The normal vector to the plane x + 3y + z = 5 is n = (1, 3, 1). The line we want is parallel to this normal vector.
Scale this normal vector by any real number t to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:
(1, 0, 6) + (1, 3, 1)t = (1 + t, 3t, 6 + t)
This is the vector equation; getting the parametric form is just a matter of delineating
x(t) = 1 + t
y(t) = 3t
z(t) = 6 + t
The vector equation for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5 is v =(1+t)i + (3t)j + (6+t)k
The parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5
x(t) = 1+ty(t) = 3tz(t) = 6+tThe parametric equation of a line through the point A(x, y, z) perpendicular to the plane ax+by+cz= d is expressed generally as:
A + vt where:
A = (x, y, z)
v = (a, b, c) (normal vector)
This can then be expressed as:
s = A + vt
s = (x, y, z) + (a, b, c)t
Given the point
(x, y, z) = (1,0,6)
(a, b, c) = (1, 3, 1)
Substitute the given coordinate into the equation above:
s = (1,0,6) + (1, 3, 1)t
s = (1+t) + (0+3t) + (6+t)
The parametric equations from the equation above are:
x(t) = 1+t
y(t) = 3t
z(t) = 6+t
The vector equation will be expressed as v = xi + yj + zk
v =(1+t)i + (3t)j + (6+t)k
Learn more here: brainly.com/question/12850672
a kicker starts a football game by "kicking off". The quadratic function y = -10x^2 + 25x models football's height after x seconds. How long, in seconds, is the football in the air?
Answer: 2.5 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) for the ball to land on the ground (y = 0)
0 = -10x² + 25x
0 = -5x(2x - 5)
0 = -5x 0 = 2x - 5
[tex]0 = x\qquad \dfrac{5}{2}=x[/tex]
x = 0 seconds is when the ball was kicked
x = 5/2 --> 2.5 seconds is when the ball landed on the ground
Help someone please!!
Answer:
A. 5:4
Step-by-step explanation:
Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.
If 2y = 6 - 3x, find y when x = 0
Answer:
2y= 6-3x when x=0
2y= 6-3(0)
2y= 6-0
2y= 6
y= 6/2
y= 3
#i'm indonesian
#hope it helps.
Answer:
[tex] \boxed{y = 3}[/tex]
Step-by-step explanation:
Given, x = 0
[tex] \mathsf{2y = 6 - 3x}[/tex]
plug the value of x
⇒[tex] \mathsf{2y = 6 - 3 \times 0}[/tex]
Multiply the numbers
⇒[tex] \mathsf{2y = 6 - 0}[/tex]
Calculate the difference
⇒[tex] \mathsf{2y = 6}[/tex]
Divide both sides of the equation by 2
⇒[tex] \mathsf{ \frac{2y}{2} = \frac{6}{2} }[/tex]
Calculate
⇒[tex] \mathsf{y = 3}[/tex]
Hope I helped!
Best regards!
Help plz! Jim is climbing a mountain that has a base 150 feet above sea level. If he climbs 233 feet then descends into a cave 64 feet, how far above sea level is Jim
Answer:
150+233-64=319
Jim is 319 ft above sea level.
Step-by-step explanation:
Write a differential equation that fits the physical description. The at time t is proportional to the power of its .
Complete Question
The complete question is shown on the first uploaded image
Answer:
The differential equation that fits the physical description is [tex]\frac{d (v(t))}{dt} = z [v(t)]^2[/tex]
Step-by-step explanation:
From the question we are told that
The acceleration due to air resistance of a particle moving along a straight line at time t is proportional to the second power of its velocity v, this can be mathematically represented as
[tex]a(t) \ \ \alpha \ \ \ [v(t)]^2[/tex]
Where [tex]a(t)[/tex] is the acceleration at time t
and [tex]v(t)[/tex] is the velocity at time t
So
=> [tex]a(t)= z [v(t)]^2[/tex]
Where z is a constant
Generally acceleration is mathematically represented as
[tex]a(t) = \frac{d (v(t))}{dt}[/tex]
So
[tex]\frac{d (v(t))}{dt} = z [v(t)]^2[/tex]
The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of and use a class width of . Does the frequency distribution appear to be roughly a normal distribution?
Answer:
The frequency distribution does not appear to be normal.
Step-by-step explanation:
The data provided is as follows:
S = {0.38 , 0 , 0.22 , 0.06 , 0 , 0 , 0.21 , 0 , 0.53 , 0.18 , 0 , 0 , 0.02 , 0 , 0 , 0.24 , 0 , 0 , 0.01 , 0 , 0 , 1.28 , 0.24 , 0 , 0.19 , 0.53 , 0 , 0, 0.24 , 0}
It is provided that the first lower class limit should be 0.00 and the class width should be 0.20.
