The lengths of a lawn mower part are approximately normally distributed with a given mean Mu = 4 in. And standard deviation Sigma = 0. 2 in. What percentage of the parts will have lengths between 3. 8 in. And 4. 2 in. ? 34% 68% 95% 99. 7%.
Empirical rule is defined for normal distributions. The percentage of the parts the lengths between 3.8 inches and 4.2 inches lie is: Option B: 68%
What is empirical rule?According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]
where we had
[tex]X \sim N(\mu, \sigma)[/tex]
where mean of distribution of X is [tex]\mu[/tex] and standard deviation from mean of distribution of X is [tex]\sigma[/tex]
For the given case, as it is given that the lengths of a lawn mower part are approximately normally distributed, let its lengths be tracked by a random variable X
Then, [tex]X \sim N(\mu =4, \sigma = 0.2)[/tex]
The needed percentage is
[tex]P(3.8 < X < 4.2)[/tex]
We can rewrite it as:
[tex]P(4-0.2 < X < 4 + 0.2)[/tex]
This is the percent of values lying under one standard deviation about the mean of X. Using the empirical rule, we get the percentage as:
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%[/tex]
Thus,
[tex]P(4-0.2 < X < 4 + 0.2) = 68\%[/tex]
Thus, The percentage of the parts the lengths between 3.8 inches and 4.2 inches lie is: Option B: 68%
Learn more about empirical rule here:
https://brainly.com/question/13676793
how do you find A? will give brainliest.
Answer:
a = -2/9
Step-by-step explanation:
Locate two points that cross grid intersections and compute the slope of the line between them. I would choose the vertex (4, 4) and the point (-5, 2) as being points where the graph crosses grid intersections.
The slope of the line between those points is given by the slope formula ...
m = (y2 -y1)/(x2 -x1)
m = (2 -4)/(-5 -4) = -2/-9 = 2/9
We note that this representation of the absolute value function appears inverted (reflected across the x-axis). That means the coefficient 'a' will be negative. The slope of an unmodified absolute value function is -1 to the left of the vertex. It will only be 2/9 if the function has been multiplied by -2/9.
a = -2/9
__
Additional comment
The vertex on the graph is at (4, 4), so the values of (h, k) are (4, 4).
Answer:
[tex]-\frac{2}{9}[/tex]
Step-by-step explanation:
Using the points (-5,2) and (4,4), the slope is given as 2/9. This is an absolute value graph, so from this information the slope is either 2/9 or -2/9. The graph faces downwards, so the slope is negative and therefore [tex]-\frac{2}{9}[/tex].
which is greater 5/7 or 3/4?
Answer:
3/4
Step-by-step explanation:
common denominator is 28
20/28 and 21/28 so 3/4 is greater
5/7 = 0.71
3/4 = 0.75
¾ is greater.
- Toodles!~
Find the volume of the prism.
6 m
7 m
8 m
Step-by-step explanation:
hello,
simply knowing the formula will lead you to the answer easily.
formula to find the volume of a prism:
v = bh, where b = base area and h = height.
here, in the picture given, the :
h of the prism = 6m
base area = length * width
b = 8 cm × 7 cm
b = 56 cm²
thus, using v = bh,
v = 56 × 6
v = 336 cm³
please try to understand, and let me know if you have any questions,
have an amazing day! au revoir!
The ratio of the measures of three sides of a triangle is 2:5:4, and its perimeter is 154 units. Find the measure of each side of the triangle.
Answer:30, 75, 60.
Step-by-step explanation:
Can someone please help Tysm!!
Answer:
[tex]y - 6 = 5[/tex]
equation are màthematical statements containing two algebraic expression on both sides of an "equal to (=)" sign.
Answer:
the answer is C/3
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
v/5-4-(v/4)=0
v
Simplify —
4
v v
(— - 4) - — = 0
5 4
STEP 2:
v
Simplify —
5
Equation at the end of step
2
:
v v
(— - 4) - — = 0
5 4
STEP 3:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 5 as the denominator :
4 4 • 5
4 = — = —————
1 5
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
v - (4 • 5) v - 20
——————————— = ——————
5 5
Equation at the end of step 3:
(v - 20) v
———————— - — = 0
5 4
STEP 4:
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 4
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
5 1 0 1
2 0 2 2
Product of all
Prime Factors 5 4 20
Least Common Multiple:
20
Calculating Multipliers :
4.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 4
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
4.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (v-20) • 4
—————————————————— = ——————————
L.C.M 20
R. Mult. • R. Num. v • 5
—————————————————— = —————
L.C.M 20
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
(v-20) • 4 - (v • 5) -v - 80
———————————————————— = ———————
20 20
STEP 5:
Pulling out like terms :
5.1 Pull out like factors :
-v - 80 = -1 • (v + 80)
Equation at the end of step 5:
-v - 80
——————— = 0
20
STEP 6:
When a fraction equals zero :
6.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
-v-80
————— • 20 = 0 • 20
20
Now, on the left hand side, the 20 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
-v-80 = 0
Solving a Single Variable Equation:
6.2 Solve : -v-80 = 0
Add 80 to both sides of the equation :
-v = 80
Multiply both sides of the equation by (-1) : v = -80
What is the quotient?
x-3) 4x2+3x+2
PLS HELP HURRYYY (100 POINTS)
Answer:
I think that the selected answer is correct
Step-by-step explanation:
Answer:
Its step 3 which needs correction.
Step-by-step explanation:
step 3 is deeply a mistake, the step 3 correction is correct that the total sum of interior angles which is 180 degrees is equal to the angle of total straight line angle. Step 2 is correct that when angle m plus angle p sums, they mix up to 180 degrees and its adjacent supplementary angles.
The radius r of a sphere is 6 units. find the volume of a sphere right your answer in terms of π
Answer:
904.77
Step-by-step explanation:
(4/3) · π · r3 = (4÷3)×π×(6^3) = 904.778684 = 904.77
ray is not part of a line.
true or false
Answer:
false
Step-by-step explanation:
ray is a part of a line
hope it helps
HELP ASAP PLEASE For the inequality, find two values for x that make the inequality true: x+3<70
A. 80
B. O
C. 70
D. 60
E. 69
Answer:
b,d
Step-by-step explanation:
80+3= 83 false
0+3=3 true
70+3= 73 false
60+3=63 true
69+3= 72 false
Hope this helps
[tex]\large\text{Hey there!}[/tex]
[tex]\large\textsf{x + 3}<\large\textsf{70}\\\\\huge\textbf{SUBTRACT 3 to BOTH SIDES}\\\\\large\textsf{x + 3 - 3}<\large\textsf{70 - 3}\\\\\huge\textbf{CANCEL out: 3 -3 because it give you 1}\\\\\huge\textbf{KEEP: 70 - 3 because it help what is}\\\huge\textbf{being compared to the x-value}\\\\\large\text{NEW EQUATION: \textsf{x}} < \large\textsf{70 - 3}\\\\\large\text{SIMPLIFY IT!}\\\\\large\textsf{x}< \large\textsf{67}\\\\\huge\textbf{Thus, your answer is: \boxed{\mathsf{x < 67}}}\huge\checkmark[/tex]
[tex]\large\textbf{It is an (O)(P)(E)(N) circle shaded to the LEFT side of the}\\\large\textbf{number starting at point 67.}[/tex]
[tex]\large\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Write the first 5 terms for this sequence:
Answer:
3, -6, 12, -24, 48
Step-by-step explanation:
Given:
[tex]a_1=3[/tex][tex]a_{n+1}=-2 \cdot a_n[/tex]Therefore,
[tex]a_1=3[/tex]
[tex]a_2=-2 \cdot a_1=-2 \cdot 3=-6[/tex]
[tex]a_3=-2 \cdot a_2=-2 \cdot -6=12[/tex]
[tex]a_4=-2 \cdot a_3=-2 \cdot 12=-24[/tex]
[tex]a_5=-2 \cdot a_4=-2 \cdot -24=48[/tex]
Tell how much each person gets when they share equally.
2 sisters share 3 hours of babysitting.
When a number is trebled and then decreased by 5, the answer is 19. find the original number.
Answer: i think 8
Step-by-step explanation: trebled means three times so 8x3=24 then 24-5=19
Please help I tried doing this. It’s due tomorrow please help! Give me an explanation please by the way!
Example of sphere with a volume
[tex]\pi = 6.15[/tex]
V volumeI need an answer to this math problem.
Answer:
c²
Step-by-step explanation:
Finding the factors:
7c³=7×c×c×c
8c²=2×2×2×c×c
Here,
c×c is common in both terms
Hence,GCF=c²
Two brothers, Mark and Charles, each inherit $27000. Mark invests his inheritance in a savings account with an annual return of 1.8%, while Charles invests his inheritance in a CD paying 4.8% annually. How much more money than Mark does Charles have after 1 year?
A book sold 38,300 copies in its first month of release. Suppose this represents 6.3% of the number of copies sold to date. How many copies have been sold to date?
Round your answer to the nearest whole number.
Answer:
35,887.1 because 38300×93.7 ➗ 100
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS HELP ASAP THANKS
Answer:
the answer is 2
im sure of it
For a ΔABC, ∠A + ∠B + ∠C = .......................
PLS ANSWER AS SOON AS POSSIBLE
180°
sum of angles of triangle = 180°
Answer:
∠A + ∠B + ∠C = 180⁰
Step-by-step explanation:
The sum of the angles in a triangle is 180. This sum is a semicircle or a straight angle. The angle of the semicircle is × 360⁰.
________________
Write the equation of the lines described.
The line has a y-intercept of (0,3) and goes
through the point (2,7)
Answer:
y=2x+3
Step-by-step explanation:
Hi there!
We want to write the equation of the line
We are given that the y-intercept of the line is (0,3) and that the line also goes through the point (2,7)
There are many ways to write the equation of the line, but the most common way is slope-intercept form, which is given as y=mx+b, where m is the slope and b is the y intercept
The value of b is actually the value of y in the point making point of the y intercept
In this case, that point would be 3
So the value of b in this case is 3
Substitute 3 as b into the equation:
y=mx+3
Now we need to find m
As the equation passes through the point (2,7), we can use it to help solve for the value of m
Substitute 2 as x and 7 as y into the equation:
7=2m+3
Subtract 3 from both sides
4=2m
Divide both sides by 2
m=2
Substitute 2 as m into the equation:
y=2x+3
Hope this helps!
Take a look here if you wish to have a similar problem for practice (n.b., the solution uses a different method than the one shown here): https://brainly.com/question/7457022
Solve the problem and explain the steps taken. There are four students working on a project in math class. Miguel has completed 1/8 of the project, Gina has completed 13% of the project, Jatziry has completed 0.10 of the project, and Kwa has completed 19 of the project. Makw a list of students in order from least to greatest by the amount of the project they have completed.
Answer:
10%
12.5%
13%
19%
Step-by-step explanation:
First write all of the amounts as a percent.
1/8 = 12.5%
13%
.10 = 10%
19%
Then you can order them from least to greatest.
10%, 12.5%, 13%, and then 19%
hope this helps
A high school championship football game was attended by 1580 fans. there were 640 were out of state fans at the game. the other fans were local. What is the ratio?
A) 15/14
B) 32/79
C) 49/79
D) 32/47
CORRECT ANSWER GETS BRANLIEST!
ill give 5 stars if u correct
Answer:
A.
Step-by-step explanation:
On graph A, all 4 points (G, P, R, and S) are all in the correct order. Options B and D are easy to eliminate because we know that none of the nests are actually at the center.
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let me know if you have any questions! Spread the love.
Answer:
A.
Step-by-step explanation:
Options A and B are the only number lines with the blue point at the right spot (You can see it is 1/2 mile away so it goes in the middle of 1 and 2). Between these 2 only number line A has the red dot in the right spot (it belongs at -0.25 which is 1 spot left of the center 0).
Which statement shows how the product of (x 3)2 demonstrates the closure property of multiplication? x2 9 may or may not be a polynomial x2 6x 9 may or may not be a polynomial x2 9 is a polynomial x2 6x 9 is a polynomial.
The product of (x + 3)² demonstrates the closure property of multiplication. [tex]\rm x^{2} + 6x + 9[/tex] is a polynomial. Option D is correct.
What is polynomial?Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
What is the closure property of multiplication?A set is closed under an operation when we do that operation on the member of the set and we always get a set member.
Given
An expression is (x + 3)²
On simplifying, we have
[tex]\rm (x + 3)(x + 3)\\\\x (x + 3) + 3 (x + 3)\\\\x^{2} +3x +3x +3^2\\\\x^{2} +6x + 9[/tex]
Thus, [tex]\rm x^{2} + 6x + 9[/tex] is a polynomial.
More about the polynomial link is given below.
https://brainly.com/question/17822016
Answer:
Option D
Step-by-step explanation:
Find a polynomial that represents the area of the triangle in inches.
Answer:
(3x²-3.5x+1)in²
Step-by-step explanation:
area of a triangle = ½(base × height)
= ½(2x-1)(3x-2)
= ½(6x²-4x-3x+2)
= ½(6x²-7x+2)
= 3x²-3.5x+1
A polynomial that represents the area of the triangle is (3x²-3.5x+1)in²
Help is it A or B? pls help
Answer:
[tex]f(x)=-(x+8)(x-2)[/tex]
Step-by-step explanation:
Start by factoring out a -1...
[tex]f(x)=-(x^2+6x-16)[/tex]
Now, we have to find two integers that multiply to get -16 and have a sum of 6:
(-2)*8=-16
-2+8=8-2=6
Using this, we can split 6x into -2x and 8x...
[tex]f(x)=-(x^2-2x+8x+16)[/tex]
Factor the first and second half separately...
[tex]f(x)=-[(x^2-2x)+(8x-16)]\\f(x)=-[x(x-2)+8(x-2)]\\[/tex]
Since both x and 8 are being multiplied by x-2, we can combine them to get...
[tex]f(x)=-(x+8)(x-2)[/tex]
What is the value of a?
a-470°
a+250°
a-45°
a =
Answer:
a = 117°
Step-by-step explanation:
The exterior angle of a triangle = the sum of the remote interior angles.
a + 25° = (a - 47°) + (a - 45°)
a + 25° = (a + a) + (-47 - 45)
a + 25° = 2a - 92°
-2a = -2a
-a +25 = -92
-25 = -25
-a = -117°
a = 117°
what is 1/9x5/4??? i need this so i can pass one of my math standards so i do not go to summer school HELP ME!!!!
Answer:
Step-by-step explanation:
1/9x5/4
5/36
You multiply across
5*1 = 5
9*4 = 36
5/36
Hope this helps!
WILL GIVE A BRAINLY AND THANKS
Answer:
190
Step-by-step explanation:
If the ratio is given 1:200
x : 38000 = 190 times the ratio 1:200
1*190 : 200 * 190
190 : 38000
The answer is 190 security personnels
Hope this helps :)
Have an excellent day!