Answers
5^-3 = 0.008
2^2 = 4
5^6 = 15625
0.008*4*15625 = 500
2^3 = 8
5^2 = 25
25*8 = 200
500/200 = 5/2 = 2 1/2
Related Questions
A diver descends from an elevation of 6 feet below sea level to an elevation
of 98 feet below sea level in 4 equal intervals. What was the diver’s change in
elevation in each interval? Explain how you solved this problem.
Answers
Now, since he descended in four equal intervals, we can just divide 92 into four equal parts, or divide by 4, to get 23 feet.
So the diver's change in elevation in each interval was (negative?) 92 feet.
Khalid invested $9500 in a savings account with a yearly interest rate of 3% for 8 years. How much simple interest did he earn?
Answers
9500*[1+(0.03*8)]
giving us 9500*1.24 = $11,780
Answer:
$2280
Step-by-step explanation:
Which of the following is an odd function? f(x) = x3 + 5x2 + x mc023-1.jpg f(x) = x2 + x f(x) = –x
Answers
(a) f(x) = x³ + 5x² + x
(b) f(x) = x² + x
(c) f(x) = -x
Function (a)
f(-x) = (-x)³ + 5(-x)² + (-x)
= -x³ + 5x² - x
= -(x³ - 5x² + x)
The function is neither even nor odd.
Function (b)
f(-x) = (-x)² + (-x)
= -(-x² + x)
The function is neither even nor odd.
Function (c)
f(-x) = -(-x)
= x
= -f(x)
Because f(-x) = -f(x) the function is odd.
Answer: f(x) = -x is an odd function.
By evaluating each function in -x, we will see that the only odd one is:
f(x) = -x
What is an odd function?
We say that a function is odd if:
f(-x) = f(x)
Then we just need to check that for the given functions, let's see what we get:
1) f(-x) = (-x)^3 + 5*(-x)^2 + (-x) = -x^3 + 5x^2 - x ≠ -f(x)
2) f(-x) = (-x)^2 - x= x^2 - x ≠ -f(x)
3) f(-x) = -(-x) = x = -f(x)
So the only odd function is the third one, one useful thing that you may need to know is that usually when you see even exponents, that function will not be odd.
If you want to learn more about odd functions, you can read:
https://brainly.com/question/1561362
The __________ is the score that occurs most frequently in a distribution.
Answers
for geometric sequence below, determine the explicit formula. be sure to enter your answer as a formula of the form a_n= a_1(r)^(n-1) with the correct a_1 and r values.
5/8, 25/8, 125/8, 625/8, . . ., a_n
Answers
Let's calculate r:
r = a₂ / a₁
r = (25/8) / (5/8)
r = 5.
Since a₁ = 5/8
[tex]\boxed{\mathsf{a_n = \frac{5}{8}\cdot 5 ^{n-1}}}[/tex]
Approximately how many times greater is 9.75 * 10^6 than 1.25 * 10^2?
Answers
9.75 / 1.25 = 7.8
10^6 - 10^2 = 10^4
= 7.8 x 10^4 greater
Which lines must be parallel if angle 10 is supplementary to angle 11?
Answers
You have just won the lottery and will receive $1,000,000 in one year. you will receive payments for 30 years, and the payments will increase 3 percent per year. if the appropriate discount rate is 7 percent, what is the present value of your winnings?
Answers
Final answer:
The student's question involves determining the present value of annuity payments from a lottery winning, which increase over time and are discounted by a particular rate. The present value is calculated using a formula for a growing annuity, taking into account factors like the growth rate of the payments, the discount rate, and the number of periods. An example with a simple bond issue is provided to illustrate the process of calculating present value at different discount rates.
Explanation:
The student's question pertains to calculating the present value of annuity payments that increase at a fixed percentage rate over time, using a specified discount rate. This is a common exercise in finance and economics, especially related to determining the value of future cash flows given a particular rate of return (or discount rate). To solve the problem, we use the present value formula for a growing annuity.
For the lottery winnings scenario, we would calculate the present value of each individual payment and then sum them up. The first payment of $1,000,000 is received in one year, and it increases by 3 percent each year for 30 years. The discount rate is 7 percent. To analyze this, we must consider the effects of inflation and the time value of money, which is why the payments are 'discounted' back to their present value at the prevailing discount rate.
The general formula for the present value of a growing annuity is:
PV = P * [(1 - ((1 + g)/(1 + r))^n) / (r - g)]
where PV is the present value, P is the first payment, g is the growth rate of the payments, r is the discount rate, and n is the number of periods.
Using the simple two-year bond example provided, the present value calculations at an 8% discount rate are:
$240/(1+0.08) = $222.22
$3,240/(1+0.08)^2 = $2,777.78
Total present value = $222.22 + $2,777.78 = $3,000
If the discount rate increases to 11%, the new present values would be calculated using the higher rate, resulting in a lower total present value for the bond. The calculations reflect the principle that if the cost of borrowing money increases (higher discount rate), the present value of future payments decreases.
A puzzle contains a triangular piece with a base of 3 in. and a height of 4 in. A manufacturer wants to make 80 puzzles. Find the amount of wood used if each puzzle contains 20 triangular pieces.
Answers
Answer:
9600 square inches.
Step-by-step explanation:
We have been given that a puzzle contains a triangular piece with a base of 3 in. and a height of 4 in.
The would used for each triangular piece would be equal to area of triangle.
[tex]\frac{1}{2}\times 3\text{ in}\times 4\text{ in}=3\text{ in}\times 2\text{ in}=6\text{ in}^2[/tex]
Each puzzle contains 20 triangular pieces, so wood used for each piece of puzzle would be 20 times 6 square inches.
[tex]\text{Wood used for each puzzle}=20\times 6\text{ in}^2[/tex]
[tex]\text{Wood used for each puzzle}=120\text{ in}^2[/tex]
[tex]\text{Wood used for 80 puzzles}=80\times 120\text{ in}^2[/tex]
[tex]\text{Wood used for 80 puzzles}=9600\text{ in}^2[/tex]
Therefore, 9600 square inches of wood is needed to make 80 puzzles.
What is negative three divided by zero fraction form should i just remove the zero?
Answers
If i multiply the numerator do i have to multiply the denominator
Answers
Three orders are placed at a pizza shop. two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas, a liter of soda, and two salads cost $22. how much does each item cost?
Answers
let x cost of small pizzas
y cost of soda
z cost of salad
two small pizzas, a liter of soda, and a salad cost $14
2x + y + z = 14
one small pizza, a liter of soda, and three salads cost $15
x + y + 3z = 15
three small pizzas, a liter of soda, and two salads cost $22
3x + y + 2z = 22
Solving for x, y and z, we will have:
x = $ 5
y = $ 1
z = $ 3
We can solve this problem by setting up a system of equations using the given information and using algebraic methods to solve for each variable, which represent the cost of the individual items.
Explanation:This question can be solved by using the method of linear equations. Let's denote the cost of a small pizza as P, a liter of soda as S, and a salad as A. From the given information, we can create three equations:
2P + S + A = $14 P + S + 3A = $15 3P + S + 2A = $22
By solving these equations, we can determine the prices of the individual items. The details of solving these equations may vary based on your level of comfort with algebra and systems of equations, but the general method involves isolating one variable in one equation and then substituting it into the other equations to eventually solve for each variable.
Learn more about System of Equations here:https://brainly.com/question/21620502
#SPJ3
At Susie's school, 5/8 of all students play sports. Of the students who play sports, 2/5 play soccer. What fraction of the students in Susie's school play soccer?
Answers
If a car travels 23 miles on 1.0 gal of gas, how many liters of gasoline are needed for a 135 mile trip?
Answers
Solve for y.
d = 5x + 5y
Answers
5y = d - 5x
y = (d - 5x) / 5
The solution for y of the given equation is y = (d - 5x)/ 5.
What are Arithmetic operations?Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
The operator that performs the arithmetic operations are called arithmetic operators.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
Given that the equation as
⇒ d = 5x + 5y
Rearrange the terms in the above equation
⇒ 5y = d - 5x
Divided by 5 both sides of the equation
⇒ y = (d - 5x)/ 5
Hence, the solution for y of the given equation is y = (d - 5x)/ 5.
Learn more about Arithmetic operations here:
brainly.com/question/25834626
#SPJ2
Loretta invested $1000 in a simple interest account yielding 5% paid annually. In 2 years, she will have $1100 in her account. From this example, we can conclude that 5% represents the:
Answers
Final answer:
The 5% represents the annual interest rate on Loretta's investment in a simple interest account.
Explanation:
The 5% represents the annual interest rate on Loretta's investment. In simple interest, the interest is calculated as a percentage of the initial investment. So, if Loretta invested $1000, and after 2 years her account has grown to $1100, the interest earned would be $100 (1100 - 1000).
To find the interest rate, we can use the formula:
Interest = Principal * Rate * Time
Using the given information, we can plug in the values and solve for the rate:
100 = 1000 * Rate * 2
Simplifying the equation, we get:
Rate = 100 / (1000 * 2) = 0.05 or 5%
Therefore, the 5% represents the annual interest rate in this scenario.
Find all values of thetaθ, if thetaθ is in the interval [0degrees°, 360degrees°) and has the given function value cot thetaθ=1
Answers
The 2 angles are 45 and 180+45 = 225 degrees
Answer 45 , 225 degrees.
Find the point-slope form of the equation of the line passing through the points (–1, –3) and (4, 1).
Answers
Your y1 value is -3 and your x1 value is -1.
Before we can solve the equation, we need the slope first. To find the slope of a line, we need to use the equation y2-y1/x2-x1.
That would be 1-(-3)/4-(-1) which translates to 4/5. Your slope is 4/5.
Now we can plug this into the point slope form.
y-(-3)=4/5(x-(1))
That would be y+3=4/5x+4/5. You must then subtract 3 from 4/5.
This would mean that y=4/5x-2.2
Hope this helps.
A segment has an endpoint (14,-8) and (4,12) what are the coordinates of its midpoint
Answers
The coordinates of the midpoint of the segment that has endpoints as (14,-8) and (4,12) are (9,2).
What are the coordinates of the midpoint of the line segment AB?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
Suppose we've two endpoints of a line segment:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
x = (p+m) / 2
and
y = (q+n) / 2
Given that a segment has an endpoint (14,-8) and (4,12). Therefore, The coordinates of the midpoint of the segment can be written as,
X- coordinate = (14+ 4)/2
= 18/2
= 9
Y- coordinate = (-8+12)/2
= 4/2
= 2
Hence, the coordinate of the midpoint of the segment that has endpoints as (14,-8) and (4,12) is (9,2).
Learn more about Midpoint here:
https://brainly.com/question/5127660
#SPJ2
Group A has an elevation of -282 feet. group B has an elevation of 279 feet. which is closer to sea level
Answers
--- sea level ---
~ -282 feet
distance of group B = 279 ft
So group B is closer
Simplify 5x + 50/x+5 · 1/x+10
A. 5/x+5
B. 5x^{2}
C. x-3/x+7
D. x-2
Answers
the base of a pyramid has n sides write an expression for the number of faces of the pyramid
Answers
This means that a pyramid always have the number of face which is one more than the number of sides of the base.
Therefore, given that a pyramid has n number of sides of the base, the expression for the number of faces of the pyramid is given by
number of faces = n + 1.
Express the set of real numbers between but not including 2 and 5 as follows.
Answers
i think this is the answer
Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined value of $8.85. How many of each does he have
Answers
Answer:
Dustin has 17 nickels and 32 quarters.
Explanation:
Let's denote the number of nickels as [tex]\(n\)[/tex] and the number of quarters as [tex]\(q\).[/tex]
We can set up a system of equations based on the given information:
1. The total number of coins: [tex]\(n + q = 49\)[/tex]
2. The total value of the coins: [tex]\(0.05n + 0.25q = 8.85\)[/tex]
We can solve this system of equations to find the values of [tex]\(n\) and \(q\).[/tex]
From equation (1), we can express [tex]\(n\)[/tex] in terms of [tex]\(q\):[/tex]
[tex]\[n = 49 - q\][/tex]
Now, substitute this expression for [tex]\(n\)[/tex] into equation (2):
[tex]\[0.05(49 - q) + 0.25q = 8.85\][/tex]
[tex]\[2.45 - 0.05q + 0.25q = 8.85\][/tex]
Combine like terms:
[tex]\[0.20q + 2.45 = 8.85\][/tex]
Subtract 2.45 from both sides:
[tex]\[0.20q = 6.40\][/tex]
Now, divide both sides by 0.20:
[tex]\[q = \frac{6.40}{0.20} = 32\][/tex]
So, Dustin has 32 quarters.
To find the number of nickels, we can substitute the value of \(q\) into the equation [tex]\(n + q = 49\):[/tex]
[tex]\[n + 32 = 49\][/tex]
[tex]\[n = 49 - 32\][/tex]
[tex]\[n = 17\][/tex]
So, Dustin has 17 nickels.
Which equation represents the line that passes through the points (–3, 7) and (9, –1)?
A) y = - 2/3 x + 5
B) y = - 2/3 x - 7
C) y = 2/3 x - 7
D) y = 2/3 x - 5
Answers
y = mx + b
7 = -2/3(-3) + b
7 = 2 + b
b = 5
equation
y = -2/3x + 5
answer
A) y = - 2/3 x + 5
The equation represents the line that passes through the points (–3, 7) and (9, –1) will be A) y = - 2/3 x + 5.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
The slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
The slope = (7 + 1)/(-3 - 9)
= 8 / -12
= -2/3
The equation of a line
[tex]y = mx + b\\7 = -2/3(-3) + b\\7 = 2 + b\\b = 5[/tex]
y = -2/3x + 5
Learn more about slope;
https://brainly.com/question/3605446
#SPJ2
define a variable and write an inequality to model each situation. The school auditorium can seat at most 1200 people.
Answers
If 6 cats can kill 6 rats in 6 minutes, how many cats will it take to kill 100 rats in 50 minutes? previous next
Answers
200
Bethany sells roses and petunias. The expression 3r+2.5p gives the cost (in dollars) of r roses and p petunias.What is the cost of 7 roses and 8 petunias?
Answers
21 + 20
41
Hope this helps!
3(7)+2.5(8)
21+20
41
your answer would be $41
What is the length of a rectangle with area 402 ft^2
and width 12 ft?
Answers
402 / 12 = 33.5
So the length is 33.5 feet.
Hope this helps! :)
The length of the rectangle is 33.5 feet.
To find the length of the rectangle, we can use the formula for the area of a rectangle:
Area = length * width
Given:
Area = 402 ft^2
Width = 12 ft
Let's solve for the length:
402 ft^2 = length * 12 ft
To find the length, divide both sides by 12 ft:
length = 402 ft^2 / 12 ft
length = 33.5 ft
So, the length of the rectangle is 33.5 feet.
To know more about length:
https://brainly.com/question/17201180
#SPJ2
0.90 divided by 0.30 PLEASE SHOW WORK OR EXPLAIN YOUR REASONING!
Answers
Hope this helps!
first write it as a fraction =0.9/0.3
then you multiply the numerator and the denominator by 10= 9/3
divide the 9 and the 3 =3
hope this helps