[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=500\left(1+\frac{0.05}{1}\right)^{1\cdot 4}\implies A=500(1.05)^4\implies A\approx 607.75[/tex]
The final amount will be $607.75 after 4 years if the principal amount is $500 and it compounded annually with interest rate of 5%
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+r)^t[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have in the problem:
P = $500, r = 5% = 0.05, and n = 4 years
[tex]\rm A = 500(1+0.05)^4[/tex]
A = $607.75
Thus, the final amount will be $607.75 after 4 years if the principal amount is $500 and it compounded annually with interest rate of 5%
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Find the solution of the system of equations.
8x – 2y = -30
–9x + 4y = 18
Step-by-step explanation:
8x – 2y = -30 } ×2
16x - 4y = -60
–9x + 4y = 18
___________
7x=-42
x=-6
8(-6)-2y=-30
-2y=-18
y=9
Answer:
(-6,-9)
Step-by-step explanation:
The quickest way is to solve with elimination. Multiply the top equation by 2.
2(8x – 2y = -30)
16x-4y=-60
16x-4y=-60
–9x + 4y = 18
7x=-42
x=-6
8x – 2y = -30
8(-6) – 2y = -30
-48-2y=-30
-2y=18
y=-9
Mary walks to her garage. The distance to the garage as a function of time is shown in this graph
A. Mary starts 8 meters from the garage.
B. Mary walks 8 meters every 4 seconds.
C. Mary arrives at the garage after 4 seconds.
D. Mary walks at a speed of 2 meters per second.
Answer:
d
Step-by-step explanation:
so if you look at the bottom left corner you can see 1 box is the same as saying for every second someone walks its one metre.
thats not how i got the answer though.
if you look at the starting point at 8 because she was 8 meters away you need to see when she comes across her first second which after 2 meters (Goes down two squares before reaching the first second)
now technically soe of the other answers are correct too but heres how i thought about it.
A. its correct but i dont think that's what its asking you for tbh
B. This we don't know for sure. eg she could take 890 seconds walking back to her starting point we just don't know for sure.
C. This is also true but once again it's easily given to you so i dont think that's what you're being asked.
D. This is the only option where you had to do any for of working out because s=d/t so s=8/4=2m/s
What is the measure of arc XZ if the angle equals 135 and the radius is 17 km
now, let's make the assumption that the arcXZ has a central angle of 135° and a radius of 17.
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=17\\ \theta =135 \end{cases}\implies s=\cfrac{(135)\pi (17)}{180}\implies s=\cfrac{51\pi }{4}\implies s\approx 40.06[/tex]
Farm workers plant 980 beans in 35 rows. How many beans do they plant in one row
please help
i added a picture
A student wants to survey the sophomore class of 200 students about whether the school should require uniforms. A
random sample of 50 sophomores is surveyed and asked whether they support the school adopting uniforms. Of
the 50 sophomores, 12 say they would favor school uniforms. Assuming the conditions for inference have been met,
what is the 90% confidence interval for the true proportion of sophomores who favor the adoption of uniforms?
0.24 +1.96
0.24(1-0.24)
200
O 0.7601.964
0.76(1 -0.76)
200
O 0.24 +1.657
0.24(1-0.24)
50
O 0.76 +1.95
0.76(1-0.76)
50
Answer: C
Step-by-step explanation:
Given:
Sample size (n) = 50
x = 12
[tex]\widehat{\mathbf{p}}=\frac{\mathbf{x}}{n}=\frac{12}{50}=0.24[/tex]
Confidence level = 90%
α = 1 − 0.90 = 0.10
α/2 = 0.05
[tex]\text { Critical value }\left(z_{c}\right)=z_{\frac{\alpha}{2}}=z_{0.05}=1.6449[/tex]
(from standard normal table)
90% Confidence interval is,
[tex]\begin{aligned}&\text { Confidence interval }=\widehat{\mathbf{p}} \pm z_{c} \times \sqrt{\frac{\hat{\mathbf{p}}(1-\hat{\mathbf{p}})}{n}} \\&\text { C. I }=0.24 \pm 1.6449 \times \sqrt{\frac{0.24(1-0.24)}{50}} \\&\text { C. I }=0.24 \pm 1.65 \times \sqrt{\frac{0.24(1-0.24)}{50}}\left\end{aligned}[/tex]
Therefore, 90% confidence interval for the true proportion of sophomores who favour the adoption of uniforms is C
Mr. Wilson bought a bag of birdseed and put half of it in his bird feeder. He split the other half equally among his 4 pet birds. How much of the bag did each pet bird get?
Answer:
each pet bird got 1/8 of the bag of birdseed
Step-by-step explanation:
the easiest way to do this is to divide the bag into eighths. if you divide the bag into eighths, 4/8 of the bag, being half, goes into the bird feeder. the other 4/8 of the bag is divided among Mr. Wilson's four pet birds, leaving each bird to get 1/4 of the bag when split evenly.
hope this helps
Translate the following phrase to an expression: the difference between twenty and twice a number.
Answer:
20 - 2n
n = a number
7k^2=21,952
Volume of cylinders, cones, and spheres
What is the answer please
Answer:56Step-by-step explanation:7k²=21952
k²=21952/7
k²=3136
k=√3136
k=56
PLS MARK ME AS BRAINLIEST
UNIQUE
SIZE
What Does Cate Often
Call Her Twin Sister?
Answer:
a dupli-CATE
Step-by-step explanation:
HAHAHAHA OMG THIS IS ACTUALLY FUNNY
A triangular bandana has an area of 38 square inches. The height of the triangle is 9
inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base.
Answer:
Base=8.4 inches
Step-by-step explanation:
Area of triangular bandana is 38sq inches
Height of triangle is 9 inches
Area of ∆ =½×b×h
38=½×b×9
38×2=b×9
76/9=b
b=8.4 inches
1) Find the slope of the line
2) find the slope between the two points
help please, thank you
Answer:
1 = 3/2
2 = -1/14
Step-by-step explanation:
The equation for the slope of a line is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] (difference in Y divided by the difference in X) or simply just Rise/Run.
For the first one, we have to pinpoint two points on the graph. There's one point placed on the x-axis 2 units away from the origin (2,0) and one four units to the right and 3 units up from the origin (4,3). Since it's on a graph, the easiest way to calculate it is by counting the units up and then right from (2,0) to (4,3). You can count that (4,3) is 3 units up and 2 units right from (2,0). Since slope is Rise/Run, the slope is 3/2.
For the second one, you can use the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. The Y of the second point is 2, and the Y of the first point is 1. The X of the second point is -17, and the X of the first point is -3.
You can plug all 4 numbers in to get (2-1)/(-17- -3)
2-1 = 1 and -17 - -3 = -14. So your slope is 1/-14 or -1/14.
Researchers randomly surveyed people at two amusement parks, Funland and Thrillville, to find out how many times they visit the park per year. Following are the data from the two surveys.
Funland: 4,1,2,1,5,6,3,2,4,3,2,6,1,3,2
Thrillville: 8,6,5,7,2,5,4,2,1,9,3,8,3,7,5,2,9,4,2,8
How many more times per year, on average, do people visit Thrillville than Funland?
On average, people visit Thrillville 2 more times per year than Funland.
AveragesTo determine how many more times per year, on average, do people visit Thrillville than Funland, the following calculation must be performed:
Funland: 4,1,2,1,5,6,3,2,4,3,2,6,1,3,2 = 4545 / 15 = 3Thrillville: 8,6,5,7,2,5,4,2,1,9,3,8,3,7,5,2,9,4,2,8 = 100100 / 20 = 55 - 3 = 2Therefore, on average, people visit Thrillville 2 more times per year than Funland.
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Estimate the difference.
Answer:
498. 498/6 = 83.
Step-by-step explanation:
Amy earns £10.00 per hour. She gets a raise, and her new hourly rate is £11.50 What is the percentage change in her hourly rate?
Percentage Change = (new rate - old rate) / (old rate)
New Rate = 11.5
Old Rate = 10
(11.5 - 10) / 10
1.5 / 10 = 15 / 100 = 0.15 = 15%
The percentage change in her hourly rate is 15%.
Hope this helps!
A board-game club meets each week at the local library. People bring different board games to play, like checkers and chess. Out of the 50 people that meet each week, 67% prefer to play checkers over chess. Construct an 83% confidence interval for the population mean of people that prefer to play checkers over chess.
Using the z-distribution, as we are working with a proportion, it is found that the 83% confidence interval is (0.5789, 0.7611).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have an 83% confidence level, hence[tex]\alpha = 0.93[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.83}{2} = 0.915[/tex], so the critical value is z = 1.37.
