Answer:
year 1: 90% × 245000 = 220500
year 2: 90% × 220500 = 198450
year 3: 90% × 198450 = 178605
∴ the car price after 3 years is 178605
explanation:
the value of car decreases 10%. that means the car price is 90%
The price of the car after 3 years will be 178605
We can calculate the value in the following way
Rate of decrease in car's price: 10%
Current price of the car: 245000
Value after 1 year, say value1= current value-10% of current value
[tex]value1=245000-\frac{10*245000}{100}[/tex]
=245000-24500
=220500
After 1 year, the next decrement in the price will be based on the value of the car in that year. In other words, we calculate the value after the second year by decreasing by 10% of value1.
Value of car after 2 years, say value2= value1- 10% of value1
[tex]value2=220500- (\frac{10*220500}{100})[/tex]
=220500-22050
=198450
Similarly,
Value of car after 3 years, say value3= value2- 10% of value2
[tex]value3=198450- (\frac{10*198450}{100})[/tex]
=198450-19845
=178605
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The model t = 16.708 ln(x/(x-705)) approximates the term of a mortgage of $150,000 at 6% interest rate, where t is the term of the mortgage in years and x is the monthly payment plan in dollars.
a. Approximate in terms (in yr) of a $150,000 mortgage at 6% when the monthly is $897.72 and when the monthly payment is $1526.49 (Round your answers to the nearest whole number).
$897.72 ________ yr
$1526.49_________ yr
b. Approximate the total amounts paid (in dollars) over the term of the mortgage with a monthly payment plan of $897.72 and with a monthly payment plan of $1526.49. (Round your answers to 2 decimal places.)
$897.72 $_____________
$1526.49 $_____________
What is the amount of the total is interest costs (in dollars) in each case? (Round your answers to 2 decimal places)
$897.72 $__________
$1526.49 $__________
c. What is the vertical asymptote for the model? ____________
Interpret its meaning in the context of the problem.
The monthly payment must be (more or less) than $________, and the close to this value is, the (quicker you will be able or longer it will take) to pay off the mortgage.
Answer:
(a) $897.72: 26 yr
$1526.49: 10 yr
(b) See below.
(c) x = 705
more, $705, longer it will take
Step-by-step explanation:
Given equation:
[tex]t=16.708 \ln \left(\dfrac{x}{x-705}\right)[/tex]
where:
t = term of the mortgage (in years)x = monthly payment plan (in dollars)Part (a)[tex]\begin{aligned}x=897.72 \implies t& =16.708 \ln \left(\dfrac{897.72}{897.72-705}\right)\\& =16.708 \ln \left(4.65815691...\right)\\&=16.708(1.53861985...)\\&=25.70726...\\&=26\; \rm years\end{aligned}[/tex]
[tex]\begin{aligned}x=1526.49 \implies t& =16.708 \ln \left(\dfrac{1526.49}{1526.49-705}\right)\\& =16.708 \ln \left(1.85819669...\right)\\& =16.708(0.619606496...)\\&=10.352385...\\&=10 \; \rm years\end{aligned}[/tex]
Part (b)To approximate the total amounts paid (in dollars) over the term of the mortgage, multiply the monthly payment by the term.
Please note I have provided two calculations per monthly payment:
(1) by using the exact term, and (2) using the rounded term from part (a).
[tex]\implies \$897.72 \times 25.7072605... \times 12 =\$276935.06[/tex]
[tex]\implies \$897.72 \times 26 \times 12=\$280088.64[/tex]
[tex]\implies \$1526.49 \times 10.3523853... \times 12=\$189633.75[/tex]
[tex]\implies \$1526.49 \times 10 \times 12 =\$183178.80[/tex]
To calculate the amount of interest costs (in dollars) in each case, subtract $150,000 from the total amounts paid:
[tex]\$897.72\implies 276935.06-150000=\$126935.06[/tex]
[tex]\$897.72 \implies 280088.64-150000=\$130088.64[/tex]
[tex]\$1526.49 \implies 189633.75-150000=\$39633.75[/tex]
[tex]\$1526.49\implies 183178.80-150000=\$33178.80[/tex]
Part (c)The natural logarithm of a negative number cannot be taken.
Therefore, x > 705.
So the vertical asymptote for the model is:
x = 705The monthly payment must be more than $705, and the closer to this value the payment is, the longer it will take to pay off the mortgage.
Kelvin spends 1/4 of his $100 on a ticket to a play and then buys a shirt for $22.50. How much
of the $100 does Kelvin have left?
A $5.50
B $10.00
C $52.50
D $73.50
need answer right now
An experiment consists of drawing one card from a bridge deck. The sample space contains 52 outcomes, one for each of the 52 cards. Suppose we assign a probability of 1/52 to each of the cards. Find the probability that the following happens.
(a) A king is drawn
(b) The card drawn is a king or a queen.
(c) The card drawn is a diamond.
(d) The card drawn is a black card.
The probability of drawing a king, a king or queen, a diamond, or a black card from a deck of 52 cards is 1/52, 4/52, 13/52, and 26/52, respectively.
(a) The probability that a king is drawn is 1/52, since there is only one king in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a king is 1/52.
(b) The probability that a king or a queen is drawn is 4/52, since there are four kings and queens in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a king or queen is 4/52.
(c) The probability that a diamond is drawn is 13/52, since there are 13 diamonds in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a diamond is 13/52.
(d) The probability that a black card is drawn is 26/52, since there are 26 black cards in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a black card is 26/52.
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Replace the loading system acting on
the beam by an equivalent resultant
force and couple moment at point O.
The answers are a) FR = 365 N b) u = 70.8° d and c) (MR)O = 2364 N m (counterclockwise)
What is resultant force?When an object is subject to several forces, the resultant force is the force that alone produces the same acceleration as all those forces.
Given is a figure, we need to find equivalent resultant force and couple moment at point O
Equivalent Resultant Force And Couple Moment At O.
+→ (FR)x = ΣFx; (FR)x = 600 cos 60° - 455(12 / 13)
= -120 N = 120 N ←
+ ↑ (FR)y = ΣFy; (FR)y = 455(5/13) - 600 sin 60° = -344.62 N = 344.62 N ↓
As indicated in Fig (attached)
a) FR = √F(R)x²+F(R)y²
= √2120² + 344.62² = 364.91 N = 365 N
And
b) θ = tan-1{(FR)y / (FR)x}
= tan-1 {344.62/120}
= 70.80°
Also,
c) a+(MR)O = ΣMO; (MR)O = 455(12/13)(2) + 600 cos 60° (0.75) + 600 sin 60° (2.5)
= 2364.04 N m
= 2364 N m (counterclockwise)
Hence, The answers are a) FR = 365 N b) u = 70.8° d and c) (MR)O = 2364 N m (counterclockwise)
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4 times the difference of x and 2
Answer: 2x-4
Step-by-step explanation:
Answer:
solution
you must multiply a difference of x and 2 which is. >{x-2}
mathematical
4 x {x-2}
Using the definitional formula, compute Ss, variance and the standard deviation for the following population of scores. Scores: 1, 8, 0, 4,2 SS 40 variance 10 standard deviation 3.16
Ss, variance and the standard deviation for the population of scores is 2.83 and 8 respectively
What is standard deviation and variance?
Standard deviation is a measure of the distribution of statistical data, whereas variance is a measure of how data points differ from the mean. The fundamental distinction between the two is that although the variance is expressed in squared units, the standard deviation is expressed in the same units as the data's mean.
Given,
SS = 40
Variance = 10
Standard Deviation = 3.16
Using Population Variance Formula :
= [tex]\frac{1}{n}[/tex]∑( x-xbar)² where i is 1
For the complete solution see the attachment of table
sum ( x - x bar)² = 40
so, variance = 40/5
= 8
standard deviation = [tex]\sqrt{8}[/tex]
= 2.83
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let
[tex]A=(\sqrt{2} +\sqrt{3} )(\sqrt{4} +\sqrt{5} )...(\sqrt{2020} +\sqrt{2021} )\\B=(\sqrt{2021} -\sqrt{2020} )(\sqrt{2019} -\sqrt{2018} )...(\sqrt{3} -\sqrt{2} )[/tex]
what is A times B?
Answer:
1
Step-by-step explanation:
A)
[tex]( \sqrt{3 } - \sqrt{2} )( \sqrt{3} + \sqrt{2} )( \sqrt{5 } - \sqrt{4} )( \sqrt{5} + \sqrt{4} )....[/tex]
using difference of two squares
[tex]( \sqrt{a} + \sqrt{b} )(\sqrt{a} - \sqrt{b} ) = a - b[/tex]
we can rewrite the A) to 1×1×1×1.... so the answer would be 1
determine the 97.5th percentile of the standard normal distribution as a decimal rounded to the nearest hundredth.
What is the solution of the system? Use elimination.
3x +9y=33
-10x-6y=-14
a. (-4,5)
b. (4,-1)
c. (-10, 3)
d. (-1,4)
To solve the given system of equations using elimination, we can add the two equations together to eliminate one of the variables. Doing this, we get 3x + 9y + (-10x - 6y) = 33 + (-14), which simplifies to -7x + 3y = 19. We can then solve for y by dividing both sides of the equation by 3, giving us y = 19/3 = 6.33. We can substitute this value for y in either of the original equations to solve for x. For example, if we substitute 6.33 for y in the first equation, we get 3x + 9 * 6.33 = 33, which simplifies to 3x = 3.67. Dividing both sides of the equation by 3, we get x = 1.22. Therefore, the solution of the system is (1.22, 6.33), which is approximately (1, 6). The answer choice that is closest to this solution is (d) (-1, 4). Thus, the solution of the system is (-1, 4).
A small town has two local high schools. High School A currently has 700 students and is projected to grow by 65 students each year. High School B currently has 900 students and is projected to grow by 40 students each year. Let A(t) represent the number of students in High School A in t years, and let B(t) represent the number of students in High School B after t years. Write the equation for each function and determine how many students would be in each high school in the year they are projected to have the same number of students. A(t) = B(t) =
Answer:
1. A(t) = 65t + 700
2.B(t) = 40t + 900
3. High School A and High School B will both have 1,220 students in the 8th year
Step-by-step explanation:
1. The equation for the number of students in High School A represents a linear function.
⭐ What is a linear function?
A linear function is a type of equation where every y-value increases by a constant, additive amountOne way to write the equation for a linear function is: [tex]y = mx+b[/tex], where m is the constant, additive amount, and b is the y-intercept, or the initial value.Let's write the equation for High School A in the [tex]y = mx+b[/tex] format, known as slope-intercept form:
The constant, additive amount for High School A is 65 (m)The initial value for High School A is 700 (b)∴ High School A: [tex]y = 65x + 700[/tex]
2. Let's write the equation for High School B in the [tex]y = mx + b[/tex] format, known as slope-intercept form:
The constant, additive amount for High School B is 40 (m)The initial value for High School B is 900 (b)∴ High School B: [tex]y = 40x + 900[/tex]
3. To find at what year High School A and High School B will have the same number of students, we need to solve a system of linear equations.
⭐What is a system of linear equations?
A system of linear equations is two or more linear equations that intersect at one point (x,y)For this problem, let's set both linear equations equal to each other to see at what point will the high school populations be the same.
[tex]A(t) = B(t)[/tex]
[tex]65t + 700 = 40t + 900[/tex]
[tex]25t = 200[/tex]
[tex]t = 8[/tex]
Now we know that in the 8th year, High School A will have the same population as High School B.
We need to find what the population will be in year 8.
Thus, substitute the value of t into one of the functions and solve.
I am choosing to substitute t into A(t), but you can also do B(t).
[tex]A(8) = 65(8) + 700[/tex]
[tex]A(8) = 520 + 700[/tex]
[tex]A(8) = 1,220[/tex]
⚠️!!! CAUTION !!! ⚠️
Some people may stop at this point and write that in the 8th year, both high schools will have a population of 1,220 students.
However, you should also substitute 8 into the other function you didn't substitute it into to make sure that 8 is correct.
[tex]B(8) = 40(8) + 900[/tex]
[tex]B(8) = 320 + 900[/tex]
[tex]B(8) = 1,220[/tex]
∴ In the 8th year, both high schools will have a population of 1,220 students.
What sides are similar to this triangle with the side dimensions of 6cm, 12cm, and 15cm?
Answer: Pythagorean triplets.
Step-by-step explanation:
not sure but this is the triangle that helps at all.
Below is the table of values of a function. Write the output when the input is n.
input 1,4,6,n
output 2,8,12,?
Answer:
Step-by-step explanation:
Kyra is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve large rooms that can hold 8 people, and small rooms that can hold 6 people. Kyra reserved twice as many large rooms as small rooms, which altogether can accommodate 88 guests. Determine the number of small rooms reserved and the number of large rooms reserved.
The number of small rooms reserved is 4.
The number of large rooms reserved is 8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Small rooms are denoted as S.
Large rooms are denoted as L.
Now,
We will make two equations.
L = 2S _____(1)
8L + 6S = 88 ______(2)
Putting (1) in (2) we get,
8L + 6S = 88
8 x (2S) + 6S = 88
16S + 6S = 88
22S = 88
S = 88/22
S = 8/2
S = 4
Now,
Putting S = 4 in (1) we get,
L = 2 x 4
L = 8
Thus,
The number of small rooms and large rooms reserved is 4 and 8.
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Rain is flowing into 2 containers at different rates. The figure below shows the volume of water in each container what is the difference in rate of change between the two containers
With the help of Linear relationships The difference in the rate of change between the two containers is 1/5 gallon per minute.
what is Linear relationships?
A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships. In everyday life, linear relationships are quite prevalent.
Given:
Volume of water in each container.
To find:
Difference in the rate of change.
Solution:
Take any two points on container 1.
Let the points are (10, 2) and (20, 4).
m = (y2 - y1) / ( x2 - x1 )
= ( 4 - 2 ) / ( 20 - 10 )
= 2/ 10
= 1/ 5
Rate of change for container 1 is .
Take any two points on container 2.
Let the points are (5, 2) and (10, 4).
m = (y2 - y1) / ( x2 - x1 )
= ( 4 - 2 ) / ( 10 - 5)
= 2 / 5
Rate of change for container 2 is 2/5
Difference = (2 /5 ) - ( 1/ 5 )
= 1 / 5
Hence, The difference in the rate of change between the two containers is 1/5 gallon per minute.
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how many 3 digit multiple of 11 ends in 2
Answer:
22
There are 22 multiples that end in 22.
Determine if the following equation has one, none, or many solutions.
2(2x+-1)=4x-4
Answer: no solutions
Step-by-step explanation:
can some one please help me with this question
The measure of the largest exterior angle of the triangle will be 162°.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The exterior angles of the triangle are 3x°, 8x°, and 9x°. Then the measure of the interior angle of the triangle will be 180° - 3x°, 180° - 8x°, and 180° - 9x°.
The sum of the interior angle of the triangle is 180°. Then the equation is given as,
180° - 3x° + 180° - 8x° + 180° - 9x° = 180°
360° - 20x° = 0
x = 18°
Then the measure of the exterior angles of the triangle will be given as,
3x° = 3 × 18° = 54°
8x° = 8 × 18° = 144°
9x° = 9 × 18° = 162°
The measure of the largest exterior angle of the triangle will be 162°.
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a. Use the points (1, 226.9) and (4, 275.2) to write an equation for the line of fit in slope-intercept form, where x is the number of years since 2010 and y is the median price in thousands of dollars. what will be the approximate price by 2025?
The Equation of line is y= 16.1x + 210. 8.
The approximate price by 2025 is 452.3.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
The points are (1, 226.9) and (4, 275.2).
So, Slope for line
m = ( 275.2- 226.9)/( 4-1)
m = 48.3/ 3
m= 16.1
Now, using the slope- intercept form
y= mx+ b
y = 16.1x + b
Now, x= 1 and y= 226.9
By, y = 16.1 + x
226.9 = 16.1(1)+ b
b= 210.8
So, the equation of line is y= 16.1x + 210. 8
Now, x is the number of years since 2010 and by 2025
x= 2025 - 2010 = 15
Then, the approximate price by 2025
y= 16.1(15) + 210.8
y= 452.3
Hence, the approximate price by 2025 is 452.3.
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Leslie wants to invest $3,800.00 in a savings account that pays 4.8% simple interest.
How many years will it take for this investment to triple in value? Round your answer to the nearest tenth of a year.
It will take _______ years for this investment to triple in value.
Answer:
It will take 41.7 years for this investment to triple in value.
Step-by-step explanation:
Here is the formula for simple interest
[tex]A=P(1+rt)[/tex]
Lets solve for [tex]t[/tex].
Divide both sides by [tex]P[/tex].
[tex]\frac{A}{P}=rt+1[/tex]
Subtract 1 from both sides.
[tex]\frac{A}{P}-1=rt[/tex]
Divide both sides by [tex]r[/tex].
[tex]\frac{\frac{A}{P}-1}{r} =t[/tex]
To write [tex]-1[/tex] as a fraction with a common denominator, multiply by [tex]\frac{P}{P}[/tex] .
[tex]\frac{\frac{A}{P}-1*\frac{P}{P}}{r} =t[/tex]
[tex]\frac{\frac{A}{P}*\frac{-P}{P}}{r} =t[/tex]
Combine the numerators over the common denominator.
[tex]\frac{\frac{A-P}{P} }{r} =t[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]t=\frac{A-P}{Pr}[/tex]
We are given
[tex]P=3800\\r=0.048[/tex]
We need to find what amount is triple his money.
[tex]3800*3=11400[/tex]
[tex]A=11400[/tex]
Substitute our numbers into the equation for [tex]t[/tex].
[tex]t=\frac{11400-3800}{3800*0.048}[/tex]
Factor 3800 out of 11400.
[tex]t=\frac{3800*3-3800}{3800*0.048}[/tex]
Factor 3800 out of −3800.
[tex]t=\frac{3800*3-3800*-1}{3800*0.048}[/tex]
Factor 3800 out of [tex]3800*3-3800*-1[/tex].
[tex]t=\frac{3800*(3-1)}{3800*0.048}[/tex]
Cancel the common factor of 3800.
[tex]t=\frac{3-1}{0.048}[/tex]
Simplify.
[tex]t=\frac{2}{0.048}[/tex]
[tex]t=41.666[/tex]
Merry Christmas!
What are the values of t and u?
t = ?°
u= ?°
The career placement office at a large university tracks the number of job applications graduating seniors complete before getting their first job. Data on college graduates suggests that most will send out a large number of applications before getting their first job. Which one of the following histograms best represents the distribution of job applications for graduating seniors?
a.Histogram III
b.Histogram II
c.Histogram IV
d.Histogram I
The histogram that best represents the distribution of job applications for graduating seniors is given as follows:
a. Histogram III.
How to identify the correct histogram?An histogram shows the number of times that each observation appears in a data-set.
Data on college graduates suggests that most will send out a large number of applications before getting their first job, hence the left bins on the histogram should have small numbers, while the right bins on the histogram should have greater numbers.
The only histogram that follows this pattern is Histogram III, hence option A gives the histogram that best represents the distribution of job applications for graduating seniors.
Missing InformationThe histograms are given by the image shown at the end of the answer.
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40 POINTS
Use the image to determine the type of transformation shown.
Image of polygon ABCD and a second polygon A prime B prime C prime D prime to the right.
Horizontal translation
Vertical translation
Reflection across the y-axis
270° counterclockwise rotation
Reflection across the y-axis is the transformation used to the polygon ABCD.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that Image of polygon ABCD and a second polygon A prime B prime C prime D prime to the right.
ABCD is the original image and prime B prime C prime D prime is the transformed image.
ABCD rectangle is transformed to A'B'C'D'.
As we observe the diagram, the two rectangles look the same which means the shape remains constant.
The translation is applied to the original image which move to the right side.
A translation is a movement of the graph either horizontally parallel to the x axis or vertically parallel to the y axis.
We can reflect the graph of any function f about the x-axis by graphing y=-f(x) and we can reflect it about the y-axis by graphing y=f(-x).
Hence, Reflection across the y-axis is the transformation used to the polygon ABCD.
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Answer: reflection across the y axis
Step-by-step explanation: I hope that helps :)
Though 70% of women with children younger than 18 years participate in the labor force, society still upholds the stay-at-home mother as the traditional model. Some believe that employment distracts mothers from their parenting role, affecting the well-being of children. In the GSS 2014, respondents were asked to indicate their level of agreement to the statement: "A working mother hurts children". Of the 435 male respondents who answered the question, 18% strongly agreed that a working mother does not hurt children. a, What is the 90% confidence interval for this statistic for males? b. Of the 566 respondents who answered the question, 40% strongly agree that a working mother does not hurt children. What is the 90% confidence level for this statistic?
a) The 90% confidence interval for this statistic for males is of: (0.1497, 0.2103).
b) The 90% confidence level for this statistic is of: (0.3661, 0.4339).
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
For males, the parameters are given as follows:
[tex]\pi = 0.18, n = 435[/tex]
Hence the lower bound of the interval is given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 - 1.645\sqrt{\frac{0.18(0.82)}{435}} = 0.1497[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 + 1.645\sqrt{\frac{0.18(0.82)}{435}} = 0.2103[/tex]
For the statistic, the parameters are given as follows:
[tex]\pi = 0.4, n = 566[/tex]
Hence the lower bound of the interval is given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.645\sqrt{\frac{0.4(0.6)}{566}} = 0.3661[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.645\sqrt{\frac{0.4(0.6)}{566}} = 0.4339[/tex]
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(20points) Let A be a 4 x 4 matrix and let A be a eigenvalue of multiplicity 3. If A - AI has rank 1, is A defective? Explain.
No, A is not defective.
What is the rank nullity theorem?The rank–nullity theorem is a theorem in linear algebra, which asserts that the dimension of the domain of a linear map is the sum of its rank (the dimension of its image) and its nullity (the dimension of its kernel).
Given here A be a 4 x 4 matrix and let λ be an eigenvalue of multiplicity 3 and rank 1, then by rank nullity theorem we have
Rank(A-λI) + Nullity((A-λI) =4
⇒dimN(N-λI) = Nullity(A-λI)
⇒dimN(N-λI) = 4 - Rank(A-λI)
⇒dimN(N-λI) = 4-1
⇒dimN(N-λI) = 3
Therefore 3 linearly independent eigenvectors belong to eigenvalue λ. Since λ is an eigenvalue of multiplicity 3, this ensures that there is a different eigenvalue different from λ. Along with 3 linearly independent eigenvectors in the eigenspace of λ, this gives us 4 linearly independent eigenvectors in the matrix A. Now we An n × n matrix A is diagonalizable if and only if A has n linearly independent eigenvectors. Thus A is nondefective
Hence, matrix A is not defective.
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To estimate the number of bass in a lake, a biologist catches and tags 32 bass. Several weeks later, the biologist catches a new sample of 55 bass and finds that 5 are tagged. How many bass are in the lake.
If a share of a stock jumped from $9 to $25, what was the percent increase of this stock (rounded to the
nearest tenth)?
Answer: 177.8
Step-by-step explanation: To find the percent increase, we have to use this formula:
New value-old value/ old value x 100
So, following this formula, we would do 25-9, which, is 16, divided by 9. That would be 1.777... So now let's round that to 1.78, so 1.78 x 100 = 177.8. I hope this helped.
A-Level Cambridge
PURE MATHEMATICS - PI
CH1 COORDINATES GEOMETRY
1-(9709-S 2012-Paper 1/2-Q4) COORDINATES GEOMETRY
[6]
The point A has coordinates (-1, -5) and the point B has coordinates (7, 1). The perpendicular
bisector of AB meets the x-axis at C and the y-axis at D. Calculate the length of CD.
ШОә
Answer:
either 8.6 or 9. check if it's correct?
7² + 5² = 74
square root 74 = 8.6
4x+6y=8
y = -2/3x+1/3
how do i graph this and what is the solution please help it’s urgent
Find the point on the line 3x + y = 8 that is closest to the point
(−3, 1)
The point on the line 3x + y = 8 that is closest to the point (-3, 1) is (1.8, 2.6).
What is Quadratic Equations?Quadratic equations are equations of the form a x² + b x + c = 0 where a, b and c are real numbers.
Given line is,
3x + y = 8 ⇒ y = -3x + 8
So we have any point (x, -3x + 8).
We have to find a point (x, -3x + 8) such that distance of this point from (-3, 1) is minimum.
Distance between (-3, 1) and (x, -3x + 8) = √[(x - -3)² + (-3x + 8 - 1)²]
= √[(x + 3)² + (-3x + 7)²]
= √(x² + 6x + 9 + 9x² - 42x + 49)
= √(10x² - 36x + 58)
So the distance between (-3, 1) and (x, -3x + 8) is √(10x² - 36x + 58) should be minimum.
We minimize the function f(x) = 10x² - 36x + 58.
A quadratic function represents the equation of a parabola.
Coefficient of x² is positive, so parabola opens upward. So we will be having the minimum value.
Minimum value at the point x = -b / 2a for the quadratic equation a x² + b x + c.
Minimum value is at x = - (-36) / (2 × 10) = 36/20 = 9/5 = 1.8.
To find the y coordinate,
y = -3x + 8 = 2.6
So the required point is (1.8, 2.6).
Hence the point on the line closest to the point (-3, 1) is (1.8, 2.6)
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What is the maximum height of the firework? How long is the firework in the air before it explodes?
See attached picture
The maximum height of the firework is; 387.78 ft
The time for which the firework is in the air before it explodes is; 1 second
How to solve projectile equations?
We are given the function;
h = -(500/9)t² + (1000/3)t + 10
where;
h is height after time of t seconds
At height of zero, the firework would either be about to launch or when it has come down.
Thus, let us set h = 0 to find the times.
0 = -(500/9)t² + (1000/3)t + 10
Using quadratic equation calculator, we have;
t ≈ 2 seconds
Now the firework explodes at the highest point which will be the mid point of where the launching started and the endpoint where it stopped.
This means time at midpoint = (0 + 2)/2 = 1 sec
It explodes after 1 second.
Thus maximum height at this time is;
h = -(500/9)(1)² + (1000/3)(1) + 10
h = 387.78 ft
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