function,
{(5, 1), (4, -3), (3, -1)}
We know, a domain is the set of all "x" values.
Therefore, domain of the function are, 5, 4 and 3
But, if we see, 1 is one of the values of y.
Hence, 1 is not a domain.
For more references on domain, click,
https://brainly.com/question/28135761
#SPJ1
Witch expression is equivalent to (-10/9t+1/8)-(-6/18t+3/4) (I NEED THIS FAST!)
Answer: ( -56 - 45t ) / 72t
Step-by-step explanation:
attached a picture for explaination.
hope that helps...
Which relationships have the same constant of proportionality between yyy and xxx as the following table?
x y
7 24.5
9 31.5
Choose 3 answers
Answer:
A,D,E
Step-by-step explanation:
A:
14/4 = 3.5
D:
7/2 = 3.5
E: 14/4 = 3.5
The constant of proportionality for the table is 3.5. Any other table that satisfies the equations x/y = 3.5 will have the same constant of proportionality.
Explanation:To find the constant of proportionality, we can divide the y-values by the corresponding x-values and see if they are the same for all given points. In this case, if we divide 24.5 by 7, we get approximately 3.5. If we divide 31.5 by 9, we also get approximately 3.5. Therefore, the constant of proportionality is 3.5 for this table.
Now, we need to find the relationships that have the same constant of proportionality.
For example, if we have a table with the following values:
x1 y1
x2 y2
x3 y3
and the constant of proportionality is k, then we have the following equations:
x1/ y1 = k
x2/ y2 = k
x3/ y3 = k
So, any other table that satisfies these equations will have the same constant of proportionality as the given table.
Learn more about Mathematics here:https://brainly.com/question/26854035
#SPJ2
Suppose that the relation S is defined as follows.
S= {(4,n), (8,q), (4,m)}
Give the domain and range of S.
Write your answers using set notation.
Domain=
Range=
The domain of the relation is {4,8} and the range of the relation is {n,q,m}.
What is domain?A function or relation's domain is the set of all potential independent values that it can have.
Suppose that the relation S is defined as follows.
S= {(4,n), (8,q), (4,m)}
The first term at the point represents the input and the second term at the point represents the output.
So,
the input values are 4,8 and 4 and their respective outputs are n, q and m,
The collection of all conceivable independent values that a function or relation may take is known as its domain.
So, the domain is {4,8}.
The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.
So, the range is {n,q,m}
Therefore, the domain is {4,8} and the range is {n,q,m}.
To learn more about the domain;
https://brainly.com/question/28135761
#SPJ1
A school requires 2 iPads for every 5 students. How many iPads are needed for 145 students?
Answer:
58 iPads
Step-by-step explanation:
To calculate how many iPads are needed for 145 students, we can use the given ratio of 2 iPads for every 5 students.
First, find out how many groups of 5 students are in 145 students by dividing 145 by 5:
[tex]\sf \dfrac{145\; students}{5\; students/group} = 29\;groups\; of \;5 \;students[/tex]
Now, for each group of 5 students, we need 2 iPads. So, multiply the number of groups of 5 students by 2 to find the total number of iPads needed:
[tex]\sf 29 \;groups \times2\; iPads/group = 58\; iPads[/tex]
Therefore, 58 iPads are needed for 145 students.
Geometry is hard help
You recently joined a gym. You had to pay a joining fee of $40, and you will pay $20 per month to maintain the membership.
What is the one-time charge? What does it represent in slope-intercept form?
What is the recurring charge? What does it represent in slope-intercept form?
What does x represent?
What does y represent?
The number 40 represents the one-time charge which is the y-intercept. And the number 20 presents the fee for gym per month. The x-intercept represents that you need to pay 14 monthly fees for a year.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' represents the number of months and 'y' be the total cost. Then the equation is given as,
y = 20x + 40
The number 40 addresses the one-time charge which is the y-capture. Also, number 20 presents the charge for the exercise center each month. The x-block addresses that you really want to pay 14 month-to-month charges for a year.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ1
10 points if you answer his question
The sum of 18 and a number, x, equals negative 40.
Answer:
x = -58
Step-by-step explanation:
18 + x = -40
-18 -18
x = -58
The library at your school has MP3 players pre-loaded with audio and digital books
to check out. When the librarian starts downloading new books at 11:00 am, there
are 15 already loaded. When she checks at noon, there are 25 books completely
loaded. Assuming that the computer downloads books at a consistent rate, how
many complete books will have downloaded at 2:45 pm?
Write a function of books downloaded, y, based on time passed, x (in hours), as well
as the total number of books that will be completed by 2:45 pm.
The total number of books completed by 2:45 pm will be 42.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that when the librarian starts downloading new books at 11:00 am, there are 15 already loaded. When she checks at noon, there are 25 books completely loaded.
The number of books loaded in 1 hour is calculated as,
N = 25 - 15
N = 10 books
Now from 12 noon to 2:45 pm, the time in hours will be,
T = 165 minutes or 165 / 60 = 2.75 hours
The equation for the number of books loaded will be written as,
y = 15 + 10T
y = 15 + ( 10 x 2.75)
y = 15 + 27.5
y = 42.5 or 42
The completely loaded books are 42 in number.
To know more about an expression follow
https://brainly.com/question/26310043
#SPJ1
a ferris wheel 50 ft in diameter makes one revolution every 40 sec. if the center of the wheel is 30 ft above the ground, how long after reaching the low point is a rider 50 ft above the ground
So, it will take the rider 5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.
The circumference of the ferris wheel is equal to the diameter times pi, or 50*pi=157.08 ft. Since the ferris wheel makes one revolution every 40 seconds, the speed of the ferris wheel is 157.08/40=3.92 ft/sec.
Since the rider starts at a height of 30 ft above the ground and ends up 50 ft above the ground, the total change in height is 50-30=20 ft. Since the speed of the ferris wheel is 3.92 ft/sec, it will take the rider 20/3.92=5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.
To know more about revolutions,
visit; brainly.com/question/28203876
#SPJ4
What is the name given to the exponent to which 3 must be raised to obtain 11?
The number which can be raised by 3 to give the value of 11 is 2.224.
What are exponential functions?The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.
Given:
The exponent to which 3 must be raised to obtain 11,
Assume the number is x then, According to the statement,
x³ = 11
x = ∛11
x = 2.224
Thus, the number is 2.224.
To know more about exponential functions:
https://brainly.com/question/15352175
#SPJ1
