The amount of money in the account after 10 years is $278,814.10.
What will be the value of the account after 10 years?The first step is to determine the amount she has left to invest.
Amount invested = amount won - amount spent on vacation
$250,000 - $10,000 = $240,000
The second step is to determine the future value of the account. The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate = 1/5/12 = 0.125%m = number of compounding =12N = number of years240,000 x 1.00125^(12 x10) = $278,814.10
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Set W consists of the even whole numbers from 2 to 20, inclusive. If a number is selected at random from set W, then what is the probability that the number is a
multiple of 4 and also a multiple of 6?
Answer:
1/19
Step-by-step explanation:
The number in the set that are a multiple of both 4 and 6 is 12.
This is one number out of the 19 numbers in the set, so the probability is 1/19.
If log103 0.4771,
evaluate log100.0003.
Round your answer to four decimal
places.
Answer:
log(0.0003) = -3.5229
Step-by-step explanation:
The rules of logarithms tell you ...
log(ab) = log(a) +log(b)
Applicationlog(0.0003) = log(3×10^-4) = log(3) +log(10^-4)
= log(3) -4 = 0.4771 -4
log(0.0003) = -3.5229
__
Additional comment
If you do much work with logarithms, you find that negative logarithms are generally expressed using a positive mantissa with a negative add-on. Often, that negative add-on is -9, so this would be ...
5.4771-9
This helps when taking antilogs, as you look up 0.4771 in the table to see that the multiplier is 3.
If you were to look up 0.5229, you would find 3.333, meaning the multiplier is 1/3.333 and the antilog of -3.5229 is (10^-3)/3.333. This may not be a convenient value to work with.
Find the simple interest earned after 4 years on $2,250 invested at an interest rate of 5%.
simple interest= principal x time x rate/100
If f ( x ) = x 2 and g ( x )= 2x - 2,
find f ( g ( 7 ) )
Answer:
144
Step-by-step explanation:
First find g(7) --
[tex]g(7)=2(7)-2\\=14-2\\=12[/tex]
Then plug 12 into f(x) --
[tex]f(12)=(12)^{2} \\=144[/tex]
Which choice is equivalent to the expression below?
√6 +2√√3+√27-√12
A. 53-6
OB. 2√3-√21
OC. 3√3+√6
OD. 5√3
The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.
According to the statement
We have given that one evaluating expression which is √6 +√6+√27-√12
And we have to simplify this expression by evaluating it.
So, Given expression is:
√6 +√6+√27-√12
√6 +√6+√(9*3)-√(4*3)
√6 +√6+3√(3)-2√(3)
√6 +√6+√3( 3-2)
After evaluating the expression it become
√6 +√6+√3(1)
√(3*2) +√(3*2) +(1)√3
Take common from above expression then
√3(√2 +√2 ) +√3
√3(2√2) +√3
√3(2√2+ 1)
Now the expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.
So, The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Which choice is equivalent to the expression below?
√6 +√6+√27-√12
A. √3(2√2+ 1)
B. 2√3-√21
C. 3√3+√6
D. 5√3
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Which of the following is not irrational? (a) (2-√3)2 (b)(√2+√3)2 (c) (√2-√3)(√2+√3) (d)27√7
Answer: (c)
(√2-√3)(√2+√3)
Step-by-step explanation:
An irrational number is one that cannot be expressed as the ratio of two integers. In other words it cannot be expressed as [tex]\frac{x}{y}[/tex] where x and y are integers
[tex]\sqrt{2}[/tex] is irrational
[tex]\sqrt{3}[/tex] is irrational
In fact the square root of any prime number is irrational. So [tex]\sqrt{5}[/tex], [tex]\sqrt{7}[/tex] etc are irrational. But [tex]\sqrt{9}[/tex] is not irrational since it evaluates to 3 which can be expressed as [tex]\frac{3}{1}[/tex]
Any expression that contains the square root of a prime number is also irrational
Looking at the choices we see that choices (a), (b) and (d) all evaluate to expressions containing square roots of primes
(a) (2-√3)2 = 4 - 2√3 . Hence irrational
(b) √2+√3)2 = 2√2+2√3. Hence irrational
(d) 27√7 is irrational
Let's look at choice (c)
(√2-√3)(√2+√3)
An expression [tex](a+b)(a-b)[/tex] can be evaluated as [tex]a^{2} - b^{2}[/tex]
Here a = √2, [tex]a^{2}[/tex] =[tex]a = \sqrt{2}\\ a^2 = (\sqrt{2} )^2 = 2\\\\b = \sqrt{3} \\b^2 = (\sqrt{3} )^2 = 3\\\\a^2 - b^2 = 2-3 = -1\\[/tex]
This is a whole number(integer) and all integers are rational numbers
Hence correct answer is (c)
If one angle in a parallelogram is a right angle prove the other are the same.
