Justin deposited $4000 into an account with 5.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have inthe account after 10 years?Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
First, divide the annual interest rate by 2 to find the semiannual interest rate:
[tex]\frac{5.5}{2}=2.75[/tex]Next, identify the number of periods when the 2.75% increase will be appliad. In a period of 10 years, there are 20 semiannual periods.
Each period, the initial investment gets multiplied by a factor of:
[tex]1+\frac{2.75}{100}=1+0.0275=1.0275[/tex]Over 20 semiannual periods, the initial investment will get multiplied by a factor of:
[tex]1.0275^{20}[/tex]Therefore, after 10 years, the amount of money in the account is:
[tex]\begin{gathered} 4000\times(1.0275)^{20}=4000\times1.7204\ldots \\ =6881.7137\ldots \end{gathered}[/tex]To the nearest cent, the amount of money in the account will be:
[tex]6881.71[/tex]Related Questions
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Answers
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
The number of bats in a colony is growing exponentially. After 2 years, there were 120 bats. After 5 years, there were 960 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 8 years? do not include units in your answer.
Answers
7680 bats are expected to be in the colony after 8 years
What is Exponential Decay?A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
The formula for exponential growth
[tex]y=ab^{t}[/tex]
Given,
After 2 years, there were 120 bats.
120=ab²...1
After 5 years, there were 960 bats.
960=ab⁵....2
Hence:
120/960 = ab²/ab⁵
1/8 = b²/b⁵
1/8 = 1/ b³
1/2³ =1/ b³
2³=b³
b=2
We solve for a
120 = ab²...... Equation 1
120 = a × 2²
120 = 4a
a = 120/4
a = 30
Now put a, b and t value in the formula
y = 30 × 2⁸
y = 7680 bats
Hence, 7680 bats are expected to be in the colony after 8 years
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Benjamin believes that [tex] \frac{1}{2} [/tex]% is equivalent to 50%. is he correct? why or why not?
Answers
First, we convert 1/2% to a decimal.
[tex]\frac{1}{2}\%=\frac{0.5}{100}=0.005[/tex]Similarly:
[tex]undefined[/tex]Write an equation for the line parallel to the given line that
contains C.
C(4,6); y= -4x+1
The equation of the parallel line is
Answers
The equation of the line parallel to the given line is y + 4x = 22
The given line is y= -4x+1
Slope of the line = -4
Slope of the parallel line= -4
Equation of the line parallel to the given line which passes through C(6,4)
y - 6 = - 4 ( x - 4 )
y - 6 = -4x + 16
y + 4x = 22
Hence the equation of the parallel line is y + 4x = 22
One that stretches on all sides and has no width is referred to in geometry as a line. A straight line is, to put it simply, a line without bends. An non-curved line that extends to infinity on both sides is said to be straight.
The general equation for a straight line is y = mx + c, where m stands for the line's slope and c for its y-intercept. The most frequently used straight line equation is one that has to do with geometry.
The equation of a straight line can be written in a number of different ways, such as point-slope form, slope-intercept form, general form, standard form, etc.
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12. Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. Youchoose a ball at random.aa. What is the probability that you choose a red or even numbered ball? (3 points)b. What is the probability you choose a green ball or a ball numbered less than 5?(3 points)
Answers
Given
A bag contains 13 red balls numbered 1-13 and 5 green balls numbered 14-18.
And a ball is chosen at random.
To find:
a) The probability that you choose a ren or even numbered ball.
b) The the probability you choose a green ball or a ball numbered less than 5.
Explanation:
It is given that,
The total number of balls is (13+5)=18.
The number of red balls is 13 numbered from 1-13.
The number of green balls is 5 numbered from 14-18.
i) Then, the probability of getting a a red or even numbered ball is,
[tex]\begin{gathered} P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right) \\ =\frac{n\left(A\right)}{n\left(S\right)}+\frac{n\left(B\right)}{n\left(S\right)}-\frac{n\left(A\cap B\right)}{n\left(S\right)} \end{gathered}[/tex]Here,
[tex]\begin{gathered} n\left(A\right)=n\left(red\text{ balls}\right) \\ =13 \\ n\left(B\right)=n\left(even\text{ numbered balls}\right) \\ =9 \\ n\left(A\cap B\right)=n\left(red\text{ balls and even numbered balls}\right) \\ =6 \\ n\left(S\right)=n\left(Total\text{ number of balls}\right) \\ =18 \end{gathered}[/tex]That implies,
[tex]\begin{gathered} P\left(A\cup B\right)=\frac{13}{18}+\frac{9}{18}-\frac{6}{18} \\ =\frac{16}{18} \\ =\frac{8}{9} \\ =0.89 \end{gathered}[/tex]Hence, the probability of getting a red or even numbered ball is 0.89.
ii) Also,
The probability of getting a green ball or a ball numbered less than 5 is,
[tex]\begin{gathered} P\left(C\cup D\right?=P\left(C\right)+P\left(D\right)-P\left(C\cap D\right) \\ =\frac{n\left(C\right)}{n\left(S\right)}+\frac{n\left(D\right)}{n\left(S\right)}-\frac{n\left(C\cap D\right)}{n\left(S\right)} \end{gathered}[/tex]Here,
[tex]\begin{gathered} n\left(C\right)=n\left(green\text{ balls}\right) \\ =5 \\ n\left(D\right)=n\left(balls\text{ numbered less than 5}\right) \\ =4 \\ n\left(C\cap D\right)=n\left(a\text{ }green\text{ }ball\text{ }or\text{ }a\text{ }ball\text{ }numbered\text{ }less\text{ }than\text{ }5\right) \\ =0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} P\left(C\cup D\right)=\frac{5}{18}+\frac{4}{18}-0 \\ =\frac{9}{18} \\ =\frac{1}{9} \\ =0.11 \end{gathered}[/tex]Hence, the probabilty of getting a green ball or a ball numbered less than 5 is 0.11.
Solve -4 1/5 ÷ 2 1/4.
one and 39 over 45
negative one and 39 over 45
negative eight and one twentieth
negative nine and 9 over 20
Answers
Answer:
Step-by-step explanation:
A square has each side equal to 2x-3. The expression that will calculate its area is:
A. 2x² + 6x + 9
B. 4x² + 9
C. 4x² + x - 6
D. 4x² - 6x + 9
E. 4x² - 12x + 9
Answers
The expression that will calculate its area is Option D. 4x² - 6x + 9.
The region is the amount that expresses the extent of vicinity on the aircraft or on a curved surface. The region of a plane vicinity or plane location refers to the area of a shape or planar lamina, whilst floor vicinity refers back to the region of an open surface or the boundary of a 3-dimensional item.
Calculation:-
side of square is given by = 2x-3
area of square = side²
= ( 2x-3)²
= 4x² + 3² - 2× 2x×3
= 4x² + 9 - 12x
The area is the quantity of area occupied by means of a two-dimensional figure. In other phrases, it's far the amount that measures the range of unit squares that cowl the surface of a closed determine. the same old unit of the vicinity is square devices that's usually represented as rectangular inches, square feet, etc.
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3 A of ch 75 -5 A study of traffic patterns in a large city shows that if the weather is rainy, there is a 50% chance of an automobile accident occurring during the morning commute. If the weather is clear, the chance of an accident is reduced to 25%. Suppose the weather forecast for tomorrow predicts a 75% chance of rain. Draw a tree diagram based on the information in the work space. (Level 4) Show Your Work US be A of ch
Answers
Solution
We can create the solution with the following tree diagram:
Part 2
For this case we want this probability:
P(rain and accident)
And we can do this operation:
P(rain and accident) = 0.75 *0.5 = 0.375
Part 3
For this case we want this probability:
P( no rain and accident)
And we can do this operation:
P(no rain and accident) = 0.25 *0.25 = 0.0625
Part 4
P(Accident) = 0.5*0.75 + 0.25*0.25= 0.4375
In the following figures, solve for x. Complete parts (a) through (c)
Answers
Explanation:
Part A:
The image is given below as
Concept:
Using the linear pairs theorem, we will have that
[tex]\begin{gathered} z+80^0=180^0 \\ substract\text{ 80 from both sides} \\ z+80-80=180-80 \\ z=100^0 \end{gathered}[/tex]Also from the image of the question, we can deduce that
[tex]y=55^0(vertical\text{ angles are equal\rparen}[/tex]Hence,
To calculate the value of x, we will use the sum of angles in a triangle
The sum of angles in a triangle gives
[tex]180^0[/tex]By substtituting the values, we will have
[tex]\begin{gathered} x+y+z=180^0 \\ y=55^0 \\ z=100^0 \\ x+y+z=180^{0} \\ x+55+100=180^0 \\ x+155=180^0 \\ x=180-155 \\ x=25^0 \end{gathered}[/tex]Hence,
The final answer for x in part A is
[tex]x=25^0[/tex]Part B:
From the image in the question we can see that angle segmen makes up a right angle
Hence,
We will have the relation below
[tex]\begin{gathered} 7x+2x=90^0 \\ 9x=90^0 \\ \frac{9x}{9}=\frac{90}{9} \\ x=10^0 \end{gathered}[/tex]Hence,
The final answer for x in part B is
[tex]x=10^0[/tex]Transform y = f(x) by reflecting it across the x-axis. Label the newfunction h(x). Compare the coordinates of the corresponding pointsthat make up the two functions. Which coordinate changes, x ory?
Answers
y = f(x)
Reflection, change the sign of the function
y = - f(x)
f(x) -f(x)
1 -1
2 -2
3 -3
8 -8
20 -20
The x coordinate will change.
Mika used division to rewrite 5/40
as 0.125. Explain what she should do next to convert 0.125 to a percent.? HELPPP
Answers
Answer:
12.5%
Step-by-step explanation:
So, Mika did do the division right. So we can get that out of the way. In order to convert to a percent, you just simply move the decimal point over two times. In this case, we have 0.125. We move it over twice to get 12.5. Now, we just plop the percentage next to it to get: 12.5%.
May I have Brainliest please? I am so close to getting my next ranking! I just need 2 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
12.5%
(can also be written as:)12[tex]\frac{1}{2}[/tex]%
Step-by-step explanation:
She should bring the decimal point over two places to the right.
To convert decimals to percents ALWAYS bring the decimal point two places to the right and and a percentage sign.
Number 9, Im not quite sure on how to do these
Answers
Solution:
Given:
[tex]f(x)=2(x-3)^2+1[/tex]The equation of a parabola in vertex form is given by:
[tex]y=a(x-h)^2+k[/tex]The coordinates of the vertex is given by (h,k).
Hence, comparing both equations,
[tex]\begin{gathered} f(x)=2(x-3)^2+1 \\ y=a(x-h)^2+k \\ a=2 \\ h=3 \\ k=1 \end{gathered}[/tex]Therefore, the coordinates of the vertex is;
[tex](h,k)=(3,1)[/tex]prime or composite
number 1
67
Answers
Answer:
167 is a prime number. However, if you're looking for if 1 or 67 is prime or composite, 1 is neither prime nor composite, and 67 is also prime.
Step-by-step explanation:
To find if a number is prime, you check if the only factors of the number are 1 and itself. If a number has more than two factors, it is composite. The only exception to this rule is if the number is 1 or 0, then it will be neither prime nor composite.
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Please help,quick! *I need an equation!*
Any 1 solved is appreciated please:)
2.If a number decreased by 20, the result is 13. What is the number?
3. This week, a construction company had expenses of $900, which was $50 more than the expenses from last week. What were last week's expenses?
4.Sara's mom split her gift card among her 4 children. If each child received $15, how much was on the gift card originally?
I'd appreciate it if you just solved 1, or all of them. Either way, thank you.
Answers
Answer: for 2 its 33, for 3 its 850, for number 4 its 60
Step-by-step explanation:
1: 20+13=33, so 33-20=13
2: 900-50=850
4: 15x4=60
a student says that the solution of 375=x-28 is 347 explain the students error and find the correct answer
Answers
The given equation is:
375 = x - 28
To solve the equation:
Collect like terms
The -28 crosses the equality sign to the left and becomes 28
The equation then becomes:
375 + 28 = x
x = 403 (correct answer)
The students error is that when he collected like terms, he did not change the "-" sign in -28 to +
He did 375 - 28 = x
x = 347 (wrong)
Two-thirds of the gross of 144 plates was used at the wedding reception. How many plates were not used?
Answers
Answer:
47 ? (might b wrong_?
Step-by-step explanation:
2/3 divided by 144= 0.00462962963, if you round its 47.
Answer:48
Step-by-step explanation: because two third of 144 plates is 96 so you subtract 96 from 144.
If you want to go on a field trip to the Bronx Zoo with your science class in 3 months and the trip is $36.00, how much money do you have to save per month?
Answers
Answer: you would have to save 12 dollars per month
Step-by-step explanation:
36 divided by 3
Can someone help me please
Answers
Answer:
A,D
Step-by-step explanation:
irrational is a number that never repeats and just goes on and on and these 2 numbers are the only ones
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25% of the students in a school are in sixth grade.A. How many sixth graders are there if the school has160 students?B. How many sixth graders are there if the school has28 students?C. If the school has x students, write an expression for the number of sixth graders in terms of x. D. How many students are in the school is 42 of them are sixth graders.
Answers
A.
Multiply the number of students (160) by the percentage that are in sixth grade (25%)
Express the percentage in decimal form = 25/100 = 0.25
160 x 0.25 = 40 students
B. Same process
28 x 0.25 = 7 students
C.
Multiply 0.25 by x
0.25x
D.
0.25x = 42
Solve for x
x =42/0.25
x= 168
What is the total surface area of the rectangular prism in square feet?39.25 ft?© 45 ft?B 78.5 ft?DNot here
Answers
We have that the total surface area of the rectangular prism is:
[tex]\begin{gathered} A_T=\text{ 2(4.5ft }\cdot\text{ 4ft) + 2(4.5 ft }\cdot\text{ 2ft)} \\ =2(18ft^2)+2(9ft^2) \\ =36ft^2+18ft^2 \\ =54ft^2 \end{gathered}[/tex]So the answer is 54 ft^2.
Daniel took 12 index cards and wrote the number 1 through 12 on them 1 number of each card. he then collected the cards, shuffled them, and drew one card from the stack. what is the probability that the number on the card is greater than 0
Answers
We have 12 cards, each one with a different number, so the probability of each card being picked is 1/12.
Since all these cards have numbers that are greater than 0, all the 12 cards are correct options to being picked.
Adding the probability of all 12 cards, we have 12/12, that is, 1 or 100%.
So the probability of picking a card with a number greater than 0 is 1 or 100% (that is, every card has a number greater than 0).
Select the correct answer. Choose the number sentence that illustrates the distributive property of multiplication over addition. 6 × (5 + 8) = (6 × 5) + 8 6 × (5 + 8) = (6 + 5) × (6 + 8) 6 × (5 + 8) = (6 × 5) + (6 × 8)
Answers
The numeric sentence (A) 6 × (5 + 8) = (6 × 5) + 8 represents the distributive property of multiplication.
What is the distributive property of multiplication?The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true. According to the distributive property of multiplication, the first number can be distributed among both of the other numbers and multiplied by each of them independently before adding the results to produce the same outcome as multiplying the first number by the sum.So, the distributive property of multiplication:
a × (b + c) = (a + b) × cSo, in the given options, only option (A) is similar to the distributive property of multiplication.
Therefore, the numeric sentence (A) 6 × (5 + 8) = (6 × 5) + 8 represents the distributive property of multiplication.
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Correct question:
Select the correct answer. Choose the number sentence that illustrates the distributive property of multiplication over addition.
(A) 6 × (5 + 8) = (6 × 5) + 8
(B) 6 × (5 + 8) = (6 + 5) × (6 + 8)
(C) 6 × (5 + 8) = (6 × 5) + (6 × 8)
100% D IN Use the information to answer the question. A store sells jump ropes. Each jump rope costs the same amount. During a sale, the store reduces the price of each jump rope by $1.90. Ma spends $12.78 on 2 jump ropes at the sale price. What was the price of 1 jump rope before the sale? Enter the answer in the box. $
Answers
Answer : $8.29
A shop sells jump ropes
Ma spends $12.78 on 2 jump ropes after removing $1.90 on each jump rope
Since, she spents $12. 78 on two jump ropes
$1.90 is removed from each
For the two jump rope, we have
2 x 1.90 = $3.80
This means $3.80 is removed from the two jump ropes
The total amount spents on the two jump rope before the removal is
$12.780 + $3.80
The total amount = $16.58
The total amount spents on the two jump ropes before the sales is $16.58
Since each jump rope cost the same price
Then
16.58/2 = $8.29
Therefore, the price of each jump rope is $8.29
what is the slope of this line? y= -2x +6
Answers
Answer:
-2
Step-by-step explanation:
Slope is y = mx + b
Your equation is y = -2x + 6, simply pull the 'm' from the equation, that being -2.
Hope that helps.
THESE IS DUE TODAY PLEASE IM IN A RUSH
Answers
Answer:
3/8 gal
Step-by-step explanation:
[tex]5\frac{1}{4} \times \frac{1}{6} = \frac{21}{4} \times \frac{1}{6} = \frac{21}{24} = \frac{3}{8} [/tex]
Janice buys a stuffed animal for $16.20. There was a 8% tax on the toy. What was the cost of the stuffed animal before tax?
Answers
Answer:
$15
Step-by-step explanation:
After tax cost is $16.20
Since 8% tax this is 108% of before tax cost
16.20/1.08 = 15
help
please it’s due tmrw
Answers
Answer: -3
Step-by-step explanation:
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Answers
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
-2(t+-4)=10-2t how many solutions does this equation have.
Answers
the given expression is
-2 (t + (-4) ) = 10 -2t
= -2t + 8 = 10 - 2t
Aaliyah is trying to solve (2 – -3)? lbut is stuck on the first step. Finish solving the equationusing the Complete the Square Method and select the correct value of x below.O2=3 -OD=3+Oc=i - 3O2=334567891011 12NE
Answers
Given:
[tex](x-3)^2=-1[/tex]To solve for x:
Taking square root on both sides we get,
[tex]\begin{gathered} x-3=\sqrt[]{-1} \\ x-3=i \\ x=3+i \end{gathered}[/tex]Hence, the correct option is, B.