The frequency distribution table is as follows:
Class Interval Count
0.00 - 0.19 21
0.20 - 0.39 6
0.40 - 0.59 2
0.60 - 0.79 0
0.80 - 0.99 0
1.00 - 1 . 19 0
1.20 - 1. 39 1
The frequency distribution does not appear to be normal. This is because the frequencies does not start and end at almost equivalent points and the mid-distribution does not consist of the highest frequency.
Thus, the frequency distribution does not appear to be normal.
Solve for x: x/25 > 5
Answer:
x>125
Step-by-step explanation:
Answer:
x > 125
Step-by-step explanation:
Multiply each side by 25, so it now looks like this: x > 125I hope this helps!
What is an equation of the line that passes through the points (-5, 8) and (5,0)?
Answer:
y= -0.8x + 4
Midpoint is 0,4
A middle school has 470 students. Regina surveys a random sample of 40 students and finds that 28 have cell phones. How many students at the school are likely to have cell phones? A. 132 students B. 188 students C. 329 students D. 338 students Please include ALL work! <3
Answer:
C. 329
Step-by-step explanation:
So 28 is 70% of 40
so we know that 70% percent of students have phones
70% of 470
329
Thats how I solved it have a great day :)
The mean area of 7 halls is 55m².If the mean of 6 of them be 58m², find the area of the seventh all.
Answer:
Area of 7th hall = 37 m^2
Step-by-step explanation:
Total area of 7 halls = 7*55 = 385
Total area of 6 halls = 6*58 = 348
Area of 7th hall = 385-348 = 37 m^2
Answer:
The area of the seventh hall = 37m²
Step-by-step explanation:
for 6 halls
Mean area of 6 halls = 58m²
[tex]Mean\ area = \frac{sum\ of\ areas}{Number\ of\ halls} \\58\ =\ \frac{sum\ of\ areas}{6} \\sum\ of\ areas\ of\ 6\ halls\ = 58\ \times\ 6 = 348\\sum\ of\ areas\ of\ 6\ halls\ = 348[/tex]
Let the area of the 7th hall be x
The sum of the areas of 7 halls = 348 + x - - - - - - (1)
[tex]Mean = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\55 = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\sum\ of\ the\ areas\ of\ 7\ halls\ = 55\ \times\ 7\ = 385\\sum\ of\ the\ areas\ of\ 7\ halls\ =\ 385 - - - - (2)[/tex]
notice that equation (1) = equation (2)
348 + x = 385
x = 385 - 348 = 37m²
Therefore, the area of the seventh hall = 37m²
Help!!!!!!! Thank you!!!!!!!
Answer:
D
Step-by-step explanation:
The ratio of yellow paint to blue paint is 4:3. We can make the largest amount of green paint by using all of the 20 quarts of yellow paint so we have to solve for x in 4:3 = 20:x, since 4 * 5 = 20, 3 * 5 = x so we use 15 qts of blue paint, therefore we will have 20 + 15 = 35 qts of green paint.
Answer:
D
Step-by-step explanation:
Can somebody please solve this problem for me!
Answer:
x = 200.674
Step-by-step explanation:
tan∅ = opposite/adjacent
Step 1: Find length of z
tan70° = 119/z
ztan70° = 119
z = 119/tan70°
z = 43.3125
Step 2: Find length z + x (denoted as y)
tan26° = 119/y
ytan26° = 119
y = 119/tan26°
y = 243.986
Step 3: Find x
y - z = x
243.986 - 43.3125 = x
x = 200.674
I need help on this question
Answer:
Figure G.
Step-by-step explanation:
Let's check through the values and calculate the radius and area for all the circle.
For circle R
Diameter = 2 feet
Radius= 1 feet
Area= πr²
Area= 3.14*1
Area= 3.14 feet²
CircleS
Diameter= 4 feet
Radius= 2 feet
Area= πr²
Area= 3.14*2²
Area= 12.56 feet²
Circle T
Diameter= 8 feet
Radius= 4 feet
Area = π r²
area= 3.14*4²
Area=50.24 feet²
Circle U
Diameter= 12 feet
Radius= 6 feet
Area = π r²
area= 3.14*6²
Area=113.04 feet²
The values of the radius and Area all match the graph in figure G
“Type ‘equal, supplementary, complementary, or vertical in the space provided’”
Answer:
Supplementary
Step-by-step explanation:
When the sum of 2 angles equal 180°, they are called supplementary angles. And they also form a straight line together.
<AOB (40°) and <BOC (140°) are not equal angles.
<AOB (40°) and <BOC (140°) are not complementary angles. Complementary angles add up to equal 90°.
<AOB (40°) and <BOC (140°) are not vertical angles. Vertical angles are opposite angles formed when two lines intersect.
<AOB (40°) and <BOC (140°) are supplementary angles. They add up to equal 180°.
Write a variable expression for a number w increased by 4 (A) 4 ÷ w (B) w + 5 (C) w + 4
Answer:
C) w+4
Step-by-step explanation:
w=the variable
+4= increased by 4
HOPE THIS HELPS!!!!!! :)
<33333333333
Mark each of the following as true or false and explain how you know.
true false false true...is the quick answer
Remember that negatives are always less than positive numbers.
In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?
Answer:the mean is greater than the median
Step-by-step explanation:
The mean is less than the median. Then the correct option is A.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
Half the students scored 87.
The next highest score is 71.
Then the median will be
(71+ 87) / 2 = 79
A few students scored 52, so the mean is slightly lower than the mean of 71 and 87.
Thus, the mean is less than the median.
Then the correct option is A.
The missing options are given below.
A. The mean is less than the median.
B. The mean and the median is the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
More about the statistics link is given below.
https://brainly.com/question/10951564
#SPJ2
If x represents the rate that Joy traveled at for the first half of the trip, write an
expression that represents the amount of time it takes Joy to complete the second half of the
trip at the slower rate.
Answer:
time taken for trip 2nd half > time taken for trip 1st half
Step-by-step explanation:
Let the total distance of Joy's trip be = D
Then, the first half distance travelled = D/2
The rate (speed) at which Joy travels during first half = x
So, time taken to travel first half = Distance / Speed
= (D/2) / x = D / 2x
Second half of trip distance travelled = remaining D/2Let the rate (speed) at which Joy travels during second half = x'
As given, x' (second half speed) < x (first half speed)
So, time taken to travel first half = Distance / Speed
(D/2) / x' = D / 2x'
As x' < x : D / 2x' > D / 2x .
Trip 1st half Time taken trip < 2nd half ; or trip 2nd half time taken > 1st half
In a factory there are 100 units of a certain product, 5 of which are defective. We pick three units from the 100 units at random. What is the probability that none of them are defective
Answer:
Probability of picking all three non-defective units
= 7372/8085 (or 0.911812 to six decimals)
Step-by-step explanation:
Let
D = event that the picked unit is defective
N = event that the picked unit is not defective
Pick are without replacement.
We need to calculate P(NNN) using the multiplication rule,
P(NNN)
= 97/100 * 96/99 * 95/98
=7372/8085
= 0.97*0.969697*0.9693878
= 0.911812
The probability that none of the picked products are defective is;
P(None picked is defective) = 0.856
We are told that 5 are defective out of 100.This means the number of good products that are not defective are 95.
Probability of the first picked product not being defective is written as; P(First picked not defective) = 95/100Since the good ones have been picked, there will be 99 left of which the good ones are now 94. Thus, probability of second one not being defective = 94/99Since two good ones have been picked, there will be 98 left and 93 good ones left. Thus, probability of third one not being defective = 93/98Finally, Probability of none of the three being defective is;95/100 × 94/99 × 93/98 = 0.856
Read more at; https://brainly.com/question/14661097
Gavin goes to the market and buys one rectangle shaped board. The length of the board is 16 cm and width of board is 10 cm. If he wants to add a 2 cm wooden border around the board, what will be the area of the rectangle board?
Answer:
The answer is 216
Step-by-step explanation:
if there is a 2 cm border, that means that the sides will both become 2 centimeters longer. so (16+2)*(10*2) = 18*12 = 216.
Emily made a pot cream of pumpkin soup for thanksgiving dinner she put 5 cups of cream in the soup she poured the soup into 24 small bowl show much cream measured in oz is used for each small bowl of soup?
Answer:
each bowl can contain 5/3 oz. of soup.
Step-by-step explanation:
1 cup = 8 oz.
8 oz.
5 cups x -------------- = 40 oz.
1 cup
to get the measurement of each bowl,
40 oz. divided into 24 bowls.
therefore, each bowl can contain 5/3 oz. of soup.
Q-The general solution of inequality cos 2 x≤- sin x is
Answer:
x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I
Step-by-step explanation:
1−2sin2 x≤−sin x ⇒ (2sin x+1)(sin x−1)≥0
sin x≤−1/2 or sin x≥1
−5π/6+2nπ≤x≤−π/6+2nπ or , n ϵ I x=(4n+1)π/2, n ϵ I⇒ -5π6+2nπ≤x≤-π6+2nπ or , n ϵ I x=4n+1π2, n ϵ I (as sin x = 1 is valid only)
In general⇒ In general x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I
Joy is preparing 20 liters of a 25% saline solution. She has only a 40% solution and a 10% solution in her lab. How many liters of the 40% solution and how many liters of the 10% solution should she mix to make the 25% solution?
Answer:
10 Liters of 40% solution
Step-by-step explanation:
Answer:
10 liters of the 40% solution, and 10 liters of the 10% solution
Step-by-step explanation:
Let us say that x = the liters of the 40% solution, and y = liters of the 10% solution in her lab. We know that Joy is preparing a solution containing a total 20 liters, so x + y = 20. We can respectively create the following system of equations,
x + y = 20,
0.40x + 0.10y = 0.25 ( 20 )
And now we have to solve this system of equations for x and y, the liters of the 40% solution and the liters of the 10% solution,
[tex]\begin{bmatrix}x+y=20\\ 0.4x+0.1y=0.25\left(20\right)\end{bmatrix}[/tex] ( Substitute x as 20 - y )
[tex]0.4\left(20-y\right)+0.1y=0.25\cdot \:20\end{bmatrix}[/tex] ( Isolate y )
[tex]8-0.3y=5[/tex] ⇒ [tex]80-3y=50[/tex] ⇒ [tex]-3y=-30[/tex] ⇒ y = 10
[tex]x=20-10 = 10[/tex] ⇒ x = 10
Therefore, there are 10 liters of both the 40% and 10% solution.
A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result. Exactly 3 fours.
A. 0.161
B. 0.002
C. 0.116
D. 0.216
Answer:
0.0321
Step-by-step explanation:
This can be found by binomial probability distribution as the probability of success is constant. There are a given number of trials. the successive tosses are independent.
Here n= 5
The probability of getting a four in a roll of a die = 1/6
The probability of not getting a four in a roll of a die = 5/6
The probability of getting exactly three 4s in five throws is given by
5C3 (1/6)³ (5/6)² = 10 (0.0046) (0.694)= 0.0321
A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped10 times and the man is asked to predict the outcome in advance. He gets 7 out of10 correct. What is the probability that he would have done at least this well if hehad no ESP?
Answer:
I would say 70%
Step-by-step explanation:
He got 7 of of 10 (7/10 = 70%) right so I would say he would do just as well without ESP since it doesn't exist.
please help me to answer this question
Answer:
I can not see any questions
Please answer this correctly without making mistakes
Answer:
2 13/15 miles
Step-by-step explanation:
Hey there!
Well first we need to find the distance between Lancaster and Hillsdale and Lancaster to Silvergrove.
9 + 7 13/15
= 16 13/15
LS is just 14 miles.
Now we can do,
16 13/15 - 14
= 2 13/15 miles
Hope this helps :)
Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)
What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.
Answer:
The chi - square test can be [tex]\approx[/tex] 0.667
Step-by-step explanation:
From the given data :
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis: The number of customers does follow a uniform distribution
Alternative hypothesis: The number of customers does not follow a uniform distribution
We learnt that: Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
The above given data was the observed value.
However, the question progress by stating that : He expected to have 15 customers each day.
Now; we can have an expected value for each customer as:
Observed Value Expected Value
Day Customers
Monday 17 15
Tuesday 13 15
Wednesday 14 15
Thursday 16 15
The Chi square corresponding to each data can be determined by using the formula:
[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]
For Monday:
[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Tuesday :
[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Wednesday :
[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
For Thursday:
[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
Observed Value Expected Value chi - square
Day Customers
Monday 17 15 0.2666666667
Tuesday 13 15 0.2666666667
Wednesday 14 15 0.06666666667
Thursday 16 15 0.06666666667
Total : 0.6666666668
The chi - square test can be [tex]\approx[/tex] 0.667
At level of significance ∝ = 0.10
degree of freedom = n - 1
degree of freedom = 4 - 1
degree of freedom = 3
At ∝ = 0.10 and df = 3
The p - value for the chi - square test statistics is 0.880937
Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis
Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.
Answer:.67
Step-by-step explanation:
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive
Complete Question
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive
Answer:
Yes the company conclude that the correlation is positive
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The correlation is r = 0.65
The null hypothesis is [tex]H_o : r < 0[/tex]
The alternative hypothesis is [tex]H_1 : r > 0[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]Sr = \sqrt{1- r}[/tex]
[tex]Sr = \sqrt{1- 0.65}[/tex]
[tex]Sr = 0.616[/tex]
The degree of freedom for the one-tail test is
[tex]df = n- 2[/tex]
[tex]df = 14- 2[/tex]
[tex]df = 12[/tex]
The standard error is evaluated as
[tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]
[tex]SE =0.1779[/tex]
The test statistics is evaluated as
[tex]t = \frac{r }{SE}[/tex]
[tex]t = \frac{0.65 }{0.1779}[/tex]
[tex]t = 3.654[/tex]
The p-value of of t is obtained from the z table, the value is
[tex]p-value = P(t < 3.654) = 0.00012909[/tex]
Given that [tex]p-value < \alpha[/tex] then we reject the null hypothesis
Hence the company can conclude that the correlation is positive
What is the x-intercept?
