A directed line segment AB with A (1,3) and B (8,4) is partitioned by point C such that AC and CB form a 4:1 ratio. Find C
Write your answer as a coordinate point.
Do not include spaces in your answer.
Write your answer as a decimal if necessary.
Answer:
[tex]C = (\frac{33}{5},\frac{19}{5})[/tex]
Step-by-step explanation:
Given
[tex]A = (1,3)[/tex]
[tex]B = (8,4)[/tex]
[tex]AC : BC = 4 : 1[/tex]
Required
Determine the coordinates of C
To do this, we make use of:
[tex]C = (\frac{nx_1 + mx_2}{n+m},\frac{ny_1 + my_2}{n+m})[/tex]
Where:
[tex]A = (1,3)[/tex] ---- [tex](x_1,y_1)[/tex]
[tex]B = (8,4)[/tex] ---- [tex](x_2,y_2)[/tex]
[tex]m:n = 4 : 1[/tex]
So:
[tex]C = (\frac{1 * 1 + 4*8}{1+4},\frac{1*3 + 4*4}{1+4})[/tex]
[tex]C = (\frac{33}{5},\frac{19}{5})[/tex]
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 51.5 and 51.7 min. P(51.5 < X < 51.7)
Answer:
0.1 = 10% probability that the class length is between 51.5 and 51.7 min, that is, P(51.5 < X < 51.7) = 0.1.
Step-by-step explanation:
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distributon has two bounds, a and b, and the probability of finding a value between c and d is given by:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min.
This means that [tex]a = 50, b = 52[/tex]
If one such class is randomly selected, find the probability that the class length is between 51.5 and 51.7 min.
[tex]P(51.5 \leq X \leq 51.7) = \frac{51.7 - 51.5}{52 - 50} = \frac{0.2}{2} = 0.1[/tex]
0.1 = 10% probability that the class length is between 51.5 and 51.7 min, that is, P(51.5 < X < 51.7) = 0.1.
Use calculus to evaluate (lhopitals rule)
lim x>infinity x^2 - ln(2/x)/3x^2 + 2x
Answer:
1/3
Step-by-step explanation:
[tex][x^2 - ln(2/x)]/[3x^2 + 2x]\\[/tex]
∞/∞
[tex]\frac{d}{dx}[x^2-ln(2/x)] =2x+\frac{1}{x}\\ \frac{d}{dx}[3x^2+2x]=6x+2\\\frac{2x+\frac{1}{x}}{6x+2}[/tex]
Also ∞/∞
[tex]\frac{d}{dx}[2x+\frac{1}{x}]=2-1/x^2\\\frac{d}{dx}[6x+2]=6\\\\[/tex]
[tex]\lim_{x \to \infty} \frac{2-\frac{1}{x^2} }{6}\\=\frac{2}{6} \\=\frac{1}{3}[/tex]
3/4 of 1/3 =? please show me how to do it
A friend owes $10,000 on his credit card. He plans to stop making charges and pay off the balance. The card has a minimum payment of 5%. He figures correctly that 5% of $10,000 is $500. From that he concludes that he needs to make the 5% minimum payment for only 20 months Is your friend right? If not, explain the error in his reasoning.
Answer:
yes he is correct
Step-by-step explanation:
10000x0.05=500 so thats correct
he will pay 500 for 20 month= 10,000
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: Should be 150mm
Step-by-step explanation:
Find the surface area of each figure. Round answers to the nearest tenth, if necessary
2 mm-
2/5 mm
10 mm
3 mm
O
75 mm2
150 mm2
92 mm2
86 mm2
I have tried a while to figure this out, but I have had no luck!
Dianne runs around a circular track that has a radius of 55 feet. After running three quarters of the distance around the track, how far has she run?
Answer:
She has run 259.18m
Step-by-step explanation:
Since Dianne is running around the circular track, she is running around the perimeter of the circle.
Now, we know that the perimeter of a circle is given by;P = 2πr
Thus the perimeter of the track = total distance that the man travels = 2 x π x 55 = 345.575 meters
Now,since she has run 3/4 of the distance, thus, she has run;
(3/4) x 345.575 = 259.18m
pls pls pls pls helpppp
What is the conjugate of (x2-6)?
Answer:
2(x - 3)
Step-by-step explanation:
A $7.00 item is marked down by 10%.
What is the new cost of the item?
Round to two decimals if needed.
$
Answer:
6.3
Step-by-step explanation:
Derek has a bank account that pays 4.1% simple interest. He deposits $910 and leaves it in for 2.5 years. How much interest does he earn.
Answer:
After 2 and a half years, Derek's bank account will have earned interest of $ 93.27.
Step-by-step explanation:
Given that Derek has a bank account that pays 4.1% simple interest, and he deposits $ 910 and leaves it in for 2.5 years, to determine how much interest does he earn, the following calculation must be performed, knowing that simple interest is not added to the initial capital:
(910 x 0.041) x 2.5 = X
37.31 x 2.5 = X
93.275 = X
Thus, after 2 and a half years, Derek's bank account will have earned interest of $ 93.27.
In ΔJKL, j = 520 inches, k = 730 inches and l=640 inches. Find the measure of ∠K to the nearest degree.
Answer:
It’s 56.7
Step-by-step explanation:
Fudisks
a savings account increases from $200 to $212. what is the percent increase of the savings account?
Answer:
6% increase
Step-by-step explanation:
To find the percent increase, divide the difference by the original:
12/200
= 0.06
Multiply this by 100:
0.06(100)
= 6
So, the percent increase was 6%
Which is a perfect square?
61
62
63
65
Answer:
None of them really,
A perfect square is a number that can be expressed as the product of two equal integers...which is not seen here.
Th closest perfect square that could be possible would be 64, but thats not an option, so go with none.
30°
8 + 6x
4x + 2
in a triangle
Answer:
x=12
Step-by-step explanation:
Simplifying
30 + 4x + 2 = 8 + 6x
Reorder the terms:
30 + 2 + 4x = 8 + 6x
Combine like terms: 30 + 2 = 32
32 + 4x = 8 + 6x
Solving
32 + 4x = 8 + 6x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6x' to each side of the equation.
32 + 4x + -6x = 8 + 6x + -6x
Combine like terms: 4x + -6x = -2x
32 + -2x = 8 + 6x + -6x
Combine like terms: 6x + -6x = 0
32 + -2x = 8 + 0
32 + -2x = 8
Add '-32' to each side of the equation.
32 + -32 + -2x = 8 + -32
Combine like terms: 32 + -32 = 0
0 + -2x = 8 + -32
-2x = 8 + -32
Combine like terms: 8 + -32 = -24
-2x = -24
Divide each side by '-2'.
x = 12
Simplifying
x = 12
A psychology professor assigns letter grades on a test according to the following scheme. A: Top 9% of scores B: Scores below the top 9% and above the bottom 56% C: Scores below the top 44% and above the bottom 20% D: Scores below the top 80% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 79.3 and a standard deviation of 8.4. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
Answer:
You get a D if you have a grade between 66 and 72.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Scores on the test are normally distributed with a mean of 79.3 and a standard deviation of 8.4.
This means that [tex]\mu = 79.3, \sigma = 8.4[/tex]
D: Scores below the top 80% and above the bottom 6%
So between the 6th and the 20th percentile.
6th percentile:
X when Z has a pvalue of 0.06. So X when Z = -1.555.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.555 = \frac{X - 79.3}{8.4}[/tex]
[tex]X - 79.3 = -1.555*8.4[/tex]
[tex]X = 66.2[/tex]
Rounds to 66
20th percentile:
X when Z has a pvalue of 0.2. So X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 79.3}{8.4}[/tex]
[tex]X - 79.3 = -0.84*8.4[/tex]
[tex]X = 72.2[/tex]
Rounds to 72
You get a D if you have a grade between 66 and 72.
Helpppp!!! Pleaseeee
Answer:I’m pretty sure it’s 90
Step-by-step explanation:
Answer:
tan 60=√3/t
t=√3/√3=1 is your answer
I WILL GVE BRAINLIEST JUST HELP ASAP
Use the Rational Zeros Theorem to write a list of all potential rational zeros
f(x) = 14x3 + 56x2 + 2x - 7
Answer:
± 1 , ± 1/2 , ± 1/7 , ± 1/14 , ± 7 , ± 7/2
Step-by-step explanation:
whoever gets these 2 right gets brainliest!!
Answer: c,b
Step-by-step explanation:
Answer:
the correct and reasonable answer should be B and C.
Step-by-step explanation:
what is the quotient of 3 to the 5 power ÷ 3 to the 3 power
If a central angle measures 87°, then its arc will measure _____.
twice as much
the same
half as much
The same!
Hope This Helps! <3
Good Luck Studying ^-^
Jennifer is attending a school orchestra concert.She sees her math teacher seated 4.5 meters ahead of her and her science teacher seated 1.1 metes to her right.how far apart are the two teachers?
Answer:
j
Step-by-step explanation:
jj
Simplify the expression: (-4x^10y^-8)^2
Answer:
(-8x)(20y)-16
Step-by-step explanation:
(-4x10y-8)2
distribute the two to all terms inside the parentheses
(-8x)(20y)-16
you cannot simplify this further
PLZ HELP DUE IN 8 MINS PLZ HELP
Answer: for number 1 its negative 14
Step-by-step explanation:
i will give you brainliest whoever answers correct first!!
Answer:
x=16
Step-by-step explanation:
ok yeah lololol
5 members or 20% of the math league did not come to the meet. how many total members are there
Find x. Please and thank you!
What is the area of the triangle?
6
2
3
Answer:
6
Step-by-step explanation:
Find the area of both triangles inside the bigger triangle and add them together.
Use the Pythagorean theorem to find the missing length of the leg in the smallest triangle:
a² + b² = c²
2² + b² = 3²
4 + b² = 9
5 = b²
2.2 ≈ b
Calculate the area of the smaller triangle:
1/2(bxh)
1/2(2 x 2.2)
1/2(4.4)
2.2
Calculate the area of the bigger triangle:
We know that the longer leg is 3.8 units because we were able to subtract the length of the smaller triangle's leg from 6.
1/2(bxh)
1/2(2 x 3.8)
1/2(7.6)
3.8
Add both areas to find the area of the largest triangle:
3.8 + 2.2 = 6
HELP ASAP!! In a right triangle, the longer leg is twice the shorter leg and the hypotenuse is 8 more than the shorter leg. Find the length of the shorter leg.
Answer:
We can't find an exact number, but the answer is x.
What is a angle called when two angles share a common side and a common vertex
Answer:
Adjacent Angles
Step-by-step explanation:
Adjacent angles are two angles that have a common vertex and a common side but do not overlap. They share the same vertex and the same common side.