Answer:
Step-by-step explanation:
2x=x(1.07)^t
2=(1.07)^t
t=log2/(log 1.07) ≈10.2 4 years
so it doubles in approximately in 10.2 years
To solve the problem we must know about Compounding.
What is compounding?Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.
It is given by the formula,
[tex]A = P(1+r)^t[/tex]
where A is the value after t period of time,
P is the value of the asset at the beginning, and,
r is the rate of interest.
The value of the home doubles once each decade.
Given to us
As it is given that the value of a home increases by 7% each year, therefore, the value of the home is compounding every year.
We know the formula of compounding,
[tex]A = P(1+r)^t[/tex]
Why does the value doubles?Now, let's assume a house whose value is 'P' today, therefore, substitute the value of the house in the formula of compounding,
[tex]A = P(1+r)^t[/tex]
Substitute the rate at which the value is increasing,
[tex]A = P(1+0.07)^t[/tex]
We know that in a decade there are 10 years,
[tex]A = P(1.07)^{10}[/tex]
[tex]A = 1.967P\approx 2P[/tex]
As we can see that the value of the home is almost 2 times the 'P' therefore, twice the value of the home at the beginning.
Hence, the value of the home doubles once each decade.
Learn more about Compounding:
https://brainly.com/question/25857212
Point D'' (-4,-2) is a vertex of a quadrilateral A'' B'' C'' D''. The original image was rotated 270 degress counterclockwise around the origin and then reflected over the x-axis.
Part A: What are the coordinates of the original image's point D before the composition of transformations?
A. (-4,-2)
B. (-2,-4)
C. (-2,4)
D. (2,-4)
Part B: The original image is quadrilateral ABCD. Point C is on the same y-axis of point D, but five units to the right of point D. If quadrilateral A'' B'' C'' D'' is transformed following the rule (x,y)---> (x-4, y+2), what are the coordinates of point C''?
Answer:
steps below
Step-by-step explanation:
part A: D'' (-4 , -2) (reverse) reflection over x axis -> (-4 , 2)
(-4 , 2) rotated 270 degrees clockwise: -> D (-2 , -4)
Part B: C (-2+5 , -4) = (3 , -4)
C" (3-4 , -4+2) = (-1 , -2)
Lian was asked to write an equation and solve this problem.
Shonda has some small spoons and 40 large spoons. If she has 68 spoons total, how many small spoons does Shonda have?
Lian’s work is shown below.
Steps
Lian’s Work
Step 1
s + 40 = 68
Step 2
s + 40 minus 40 = 68 minus 40
Step 3
s = 28
In which step, if any, did Lian first make a mistake in her work?
step 1
step 2
step 3
no mistake Who wanna mha (my hero academia anime rp wit me plz dont report)
Answer:
Its no mistake
Step-by-step explanation:
I got it right
The data represents the height, in feet, of various buildings. Find the Interquartile Range.
60, 58, 54, 56, 63, 65, 62, 59, 56, 58
Plsss helpppppp :(
This is a testt!
Answer: 6
Step-by-step explanation:
hii please help i’ll give brainliest
Answer:
Answer C or "7+3c"
Explanation:
This is because, 7 more would mean its independent on its own side of the plus sign and 3c mean 3 multiplied by ... (any number)
Hope this helps and please mark brainliest!Same as before this test... is just driving me crazy I'm blowing all my points through these so...
Answer and Step-by-step explanation:
For this, you would need to use the trigonometric function Sine and cosine.
The trig equations are:
sin(θ) = [tex]\frac{opposite - side}{hypotenuse}[/tex]
cos(θ) = [tex]\frac{adjacent-side }{hypotenuse}[/tex]
Let's start with Sine:
sin(60) = [tex]\frac{x}{10\sqrt{3} }[/tex]
Multiply both sides of the equation by [tex]10\sqrt{3}[/tex].
[tex]10\sqrt{3} (sin(60)) = x[/tex]
Input into calculator and solve.
x = 15
Now for Cosine:
cos(60) = [tex]\frac{y}{10\sqrt{3} }[/tex]
Multiply both sides of the equation by [tex]10\sqrt{3}[/tex].
[tex]10\sqrt{3} (cos(60)) = x[/tex]
Input into calculator and solve.
y = [tex]5\sqrt{3}[/tex]
x = 15
y = [tex]5\sqrt{3}[/tex]
These are the answers.
I hope this helps!
#teamtrees #PAW (Plant And Water)
Step-by-step explanation:
It's a right triangle with one of the angles being 60°. This means that the leftover angle is 30°. This allows me to use the attached screenshot as a reference, so please check it out if you want to understand how to easily solve those types of equations in the future. Anyway, we can specify the hypotenuse as [tex]a[/tex] .
First, let's calculate the value of [tex]y[/tex].
[tex]a[/tex] = [tex]10\sqrt{3}[/tex]
[tex]y[/tex] = [tex]\frac{a}{2}[/tex]
[tex]y[/tex] = [tex]\frac{10\sqrt{3} }{2}[/tex]
[tex]y[/tex] = [tex]5\sqrt{3}[/tex]
----
Now, let's get to [tex]x[/tex]
[tex]a[/tex] = [tex]10\sqrt{3}[/tex]
[tex]x[/tex] = [tex]\frac{a\sqrt{3} }{2}[/tex]
[tex]x[/tex] = [tex]\frac{10 \sqrt{3} * \sqrt{3}}{2}[/tex]
[tex]x[/tex] = [tex]\frac{10 * 3}{2}[/tex]
[tex]x[/tex] = [tex]\frac{30}{2}[/tex]
[tex]x[/tex] = [tex]15[/tex]
----
[tex]x[/tex] = [tex]15[/tex] and [tex]y[/tex] = [tex]5\sqrt{3}[/tex]
Please help will give you Brainliest *image
i really need help with this:
Jasmine drew a rectangle with an area of 4 square inches. Jasmine drew a new scaled version of the original rectangle using a scale factor of 5. What is the area, in square inches, of the new rectangle?
Answer:20
Step-by-step explanation:
i wrote 10 for some reason
Multiply (5x-2)^2
A: 25x^2 - 4
B: 25x^2 - 10x + 4
C: 25x^2 - 20x + 4
D: 25x^2 + 20x + 4
Say a answer not a website
the number of wolves in a wildlife refuge can be modeled by an exponential function where x is the number of decades since population counts began and y is the average annual number of wolves during the decade is given in the table
WHICH GRAPH IS THE GRAPH OF THE FUNCTION??
can some pls help me find the slope of this line i really really need help
Answer:
Slope = Rise over Run
Rise = 2
Run = 3
Slope = 2/3
Let me know if this helps!
Need help asap thank you
The area of rectangular is 64m the length of the pool is 12 m less that the width .The situation can be represented by the equation x
Answer:
Width = 16 m
Length = 4 m
Step-by-step explanation:
The area of rectangular is 64m² the length of the pool is 12 m less that the width . The situation can be represented by the equation x
Area of a rectangle = Length × Width
L = W - 12
Hence:
64 = (W - 12) × W
64 = W² - 12W
W² - 12W - 64 = 0
Factor using
(W + 4)(W - 16) = 0
Width = 16m
Length = W - 12
Length = 16 m - 12 m
= 4 m
Submarines use sonar systems, which are similar to radar systems, to detect obstacles. Sonar systems use sound to detect objects underwater.
a. You are traveling underwater in a submarine. The sonar system detects an iceberg 4000 meters ahead, with an angle of depression of 34∘ to the bottom of the iceberg. How many meters must the submarine lower to pass under the iceberg?
The submarine must lower at least ____ meters.
Question 2
b. The sonar system then detects a sunken ship 1500 meters ahead, with an angle of elevation of 19∘ to the highest part of the sunken ship. How many meters must the submarine rise to pass over the sunken ship?
The submarine must rise at least ____ meters.
Answer:
a. tan(34)= O/4000 and follow the solving to get the distance it must be lowered
b. (Same idea as a) tan(19)=1500/A and solve to get the distance
The submarine must lower at least 2698 meters and the submarine must rise at least 516.45 meters.
Given that, the sonar system detects an iceberg 4000 meters ahead, with an angle of depression of 34∘ to the bottom of the iceberg.
What are trigonometric angles?Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.
a) We know that, tan θ = (Perpendicular/Base)
Let the number of meters must the submarine lower to pass under the iceberg be x.
tan θ = x/4000
⇒ tan 34° = x/4000
⇒ 0.6745 = x/4000
⇒ x = 0.6745 × 4000
⇒ x = 2698 meters
b) Let the number of meters must the submarine rise to pass over the sunken ship be y.
tan θ = y/1500
⇒ tan 19° = y/1500
⇒ 0.3443 = y/1500
⇒ y = 0.3443 × 1500
⇒ y = 516.45 meters
Therefore, the submarine must lower at least 2698 meters and the submarine must rise at least 516.45 meters.
Learn more about the trigonometric angles visit:
https://brainly.com/question/24174128.
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Write the equation of the line in fully simplified slope-intercept form?
Answer:
y=-[tex]\frac{1}{2}[/tex]x+1
Step-by-step explanation:
So the first number after the y= is the slope which is - 1/2 then you add an X after that. Then you add the y-intercept point which on this graph is 1.
what is (1 5th) divided by 6 ps.1 5th is my fraction
Answer:
The answer is 0.3 repeating or in a fraction 1/3
Step-by-step explanation:
All you have to do is divide 1/5 th by 6 and then make it a fraction it's not that hard.
How are angles 7 and 8 related
Answer:
∠8 and ∠7 are a linear pair; they are supplementary. Their measures add up to 180°. Therefore, ∠7 = 180° – 53° = 127°.
Step-by-step explanation:
Have great day!!!!
Find the slope and y intercept on the graph
Answer:
slope should more than likely be y = -2 + x = 1
Step-by-step explanation:
Explain why rational expressions have restrictions
Answer:
Mostly for simplifying, the restrictions are the same no matter is being simplified or not. The restriction of a rational expression is always in the denominate
Step-by-step explanation:
factor completely 21x^3+35x^2+9x+15
Answer:
(3x+5)(7x^2+3)
Step-by-step explanation:
Factor : 21x^3+35x^2+9x+15
21x^3+35x^2+9x+15
=(3x+5)(7x^2+3)
______________________
Hope this helps!
Can someone help me with this please?
Answer:
the function is linear
Step-by-step explanation:
now you figure this out in many ways,
but the easiest is to plot the points on a Cartesian x-y plane, rule a line through the points,if it's in a straight line then its linear if it's a curve its cubic
from the question, after plotting your points.ie (-9,-2),(-5,-7),(-1,-12),(3-17)
we get a straight line pointing downwards.
I hope this is convenient enough
The expression 9a + 7c gives the cost (in dollars) for a adults and c children to eat at a buffet restaurant.
a. The cost for 1 adult is?
The cost for 1 child is?
b. The total cost for 1 adult and 3 children is?
c. Is $30 enough for a family of 2 adults and 2 children to eat at the buffet?
Answer:
a. $16
b. $30
c. for 2 adults and 2 children it is $32, so they are $2 short.
Step-by-step explanation:
i hope this helps :)
Makenzie leaves her home at 10am. She has to be at her grandmother's house, which is 42 miles away. The
speed limit is 65mph on the highway between their houses. Can she make it to her grandmother's house by
10:30 without speeding?
Answer:
no
Step-by-step explanation:
will take approximately 1-2 hours or even longer
If an = a1 x 5^n-1 and a1=1
what is the value of a5?
what is 2+2
haha take all the points and mark me brainliest and like
Answer:
4
Step-by-step explanation:
please please please please helppppp
Answer:
3: D 4: A 5: B not completely sure about 5 though
is statistics class hard? i signed up for it and kinda regretting it
Answer:
yes it is hard
Step-by-step explanation:
Most people don’t really learn statistics until they start analyzing data in their own research.
Use the long division method to find the result when 12x^3+17x^2+12x+4 is divided by 3x + 2.
Answer:
Step-by-step explanation:
not sur
e
Answer: 307 ÷ 24 = 209 ÷ 32 = 456
Step-by-step explanation:
9 less than m squared
Answer: b = m
(3 + m)(3 - m)
Step-by-step explanation:
please i have a hw and i need help
Answer:
11: A. Some ferrets are longer than some fishers.
12: The range for the fisher is 25cm greater than for the ferret.
13. The mean for the ferret is 11cm less than for the fisher.
5. Probably 18 members.
6. Probably 210
What is the measure of an angle that is the supplement of angle K?
A.
30°
B.
50°
C.
None of the above
D.
60°
E.
40°
Answer:
is the measure of an angle that is the supplement of angle K=180-150=30
A.is your answer