To earn $500 in interest at a 4% annual rate, you need to leave $2000 in the account for approximately 6.25 years.
The formula for simple interest is given by:
[tex]\[ I = P \times r \times t \][/tex]
Where:
- I is the interest earned,
- P is the principal amount (initial deposit),
- r is the annual interest rate (expressed as a decimal), and
- t is the time the money is invested or borrowed in years.
In this case, you want to find t, so rearrange the formula to solve for t:
[tex]\[ t = \frac{I}{P \times r} \][/tex]
Given that P = $2000, r = 0.04 (4% as a decimal), and I = $500, plug these values into the formula:
[tex]\[ t = \frac{500}{2000 \times 0.04} \][/tex]
Calculate the result to find out how long you must leave the money in the account to earn $500 in interest.
[tex]\[ t = \frac{500}{2000 \times 0.04} \]\[ t = \frac{500}{80} \]\[ t = 6.25 \][/tex]
Therefore, you must leave the money in the account for approximately 6.25 years to earn $500 in interest at a simple annual rate of 4%.
The seventh grade math classes are going on a field trip. the field trip will cost $7 per student. write an expression to find the cost of the field trip for s students. what is the total cost if 26 students go on the trip?
7s is the expression to find the cost of the field trip for s students and 182 is the total cost if 26 students go on the trip
What is Expression?An expression is combination of variables, numbers and operators.
Given,
The seventh grade math classes are going on a field trip.
the field trip will cost $7 per student.
Given s is number of students.
7s is the expression to find the cost of the field trip for s students.
When number of students are twenty six 26, i.e s=26
Total cost=7×26
seven times of twenty six
182
Hence 7s is the expression to find the cost of the field trip for s students and 182 is the total cost if 26 students go on the trip
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What is the meaning of life? What makes this world so great? Is there something to look forward to in the future?
The office manager ordered145 packs of printer paper. Based on average daily use, she knows that the paper will last 65 days. What graph represents this situation? How many packs of printer paper should the manager expect to have after 25 days?
Select the postulate that is illustrated for the real numbers.
6 + 0 = 6
The commutative postulate for multiplication
Multiplication by one
The addition inverse postulate
Commutative postulate for addition
The distributive postulate
The additive identity postulate
The multiplication inverse
Answer:
The additive identity postulate
Step-by-step explanation:
6 + 0 = 6
Any number added with zero, we get the same number.
That is, a + 0 = a, where "a" is any real number.
Let's take a = 9, we get
9 + 0 = 9
Let's check out a few more examples:
-9 + 0 = -9
2/3 + 0 = 2/3
22 + 0 = 22
You can see any number added with 0, we get the same number.
Here 0 is additive identity, this is called additive identity postulate.
We are given 6 + 0 = 6 which illustrated by "The additive identity postulate."
Therefore, answer is "The additive identity postulate"
What number gives you the same result when multiplied by 6 as it does when 6 is added to it?
Find the total amount in the compound interest account.
$1740 is compounded daily at a rate of 12% for 5 years. Let 1 yearequals=365 days.
=$
Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.
Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answer:
A: r-14x-1=0
B: r(x)=14x+1
C: x= left to right axis
y= up to down axis
domain= x,0
range= r,0
slope= 14
x-intercept= r=0 ==> 0=14x+1 ==>x=(-1/14,0)
r-intercept= x=0 ==> r=14(0)+1= (0,1)
make sure to right it in your own.
If two angles of a triangle are complementary, then the triangle must be
please help me
An irregular polygon is shown below:
The area of the irregular polygon is ____ square units.
Answer:
26
Step-by-step explanation:
well we see that it is at its longest is 9, and the tallest is four
we have two missing sides...
so for the top left on long, it is 5
the full length is 9, and we have a 4 on the top, so we have 5 left, the top right line is 5
the one on the left side is two, because the middle line is a 2, and the full items height is 4.
4x2=8
2x2=4
5+9=14
8+4=12
14+12=26
HELP PLEASE!!!!!
Find the radius of a circle if a central angle of 3π/2 intercepts an arc of 26.4 centimeters.
0.19 cm
3.14 cm
5.6 cm
Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.
5 rad16 rad65 radFind the arc length intercepted by a central angle of 3π/4 radians in a circle whose radius is 18.4 inches.
13.8π15.2π24.5πAnswer:
Find the radius of a circle if a central angle of 3π/2 intercepts an arc of 26.4 centimeters.
Ans: 5.6 cm
Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.
Ans: 5 rad
Find the arc length intercepted by a central angle of 3π/4 radians in a circle whose radius is 18.4 inches.
Ans: 13.8π
Find two numbers whose product is 20 and whose sum is 12
The numbers are 10 and 2 if the product is 20 and whose sum is 12 after making the two equations.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The product of two numbers is 20 and whose sum is 12
Let the numbers are x and y
xy = 20
x + y = 12
y = 12 - x
x(12 - x) = 20
x² - 12x + 20 = 0
After solving the above quadratic equation, we get:
x = 10, 2
y = 2, 10
Thus, the numbers are 10 and 2 if the product is 20 and whose sum is 12 after making the two equations.
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For which value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers
25/8 is the value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
We need to find the value of k will the roots of the equation 2x²-5x+k=0 be real and rational numbers.
A quadratic equation has real roots when the discriminant is positive or zero (not negative).
b²-4ac≥0
b=-5, a=2, c=k
(-5)²-4((2.k)≥0
25-8k≥0
25≥8k
Divide both sides by 8
25/8≥k
k≤25/8
Hence, 25/8 is the value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers
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At one point on the trip, the miles are recorded as 15,121 when the gas tank is 75% full. Use a ratio equation to determine the miles per gallon the sedan averages. Round your answer to the nearest whole number.
The most common size of a sedan tank is 18.5 gallons. So if it is 75% full, it contains 13.875 gallons of gas. If it recorded a mileage of 15,121 miles, mileage per gallon, therefore, is 1090 rounded off to the nearest whole number.
Given: Gas full tank of a sedan – 18.5 gallons
75% full = 13.875 gallons
Mileage using 13.875 gallons of fuel = 15,121 miles
The mileage per gallon computation using the ratio equation:
Ratio is 15121:13.875 or
X/1= 15121/13.875
13.875x = 15121
X = 15121/13.875
X =1089.80 or 1090 miles per gallon (rounded off)
To support a shelf, the diameter of a bolt can be measured anywhere from 0.2 cm less than 1.5 cm to 0.2 greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt
Answer:
The answer is A.
Step-by-step explanation:
We use filled in dots because it can be anything .2 and less or, .2 or more.
What transformation takes
f(x)=15x+3 to g(x)=5x+3 ?
Question 1 options:
a horizontal compression by a factor 1/3
a translation 6 units right
a horizontal stretch by a factor of 3
a translation 6 units down
I don't get how to do this please help
the answer is D
the exponent is 8.869 where the 9 is 9/1000, the 6 is 6/100 and the 8 to the right od the decimal point is 8/10
What number appears 7 times in the multiplication table?
In a multiplication table, each number from 1 to 12 would appear 12 times corresponding to each multiplier. In a table specific for a single number, that number would repeat 12 times.
Explanation:The question is asking about a number that appears 7 times in a multiplication table. In a multiplication table, numbers 1 through 12 are repeated 12 times, once for each multiplier. However, in a multiplication table between 1 and 10, the number 1 appears multiple times as it is a factor for every other number. As an exception, if we have a multiplication table that is specific to a certain number, for example, the number 7, then number 7 would appear 12 times as it is the constant multiplier for each number in the table.
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What three consecutive integers have a sum of 252?
252/3 = 84
84-1 = 83
84+1=85
83 +84 +85 = 252
the numbers are 83, 84, 85
What are the coordinates for the x and y intercepts of the function 4y - 2x = 24?
Solve for PQ 4x+19=2x+32
Stan, a local delivery driver is paid $3.50 per mile driven plus a daily amount of $75. On Monday he is assigned a route that is 30 miles longer. How much is he being paid for that day? Independent and dependent variables?
Ou can draw a quadrilateral with two sets of parallel lines and no right angles.
a. True
b. False
Please help ;-;!!
Math Algebra
(Image)
Eighteen cement squares cover a patio with an area of 40.5m^2. What is the side length of one of the squares
The side length of each of the cement squares is 1.5m. This is calculated by dividing the total area by the number of squares to find the area of each square, and then taking the square root to find the side length.
Explanation:To solve this question, we need to first understand that the total area of the patio equals the sum of the areas of each individual cement square. There are eighteen squares, and the total area is 40.5 square meters. This means that the area of one cement square can be acquired by dividing the total area by the quantity of the squares.
So, the calculation would be 40.5m² / 18, giving us an area of 2.25m² for each square.
Now, since these are squares and all sides of a square are equal, their area is represented by the square of one side length. Therefore, to get the length of one side, we extract the square root of the area.
The calculation is √2.25, which equals 1.5. So, the side length of one of the cement squares is 1.5m.
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The declaration opens with a rational statement of its purpose. in a document with such radical intent, its is not surprising that supporting details often use emotionally laden language.Find at least 5 details in the document that use loaded words to cite factual support . What emotions are revealed in the use of charged language ?
The document uses emotionally loaded language to support its claims. This creates a strong emotional impact on readers and helps persuade them.
Explanation:When analyzing a document, it is important to pay attention to emotionally loaded language used as factual support. Here are five details in the document that use loaded words:
Quoting from interviews with government workers and bystanders who were hiding behind locked doors and had no police protection, appealing to the emotion of fear.Recreating images with vivid descriptions and concrete language of lone officers overwhelmed by crowds of people and beaten, appealing to the emotions of fear and empathy.Using nonaggressive language to address opposing views, showing empathy and attempting to convince others to support the author's position.Adhering to descriptive diction and employing sensory detail, creating a rhetorical effect.Refuting counterclaims and appealing to readers' logic and emotions, demonstrating fairness and advanced skill at persuasion.The use of emotionally charged language reveals the emotions of fear, empathy, conviction, and persuasion in the document.
30 POINTS PLEASE HELP! An investment in a savings account grows to three times the initial value after t years.
If the rate of interest is 5%, compounded continuously, t = (blank) years.
Solve the system:
p-3q=-1
-5p+16q=5
a. (2,1)
b.(3,3)
c. (-1,0)
d.(5,2)
Answer: The correct option is
(c) (-1, 0).
Step-by-step explanation: We are given to solve the following system of equations :
[tex]p-3q=-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-5p+16q=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (i), we have
[tex]p-3q=-1\\\\\Rightarrow p=3q-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of p from equation (iii) in equation (ii), we get
[tex]-5(3q-1)+16q=5\\\\\Rightarrow -15q+5+16q=5\\\\\Rightarrow q=5-5\\\\\Rightarrow q=0.[/tex]
From equation (i), we get
[tex]p=3\times0-1=-1.[/tex]
Thus, the required solution is (p, q) = (-1, 0).
Option (c) is CORRECT.
Help with finding value of x?
Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use: Step 1: Choose a point on the line, such as (2, 5). Step 2: Choose another point on the line, such as (1, 3). Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is . Step 4: Substitute those values into the point-slope form. y – y1 = m(x – x1) y – 3 = (x – 1) Which of Talia’s steps is incorrect? Step 1 is incorrect because it uses a point that is not on the line. Step 2 is incorrect because it uses a point that is not on the line. Step 3 is incorrect because it shows an incorrect ratio for the slope. Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.
Answer:
Step 3 is incorrect because it shows an incorrect ratio for the slope.
Step-by-step explanation:
Find the product.
-mnp(3m - 5n + 7p)
-3m + 5n^2+ 7p^2
3mnp - 5mnp + 7mnp
-3mnp + 5mnp - 7mnp
-3m^2np + 5mn^2p - 7mnp^2