Answers
Answer:
1 C
2 A
Step-by-step explanation:
1 C No it cannot be defined because A and B are not congruent
2 A Yes, the lines will remain parallel
PS. It's only 50 points because two answers are allowed. Each answerer gets half.
Related Questions
Rachel invests $25,000 at age 25. She hopes the investment will be worth $125,000 when she turns 50. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Answers
The rate of growth will she need to achieve her goal is 2.8%
The formula for finding the compound amount is expressed as:
[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]
P is the amount invested = $25000
t is the time in years = 25 years
A is the amount = $125000
r is the rate in %
Substitute the given parameters into the formula to have:
[tex]125000 =25000(1+r )^{25}\\5 =(1+r)^{25}\\log5=25log(1+r)\\log(1+r)=\frac{log5}{25} \\log(1+r)=0.02796\\1+r = e^{0.02795}\\1+r=1.0283\\r = 1.0283 -1\\r = 0.0283\\[/tex]
Hence the rate of growth will she need to achieve her goal is 2.8%
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Anita is filling a small pool for her kids. Currently, there are 60 gallons of water in the pool and she is filling
the pool at a rate of 50 gallons every 5 minutes. The pool holds 200 gallons of water.
Which equation represents the amount of minutes (m) that it will take to fill the pool?
A. -10m + 200 = 60
B. -50m + 200 = 60
C.-10m + 140 = 60
D. -50m + 140 = 60
Answers
Answer:
M/140 = 50/60 or C
Step-by-step explanation:
Since the total is 200 it will be the denominator but we already have 60 gallons so we do 200-60=140
the ratio is 50 per 60
What is 0.14 as a fraction
Answers
Answer:
7/50
Step-by-step explanation:
Here is an easy way of converting a decimal number to fraction.
Step 1:
Write it down as 0.14/1
Step 2:
Multiply bottom and top by 10 for every number after the decimal, since there is 2 numbers after the decimal you do 10*10 = 100
[tex]\frac{0.14(100)}{1(100)}[/tex] = 14/100
Step 3:
You can simplify 14/100 to 7/50 and thats why 7/50 is the answer
Answer:
[tex]\frac{14}{100}[/tex] or [tex]\frac{7}{50}[/tex]
Step-by-step explanation:
To find 0.14 we have to see what place it's in, since it was in the hundredths place, we put 14 over 100, which is 14/100.
To simplify this fraction we have to find the GCM (Greatest Common Factor), the GCM of 14 and 100 is 2. Then we divide both the bottom and the top by 2 (whatever you do to the bottom, you do to the top), which gives us 7/50.
To conclude, 0.14 as a fraction is 14/100 or 7/50.
Simplify -3(xy + 2y) + 5y - x.
Answers
Answer:
Step-by-step explanation:
-3 (xy+2y)+5y-x
-3xy-6y+5y-x
-3xy-y-x
The probability that a man will be alive in 25 years is 3/5. and the probability that his wife will be alive is 2/3. Determine the probability that in 25 years:
a. both will be alive
b. at least one will be alive
c. only the wife will be alive
Answers
Answer:
e
Step-by-step explanation:
chicken nuggets
A) 6/25
B) 13/15
C) 4/15
Explanation:
A) P(both will be alive) = (3/5)(2/5) = 6/25
B) P(at least one will be alive) = 1-P(both die) = 1-(2/5)(1/3) = 13/15
C) P(only the wife will be alive)=(2/5)(2/3) = 4/15
Estimate the limit 1/x+2-1/4/x-1
Answers
Answer:
Step-by-step explanation:
Begin by finding a common denominator in the numerator of that rational expression. The common denominator is 3(x+2):
[tex]\frac{\frac{(3)1}{(3)x+2} -\frac{(x+2)1}{3(x+2)} }{x-1}[/tex] which simplifies to
[tex]\frac{\frac{3}{3x+6} -\frac{(x+2)}{3x+6} }{x-1}[/tex] which simplifies further to
[tex]\frac{\frac{3-x-2}{3x+6} }{x-1}[/tex] and
[tex]\frac{\frac{1-x}{3x+6} }{x-1}[/tex] Bring up the lower fraction and flip it and multiply:
[tex]\frac{1-x}{3x+6}*\frac{1}{x-1}[/tex] In order to make the 1-x into x-1, multiply the numerator of that fraction on the left by -1 to get:
[tex]-\frac{x-1}{(3x+6)(x-1)}[/tex] and now the x-1 terms cancel out, leaving us with:
[tex]-\frac{1}{3(1)+6}=-\frac{1}{9}=-.1111[/tex]
The following section is a statement from the rental agreement Tim signed when he rented his car this past weekend.
"Upon checkout, the fuel level of the vehicle will be determined by turning the vehicle on and visually inspecting the fuel gauge. The approximate fuel level will be recorded on the Check-Out sheet and verified with initials by the vehicle Renter. One copy of the Check-Out sheet will be given to the customer. Another copy will be kept with the on-site records of the vehicle.
"The rented vehicle must be returned with a minimum fuel level the same as that indicated on the Check-Out sheet. A vehicle returned with a fuel level less than the approximate level indicated on the Check-Out sheet will be completely refueled with on-site pumps. The price of the fuel used to refuel the vehicle will be added to the Renter's total charge at a cost of $4.50 per gallon plus a $5.00 refueling charge."
Tim forgot to refuel the vehicle when he returned it. His Check-Out sheet indicates that the vehicle had about 1/2 of a tank left. The tanks is now nearly empty.
If it takes 11.75 gallons of gas to refuel the car Tim rented, how much extra should he expect to pay because he forgot to get gas?
a.
$26.44
b.
$31.44
c.
$52.88
d.
$57.88
Answers
Answer: D
Step-by-step explanation:
Tim should expect to pay an extra $52.88 because he forgot to refuel the car. option D is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The car that Tim rented needed 11.75 gallons of gas to refill to the same fuel level as indicated on the Check-Out sheet.
Since the rental agency charges $4.50 per gallon of gas plus a $5.00 refueling charge, the cost of refueling the car will be:
11.75 gallons x $4.50/gallon + $5.00
= $57.88
Therefore, Tim should expect to pay an extra $57.88 because he forgot to refuel the car. The correct answer is (d).
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A patio measures 4 yd long and 3 yd wide. What is the area in square meters? Round final answer to two decimal places
Answers
Answer:
Step-by-step explanation:
1 yd(36 in/yd)(2.54 cm/in) / (100cm/m) = 0.9144 m
(4(0.9144)) x (3(0.9144)) = 10.03352832 = 10.03 m²
Evaluate the following expression. 12!
Answers
Answer:479001600
Step-by-step explanation:
12 factorial is 12 * 11 * 10 ..... all the way to one
A way to do it by hand is
12 * 1
11 * 2
10 * 3
9 * 4
8 * 5
7 * 6
stop here because 6 * 7 and 5 *8 are already listed
This gives you 6 products then multiply those 6 products by pairs which gives you three pairs which gives you three products then compute a pair then multiply by last product.
Easy math but a lot of written work
Can you help me with this ?:)
With explanation step-step Thanks
Answers
Part A
The given angle is 4pi/3. Multiply it by the factor 180/pi to convert from radians to degree mode.
Note how the given angle has pi in the numerator, while the conversion factor has pi in the denominator. The two pi terms will cancel.
(4pi/3)*(180/pi)
(4/3)*(180/1)
(4*180)/(3*1)
720/3
240
The angle 4pi/3 radians is equivalent to 240 degrees. This 240 degree angle is in quadrant 3. Any angle in this quadrant is between 180 degrees and 270 degrees, excluding both endpoints. This is the bottom left quadrant, aka the southwest quadrant.
Answer: Quadrant 3===========================================================
Part B
To find the reference angle, we'll subtract off pi. This only works for angles in quadrant 3. This is because the first pi radians, aka 180 degrees, is taken up by the first two upper quadrants. The remaining bit in the third quadrant is all we care about to find the reference angle.
reference angle = (given angle in quadrant 3) - pi
reference angle = (4pi/3) - pi
reference angle = (4pi/3) - (3pi/3)
reference angle = (4pi - 3pi)/3
reference angle = pi/3
Answer: pi/3 radians===========================================================
Part C
Use a calculator or a reference table to find that
tan(4pi/3) = tan(pi/3) = sqrt(3)
Alternatively, you can compute the sine and cosine values first
sin(pi/3) = sqrt(3)/2cos(pi/3) = 1/2Dividing the two items in the order mentioned will get us the tangent value
tan = sin/cos
tan(pi/3) = sin(pi/3) divide cos(pi/3)
tan(pi/3) = sqrt(3)/2 divide 1/2
tan(pi/3) = sqrt(3)
In the jump from the second to last step, to the last step, the denominators '2' cancel out when dividing.
Answer: sqrt(3)9/10 - _ = 1/5 mathematics
Answers
Answer:
x=7/10
Step-by-step explanation:
1/5=2/10
9/10- =2/10
Substitute the blank with X
9/10- X =2/10
x=7/10
Answer:
7/10
Step-by-step explanation:
9/10 - _ = 1/5
Let's represent the unknown as x
Therefore,
9/10 - x = 1/5
9/10 - 1/5 = x
x = 9/10 - 1/5 = 7/10
(5,3)(6,r) m=-1
Find the value of r so that the line that passes through the pair of points has the given slope
Answers
Answer:
Step-by-step explanation:
Slope is change in y over the change in x
(r - 3) / (6 - 5) = -1
(r - 3) / (1) = -1
r - 3 = -1
r = 2
write this fraction as a decimal use bar notation if neccesary
3 15/44
Answers
Answer:
3.34
Step-by-step explanation:
First step: 3x44=132, 132+15=147. Then use 147 as numerator and 44 as denominator.
Second step: Divide 147/44= 3.3409090909091, round and get 3.34.
Hope this helps.
Which statement best describes what the volume of an object represents? Volume is the length of an object. Volume is the amount of matter in an object. Volume is the amount of space taken up by an object. Volume is the ability of an object to floa
Answers
Answer:
Volume is the amount of space taken up by an object
You are asked to prepare 900mls of 3% sucrose. How much sucrose do you need?
Answers
Answer:
27g of sucrose
Step-by-step explanation:
You would need 3g of sucrose per ever 100ml and you have 900ml therefore 27g
Find the equation of the line through P=(8,7) such that the triangle bounded by this line and the axes in the first quadrant has the minimal area.
Answers
The area of the triangle is given by the product of 0.5 and the distances of the x and y intercepts from the origin.
[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]Reasons:
The area of the triangle, A = 0.5·x·y
Where;
x and y are the values of the line at the intercepts
The equation of the line is; (y - 7) = m·(x - 8)
At the y-intercept, x = 0, therefore;
(y - 7) = m·(0 - 8) = -8·m
At the y-intercept, y = 7 - 8·m
At the x-intercept, y = 0, therefore;
(0 - 7) = m·(0 - 8) = -8·m
At the x-intercept, -7 = m·x - 8·m
8·m - 7 = m·x
[tex]\displaystyle x = \mathbf{8 - \frac{7}{m}}[/tex]
Therefore;
[tex]\displaystyle A = 0.5 \times \left(7 - 8 \cdot m\right) \times \left(8 - \frac{7}{m} \right) = \mathbf{\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}}[/tex]
When the area is minimal, we have;
[tex]\displaystyle \frac{dA}{dm} =0 = \frac{d}{dm} \left(\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}\right) = \mathbf{-\frac{32 \cdot m^2 - 24.5}{m^2}}[/tex]
m² × 0 = 24.5 - 32·m²
[tex]\displaystyle m^2 = \frac{24.5}{32} = \frac{49}{64}[/tex]
[tex]\displaystyle m = \sqrt{\frac{49}{64}} = \frac{7}{8}[/tex]
[tex]\displaystyle m = \pm \frac{7}{8}[/tex]
The equation of the line when [tex]\displaystyle m = + \frac{7}{8}[/tex] is therefore;
(y - 7) = m·(x - 8)
[tex]\displaystyle (y - 7) = \mathbf{\frac{7}{8} \cdot (x - 8)}[/tex]
[tex]\displaystyle (y - 7) = \frac{7}{8} \cdot (x - 8) = \frac{7}{8} \cdot x - \frac{7}{8} \times 8 = \frac{7}{8} \cdot x - 7[/tex]
[tex]\displaystyle y = \frac{7}{8} \cdot x - 7 + 7 = \frac{7}{8} \cdot x[/tex]
[tex]\displaystyle y = \mathbf{\frac{7}{8} \cdot x}[/tex]
The x and y intercept of the above line are 0
When [tex]\displaystyle m = - \frac{7}{8}[/tex], we have;
[tex]\displaystyle (y - 7) = -\frac{7}{8} \cdot (x - 8) = -\frac{7}{8} \cdot x + \frac{7}{8} \times 8 = -\frac{7}{8} \cdot x + 7[/tex]
Which gives;
[tex]\displaystyle y = \frac{7}{8} \cdot x + 7 + 7 = \frac{7}{8} \cdot x + 14[/tex]
[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ y = \mathbf{14 - \frac{7}{8} \cdot x}[/tex]
The equation of the line through P = (8, 7) such that the triangle bounded by the line and the axes in the first quadrant has minimal area is therefore;
[tex]\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]
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The population of a city decreases by 1.1% per year. If this year's population is
79,000, what will next year's population be, to the nearest individual?
Answers
Answer:
Step-by-step explanation:
100% - 1.1% = 98.9% = 0.989
79000(0.989)¹ = 78,131
or
1.1% = 0.011
79000(0.011) = 869
79000 - 869 = 78,131
Some home computers can do a calculation in 2 x 10 ? seconds. Write this number in standard form.
Answers
2 × 10 = 20
see Picture.
1.
Identify the point corresponding to P.
A. P′ (−3, −1)
B. P′ (−4, 0)
C. P′ (−5, −3)
D. P′ (−2, 0)
Answers
Answer:
B. P′ (−4, 0)
Step-by-step explanation:
You can look at the graph. The X-axis always goes first. SO -4 is first because it's on the x-axis. ANSWER= (-4, 0)
A set of stickers contains 4 shamrocks for every 6 rainbows. Which choice contains an equivalent ratio of shamrocks to rainbows?
shamrocks : rainbows
1. 2 : 4
2. 6 : 9
3. 1 : 3
4. 8 : 18
Answers
because 4/6 is equal to 2/3 and so is 6/9
Find two numbers x and y with a sum of 2 and a difference of 12
Answers
Answer:
x = 7
y = -5
Step-by-step explanation:
x + y = 2
x - y = 12
( x + y ) + ( x - y ) = 2 + 12
2x = 14
x = 7
7 + y = 2
y = -5
Check:
7 + -5 = 2
7 - (-5) = 12
Correct
-Chetan K
____________is the exact average deviation of data values from the mean in squared units, and ____________ is the approximate average deviation of data values from the mean in regular units.
Answers
Variance is the exact average deviation of data values from the mean in squared units and the Standard deviation of data values from the mean in regular units.
Variance is a statistical measure of the dispersion of numbers in a data collection. Variance estimates how much more each number in the set deviates from the mean, and from each and every other number in the set.
The variance is a measure of the degree of variability. It is determined by averaging the squared deviations out of the mean.
The greater the spread of the data, the greater the variance in proportion to the mean.
The standard deviation is determined as the square root of variance by calculating the departure of each data point from the mean. The standard deviation represents the average level of variation in your dataset. It informs you how far each number deviates from the mean on average.
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Amelia had 22 sea shells. Then, she collected 9 more sea shells. After that, she gave S sea shells to her little sister. Which of the following shows how many sea shells she has currently?
Answers
Answer:
22 + 9 - S
Step-by-Step Explanation:
Amelia started with 22 seashells and found 9 more so you add that together then since she gave S amount of seashells away to her sister you minus it.
On a coordinate plane how are the location of points -6,7 and -6,-7 related
Answers
Answer:both involving 6 and 7. (-6,-7) would be in quadrant 3 while point (-6,7) would be on top of it in quadrant 2.
Step-by-step explanation:
So um anyone know how to do this?
Answers
We need to find distance they travel as a function of time. This simply means that x is the function of time. The destination is 120 miles away, this is irrelevant for the question that is currently being asked. However, we know that they have already travelled 20 miles and are going 50 miles and hour. So lets plug in what we have.
50 is our rate of change, so we match that with the x.
20 is our constant, the distance already travelled.
This means our function is:
f(x) = 50x + 20
This means our answer is D) f(x) = 50x + 20
Lets also plug in 120 to solve how much further they need to travel before arriving.
120 is our f(x) as it is the final distance travelled.
120 = 50x + 20
120-20 = 50x
100 = 50x
100/50 = x
2 = x
This means that they need to travel 2 hours in addition to the 20 miles they have already gone.
I hope I've helped! :)
5(x+6)-8x=3(10-x)n no solution, one solution, or all real numbers are solutions
Answers
Answer:
Infinite, any number
Step-by-step explanation:
Simplify
30 - 3x = 30 - 3x
As a bonus question on a test, Mr. Smith wrote 8z + (5y6w). He told his students the values of each variable: w=6, y=2, and z = 7. What is the simplification of Mr. Smith's expression?
Answers
Answer:
416
Step-by-step explanation:
Plug in the variables
8(7) + (5*2 * 6*6)
56 + (10 * 36)
56 + 360
416
what is 0.5734 rounded to the nearest thousandth
Answers
Answer:
0.573
Hope that helps :)
Explanation:
3 is the thousandths, so you would round up by looking at the number to the right which is 4. Since 4 is not greater than 5, it wouldn’t change the 3.
If you get this right i'll give u 40 :)
Answers
Answer:
1.NO 2. Yes
Step-by-step explanation:
Answer:
The first and second one is no
Step-by-step explanation:
(1/5) to the second power is 1/25 and adding 25/25 gets 26/25 which is not equal to 24/25
1 to the second power is still one and (1/4) to the second power is 1/16. 16/16 plus 1/16 is 17/16 which is not equal to 25/26
please help! i don’t understand!
Answers
Answer:
£0.00 probably is the answer
Answer:
7158
Step-by-step explanation: