Answer:
The minimum sample size is 239.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Population standard deviation is equal to 1.5
This means that [tex]\sigma = 1.5[/tex]
Margin of error of 0.25
This means that [tex]M = 0.25[/tex]
What's the minimum size of the sample?
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.25 = 2.575\frac{1.5}{\sqrt{n}}[/tex]
[tex]0.25\sqrt{n} = 2.575*1.5[/tex]
[tex]\sqrt{n} = \frac{2.575*1.5}{0.25}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*1.5}{0.25})^2[/tex]
[tex]n = 238.7[/tex]
Rounding up:
The minimum sample size is 239.
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]
Find the length of the third side. If necessary, write in simplest radical form.
Let the third side be x :
( 3√5 )^2 = 6^2 + x^2
45 = 36 + x^2
x^2 = 45 - 36
x^2 = 9
x = 3
PLEASE HELP I WILL GIVE BRAINLIEESTTTT
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 !!!!!
#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
An experimenter is studying the effects of temperature, pressure, and type of catalyst on yield from a certain chemical reaction. She considers 6 different temperatures, 5 different pressures, and 4 different catalysts are under consideration.
a. If any particular experimental run involves the use of a single temperature, pressure, and catalyst, how many experimental runs are possible?
b. How many experimental runs are there that involve use of the lowest temperature and two lowest pressures?
c. Suppose that five different experimental runs are to be made on the first day of experimentation. If the five are randomly selected from among all the possibilities, so that any group of five has the same probability of selection, what is the probability that a different catalyst is used on each run?
Answer:
a) 120 possible experimental runs
b) 8 possible experimental runs
c) 0
Step-by-step explanation:
a. For the experiment, there are 6 different temperatures (T), 5 different pressures (P), and 4 different catalysts (C). We can find the total number of combinations using the product rule.
N = T × P × C
N = 6 × 5 × 4 = 120
b) If we use only the lowest temperature, we have T = 1, and if we use the two lowest pressures, we have P = 2. We can find the total number of combinations using the product rule.
N = T × P × C
N = 1 × 2 × 4 = 8
c) If we perform 5 experimental runs with 4 possible catalysts, it is not possible to use a different catalyst each time. At least, 1 catalyst must be repeated twice. Then, the event "a different catalyst is used on each run" has a probability of 0.
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
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!!!
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
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!!!!
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 me find the answer
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
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
____ 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:
how to expand (3x-4y)^6
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.
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
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.
Marie had 12 pizzas. She wanted to give each person of a 1/4
pizza. How many people would receive a piece of pizza?
Answer:
48 people.
Step-by-step explanation:
Each person gets 1/4 of a pizza meaning that one pizza can serve 4 people. If one pizza can serve 4 people, 12 pizzas can serve 48 people, because 4x12=48.
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.
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
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
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
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)
which expression is equivalent to (5^-2) ^5 x 5^4
Answer:
6.4 × 10 ^-5
Step-by-step explanation:
(0.04)^5 × 625 = 6.4 × 10^-5 (6.4e-5)
HELP!! these two questions I've been stuck on! Please help!
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;
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