Susan invests
2
times as much money at
8%
as she does at
4%
. If her total interest after
1
year is
$800
, how much does she have invested at each rate?
Final answer:
To find how much Susan has invested at each rate when she invests 2 times as much money at 8% as she does at 4%, create and solve an equation based on the total interest earned.
Explanation:
Susan has invested $x at 4% interest rate and $2x at 8% interest rate.
Given that the total interest after 1 year is $800, we can create the equation: $x(0.04) + $2x(0.08) = $800.
Solving the equation, we find that Susan has $3,000 invested at 4% and $6,000 invested at 8%.
What is the next number in the series? 71 62 53 44 35 ?
Please help quick !!
PLEASE HELP!!!!!! The line of symmetry for the quadratic equation y = ax 2 - 8x - 3 is x = 2. What is the value of "a"?
A) -2
B) -1
C) 2
If f(x)=2x^2sqrt(x-2), complete the following statement f(6)
The value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82
How to determine the function value?The function is given as:
[tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]
Substitute 6 for x
[tex]f(6)=2 * 6^2 + 5\sqrt{6-2}[/tex]
Evaluate the difference
[tex]f(6)=2 * 6^2 + 5\sqrt{4}[/tex]
Evaluate the exponents
f(6)=2 * 36 + 5 * 2
Evaluate the sum of products
f(6) = 82
Hence, the value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82
Read more about functions at:
https://brainly.com/question/13136492
#SPJ2
for f(x) = x^3-7X^2+8x+16 find f(10) using synthetic division
If 12 bumper stickers cost $8.64, then how much do 18 cost
The proportion is solved and the cost of 18 bumper stickers is $ 12.96.
Given data:
To find out how much 18 bumper stickers cost, use a proportion since the cost of bumper stickers is directly proportional to the number of stickers.
Cost of 12 bumper stickers / Number of 12 bumper stickers = Cost of 18 bumper stickers / Number of 18 bumper stickers
On simplifying the proportion:
$8.64 / 12 = x / 18
Now, solve for x (the cost of 18 bumper stickers):
x = ($8.64 / 12) * 18
x = $12.96
Hence, 18 bumper stickers cost $12.96.
To learn more about proportion, refer:
https://brainly.com/question/7096655
#SPJ5
The Greasy Grab Bag claims that customers can make 20 different meal combinations from the menu items. If the Greasy Grab Bag has 4 sandwiches, 3 sides, and 2 drinks, which of the following is correct?
The correct number of different meal combinations that customers can make from the menu items at the Greasy Grab Bag is 24.
To determine the number of different meal combinations, we need to consider that each meal consists of one sandwich, one side, and one drink. Given that there are 4 sandwiches, 3 sides, and 2 drinks to choose from, we can calculate the total number of combinations by multiplying the number of choices for each category together.
The number of sandwich choices is 4, the number of side choices is 3, and the number of drink choices is 2. Therefore, the total number of meal combinations is calculated as follows:
Total combinations = Number of sandwich choices — Number of side choices — Number of drink choices
Total combinations = [tex]$4 \times 3 \times 2$[/tex]
Now, let's calculate the total number of combinations:
Total combinations =[tex]$4 \times 3 \times 2 = 12 \times 2 = 24$[/tex]
Thus, there are 24 different meal combinations that customers can make, which means the Greasy Grab Bag's claim of 20 different meal combinations is incorrect. The correct number is 24.
In a certain grocery store, strawberries cost $5.92 per pound ( 5.92 dollars/lb ). what is the cost per ounce?
Answer:
$,37 dollars per ounce of strawberries
Step-by-step explanation:
We have to remember that there are 16 ounces in one pound so in order to calculate the cost per ounce, we just divide the cost per pound by 16:
5,92/16= ,37
SO the cost per ounce of strawberries when the price per pound is 5,92 dollars will be 0,37 dollars.
find the equation of a line containing the given point and slope (10,5); m=9/20
The value of y is inversely proportional to the value of x. When y=40, x=5. What is the value of y when x=8
Answer: 64
Step-by-step explanation:
i put it into math-way
Convert the measurement as indicated.
26ft= _ yd _ ft
When Sharon began shopping this morning, she had $40.00. She purchased five paperback books and had lunch. The books were all the same price, and lunch cost $3.25. She now has $7.00 left over. What was the price of each of the books? A. $5.95 B. $6.60 C. $7.35 D. $8.75
A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases. If x represents the original price of the jacket, which expression represents the final price of the jacket during this sale? 0.2x – 3 0.8x – 12 0.8x – 15 0.2x – 15
0.8x – 12
Explanation:The sale price is (x-15). After the 20% discount, the final price is 0.80 times the sale price, so is ...
... final price = 0.80×(x -15) = 0.80x -12
Answer:
The correct option is B.
Step-by-step explanation:
Let the original price of the jacket be x.
A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases.
The price of jacket after $15 off is [tex]x-15[/tex].
Then 20% discount is applied, so the final price of the jacket is
[tex]P=(x-15)(1-\frac{20}{100})[/tex]
[tex]P=(x-15)(1-0.2)[/tex]
[tex]P=(x-15)(0.8)[/tex]
[tex]P=0.8x-12[/tex]
The final price of the jacket during this sale is 0.8x-12. Therefore the correct option is B.
Write an equation of a line that is perpendicular to the given line and that passes through the given point.
-x + 5y= 14; (-5, -2)
A. Y=-5x-27
B.y=-1/5x-27
C. Y=-1/5x-15
D. Y=5x-27
A motorboat takes 3 hours to travel 108 km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Convert 5.6 liters to milliliter
5,600 ml
560 ml
0.056 ml
0.0056
what is the value of x in the equation 5(4x-10)+10x=4(2x-3)+2(x-4) ?
-7/4
-1/4
3/20
3/2
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Here, the given expression is,
[tex]5(4x-10)+10x=4(2x-3)+2(x-4)[/tex]
By distributive property,
[tex]20x - 50 + 10x = 8x - 12 + 2x - 8[/tex]
By combining like terms,
[tex]30x -50=10x-20[/tex]
Adding 50 on both sides,
[tex]30x=10x-20+50[/tex]
[tex]30x = 10x + 30[/tex]
Subtracting 10x on both sides,
[tex]20x = 30[/tex]
Divide both sides by 20,.
[tex]x=\frac{3}{2}[/tex]
Hence, LAST option is correct.
Explain why we need more than one digit to express certain quantities
Calculator Reference A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed?
Answer: The expression that represents the number of hours the mountaineer climbed is given by
[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]
Step-by-step explanation:
Since we have given that
Distance covered by mountaineer = 1000 feet
Speed at which he climbed = x feet per hour
Time taken by him would be
[tex]\dfrac{1000}{x}[/tex]
Additional distance covered by him = 5000 feet
Speed at which he climbed this time = 2x-10
So, Time taken is given by
[tex]\dfrac{5000}{2x-10}\\\\\\=\dfrac{5000}{2(x-5)}\\\\\\=\dfrac{2500}{x-5}[/tex]
Hence, the expression that represents the number of hours the mountaineer climbed is given by
[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]
What is the integral of 1/x?
Final answer:
The integral of 1/x is the natural logarithm of the absolute value of x, plus an integration constant C. This expression is central to calculations in many areas of science and mathematics.
Explanation:
The integral of 1/x is known as the natural logarithm of the absolute value of x, plus a constant of integration, commonly referred to as C. In mathematical terms, this is expressed as:
[tex]\( \int \frac{1}{x} dx = \ln(|x|) + C \)[/tex]
The natural logarithm arises due to the fundamental properties of the integral, and it's significant as it appears frequently across various fields of science and mathematics. While the basic form of integration of 1/x involves the natural logarithm, in applied examples like the cases mentioned above, where one works with additional functions or domain restrictions, the integral may lead to more complex expressions or even vanish under certain symmetry conditions.
Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta?
What is 4.76 hours converted to min and sec
53 ℃ below zero degrees
What is after 100,99,07,94,90
Each canvas bag will hold exactly 5 pounds of kings tomatoes. How many bags will be necessary to hold 5 kg worth of these same tomatoes? (1 kg = 2.25 pounds)
1 kg = 2.25 pounds
5*2.25 = 11.25 pounds
11.25/5 = 2.25 bags
so you would need 3 bags
If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f – g)(x).
Answer: The required value is
[tex](f-g)(x)=x^2+8.[/tex]
Step-by-step explanation: The given functions are:
[tex]f(x)=2x^2+1,\\\\g(x)=x^2-7.[/tex]
We are given to find the value of [tex](f-g)(x).[/tex]
We know that, if s(x) and t(x) are any two functions of a variable x, then we have
[tex](s-t)(x)=s(x)-t(x).[/tex]
Therefore, we have
[tex](f-g)(x)\\\\=f(x)-g(x)\\\\=(2x^2+1)-(x^2-7)\\\\=2x^2+1-x^2+7\\\\=x^2+8.[/tex]
Thus, the required value is
[tex](f-g)(x)=x^2+8.[/tex]
Answer:
3x2 - 6 its the answer
If the parent function f(x) = (2x − 3)3 is transformed to g(x) = (-2x + 3)3, which type of transformation occurs?
The leader of the group brought 8.03 ounces of trail mix. The hikers only ate 5.26 ounces of the trail mix. How much trail mix was left?
A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.
Which equation can be used to solve for x, the increase in side length of the square in inches?
x2 + 4x – 81 = 0
x2 + 4x – 65 = 0
x2 + 8x – 65 = 0
x2 + 8x – 81 = 0
Answer:
[tex]x^2+8x-65=0[/tex]
Step-by-step explanation:
Side length of square = 4 inches
Let x be the increase in length
So, New length = x+4
Area of square = [tex]Side^2[/tex]
Area of enlarged square = [tex](x+4)^2[/tex]
Using identity : [tex](a+b)^2=a^2+b^2+2ab[/tex]
Area of enlarged square = [tex]x^2+16+8x[/tex]
We are given that The final area needs to be 81 square inches.
So, [tex]x^2+16+8x=81[/tex]
[tex]x^2+16+8x-81=0[/tex]
[tex]x^2+8x-65=0[/tex]
So, Option C is true
Hence equation can be used to solve for x, the increase in side length of the square in inches is [tex]x^2+8x-65=0[/tex]