Answer:
95.44% of the grasshoppers weigh between 86 grams and 94 grams.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 90 grams and a standard deviation of 2 grams.
This means that [tex]\mu = 90, \sigma = 2[/tex]
What percentage of the grasshoppers weigh between 86 grams and 94 grams?
The proportion is the p-value of Z when X = 94 subtracted by the p-value of Z when X = 86. So
X = 94
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{94 - 90}{2}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
X = 86
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{86 - 90}{2}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
0.9772 - 0.0228 = 0.9544
0.9544*100% = 95.44%
95.44% of the grasshoppers weigh between 86 grams and 94 grams.
What is a dialation?
A Making a shape bigger or smaller based on a scale factor.
A slide of a point in a certain direction.
A turn of a point around the origin.
A flip of a point across a line.
A family of pdf's that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. One such member of the Pareto family is the following pdf.
f(x) = { c//x^3 x≥2
0 x<2
Find the mean of X.
(a) 2
(b) 3
(c) 5
(d) 6
(e) 4
Answer:
[tex]Mean = 4[/tex]
Step-by-step explanation:
Given
[tex]f(x) =\left \{ {{\frac{c}{x^3} \ x\ge 2} \atop {0\ x<2}} \right.[/tex]
Required
The mean of x
Given that:
[tex]f(x) = \frac{c}{x^3}[/tex] [tex]x \ge 2[/tex]
First, solve for c using;
[tex]\int\limits^a_b {f(x)} \, dx = 1[/tex]
Substitute [tex]f(x) = \frac{c}{x^3}[/tex] and [tex]x \ge 2[/tex]
[tex]\int\limits^{\infty}_2 {\frac{c}{x^3}} \, dx = 1[/tex]
Isolate c
[tex]c\int\limits^{\infty}_2 {\frac{1}{x^3}} \, dx = 1[/tex]
Rewrite as:
[tex]c\int\limits^{\infty}_2 {x^{-3}} \, dx = 1[/tex]
[tex]c[\frac{x^{-3+1}}{-3 +1}]|\limits^{\infty}_2 = 1[/tex]
[tex]c[\frac{x^{-2}}{-2}]|\limits^{\infty}_2 = 1[/tex]
[tex]-\frac{c}{2} [x^{-2}]|\limits^{\infty}_2 = 1[/tex]
Expand
[tex]-\frac{c}{2} [{\infty}^{-2} - {2}^{-2}]= 1[/tex]
[tex]-\frac{c}{2} [0 - \frac{1}{4}]= 1[/tex]
[tex]-\frac{c}{2} *- \frac{1}{4}= 1[/tex]
[tex]\frac{c}{8}= 1[/tex]
Solve for c
[tex]x = 8 * 1[/tex]
[tex]x = 8[/tex]
So, we have:
[tex]f(x) = \frac{c}{x^3}[/tex] [tex]x \ge 2[/tex]
[tex]f(x) = \frac{8}{x^3}[/tex] [tex]x \ge 2[/tex]
So, the mean is calculated as:
[tex]Mean = \int\limits^a_b {x * f(x)} \, dx[/tex]
This gives;
[tex]Mean = \int\limits^{\infty}_2 {x * \frac{8}{x^3}} \, dx[/tex]
[tex]Mean = \int\limits^{\infty}_2 {\frac{8}{x^2}} \, dx[/tex]
[tex]Mean = 8\int\limits^{\infty}_2 {\frac{1}{x^2}} \, dx[/tex]
Rewrite as:
[tex]Mean = 8\int\limits^{\infty}_2 {x^{-2} \, dx[/tex]
Integrate
[tex]Mean = 8 {\frac{x^{-2+1}}{-2+1}|\limits^{\infty}_2[/tex]
[tex]Mean = 8 {\frac{x^{-1}}{-1}}|\limits^{\infty}_2[/tex]
[tex]Mean = -8x^{-1}|\limits^{\infty}_2[/tex]
Expand
[tex]Mean = -8[(\infty)^{-1} - 2^{-1}][/tex]
[tex]Mean = -8[0 - \frac{1}{2}][/tex]
[tex]Mean = -8* - \frac{1}{2}[/tex]
[tex]Mean = 8* \frac{1}{2}[/tex]
[tex]Mean = 4[/tex]
PLEASE HELP
what is the perimeter of a quadrilateral with vertices at (1,5), (6,5), (1,11), and (6,11)? enter the answer in the Ⴆσx
Answer:
perimeter = 25.62 units
Step-by-step explanation:
Let the quadrilateral be ABCD
A = (1, 5), B = (6, 5), C= (1, 11) , D = (6, 11)
To find the perimeter we need to add the lengths of sides AB , BC, CD, and AD.
