a total of $9500 is invested, part at 10% simple interest and part at 9%
if the total annual return from the two investments is $914.00
Amount invested = 9500
Total amount return means total yield = $914
Let x amount is invested at 10% simple interest
Interest for first part = 10 % times x = 0.10x
Remaining part invested is 9500 -x
Interest for remaining amount = 9% (9500 -x) = 0.09(9500-x)
Total interest yield is 914. Now we frame an equation
0.10x + 0.09(9500-x) = 914
0.10x +855 - 0.09x = 914 (combine like terms)
0.01 x + 855 = 914 (subtract 855)
0.01x = 59 ( divide both sides by 0.01)
So x = 5900
$5900 is invested in 10% simple interest
9500 - 5900 = $3600 is invested in 9% simple interest
Final answer:
To solve the problem, we set up a system of equations based on the provided information. After simplifying and solving the system, we find that $5900 is invested at 10% and $3600 is invested at 9%.
Explanation:
Investment Allocation Problem
Let's denote the amount of money invested at 10% as $x and the amount of money invested at 9% as $y. Since the total amount invested is $9500, we can write the first equation as:
x + y = 9500
The total annual return from the investments is $914. We know that the interest from the first investment is 0.10x and from the second investment is 0.09y. Thus, our second equation, based on the total interest earned is:
0.10x + 0.09y = 914
Now we can solve the system of equations:
x + y = 9500 (Equation 1)
0.10x + 0.09y = 914 (Equation 2)
Multiplying Equation 1 by 0.10 gives us a new equation:
0.10x + 0.10y = 950 (Equation 3)
Now, we subtract Equation 2 from Equation 3:
(0.10x + 0.10y) - (0.10x + 0.09y) = 950 - 914
0.10y - 0.09y = 36
0.01y = 36
y = 3600
Substitute y = 3600 into Equation 1 to find x:
x + 3600 = 9500
x = 5900
Therefore, $5900 is invested at 10% and $3600 is invested at 9%.
1,760 yards =
miles
If A =bc+us,which equation is solved for s?
steven spent $90on clothes.he bought a pair of jeans that cost $34 and spent the rest on t shirts that cost $8.
I'm not sure what the question is but if your trying to find out how many t-shirts he bought it would be 7.
Here's why...
90$-34$= 56
56/8= 7
He could buy 7 shirts with the left over money he had.
Hope this answered your question. :)
~Noodles~
Final answer:
Steven spent $90 in total, bought jeans for $34, and used the remaining $56 to buy T-shirts that cost $8 each, allowing him to purchase 7 T-shirts.
Explanation:
The student’s question is a simple mathematics word problem involving subtraction and division. Steven spent a total of $90 on clothes. After purchasing jeans for $34, he used the remainder of his money to buy T-shirts costing $8 each. To solve this, we first subtract the cost of the jeans from the total amount to find out how much money was left for T-shirts:
$90 (total amount) - $34 (cost of jeans) = $56
Next, we calculate the number of T-shirts Steven could buy with the remaining $56 by dividing this amount by the cost of one T-shirt:
$56 ÷ $8 (cost per T-shirt) = 7 T-shirts
Therefore, Steven was able to purchase 7 T-shirts with the rest of his money.
-9/10 - 2/5 I NEED HELPPP NOWWWWWW
-9/10 - 2/5 is -13/10... or -1 3/10
25 POINTS AND BRAINLIEST.
relations 3,2 0,-4 5,6 1,2 1,7
Please justify this answer for me!! and quick!.
If I were to graph this as a venn diagram I would be able to see a relationship between these sets of numbers because 2 and -4 are an ordered pair. Most relations in math are between two sets and is a collection of ordered pairs.
how do you do this?
0.3
0..2
0.80
but yeah lol XD gooda dala
For every five yardsyou run Jill run 6 yards if you run 30 yards then how far has jill run
question a - you run 30 yards (divide by 5 then muliply by 6) so Jill runs 36 yards.
question b - Jill runs 54 yards (divide by 6 then multiply by 5) so you run 45 yards.
