Answer:
The equation of the plane is
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 7y - 5z + 13 = 0
Step-by-step explanation:
Given 3 points, P(x₁, y₁, z₁), Q(x₂, y₂, z₂), and R(x₃, y₃, z₃).
We can calculate the equation of the plane through those points as
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0, where (x₀, y₀, z₀) are the coordinates of any one of the points P, Q, or R, and <a,b,c> is a vector perpendicular to the plane.
The vector perpendicular to the plane is obtained by writing vector PQ and PR and taking the cross or vector product.
For this question,
P = (5, 4, 5)
Q = (-5, -1, -4)
R = (-2, 1, -2)
PQ = (-5, -1, -4) - (5, 4, 5) = (-10, -5, -9)
= (-10î - 5ĵ - 9ķ)
PR = (-2, 1, -2) - (5, 4, 5) = (-7, -3, -7)
= (-7î - 3ĵ - 7ķ)
PQ × PR is then
| î ĵ ķ |
|-10 -5 -9|
|-7 -3 -7|
= î [(-5×-7) - (-9×-3)] - ĵ [(-10×-7) - (-9×-7)] + ķ [(-10×-3) - (-7×-5)]
= î (35 - 27) - ĵ (70 - 63) + ķ (30 - 35)
= 8î - 7ĵ - 5ķ
Hence, (a, b, c) = (8, -7, -5)
And using point P as (x₀, y₀, z₀) = (5, 4, 5)
The equation of the plane is
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 40 - 7y + 28 - 5z + 25 = 0
8x - 7y - 5z = 40 - 28 - 25 = -13
8x - 7y - 5z + 13 = 0
Hope this Helps!!!
Isabella averages 152 points per bowling game with a standard deviation of 14.5 points. Suppose Isabella's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(152,14.5)______.
If necessary, round to three decimal places.
Suppose Isabella scores 187 points in the game on Sunday. The z-score when x=187 is ___ The mean is _________
This z-score tells you that x = 187 is _________ standard deviations.
Answer:
The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.
Step-by-step explanation:
Problems of normally distributed samples are 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.
In this question:
[tex]\mu = 152, \sigma = 14.5[/tex]
The z-score when x=187 is ...
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{187 - 152}{14.5}[/tex]
[tex]Z = 2.41[/tex]
The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.
A rhombus is a quadrilateral with four congruent sides. The perimeter of rhombus WXYZ is less than 32 inches. Which inequality can be used to find all possible side lengths, s, for rhombus WXYZ? s squared greater-than 32 s squared less-than 32 4 s less-than 32 4 s greater-than 32
Answer:
4s< 32
Step-by-step explanation:
Congruent sides mean they are all the same length
Let the length be s
Perimeter means add the sides
s+s+s+s < 32
4s< 32
Answer:
4s>32
Step-by-step explanation:
your welcome dears
12
? Select three options.
Which phrases can be represented by the algebraic expression
W
12 divided by a number
the quotient of 12 and a number
a number divided by 12
a number divided into 12
the product of 12 and a number
Answer:
Step-by-step explanation: its 24
1,2,5
Step-by-step explanation:
Pernyataan berikut yang benar adalah ....
A. Garis bagi membagi sisi menjadi dua sama panjang
B. Garis bagi membagi sudut menjadi dua sama besar
C. Garis berat membagi sudut menjadi dua sama besar
D. Garis tinggi membagi sudut menjadi dua sama besar
Assume that the probability of a driver getting into an accident is 7.1%, the
average cost of an accident is $14,886.05, and the overhead cost for an
insurance company per insured driver is $110. What should the driver's
insurance premium be?
O A. $1276.27
O B. $1242.93
O C. $1165.49
O D. $1156.43
Answer:
C - $1165.49
Step-by-step explanation:
We have that the probability of a driver getting into an accident = 7.1% i.e. 0.071.
Now, the average cost of an accident = $14,886.05
Then, the expected cost of an accident = $14,886.05 × 0.071 = $1056.91
As, the overhead cost for insurance = $110
Therefore, the driver's insurance premium = $1056.91 + $110 = $1166.91
Since, the closest option to $1166.91 is option C.
Hence, the driver's insurance premium will be $1165.49.
the driver's insurance premium will then be,
⇒ $1166.91
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Now, The following can be deduced from the question:
Average cost of an accident = $14,886.05
Probability of a driver getting into an accident = 7.1%
= 7.1/100
= 0.071.
Overhead cost for insurance = $110
Therefore, the expected cost of an accident will be calculated as:
= Average cost of an accident × Probability of a driver getting into an accident
= $14,886.05 × 0.071
= $1056.91
Therefore, the driver's insurance premium will then be:
= $1056.91 + $110
= $1166.91
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ5
Which is equivalent to 8−+3
8
x
-
y
+
3
x
?
Answer:
DIDNT UNDERSTAND THE QUESTION PROPERLY BRO..
KEEP THE QUESTION AGAIN
is 7.68 bigger than 7.680
Answer:
literally 7.68=7.680
The population of Boomtown is currently 3000 and expected to grow by 2.3% over the
next year. What will its population be by then?
The population of Dullsville, on the other hand, is currently 13000 and expected to
decrease by 4.1% over the next year. What will its population be by then?
Answer:
a) The Expectation of the Population to grow in the next year
= 3069
b) The Expectation of the Population decrease in the next year
= 12,467
Step-by-step explanation:
Explanation:-
a)
The population of Boom town is currently 3000
Given expected to grow by 2.3 % over the next year
= [tex]3000 X \frac{2.3}{100} = 69[/tex]
= 69
The Expectation of the Population growth in the next year
= 3000 +69 = 3069
b)
The population of town is currently 13000
Given expected to grow by 4.1 % over the next year
= [tex]13000 X \frac{4.1}{100} = 533[/tex]
The Expectation of the Population decrease in the next year
= 13000 - 533 = 12,467
HI!!! CAN SOMEONE HELP ME ON GRAPHING THIS? THANKS, i WILL GIVE YOU 5 STARS AND OTHERS: f(x) = sin(x) – 5
Answer:
The graph is shown below.
Step-by-step explanation:
The trigonometric expression is:
[tex]f(x)=sin\ (x)-5[/tex]
The general form is:
[tex]f(x)=a\ \text{sin}\ (bx-c)+d[/tex]
Comparing the two expression we know:
a = 1
b = 1
c = 0
d = -5
Compute the value of amplitude, |a | as follows:
[tex]\text{Amplitude}=|a|=|1|=1[/tex]
Compute the period of the function as follows:
[tex]\text{Period}=\frac{2\pi}{|b|}=\frac{2\pi}{|1|}=2\pi[/tex]
Compute the phase shift as follows:
[tex]\text{Phase Shift }=\frac{c}{b}=\frac{0}{1}=0[/tex]
The vertical shift is:
[tex]\text{Vertical Shift}=d=-5[/tex]
The properties of the trigonometric function are:
Amplitude = 1
Period = 2π
Phase shift = 0
Vertical shift = -5
Plot the graph of the trigonometric function by selecting a few points.
x : [tex]0[/tex] [tex]\frac{\pi}{2}[/tex] [tex]\pi[/tex] [tex]\frac{3\pi}{2}[/tex] [tex]2\pi[/tex]
f (x) : -5 -4 -5 -6 -5
The graph is shown below.
The functions s and t are defined as follows. s(x)=3x-4 t(x)=-5x+3 Find the value of s(t(-1)).
t(x)=-5x+3
t(-1)=-5*(-1)+3=5+3=8
s(x)=3x-4
s(t(-1))=s(8)=3*8-4=24-4=20
answer is 20
What is the vertex of f(x) = |x+ 8|– 3?
(-8, -3)
(-8,3)
(8, -3)
(8,3)
Answer:
The vertex is at (-8,-3)
Step-by-step explanation:
The function is of the form
y = a|x-h| + k where (h,k) is the vertex
f(x) = |x+ 8|– 3
f(x) = |x - - 8|– 3
The vertex is (-8,-3)
Determine the interest earned on a 3 and 1/4 year investment of $2880 at a rate of 4.5%
Answer:
The interest earned is $421.2.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
In this question:
[tex]P = 2880, I = 0.045, t = 3 + \frac{1}{4} = 3.25[/tex]
So
[tex]E = P*I*t[/tex]
[tex]E = 2880*0.045*3.25[/tex]
[tex]E = 421.2[/tex]
The interest earned is $421.2.
How many days are there in 12 weeks? Use the following information to convert this time to days. 1 week = 7 days
Answer:
84days
Step-by-step explanation:
1 week = 7days =>12 weeks = 12×7 = 84days
Answer:
84 days are in 12 weeks
Step-by-step explanation:
1 week = 7 days
4 weeks = 28 days
So 28 + 28 + 28 = 84 days
The energy, E, of a body of mass m moving with speed v is given by the formula below. The speed is nonnegative and less than the speed of light, c which is constant. Use lower case letters here. E = mc^2 (1/Squareroot1 - v^2/c^2 - 1)
(a) Find E/m = c^2Squareroot1 - v^2/c^2 - c^2/1 - v^2/c^2 what is the sign of this partial? Positive negative
(b) Find E/v =?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]\frac{\delta E}{\delta m}= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ][/tex]
b
[tex]\frac{\delta E}{\delta V} = \frac{mc^3 v}{(c^2 - v^2 )^{\frac{3}{2} }}[/tex]
Step-by-step explanation:
From the question we are given
[tex]E = mc^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } }- 1 ][/tex]
So we are asked to find [tex]\frac{\delta E}{\delta m}[/tex]
Now this is mathematically evaluated as
[tex]\frac{\delta E}{\delta m} = \frac{\delta }{\delta m} [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 )][/tex]
[tex]= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2 } } } -1 ] \frac{\delta m}{\delta m}[/tex]
[tex]= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ][/tex]
Also we are asked to find [tex]\frac{\delta E}{\delta V}[/tex]
Now this is mathematically evaluated as
[tex]\frac{\delta E}{\delta V} = \frac{\delta }{\delta v } [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } - 1 )][/tex]
[tex]\frac{\delta E}{\delta V} = mc^2 [\frac{\delta }{\delta v} (\frac{c}{\sqrt{c^2 -v^2} } - 1 )][/tex]
[tex]= mc^2 [c* [\frac{\delta }{\delta v} (c^2 - v^2 )^{-\frac{1}{2} }] - 0][/tex]
[tex]= mc^3 [- \frac{1}{2} (c^2 - v^2 )^{-\frac{3}{2} } * (-2v)][/tex]
[tex]= \frac{mc^3 v}{(c^2 - v^2 )^{\frac{3}{2} }}[/tex]
5. (03.02 MC)
If f(x) = 2х2 - 30, find f(4). (1 point)
НА
Мен
ка
ООО
Амер
-14
2
o17
Answer:
f(4) =2
Step-by-step explanation:
f(x) = 2х^2 - 30,
Let x=4
f(4) = 2 (4)^2 -30
= 2*16 -30
=32-30
= 2
What is the general form of this equation:
The line passes through the point (-2,4) with a slope -2/3
Answer: y= -2/3 + 8/3
Step-by-step explanation:
-2/3 is the slope so you just need the y-intercept to write the equation in general form or slope intercept form
4= -2/3(-2) +b
4 = 4/3 + b
-4/3 -4/3
b= 8/3
general form is y= -2/3 + 8/3
A soccer league has 180 players. Of those players 50% are boys. How many boys are in the soccer league?
Answer:
90 boys
Step-by-step explanation:
There are 180 players
Multiply by the percent that are boys to find the number of boys
180 * 50%
180 * .50
90
Answer:
90 boys
Step-by-step explanation:
The soccer league has 180 players, and 50% or half are boys.
Multiply the total number of players in the league by the percent that are boys.
total number of players * percent of boys
180* 50%
Convert 50% to a decimal by dividing by 100, or moving the decimal place 2 spaces to the left.
50/100=0.50
50.0–>5.0–>0.50
180*0.50
Multiply
90
There are 90 boy soccer players in the league.
Wisconsin Public Radio wants to duplicate a survey conducted in 2011 that found that 68% of adults living in Wisconsin felt that the country was going in the wrong direction. How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 3%? Be sure to show all your work and round appropriately
Answer:
655 people would need to be surveyed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
In this question, we have that:
[tex]\pi = 0.68[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 3%?
We need to survey n adults.
n is found when M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.68*0.32}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.68*0.32}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.68*0.32}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645\sqrt{0.68*0.32}}{0.03})^{2}[/tex]
[tex]n = 654.3[/tex]
Rounding up
655 people would need to be surveyed.
Which value of a in the exponential function below would cause the function to shrink? f(x) = a(three-halves) Superscript x Four-fifths Five-fourths Three-halves Seven-fourths
Answer:
Four-fifths
Step-by-step explanation:
As we know that
By multiplying the function by a constant, we may expand or shrink the function in the y-direction.
Now we have
[tex]y=a(b^{x})[/tex]
if [tex]a> 1[/tex] > the function would enlarge
if [tex]0< a < 1[/tex] > the function would shrinks
Now
For case A
[tex]a = \frac{4}{5}[/tex]
[tex]0 < (\frac{4}{5} )< 1[/tex] ....... > the function would shrinks
For case B
[tex]a = \frac{5}{4}[/tex]
[tex](\frac{5}{4} )>1[/tex] .......> the function would enlarge
For case C
[tex]a = \frac{3}{2}[/tex]
[tex](\frac{3}{2} )>1[/tex] .........> the function would enlarge
For case D
[tex]a = \frac{7}{4}[/tex]
[tex](\frac{7}{4} )>1[/tex] .........> the function would enlarge
Therefore the second option is correct
Answer: 4/5
Step-by-step explanation: E2020
What is the MEDIAN of this data?
Answer:
I think the median is 7
if it is not im so sorry
The median of the data is 7.
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
If an icecream cone starts at $2 and an additional $0.50 for each scoop, what is
the cost of a 3-scoop cone?
Answer:
$3.50
Step-by-step explanation:
$2 + (3 x $0.50) = x
$2 + $1.50 = x
x = $3.50
Answer:$3:50
Step-by-step explanation: 2+0.50+0.50=3+0.50=$3.50
Which of the options is the response variable?
A. The number of adults.
B. The type of training exercises performed by each participant.
C. The size of the physiological blind spot.
D. The number of times an adult performed training exercises.
Question:
The physiological blind spot refers to a very small zone of functional blindness in the eye where the optic nerve passes through the retina. We do not notice it because our nervous system compensates for it. Can eye training reduce the size of a person's physiological blind spot? Researchers recruited a representative sample of 10 adults with normal vision. Each participant performed training exereises with one eye for three weeks. The size of the physiological blind spot was measured (in degrees of visual angle squared) with a motion detection task both prior to training and again after the training was completed. Which of the options is the response variable?
A) The size of the physiological blind spot
B) The number of adults.
C) The type of training exercises performed by each participant.
D) The size of the physiological blind spot.
E) The number of times an adult performed training exercises.
Answer:
The correct answer is A)
Explanation:
The response variable (when experimenting) is the variable or factor about which the researcher is concerned. It can also be (as the name entails) the variable which respond to changes in the experiment.
The changes in the experiment is the training. The variable which the researcher is concerned about and which may or may not change with the introduction of training is the size of the physiological blind spot.
Cheers!
can someone help me please? its urgent
Answer:
Step-by-step explanation:
Answer:
972^1/4 = 4 ⁴√3
448^1/3 = 4 ³√7
3528^1/2 = 42√2
4050^1/4 = 3 ⁴√50
Hope this helps.
Which statements are true?
If all angles of a quadrilateral are right angles, then the quadrilateral must be a square.
Two shapes are similar if and only if their corresponding angles are equal.
All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180º.
if the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus.
There are three vertices in a triangle, or there are four sides in a pentagon.
Any two triangles are either similar or congruent.
Answer:
Step-by-step explanation:
1) If all angles of a quadrilateral are right angles, then the quadrilateral must be a square. This is not true because the quadrilateral can also be a rectangle.
2) Two shapes are similar if and only if their corresponding angles are equal. This is true.
3) All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180º. This is false because the sum of the angles is 360°
4) if the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus. This is true.
5) There are three vertices in a triangle, or there are four sides in a pentagon. This is false because a Pentagon has 5 sides.
6) Any two triangles are either similar or congruent. This is not true. Congruent triangles are always similar
Therefore, the true statements are 2 and 4
Answer:
its B and D
Step-by-step explanation:
Suppose you buy a CD for $500 that earns 3% APR and is compounded quarterly. The CD matures in 3 years. Assume that if funds are withdrawn before the CD matures, the early withdrawal fee is 3 months' interest. What is the early withdrawal fee on this account?
Answer:
$3.75
Step-by-step explanation:
I = Prt
I = $500·0.03·(3/12) = $3.75
The early-withdrawal fee is $3.75 for the first quarter.
_____
Each quarter after that, the principal amount will be larger, so the interest penalty will be larger. The fee would be the amount of interest that would be credited at the end of the next quarter, or at the end of the quarter currently in progress.
Distribute and simplify these radicals. square root of 60
Answer:
2 sqrt(15)
Step-by-step explanation:
sqrt(60) = sqrt(4*15) = 2 sqrt(15)
What is the mode of this set of data?
Answer:
The mode is 15
Step-by-step explanation:
The mode is the number which appears most often in a set of numbers. Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often).
Answer:
The mode of this set is 15.
Step-by-step explanation:
the mode is 15 bcoz 15 is repeated two times where as other numbers aren't repeated..
Quinn used a scale drawing to build a soccer field near his school. Initially, he wanted the field to be 28 yards long and 17.5 yards wide. He decided to change the length of the field to 36 yards.
If the width is to be changed by the same scale factor, what is the new width of the field? Express your answer to the nearest tenth.
18.5
22.5
25.5
57.6
Answer:
So the answer is going to be B. AKA 22.5
Step-by-step explanation:
I took the test on ed and got this answer right! hth (hope this helps)
Answer:
B, second option, 22.5
Step-by-step explanation:
1.)because
2.)i'm
3.)kinda
4.)smart
answer=22.5:))))))))
Solve 23 - Q >-3(2-6)
Answer:
q < 11
Step-by-step explanation:
Distribute the -3
23 - q > 12
Add q and subtract 12
q < 11
Step-by-step explanation:
the answer is
q<11
23-q>12
A campaign strategist wants to determine whether demographic shifts have caused a drop in allegiance to the Uniformian Party in Bowie County. Historically, around 62% of the county's registered voters have supported the Uniformians. In a survey of 196 registered voters, 57% indicated that they would vote for the Uniformians in the next election. Assuming a confidence level of 95% and conducting a one-sided hypothesis test, which of the following should the strategist do?
a. Accept the hypothesis that the proportion of Uniformian voters has not changed.
b. Accept the hypothesis that the proportion of Uniformian voters has decreased.
c. Conclude that the proportion of Uniformian voters is now between 56% and 62%.
d. There is not enough evidence to support the hypothesis that the proportion of Uniformian voters has decreased.
Answer:
d. There is not enough evidence to support the hypothesis that the proportion of Uniformian voters has decreased.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that there is a significant drop in allegiance to the Uniformian Party in Bowie County.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.62\\\\H_a:\pi<0.62[/tex]
The significance level is 0.05.
The sample has a size n=196.
The sample proportion is p=0.57.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.62*0.38}{196}}\\\\\\ \sigma_p=\sqrt{0.001202}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.57-0.62+0.5/196}{0.035}=\dfrac{-0.047}{0.035}=-1.369[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.369)=0.0855[/tex]
As the P-value (0.0855) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that there is a significant drop in allegiance to the Uniformian Party in Bowie County.