the amount (a) that principal (p) will be worth after t years at interest rate (r) compounded annually is
a = p(1 + r)^t
suppose $6,000 is invested at 5.5% and yields a total of $7,255. how many was it invested
The number of years the money was invested with annual compounding is 3.45 years.
How many years was it invested?When an amount earn interest compounded annually, it means that both the amount invested and the interest earned increases in value once a year.
Number of years = (In FV / PV) / r
Where:
FV = future valuePV = present valuer = interest rate(In 7255 / 6000) 0.055 = 3.45 years
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Find each square (x+4)^2
Answer:
[tex]x^{2} +8x+16[/tex]
Step-by-step explanation:
There are 2 ways to find the square of a binomial. You can use FOIL or use a formula. Just remember that the square of a binomial will always be a trinomial.
FOIL
Since we are squaring a binomial we can rewrite the expression as (x+4) * (x+4). FOIL stands for First, Outside, Inside, Last. This explains how to multiply out 2 binomials. This method will give you 4 different terms that can then be combined to find the answer.
First - multiply the first terms of each binomial
x * x = [tex]x^{2}[/tex]Outside - multiply the terms on the outside of both binomials
x * 4 = 4xInside - multiply the terms on the inside of both binomials
4 * x = 4xLast - multiply the last terms of each binomial
4 * 4 = 16Now we can combine these terms to create the new polynomial [tex]x^{2} +4x+4x+16[/tex]. Then, combine like terms for the final answer: [tex]x^{2} +8x+16[/tex].
Shortcut
Another way to square binomials is to use the formula [tex]a^{2} +2ab+b^{2}[/tex], where a is the first term and b is the second term. So, for this formula, the binomial would look like (a+b).
So, we can apply this formula by plugging in x for a and 4 for b.
[tex]x^2+2*4*x+4^2[/tex]Then, multiply the middle term
[tex]x^{2} +8x+4^2[/tex]Finally, square 4
[tex]x^2+8x+16[/tex]This gives us the same final answer as the method above.
Step-by-step explanation:
(x+4)^2
you can also expand it
(x+4)(x+4)
x^2+4x+4x+16
x^2+8x+16
can someone help me on this question?
Answer:
first line: 0, 4
explanation: middle of -12 and 12 is 0, then 12/3 = 4
second line: -9, 6
explanation: split into 4 sections per each 12 so 12/4 is 3 and the location of the first unknown point is one section away from 12 so we know the distance between there is 3, leaving -12+3 = -9. Then two sections less than 12 is 12-6 = 6
third line: -12, 4
explanation: 24/6 = 4, -24 + 12 = -12 so 4 units each sections 0 + 4 = 4
You toss a coin and roll a number cube. The table shows the sample space,
where H means heads, T means tails, and the numbers represent the number
cube roll?
What is the probability of tossing heads and rolling a number less than 3?
A.1/4
B.1/3
C.1/6
D.1/2
Please help me on this and answer quickly if you get it correct and I’ll give brainlist if you don’t I won’t give brainlist but hurry please!!
Using it's concept, it is found that the probability of tossing heads and rolling a number less than 3 is given by:
C. 1/6
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there were 12 trials. Of those, 2 are H1 and H2, which are heads and a number less than 3, hence the probability is given by:
p = 2/12 = 1/6.
Which means that option C is correct.
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The graphs of f(x) = -2x and g(x)=()* are shown.
What are the solutions to the equation -2x = ()*?
Select each correct answer.
0-2
0 -1
02
04
-10-8-6-4
10
8
6-
72
-4
6
in
8
10+
2 4 6 8 10
The solutions to the equation -2x = 2^x are (1,2) and (2,4)
How to determine the solutions?The attached graph represents the missing part of the question
The equations are given as:
f(x) = -2x
g(x) = 2^x
The solution to -2x = 2^x is the points where the graphs of f(x) and g(x) intersect
From the attached graph, the points of intersection are:
(1,2) and (2,4)
Hence, the solutions to the equation -2x = 2^x are (1,2) and (2,4)
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The charge for renting a hedge trimmer is $10 plus $5 per day the total for renting a trimmer was $85. Which equation can you use to find the number of days the trimmer was rented? Please help !!!!
Answer:
15days.
Step-by-step explanation:
total amount=$85
renting amount=$10
amount per day=$5
to find the number of days the trimmer was rented it will be;
total amount-renting amount ÷$5
$85-$10÷$5
$75÷$5
=15days
A car travelled a distance of 50km in an hour.what distance did it travel in 30min at the same speed?
Answer:
The car would have traveled 25 km.
Step-by-step explanation:
Set up the Proportion [tex]\frac{50}{60} = \frac{x}{30}[/tex]. Solving that proportion gets you an answer of 25, getting you the answer 25 km in 30 minutes. I hope this helps! :)
The points E(- 4, 6), F(- 6, - 2), G(2, - 4) , and H(4, 4) form quadrilateral EFGH. Plot the points then click the "Graph Quadrilateral " button.
The slope of EF, FG, GH, and HE is 4, -1/4, 4, and -1/4 respectively. And the length of sides EF, FG, GH, and HE will be √68, √68, √68, and √68 units respectively.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The points E(-4, 6), F(-6, -2), G(2, -4) , and H(4, 4) form quadrilateral EFGH.
Then the slopes are calculated below.
Slope of EF = (6 + 2)/(-4 + 6)
Slope of EF = 8/2
Slope of EF = 4
Slope of FG = (-4 + 2)/(2 + 6)
Slope of FG = -2/8
Slope of FG = -1/4
Slope of GH = (4 + 4)/(4 - 2)
Slope of GH = 8/2
Slope of GH = 4
Slope of HE = (6 - 4)/(-4 - 4)
Slope of HE = -2/8
Slope of HE = -1/4
Then the distance between the point will be
EF² = (-6 + 4)² + (-2 - 6)²
EF² = (-2)² + (-8)²
EF² = 4 + 64
EF = √68
FG² = (2 + 6)² + (-4 + 2)²
FG² = (8)² + (-2)²
FG² = 64 + 4
FG = √68
GH² = (4 - 2)² + (4 + 4)²
GH² = (2)² + (8)²
GH² = 4 + 64
GH = √68
FG² = (4 + 4)² + (4 - 6)²
FG² = (8)² + (-2)²
FG² = 64 + 4
FG = √68
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Mr. Fishie bought a tank for $15 and 10 fish which cost $f each. If he gave the cashier two 20-dollar bills, what was his change in terms of f?
Answer:
$25 - $10f
Step-by-step explanation:
Fishie's name is fishy.
We know Mr. Fishie spent $15 on a tank. His 10 fish cost 10*$f. His total is:
Total =15 + 10*f
His change after 2 $20 would be:
$40 - ($15 - $10f), or
$25 - $10f
1. if axb = 0 then either a or b or both must equal....
Fill in the missing number in this sequence:
{ } 45, 15, 5
Answer:
135
Step-by-step explanation:
every njmber is divided by 3
If 135 is divised by 3 it becomes 45
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to fill in the missing number in the following sequence:
[tex]\pmb{(~~~),45,15,5}[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Look at the common ratio.Since every number here is divided by 3, the common ratio is 3.
To find the missing number, we should multiply 45 times the common ratio, 3:
[tex]\star~\mathrm{\overline{\underline{\overline{\underline{135}}}}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
The value of the expression -a -bl when a = 7
and b = -3
Answer:
Option 1 -----> -10
Step-by-step explanation:
Substitute a and b into the equation :
-{a-b} =
-{7-(-3)} =
-{7+3} =
-{10} =
-10 ---> Option 1
Hoep this helped and brainliest please
Gavin has nickels, dimes, and quarters in the ratio of 1:3:6.If 57of Gavin’s coins are dimes , how many nickels and quarters does he have?
Answer:
19 nickels, 57 dimes, and 114 quarters
Step-by-step explanation:
57/3 = 19
1 × 19 = 19
3 × 19 = 57
6 × 19 = 114
What is 6x-6x56 =?
Show all work.
Answer:
6x-6x56 =-2016
Step-by-step explanation:
You have to subtract, then multiply by 56 to get -2016, as it shows a negative.
Can * x ^ 2 + 25 be factored using a difference of two squares?
No it can't be factored , whenever there is addition between two squares , the expression can't be factored
Mike purchased a vehicle for Rs 59425 and spent Rs 8652 on repairs. How much did the vehicle cost him?
Answer:
68077
Step-by-step explanation:
he had spent 68077 because by 59425+8652 makes 68077
Paula walks 1/12 mile in 5/3 minutes. What rate is equivalent to the rate she walked?
The rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute
Calculating RateFrom the question, we are to determine the rate which is equivalent to the rate Paula walked
Using the formula,
[tex]Rate = \frac{Distance}{Time}[/tex]
From the given information,
Distance = 1/12 mile
Time = 5/3 minutes
Putting the parameters into the formula, we get
[tex]Rate =\frac{\frac{1}{12} }{\frac{5}{3} }[/tex]
[tex]Rate = \frac{1}{12} \div \frac{5}{3}[/tex]
[tex]Rate = \frac{1}{12} \times \frac{3}{5}[/tex]
[tex]Rate = \frac{3}{60}[/tex]
[tex]Rate = \frac{1}{20}[/tex] mile/minute
Hence, the rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute
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Brent sells an avarage of 52 pot holders each week. about how many pot holders does he sell in 58 weeks.
The amount of pot holders Brent sold for 58 weeks is 3016
How to find the amount of pot holders Brent sold?He sells 52 pot holders each week.
This means for every week, he sold 52 pot holders. Therefore, the amount of pot holders he sold for 58 weeks can be solved as follows:
1 week = 52 pot holders
58 weeks = ?
cross multiply
number of pot sold for 58 weeks = 58 × 52
number of pot sold for 58 weeks = 3016
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!!20 POINTS AND BRAINLIEST!!! HELP ASAP!!!
How much ribbon would be needed to go around a package that had a length 2x^2+3x-5/x^2+x-3 centimeters and width x^2-x-5/x^2+x-3 centimeters?
(show work)
Answer:
23cm
Step-by-step explanation:
If you multiply like terms you will get the answers. Then you add last to get 23cm
The required length ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).
Given that,
Package that had a length of 2x^2+3x-5/x^2+x-3 centimeters and width x^2-x-5/x^2+x-3.
How much ribbon would be needed to go around the package in centimeters is to be determined.
Perimeter is the measure of the figure on its circumference.
The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
Quantity of ribbon = perimeter of the rectangular package
= 2 * length + 2* width
= 2 * (2x^2+3x-5/x^2+x-3) + 2(x^2-x-5/x^2+x-3)
= 2 (3x^2 + 2x -10) / (x^2 + x - 3)
Thus, the required length of ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).
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A square notepad has sides that are 10 centimeters long. What is the notepad's area?
Answer:
100cm²
Step-by-step explanation:
The notepad is square.
The area of a square = length X width.
All the sides of a square are the same length.
Therefore, the area of the notepad = 10 X 10 which equals 100.
Don't forget the units!
The units for area is cm².
The units for volume is cm³.
This is area so your answer is 100cm².
Hope this helped, have a nice day!
Convert 5.6 times 10 to power of 4 to ordinary form
please answer the question below, will give brainliest to first answer :)
Answer:
None of these answers are correct
Step-by-step explanation:
neither of them are rays.
a ray goes from the center to the edge of a circle.
Factor completely AND solve for the solutions of the quadratic.
HELP ME AND ANSWER BOTH PARTS PLEASE!
A physical therapist claims that 75% of people lose their balance if they close their eyes while standing on one foot. A gymnast feels that the rate is less than 75%. To test this, she randomly selects 100 people and finds that 80 of them lose their balance while standing on one foot. To determine if these data provide convincing evidence that the proportion of people who lose their balance while standing on one foot and closing their eyes is less than 75%, 150 trials of a simulation are conducted. The gymnast is testing the hypotheses: H0: p = 75% and Ha: p < 75%, where p = the true proportion of people who will lose their balance while standing on one foot and closing their eyes. Based on the results of the simulation, what is the estimate of the P-value of the test? A dotplot. A number line labeled simulated sample percentage of people who lose balance goes from 64 to 88 percent. 64, 3; 66, 3; 67, 4; 68, 8; 69, 5; 70, 7; 71, 8; 72, 11; 73, 15; 74, 12; 75, 11; 76, 8; 77, 18; 78, 10; 79, 10; 80, 5; 81, 4; 82, 2; 83, 2; 84, 1; 85, 2; 87, 1. 0.1133 0.17 0.887 0.92
Answer:
75
Step-by-step explanation:
becAUSE IF YOU TEST IT THATS UR ANSWER
Drag the tiles to the correct boxes to complete the pairs.
Match the subtraction expressions with their answers.
From simplification of the given algebra, the correct answers are as shown below.
How to solve algebra problems?1) (a² - b)/(a³b²)
This reduces to;
(a²/(a³b²)) - b/(a³b²)
⇒ a/(ab²) - 1/(a³b)
2) The algebraic expression is;
(b - a)/a³b³
⇒ b/a³b³ - a/a³b³
⇒ 1/a³b² - 1/a²b³
3) The algebraic expression is;
(2 - ab²)/(a²b³)
⇒ (2/(a²b³)) - (ab²)/(a²b³)
⇒ 2/(a²b³)) - 1/(ab)
4) The algebraic expression is;
(2 - ab²)/(a²b³)
⇒ 2/(a²b³) - 1/ab
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Factor: 5x2 – 15x – 20.
(a) 5(x-4)(x+1),
(b) -2(x-4)(x+5),
(c) -5(x+4)(x-1),
(d) 5(x+4)(x+1).
Answer:
[tex]a)~5(x-4)(x+1)[/tex]
Step-by-step explanation:
[tex]~~~5x^2 -15x -20\\\\=5(x^2 -3x -4)\\\\=5(x^2 -4x +x -4)\\\\=5\textbf{[}x(x-4) +(x-4)\textbf{]}\\\\=5(x-4)(x+1)[/tex]
solve these algebraic fractions please with step by step explanation would be great
Answer:
first ans =x-7
second ans= x+y/x-y
Step-by-step explanation:
I think you would get it and it doesn't need explanation.
Keith is working two jobs this summer as a lifeguard and a tutor. he earns $16 an hour as a lifeguard and $18 an hour as a tutor. he wants to earn at least $250 to put towards his car. what is one possible combination of hours he can work at each job to earn at least $250?
Answer:
He could work 10 hours as a lifeguard, and 5 hours as a tutor
Step-by-step explanation:
If he makes $16 an hour as a lifeguard
and $18 an hour as a tutor,
He could work 10 times $16, to make $160 for 10 hours.
Now we subtract this from $250, this makes $90.
We know need to find out how many times 18 goes into 90, 5 times.
So we know that he could work 10 hours as a lifeguard and 5 hours as a tutor.
I hope this is right.
I hope this helps too, have a nice day!
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
c. diameter
because when a line intersects the center and even touches the centre is called a diameter
hope it helps.
Answer:
C
Step-by-step explanation:
Diameter