Lets find the length of all sides using distance formula;
[tex]distance = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
[tex]AB = \sqrt{(1-6)^2+(5-5)^2} = \sqrt{25} = 5units\\\\BC= \sqrt{(6-1)^2+(5-11)^2} = \sqrt{25+36} =\sqrt{61} units\\\\CD=\sqrt{(1-6)^2 + (11-11)^2} = \sqrt{25} = 5units\\\\AD = \sqrt{(1-6)^2+(5-11)^2} = \sqrt{25+36} = \sqrt{61}units[/tex]
Perimeter = AB + BC + CD + AD
[tex]=10 + 2\sqrt{61} units[/tex] = 25.62 units
HELP!! these two questions I've been stuck on! Please help!
Can someone please answer
Answer:
6 - 5 = 7 - 61 = 1 (TRUE)Step-by-step explanation:
13 - 6 = 6 - 1
7 = 5 (FALSE)
-----------------------------
6 - 5 = 7 - 6
1 = 1 (TRUE)
------------------------------
8 - 4 = 11 - 8
4 = 3 (FALSE)
Question 3 of 25
If f(x) = 3x + 2, what is f(5)?
O A. 10
O B. 17
O c. 1
O D. 13
Answer:
I believe it's 17 :)
Step-by-step explanation:
5×3= 15 +2 = 17
in the triangle EFG,
Answer:
[tex]4.\ \sin E = \cos G[/tex]
Step-by-step explanation:
Given
[tex]\triangle EFG[/tex]
[tex]\angle F = 90^o[/tex] --- right angle
Required
Which of the options is true
In a triangle, we have:
[tex]\angle E + \angle F + \angle G = 180^o[/tex] --- angles in a triangle
Substitute [tex]\angle F = 90^o[/tex]
[tex]\angle E + 90^o + \angle G = 180^o[/tex]
Collect like terms
[tex]\angle E + \angle G = 180^o -90^o[/tex]
[tex]\angle E + \angle G =90^o[/tex]
This implies that E and G are complementary angles.
For complementary angles, E and G;
[tex]\sin E = \cos G[/tex] and [tex]\sin G = \cos E[/tex]
Hence, (4) is true
Suppose the line with slope 1 crosses the x -axis at x=2.
(a) Find the equation of the line in slope-intercept form and enter the answer in the space:
(b) What is the y -intercept of the graph of the line? Enter your answer in the space:
Answer:
a. y=x-2 b. -2
Step-by-step explanation:
a.) if the slope is 1, the x-int is always the negative of the y-int so y=x-2
b.) in y=mb+b (slope intercept form) b is the y-int so -2
Brainliest Plz??
Find the sum sn of the arithmetic sequence a7＝14/3 d＝-4/3 n＝15
Answer:
[tex]S_{15}= 50[/tex]
Step-by-step explanation:
Given
[tex]a_7 = \frac{14}{3}[/tex]
[tex]d = -\frac{4}{3}[/tex]
[tex]n = 15[/tex]
Required
The sum of n terms
First, we calculate the first term using:
[tex]a_n = a + (n - 1)d[/tex]
Let [tex]n = 7[/tex]
So, we have:
[tex]a_7 = a + (7 - 1)d[/tex]
[tex]a_7 = a + 6d[/tex]
Substitute [tex]a_7 = \frac{14}{3}[/tex] and [tex]d = -\frac{4}{3}[/tex]
[tex]\frac{14}{3} = a + 6*\frac{-4}{3}[/tex]
[tex]\frac{14}{3} = a -8[/tex]
Collect like terms
[tex]a =\frac{14}{3} +8[/tex]
Take LCM and solve
[tex]a =\frac{14+24}{3}[/tex]
[tex]a =\frac{38}{3}[/tex]
The sum of n terms is then calculated as:
[tex]S_n = \frac{n}{2}(2a + (n - 1)d)[/tex]
Where: [tex]n = 15[/tex]
So, we have:
[tex]S_n = \frac{15}{2}(2*\frac{38}{3} + (15 - 1)*\frac{-4}{3})[/tex]
[tex]S_n = \frac{15}{2}(2*\frac{38}{3} + 14 *\frac{-4}{3})[/tex]
[tex]S_n = \frac{15}{2}(2*\frac{38}{3} - 14 *\frac{4}{3})[/tex]
[tex]S_n = \frac{15}{2}(\frac{2*38}{3} - \frac{14 *4}{3})[/tex]
Take LCM
[tex]S_n = \frac{15}{2}(\frac{2*38-14 *4}{3})[/tex]
[tex]S_n = \frac{15}{2}(\frac{20}{3})[/tex]
Open bracket
[tex]S_n = \frac{15*20}{2*3}[/tex]
[tex]S_n = \frac{300}{6}[/tex]
[tex]S_n = 50[/tex]
Hence,
[tex]S_{15}= 50[/tex]
Name
Date
Unit 2 Mid-Unit Assessment continued
Form A
6
Ben has 5 comic books. His cousin Kurt has 6 times as many comic books
as Ben has.
Part A
Draw and label a bar model to show the number of comic books
each boy has.
Answer:
das
Step-by-step explanation:
adsasc
#6 - 8 ASAP first answer gets brainliest
Answer:
6. 8 in.²
7. 47.6 m²
9. 20 cm²
Step-by-step explanation:
6. Area of triangle = ½*base*height
base = 4 in.
height = 4 in.
Area = ½*4*4
Area = 2*4
Area = 8 in.²
7. Area of triangle = ½*base*height
base = 13.6 m
height = 7 m
Area = ½*13.6*7
Area = 47.6 m²
9. Area of the shaded figure = area of triangle + area of rectangle
= ½*b*h + L*W
b = 2 cm
h = 4 cm
L = 8 cm
W = 2 cm
Area of the shaded figure = ½*2*4 + 8*2
= 4 + 16
= 20 cm²
a garden and a bench cost 725 combined. the garden table cost 75 more than the bench. What is the cost of the bench
Answer: feugfberuyvfeygcreuyug
Step-by-step hththrhfhr
The total points scored for the Warriors basketball team for each game during the season were 42, 20, 13, 64, 27, 35, 45, 40, 23, 12, 12, and 39. What is the standard deviation (6x)? A) 15.31 points B) 31 points © 15.99 points D) 12 points
Answer:
A. 15.31
I did the standard deviation calculator and this is what I got
Find the slope please and thank you!! :))
Answer:
3/2
Step-by-step explanation:
(y-y)/(x-x)=-1+7/2+2=6/4=3/2
Answer:
Slope = 1.5
Step-by-step explanation:
m = (y₂ -y₁) / (x₂-x₁)
m = (-1+7) / (2+2)
m = 1.5
Evaluate f(x)= 4x-2 when x= -2
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{If x = -2, then substitute it into the given equation}[/tex].
[tex]\large\textsf{f(x) = 4(-2) - 2}[/tex]
[tex]\large\textsf{y = 4(-2) - 2}[/tex]
[tex]\large\textsf{4(-2) = \boxed{\bf -8}}[/tex]
[tex]\large\textsf{y = -8 - 2}[/tex]
[tex]\large\textsf{-8 - 2 = \boxed{\bf -10}}[/tex]
[tex]\boxed{{\large\text{y = \bf -10}}}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \textsf{\huge \bf y = -10}}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex]\quad\quad\quad\quad \tt{f(x) = 4x - 2}[/tex]
[tex]\quad\quad\quad\quad \tt{f( - 2) = 4( - 2)- 2}[/tex]
[tex]\quad\quad\quad\quad \tt{f( - 2) = ( - 8)- 2}[/tex]
[tex]\quad\quad\quad\quad \tt{f( - 2) = - 10}[/tex]
Hence, the answer is -10.[tex]\quad\quad\quad\quad\boxed {\tt{\color{green}f( - 2) = - 10}}[/tex]
__________
#LetsStudy
A sector of a circle has a diameter of 12 feet and an angle of 3pi/4 radians. Find the area of the sector.
Answer:
42.39 ft²
Step-by-step explanation:
area of sector= 3/8 × 3.14 × 6²
= 42.39 ft²
The area of the sector is 42.39 ft²
Given that, a sector of a circle has a diameter of 12 feet and an angle of 3pi/4 radians, we need to find the area of the sector,
Area of the sector = θ/360° / π·radius²
area of sector= 3/8 × 3.14 × 6²
= 42.39 ft²
Hence, the area of the sector is 42.39 ft²
Learn more about the sector of the circle, click;
https://brainly.com/question/15591260
#SPJ2
In the triangle below, suppose that m angle L=(5x-3)m angle M=(4x-7)^ , and m angle N=x Find the degree measure of each angle in the triangle .
Please I need this done in 15 minutes !!!!!
birth weights in norway are normally distributed with a mean of 3570 g and a standard deviation of 500g. if the hospital officials plan to require special treatment for the lightest 3% of newborn babies, what birth weight seperates those requiring special treatment from those who do not
Answer:
2630 g
Step-by-step explanation:
From the given information:
Given that:
mean (μ) = 3750 g
Standard deviation (σ) = 500
Suppose the hospital officials demand special treatment with a percentage of lightest 3% (0.03) for newborn babies;
Then, the weight of birth that differentiates the babies that needed special treatment from those that do not can be computed as follows;
P(Z < z₁) = 0.03
Using the Excel Formula; =NORMSINV(0.03) = -1.88
z₁ = - 1.88
Using the test statistics z₁ formula:
[tex]z_1 = \dfrac{X-\mu}{\sigma}[/tex]
[tex]-1.88 = \dfrac{X-3570}{500}[/tex]
By cross multiply, we have:
-1.88 × 500 = X - 3570
-940 = X - 3570
-X = -3570 + 940
-X = -2630
X = 2630 g
Hence, 2630 g is the required weight of birth that differentiates the babies that needed special treatment from those that do not
Consider the equation y=-x2 - 7x + 12. Determine whether the function has a
maximum or a minimum value. State the maximum or minimum value. What are
the domain and range of the function?
Answer:
Max (-7/2, 97/4)
Domain: all real numbers
Range: (negative infinity, 97/4)
Step-by-step explanation:
Im assuming this is a quadratic equation y = -x^2-7x+12
The max/min are the vertex (-b/2a)
Ignore the answer I put please help and I’ll give brainliest
Answer:
B.
Step-by-step explanation:
3/12 reduces to 1/4.
1/2 alone is greater than 1/4, so when 2/10 is added to 1/2, it is certainly greater than 3/12.
Answer: B.
how to expand (3x-4y)^6
Find the missing length. The triangles in each pair are similar.
I think the answer should be 12
this is because CH length is 6 x 5 is 30 so 60/5 is 12 for BH.
By what percent will a fraction decrease if its numerator is decreased by 40% and its denominator is decreased by 25%?
Answer: 80%
Step-by-step explanation:
Hence, if the numerator is decreased by 40% and the denominator is decreased by 25%, the original fraction is decreased by 80 percent.
13 of 20 QID: 26864 What is the radius of a right circular cylinder with a volume of 12 in3 if it has a minimum surface area
Answer:
r = 1,248 in
Step-by-step explanation:
v(c) = 12 in³
The surface area of a right cylinder is:
Area of the base and top + lateral area
S(a) = 2*π*r² + 2*π*r*h (1)
v(c) = 12 in³ = π*r²*h h is the height of the cylinder, then
h = 12 / π*r²
By substitution, in equation (1) we get the Surface area as a function of r
S(r) = 2*π*r² + 2*π*r* ( 12 / π*r²)
S(r) = 2*π*r² + 24 /r
Tacking derivatives on both sides of the equation we get:
S´(r) = 4*π*r - 24 /r²
S´(r) = 0 4*π*r - 24 /r² = 0 π*r - 6/r² = 0
π*r³ - 6 = 0
r³ = 1,91
r = 1,248 in
How do we know that the value r = 1,248 makes Surface area minimum??
We get the second derivative
S´´(r) = 4*π + 48/r³ S´´(r) will be always positive therefore we have a minumum of S at the value of r = 1,248 in
16 meters of rope, i want to cut pieces of rope 0.2meters long. how many pieces can cut?
Answer:
80
Step-by-step explanation:
because 16 decided by 0.2 is 80
hope this helps!!!!
PLEASE HELP I WILL GIVE BRAINLIEESTTTT
____ 2. The set of numbers {9, 8, 7, …}
A. x > ‐4
B. x < ‐4
C. x >_ ‐4
D.x <_ ‐4
Answer:
A. x > -4
Step-by-step explanation:
< less than
>greater than
the unknown number x is greater than -4
{9, 8, 7, ...} the number is counting down. So the next number is 6.
is 6 greater than -4
or less than -4
therefore
x(which is 6) is greater than -4
x > -4
Answer:
c
Step-by-step explanation:
Given: mĐIED = 116° and mÐJFG = 100° Find the measure of each unknown angle. (not drawn to scale) O m
Answer:
B is the answer
Step-by-step explanation:
Please help me find the answer
6.b.Find the equation of the circle lies on 2x-3y+1=0 and the circle passing through the points (-1,2) and (2,3).
Answer:
(x + 1)² + (y - 7)² = 25Step-by-step explanation:
Perpendicular bisector of the chord connecting the the points (-1,2) and (2,3) is also passing through the center of the circle.
We'll find the equation of the line and solve the system to find the center.
Midpoint of the chord:
((-1 + 2)/2, (2 + 3)/2) = (0.5, 2.5)Equation of the line through chord (-1,2) and (2,3):
m = (3 - 2)/(2 + 1) = 1/3y - 2 = 1/3(x + 1)y = 1/3x + 7/3Perpendicular bisector is:
y - 2.5 = -3(x - 0.5)y = -3x + 4 >> (1)And the given line is:
2x - 3y + 1 = 0y = 2/3x + 1/3 >> (2)Solve the system:
-3x + 4 = 2/3x + 1/3-9x + 12 = 2x + 111x = -11x = -1Find y:
y = -3(-1) + 4 = 3 + 4 = 7The center is (-1, 7)
Find the radius, the distance from center to one of points on circle
(-1, 7) and (-1, 2) 7 - 2 = 5The equation of circle is:
(x + 1)² + (y - 7)² = 5²(x + 1)² + (y - 7)² = 25
Hope This Helps!!!
Hope This Helps!!!Have A GREAT DAY!!!