Using the normal distribution, it is found that there is a 0.84 = 84% probability that a randomly selected high jumper has a personal best between 227 and 265 cm.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 208, \sigma = 19[/tex]
The probability that a randomly selected high jumper has a personal best between 227 and 265 cm is the p-value of Z when X = 265 subtracted by the p-value of Z when X = 227, hence:
X = 265:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{265 - 208}{19}[/tex]
Z = 3
Z = 3 has a p-value of 0.9987.
X = 227:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{227 - 208}{19}[/tex]
Z = 1
Z = 1 has a p-value of 0.1587.
0.9987 - 0.1587 = 0.84.
0.84 = 84% probability that a randomly selected high jumper has a personal best between 227 and 265 cm.
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The surface area of a cube is 96 square units. What is the volume of the cube?
Answer:
volume=64
Step-by-step explanation:
surface area of cube =96
6l²=96
l²=16
l=4
now, by the question
volume of cube =l³
=(4)³
=64
A line passes through the points (3,0) and (4,2). What is its equation in slope-intercept form?
Answer:
y = 2x - 6
Step-by-step explanation:
Slope intercept form:Equation of the line:
[tex]\sf \boxed{ y = mx +b}[/tex]
Here m is the slope and b is the y-intercept.
Step 1: Find the slope
(3 , 0) ⇒ x₁ = 3 & y₁ = 0
(4 , 2) ⇒ x₂ = 4 & y₂ = 2
[tex]\sf \boxed{Slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{2 -0}{4-3}\\\\= \dfrac{2}{1}\\\\=2[/tex]
m = 2Step2: Now, substitute the value of 'm' in the equation.
y = 2x + b
Step3: In the above equation plug in any point. Here, (3 ,0) is chosed.
0 = 2*3 + b
0 = 6 + b
-6 = b
b = -6Step4: Equation of the line:
y = 2x - 6
Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin
The standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin and directrix is y² = 16x.
What is the parabola?It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
Given that the parabola's vertex is located at the origin and that the directrix is at x = -4, the focus is at (4,0).
Then the equation can be written as
[tex]\rm \sqrt{(x-4)^2 +(y-0)^2} = \sqrt{(x+4)^2 + (y-y)^2}\\\\\sqrt{(x-4)^2 +(y-0)^2} = \sqrt{(x+4)^2}[/tex]
On squaring both sides, we have
[tex]\begin{aligned} (x-4)^2 +(y-0)^2 &= (x+4)^2 \\\\x^2 + 16 - 8x +y^2 &= x^2 + 16 + 8x\\\\y^2 &= 16x \end{aligned}[/tex]
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Xaiver earns 45$ to walk the neighbors dog 8 hours during the week how much does xaiver earn ler hour
Answer:
$5.625 (per hour)Step-by-step explanation:
45÷8 = 5.625
What best describes arc ZMF? ARC TFM and ARC TZ? I have no clue which is which.
1. Major Arc
2. Semicircle
3. Minor Arc
What is minor arc?An arc whose measure is less than 180 degrees is called a minor arc.
What is major arc?An arc whose measure is greater than 180 degrees is called a major arc.
What is semicircle?An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two.
1. The arc ZMF defines a major arc as the measure is more than 180.
2. Arc TFM defines semicircle as it measure 180 degrees.
2. Arc TZ defines a minor arc as the measure is less than 180.
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State the equation of a line perpendicular to y = -3 going through (-5, -3).
Answer:
x=-5
Step-by-step explanation:
Answer:
Equation of the perpendicular line is x = -5
Step-by-step explanation:
The equation of the given line is y =-3
This means that the given line is parallel to the x axis. Imagine a horizontal line and for all values of x, the y value is constant -3. So the line perpendicular to this line would be one that is parallel to the Y axis. Imagine a vertical line. This line would have the same x value for all values of Y. Equation would be of the form
x = constant.
It is given that the line passes through (-5, -3), from which we get that constant value as -5.
Equation of the perpendicular line is x = -5
helppp need answers asap
The number of cookies baked by Tanya in 12 batches of 18 cookies per batch including 70 cookies of Monday is 286.
What is mathematical model or function?A mathematical model or function is the model which is used to explain any system, the effect of the components by study and estimate the functions of systems.
The total number of cookies made by Tania on the Monday is 70 and want to make more than this on Tuesday.
The capacity of the pan is to cook 18 cookies per batch. The function she used to predict the number of cookies is,
y=70+18(x)
Here, x is the number of batches.
