Answer:
A
Step-by-step explanation:
To solve this problem, we need to first find out how much interest the account earns each year. If the account earns 2.5% simple interest per year, and it starts with an initial balance of $260, then the interest earned each year is 0.025 * $260 = $6.50.
Over 5 years, the account will earn a total of 5 * $6.50 = $<<5*6.5=32.50>>32.50 in interest.
To find the total amount of money in the account at the end of the 5 years, we need to add the interest earned to the initial balance of the account. The total amount of money in the account will be $260 + $32.50 = $<<260+32.5=292.50>>292.50.
Therefore, the total amount of money in the account at the end of the 5 years is $292.50.
Answer:
A) $292.50
Step-by-step explanation:
Simple Interest Formula
A = P(1 + rt)
where:
A = Final amountP = Principal amountr = Interest rate (in decimal form)t = Time (in years)Given:
P = $260.00r = 2.5% = 0.025t = 5 yearsSubstitute the given values into the formula and solve for A:
⇒ A = 260(1 + 0.025 · 5)
⇒ A = 260(1 + 0.125)
⇒ A = 260(1.125)
⇒ A = 292.50
Therefore, the total amount of money in her savings account at the end of 5 years is $292.50.
Is (1,10) a solution to
y=7x+5
y=x+9
No or yea
Answer:
no
Step-by-step explanation:
we can test it
10=7(1)+5
10=7+5
10=12
not a solution
hopes this helps
If k is a negative integer, which of these is DEFINITELY NEGATIVE? A. k* (k-1) * (k - 2) B. k* (k+1) C. k* (-50) D. (50-k)
Answer:
only A ans bellow
Step-by-step explanation:
let k= -4
A. k * (k - 1) * ( k - 2)
= -4 * (-4 -1) * ( -4 -2)
= -4* (-5) * (-6)
= 20*-6
= -120
B. k * ( k+1)
= -4 * ( -4+1)
= -4 * (-3)
= + 12
C. k * (-50)
= -4 * (-50)
= + 200
D . (50 - k)
= 50 - (-4)
= 50 + 4
= + 54
Mark me the brainliest
if k is negative then k(k-1)(k - 2) will be definitely negative.
What is Number system?A number system is defined as a system of writing to express numbers.
Given that k is a negative integer.
We need to find which of the given options are defnitely negative.
Let us consider k as -3.
k(k-1)(k - 2)
-3(-3-1)(-3-2)
-3(-4)(-5)=-60
Which is negative.
k(k+1)=-3(-3+1)=6 +ve
k (-50)=-3(-50)=150 +ve
(50-k)=50-(-3)=53 +ve.
Hence, if k is negative then k(k-1)(k - 2) will be definitely negative.
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this will be my last question of the day.
Answer:
x = -3
Step-by-step explanation:
See the picture below
Identify the angles shown
A. Corresponding angles
B. Alternate interior angles
C. Same side interior angles
D. Alternate exterior angles
Help!!!
please solve theta
csc^2 theta=cot theta+3
The value of θ will -45° or 26.56°
What are trigonometric identities?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.
Given that, cosec²θ = cotθ + 3
Solving for θ,
∵ cosec²θ = cot²θ+1
∴ cot²θ+1 = cotθ + 3
cot²θ-cotθ-2 = 0
Factorizing and solving, we get
(cotθ+1)(cotθ-2) = 0
cotθ+1 = 0
cotθ = -1
θ = -45°
or, cotθ-2 = 0
cotθ = 2
θ = 26.56°
Hence, The value of θ will -45° or 26.56°
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Answer the questions about the following polynomial..... please help!
Answer:
x⁵ - 1/3x² -1
Step-by-step explanation:
In order to write polynomials in standard form:
1) Find the degree (power) of each term
2) Arrange them in descending order (largest to smallest)
We have : -1 + x⁵ - 1/3x²
The degree of -1 is 0 since there is no power.
The degree of x⁵ is 5.
The degree of - 1/3x² is 2.
Now arranging them in descending order:
x⁵ has the largest degree, followed by - 1/3x² and then -1, so the polynomial in standard form is:
x⁵ - 1/3x² -1
A basketball team has a winning percentage of 62.5% after 8 games. How many games in a row must be won to raise the winning percentage to 75%?
