Final answer:
To determine the initial amount needed in a bank account to reach $10,000 in ten years with 10% compound interest, use the compound interest formula.
Explanation:
To find out how much money you need to put in a bank account to have $10,000 in ten years with 10% interest compounded annually:
Use the formula for compound interest: A = P(1 + r/n)^(nt)
Plug in the values: $10,000 = P(1 + 0.10/1)^(1*10)
Solve for P: P = $10,000 / (1.10^10)
Calculation:
PV = FV / (1 + r/n)^(n*t)
Inserting the known values:
PV = $10,000 / (1 + 0.10/1)^(1*10)
PV = $10,000 / (1.10)^10
Calculating the exponent:
PV = $10,000 / 2.59374
Finally:
PV = $3,855.43 (approximately)
Therefore, you need to put approximately $3,855.53 into the bank account initially.
A portion of a city map is shown in the figure at the right. If you walk along Maple Street between 2nd Street and Elm Grove Lane, how far do you walk? Round your answer to the nearest tenth of a yard.
The length is 259.4 yd.
We have to find the length of AC.
using sin rule,
we have
[tex]\frac{c }{Sin C} = \frac{b}{sinB}[/tex]
[tex]\frac{210}{sin 54} = \frac{b}{sin 88}[/tex]
[tex]b =\frac{210 sin 88}{sin 54}[/tex]
[tex]b = 259. 4161\\b = 259.4[/tex]
The length is 259.4 yd.
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Question
Given quadrilateral RSTU, determine if each pair of sides (if any) are parallel and which are perpendicular for the coordinates of the vertices.
R(1, -3), S(4, -1), T(2, 2), U(-4, -2)
Click on the graphic to complete the answer.
If the polynomial x^5 − 10^5 can be split as the product of the polynomials x − 10 and a, what is a?
a) x^4 - 99,990
b) x^4+10x^3+100x^2+1000x -10,000
c) x^4+10x^3+100x^2+1,000x+10,000
d)x^4+10x^3+100x^2+1000x + 10000/x-10
e)x^4 - 99990/x-10
please help !,
Rugs sell for $8 per square foot. Beth bought a 9-foot-long rectangular rug for $432. How wide was the rug?
You flip 2 coins.what is the probability that one coin will land on heads and one coin will land on tails?createa sample space of outcomes.
Which equation is in slope-intercept form and represents a line with slope 3 through the point (9, –4)?
y=3x+21
y=3x-31
-3x+y=-31
-3x+y=21
The equation in slope-intercept form representing a line with a slope of 3 and passing through the point (9, -4) is y = 3x - 31. This is found by substituting the point coordinates into the slope-intercept equation and solving for the y-intercept.
The question involves finding an equation in slope-intercept form that represents a line with a given slope that passes through a specific point. Slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept. Given the slope of 3 and the point (9,
–4), we can find the correct equation by substituting into the slope-intercept form and solving for b.
The correct equation must satisfy the condition that when x is 9, y is –4. Let's use this condition to solve for b:
y = mx + b
–4 = 3(9) + b
–4 = 27 + b
b = –4 - 27
b = –31
Therefore, the equation of the line is y = 3x – 31. This is the only equation among the choices that is in slope-intercept form and satisfies the given conditions.
What is the factored form of the following expressions x^2-100xy+24y^2
Ribbon candy costs 2.50 per foot how many feet can you buy if you have 11.25
Solution :
Given that , Ribbon candy costs 2.50 per foot.
To calculate the length of Ribbon candy you can buy with 11.25, first you need to calculate the length of Ribbon candy you can buy with 1.
Solving it by Unitary Method,
In 2.50 you can buy 1 foot Ribbon candy,
In 1 you can buy [tex] \frac{1}{2.50} [/tex] foot Ribbon candy,
So, In 11.25 you can buy [tex] \frac{1}{2.50} \times 11.25 =4.5 [/tex]
Hece , In 11.25 you can buy 4,5 foot of ribbon candy.
The number 12,089 is?
< 12,098.
= 12,098.
> 12,098.
Or none of these is correct
Final answer:
The numbers 12,089 is less than 12,098, as determined by comparing the ones place of each number., hence the correct option is A
Explanation:
The student asks for the correct comparison between the numbers 12,089 and 12,098. To generate an accurate answer, we compare the digits from left to right.
Since the thousands, hundreds, and tens places are the same, we look at the ones place to determine which number is greater. Comparing the ones digits, we see that 9 (in 12,098) is greater than 8 (in 12,089), therefore 12,089 is less than 12,098.
The correct answer is:
12,089 < 12,098.
What do you need to do to solve x/6=18
Ms. Gartland bought x number of shirts for the new members of her chorus. The cost for the x number of shirts, including $3.99 shipping, was $77.49. Each shirt cost $12.25. There was no sales tax on this purchase. Write an equation that can be used to find x.
5. given no other restrictions, what are the domain and range of the following funtction? f(x)=x^2-2x+2 if your in connexus and have done the algebra 2 final could you give me the awnsers
here Choose the point-slope form of the equation below that represents the line that passes through the points (−6, 4) and (2, 0).
y − 4 = −one half(x + 6)
y − 4 = 2(x + 6)
y + 6 = −one half(x − 4)
y + 6 = 2(x − 4)
Question 2 (Multiple Choice Worth 2 points)
Given the equation y − 3 = one half(x + 6) in point-slope form, identify the equation of the same line in standard form.
x − 2y = −12
y = one halfx
y = one halfx + 6
y = one halfx + 9
Question 3 (Multiple Choice Worth 2 points)
Given the equation y − 4 = three fourths(x + 8) in point-slope form, identif
Mickey is 40 years old and has his retirement savings in a 401(k). If he makes $55,000 annually, what is the maximum percentage of his income that he can contribute to his 401(k) plan per year? (The current maximum contribution limit is $16,500.)
Answer:
30%.
Step-by-step explanation:
We have been given that Mickey makes $55,000 annually and the current maximum contribution limit to 401(k) plan is $16,500. We are asked to find the maximum percentage Mickey can contribute of his 401(k) plan.
To find the maximum contribution percentage, we need to figure out $16,500 is what percent of $55,000.
[tex]\text{The maximum contribution percentage}=\frac{\$16,500}{\$55,000}\times 100[/tex]
[tex]\text{The maximum contribution percentage}=0.30\times 100[/tex]
[tex]\text{The maximum contribution percentage}=30\%[/tex]
Therefore, Mickey can contribute 30% of his annual income to his 401(k) plan at maximum.
What is the formula of quadratic equations?
Final answer:
The quadratic formula is used to find the solutions of quadratic equations. It is x = (-b ± √(b² - 4ac)) / (2a). The discriminant determines the nature of the solutions.
Explanation:
The formula for quadratic equations is:
x = (-b ± √(b² - 4ac)) / (2a)
Quadratic equations are equations of the form ax² + bx + c = 0. The quadratic formula is used to find the solutions or roots of these equations. The discriminant, b² - 4ac, determines the nature of the solutions: if it is positive, there are two real solutions; if it is zero, there is one real solution; and if it is negative, there are two complex solutions.
write the number 0.5 in the form a/b using integers to show it is a rational number
A.5/11
B.5/10
C.5/100
D.2/1
Answer:
The correct option is B.
Step-by-step explanation:
The given number is 0.5.
If a number can be defined as a/b where b≠0, then it is called a rational number.
We need to rewrite the given number in the form of a/b using integers.
Multiply and divide the given number by 10 to remove the decimal from the given number.
[tex]0.5\times \frac{10}{10}[/tex]
On simplification we get
[tex]\frac{0.5\times 10}{10}[/tex]
[tex]\frac{5}{10}[/tex]
Here a=5 and b=10 both are integers.
The given number 0.5 is a ration number because it can be written as 5/10.
Therefore the correct option is B.
If you pick a gumball at random, put it back, and then pick another gumball at random, what is the probability of picking a blue gumball then picking a yellow gumball?
Answer:
its 1/50
Step-by-step explanation:
Dilation dv, 2/5 (look at picture) was performed on a rectangle. How does the image relate to the pre-image? Check all that apply. (i included picture of the above dilation because i wasnt sure if it would be helpful)
A. The image is a reduction because n < 1.
B. The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.
C. The angles of the image are two-fifths the size of the angles of the pre-image.
D. The center of dilation is at point Q.
E. The base of the image is two-fifths the size of the base of the pre-image.
Answer:
Dilation =[tex]\frac{2}{5}[/tex] was done on a rectangle.
→As Factor of Dilation is 0.4, which is less than 1.
→So, the image will be smaller in size than Pre image.
→As, the two rectangles , Pre image and image are similar so their sides will be proportional.
As in similar figures the interior angles are congruent.
As the images are similar , so Base of the image will be two fifths of the size of the base of preimage.
Option A,B and E are Correct.
A: The image is a reduction because n < 1.
B : The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.
E. The base of the image is two-fifths the size of the base of the pre-image.
You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. You want the mixture to be 50% white vinegar and 50% water. How many cups of white vinegar do you need to add to the mixture?
To change a mixture that is 10% vinegar and 90% water to a 50-50 mixture, one would have to add 8 more cups of vinegar. This is because there are already 9 cups of water in the 10 cup solution, so adding 8 more cups of vinegar will total to 9 cups of vinegar and 9 cups of water.
Explanation:This question can be tackled using a simple mathematical approach. You already have a mixture that is 10% vinegar and 90% water, which means you have 1 cup of vinegar in your 10 cups of solution (because 10% of 10 cups is 1 cup). To get a 50-50 mixture, you also need the amount of water to equal the amount of vinegar. Since you already have 9 cups of water in the solution, you need to add 8 more cups of vinegar to balance it out and get a 50% solution. So you'll need to add 8 cups of white vinegar to your mixture in order to attain a balance of 50% vinegar and 50% water.
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Working together, it takes two roofers 10 hours to put a new roof on a portable classroom. if the first roofer can do the job by himself in 12 hours, how many hours will it take the second roofer to do the job by himself?
Number of hours the second roofer to do the job by himself is 60 hours.
Given that, working together, it takes two roofers 10 hours to put a new roof on a portable classroom.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Working together 1/10 roofs per hour
First roofer 1/12 roofs per hour
So, equation is x + 1/12 = 1/10
x = 1/10 - 1/12
= 6/60 - 5/60 = 1/60
Together, they work 1/60 + 1/12
= 1/60 + 5/60
= 6/60 = 1/10
Therefore, number of hours the second roofer to do the job by himself is 60 hours.
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A stadium can seat 46,000 people for a baseball game. One day, 49,442 people attended a game. How many people had to stand because they did not have a seat? 3. Draw a picture or a chart that shows the information and the question
An expression is shown below:
3x3y + 15xy − 9x2y − 45y
Part A: Rewrite the expression so that the GCF is factored completely. Show the steps of your work. (4 points)
Part B: Rewrite the expression completely factored. Show the steps of your work.
Using the graph below, calculate the average rate of change for f(x) from x = 2 to x = 6.
exponential function going through points 2, 2 and 6, 6
−4
−1
1
4
Answer:
The average ate of change for f(x) from x=2 to x=6 is one, (1). Also seen as choice c.
Step-by-step explanation:
I need help making a linear equation for this scenario?
"You have relatives living in the United Kingdom and in France. Suppose that you have purchased a prepaid phone card with a value of $75. Calls to the United Kingdom cost 23 cents per minute, while calls to France cost 21 cents per minute."
"Write a linear equation in two variables to represent the number of minutes you can use to call those two locations.",
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
Hi, can somebody please help me with this problem? Thank you.
"which answer is not a theorem or postulate used to prove triangles' similarity?"
in simple words it is SSA
Could anyone assist me here?
The table shows ordered pairs for a polynomial function, f.
x f(x)f(x)
−2−2 30
−1−1 0
0 −2−2
1 0
2 30
3 160
4 510
What is the degree of f?,
Answer:
The degree of the polynomial function will be 4.
Step-by-step explanation:
The table shows the ordered pairs for a polynomial function, f.
[tex]x[/tex] -2 -1 0 1 2 3 4
[tex]f(x)[/tex] 30 0 -2 0 30 160 510
Now, to get the degree of the polynomial, it is required to get the difference of the value of function. When the value of the function becomes equal, then the number of step or difference will be its degree.
So, the first difference of the function will be,
[tex]0-30=-30\\ -2-0=-2\\0-(-2)=2\\30-0=30\\160-30=130\\510-160=350[/tex]
Now, the second difference of the function will be,
[tex]-2-(-30)=28\\2-(-2)=4\\30-2=28\\130-30=100\\350-120=220[/tex]
Now, the third difference of the function will be,
[tex]4-28=-24\\28-4=24\\100-28=72\\220-100=120[/tex]
Now, the fourth difference of the function will be,
[tex]24-(-24)=48\\72-24=48\\120-72=48[/tex]
So, the fourth difference of the function is equal and hence, the degree of the polynomial function will be 4.
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So I just wanna see if I got this one correct my question is.... Each volume of an encyclopedia is 2 1/3 inches wide. How many volumes will fit on a shelf 18 inches wide?
Jamal wrote the following statements: Statement 1: Perpendicular lines are two lines that intersect at 90° angles. Statement 2: All right angles are congruent. Which geometry term does each statement represent?