Answer:
After 11 years the value of the investment reaches $1500.00
.
Step-by-step explanation:
The formula used for finding time (when the value reaches certain amount) is:
[tex]A= P(1+\frac{r}{n})^{nt}[/tex]
where A= Future VAlue
P= Principal Value
r= rate of interest (in decimal)
n= no of times investment is compounded
t= time
Putting the values given and finding Time t,
A= $1500
P= $1200
r= 2% or 0.02
n= 4 (compound quarterly)
[tex]A= P(1+\frac{r}{n})^{nt}[/tex]
[tex]1500= 1200(1+\frac{0.02}{4})^{4t}[/tex]
Dividing both sides by 1200 and solving 0.02/4 = 0.005
[tex]1.25= (1+0.005)^{4t}[/tex]
[tex]1.25= (1.005)^{4t}[/tex]
Since t is in power we take the logarithm ln on both sides.
The rule of logarithm says that the exponent can be multiplied with the base when taking log
[tex]\ln1.25=ln( 1.005)^{4t}\\\ln1.25=4t * ln( 1.005)\\0.22 = 4t * 0.005\\Solving\,\,\\\frac{0.22}{4*0.005} = t\\=> t= 11\, years[/tex]
Angelo runs 7 miles per week and increases his distance by 1 mile each week. Marc runs 4 miles per week and increases his distance by 2 miles each week. In how many weeks will Angelo and Marc be running the same distance? What will that distance be?
Answer:
Step-by-step explanation:
You have to set each runner's plan equal to each other because they are equal in the end. You start with 7 miles for Angelo and 4 miles for Marc.
x is a variable that is multiplied by the number of weeks it takes for both runners' distances to be equal. So multiply x by the miles increased every week.
Marc = Angelo
2x + 4 = x + 7
x = 3
In 3 weeks each runner will run 10 miles for the week.
To find when Angelo and Marc will be running the same distance and what that distance will be, set up and solve equations.
Explanation:To find out in how many weeks Angelo and Marc will be running the same distance, we can set up an equation. Let's assume the number of weeks is x. Angelo's distance can be represented by the equation 7 + 1x, and Marc's distance can be represented by the equation 4 + 2x. To find when their distances are equal, we can set the two equations equal to each other and solve for x.
Setting the equations equal: 7 + 1x = 4 + 2x
Simplifying the equation: x = 3
Therefore, Angelo and Marc will be running the same distance in 3 weeks. To find the distance, we can substitute the value of x back into either of the original equations. Let's use Angelo's equation: 7 + 1(3) = 10
So, Angelo and Marc will be running 10 miles in the same distance.
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Comstock nut company has 500 pounds of peanuts to package if each package contains one and one four pounds how many packages are needed?
Answer:
2000
Step-by-step explanation:
500/0.25. :) hope this helped
Comstock Nut Company can make 400 packages of peanuts by dividing the total weight of peanuts (500 pounds) by the weight of each package (1.25 pounds). Ounces or grams would be suitable to measure a handful of peanuts.
Explanation:To calculate how many packages Comstock Nut Company can make, we simply divide the total weight of the peanuts by the weight of each package. They have 500 pounds of peanuts and each package weighs 1 and 1/4 pounds (which is the same as 1.25 pounds).
Number of packages = Total weight of peanuts ÷ Weight per package
Number of packages = 500 pounds ÷ 1.25 pounds/package
When you divide 500 by 1.25, you get 400. Therefore, Comstock Nut Company can make 400 packages of peanuts.
When it comes to choosing the best unit of measurement, for a handful of peanuts, we would typically use ounces or grams since they are small quantities that don't weigh much, similar to how Jeffrey should use ounces to label packages of steak when most are less than a pound.
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Re-arrange this polynomial so it’s terms are in order from highest to lowest. 4x to the 5th power + 2x to the 3rd power - 15 - 7x to the second power
Answer:
[tex]4x^5+2x^3-7x^2-15[/tex]
Step-by-step explanation:
Look at the degrees of each term.
[tex]4x^5=5 \\ \\ 2x^3=3 \\ \\ -7x^2 = 2 \\ \\ -15=1[/tex]
Rearrange them from greatest to least.
[tex]4x^5+2x^3-7x^2-15[/tex]
if you start on the unit circle at (0,-1) and move 360° in the counterclockwise direction, at what angle measure on the unit circle will you end up? Answer should be the angle measure in degrees.
Answer:
270°
Step-by-step explanation:
(0, -1) is at the 270° angle. If you do a 360°, you end up back where you started, so the angle is still 270°.
Marilyn has a bag of coins. The bag contains 25 wheat pennines, 15 Canadian pennies, 5 steel pennies, and 5 Lincoln pennies. She picks a coin randomly from the bag. What is the probability that she picked a steel penny or a lincoln penny? A.) 10% B.) 20% C.) 50% D.) 30%
Answer:
B
Step-by-step explanation:
In probability, "AND" means to multiply and "OR" means to add.
Here they want probability of steel penny ( P(s) ) "OR" probability of lincoln penny ( P(l) ).
Let's find the individual probabilities and "ADD" them.
P(s) = 5/50 (since there are 5 steel pennies and there are 50 coins in total)
P(l) = 5/50 (since there are 5 lincoln pennies and there are 50 coins in total)
So probability of 5 steel penny and 5 lincoln penny = 5/50 + 5/50 = 10/50 = 1/5
1/5 is equal to 20%, correct answer is B
solve for x.
9(x - 6) = 8(x + 6)
Answer:
x=102
Step-by-step explanation:
9x-54=8x+48
subtract 8x from both sides
x-54=48
add 54 to both sides
x=102
Answer:
x = 102
Step-by-step explanation:
9(x + -6) = 8(x + 6)
Reorder the terms:
9(-6 + x) = 8(x + 6)
(-6 * 9 + x * 9) = 8(x + 6)
(-54 + 9x) = 8(x + 6)
Reorder the terms:
-54 + 9x = 8(6 + x)
-54 + 9x = (6 * 8 + x * 8)
-54 + 9x = (48 + 8x)
Solving
-54 + 9x = 48 + 8x
Add '-8x' to each side of the equation.
-54 + 9x + -8x = 48 + 8x + -8x
Combine like terms: 9x + -8x = 1x
-54 + 1x = 48 + 8x + -8x
Combine like terms: 8x + -8x = 0
-54 + 1x = 48 + 0
-54 + 1x = 48
Add '54' to each side of the equation.
-54 + 54 + 1x = 48 + 54
Combine like terms: -54 + 54 = 0
0 + 1x = 48 + 54
1x = 48 + 54
Combine like terms: 48 + 54 = 102
1x = 102
Divide each side by '1'.
x = 102
A recipe calls for 2/3 cup of sugar for every 2 teaspoons of vanilla. What is the unit rate in cups per teaspoon?
Answer:
2/3 to 2 or 2/3:2 or two thirds to 2 or (2/3,2)
Step-by-step explanation: hope this helped
can i have some help please?
Answer:
C is the correct answer
Please I need help with this one
Answer:
Cone
Step-by-step explanation:
the base is formed when the triangle is turned in a circle. the base is a triangle.
Jefferson High School is looking to expand its student parking lot by expanding the existing lot as shown above. The size of the new parking lot will be twice the size of the old parking lot. How many feet, x, was the old parking lot expanded by?
Answer:
60
Step-by-step explanation:
identify an equation in point-slope intercept form for the line perpendicular to y=3x+5 that passes through (4,-1)
Answer:
y + 1 = - [tex]\frac{1}{3}[/tex](x - 4)
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 5 is in this form
with slope m = 3
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex]
The equation of a line in point slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here (a, b) = (4, - 1), thus
y - (- 1) = - [tex]\frac{1}{3}[/tex](x - 4), that is
y + 1 = - [tex]\frac{1}{3}[/tex](x - 4) ← in point- slope form
3x+4(x-8)-14 evaluate for x=11
Answer:
For X = 11, the expression is equal to 31
Step-by-step explanation:
Hello
For X = 11 you only have to replaced the value into the expression, so:
3(11) + 4(11-8) - 14
33 + 4(3) - 14
33 + 12 - 14
31
Best regards
Hello there!
Plug 11 into the equation, by replacing x with it and simplify.
3x+ 4(x-8) - 14
3(11) + 4(11-8) - 14 -- Remember PEMDAS, start by subtracting 11 - 8.
3(11) + 4(3) - 14 -- Next, multiply 3 by 11.
33 + 4(3) - 14 -- Now, multiply 4 by 3.
33 + 12 - 14 -- Now, add 33 to 12.
45 - 14 -- Now, take 14 away from 45.
31 -- This is your final answer.
I hope this was helpful and have a great rest of your day! ~ saturns
Which would best illustrate the percentage of students that received As, Bs, Cs, Ds, and Fs on recent test ?
A) pie graph
B) histogram
C) data table
D) line graph
A) pie graph is ur answer
A) pie graph
Pie graphs are best used when comparing percentages, so it would be best to compare values using a pie graph in this situation.
Help please
“What are my chances of drawing a g”
Answer:
0.1
Step-by-step explanation:
There are a total of 10 tiles, of which 1 is the letter G
P(G) = [tex]\frac{1}{10}[/tex] = 0.1
0.1
Explanation step by step:
There is a total of 10 tiles of which 1 is the letter G
[tex]P(G) = \ \frac{1}{10} = 0.1[/tex]
The perimeter of the rectangular state is 42 miles . A ranger estimates that there are 9 deer in each square mile of the park . If this estimates is correct ,how many total deer are in the park ,explain your answer using numbers ,symbols, and words
P.S this questions is important ,so answer it fast
Thank you
Answer:
990 deers is ONE possible answer.
Step-by-step explanation:
Since we don't know anything else than the perimeter, we don't know the exact dimensions of the park.
For example, it could be 10 x 11 miles, perimeter is 42, but the area is 110 sq miles.
It could also be 9 x 12 miles, perimeter is again 42, but the area is now 110 sq miles.
It could be a 1 x 20 miles park, perimeter is again 42, but the area is just 20 sq miles.
And it could be many other dimensions scenarios. That affect of course the calculation result.
For this answer, I'll assume the park is 10x11 miles, for an area of 110 sq miles.
Since the estimation is that there's 9 deeps for square mile... that means that for a park measuring 10x11 miles, there would be 990 deers (9 * 110).
Which runner has the fastest pace?
Answer:
the correct answer is distance 2 and time 18
Step-by-step explanation:
Answer:
answer is distance 2 and time 18
Step-by-step explanation:
Consider the equations: y = 3x + 2 and y = 2x + 1.
Solve the system of equations by completing the table of values to find an ordered pair that satisfies both equations.
Answer:
(-1,-1)
Step-by-step explanation:
y = 3x + 2x y-1 -10 21 52 83 11y = 2x + 1x y-1 -10 11 32 53 7Sample calculation
y = 3x + 2 y = 2x + 1
x = 2 x = 2
y = ? y = ?
y = 3*2 + 2 y = 2*2 + 1
y = 6 + 2 y = 4 + 1
y = 8 y = 5
The two that give exactly the same answer is
(-1, - 1)
Step-by-step explanation:
Given : Consider the equations [tex]y=3x+2[/tex] and [tex]y=2x+1[/tex]
To find : Solve the system of equations by completing the table of values to find an ordered pair that satisfies both equations ?
Solution :
For the equation, [tex]y=3x+2[/tex]
[tex]y(-1)=3(-1)+2=-1[/tex]
[tex]y(0)=3(0)+2=2[/tex]
[tex]y(1)=3(1)+2=5[/tex]
[tex]y(2)=3(2)+2=8[/tex]
[tex]y(3)=3(3)+2=11[/tex]
We create a table,
x y
-1 -1
0 2
1 5
2 8
3 11
For the equation, [tex]y=2x+1[/tex]
[tex]y(-1)=2(-1)+1=-1[/tex]
[tex]y(0)=2(0)+1=1[/tex]
[tex]y(1)=2(1)+1=3[/tex]
[tex]y(2)=2(2)+1=5[/tex]
[tex]y(3)=2(3)+1=7[/tex]
We create a table,
x y
-1 -1
0 1
1 3
2 5
3 7
How to fill in the prime factor tree?????? Answer???
Step-by-step explanation:
On the 8 branch, to the left is 2, and on the right is 4. On the left branch, and on the left, it is 2, and there is a 2 for the 6 branch.
Will give Brainlest! Help plz
41000 is 100%
29000 is ? %
?=29000x100/41000~70.73%
Find the 13th term of the sequence 5, 8, 11, 14, 17...
A 13th term does not exist
41
46
49
5,8,11,14,17,20,23,26,29,32,35,38,41
Add each number by 3
13th term is 41 ( first choice)
Answer:41
Step-by-step explanation:
The numbers go up by 3
What is the zero of the following function?
Answer:
D
Step-by-step explanation:
The zero of the function is the point on the x- axis where the graph crosses
That is x = - 5
Answer: OPTION D
Step-by-step explanation:
The zero of the function is the intersection of the function with the x-axis.
A function intersects the x-axis when the value of y is zero ([tex]y=0[/tex])
Then, you can observe in the graph attached that the function intersects the x-axis at the point (-5,0), where the x-coordinate is -5 and the y-coordinate is 0:
[tex]x=-5\\y=0[/tex]
Therefore, you can identify that the zero of the function shown in the figure is:
[tex]x=-5[/tex]
This matches with the option D.
Rhea had a score of a 70 on her first quiz and a score of a 77 on her second quiz. What is the percent increase from her first quiz score to her second quiz score?
The answer is:
The percent increase from her first quiz score to her second quiz score is 10%.
Why?To know what is the percent increase from her first quiz to her second quiz, first we need to calculate the increase points, then, represent it in porcentage value.
Then, calculating her increas in points, we have:
[tex]Increase=SecondQuizScore-FirstQuizScore\\Increase=77points-70points=7points\\Increas=7points[/tex]
Now, calculating the percent increase, we have:
[tex]Increase(Percentage)=\frac{Increase(points)}{FirstScore}*100\\\\Increase(Percentage)=\frac{7}{70}*100\\\\Increase(Percentage)=0.10*100=10[/tex]
Hence, the percent increase from her first quiz score to her second quiz score is 10%.
Have a nice day!
Answer:
10%
Step-by-step explanation:
increase percentage is = difference /initial value x 100
=77-70/70 x 100
=10
This graph shows the temperature in city for eight days what was the temperature range for this period 67 73 80 73 76 75 73 67 answers 12,13,15,16
Answer: The answer is 13
Step-by-step explanation: The range means to find the difference from the largest number and smallest number
1) line all the numbers from biggest to smallest
80,76,75,73,73,73,67,67
2) take the largest number and smallest number
largest=80
smallest=67
3) then subtract the two to find your range
80-67= 13Checking account A charges a monthly service fee of $23 and a wire transfer fee of $7.50, while checking account B charges a monthly service fee of $14 and a wire transfer fee of S9.50. Which checking account is the better deal if 4 wire transfers are made per month?
Answer:
Checking account B
Step-by-step explanation:
If you do 7.50 times 4 plus 23 you get 53 dollars. With plan B you go 9.50 times 4 plus 14 to get 52 dollars.
find the height of the cylinder V=271.4in3
h=271.4/6π≈14.4 inches.
If the volume and the rafius of the cylinder is 271.4 cubic inches and 6 inches. Then the height of the cylinder will be 2.4 inches.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
If the volume of the cylinder is 271.4 cubic inches and the radius of the cylinder is 6 inches.
Then the height of the cylindr will be
We know the volume of the cylinder is given as
V = πr²h
Then we have
271.4 = π x 6² x h
271.4 = 36π x h
271.4 = 113.1 x h
h = 2.4
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Hobby Shop is selling model cars and model trucks for 50% off this week. At the sale price, you can buy one car and one truck for $13.00. Also at the sale price, you can buy 4 trucks and 2 cars for $42.00. What is the sale price and the original price of the model car and the model truck?
Answer:
The truck original price is $16.00 and the car price is $5.00.
The truck sale price is $8.00 and the car price is $10.00.
Step-by-step explanation:
We need to find the original price of the truck (T) and car (C)
Sale price of the truck is 50% so that means it is half the original price.
Now let's see the equations we can come up with there:
At sale price:
[tex]T + C = \$13.00\\\\4T + 2C = \$42.00[/tex]
We can solve this through substitution.
Using the first equation, we can come up with an equation for one of the missing variables.
[tex]T + C =\$13.00\\\\C = \$13.00 - T[/tex]
We can use this equation on the second one, to solve for one variable. [tex]4T + 2C = \$42.00\\\\4T + 2(\$13.00-T) = \$42.00\\\\4T + \$26.00 - 2T = \$42.00\\\\4T - 2T = \$42.00 - \$26.00\\\\2T = \$16.00\\\\\dfrac{2T}{2}=\dfrac{\$16.00}{2}\\\\T = \$8.00[/tex]
The sale price of the model truck is $8.00.
Now can use this on the first equation again.
[tex]T + C = \$13.00\\\\\$8.00 + C = \$13.00\\\\C = \$13.00 - \$8.00\\\\C = \$5.00[/tex]
The sale price of the model car is $5.00.
Because it is 50% off on both models, the original price is twice the sale price. So we can solve it by multiplying the sale prices by 2.
Original price of model truck: $8.00 x 2 = $16.00
Original price of model car: $5.00 x 2 = $10.00
Answer:
The truck's original is $16. The sale price is $8. The car's original is $10. It's sale is $5.
Step-by-step explanation:
Please give me five stars, heart, and mark me brainliest! The other guy is incorrect.
how do you rewrite 1/27 as an expression with a negative exponent
Answer:
3^-3
Step-by-step explanation:
27 = 3^3
so
1/ 27= 1 / 3^3 = 3^-3
To write the fraction \( \frac{1}{27} \) as an expression with a negative exponent, you can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \), where \( a \) is any non-zero real number and \( n \) is a positive integer.
Applying this property to \( \frac{1}{27} \), we can see that the fraction is the reciprocal of \( 27 \) raised to the first power. Thus, we rewrite the expression \( \frac{1}{27} \) by flipping the position of \( 27 \) to the numerator and making the exponent negative:
\( \frac{1}{27} = 27^{-1} \)
So, \( 27^{-1} \) is the same as \( \frac{1}{27} \). When you calculate \( 27^{-1} \), you get the value of approximately \( 0.037037037037037035 \), which represents the decimal equivalent of the fraction \( \frac{1}{27} \).
What is the ratio of 7 nickles to 70 cents
This ratio can be presented as:
7:70
or
1:7
To make six cakes Fred uses four and a half cups of sugar. How much sugar does he need for one cake?
Answer:
1.333 cups
Step-by-step explanation:
if you divide 6 by 4.5 you get 1.333
pls pls pls help
I need help
Use the formula A = bh to determine which parallelograms have the same area.
What is that area?
Answer: Parallelograms
have an area of
square units.
Answer:
Parallelograms I, II, and IV
Step-by-step:
Area of parallelograms:
I. A=3*5=15 units squared
II. A=5*3=15 units squared
III. A=4*4=16 units squared
IV. A=5*3=15 units squared
So, parallelograms I, II, and IV have the same area of 15 units squared.
Answer:
Parallelograms I, II, and IV have an area of 15 square units
Step-by-step:
Area of parallelograms:
I. A=3*5=15 units squared
II. A=5*3=15 units squared
III. A=4*4=16 units squared
IV. A=5*3=15 units squared
So, parallelograms I, II, and IV have the same area of 15 units squared.