Answer: 11
Step-by-step explanation: To raise the winning percentage to 75%, the team needs to win 3 more games out of 4, for a total of 3/4=75% of the games. Since the team has already won 8 games, they need to win 8+3=11 games in a row to raise the winning percentage to 75%
identify the value of f(x) and x from the given coordinates
Answer:
1
Step-by-step explanation:
For function f(x), the average rate of change from x = a to x = b is:
average rate of change = (f(b) - f(a))/(b - a)
Here we have:
f(a) = f(-3) = -2.88
f(b) = f(2.5) = 2.62
average rate of change = (2.62 - (-2.88))/(2.5 - (-3)) = 1
y is directly proportional to x. When x = 2, y = 64. Find x when y = 80
Answer:
64 divided by 2= 32 80 divided by 32= 2.5
mince pies and 2 jars of cranberry sauce costs £4.80 10 mince pies and 3 jars of cranberry sauce costs £7.60 How much does a mince pie and a jar of cranberry sauce cost each?
Answer:
£2.53 just divide£7.60by 3
three calculus students entered a pizza parlor. they were quite hungry and ordered an entire pie, but instead of having the pizza maker cut the pie in the usual manner they asked her to slice the pie into three equal areas using only two parallel slices. where should these slices be made in order to accomplish this?
As per the Newton's method, the equal ration of the Pizza is 3: 2: 3
In math, Newton's method states that a technique for solving equations of the form f(x)=0 by successive approximation
Here we have given that three calculus students entered a pizza parlor. they were quite hungry and ordered an entire pie, instead of having the pizza maker cut the pie in the usual manner they asked her to slice the pie into three equal areas using only two parallel slices.
And we need to find these slices be made in order to accomplish this
Here let us assuming that the pizza has unit radius, and the area of the pizza is π and each piece has to have area π/3.
Therefore, the given details is enough to find the height of a circle segment such that its area is one third of the original circle,
As per the Newton's method, we get the value of h as,
=> h ≈ 0.735068 ≈ 4492/6111,
Therefore the three slices have widths approximately proportional to 3:2:3.
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An airplane is descending from 35600 ft at 3200ft per mile,
how long would it be until the plane reaches 18,000 ft? I dont remember the exact ft but i just need a example such as a equation to solve please! please help! T>T
Answer:
To calculate how long it will take for the plane to reach 18,000 ft, first find the difference between the plane's current altitude and its target altitude:
35,600 ft - 18,000 ft = 17,600 ft
Then, divide this difference by the rate of descent to find the time it will take for the plane to reach its target altitude:
17,600 ft / 3,200 ft/mile = 5.5 miles
Since the rate of descent is given in feet per mile, this result is equivalent to the time it will take for the plane to reach its target altitude. Therefore, it will take the plane 5.5 miles (or a similar amount of time) to reach 18,000 ft.
Question 1-8
Cameron goes to the grocery store every 15 days. Brooks goes to the grocery store every 12 days. If both Cameron and Brooks go to the grocery
store today, how many days until they go to the grocery store on the same day again? Enter the answer in the box.
days
Answer:
60
Step-by-step explanation:
To find the least common multiple of 15 and 12, we can list the multiples of 15 and 12 and find the smallest number that appears in both lists:
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
The least common multiple of 15 and 12 is 60, so Cameron and Brooks will go to the grocery store on the same day every 60 days.
a company wants to encrypt a document containing important passwords. to do this, the sum of two positive numbers will need to be minimized. if the product of both numbers is 47, what is the minimum sum?
The requried, "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.
To find the minimum sum of two positive numbers whose product is 47, we can use the concept of the arithmetic mean-geometric mean inequality (AM-GM inequality).
The AM-GM inequality states that for any two positive numbers, the arithmetic mean (average) is always greater than or equal to the geometric mean. Mathematically, it can be expressed as:
AM ≥ GM
For two positive numbers "a" and "b," the arithmetic mean is (a + b) / 2, and the geometric mean is √(ab).
Given that the product of the two numbers is 47 (ab = 47), we want to find the minimum value of their sum (a + b).
Using the AM-GM inequality:
(a + b) / 2 ≥ √(ab)
Substitute ab = 47:
(a + b) / 2 ≥ √47
Now, let's solve for the minimum sum (a + b):
a + b ≥ 2(√47)
a + b ≥ 2 * √(47)
a + b ≥ 13.711.
Since "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.
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a fast-food restaurant runs a promotion in which certain food items come with game pieces. according to the restaurant, 1 in 4 game pieces is a winner. if jeff keeps playing until he wins a prize, what is the probability that he has to play the game exactly 5 times?
The probability that Jeff has to play the game exactly 5 times i.e he keeps playing until he wins prize is (0.25)⁵.
We have, a fast-food restaurant runs a promotion which consists some food items with games pieces. 1 in 4 game pieces is a winner. This means, probability of winning game or sucess (p) = 1/4 . Since number of trials is fixed, trials are independent and probability of success is constant in each trial, we can use Binomial distribution. The Binomial distribution probability formula is
P(X= x) = ⁿCₓ(p)ˣ(1-p)⁽ⁿ⁻ˣ⁾
where,n --> number of trials
p --> probability of success
x --> number of times for a specific outcome within n trials
ⁿCₓ --> number of combinations
we have calculate the probability that he has to play the game exactly 5 times, i.e
x = 5 . Jeff keeps playing until he wins and he wins when he play exactly 5 times so,n= 5
Now, plugging all known values in above formula we get,
P(X= 5) = ⁵C₅(0.25)⁵(1-0.25)⁰
=> P(X= 5) = ⁵C₅(0.25)⁵(0.75)⁰
=> P(X= 5) = 1× (0.25)⁵× 1 = (0.25)⁵
Hence, required probability is (0.25)⁵
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HELPPPP!! how do i find the angle measure ?
Answer:
1. m<AOB = 50 degree
2. m<COD = 90 degree
3. m<BOD = 130 degree
4. m<AOD = 180 degree
Step-by-step explanation:
1. We see that <AOB has one leg at 0 and the other leg at 50 degrees, so the <AOB is 50 degrees.
2. We see that <COD has one leg at 0 and the other leg at 90 degrees, so the <COD is 90 degrees
3. We see that <BOD has one leg at 50 and the other leg at 180 leg, so the <BOD is 180 - 50 = 130 degree
4/ We see that <AOD has one leg at 0 and the other leg at 180 degrees, so the <AOD is 180 - 0 = 180 degrees
How do I solve for x in #34 and #35?
Answer:
34. x = 3 1/3
35. x = 5.2
Step-by-step explanation:
Given figures involving triangles with angle bisectors and parallel segments, you want to solve for x.
In each case, you need to make use of two proportional relationships. An angle bisector divides the triangle proportionally. An segment parallel to one side of the triangle divides it proportionally.
34.Using the angle bisector relation, you have ...
QP/PT = QS/ST
x/3 = 5/ST ⇒ x = 15/ST
Using the parallel segment relation, you have ...
PT/QR = ST/SR
3/2 = ST/3 ⇒ ST = 9/2
Using the value of ST in the equation for x gives ...
x = 15/(9/2) = 30/9 = 10/3
x = 3 1/3
35.Using the angle bisector relation, you have ...
EF/ED = CF/CD
7.2/9 = CF/6 ⇒ CF = 6(7.2/9) = 4.8
Using the parallel segment relation, you have ...
CB/BA = CF/FE
x/7.8 = 4.8/7.2
x = 7.8(4.8/7.2)
x = 5.2
__
Additional comment
In each case, we assigned a numerical value to the intermediate variable (ST, CF). We didn't actually need to do that.
Write a linear function f(x) = mx + b for the table.
The linear function is f(x) = 3x -5.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given linear function expression,
f(x) = mx + b
From the table,
x = -2
then, 1 = -2m +b ......equation 1
Put x = 0
then, b = -5
Substitute the value of b to the equation 1, we get
m = 3
Finally, the function is f(x) = 3x -5
Therefore, the linear function is f(x) = 3x -5
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if x^2 + y^2 = 289, find the value of dy/dt at (8,15)
Answer: a)
Step-by-step explanation:
To find [tex]\frac{dy}{dx}[/tex], we will have to use implicit differentiation, and because the base is [tex]dx[/tex], we will take the deriviative of both sides with respect to [tex]x[/tex].
To derive [tex]y[/tex] with respect to [tex]x[/tex], just derive the term with respect to y then multiply the term with [tex]\frac{dy}{dx}[/tex].
So [tex]\frac{d}{dx} x^{2}[/tex] is just [tex]2x[/tex], [tex]\frac{d}{dx} y^{2}[/tex] is [tex]2y \frac{dy}{dx}[/tex], and [tex]\frac{d}{dx} 289[/tex] is 0. Now substitue each term with it's deriviative.
[tex]2x + 2y \frac{dy}{dx} = 0[/tex]
Now, just solve for [tex]\frac{dy}{dx}[/tex] when [tex]x[/tex] is 8 and [tex]y[/tex] is 15
[tex]2(8) + 2(15)\frac{dy}{dx} = 0[/tex]
[tex]16 + 30\frac{dy}{dx} = 0[/tex]
[tex]\frac{dy}{dx} = \frac{-16}{30} = \frac{-8}{15}[/tex]
So the answer is choice a)
Which statement is true?
Answer:
Correct Statement : The y- intercept of Function A is greater than the y- intercept of Function B
What is x+3y ≥ 3
Help?
Answer: x
≥
3
−
3
y
Step-by-step explanation:
Please help me with this
Answer:
d = 0
Step-by-step explanation:
7.5d = 2.5d
Divided both sides by factors and we get
d = 0
4) The instantaneous rate of change of f(x)=x³−5 at (2,3) is:
a) 4
b) 12
c) 48
d) 60
The instantaneous rate of change of f(x) = x³ − 5 at (2,3) is (b) 12
How to determine the instantaneous rate of changeFrom the question, we have the following parameters that can be used in our computation:
Function: f(x) = x³ − 5
Point = (2, 3)
Differentiate the function to get the instantaneous rate
This is represented as
f'(x) = 3x²
Substitute 2 for x in the equation
The 2 is coming from the x-coordinate in (2, 3)
So, we have
f'(2) = 3(2)²
Evaluate
f'(2) = 12
Hence, the instantaneous rate of change is 12
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the booking limits for four fare classes in a flight are given as . (a) what is the available capacity for these four classes, i.e., what is the booking limit for classes {1, 2, 3, 4}? [ select ] (b) from this available capacity, how many seats are protected for class 1, i.e., what is the protection level for class 1?
The function available capacity for the four classes is 40 seats each. The protection level for class 1 is 40 seats, meaning that 40 seats are protected for class 1. 40 + 40 + 40 + 40 = 160
The booking limits for the four fare classes in a flight are given as 40, 40, 40, and 40, respectively. This means that the available capacity for these four classes is 40 seats each. The protection level for class 1 is 40 seats, meaning that 40 seats are specifically reserved for passengers in class 1. This ensures that passengers in class 1 are guaranteed at least 40 seats on the flight. The protection level for the other classes is also 40 seats each, ensuring that at least 40 seats are available for each class. This allows airlines to ensure that all of their classes have sufficient seating capacity for their passengers. 40 + 40 + 40 + 40 = 160
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a line with a slope of 2 passes through the points (10,8) and (w,6). what is the value of w?
Answer:
w = 9
Step-by-step explanation:
Use a slope formula to solve. Subtract the y's put that on top and subtract x's and put that on the bottom. This calc should equal 2 that was given.
(8-6)/(10-w) = 2
2/(10-w) = 2
Cross-multiply.
2 = 2(10-w)
Distributive property
2 = 20 - 2w
Add 2w
2 + 2w = 20
Subtract 2
2w = 18
divide by 2
w = 18/2 = 9
Or you can logic it out...8-6 is 2 on top. Need a 1 on the bottom (bc 2/1 is 2) 10-9 is 1 for on the bottom. w = 1
A train leaves the station at time t=0. Traveling at a constant speed, the train travels 260 kilometers in 2 hours. Answer parts a and b
The function which can be used to find the relation between distance and time is f(t) = 130t.
As we know the train travels 260 kilometers in 2 hours,
then the distance traveled in one hour will be 130 kilometers.
distance = 130
when time = 0 ,
distance also = 0 , as the train has not started moving yet.
Then , the function which can tell bout the relation will be ,
f(t) = 130t
where d = f(t)
Distance is a scalar quantity which tells us about how far an object is from its starting position. Distance don't have a direction.
The distance unit of measurement in the SI
SI unit of distance is meter in the International System of Units.
Using this as the fundamental unit and a few formulae, a large number of different derived units or quantities are produced, including volume, area, acceleration, and speed.
Distance is measured also using the C.G.S. and M.K.S in metric unit system.
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select the correct answer from each drop down menu
choices: the rate of function eight is (greater than), (less than), (equal to) the rate of change a function b
(neither function is ), (only function b is) , (only function a is) , (both functions are) increasing.
The y intercept of function a is (less than) , (greater than), (equal to) the y-intercept of function B
whatever is in the parentheses are the choices. please help
The rate of change of function A is greater than the rate of change of function B.
The y-intercept of function A is less than the y-intercept of function B.
How to calculate the rate of change of the function?The rate of change is also called the slope of a linear equation and is defined as the rate of change of y-values divided by the corresponding change in x-values.
For function A, we are told that the line passes through the points (2, 3) and (-1, -3). The rate of change is gotten from the formula;
Rate of change = (y₂ - y₁)/(x₂ - x₁)
Rate of change = (-3 - 3)/(-1 - 2)
Rate of change = -6/-3
Rate of change = 2
For function B, we are given that the equation of the line is;
y = ¹/₂x + 2
Now, formula for equation of a line in slope intercept form is;
y = mx + c
where ;
m is slope and c is y-intercept
Thus, slope is 1/2 and y-intercept is 2
For function A, we can find the y-intercept as;
3 = 2(2) + c
c = 3 - 4
c = -1
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Tritan purchaed a new car in 2000 for $22,800. The value of the car ha been depreciating exponentially at a contant rate. If the value of the car wa \$10,400$10,400 in the year 2006, then what would be the predicted value of the car in the year 2016, to the nearet dollar?
Tritan purchased a new car in 2000 for $22,800. The value of the car ha been depreciating exponentially at a constant rate then the Cost of the car in year 2016 will be $2811.
Cost price of the car = $22800
Value of the car has been depreciating exponentially, so the formula for value of the car after t years,
Here P(t) = Final value after t years
A = Cost price or initial value
r = rate of depreciation
t = duration in years
r = 100(1 - 0.87737)
r = 12.26%
Now cost of the car in year 2016 (After 16 years)
P(16) = 2810.99
= $2811
Therefore, cost of the car in year 2016 will be $2811.
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A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8, –4). Answer the questions about line t to write the equation.
What is the slope of line t?
–0.75
What is the y-intercept of line t?
2
What is the equation in slope-intercept form of line t?
y = –0.75x + 2
The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.
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.
The line t that passes through the points (0, 2) and (8, -4) is given as,
(y - 2) = [(- 6 - 2) / (8 - 0)](x - 0)
y - 2 = - 0.75x + 0
y = -0.75x + 2
The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.
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The prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500.
The price that is 3 standard deviations above the mean is $_
The price that is 2 standard deviations below the mean is $_
The percentage of buyers who paid between $16,500 and $17,500 is %___
The percentage of buyers who paid between $17,000 and $18,000 is %___
The percentage of buyers who paid less than $16,000 is %__
Answer: If the prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500, it means that the majority of the prices paid for the car will fall within a certain range around the mean. Specifically, approximately 68% of the prices paid will be within one standard deviation of the mean, which in this case would be between $16,500 and $17,500. Approximately 95% of the prices paid will be within two standard deviations of the mean, which would be between $16,000 and $18,000. And approximately 99.7% of the prices paid will be within three standard deviations of the mean, which would be between $15,500 and $18,500. This shows that the prices paid for the car are relatively consistent, with only a small percentage falling outside of the range determined by the mean and standard deviation.
Step-by-step explanation: