What is the annual interest for a principal of $3,500 at a simple annual interest
rate of 2.3%?
Answer:
Step-by-step explanation:
Given principal p =$3500
Time t =1 year
Rate of interest r =2.3%
So annual interest=p×r×t/100
=3500×2×2.3/100
=7000×2.3/100
=16100/100
=161.
So annual interest is $161
In science class, Polly learned that trees help make the oxygen that people breathe. One tree makes about 250 pounds of oxygen each year. Polly wonders how much oxygen the trees on her street make. When she gets home, she counts 32 trees on her street. How many tons of oxygen do they make in a year?
Answer:
They make 4 approximately tons of oxygen each year.
Step-by-step explanation:
( 250lbs × 32 ) ÷ 2000 = 4t
250 pounds because each tree makes about 250 pounds of oxygen a year.
× 32 because there are 32 trees, so they'll make 32 times more oxygen than one tree.
÷ 2000 because before that everything was in pounds, and the question asks about tons. There are 2000 pounds in a ton, so you divide by 2000 to get the answer, which is 4 tons.
A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola yx. What are the dimensions of the rectangle with the maximum area? What is that area?
Answer:
The answer is below
Step-by-step explanation:
The question is not complete, the complete question is:
A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y 81-x², what are the dimensions of the rectangle with the maximum area? what is the area?
Solution:
Given the parabola:
y = 81 - x²
Let the points (a,0) and (-a, 0) be points on the axis, this points touch the parabola at (a, 81 - a²) and (-a, 81 - a²).
Points (a,0), (-a, 0), (a, 81 - a²), (-a, 81 - a²) form the rectangle.
The length of rectangle = distance between (a,0) and (-a, 0) or between (a, 81 - a²) and (-a, 81 - a²) = 2a
The breadth of rectangle = distance between (a,0) and (a, 81 - a²) or between (-a, 0) and (-a, 81 - a²) = 81 - a²
Area of rectangle (A) = length × breadth = 2a × (81 - a²) = 162a - 2a³
A = 162a - 2a³
The maximum area is at dA / da = 0
dA / da = 162 - 8a² = 0
162 - 6a² = 0
6a² = 162
a² = 27
a = 5.2 units
Length = 2a = 2(5.2) = 10.4 units
Breadth = 81 - a² = 81 - 5.2² = 54 unit
Area = length × breadth = 54 × 10.4 = 561 unit²
A random survey of 30 students found that 17 played a musical instrument. If the school has 450 students, predict how many do not play an instrument.
Given:
A random survey of 30 students found that 17 played a musical instrument.
Total number of students = 450
To find:
Estimated number of students who do not play an instruments.
Solution:
A random survey of 30 students found that 17 played a musical instrument.
Let E be the event that student play an instrument.
So, probability that a student plays an instrument is
[tex]P(E)=\dfrac{17}{30}[/tex]
Probability that a student do not play an instrument is
[tex]P(E')=1-P(E)[/tex]
[tex]=1-\dfrac{17}{30}[/tex]
[tex]=\dfrac{13}{30}[/tex]
Now, number of students who do not play an instruments is
[tex]450\times P(E')=450\times \dfrac{13}{30}[/tex]
[tex]450\times P(E')=195[/tex]
Therefore, 195 students do not play an instrument.
ANSWER PLS OR NOTHING WILL HAPPEN
Answer: 8
Step-by-step explanation:
Answer:
[tex]( - 4)( - 2) = \boxed{8}[/tex]
There are a total of 120 bicycles and tricycles in a shop. There are 302 wheels in allmany bicycles and how many tricycles are in the shop?
Answer: There are 62 tricycles in the shop.
Step-by-step explanation:
Given: Number of wheels in a bicycle = 2
Number of wheels in a tricycle = 3
Let x = Number of bicycles , y = Number of tricycles.
As per given , we have
x+y =120 (i)
2x+3y=302 (ii)
Multiplying 2 on both sides of (i)
2x+2y=240 (iii)
Subtract (iii) from (ii) , we get
y= 62
Put value of y in (i) , we get
[tex]x+62=120\\\\\Rightarrow\ x=120-62\\\\\Rightarrow\ x= 58[/tex]
Hence, there are 58 bicycles and 62 tricycles in the shop.
In late June 2012, Survey USA published results of a survey stating that 55% of the 579 randomly sampled Kansas residents planned to set off fireworks on July 4th. Determine the margin of error for the 55% point estimate using a 95% confidence level. The margin of error is: _____% (please round to the nearest percent)
Answer:
The Margin of Error E [tex]\simeq[/tex] 4.1 %
Step-by-step explanation:
Given that:
The sample size = 579
The sample proportion [tex]\hat p = 55\%[/tex] = 0.55
From the confidence interval of 95%
The level of significance ∝ = 1 - C.I = 1 - 0.95 = 0.05
The critical value of [tex]Z_{\alpha/2 } = Z_{0.025} = 1.96[/tex]
Thus;
The Margin of Error E = [tex]Z_{\alpha/2 } \times \sqrt{{\dfrac {\hat p ( 1 - \hat p }{n}}[/tex]
The Margin of Error E = [tex]1.96 \times \sqrt{{\dfrac {0.55 ( 1 - 0.55) }{579}}[/tex]
The Margin of Error E = [tex]1.96 \times \sqrt{{\dfrac {0.55 ( 0.45 )}{579}}[/tex]
The Margin of Error E = [tex]1.96 \times \sqrt{{\dfrac {0.2475}{579}}[/tex]
The Margin of Error E = [tex]1.96 \times \sqrt{{4.2746114 \times 10^{-4}}[/tex]
The Margin of Error E = [tex]1.96 \times .020675[/tex]
The Margin of Error E = 0.040523
The Margin of Error E [tex]\simeq[/tex] 0.041
The Margin of Error E [tex]\simeq[/tex] 4.1%
Helpppppppp pleaseeeee
Answer:
108 cm^2
Step-by-step explanation:
A= 1/2 b×h
so
1/2 12×18
Please answer this correctly without making mistakes
Answer:
The answer is $0.07 cents per inch
Step-by-step explanation:
If you take 6 feet into inches (72)
and divide the total cost by the amount of inches (5.04 / 72)
You get the answer
9a + 8 - 20-3-50
Answer
Answer:
9a-65
Step-by-step explanation:
simply write 9a+(add the remaining numbers all together)
Hadley paddled a canoe 2 miles in 1/9 of
an hour How far could Hadley paddle in
1 hour?
Answer: 18 miles
explanation: set up a proportion. (2 over 1/9 = x over 1). cross multiply, 2x1=2, then divide 2/(1/9)=18.
Put brackets in the expression to make the following true. 4 - 7 - 8 + 6 = -17
solve (x-4)^2=5.
Answers:
A. x=9 and x=1
B. x=5+(square root)4
C. x=-4+(square root)5
D. x=4+(square root)5
Answer:
don't dout yourself
Step-by-step explanation:
never give up thanks for the free points
How are prism and cylinders are alike ?
Answer:
They are both 3 dimensional shapes. A cylinder is essentially a prism for a circle.
Step-by-step explanation:
Step-by-step explanation:
- They are both 3 dimensional
-They both have 2 bases
Which ordered pairs are solutions to the equation 5x+12y=15?
A rocket is launched from a tower. The height of the rocket , y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
Y=-16x^2+147x+118
========================================================
Explanation:
The general equation
y = ax^2 + bx + c
has the vertex (h,k) such that
h = -b/(2a)
In this case, a = -16 and b = 147. This means,
h = -b/(2a)
h = -147/(2*(-16))
h = 4.59375
The x coordinate of the vertex is x = 4.59375
Plug this into the original equation to find the y coordinate of the vertex.
y = -16x^2+147x+118
y = -16(4.59375)^2+147(4.59375)+118
y = 455.640625
The vertex is located at (h,k) = (4.59375, 455.640625)
The max height of the rocket occurs at the vertex point. Therefore, the max height is y = 455.640625 feet which rounds to y = 455.6 feet
A fair six-sided die is rolled. Find the probability of getting a 4.
Answer:
A fair six-sized die is rolled. Find the probability of getting at least a 4.
There are 6 outcomes and three of them are 4, 5 or 6, so the probability of greater than or equal to 4 is 3/6=½.
If a polynomial has four terms, 3x3 + 5x + 6x2 + 10, which factoring method can be considered? perfect-square trinomial difference of squares factor by grouping sum of cubes
Answer:
c
Step-by-step explanation:
just took the quiz
Answer:
The answer is C) factor by grouping
Step-by-step explanation:
Edge 2020
shasha worked in the garden for 3 hours and 40 minutes. she started at 8:30am. at what time did she stop?
Answer:
Sasha stopped working at 12:10 PM
Step-by-step Explanation
8:30 + 3 hours and 40 minutes = 12:10 PM
Mark as brainliest if it's right!
Answer:
12:10 p.m
Step-by-step explanation:
3 hours from 8:30 is 11:30 a.m.
Now we add 30 minutes to 11:30 and you get 12:00
Add the remaining 10 minutes and you get 12:10 p.m
I hope this helped, please mark Brainliest, thank you!
A line passes through the point (-6,7) and has a slope of -4/3. Write an equation in slope-intercept form for this line.
Answer:
Step-by-step explanation:
y-7= -4/3 (x+6)
y-7= -4/3x-8
add 7 to both sides
y= -4/3x-1
The equation in slope-intercept form for the given line is 3y = -4x -3
What is Equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that a line passes through the point (-6,7) and has a slope of -4/3.
Standard equation of a line = y = mx + c where m is the slope,
Therefore, putting values of x and y to get the value of c
7 = -6*-4/3 + c
c = 7 - 8
c = -1
Equation = y = -4x/3 -1
Or, 3y = -4x -1
Hence, the equation of a line passing through the point (-6,7) and has a slope of -4/3 is 3y = -4x -1
For more references on Equation, click;
https://brainly.com/question/10413253
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i need help with this plz i have no idea what to do
Answer:
When Item Price * (%) is < or > to $ Off
Step-by-step explanation:
What is the angle of elevation?
Answer:
Step-by-step explanation:
tan x° = [tex]\frac{3}{4}[/tex] ⇒ x° ≈ 36.87° ≈ 36.9°
Write an equation in standard form for the line, where the points (-2, -1) and (0, 4) are on the line
Answer:
An equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
Step-by-step explanation:
Given the points
(-2, -1) and (0, 4)The slope between two points
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)[/tex]
[tex]m=\frac{4-\left(-1\right)}{0-\left(-2\right)}[/tex]
[tex]m=\frac{5}{2}[/tex]
Writing the equation in point-slope form
As the point-slope form of the line equation is defined by
[tex]y-y_1=m\left(x-x_1\right)[/tex]
Putting the point (-2, -1) and the slope m=1 in the line equation
[tex]y-\left(-1\right)=\frac{5}{2}\left(x-\left(-2\right)\right)[/tex]
[tex]y+1=\frac{5}{2}\left(x+2\right)[/tex]
[tex]y=\frac{5}{2}x+4[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
so
[tex]y=\frac{5}{2}x+4[/tex]
[tex]\frac{5}{2}x-y=-4[/tex]
Therefore, an equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
6/root of 12. Rationalize the denominator
Answer:
Step-by-step explanation:
hi
[tex]\dfrac{6}{\sqrt{12}}=\dfrac{2\times 3}{\sqrt{2^2\times 3}}=\dfrac{3}{\sqrt{3}}=\sqrt{3}[/tex]
thanks
Houses can be either domed or octagonal.
True
False
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Houses can be either domed or octagonal: True
about how many 18s are there in 250?a.10 b.12 c.15
Answer:
C. 15
Step-by-step explanation:
It's 13.888 about 14, so 15 is the closest answer.
b
Step-by-step explanation:
taking 250÷18=13.88~
CAN SOMEONE PLEASE HELP ME ON THE TOP ONE !!!!!!
Answer:
[tex]the \: slope \: is \to \boxed{-3} \\ the \: y \: intercept \to \boxed{18}[/tex]
Step-by-step explanation:
[tex]the \: solpe \: \boxed{m} = \frac{9 -1 2}{3 - 2} = -3 \\ y = mx + c \\ 12 = (-3)(2) + c \\ c = 12 + 6 = 18[/tex]
What is the value of the function at x=−2?
Answer:
y = 3
General Formulas and Concepts:
Reading a Cartesian PlaneReading and labeling coordinatesStep-by-step explanation:
The question is asking us what the y-value is when x = -2.
According to the graph, when x = -2, y = 3.
Therefore, y = 3.
A fox leaves its den and travels 725 yards northeast, then 950 yards west. How far, in yards is the fox from its den
Answer:
1,675
Step-by-step explanation:
add it
Using Pythagoras, the distance of the fox from its den would be 533.26 yards
Hypotenus = 900 yards Adjacent = 725 yards Distance from den = oppositeOpposite = √hypotenus² - adjacent²
Distance = √(900)² - (725)²
Distance = √810000 - 525625
Distance = √284375
Distance = 533.26 yards
Therefore, the fox is 533.26 yards from his den.
Learn more : Opposite = √hypotenus² - adjacent²
Luke likes running. He runs 2 1⁄2 miles every 1⁄2 hour. Complete the table to find out how far he runs in each time interval. Which one shows his unit rate (miles per hour)?