Answer:
8 in
Step-by-step explanation:
The ratio of sides and perimeter in similar figures are equal.
let x be the perimeter of the smaller figure, then by proportion
[tex]\frac{7}{28}[/tex] = [tex]\frac{2}{x}[/tex] ( cross- multiply )
7x = 56 ( divide both sides by 7 )
x = 8
The perimeter of the smaller pentagon is 8 in
which answer choice shows the number four hundred sixty -five ten - thousandths in standard from
Answer:
4.65 x 10^-5
Step-by-step explanation:
.00465
[tex]4.65 x 10^{-5}[/tex]
When proving the product, quotient, or power rule of logarithms, various properties of logarithms and exponents must be used.
Which property listed below is used in all of these proofs?
Answer:
d
Step-by-step explanation:
Leah has just inherited 12000 she wants to invest the money so that she can increase the value of her inheritance what are some of the ways she can do this
Answer:
she can put it in a bank to gain interest
she can invest in the stock market
she can loan out money
Step-by-step explanation:
Depending on the compounding frequency, Leah's investment of $12,000 with a 4.5% annual interest rate would yield the following amounts after 10 years:
- Continuous compounding: approximately $18,843.48
- Daily compounding: approximately $19,212.03
- Monthly compounding: approximately $18,867.02
Leah's inheritance presents her with a golden opportunity to grow her wealth through strategic investment. With $12,000 at her disposal, she can explore various avenues to maximize the value of her funds. One option she's considering is investing in an account that offers a 4.5% annual interest rate.
To evaluate the potential returns from this investment, she needs to understand how different compounding frequencies affect the growth of her investment over time.
Let's start by defining the equations for the amount A(t) in the account after t years, using continuous compounding, daily compounding, and monthly compounding.
1. Continuous Compounding:
The formula for continuous compounding is given by:
[tex]\[ A(t) = P \times e^{rt} \][/tex]
where:
- A(t) is the amount of money in the account after t years,
- P is the principal amount (initial investment),
- r is the annual interest rate (expressed as a decimal),
- t is the time in years, and
- e is the base of the natural logarithm, approximately equal to 2.71828.
Using Leah's values:
P = $12,000
r = 0.045 (4.5% expressed as a decimal)
Substituting these values into the formula, we get:
[tex]\[ A(t) = 12000 \times e^{0.045t} \][/tex]
To find the amount after 10 years, we can plug t = 10 into the equation and calculate the result.
[tex]\[ A(10) = 12000 \times e^{0.045 \times 10} \][/tex]
[tex]\[ A(10) \approx 12000 \times e^{0.45} \][/tex]
[tex]\[ A(10) \approx 12000 \times 1.57029 \][/tex]
[tex]\[ A(10) \approx \$18,843.48 \][/tex]
So, after 10 years of continuous compounding, Leah's investment would be approximately $18,843.48.
Next, let's consider daily compounding. In this case, interest is compounded 365 times per year, so the formula becomes:
[tex]\[ A(t) = P \times \left(1 + \frac{r}{365}\right)^{365t} \][/tex]
Using the same values as before, we can calculate:
[tex]\[ A(10) = 12000 \times \left(1 + \frac{0.045}{365}\right)^{365 \times 10} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + \frac{0.045}{365}\right)^{3650} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + 0.00012328767123\right)^{3650} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.00012328767123)^{3650} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.60100220887) \][/tex]
[tex]\[ A(10) \approx \$19,212.03 \][/tex]
After 10 years of daily compounding, Leah's investment would be approximately $19,212.03.
Finally, let's explore monthly compounding. With monthly compounding, interest is compounded 12 times per year, so the formula becomes:
[tex]\[ A(t) = P \times \left(1 + \frac{r}{12}\right)^{12t} \][/tex]
Using the same values as before, we can calculate:
[tex]\[ A(10) = 12000 \times \left(1 + \frac{0.045}{12}\right)^{12 \times 10} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + \frac{0.045}{12}\right)^{120} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + 0.00375\right)^{120} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.00375)^{120} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.5722520173) \][/tex]
[tex]\[ A(10) \approx \$18,867.02 \][/tex]
After 10 years of monthly compounding, Leah's investment would be approximately $18,867.02.
In summary, depending on the compounding frequency, Leah's investment of $12,000 with a 4.5% annual interest rate would yield the following amounts after 10 years:
- Continuous compounding: approximately $18,843.48
- Daily compounding: approximately $19,212.03
- Monthly compounding: approximately $18,867.02
These calculations illustrate how different compounding frequencies can affect the growth of an investment over time. Daily compounding typically results in slightly higher returns compared to monthly compounding, while continuous compounding offers the highest potential returns due to its continuous nature.
By understanding these dynamics, Leah can make an informed decision about how to maximize the growth of her inheritance based on her investment preferences and goals.
The complete question is:
Leah has just inherited $12,000. She wants to invest the money so that she can increase the value of her inheritance. What are some of the ways she can do this?
1. Leah wants to invest the $12,000 in an account that pays 4.5% annual interest.
a. Write equations for the amount A(t) that will be in the account after t years, if the interest is
compounded continuously, daily, and monthly. Then, find the amount after 10 years, rounded
to the nearest cent, for each method of compounding.
How many leaves are there if you have 9 clovers?
Answer:
36 leaves
Step-by-step explanation:
1 clover has 4 leaves
so if you have 9 clovers multiply the leaves by clovers by 4
1:4
9:36
d(1)=13 d(n)=d(n−1)+17 Find the 4 th term in the sequence.
Answer:
the 4th term is 64
Step-by-step explanation:
Given
d(1) = 13
d(n) = d( n -1) +17
First
d(2) = d(2-1) + 17
= d(1) + 17
= 13 + 17
= 30
d(3) = d(3-1) +17
= d(2) + 17
= 30 +17
= 47
d(4) = d(4-1) + 17
= d(3) + 17
= 47 +17
=64
To find the 4th term in the sequence defined by d(n)=d(n-1)+17, we can use the formula recursively to compute the subsequent terms. Starting with d(1)=13, we can find d(4) by adding 17 repeatedly.
Explanation:The sequence is defined by the formula d(n)=d(n-1)+17, with d(1)=13. To find the 4th term in the sequence, we can use the formula recursively. Starting with d(1)=13, we can find d(2) by adding 17 to d(1): d(2)= d(1) + 17 = 13 + 17 = 30. Continuing this pattern, we find d(3) = d(2) + 17 = 30 + 17 = 47. Finally, we find d(4) = d(3) + 17 = 47 + 17 = 64.
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Please help!
What is the median of the data?
Answer:
15 hope it helps:)
Step-by-step explanation:
because it divides 5 in each side
GUEST
An equation is given.
6-x=y
Complete the table to show the relationship between values of x and y.
O
2
Answer: 6 and 4
Step-by-step explanation:
Fill in the numbers with the correct variable and you get your answer. 6-0=6 6-2=4
Select the expression that is equivalent to the polynomial given below.
(4x + 3) (3x – 8)
O A. 128 - 23x-24
23x + 24
C.
128²-41x-24
D.
12x +41x + 24
Look at the attached picture⤴
Hope it will help u...
Can you help me with this question please
Answer:
516
Step-by-step explanation:
First
34% small and 40% large means that 100 - (34 + 40) = 26% medium
26% of 600 = 0.26 × 600 = 156
----------------------------------------------------
Second
[tex]\frac{3}{10}[/tex] are small and [tex]\frac{1}{10}[/tex] are large, which means [tex]\frac{6}{10}[/tex] are medium
[tex]\frac{6}{10}[/tex] × 400 = 0.6 × 400 = 240
-----------------------------------------------------
Third
sum the parts of the ratio, 3 + 4 = 7
Divide 210 by 7 to find the value of one part of the ratio
210 ÷ 7 = 30 ← value of 1 part of ratio
Thus medium = 4 × 30 = 120
Total number of medium packets = 156 + 240 + 120 = 516
a spere has a diameter of 24 units what is the volume in cubic units
Answer: 7238.23
Step-by-step explanation:
volume of a sphere is (4/3)(pie)(r^3)
so if the diameter is 24 than the radius is 12 so u would substitute that into the formula and you should get 7238.23
The correct answer is option D: 6,912π cubic units.
To find the volume (V) of a sphere, you use the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where (r) is the radius of the sphere.
Given that the sphere has a diameter of 24 units, the radius (r) is half of the diameter, which is 24/2 = 12 units.
Now, substitute the value of the radius into the formula:
[tex]\begin{aligned}V & =\frac{4}{3} \pi(12)^3 \\V & =\frac{4}{3} \pi 1728 \\V & =\frac{6912}{3} \pi\end{aligned}[/tex]
Complete Question:
A sphere has a diameter of 24 units. What is its volume in cubic units?
A. 576π cubic units
B. 1,728π cubic units
C. 2,304π cubic units
D. 6,912π cubic units
express the first quantity as a percentage of the second
a) 35 minute 2 hour
b )650g.3 kg
Answer:
a) 29% b) 22%
Step-by-step explanation:
The quantities must be expressed in the same units.
a) compare 35 minutes to 2 hours. 2 hours is 2 x 60 = 120 minutes.
35/120 = .291667 = 29%
b) compare 650 grams to 3 kilograms. 3 kg = 3 x 1000 = 3000 g.
650/3000 = .21667 = 22%
Answer:
see explanation
Step-by-step explanation:
To express as a percentage, first express as a fraction and multiply by 100%
The quantities must be expressed in the same units.
(a)
2 hours = 2 × 60 = 120 minutes, thus
[tex]\frac{35}{120}[/tex] × 100% ≈ 29.2% ( to 1 dec. place )
(b)
3 Kg = 3 × 1000 = 3000 g, thus
[tex]\frac{650}{3000}[/tex] × 100% ≈ 21.7% ( to 1 dec. place )
Here are six number cards.
-7 -5 -3 3 1 -1
Arrange the cards into three pairs with the same total.
Answer:
-7 3=-4
-5 1=-4
-3 -1=-4
-7 and 3 make -4. -5 and 1 make -4. -3 and -1 make -4.
The three pairs with the same total are as follow:
-7 + (3) = -4-5 + 1 = -4-3 -1 = -4What are integers?An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes:
Positive Numbers: A number is positive if it is greater than zero. Example: 1, 2, 3 . . .Negative Numbers: A number is negative if it is less than zero. Example: -1, -2, -3 . . .Zero is defined as neither a negative number nor a positive number. It is a whole number.Given:
Number on cards -7 -5 -3 3 1 -1
Now, we have to make the pair according it gives the same total
-7 + (3) = -4
-5 + 1 = -4
-3 -1 = -4
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What is the expression in scientific notation? (7 x 10^−12)(4 x 10^5)?
Answer:2.8 x 10^-6. hope this helps :)
Final answer:
The expression (7 x 10⁻¹²)(4 x 10⁵) in scientific notation is 2.8 x 10⁻⁷.
Explanation:
The expression in scientific notation for the product (7 x 10⁻¹²)(4 x 10⁵) is found by multiplying the coefficients (7 and 4) and then adding the exponents of 10 (as they have the same base). Multiplying the coefficients gives us 28, and adding the exponents of 10 (-12 + 5) gives us -7 as the new exponent.
The final result in scientific notation is 2.8 x 10⁻⁷. Note that 28 is adjusted to 2.8 to maintain the correct form for scientific notation, which is one non-zero digit to the left of the decimal point.
There are 5280 feet in 1 mile. How many inches are in 4 feet
Answer:
253,440
Step-by-step explanation:
12inches make a foot
So, in 1 miles, total inches equal
5280 × 12 = 63360 inches in one mile
In 4 miles then, total inches would be
63360 × 4 = 253440 inches
The graph shows f(x) = (x - 5)2. What is the value of h?
h=
Answer:
-5
Step-by-step explanation:
H is the value that is being added or subtracted from x in the equation
f(x)=a(x-h)^2 +k
The human population of Earth was approximately 6 billion in 1998. If the rate of
population growth from then on was 2.3% per year, what would be the best
approximation for the human population (in billions) of Earth in 2020?
Answer:
9.89 billion
Step-by-step explanation:
At that rate of growth, the population is multiplied by 1.023 each year. After 22 years, the population would be ...
6·1.023^22 ≈ 9.89 . . . billion
Answer:
Let the equation for the population (P) growth be given by
P = P0ert, where P0 is the initial population in billioins at time t,
t is the number of years since 1987,
r is the rate of growth of population/year
In this case P0 = 5 billion and r = 0.02. Putting these values into the equaation:
P = 5e0.02t
Year 1995 is 8 years after 1987, then the population would be
P = 5e0.02*8 = 5e0.16 ≈ 5.87 billion people
Step-by-step explanation:
What is 0.0068 in scientific notation?
Answer:
6.8 x 10^-3
Step-by-step explanation:
Answer:
6.8 x 10³
Step-by-step explanation:
Quadrilateral DUCK is inscribed in circle O what is the measure of
Answer:
95°
Step-by-step explanation:
Since, quadrilateral DUCK is inscribed in circle O
sum of the opposite angles of the quadrilateral is 180°
m<K +m<U= 180°
m<K= 180°- 85°= 95°
Answer:
95 degrees
Step-by-step explanation:
Quadrilaterals that are inscribed in circles are often called "cylic". Cyclic quadrilaterals have many unique properties. One of these is that opposite angles add up to 180 degrees.
Here, DUCK is a cyclic quadrilateral. "Opposite angles" are < U and < K, as well as < D and < C. So, since < U and < K are opposite angles in this inscribed quadrilateral, they add up to 180 degrees:
< U + < K = 180
We already know that < U = 85, so:
85 + < K = 180
< K = 95
Thus, < K is 95 degrees.
Hope this helps!
If the measure of Angle C A E is 95°, what is the measure of Arc C B A?
90°
95°
190°
195°
Answer: the answer is 190
Step-by-step explanation: I multiplied 95 by two
Answer:
C) 190
Step-by-step explanation:
Transformers the following equation into slope-intercept. I need help ASAP
Answer:
Look at the attached work for a step by step solution and answer.
Step-by-step explanation:
If this fish tank is filled only halfway, how much water will it hold?
A. 1920 cubic inches
B. 42 cubic inches
C. 5880 cubic inches
D. 969 cubic inches
Answer:
I believe you typed your final answer choice incorrectly, as it should read 960 which is the correct answer
Step-by-step explanation:
the volume is 1920
1920/2=960
Answer:
960 cubic inches
Step-by-step explanation:
I took the test
Question 1 0 / 5 pts (06.07A LC) The legs of a right triangle are 3 units and 8 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. (5 points) 8.54 units 9.54 units 11.00 units 24.00 units
Question 2 5 / 5 pts (06.07A LC) Jacob calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle was it? (5 points) A B C D
Question 3 5 / 5 pts (06.07A MC) What is the length of the third side of the window frame below? (5 points) (Figure is not drawn to scale.) 15 inches 27 inches 25 inches 32 inches
Question 4 5 / 5 pts (06.07A MC) The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown. (Figure is not drawn to scale.) Which of the following options is closest to the distance (in miles) between points A and B? (5 points) 2.24 miles 2.65 miles 3.74 miles 5.29 miles
Answer: H
Step-by-step explanation:Question 1(Multiple Choice Worth 5 points) (06.07A MC) What is the length of the third side of the window frame below? (Figure is not drawn to scale.) A picture of a right triangular window frame is shown. The longest side has length labeled as 87 inches. The height of the frame is labeled as 63 inches. 48 inches 60 inches 70 inches 75 inchesanswer - 60Question 2(Multiple Choice Worth 5 points) (06.07A MC) The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown. (Figure is not drawn to scale.) A picture of a right triangle ABC with right angle at B is shown. The length of the side AC is labeled as 9 miles. The length BC of the triangle is labeled as 6 miles. This length BC is also the length of an irregular gray shaded shape. Which of the following options is closest to the distance (in miles) between points A and B? 6.71 miles 7.35 miles 8.66 miles 10.82 miles answer - 6.71Question 3(Multiple Choice Worth 5 points) (06.07A LC) The legs of a right triangle are 3 units and 8 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. 8.54 units 9.54 units 11.00 units 24.00 units answer - 8.54Question 4(Multiple Choice Worth 5 points) (06.07A LC) Jessica calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle was it? Four triangles E, F, G, H are shown from left to right. Triangle E has one side labeled as 2 and the other as 3, and the included acute angle is shown. Triangle F has both sides labeled as 3, and the included acute angle is shown. Triangle G has one side labeled as 4 and the other as 2, and the included right angle is shown. Triangle H has one side labeled as 6 and the other as 7, and the included obtuse angle is shown. answer h
Which statement could be used to describe the functions?
O Both original functions have a domain of (-0,-).
O Both original functions have a domain of [-0, 2).
The domain of f(x) is [2, o), while the domain of g(x) is
(-0, 2]
O The domain of f(x) is (-00, 2], while the domain of g(x)
is [2, 0).
Answer:
number d im (pretty sure)
Step-by-step explanation:
|7m+4| =1 pls pls.
|7m + 4| = 1
It can equal either 1 or -1, so:
7m + 4 = 1
7m = -3
m = -3/7
7m + 4 = -1
7m = -5
m = -5/7
Which phrase is a hit about what might happen later in the story?
Answer:
foreshadowing
Step-by-step explanation:
Is that what you're looking for?
If it is:
Foreshadowing includes the clues the author throws into a story to hint at what may happen in the future, or further in the book. For instance, Character A says to Character B that "I've never broken a bone before! I've never even been hospitalized" but does so near the climax of the story.
Find the sum or difference.
(6x + 5) + (-3x + 7)
Answer:
3x+12 is the sum
9x-2 is differences
Step-by-step explanation: Combine like terms
To calculate the height of a tree, Ryan measures the
angle of elevation from a rock on the ground to be 34°
He measures his distance from the rock on the ground
to the base of the tree to be 8 meters. How high is the
tree to the nearest tenth of a meter?
The height of the tree is 5.4 m
Step-by-step explanation:
Let the height of the tree be 'h'
Angle of elevation= 34°
distance from the rock on the ground
to the base of the tree = 8 m
we can use the tan function of trigonometry to find the height of the tree,
tan 34° = h/8
tan 34° = 0.67
tan 34° = h/8
0.67 = h/8
h = 8 x 0.67
h = 5.4m
The height of the tree is 5.4 m
The height of the tree to the nearest tenth of a meter is approximately 5.6 meters.
To calculate the height of the tree, we can use trigonometry, specifically the tangent function since we have the angle of elevation and the distance from the observer to the base of the tree.
Let's denote:
h as the height of the tree,d as the distance from the observer to the base of the tree.According to trigonometry,
[tex]\[ \tan(\text{angle of elevation}) = \frac{\text{height of the tree}}{\text{distance to the tree}} \][/tex]
Substituting the given values:
[tex]\[ \tan(34^\circ) = \frac{h}{8} \][/tex]
Now, let's solve for h:
h = 8 × tan(34°)
Using a calculator, we find:
h ≈ 8 × 0.6947
≈ 5.5576
Therefore, the height of the tree to the nearest tenth of a meter is approximately 5.6 meters.
I completed 2/3 of my project last month and 1/4 of it this week
Answer:
You've completed 11/12 of your project
Only 1/12 left to go!
Step-by-step explanation:
2/3 + 1/4 = 11/12
Answer:
Step-by-step explanation:
2/3+1/4=11/12
Coleman graphed the relationship between the number of rotations of his front bike tire and the distance
he traveled past a tree. Negative distance means the tree is in front of Coleman and positive distance
means the tree is behind Coleman
Answer:
I feel like its either c or d but i'm not sure? I'm sorry for the inconvenience. I really did try.
Step-by-step explanation:
Answer:
the anwser is d none of the above
Step-by-step explanation:
What does the yyy-intercept represent?The yyy-intercept tells us the value of the yyy-variable when the xxx-variable equals 000.Hint #22 / 3In this context, xxx represents the number of tire rotations, and yyy represents the distance past the tree. So the y-intercepty-interceptstart color #ca337c, y, start text, negative, i, n, t, e, r, c, e, p, t, end text, end color #ca337c at (0,−15)(0,−15)left parenthesis, 0, comma, minus, 15, right parenthesis says after 000 tire rotations, Coleman was 151515 meters away from the tree and the tree was in front of him.55101015152020252510102020303040405050-10-10Tire rotationsDistance past the tree (m)(0,−15)(0,−15)The first and fourth quadrants of a coordinate plane. The horizontal axis is from zero to thirty with a scale of five and is titled Tire rotations. The vertical axis is from negative twenty to sixty with a scale of five and is titled Distance past the tree in meters. The graph of the line is y equals two point two five x minus fifteen. The point zero, negative fifteen is plotted and labeled.Hint #33 / 3The answerThe yyy-intercept represents the distance Coleman was away the tree when he started traveling.Since that was not an option, the answer is none of the above.
4 + x/7 = 2 plz solve
Answer x=-14.
Step-by-step explanation:
4+x/7
4+ -14/7
4+-2
2
Answer:
[tex]4 +\frac{x}{7}=2[/tex]
[tex]\frac{28 + x}{7} = 2[/tex]
28 +x = 14
x =14 - 28
x = -14
Hope this helped.
Step-by-step explanation: