a retired biologist withdraws money from a retirement account at a constant rate. 15 months after she starts withdrawing money, she has $785,000 in the account. she has $630,000 in her account 40 months after she starts withdrawing money. let a(t) represent the dollar amount in the account t months after she begins withdrawing money from the account. a. find the linear function that gives a(t), the dollar amount in the account t months after she starts withdrawing money. (8 points) b. how much money is in the account 80 months after she starts withdrawing money? (2 points)
The linear function that gives a(t), the dollar amount in the account t months after she starts withdrawing money is [tex]a(t)=785000-3875t[/tex]
The money in the account 80 months after she starts withdrawing money is [tex]a(80) & =\$ 475000\end{aligned}$$[/tex]
The amount of money she withdraw in 40 months
[tex]& \Rightarrow \$(785000-630000) \\& =\$ 155000\end{aligned}$$[/tex]
She withdraw money per month at constant rate
[tex]=\frac{155000}{40}$$[/tex]
The amount of money a(t) in t months.
[tex]a(t)=785000-\frac{155000 t}{40}$$[/tex]
[tex]a(t)=785000-3875t[/tex]
Therefore the linear function that gives a(t), the dollar amount in the account t months after she starts withdrawing money is [tex]a(t)=785000-3875t[/tex]
(b) The money in the account after 80 months.
[tex]$$\begin{aligned}a(80) & =785000-3875(80) \\& =785000-310000 \\a(80) & =\$ 475000\end{aligned}$$[/tex]
Therefore the money in the account 80 months after she starts withdrawing money is [tex]a(80) & =\$ 475000\end{aligned}$$[/tex]
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6√-48
please help with this question
Answer:
24i√3
Step-by-step explanation:
simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
I tried.
What is 3N?
Help please
The required matrix is obtained by scalar multiplication as [tex]\left[\begin{array}{ccc}-6&0\\9&15\\\end{array}\right][/tex].
What is a matrix?A matrix can be defined as a rectangular array of elements written in the form of rows and columns. For m rows and n columns the order of the matrix can be written as m × n.
The number of rows and columns for a square matrix are always equal.
Two matrix can only be added when their orders are equal.
The given matrix can be written as follows,
N = [tex]\left[\begin{array}{ccc}-2&0\\3&5\\\end{array}\right][/tex]
Where its elements are a₁₁ = -2, a₁₂ = 0, a₂₁ = 3 and a₂₂ = 5.
Since, the scalar multiplication of a matrix is equivalent to the matrix each of which elements are multiplied by that scalar.
As per the problem the matrix 3N can be evaluated as follows,
3N = [tex]\left[\begin{array}{ccc}-2\times3&0\times3\\3\times3&5\times3\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-6&0\\9&15\\\end{array}\right][/tex]
Hence, the matrix 3N is obtained by multiplying all of the terms of matrix by 3 as [tex]\left[\begin{array}{ccc}-6&0\\9&15\\\end{array}\right][/tex].
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What answer is the best one? Pls help me
we know ,
the probability=no of repeated value/total number
factorial of 3 and 2
and factorial of total number
=3ḷ×2ḷ/7ḷ
=3×2×1×2×1/7×6×5×4×3×2×1
=1/7×5×4×3
=1/420
=0.23809
or
=0.238
what is Probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.
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nearly a quarter of the texas gulf coast is national seashore or state park. At 372 miles long, it is undergoing a seaward advance at the rate of about .0095 mile per year. find the length of the texas shoreline in km. 1 mile = 1.61 km
If one quarter of the Texas Guff coast is national seashore or state park at the given figures, the length of the Texas shoreline is 0.8835km
How to determine the length?The length is the measure of how long the shoreline is.
The given parameters sare
mileage of the seashore = 372 miles
Advancement of 0.0095 miles per year.
1/4 taken as gulf coast
Applying these parameters we have
372*0.0095*1/4*12
⇒ 96.102 miles
= 96.102/1000 = 0.96102 km
1000 miles = 1km
Therefore divide the value by 1000 to get
Therefore the length is 0.96102km
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Suppose you deposit $100 in Account A with
a simple interest rate of 3.4%, and $300 in
Account B with a simple interest rate of 1.8%.
One year later, you get
a bank statement
that
shows the interest for Account A is
$3.40 and the
interest for Account B is $540.00.
a. Which account statement is incorrect?
b. What may have been the bank's error?
The account statement for Account B is incorrect.
What is simple rate of interest?
Simple rate of interest is a type of interest calculation where interest is calculated only on the principal amount of a loan. Simple interest is calculated periodically, usually monthly or annually, as a fixed percentage of the principal. It is different from compound interest, which applies interest to both the principal and the accumulated interest. It is simpler to calculate than compound interest, and is generally used for short-term loans.
Given: Account A: $100, 3.4% and Account B: $300, 1.8%
We know, Simple Interest = Principal × Rate × Time
Interest for Account B = $300 × 1.8%
= $5.40
The bank statement after one year should be $5.40 instead of $540.00.
Hence, Account B's statement is incorrect.
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Graph y=-4x+8 please.
Answer:
attached is the graph and other data
Step-by-step explanation:
n is m% of what? Help please :)
Answer:
Step-by-step explanation:
m% = m/100
what = a variable ... "x". for example.
"is" means "="
"of" means multiply
n = (m/100)•x
it says i need the regression equation and the final answer
please help i dont understand this at all :(
A linear regression equation that represents the data set is y = -29.97x + 1048.80. Also, the number of new cases for 2026 is equal to 689 cases.
How to write the linear regression equation?In this scenario, the Year since 2014 (x) would be plotted on the x-axis of the scatterplot while the New cases (y) would be plotted on the x-axis of the scatterplot.
On the Excel sheet, you should right click on any data point on the scatterplot, select format trend line and then tick the box to display an equation for the linear regression (line of best fit) on the graph.
By critically observing the scatterplot (see attachment) which models the relationship given in the table, an equation for the linear regression is given by:
y = -29.97x + 1048.80
For 2026, the value of x is given by:
x = 2026 - 2014 = 12 years.
Now, we can determine the new cases for 2026:
y = -29.97(12) + 1048.80
y = -359.64 + 1048.80
y = 689.16 ≈ 689 cases.
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- 1/4 * (x - 26) = - 200 Solve the equation for x.
Answer:
x=826
Step-by-step explanation:
"9 less than a number is
zero."
I need help
Answer:9 less than 9 is 0
Step-by-step explanation:
9-9=0
Answer:
9
Step-by-step explanation:
Less means minus, so basically X ( something ) - 9 is 0
X - 9 = 0
You add 9 on each side
X = 0 + 9
X = 9
Basically, all you're doing is the reverse, you start with 0 and do the opposite of taking away 9 which is adding nine so that you get the number:
0 + 9 = 9
Hence the number is 9
:)
( sorry if I misunderstood )
Could Someone Help Me with this rewrite dis equation into y=mx+b
y< -3/4x+2 pls help me
The equation written in slope-intercept form is y = -(3/4)x +2.
What is the slope-intercept form of a line?The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.
The given inequality is y < -3/4x + 2
Rewrite the inequality as an equation in slope-intercept form:
y < (-3/4)x + 2
y = (-3/4)x + 2
Where m = -3/4 and b = 2
Hence, the equation written in slope-intercept form is y = -(3/4)x +2.
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Find y she c=10 if y=8 when’s=20
The value of x=10 is y=4 if y=8 if x=20.
What is an algebra?Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics. It is also used to name specific types of algebraic structures, such as an algebra over a field, which is frequently referred to as an algebra. The word algebra is used to name both a mathematical field and some of its subfields.
When x=20, y=8
The value of y is 0.4 times of x.
y=0.4×20
y=8
So, when x=10
y=0.4×10
y=4
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Hellllalalap pls happy holidAys
Answer:
Federal Reserve banks
Step-by-step explanation:
Hope it helps!
4) You are running the concession stand for the basketball game. You sell hot dogs for $1.50 and drinks
for $2. At the end of the night you made $250.
a) Write an equation in standard form that models this situation, be sure to define your variables.
b) If you sold 47 drinks, how many hot dogs did you sell?