Answer: If one angle of a parallelogram is a right angle, then all other angles would also be right angles and the parallelogram would be a rectangle.
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.2 and a standard deviation of 2.5. Answer parts (a)–(d) below.
The probability that a randomly selected study's participant was less than 4 is 0.2266.
How to compute the probability?Given that:
mean = 5.8
standard deviation = 2.4
a) P(x < 4) = P[(x - mean ) /sd < (4 - 5.8) / 2.4]
= P(z < -0.75)
Using z table,
= 0.2266
b) P(4 < x < 6) = P[(4 - 5.8)/ 2.4) < (x - \m ) /sd < (6 - 5.8) / 2.4) ]
= P(-0.75 < z < 0.08)
= P(z < 0.08) - P(z < -0.75 )
Using z table,
= 0.5319 - 0.2266
= 0.3053
c) P(x > 8) = 1 - p( x< 8)
=1- p P[(x - \m ) / sd< (8 - 5.8) / 2.4]
=1- P(z < 0.92)
Using z table,
= 1 - 0.8212
= 0.1788
Lastly, there are no unusual events because all the probabilities are greater than 0.05.
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A store is having a 20% off sale. The sale price of an item with price p is p - 0.2p. What is an equivalent expression.
Although all of the following systems can be solved via the substitution method, substitution would be the best method for solving which system.
Group of answer choices
Using the substitution method, the system of equation that is easily solved is:
c. y = 2x + 3
2x + y = 5
How to Solve A System of Equations Using the Substitution Method?Using the substitution method to solve a system of equations is best when one of the equations have one isolated variable that we can simply plug its value into the second equation.
For example, given the system of equations:
y = 2x + 3 --> eqn. 1
2x + y = 5 --> eqn. 2
Substitute y = (2x + 3) into eqn. 2 and find x:
2x + y = 5 --> eqn. 2
2x + 2x + 3 = 5
4x + 3 = 5
4x = 5 - 3
4x = 2
x = 2/4
x = 1/2
Substitute x = 1/2 into eqn. 1 to find y
y = 2x + 3 --> eqn. 1
y = 2(1/2) + 3
y = 1 + 3
y = 4
From the above, we can see that the system of equations that is quite easy to solve using the substitution method is:
c. y = 2x + 3
2x + y = 5
The rest of the equations are quite different and not as straightforward as solving as this using the substitution method.
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If 7 and 9 are the remainders when 98 and 165
respectively, are divided by a positive integer a, then a =
Answer:
Step-by-step explanation:
98-7=91
165-9=156
(91/156)/13=7/12
Answer = 13
It is divided by a positive integer a, which will equal the number 13.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data provided by the question,
The number are 98 and 165.
The remainders are 7 and 9.
So, the actual number is,
98 - 7 = 91 and,
165 - 9 = 156
They are divided by the number 13, so the value of a will be equal to 13.
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Briana received a 10-year subsidized student loan of $26,000 at an annual interest rate of 4.125%. Determine her monthly payment (in dollars) on the loan after she graduates in 2 years. (Round your answer to the nearest cent.)
Answer:
$264.78
Step-by-step explanation:
The government pays the interest on Briana's loan while she is in school. Her monthly payments will be for a loan of $26,000. The amount of the payment can be found from the amortization formula, or using a calculator or spreadsheet.
Payment amountFor a loan of principal amount P at annual rate r for t years, the monthly payment is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t)) = $26000(0.04125/12)/(1 -(1 +0.04125/12)^(-120)) = $264.78
Briana's monthly payment after she graduates is $264.78.
Please help, type your answers in order .
Step-by-step explanation:
we know from the laws of motion that in the equation
h = 20t - 1.86t²
the gravitational acceleration is in the factor of the t² term.
h = v0t + 1/2 × g × t²
v0 being the initial velocity (20 m/s).
and we can therefore see, that the gravitational acceleration "a" on Mars is 2×1.86 = 3.72 m/s²
(a)
the velocity v after 2 seconds is (first law of motion)
v = v0 + at = 20 - 3.72×2 = 12.56 m/s
gravity pulling down, so negative acceleration.
(b)
first we need the time when the rock is at 25 m.
25 = 20t - 1.86t²
0 = -1.86t² + 20t - 25
the solution to a quadratic equation is always
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = t
a = -1.86
b = 20
c = -25
t = (-20 ± sqrt(400 - 4×-1.86×-25))/(2×-1.86) =
= (-20 ± sqrt(214))/-3.72
t1 = (-20 + 14.62873884...)/-3.72 =
= 1.443887409... s ≈ 1.44 s
t2 = (-20 - 14.62873884...)/-3.72 =
= 9.308800763... s ≈ 9.31 s
that means, on its way up the rock reached 25m after
1.44 s.
on its way down the rock reached 25 m after
9.31 s.
velocity 0 (the rock came to a stop before falling back down) was after
0 = 20 - 3.72t
3.72t = 20
t = 20/3.72 = 5.376344086... s
that means the rock was falling after this point back to the ground and was gaining speed again.
that accelerating phase until the rock was again at 25 m was
9.308800763... - 5.376344086... = 3.932456677... s
long
the velocity at these points was
v-up = 20 - 3.72×1.443887409... = 14.62873884... m/s ≈
≈ 14.63 m/s
v-down = 0 + 3.72×3.932456677... = 14.62873884... m/s ≈
≈ 14.63 m/s
as expected : the rock did a perfectly symmetric flight path between the two 25 m marks.
so time and speed on both sides had to be identical.
but we have proven it.
Answer:
a) 12.56 m/s
b) up: 14.63 m/s (2 d.p.)
down: -14.63 m/s (2 d.p.)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{The Constant Acceleration Equations (SUVAT)}\\\\s = displacement in m (meters)\\u = initial velocity in m s$^{-1}$ (meters per second)\\v = final velocity in m s$^{-1}$ (meters per second)\\a = acceleration in m s$^{-2}$ (meters per second per second)\\t = time in s (seconds)\\\\When using SUVAT, assume the object is modeled\\ as a particle and that acceleration is constant.\end{minipage}}[/tex]
The average gravitational acceleration on Mars is 3.721 m/s² (about 38% of that of Earth). The fact that the rock is thrown from the surface of Mars rather than the surface of Earth is of no consequence when using the equations of constant acceleration (SUVAT equations) as long as acceleration is not used in the calculations.
Part (a)Given:
[tex]s=20t-1.86t^2, \quad u=20, \quad t=2[/tex]
[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies 20(2)-1.86(2)^2 & = \dfrac{1}{2}(20+v)(2)\\\\32.56 & = 20+v\\\\v & = 32.56-20\\\\v & = 12.56\:\: \sf m/s\end{aligned}[/tex]
Therefore, the velocity of the rock after 2 s is 12.56 m/s.
Part (b)Find the time when the height of the rock is 25 m:
[tex]\begin{aligned}20t-1.86t^2 & = s\\\implies 20t-1.86t^2 & = 25\\1.86t^2-20t+25 & = 0\end{aligned}[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1.86, \quad b=-20, \quad c=25[/tex]
[tex]\implies t=\dfrac{-(-20) \pm \sqrt{(-20)^2-4(1.86)(25)} }{2(1.86)}[/tex]
[tex]\implies t=\dfrac{20 \pm \sqrt{214}}{3.72}[/tex]
[tex]\implies t=9.308800763..., 1.443887409...[/tex]
Therefore, the height of the rock is 25 m when:
t = 9.31 s (2 d.p.)t = 1.44 s (2 d.p.)To find the velocity (v) of the rock at these times, substitute the found values of t into the equation, along with s = 25 and u 20 m/s:
[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies v & = \dfrac{2s}{t}-u\\\\v & = \dfrac{2(25)}{t}-20\\\\v & = \dfrac{50}{t}-20\\\\\end{aligned}[/tex]
When t = 1.443887409...s
[tex]\implies v=\dfrac{50}{1.443887409...}-20=14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]
When t = 9.308800763...s
[tex]\implies v=\dfrac{50}{9.308800763...}-20=-14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]
Therefore, the velocity of the rock when its height is 25 m is:
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SUPER URGENT PLEASE ANSWER ASAP
Answer:
shown below
Step-by-step explanation:
Look at the white squares, count them. 1, 2, 3. the next will be 4 and 5. draw 4 white squares, then house it in black squares like the others. to know if u did it right, count the black squares, there should be 8, then 9.
Find the value of 8!
Hey there!
8!
= 8(7)(6)(5)(4)(3)(2)(1)
= 56(6)(5)(4)(3)(2)(1)
= 336(5)(4)(3)(2)(1)
= 1,680(4)(3)(2)(1)
= 6,720(3)(2)(1)
= 20,160(2)(1)
= 40,320(1)
= 40,320
Therefore, your answer should be:
40,320
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
what’s the approximate value of tan 1
Answer: tan 1 radians = 1.557, tan 1 degrees = 0.017
NO LINKS!! Please help me with this problem
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :
Length of transverse axis is :
[tex]\qquad \sf \dashrightarrow \: 2b = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: b = 6[/tex]
length of conjugate axis is :
[tex]\qquad \sf \dashrightarrow \: 2a = 8[/tex]
[tex]\qquad \sf \dashrightarrow \: a = 4[/tex]
Equation of hyperbola ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{ {x}^{2} }{ {a}^{2} } = 1[/tex]
plug in the values ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{ {x}^{2} }{ {4}^{2} } = 1[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{ {x}^{2} }{ {16}^{} } = 1[/tex]
Answer:
[tex]\dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]
Step-by-step explanation:
Standard form equation of a vertical hyperbola
[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]
where:
center = (h, k)vertices = (h, k±a)co-vertices = (h±b, k)foci = (h, k±c) where c² = a² + b²[tex]\textsf{asymptotes}: \quad y =k \pm \left(\dfrac{a}{b}\right)(x-h)[/tex]Transverse axis: x = hConjugate axis: y = kFrom inspection of the graph:
center = (0, 0) ⇒ h = 0, k = 0vertices = (0, 6) and (0, -6) ⇒ a = 6co-vertices = (4, 0) and (-4, 0) ⇒ b = 4Substitute the found values into the formula:
[tex]\implies \dfrac{(y-0)^2}{6^2}-\dfrac{(x-0)^2}{4^2}=1[/tex]
[tex]\implies \dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]
1) La suma de dos números es 58. Si uno de los números es 12 más que el otro
número,
cuáles son los números?
Answer:
Los números son 23 y 35.
Step-by-step explanation:
Q: The sum of two numbers is 58. If one of the numbers is 12 more than the other number, what are the numbers?
Set the numbers as x and y. Using the given information, we have two equations:
x+y=58
x=y+12
Solving using substitution, we have:
y+y+12=58 -> y=23
Substituting, x=23+12=35
The numbers are 23 and 35.
In a unit circle, 0 = 90°. Identify the terminal point and sin 0.
A. Terminal point: (0, 1); sin 0 = 1
B. Terminal point: (1, 0); sin 0 = 0
C. Terminal point: (1, 0); sin 0 = 1
OD. Terminal point: (0, 1); sin 0 = 0
SUBMI
Terminal point: (0, 1); sinФ = 1 ⇒ A
How do you find the terminal point?P(a, b) is the terminal point indicated by t, and the signs are selected based on the quadrant in which this terminal point is located. For each actual number t that is given.The terminal point on the positive x-axis is (1, 0), which denotes that cos(x) = 1, sin(x) = 0 and = 0° or 360°.The terminal point (0, 1) on the positive y-axis indicates that = 90° and cos = 0, sin = 1.The x-terminal axis's point on the negative side is (-1, 0), which indicates that the angle is 180 degrees, cos is -1, and sin is 0.(0, -1), which denotes the terminal point on the negative y-axis, indicates that = 270° and cos = 0, sin = -1.On a unit circle Ф = 90°
Using the second rule listed above
The terminal point is (0, 1)
sinФ = 1
Terminal point: (0, 1); sinФ = 1
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Which equation is correct?
O sin gº =z/x
O sin gº=x/z
O tan gº =z/x
O tan gº = x/z
The value of your stock investment in a certain company decreased 10 % over the last year. If the value of your stock investment is $7000
today, then what was the value of your stock investment a year ago
The value of the stock a year ago is $7778
How to determine the value of the stock a year ago?The given parameters are:
Depreciation rate, r = 10%
Value of investment today, V(t) = $7000
The value of the stock a year ago is then calculated as:
Value of investment today = Value of investment last year * (1 - Depreciation rate)
Substitute the known values in the above equation
7000 = Last year * (1 - 10%)
Evaluate the difference of 1 and 10%
7000 = Last year * (90%)
Divide both sides by 90%
Last year = 7778
Hence, the value of the stock a year ago is $7778
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List these fractions from
least to greatest 3/8 5/8 4/8 2/8 7/8
Answer: 2/8, 3/8, 4/8, 5/8, 7/8
Step-by-step explanation:
Since they all have a common denominator, we can list them based on their numerator without having to worry about the denominator.
2/8 < 3/8 < 4/8 < 5/8 < 7/8
If the lengths of a triangle are 8, 12, and 18 can it be a right triangle?
Hello,
The triangle be right only if : 18² = 8² + 12²
We have : 18² = 18 × 18 = 324
and 8² + 12² = 8 × 8 + 12 × 12 = 208
324 ≠ 208 → the triangle can not be a right triangle
If u spend $25 per day. How many days will it take you to spend $1,000
Answer:
4days atlases in the week
Quantity day
25------------------1
1000---------------x
We solve
[tex]\boldsymbol{\sf{x=\dfrac{1000\times1}{25}=\dfrac{1000}{25}=40 }}[/tex]
Answer: To spend $1,000 it will take 40 days.
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find the domain of the function expressed by the formula:
y=1/x-7
The domain of the function is x ≠ 7
How to determine the domain?The function is given as:
y = 1/x - 7
Set the denominator not equal to 0
x - 7 ≠ 0
Add 7 to both sides
x ≠ 7
Hence, the domain of the function is x ≠ 7
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Amanda rented a bike from Ted's Bikes.
It costs $10 for the helmet plus $4.25 per hour.
If Amanda paid about $33.38, how many hours did she rent the bike?
a) Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.
Answer:
5.5 hours
Step-by-step explanation:
I am going to assume that a helmet is necessary prerequisite for renting the bike.
I also am assuming that the hourly rate can be turned into a sub hourly rate if the full hour isn’t used.
10+4.25h=33.38
4.25h=23.38
h=23.38/4.25
h=5.5
Write an inequality for the following statement, 1 is greater than x
The inequality suitable if 1 is greater than x is x<1.
Given that 1 is greater than x.
We are required to form an inequality which shows that 1 is greater than x.
Inequality is like an equation showing relationship between two or more variables.It is mostly not found in equal to form.
It shows the range of quantities.
When 1 is greater than x means the greater than sign will be used for 1 not x and the inequality will be as under:
x<1
We have not used equal to sign because 1 is greater than x not equal to x.
Hence the inequality suitable if 1 is greater than x is x<1.
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need heeeelp please
Answer:
4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])
Step-by-step explanation:
28[tex]v^{7}[/tex]x³[tex]y^{6}[/tex] - 12[tex]v^{9}[/tex][tex]x^{9}[/tex] ← factor out 4[tex]v^{7}[/tex]x³ from each term
= 4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])
1) The following scatterplot shows the percentage of the vote a candidate received in the 2016 senatorial elections
according to the voter's income level based on an exit poll of voters conducted by a news agency. The income
levels 1-8 correspond to the following income classes:
1 = Under $15,000; 2 = $15-30,000; 3 = $30-50,000; 4 = $50-75,000; 5 = $75-100,000;
6 = $100-150,000; 7 = $150-200,000; 8 = $200,000 or more.
Use the election scatterplot to determine whether there is a correlation between percentage of vote and income
level at the 0.01 significance level with a null hypothesis of ρs = 0.
A) The test statistic is between the critical values, so we fail to reject the null hypothesis. There is no
evidence to support a claim of correlation between percentage of vote and income level.
B) The test statistic is not between the critical values, so we fail to reject the null hypothesis. There is no
evidence to support a claim of correlation between percentage of vote and income level.
C) The test statistic is between the critical values, so we reject the null hypothesis. There is sufficient
evidence to support a claim of correlation between percentage of vote and income level.
D) The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient
evidence to support a claim of correlation between percentage of vote and income level
The answer to the question is B. The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level.
What is the scatter plot?This is the plot that shows the relationship between two different variables along a straight line. All of the points that are known to have a relationship between these variables would fall under this line. Other parts that fall outside the line are regarded as the outliers in the plot.
In this particular question, the outlier is seen to be outside of the critical values so we have to conclude that the solution is B. We fail to reject the null hypothesis.
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Which of the following is the solution to the inequality below? 9 - 3x >= 2(x - 3) A . x <= 15 B. x >= 15 C. x >= 3 D. x <= 3
Answer: [tex]x \leq 3[/tex]
Step-by-step explanation:
[tex]9-3x \geq 2(x-3)\\\\9-3x \geq 2x-6\\\\15-3x \geq 2x\\\\15 \geq 5x\\\\3 \geq x\\\\x \leq 3[/tex]