Answer:
the answer to that question is 3
You put $ 1500 into an account that pays 7% annual interest compounded continuously. How long will it be before you have $2000 in your account?
The answers to all the subparts are:
Equation formed: A= 1500e(.07)(4)Money in the account after 4 years: $1984.69Time until there is $5000 in the account: 30 yearsWhat is compounding?Compound interest is the contribution of interest to the principal sum of a loan or deposit or interest on interest plus interest. It is the result of reinvesting interest, or adding it to the loaned capital, rather than paying it out or requiring payment from the borrower, so that interest is earned on the principal sum plus previously accumulated interest in the following period. In finance and economics, compound interest is the norm.Compound interest differs from simple interest in that previously accrued interest is not added to the principal amount of the current period, resulting in no compounding.So,
Given:
A = pertA= future amountp = principal investment = 1500e = Euler's numberr = interest rate = .07t = time in years = 4(1) An equation to model the situation:
Then, according to given information, A= 1500e(.07)(4).(2) Money in the account after 4 years:
A= 1500e.28 = $1984.69(3) To find how will it be until there is $5000 in the account:
5000 = 1500e.04te.04t = 5000/1500e.04t = 10/3ln(e.04t) = ln(10/3).04t = ln(10/3)t = ln(10/3)/.04t = 30 yearsTherefore, the answers to all the subparts are:
Equation formed: A= 1500e(.07)(4)Money in the account after 4 years: $1984.69Time until there is $5000 in the account: 30 yearsKnow more about compounding here:
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The complete question is given below;
$1500 is put into an account earning 7% annual interest, compounded continuously.
1. Write an equation to model the situation
2. How much money will be in the account after 4 years?
3. How will it be until there is $5000 in the account?
What’s 7+5p+4r+6s I need to fast
Answer:
7+5p+4r+6s
Step-by-step explanation:
the same thing cause their variables are different, you can't add if the variables are different
variables are those letters that are at the end of the coefficient
Which is the more economical purchase: an
18-ounce box of corn flakes for $3. 49 or a 24-ounce box of
corn flakes for $3. 89?
The more economical purchase is the 24-ounce box of cornflakes for $3.89.
The more economical purchase can be determined by calculating the unit rate for each box of cornflakes.
The unit rate can be calculated by the division of the total ounce of the box by the price of the box
Hence the unit rate for the 18-ounce box is calculated as,
unit rate of 18-ounce box = 18 / 3.49
unit rate of 18-ounce box = 5.16 ounce/$
The unit rate for the 24-ounce box is calculated as,
unit rate of 24-ounce box = 24 / 3.89
unit rate of 24-ounce box = 6.17 ounce/$
As the rate of 6.17 ounce/$ is more economical than 5.16 ounce/$, the more economical purchase is the 24-ounce box of corn flakes.
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Tanya is training a turtle for a turtle race. For every of an hour that the turtle is crawling, he can travel of a mile. At what unit rate is the turtle crawling answer in fractions
The unit rate for the turtle crawling is 1 mile per hour
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Unit rate is the ratio of two different units, and also having a denominator of one.
For every of an hour that the turtle is crawling, he can travel of a mile. Hence:
Unit rate of crawling = 1 mile / 1 hour = 1 mile per hour
The unit rate for the turtle crawling is 1 mile per hour
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Evaluate. Write your answer as a mixed number.
2 2/3 × 3 1/4=
(They are fractions with whole numbers)
The value of the fractional expression as a mixed numbers is: 2⅔ × 3¼ = 8⅔.
What are Mixed Numbers?A mixed number is a combination of a whole number together with a fraction. It can also be referred to as mixed fractions.
How to Evaluate Fractions?Given the fractional expression, 2⅔ × 3¼, evaluate the fractions as explained below:
Convert the mixed numbers to improper fractions
2⅔ × 3¼ = 8/3 × 13/4
2⅔ × 3¼ = 2/3 × 13/1
Multiply the denominators together and the numerators together
2⅔ × 3¼ = 26/3
Divide
2⅔ × 3¼ = 8⅔
Therefore, the value of the fractional expression as a mixed numbers is: 2⅔ × 3¼ = 8⅔.
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Given that 1 inch = 2.54 cm, how
many
centimeters are there in 6 feet? Answers may
be written using decimal form and should be
rounded to the nearest hundredth when
necessary.
Answer:
There are 182.88 cm in 6 feet, given that 1 inch = 2.54 cm.
Step-by-step explanation:
Given that 1 inch = 2.54 cm, how many centimeters are there in 6 feet?
12 inches = 1 foot
We have 6 feet, so:
6 feet x 12 inches = 72 inches
If 1 inch is 2.54 cm, multiply by the number of inches by 2.54 to get the number of cm.
2.54 x 72 = 182.88
There are 182.88 cm in 6 feet, given that 1 inch = 2.54 cm.
For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. The formula for converting from Celsius to Fahrenheit temperatures is F=\frac{9}{5} C+32 .
a. Find the inverse of the formula. Is the inverse a function?
A function is one-to-one if each horizontal line crosses the function's graph no more than once. The inverse function of F = 9/5C +32 is a one to one function.
What is meant by one-to-one function?A function is one-to-one if each horizontal line crosses the function's graph no more than once.
If the graph of a function f is known, determining whether the function is 1 -to-1 is simple. Make use of the Horizontal Line Test. If no horizontal line intersects the graph of the function f more than once, the function is one-to-one.
If f(x) = f(y)
⇒ x = y, then f is one to one.
Let the Fahrenheit temperatures be F = 9/5C +32
Subtract 32 from both sides of the above equation
F-32 = 9/5C
Multiply both sides by 5:
5(F-32) = 9C
Divide both sides by 9:
C = 5/9 (F-32)
For 27°
C = 5/9 (27-32)
simplifying the above equation, we get
⇒ C = 5/9 (-5)
⇒ C = -25/9
The value of C = -25/9.
= -2.78C°
⇒ 2dp
Yes, the inverse is a one to one function.
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A classroom of students can be divided into two, three, and five groups, with no students left over. How many students are likely in the class?
The number of students that are likely to be in the class will be 30 students.
How to calculate the value?From the information, it was stated that the classroom of students can be divided into two, three, and five groups, with no students left over.
Therefore, the number of students that are likely to be in the class will be:
= 2 × 3 × 5
= 30
Therefore, the number of students that are likely to be in the class will be 30 students.
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Which inequality is represented by the graph?
y≥−3/2x−2
y<−3/2x−2
y>−3/2x−2
y≤−3/2x−2
Answer:
y≥−3/2x−2
Step-by-step explanation:
the inequality is represented by the graph is y≥−3/2x−2
help!!!!
What is the expanded form of the number 34.576?
A: An expression that reads three times ten, plus four times one plus five times one-tenth, plus seven times one-hundredth, plus six times one-thousandth
B: An expression that reads three times ten, plus five times one, plus four times one-tenth, plus six times one-hundredth, plus seven times one-thousandth
C: An expression that reads four times ten, plus three times one, plus seven times one-tenth, plus five times one-hundredth, plus six times one-thousandth
D: An expression that reads five times ten, plus four times one, plus three times one-tenth, plus seven times one-hundredth, plus six times one-thousandth
The expanded form of the number 34.576 is A: An expression that reads three times ten, plus four times one plus five times one-tenth, plus seven times one-hundredth, plus six times one-thousandth.
How to illustrate the information?It should be noted that the correct form of the expression will be:
= (3 × 10) + (4 × 1) + (5 × 1/10) + (7 × 1/100) + (6 × 1/1000)
= 34.576
Therefore, the expanded form of the number 34.576 is an expression that reads three times ten, plus four times one plus five times one-tenth, plus seven times one-hundredth, plus six times one-thousandth.
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Find the inverse of each function. Is the inverse a function?
f(x)=x³
To have an inverse function, a function must be one-to-one.
[tex]$$f^{-1[/tex](x) = x³ is the inverse of f(x) = x³
What is meant by inverse function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by [tex]$$f^{-1[/tex] or F-1 if the function is denoted by ' f ' or ' F '.
To find the inverse, interchange the variables and solve for y.
f−1(x)=3√x
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
Replace y with [tex]$$f^{-1[/tex](x) then we get
[tex]$$f^{-1[/tex](x) = 3√x
[tex]$$f^{-1[/tex](x) = x³ is the inverse of f(x) = x³
The result of a mathematical operation, such as addition and subtraction, multiplication and division, is reversed. These are referred to as inverse operations. Typically, the inverse of a number is its reciprocal, or x - 1 = 1/x. A number and its reciprocal (inverse) product yield one.
To have an inverse function, a function must be one-to-one.
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Which function has an inverse that is also a function?
{(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}
{(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)}
{(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)}
{(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}
The function has an inverse that is also a function would be {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} so correct option will be (A).
What is a function?A certain kind of relationship called a function binds inputs to essentially one output. In other words, the function is a relationship between variables and the nature of the relationship.
We have been given that a function is only a function such that there is a unique value of y corresponding to x.
An inverse function is only be a function if the function which is going to be inverse is a function.
The inverse of a function: (x, y) → (y, x)
1. {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}
It has unique y- values, the inverse won't repeat x-values, so the inverse is also a function.
Hence, The function has an inverse that is also a function would be {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} so correct option will be (A).
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Izzy runs on the school track team. She runs 4 miles in hour.
3
What is Izzy's speed in miles per hour?
Izzy's speed in miles per hour is ?
10
69
9
10
3
1
15
9
10
Answer: Izzy's speed is [tex]6\frac{9}{10}[/tex] mph.
Step-by-step explanation: You have to divide the number of miles by the number of hours.
[tex]4\frac{3}{5} / \frac{2}{3}\\[/tex]
Convert the mixed fraction [tex]4\frac{3}{5}[/tex] to an improper fraction.
[tex]\frac{4 * 5 + 3}{5} / \frac{2}{3} = \frac{23}{5} / \frac{2}{3}[/tex]
Multiply the first fraction by the reciprocal of the second fraction (the second fraction upside down).
[tex]\frac{23}{5} / \frac{2}{3} = \frac{23}{5} * \frac{3}{2} = \frac{23 * 3}{5*2} = \frac{69}{10}[/tex]
Convert the result into a mixed fraction.
69 / 10 = 6 with a remainder of 9
A: [tex]6\frac{9}{10}[/tex]
Use the interactive to graph a line with a slope of zero and passing through the point (0,4).
Which statements are true for the graph? Check all that apply.
The line is horizontal.
The line is vertical.
The line goes through (0,0).
The line goes through (4,4).
The x-values are all 0.
The y-values are all 4.
Answer:
THE CORRECT ANSWER'S ARE A,D AND F
Step-by-step explanation:
did the test on edge .
What’s the answer for number 8? Show work and explain
Answer:
so simple do it yourself and use the formula when is given in the text book to solve
2. Use Structure Why do you multiply by a power
of 10 when writing a repeating decimal as a
rational number?
ext
Answer: Use Structure multiply by a power of 10 when writing a repeating decimal as a rational number is 1/5.
Step-by-step explanation:
Define Decimal number :
A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.
Example: the numbers we use in everyday life are decimal numbers, because they are based on 10 digits (0,1,2,3,4,5,6,7,8 and 9). "Decimal number" is often used to mean a number that uses a decimal point followed by digits that show a value smaller than one. Example: 45.6 (forty-five point six) is a decimal number.
Define Rational numbers :
Rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.
Example : a rational number is a type of real number, which is in the form of p/q where q is not equal to zero. Any fraction with non-zero denominators is a rational number. Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on.
So, Given data,
Use Structure Why do you multiply by a power of 10 when writing a repeating decimal as a rational number?
Then we can write,
Let us assume to multiply by some number (10, 100, 1000, etc.)
so that,
when we subtract the original number from the multiple, the repeating part cancels out.
If we multiply by 10.
we get 10x = 2
x = 2/10
x = 1/5
Therefore ,
x = 1/5 is Rational number.
So,
Use Structure multiply by a power of 10 when writing a repeating decimal as a rational number is 1/5.
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Choose the correct description of the graph of the compound inequality (1 point) x − 3 < −11 or x + 5 greater than or equal to 14. Group of answer choices A number line with a closed circle on −8, shading to the left, and an open circle on 9, shading to the right A number line with an open circle on −8, a closed circle on 9, and shading in between A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right A number line with a closed circle on −8, an open circle on 9, and shading in between
The graph of the compound inequality is described by the third choice. A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right
From the question, we are top determine the graph of the given compound inequality
First, we will determine the solution to the compound inequality
Solving the first inequality
x - 3 < - 11
Add 3 to both sides
x - 3 + 3 < - 11 + 3
x < -8
Solving the second inequality
x + 5 ≥ 14
Subtract 5 from both sides
x + 5 - 5 ≥ 14 - 5
x ≥ 9
Thus,
The solution to the given compound inequality is x < -8 or x ≥ 9
Hence, the graph of the compound inequality is described by the third choice. A number line with an open circle on −8, shading to the left, and a closed circle on 9, shading to the right.
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Find the distance between the two points in simplest radical form.
906/2so what is your name
You have solved equations containing square roots by squaring each side. You were using the property that if a=b then (a²=b²). Show that the following statements are not true for all real numbers.
b. If a ≤ b then a²≤ b² .
If a ≤ b, then it is not true for all real numbers that a²≤ b² .
Consider a ≤ b.
Then squaring on both sides,
⇒ a²≤ b² .
But this is true only when both a and b are non-negative numbers.
For example, if we take a = 2 and b = 5, then clearly,
2² = 4 ≤ 5² = 25
Now we need to prove that this result is not true for all real numbers. So we find two real numbers a and b which does not follow this result.
Let a = -7 and b = 3
So here, a < b
Now a² = (-7)² = 49
and b² = 3² = 9
So here, a² > b².
Thus a = -7 and b = 3 is the required counter example to show that the given result is not true for all real numbers.
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Highlight the first step that shows an error in solving 2(2+q)−2=8. Then find the solution of the original equation. The solution is q=.
please help!!!!
Answer:
q=3
Step-by-step explanation:
im very bad at explaining step by step.
a ladybug flies in a straight line from (2, 7, 1) to (4, 1, 5) (with units in meters); the ladybug flies at a constant speed and the flight takes 4 seconds. (a) give a parametrization for the path the ladybug flies between the points, including domain. (b) how much distance does the ladybug travel per second?
As per coordinate geometry, a) 7.48 meters is the parameter for the path the ladybug flies between the points, including the domain. b) 1.87-meter distance does the ladybug travel per second
This is a problem from coordinate geometry and we can crack it with a few steps. First of all, the required formula to solve it is,
l = √ ( x₁ - x₂ )² + ( y₁ - y₂ )² + ( z₁ - z₂)²
where, x₁, y₁, z₁ is the coordinate of the first point and x₂, y₂, z₂ is the coordinate of the second point and l is the distance between two points.
Here x₁ = 2, y₁ = 7, z₁ = 1
and x₂ = 4, y₂ = 1, z₂ = 5
Now we have to put values in the formula,
l = √ ( 2 - 4 )² + ( 1 - 7 )² + ( 5 - 1 )²
l = √ 2² + 6² + 4²
l = √ 4 + 36 + 16
l = √ 56 = 7.48 meter
So, the ladybug flies 7.48 meters while traveling from point one to point two.
The speed taken to fly along this path is, l/t = S, where S is denoted as speed.
S = 7.48 / 4 = 1.87 meters/ second.
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Comparing ratio tables
How much faster does laura type than robert
Answer:
The following tables show how many words each person can text in a given amount of time. Compare the rates of texting for each person using the ratio table.
Step-by-step explanation:
Can you solve this ?
Answer:
2x^2 + 6x - 2
Step-by-step explanation:
It's the second option using like terms
Answer:
The answer is 2x² + 6x - 2. which means it's B.
The mass of a bar of chocolate is 1800g
The density of the chocolate is 9g/cm
Find the mass of the ball in kg
The mass of the bar of chocolate in kilogram, kg is calculated to be 1.8kg
How to find the mass of the bar in kgGiven data
mass of a bar of chocolate is 1800g
density of the chocolate is 9g/cm
density is defined the ratio of mass and volume. therefore the density of the chocolate will be the ratio of the mass of the chocolate bar to the volume of the chocolate. this represented mathematically as:
The mass of the bar of chocolate is given in grams as 1800g
converting the unit to kg is done as follows
if 1kg is equal to 1000g, then how many kg is 1800g
= 1800 / 1000
= 1.8 kg
hence the mass of the chocolate bar in kg is 1.8 kg
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solve the literal equation for y, 8x + 2y = 18
Answer:
y=-4x+9
Step-by-step explanation:
8x+2y=18
-8x -8x
2y=-8x+18
Divide by 2.
2y/2=y
-8x/2=-4x
18/2=9
Put the pieces back together.
y=-4x+9
Hope this helps.
Answer:
x = 9-y / 4
Step-by-step explanation:
What is the value of the expression (-2 3/5)(-0.5)?
Answer:
1.3
Step-by-step explanation:
(−2 3/5)(−0.5)
=(−13/5)(−0.5)
=−13/5(−0.5)
=1.3
=1.3
Solve each equation. Round to the nearest ten-thousandth. 2 log₃x=54
The solution for the given Logarithms equation 2 log₃x=54 is x = 3²⁷ in the nearest ten-thousandth = 7625597484987.
The exponential logarithmic form:Exponential functions have logarithmic inverses. A log is thus an exponent! y=logbx if and only when by=x for all x greater than zero and 0b1.
Why are logarithms used?Logarithms depict changes in terms of multiplication: each step in the preceding instances is 10x larger. Each step is "e" (2.71828...) times longer using the natural log. When dealing with such a sequence of multiplications, logarithms assist in "counting" them in the same way as addition assists us in counting when effects are added.
According to the given equation:Given 2 log₃x=54
Divide both side by 2:
(2 log₃x)2 = 54/2
simplify.
log₃(x) = 27
apply log rule:
x = 3²⁷
Decimal value of x = 3²⁷ = 7625597484987
The solution for the given Logarithms 2 log₃x=54 is x = 3²⁷ in the nearest ten-thousandth = 7625597484987
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Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
3 f(x)-2
For f(x)=2 x+5 and g(x)=x²-3 x+2 , the values of the composite function 3 f(x)-2 = 6x+ 13
What is the domain of the function 3 f(x)-2 ?
The domain of a function is the set of input values, the function can take.
The functions are given as:
f(x)=2 x+5
g(x)=x²-3 x+2
To find:
3 f(x)-2 = ?
3 ×(2 x+5) - 2 = 6x + 15 - 2
= 6x+ 13
Therefore,
The function operation of 3 f(x)-2 = 6x+ 13
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HELP ME YALLLL I HAVE A QUESTION ❓⁉️❓❓
Multiple choice :
A) k=2
B) k=0
C) k<4
D) k<or = 0
E)k< or = 4
====================================================
Explanation:
Recall the discriminant formula is
d = b^2 - 4ac
which is the stuff found under the square root in the quadratic formula.
If d > 0, then the equation ax^2+bx+c = 0 will have two different real number roots.
So,
d > 0
b^2 - 4ac > 0
4^2 - 4(1)(k) > 0
16 - 4k > 0
16 > 4k
4k < 16
k < 16/4
k < 4 which points us to choice C
For example, if k = 0, then the equation x^2+4x+k = 0 becomes x^2+4x = 0. This has the two different roots of x = 0 and x = -4.
Please help me find the value of x.
[tex]\huge\boxed{\sqrt5}[/tex]
To find the value of [tex]x[/tex], we'll use the Pythagorean theorem.
The following formula applies, with the lengths of the sides with the right angle being [tex]a[/tex] and [tex]b[/tex], and the hypotenuse being [tex]c[/tex]:
[tex]a^2+b^2=c^2[/tex]
Substitute the values in.
[tex]x^2+(\sqrt{11})^2=4^2[/tex]
Square the numbers as possible.
[tex]x^2+11=16[/tex]
Subtract 11 from both sides of the equation.
[tex]x^2=5[/tex]
Take the square root of both sides of the equation to solve for [tex]x[/tex].
[tex]x=\sqrt5[/tex]