A reflection over a line l moves every point P of the plane to the point P ′ on the perpendicular from P to the line l and on the same distance from l .
If the line is the x -axis, a point P = ( p 1 p 2 ) moves to the point P ′ = ( p 1 , − p 2 ) .
The image of the triangle A B C is the triangle A ′ B ′ C ′ with B ′ = ( 9 , − 5 )
The article "Snow Cover and Temperature Relationships in North America and Eurasia"† used statistical techniques to relate the amount of snow cover on each continent to average continental temperature. Data presented there included the following ten observations on October snow cover for Eurasia during the years 1970-1979 (in million km2): 6.5 12.0 14.9 10.0 10.7 7.9 21.9 12.5 14.5 9.2 What would you report as a representative, or typical, value of October snow cover for this period, and what prompted your choice?
Answer:
Step-by-step explanation:
From the given information,
The ten observation data on october snow cover for Eurasia during the years is 6.5, 12.0, 14.9, 10.0, 10.7, 7.9, 21.9, 12.5, 14.5, 9.2
What would you report as a representative, or typical, value of October snow cover for this period, and what prompted your choice?
For the given data, 21.9 is an outlier, so trimmed mean would be good choice for the researcher,
Remove the smallest and the largest values to compute the trimmed mean
[tex]\bar x = \frac{12.0+14.9+10.0+10.7+7.9+12.5+14.5+9.2}{8} \\\\=\frac{91.7}{8} \\\\=11.465[/tex]
A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares.
Once George has put rice on the 10th square, he has placed a total of _____ grains of rice on the chess board.
Hey there! I'm happy to help out!
As you can see, our number keeps on doubling. It's like 2×2×2×2.... so on and so forth. Whenever we multiply a number by itself, we can model it as an exponent, so if we had 2², it is two twos being multiplied, and 2×2=4. If it was 2³, it would be 2×2×2=8.
However, we have a one. This signifies a starting point and exponents have our back. Anything to the 0th power is always equal to one! So, this situation would look something like this:
[tex]2^0, 2^1, 2^2, 2^3,2^4,... etc.[/tex]
So, for the second square, we are going to the first power. For the fourth square it's going to the third power. Therefore, the 10th square will be the 9th power!
[tex]2^9=[/tex] 2×2×2×2×2×2×2×2×2= 512
However, we want to find how much he has done in total! So, let's find how much he did on the other squares!
[tex]2^8[/tex]= 256
[tex]2^7[/tex]=128
[tex]2^6[/tex]=64
[tex]2^5[/tex]=32
[tex]2^4[/tex]=16
2³=8
2²=4
[tex]2^1[/tex]=2
[tex]2^0[/tex]=1
Now, we add these all up to find the total grains of rice!
512+256+64+32+16+8+4+2+1=895
Therefore, George has placed a total of 895 grains of rice on the chess board.
I hope that this helps! Have a wonderful day!
Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
We have,
On the first square, George placed 1 grain of rice.
On the second square, he placed 2 grains.
On the third square, he placed 4 grains.
On the fourth square, he placed 8 grains.
In general, on the nth square, he places [tex]2^{n-1}[/tex] grains.
So,
On the first 10 squares,
1 + 2 + 4 + 8 + ... + [tex]2^9[/tex]
This is a geometric series with a first term of 1 and a common ratio of 2.
The sum of the first n terms of a geometric series.
[tex]S_n[/tex] =[tex]a(1 - r^n) / (1 - r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
Substituting the values,
[tex]S_{10}[/tex] = 1(1 - 2^10) / (1 - 2)
= 1(1 - 1024) / (-1)
= 1023
Therefore,
Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.
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Which expressions are equivalent to 7.7.7.7.7.7 ?
Answer:
1.84877
Step-by-step explanation:
tnvvvvvvvvvvv4kvjk5nvj5tnnjt5
Answer:
A and C
Step-by-step explanation:
Evaluate each geometric
series described
3 + 6 +12 + 24 n=7
F(4) =
if g(x) = 2, x =
Answer:
Shown from the explanation below..
Step-by-step explanation:
From the graph, it's a graph with a vertex hence its a quadratic equation without
When g(X)=2; x=0
F(4) =-10; from x=4 on the graph of f(x)
The required value of f(4) = -10, value of function evaluated from the graph.
A graph has been shown of f(x) and g(x).
g(x) = 2 is given and f(4) is to determine with the help of the graph.
The graph is a demonstration of curves which gives the relationship between x and y axis.
The graph has been shown to find the value of f(x) coordinates located on the curve for every x on the number line of the x-axis.
In manner to locate f(4) draw the verticle from x = 4 the intersect at cover f(x)(yellow point). Now, draw the horizontal line from the yellow mark the line intersects at y = -10 on the y axis. i.e.
f(4) = -10
Thus, the required value of f(4) = -10, value of function evaluated from the graph.
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Let T: R^3 --> R^3 be a linear transformation. Let {v1, v2, v3} be a set of linearly dependent vectors in R^3. Show that the set {T(v1), T(v2), T(v3)} is also linearly dependent.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
She used 25 equally sized stones to make a path that is 12 feet long. How long is each stone
Answer:
The length of each stone is
L = 12/25 = 0.48 ft
Hope this helps!
:)
Each stone measures 0.48 feet.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here, the number of stones is 25 and it is used to construct 12 feet long then measure of each stone =12/25
=0.48 feet
Hence, Each stone measures 0.48 feet.
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You roll two dice. How many ways can you
roll a sum of 8 or a sum of 10?
Answer:
5 different ways
Step-by-step explanation:
for the 8
2 and 6
3 and 5
4 and 4
for then tens
5 and 5
4 and 6
PLZ HELP ...............
Answer:
Centimeters Mapped: 8.4 cm
Step-by-step explanation:
Let us plan out our steps, and solve for each:
1. If we want to determine the cm of the route on the map, let us first convert 2.1 kilometers ⇒ centimeters: 2.1 km = 210,000
2. Given such, let us create a proportionality as such:
1 = 25,000 ⇒ x - route in cm mapped out
x 210,000
3. Now let us cross multiply, and solve through simple algebra:
210,000 = 25,000 * x,
x = 8.4 centimeters marked by a route on the map
According to the Florida Agency for Workforce, the monthly average number of unemployment claims in a certain county is given by ????????(tt) = 24.31tt2 − 276.58tt + 2035, where t is the number of years after 1990. a) During what years did the number of claims decrease? b) Find the relative extrema and interpret it.
Answer:
a) The number of claims decrease from 1990 to 1996.
b) The relative extrema is a minimum and happens approximately in 1996 (t=5.688). This means the moment when the number of claims stop decreasing and start to increase.
Step-by-step explanation:
The monthly average number of unemployment claims in a certain county is given by:
[tex]C(t)=24.31t^2-276.58t+2035[/tex]
With t: number of years after 1990.
We have to determine in what years the number of claims decrease and the relative extreme value.
We can find this by analizing the first derivative.
When the first derivative is equal to zero, this indicates an extreme value, which can be a maximum or minimum.
When the first derivative is positive, it indicates that the function is increasing. On the contrary, when the first derivative is negative, it indicates that the function is decreasing.
The first derivative is:
[tex]\dfrac{dC}{dt}=24.31(2t)-276.58(1)+0\\\\\\\dfrac{dC}{dt}=48.62t-276.58[/tex]
Then, we can calculate the extreme value:
[tex]\dfrac{dC}{dt}=48.62t-276.58=0\\\\\\48.62t=276.58\\\\\\t=\dfrac{276.58}{48.62}=5.688\approx 6[/tex]
This extreme value happens for t=6 (year 1996).
If we calculate the value of the first derivative for t=5, that is previous to the extreme value, we can find if the function was increasing or decreasing:
[tex]\dfrac{dC}{dt}(5)=48.62*5-276.58=243.10-276.58=-33.48<0[/tex]
As the value is negative, we know that the number of claims was decreasing from t=0 to t=6 (from 1990 to 1996), and then reach a minimum and start to increase from them (from 1996 onwards).
5. Refer to the image in question #2. Determine whether the following
statement is true or false, "If the front base edge of the rectangular prism is
decreased by 1 inch, it will hold more than the triangular prism."*
True
False
What’s the correct answer for this?
Answer:
(A)
Step-by-step explanation:
Using the formula :
Area = 1/2 [-1(1 - 6) -7(6 - 1) -3(1 - 1)]
Area = 1/2 [5 - 35]
Area = 1/2 × -30 = |-15| = 15 units²
Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6.
Write a probability model for this experiment, and use the probability model to predict how many times Stacy would spin a 6 if she spun 50 times. Give the probabilities as decimals, rounded to 2 decimal places
Answer:
Hence, Stacy will spin 6, 8.33 times out of her n = 50 attempts.
Step-by-step explanation:
Let us consider a success to get a 6. In this case, note that the probability of having a 6 in one spin is 1/6. We can consider the number of 6's in 50 spins to be a binomial random variable. Then, let X to be the number of trials we get a 6 out of 50 trials. Then, we have the following model.
We will estimate the number of times that she spins a 6 as the expected value of this random variable.
Recall that if we have X as a binomial random variable of n trials with a probability of success of p, then it's expected value is np.
Then , in this case, with n=50 and p=1/6 we expect to have number of times of having a 6, which is 8.33.
$2,000 at 9% simple interest; deposit $1,600
oops sorry.
180 was the 9% interest.
Evaluate the log by thinking “3 to what power is 1/9 so log3(1/9) =
Answer:-2
Step-by-step explanation:
Log3(1/9)
Log(1/9) ➗ Log3
Log(1/3^2) ➗ Log3
Log3^(-2) ➗ Log3
-2Log3 ➗ Log3
-2(Log3 ➗ Log3)
-2
The solution of the expression by taking a log is, log₃ (1/9) = - 2
Used the formula for the logarithmic function,
log₃ (a)ⁿ = n log₃ (a)
log₃ (3) = 1
Given that,
The logarithmic function is,
log₃ (1/9)
It can be written as,
log₃ (3⁻²)
Since, log₃ (a)ⁿ = n log₃ (a)
So, we get;
- 2 log₃ (3)
- 2 × 1
- 2
Therefore, the solution is - 2.
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The area of a rectangular wall of a barn is 171 square feet . It’s length is 10 feet longer than the width . Find the length and width of the wall of the barn
Answer:
10 x 17.1 = 171
Step-by-step explanation:
10 x 17.1 = 17.1
If a coin is flipped three times, how many possible outcomes will include exactly 2 tails?
Answer:
If a coin is flipped three times, possible outcomes would be:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
=> possible outcomes that will include exactly 2 tails:
HTT
THT
TTH
TTT
Hope this helps!
:)
Answer:
The answer is 3 or option B.
Step-by-step explanation:
I just answered the question.
Determine two pairs of polar coordinates for (4,4) when 0° < θ < 360°
a(4√2, 45°), (-4√2, 225°)
b(4√2, 315°), (-4√2, 135°)
c(4√2, 135°), (-4√2, 315°)
d(4√2, 225°), (-4√2, 45°)
Answer: option a.
Step-by-step explanation:
In polar coordinates we have that:
x = r*cos( θ)
y = r*sin( θ)
we know that x = 4 and y = 4. now let's analyze the options:
a) x = 4√2*cos(45°) = 4 nice.
y = -4√2*sin(225°) = 4 nice
Option a is correct
b) x = 4√2*cos(315°) = 4 nice
y = -4√2*sin(135°) = -4 incorrect
option b is not correct
c) x = 4√2*cos(135°) = -4 incorrect
Option c is not correct
d) x = 4√2*cos(225°) = -4 incorrect
option d is not correct
Solve (x + 6)2 = 64.
Answer:
x=26
Step-by-step explanation:
(x+6)2=64
x+6=32
x=26
Answer:
Here is the solution. Mark as brainlist please.
the angle measurements in the diagram are represented by the following expressions
Answer:
x = 12
∠A = 144
Step-by-step explanation:
+ We have: ∠A = ∠C (alternate interior)
∠D = ∠C ( vertically opposite angles)
=> ∠A = ∠C (because = ∠C)
=> 10x + 24 = 6x + 72
=> 10x - 6x = 72 - 24
4x = 48
x = 12
+ ∠A = 10x + 24
∠A = 10 x 12 + 24
∠A = 144
In the phrase “rise over sun” shat does “rise” indicate?
ASAP PLEASE
simplify the equation
Answer:
Option A is correct
Step-by-step explanation:
a^(6/4) = a^(3/2)
b^(4/4) = b
c^(8/4) = c^2
Hope this helps!
:)
Simplify (-2x^3)2•y•y^9
Simplify (-2x^3)^2 •y•y^9 Answer 4x^6y^10
The linear plot shows how water pressure changes as a diver's depth increases. What is the best
description of the effect on the water pressure experienced by a diver based on the diver's depth?
Water Pressure vs. Depth
For overy 33 feet a diver descends, the pressure
increases by 1 atmosphere.
Pressure
(in atmospheres)
Nex
For every 33 feet a diver ascends, the pressure
increases by 1 atmosphere.
For every 33 units of increase in atmospheric
pressure, the diver ascends by 1 foot.
25 50 75
Depth (in feet)
100 x
For overy 33 units of increase in atmospheric
pressure, the diver descends by I foot.
The solution is Option A.
The slope of the equation is 1/33 and For every 33 feet a diver descends, the pressure increases by 1 atmosphere
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the first point be A
The value of A = A ( 0 , 1 )
Let the second point be = B
The value of B = B ( 100 , 4 )
Now , the slope of the points of the line is given by the equation
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 4 - 1 ) / ( 100 - 0 )
Slope m = 3 / 100
Slope m = 1/33
Therefore , the value of slope of the line is 1/33
And , when the diver swims a depth of 33 feet , the atmospheric pressure increases by 1
Hence , The slope of the equation is 1/33 and For every 33 feet a diver descends, the pressure increases by 1 atmosphere
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Answer:
For every 33 feet a diver descends, the pressure increases by 1 atmosphere
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
the answer is either x=√3+5 or -√ 3+5
Step-by-step explanation:
split it into 2 equations
Answer:
(x-5)(x-5) =3
X^2 -5x -5x +25 = 3
x^2 -10x +22 = 0
x1 = (-b + sqrt(b^2 - 4ac))/2a
a=1
b=-10
c= 22
x1 = (10 +sqrt((-10)^2- 4(1)(22))/2(1)
x1 = (10 + sqrt(100-88))/2
x1= (10 + sqrt(22))/2
x1= (10 + sqrt(4) x sqrt(3))/2
x1=(10 + 2 x sqrt(3))/2
x1 =5 +sqrt(3)
x2 = (-b - sqrt(b^2 - 4ac))/2a
x2 = 5 - sqrt(3)
Answer is C
Step-by-step explanation:
Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A1 be the event that the receiver functions properly throughout the warranty period, A2 be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A1)= .95, P(A2) = .98, and P(A3) = .80.a. What is the probability that all three components function properly throughout the warranty period?b. What is the probability that at least one component needs service during the warranty period?c. What is the probability that all three components need service during the warranty period?
Answer:
that is alot the prob. is 20
Step-by-step explanation:
Write the formula for absolute value function if its graph has the vertex at point (0,6) and passes through the point (−1,−2).
Answer:
y = -8|x| + 6
Step-by-step explanation:
y = a|x-b| + c; (b,c) = vertex and a = constant
y = a|x-0| + 6 -->
y = a|x| + 6 -->
-2 = a|-1| + 6 -->
-2 = a + 6 -->
-8 = a -->
y = -8|x| + 6
What is the fractionation of X2 - 6X + 5
Answer:
(x -1)(x -5)
Step-by-step explanation:
We recognize that 6 is the sum of the factors of 1·5, so we can write the factorization as ...
x^2 -6x +5 = (x -1)(x -5)
_____
The product of factors will be ...
(x +a)(x +b) = x^2 +(a+b)x +ab
So, the binomial constants "a" and "b" are factors of the trinomial constant that have a sum equal to the coefficient of the linear term. Here, those are factors of +5 that have a sum of -6. The factors of interest are -1 and -5: 5 = (-1)(-5); -6 = (-1) +(-5).
I really need some help............!!!!!!!!!
Answer:
1.25
Step-by-step explanation:
Answer:
1.25 cm
Step-by-step explanation:
The blow up snow flake is 15 cm
The blow up ratio is 12 to 1
Divide the 15 cm by 12 to determine the size in real life
15/12 =1.25 cm
A dietician believes that people who eat a high-fiber cereal as part of their breakfast will consume, on average, fewer calories at lunch than people who do not eat a high-fiber cereal as part of their breakfast. To test this claim, he measured the lunchtime calorie intake of 49 adults who did eat a high-fiber cereal for breakfast on a given day (group 1). For those individuals, the average number of calories consumed at lunch was 609.86, with a standard deviation of 55.96 calories. He also measured the lunchtime calorie intake of 78 adults who did not eat a high-fiber cereal for breakfast on a given day (group 2). For those individuals, the average number of calories consumed at lunch was 641.02, with a standard deviation of 109.14 calories. The dietician wishes to test this claim at the 5% significance level.
If Welch's two-sample test for equality of means is used, then what is the value of the test statistic tobs, rounded to two decimal places?
Answer:
The calculated value Z = 1.8368 < 1.96 at 0.05 level of significance
The null hypothesis is accepted
The samples have been drawn from the same Population
Step-by-step explanation:
Step(i):-
Given first sample size 'n₁' = 49
Mean of the first sample 'x₁⁻ = 609.86
Standard deviation of the sample S₁ = 55.96 calories
Given first sample size 'n₂' = 78
Mean of the first sample 'x₂⁻ = 641.02
Standard deviation of the sample S₂ = 109.14 calories
Step(ii):-
Null hypothesis : H₀: x₁⁻ = x₂⁻
Alternative Hypothesis : H₁: x₁⁻ ≠ x₂⁻
Level of significance ∝ = 0.05
Test statistic
[tex]Z = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{S.D^2(\frac{1}{n_{1} } }+\frac{1}{n_{2} } }[/tex]
where
[tex]S.D^{2} = \frac{n_{1} S^2_{1}+ n_{2} S^2_{2} }{n_{1} + n_{2} -2}[/tex]
[tex]= \frac{49 X (55.96)^2+ 78X(109.14)^2 }{49 + 78 }[/tex]
σ² = 8660.357
Step(iii):-
Test statistic
[tex]Z = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{S.D^2(\frac{1}{n_{1} } }+\frac{1}{n_{2} } }[/tex]
[tex]= \frac{ 609.86-641.02 }{\sqrt{8660.357(\frac{1}{49 } }+\frac{1}{78 } ) }[/tex]
[tex]Z = \frac{-31.16}{16.9638} = -1.8368[/tex]
|Z| = |-1.8368| = 1.8368
The tabulated value Z₀.₉₅ = 1.96
The calculated value = 1.8368 < 1.96 at 0.05 level of significance
The null hypothesis is accepted
Final answer:-
The samples have been drawn from the same Population
