Given:
The vertices of a parallelogram are P(1,2,1), Q(1,0,-1), R(2,2,0).
PQ and PR are the adjacent sides of the parallelogram.
To find:
The coordinates of vertex S.
Solution:
We know that, the diagonals of a parallelogram bisect each other.
Let the coordinates of the vertex S are (a,b,c).
In the given parallelogram PS and QR are the diagonals. It means their midpoints are same.
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{1+2}{2},\dfrac{0+2}{2},\dfrac{-1+0}{2}\right)[/tex]
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{3}{2},\dfrac{2}{2},\dfrac{-1}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{1+a}{2}=\dfrac{3}{2}[/tex]
[tex]1+a=3[/tex]
[tex]a=3-1[/tex]
[tex]a=2[/tex]
Similarly,
[tex]\dfrac{2+b}{2}=\dfrac{2}{2}[/tex]
[tex]2+b=2[/tex]
[tex]b=2-2[/tex]
[tex]b=0[/tex]
And,
[tex]\dfrac{1+c}{2}=\dfrac{-1}{2}[/tex]
[tex]1+c=-1[/tex]
[tex]c=-1-1[/tex]
[tex]c=-2[/tex]
Therefore, the coordinates of vertex S are (2,0,-2).
write your answer in simplest radical form
How do I solve this
4 - 2 3/9 =
Answer:
1 2/3.
Step-by-step explanation:
4 - 2 3/9
= 4 - 2 1/3
= 4 - 7/3
= 12/3 - 7/3
= 5/3
= 1 2/3
prove that:cos^2(45+A)+cos (45-A)=1
Step-by-step explanation:
[tex] \boxed{cos^2x=\frac{1-cos2x}{2}}\\cos^2(45+A)+cos^2(45-A)=\frac{1-cos2(45+A)}{2}+\frac{1-cos2(45-A}{2}\\=\frac{1 - cos(90 +2A) }{2} + \frac{1 - cos(90 - 2A) }{2} \\ = \frac{2- ( - sin 2A) - sin2A}{2} \\ = \frac{2 + sin2A -sin2A }{2} \\ = \frac{2}{2} \\ = 1[/tex]
Step-by-step explanation:
Prove that
[tex]\cos^2(45+A)+\cos^2(45-A) =1[/tex]
We know that
[tex]\cos (\alpha \pm \beta) = \cos \alpha\cos \beta \mp \sin \alpha \sin\ beta)[/tex]
We can then write
[tex]\cos (45+A)=\cos 45\cos A - \sin 45\sin A[/tex]
[tex]\:\:\:\:\:\:\:\:= \frac{\sqrt{2}}{2}(\cos A - \sin A)[/tex]
Taking the square of the above expression, we get
[tex]\cos^2(45+A) = \frac{1}{2}(\cos^2A - 2\sin A \cos A + \sin^2A)[/tex]
[tex]= \frac{1}{2}(1 - 2\sin A\cos A)\:\:\;\:\:\:\:(1)[/tex]
Similarly, we can write
[tex]\cos^2(45-A) =\frac{1}{2}(1 + 2\sin A\cos A)\:\:\;\:\:\:\:(2)[/tex]
Combining (1) and (2), we get
[tex]\cos^2(45+A)+\cos^2(45-A)[/tex]
[tex]= \frac{1}{2}(1 - 2\sin A\cos A) + \frac{1}{2}(1 + 2\sin A\cos A)[/tex]
[tex]= 1[/tex]
Nadia needs 3/4 cup of orange juice for a punch recipe. She will double the recipe to make
punch for a party. Which statement is true?
Answer:
she will be using more orange juice
Answer:
she will be using more orange juice
Ms.Griffin has a class of 18 students. She can spend $19 on each student to buy math supplies for each year. She first buys all of her students calculators, which costs a total of 88.02. After buying the calculators, how much does she have left to spend on each student
which polynomial represents the difference below?
Answer:
c. -[tex]x^{2}[/tex] + 8x + 6
Step-by-step explanation:
2[tex]x^{2}[/tex] + 7x + 6 - (3[tex]x^{2}[/tex] - x)
2[tex]x^{2}[/tex] + 7x + 6 - 3[tex]x^{2}[/tex] + x (Distributed the negative to terms inside parentheses)
-[tex]x^{2}[/tex] + 8x +6 (Combine like terms)
Identify the coordinates of H' after a 180° rotation about the origin.
Answer: (4, -2) which is choice A
Explanation:
The rule I used is [tex](x,y) \to (-x,-y)[/tex]
Simply swap the sign of each x and y coordinate to go from (-4, 2) to (4, -2)
This rule only works for 180 degree rotations. It doesn't matter if you go clockwise or counterclockwise.
Suppose your marketing colleague used a known population mean and standard deviation to compute the standard error as 52.4 for samples of a particular size. You don't know the particular sample size but your colleague told you that the sample size is greater than 70. Your boss asks what the standard error would be if you quintuple (5x) the sample size. What is the standard error for the new sample size? Please round your answer to the nearest tenth. Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.
Answer:
The standard error for the new sample size is of 23.4.
Step-by-step explanation:
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.
Interpretation:
From this, we can gather that the standard error is inversely proportional to the square root of the sample size, that is, for example, if the sample size is multiplied by 4, the standard error is divided by the square root of 4, which is 2.
Standard error of 52.4, sample size multiplied by 5. What is the standard error for the new sample size?
The standard error of 52.4 divided by the square root of 5. So
[tex]s = \frac{52.4}{\sqrt{5}} = 23.4[/tex]
The standard error for the new sample size is of 23.4.
The value of 33 + 42 = ___.
Numerical Answers Expected!
Answer for Blank 1:
[tex] \sf Q) \: {3}^{3} + {4}^{2} = {?}[/tex]
[tex] \sf \to \: {3}^{3} + {4}^{2} [/tex]
[tex] \sf \to \: 27 + 16= 43 [/tex]
Thus, the value is 43.
Consider the series ∑n=0∞54n. The sum of a series is defined as the limit of the sequence of partial sums, which means
(a) The n-th partial sum of the infinite series,
[tex]\displaystyle\sum_{n=0}^\infty\frac5{4^n}[/tex]
is
[tex]S_n = \displaystyle\sum_{k=0}^n\frac5{4^k} = 5\left(1+\frac14+\frac1{4^2}+\cdots+\frac1{4^n}\right)[/tex]
Multiplying both sides by 1/4 gives
[tex]\dfrac14S_n = \displaystyle\sum_{k=0}^n\frac5{4^k} = 5\left(\frac14+\frac1{4^2}+\frac1{4^3}+\cdots+\frac1{4^{n+1}}\right)[/tex]
Subtract this from [tex]S_n[/tex] and solve for [tex]S_n[/tex] :
[tex]S_n-\dfrac14S_n = 5\left(1-\dfrac1{4^{n+1}}\right)[/tex]
[tex]\dfrac34 S_n = 5\left(1-\dfrac1{4^{n+1}}\right)[/tex]
[tex]S_n = \dfrac{20}3\left(1-\dfrac1{4^{n+1}}\right)[/tex]
(your solution is also correct)
(b) The infinite sum is equal to the limit of the n-th partial sum:
[tex]\displaystyle\sum_{n=0}^\infty \frac5{4^n} = \lim_{n\to\infty} \boxed{\sum_{k=0}^n \frac5{4^k}}[/tex]
and the sum indeed converges to 20/3.
Choose the graph of y = 2 tan x.
Answer:
The image shows the graph of y = 2 tan x.
20 slips of paper are put into a bag numbered from 1 to 20. One slip is randomly selected from the bag. We are interested in selecting even numbers. What is the probability of selecting an even number from the bag?
Answer:
2/5
Step-by-step explanation:
Answer:
Step-by-step explanation:
There are 10 even numbers from 1 to 20
2 4 6 8 10 12 14 16 18 20
There 20 possible choices.
P(Even) = 10 /20 = 1/2
A farmer wants to build a rectangular pen and then divide it with two interior fences. The total area inside of the pen will be 264 square meters. The exterior fencing costs $15.60 per meter and the interior fencing costs $13.00 per meter. Find the dimensions of the pen that will minimize the cost.
Answer:
x = 12 m and y = 22 m
Step-by-step explanation:
Total area = 264 [tex]m^2[/tex]
∴ xy = 264
[tex]$y=\frac{264}{x}$[/tex] ............(1)
Cost function = [tex]C(x,y) = 2 x (15.60) + 2y(15.60) + 2x(13)[/tex]
[tex]C(x,y) = 57.2 x + 31.2y[/tex]
Therefore, using (1),
[tex]$C(x) = 57.2x+31.2 \left(\frac{264}{x} \right)$[/tex]
[tex]$C(x) = 57.2x+\frac{8236.8}{x} \right)$[/tex]
So, cost C(x) minimum where C'(x) = 0
[tex]$C'(x) = 57.2 - \frac{8236.8}{x^2}=0$[/tex]
[tex]$x^2=\frac{8236.8}{57.2}$[/tex]
[tex]$x^2=144$[/tex]
[tex]$x=12$[/tex] m
Therefore, [tex]$y=\frac{264}{x}$[/tex]
[tex]$=\frac{264}{12}$[/tex]
= 22 m
So the dimensions are x = 12 m and y = 22 m.
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.5 years with a standard deviation of 0.7 years. Step 2 of 2 : If a sampling distribution is created using samples of the ages at which 43 children begin reading, what would be the standard deviation of the sampling distribution of sample means
Answer:
[tex]S.E = 0.108[/tex]
Step-by-step explanation:
From the question we are told that:
Mean age [tex]\=x=5.5[/tex]
standard deviation [tex]\sigma= 0.7 years.[/tex]
Sample size [tex]n=43[/tex]
Generally the equation for Standard error is mathematically given by
[tex]S.E= \sigma \bar x[/tex]
[tex]S.E= \frac{\sigma}{\sqrt n}[/tex]
[tex]S.E= \frac{0.7}{\sqrt 43}[/tex]
[tex]S.E = 0.108[/tex]
A trough has ends shaped like isosceles triangles, with width 2 m and height 5 m, and the trough is 18 m long. Water is being pumped into the trough at a rate of 8 m3/min. At what rate (in m/min) does the height of the water change when the water is 2 m deep
9514 1404 393
Answer:
5/9 m/min
Step-by-step explanation:
The depth of the water is 2/5 of the depth of the trough, so the width of the surface will be 2/5 of the width of the trough:
2/5 × 2 m = 4/5 m
Then the surface area of the water is ...
A = LW = (18 m)(4/5 m) = 14.4 m²
The rate of change of height multiplied by the area gives the rate of change of volume:
8 m³/min = (14.4 m²)(h')
h' = (8 m³/min)/(14.4 m²) = 5/9 m/min
Find the slope of the line #67
difference between mutually exclusive
Answer:
A mutually exclusive event is when there are two events that can occur, such as flipping a coin, either it will be a head or a tail. Hence, both the events here are mutually exclusive.
An independent event is termed as an event that occurs without being affected by other events. The happening of one event has nothing to do with the happening of the other and there is no cause-effect between the two.
The wholesale price of 6 oz plastic bottles is 6 cents how many plastic bottles can be purchased for $98.41
Answer:
1640
Step-by-step explanation:
Take the total amount and divide by the amount for one
Make sure to write 6 cent in dollar form (.06)
98.41 / .06
1640.1666
Round down since we need to buy whole bottles
1640
Male Color Blindness When conducting research on color blindness in males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness (based on data from the National Institutes of Health).X Px0 0.6591 0.2872 0.0503 0.0044 0.0015 0+In determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Answer:
The sum of the probabilities of all possible outcomes is not 1, which means that a probability distribution is not given.
Step-by-step explanation:
We are given these following probabilities:
[tex]P(X = 0) = 0.6591[/tex]
[tex]P(X = 1) = 0.2872[/tex]
[tex]P(X = 2) = 0.0503[/tex]
[tex]P(X = 3) = 0.0044[/tex]
[tex]P(X = 4) = 0.0015[/tex]
Determine whether a probability distribution is given.
We have to see if the sum of the probabilities of all possible outcomes is 1. So
[tex]0.6591 + 0.2872 + 0.0503 + 0.0044 + 0.0015 = 1.0025[/tex]
The sum of the probabilities of all possible outcomes is not 1, which means that a probability distribution is not given.
Find the medien: 16,12,10,15,7,9,16
Answer:
12
Step-by-step explanation:
arrange the numbers in ascending order and cross out from either side till you have a middle line
FINAL ANSWER:
12
Step-by-step explanation:
Median is the middle number in the data set.
so first of ... we need to arrange the group of numbers from lower to greater.
16, 12, 10, 15, 7, 9, 16 ⇒ 7, 9, 10, 12, 15, 16, 16
Now that we have arranged the numbers from least to greatest all we need to do is to find the middle number of the data set (data set? they are the group of numbers)
Ok, so what you want to do here is to just count the numbers until you get to the middle number of the data set...
7, 9, 10, 12, 15, 16, 16
the median in the given data set is 12.
I hope this helps you!!! Let me know if my answer is incorrect or not...
HAVE A GREAT DAY AND GOD BLESS YOU ;)!!!
Britany wants to read a book. In her room, she has 5 mysteries, 15 historical fictions, 12 modern fantasies, and 7 blographies.
How many different choices are available?
pleaseee
Answer:
39
Step-by-step explanation:
5 + 15 + 12 + 7 = 39
Answer:
39
Step-by-step explanation:
5 + 15 = 20, 12 + 7 = 19, 20 + 19 = 39.
Simplify: 3.5 x 10^-2 + 2.3 x 10^-2
Given:
The given expression is:
[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]
It can be written as:
[tex]=(3.5+2.3)\times 10^{-2}[/tex]
[tex]=5.8\times 10^{-2}[/tex]
Therefore, the simplified form of the given expression is [tex]5.8\times 10^{-2}[/tex].
Michael drove 210 miles in 3 1/2. Jordan drove 330 miles in 6 hours. Which is an accurate comparison of the rates at which the two people drove?
Michael = 210 / 3.5 = 60 miles per hour
Jordan = 330/ 6 =55 miles per hour
Jordan drove 5 miles per hour slower than michael
Find the area of a circle having a radius of 9 cm
Answer:
81 pi cm^2
or approximately 254.34 cm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi (9)^2
A = 81 pi
Using 3.14 as an approximation for pi
A = 81 (3.14)
A =254.34 cm^2
Answer:
81pi cm^2
Step-by-step explanation:
formula : pi*r^2
pi*9^2
pi*81
What is the value of the expression (2x + y) (2x - y) when x = 4 and y = -5?
Answer:
39
Step-by-step explanation:
1. (2(4)-5)(2(4)+5)
2.(3)(13)
3.39
Answer:
Step-by-step explanation:
This is a difference of squares question. You should 64 = 25 = 39 Let's see if that happens.
Difference of squares
(2x - y) ( 2x + y) = 4x^2 - y^2
4(4)^2 - (5)^2
64 - 25 = 39
Now do the question exactly as it is written.
(2*4 - -5)(2*4 + -5)
(8 +5)(8 - 5)
3 * 13
39
They really do give the same answer.
Find the area of athletic field if it's length is 120cm and its width is 28cm .A. 397.6cm B. 3360cm C. 296 cm D. 4592cm E. 3356cm
Answer:
B 3360
Step-by-step explanation:
Area of Rectangle = Length X Width
120 X 28
= 3360 cm
Answered by Gauthmath
Select the correct answer.
Which is the minimum or maximum value of the given function?
dndnsn
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the function is not given. So, I will make an assumption.
A quadratic function is represented as:
[tex]f(x) = ax^2 + bx + c[/tex]
If [tex]a > 0[/tex], then the function has a minimum x value
E.g. [tex]f(x) = 4x^2 - 5x + 8[/tex] ------ [tex]4 > 0[/tex]
Else, then the function has a maximum x value
E.g. [tex]f(x)= -4x^2 -5x + 8[/tex] ---- [tex]-4 < 0[/tex]
The maximum or minimum x value is calculated using:
[tex]x = -\frac{b}{2a}[/tex]
For instance, the maximum of [tex]f(x)= -4x^2 -5x + 8[/tex] is:
[tex]x = -\frac{-5}{2*-4}[/tex]
[tex]x = -\frac{5}{8}[/tex]
So, the maximum of the function is:
[tex]f(x)= -4x^2 -5x + 8[/tex]
[tex]f(-\frac{5}{8}) = -4 * (-\frac{5}{8})^2 - 5 *(-\frac{5}{8}) +8[/tex]
[tex]f(-\frac{5}{8}) = 9.5625[/tex]
Which expression is equal to
(3x – 4)(2x – 5)?
Answer:
6x^2-23x+20
Step-by-step explanation:
i think the expanded form of that equation is equal to it.
(3x-4)(2x-5)
3x(2x-5)-4(2x-5)
6x^2-15x-8x+20
6x^2-23x+20
I hope this helps and sorry if it's wrong
The line l with equation x - 2y + 2 = 0 crosses the y-axis at the point P. The line
m with equation 3x + y - 15 = 0 crosses the y-axis at the point Q and intersects
l at the point R. Find the area of triangle PQR.
Answer:
Area of ΔPQR is 28 units²
Step-by-step explanation:
-P is the point with coordinates ( 0, y-intercept for line x-2y+2 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point P( 0, b)
x-2y+2 = 0, subtract x and 2 from both sides
-2y = -x-2, divide by -2 both sides
y= (1/2)x +1 so b=1 and P (0, 1)
-Q is the point with coordinates ( 0, y-intercept for line 3x+y -15 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point Q( 0, b)
3x +y -15 =0, subtract 3x and add 15 to both sides
y= -3x +15 so b=15 and Q(0,15)
-R is the intersection of the two lines so is the solution of the system of equations y= (1/2)x +1 and y= -3x +15
(1/2)x +1 = -3x +15, add 3x and subtract1
(1/2) x+3x = 15-1, combine like terms
(7/2)x = 14 , multiply both sides by 2
7x = 28, divide both sides by 7
x= 4
y= (1/2)x +1 = (4/2) +1 =3 so R(4,3)
- the area of ΔPQR is (base *height)/2
base= 15-1= 14
height = 4
A= (14*4)/2 = 14*2 = 28
Which of the following is the point and slope of the equation y + 14 = 7(x - 18)?
Answer:
y = 7x - 140
The slope is 7
The y-intersept is -140
= (7, -140)
Step-by-step explanation:
y + 14 = 7(x - 18)
y + 14 = 7x - 126
y =7x - 126 - 14
y = 7x - 140