You are running the concession stand for the basketball game. You sell hot dogs for $1.50 and drinks for $2.
a) an equation in a standard form that models this situation is
1.5H + 2D = 250
b) Hot dogs sold 104
What is the equation?Generally, a) Let H be the number of hot dogs sold and D be the number of drinks sold. The equation that models this situation is:
1.5H + 2D = 250
b) To find the number of hot dogs sold, we can solve the equation for H:
1.5H = 250 - 2D H = (250 - 2D) / 1.5
Substituting D = 47 into this equation gives us:
H = (250 - 2*47) / 1.5 H = (250 - 94) / 1.5 H = 156 / 1.5 H = 104
Therefore, you sold 104 hot dogs.
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what is 5 divided by 1 7/9
Rick bought a photo printer and supplies for $186. 90, which will allow him to print photos for $0. 29 each. A photo store charges $0. 55 to print each photo. How many photos must Rick print before his total cost is less than getting prints made at the photo store? More than 718 photos. Less than 718 photos. More than 900 photos. Not enough information to solve
The 718.85 < x inequality says that : He must print 719 photos or more.
Given,
In the question:
Rick bought a photo printer and supplies for $186. 90, which will allow him to print photos for $0. 29 each.
and, A photo store charges $0. 55 to print each photo.
To find the how many photos must Rick print before his total cost is less than getting prints made at the photo store?
Now, According to the question:
Let the photos be x
Rick bought a photo printer be $186.90
A photo store charges $0. 55 to print each photo.
The question is based on inequality:
Photo Printer < photo store
1.86.90 + 0.29x < 0.55x
- 0.29x - 0.29x
______________________
1.86.90 < 0.26x
Divide by 0.26x on both sides
= 718.85 < x
Hence, The 718.85 < x inequality says that : He must print 719 photos or more.
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Timmy received $50 for his birthday. Following the birthday party, his parents promised him $5 each week for completing his chores. Assuming timmy completes all chores, use a linear equation to determine the number of dollars timmy will have 7 weeks after his birthday.
Assuming timmy completes all chores, the number of dollars timmy will have 7 weeks after his birthday is 85 dollars.
What are equations?In mathematics, an equation is a claim that two expressions are equivalent. It is a mathematical expression that employs the equals symbol, "=", to indicate that two quantities have values that are equal. Problems in algebra, geometry, calculus, and other branches of mathematics are frequently solved using equations. In algebra, equations are frequently used to depict the connection between variables and constants, as well as to discover the value of an unknown variable. For example, the equation x + 2 = 5 may be utilised to get the value of x, which is 3. Equations can be linear, quadratic, or higher-degree, and they can involve multiple variables.
How to solve?
Let x be the number of weeks after Timmy's birthday.
The total number of dollars Timmy will have after x weeks is 50 + 5x.
Therefore, Timmy will have 50 + 5(7) =85 dollars after 7 weeks
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Which statement about 56 – 34 is true?
A The least common denominator is 6.The least common denominator is 6.
B The difference is a whole number.The difference is a whole number.
C The least common denominator is 12.The least common denominator is 12.
D The difference is a mixed number.The difference is a mixed number.
Since, Both the numbers used for the difference calculation are whole numbers, The answer is B) The difference is a whole number.
What are real numbers?Both rational and irrational numbers are considered to be real numbers. Real numbers include all rational and irrational numbers, including integers (-2, 0, 1) and fractions (1/2, 2.5).
What are whole numbers?Whole numbers are natural numbers including zero with it.
56 is a whole number
34 is a whole number
the difference, 56-34 = 22 is also a whole number.
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(-12, -2) and (k, 8)
Answer: The answer is -2
Step-by-step explanation: Common sense
Determine the point and slope from the equation
y-4-5(x + 7)
point (-7.4) slope: -5
point (7.4) slope: -5
point (7.-4) slope: -5
To determine the point and slope from the given equation, we can rewrite the equation in the standard form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).
In this case, the equation is already in the standard form, so we can immediately see that the slope is -5 and the y-intercept is (0, 4). This means that the point at which the line crosses the y-axis is (0, 4), and the slope of the line is -5.
Therefore, the correct answer is:
Point: (0, 4)
Slope: -5
In Exercises 7-10, find the zeros of the function. Then sketch a graph of the function.
7. f(x) = - 5x ^ 4 + 20x ^ 3 + 60x ^ 2
8. g(x) = - x ^ 3 - x ^ 2 + 30x
9. k(x) = x ^ 3 + x ^ 2 - 4x - 4
10. f(x) = x ^ 1 - 4x ^ 2 - 9x + 36
Answer:
Step-by-step explanation:
7 1+1
8 2+2
9 4+4
10 1+1+2+2+4+4=69
UDENT EXAM
Roy is 30 miles from Dallas, ready to leave for Pecos. Travis is in Pecos, ready to leave for Dallas. To qualify for a trip to Costa Rica, Roy
vill meet Travis somewhere along the highway to give him the key to a treasure chest in Pecos. The distance, d, in miles, from Dallas is a
unction of the hours, h, since Travis left Pecos. What does the point (4,270) represent?
In the diagram, ∠4 ≅ ∠5 and SE — bisects
∠RSF. Find m∠1. Explain your reasoning.
Answer:
60°
Step-by-step explanation:
You want the measure of angle 1 in the given diagram.
Angle relationsTransversal TR creates corresponding angles 1 and 5, so those are congruent.
It is given that angles 4 and 5 are congruent.
Transversal SE creates alternate interior angles 2 and 4, so those are congruent.
Angle bisector SE creates angles 2 and 3 congruent.
Now we have ∠1≅∠5≅∠4≅∠2≅∠3.
Hence all of the angles are congruent to each other, and angle 1 is 1/3 of 180°.
m∠1 = 60°
Line Q: y= 3x+7
Line R: y=1/3x-10
Answer:
what we have do with these lines?... please complete your questions
Answer:
neither
Step-by-step explanation
3*1/3= 1
3 and 1/3 are multiplicative inverses
it is supposed to be 3*(-1/3) or -3*(1/3) = -1
Value of [ 1234568 * 198765432 + 98765432 * 98765432 ]^{1/4}
Answer: 10000
Step-by-step explanation:
((1234568)(198765432)+(98765432)(98765432))^1/4
=(245389441853376+(98765432)(98765432))^1/4
=(245389441853376+9754610558146624)^1/4
=10000000000000000^1/4
=10000
Hope this helps!!! :)
pls help due asap plsss
Answer:
Option D delta is correcto
PLEASE HELP!!!! ASAP!!
Answer:
2
Step-by-step explanation:
This question is asking about the multiplication rule of exponents. When you multiply two exponents of the same base, the exponents add. With the parameters x=4, y=6, and z=8, the first one is true because 2+4=6. The third one is true because 6+6=12. The second one isn't true because 6+8=14, not 4.
A model car is 12 inches long. Using a scale of 3 inches : 4 feet ,how long is the actual car
The basic unit of length in the metric system is the meter. All units of length in the metric system are derived from the meter.
What is unit of length?Using measuring instruments like a ruler, measuring tape, etc., one can measure the length of any object. A ruler can be used to determine, for instance, how many inches a pencil is long. A feet scale can be used to gauge the height of each student in a class.The inch, foot, yard, and mile are the fundamental units of length and distance measurement in the English system. The rod, furlong, and chain are additional length units.Length of the car is 12 inches equal to 192 feet.
Given ,
3 inches : 4 feet
3 inches : 4*12
3 inches :48
1 inches : 16 feet
Length of the car is 12 inches = 12 * 16
Length of the car is 12 inches = 192 feet
The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For instance, a rectangle's length and width are its dimensions.In the metric system, the SI unit of length is a metre which is defined as: “The length of the path travelled by light in a vacuum within 1⁄299792458 seconds.”The SI unit of length is a metre (m). One metre (m) is divided into 100 equal parts called centimetre (cm). One centimetre (cm) has 10 equal parts called millimetre (mm). For measuring longer distances, we use a larger unit of length called, kilometre (km).To learn more about unit of length refer to:
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If ur good at geometry can u help Solve for m given that the perimeter of the triangle is 19 centimeters.
Answer:
m = 7cm
Step-by-step explanation:
Perimeter of a triangle is all the sides added up, so a+ b + c.
Given that a= 6 and b= 6, that's 12cm together. So just subtract the perimeter 19cm by 12cm to get your answer of 7cm.