Ludlow's z-score is z = 13.5
Given that the heights of American men are approximately normal.
Mean of the population, μ = 69.3 inches
Standard Deviation of the population, σ = 2.8 inches
Height of Robert Ludlow is 8 feet 11.1 inches = 107.1 inches [since 1 feet = 12 inches and 8 feet = 96 inches. 96 + 11.1 = 107.1 inches]
So [tex]\bar x[/tex] = 107.1 inches.
Since the population is assumed to be normal, we can find the z-score,
z = [tex]\frac{\bar x-\mu}{\sigma}[/tex]
= (107.1-69.3)/2.8
= 37.8 / 2.8
= 13.5
Learn more about z-score at https://brainly.com/question/25638875
#SPJ4
Which equation justifies why ?
The equation that justifies [tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex] is [tex](7^{\frac{1}{3} } )^{3} = 7^{\frac{1}{3} .3} = 7[/tex]
How to find the equation that justify another equation?The equation is as follows;
[tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex]
using laws of indices, the equation can be simplified.
[tex]a^{1 / b} = \sqrt[b]{a}[/tex]
Therefore,
[tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex] are the same.
Hence, it means the equation that justifies [tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex] is as follows:
[tex](7^{\frac{1}{3} } )^{3} = 7^{\frac{1}{3} .3} = 7[/tex]
learn more on equation here: https://brainly.com/question/24284103
#SPJ1
Find the inverse of each function. Is the inverse a function?
f(x)=2x² /5 +1
Yes , the given function is an inverse function which is given by [tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f-1 or F-1.A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.An inverse function returns the original value that the function provided the output for.We have given a function [tex]f(x)=\frac{2x^2}{5} +1[/tex]. ....(1)
Let y = f(x)
[tex]y=\frac{2x^2}{5} +1\\y-1=\frac{2x^2}{5} \\\\\frac{5(y-1)}{2} =x^2\\\\\sqrt{\frac{5(y-1)}{2} } =x[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]x=f^{-1}(y)[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex]
We can check that this is really an inverse function or not
Putting in [tex]x=\sqrt{\frac{5(y-1)}{2} }[/tex] equation (1) , we get
[tex]f(f^{-1}(y))=\frac{2(\sqrt{\frac{5(y-1)}{2} })^2}{5} +1\\\\\y=\frac{2\frac{5(y-1)}{2} }{5} +1\\\\y=\frac{5(y-1)}{5} +1\\\\y=y-1+1\\\\y=y[/tex]
As LHS = RHS which means inverse function is correct .
Learn more about inverse function here :
brainly.com/question/14391067
#SPJ4
Determine which of the following relations is a function.
x
-10
50
-5
50
10
y
10
5
0
-5
-10
D
x
-3
-1
0
0
3
NE
2
1
2
4
0
x
-8
-2
1
2
4
y
-4
-2
3
4
6
x
0
1
2
2
LO
5
92
42
2
6
7
We need to know about the difference between relation and function to solve this problem. Options 1 and 3 are functions but 2 and 4 are just relation not functions.
A relation is a relationship between two or more sets of values. A function is an expression that defines the relationship between two variables. The main difference between a relation and a function is that a relation can have multiple output for a single input but a function only has single output for a single input. Every function is a relation but every relation is not a function. In this question x is the input variable and y is the output variable,for option (1) all the input values have single output values, for option (2) the value x=0 has two different output values so this relation is not a function, for option (3) all input values have single output values, so it is a function and for option (4) the input value x=2 has two different output values so it is not a function.
Therefore we found out that options (1) and (3) are functions and the rest are just relations.
Learn more about relation and function from here:
https://brainly.com/question/28226267
#SPJ9
Answer:
its simply a, and c
Step-by-step explanation:
yiippeeeeee
2. The product of √5 and which of the following numbers will result in an irrational number? A. √5 B. -√5 C. √2 D. 3√5
Answer:
C
Step-by-step explanation:
The radicands have at least one prime-factor that is not in common.
turn 4 3/5 into a decimal
Answer:
4.6
Step-by-step explanation:
1. Multiply the whole number by the denominator
4 x 5 = 20
2. Add the result of step 1 to the numerator
20 + 3 = 23
3. Divide the result of step 2 by the denominator
23 ÷ 5 = 4.6
Quotients Great and Small
Diving fractions
Thanks so much please show work!
1. 5/6 ÷ 5/8 or. 5/6 x 8/5=
2. 5/9 ÷ 1/2 or. 5/9 x 2/1 =
3. 9/10 ÷ 3/5 or. 9/10 x 5/3=
Step-by-step explanation:
GOOD RIGHT?
A square with side length ppp has an area of 169169169 square centimeters. The following equation shows the area of the square.
p^2 = 169p
2
=169p, squared, equals, 169
What is the side length of the square in centimeters?
The side length of the square in centimeters is 13 centimeters
What are areas?The area of a shape is the amount of space on the shape
How to determine the side length?The equation of the area of the square is given as
p² = 169
The area of a square is the product of its length
This means that we simply take the square root of both sides of the equation to determine the side length
Next, we take the square root of both sides of the equation
So, we have
√p² = √169
Evaluate the square roots
So, we have
p = 13
Hence, the side length of the square in centimeters is 13 centimeters
Read more about areas at:
https://brainly.com/question/22972014
#SPJ1
h3lp
Which graph is the graph of the function [tex]g(x)=\frac{x^{2}-x }{x^{2} -1}[/tex]
see screenshot for answer choices
Answer:
A function is a mathematical relation that maps a value in a set of input numbers to a value in a set of output numbers. Some functions can map multiple values in one set to one value in the other set.
Step-by-step explanation:
How much water would you have if you combine all wars together of 1/2 ,1/3 and 1/6 but you have to rewrite with common denominators and then solve
The addition of the fractions means that the value when combined is 1.
How to calculate the fraction?It should be noted that based on the information given, we simply have to add the fractions that are given and this will be:
= 1/2 + 1/3 + 1/6
= 3/6 + 2/6 + 1/6
= 6/6
= 1
Therefore, the addition of the fractions means that the value when combined is 1.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
Someone answer this plsss
The equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6
From the question, we are to determine the equation of the line that is perpendicular to the given equation.
A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.
That is,
If m₁ is the slope of one of the lines
and m₂ is the slope of the other line
Then,
m₁ = -1/m₂
First, we will determine the slope of the given line
The equation of the given line is
y = 3x - 9
Compare the equation to the general form of the equation of a straight line
y = mx + b
Where m is the slope
and b is the y-intercept
By comparison,
m = 3
∴ The slope of the given line is 3
Thus,
The slope of the line that is perpendicular to this line is -1/3
Now,
To determine the equation this line,
We have that the line passes through the point (3, 1)
Using the point-slope form of the equation of a straight line,
y - y₁ = m(x - x₁)
m = -1/3
x₁ = 3
y₁ = 1
Putting the parameters into the equation,
y - 1 = -1/3(x - 3)
Expressing the equation in standard form
3(y -1) = -1(x - 3)
3y - 3 = -x + 3
3y + x = 3 + 3
x + 3y = 6
Hence, the equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6
Learn more on Equation of a line here: https://brainly.com/question/11752607
#SPJ1
describe some possible random variables (other than the ones mentioned previously) and discuss whether they are continuous random variables or discrete random variables.
Random variables can be either discrete or continuous.
Sample spaces need not consist of numbers. In statistics, we are most often interested in numerical outcomes such as the "count" of an occurrence. We call X a random variable because its values vary when the phenomenon is repeated. We use capital letters near the end of the alphabet like X or Y.
A random variable is a variable whose value is a numerical outcome of a random phenomenon. When a random variable describes a random phenomenon the sample space S just lists the possible values of the random variable. There are two ways of assigning probabilities to the values of a random variable that will dominate our application of probability as we study statistical inference.
Random variables can be either discrete or continuous. A discrete random variable X has a "countable number of possible values. The probability distribution of X lists the values and their probabilities in table form. The probabilities must satisfy two requirements:
1) every probability pi is a number between 0 and 1
2) p1 + p2 +,,,+pk = 1.
The probability of any event is found by adding the probabilities pi of the particular values xi that makes up the event.
For more information on random variables click on the link below:
https://brainly.com/question/17217746
#SPJ4
Solve for w.
0.43 +2.7w = 3.7w - 0.47
Answer:
w = 0.9
Step-by-step explanation:
What I did is I subtracted 2.7 from 3.7 bc it was the least number and that gave me 1 so that left me with 0.43 = w - 0.47. Then I added 0.47 to 0.43 and that gives me 0.9 which would be the answer
If you don't understand how I got it I can try to explain a little better, but hopefully, you understand:)
what is the slope of the line that passes through the points (6, -5) and (6, -4)?
Answer (y2 -y1) / (x2 - x1)
hope this helps
Answer:
(y2 -y1) / (x2 - x1)
Step-by-step explanation:
Use that formula. The answer should be -3/0 which doesn't make sense. Are you sure you have your x values correct? Since in that case, it would be a straight line and the equation for that would be x = 6 since it is a straight line up with no y-intercept.
About how much farther did she bike on Wednesday than Thursday?
the answer is 71 miles far
For the function f(x)=∛2x , find f⁻¹(x) . Then determine the value of x when f(x)=16 .
The value of [tex]f^{-1}(x)[/tex] is [tex]\frac{x}{\sqrt[3]{2} }[/tex] when f(x) = 16 is [tex]x=2^\frac{11}{3}[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f^-1.A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.An inverse function returns the original value that the functionWe have given a function [tex]f(x)=x\sqrt[3]{2}[/tex]. ....(1)
Let y = f(x)
[tex]y=x\sqrt[3]{2} \\\\x=\frac{y}{\sqrt[3]{2} }[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]y=\frac{x}{\sqrt[3]{2} }[/tex]
[tex]f^{-1}(x)=y[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(x)=\frac{x}{\sqrt[3]{2} }[/tex]
It is given that f(x) = 16 on comparing it with equation (1) , we get
[tex]x\sqrt[3]{2}=16\\x=\frac{2^4}{2^\frac{1}{3} } \\x=2^{4-\frac{1}{3} }\\x=2^\frac{11}{3}[/tex]
Learn more about inverse function here :
brainly.com/question/14391067
#SPJ4
Please helppppp nowwwwww
Answer:
It has 2 angles right and acute
A school dedicated 50% of the courtyard area for students to start a garden. The students want to know how much of the 632 yard the will be able to use?
The students will have 316 yards of the courtyard
The number of yards left for the students can be calculated as follows;
A school dedicated 50% of the courtyard area for students to start a garden
= 50/100
= 0.5
The number of yards is 632, the number of yards left for the students can be calculated as follows
= 0.5 × 632
= 316
Hence 316 yards are left for the students
Read more on yards here
https://brainly.com/question/14411482
#SPJ1
What would happen to a monthly payment if the interest rate increased?
OA. The payment would go up.
B. The payment would go down.
OC. The payment would remain the same.
OD. None of the above
i need all 3 im confused on them
Answer:
1. 5/12 in exact form and 0.416 in decimal form
2. 26/3 in exact form and 8.6 in decimal form and 8 2/3 in mixed number form.
On each "6" there's a - on top!
Given the algebraic expression ----- create an equivalent expression.
The equivalent expression of (64x^2/3)^-1/3 is 1/(4x^1/9)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
What are rational expressions?Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.
This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals
How to determine the equivalent expression?The expression is given as
(64x^2/3)^-1/3
Evaluate the product of the exponents
So, we have
(64x^2/3)^-1/3 = 64^-1/3 * x^(2/3*-1/3)
Evaluate the product of the exponents
So, we have
(64x^2/3)^-1/3 = 64^-1/3 * x^-1/9
Evaluate the exponent
So, we have
(64x^2/3)^-1/3 = 1/4 * x^-1/9
Evaluate the product
So, we have
(64x^2/3)^-1/3 = 1/4x^-1/9
Rewrite as
(64x^2/3)^-1/3 = 1/(4x^1/9)
Hence, the equivalent expression of (64x^2/3)^-1/3 is 1/(4x^1/9)
Read more about equivalent expression at
https://brainly.com/question/2972832
#SPJ1
Find the midpoint of the segment with the following endpoints (4,6) (1,3)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +4}{2}~~~ ,~~~ \cfrac{ 3 +6}{2} \right) \implies \left(\cfrac{ 5 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies \left(2\frac{1}{2}~~,~~4\frac{1}{2} \right)[/tex]
10,645 divided by 5?
Answer:
2,129
5 times 2129 = 10645
Step-by-step explanation:
Hope it helps! =D
REMEMBER: f(2
1) If f(x) = 2x - 3,
a) f(-2) =
which option/graph
PLEASE PLEASE HELP
Alexander is drawing a map of the Federal Triangle in Washington, D.C. The actual Federal Triangle has a base of 3000feet and height of 1200 feet. Alexander needs his drawing to fit on his paper, so he decides to make the base of his triangle 10 inches.
What scale is Alexander using?
The scale of the drawing is 1 inch represents 300 feet .
What is the scale of the drawing?A scale drawing is a smaller image of a larger diagram or object in terms of dimensions. The scale drawing is usually reduced at a constant dimension.
In order to determine the scale of the drawing, divide the base of the actual Federal triangle by the base of the drawing.
Scale of the drawing = original dimensions / dimensions of the scale drawing
3000 / 10 = 300
1 inch represents 300 feet
1 inch : 300 feet
The scale of a drawing is usually written in this format - one a colon (:), the result of the division of the original dimension and the dimension of the scale.
To learn more about scale drawings, please check: https://brainly.com/question/26388230
#SPJ1
Simplify. (3⁻²) (3⁵) .
The Brandywine Dance Team is buying equipment and T-shirts. The equipment costs $356 and the T-shirts cost $12 each. The team spent a total of $644
The number of T-shirts bought by the Brandywine Dance Team is 24.
How is the number of T-shirts determined?The number of the T-shirts that the Brandywine Dance Team purchased is determined using basic mathematical operations of division, subtraction, addition, and multiplication.
First, the cost of the equipment is subtracted from the total cost spent by the team. The remainder refers to the cost of the T-shirts. Since one T-shirt costs $12, the total quantity of T-shirts bought is 24.
Data and Calculations:The total amount spent = $644
The cost of the equipment = $356
The remainder after the equipment = $288 ($644 - $356)
Unit cost of T-shirts = $12
The number of T-shirts bought = 24 ($288/$12)
Thus, the Brandywine Dance Team bought 24 T-shirts.
Learn more about mathematical operations at https://brainly.com/question/20628271
#SPJ1
Question Completion:How many T-shirts were purchased by the Team?
Which expression is equivalent? Please help!
Answer:
I am pretty sure it is y^14/z^14
Answer
y^14 / z^14 (Option 3)
Step-by-step explanation:
The z^-4 adds to the z^3, making z^7
The y^-2 adds to the y^5 making y^7
The negative square flips the equation and essentially doubles it. leaving the Y on the numerator and Z on the denominator, doubling the 7 into 14
Enterprise will allow you to rent a car for $10 per day plus a $20 fee. Hertz will allow you to rent a car for $40 a
day. After how many days, x, will Enterprise cost more than Hertz?
Yes..............................
-5; -1/2; -0.05; -45% least to greatest
Answer:
-5, 1/2, -0.45, -0.05 would be the solution