The cookies baked by her in 12 batches,
y=70+18(x)
y=70+18(12)
y=286.
Thus, the number of cookies baked by Tanya in 12 batches of 18 cookies per batch including 70 cookies of Monday is 286.
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Find the missing measures in each parallelogram
help!!
Answer:
y=8
Step-by-step explanation:
SR=2×SG
AND SG=GR
3y-16=2×4
3y-16=8
3y=8+16
3y=24
y=8
7. Solve the equation 2x + 4 = 9. Explain the
and properties you used.
A local restaurant owner can purchase tea for $16 per pound and coffee for $8 per pound. His budget does not allow him to spend more than $280 on coffee and tea. Which graph shows the possible combinations of pounds of tea, x, and pounds of coffee, y, that the restaurant owner can purchase?
Answer:
answer is 152
Step-by-step explanation:
i mutiplied $16 and $8 and got 128 the subtracted 128 and 280 and final answer is 152
Please hurry!A flagpole casts a shadow that is 28 fery long. At the same time,a stick that is 2 feet tall casts a shadow that is 3.5 feet long how tall is the flagpole?
Answer - The flagpole is 16 feet tall.
Explanation -
2/3.5 =1.75
1.75x16 =28
What is the sum of the numbers in the series below? 15 11 7 . . . (–129)
Using Gauss's method, the sum of the numbers in the given series [ 15 11 7 . . . . ( –129 ) ] is -2664.
What is an arithmetic sequence?An arithmetic sequence is simply a sequence of numbers in which the difference between the consecutive terms is constant.
From Gauss's method nth term is an arithmetic sequence is expressed as;
n = (( first term - last term )/d) + 1
d is the common difference between terms.
Given the series in the question;
15 11 7 . . . (–129)
d = 15 - 11 = 4
Next, we find n
n = (( first term - last term )/d) + 1
n = (( 15 - (-129))/4) + 1
n = ( 144/4 ) + 1
n = 36 + 1
n = 37
Now, using the common difference between terms the sun will be;
S = 15 + 11 + 7 . . . -125 -129
Also
S = -129 -125 . . . + 7 + 11 + 15
We add
2S = -114, 114, 114 . . . . n
Hence, the sum will be;
2S = ( -114 ) × n
2S = ( -114 ) × 37
2S = -5328
S = -5328 / 2
S = -2664
Therefore, using Gauss's method, the sum of the numbers in the series [ 15 11 7 . . . (–129) ] is -2664.
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Maths question
Write an algebraic expression for each of the following
Answer:
a) 3n+5
b) n+16
c) [tex]\frac{n-9}{2}[/tex]
d) [tex]\frac{x-u}{x+u}[/tex]
Question attached and investigates relationship between zeroes and tangents of cubic function
The tangent lines of the cubic function f(x) = x(x - 2)(x - 6) at the zeros 0, 2 and 6 are y = 12x, y = -8x + 16 and y = 24x - 144
Part A: The tangent lines of f(x) = x(x - 2)(x - 6)The cubic function is given as:
f(x) = x(x - 2)(x - 6)
Expand
f(x) = x³ - 8x² + 12x
Differentiate the function
m = 3x² - 16x + 12
At the point x = 0, we have:
m = 3(0)² - 16(0) + 12
m = 12
Also, we have:
f(0) = 0
A linear equation is represented as:
y = m(x - x₁) + y₁
So, we have:
y = 12(x - 0) + 0
y = 12x
At the point x = 2, we have:
m = 3(2)² - 16(2) + 12
m = -8
Also, we have:
f(2) = 0
A linear equation is represented as:
y = m(x - x₁) + y₁
So, we have:
y = -8(x - 2) + 0
y = -8x + 16
At the point x = 6, we have:
m = 3(6)² - 16(6) + 12
m = 24
Also, we have:
f(6) = 0
A linear equation is represented as:
y = m(x - x₁) + y₁
So, we have:
y = 24(x - 6) + 0
y = 24x - 144
The above means that the tangent lines are:
y = 12x, y = -8x + 16 and y = 24x - 144
From the attached graph, we can see that the tangent lines at the zero values x = 0 and x = 2 intersect the graph of f(x) at the zero value x = 6
Part B: The tangent lines of f(x) = (x - a)(x - b)(x - c)The equation is given as:
f(x) = (x - a)(x - b)(x - c)
To prove the statement using a computer algebra system, simply follow the next steps:
Set values for a, b and cInclude the following vertices in the plane: (a,f(a)), (b,f(b)) and (c,f(c))Differentiate f(x) i.e g(x) = f'(x)Include the following vertices in the plane: (a,g(a)), (b,g(b)) and (c,g(c))Lastly, plot the following equations: y = g(a)(x - a) + f(a), y = g(b)(x - b) + f(b) and y = g(c)(x - c) + f(c)See attachment (2) for proof
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Which inequality describes the graph?
The graph is a linear inequality, and the inequality that describes the graph is y < 2x - 1
How to determine the inequality?From the graph, we have the following features:
y-intercept, b = -1It passes through the points (0,-1) and (1,1)The line is a dotted line and the lower region are shaded; so, we make use of the < inequalityNext, we calculate the slope using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{1 + 1}{1 - 0}[/tex]
m = 2
The inequality is then calculated using:
y < mx + b
This gives
y < 2x - 1
Hence, the inequality that describes the graph is y < 2x - 1
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A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a square. Which of the following solids could have resulted in that cross section?
Answer:
It's A.
Step-by-step explanation:
This is because the cross section of the shape is a square, which is why it is A.
Eric is painting & wooden cylinders. Each cylinder has a radius of 6.2 inches and a
height of 12.4 inches. Eric can paint 50 square inches of wood using one pint of paint.
How much paint will Eric need to paint all the wooden cylinders?
2특
5
5) What is 2 and 5/7as an improper fraction?
17
a) 15
a
b) 3
b
c) 15
5
d)
3. Write the polynomial function with the given degree and zeros. Degree: 8 zeros: 7 multiplicity 2
Step-by-step explanation:
I think answer is 14 please give me a brain list
what is the projected population for 2015
Answer:
the answer is b
Step-by-step explanation:
ive did it before
Two consecutive integers have a sum of 195. Find the integeres
Hey ! there
Answer:
First Integer is 97Second Integer is 98Step-by-step explanation:
The question says that two consecutive Integer have a sum of 195 . And we are asked to find the integers.
For finding integers we are assuming them . So ,
Let the first integer be x .Let the second integer be x + 1 ( This is because in question it's given that they are consecutive integers )Solution : -
According to question ,
First Integer + Second Integer = 195So ,
[tex] \dashrightarrow \qquad \: x + x + 1 = 195[/tex]
Step 1 : Adding like terms ( x and x ) on left side :
[tex] \dashrightarrow \qquad \: 2x + 1 = 195[/tex]
Step 2 : Subtracting 1 on both sides :
[tex] \dashrightarrow \qquad \: 2x + \cancel{1} - \cancel{1} = 195 - 1[/tex]
Simplifying it ,
[tex] \dashrightarrow \qquad \: 2x = 194[/tex]
Step 3 : Dividing with 2 on both sides :
[tex] \dashrightarrow \qquad \: \dfrac{ \cancel{2}x}{ \cancel{ 2}} = \cancel{\dfrac{194}{2} }[/tex]
On further calculations , We get :
[tex] \dashrightarrow \qquad \: \purple{\underline{\boxed{\frak{ x = 97}}}} \quad \: \bigstar[/tex]
We know that ,
x = first number✰ Therefore , first number is 97 .
x + 1 = second number97 + 1 98✰ Therefore , second number is 98.
Verifying : -
Now , we are verifying our answer by substituting value of first and second number and equating it with 195 . So ,
97 + 98 = 195195 = 195L.H.S = R.H.SHence , Verified .Therefore , our solution is correct .
#Keep Learning- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Two consecutive integers have a sum of 195. Find the integers
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]
The integers are 97 and 98.
[tex]\blue{\textsf{\textbf{\underline{\underline{How to Solve:-}}}}[/tex]
If integers are [tex]\textbf{consecutive,}[/tex] they stand right next to each other.
Example:- 7 and 8. 7 and 8 are consecutive integers because they stand right next to each other.
Now, let the integer be n.
The integer next to n is 1 greater than n, or n+1.
So we set up the following equation:-
[tex]\bigstar{\fbox{n+n+1=195}[/tex]
[tex]\textsf{\underline}}[/tex]Add the n's:-
[tex]\Longrightarrow[/tex] [tex]\sf{2n+1=195}[/tex]
Subtract 1 on both sides:
[tex]\sf{2n=195-1}[/tex]
[tex]\sf{2n=194}[/tex]
Divide by 2 on both sides:-
[tex]\bigstar{\fbox{n=97}[/tex]
Now that we've found the first integer, finding the second integer is easy, because we can subtract the first integer from the sum of both integers:-
195-97=98
So the second integer is 98.
Quick Check:-
97 and 98 are consecutiveThey add up to 195:-97+98=195[tex]\textbf{195=195}[/tex]Since the LHS (left-hand side) equals the RHS (right-hand side), the integers are indeed 97 and 98.Good luck.
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The width of a rectangle measures (36 + 5) centimeters, and its length measures
(86 + 6) centimeters. Which expression represents the perimeter, in centimeters, of
the rectangle?
Answer:
Step-by-step explanation:
36+5=41
86+6=92
41*2=82
92*2=184
82+184=266
What Is The Volume? Show Your Work Please
Answer:
406[tex]ft^{2}[/tex]
Step-by-step explanation:
Find the midpoint of the 2 coordinates (0,5) and (4,17)
Answer:
(2, 11)
Step-by-step explanation:
Using the information you were give, plug it into this formula:
(x₁ + x₂)/2, (y₁ + y₂)/2
This should give you a new coordinate.
so i have this question this math problem is: James works in a factory and wraps 8 packages every hour. How many hours will it take James to wrap 3,736 packages THIS IS CONFUSING someone help
Answer:
467 hours.
Step-by-step explanation:
3736 / 8
= 467.
4.what is the equation of the line perpendicular to y = 3/4x + 2 and goes
through the point (6, 3)?
a.y = 3/4x + 11
ob.y = 4/3x - 5
o c. y = -3/4x - 5
od. y = -4/3x +11
This is easy answer this and you will get points!!love you guys
Answer:
4. 56 is 8 times as many as 7.
56 = 8 x 7
5. 6, 12, 18, 24, and 30
6. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Hope this helps!
Hey there!
SIMPLIFYING #4
Question reads….
“56 is _____ times as many as _____”
~ The factors of 56 is/are
• 1, 2, 4, 7, 8, 14, 28, & 56
~ The factor pairs of 56 is/are
• 1 × 56 = 56
• 2 × 28 = 56
• 4 × 14 = 56
• 7 × 8 = 56
~ So, for the FIRST portion we can day
“56 is _2_ times as many as _28_”
(or you could choose any numbers from your factoring pair !)
SIMPLIFYING #5
Question reads….
“List the first five multiples of 6”
~ Meaning of multiples
• Multiples is any number that can be divided EVENLY without any remainders.
~So, the first five multiples are….
• 6, 12, 18, 24, & 30
SIMPLIFYING #6
Question reads….
“Name all the factors of 72”
~ Meaning of factoring/factor
• Factoring is another name for factorizing/factorization. It is basically a number that when you’re multiplying with another number that produces a number or expression
~ So, the factors of 72 is/are….
• 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 , & 72
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The integer succeeding -9 is
The integer succeeding -9 is - 8.
Answer:
-8 is the answer as it goes like -10,-9,-8 etc
Which statements are true for the given geometric sequence? Check all that apply.
The domain is the set of natural numbers.
The range is the set of natural numbers.
The recursive formula representing the sequence is f(x + 1) = Three-halves(f(x )) when f(1) = 4.
An explicit formula representing the sequence is
f(x) = 4(three-halves) Superscript x
The sequence shows exponential growth.
The statements are true for the given geometric sequence.
The domain is the set of natural numbers.
The recursive formula representing the sequence is f(x + 1) = 3/2(f(x )) when f(1) = 4.
The sequence shows exponential growth.
We have given the graph.
What is the geometric sequence?
A geometric sequence is a sequence in which the ratio of every two successive terms is a constant.
The graph is given below we can see that
The domain is the set of natural numbers.
The recursive formula representing the sequence is
f(x + 1) = 3/2(f(x )) when f(1) = 4.
The given graph grows exponentially.
The sequence shows exponential growth
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Answer:
a, c, e
The domain is the set of natural numbers.
The recursive formula representing the sequence is f(x+1) = Three-halves(f(x)) when f(1) = 4
The sequence shows exponential growth.
Step-by-step explanation:
PLEASE SOMEBODY HELP! I’ve been stuck on this question for nearly 5 hours because I literally have no idea what to do somebody please help
Answer:
Well We need to get rid of 1200 mb so your estimated guess would be to delete~2523~ photos If i get this wrong Im very sorry.
Step-by-step explanation:
