Using the z-distribution, since the p-value of the test is less than 0.01, there is enough evidence to conclude that the claim is correct.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the proportion is above 0.5, hence:
[tex]H_0: p \leq 0.5[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the proportion is above 0.5, hence:
[tex]H_1: p > 0.5[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]n = 825, \overline{p} = \frac{500}{825} = 0.606, p = 0.5[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.606 - 0.5}{\sqrt{0.5(0.5)}{825}}}[/tex]
z = 6.1.
What is the p-value?We have a right-tailed test, as we are testing if the proportion is greater than a value. Using a z-distribution calculator, with z = 6.1, the p-value is of 0.
Since the p-value is less than 0.01, there is enough evidence to conclude that the claim is correct.
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Time to use my tools
96 100 132
6 ... 4 ....6
5....7......3
21...32...?
1)32
2)20
3)25
4)30
find the missing one
Answer:
the correct answer is 25
Find the difference between 0.84 and 17.1. (a) Give your answer as a mixed number in its simplest form. (b) Divide your answer by 9 and give your answer correct to 2 decimal places.
Answer:
in case you don't understand feel free to ask bye.
Question: You can work 40 hours per pay period while attending school earning $12.50 an hour. There are two pay periods per month. NOW Assume you have deductions for health care of $25 per pay period and 401K deduction of $50 per pay period. These deductions are pretax.
Gross Pay per pay period: $
Taxable Income per pay period:
You pay 11% in federal taxes. Federal tax withholding per pay period: $
___
Use the state tax rates below and calculate State tax withholding per pay period: $
(round to two decimals)
_____
From the image:
Calculate FICA withholding per pay period: $
Calculate Medicare withholding per pay period: $
(round to two decimals)
What is your Net pay per pay period: $
(round to two decimals)
1) Based on the information, the following taxation calculations can be made:
a) Gross Pay per pay period: $500
b) Taxable Income per pay period: $425
c) Since you pay 11% in federal taxes, the Federal tax withholding per pay period is $46.75.
2) The State tax withholding per pay period is $20.
3) The calculation of FICA, Medicare, and the Net Pay per pay period is as follows:
FICA withholding per pay period: $25.50
Medicare withholding per pay period: $6.16
Net Pay per pay period = $326.59
Data and Calculations:Total hours worked per pay period = 40 hours
Rate per hour = $12.50
Pay periods per month = 2
Gross pay per pay period = $500 (40 x $12.50)
Deductions per pay period:Health care = $25
401K deduction = $50
Total deductions per pay period = $75
Taxable income per pay period = $425 ($500 - $75)
Federal taxes = 11%
Federal tax withholding per pay period: $46.75 ($425 x 11%)
Annual taxable income = $10,200 ($425 x 24)
State withholding tax (annual) = $480 {$120 + ($10,200 - $5,000) x 5%}
State withholding tax per pay period = $20 ($480/24)
FICA withholding per pay period: $25.50 ($425 x 6.2%)
Medicare withholding per pay period: $6.16 ($425 x 1.45%)
Net Pay per pay period:Gross Pay $500
Total deductions $75
Taxable income = $425
Federal Withholding = $46.75
State Withholding = $20
]FICA Withholding = $25.50
Medicare Withholding = $6.16
Net Pay per pay period = $326.59
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(3x+1)^2-2(3x+1)(3x+5)^2+(3x+5)^2
Answer:
soln,
write the question
=9x^2+1-6x-2×9x^2+25+9x^2+25
=9x^2+1-6x-18x^2+25+9x^2+25
=9x^2-18x^2+9x^2+1+25+25-6x
=51-6x
if(3x+1)^2 mean that (3x+1)has power of 2 and u don't have to use the formula this is the answer
Step-by-step explanation:
it's just BODMAS method
need help please...
Answer:
[tex]\sf 28 \frac{1}{3} \:ft=28.3\:ft\:(nearest\:tenth)[/tex]
Step-by-step explanation:
Given information:
It takes Mr Kelly 6 strides to walk 20 ft.It takes Mr Kelly 8.5 strides to walk the other side of his house.Let x be the unknown length of the other side of Mr Kelly's house.
To solve, set up a ratio with the given information and the defined unknown, then solve for x:
[tex]\textsf{20 ft : 6 strides = x ft : 8.5 strides}[/tex]
[tex]\implies \sf 20:6 = x:8.5[/tex]
[tex]\implies \sf \dfrac{20}{6}=\dfrac{x}{8.5}[/tex]
[tex]\implies \sf x=\dfrac{20 \cdot 8.5}{6}[/tex]
[tex]\implies \sf x=\dfrac{170}{6}[/tex]
[tex]\implies \sf x=28 \frac{1}{3} \:ft[/tex]
[tex]\implies \sf x=28.3\:ft\:(nearest\:tenth)[/tex]
Therefore, the length of the other side of Mr Kelly's house that takes him 8.5 strides to walk is 28.3 ft (nearest tenth).
Let that be x
20:x=6:8.520/x=6/8.520/x=12/1712x=17(20)12x=340x=340/12x=28.3ftThe hypotenuse of an isosceles right triangle is 14 centimeters longer than either of its legs. Find the exact length of each side. (Hint: An isosceles right triangle is a right triangle whose legs are the same length.)
The Pythagorean theorem states that:
[tex]a^2+b^2=c^2[/tex]
a and b are two legs of a right trianglec is the hypotenuseThe Quadratic Formula[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Solving the QuestionLet a represent the length of one leg.
Because the hypotenuse is 14 cm longer than a leg, we can say that the hypotenuse's length is 14 + a.
Plug these into the Pythagorean theorem:
[tex]a^2+b^2=c^2\\a^2+a^2=(14+a)^2\\2a^2=14^2+2(14)a+a^2\\2a^2=196+28a+a^2\\a^2=196+28a\\a^2-196-28a=0\\a^2-28a-196=0[/tex]
Factor using the quadratic formula:
[tex]a=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]a=\dfrac{-(-28)\pm \sqrt{(-28)^2-4(1)(-196)}}{2(1)}\\\\a=14\pm14\sqrt{2}\\\\a=14+14\sqrt{2}[/tex]
We know that it's plus because subtracting results in a negative value, and length cannot be negative.
This is the length of each side.
Because the hypotenuse is 14 cm longer, we can say that the hypotenuse is [tex]28+14\sqrt{2}[/tex].
AnswerLeg length = [tex]14+14\sqrt{2}[/tex]
Hypotenuse length = [tex]28+14\sqrt{2}[/tex]
can someone answer this?
Step-by-step explanation:
f(x)=-3x+4
f(a)= -3a +4
So,
2f(a)= f(a) + f(a)
=(-3a +4) +(-3a + 4)
=-3a + 4 -3a - 4
=-6a
f(2a)=2(-3a + 4)
=-6a +8
f(a+2)=(-3a + 4) + 2
= -3a +4 +2
= -3a + 6
f(a) + f(2)= -3a +1+5
because, f(2)= -3(2)+1
=-6+1
=5
and f(a)= -3a+1
5 + 4 ⋅ ( 8 − 6 ) ^2
[tex]\boldsymbol{\sf{5+4\cdot(8-6)^{2} \ \ \longmapsto \ \ [Subtract \ 6 \ from \ 8.] }}[/tex]
[tex]\boldsymbol{\sf{5+4\cdot2^{2} }}[/tex]
Calculates 2 to the power of 2 and gets 4.
[tex]\boldsymbol{\sf{5+4\cdot4 \ \ \longmapsto \ \ [Multiply] }}[/tex]
[tex]\boldsymbol{\sf{5+16 \ \ \longmapsto \ \ [Add]}}[/tex]
[tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ 21}}}}[/tex]
Answer:
5+16x
Step-by-step explanation:
5+4x(8−6)
2
Subtract 6 from 8 to get 2.
5+4x×2
2
Calculate 2 to the power of 2 and get 4.
5+4x×4
Multiply 4 and 4 to get 16.
5+16x
If a square root parent function is vertically stretched by a factor of 6, what is
the equation of the new function, G(x)?
OA. G(x) = -6√√x
O B. G(x)=√x
OC. G(x) = √6x
O D. G(x) = 6-√x
Parent function = √x
On stretching vertically by factor of 6
New function G(x) = 6√x
HELP NEED ANSWERS QIUCKLY! WILL GIVE BRAINLEST!
1. What is the difference between arithmetic and geometric?
2. Which formulas are used for each? Explain ratio and difference.
3. Given 4, 8, 16, 32 identify the next term and if its a ratio or difference
4. Explain the steps in using the sigma notation.
Answer:
Arithmetic => each new term differs from the previous term by a fixed amount
an = a1 + d (n − 1)
Geometric => each element after the first is obtained by multiplying the previous number by a constant factor
an = a1 (r)^(n − 1)
4,8,16,32 the difference is not fixed so it is a geometric so it is ratio
the ratio is 2 and n is 5 so 4*(2)^4 =4*16=64
To generate the terms of a series given in sigma notation, replace the index of summation with consecutive integers from the first value to the last value of the index.
if you also want the sum of them
arithmetic -> (n/2)(a1+an)
geometric -> (a1*(1-r^n))/(1-r) or
when the sequence is infinite you can use a1/(1-r)
Step-by-step explanation:
Arithmetic => 1,3,5,7,9,11,13,15....
Geometric => 1,2,4,8,16,32,64....
Neil emptied his change jar and noticed he only had pennies, nickels, and quarters. He had coins for a total of . He had fewer quarters than nickels. How many pennies did Neil have? The solution is
Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total are 4.60. How many of each coin does he have.
Let x represent dimes (0.1), y represent nickels (0.5) and z represent quarter (0.25)
Hence:
0.1x + 0.05y + 0.25z = 4.6 (1)
Also:
x = 3y (2)
And:
z = y + 4 (3)
From the equations:
x = 18, y = 6, z = 10
Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies
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please I need help in these exercises and I tried to solve them but I can't, crown to the best answer <'3
(a) The result of the long division is a - b + c.
(b) The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).
How to find an algebraic expression by long division
Long division is an algebraic procedure with which we can find the result of a division of two polynomials. Now we proceed to present the entire procedure explained:
(a) a² - b² + 2 · b · c - c² divided by a + b - c.
1) Multiply a + b - c by a and subtract it from a² - b² + 2 · b · c - c²: Result: a / Remainder: - b² - a · b + 2 · b · c + a · c - c²
2) Multiply a + b - c by - b and subtract it from the result of 1): Result: a - b / Remainder: b · c + a · c - c²
3) Multiply a + b - c by c and subtract it from the result of 2): Result: a - b + c / Remainder: 0
The result of the long division is a - b + c.
(b) 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4 divided by m⁴ - 3 · m² + 4.
1) Multiply m⁴ - 3 · m² + 4 by 3 · m³ and subtract it from 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4: Result: 3 · m³ / Remainder: 2 · m⁵ + m⁴ + 6 · m³ - 8 · m + 3 · m² + 4.
2) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 1): Result: 3 · m³ + 2 · m / Remainder: m⁴ + 12 · m³ - 16 · m + 3 · m² + 4.
3) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 2): Result: 3 · m² + 2 · m + 1 / Remainder: 12 · m³ - 16 · m + 6 · m².
The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).
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the sum of three consecutive integers is 78. what are the three Integers
Answer:
25, 26, and 27 are the three consecutive integers.
Step-by-step explanation:
Let the numbers be represented as x, x + 1 and x + 2.
We can write the equation:
[tex]x+(x+1)+ (x+2)=78[/tex]
Opening the brackets and simplifying:
[tex]x+x+1+x+2=78[/tex]
[tex]3x+3=78[/tex]
Subtract 3 from both sides.
[tex]3x=75[/tex]
Divide both sides by 3.
[tex]x=25[/tex]
Since the three consecutive integers are x, x + 1 and x + 2, replace x with 25.
∴ 25, 26 and 27 are the three consecutive integers.
Answer:
25 , 26 and 27
Step-by-step explanation:
Which expression has a value of -24 when a = -2 and b = 3?
A. a√16 + b - 10
B. a(√16 + b) -10
C. a√16 + (b - 10)
D. (a√16) + b - 10
The option B is correct, The second expression gives the correct value -24.
According to the statement
we have given that the some expression and a = -2 and b = 3 and we have to which expression gives a output of answer -24 after put the values in the expressions.
So, For this purpose
First expression:
[tex]a\sqrt{16} + b - 10[/tex]
Put a = -2 and b = 3
then
[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]
Second expression:
[tex]a(\sqrt{16} + b) -10[/tex]
Put a = -2 and b = 3
then
[tex]a(\sqrt{16} + b) -10\\-2(4 +3) -10\\-14-10\\-24[/tex]
Now,
Third expression:
[tex]a\sqrt{16} + (b - 10)[/tex]
Put a = -2 and b = 3
then
[tex]a\sqrt{16} + (b - 10)-2*4 + (-7)\\-8-7\\-15[/tex]
Now,
Fourth expression and first expression are same,
So,
Fourth expression:
[tex]a\sqrt{16} + b - 10[/tex]
Put a = -2 and b = 3
then
[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]
The second expression gives the correct value -24.
So, The option B is correct, The second expression gives the correct value -24.
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Fertiliser is applied at the rate of a grams per square metre. It
takes b kilograms to cover a field of area c square metres. Find a
formula for b in terms of a and c.
Step-by-step explanation:
1 kilogram (kg) = 1000 grams (g)
as "kilo" means 1000.
b = a × c / 1000
it is simple : we have "c" square meters. as we need to apply "a" grams per square meter, we need to multiply both numbers to know how many grams we need for that many square meters. hence a × c.
and to get kg, we need to divide this number of grams by 1000.
that's it.
a storage room measures 20 feet by 15 feet. the floor is covered by tiles that cost $7.50 per square foot. what will be the cost of the entire floor with tiles?
Answer: $2250
Step-by-step explanation:
Given information
Dimension of the room = 20 feet × 15 feet
Cost of tiles = $7.50 / ft²
Derived formula from the given information
Total cost = Floor area × Cost of tiles
Substitute values into the formula
Total cost = Floor area × Cost of tiles
Total cost = (20 × 15) × (7.5)
Simplify by multiplication
Total cost = 300 × (7.5)
[tex]\Large\boxed{Total~cost~=~2250~Dollars}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Please i need help for this calculus
Step-by-step explanation:
First thing first, let find the x value of where P and Q both meet y=5, we know that y=5, and y=2x^2+7x-4, so using transitive law,
[tex]5 = 2 {x}^{2} + 7x - 4[/tex]
[tex]2 {x}^{2} + 7x - 9[/tex]
[tex]2 {x}^{2} - 2x + 9x - 9[/tex]
[tex]2x(x - 1) + 9(x - 1)[/tex]
[tex](2x + 9)(x - 1) = 0[/tex]
[tex]x = 1[/tex]
[tex]2x + 9 = 0[/tex]
[tex]x = - \frac{9}{2} [/tex]
Now, to find the gradient of the curve let take the derivative of both sides
[tex]5 = 2 {x}^{2} + 7x - 4[/tex]
[tex]0 = 4x + 7[/tex]
[tex]4x + 7[/tex]
Plug in -9/2, let call that point P
[tex]4( \frac{ - 9}{2} ) + 7 = - 11[/tex]
Plug in 1, let call that point Q
[tex]4(1) + 7 = 11[/tex]
So the gradient of the curve at point P (-9/2,5) is -11
The gradient of the curve at point Q (1,5) is 11.
The formula =MID("ABCDEFGHI",3,4) would yield the result
If the formula, =MID("ABCDEFGHI",3,4) is used, the result yielded would be CDEF.
What would =MID("ABCDEFGHI",3,4) yield?When using the =MID function on a spreadsheet, the number after the text in the formula would show the position of the text from the left that the function would begin to count from.
The text in the third position from the left as shown in ABCDEFGHI is C so we need to start counting from letter C.
The second number in the function would then show the number of texts that needs to be counted and selected from the row of letters. That number is 4.
So from the letter C, you'll count 4 letters including the letter C itself.
The result you get would therefore be C, D, E, F which are the four letters from C.
In conclusion, the formula =MID("ABCDEFGHI",3,4) would yield the result, "C, D, E, F,."
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4x-12y=-20 substitution method
If we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.
Given two equations x-2y=5 and 4x+12y=-20.
We are required to find the value of x and y through substitution method.
Equation is like a relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Equation can be a linear equation,quadratic equation, cubic equation or many more depending on the power of variable.
They can be solved as under:
x-2y=5---------------1
4x+12y=-20--------2
Finding value of variable x from equation 1.
x=5+2y--------------3
Use the value of variable x in equation 2.
4x+12y=-20
4(5+2y)+12y=-20
20+8y+12y=-20
20y=-20-20
20y=-40
y=-40/20
y=-2
Use the value of variable y in equation 3.
x=5+2y
x=5+2*(-2)
x=5-4
x=1
Hence if we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.
Question is incomplete as it should include one more equation x-2y=5.
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Find the cube root of 1+¡^5
Number #2 please, I don’t know how to solve it.
Answer:
See below
Step-by-step explanation:
Here is HOW to solve this problem:
b = pounds of blue candy then r = 11-b = pounds of red candy
.79b = cost of blue candy 1.29 (11-b) = cost of red candy
these two costs sum to 11.19
.79b + 1.29 ( 11-b) = 11.19 Now you can solve for 'b' the 'r' = 11-b
Answer:
Red candy =5
Blue candy = 6
Step-by-step explanation:
Let the pounds of red candy be x and blue candy y. Then y=11-x
Also 1.29x + 0.79y=11.19
1.29x+0.79(11-x)=11.19
0.5x=11.19–8.69
0.5x=2.5
X=5
Red candy =5
Blue candy = 6
A television is identified by the diagonal measurement of the screen. A television has a length of 57-inches and a height of 33 inches. What is the length of the diagonal of the television screen?
Answer: 65.86 inches
Step-by-step explanation:
Length of the hypotenuse (length of diagonal) : a^2 + b^2 = c^2
The length (a)= 57
The height (b) =33
57^2= 3,249
33^3= 1,089
3,249 + 1,089 = c^2
4,338 = c^2
We next square root both sides to find c by itself (length of the diagonal)
[tex]\sqrt{4,338} = c[/tex]
c= 65.8634952...
You can then round to however many decimals are required.
To the hundreds place: 65.86 inches
If the measure of WZX is 262 what is the measure of XWY?
Answer:
49°
Step-by-step explanation:
The circumference of a circle measures 360 degrees, so arc XW is 98°.
So, angle XWY is 49°.
three times the difference between t and y"
Answer: 3(t-y)
Step-by-step explanation:
The term difference refers to subtraction, so that means t-y in parenthesis since you would have to solve that first.
Then after you'd solve that, then you would multiply it by 3
Hope I helped :)
QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
a. Central angle: Angle BAC
b. Major arc: Arc BEC
c. Minor arc: Arc BC
d. m(BEC) = 260°
e. m(BC) = 100°
What is a Major Arc?A major arc can be defined as an arc that has a measure that is greater than a semicircle (half a circle) or greater than 180 degrees.
What is a Minor Arc?A minor arc can be defined as an arc that has a measure that is less than a semicircle (half a circle) or less than 180 degrees.
What is a Central Angle?An angle whose vertex is at the center of a circle and has two radii of as its sides is called a central angle of a circle.
a. Central angle in the image given is: Angle BAC
b. Major arc of the circle is: Arc BEC
c. Arc BC is a minor arc.
d. m(BEC) = 360 - 100 [based on the central angle theorem]
m(BEC) = 260°
e. angle BAC = 100°
m(BC) = angle BAC [based on the central angle theorem]
m(BC) = 100°
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The price of a train ticket consists of an initial fee plus a constant fee per stop. The table compares the number of stops and the price of a ticket (in dollars). Stops Price (dollars) 333 6.506.506, point, 50 777 12.5012.5012, point, 50 111111 18.5018.5018, point, 50 What is the fee per stop?
Based on the task content given; the initial fee and the fee per stop is $2 and $1.5 respectively.
Equationlet
Initial fee = xFee per stop = yx + 3y = 6.50
x + 7y = 12.50
Subtract both equation to eliminate x7y - 3y = 12.50 - 6.50
4y = 6
y = 6/4
y = 1.5
Substitute y = 1.5 intox + 3y = 6.50
x + 3(1.5) = 6.50
x + 4.5 = 6.50
x = 6.50 - 4.5
x = 2
Therefore, the initial fee and the fee per stop is $2 and $1.5 respectively.
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Heyy i just need some help with questions 21and 25 if anyone could help me and show the work that would be amazing thank you!!
Step-by-step explanation:
21) f(x)=1/x-6. g(x)=7/x+6
f(g(x))=f(7/x+6)=1÷7/x+6 - 6=x+6/7 - 6
g(f(x))=g(1/x-6)=7÷1/x-6 - 6 =7(x-6) - 6
simplify forward
25)f(x)=|x| g(x)=5x+1
f(g(x))=f(5x+1)=|5x+1|=5x+1=g(x)
g(f(x))=g(|x|)=5|x|+1=5x+1=g(x)
A company reports cost of goods manufactured of $918,700 and cost of goods sold of $955,448. Compute the average manufacturing cost per unit assuming 18,374 units were produced.
If the cost of goods manufactured of $918,700 and cost of goods sold is $955,448. The average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.
Average manufacturing cost per unitUsing this formula to determine the average manufacturing cost per unit
Average manufacturing cost per unit= Total cost/Number of units produced
Where:
Total cost=$918,700+$955,448=$1,874,148
Number of units produced=18,374 units
Let plug in the formula
Average manufacturing cost per unit=$918,700+$955,448/18,374
Average manufacturing cost per unit=$1,874,148/18,374
Average manufacturing cost per unit=$102 per unit
Therefore the average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.
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Rearrange the equation (x-1)(x-1)(x-1)=y to solve for x express x in terms of y
Answer:
[tex]x=1+\sqrt[n]{y}[/tex]
Step-by-step explanation:
Since: [tex](x-1)*(x-1)*(x-1)=y[/tex]
that would imply: [tex](x-1)=\sqrt[3]{y}[/tex]
This is a bit more clear, if you write the equation as:
[tex](x-1)^3=y[/tex]
and then take the cube root of both sides
[tex]\sqrt[3]{(x-1)^3}=\sqrt[3]{y}[/tex]
Which simplifies to
[tex]x-1=\sqrt[3]{y}[/tex]
Now add 1 to both sides, and you get the equation:
[tex]x=1+\sqrt[n]{y}[/tex]
A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Use the Empirical Rule to estimate the proportion.
Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the mean of 110 and the standard deviation of 15, we have that:
80 = 110 - 2 x 15.140 = 110 + 2 x 15.These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
More can be learned about the Empirical Rule at brainly.com/question/24537145
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