Answer:
The pvalue of the test is 0.177 > 0.02, which means that at α=0.02, you cannot reject the company's claim.
Step-by-step explanation:
A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 35 milligrams. You want to test this claim.
At the null hypothesis, you test that the mean caffeine content is of 35 milligrams, that is:
[tex]H_o: \mu = 35[/tex]
And at the alternate hypothesis, you test if the content is different from 35, so:
[tex]H_a: \mu \neq 35[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
35 is tested at the null hypothesis:
This means that [tex]\mu = 35[/tex]
During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 36.8 milligrams. Assume the population is normally distributed and the population standard deviation is 7.3 milligrams.
This means that [tex]n = 30, X = 36.8, \sigma = 7.3[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{36.8 - 35}{\frac{7.3}{\sqrt{30}}}[/tex]
[tex]z = 1.35[/tex]
Pvalue of the test and decision:
The pvalue of the test is the probability of the mean caffeine content differing from the mean by at least 36.8 - 35 = 1.8, which is P(|z| > 1.35), which is 2 multiplied by the pvalue of z = -1.35.
Looking at the z = -1.35 has a pvalue of 0.0885
2*0.0885 = 0.177
The pvalue of the test is 0.177 > 0.02, which means that at α=0.02, you cannot reject the company's claim.
which angle corresponds to <OJH
Answer:
line parallel to OJ or JH
An investor wants to invest up to $100,000 as follows:
X amount into a Certificate of Deposit (CD) that yields an expected annual return of 1% with a risk index of 1,
Y amount into a Bond with an expected annual return of 3% and a risk index of 4,
Z amount into a Stock with an expected annual return of 7% and a risk index of 8.
The investor’s objective is to maximize the total expected annual return of the investment.
However, to be prudent, the investor requires that:
The fraction of the total investment in X must be at least 20%.
The fraction of the total investment in Z must not exceed 50%.
The combined portfolio risk index must not exceed 5.
Required:
a. Set up this investment problem as a linear program, which has 3 variables, 3 basic constraints, and 4 special constraints.
b. Use an LP software to find the maximum expected annual return in dollars and the dollar values of X, Y, and Z for this best investment.
c. From the software solution, show the values of the dual variables for the four special constraints.
Answer:
a-The Linear Model is as follows:
[tex]X+Y+Z\leq 100,000\\{0.001X}\geq 20\\{0.001Z}\leq 50\\0.00001X+0.00004Y+0.00008Z\leq5\\X\geq0\\Y\geq0\\Z\geq0[/tex]
b-The values are
X=$33,333.33
Y=$16,666.67
Z=$50,000.00
Leading to a total expected return of $4333.33.
c-The values of constraints are as follows
X+Y+Z=33333.33+16666.67+50000=100,000
X=33%, Y is 16.67% and Z is 50%
Risk component of X is 0.33
Risk component of Y is 0.66
Risk component of Z is 4.00
Step-by-step explanation:
a
From the conditions, the first special constraint is the total amount which is that the sum of investments must not be more than the total available amount of $100,000 so
[tex]X+Y+Z\leq 100,000[/tex]
The second special constraint is that the percentage of X must be at least 20% So
[tex]\dfrac{X}{100,000}\times100 \geq20\\\dfrac{X}{1000} \geq20\\{0.001X}\geq 20[/tex]
The third special constraint is that the fraction of total investment of Z must not exceed 50% So
[tex]\dfrac{Z}{100,000}\times100 \leq50\\\dfrac{Z}{1000}\leq 50\\0.001Z\leq50[/tex]
The fourth special constraint is that the combined portfolio risk index must not exceed 5 so
[tex]\dfrac{X}{100,000}\times1+\dfrac{Y}{100,000}\times4+\dfrac{Z}{100,000}\times8\leq5\\0.00001X+0.00004X+0.00008Z\leq5[/tex]
As the investments cannot be negative so three basic constraints are
[tex]X\geq0\\Y\geq0\\Z\geq0[/tex]
The maximization function is given as
[tex]f(X,Y,Z)=\dfrac{X}{X+Y+Z}\times1\%+\dfrac{Y}{X+Y+Z}\times3\%+\dfrac{Z}{X+Y+Z}\times7\%\\f(X,Y,Z)=\dfrac{X}{X+Y+Z}\times0.01+\dfrac{Y}{X+Y+Z}\times0.03+\dfrac{Z}{X+Y+Z}\times0.07[/tex]
b
By using an LP solver with BigM method the solution is as follows:
X=$33,333.33
Y=$16,666.67
Z=$50,000.00
Leading to a total expected return of $4333.33.
c
The values of constraints are as follows
X+Y+Z=33333.33+16666.67+50000=100,000
X=33%, Y is 16.67% and Z is 50%
Risk component of X is 0.33
Risk component of Y is 0.66
Risk component of Z is 4.00
y = x2 – 3x + 2
use the discriminant to determine the number of solutions
Answer:
2 real solutions
Step-by-step explanation:
The formula for determining the discriminant is b² - 4ac.
So, let's identify our variables.
a = 1
b = 3
c = 2
Now, we can plug in our values.
3² - 4(1)(2)
9 - 8
1
1 is the discriminant of this function, and since 1 is positive, this indicates that there are two distinct real number solutions.
In triangle ABC, m∠A=(6x+9)∘, m∠B=(x−8)∘, and the exterior angle at C is 141∘.
What is the measure of angle B?
12∘
20∘
141∘
129∘
Answer:
12°
Step-by-step explanation:
Let's start with the easy first.
We know that m∠C is 39° because together ∠C and the exterior angle equal 180°. And 180 - 141 = 39.
Now, we can use this to find the remaining two angles.
180° - 39° = 141°
So, this means that we can set up m∠A + m∠B = 141°.
6x + 9 + x - 8 = 141
7x + 1 = 141
7x = 140
x = 20
Finally, we can plug in for our x value and find m∠B.
m∠B = x - 8
m∠B = 20 - 8
m∠B = 12°
Answer:
12
Step-by-step explanation:
Question 4
1 points)
The high school football game started at 7:15 P.M. and ended at 10:44 P.M. How
long did the game last?
A. O 3 hours 29 minutes
B. O 3 hours 9 minutes
C. O 2 hours 29 minutes
D. O 2 hours 9 minutes
Next >
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Clear Answer
DetermIne the inverse function of f(x) = 1/3 + 6
Please show work
Answer:
f(x)⁻¹ = 3x - 18
Step-by-step explanation:
I'm going to assume that 1/3 is the coefficient of the x.
f(x) = 1/3x + 6
y = 1/3x + 6
x = 1/3y + 6
x - 6 = 1/3y
3x - 18 = y
f(x)⁻¹ = 3x - 18
work out the value of (6-2.5)( 8+4)
Answer:
42
Step-by-step explanation:
Uh, I'm guessing what is being asked here is to solve, so, time to distribute.
(6 - 2.5)(8 + 4)
48 + 24 - 20 - 10
42
PLS HELP Find the value of x .
the answer is 6
8+10=18
12+?=18
12+6=18
What is factor for 7x^2-21-280
What is the area of this polygon? Im really bad a geometry so can I have help please.
What is 24 – 6х3+52 - (16+ 2)?
ОА.
9
ОВ.
23
Ос.
71
OD.
496
Answer:
40
Step-by-step explanation:
24 – 6х3+52 - (16+ 2)
PEMDAS states we do the paranthesis 1st
24 – 6 х 3 + 52 - (18)
Next, we do the multiplication
24 - 18 + 52 - 18
Since it's just adding & subtracting, we go from left to right
40
Simplify (2^-6)(5)(2^3x5)^2
Answer:
-32000x^2
Step-by-step explanation:
Answer:
-32000x^2
Step-by-step explanation:
Pls help
If a varies jointly as b and c, find a when b = 4 and c = -3.
a = -96 when b = 3 and c = -8
a=
Answer:
a=4bc
a=4(4)(-3)=-48
a= - 48 when b equals to 3 is equals to - 8
The required answer by direct variation a is equal to 96. In other words, when b = 4 and c = -3, the value of a is 96.
When a variable varies jointly as two other variables, it means that the relationship between the variables can be expressed using direct variation. In this case, we have that "a varies jointly as b and c."
To find the value of a when b = 4 and c = -3, we can set up the proportion based on the direct variation relationship:
a/bc = k
where k is the constant of variation.
Substituting the given values:
a/(4)(-3) = k
Simplifying, we have:
a/-12 = k
Now, we can find the value of a when b = 4 and c = -3 by substituting these values into the equation and solving for a:
a/(-12) = k
a/(-12) = -96/-12 (since k = -96 when b = 3 and c = -8)
a = 96
Therefore, the required answer by direct variation a is equal to 96. In other words, when b = 4 and c = -3, the value of a is 96.
Learn more about direct variation here:
https://brainly.com/question/29150507
#SPJ2
Which linear inequality is represented by the graph?
Oys 2x + 4
Oyszx+ 3
O yz {x + 3
O y 2x + 3
The linear inequality that represents the graph is: [tex]y \le \frac 23x + \frac 15[/tex]
The line of the inequality passes through the points:
(0,0.2) and (3,2.2)
So, the slope of the line is:
[tex]m = \frac{2.2 - 0.2}{3 - 0}[/tex]
[tex]m = \frac{2}{3 }[/tex]
The equation is then calculated as:
[tex]y =mx + c[/tex]
Where c represents the value of y, when x = 0.
So, we have:
[tex]y =\frac 23x + 0.2[/tex]
Rewrite as:
[tex]y =\frac 23x + \frac 15[/tex]
The down region is shaded, and the line is a closed line.
So, the inequality is:
[tex]y \le \frac 23x + \frac 15[/tex]
Read more about inequalities at:
https://brainly.com/question/9774970
u = 63 cm, t = 34 cm and ∠T=158°. Find all possible values of ∠U, to the nearest 10th of a degree.
Answer:
{}
Step-by-step explanation:
Thats actually the answer believe it or not :)
1. Force is a push or a
upon an object
A heat
C. pull
B. motion
D. transfer
2 Which is needed to make an object move?
A density
C. porous
B. force
D. non-porous
Answer:
1. C
2.B
Step-by-step explanation:
Force is a push or a pull.. can be a twist too
to make an object move you have to apply force by pushing of pulling the object.
brainiest exchange give me and I will give you 2+2
Answer:
4
Step-by-step explanation:
and sure
Answer:
4
Step-by-step explanation:
Ann races her bicycle for 58m. A wheel of her bicycle turns 29 times as the bicycle travels the distance. What is the diameter of the wheel
Answer:
0.637 m or 63.7 cm
Step-by-step explanation:
Formula
d = n * pi di
Givens
di = diameter and is unknown
n = 29 times
d = 58 meters
Solution
58 = 29 * 3.14 * di
2 = 3.14 * di
2/3.14 = di
d = 0.637 meters
or
d = 63.7 cm
Two planes just took off from Boston, MA. The first plane is traveling 2.5 times as fast as the second plane. After traveling in the same direction for 5 hours, they are 735 miles apart. What is the average speed of each plane? (Hint: Since they are traveling in the same direction, the distance between them will be the difference of their distances.)
Answer:
Plane 1: rate = 245 mph
Plane 2: rate = 98 mph
Step-by-step explanation:
Plane 2: Let r = rate
d = 5r
Plane 1: 2.5r = rate
d = 5(2.5r)
5(2.5r) - 5r = 735
12.5r - 5r = 735
7.5r = 735
r = 98
A pair of weak earthquakes is modeled by a system of inequalities. One earthquake occurred roughly 20 km east and 14 km north of the center of Columbia, NC. The quake could be felt from 25 km away. A couple days later, another earthquake occurred 8 km west and 3 km north of the center of Columbia and could be felt from 14 km away. If Columbia is located at (0, 0) on a coordinate grid, the system of inequalities represents this scenario.
StartLayout Enlarged left-brace first row (x minus 20) squared + (y minus 14) squared less-than-or-equal-to 625 second row (x + 8) squared + (y minus 3) squared less-than-or-equal-to 196 EndLayout
Which location relative to Columbia felt both earthquakes?
4 km west and 12 km south
6 km west and 4 km north
2 km east and 10 km north
6 km east and 8 km north
Answer:
2 km east and 10 km north
Step-by-step explanation:
I did the activity and got the right answer.
By evaluating the inequalities, we will see that the correct option is: 2 km east and 10 km north
Which location will feel both earthquakes?
Here we have the inequalities:
(x - 20)^2 + (y - 14)^2 ≤ 625
(x + 8)^2 + (y - 3)^2 ≤ 196
Where, x is the distance due east, and y is the distance due north.
So we just need to find which of the given options makes both inequalities true, for example, for the first one we have:
x = -4
y = -12
Replacing that on the first inequality we get:
(-4 - 20)^2 + (-12 - 14)^2 ≤ 625
1,252 ≤ 625
This is false, so this option is not correct.
Now we just need to check the other options. Particularly for the third we have:
x = 2
y = 10
Replacing that in both inequalities we get:
(2 - 20)^2 + (10 - 14)^2 ≤ 625
340 ≤ 625 (true).
(2 + 8)^2 + (10 - 3)^2 ≤ 196
149 ≤ 196 (true)
So at 2km east and 10km north of Columbia, the two earthquakes can be felt.
If you want to learn more about inequalities, you can read:
https://brainly.com/question/18881247
Explain the importance of putting your data set in order from least to greatest.
Answer:
In order to make it easier for you to understand and helps in making problems more easier and faster to do
please help me I've been asking for this question for a while and I keep getting those spam messages please help me 15pts
How would you go about finding the confidence interval of say 90% or 95% for any given distribution scenario?
Answer:
You'd want to divide.
Step-by-step explanation:
Let's say you got a 9/10 on a test.
You'd do 9 divided by 100 and multiply it by 10 to get 90%
That is how you solve a percentage problem
FORMAT IN LESS DETAILED EXPLANATION:
9/100x10=90%
Nine divided by one-hundred times ten equals ninety percent
What is the mode of this
data?
5, 3, 3, 6, 7, 9, 10
uh help
Answer:
3
Step-by-step explanation:
3 appears the most (twice)
The rest of the numbers only appear once
a cylinder shaped water pitcher has a radius of 5 inches and a height of 12.5 inches find the surface area of the pitcher
A.5495 in² B. 54.95 in²
C.549.5 in² D. 5.495 in²
A cylinder shaped water pitcher has a radius of 5 inches and a height of 12.5 inches. Find the surface area of the pitcher.
Answer:-Given:-[tex] \bullet [/tex] Radius (r) of a cylinder shaped water pitcher = 5 inches.
[tex] \bullet [/tex] Height (h) of a cylinder shaped water pitcher = 12.5 inches.
To Find:-The surface area of the pitcher.
Solution:-We know,
Formula of Surface area of a cylinder is 2πr(r + h) sq. units.
So,
Surface area of the pitcher = 2 × 3.14 × 5(5 + 12.5)
Surface area of the pitcher = 31.4 × 17.5
Surface area of the pitcher = 549.5 in²
[tex] \therefore [/tex] The surface area of the pitcher is 549.5 in².
Hence, the option (C) 549.5 in² is correct. [Answer]
The surface area of the cylinder is 549.50 in².
What is the surface area of the cylinder?A cylinder is a three-dimensional object. It is made up of a prism with a circular base. The total surface area is the sum of the areas of the faces or surfaces of a 3-dimensional object
Total surface area = 2πr(r + h)
Where:
π = 3.14r = 5 h = height2 x 3.14 x 5 (5 + 12.5) = 549.50 in²
Not if this correct????
Step-by-step explanation:
(o, -2) is the correct answer because in -90°
P [x,y] =P' [y,-x ]
hope it is helpful to you
Please helppp!!!
what is the perimeter of the triangle?
what is the area or the triangle?
Answer:
The perimeter is 27 km
The area is 21 km^2
Step-by-step explanation:
The perimeter of a triangle will just be all of the sides added up.
12 + 9 + 6 = 27 km
The area of a triangle is:
A = 1/2 * base * height
The base is 6 km, and the height is 7 km. Substituting the values in and solving, we get:
A = 1/2 * 6 * 7
A = 3 * 7
A = 21 km^2
A student has been tracking his progress in French class. He notes each
grade he receives along with the date he received it. At the end of the
semester, he decides to create a data display to illustrate how his grades
have improved over time. What kind of display is his best choice?
O A. Stem-and-leaf plot
O B. Line graph
O C. Bar graph
D. Circle graph
Answer:
B) Line graph
what is:
k/3 + 17 = 12?
Answer:
-15
Step-by-step explanation:
yan po ang answer thank you na lang po
Please help I’m stuck
Answer:
96
Step-by-step explanation:
Its a pattern :) BTW can you help with mine please
A quarter has a diameter of 24 mm.
Which measurement is closest to the
circumference of the quarter in
millimeters?
A. 452.39 mm
B. 37.7 mm
C. 75.4 mm
D. 150.8 mm
Answer:
C or D
Step-by-step explanation: