Odette deposited $3,624.40 into a savings account with an interest rate of 2.1% compounded annual. About how long will it take for the account to be worth $7,000?
A. 31 years, 9 months
B. 30 years, 9 months
C. 28 years, 4 months
7000 = 3624*(1+0.21)^x
7000 = 3624 *1.021^x
7000/3624 = 1.021^x
875/453 = 1.021^x
xlog(1.021 = log(875/453
x = 31.677
31 years 9 months
Answer:
Option A is the answer.
Step-by-step explanation:
p = 3624.40
r = 2.1% or 0.021
n = 1
t = ?
A = 7000
Compound interest formula is :
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]
Substituting the values in formula:
[tex]7000=3624.40(1+\frac{0.021}{1})^{t}[/tex]
=> [tex]\frac{7000}{3624.40} =(1.021)^{t}[/tex]
=> [tex]1.93135=(1.021)^{t}[/tex]
[tex]t=\frac{log1.93135}{log1.021}[/tex]
=> t = 31.670 years.
Closest to option A.
Evaluate the function f(x)=−4x−3 f(x)=−4x−3 for x=−6x=−6.
In a class of 10, there are 2 students who forgot their lunch.
If the teacher chooses 2 students, what is the probability that both of them forgot their lunch?
Answer:2/10
Step-by-step explanation: 10 students, 2 of them forgot their lunch. So 2/10 of the students will be chosen by the teacher
Simplify 7t · s · 3rt.
10rst
10rst2
21rst2
An expression is defined as a set of numbers, variables, and mathematical operations. The given expression 7t · s · 3rt, when simplified will be equal to 21rst². The correct option is C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression 7t · s · 3rt can be written as,
7t · s · 3rt
= 7 × t × s × 3 × r × t
= 21rst²
Hence, the given expression 7t · s · 3rt, when simplified will be equal to 21rst².
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The length of a rectangle is four times its width. If the perimeter is at most 100 centimeters, what is the greatest possible value for the width? Question 17 options:
Important state labor laws and safety regulations came about as a result of the 1911 __________.
a. labor relations act
b. triangle shirtwaist factory fire
c. homestead strike
d. massachusetts child safety campaign
Answer:
Option B is correct.
Step-by-step explanation:
Important state labor laws and safety regulations came about as a result of the 1911 - Triangle shirtwaist factory fire
The Triangle shirtwaist factory fire was one of the worst industrial disasters during that time. Many people died due to a fire breakout in the factory. They could not escape the building and died due to smoke inhalation or burns.
After this incident, a Committee on Public Safety was formed that led to a legislation requiring labor laws and improved factory safety standards.
I have a box of nickels and dimes. When I counted the money, I was surprised to see that I have exactly $20. Then it occurred to me that, if my nickels were dimes and my dimes were quarters, I would have $46.25. How many dimes and nickels are in the box?
There are 150 nickels and 125 dimes in the box.
Let x = the number of nickels in the box
Let y = the number of dimes in the box
Firstly, we have to convert value of nickels and dimes into cents.
Value of 1 nickel = 5 cents
Value of 1 dime = 10 cents
Value of 1 dollar = 100 cents
Thus, the equation (1) (in cents) can be written as:
x + 2y = 400 Equation (1)
If my nickels were dimes and dimes were quarters:
A quarter is worth 25 cents.
Thus, the equation (2) (in cents) can be written as:
5x+10y =2000
5(x+2y)= 2000
x+2y = 2000/5
2x + 5y = 925 Equation (2)
Multiply Equation (1) by "2", we get:
10x +25y= 4625
5(2x+5y)=4625
2x+5y=4625/5
2x + 4y = 800 Equation (1)
Subtraction Equation (1) from Equation (2):
2x +5y-2x -4y=925-800
y= 125
2x + 5y = 925
2x + 5 × 125 = 925
2x + 625 = 925
2x = 925 - 625
2x = 300
x = 150
There are 150 nickels and 125 dimes in the box.
Here, we can check it by putting the value of x and y in Equation (1):
5x + 10y = 2000
5× 150 + 10 × 125 = 2000
750 + 1250 = 2000
2000 = 2000
There are 150 nickels and 125 dimes in the box.
PLESEEE HELP I WILL GIVE THE BRAINLIEST TO THE BEST ANWSERS
Which word sentence represents the equation?
6(x + 3) = 42
A)The sum of 3 and six times some number is 42.
B)Three plus 3 times some number is 42.
C)Six times some number plus 3 is 42.
D)Six times the sum of a number and 3 is 42.
What is the solution set for 3x + 2 = 14, given the replacement set {1, 2, 3, 4} ?
A)x = 1B)x = 2C)x = 3D)x = 4Solve the inequality
7x ≥ -7
a. x ≤ -1
b. x > -14
c. x ≥ -1
d. x ≥ 14
Answer:
A: x ≥ -1
its rightc bc
Rob cuts 15-foot wire into 8 equal pieces. About how long is each piece
vertical angles are opposite angles with the same vertex
true or false
Reuben drove 576 miles in 8 hours.
At the same rate, how long would it take him to drive 936 miles?
Reuben's driving rate is 72 miles per hour. At this same rate, it would take him 13 hours to drive 936 miles.
To determine how long it would take Reuben to drive 936 miles at the same rate, we first need to find his driving rate. Reuben drove 576 miles in 8 hours. To find his rate, we divide the distance by the time:
Rate = Distance / Time
Rate = 576 miles / 8 hours = 72 miles/hour
Next, we use this rate to find out how long it will take him to drive 936 miles:
Time = Distance / Rate
Time = 936 miles / 72 miles/hour = 13 hours
Thus, it would take Reuben 13 hours to drive 936 miles at the same rate.
What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?
find the slope of the line given:
y = mx+b
y = -3x/2 -7/2
slope = -3/2
the slope of the perpendicular line is the negative reciprocal
so answer is 2/3
What is the value of cos 45 degrees?
(answers in picture)
List an example of two events that are independent. (b) list an example of two events that are dependent. (a) list an example of two events that are independent. choose the correct answer below.
a. a father having hazel eyes and a daughter having hazel eyes
b. selecting a queen from a standard deck, not replacing it, and then selecting a queen from the deck
c. rolling a die twice
d. not putting money in a parking meter and getting a parking ticket (b) list an example of two events that are dependent. choose the correct answer below.
a. tossing a coin and getting a head, and then rolling a six-sided die and obtaining a 6
b. selecting a ball numbered 1 through 12 from a bin, replacing it, and then selecting a second numbered ball from the bin
c. rolling a die twice
d. drawing one card from a standard deck, not replacing it, and then selecting another card
When two events are dependent, this means that one event cannot occur without the other, or simply put the two events are connected to each other in one way or the other.
When two events are independent, this means that the two events can occur separately, with one event having no effect on the occurrence of the other.
Therefore the dependent and independent events are as follows:
Independent event:
c. rolling a die twice
The outcome of the first die does not affect the outcome of the second die, hence independent.
Dependent event:
d. drawing one card from a standard deck, not replacing it, and then selecting another card
By the act of not replacing the drawn card, we are changing the probability of selecting another card, hence dependent.
Eric and his work crew have 50 trees o plant. In 8 hours today, they planted 40 trees. If the work at the same rate tomorrow, how long will it take to finish planting the trees?
State a true conclusion. 1) If a ● b = 0, then a = 0 or b = 0 2) 3x = 0
Answer:
x=0
Step-by-step explanation:
Proposition 1) If a ● b = 0, then a = 0 or b = 0
Proposition 2) 3x = 0
=> 3 = 0 or x = 0
Given that 3 ≠ 0, x must be equal to 0.
Conclusion: x = 0
For all real numbers a and b if a not equal to 0 and b not equal to 0 then a^2 + b^2 does not equal (a+b)^2
Use the graph shown to fill in the blank.
When x = -3, then y = a0.
What’s the reciprocal of 7/2a
2a/7
-2a/7
7/2a
-7/2a
The expression 3x² represents
Final answer:
The expression 3x² signifies a quadratically powered variable (x) that is multiplied by the coefficient 3, commonly seen in algebraic equations.
Explanation:
The expression 3x² represents a mathematical formula where the variable x is squared (multiplied by itself) and then multiplied by 3. The squaring of a variable is a fundamental concept in algebra that symbolizes a number raised to the power of 2.
The coefficient 3 in this case indicates that the square of x is being tripled. Therefore, if x is 2, x² would be 4, and 3x² would be 12. This type of expression is essential in solving quadratic equations and appears frequently in various mathematical contexts.
Which term describes gross pay that is calculated based on the number of hours an employee has worked?
Answer: Hourly wage
Step-by-step explanation:
The term "hourly wage" describes the gross pay that is calculated based on the number of hours an employee has worked.
The hourly wage is the amount of money that is earned by a employee for every hour worked or it is the amount of money paid by employer for every hour worked.
Here, the gross pay is calculated by multiplying the hourly wage to the number of hours worked.
Is 81 a multiple of 3 explain why
To take a taxi , it cost $3.00 plus an additional $2.00 mile traveled. you spent exactly $20 on a taxi, which includes the $1tip you left. how many miles did you travel?
A triangle has base 6 cm and area 42 cm^2 what is the height of the triangle
The height of the triangle is 14 cm.
Explanation:To find the height of the triangle, we can use the formula for the area of a triangle: Area = 1/2 * base * height. In this case, the base is 6 cm and the area is 42 cm^2. By rearranging the formula, we can solve for the height: Height = 2 * Area / Base. Plugging in the values, we get Height = 2 * 42 cm^2 / 6 cm = 14 cm.
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Calc Question :fuel cost Please help me.
What theorem or postulate can prove a triangle to be an isosceles?
Final answer:
The Converse of the Base Angles Theorem states that if two angles of a triangle are congruent, then the triangle is isosceles.
Explanation:
In geometry, the theorem that can prove a triangle to be isosceles is the Converse of the Base Angles Theorem. It states that if two angles of a triangle are congruent, then the triangle is isosceles. In other words, if the two base angles of a triangle are equal, then the triangle is isosceles. For example, if angles A and B in triangle ABC are congruent (angle A = angle B), then triangle ABC is isosceles.
A shop has a sale that offers 20% off all price. On the final day they reduce all the sale prices by 25%. Linz buys a radio on the final day. Work out the overall percentage reduction on he price of the radio.
To calculate the overall percentage reduction on the price of the radio, we need to calculate the final price after both discounts. The first discount of 20% off reduces the price by 20/100 = 0.2. The second discount of 25% off reduces the price by 25/100 = 0.25. The overall percentage reduction is 40%.
Explanation:To find the overall percentage reduction on the price of the radio, we need to calculate the final price after both discounts. The first discount of 20% off reduces the price by 20/100 = 0.2. So, the price after the first discount is 1 - 0.2 = 0.8 times the original price. The second discount of 25% off reduces the price by 25/100 = 0.25. So, the final price after both discounts is 0.8 * (1 - 0.25) = 0.8 * 0.75 = 0.6 times the original price.
To calculate the overall percentage reduction, we can subtract the final price from the original price, divide by the original price, and multiply by 100. The overall percentage reduction is ((1 - 0.6) / 1) * 100 = 40%.
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What is the probability of throwing a number greater than 4 when rolling a number cube that has sides labeled 1, 2, 3, 4, 5, 6?
The probability of rolling a number greater than 4 on a six-sided die is 1/3 or 0.33 or 33%. This is obtained by dividing the number of favourable outcomes (2, i.e., 5 and 6) by the total number of outcomes (6).
Explanation:The subject of the question is the probability in mathematics, specifically related to an experiment involving rolling a six-sided die. To answer your question, a six-sided die has numbers from 1 to 6. But you are asking about throwing a number greater than 4. There are only two outcomes that are greater than 4, the numbers 5 and 6. Therefore, the possible favorable outcomes are 2.
The total outcomes (since it's a six-sided standard die) are 6. Probability is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, it will be 2/6 = 1/3 which is approximately 0.33 or 33%.
This means, if you roll the die, on an average, you can expect to roll a number greater than 4 about 33 times if you roll it 100 times.
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Does a negative minus a negative equal positive