If the saving compounded monthly at an interest rate of 6%. The amount you need to deposit a month is $8,302.
How to find the compound interest?Using this formula to determine the principal amount
P = A / (1 + r/n) ^nt
Where:
P = principal = ?
A = amount = $50,000
r = interest rate = 6%
t = time = 30
Now let plug in the formula
P = $50,000 / (1 + 0.06/12) ^( 12 × 30 )
P = $50,000 / (1 + 0.005) ^ 360
P = $50,000 / (1.005)^360
P = $50,000 / 6.022575
P = $8,302
Therefore $8,302.10 is the amount deposited.
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this is the last one i need help with. please & thank you asap
Answer:
slope = 3/7
Step-by-step explanation:
Locations of points: (-4 , 1) and (3 , 4)
slope = rise / run
between two plotted points this means that:
slope = change in y / change in x
slope = (4 - 1) / (3 - (-4))
slope = (4 - 1) / (3 + 4)
slope = 3/7
Determine the solutions of the equation [x - 30 = 11. 1. Rewrite for two solutions: (x – 3) = 11, -(x - 3) = 11 Solve for x in each equation. What are the solutions to the equation? O x= -14, -8 O x= -14,8 O X=-8, 14 O x= 8,14
First solution
(x-3)=11
x=11+3
x=14Second solution
-(x-3)-11
multiply by -1 both sides
x-3=-11
x=-11+3
x=-8therefore
answer is
-8,14
Triangle XWY is transformed to produce triangle URL. Select all the transformations that would guarantee triangles XWY and URL are congruent.
O reflection, then a translation
O dilation, then a reflection a
O rotation, then a dilation a
O translation, then a rotation.
O rotation, then a reflection
The correct transformations are;
1. Reflection, then a translation
2. Rotation, then a reflection
3. Translation, then a rotation.
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
Triangle XWY is transformed to produce triangle URL.
Now,
The images arise from transformation should remain the same with respect to the size or shape.
So, we get;
The correct transformations are;
1. Reflection, then a translation
2. Rotation, then a reflection
3. Translation, then a rotation.
Thus, The correct transformations are;
1. Reflection, then a translation
2. Rotation, then a reflection
3. Translation, then a rotation.
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The graph depicts the growth in costs using a line segment. Use the midpoint formula to approximate the cost during the year 1987.The approximate cost during the year 1987 was $ ____.
Answer:
The approximate cost during the years 1987 was $7527
Explanation:
The midpoint formula is:
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]For two given points.
In this case, we can see in the graph the points (1983, 5021) and (1991, 10033)
Then, using the midpoint formula:
[tex]M(\frac{1983+1991}{2},\frac{5021+10033}{2})=M(1987,7527)[/tex]Thus, the approximation for the year 1987 is $7527
Multiply and combine like terms to degerming the product of these polynomials.
(2 n-3)(5 n+6)
Enter your results in the response box.
Answer:
7n-18
Step-by-step explanation:
The working out is attached. Hope it helps!
what is ST? I've included a photo of the problem
Answer
ST = 14
According to the diagram
UV = VW
ST = UT
UT = VT - UV
UV = 14 and VT = 29
UT = 29 - 14
UT = 15
SInce UT = ST, Therefore, ST = 14
help meeeeeeeeeee pleaseeeeeeeeeeeeeeeeeee
Step-by-step explanation:
I just answered this. how often did you post this basic question ?
3² +4² + 12² is equal to n² for some positive number n . Find n.
Answer:
n = 13
Step-by-step explanation:
For this, you need to square all of the numbers and then add them together. Most of the time, you can put them into a calculator but I will work it out below.
Squaring means multiplying a number by itself, so we get:
3² + 4² +12² =n²
Turns into:
(3*3) + (4*4) +(12*12) = n²
Then work out the multiplication:
9 + 16 + 144 = n²
Add everything together
169 = n²
Now take the square root of each side:
[tex]\sqrt{169} =\sqrt{n^{2}}[/tex]
This comes out to be:
± 13 = n
The question asks for the positive number, so you answer is:
n = 13
Which of the following is an example of the associative property of multiplication?7 . (3 . 5) = (7 . 3) . 507. (3+5) = 21 + 357.(3.5) = 7 . (5. 3)0.1=1
The associative property of multiplication states that you can choose any pair of numbers to multiply first when there are more than two numbers being multiplied. This doesn't change the final result:
a . b . c = (a . b) . c = a . (b . c)
So, we see an example of such property in the first option:
7 . (3 . 5) = (7 . 3) . 5
Let's check this is indeed true:
7 . (3 . 5) = 7 . 15 = 105
(7 . 3) . 5 = 21 * 5 = 105
Therefore, the first option is correct.
Notice that the second option uses the distributive property of multiplication over addition:
a . (b + c) = a . b + a . c
The third uses the commutative property of multiplication:
a . b = b . a
The fourth is wrong since zero multiplied by any number is zero, not one:
0 . a = 0, for all values of a.
Write an equation. Let X represent the number described in the exercise. Then solve the equation & find the number. Four subtracted from the product of 5 and a number is 51.Write an equation.
We have to write an equation from the word problem,
Four subtracted from the product of 5 and a number is 51
Let's break it down:
--- product of 5 and a number can be written as,
[tex]\begin{gathered} 5\times x \\ =5x \end{gathered}[/tex]--- four subtracted from "product of 5 and a number" can be written as,
[tex]5x-4[/tex]^^ All this is equal to 51, so we can write,
[tex]5x-4=51[/tex]To find the unknown number, we solve the above equation. The steps are shown below:
[tex]undefined[/tex]<
Tobin's friend Rose claims that she can read minds. To test
Rose's abilities, Tobin draws 3 cards without replacement
from a standard deck of 52 playing cards. Tobin asks Rose
to identify each of the 3 cards she drew in order.
Assume that Rose has no special abilities and is randomly
guessing the cards.
What is the probability that Rose identifies all 3 cards in
the correct order?
The probability that rose identifies all 3 cards in the correct order is 1/132,600 by the concept of permutation.
What is permutation?It is the separate arrangements of a given number of associates taken all at once, or some of them, or just a few of them. There are two possible meanings, AB and BA, for instance, if we have the two elements A and B.
Following the arrangement of 'r' items from a total of 'n' elements, the number of permutations is,
nPr = n! / (n – r)!
Here to obtain the probability in correct order use permutation formula
Recall that, Probability is calculated as favorable outcomes divided by all possible outcomes.
Favorable number of outcomes = 1 (as only one order is correct)
Total outcomes = 52p3 (since 3 cards to be arranged from pack of 52)
So, the probability of rose identifies all 3 cards in correct order =1/52p3
Probability = [tex]\frac{1}{52!/(52-3)!}[/tex]
Probability = 49! /52!
Probability = 49! /52*51*50*49!
Probability = 1/52*51*50
Probability = 1/132,600
Therefore, the probability that rose identifies all 3 cards in the correct order is 1/132,600.
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A line intersects the points
(-2, 9) and (3, -11).
m = -4
Write an equation in point-slope form
using the point (-2, 9).
y - [?] =(x-)
Answer: (3,11)
Step-by-step explanation:
For the following, find f(2.1) and f(4).
Answer:
option A
Step-by-step explanation:
put x= 4 in condition 4<=x<8
as it satisfied condition
and put x= 2.1 in condition 2<x<4
Michael has a twelve gallon gas tank. When he filled
his tank up, he pumped nine gallons of gas. What
fraction of his tank had been empty?
Answer:
3/4
Step-by-step explanation:
9/12 Divide the top and bottom by 3
3/4
)) Sonoma bikes 5 miles to Paige's house. On a map, 5 they measure that distance as 7 cm. The same map shows that the mall is 3 cm from Paige's house. What is the actual distance between Paige's house and the mall?
Find the scale factor by dividing the real length by the map length. Since Sonoma's house is 5 miles away from Paige's house but they appear 7cm appart in the map, then the scale factor is:
[tex]undefined[/tex]A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of 10 corn plants. He labels the 100 plants 00–99. Refer to the given line from a random number table. Which numbers represent the sample of 10 corn plants?
58160 09695 38399 40400 32662 46254
58, 16, 00, 96, 95, 38, 39, 94, 04, 00
58, 16, 00, 96, 95, 38, 39, 94, 04, 32
58, 16, 96, 95, 38, 39, 94, 04, 32, 66
58, 16, 09, 69, 38, 39, 40, 32, 66, 46
Answer: Here the correct option is 2) 58, 16, 00, 96, 95, 38, 39, 94, 04, 32
Step-by-step explanation:
−2 4/5×(−3 1/2)
I really need help.
!!PLEASE HELP!!
Stefan is baking taquitos for a school fundraiser. The recipe calls for 2 1/2 cups of beans and 3 1/4 cups of rice. What is the ratio between cups of beans and cups of rice?
The ratio between cups of beans and cups of rice is 10/13 . Option C
What is ratio?
A ratio can described as an ordered pair of numbers, like y and z, that is written mathematically in the form y / z where the denominator of the fraction is not equal to zero.
It is known to describe the number of times an element or number contains another number proportionally.
It is also seen as the comparison of two quantities, elements or numbers that has the same units and likewise, explains how much one of the elements or quantity is found in the another one.
This is done based on their sizes or magnitudes.
A proportion is a mathematical equation with two ratios set equivalent or equal to each other.
Given that;
Beans = 2 1/ 2 cups
Rice = 3 1/4 cups
Convert to mixed fractions;
Beans = 5/2
Rice = 13/4
Now, divide the cups of beans by that of rice;
= 5/ 2 ÷ 13/4
= 5/2 × 4/13
= 10/13
Hence, the ratio is 10/13
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Please help if you can!!!
Use the function below to find f(-2).
f(x) = 3x
A. -6
B. -9
O C.
O D.
996
610
9
Answer:
option d is the correct answer
What what solid is generated when the semi circle is rotated about the line
Sphere solid is generated when the semicircle is rotated about the line.
Given,
The semi circle is rotated about the line.
To find the what solid is generated?
Now, According to the question:
We know that when a semicircle is rotated about any line then the three dimensional figure or a solid that is formed on this rotation transformation is Sphere.
Hence, Sphere solid is generated when the semicircle is rotated about the line.
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A bag with 10 marbles has 3 yellow marbles, 2 blue marbles, and 5 red marbles. A marble is chosen from the bag at random. What is the probability that it is yellow or blue? Write your answer as a fraction in simplest form.
I need help with this practice problem The subject is trigonometry It asks to graph the function If you can ❗️ use Desmos to graph
We will have the following:
The total bill for dinner was $43.75 (including tax and a tip). paid a 22.9% tip, what was his bill before adding the tip?
Answer:
$33.75
Step-by-step explanation:
22.9% of $43.75 = $10.0
43.75 - 10.0 = $33.75
Hope that helps
Answer:
$35.60
Step-by-step explanation:
I cross multiplied related numbers:
[tex]\frac{43.75}{x}[/tex]=[tex]\frac{122.9}{100}[/tex] cross multiply
4375=122.9x, divide both sides by 122.9
35.598=x round to hundredths
35.60
Find the slope of the line passing through the pair of points or state that the slope is
undefined. Then indicate whether the line through the points rises, falls, is horizontal, or
is vertical.
(3,-5) and (-7,-5)
...
Select the correct choice below and, if necessary, fill in the answer box within your
choice.
Answer:
The slope is o. The line will be vertical and the equation of the line is y = -5
Step-by-step explanation:
Find three number in arithmetic progression whose sun is 21 and product is 315
Answer:
Step-by-step explanation:
It should be option D
Barnaby decided to count the number of ducks and geese flying south for the winter. Thefirst day he counted 175 ducks and 63 geese. What is the ratio of ducks to the total num-ber of birds flying overhead in simplest terms?
So, here we have that there are 175+63 = 238 birds in total.
We want to know the ratio of ducks to the total number of birds flying overhead. There are 175 ducks for a total of 238, so the ratio is:
175:238
Sue traveled 96 miles in 12 hours. A unit rate to describe Sue's travel is 8 miles per hour. What is another unit rate in this situation?
Answer:
Sue travels 8 miles per hour.
Step-by-step explanation:
Part 3: Solve a real-world problem using a cube root function.
Once Isabel rented the warehouse space, she decided to post ads on several social media sites to advertise her online bookstore. Let x represent the number of months the ads have been posted. Isabel finds that the function below describes the number of books sold as a function of the number of months her ads have been posted.
f(x) = 1000 + 1000
⦁ How many books were sold after 8 months? (3 points)
⦁ Graph the function. (10 points)
Considering the given function, it is found that 3000 books were sold after eight months.
FunctionThe function in this problem is defined as follows:
f(x) = 1000(∛x) + 1000
In which f(x) represents the number of books sold after x months.
After eight months, we have that x = 8, hence the number of books is calculated as follows:
f(8) = 1000(∛8) + 1000
The lone instance of x in the function was replaced by eight to find the numeric value.
The cube root of eight is calculated as follows:
8 = 2 x 2 x 2 = 2³
Hence:
∛8 = 2
Thus the numeric value of the expression is:
f(8) = 1000(∛8) + 1000 = 1000 x 2 + 1000 = 2000 + 1000 = 3000 books.
The graph of the situation is given by the image at the end of the answer, at a domain of x >= 0, as the number of months cannot assume negative values.
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Need help answering the following polynomial
The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
The given expression is [tex]-x^{2}-\frac{1}{6}[/tex].
We have to complete the given sentence;
The expression represents a ........... polynomial with ........terms. The constant term is .........., the leading term is..........., and the leading coefficient is .................... .
we first complete the given sentence then we explain the sentence.
The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
Firstly about Quadratic Polynomial
When the highest degree term in a second-degree polynomial equals to 2, the polynomial is said to be quadratic.
Now about Constant Term
A number that is constant and does not have any variables in an algebraic expression is a constant term.
Now about Leading Coefficient
The numbers placed in front of the variable with the biggest exponent are known as leading coefficients.
Hence, the expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
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