The other parameters are [tex]n = 50, \pi = 0.67[/tex].
Then, the bounds of the interval are given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 - 1.37\sqrt{\frac{0.67(0.33)}{50}} = 0.5789[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 + 1.37\sqrt{\frac{0.67(0.33)}{50}} = 0.7611[/tex]
The 83% confidence interval is (0.5789, 0.7611).
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Answer:
CI = (57.89%, 76.14%)
Step-by-step explanation:
First, solve for the 83% critical z-value (za/2). Second, solve for the margin of error. Third, solve for the confidence interval by subtracting and adding the margin of error with the sample probability of success.
which is larger 0.849 or 1.08
Answer:
the answer to this question is 1.08
help please thank you!!!
Answer:
3/4 · 1/4 = 3/16
Step-by-step explanation:
We can see from the picture that
yellow is
4 boxes out of the entire group of 16 boxes, hence 4/16
OR simplified
1 horizontal strip out or 4 total same horizontal strips, hence 1/4
blue is
12 boxes out of the entire group of 16 boxes, hence 12/16
OR simplified
3 vertical strips out or 4 total vertical strips, hence 3/4
The multiplication problem is
1/4 · 3/4 = 3/16 or 3/4 · 1/4 = 3/16
The result is 3 green boxes out of all 16 boxes.
(3/16 can not be simplified)
HELLLPPPPPPPP!!!!!!!!
An experiment consists of randomly drawing a card from a standard deck and recording its color, then rolling a die and recording its value.
The following tree diagram shows the possible outcomes.
A 2-column tree diagram: card & die. The card column has B & R. B & R each branch to the numbers 1 through 6 in the die column.
What is the probability of selecting a red card and rolling a number less than 3?
Enter your answer as a reduced fraction, like this: 3/14
The experiment of rolling the dice and selecting a card is an illustration of probabilities
The probability of selecting a red card and rolling a number less than 3 is 1/6
How to determine the probability?From the figure, we have:
Total outcomes = 12
Red card with a number less than 3 = 2
So, the probability of selecting a red card and rolling a number less than 3 is:
p = 2/12
Simplify
p = 1/6
Hence, the probability of selecting a red card and rolling a number less than 3 is 1/6
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What are the new coordinates of the figure above if it is rotated 90 degrees clockwise about the origin ?
A. A’(1,-3), B’(1,-7),C’(-3,-7),D’(-3,-3)
B. A’(-3,-1),B’(-7,-1), C’(-7,3) D’(-3,3)
C. A’(-3,-1),B’(-7,-1),C’(-7,3),D(-3,3)
D.A’ (1,-3),B’(1,-7),C’(3,-7),D’(3,-3)
Answer: A
Step-by-step explanation:
A vessel is in the shape of a right circular cone. The
radius of the top is 8 cm and the height is 40 cm.
Water is poured into the vessel at a rate of 20 cm /s.
Calculate the rate at which the water level is rising
when
(i) the water level is 12 cm from the vertex,
(ii) the vessel is one-quarter full.
The conic water vessel of height 40 cm and radius 8 cm filled at 20 cm^3/s gives;
The rate at which the water level is rising when the water level is 12 cm from the vertex is approximately 1.1 cm/s.When the vessel is one-quarter filled the rate at which the water level is rising is approximately 0.21 cm/s.How can the water level rate be found?The volume of the vessel, v = π•r^2•h/3
[tex] \frac{h}{r} = \frac{40}{8} = 5[/tex]
h = 5•r
Therefore;
v = π•r^2•(h)/3 = π•(h/5)^2•h/3
v = π•h^3/75
By chain rule of differentiation, we have;
[tex] \frac{dv}{dh} = \frac{dv}{dt} \times \frac{dt}{dh} [/tex]
Which gives;
[tex]π• \frac{ {h}^{2} }{25} = 20 × \frac{dt}{dh} [/tex]
[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {h}^{2} }{25} } [/tex]
When the height is 12 cm from the vertex, we have;
[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {12}^{2} }{25} } = 1.1 [/tex]
The rate at which the water level is rising when the water level is 12 cm from the vertex is approximately 1.1 cm/s.When the vessel is one-quarter filled, we have;
v = π•h^3/75
π•(40)^3/(75×4) = π•h^3/75
10•(40)^2 = 16,000 = h^3
h = (16,000)^(1/3) = 25 (approx)
Which gives;
[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {25}^{2} }{25} } = 0.21 [/tex]
When the vessel is one-quarter filled the rate at which the water level is rising is approximately 0.21 cm/s.
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There are 777 students in a class: 222 boys and 555 girls. If the teacher picks a group of 333 at random, what is the probability that everyone in the group is a girl?
The probability is 0.1429.
The probability that the first person chosen is a boy is 5/7. The probability that the second is a boy is 4/6; the third, 3/5; and the fourth, 2/4. Both the numerator and denominator decrease every time, because you lose a boy to choose from and you lose a student to choose from as well. This gives us:
5/7(4/6)(3/5)(2/4) = 120/840 = 0.1429.
The probability that everyone in the group is a girl is 2/7.
What is probability?Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.
Total number of students in a class = 7
Number of boys students = 2
Number of girls students = 5
The probability that everyone in the group is a girl is;
[tex]\rm Probability =\dfrac{Total \ number \ of \ girls}{Total \ number \ of \ boys}\\\\Probability=\dfrac{2}{7}[/tex]
Hence, the probability that everyone in the group is a girl is 2/7.
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i am stuck on this question please help me
Answer:
h = 8 units, b = 20 units
Step-by-step explanation:
h = 2 units
2 x 4 = 8
b = 5 units
5 x 4 = 20 units
Therefore, h = 8 units and b = 20 units
Hope this helps :)
Find the Circumference ddddddddddddddddddddddddddddd
Answer:
25.12
Step-by-step explanation:
C = π2r
C = 3.14*2*4
C = 25.12
Hope this helps :)
Given the function g(x)=√x+4, which of the following values cannot be the domain of g?
A. X=1
B. X=2
C. X=12
D. X=-5
Answer:
D. x = -5
Step-by-step explanation:
The square root function is only defined for non-negative arguments. For the function ...
[tex]g(x)=\sqrt{x+4}[/tex]
this means we must have ...
x +4 ≥ 0
x ≥ -4 . . . . . . subtract 4 from both sides
All of the numbers on your answer choice list are more than -4 except -5.
x = -5 is not in the domain of g(x)
Given g(x)=5x-3g(x)=5x−3, find g(-4)g(−4).
g(x)=5x-3
g(x)=5x−3
g(\color{green}{-4})=5(\color{green}{-4})-3
g(−4)=5(−4)−3
Plug input into x
-20-3
−20−3
Multiply
-23
−23
Answer:
the answer is 529
Step-by-step explanation:
see the explanation photo
Spencer owns a taxi cab company. He charges customers a base fee of $5 and an extra $2 for each mile traveled. If F represents a customer's fare (in dollars) and d represents the distance traveled (in miles draw a graph representing the relationship between F and d
Answer:
Let F = customer's fare (in dollars)
Let d = distance traveled (in miles)
Given:
Base fee = $5Charge per mile = $2 per mileCreating an equation from given information:
F = 2d + 5
This is a linear equation, with slope of 2 and y-intercept of (0, 5)
**see attached graph**
Answer:
See below ↓
Step-by-step explanation:
Given :
Base fee = $5Per extra mile = $2Solving :
With F as the total customer fare and d is the distance covered the equation will be :-F = 2d + 5In terms of x and y, it can be written as :y = 2x + 5Graph is given belowif you could just tell me what I should say in the presentation, that would be great :) thx
Answer:
we're u asking for this
What is ur statistical question
Find the distance between the two points in simplest radical form.
Answer:
13 units
Step-by-step explanation:
A right triangle can be drawn using the grid lines for legs and the line segment between the two points as the hypotenuse. You can count grid squares or subtract coordinates to find the vertical leg is 12 units and the horizontal leg is 5 units. The Pythagorean theorem tells you the length of the hypotenuse (distance between the points) is ...
d² = 12² +5² = 144 +25 = 169
d = √169 = 13
The distance between the two points is 13 units.
_____
Additional comment
This set of dimensions, {5, 12, 13}, is one of several "Pythagorean triples" that often show up in math problems. Other common triples are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, and multiples of these.
giving brainlist please help me out
Answer:
681 m^3
Step-by-step explanation:
Winder only found part of the volume. He also needs to find the volume of the hemisphere.
I would first find the volume of the cylinder like Winder, then proceed to calculate the volume of the hemisphere, which is V = 4/3π(4^3)=27.16 m^3. The total volume inside the storage tank is 681 m^3 when rounded to the nearest cubic meter.