The scores on the statistics test was normally distributed with a mean of 86 and a standard deviation of 5. Jose scored a 93 on his test then 1.4% of the class scored less than he did.
What is Normal Distribution?A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
The scores on the statistics test was normally distributed with a mean of 86, a standard deviation of 5, and Jose scored a 93 on his test.
We need to find the percentage of the class scored less than he did
z=(x-mean)/ S.D
=93-86/5
=7/5
=1.4
Therefore 1.4 percentage of the class scored less than Jose did.
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Determine whether the regular polygon will tessellate in the plane. Write yes or no. Explain.
triangle
Yes , Triangles are all tessellated. The triangle's three corners (A, B, and C) meet together to form a 180° angle, or a straight line, which is why the image is successful.
Is a triangle capable of tessellation?
Triangles are all tessellated. The triangle's three corners (A, B, and C) meet together to form a 180° angle, or a straight line, which is why the image is successful. We state it here since it will serve as the cornerstone of our investigation into polygon tessellations: Any triangle's total angles come to 180 degrees.To create a regular tessellation, it is necessary that the tiles may fill 360 degrees around a point (all the tiles regular polygons with same number of sides) Only 60 degree angle triangles, 90 degree squares, and 120 degree hexagons will work.
Every vertex, edge, and tile in a regular tesselation are identical.
However, there are semiregular tesselations that use more than one regular polygon, but since they must be able to fill 360 degrees around a point, it turns out that only the octagon (8 sides, 135 degrees) and dodecagon can be used as additional polygons (12sides, 150 deg).
Note that just these 5 tesselations can be utilized to fill the plane entirely with regular polygons.
Each vertex in the semiregular tessellations is the same.
Eight of them are (3,3,3,3,6), (3,3,3,4,4), (3,4,6,4), (3,6,3,6), (3,12,12), and (4,6,12). (4,8,8)
The Octagon & square tiling (4,8,8) is a very common floor tiling.
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Determine which line passing through the given points has a steeper slope.
Line 1: (-9,-4) and (7,0)
Line 2:(0,1) and (7,4)
The line which have a steeper slope is Line 1.
It is given in the question that the points on the line are given by:-
Line 1: (-9,-4) and (7,0)
Line 2:(0,1) and (7,4)
We have to find which line has a steeper slope.
First we will find the slope of each line.
We know that slope of a line with points (a,b) and (c,d) is given by:-
(d-b)/(c-a)
Slope of Line 1:
(0-(-4))/(7-9) = 4/(-2) = -2 (we will take the absolute value)
Slope of Line 2:
(4-1)/(7-0) = 3/7
We know that greater the slope of the line means greater the steep of the line.
As,
2 > 3/7
Hence, Line 1 is steeper than Line 2.
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if 3.99 x 10 ^ 13 was written in standard notation how many zeros does it contain before the decimal point
Answer:
11 zeros
Step-by-step explanation:
10^13 = 100 000 000 000 000
Round the two first numbers(which makes 11 zeros left), then lastly the zeros
A circle with radius 3 is contained in a square with side length 9 . What is the probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle?
A. 1/9
B. 1/3
C. π/9
D. 9/π
The probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle is π/9 .
Probability of an event is defined as the Number of favorable outcomes divided by total number of outcomes.
It is denoted by P(E).
Given that
radius of circle = 3
side of the square = 9
Let E be the event that a randomly chosen point in the interior of the square will also lie in the interior of the circle
then
[tex]P(E)=\frac{AreaOfCircle}{AreaOfSquare}[/tex] ...(i)
Area of Circle = πr² = π(3)² = 9π
Area of Square = (side)²=(9)²=81
Substituting the values in equation (i) we get
[tex]P(E)=\frac{9\pi }{81}[/tex]
[tex]=\frac{\pi }{9}[/tex]
Therefore , the probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle is π/9 .
The correct option is (C) π/9
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round 8.6 to the nearest whole number
Answer:
9
Step-by-step explanation:
Since one place to the right is greater than or equal to 5 you round up.
6. What's the product of 3 2/3 and 14 2/5 ?
A. 52 415
B. 42 45
C. 54
D. 52 45
Answer:
D. 52 45
Step-by-step explanation:
Write an explicit and a recursive formula for each sequence. 1,1 1/3, 1 2/3, 2, . . . . . .
an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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Use the given information to write an equation of the circle.
center (2,1) , through (6,4)
Using the given information, the equation of the circle with center located at point (2 , 1) and passes through the point (6 , 4) is (x - 2)^2 + (y - 1)^2 = 25
Using the distance formula, get the radius of the circle by solving for the distance between the center (2 , 1) and the point (6 , 4).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(6 - 2)^2 + (4 - 1)^2
radius= √16 + 9
radius = √25
radius = 5
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (2 , 1)
r = 5
(x - 2)^2 + (y - 1)^2 = 5^2
(x - 2)^2 + (y - 1)^2 = 25
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5n+ 1 = 5n -1
Solve for n
Answer:
no solution
Step-by-step explanation:
5n + 1 = 5n - 1 ( subtract 1 from both sides )
5n = 5n - 2 ( subtract 5n from both sides )
0 = - 2 ← not possible
this indicates that the equation has no solution
The pivot or midpoint of a seesaw on a playground is 13.5 feet from the swing set. If the swing set is 8 feet from the edge of the seesaw when the seesaw is level, how long is the seesaw.
The length of seesaw will be equal to 11 feet.
It is given that midpoint of the seesaw is 13.5 feet from the swing set and swing set is 8 feet from the edge of the seesaw.
We have to find out the length of seesaw.
What do you mean by midpoint of a line segment ?
The midpoint is halfway between the two end points , whose x value is halfway between the two x values and y value is halfway between the two y values.
As per the question ;
The midpoint of the seesaw is 13.5 feet from the swing set.
and
The swing set is 8 feet from the edge of the seesaw.
So ;
The distance from the midpoint to the edge will be ;
13.5 – 8 = 5.5.
And
The length of the seesaw will be ;
= 2× (5.5)
= 11 feet
Thus , the length of seesaw will be equal to 11 feet.
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Evaluate the expression and enter your answer in the box below.
[(5+11) 4]+9. (6-4)
÷
Answer here
Answer:
22 :)
Step-by-step explanation:
I've attached an image to help break down the answer. (credit to cymath.com)
Hope this helps!
E represents the anchors elevation relative to the waters surface (in meters)
A large ship lowered its anchor, The anchor's elevation (in meters) in relation to the water's surface is represented by E as a function of time t. (in sec) E=-2.4t+75. The anchor drop 12 meters every 5 seconds.
Given that in the picture we can see the question that is
A large ship lowered its anchor,
The anchor's elevation (in meters) in relation to the water's surface is represented by E as a function of time t. (in second).
E=-2.4t+75
According to the function E=-2.4t+75
We assume that [tex]t_{1}[/tex].
So, every 5 second [tex]t_{1}[/tex]=t+5.
So, we get
ΔE=E(t)-E(t+5)
ΔE=-2.4t+75-(-2.4(t+5)+75)
ΔE=-2.4t+75+2.4t+12-75
ΔE=12
Therefore, the anchor drop 12 meters every 5 seconds.
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A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 18 minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 22 minutes.
write this as an equation
Answer:
Step-by-step explanation:
Givens
Flight speed there = 12 feet / second
Flight speed back = 8 feet / second
Total time = 22 minutes
Time at rest = 18 minutes
Time in flight = 22 - 18 = 4 minutes
Equation
Let the time going to the flowerbed = t
12*t + 8*t + 18 = Distance travelled + time at rest.
Answer
12*t + 8*t + 18 = Distance travelled + time at rest
Find the measure of the combined angle.
27°
44°
Measure of the combined angle of 71° .
71 degrees is an acute angle .
Given, that two measure of angles 44 degrees and 27 degrees .
Classification of angles :
Acute angle : 0° ≤ Ф ≤ 90°
Right angles : Ф = 90 degrees
Obtuse angles : 90° ≤ Ф ≤ 180°
Reflex angle : 180° ≤ Ф ≤ 360°
Here the angles given are 44 degrees and 27 degrees.
Combined measure of two angles = 44 + 27
= 71 degrees.
Acute angle : 0° ≤ Ф ≤ 90°
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PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
The equation and the solution are 2 = -8 * -x and x = 1/4, respectively
How to determine the equation and the solution?On the model, we have the following representations
[1][1] [-1][-1][-1][-1][-1][-1][-1][-1][-x]
When represented as an equation, we have the following equation
So, we have
2 = -8 * -x
Evaluate the product in the above equation
So, we have
2 = 8x
Divide both sides of the above equation by 8
So, we have
1/4 = x
Rewrite the above expression as
x = 1/4
Hence, the equation and the solution are 2 = -8 * -x and x = 1/4, respectively
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Write a function g whose graph represents the indicated transformation of the graph of f(x)=-2|x-4|+2
Using translation concepts, the function g is given as follows:
g(x) = -|x - 4| + 1
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, we have that function g(x) is the function f(x) vertically compressed by a factor of 2, hence:
g(x) = 0.5f(x)
g(x) = 0.5(-2|x - 4| + 2)
g(x) = -|x - 4| + 1
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A zoo has two elephants, Sally and Joe. Sally weighs 7,645 pounds, and Joe weighs 12,479 pounds. How much do Sally and Joe weigh in all?
As per given data of two elephants, Sally weighs 7,645pounds and Joe weighs 12,479 pounds then total weight of Sally and Joe is equal to 20,124pounds.
As given in the question,
Number of elephants in zoo = 2
Sally weighs = 7,645 pounds
Joe weighs = 12, 479 pounds
Total weight of Sally and Joe is equal to
= ( 7,645 + 12,479 ) pounds
= ( 20,124 ) pounds
Therefore, as per given data of two elephants, Sally weighs 7,645pounds and Joe weighs 12,479 pounds then total weight of Sally and Joe is equal to 20,124pounds.
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Determine whether each formula is explicit or recursive. Then find the first five terms of each sequence. a₁ =-2, a n =a n₋₁ -5
This is recursive sequence and -2, -7, -12, -17, -22, -37 these are the first five terms of sequence.
How to find the first five terms of sequence a₁ = -2, a (n) =a (n-1)-5 ?A recursive formula is one that defines each term in a sequence by reference to the one before it. The following parameters are defined using the recursive formulas:
1. The initial term in the series.
2. The general rule for determining any term from its preceding term.
Recursive Arithmetic Sequence Formula
The following is the recursive formula to determine the nth term in an arithmetic series:
an = an-1 + d for n ≥ 2
where
The common difference is d, and an is the nth term of an A.P.
given that
a₁ = -2
a (n) =a (n-1) -5 so, d = -5
For example, we need to extend the sequence term by term in order to find the first five terms:
a(1) = -2
a(2) = a(1) + d = -2 + (-5) = -7
a(3) = a(2) + d = -7 + (-5) = -12
a(4) = a(3) + d = -12 + (-5) = -17
a(5) = a(4) + d = -17 + (-5) = -22
a(6) = a(5) + d = -22 + (-5) = -27
Hence,this is recursive sequence and -2, -7, -12, -17, -22, -37 these are the first five terms of sequence.
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Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 50+55+60+ . . . ; n=7
The summation notion of given series is ∑50+5n , here n starts from 0 and the sum of given arithmetic series is 455.
The given arithmetic series is 50+55+60+ . . .
The summation notion of given series is ∑50+5n , here n starts from 0.
The sum of arithmetic series can be written as,
[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]
n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.
We have, n=7, [tex]a_{1}[/tex] = 50
To calculate sum of arithmetic series, we need to find [tex]a_{7}[/tex] .
[tex]a_{7} = a_{1} + (n-1)d[/tex]
d = 5 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get
[tex]a_{7}[/tex] = 50 + (7-1)(5)
[tex]a_{7}[/tex] = 50 + 30 = 80
On substituting values in sum of arithmetic series formula, we get
[tex]S_{7}[/tex] = (7(50 + (80)))/2 = 455
The summation notion of given series is ∑50+5n , here n starts from 0 and the sum of given arithmetic series is 455.
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Kayla buys candy that costs $7 per pound. She will buy less than 8 pounds of candy. What are the possible amounts she will spend on candy? 
Use c for the amount (in dollars) Kala will spend on candy. Write your answer as in inequality solved for c.
Answer:
[tex]0 \leqslant c \leqslant 56[/tex]
Step-by-step explanation:
Since candy costs $7 per pound, and Kayla will buy less than 8 pounds, she will spend no more than $7 × 8, or $56.
HELP ASP SHOW UR WORK YOULL GET BRAINLEST
Answer:
X=2
Step-by-step explanation:
Add four to both sides
2x-4=0
2x-4+4=0+4
Add the numbers 2x = 4
2x =4
2x/2 = 4/2
cancel the terms
divide the numbers
= x=2
If Y=3x+5 and x=0 what is y
The heights of a sample of 15 students are recorded in
the stemplot below.
Heights of Students
What is the mean height, in inches, of this sample?
65
65.2
66
67
The mean height of the given sample of values is approximately 65.20.
The heights of the 15 students are as follows:
{59, 61, 62, 63, 63, 64, 65, 65, 66, 67, 67, 67, 67, 69, 73}
To find the mean (average) height of the given values, we need to add up all the heights and then divide the sum by the total number of heights:
59 + 61 + 62 + 63 + 63 + 64 + 65 + 65 + 66 + 67 + 67 + 67 + 67 + 69 + 73
= 978
So, the mean height can be calculated as:
Mean height = Total height / Number of heights = 923 / 15 = 65.2
Therefore, the mean height is approximately 65.20.
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6n² - 15 = 6 (5)² - 15
Answer:
6n2-15=150-15
6n2-15=135
6n2=150
divied both side by 6
n2=25
sqrt both side
n=-5 or 5 bc sqrt so 2 answer
Step-by-step explanation:
Jessica tan 52,520 feet in 50 minutes. What is Jessica’s rate in miles per hour
Simplify by combining like terms. -(3 x-4 y)+x
By combining the like terms, the simplified form of the expression -(3x-4y)+x is -2x+4y
Given,
The algebraic expression = -(3x-4y)+x
Expand the terms
-(3x-4y)+x= -3x+4y+x
Combine the like terms
-3x+4y+x= (-3+1)x+4y
=-2x+4y
Hence, by combining the like terms, the simplified form of the expression -(3x-4y)+x is -2x+4y
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Prove or disprove that the product of a nonzero rational number and an irrational number is irrational.
Answer: The claim is true
The proof is below
=====================================================
A = some nonzero rational number
B = some irrational number
Because value A is rational, this means A = p/q where p,q are nonzero integers.
Let's do a proof by contradiction. The claim is that A*B is irrational, but let's do the opposite and assume A*B is rational. We should get to a contradiction somewhere based on this assumption.
If A*B is rational, then A*B = r/s for some integers r and s
Then we can have the following steps
A*B = r/s
(p/q)*B = r/s
B = (r/s)*(q/p)
B = (rq)/(sp)
B = (some integer)/(some other nonzero integer)
B = some rational number
Recall we made B irrational. There's no way to have B rational and irrational at the same time. This is where the contradiction happens. This causes the original assumption of "A*B is rational" to be false. Therefore, the opposite must be the case and A*B has been proven to be irrational.
Therefore, the product of a rational number and an irrational number is irrational.
------------------------
Example:
5 is rational
sqrt(3) is irrational
5*sqrt(3) is irrational
Determine the slope of the line that contains the given points.
G(-4,3), H(-4,7)
The slope of the line that contains the points G(-4,3), H(-4,7) is not defined.
Slope of a line containing two points (a,b) and (c,d) is denoted by
[tex]slope=\frac{d-b}{c-a}[/tex]
In the given question
The points given are G(-4,3), H(-4,7)
a=-4, b= 3 and c= -4 and d=7
Substituting the values in formula of slope we get
[tex]slope=\frac{d-b}{c-a}[/tex]
[tex]slope=\frac{7-3}{-4-(-4)}\\ \\ =\frac{4}{-4+4} \\ \\ =\frac{4}{0}[/tex]
Since the division of any number by zero is not defined .
Therefore , the slope of the line that contains the points G(-4,3), H(-4,7) is not defined.
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Please help me with this math problem! Will give brainliest!! :)
Answer:
f (x^2-4) = 2x^2 - 5
Step-by-step explanation:
Given f (x) = 3x – 5 and g(x) = 2x + 1, find g(f(x)).
Answer:
g(f(x)) = 6x -9
Step-by-step explanation:
Given f(x) = 3x –5 and g(x) = 2x +1, you want to find g(f(x)).
Function evaluationA function is evaluated by simplifying the result of substituting the argument for the function's variable.
g(f(x)) = 2·f(x) +1 = 2(3x -5) +1 = 6x -10 +1
g(f(x)) = 6x -9
