After approximately 16 years, the principal amount of $500 double.
What do we mean by compound interest?Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate multiplied by the number of compound periods multiplied by one. The total initial loan amount is then deducted from the resulting value. The amount of interest added in each compounding period is determined by the interest rate, compounding period, and account balance. The basic formula is as follows: added interest = (interest rate for one period) × (balance at the beginning of the period).So, to find out how many years will a principal of $ 500 double:
Let x be the principal amount.The formula for calculating compound interest is as follows:
A = P(1 + r)^tThe value of r is 0.0462. In the equation, substitute this and x:
2x = x(1 + 0.0462)^t2 = (1.0462)^t (1.0462)^16 = (1.0462)^t t = 16Therefore, after approximately 16 years, the principal amount of $500 double.
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Determine whether each function is an example of exponential growth or decay. Then, find the y -intercept. y=0.0015(10) x
The function y=0.0015(10)ˣ showcases exponential growth.
What do we mean by exponential function?An exponential function is a mathematical function with the formula f (x) = ax.Where an is the function's base constant and x is a variable.The most common exponential-function base is the transcendental number e, or approximately 2.71828.So,
Given function: y=0.0015(10)ˣ
If we put x = 1 as follows:
y = 0.0015×10y = 0.015Then, if we put x = 2 as follows:
>>y = 0.0015×(10)²>>y = 0.0015×100>>y = 0.15Hence, we see that 0.15 > 0.15.
So, when x increases, y also increases.Therefore, the function y=0.0015(10)ˣ showcases exponential growth.
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If triangle is rotated 90° clockwise about the origin what will be thr new coordinates of vertex B?
(-1,-4)
(1,4)
(4,1)
(4,-1)
Answer:
The answer to your question is going to be c
Solve each equation.
4^{3 x}=64
value of x in given exponential equation is = 1
What is exponential equation ?In, mathematics a exponential function or equation is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]a^x[/tex] .
where, a is the base of function
x is the expression
Mathematically, if [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as [tex]a^x = N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.
Some important formulas of exponents :
[tex]a^x . a^y = a^{x+y}[/tex][tex]\frac{a^x}{a^y} = a^{x-y}[/tex][tex]a^x.b^x=(ab)^x[/tex][tex](a^x)^y = a^{xy}[/tex][tex]a^0 =1[/tex]According to given statement,
4^3x = 64
=> 4^3x = 4³
=> 3x = 3
=> x = 1
Thus solution for this equation is x =1.
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Find the inverse of each function. Is the inverse a function? g(x)=3 x³-4
Inverse of the given function F(x) = 3 x³- 4 is F⁻¹(x) = ∛[ ( y + 4 ) / 3 ]
Given is a function of x, F(x) = 3 x³- 4
These question can be solved by following 4 easy steps
Step 1 : Switch the F(x) with the variable y
This implies, F(x) = 3 x³- 4 becomes y = 3 x³- 4
Step 2 : Interchange the variable x and y in the above obtained equation
This implies, from the equation y = 3 x³- 4, we get
x = 3 y³- 4
Step 3 : Solve the new obtained equation for y
This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.
x = 3 y³- 4
=> x + 4 = 3 y³
=> 3 y³ = x + 4
=> y³ = ( x + 4 ) / 3
=> y = ∛( x + 4 ) / 3
Hence we obtain the required equation.
Step 4 : Switch the variable y with F⁻¹(x)
This implies, y = ∛( x + 4 ) / 3 becomes F⁻¹(x) = ∛( x + 4 ) / 3
Therefore, we get the inverse of the given function F(x) = 3 x³- 4 as F⁻¹(x) = ∛( x + 4 ) / 3
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Suppose the function f(x)=0.15 x represents the number of U.S. dollars equivalent to x Chinese yuan and the function g(y)=14.07 y represents the number of Mexican pesos equivalent to y U.S. dollars.
b. Find the value in Mexican pesos of an item that costs 15 Chinese yuan.
The value in Mexican pesos of an item that costs 15 Chinese yuan is 0.474 x.
What is the value in Mexican pesos of an item that costs 15 Chinese yuan?
x yuan to y dollars = f(x)
f(x) = 0.15 x
y dollars to x yuan =
y= 0.15 x
x = [tex]\frac{y}{0.15}[/tex]
y dollars to x pesos =g(y)
g(y) =14.07 y
x pesos to y dollars
x = 14.07 y
y = [tex]\frac{x}{14.07}[/tex]
Substituting the result of second into first,
pesos → dollars → yuan
Lets call this function, h(x) = converts x pesos into y yuan.
h(x) = ( [tex]\frac{x}{14.07}[/tex] )/ 0.15
= 0.474 x
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Solve for x, what is the measure of angle J.
The value of x is 14 and the measure of angle J s 103
How to solve for x and the measure of angle J?The given angles are external angles of parallel lines and a transversal
So, we have:
6x - 7 + 7x + 5 = 180
Evaluate the like terms
13x = 182
Divide both sides by 13
x = 14
Substitute x = 14 in J = 7x + 5
J = 7 x 14 + 5
Evaluate
J = 103
Hence, the value of x is 14 and the measure of angle J s 103
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The values of x and angle J are 14 and 103 degrees respectively.
How to determine the angleIt is important to note that angles on a transversal line are supplementary, that is, they sum up to 180 degrees
Given the angles as;
6x - 77x + 5Equate the angles
6x - 7 + 7x + 5 = 180
collect like terms
6x + 7x = 180 +2
13x = 182
Make 'x' the subject
13x/ 13 = 182/ 13
x = 14
But angle J = 7x + 5 = 7(14) + 5 = 98 + 5 = 103
Thus, the values of x and angle J are 14 and 103 degrees respectively.
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Please help I’m gonna cry
SportCo manufactures basketballs. The fixed expenses are $46,270 and the variable expenses are $6.50 per basketball produced. How many basketballs did they produce if their expenses total $87,870?
SportCo manufactured 6400 basketballs
SportCo manufacturers fixed expenses for producing basketballs = $46,270
Variable expense incurred per basketball produced = $6.50
Total expenses incurred by SportCo for producing basketballs= $87,870
Fixed costs are costs that remain constant regardless of whether more or fewer goods or services are produced or sold.
An expense for the company that varies according to how much is produced or sold is called a variable cost. Depending on a company's production or sales volume, variable costs grow or fall. They climb as production rises and reduce as production declines.
Let x be the number of basketballs produced by the manufacturer SportCo.
Formulating the equation we get:
Fixed cost + Variable cost*Number of basketballs produced = Total expenses incurred by the manufacturer
46270 + 6.5(x) = 87870
6.5(x) = 41600
x = 6400
Therefore, the number of basketballs produced is 6400 by the manufacturer.
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Here is some information about a group of 20 children.
Boys
Girls
3
2
Left-handed
Right-handed
9
6
A child is chosen at random from the group.
a
What is the probability that the chosen child is a girl?
Give your answer as a fraction.
B
What is the probability that the chosen child is a left-handed girl?
Give your answer
The probability that a girl is chosen is 1/10 and the probability that a left-handed girl is chosen is 11/20.
Probability may be defined as the possibility of occurrence of an event. Probability of an event can be 0 or 1 but it can never be negative. If probability is 0 then the event will not occur and if probability is 1 then the event will definitely occur. Probability is given by the formula.
Probability = Favorable outcomes/Total number of outcomes.
Here, total number of outcomes = 20.
Now in the first case we need to find probability of picking a girl so favorable outcome is 2.
Probability of picking a girl = 2/20
Probability of picking a girl = 1/10
In the second case we need to find probability of picking a left-handed girl, so the favorable outcomes are 2 + 9 = 11 as total number of girls are 2 and total number of left-handed people are 9.
Probability of picking left-handed girl = 9 + 2/20
Probability of picking left-handed girl = 11/20
Thus, probability that a girl is chosen is 1/10 and the probability that a left-handed girl is chosen is 11/20.
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write two ratios that are equvilent to 3:11
Answer:
6:22, 9:33
Step-by-step explanation:
When writing equivalent ratios, you use two of the numbers from the original ratio and multiply them evenly to get an equivalent ratio.
[tex]\mathrm{p:q~or~\frac{p}{q} = \frac{x(p)}{x(q)}}\\\mathrm{\frac{6 \times 2}{11 \times 2} = 6:22}\\\mathrm{\frac{6 \times 3}{11 \times 3} = 9:33}[/tex]
Answer:
6:22 and 9:33
Step-by-step explanation:
Answer: 6:22 and 9:33
Think of the ratio like a fraction, one way to find an equivalent ratio is to simplify the current ratio. But in this case, we are unable because we can divide 3 by 3 to get one, but not 11 by 3.
3 divided by 3 = 1
11 divided by 3 = does not evenly divide
Another way is to multiply both numbers by the same number.
3 times 2 = 6
11 times 2 = 22
And we can just keep doing the same with different numbers.
3 times 3 = 9
11 times 3 = 33
800/____ =200. Mathematical questions.
Answer:
X = 4
Step-by-step explanation:
harvey porter is a wizard. he waved his wand and made a grain of sand that had a diameter of 0.00002 meters grow to a diameter 0.006meters. approximately how many times as large is the diameter of the grain of sand now as it was before harvey porter waved his wand
Answer:
Step-by-step explanation:
rgvm
Answer:the answer is A haha
Step-by-step explanation:
i just did this kahn academy lesson-
Solve each inequality using a table.
(Hint: For more accurate results, set ΔTbl=0.001. )
2(4) x⁺³ ≤ 8
After solving the given inequality the answer is x∈(-∞, 1].
What do we mean by inequality?An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.To solve the inequality:
Given: 2(4)x⁺³≤8
Then,
[tex]\begin{aligned}&2 \cdot 4 x^3 \leq 8\\&8 x^3 \leq 8\\&8 x^3+(-8) \leq 8+(-8)\\&8 x^3-8 \leq 8-8\\&8 x^3-8 \leq 0\\&2^3 \cdot x^3-2^3 \leq 0\\&2^3\left(\frac{2^3 \cdot x^3}{2^3}-\frac{2^3}{2^3}\right) \leq 0\\&8\left(x^3-1\right) \leq 0\\&x^3-1 \leq 0\\&x^3-1^3 \leq 0\end{aligned}[/tex]
Then,
[tex]\begin{aligned}&(x-1)\left(x^2+x+1\right) \leq 0\\&\left\{\begin{array}{l}x-1=0 \\x^2+x+1=0\end{array}\right.\\&\left\{\begin{array}{l}(x-1)+1=1 \\x_1=\frac{-1+\sqrt{1-4}}{2} \\x_2=\frac{-1-\sqrt{1-4}}{2}\end{array}\right.\\&\left\{\begin{array}{l}x-1+1=1 \\x_1=\frac{-1+\sqrt{-3}}{2} \\x_2=\frac{-1-\sqrt{-3}}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=\frac{-1+\sqrt{3} \cdot \sqrt{-1}}{2} \\x_2=\frac{-1-\sqrt{3} \cdot \sqrt{-1}}{2}\end{array}\right.\end{aligned}[/tex]
So,
[tex]\begin{aligned}&\left\{\begin{array}{l}x=1 \\x_1=\frac{-1+\sqrt{3} \cdot i}{2} \\x_2=\frac{-1-\sqrt{3} \cdot i}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=-\frac{1}{2}+\frac{\sqrt{3}}{2} i \\x_2=-\frac{1+\sqrt{3} \cdot i}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=-\frac{1}{2}+\frac{\sqrt{3}}{2} i \\x_2=-\frac{1}{2}-\frac{\sqrt{3}}{2} i\end{array}\right.\\&\left\{\begin{array}{l}x \leq 1 \\x \geq 1\end{array}\right.\end{aligned}[/tex]
So, finally, it gives:
[tex]2 \cdot 4 x^3 \leq 8\\2 \cdot 4 \cdot 0^3 \leq 8\\\begin{aligned}&x \leq 1 \\&x \in(-\infty, 1]\end{aligned}[/tex]
Therefore, after solving the given inequality the answer is x∈(-∞, 1].
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The length of a bacterial cell is about 4 x 10−6 m, and the length of an amoeba cell is about 2.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
The bacterial cell length is 62.5 times smaller than the amoeba cell.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The length of a bacterial cell is about 4 x 10⁻⁶ m, and the length of an amoeba cell is about 2.5 x 10⁻⁴ m
Hence:
Ratio of Amoeba length to bacteria length = (2.5 x 10⁻⁴ m) / (4 x 10⁻⁶ m) = 62.5
The bacterial cell length is 62.5 times smaller than the amoeba cell.
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Answer:
the answer in scientific notation with the significant amount of digits is 6.25 x 10^2.
Step-by-step explanation:
you have to solve the equation and divide 0.00025 by 0.00004
you will get 6.25
and if you divide 2.5 by 4 you get 0.625 you have to move the decimal over to the right by 2 so you get the exponent of 2
The answer in scientific notation with the significant amount of digits is 6.25 x 10^2
Valeria has a points card for a movie theater.
She receives 80 rewards points just for signing up.
She earns 7.5 points for each visit to the movie theater.
She needs 185 points for a free movie ticket.
Write and solve an equation which can be used to determine v, the number of visits
Valeria must make to earn a free movie ticket.
According to the linear equation , the number of visits Valeria must make to earn a free movie ticket is 14.
According to the statement
We have to find that the linear equation.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
She receives 80 rewards points just for signing up.She earns 7.5 points for each visit to the movie theater.She needs 185 points for a free movie ticket.
then
The linear equation becomes:
The equation that can be used to represent the explanation given in the question is : 185 = 80 + 7.5x
Then
Combine similar terms
185 = 80 + 7.5x
185 -80 = 7.5x
105 = 7.5x
x = 105 /7.5
x = 14.
So, According to the linear equation , the number of visits Valeria must make to earn a free movie ticket is 14.
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Give me a entire guide for 3.82 x 0.63 (my teacher wants me to show work on paper so I need every little step)
The product of 3.82 x 0.63 is 2.4066.
What is multiplication?One of the four fundamental mathematical operations, along with addition, subtraction, and division .In mathematics refers to the continual addition of sets of identical size Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication is called as multiplication.
Given that,
The product of
3.82
x 0.63
1146
2292 x
000 x x
2.4066
Therefore, the product of 3.82 x 0.63 is 2.4066.
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Use the properties of logarithms to evaluate each expression.
log₂4- log₂16
Using the properties of logarithm the value of the expression is [tex]log_{2}4 - log_{2}16 = -2[/tex]
We have been given two logarithm terms that is the first term is [tex]log_{2}4[/tex] and second term is [tex]log_{2}16[/tex].
The propertied of logarithm that we are going to use are
[tex]log a^{m} = m * log a[/tex] and [tex]log_{a} a = 1[/tex]
First we will find the value of the two terms and operate the above mentioned properties of logarithm to obtained the values of the logarithm.
Thus,
[tex]log_{2}4 = log_{2}2^{2} \\ = 2* log_{2}2\\ = 2*1\\ = 2[/tex]
Similarly,
[tex]log_{2}16 = log_{2}2^{4} \\ = 4* log_{2}2\\ = 4*1\\ = 4[/tex]
Now subtracting both the terms by substituting its respective values which we have calculated above, we get
[tex]log_{2}4 - log_{2}16 = 2 - 4 = -2[/tex]
Thus the value of the expression is [tex]log_{2}4 - log_{2}16 = -2[/tex]
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1. Which square-large, medium, or small-covers more of the plane? Explain your reasoning.
The large square covers more
(See attachment below)
Explanation- The large square has the highest dimension and by extension, it has the highest area.
This means that, less large squares will be needed to cover more areas compared to other sizes of the squares
Area of the square =(side)².
square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle and a special kind of parallelogram.
By observation,
9 small squares are equivalent to one large square, implying that the 5 large squares are giving us 45 small squares.
4 small squares can fit into one medium square, implying that the 10 medium squares are giving us 40 small squares.
There are only 10 small squares.
Hence, the large square covers more of the plane
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Assessment
Practice
11. On a recent homework assignment, Eli needed to solve the equation
g² = 49. He incorrectly wrote g = -7.
PART A
What is the correct solution?
PART B
Critique Reasoning What error did Eli likely make?
He did not take the square root of 49 correctly since (-7)2 49.
® He did not solve the equation completely since there is a positive
solution as well.
He did not solve the equation completely since there are two positive solutions.
He did not solve the equation completely since there are two
negative solutions.
Answer:
Step-by-step explanation:
Answer:
what is the correct solution
Step-by-step explanation:
Each year a certain amount of money is deposited in an account which pays an annual interest rate of so that at the end of each year the balance in the account is multiplied by a growth factor of . $500 is deposited at the start of the first year, an additional $200 is deposited at the start of the next year, and $600 at the start of the following year. Write an expression for the value of the account at the end of three years in terms of the growth factor . What is the amount (to the nearest cent) in the account at the end of three years if the interest rate is 2%?
The answer to the question is 1350.68
so we are given $500 is deposited at the start of the first year and the interest rate is 2 percent
so the interest =2/100×500 =$10
total amount =$510
we are given that $200 is deposited at the start of the next year, now total amount =$710
interest rate is 2 percent
so the interest =2/100×710 =$14.2
total amount =$724.2
we are given that $600 is deposited at the start of the following year now total amount =1324.2
interest rate is 2 percent
so the interest =2/100×1324.2 =$14.2
total amount =$1350.68
Hence the answer is $1350.68
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Suppose you pick a marble from a box containing five red and seven blue marbles. You record the color and put the marble back in the box. What is the probability of getting a red marble both times if you do this twice?.
Answer:The probability would be 5 out of 12.
a cyclist is traveling north down the road at 23 ft per second as he approaches his destination 20 minutes (minutes need to be changed to seconds) later he comes to a complete stop. what is his acceleration?
Please help
--------------------------
Answer:
Step-by-step explanation:
Answer:
y = 8.40x
y = the total amount that he earned and x = the number of hours that he worked.
Step-by-step explanation:
Which statement about the function y = −14x − 2 is true? A. As the value of x increases, the value of y increases. B. As the value of x decreases, the value of y stays the same. C. As the value of x increases, the value of y decreases. D. As the value of x decreases, the value of y decreases.
The statement about the function y = −14x − 2 that is true is that A. As the value of x increases, the value of y increases. B.
How to illustrate the information?It should be noted that the information is to get the dtatement about the function y = −14x − 2 that is true.
y = −14x − 2
Let's use x = 1
y = −14x − 2
y = -14(1) - 2 = -16
When x = 2, y = −14x − 2.
y = -14(2) - 2 = -40
It shows that as x increases, y will also increase.
Therefore, the correct option is A.
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Rick paddles a kayak 20 miles upstream in 4 hours. the return trip downstream takes him 2.5 hours. what is the rate that rick paddles in still water? what is the rate of the current
Rick paddles in still water at a rate of 6.5 mph. The rate of the current is 1.5 mph.
The rate at which an object moves from one point to another is also called speed. It can be measured by dividing the distance over time.
rate = distance/time
Let x = rate at which Rick paddles
c = rate of the current
If Rick paddles a kayak 20 miles upstream in 4 hours, and going upstream means the current is against your direction, then the equation for the travel is:
x - c = 20 miles/4 hours
x - c = 5 (equation 1)
If the return trip downstream takes him 2.5 hours, and downstream means that the current is going the same direction as you are, then the equation for the downstream travel is:
x + c = 20 miles/2.5 hours
x + c = 8 (equation 2)
Using elimination method, solve the two equations.
x + c = 8
x - c = 5
2x = 13
x = 6.5
rate at which Rick paddles = 6.5 mph
Substitute x in equation 1 and solve for c.
x - c = 5 (equation 1)
6.5 - c = 5
c = 6.5 - 5
c = 1.5
rate of the current = 1.5 mph
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Simplify each number. -(-27)⁻⁴/₃
The result of simplifying the expression -(-27)⁻⁴/₃ using the exponent rules is 1/81
To solve this exercise we have to resolve algebraic operations following the exponent rules.
-(-27)⁻⁴/₃ =
(27)⁻⁴/₃
As we have a negative exponent, you have to pass the exponent to the denominator:
1/(27)⁴/₃
As we have a fractional exponent, you must convert the exponent to root:
1/[tex]\sqrt[3]{}[/tex](27)⁴
1/[tex]\sqrt[3]{}[/tex](531441)
1/81
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Please answer this I have had this assignment open for 4 days, 9 hours, 30 minutes, and 25 seconds
The value of f(0) = 2 and f(-2) = -2 given the equation that we have in this image.
How to solve for the functionThe function that we have here is given as
[tex]\frac{2x-2}{(x + 1)(x-1)}[/tex]
We have to find the value of f(-2)
= 2(-2) - 2 / (-2 + 1) (-2 - 1)
= - 4 - 2 / -1(-3)
= -6 / 3
= -2
Hence f(-2) = -2
Next we have to find f(0)
2(0) - 2 / (0 + 1) (0 - 1)
= -2 / 1 * -1
= -2 / -1
= 2
Hence we can say that the value of f(0) = 2 and f(-2) = -2 given the equation that we have in this image.
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Will mark brainiest help hurry pls
Answer:
d=-2/3f+7
Step-by-step explanation:
A diver jumps from a cliff that is 48 ½ feet above the surface of the water. She stops descending
12 ½ feet under the water. What was the total distance of her jump?
Answer:
61
Step-by-step explanation:
1. 4 times the sum of x and 2
4(x+2)
hope this helps