Given :
Two points [tex]P_1(-2,3,2)\ and\ P_2(1,2,0)[/tex] .
To Find :
The direction of [tex]P_1P_2[/tex] and midpoint of line segment [tex]P_1P_2[/tex] .
Solution :
Direction of [tex]P_1[/tex] and [tex]P_2[/tex] is given by :
[tex]\vec{D}=\dfrac{P_2-P_1}{|P_2-P_1|}\\\\\vec{D}=\dfrac{(-2i+3j+2k)-(i+2j+0)}{P_2-P_1}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{3^2+1^2+2^2}}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{14}}[/tex]
Now , mid point is given by :
[tex]M(\dfrac{-2+1}{2},\dfrac{3+2}{2},\dfrac{2+0}{2})\\\\M(\dfrac{-1}{2},\dfrac{5}{2},1)[/tex]
Hence , this is the required solution .
Find an equation of a plane through the point (3, 0, 2) which is orthogonal to the linex=?2+3t,y=2+4t,z=?1?3tin which the coefficient of x is 3.
Answer: 3x + 4y - 3z - 3 = 0
Step-by-step explanation:
with the given point (3, 0, 2), the plane is orthogonal to this line so it
has directional ratios (3, 4, -3)
therefore the given equation can be written as;
(x+2)/3 = (y-2)/4 = (z+1)/-3
so equation of the plane passing through point x1, y1 and z1 in the one point form is given as;
a(x-x1) + b(y - y1) + c(z -z1) = 0
abc represent the direction ratio
so we substitute
3(x-3) + 4(y-0) + (-3(z-2)) = 0
3x - 9 + 4y - 0 - 3z + 6 = 0
3x + 4y - 3z - 3 = 0
therefore the equation of the plane through the point is 3x + 4y - 3z - 3 = 0
TUV = 9x + 1 TUW = 7x-9 WUV 5x-11
Answer:
7
Step-by-step explanation:
9x + 1 = 7x - 9 + 5x - 11
9x + 1 = 12x - 20
9x + 1 - 1 = 12x - 20 - 1
9x = 12x - 21
9x - 12x = 12x - 12x -21
-3x = -21
-3x/3 = -21/-3
x = 7
Hope that helps!
The product of -4 and d
Answer:
-4d
Step-by-step explanation:
Six classes of 31,28,27,32,24 and 26 students are to travel on buses that each hold 36 students. How many buses are needed?
Answer:
5 buses
Step-by-step explanation:
You add all the students up to get 168, because that's the total number of students, and divide it by 36. The buses can only carry 36 people, so you will need 4.666 buses, but you can't have 0.666 of a bus, so you will need 5 buses to fit everyone.
15 POINTS FOR CORRECT PERSON!! PLEASE HELP The product (5+ i ) (5-i) is a real number, 26. What are the factors (5+i) and (5-i) called? Imaginary units Complex conjugates Imaginary numbers Or complex numbers?
Answer:
Complex numbers
Step-by-step explanation:
Given
[tex](5 + i)[/tex] and [tex](5 - i)[/tex]
Required
Determine what both factors are called
From the list of given options. option "complex numbers" answer the question correctly
This is because when numbers are written in form [tex]a + bi[/tex] where [tex]b \neq 0[/tex] and [tex]i = \sqrt{-1}[/tex]; such a number are referred to as complex number
Some other examples are:
[tex]-7 + 3i[/tex]
[tex]2 - 7i[/tex]
[tex]4 + i[/tex]
And lots more
-4.5 x (-2)???????????????????????
Answer:
9
Step-by-step explanation:
-4.5 x (-2) is equal to 9
If John has drank three drinks per day how many will he have drank in 3 day's?
Answer:
9 drinks
Step-by-step explanation:
3+3+3=9
Or 3*3=9
Answer:
9
Step-by-step explanation:
which of the following verifies that triangle YXZ is similar to triangle QPR?
Answer:
AA postulate
Step-by-step explanation:
Because both the angle are identical?
4(z – 2) + 3z
Need help
Answer:
5z-8
Step-by-step explanation:
(8z-8)+3z=
5z-8
Answer:
z-8
Step-by-step explanation:
4(z -2)+3z
4z -8 +3z
-3 -3
z -8
Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to:________
a. manipulation; chance
b. manipulation; experimental error
c. sampling error; independent variable
d. independent variable; experimental error
Answer:
Option (A)
Step-by-step explanation:
There are 2 main branches of statistics. They are:
1. Descriptive Statistics
2. Inferential Statistics
Descriptive statistics describes the characteristics of observed subjects or items while Inferential statistics makes inferences, based on given or derived data.
Inferential Statistics allow you to decide whether a difference between the experimental group and control group is due to manipulation or chance.
The Experimental group is the group that an effect is tested on while the Control group is the group that is left untested or uninfluenced. Inferential statistics allow you to decide whether a difference between these 2 groups is due to
- manipulation or interference by any force (which may be the experimenter/researcher)
or
- probability which is chance.
Option a. manipulation; chance
Inferential statistics is a statistical method for estimating the characteristics of a larger population from a small but representative sample. In other words, it enables the researcher to make generalizations about a larger group based on a smaller subset of that group.
Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to a. manipulation; chance
For more information:
https://brainly.com/question/20982963?referrer=searchResults
what is 12.3 -(-9.6) =12.3 + 9.6 simplified?
Answer:
Step-by-step explanation:
12.3 + 9.6 = 21.9
The expression 12.3 - (-9.6) is equivalent to 21.9.
Given is an expression 12.3 -(-9.6) = 12.3 + 9.6, we need to simplify it,
To simplify the expression 12.3 - (-9.6), we can rewrite it as 12.3 + 9.6.
When subtracting a negative number, it is equivalent to adding the positive value of that number.
So, -(-9.6) becomes +9.6.
Therefore, 12.3 - (-9.6) simplifies to 12.3 + 9.6.
Adding 12.3 and 9.6 gives us 21.9.
So, 12.3 - (-9.6) = 21.9.
Learn more about expression click;
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Veronica has been wanting to learn to ice skate for years!
When the Glacier Zone Ice Rink opened, Veronica bought 12
ice-skating lessons during their grand-opening sale. Veronica
paid $305.40 in all. How much did each lesson cost?
Answer:
25.45 per lesson
Step-by-step explanation:
divide $305.40 by 12
HURRRRYYYYYYY PLEASE Write the equation of the line that passes through the points (-8,-1) and (5,−7). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
y + 8 = 2x + 2
Step-by-step explanation:
Use the points given to find the slope. Divide the difference in y-values by the difference in x-values.
(-1) - (-7) = 6
5 - (-8) = 3
6/3 = 2
The slope is 2.
Now, pick one of the points to put in point-slope form. It doesn't matter which. You will get the right answer either way. I will use (-1, -8).
y - y₁ = m(x - x₁)
y - (-8) = 2(x - (-1))
y + 8 = 2(x + 1)
y + 8 = 2x + 2
Help please if u can
Answer:
Negative infinity
Step-by-step explanation:
The line points down infinitely in the graph.
Find the domain of the function.
f(x)=9x+7
ILL GIVE YOU BRAINLIST !!!
Evaluate the expression given the replacement values.
Answer:
24
Step-by-step explanation:
[tex]a^{2}[/tex]= 49 because any number squared is positive.
Since b=2,
2(-4)= -8.
Then this is 49-8-17, which equals 24.
Answer:
24
Step-by-step explanation:
what five parts make up a data table
Answer:
Step-by-step explanation:
Check boxes.
Sorting (on columns)
Icons that communicate alerts.
Pagination.
Headers Row.
A bakery wants to determine the best placement for day-old goods. What type of data collection source do you think the bakery should use? Choose the correct answer below. A. The bakery should conduct an experiment. B. The bakery should collect information from operational or transactional systems. C. The bakery should conduct an observational study. D. The bakery should obtain information that was distributed by an organization or individual. E. The bakery should conduct a survey
Answer: C. The bakery should conduct an observational study
Step-by-step explanation:
From the question, we are informed that a bakery wants to determine the best placement for day-old goods. The type of data collection source that the bakery should use is an observational study.
An observational study is a form of study whereby the individuals who are to be observed are being studied by the researcher and certain conclusions are derived about them. When the bakery conductd an observational study, the behavior of the customers regarding goods placement can be observed.
What percent of 150 is 33.5?
Answer:
22.33
Step-by-step explanation:
x%(150)=33.5
x/100 x 150=33.5
x/2 x 3=33.5
x=2/3 x 33.5
x=67/3
x=22.33
Answer:
Click at the above pic and the ans will appear.
Hope it helps :)
Write each improper fraction as a mixed number in simplest form -72/27=
Alisa types 900 words in 20 minutes. What is her typing speed words per minute?
Answer:
45 words per minute!
Step-by-step explanation:
Divide 900 by 20!
Answer:
Her typing speed is 45 word per minute
Step-by-step explanation:
20x = 900
divided 20 on both sides
x = 45
Find an equation of the plane.
The plane through the point (1, -1, - 1 ) and parallel to the plane 5x - y - z = 6
Answer: equation of the plane is 5x - y - z - 7 = 0
same as ( 5x - y - z = 7 )
Step-by-step explanation:
Given data;
5x - y - z = 6
therefore vector of plane is n° = ( 5, -1, -1)
so equation will be
n°(x-x₀, y-y₀, z-z₀) = 0
( 5, -1, -1) (x-x₀, y-y₀, z-z₀) = 0
5(x- (1)) -1(y - (-1)) -1(z - (-1)) = 0
5x - 5 - y - 1 - z - 1 = 0
5x - y - z - 7 = 0
Therefore equation of the plane is 5x - y - z - 7 = 0
same as ( 5x - y - z = 7 )
Drag the fraction that is equivalent to each repeating decimal. Each fraction may be used only once.
Answer:
Step-by-step explanation:
The easiest way to do any of these is to put the fraction into your calculator and see what comes up.
So for 32/9 you get 3.5555555555 which is the same as 3.5 with a bar over it.
7/30 is the same as .23333333333 which is the same as 0.23 with a bar over the three.
5/3 = 1.6666666 which is 1.6 with a bar over the 6
4/9 is 0.4444444 which is the same as 0.4 with a bar over the 4.
What is the difference between math content and math skills
Answer
B
Step-by-step explanation:
Took quiz
A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 510-meter head start. When the start gun is fired the hare begins running at a constant speed of 8 meters per second and the tortoise begins crawling at a constant speed of 6 meters per second. -Let t represent the number of seconds that have elapsed since the start gun was fired. 1) Write an expression in terms of t that represents the hare's distance from the starting line (in meters) 2) Write an expression in terms of t that represents the tortoise's distance from the starting line (in meters) 3) Write an expression in terms of t that represents the number of meters the tortoise is ahead of the hare.
Answer:
1. 8t
2. 510 + 6t
3. 510 - 2t
Step-by-step explanation:
1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t
2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t
3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.
d' = 510 + 6t - 8t
= 510 - 2t
please help me with this problem
Answer:
A) sin 70 = x/10
Step-by-step explanation:
From the angle 70 degrees, 10 is the hypotenuse and x is the opposite and if we go by SOH-CAH-TOA I have an O and a H so its sin.
so we know it's sin so we need to figure out the equation. since we have a hypotenuse as a factor it is on top. and the other number is on the bottom.
so,
A) sin 70 = x/10
Evaluate the integral by interpreting it in terms of areas. integral -3 to 0(1+(9-x^2)^1/2)dx
Answer:
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]
Step-by-step explanation:
We need to evaluate the following integral by interpreting it in terms of areas :
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx[/tex]
The first step is to separate the integral into two easier integrals
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=\int\limits^0_{-3} 1 \, dx+\int\limits^0_{-3}\sqrt{9-x^{2}}\, dx[/tex] (Integral of the sum)
Now we can calculate each integral by studying the area below each function.
For the first integral the function is [tex]f(x)=1[/tex]
(I will attach a file with the functions)
The area below this function is the area of a rectangle with sides 1 and 3 ⇒
[tex]\int\limits^0_{-3}1 \, dx=3[/tex]
For the second integral the function is
[tex]f(x)=y=\sqrt{9-x^{2}}[/tex]
If we study this function :
[tex]y=\sqrt{9-x^{2}}[/tex]
[tex]y^{2}=9-x^{2}[/tex] (I)
[tex]x^{2}+y^{2}=9[/tex]
Which is the equation of a circle centered at (0,0) with radius equal to 3
From the equation (I)
[tex]y^{2}=9-x^{2}[/tex]
[tex]|y|=\sqrt{9-x^{2} }[/tex]
The two possible solutions are :
[tex]y=\sqrt{9-x^{2}}[/tex] (II) and [tex]y=-\sqrt{9-x^{2}}[/tex]
We will use (II) to solve the integral (which is the upper part of the circle)
The area of a circle with radius equal to 3 is
[tex]\pi.3^{2}[/tex]
In the integral we only need a quarter of circle ⇒ We divide the total area by 4 ⇒ [tex]\frac{\pi.3^{2}}{4}[/tex] ⇒ [tex]\frac{9\pi }{4}[/tex]
Finally the integral is equal to
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]
Wayne flips a weighted magic trick coin 100 times. If the coin landed on heads just 19 times out of 100 , how many times is the coin expected to land on tails out of 800 flips? (Hint: the probability that the coin will land on heads is not equal to 0.5 .) A 152 B 648 C 800 D 912
Answer:
152 (Answer A)
Step-by-step explanation:
The experimental probability of obtaining a head is 19/100, or 0.19.
If the coin is flipped 800 times, the expected number of heads will thus be:
0.19(800 flips) = 152 (Answer A)
drag each statement to show it true,based on the graph.
Answer:
1). Cinnamon costs $7 per one pound
2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].
Step-by-step explanation:
x-values on the graph define the weight of cinnamon and y-values define the price.
Slope of the line drawn from the origin (0, 0) and (0.75, 5.25) will determine the per lb price of the cinnamon.
Slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] will be,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
If the points on the given line re (0,0) and (0.75, 5.25),
Slope = [tex]\frac{5.25-0}{0.75-0}[/tex]
= 7
Therefore, two options are the correct options.
1). Cinnamon costs $7 per one pound
2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].
EVALUATE !!!! ILL GIVE YOU BRAINLIST HAVE TO GET IT RIGHT !!!!
N = 3/4 , x = 8 , y = 6 , m = 3
Answer:
12Step-by-step explanation:
[tex]nxy\div m\\\\n =3/4\\x =8\\y =6\\m=3\\\\\frac{3}{4} \times 8 \times 6 \div 3\\\\\mathrm{Divide\:the\:numbers:}\:6\div \:3=2\\=\frac{3}{4}\times \:8\times \:2\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:8=\frac{8}{1}\\=2\times \frac{3}{4}\times \frac{8}{1}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2}{1}\\=\frac{3}{4}\times \frac{8}{1}\times \frac{2}{1}\\\\Multiply\:fractions\\=\frac{3\times \:8\times \:2}{4\times \:1\times \:1}\\\\=\frac{48}{4}\\\\Simplify\\=12[/tex]
Answer:
it is 12
Step-by-step explanation:
3/4×8×6÷3=12
I HOPE this help plz mark me as brainliest