Answer:
Mary Seitz invested $ 2,000 in the savings account.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Interest rate = 5% simple = 0.05
Time of the investment = 3 years
Amount of interest = $ 300
2. How much money did Mary place in the savings account?
Let's recall the formula of the simple interest:
A = P * (1 + rt), where:
A = Final value of the investment
P = Initial investment
r = Interest rate
t = Time
Replacing with the values we know:
A = P * (1 + 0.05 * 3)
A = P * (1 + 0.15)
P + 300 = 1.15P (A = P + 300)
P - 1.15P = -300
-0.15P = -300
P = -300/-0.15
P = 2,000
Mary Seitz invested $ 2,000 in the savings account.
Find the first and second derivative of the function defined by the parametric equation.
x = 3e and y= 3^3t - 1
Answer:
Step-by-step explanation:
Given two parametric equations [tex]x(t)[/tex] and [tex]y(t)[/tex], the first derivative can be found using the following equation:
[tex]\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
In this problem, [tex]x(t) = 3e[/tex] and [tex]y(t) = 3^{3t} - 1[/tex]. Finding the derivative of each of these functions with respect to [tex]t[/tex] gives us the following:
[tex]\frac{dx}{dt} = 0[/tex]
[tex]\frac{dy}{dt} = 3^{3t + 1}\log{3}[/tex]
Because [tex]\frac{dx}{dt} = 0[/tex], that means the function is a vertical line and has an infinite first derivative.
Final answer:
The first derivative of the x-component is zero, and the first derivative of the y-component is 27. The second derivatives of both components are zero.
Explanation:
To find the first and second derivatives of the function defined by the parametric equation, we need to differentiate each component with respect to the parameter (in this case, t). Let's start with x = 3e, which is a constant, so its derivative is zero. Next, let's differentiate y = 3^3t - 1. The derivative of 3^3t with respect to t is (3^3)(1) = 27, and since the derivative of -1 with respect to t is 0, the y-component's derivative is 27.
Now, to find the second derivative, we differentiate the derivatives we found. The second derivative of x is still zero since the first derivative is zero. The second derivative of y (27) is also zero since it is a constant. Therefore, the first and second derivatives of the parametric equation are dx/dt = 0 and dy/dt = 27, respectively.
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Select the table of values where the quadratic function changes direction at a different value of x than the others.
Imagine that this is a graph.
A.
x -3 -2 -1 0 1 2 3
y 2 3 2 -1 -6 -13 -22
B.
x -3 -2 -1 0 1 2 3
y 2 3 2 -1 -6 -13 -22
C.
x -3 -2 -1 0 1 2 3
y 4 3 4 7 12 19 28
D.
x -3 -2 -1 0 1 2 3
y 1 -1 1 7 17 31 49
D,the quadratic function turning point is (-2,-1) while the other graphs change direction at (-2,3)
Step-by-step explanation:
The point where the graph of a quadratic function changes direction is called a turning point.This is the point where the curve changes to face up or down according to the function.The functions in A,B and C have a common turning point (-2,3) that also appears in the table.The function in D has a turning point at (-2,-1) that is different from the other three functions.
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When rounding to the nearest hundred, what is the least whole number that rounds to 900?
Answer:
850 rounds up to 900
Step-by-step explanation:
if it's 5 or more it will go up, if it were 840 it'll drop to 800
A restaurant has 36 tables. If each can sit five people, how many can be seated at the restaurant?
Answer:
180 people
Step-by-step explanation:
If there are 5 people for each table and there are 36 tables, so then you would need to multiply 36 by 5, because you wouldn't want to add 5 people 36 times lol, so then when you multiply them together, you would get 180 people in total in the restaurant. :-)
hope this helped! ♡
What is the value of x?
12 units
15 units
20 units
24 units
Answer:
Answer: The value of x is 15 units. Step-by-step explanation: In the given triangle RSQ and ΔRST it is given that. ∠RTS ≅ ∠SRQ ≅ 90°.
Step-by-step explanation:
Answer:
20 units
Step-by-step explanation:
I got it wrong with 15 for the cumulative exam on EDGE 2020/2021
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)?
can someone help me solve this?
1.8
to find the circumference of a circle you have to multiple the diameter by pi (3.14). so if you have the circumference already just switch around the equation (since you don’t know the diameter) to 10.99 divided by 3.14 to find the diameter and you get 3.5. but thats the diameter and you have to find the radius so divide 3.5 by two and you get 1.75 and 1.75 rounded to the nearest tenths is 1.8
Answer is provided in the image attached.
You are given the expressions 76+ n and 2n + 26 what is the smallest value of n that will make each number rational ?
Answer:
A proof that square root of 2 is irrational. ... An equation x² = a, and the principal square root ... The number under the radical sign is called the radicand. ... the given square numbers, each product of square numbers is equal to what square ... are relatively prime -- and it will be impossible to divide n· n into m· m and get 2.
Step-by-step explanation:
Rational numbers are numbers that can be represented as a fraction of two integers. For [tex]\sqrt{76 + n}[/tex] and [tex]\sqrt{2n + 26}[/tex] to be rational, the smallest value of n is 5
Given that:
[tex]\sqrt{76 + n}[/tex] and [tex]\sqrt{2n + 26}[/tex] --- correct expressions
For both numbers to be rational, we should be able to represent the numbers as a fraction of two integers.
There are no straight ways to solve this, except trial by error.
When [tex]n = 1[/tex]
[tex]\sqrt{76 + n} = \sqrt{76 + 1} = \sqrt{77} = 8.77496.......[/tex]
The above is not rational
When [tex]n = 2[/tex]
[tex]\sqrt{76 + n} = \sqrt{76 + 2} = \sqrt{78} = 8.83176......[/tex]
The above is not rational
When [tex]n = 3[/tex]
[tex]\sqrt{76 + n} = \sqrt{76 + 3} = \sqrt{79} = 8.88819......[/tex]
The above is not rational
When [tex]n = 4[/tex]
[tex]\sqrt{76 + n} = \sqrt{76 + 4} = \sqrt{80} = 8.944271......[/tex]
The above is not rational
When [tex]n = 5[/tex]
[tex]\sqrt{76 + n} = \sqrt{76 + 5} = \sqrt{81} = 9[/tex]
The above is rational
So, we try [tex]n = 5[/tex] for the second expression
[tex]\sqrt{2n + 26} = \sqrt{2\times 5 + 26} = \sqrt{10 + 26}=\sqrt{36}= 6[/tex]
The above is also rational
Hence, the smallest value of n that makes each of the expression rational is [tex]n = 5[/tex]
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what is the slope of the line that passes through the points (-8,-6) and (-18,6)? write your answer in simplest form.
Slope = -6/5
Work is provided in the image attached.
The slope of the line passing through the given points is -6/5.
Explanation:The slope of a line can be found using the formula: m = (y2 - y1) / (x2 - x1).
In this case, the coordinates of the two points are (-8, -6) and (-18, 6). Applying the formula, we have: m = (6 - (-6)) / (-18 - (-8)) = 12 / (-10) = -6/5.
Therefore, the slope of the line that passes through the points (-8, -6) and (-18, 6) is -6/5.
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Kendra wants to know the average height of the 30,000 ninth grade students in Florida. She randomly selects 1,000 ninth graders in Florida, assuring that the group accurately represents all ninth grade students in Florida. Kendra finds their average height to be 65 inches. What assumption can be made regarding the approximate average height of all ninth grade students in Florida?
Based on Kendra's random selection of 1,000 ninth graders in Florida and finding their average height to be 65 inches, we can make the assumption that the approximate average height of all ninth-grade students in Florida is close to 65 inches.
We have,
The assumption is based on the principle of random sampling, where a representative sample from a larger population can provide valuable insights into the characteristics of the entire population.
By randomly selecting 1,000 ninth graders, Kendra aimed to ensure that the group accurately represents all ninth-grade students in Florida.
While there might be some variation or margin of error, the average height of the sampled group can provide a reasonable estimate of the average height of all ninth-grade students in Florida.
Therefore,
Based on the random sample, we can assume that the approximate average height of all ninth-grade students in Florida is around 65 inches.
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factorise 3×15×1/15
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
[tex]3.15.\frac{1}{15}\\\\3.\frac{15}{15}\\\\3.1\\\\3[/tex]
(20 POINTS PLZ HELP!!) plz answer all questions
(question A) What is the absulote value of |-10 + -4|
(question B) what is the absolute value of |5+2|
(question C) what is the absolute value of |--8.7|
(question D) what is the absolute value of -|-9.2|
Answer:
answer to question a is -14
answer to question b is 10
answer to question c is -56
answer to question d is -18
Step-by-step explanation:
Answer:
The answer to your question is below
Step-by-step explanation:
Absolute value of a number, is the value without considering its sign. For example, when we measure distance, we do not say -50 meters, we say "50 meters" because for distance, do not exist negative values.
(A) What is the absolute value of |-10 + -4|
| - 10 + -4| = | - 10 - 4| = | - 14 | = 14
(B) what is the absolute value of |5+2|
| 5 + 2 | = |7| = 7
(C) what is the absolute value of |--8.7|
| - - 8.7 | = | 8.7 | = 8.7
(D) what is the absolute value of -|-9.2|
- | - 9.2 | = - 9.2
A printer cartridge with 2 1 ⁄2 milliliters of ink will print off 2 ⁄3 of a box of paper. How many milliliters of ink will it take to print an entire box?
