Answer:
The vector equation
[tex]r = (2 + 3t)i+ (2.4 + 2t)j+ (3.5 - t)k[/tex]
The parametric equation
[tex]x = 2 + 3t\\y = 2.4 + 2t\\z = 3.5-t[/tex]
Step-by-step explanation:
Given
[tex]Point = (2,2.4,3.5)[/tex]
[tex]Vector = 3i + 2j - k[/tex]
Required
The vector equation
First, we calculate the position vector of the point.
This is represented as:
[tex]r_0 = 2i + 2.4j + 3.5k[/tex]
The vector equation is then calculated as:
[tex]r = r_o + t * Vector[/tex]
[tex]r = 2i + 2.4j + 3.5k + t * (3i + 2j - k)[/tex]
Open bracket
[tex]r = 2i + 2.4j + 3.5k + 3ti + 2tj - tk[/tex]
Collect like terms
[tex]r = 2i + 3ti+ 2.4j + 2tj+ 3.5k - tk[/tex]
Factorize
[tex]r = (2 + 3t)i+ (2.4 + 2t)j+ (3.5 - t)k[/tex]
The parametric equation is represented as:
[tex]x = x_0 + at\\y = y_0 + bt\\z = z_0 + ct[/tex]
Where
[tex]r = (x_0 + at)i +(y_0 + bt)j+(z_0 + ct)k[/tex]
By comparison:
[tex]x = 2 + 3t\\y = 2.4 + 2t\\z = 3.5-t[/tex]
Find the Greatest common factor of 120? Show your work!
Answer:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60
Step-by-step explanation:
1x120, 2x60, 3x40, 4x30, 5x24, 6x20, 8x15, 10x12, 12x10,15x8, 20x6, 24x5, 30x4, 40x3, 60x2
The function in the table is exponential:
True
False
Answer:
true ...
believe it or not there is an exponential sequence that can make that
result
f(x) = [tex]2^{(2(x+2) -1)}[/tex]
x /// 2(x+2) -1
-1 /// 1
0 /// 3
1 /// 5
2 /// 7
[tex]2^{1} = 2\\2^{3} = 8\\\\2^{5} = 32\\\\2^{7 = 128\\\\[/tex]
Step-by-step explanation:
Domain and range
O Function
O Not a function
Answer:
Radiation 1- Function
Radiation 2- Not a function
Radiation 3- function
Radiation 4- function
Answer:
1 - Function
2 - Not a function
3 - function
4 - function
Step-by-step explanation:
Hw help ASAP PLZZZZZZ
Answer:
Your answer is C. X = 29/8c
Step-by-step explanation:
2/3(cx + 1/2) - 1/4 = 5/2
2cx/3+1/3-1/4=5/2
2cx3+1/12=5/2
2cx/3=5/2-1/12
2cx/3=29/12
(3)2cx/3=29/12(3)
2cx= 31/4
(2c)2cx=29/4(2c)
X=29/8c
Your answer is C. X = 29/8c
What is the equation of the line that is perpendicular to
the given line and has an x-inter cept of 6?
O y = x + 8
O y = x + 6
O y = fx-8
O y=x-6
Answer:
the last one, y=x-6
Step-by-step explanation:
it is the only answer with an x-intercept of 6. you did not provide the line, but I'm assuming it is y=-x.
find the equation of the circle centre (3-2)radius 2 unit
Answer:
(x - 3)^2 + (x + 2)^2 = 4
Step-by-step explanation:
Equation of circle:
(x - h)^2 + (x - k)^2 = r^2
(h, k) = (3, -2)
r = 2
(x - 3)^2 + (x - (-2))^2 = 2^2
(x - 3)^2 + (x + 2)^2 = 4
enter the number that belongs in the green box. m
==========================================================
Explanation:
Let's find angle D. Recall that for any triangle, the interior or inside angles always add to 180 degrees.
A+D+C = 180
32+D+41 = 180
D+73 = 180
D = 180-73
D = 107
Now notice that triangle ADC is congruent to triangle ABC. We can use the SSS congruence theorem to prove this.
The identical triangles must have corresponding angles that are the same measure, meaning angle D = angle B = 107 degrees.
Side note: This quadrilateral is a kite because it has two pairs of adjacent congruent sides, but not all four sides are the same length (or else it would be a rhombus).
Suppose 46% of politicians are lawyers. If a random sample of size 662 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Answer:
0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose 46% of politicians are lawyers.
This means that [tex]p = 0.46[/tex]
Sample of size 662
This means that [tex]n = 662[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.46[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.46*0.54}{662}} = 0.0194[/tex]
What is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%?
p-value of Z when X = 0.46 + 0.04 = 0.5 subtracted by the p-value of Z when X = 0.46 - 0.04 = 0.42. So
X = 0.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.46}{0.0194}[/tex]
[tex]Z = 2.06[/tex]
[tex]Z = 2.06[/tex] has a p-value of 0.9803
X = 0.42
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.42 - 0.46}{0.0194}[/tex]
[tex]Z = -2.06[/tex]
[tex]Z = -2.06[/tex] has a p-value of 0.0197
0.9803 - 0.0197 = 0.9606
0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Help please!!!!! I’m using Plato
Answer:
[tex]\frac{y^{6} }{ x^{2} }[/tex]
Step-by-step explanation:
[tex]y^{6} x^{-2}[/tex]
Answer and Step-by-step explanation:
When there is a set of values within parenthesis, and an exponents on the values and on the parenthesis, you multiply the outer exponent with the inner exponent.
When a value has a negative exponent, the value that has the negative exponent will become a fraction and go to the denominator of the fraction (or go immediately to the denominator), or if it is already a fraction, goes to the denominator. If the value that has the negative exponent is in the denominator, the value will go to the numerator. In both instances, the negative exponent will then change to positive.
First, we need to simplify the expression inside the parenthesis.
[tex]y^{\frac{3}{2} } x^{-\frac{1}{2} } --> \frac{y^{\frac{3}{2} } }{x^{\frac{1}{2}} }[/tex]
Now we multiply the 4 to the exponents.
[tex]\frac{y^{\frac{3}{2} *\frac{x4}{1} } }{x^{\frac{1}{2}}*\frac{4}{1} } = \frac{y^{\frac{12}{2}} }{x^{\frac{4}{2}}} = \frac{y^6}{x^2}[/tex]
[tex]\frac{y^6}{x^2}[/tex] is the answer.
#teamtrees #PAW (Plant And Water)
At an intersection, the red light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25 minutes. Approximately what percent of red lights last between 2.5 and 3.5 minutes? (2 points)
Answer:
95.4%
Step-by-step explanation:
Z(low)=-2 0.022750132
Z(upper)=2 0.977249868
Select the correct answer.
Tom gets $12 off a box of chocolates that had an original price of $48. What percentage is the discount
Answer:
25
Step-by-step explanation:
divide 48 by 4 which is 25%
lenguaje coloquial de x-y
Answer:
Uhh what??
Step-by-step explanation:
I dont understand you ●___●
is the equation x^3 - 2x^2 + 1 = 0 a quadratic equation?
Answer:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
STEP
1
:
Equation at the end of step 1
(((x3) - 2x2) + 2x) - 1 = 0
STEP
2
:
Checking for a perfect cube
2.1 x3-2x2+2x-1 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3-2x2+2x-1
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 2x-1
Group 2: -2x2+x3
Pull out from each group separately :
Group 1: (2x-1) • (1)
Group 2: (x-2) • (x2)
Which of the following numbers are less than -0.65? Select all that apply.
-0.99
-4/5
-1/6
NEXT QUESTION
Answer -0.99 and -4/5
Step-by-step explanation:
-4/5 is equal to -0.8
Both -0.8 and 0.99 are to the left of -0.65, which is why they're less than 0.65.
1/6 = -0.16
Since -0.16 is to the right of -0.65 it is more than, not less
My reason:
As you go rightward, you increase the numbers by 1, which is why the numbers closer to the right are bigger than the numbers closer to the left.
(sorry for answering when it's already been two weeks lol. I felt the urge to answer-)
if log 2=x express 12.5 in terms of x
Answer:
b
Step-by-step explanation:
thbte
A cylinder has a radius of 2.5 inches (in.) and a height of 11 in., as shown.
2.5 in.
11 in.
What is the surface area, in square inches, of the cylinder?
Answer:
212.06
Step-by-step explanation:
can't really explain since the formula is fricking long but trust me that's uts 212.06 in²
Which graph represents the function below?
y= { -x if x > -3
x+6, if x<(or equal to)3
Answer:
second option
Step-by-step explanation:
I'm not sure how to explain but if you really need an explanation please message me
The function that represents the absolute function will be y = -|x + 3| + 3. Then the function is represented by graph A.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = | x - h| + k
The function is given below.
y = -x, if x > -3
y = x + 6, if x ≤ -3
The value of the functions at x = -3 is calculated as,
y = - (-3)
y = 3
y = -3 + 6
y = 3
The capability that addresses the outright capability will be y = - |x + 3| + 3. Then the capability is addressed by diagram A.
The graph is given below.
More about the absolute function link is given below.
https://brainly.com/question/10664936
#SPJ2
Please help! Thank you!
Answer:
hi
Step-by-step explanation:
Two methods, A and B, are available for teaching Spanish. There is a 70% chance of successfully learning Spanish if method A is used, and a 85% chance of success if method B is used. However, method B is substantially more time consuming and is therefore used only 20% of the time (method A is used the other 80% of the time). The following notations are suggested:
A—Method A is used.
B—Method B is used.
L—Spanish was learned successfully. A person learned Spanish successfully.
What is the probability that he was taught by method A?
Answer:
0.7671 = 76.71% probability that he was taught by method A
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Person learned Spanish successfully.
Event B: Method A was used.
Probability of a person learning Spanish successfully:
70% of 80%(using method A)
85% of 20%(using method B)
So
[tex]P(A) = 0.7*0.8 + 0.85*0.2 = 0.73[/tex]
Probability of a person learning Spanish successfully and using method A:
70% of 80%, so:
[tex]P(A \cap B) = 0.7*0.8 = 0.56[/tex]
What is the probability that he was taught by method A?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.56}{0.73} = 0.7671[/tex]
0.7671 = 76.71% probability that he was taught by method A
what is completely factored form or this expression?
y^2-12y+32
a.(y+4)(y+8)
b.(y-4)(y-8)
c.(y+18)(y+2)
d.(y-18)(y-2)
[tex]\\\\\\[/tex]
Therefore [tex]\sf{option~ B~ is ~correct }[/tex][tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
Answer:
(y-4) (y-8)
Step-by-step explanation:
y^2-12y+32
What two numbers multiply to 32 and add to -12
-8*-4 = 32
-8+-4 = -12
(y-4) (y-8)
Determine how much interest you would earn on the following investment:
$190,000 invested at a 6.9% interest rate for 9 months.
The mean points obtained in an aptitude examination is 167 points with a standard deviation of 20 points. What is the probability that the mean of the sample would differ from the population mean by less than 3.8 points if 76 exams are sampled
Answer:
0.9029 = 90.29% probability that the mean of the sample would differ from the population mean by less than 3.8 points if 76 exams are sampled
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
The mean points obtained in an aptitude examination is 167 points with a standard deviation of 20 points
This means that [tex]\mu = 167, \sigma = 20[/tex]
Sample of 76:
This means that [tex]n = 76, s = \frac{20}{\sqrt{76}}[/tex]
What is the probability that the mean of the sample would differ from the population mean by less than 3.8 points?
P-value of Z when X = 167 + 3.8 = 170.8 subtracted by the p-value of Z when X = 167 - 3.8 = 163.2. So
X = 170.8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{170.8 - 167}{\frac{20}{\sqrt{76}}}[/tex]
[tex]Z = 1.66[/tex]
[tex]Z = 1.66[/tex] has a p-value of 0.9515
X = 163.2
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{163.2 - 167}{\frac{20}{\sqrt{76}}}[/tex]
[tex]Z = -1.66[/tex]
[tex]Z = -1.66[/tex] has a p-value of 0.0485
0.9514 - 0.0485 = 0.9029
0.9029 = 90.29% probability that the mean of the sample would differ from the population mean by less than 3.8 points if 76 exams are sampled
The sum of 4 consecutive multiples of 6 is 540. What is the greatest of these numbers?
Answer:
144
Step-by-step explanation:
First: 6x
Second: 6x+6
Third: 6x+12
Fourth: 6x+18
- Since they're multiples of 6
[tex]6x+6x+6+6x+12+6x+18=540[/tex]
[tex]24x+36=540\\[/tex]
Subract 36 from each side give us...
[tex]24x=504\\x=21[/tex]
[tex]21(6)+18=144[/tex]
Hope this helped! Please mark brainliest :)
A car originally costs $20,000. Its price went up by 20% and then by another $8,000. How much did the price go up as a percentage of the original price?
Answer:
60%
Step-by-step explanation:
20,000
we can move the decimal place one to the left to find 10 percent
2,000
multiply 10 x 2 to find twenty percent or 4,000
we add this to the original total. 24,000
then add the 8,000
32,000
we know find one percent of the original total
200
and find the difference between the two totals
32000-20000 = 12,000
12000 divided by 200 which is 6
multiply six by ten to get
60 percent
Need help on last question
Answer:
Step-by-step explanation:
so let the equation equal 13
13 = 3[tex]x^{3}[/tex]-12x+13
so when ever 3[tex]x^{3}[/tex]-12x=0 then this is equation is true, soooo
x (3[tex]x^{2}[/tex] - 12) =0
so when x = 0 this is true, but also when
3[tex]x^{2}[/tex]-12=0 also
3[tex]x^{2}[/tex] = 12
[tex]x^{2}[/tex] = 4
x = 2
so when x = 2 or -2 or 0 , then this is true
Simplify:
-5x+6y-9y+4x
Answer:
-x-3y
Step-by-step explanation:
-5x+6y-9y+4x
-5x+4x+6y-9y
-x-3y
Tell whether the following two triangles can be proven congruent through SAS.
A.Yes, the two triangles are congruent because they’re both right triangles.
B.Yes, the two triangles are congruent because two sides and their included angle are congruent in both triangles.
C.No, the two triangles can only be proven congruent through SSS.
D.No, the two triangles can only be proven congruent through AAA.
Answer:
C.No, the two triangles can only be proven congruent through SSS.
Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)
The x y-coordinate plane is given.
The function enters the window in the second quadrant, goes up and right becoming less steep, crosses the y-axis at approximately y = 3.2, changes direction at the approximate point (0.7, 3.3), goes down and right becoming more steep, and stops at the closed point (2, 3).
The function starts again at the open point (2, 1), goes up and right becoming more steep, goes up and right becoming less steep, passes through the open point (4, 4), changes direction at the approximate point (4.2, 4.1), goes down and right becoming more steep, and exits the window in the first quadrant.
(a) lim x → 2− f(x)
(b) lim x → 2+ f(x)
(c) lim x → 2 f(x)
(d) f(2)
(e) lim x → 4 f(x)(f) f(4)
Answer:
Hence the answer is given as follows,
Step-by-step explanation:
Graph of y = f(x) given,
(a) [tex]\lim_{x\rightarrow 2^{-}}f(x)=3[/tex]
(b) [tex]\lim_{x\rightarrow 2^{+}}f(x)=1[/tex]
(c) [tex]\lim_{x\rightarrow 2}f(x)= DNE \left \{ \therefore \lim_{x\rightarrow 2^{-}} f(x)\neq \lim_{x\rightarrow 2^{+}}f(x) \right.[/tex]
(d) [tex]f(2)=3[/tex]
(e) [tex]\lim_{x\rightarrow 4}f(x) = 4[/tex]
(f) [tex]f(4)= DNE.[/tex]{ Hole in graph}
Hence solved.
Help asap please!!..
Answer:
9x² - 4/3x + ¼
Step-by-step explanation:
(3x - ½)²
(3x - ½)(3x -½)
9x² - ⅔x - ⅔x + ¼
9x² - 4/3x + ¼
Find two positive numbers whose difference is 3 and whose product is 1638.
Answer:
42 and 39
Step-by-step explanation:
The best method in my opinion is to guess and check. So, you would start off by dividing 1638 by any number you see fit (I started with 34), and keep increasing or decreasing until you get whole numbers that are three integers apart. I understand that this is a little tedious but I'm not aware of a better solution as of right now, so that's the best that I've got! Please let me know if you need more help and I will be happy to help!