Using compound interest, it is found that Claire will have $6,186 in her account when Henry's money has tripled in value.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For Henry, we have that r = 0.0675, n = 12. The time it takes for the amount to triple is t when A(t) = 3P, hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]3P = P\left(1 + \frac{0.0675}{12}\right)^{12t}[/tex]
[tex](1.005625)^{12t} = 3[/tex]
[tex]\log{(1.005625)^{12t}} = \log{3}[/tex]
[tex]12t\log{(1.005625)} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{12\log{(1.005625)}}[/tex]
t = 16.32.
Then, for Claire, we have that the parameters are as follows:
P = 2300, r = 0.0625, n = 1, t = 16.32.
Hence, the amount is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(t) = 2300\left(1 + \frac{0.0625}{1}\right)^{16.32}[/tex]
A(t) = 6186.
Claire will have $6,186 in her account when Henry's money has tripled in value.
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The ratio of the measures of the sides of a triangle is 9:12:5. If the perimeter of the triangle is 130 feet, find the measure of the sides.
Answer:
The sides of the triangle are 45, 60, and 25 ft
Step-by-step explanation:
9 + 12 + 5 equals 26.
Now we need to get the first two sides.
9/26 × 130 = 1170/26 = 45
In order to obtain the other side;
12/26 = 1560/26 = 60
And to obtain the third side:
5/26 × 130 =650/26 = 25
Therefore, the sides of the triangle are 45, 60, and 25 ft
I hope this helps! ^-^
the sum of two rational number is -8 ,if one of the number is -10/1, find the other number.
Answer:
2
Step-by-step explanation:
-10 + x = - 8 add 10 to both sides of the equation
x = 2
PLEASE I NEED HELP!!!
The original cost for a pair of sneakers is $65. After discounts, the total price for the sneakers came to $55.25. What percentage discount is that?
15%
20%
18%
5%
Korey is planning to open a comic book store near his home. after completing a population survey for 3,520 homes in a 5 mile radius, korey created the chart below to include in the market analysis section of his business plan. korey expects 75% of his business to come from kids in high school and grade school. about how many of homes surveyed fit into one of these two categories? a pie chart titled population surveys. retired (55 plus), 10 percent; family (kids in college), 8 percent; family (kids in high school), 18 percent; family (kids in grade school), 32 percent; family (no kids), 20 percent; single, 12 percent. a. 493 b. 637 c. 1,126 d. 1,760
Kids in grade school have a maximum percentage of 32 reasons that Option (d) is the correct answer.
why are the grade-school-aged kids surveyed?Korey did the market analysis section of his business plan after conducting a population survey of 3,520 homes within a 5-mile radius.
He discovered that younger children who read comic books as children are more likely to read them as adults, resulting in a current and future client base.
For more information about the market analysis survey, refer below
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Find the area! (Don’t need to explain)
Area of vertical rectangle:-
13(5)65mm²Area of horizontal rectangle:-
13(2)26mm²Area of triangle:-
1/2(13-10)(5)1/2(3)(5)15/27.5mm²Total area:-
7.5+26+6598.5mm²What I'd the value of x
Answer:
Can you please give us figure so that i can help you
A cylinder has a base radius of 10in and a height of 20in. What is its volume in cubic in, to the nearest tenths place?
Answer:
6283.2
Step-by-step explanation:
[tex]V=\pi r^{2} h[/tex]
[tex]= \pi*10^{2} *20=6283.2[/tex]
Answer:
V=1570.8in³
Step-by-step explanation:
The formula for finding a cylinder using base diameter and height: V= π(d/2)² • h
if the:
D-10in
H-20in
V=π(10/2)²•20
which equals 1570.8in³
-my bad thought it said base diameter no radius
which of the following is a property of all rectangles
Answer:
The fundamental properties of rectangles are:
A rectangle is a quadrilateralThe opposite sides are parallel and equal to each otherEach interior angle is equal to 90 degreesThe sum of all the interior angles is equal to 360 degreesThe diagonals bisect each otherBoth the diagonals have the same lengthA rectangle with side lengths a and b has the perimeter as 2a+2b unitsA rectangle with side lengths a and b has the area as: ab sin 90 = ab square unitsThe sum of the interior angles is equal to 360 degreesA diagonal of a rectangle is a diameter of its circumcircleIf a and b are the sides of a rectangle, then the length of each diagonal is: [tex]\begin{array}{l}d = \sqrt{a^{2}+b^{2}}\end{array}[/tex]The diagonals bisect each other at different angles. One is acute, and another one is an obtuse angleIf the two diagonals bisect each other at right angles, then the rectangle is known as a squareA cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the longer parallel sides. In this case, the height of the cylinder is equal to the width of a rectangle. Also, the cylinder diameter is equivalent to the length of a rectangleA cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the shorter parallel sides. In this case, the height of the cylinder is equal to the length of a rectangle. Similarly, the cylinder diameter is equivalent to the width of a rectangleStep-by-step explanation:
Since you said, which of the following, I don't see any attachment. Yet, this is my best try at giving you an answer. Please mark my answer brainliest :)
Identify the y-intercept and slope of
the line.
y= 2x - 5
Answer:
y-intercept = -5
slope = 2
Step-by-step explanation:
Hello!
The y-intercept is always the y-coordinate when the line touches the y-axis. You can find this by plugging in 0 for x in the equation or choosing the last term in slope-intercept form.
Slope intercept form: y = mx + b
y = outputx = inputm = slopeb = y - interceptGiven this info, we can see that the slope, m, is 2, from our equation of y = 2x - 5, and the y-intercept is -5
John put away 36 of 48 shirts in his closet. Don has 84 shirts. If he put away the same percent, how many shirts did Don put in his closet?
Answer:
63
Step-by-step explanation:
John's percentage:
36 and 48 have a common factor of 12 so divide both of them by 12.
36/12= 3 and 48/12=4 therefore
so 36/48= 3/4 which is 75% but we don't need to focus on the percent.
Don's no. of shirts:
we know Don has 84 shirts so we say
3/4 of 84= no. of shirts that Don put in his closet
84/4=21 21x3=63
Don put 63 shirts in his closet.
Hope that helped! Anymore questions just ask! :)
Find the value of x.
Y
23
X
L
K
29
N
11x + 2
W
35
3
33
None of these
Answer: 3
Step-by-step explanation:
The answer to the question including equations is "None of these."
The value of x cannot be determined from the information given. The answer choices are all numbers, but they do not follow any obvious pattern. There is no mathematical operation that can be performed on the answer choices to arrive at a single value for x.
If we were given more information about the problem, such as the relationship between the answer choices, then we might be able to determine the value of x. For example, if we were told that the answer choices are all prime numbers, then we could rule out all of the answer choices except for 2 and 3. However, without more information, the value of x cannot be determined.
Here is a more detailed explanation of why the value of x cannot be determined:
The answer choices are all numbers, but they do not follow any obvious pattern. For example, the answer choices are not consecutive numbers, nor are they all even or odd numbers.
There is no mathematical operation that can be performed on the answer choices to arrive at a single value for x. For example, we cannot add, subtract, multiply, or divide the answer choices to get a single value for x.
If we were given more information about the problem, such as the relationship between the answer choices, then we might be able to determine the value of x. For example, if we were told that the answer choices are all prime numbers, then we could rule out all of the answer choices except for 2 and 3. However, without more information, the value of x cannot be determined.
Therefore, the answer to the question is "None of these."
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PLEASE HELP I'M SO CLOSE TO BEING DONE
Answer:
see explanation
Step-by-step explanation:
the perimeter (P) is the sum of the 3 sides of the triangle.
P = 4x² + 1 + 26x + 6 + x² + 10x ← collect like terms
= 5x² + 36x + 7
to factor the expression, consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 5 × 7 = 35 and sum = 36
the factors are + 35 and + 1
use these factors to split the x- term
5x² + 35x + 1x + 7 ( factor the first/second and third/fourth terms )
= 5x(x + 7) + 1 (x + 7) ← factor out (x + 7) from each term
= (x + 7)(5x + 1) , then
P = (x + 7)(5x + 1) ← in factored form
What is the area of a trapezoid based right prism that has the volume of 30cm cubed
Answer:
6 cm²
Step-by-step explanation:
V = Bh
30 = B (5)
[tex]b \: = \frac{30}{5} = 6 \: cm {}^{2} [/tex]
Tina buys tickets to an amusement park. Adult tickets cost $18.50 each and children tickets cost $12.25 each. Tina has $280 to purchase both adult and children's tickets. If she purchases 6 children's tickets, determine algebraically the maximum number of adult tickets that Tina can purchase.
Answer: 11 adult tickets
Step-by-step explanation:
First, we will write an equation. Let x be adult tickets and y be children tickets.
$280 ≥ 18.5x + 12.25y
Now I will graph it!
-> See attached
If she bought 6 children's tickets, we can look to the y value of 6 (children's tickets) to find our maximum value of x (adult tickets).
This means she can buy a maximum of 11 tickets because we will assume she cannot buy part of a ticket.
She can buy 11 adult tickets.
Which equation has a graph that lies entirely above the x-axis?
y = –(x + 7)2 + 7
y = (x – 7)2 – 7
y = (x – 7)2 + 7
y = (x – 7)2
Answer:
[tex]y = (x - 7)^{2} + 7[/tex].
Step-by-step explanation:
Let [tex]a[/tex], [tex]h[/tex], and [tex]k[/tex] be constants, and let [tex]a \ne 0[/tex]. The equation [tex]y = a\, (x - h)^{2} + k[/tex] represents a parabola in a plane with vertex at [tex](h,\, k)[/tex].
For example, for [tex]y = -(x + 7)^{2} + 7 = -(x - (-7))^{2} + 7[/tex], [tex]a = (-1)[/tex], [tex]h = (-7)[/tex], and [tex]k = 7[/tex].
A parabola is entirely above the [tex]x[/tex]-axis only if this parabola opens upwards, with the vertex [tex](h,\, k)[/tex] above the [tex]x\![/tex]-axis.
The parabola opens upwards if and only if the leading coefficient is positive: [tex]a > 0[/tex].
For the vertex [tex](h,\, k)[/tex] to be above the [tex]x[/tex]-axis, the [tex]y[/tex]-coordinate of that point, [tex]k[/tex], must be strictly positive. Thus, [tex]k > 0[/tex].
Among the choices:
[tex]y = -(x + 7)^{2} + 7[/tex] does not meet the requirements. Since [tex]a = (-1)[/tex], this parabola would open downwards, not upwards as required.[tex]y = (x - 7)^{2} - 7[/tex] does not meet the requirements. Since [tex]k = (-7)[/tex] and is negative, the vertex of this parabola would be below the [tex]x[/tex]-axis.[tex]y = (x - 7)^{2} + 7[/tex] meet both requirements: [tex]a = 1[/tex] and [tex]k = 7[/tex].[tex]y = (x - 7)^{2}[/tex] (for which [tex]k = 0[/tex]) would touch the [tex]x[/tex]-axis at its vertex.Answer:
its c
Step-by-step explanation:
round to the nears hundrend .7,666
Answer:
.767
Step-by-step explanation:
0. ones, tens, hundreds, thousands
Surface area- Rectangle
Please help ASAP
Answer:
The surface area of the rectangle is 2670
Find the volume of the prism below.
7 cm
3 cm
16 cm
A cubic cm
Answer:
i dont have the answer but heres a little help to find your answer:)
Step-by-step explanation:
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle.
what comes first i genuinely forgot, like is (2,3) on a graph (x,y) or is it (y,x)
Answer:
(x,y)
Step-by-step explanation:
x comes first always
(x,y)
so 2 would be the x value and 3 would be the y value
Which statement is correct? twenty-nine seventh-grade students chose a sports activity. twenty-eight eighth-grade students chose a sports activity. twenty-four seventh-grade students chose a non-sports activity. thirty-nine eighth-grade students chose a non-sports activity.
There are 24 students in the 7th grade who chose non-sports. Then the correct option is C.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
A group of 120 seventh- and eighth-grade students were asked whether they participate in sports or in non-sports-related activities. The two-way table shows.
Participation in Sports or Non-Sports
There are 24 students in the 7th grade who chose non-sports.
More about the statistics link is given below.
https://brainly.com/question/10951564
Answer:
C
Step-by-step explanation:
Type the correct answer in the box. the volume of clay used to build a cylindrical pillar with a height of 9 centimeters is 324π cubic centimeters. the area of the base of the pillar is π square centimeters.
Answer:
113.04
Step-by-step explanation:
Given:V = 324 cu
cmh = 9 cm
Since the formula for the volume of a cylinder is V = AreaBase*heightAreaBase = V/height = 324cu cm/ 9 cmAreaBase = 113.04 square centimetresTherefore, the area of the pillar in square centimeters is 113.04
The base area of the cylindrical pillar would be; 113.04 cm²
What is the Volume of a cylinder?The volume of the cylinder is the product of the height, pie, and square of the radius.
v = πr²h
where, r = radius, h = height
Therefore,
v = 324π cm³
h = 9cm
Consider find the radius;
324π = 9πr²
r² = 324π /9π
r² = 36
r = √36
r = 6 cm
Base area of the pillar = πr²
Base area of the pillar = 36π
Base area of the pillar = 36 × 3.14
Base area of the pillar is 113.04 cm²
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a store found out that 10% of people who had bought a certain brand of a coffee grinder were unhappy with it. if there were 72 people who were happy with it, then how many people in total had bought that brand
Answer:
the answer is 720
Step-by-step explanation:
you multiply 72 × 10.
Marcus traveled 45.5 miles in 3.25 hours. Part A: How many feet did Marcus travel? (1 mile = 5,280 feet) feet Part B: How many minutes did Marcus travel? minutes
Answer:
part a is 240240
Step-by-step explanation:
multiply the value in miles by the conversion factor '5280'.
help me please please
Answer:
x + 1, y - 4
Step-by-step explanation:
Look at a point on EFGH, then its corresponding point on E'F'G'H'. Taking E, you can see that E' is one to the right and four down from it.
If you want it in math terms instead of visual ones, you can see that E is (-1, 1) and E' is (0, -3). How do you get from (-1, 1) to (0, 3)? You add 1 to x and subtract 4 from y. You can then go through all 4 points and see this is the relationship between all of them! :-)
When Joseph first starts working at a grocery store, his hourly rate is $10dollar sign, 10. For each year he works at the grocery store, his hourly rate increases by $0.50dollar sign, 0, point, 50.
Joseph's hourly rate R, in dollars, is a function of t, the number of years he works at the grocery store.
Write the function's formula.
Answer:
R(t)=10+0.50t
Step-by-step explanation:
Let t be the number of years.
We have been given that When Joseph first starts working at a grocery store, his hourly rate is $10.
For each year he works at the grocery store, his hourly rate increases by $0.50.
So the hourly rates after t years will be 10 plus 0.50t.We can represent this information in an equation as: R(t)=10+0.50t
Therefore, the function R(t)=10+0.50t represents Joseph's hourly rates after t years.
(Hope this helps pls can I have brainlist have a great day )
The polynomial −2x3 − x2 13x in the last line is the result of dividing x2 3x 1 by 3x2 and bringing down 13x. subtracting 3x4 9x3 3x2 from the dividend and bringing down 13x . multiplying 3x2 by x2 3x 1.
Subtracting 3x^4+9x^3x^2 from the dividend and bringing down by 13x, the quotient is 3x^2-2x+5, and the term 3x^2 in the quotient is the result of dividing 3x^4 by x²
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have a polynomial:
[tex]=\rm -2x^3-x^2+13x[/tex]
The dividend polynomial:
[tex]\rm = 3x^4+7x^3+2x^2+13x+5[/tex]
If we subtract the polynomial [tex]\rm 3x^4+9x^3+3x^2[/tex] from the dividend polynomial, we will get:
[tex]\rm = (3x^4+7x^3+2x^2+13x+5)-(3x^4+9x^3+3x^2)[/tex]
[tex]\rm = -2x^3-x^2+13x+5[/tex]
After bringing down 13x, we will get the polynomial:
[tex]=\rm -2x^3-x^2+13x[/tex]
If complete the division of the polynomial, we will get:
[tex]\rm = \frac{(3x^4+7x^3+2x^2+13x+5)}{x^2+3x+1}[/tex]
= [tex]=\rm 3x^2-2x+5[/tex]
Thus, the subtracting 3x^4+9x^3x^2 from the dividend and bringing down by 13x, the quotient is 3x^2-2x+5, and the term 3x^2 in the quotient is the result of dividing 3x^4 by x²
Learn more about Polynomial here:
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Mia placed a point P on the number line give the value of the number P as a fraction what does the denominator denominator of a fraction present on the number line what does the numerator of a fraction represent a number one answer answer and explain your explanation boat space provided
Mia's fraction is an illustration of number lines
The fraction present on the number line is 5/6
How to determine the fraction?From the complete question, we have the following parameters:
Sections on the number line = 6Section on the point P = 5This means that, the fraction represented by the point P is:
P = 5/6
Hence, the fraction present on the number line is 5/6
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Which correctly applies the distributive property to show an equivalent expression to (8.6)(–2.5)?
(8)(2) – (0.6)(0.5)
(8)(–2) – (0.6)(–0.5)
(8.6)(2) – (8.6)(0.5)
(8.6)(–2) + (8.6)(–0.5
Answer:
(8.6)(-2)+(8.6)(-0.5)
Step-by-step explanation
Since -2+-0.5= -2.5, we need to use a plus sign. Also, since we multiply both by 8.6, that is the answer.
What is the slope of the line?
Answer:
[tex]\text{slope} =\frac{3}{2}[/tex]
Step-by-step explanation:
Firstly ,check the image I provided.
we notice that the points A(1 , -3) and B(3 , 0) lie on the line
then
[tex]\text{slope} =\frac{0-\left( -3\right) }{3-1} =\frac{3}{2}[/tex]
can someone please help my solve for x?
x= 41
Break the shape into two triangles
Use Pythagoras theorem to solve for the hypotenuse of the first triangle (the triangle with sides 32 and 24). You should have 40
Get to the second triangle. Use Pythagoras theorem to solve for the hypotenuse which, in this case, is x. Note that the sides of the second triangle are 40 (the hypotenuse of the last triangle. Look closely. ) and 9