Answer:
[tex]\$487.48[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ A=\$1,000\\ r=7.25\%=7.25/100=0.0725\\n=4[/tex]
substitute in the formula above
[tex]1,000=P(1+\frac{0.0725}{4})^{4*10}[/tex]
[tex]1,000=P(\frac{4.0725}{4})^{40}[/tex]
[tex]P=1,000/(\frac{4.0725}{4})^{40}[/tex]
[tex]P=\$487.48[/tex]
2/3=n/12
solve the proportion
Answer: [tex]n=8[/tex]
Cross-multiply
[tex]2/3=n/12[/tex]
[tex](2)*(12)=n*(3)[/tex]
[tex]24=3n[/tex]
Flip the equation
[tex]24=3n---->3n=24[/tex]
Divide both sides by 3
[tex]3n/3=24/3[/tex]
[tex]24/3=8----> n=8[/tex]
Final answer:
To solve the proportion 2/3 = n/12, cross multiply to get 2×12 = 3×n. Simplify the equation to 24 = 3×n, and divide both sides by 3 to get n = 8.
Explanation:
To solve the proportion 2/3 = n/12, you begin by cross multiplying to find the value of n. This means you multiply 2 by 12 and 3 by n. The equation now looks like this: 2×12 = 3×n.
Next, simplify the left side of the equation, which results in 24 = 3×n.
Finally, solve for n by dividing both sides of the equation by 3, leading to n = 8.
This method of cross multiplication and division is a common technique used to solve proportions and find missing values in ratios.
Which statements are true?
Select each correct answer.
a. 30x4−12x3=6x3(5x−2)
b. 4x2+10x=2x(2x+5)
c. 100x3+5=5x3(20x+1)
d. 8x3−6x=2x3(4−3x3)
Answer:
30x^4−12x^3=6x^3(5x−2) = True
4x^2+10x=2x(2x+5) = True
100x^3+5=5x^3(20x+1) = False
8x^3−6x=2x^3(4−3x3) = False
Step-by-step explanation:
The statements which are true are 30x4−12x3=6x3(5x−2) , 4x2+10x=2x(2x+5) and 100x3+5=5x3(20x+1)
To determine which of the statements are true, we can simplify each equation and compare.
Option a :
30x4−12x3=6x3(5x−2): Factoring out the common term we can see this equation is true.
Option b:
4x2+10x=2x(2x+5): After simplifying both sides we find that 2x(2x + 5) = 4x2 + 10x, so statement (b) is true.
Option c:
100x3+5=5x3(20x+1): Attempt to simplify this equation as 5x3(20x + 1). Since this simplification holds, statement (c) is also true.
Option d:
8x3−6x=2x3(4−3x3): Simplifying the right side does not give us the left side; thus, statement (d) is false. The correct form would be 2x(4x2 - 3), assuming a typo in exponent notation.
£2300 is invested for 4 years at 5% per year simple interest. Work out the total interest
Answer: £460
Step-by-step explanation:
Use this formula to find the total interest [tex]I=\frac{P*R*T}{100}[/tex]
I stands for interest, P is principal, R is rate, and T is time.
Principle = £2300
Rate = 5%
Time = 4 years
[tex]\frac{2,300*5*4}{100} =\frac{46,000}{100} =460[/tex]
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)
- Cutiepatutie ☺❀❤
Answer:
£460
Step-by-step explanation:
Simple interest =PRT/100
Where P = principal
R= rate
T = Time
Given
P= £2300
T= 4yrs
R = 5%
Interest = 2300 x 5 x 4/100
Multiply through
Interest = 46000/100
Interest = £460
write an expression that represents the edge length of jewelry box
Answer:
The cubed-root of v (/v)
Step-by-step explanation:
Like your work on the second question illustrated, the cubed root of v (which is 216) is your expression for the edge length of the box in inches.
Hope this helps!
Step-by-step explanation:
Part A
Since volume of jewelry box is v cubic inches
Therefore,
Answer: Length of edge = v inches
Part B
Answer: 6 inches
Which of the following is the solution to the compound inequality below? 5+ x >3 or 6x +1 <-29
The solution to the compound inequality is x > -2 and x < -5, or (-∞, -5) ∪ (-2, ∞).
Explanation:To find the solution to the compound inequality, we need to solve the individual inequalities separately and then find the intersection of their solution sets.
First, solve the inequality 5 + x > 3:The solution to the compound inequality is the intersection of the solution sets of the individual inequalities, so the solution is x > -2 and x < -5. To express this in interval notation, we write (-∞, -5) ∪ (-2, ∞).
Learn more about Compound inequality here:https://brainly.com/question/20296065
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the root of quadratic equation are (3-√3) and (3+√3). find its equation
Answer: [tex]x^{2} - 6x +6 = 0[/tex]
Step-by-step explanation:
The formula for finding quadratic equation is given as :
[tex]x^{2}[/tex] - sum of roots[tex](x)[/tex] + product of roots = 0
sum of roots implies :
(3-√3)+(3+√3) =6
product of roots implies :
(3-√3) x (3+√3) = 9 +[tex]3\sqrt{3}[/tex] - [tex]3\sqrt{3}[/tex] - 3
(3-√3) x (3+√3) = 6
substituting into the equation we have:
[tex]x^{2} - 6x +6 = 0[/tex]
The sum of six different natural numbers is 22. Find these numbers.
Answer:
1,2,3,4,5,7
Step-by-step explanation:
1+2+3+4+5+7 = 22
Final answer:
Six different natural numbers that add up to 22 are 1, 2, 3, 4, 5, and 7. The process involved starting with the smallest natural numbers and then incrementally adjusting the sequence to arrive at the sum of 22.
Explanation:
The question asks to find six different natural numbers whose sum equals to 22. We can begin with the smallest natural numbers, knowing that 1 cannot be included because the sum of the next five natural numbers (2, 3, 4, 5, and 6) already exceeds 22. If we start with 2 and follow with the next smallest numbers (3, 4, 5, and 6), the sum would be 20, which is close but not quite the target sum. To reach the sum of 22, we need to replace one of these numbers with a slightly larger number while still maintaining the rule that every number must be different.
Let's replace the 6 with a 7, so our numbers are now 2, 3, 4, 5, and 7. If we sum these up (2 + 3 + 4 + 5 + 7), we get 21. We need to add one more number to reach 22. The smallest number we haven't used yet is 1, but adding 1 to our sequence would require us to adjust another number as follows: 1, 2, 3, 4, 5, and 7 add up to 22. Therefore, the six different natural numbers whose sum is 22 are 1, 2, 3, 4, 5, and 7.
Is 5(2x-3y) and 10x-3y equivalent?
Answer:
No
Step-by-step explanation:
Apply the distributive property to 5(2x - 3y):
Multiply 5 by each term inside the parentheses.
5(2x - 3y) = 10x - 15y
The other expression is 10x - 10y.
The terms 10x in both expressions are equal.
Since the term -15y is not equal to the term -10y, the expressions are not equivalent.
Let event A = the place is a city let B = the place is in North America what is P(A and B)
A. 5/7
B. 3/7
C.4/7
D.2/7
Answer:
D. 2/7
Step-by-step explanation:
We assume that the intention is that one of the places is chosen at random from the list of 7 places.
2 of those are cities in North America, so the probability that a place randomly chosen from this list is a city in North America is ...
P(A & B) = 2/7
Answer: 4/7
Step-by-step explanation:
A person buys 3 shirts for 42.00 how much would 8 shirts costs at that same price
Answer:
$112
Step-by-step explanation:
Let f(x)= x2 - 14 and g(x) = 6-X.
Find (fq)(7).
Answer:
[tex](fg)(7) = - 35[/tex]
Step-by-step explanation:
The given functions are:
[tex]f(x) = {x}^{2} - 14[/tex]
and
[tex]g(x) = 6 - x[/tex]
We want to to find
[tex](fg)(7)[/tex]
Note that:
[tex](fg)(x) = f(x) \times g(x)[/tex]
We substitute the functions to obtain:
[tex](fg)(x) = ( {x}^{2} -1 4 ) \times (6 - x)[/tex]
We now substitute x=7, to get:
[tex](fg)(7) = ( {7}^{2} -1 4 ) \times (6 - 7)[/tex]
This implies that
[tex](fg)(7) =( 49-1 4 ) \times (6 - 7)[/tex]
[tex](fg)(7) = 35 \times - 1 = - 35[/tex]
You have 20 quarters. You find 40% more quarters in your room. Then you go shopping and spend 50% of the total number of quarters. Write a expression that represents the total number of quarters you take with you when you go shopping. How much money do you have left
Answer:
a) 28 quarters
b) 14 quarters
Step-by-step explanation:
We are given the following in the question:
Number of quarters = 20 quarters
Number of quarters in room = 40%
Total number of quarter in room =
[tex]=40\%\times (20)\\\\=\dfrac{40}{100}\times 20\\\\=8[/tex]
Thus, the total quarters taken to shopping =
[tex]=20 +40\%\times (20)\\\\=20+8\\=28[/tex]
Thus, 28 quarters were taken to shopping.
Quarter spent on shopping = 50%
Total number of quarter spent in shopping =
[tex]=50\%\times (28)\\\\=\dfrac{50}{100}\times 28\\\\=14[/tex]
Money left =
Money taken for shopping - Money spent
[tex]= 28-14\\=14[/tex]
Thus, we are left with 14 quarters after shopping.
a bag is filled with 191 silver coins and 33 gold coins for what is the theoretical probability of pulling out a silver coin
Answer:
191/224
Step-by-step explanation:
1991+33= 224
191/224
Answer:
191/240\
Step-by-step explanation:
In the diagram, shown below:
If ∠ABC = 63° and ∠BCA = 54° , then what is ∠DAB?
Answer:
DAB is 117.
Step-by-step explanation:
You can solve 2 ways, either by adding the opposite angles together or by finding the 3rd angle of the triangle and using linear pair.
First Method: 63 + 54 = 117
Second Method:
180 - 63 - 54 = 63 (All triangles = 180)
180 - 63 = 117 (All linear pairs = 180)
fraction between - 3/4 and - 1/3
Solve y = 1/-25 x 8 + 175
Answer:
174.68
Step-by-step explanation:
Use PEMDAS. First, multiply 1/-25 by 8. (-8/25 or-.32)
Then, add 175 and y should= 174.68.
Use the distributive property to write an expression that is equivalent to each given expression.
-3(2x - 4)
Answer:-6x+12
Step-by-step explanation:-3 • 2x = -6x
-3 • -4 = 12. Distribute the -3 to both numbers in the parentheses
A mother gives birth to a 9 pound baby. Every 4 months, the baby gains 2 pounds.
If x is the age of the baby in months, then y is the weight of the baby in pounds.
Find an equation of a line in the form y = mx + b that describes the baby's weight.
Answer:
y=2/4x+9
Step-by-step explanation:
Vanessa's cell phone company charges $45 for a monthly fee and $0.03 for each text sent If Vanessa's bill is $76.23, how many texts did Vanessa send?
A.)94
B.)141
C.)1,041
D.)3,974
Answer:
C
Step-by-step explanation:
I chose C and got it right.
Jill drove the 200 miles to Cincinnati at an average speed of 10 miles per hour faster than her usual average speed. If she completed the trip in 1 hour less than usual, what is her usual driving speed, in miles per hour
Let [tex]v[/tex] be the usual speed, and [tex]t[/tex] be the usual time.
Following the equation [tex]s=vt[/tex], where s is the space, v is the velocity and t is time, we know that usually we have
[tex]200=vt[/tex]
But this time we were 10mph faster and it took one hour less, so we have
[tex]200=(v+10)(t-1)[/tex]
Since both right hand sides equal 200, they must equal each other:
[tex]vt=(v+10)(t-1)=vt+10t-v-10 \iff 10t-v-10=0 \iff v=10t-10[/tex]
Plug this value in the first equation and we have
[tex]200=vt=(10t-10)t \iff 10t^2-10t-200=0[/tex]
This equation has solutions [tex]t=-4,\quad t=5[/tex]. We can only accept positive solutions, so we have t=5. We finally deduce, again from the first equation,
[tex]200=5v \iff v=\dfrac{200}{5}=40[/tex]
4x+6=2x+10 find value of x makes equation true
Answer:
x = 2
Step-by-step explanation:
[tex]4x + 6 = 2x + 10 \\ \\ 4x - 2x = 10 - 6 \\ \\ 2x = 4 \\ \\ x = \frac{4}{2} \\ \\ x = 2[/tex]
Jacob copies 30% of a document. He copies 8 pages. Write the number of pages in the
document.
Answer:
27
Step-by-step explanation:
Number of documentsjacob copies 30% of a document which is 8 pages
we can solve this using cross multiplication
30 % : 8
100% : x
30%x = 100%*8
30% x = 8
x = 8/ 30%
x = 26.667
to 2sf
number of pages in the documents 27Find the sum or difference. Write your answer in the simplest form. 5 1/3 + 6 1/6
Answer:
The answer for addition one is 11 1/2. The answer for subtraction would be -5/6.
Hope this helps. Can I please get brainliest if possible?
The answer you are looking for is 11 and 1/2.
To find this answer, you must first add the fractions together. Before you do so, you must make sure they have a common denominator. So, multiply 1/3 by 2/2 to get 2/6. Now, add 2/6 and 1/6 to get 3/6. 3/6 simplified (divided by 3/3) is 1/2.
Next, add the whole numbers. 5 + 6 is 11. Thus making your final answer 11 and 1/2.
I hope this helps!
If 3 hamburgers cost $4.20, then how much does 1 hamburger cost?
Answer:
$1.40
Step-by-step explanation:
Divide 4.20 by 3.
Answer:
$1.4
Step-by-step explanation:
The price of one hamburger will be equal to the total price of the hamburgers divided by the number of hamburgers .
Therefore $4.20/3
$1.4
So each hamburger cost $1.4
Tom rented a truck for one day. There was a base fee of 19.95 , and there was an additional charge of 85 cents for each mile driven. Tom had to pay 216.30 when he returned the truck. For how many miles did he drive the truck?
Answer:
231 miles.
Step-by-step explanation:
Tom rented a truck with a base fee of 19.95. You will subtract this from the total since you just want to get the mileage.
Tom is getting charged .85 cents per mile driven.
Tom payed 216.30 subtotal minus the 19.95 base fee since we are trying to only see how many miles he drove.
(216.30-19.95=196.35) This will be total for each mile. All we need to do is divide to get the total of miles
(196.35÷.85= 231)
231 is the number of miles Tom drove.
What is the slope intercept form of 11x+3y=-32
Answer:
y=−113x−323
Step-by-step explanation:
there u go
Solve for the equation for x: 4.5x-2.3=6.7
Step-by-step explanation:
4.5x-2.3=6.7 (add 2.3 so no number in the equation)
6.7+2.3 is 9
4.5x=9 (divide by 4.5 as it's 9 is divisible by 4.5
9/4.5 is 2
X=2
put it back into the equation
4.5*2 is 9
9-2.3 is 6.7
Therefore X=2
Answer:
x = 2
Step-by-step explanation:
Add 2.3 to both sides. We get:
4.5x = 6.7 + 2.3 = 9
If 4.5x = 9, then x = 2
I need help fast (26 POINTS!!)
What’s the answer to this?
Answer:
P'(-3, 5)
Step-by-step explanation:
The transformation for a 90° rotation CCW is ...
(x, y) ⇒ (-y, x)
(5, 3) ⇒ (-3, 5)
The coordinates of the rotated point are (-3, 5).
Two cylinders are similar. The volume of the larger cylinder is 343ft3 and the volume of the smaller cylinder is 125ft3. The height of the smaller cylinder is 5ft. What is the height of the larger cylinder? Enter your answer in the box.
Answer:
The answer would be 7ft.
Step-by-step explanation:
Let the radius of the cylinder be rft. and its height be hft. Again the radius of the larger cylinder is R ft and its height is H ft. Given h = 5 ft.
As the cylinders are similar we can say [tex]R/r[/tex] = [tex]H/h[/tex]
Now the volume of the smaller cylinder is πr²h = 125
and that of larger one is πR²H = 343
SO πR²H/πr²h = 343/125
⇒ H²/h² × H/h = 343/125
⇒ H³/h³ = 7³/5³
⇒ H/h = 7/5
⇒ H = 7/5 × h = 7/5 × 5 = 7ft
Hope this Helped:)