Answer:
8.7m
Step-by-step explanation:
Let's say the height of the tree is h and apply pythagoras:
18² + h² = 20² =>
h = √76 ≈ 8.7m
You have $600,000 saved for retirement. Your account earns 5.5% interest. How much, to the nearest dollar, will you be able to pull out each
month, if you want to be able to take withdrawals for 20 years?
9514 1404 393
Answer:
$4127
Step-by-step explanation:
The amortization formula is good for finding this value.
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where P is the amount invested at rate r for t years.
A = $600,000(0.055/12)/(1 -(1 +0.055/12)^(-12·20)) = $4127.32
You will be able to withdraw $4127 monthly for 20 years.
How do you write 19/25 as a percentage?
Answer:
76%
Step-by-step explanation:
25*4=100
19*4=76
At Turtle Elementary, the kindergarten teachers lined up their students by 6s and there
were none left over. They lined them up again by 8s and there were none left over. They
tried to line them up again by 10s, but there were 2 left over. What is the least number
of students that could be in kindergarten at Turtle Elementary?
Answer:
Step-by-step explanation:
denote x as total students
lcm of 6 and 8 is 24 (so none left over)
keep trying becuz you wanna find the lowest possible number
48, 72
72 works.
Find the slope of the line passing through the points (-8,3) and (-8,-6)
Answer:
-9/0
Step-by-step explanation:
(x1, y1) and (x2, y1)
(-8, 3) and (-8,-6)
slope/m = y2 - y1 / x2 -x1
= -6 -3 / -8 -(-8)
= -6 -3 / -8 + 8
= -9 / 0
simplify y=(x+3)^2, x=1
Kevin plans to retire in 30 years, and he plans to save up $250,000 for retirement. He has two options
• Plan 1: compounded monthly with an APR of 3.3%
• Plan 2: compounded quarterly with an APR of 3.5%
Compare these two options to see which one is more beneficial for Kevin. When you make the comparison,
you should at least calculate
1. the amount he needs to deposit each time period
2. the total interest accrued
The rate of growth of the amount invested with time in Plan 1 is slightly higher than the amount invested in Plan 2.
The option most beneficial to Kevin by comparison is Plan 1Reasons:
The number of years for the investment = 30 years
The amount he plans to save = $250,000
The investment plan options are;
Plan 1: Compounded monthly investment with APR, r = 3.5%
The formula for monthly contributions is presented as follows;
[tex]\displaystyle FV = \mathbf{\frac{PMT \cdot \left( 1 + \frac{r}{n}\right)^{n\cdot t} - 1}{\frac{r}{n} }}[/tex]
Which gives;
[tex]\displaystyle 250,000 = \mathbf{\frac{PMT \cdot \left( 1 + \frac{0.033}{12}\right)^{360} - 1}{\frac{0.033}{12} }}[/tex]
Solving gives;
The amount he needs to deposit each month, PMT ≈ $256.18The total deposit = 360 × $256.18 = $92,224.2
Total interest accrued = $250,000 - $92,224.2 ≈ $157,775.78Plan 2: Compounded quarterly, with APR, r = 3.3
Which gives;
[tex]\displaystyle 250,000 = \mathbf{\frac{PQT \cdot \left( 1 + \frac{0.035}{4}\right)^{120} - 1}{\frac{0.033}{4} }}[/tex]
The amount he needs to deposit each quarter ≈ $769.34The total deposit = $769.34 × 120 = $92,321.3336
Total interest accrued = $250,000 - $92,321.3336 ≈ $157,678.67
The total interest accrued by investing in plan 1 which is approximately
$157,775.78 is larger than the interest accrued on Plan 2 which is
approximately $157,678.67
The option most beneficial to Kevin is Plan 1, due to the higher total interest accruedLearn more here:
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Please help I will give brainliest
Answer: It goes 1/2 up each time
a train moves at a constant speed. it can travel 150 miles in 2 1/2 hours. how long will it take for the train to travel 360 miles
Answer:
6 hours
Step-by-step explanation:
It travels 150 miles in 2.5 hours. 150 ÷ 2.5 = 60. 360 ÷60 = 6
Answer:
6 hours
Step-by-step explanation:
Which statement correctly uses ratio language to describe a part-to-whole ratio of 7:10?
What is the product of 10 and 1/10 in lowest term? a. 1
b. 10
c. 11/10
d. 1/10
Answer:
11/10
Step-by-step explanation:
you can't reduce
MATH.QUESTION.HELP. BRAINILEST WILL BE GIVEN!!!
Answer:
C. [tex] 2 \dfrac{1}{3} [/tex]
Step-by-step explanation:
[tex]\dfrac{1}{3} \cdot 7 = \dfrac{1}{3} \cdot \dfrac{7}{1} = \dfrac{7}{3} = 2 \dfrac{1}{3}[/tex]
Karen is throwing an orange to her brother Saul, who is standing on the balcony of their home. The height h, in feet, of the orange above the ground t seconds after it is thrown is given by
h(t) = −16t2 + 32t + 2, 0 ≤ t ≤ 2.118.
If Saul's outstretched arms are 16 feet above the ground, will the orange ever be high enough so that he can catch it?
a. No. The orange will reach a maximum height of 4 feet.
b. Yes. The orange will reach a maximum height of 18 feet.
c. There is not enough information given to answer the question.
d. No. The orange will reach a maximum height of 2 feet.
e. Yes. The orange will reach a maximum height of 36 feet.
Answer:
Yes, the orange will be high enough so
that he can catch it because maximum height
attained if 20 ft.
Step-by-step explanation:
I need help with this question please
Answer:
w = [tex]\frac{t}{4}[/tex]
Step-by-step explanation:
We have t = 4w, the question is asking to rearrange the equation to make "w" the subject, meaning that we have to isolate the variable w.
When we have a number (usually known as a coefficient) next to a variable and want to get rid of it, we need to divide it by both sides. Therefore :
t = 4w
[tex]\frac{t}{4} =\frac{4w}{4}[/tex]
[[tex]\frac{t}{4} =w[/tex]]
Since "t" is an undefined variable and has no initial value, you cannot divide it by anything, therefore it'll stay as [t/4 = w]
Imma leave this here until someone answer it :))
Answer:
Step-by-step explanation:
1) x +y = 3
Subtract 'x' from both sides
y = -x + 3
2) x - 3y = 12
Subtract 'x' form both sides.
-3y = -x + 12
Divide the entire equation by (-3)
[tex]\dfrac{-3y}{-3}=\dfrac{-x}{-3}+\dfrac{12}{-3}\\\\\\y = \dfrac{1}{3}x-4[/tex]
3) 5x + 2y = 10
Subtract 5x from both sides
2y = -5x + 10
Divide the entire equation by 2
[tex]\dfrac{2y}{2}=\dfrac{-5x}{2}+\dfrac{10}{2}\\\\\\y = \dfrac{-5}{2}x + 5[/tex]
4) y = 6x + (1/3)
It is already in y =mx +b form
5)
[tex]y=\dfrac{1}{x}*x-15\\\\\\y = 1-15\\\\y = -14\\\\y=0x -14[/tex]
Help me with this question pls
Answer:
y=-0.25x+2
Step-by-step explanation:
the slope is down one over 4, or -0.25. The y intercept is 2, so b is +2
M=-1, b=2 write an equation of a line with the given slope m and y- intercept b
Answer:
y = - x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Here m = - 1 and b = 2 , then
y = - x + 2 ← equation of line
36 is 30% of what number?
Answer:
83?
Step-by-step explanation:
(5x + 3) (3x2 + 4x + 4)
Answer:
dggdhdhdhshsjshdhdhhshshshshdhdhsbsbsbd
Show your work, hellppp!! Thank you <3
Answer:
here
hope it helps
Step-by-step explanation:
u can pass me ur contact no. if u want help
Please help me with this
Answer:
264 cm³
Step-by-step explanation:
Consider the L-shaped end of the figure. It is 7 cm wide, and 3+4 = 7 cm high. It can be considered to be a 7 cm square with a portion cut out of the upper right corner. That portion is a square that is 4 cm by 4 cm.
Then the area of the L-shaped end is ...
(7 cm)(7 cm) -(4 cm)(4 cm) = (49 -16) cm² = 33 cm²
The volume of the figure is the product of this area and the overall length, which is 8 cm.
V = Bh = (33 cm²)(8 cm) = 264 cm³ . . . volume of the figure
_____
Additional comment
There are other ways the volume can be figured. For example, it can be considered as a 7 × 8 × 3 cm block with a 3 × 4 × 8 cm block on top. That gives a volume of ...
V = LWH . . . . for each block
V = (7 cm)(8 cm)(3 cm) +(3 cm)(4 cm)(8 cm) = 168 cm³ +96 cm³ = 264 cm³
The temperature at Violet's house is set at 76 degrees Fahrenheit but might vary as much as 5 degrees. Write an inequality to represent this situation.
The inequality to represent this situation is |x - 76| < 5.
The temperature of her house is set at 76° Fahrenheit. The temperature might vary at 5 degrees. This simply means the temperature might increase by 5 degrees or decrease by 5 degrees.
Therefore, the inequality to represent this situation can be represented below:
|x - 76| < 5
-5 < x -76 < 5
add 76
-5 + 76 < x -76 + 76 < 5 + 76
71 < x < 81
Therefore, the inequality to represent this situation is |x - 76| < 5.
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Two-Dimensional Nets and Surface Area
What is the surface area of this
square pyramid?
Answer:
The surface area of a square pyramid is the sum of the areas of all its 4 triangular side faces with the base area of the square pyramid. If a, h, and l are the base length, the height of the pyramid, and slant height respectively, then the surface area of the square pyramid = a2+ 2al (or) a2+2a √a24+h2 a 2 4 + h 2 .
If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height, then find the ratio of the curved surface areas of the new cylinder to that of the original cylinder.
Given info:-If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height.
Find the ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder ?
Explanation:-
Let the radius of the right circular cylinder be r units
Let the radius of the right circular cylinder be h units
Curved Surface Area of the original right circular cylinder = 2πrh sq.units ----(i)
If the radius of the right circular cylinder is doubled then the radius of the new cylinder = 2r units
The height of the new right circular cylinder
= (1/4)×h units
⇛ h/4 units
Curved Surface Area of the new cylinder
= 2π(2r)(h/4) sq.units
⇛ 4πrh/4 sq.units
⇛ πrh sq.units --------(ii)
The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder
⇛ πrh : 2πrh
⇛ πrh / 2πrh
⇛ 1/2
⇛ 1:2
Therefore the ratio = 1:2
The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder is 1:2
What is the slope and the y-intercept of the graph of y = 8/9x - 8
Use a coordinate plane to create a rectangular park that has one corner at (−412, 312) and a perimeter of 30 units. Label the coordinates of each corner of the park. Then plot points with mixed number coordinates inside the park to represent a swing set, a slide, and a bench. Plot the slide farthest from the x-axis and the bench closest to the x-axis. What are the coordinates of the points you plotted?
A rectangle has four sides, where the opposite sides are equal
The possible coordinates are: (-4.5, 3.5), (-4.5,10.5), (3.5,3.5) and (3.5,10.5)
The coordinate point is given as:
[tex]\mathbf{(x,y) = (-4\frac12,3\frac12)}[/tex]
Express as decimal
[tex]\mathbf{(x,y) = (-4.5,3.5)}[/tex]
The perimeter is said to be 30 units.
So, we have:
[tex]\mathbf{P = 2(L + W)}[/tex]
This gives
[tex]\mathbf{2(L + W) = 30}[/tex]
Divide through by 2
[tex]\mathbf{L + W = 15}[/tex]
This means that the sum of the dimensions is 15 units.
So, we can assume that:
Length = 8
Width = 7
So, the other coordinates are calculated as follows:
[tex]\mathbf{(x,y) = (-4.5,3.5+7) = (-4.5,10.5)}[/tex]
[tex]\mathbf{(x,y) = (-4.5 + 8,3.5) = (3.5,3.5)}[/tex]
[tex]\mathbf{(x,y) = (-4.5+8,3.5+7) = (3.5,10.5)}[/tex]
So, the possible coordinates are: (-4.5, 3.5), (-4.5,10.5), (3.5,3.5) and (3.5,10.5)
See attachment for the graph of the rectangle
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Four out of nine dogs weigh less than 20 pounds. What is the decimal equivalent to the number of dogs weighing under 20 pounds?
A.0.49
B.0.444444
C.0.2222
D.0.24
Answer:
The answer is B. 0.4444
Step-by-step explanation:
You take 4 and divide it by 9 to get 0.4444
Evaluate.
(a – 2b)^3 when a= -3 and b = -1/2 Enter your answer in the box
Answer:
- 8
Step-by-step explanation:
Substitute the values for a and b into the expression
(- 3 - 2(- [tex]\frac{1}{2}[/tex] ) )³
= (- 3 + 1)³
= (- 2)³
= (- 2) × (- 2) × (- 2)
= 4 × - 2
= - 8
What is the ratio of 8 triangles to 10 stars in simplest form?
What is 36:216 simplified?
Answer : 1/6
Explanation : If 216 is divided by 36, you will get your answer 1/6.
4. Which symbols are represented by an open circle on the number line? (Select all that apply.)
Answer:
The first and second choice since those symbols are the ones that apply to open circle on the number line and the 2 last ones are closed circles
Step-by-step explanation:
The symbols represented by the open circle on the number line are greater than ( > ) and less than ( <). The correct options are A and B.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
On the number line, the open circle stands for the symbols greater than (>) and less than (<). These symbols are used to form inequalities also.
Therefore, the symbols represented by the open circle on the number line are greater than ( > ) and less than ( <). The correct options are A and B.
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