Answer:
3 3/4 mls ink.
Step-by-step explanation:
2/3 of a box corresponds to 2 1/2 mls of ink
So one box .............................. 2 1/2 / 2/3 = 5/2 / 2/3
= 5/2 * 3/2
= 15 / 4
= 3 3/4 mls ink.
It would take approximately 3.75 milliliters of ink to print off an entire box of paper. This is based on the given that 2.5 milliliters prints off 2/3 of a box and the conversion to a full box.
Explanation:The question is asking about the amount of ink it will take to print an entire box of paper. We are given that a printer cartridge with 2.5 milliliters of ink will print off 2⁄3 of a box of paper. So, if 2.5 ml prints 2⁄3 of a box, we want to find out how much ink prints 1 full box. This is a simple ratio question.
Set up the ratios like this: 2.5 ml (ink) / (2⁄3 box) = X ml (ink) / (1 box) Simplifying this, you find that X = 2.5 ml / 2⁄3, which, when calculated, equals approximately 3.75 ml. This means it will take approximately 3.75 milliliters of ink to print off an entire box of paper.
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Need help answering this!
Answer:
Wrong
Step-by-step explanation:
Since 54 / 12 is 4.5
Answer:
Step-by-step explanation:
the answer is b
A principal evenly distributes 6 reams of copy paper to 8 fifth-grade teachers.
a. How many reams of paper does each fifth-grade teacher receive? Explain how you know using pictures, words, or numbers.
b. If there were twice as many reams of paper and half as many teachers, how would the amount each teacher receives change? Explain how you know using pictures, words, or numbers.
Answer: We start with 6 reams of copy paper and 8 teachers.
a) if we distribute the paper equally between all the teachers, then each teacher receive 6/8 (here we are dividing the total number of reams by the number of people that we are are splitting it). but 6/8 is less than one, so we must open the reams in order to split them.
b) If there were twice as many reams of paper, then we will have 2*6 = 12 reams of paper, and if there where half the number of teachers, then we have 8/2 = 4 teachers.
Doing the same procedure as before, we have 12 teams for 4 teachers, then each teacher has 12/4 = 3 reams
before, each teacher received 6/8 reams, and now, each one receive 3.
if we want to know the change, we need to see the difference between these numbers, so 3 - 6/8 = 3*8/8 - 6/8
notice that i am multiplying the 3 by 8/8, this is one, but this way i can have the same denominator in both numbers.
24/8 - 6/8 = 18/8 = 9/4 = 8/4 + 1/4 = 2 + 1/4
so each teacher receive 2 + 1/4 reams than before.
Please help me I don't know
WENDYS PAY IS $423.00 19% OF THAT IS SUBTRACTED FOR TAXES HOW MUCH IS LEFT AFTER PAYING TAXES
Answer:
$342.63
Step-by-step explanation:
0.19 * 423 = 80.37
423 - 80.37 = 342.63
Alex went to the grocery store and bought 5 avocados. He paid $10 and received $4.50 in change. How much did each avocado cost if they are each the same amount?
Answer:
$1.10
Step-by-step explanation:
We have been that Alex went to the grocery store and bought 5 avocados. He paid $10 and received $4.50 in change.
First of all, we will find amount paid for 5 avocados by subtracting $4.50 from $10.
[tex]\text{Amount paid for 5 avocados}=\$10-\$4.50[/tex]
[tex]\text{Amount paid for 5 avocados}=\$5.50[/tex]
Now, we will divide $5.50 by 5 to find cost of each avocado.
[tex]\text{Cost of each avocado}=\frac{\$5.50}{5}[/tex]
[tex]\text{Cost of each avocado}=\$1.10[/tex]
Therefore, the cost of each avocado is $1.10.
Jeremiah and Cynthia each run a lemonade stand. They decide that they will share the
money they make evenly Jeremiah makes $237 at his stand and Cynthia makes $218.
After they combine and split up their money evenly, which statement must be true
a. They each get $229 with no money left over
b. They each get $228 with $1 left over
C. They each get $910 with no money left over
d. It is not possible to share their money evenly
Answer:
I believe it's D.
Step-by-step explanation:
if you add 237 + 228 you get 455. 455 divide by 2 is 227.5 which doesn't make it even.
Consider the quadratic function:
f(x) = x2 – 8x – 9
Vertex: (StartFraction negative b Over 2 a EndFraction, f (StartFraction negative b Over 2 a))
What is the vertex of the function?
(
,
)
Answer:
vertex = (4, - 25 )
Step-by-step explanation:
Given a quadratic function in standard form : f(x) = ax² + bx + c : a ≠ 0
The the x- coordinate of the vertex is
[tex]x_{V}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² - 8x - 9 ← is in standard form
with a = 1, b = - 8, thus
[tex]x_{V}[/tex] = - [tex]\frac{-8}{2}[/tex] = 4
Substitute x = 4 into f(x) for corresponding value of y
f(4) = 4² - 8(4) - 9 = 16 - 32 - 9 = - 25
vertex = (4, - 25 )
Answer:
vertex is (4,-25)
Step-by-step explanation:
[tex]f(x) = x^2 - 8x - 9[/tex]
To find out the vertex we use formula
[tex]x=\frac{-b}{2a}[/tex]
From the given f(x), the value of a=1, b=-8 and c=-9
Plug in the values in the formula
[tex]x=\frac{-(-8)}{2(1)}[/tex]
x=4
Now find the value of y
plug in 4 for x in f(x)
[tex]f(4) = 4^2 - 8(4)- 9=-25[/tex]
The value of y is -25
The vertex is (4,-25)
Sam bought one dozen eggs from the grocery store to bake some cakes.how many eggs did Sam buy?
Answer:
He buy 12 eggs from grocery.
Because,
1 dozen of a thing(x) = 12 things(x)
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∡rst is a right angle. if rs has a slope of 3, what must be the slope of st?
Answer:
The slope of st is -1/3
Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m1*m2=-1[/tex]
we have
[tex]m1=3[/tex]
substitute and solve for m2
[tex](3)*m2=-1[/tex]
[tex]m2=-\frac{1}{3}[/tex]
therefore
The slope of st is -1/3
Find y if the line through (3,5) and (6,y) has a slope of 2
Answer:
The answer is y = 11.
43-3d = d+9
Solve the equation
Answer:
8.5 (plz give me the brainliest answer for this!!!!!!!!)
Step-by-step explanation:
43-3d=d+9
34=4d
8.5=d
Have a nice day!!!!!!!! :-)
KA
Answer: 8.5=d
Step-by-step explanation:
First u need to subtract nine on both sides of the equal sign canceling the nine on the right side, then it will leave you with 34-3d=d so then u add 3d to both sides again canceling the 3d on the left side, which leaves u with 34=4d then just divide the 4 on both sides leaving u with 8.5=d
find an equation of the line that passes through the point (3,-1) and is perpendiculor to line with slope -1/2
Answer:
perp. 2
y + 1 = 2(x - 3)
y + 1 = 2x - 6
y = 2x - 7
what is the value of the expression -2(3x-2)+x+9 when the x=-3?
Value of expression at x = -3 is 28.
What is linear equations?All the mathematical equations which have any variable and constant in them are linear equations where variables are not fixed.
Given expression -2(3x-2)+x+9 at x=-3
simplify equation
-6x+4+x+9 = -5x+13
substitute x= -3
-5(-3)+13 = 15+13= 28
Hence the value at x= -3 is 28
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What is the equation of the least squares regression line for the data set?
Answer:
y = 1.862x − 0.138
Step-by-step explanation:
The equation of the least squares regression line is ŷ = -173.51 + 4.83x.
Explanation:The equation of the least squares regression line for a data set is represented as ŷ = a + bx, where a is the y-intercept and b is the slope of the line. To calculate the values of a and b, you minimize the sum of squared errors (SSE). Using calculus, you can determine the values that make SSE a minimum. In this case, the equation of the least squares regression line is ŷ = -173.51 + 4.83x.
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What is the value of x that makes the given equation true? 2(x−8)=x+5x
Answer:
x = - 4
Step-by-step explanation:
Given
2(x - 8) = x + 5x ← distribute left side and simplify right side
2x - 16 = 6x ( subtract 6x from both sides )
- 4x - 16 = 0 ( add 16 to both sides )
- 4x = 16 ( divide both sides by - 4 )
x = - 4
PLEASEEEE ASAPP
what is g(2) = 3(2)^2 - 5(2) + 5
Answer:
Step-by-step explanation:
[tex]g(x) = 3x^{2} - 5x + 5[/tex]
[tex]g(2) = 3(2^{2}) - 5(2) + 5[/tex]
[tex]g(2) = 3(4) - 10 + 5[/tex]
[tex]g(2) = 12 - 10 + 5[/tex]
[tex]g(2) = 7[/tex]
Show all work to multiply
Answer:
-42+10i
Step-by-step explanation:
*start with the square roots
\sqrt{-25} \\ =5i
\sqrt{-100} \\ = 10i
*then insert values
(2+5i)(4-10i)
*Use FOIL to multiply
2x4 + 2x-10i + 5ix4 + 5ix10i
*Simplify
8-10i+20i+50i(squared)
*Add like terms
-42+10i
*( i squared = -1 )