An initial deposit of $1200 is put into an account that earns 5% interest compounded annually. Each year year an additional of $1200 is added to the account. Whats the value of the account after the 10th deposit if no withdraws or additional deposits are made.
Answer:
$1788
Step-by-step explanation:
1200 x 0.07 = 84
84 × 7 = 588
588 + 1200 = 1788
The value of the account after the 10th deposit if no withdraws or additional deposits are made should be $15,093.47.
Calculation of the value:Since
The initial deposit is $1.200
The rate of interest is 5%
Now the future value be like
[tex]= (1,200 \times (1 + 0.05)^{9} - 1) \div 0.05) \times (1 + 0.05) + 1,200\\\\= 1,200 \times (1.5513 - 1) \div 0.05) \times (1 + 0.05) + 1,200\\\\= (1,200 \times 11.0265) \times (1.05) + 1,200[/tex]
= 13893.4711 + 1,200
= $15,093.47
hence, The value of the account after the 10th deposit if no withdraws or additional deposits are made should be $15,093.47.
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Alex is a member of the school track and field team. His times for running various distances are shown. Create a scatter plot for the collected data. Label axes with the appropriate scales and titles. Draw a line of best fit. Predict the distance Alex can run in 20s. What type of correlation exists for the data? Give reasons. Distance (m) 50 100 150 200 250 Time 6.1 12 18.3 25.2 31.7
Answer:
(1) Please find attached the graph of the data
(2) 160.396 m
(3) The correlation that exist is a straight line correlation
Step-by-step explanation:
The given data are;
Distance, Time
(m), (s)
50, 6.1
100, 12
150, 18.3
200, 25.2
250, 31.7
(2)
Based on the linear regression formula, we have;
[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]b = \dfrac{5 \times 17215 - 93.3 \times 750}{5 \times 2156.03 -8704.89} = 7.758[/tex]
[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]
[tex]a = \dfrac{750 - 7.7581 \times 93.3}{5}= 5.234[/tex]
The line is
y = 7.7581×x+5.234
When t = 20 s, we have
y = 7.7581*20+5.234 = 160.396 m
(3) The correlation that exist is a straight line correlation
The vertex form of the equation of a parabola is y = = 6(x-2)²-8.
What is the standard form of the equation?
A. y = 12x2 - 6x + 8
B. y = 6x2 - - 24x + 16
c. y = 6x2 - 4x + 4
O D. y = 12x2 - 12x + 16
Answer:
B. y = 6x^2 - 24x + 16.
Step-by-step explanation:
y = 6(x - 2)^2 - 8
y = 6(x^2 -4x + 4) - 8
y = 6x^2 - 24x + 24 - 8
y = 6x^2 - 24x + 16.
For a class project, a teacher cuts out 15 congruent
circles from a single sheet of paper that measures 6
inches by 10 inches. How much paper is wasted?
O (60 - 152) square inches
O 150 square inches
O 45 square inches
O (60 - ) square inches
Answer:
its 60-15(pie) sq inches
Step-by-step explanation:
A polynomial is factored using algebra tiles. An algebra tile configuration. 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 8 tiles are in the Product spot in 2 columns with 4 rows: 1 is labeled + x squared, 1 is labeled + x, the 3 tiles below + x squared are labeled negative x, and the 3 tiles below the + x tile are labeled negative. What are the factors of the polynomial? (x − 1) and (x + 3) (x + 1) and (x − 3) (x − 2) and (x + 3) (x + 2) and (x − 3)
Answer:
The factors of the polynomial are:
(x + 1) and (x - 3).
Step-by-step explanation:
Consider the image attached.
The upper tiles shows: (x + 1)
And the left tiles shows: (x - 3)
So, the factors of the polynomial are:
(x + 1) and (x - 3).
Answer:
x+1 and x -3
Step-by-step explanation:
Express as a trinomial (2x-5) (3x-8)
Answer:
6x^2 -31x +40
Step-by-step explanation:
2x * 3x + 2x * - 8 + -5 * 3x -5 * -8 Distributive property
6x^2 -16x -15x + 40 Math
6x^2 -31x +40 Answer
Samatha received $500 as a graduation present and decides to invest it in an account that is
compounded continuously. How much will be in the account at the end of 5 years if the interest
rate is 3%?
Answer:
Step-by-step explanation:
m= month
3÷100= 0.03
0.03×500=$15
$15/m
$15×5×12=$900
$500-$900=
Answer: -$400
A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. The path of the projectile is modeled using the equation h(t) = –16t2 + 48t + 190. Approximately when will the projectile hit the ground? 1.5 seconds 3.2 seconds 5.3 seconds 6.2 seconds
Hello! :)
—————— ☆ ☆———————————————————————————-
Answer:
5.3 seconds
Step-by-step explanation:
The answer is 5.3 seconds because
If you solve this equation than you will see how it is 5.3 seconds.
Equation: [tex]h (t) = -16t ^ 2 + 48t + 190 [/tex]
Also if you graph it, the answer will be 5.3 seconds
—————— ☆ ☆————————————————————————————
Hope this helps! :)
By: BrainlyMember ^-^
Good luck!
Answer:
^ as the other person said, it's 5.3
Step-by-step explanation:
edge
I like really need some help dudes and dudets help a bro out please?
which of the following are solutions to the equation below 5x^2-2x+16=4x^2+6x
Answer:
x = 4Step-by-step explanation:
[tex]5x^2-2x+16=4x^2+6x\\\\5x^2-2x+16-4x^2-6x=0\\\\x^2-8x+16=0\\\\x^2-4x-4x+16=0\\\\x(x-4)-4(x-4)=0\\\\(x-4)(x-4)=0\\\\(x-4)^2=0\\\\x-4=0\\\\x=4[/tex]
A rectangular prism has a width of 3 inches, and height of 4 inches, and a width of 5 inches. if the height is is doubled, what happens to the volume?
Answer:
The volume doubles to 120
Step-by-step explanation:
Volume of Rectangular Prism Formula: V = lwh
Step 1: Find volume of given lengths
V = 3(4)(5) = 60 in²
Step 2: Find volume when we double h
4(2) = 8
V = 3(8)(5) = 120 in²
Step 3: Divide the 2 numbers to find the ratio
120/60 = 2, or double the amount.
HELP ASAP NEED HELPPP
Find the next 4 terms of this Fibonacci sequence -x, x+y, y
Answer:
see explanation
Step-by-step explanation:
Any term in a Fibonacci sequence is the sum of the previous 2 terms.
Given the first 3 terms then
a₄ = a₂ + a₃ = x + y + y = x + 2y
a₅ = a₃ + a₄ = y + x + 2y = x + 3y
a₆ = a₄ + a₅ = x + 2y + x + 3y = 2x + 5y
a₇ = a₅ + a₆ = x + 3y + 2x + 5y = 3x + 8y
Thus the next four terms are
x + 2y, x + 3y, 2x + 5y, 3x + 8y
Alberto uses the steps below to solve the equation One-half x minus 3 equals 7. Step 1: One-half x minus 3 plus 3 equals 7 plus 3 Step 2: One-half x plus 0 equals 10 Step 3: One-half x equals 0 Step 4: 2 (one-half) x equals 2 (10) Step 5: 1 x equals 20 Step 6: x equals 20 Which justifies Step 6 of his work? the addition property of equality the identity property of addition the multiplication property of equality the identity property of multiplication
Answer:
Identity property of multiplication
Step-by-step explanation:
Given
Step 5: 1x = 20
Step 6: x = 20
Required
Property that justifies step 6
It should be noted that step 6 is a result of step 5.
So, basically the question is asking for the property applied on step 5.
Given that step 5 is: 1x = 20
The property applied is the identity property of multiplication.
This is so because this property states that when 1 is multiplied to an equation, the result remains the same.
Hence;
When 1 is multiplied to x (i.e. 1x), the result is still x.
So, 1x = 20 at step 5 gives x = 20 at step 6
Answer: Option B is the correct answer.
The identity property of addition
Simplify: ( ++)2 + ( −+)2 + ( +−)2
Answer:
[tex]-2[/tex]
Step-by-step explanation:
[tex]( ++)2 + ( -+)2 + ( +-)2[/tex]
[tex]++ = +[/tex]
[tex]-+ = -[/tex]
[tex]+- = -[/tex]
[tex]( +)2 + ( -)2 + ( -)2[/tex]
[tex]2-2-2[/tex]
[tex]=-2[/tex]
Rewrite the equation by completing the square.
x^2 + 2x – 48 = 0
Answer:
(x+1)^2 = 49
x = 6 x = -8
Step-by-step explanation:
x^2 + 2x – 48 = 0
Add 48 to each side
x^2 + 2x =48
Take the coefficient of x
2
Divide by 2
2/2=1
Square it
1^2 =1
x^2 + 2x +1=48+1
x^2 +2x+1 = 49
(x+1)^2 = 49
Take the square root of each side
sqrt((x+1)^2) =±sqrt( 49)
x+1 = ±7
Subtract 1 from each side
x+1-1 = -1 ±7
x = -1+7 x = -1 -7
x = 6 x = -8
A quiz has twenty questions with 7 points awarded for each correct answer, 2 points deducted for each wrong answer and 0 for each question omitted. Jack scored 87 points. How many questions did he omit? My math teacher gave us this as an optional challenge problem for 8th grade math. I got stuck on it, so if someone could give me some hints or at least tell me what I should be doing, I’d appreciate it. Like how the heck do I know which ones are correct vs which ones are omitted? Is it a multiple answer problem?
(he got 2 wrong answers, and 13 correct answers)
=====================================================
Explanation:
c = number of correct answers
w = number of wrong answers
m = number of missing answers (ie, omitted answers)
7c = number of points awarded from just the correct answers
-2w = number of points awarded from the wrong answers. Note the negative to indicate we lose points here.
0m = 0 = points from the missing answers. We don't have to worry about this portion
In total, Jack would earn 7c-2w points. Since he actually earned 87 points, we can write the equation 7c-2w = 87. We'll come back to this later.
-----------------------
The quiz has 20 questions, so c+w+m = 20 is another equation we'll be working with. Solve for c to get c = -w-m+20. Plug this into the equation 7c-2w = 87 to get...
7c-2w = 87
7(-w-m+20)-2w = 87 ... replace c with (-w-m+20)
-7w-7m+140-2w = 87 ... distribute
-9w-7m+140 = 87
-9w-7m = 87-140
-9w-7m = -53
9w+7m = 53
----------------------
From here, you use trial and error. We don't have enough information to finish solving the system. We would need 3 equations to solve for the 3 unknowns.
What we can do is make a guess of what w could be and use that to find m. Luckily there is a small list of possible values for w.
So let's say w = 0
9w+7m = 53
9(0)+7m = 53 ... plug in w = 0
7m = 53
m = 53/7 ... divide both sides by 7
m = 7.57
We got a non-whole number, so there is no way w = 0 since we can't have 0.57 of a question missing. Jack either answers the question, or he skips it. He can't have both happen.
---------------------
Let's repeat for w = 1
9w+7m = 53
9(1)+7m = 53 ... replace w with 1
9+7m = 53
7m = 53-9 ... subtract 9 from both sides
7m = 44
m = 44/7 ... divide both sides by 7
m = 6.28
So we can see that w = 1 isn't possible either.
---------------------
However, w = 2 is possible
9w+7m = 53
9(2)+7m = 53
18+7m = 53
7m = 53-18
7m = 35
m = 35/7
m = 5
Meaning that Jack got w = 2 wrong answers and skipped over m = 5 questions. The number of correct answers is c = 20-m-w = 20-5-2 = 13
-----------------------------------
An alternative to using trial-and-error is to use a graph.
Replace w and m with x and y respectively. So we go from 9w+7m = 53 to 9x+7y = 53
Use a graphing tool, or plot the graph on graph paper, to get what you see in the diagram below. I used the program GeoGebra to graph.
Then notice how the graph goes through the point (2,5) which means x = 2 and y = 5. Replace x and y with w and m to find (w,m) = (2,5)
note: the point (5,1) looks like it also lies on the graph, but it is not a solution. It's just a point that is very close to the line. I recommend you try out (w,m) = (5,1) and you'll see it doesn't work.
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Hello names smiley!
for your answer for this is A circle with diameter 10cm will have a circumference of approximately 31.4cm
or
10cm x 3.14 = 31.4 Circumference = 3.14 x diameter
Step-by-step explanation:
its ok if you dont give brainliest i just want to help!
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The grade of a road is its slope written as a percent. A warningsign must be posted if a section of road has a grade of at least 8% and ismore than 750 feet long.a. Interpret and Apply A road rises 63 feet over a horizontal distanceof 840 feet. Should a warning sign be posted? Explain your thinking.b. Critical Thinking The grade of a section of road that stretches over ahorizontal distance of 1000 feet is 9%. How many feet does the roadrise over that distance?
Answer:
(a)Grade =7.5% (No warning sign is needed)
(b)Rise =90 feet
Step-by-step explanation:
[tex]\text{Slope = }\dfrac{Rise}{Run}[/tex]
(a)
Rise = 63 feet
Run (Horizontal distance) = 840 feet.
[tex]\text{Slope = }\dfrac{63}{840}=0.075\\\\$Grade=Slope \times 100 = 0.075 \times 100 = 7.5\%[/tex]
A warning sign should not be posted since its grade is less than 8%.
(b)
Grade = 9%
Run (Horizontal distance) = 1000 feet.
Recall that:
Grade = Slope X 100
[tex]9 =\dfrac{Rise}{1000} \times 100\\\\9 =\dfrac{Rise}{10}\\\\$Rise = 9 \times 10 \\$Rise=90 feet[/tex]
The road rises 90 feet over a distance of 1000 feet.
9. A water glass can hold 2/9 of a litre of water. How many glasses of water can be filled with a 3 litre bottle?
Answer:
13.5 glasses of water
Step-by-step explanation:
If:
1 water glass can hold 2/9 of a litre
x water glasses can hold 3 litres.
Therefore, expressing it as a litre to glass ratio, we have::
[tex]\dfrac{2/9}{1}=\dfrac{3}{x} \\\dfrac{2}{9}x=3\\$Divide both sides by$ \dfrac{2}{9}\\x=3 \div \dfrac{2}{9}\\x=3 \times \dfrac{9}{2}\\\\x=13.5[/tex]
Therefore, 13.5 glasses of water can be filled with a 3 litre bottle.
Solve the equation. Be sure to check your proposed solution by substituting it for the variable in the original equation 2(3x-3)-5-2(x-3)+ 15 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is (Type an integer or a simplified fraction.) O B. The solution set is {x x is a real number O C. The solution set is ø A chef has 10 brands of hot sauce. In how many ways can the chef pick 3 to mix into a gumbo? | different ways There are In order to start a small business, a student takes out a simple interest loan for $3000.00 for 9 months at a rate of 11.75% a. How much interest must the student pay? b. Find the future value of the loan a. The amount of interest is S (Round to the nearest cent as needed) b. The future value is $ (Round to the nearest cent as needed.) Use an algebraic equation to find the measure of each angle that is represented in terms of x. 2x+30° 2x+40 m & 2x+30° m & 2x+ 40°=
Answer and Step-by-step explanation:
(i) The solution for equation: 2(3x-3) - 5 = 2(x-3) + 15 is:
2(3x-3) - 5 = 2(x-3) + 15
6x - 6 - 5 = 2x - 6 +15
6x - 2x = - 6 + 15 + 6 + 5
4x = 20
x = 5
The solution x is a real number and equals 5.
(ii) Since the order of hot sauce that goes into the gumbo doesn't matter, use combination:
[tex]C^{10}_{3}[/tex] = [tex]\frac{10!}{3! (10-3)!}[/tex]
[tex]C^{10}_{3}[/tex] = [tex]\frac{10.9.8.7!}{3.2.1.7!}[/tex]
[tex]C^{10}_{3}[/tex] = 120
There are 120 ways of picking 3 sauces out of 10.
(iii) Interest is calculated as:
interest = principal*rate*time
Principal is the value of the loan;
Rate is how much it will increase;
Time is for how long the loan will be taken. In this case, time is 9/12 since it was for months;
Interest = 3000 * [tex]\frac{11.75}{100}*\frac{9}{12}[/tex]
Interest = 264.37
The interest the student will pay will be: $264.37.
Future Value = principal + interest
future value = 3000 + 264.37
future value = 3264.37
The future value for the student is $3264.37.
(iv) As shown in the image in the attachment, the sum of the equations equals 90:
2x + 30 + 2x + 40 = 90
4x = 20
x = 5
2x + 30 = 2.5 + 30 = 402x + 40 = 2.5 + 40 = 50The angles are 40° and 50°
help pls thx guys photo attached
Answer:
x = 18
A = 110
Step-by-step explanation:
Angles A and B are supplementary angles so they add to 180 degrees
A + B = 180
5x+20 + 9x -92 = 180
Combine like terms
14x -72 = 180
Add 72 to each side
14x-72+72 = 180+72
14x = 252
Divide each side by 14
14x/14 = 252/14
x =18
A = 5x+20
= 5*18 +20
=90 +20
= 110
The revenue, in dollars, of a company that produces jeans can be modeled by 2x2+17x−175. The cost, in dollars, of producing the jeans can be modeled by 2x2−3x−125. The number of pairs of jeans that have been sold is represented by x. If the profit is the difference between the revenue and the cost, which expression can be used to find profit and what is that profit when 75 pairs of jeans are sold? 20x−50; $500 20x−50; $1,450 20x+50; $1,550 20x+50; $5,250
Answer: $1450
The profit that is gained from the production and selling of the jeans is given to be calculated through the the equation,
P = 20x - 50
For 75 jeans, we just have to substitute 75 to the x's of the equation. This then becomes,
P = 20(75) - 50 = 1450
Thus, the company will make a profit of $1450 by production of 75 jeans.
Step-by-step explanation:
The company will make a profit of $1450 by the production of 75 jeans.
Cost functions and revenueThe profit that is gained from the production and selling of the jeans is modeled by the equation;
P = 20x - 50
If 75 jeans are produced, substitute 75 to represent the value of x in the equation.
P = 20(75) - 50 = 1450
Hence, the company will make a profit of $1450 by the production of 75 jeans.
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REALLY QUICK!!! WILL GIVE BRAINLIEST!!!20 POINTS!!1
Solve the system of equations. y=x^2-5 y=2x+3
None of these answers work. I believe you recorded the equations incorrectly.
PLEASE HELP ILL MARK YOU BRAINLIEST Given the expression: 6x10 − 96x2 Factor the entire expression completely. Show the steps of your work.
Answer:
6x¹⁰ - 96x²
6x²(x⁸ - 16)
B) 6x²(x⁸ - 16)
6x²[(x⁴)² - 4²]
6x²[(x⁴ - 4)(x⁴ + 4)]
6x²(x⁴ + 4)[(x²)² - 2²]
6x²(x⁴ + 4)(x² - 2)(x² + 2)
Answer:
Step-by-step explanation:
Part A: The rewritten expression created by factoring out the greatest common factor is 6x2(x8 – 16).
Part B: The completely factored expression is 6x2(x4 + 4) (x2 + 2) (x2 – 2).
My work for Part B:
Step 1: Using the expression from Part A, we just simplify the inside of the parentheses as much as possible by using the difference of two perfect squares pattern:
6x2(x4 + 4) (x2 + 2) (x2 – 2).
If y − 4 = 2x, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs? Which order pair is it? {(2, 1), (4, 2), (6, 3)} {(1, 2), (2, 4), (3, 6)} {(4, 0), (6, 1), (8, 2)} {(0, 4), (1, 6), (2, 8)}
Answer:
the fourth set
Step-by-step explanation:
if you plug this equation into desmos and look at the x-values, you will see that the fourth set is the only one with points that make this equation true.
Answer:
D
Step-by-step explanation:
Original grade 80 New grade 100 Find the percent of increase
Answer:
25%
Step-by-step explanation:
Percent change = 100 - 80
|80|
x 100 = 20
80
x 100 = 25
Answer:
25%
Step-by-step explanation:
the number 3^13 - 3^10 is divisible by
A hockey stick is regularly $54.99, but is on sale for 20% off. What is the price of the hockey stick, including 13% tax?
Answer:
$49.71
Step-by-step explanation:
Take $54.99 - 20% to get $43.99 add 13% and get $49.71
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plzz
Answer:
36
Step-by-step explanation:
A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.So, FD is a midsegment. (D is a midpoint and so is F)
A midsegment connecting two sides of a triangle is parallel to the third side and is half as long.This midsegment connects the two sides EC and AE. The third, remaining, side is AC.
The midsegment is half as long as the third side.
FD = 18.
FD is half of the third side.
FD times 2 = third side.
18 times 2 = 36
The third side, AC, is 35 units long.
Words of encouragement:
Good luck!