The amount invested in the account that paid 4% interest is $2,600
The amount invested in the account that paid 13% interest is $1,500.
What are the simultaneous equations that represent the equation?a + b = 4100 equation 1
0.04a + 0.13b = 299 equation 2
Where:
a = amount invested in the account that paid 4% interest
b = amount invested in the account that paid 13% interest
How much was invested in each account ?
The first step is to multiply equation 1 by 0,04
0.04a + 0.04b = 164 equation 3
Subtract equation 3 from equation 2
0.09b = 135
b = 135 / 0.09
b = $1500
a = 4100 - 1500 = $2,600
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How much should Roman invest today in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly?
Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.
First, convert R as a percent to r as a decimal
r = R/100
r = 5.65/100
r = 0.0565 per year,
Then, solve the equation for P
P = A / (1 + r/n)^(nt)
P = 22,450.15 / (1 + 0.0565/12)^{(12)(3.7)}
P = 22,450.15 / (1 + 0.0047)(44.4)
P = $18,223.97
The principal investment required to get a total amount of $22,450.15 from compound interest at a rate of 5.65% per year compounded 12 times per year over 3.7 years is $18,223.97.
Therefore, Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.
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If f(x) = 3x2 – 2x + 4 and g(x) = 5x2 + 6x – 8, find (f +g)(x).
Answer:
[tex](f+g)(x)=8x^{2} +4x-4[/tex]
Step-by-step explanation:
[tex](f+g)(x)=3x^{2} +5x^{2} -2x+6x+4-8=8x^{2} +4x-4[/tex]
Hope this helps
The annual attendance at the amusement park is initially 2 million people and is increasing at 3% per year. The park’s annual food supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.2 million people per year.
a. Write the equation that represents the food supply. Write the equation represents the park attendance.
The equation that represents food supply is
b. Based on these assumptions, in approximately what year will the amusement park first experience shortages of food?
c. If the park doubled its initial food supply and maintained the rate of increase of 0.2 million people per year, would shortages still occur? In approximately which year?
d. If the park doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? After how many years would the food supply run out?
Please show work. I will mark brainliest.
Answer:
[tex]\textsf{a)} \quad f(t) = 4+0.2t \:\: \textsf{ and }\:\:A(t)=2(1.03)^t[/tex]
b) 77 years
c) 86 years
d) 110 years
Step-by-step explanation:
Part (a)Given:
Initial food supply adequacy = 4 million peopleConstant annual growth rate = 0.2 million peopleAs the food supply grows at a constant rate of being adequate for an additional 0.2 million people per year, it can be expressed as a linear function:
[tex]f(t) = 4+0.2t[/tex]
where:
f(t) = annual food supply (in millions of people).t = time (in years).Given:
Initial attendance = 2 million peopleAnnual growth rate = 3%As the annual attendance increases by 3% per year, it can be expressed as an exponential function:
[tex]A(t)=2(1.03)^t[/tex]
where:
A(t) = annual attendance (in millions of people).t = time (in years).Part (b)Graph the two functions (see attached) and locate the value of t for which A(t) > f(t) for the first time.
From inspection of the graph, the two functions intersect at t ≈ 77. So after approximately 77 years the food supply will not be enough for the number of people attending the amusement park. Therefore, after approximately 77 years, the park will first experience shortages of food.
Part (c)If the park doubles its initial food supply and maintains the rate of increase of 0.2 million people per year, the new equation would be:
[tex]f(t) = 8+0.2t[/tex]
Again, graph the new function against A(t) and find the point where the two functions intersect. A(t) = f(t) at approximately t = 86 so the park will first experience food shortages after 86 years. So doubling the initial food supply delays the eventual food shortage by only c. 9 years.
Part (d)If the park doubled the rate at which its food supply increases in addition to doubling its initial food supply, the new equation would be:
[tex]f(t) = 8+0.4t[/tex]
Again, graph the new function against A(t) and find the point where the two functions intersect. A(t) = f(t) at approximately t = 110 so the park will first experience food shortages after 110 years. So doubling the initial food supply and doubling the rate delays the eventual food shortage by only c. 33 years compared to the initial parameters. Shortages would still occur, but it would be later in approximately 110 years' time.
Help :)
Evaluate the following expression
|−3d−6|+|−5−d2| for d=−3
The value of the expression |−3d − 6| + |−5 − d²| when d = -3 is 17.
Given expression: |-3d - 6| + |-5 - d²|, and d = -3
Substitute the value of d: |-3(-3) - 6| + |-5 - (-3)²|
Calculate the values inside the absolute value signs:
|-(-9) - 6| + |-5 - 9|
Simplify the inside calculations:
|9 - 6| + |-5 - 9|
Continue simplifying:
|3| + |-14|
Calculate the absolute values:
3 + 14
Add the values together:
3 + 14 = 17
So, the value of the expression |−3d − 6| + |−5 − d²| when d = -3 is 17.
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A student does an experiment in a lab on the boiling point of water. In the 3 trials, the student gets the temperatures of 99.2, 99.5, 100.2 degrees C. Are these measurements:
Question 2 options:
Accuracy
Neither precision nor accuracy
Both precision and accuracy
Precision
The measurements are precise. Therefore, the correct option is D.
What is precision?It should be noted that precision simply means how close a test is when it's repeated.
On the other hand, it should be noted that accuracy simply means how close the results are to the standard value.
Therefore, when the student does an experiment in a lab on the boiling point of water. In the 3 trials, the student gets the temperatures of 99.2, 99.5, 100.2 degrees, they're precise.
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A t-shirt requires 1 3/8 yards of material. How many t-shirts can be made from 41 1/4 yards of material?
Applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.
How to Divide Fractions?In the problem given, we have the following information:
Material needed for one t-shirt = 1 3/8 yards
We want to find how many 1 3/4 we would find in 41 1/4.
Applying the knowledge of fraction, we are to divide 41 1/4 by 1 3/8. Convert both mixed fractions to improper fractions then divide:
41 1/4 ÷ 1 3/8
165/4 ÷ 11/8
165/4 × 8/11
165/4 × 8/11
15/1 × 2/1
= (15 × 2)/(1 × 1)
= 30/1
= 30.
Therefore, applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.
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XZ is the perpendicular bisector of segment WY. Solve for m. Enter a NUMBER only.
2(14m-8)=180
24m-16=180
24m=196
m= 8 and 1/6
A sum of money is shared in the ratio 3:4:7.
The smallest share is £210.
What is the total amount of money shared?
Answer:
£980
Step-by-step explanation:
3 portions = 210
1 portion = 70
so 70
70 × 4 = would be 280
70 × 7 = 490
490 + 280 + 210 = 980
hope this works : )
write an expression to show the total number of songs on Iris's playlist after w weeks
120 + 4w is the expression to show the total number of songs on Iris's playlist after w weeks.
She total ahs 120 songs already
She downloads or adds 4 songs every week
An expression to show the total number of songs on Iris's playlist after w weeks is:
120 + 4w
What is an mathematical expression?An expression or mathematical expression is a limited combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.
Many authors differentiate between an expression and a formula, with the former referring to a mathematical item and the latter referring to a statement about mathematical objects.
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Given:
p: x-5= 10
q: 4x+1 = 60
Which is the inverse of p→q?
If x-5 ≠ 10, then 4x+1≠61.
If 4x+1 ≠61, then x-5≠10.
If x-5=10, then 4x+1=61.
If 4x+1=61, then x-5=10
Answer:
Step-by-step explanation:
A point A (x, y) is translated 7 units to the left and 2 units up. What is the mapping to the new point A’?
(x+2, y+7)
(x-7, y+2)
(x+2, y-7)
(x+7, y+2)
Reason:
7 units to the left means x becomes x-7
2 units up means y becomes y+2
Therefore, the old preimage (x,y) translates or shifts to the new image (x-7, y+2)
Example:
[tex](\text{x},\text{y}) = (3,5)\\\\(\text{x},\text{y})\to(\text{x}-7,\text{y}+2)\\\\(3,5)\to(3-7,5+2)\\\\(3,5)\to(-4,7)\\\\[/tex]
The preimage (3,5) moves to (-4,7) after shifting 7 units left and 2 units up.
Let f (x) = 3x2 − 2x + 4. Evaluate f (a + h) and simplify your answer as much as possible.
The expression f(x) = 3 · x² - 2 · x + 4 evaluated at x = a + h is equal to the expression f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4.
How to evaluate and simplify a quadratic equation
In this question we find a quadratic equation, which has to be evaluated at x = a + h and simplified afterwards. Then, the complete procedure is shown below:
f(x) = 3 · (a + h)² - 2 · (a + h) + 4
f(x) = 3 · (a² + 2 · a · h + h²) - 2 · a - 2 · h + 4
f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4
The expression f(x) = 3 · x² - 2 · x + 4 evaluated at x = a + h is equal to the expression f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4.
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find inequality : JoJo can eat no more than 25 carbs per meal. Which inequality describes JoJo's situation?
Answer:
Jojo is on a low carb diet
Select the correct answer. What is the solution for x in the equation? -x + 3/7=2x-25/7
Answer:
x + 3/7=2x-25/7
X=4
adam has $800 invested in two accounts. one pays 6% annual interest and the other pays 10% interest. the amount of annual interest is the same as he would earn if the entire $800 was invested at 8.25%. How much does he have invested at each rate?
Adam invested $350 at 6% and $450 at 10%
Amount invested by Adam = $800
Interest paid by one account = 6%
Interest paid by another account = 10%
Let the amount invested in one account be x and the other be y
The formula for simple interest is given by:
Simple interest = (P*R*T)/100
where P = Principal
R = rate of interest
T = number of years amount is invested
Substituting the value in the formula we get:
Simple interest in one account = (x*6*1)/100-------(1)
Simple interest in another account = (y*10*1)/100--------(2)
The question states that interest earned would be the same when $800 is invested at 8.25%, therefore
Simple interest = (800*8.25*1)/100
= 66----(3)
Equating (1), (2) and (3) we get:
x + y = 800-----(4)
6x/100 + 10y/100 = 66
6x + 10y = 6600-----(5)
Multiplying (4) with 6 and equating it with (5)
6x + 6y = 4800
6x + 10y = 6600
4y= 1800
y = 450
x = 350
So, Adam invested $350 at 6% and $450 at 10%
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Choose the measurement closest to 180 cm: 6 ft, 180 in. or 450 in
Answer:
6ft
Step-by-step explanation:
180cm=5ft10in=70in
So it's closer to 6ft
What is the sum of 2 3/4 and −2 3/4 ?
A. 0
B. 3/4
C. 5 1/2
D. I don't know.
Answer:
A. 0
Step-by-step explanation:
[tex]2 \frac{3}{4} + ( - 2 \frac{3}{4}) \\ = \frac{11}{4} - \frac{11}{4} \\ = \frac{11 - 11}{4} \\ = \frac{0}{4} = 0 \\ hope \: this \: would \: help[/tex]
Answer:
A. 0
Explanation:
Given:
[tex]2\dfrac{3}{4} +(-2\dfrac{3}{4} )[/tex]
In improper fractions:
[tex]\dfrac{11}{4} +(\dfrac{-11}{4} )[/tex]
Simplify:
[tex]\dfrac{11}{4} -\dfrac{11}{4}[/tex]
Evaluate:
[tex]0[/tex]
Tip:
As the integers are alike, when subtracted they simplify to zero as a result.
Write
4/11
as a decimal.
O 0.36
0.36
0.036
0.36
Answer:
0.36
Step-by-step explanation:
Determine the value of cscθ given that the terminal side of angle θ intersects the unit circle in the first quadrant at (7/17,y).
The value of cscθ is 1/y
In this question, we have been given that the terminal side of angle θ intersects the unit circle in the first quadrant at (7/17, y).
We know that the point on the unit circle is of the form (cosθ, sinθ)
Comparing (cosθ, sinθ) with point (7/17, y) we get,
cosθ = 7/17, and sinθ = y
also, we know that cscθ = 1/sinθ
So, cscθ = 1/y
Therefore, the value of cscθ is 1/y
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HELP PLEASE DUE TODAY
12) Z ∪ N = {Set of Integers}
13) H ∪ Q = R which is a set of real numbers
How to classify numbers?
We are told that;
R = U represents the set of real numbers
N is the set of natural numbers
W is the set of whole numbers
Z is the set of integers
Q is the set of rational numbers
H is the set of irrational numbers
12) We want to find Z ∪ N. This is a set union of the set of integers and the set of natural numbers.
A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero. Thus, an integer is also a rational number and all natural numbers are positive integers and as such;
Z ∪ N = {Set of Integers}
13) We want to find H ∪ Q. This is a set union of the irrational numbers and the set of rational numbers. Now, we know that all real numbers are classified as either rational or irrational numbers
Thus; H ∪ Q = R which is a set of real numbers
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The height above ground of a cannon is a function of the time since it was shot.
Question: When time equals 0, why is the height of the cannon ball not equal to 0? Describe the domain of this function. Describe the range.
Given is the quadratic function by its graph..
At the start point, when time is zero, the height is not zero because the cannon was shot above the ground level.
The domain is the time from the point the cannon was shot and to the point the ball lands.
The range is the height from zero to the maximum height the ball reaches.
Please help I will give anyone brainliest
Answer:
1672.50 = 37.75x + 1068.50
x = 16
There were 16 players brought to the tournament.
Step-by-step explanation:
y = mx + b
y= the total cost
m = cost of each meal
x = the number of players
b = cost of the bus
Plug in what you know and solve for x
1672.50 = 37.75x + 1068.50 Subtract 1068.50 from both sides.
604 = 37.75x Divide both sides by 37.75
16 = x
Equation: 1068.50 + 37.75x =1,672.50
Answer: X= 16
If 1,672.50 is our total it will go behind the equal sign. 37.75x and 1068.50 must be added together to help us receive our total.
Our written equation should look like this
1068.50 + 37.75x =1,672.50
X is the number of players on the team.To find out we must first subtract the amount of money spent on the bus, from the total amount spent.
1,672.50-1068.50 is 604. This means our equation now looks like this
37.75x=604. The next and final step is to divide 37.75 into 604.
604/ 37.75 is 16. Which means that there are 16 players on the team.
I hope this helps & Good luck.
I got one final question... What is -1/3x + 1 = -7
Answer Formula: x =
Answer: x=24
Step-by-step explanation:
-1/3x+1= -7
you move the negative one to the other side of the equation to get x by itself and get -1/3x= -8
then you divide both sides by -1/3 and get 24
Ileana wants to know the mean number of pets owned by students in her
grade. She conducts a survey of 20 of her classmates to see how many pets
they own. The results are shown in the dot plot.
Number of Pets In the Home
::::::
0
1 2 3 4 5 6
●●
7
H
8 9 10
Which is the best estimate of the mean number of pets owned by students in
her grade?
Based on the results shown in the dot plot on the number of pets owned by students in Ileana's grade, the mean number of pets owned by students is 2.5 pets
What is the mean number?The number of pets owned per student home according to the dot plot is:
= 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 8
The total number of pets owned is:
= 0 + 0 + 0 +1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 +8
= 50 pets
The mean number of pets owned is:
= 50 / 20 students
= 2.5 pets
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thank you so much for the help!!
The independent variable in these equations based on how they are written is x, since y is a function of x here so y depends on the value of x, while x can be changed freely.
So, for each of these questions, plug in the given value of the independent variable for x.
Independent variable equal to 10: 0.1*10 + 5 = 6
Independent variable equal to 50: 0.1*50 + 5 = 10
Independent variable equal to 120: 0.1*120 + 5 = 17
19 more than four times a number is equal to the difference between -86 and three times the number find the number
Answer:
the number is -15
Step-by-step explanation:
if you turn the word problem into an equation it would be
4x+19=-86-3x
with x being the unknown number
the next step is to move the -3x to the other side by adding it to the 4x
your equation should now be 7x+19=-86
next you should move the 19 to the other side by subtracting it from the -86
this leaves you with the equation
7x= -105
lastly you must divide the -105 by seven which leaves you with the answer x= -15
Which lists all the factors of 78?
Answer:
1, 2, 3, 6, 13, 26, 39, and 78
Step-by-step explanation:
:)
Find the average rate of change of the function f(x) = x² + 4x from x₁ = 3 to x₂ = 5.
The average rate of change of the given function is 12.
The average rate of change of function f on interval [a,b] is:
f(b) -f(a)/b-a
we have interval [x₁,x₂]
[x₁,x₂] = [3,5]
f(3) = x²₊4x
f(3) = 3²+4(3)
f(3) = 21
f(5) = x²₊4x
f(5) = 5²+4(5)
f(5) = 45
f(x₂) -f(x₁)/x₂-x₁
⇒ 45-21/5-3
= 24/2
= 12
The average rate of change of function f(x) = x²+4x on interval [3,5]
is 12.
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show that the roots of the quadratic equation given by(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0
are rea land they can not be equal unless a=b=c.
Expanding out the equation, we get
[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]
Considering the discriminant,
[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]
This is always non-negative, meaning the roots are real.
The roots are equal if and only if the discriminant is 0, which is when a=b=c.
A total of 200 and a difference of 72
According to the solving the total and the difference of the numbers:
total = 136 + 64
difference = 64
Difference in Math Definition?Mathematical difference is the outcome of one of the key operations, which is the subtraction of two numbers. It reveals the margin of difference between two numbers.
How do we find the difference?Subtract the largest number from the lowest number to determine the difference between two integers. The difference between these two numbers is the product of this sum. As a result, there are 55 between the numbers 45 and 100.
According to the given data:Let the numbers be x and y
Given,
x+y = 200_____(1)
x-y = 72_____(2)
Add above 2 eq.
2x= 272
x= 136
Substitute the value of x in eq 1,we get
136+y = 200
y = 64
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