Answer:13.9
Step-by-step explanation:
Using the compound interest formula, it will take approximately 14.9 years for an account with a $3,200 initial deposit and an 8.25% annual interest rate to grow to $9,600.
Explanation:To find out how long it will take for an account with an initial value of $3,200 and an annual interest rate of 8.25% to grow to $9,600, we can use the future value formula for compound interest:
The formula is FV = PV (1 + r)^n, where:
FV is the future value of the money after n years,PV is the present value or initial amount (which is $3,200),r is the annual interest rate (which is 0.0825), andn is the number of years.To find n when FV is $9,600, we rearrange our formula to solve for n:
n = log(FV / PV) / log(1 + r)
Now, plug in the values:
n = log(9600 / 3200) / log(1 + 0.0825)
n = log(3) / log(1.0825)
n ≈ 14.9 years
So, it will take approximately 14.9 years for the account value to reach $9,600.
What is the definition of the union of two mathematical sats ,A and B
Set contain all the elements present in both the sets.
Step-by-step explanation:
Definition:
The union of two mathematical sets can be defined as the set that consists of all the elements present in both the sets without the repetition of elements.
Consider, A and B be the sets.
A = {1,7,5,6,0}
B = {2,3,4,5,6}
U is the symbol of union of sets, so A U B = {1,2,3,4,5,6,7,0}
Here 5 and 6 are the elements present in both the sets, so written only once in the set of A U B.
If a line has a slope of 3/4, what is the
slope of the line perpendicular to the
line?
The perpendicular of the line is -4/3.
What is perpendicular?Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular sign ⊥ , can be used to visually depict the state of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.
Given a line has a slope of 3/4.
So the slope of the line perpendicular will have the opposite reciprocal as a slope,
That means perpendicular of a line = - reciprocal of slope of the line
perpendicular of a line = - (4/3)
Therefore the perpendicular of the line is -4/3.
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If the sum of the interior angles of a polygon is 3780, how many sides does it have?
Answer:
23
Step-by-step explanation:
Sum of angles = (n - 2) x 180
3780 = (n - 2) x 180 Divide both sides by 180
21 = n - 2
+ 2 + 2 Add 2 to both sides
23 = n
The shape has 23 sides.
If this answer is correct, please make me Brainliest!
The polygon having the sum of the interior angles 3780° have 23 sides.
What is interior angle?The inner of the two angles formed where two sides of a polygon come together is called the interior angle.
Given that, the sum of the interior angles of a polygon is 3780, we need to find the number of sides of the polygon,
We know that,
The formula for calculating the sum of interior angles is (n-2) × 180° where is the number of sides.
Therefore,
3780° = (n-2)×180°
n-2 = 3780° / 180°
n-2 = 21
n = 21+2
n = 23
Hence, the polygon having the sum of the interior angles 3780° have 23 sides.
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An sitplane pilot over the Pacific sights an stol at an angle of depression of 10%. At this time,
the horizontal distance from the plane to the stoll is 5.172 meters.
5084
5093
898
912
17. DIG DEEPER! The houses are identical.
Pls help me answer B and C.
(picture above)
Answer:
B: M
C: Side AB is 20ft
C: Perimeter = 96ft
6. A triangular sail has a base length of 2.5 meters. The area of the sail
is 3.75 square meters. How tall is the sail?
Answer:
3 meters
Step-by-step explanation:
Area of a Triangle
= 1/2 x b x h
Given
Base Length b = 2.5 meters
Area = 3.75 square meters
Height h = ?
Therefore
3.75 = 1/2 x 2.5 x h
3.75 = 2.5/2 x h
3.75 = 1.25 x h
Divide both sides by 1.25
3.75/1.25 = 1.25/1.25 x h
3 = h
h = 3 meters
The sail is 3 meters tall
The length of a rectangular state park is 2 miles longer than twice the width. The area of the park is 84 square miles. What is the width of the park?
Answer:
Step-by-step explanation:
hello : look this solution
Final answer:
To find the width of a rectangular state park with an area of 84 square miles where the length is 2 miles longer than twice the width, we set up a quadratic equation and solve for the width. The width of the park is 6 miles.
Explanation:
The question involves solving a quadratic equation to find the width of a rectangular state park where the length is 2 miles longer than twice its width, and the area is 84 square miles. To solve this problem, let's let w represent the width of the park.
According to the problem, the length l can be expressed as:
l = 2w + 2
The area A of a rectangle is given by the formula:
A = l × w
Substituting the given area and the expression for the length, we have:
84 = (w)(2w + 2)
Which simplifies to:
84 = 2w² + 2w
And further simplifies to:
0 = 2w² + 2w - 84
Dividing the entire equation by 2 to simplify:
0 = w² + w - 42
Now, we solve this quadratic equation for w, the width of the park. Using the quadratic formula or factoring (if possible), we find the positive value of w, which could be the width of the park since a width can't be negative:
w = 6
So, the width of the park is 6 miles.
0.44, 4/9, 0.4445, 44.5 on a number line please
The quotient of d minus 16 and 3 is 4 . Which equation shows this ?
Answer: d-16/3=4
Step-by-step explanation: thats the equation!
hope it helps please mark brainliest
Final answer:
The equation representing the statement "The quotient of d minus 16 and 3 is 4" is (d - 16) / 3 = 4. By solving the equation, we find that d = 28.
Explanation:
The question asks to find the equation that represents the statement: "The quotient of d minus 16 and 3 is 4." This translates to a mathematical equation by dividing the difference of d and 16 by 3, which equals 4. The equation that shows this relationship is (d - 16) / 3 = 4.
To solve this equation for d, you can follow these steps:
Multiply both sides of the equation by 3 to eliminate the denominator: (d - 16) = 12.
Add 16 to both sides of the equation to solve for d: d = 12 + 16.
This gives you d = 28 as the solution.
Therefore, the equation that accurately represents the given statement is (d - 16) / 3 = 4, and the value of d that satisfies this equation is 28.
erin is taking part in a play at the community theater the cast and crew ordered T-shirts for all the volunteers the cost of a t-shirt is $8 and the total delivery charges $45 for order if the center has no more than $325 to buy T-shirts how many t-shirts can they buy
Answer:
The answer is the second one because it is less than or equal to 35
Answer:
Second one
Step-by-step explanation:
A toy store buys action figures from a factory for $8.00 per action figure. If they mark-up the toys 110% before selling them, what is the price of one of the action figures in the store?
Answer:
$8.80
Step-by-step explanation:
Answer:
$8.80
Step-by-step explanation:
110% is the whole cost plus 10%. you have you're cost at 8$ add 10% and that is 80 cents.
What is the value of x?
The value of x is 3.
Solution:
In the given triangle, a = 4, b = 3, x = ? and y = 2.25.
To find the value of x:
The image of the formula is attached below.
Angle bisector theorem:
An angle bisector of a triangle divides the interior angle's opposite side into two segments that are proportional to the other two sides of the triangle.
[tex]$\frac{a}{b}=\frac{x}{y}[/tex]
[tex]$\frac{4}{3} =\frac{x}{2.25}[/tex]
Do cross multiplication.
9 = 3x
Divide by 3 on both sides,
3 = x
Switch the sides.
x = 3
The value of x is 3.
How do you graph 1.50x =60? I need to know the y and x axis
Answer:
you could graph y = 1.5x and y=60, then the intersection at (40,60) represents the solution of the equation.
can 3,4,7 make a possible right triangle?
Let's see by using the Pythagorean theorem.
3 and 4 are legs. 3 is the shortest leg.
7 is the hypotenuse.
The theorem states that:
a² + b² = c²
a = 3
b = 4
c = 7
3² + 4² = 7²
9 + 16 = 49
25 = 49 (Incorrect)
So it is not possible for 3,4,7 to be a right triangle.
The numbers 3, 4, and 7 do not satisfy the Pythagorean theorem, as the sum of the squares of 3 and 4 is 25, which does not equal the square of 7 (49). Hence, these numbers cannot form a right triangle.
To determine if the numbers 3, 4, and 7 can form the sides of a right triangle, we use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we would expect the square of the longest side (7) to be equal to the sum of the squares of the other two sides (3 and 4).
Calculating, we have:
32 + 42 = 9 + 16 = 25.
The square of the longest side is 72 = 49.
Since 25 does not equal 49, the sides 3, 4, and 7 do not satisfy the Pythagorean theorem and therefore cannot form a right triangle.
Determine whether the following statement is true or false. Explain.
All spheres are similar
Answer:
Below.
Step-by-step explanation:
They are all the same shape.
Also, the only parameter of a sphere that can vary is the radius, so they are all similar.
What is the slope of the line that passes through point (3,2)
(
3
,
2
)
and point (6,11)
(
6
,
11
)
?
Answer:
Slope=3
Step-by-step explanation:
Slope=Rise/Run=(11-2)/(6-3)=9/3=3
Answer:
The slope is 3.
Step-by-step explanation:
Use the slope formula.
[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
We use the y-coordinates of the two points as y2 and y1.
We use the x-coordinates of the two points as x2 and x1. x2 goes with y2. x1 goes with y1.
[tex] slope = m = \dfrac{11 - 2}{6 - 3} = \dfrac{9}{3} = 3[/tex]
The slope is 3.
(a) How would you characterize the relationship between money spent on advertising and items sold?
Explain.
(b) Sally uses the function y= 1.6x+ 21.5 to model the situation. What score does the model predict
should be spent in advertising to sell 30 items?
(c) What does the number 21.5 in Part (b) mean in the context of the situation?
Answer:
Answer:
a) Positive Correlation
b) 69.5
c) Base advertisement fee
Step-by-step explanation:
a) Relationship between money spent on advertising and items sold
If we spent greater amount of money on advertisement, thus, we create more awareness and thus, the number of item sold increases.
Similarly, if less money is spent on advertisement, the number of items sold will be less.
Thus, the money spent on advertisement varies directly with the number of items sold.
Thus, they have a positive relationship or a positive correlation.
b) Money spent in advertising to sell 30 items
We are given the function:
[tex]y= 1.6x+ 21.5[/tex]
We put x = 30
[tex]y(30)= 1.6(30)+ 21.5\\y(30) = 69.5[/tex]
Thus, the score predicted by model is 69.5 units.
c) Interpretation of 21.5
Comparing the equation to a general linear equation, we get
[tex]y = mx + c[/tex]
where m is the slope and c is the y-intercept.
y-intercept tells us the value of function when x is zero.
Thus, for the given scenario it will tell about the basic advertisement fee to be paid if we want to sell 0 products.
Comparing we get,
c = 21.5
Interpretation:
Thus, 21.5 units is the basic amount of advertisement fee that needed to be paid( the number of items sold is 0)
Jim earned $700 this week. This was $20 less than four times the amount he earned last week. Which equation, when solved for x, gives the amount of money Jim earned last week?
Solution:
Given that,
Jim earned $700 this week
This was $20 less than four times the amount he earned last week
To find: amount of money Jim earned last week
Let "x" be the amount of money Jim earned last week
From given,
Jim earnings this week = $20 less than four times the amount he earned last week
Therefore,
700 = 4x - 20
Thus the equation is found
Angela chooses between having $1,000 now, and investing it in a savings account so that she can have $1,050 a year from now, what is this called?
Final answer:
Compound interest is the concept discussed in this question. It refers to the interest calculated on both the initial principal amount and any accumulated interest from previous periods.
Explanation:
The subject of this question is Mathematics. Specifically, it relates to the concept of compound interest. Compound interest is the interest that is calculated on both the initial principal amount and any accumulated interest from previous periods. In this case, Angela is choosing between having $1,000 now or investing it in a savings account to have $1,050 a year from now. The $50 earned is the result of the interest earned on the initial $1,000.
What is 52,683 written in scientific notation? A. 52.683 x 10 B. 0.52683 x 10 C. 5.2683 x 10 D. 5.2683 x 10
Answer:
5.2683 x 10^4
Step-by-step explanation:
hope that help
If |OQ| = 9.4 units, |OQ’| = 17.1 units, and |P’Q’| = 17.1 units, determine |PQ|. Round your answer to the tenths place, if necessary.
Answer:
9.4 units.
Step-by-step explanation:
Given information: |OQ| = 9.4 units, |OQ’| = 17.1 units, and |P’Q’| = 17.1 units.
Dilated figure is similar to the original figure. It means the corresponding sides are proportional.
[tex]\dfrac{|OQ|}{|OQ'|}=\dfrac{|PQ|}{|P'Q'|}[/tex]
Substitute the given values.
[tex]\dfrac{9.4}{17.1}=\dfrac{|PQ|}{17.1}[/tex]
Multiply both sides by 17.1.
[tex]\dfrac{9.4}{17.1}\times 17.1=\dfrac{|PQ|}{17.1}\times 17.1[/tex]
[tex]9.4=|PQ|[/tex]
Hence, the measure of |PQ| is 9.4 units.
Can someone explain this?
Answer:
First, you know that a triangle has 180° total. So, you take 180-38-25 and that equals 117. So the corner inside the triangle is 117. So a straight line is also equal to 180. You take 180-117 and that is 63. 4x+3 = 63. You subtract 3 from both sides and get 4x = 60. To get x by itself you divide by 4 and x = 15.
Ms. Chang’s class decides to order posters that advertise a walkathon to raise money for a local charity. Ichiro obtains quotes from two different companies.Clear Prints charges $2 per poster. Posters by Sue charges $15 plus $.50 per poster.a. For each company, write an equation Ichiro could use to calculate the cost for any number of posters.b. For what number of posters is the cost the same for both companies? Explain.c. Which company do you think the class should buy posters from? Explain your reasoning.d. If Ms. Chang’s class has an $18 budget for posters, which company do you think the class should buy posters from? If Ms. Chang donates an additional $10 for ordering posters, does it impact the decision made? What factors influenced your decision?
Answer:
a. For each company, write an equation Ichiro could use to calculate the cost for any number of posters.
For Clear Prints: Cost(p) = 2pFor Sue: Cost(p) = 15 + 0.50pb. For what number of posters is the cost the same for both companies?
10 postersc. Which company do you think the class should buy posters from?
if the number of posters is less than 10 they should use Clear prints, because it costs is lower than Sue's.If the number of posters is equal to 10, the cost is the same with both companiesIf the number of posters is greater than 10 they should select Sue.d. If Ms. Chang’s class has an $18 budget for posters, which company do you think the class should buy posters from?
Clear Printe. If Ms. Chang donates an additional $10 for ordering posters, does it impact the decision made?
Yes, in this case the class must order the posters from Sue.What factors influenced your decision?
The budget and the charges of each company/Explanation:
a. For each company, write an equation Ichiro could use to calculate the cost for any number of posters.
Clear prints
Call p, the number of posters. The cost is the number of posters, p. times the unit cost per poster ($2):
Cost(p) = 2pSue
Using the same variable, p, for the number of posters, the cost is the flat rate, $15, plus the number of posters multiplied by the unit cost per poster, $0.50:
Cost(p) = 15 + 0.50pThe equations fhat Ichiro could use to calculate the cost for any number of posters, are:
For Clear Prints: Cost(p) = 2pFor Sue: Cost(p) = 15 + 0.50pb. For what number of posters is the cost the same for both companies?
Solve the system: equate both equations:
2p = 15 + 0.50p2p - 0.50p = 151.50p = 15p = 15/1.50p = 10
Conclusion: For 10 posters the cost is the same for both companies.
c. Which company do you think the class should buy posters from?
It depends on the budget and the number of posters desired.
You can calculate the range in which the cost is lower by one company of the other.
You already know that if you are ordering 10 posts, the cost is the same for both companies.
How much is that cost? Compute Cost (10):
Cost(10) = $2(10) = $20What happens if the number of posters is less or greater than 10.
Solve an inequality:
2p < 15 + 0.50p2p - 0.50p < 151.50p < 15p < 15 /1.50p < 10Hence,
if the number of posters is less than 10 they should use Clear prints, because it costs is lower than Sue's.If the number of posters is equal to 10, the cost is the same with both companiesIf the number of posters is greater than 10 they should select Sue.d. If Ms. Chang’s class has an $18 budget for posters, which company do you think the class should buy posters from?
In this case the decision is driven by the buget.
How may posters can the class order to pay $18?
With Clear Prints:
18 = 2pp = 18 / 2 = 9 postersWith Sue:
18 = 15 + 0.5p0.5p = 18 - 150.5p = 3p = 3 / 0.5p = 6 postersThen, with a budget of $18, the class should buy posters from Clear Print.
e. If Ms. Chang donates an additional $10 for ordering posters, does it impact the decision made?
Repeat the calculations:
For Clear print:
18 + 20 = 2pp = 38 / 2 = 19 postersFor Sue:
18 + 20 = 15 + 0.50p0.50p = 38 - 150.50p = 23p = 23 /0.5 = 46 postersWith a budget of $38 the class can buy more posters from Sue.
What factors influenced your decision?
The budget and the charges are the factors that influence the decision. Once you know the charges from each company, you can calculate the number of posters the class can order from each one, with a given budgent, and then make the best decision (economically speaking).The charges have two components that constitute the total cost: a flat fee (in the case of Sue) and a unit cost (in both cases).
Find the value of x...
x/6=15/20
Answer:
4 1/2
Step-by-step explanation:
x/6 = 15/20
Cross multiply
X x 20 = 6 x 15
20x = 90
Divide both sides by 20
x = 90/20
x = 9/2
x = 4 1/2
14. Mount Everest is 29,028 ft high. Mount Kilimanjaro is 19,340 ft high.
How much taller is Mount Everest?
Answer:
Mount Everest is taller by 9,688 ft.
Step-by-step explanation:
Find the difference between the heights.
29,028 - 19,340 = 9,688
:
Consider the expression 5.758−2.317. Estimate the difference by rounding each number to the nearest whole number and then subtracting.
Answer:
4
Step-by-step explanation:
5.728 rounds up to 6 because it is greater than 5.50 and 2.317 rounds down to 2 since it is less than 2.5. 6 - 2 = 4.
Final answer:
To estimate the difference between 5.758 and 2.317, you round 5.758 up to 6 and 2.317 down to 2, and then subtract to get an estimated difference of 4.
Explanation:
The student is asking how to estimate the difference between two numbers by rounding them to the nearest whole number before subtracting.
To estimate the difference between 5.758 and 2.317, we first round each number to the nearest whole number:
5.758 rounds up to 6 because the first digit after the decimal (7) is greater than 5.
2.317 rounds down to 2 because the first digit after the decimal (3) is less than 5.
After rounding the numbers, we perform the subtraction:
6 - 2 = 4
Therefore, the estimated difference is 4.
f(x) =-6x2 - 5x + 4; find f(-2)
Answer:
f(-2) = 2
Step-by-step explanation:
I'm assuming "-6x2" is actually "6x^2"
f(x) = -6x^2 - 5x + 4
Plug in -2 for the x's
f(-2) = -6(-2)^2 - 5(-2) +4
f(-2) = -6(2) - 5(-2) + 4
f(-2) = -12 + 10 + 4
f(-2) = -12 + 14
f(-2) = 2
Help pleaseeeee surface area again
Answer:
490 ft^2
Step-by-step explanation:
Base: 14 × 7 = 98 (×4 = 392)
Square faces: 7 × 7 = 49 (×2 = 98)
Add: 392 + 98 = 490
Malia's family traveled
7
10
of the distance to her uncle’s house on Saturday. They traveled
2
3
of the remaining distance on Sunday. What fraction of the total distance to her uncle’s house was traveled on Sunday?
Answer:
3/9
Step-by-step explanation:
Jenna takes a survey of students in her class to determine how many hours they studied for their Math exam. The mean of the responses is 5.6 hours. Which conclusion MUST be true?
A) No one in the class studied more than 5 hours.
B) Every member of the class studied for the exam.
C) At least one person in the class studied 1 hour.
D) At least one person in the class studied more than 5 hours.
A) No one in the class studied more then 5 hours
Answer:
d
Step-by-step explanation:
trust me