Answer:
3 years
Step-by-step explanation:
A = P(1 + r)^t
A = I + P
A = 14,000 + 4,634 = 18,634
18,634 = 14,000(1 + 0.1)^t
18,634/14,000 = 1.1^t
log (18,634/14,000) = log 1.1^t
log (18,634/14,000) = t * log 1.1
t = [log (18,634/14000)]/(log 1.1)
t = 3
Write the equation of the line that passes through (−2, 6) and (2, 14) in slope-intercept form. (2 points)
Answer:
[tex]y = 4x + 14[/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation we must first find the slope of the line
Slope of the line using points (−2, 6) and (2, 14) is
[tex]m = \frac{14 - 6}{2 + 2} = \frac{8}{2} = 4[/tex]
Now we use the slope and any of the points to find the equation of the line.
Equation of the line using point ( - 2, 6) and slope 4 is
[tex]y - 6 = 4(x + 2) \\ y - 6 = 4x + 8 \\ y = 4x + 8 + 6[/tex]
We have the final answer as
[tex]y = 4x + 14[/tex]
Hope this helps you
Preeti and Shikha have bookshelves of the same size. Preeti’s shelf is 56 full of books and Shikha’s shelf is 35 full. Whose bookshelf is more full and by how much?
Answer:
Step-by-step explanation:
No of books in Preeti's shelf = 56
No of books in Shikha's shelf = 35
56 > 35
∴ Preeti's shelf is more full by 21 books
as 56 - 35 = 21
Hope this helps
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Luis’s cedar chest measures 4 feet long, 2 feet wide, and 2 ¼ feet high. What is the volume of the chest?
Answer:
[tex]4 {ft}^{3} [/tex]
Step-by-step explanation:
[tex]2 \times \frac{1}{4} = 0.5 \\ v = lbh \\ 4 \times 2 \times 0.5 \\ = 8 \times 0.5 \\ = 4 {ft}^{3} [/tex]
The volume of Luis’s cedar chest is 18 cubic feet.
The dimensions of Luis’s cedar chest are length=4 feet, width=2 feet and height=2 1/4 feet.
What is the formula to find the volume of the cuboid?The volume of the cuboid is the measure of the space occupied within a cuboid. The cuboid is a three-dimensional shape that has length, breadth, and height. If we have a rectangular sheet and we go on stacking such sheets, we will end up getting a shape that has some length, breadth, and height.
The formula to find the volume of the cuboid is l×b×h.
Where, l=length, b=breadth or width and h=height.
Now, volume=4×2×2.25=18 cubic feet.
Therefore, the volume of Luis’s cedar chest is 18 cubic feet.
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Week 4 Assignment: Solving Systems of Linear Equations by Eliminatio
Due Aug 2 by 11:59pm
Points 10
Submitting an external tool
Solve applications of systems of equations by elimination
Question
The sum of two numbers is -17. Their difference is 41. Find the numbers.
Sorry, that's incorrect. Try again?
I
10
-5
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SUI
Content attribution
Answer:
The two numbers are 12 and -29
Step-by-step explanation:
Let x and y be the two numbers
x+y = -17
x - y = 41
Add the two equations together
x+y = -17
x - y = 41
----------------
2x = 24
Divide by 2
x = 12
Now find y
x+y = -17
12 +y = -17
Subtract 12 from each side
y = -17-12
y = -29
Find the sum of the first 10 terms of the following geometric sequences: 3,6,12,24,48
Answer:
3,069
Step-by-step explanation:
The sequence is doubling, so terms 1 through 10 are:
3, 6, 12, 24, 48, 96, 192, 384, 768, 1,536
3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1,536 = 3,069
295 feet = _____ meters ?
Answer:
Hello! I hope I am correct!
Step-by-step explanation:
295 feet will equal to 89.916 meters.
Steps in order to solve this problem:
First you have to multiply the length in feet by 0.3048.
295x 0.3048 or 295* 0.3048
(295 feet is equivalent to 89.916 meters!)
Will equal 89.916 meters.
Therefore, 295 feet = 89.916 meter
Hope this helps!
Brainliest would be appreciated!
By:BrainlyAnime
(Picture attached)
What are the roots of the quadratic equation below?
x2 + 2x= -5
Answer:
No real root.
Complex roots:
[tex] x = -1 \pm 2i [/tex]
Step-by-step explanation:
[tex] x^2 + 2x = -5 [/tex]
[tex] x^2 + 2x + 5 = 0 [/tex]
There are no two integers whose product is 5 and whose sum is 2, so this trinomial is not factorable. We can use the quadratic formula.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-2 \pm \sqrt{2^2 - 4(1)(5)}}{2(1)} [/tex]
[tex] x = \dfrac{-2 \pm \sqrt{4 - 20}}{2} [/tex]
[tex] x = \dfrac{-2 \pm \sqrt{-16}}{2} [/tex]
Since we have a square root of a negative number, there are no real roots. If you have learned complex numbers, then we can continue.
[tex] x = \dfrac{-2 \pm 4i}{2} [/tex]
[tex] x = -1 \pm 2i [/tex]
To find ∫ (x − y) dx + (x + y) dy directly, we must parameterize C. Since C is a circle with radius 2 centered at the origin, then a parameterization is the following. (Use t as the independent variable.)
x = 2 cos(t)
y = 2 sin(t)
0 ≤ t ≤ 2π
With this parameterization, find the followings
dy=_____
dx=_____
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]x=x(t)=2cos(t)\\\\dx=\dfrac{dx}{dt}dt=x'(t)dt=-2sin(t)dt[/tex]
and
[tex]y=y(t)=2sin(t)\\\\dy=\dfrac{dy}{dt}dt=y'(t)dt=2cos(t)dt[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The values of dx and dy are give as -2sin(t)dt and 2cos(t)dt respectively. The answer to the given problem can be stated as,
dy = 2cos(t)dt
And, dx = -2sin(t)dt.
What is the integration of a function?The integration can be defined as the inverse operation of differentiation. If a function is the integration of some function f(x) , then differentiation of that function is f(x).
The given integral over C is ∫ (x − y) dx + (x + y) dy.
And, the parameters for C are as follows,
x = 2cos(t)
y = 2sin(t)
0 ≤ t ≤ 2π
Now, on the basis of these parameters dx and dy can be found as follows,
x = 2cos(t)
Differentiate both sides with respect to t as follows,
dx/dt = 2d(cos(t))/dt
=> dx/dt = -2sin(t)
=> dx = -2sin(t)dt
And, y = 2sin(t)
Differentiate both sides with respect to t as follows,
dy/dt = 2d(sin(t))/dt
=> dy/dt = 2cos(t)
=> dy = 2cos(t)dt
Hence, the value of dx and dy as per the given parameters is -2sin(t)dt and 2cos(t)dt respectively.
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Which set of values could be the side lengths of a 30-60-90 triangle?
O A. {6,613, 12)
O B. {6, 12, 12.3}
O C. {6,6.12, 12}
O D. {6, 12, 12/3)
Answer:
I think :
c is 30 triangle
b is 60 triangle
d is 90 triangle
bananas cost $4 and apples close 0.60$ each if b represents the number of bunches of bananas and a represents the number of apple which of the following expressions represents the total cost? 1 4.60(b+a) 2 4b + 0.60 3 4.60 + a 4 4.60ab
Answer:
[tex]\huge\boxed{\$ (4 b + 0.60 a)}[/tex]
Step-by-step explanation:
Bananas represented by b
1 banana costs $4 so b bananas will cost $ 4 b
Apples represented by a
1 apples costs 0.60 $ so a apples will cost $ 0.60 a
Totally, they will cost:
=> $ (4 b + 0.60 a)
Answer:
hiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
Closing prices of two stocks are recorded for 50 trading days. The sample standard deviation of stock X is 4.665 and the sample standard deviation of stock Y is 8.427. The sample covariance is $35.826.
Calculate the sample correlation coefficient. (Round your answer to 4 decimal places.)
Answer:
The sample correlation coefficient r = 0.9113
Step-by-step explanation:
In this question, we are interested in calculating the sample correlation coefficient.
From the question, we are given;
We are given that,
The sample standard deviation of stock X = 4.665
The sample standard deviation of stock Y = 8.427
The sample covariance = 35.826
Mathematically, the Pearson correlation coefficient "r", it is given as;
r = (co-variance of X and Y)/(standard deviation of X * Standard deviation of Y)
Inputing these values, we have;
r = (35.826)/(4.665 * 8.427) = 0.9113
You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?
Answer: You will need 8 cup scales
Step-by-step explanation:
kg=1000 grams
2000/250=8
Answer:
8
Step-by-step explanation:
2000/250=8
The average salary of all assembly-line employees at a certain car manufacturer is $42,000 is it a sample or population
Answer:
Population parameters
Step-by-step explanation:
Population parameters usually find from the average values, in a simple way we can say that finding the average value comes in the Population Parameters.
In the given question, car manufacturing companies provide sample of average.
So, given scenario is a type of "Population parameters".
A racecar is traveling at a constant speed of 150 miles per hour. How many feet does it travel in 5 seconds? Remember that 1 mile is 5280 feet.
Answer:
distance covered in 5 seconds
= 1.4283 *10^10 feet
Step-by-step explanation:
A racecar is traveling at a constant speed of 150 miles per hour.
One mile = 5280 feet
150 miles= 5290*150
150 miles= 793500 feet
A racecar is traveling at a constant speed of 793500 feet per hour.
Converting 793500 feet per hour to feet per seconds .
793500 feet per hour
= 793500*60*60 feet per seconds
=2856600000 feet per second
In 5 seconds , distance covered
= 2856600000 *5
distance covered in 5 seconds
= 1.4283 *10^10 feet
Find the area of the shape shown below.
2
2
4
Hurry and answer plz!!!!
1
Answer:
7 square units
Step-by-step explanation:
We can break down this complex shape into smaller shapes.
I've broken it down into a rectangle, a square, and a triangle (See attached picture)
Let's first find the area of the triangle. To do this we use the formula [tex]\frac{bh}{2}[/tex]. The base is 1 (because the top is 2, and 1 is already used on the triangle - 2-1 = 1.) and the height is 2 (because 4 is already used on the left, and 2 was used on the right so 4-2=2).
[tex]\frac{2\cdot1}{2} = \frac{2}{2} = 1[/tex].
Now let's find the area of the top square - we can just square 2 which is 4.
To find the area of the bottom rectangle, we can multiply it's two side lengths of 2 and 1 = 2.
Adding these all together gets us 4+2+1 = 7.
Hope this helped!
out of the 444 Fridays Rebecca has been driven to school, only 12/37 of the time did she ever choose to sit in the back seat. How many times did she sit in the front seat?
Answer:
300
Step-by-step explanation:
We need to find 12/37 of 444.
12/37 * 444 = 12/37 * 444/1 = (12 * 444)/(37 * 1) = 5328/37 = 144
She sat in the back seat 144 times out of 444.
444 - 144 = 300
She sat in the front seat 300 times.
make a box-and-whisker plot for the data. numbers of colors in a country's flag :3,2,2,4,4,3,6,3,5,3,4,1
Answer: see attachment
Step-by-step explanation:
Put the numbers in order from smallest to biggest:
1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 6
↓ ∨ ↓
Q1 Median Q3
Q1 median = (2+3)/2 = 2.5 <---- left side of box plot
Median = (3+3)/2 = 3 <---- Vertical Line of box plot
Q3 median = (4+4)/2 = 4 <---- right side of box plot
The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 6.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 6.0 minutes.
Answer: P(X<6) = 0.3085 or 30.85%
Step-by-step explanation: Determine, first, z-score:
[tex]z = \frac{x-\mu}{\sigma}[/tex]
x is a random variable for time a student takes to find a spot, in this case, x=6:
[tex]z = \frac{6-6.5}{1}[/tex]
z = -0.5
Using z-score table, find z-score:
P(X<6) = P(z< -0.5)
P(X<6) = 0.3085
Probability of finding a parking spot in less than 6 minutes is approximately 30.85%.
Select the correct answer -1/4(12x+8) is less than it equal to -2x+11
Answer:
x ≤ [tex]\frac{9}{5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{4}[/tex](12x + 8) ≤ - 2x + 11 ← distribute parenthesis on left side
3x + 2 ≤ - 2x + 11 ( add 2x to both sides )
5x + 2 ≤ 11 ( subtract 2 from both sides )
5x ≤ 9 ( divide both sides by 5 )
x ≤ [tex]\frac{9}{5}[/tex]
-¼(12x+8) ≤ -2x+11
• Divide by 44X-¼(12x+8) ≤-2x+11
= -12x + 8 ≤ -2x + 11
• Group like terms-12x + 2x ≤ 11 - 8
= -10x/10 ≤ 3/-10
x≤ 3/-10Guys, can you help me out? I would really appreciate it! GIVING OUT BRAINLIEST!!
Answer:
C:750$
Step-by-step explanation:
The food expense is 15% of total income 5000$
=> food expense: (15/100) x 5000 = 750$
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
A10x- 10 = -10x + 10
B- 10x - 10 = -10x + 10
C-10x – 10 = -10x - 10
D10x - 10 = -10x – 10
Hey there! I'm happy to help!
An equation with infinite solutions has a solution of x=x. You can plug in any x-value and it will equal x, so there are infinitely many solutions.
ANSWER A
10x-10=-10x+10
We add 10 to both sides.
10x=-10x+20
We add 10x to both sides.
20x=20
We divide both sides by 20.
x=1
We have a solution of 1, so this is not an equation with infinitely many solutions.
Answer B
-10x-10=-10x+10
We add 10 to both sides.
-10x=-10x+20
We add 10 x to both sides.
0=20
This has no solutions because the x is gone, so there cannot be a solution.
Answer C
-10x-10=-10x-10
We add 10 to both sides.
-10x=-10x
We divide both sides by -10.
x=x
This has infinitely many solutions.
Answer D
10x-10= -10x-10
We add 10x to both sides.
20x-10=-10
We add 20 to both sides.
20x=0
We divide both sides by 20.
x=0
There is a single solution here, not infinitely many.
Therefore, the answer is C. -10x-10=-10x-10.
Have a wonderful day! :D
Find the side of a square whose diagonal is of the given measure.
Given = 15.2 cm
Answer:
15cm
Step-by-step explanation:
First, a square's diagonal is basically the hypotenuse of a 45-45-90 triangle. a 45-45-90 triangle has a really special relationship, where the side length is x, and the diagonal is x [tex]\sqrt{2}[/tex]. So, the side length is 15.
Answer:
15cm
Step-by-step explanation:
Each corner of the square would be a 90° angle so half of that would be 45°.
[tex] \sin(45) \times 15 \sqrt{2} = 15cm[/tex]
Find the missing side of the triangle. A. 321−−−√ yd B. 221−−−√ yd C. 338−−√ yd D. 21−−√ yd
Answer:
[tex] x = \sqrt{221} yd [/tex]
Step-by-step explanation:
Use Pythagorean theorem to find x.
Thus, the sum of the square of the lengths of two legs of a right triangle equal the square of the hypotenuse, which is the longest side.
Thus,
[tex] x^2 = 11^2 + 10^2 [/tex]
[tex] x^2 = 121 + 100 [/tex]
[tex] x^2 = 221 [/tex]
[tex] x = \sqrt{221} yd [/tex]
Answer:
v/221 yd
Step-by-step explanation:
11y 10yd x ?
x=v/221 yd
yippie
Do men and women run a 5 kilometer race at the same pace? Here are boxplots of the time (in minutes) for a race recently run in Chicago. Write a brief report discussing what these data show.
Answer:
yes
Step-by-step explanation:
Based on experience, the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2771 mm with a standard deviation of 0.000855 mm.
(a) A certain shipment has a diameter of 0.2742. Find the standardized z-score for this shipment. (Round your answer to 3 decimal places.)
z
(b) Is this an outlier?
Yes
No
Answer:
(a) The standardized z-score for this shipment is -3.392.
(b) Yes, this an outlier.
Step-by-step explanation:
We are given that the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2771 mm with a standard deviation of 0.000855 mm.
Let X = the metal thickness of incoming shipments.
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean thickness = 0.2771 mm
[tex]\sigma[/tex] = standard deviation = 0.000855 mm
(a) Now, it is given that a certain shipment has a diameter of 0.2742 mm and we have to find the standardized z-score for this shipment.
So, z-score = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{0.2742-0.2771}{0.000855}[/tex] = -3.392
Hence, the standardized z-score for this shipment is -3.392.
(b) Yes, we can consider this as an outlier because the standardized z-score is very large and this value is far from the population mean.
Michael records the height of 1000 people. This data is a normal distribution and the sample mean was 0.75. Identify the margin of error for this data set.
Answer:
0.0284Step-by-step explanation:
The formula for calculating the Margin of error of a dataset is expressed as;
Margin of error = [tex]Z*\sqrt{\frac{p(1-p)}{n} } \\\\[/tex] where;
Z is the z-score of 95% confidence interval = 1.96
p is the sample proportion/mean = 0.75
n is the sample size = total number of people = 1000
Note that when the confidence interval is not given, it is always safe to use 95% confidence.
Substituting this values into the formula we have;
[tex]ME = 1.96*\sqrt{\frac{0.7(1-0.7)}{1000} } \\\\ME = 1.96*\sqrt{\frac{0.7(0.3)}{1000} } \\\\ME = 1.96*\sqrt{0.00021} } \\\\ME = 1.96*0.01449\\\\ME = 0.0284[/tex]
Hence the margin error for the dataset is 0.0284
A city council consists of seven Democrats and six Republicans. If a committee of five people is selected, find the probability of selecting two Democrats and three Republicans.
Answer:
solution,
let d and r denote democrats and republicans respectively.
given,
no. of total sample space n(s) =7+6=13
no. of total democrats n(d)=7
no. of total republicans n(r)=6
no. of democrats events n(D1)=2
no. of republicans events n(R1)=3
it is a mutually exclusive event. so the probability of selecting two democrats and three republicans= {n(D1)/n(s)} * {n(r1)/n(s)}
=(2/13)*(3/13)
=6/169
Answer:
6/169
Step-by-step explanation:
If a recipe which makes 8 servings calls for 2 cups of sugar, how many cups of sugar will it take to make 18 servings?
Answer:
4.5
Step-by-step explanation:
2/8=x/18
Answer:
4.5 cups
Step-by-step explanation:
first you set up the problem like servings/cups. This would look like 8/2. Then you add the 18 servings and make it a cross multiplication problem. The expression would look like 8/2=18/x. You cross multiply and get 8x=36. Divide by 8 and get x=4.5 cups.
Write the expression as a single term, factored completely. Do not rationalize the denominator. 54x2+1−−−−−−√+20x4x2+1√ Select one: a. 5(4x2+4x+1)4x2+1√ b. 20x2+20x+1)5x+1 c. 20x2+20x+1)4x2+1√ d. 5(4x2+4x+1)5x+1
When we write expression 5√(4x² + 1) + 20x / √(4x² + 1) as singled term factorised completely, we have 5(4x² + 4x + 1) / √(4x² + 1) (Option A)
Data obtained from the question5√(4x² + 1) + 20x / √(4x² + 1)Factorised =?How to factorised 5√(4x² + 1) + 20x / √(4x² + 1)5√(4x² + 1) / 1 + 20x / √(4x² + 1)
Least common multiple (LCM) is √(4x² + 1)
[(5√(4x² + 1) × √(4x² + 1) + 20x] / √(4x² + 1)
[5(4x² + 1) + 20x] / √(4x² + 1)
[20x² + 5 + 20x] / √(4x² + 1)
[20x² + 20x + 5] / √(4x² + 1)
5(4x² + 4x + 1) / √(4x² + 1)
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Complete question
See attached photo
-50 POINTS- (5/5) Which scatter plot represents the following data?
Answer:
B is plotted correctly
Step-by-step explanation:
A point (1,2) is plotted at (1,3)
B is plotted correctly
C point (1,2) is plotted at (1,3)
D point (1,2) is plotted at (1,3)
Answer:
B.
Step-by-step explanation:
According to the table, there is a point at (0, 5), and a point at (1, 2).
A: The scatterplot has a point at (0, 5), but a point at (1, 3).
B: The scatterplot has points at (0, 5) and (1, 2).
C: The scatterplot has a point at (0, 5), but a point at (1, 3).
D: The scatterplot has a point at (0, 5), but a point at (1, 3).
Hope this helps!