Two siblings Edwin and Rhea are both going skiing but choose different payment plans. Edwin's plan charges $45 for rentals and $5.25 per lift up the mountain. Rhea's plan was a bundle where her entire day cost $108. Set up an inequality that models the number of trips, n, up the mountain for which Edwin will pay more than Rhea. Solve the inequality. Also, what is the greatest amount of trips that Edwin can take up the mountain and still pay less than Rhea? Explain how you arrived at your answer.
The greatest amount of trips that Edwin can take up the mountain and still pay less than Rhea would be 63.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Two siblings Edwin and Rhea are both going skiing but choose different payment plans.
Edwin's plan charges $45 for rentals and $5.25 per lift up the mountain.
Rhea's plan was a bundle where her entire day cost $108.
An inequality that models the number of trips, n, up the mountain for which Edwin will pay more than Rhea.
45 + 5.25n > 108
Subtract 45 on both sides
-45 + 45 + 5.25n > 108 -45
5.25n > 63
Divide both sides by 5.25
n > 12
Also,
5.25 x 12
= 63
The greatest amount of trips that Edwin can take up the mountain and still pay less than Rhea would be 63.
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The body of a person who weighs 50 kilograms contains around 2 × 10^2 grams of sodium chloride. How much sodium chloride is contained in the bodies of 1.8 × 10^3 people who each weigh 50 kilograms? Represent the answer in scientific notation
A. 3.6 × 10^5 gramsB. 1.1 × 10^1 gramsC. 36 × 10^5 gramsD. 11 × 10^1 grams
Answer:
Answer is A.[tex]3.6*10^{5}[/tex]
Step-by-step explanation:
Mass of Sodium Chloride in one 50kg person = [tex]2*10^{2}[/tex] grams
Mass of Sodium Chloride in [tex]1.8*10^{3}[/tex] 50kg people = [tex]2*10^{2}[/tex] * [tex]1.8*10^{3}[/tex]
=[tex](1.8*10^{3})*(2*10^{2})[/tex]
=[tex]3.6*10^{5}[/tex]
So the Answer is A.
Which of the following is a true statement describing the pattern 20, 25, 30, 35,…? The pattern contains only even numbers. The pattern contains only odd numbers. The pattern is decreasing. The pattern contains only factors of 5.
In this pattern all are divisible by 5
20[tex] =4×5[/tex] i.e. divisible by 5
25[tex] = 5×5 [/tex] is divisible by 5
30[tex] =2×3×5[/tex] is divisible by 5
35[tex] =7×5 [/tex] is divisible by 5
Hence the pattern contain factor 5
The statement that correctly describes the pattern 20, 25, 30, 35, ... is that it contains only factors of 5.
The given sequence of numbers is 20, 25, 30, 35,... and the correct statement describing this pattern is that it contains only factors of 5. This is because each number in the sequence is a multiple of 5 and can be divided by 5 without leaving a remainder. The sequence is not exclusively even or odd numbers, as it contains both (20 and 30 are even, while 25 and 35 are odd). Also, the pattern is not decreasing; it is instead increasing by increments of 5.
Identify the range of the function.
The range of the function is -4 < x ≤ 4.
The range of a function is all of the values of y that the graph could contain. In this case, x varies between -4 and 4. We should have a < symbol at -4 because it doesn't include -4 due to the open circle. We should have a ≤ with 4 since it has a closed dot.
Can 15 over 240 be simplified
How to solve part to whole?
what is the value of (11,982)^0
This is a trick question as I'm sure you know, so the answer is 1.
Anything to the power of 0 = 1 and here is why:
[tex](11,882)^0[/tex] Is the equation, but in reality this is what you have: [tex]1(11,982)^0[/tex]
11,982 cancels out and so you are left with just 1
pls help! will give brainliest
7) D -80
8) C -3.3
9) A 127.6
78 = -2(m + 3) + m. 0.6(y + 3) = 4.8
three more than a number is 12
hello there
i belive you are asking a number which whn added three equals 12 so your answer is 9
The statement 'three more than a number is 12' represents an algebraic equation. It can be expressed as 'x + 3 = 12'. Solving this equation, we find that the unknown number is 9.
Explanation:The question 'three more than a number is 12' is a basic algebraic equation. The unknown number is represented by a variable, let's call it x. So, the equation would read 'x + 3 = 12'. We solve for x by subtracting 3 from both sides of the equation. This gives us 'x = 12 - 3', which simplifies to 'x = 9'. Therefore, the number that, when increased by three, yields 12 is 9.
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what is 6 7/8 + 7 5/12
[tex]6 \: \frac{7}{8} \: + 7 \frac{5}{12} [/tex]
Here is your equation:
[tex]6 \frac{7}{8} + 7 \frac{5}{12}[/tex]
As you can see, the denominators, which is the bottom number in the fraction, are different. You need to have the same denominator, so that you can add it. To change the denominators, you need to find the LCM of both denominators, which is 8 and 12. To find the LCM, first list the multiples of both numbers and see what is common.
[tex]8 - 8, 16, 24, 32, 40, 48, 56 \\12-12, 24, 36, 48[/tex]
The only common number is 48. That means you need to change both fractions so that they have a denominator of 48.
[tex]6 \frac{7 \times 6}{8 \times 6} \rightarrow 6 \frac{49}{48}[/tex]
[tex]7 \frac{5 \times 4}{12 \times 4} \rightarrow 7 \frac{20}{48}[/tex]
Here is your new equation:
[tex]6 \frac{49}{56} + 7 \frac{20}{48}[/tex]
Add:
[tex]6 \frac{49}{48} + 7 \frac{20}{48} = 13 \frac{69}{48}[/tex]
Simplify:
[tex]13 \frac{69}{48} \rightarrow 14 \frac{21}{48} \rightarrow 14 \frac{7}{16}[/tex]
Your answer is 14 [tex]\frac{7}{16}[/tex]
If you have any questions, feel free to ask in the comments! :)
if tickets for a amusement park cost $10 for adults and $6 for children.What is the total cost for 2 adults ad 3 children
(10)2 x (6)3 = 38
It will cost $38 for 2 adult's and 3 children's tickets.
Juan is constructing a doghouse . He need four pieces of Ply wood that are 2 ft x 3 ft rectangles. He also needs two pieces of plywood that are 2 ft x 2 fr squares . How many square feet of plywood is he purchasing in all?
Final answer:
Juan will be purchasing 32 square feet of plywood in all for constructing the doghouse, calculated by summing the areas of four 2 ft x 3 ft rectangular pieces and two 2 ft x 2 ft square pieces.
Explanation:
Juan is constructing a doghouse and needs to calculate the total square footage of plywood required for both rectangular and square pieces. To determine this, we calculate the area of each piece of plywood and then sum them up. The area of a rectangle is given by multiplying its length by its width, and for a square, each side is of equal length, so we multiply the length of one side by itself to find the area.
The four rectangular pieces are 2 ft by 3 ft, so each one has an area of:
2 ft × 3 ft = 6 square feet
Since there are four such pieces, this amounts to:
4 pieces × 6 square feet per piece = 24 square feet
The two square pieces are 2 ft by 2 ft, so each one has an area of:
2 ft × 2 ft = 4 square feet
Thus, the total for the two square pieces is:
2 pieces × 4 square feet per piece = 8 square feet
Adding both totals together, Juan will be purchasing:
24 square feet + 8 square feet = 32 square feet of plywood in all.
8x604 using mental math
8 times 604 equals 4,832.
Factor completely 3x4y3 − 15x2y2 + 6xy.
3xy(x3y2 − 5xy + 2)
3x(x3y3 − 5xy2 + 2y)
3(x4y3 − 5x2y2 + 2xy)
Prime
3x^4y^3 - 15 x^2y^2 +6xy
we can factor out 3xy
3xy(x^3y^2 -5xy+2)
we cannot factor any further
Choice A
Answer: Choice A. Hope this helped :)
Step-by-step explanation:
Please Fill in the Blank with the simplified equation. 5/8g=40
Multiply both sides by 8
5/8g × 8 = 40× 8
5g = 320
Divide both sides by 5
5g/5 = 320/5
G = 64
how do i find the volume of the last one? density= 2.7g/cm^3 mass= 0.85g
Answer:
0.314cm³
Step-by-step explanation:
Formula,
Volume = Mass/Density
Volume = 0.85g / 2.7gcm³
Volume = 0.314cm³
a line contain the points (82,-96) and (87,-86) . what is the slope of the line in simplification form ?
y=2x−26 because the form for standard slope is: y=mx+b
you have to find the slope by doing y-y/x-x and then you plug the slope you get into m and then you pick a point; either (82,-96) or (87,-86) and you plug it in for the x and y in y=mx+b and you work out the equation from there.
what is the square root of 28x to the third power y to the third power
Hello!
√28x³y³ is equal to [tex]2xy\sqrt{7xy}[/tex]
We can find this solution through the following steps.
Rewriting the equation by factoring 4 from 28, factoring out x², and factoring out y²We then can rewrite 4 as 2² in our equation, leaving us with [tex]\sqrt{2^{2}*7*(x^{2}x)*y^{2}y }[/tex]We will then move our x and 7, and rewrite [tex]2^{2}*x^{2}* y^{2}[/tex] as [tex](2xy)^{2}[/tex]We can then pull the terms from the radical leaving us with [tex]2xy\sqrt{7xy}[/tex]what is the area of the shaded region ???
z-score fore -1.2 = 0.1151
z-score for 0.85 = 0.8023
Subtract :
0.8023 - 0.1151 =0.6872
The answer is C.
The number of yellow fish at the aquarium is 5 fewer than 3 times the number of blue fish. The table shows how the number of yellow fish, y, depends on the number of blue fish, b. Choose the equation which represents the rule.
Answer:
If you are on USATestPrep (which you most likely are) the correct answer is C.
Step-by-step explanation:
C) y = 3b − 5
It is “5 fewer than 3 times”
Answer:
y = 3b-5
Step-by-step explanation:
The number of yellow fish is 5 fewer than 3 times the number of blue fish. Using b to represent the number of blue fish, 3 times this is 3b; 5 fewer than this is 3b-5. This gives us the equation
y = 3b-5
Write the number in standard notation. 5 x 10^5
Tickets to a concert cost $2 for children, $3 for teenagers and $5 for adults. When 570 people attended the concert, the total ticket receipts were $1950. Three-fourths as many teenagers as children attended. How many adults attended?
Answer: 220
Step-by-step explanation:
Children (x): $2
Teens (y): $3, [tex]\frac{3}{4}x[/tex]
Adults: (z): $5
Quantity: x + y + z = 570 ⇒ x + [tex]\frac{3}{4}x[/tex] + z = 570 ⇒ 1.75x + z = 570
Cost: 2x + 3y + 5z = 1950 ⇒ 2x + 3[tex](\frac{3}{4}x)[/tex] + 5z = 1950 ⇒ 2x + 2.25x + 5z = 1950 ⇒ 4.25x + 5z = 1950
Qty: 1.75x + z = 570 → 5(1.75x + z = 570) → 8.75x + 5z = 2850
Cost: 4.25x + 5z = 1950 → -1(4.25x + 5z = 1950 → -4.25x - 5z = -1950
4.50x = 900
x = 200
Teens (y): [tex]\frac{3}{4}x[/tex]
y = [tex]\frac{3}{4}(200)[/tex]
= [tex]\frac{600}{4}[/tex]
= 150
Quantity: x + y + z = 570
200 + 150 + z = 570
350 + z = 570
z = 220