Answer:
c. 5.5 years, 0.51 years
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Mean of 5.5 years and a standard deviation of 2.1 years.
This means that, for the population, [tex]\mu = 5.5, \sigma = 2.1[/tex]
Random samples of size 17.
This means that [tex]n = 17[/tex]
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.
The mean is the same as the mean for the population, that is, 5.5 years.
The standard deviation is:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{2.1}{\sqrt{17}} = 0.51[/tex]
This means that the correct answer is given by option c.
Prove that the square of an odd number is always 1 more than a multiple of 4
Answer:
By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.
Step-by-step explanation:
For examples,
Let's consider squares of 3, 11, 25, 37 and 131.
[tex] {3}^{2} = 9[/tex]
8 is a multiple of 4, and 9 is more than 8.
[tex] {11}^{2} = 121[/tex]
120 is a multiple of 4 and 121 is one more than it.
[tex] {25}^{2} = 625[/tex]
624 is a multiple of 4 and 625 is one more than it.
[tex] {37}^{2} = 1369[/tex]
1368 is a multiple of 4 and 1369 is one more than 1368.
[tex] {131}^{2} = 17161[/tex]
17160 is a multiple of 4.
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. Round your answers to four decimal places. Do not round intermediate calculations.
Answer:
the operating characteristics have been solved below
Step-by-step explanation:
we have an average of 10 minutes per customers
μ = mean service rate = 60/10 = 6 customers in one hr
the average number of customers that are waiting in line
mean arrival λ = 2.5
μ = 6
[tex]Lq = \frac{2.5^{2} }{6(6-2.5)} \\[/tex]
= 6.25/21
= 0.2976
we calculate the average number of customers that are in the system
[tex]L=Lq+\frac{2.5}{6}[/tex]
= 0.2976+0.4167
= 0.7143
we find the average time that a customer spends in waiting
[tex]Wq=\frac{0.2976}{2.5}[/tex]
= 0.1190 hours
when converted to minutes = 0.1190*60 = 7.1424 minutes
[tex]0.1190+\frac{1}{6}[/tex]
=0.2857
probability that arriving customers would wait for the service
= 2.5÷6 = 0.4167
Given a parametric curve
{x = 2 cost
{y = 4 sint 0 <= t <= π
a. Set up but do NOT evaluate an integral to find the area of the region enclosed by the curve and the x-axis.
b. Set up but do NOT evaluate an integral to find the area of the surface obtained by rotating the curve about the x-axis.
(a) The area of the region would be given by the integral
[tex]\displaystyle\int_0^\pi y(t)\left|x'(t)\right|\,\mathrm dt = 8 \int_0^\pi \sin^2(t)\,\mathrm dt[/tex]
(b) The area of the surface of revolution would be given by
[tex]\displaystyle\int_0^\pi y(t)\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt = 4\int_0^\pi\sin(t)\sqrt{4\sin^2(t)+16\cos^2(t)}\,\mathrm dt[/tex]
In the following diagram HI || JK.
HELP MATES PLEASE WILL GIVE 15 POINTS
What is the measure of Zx?
Angles are not necessarily drawn to scale.
67°
H
K
46°
2°
I
A
Answer:
m∠ x = 67
Step-by-step explanation:
∠AJK = ∠AHI = 67 Corresponding Angles
180 - 67 - 46 = x
x = 67
Triangle Sum Theory - the sum of all angles in a triangle = 180
Also, when you see parallel lines look for Corresponding,
Alternate Interior or Same side Interiors.
what is the graph of this function?
Answer:
You MADE IT EASY
Step-by-step explanation:
[tex] {y - 5 \times 9}^{2} \: times \: sevem \\ n \: equals \sec(x + {}^{2} ) [/tex]
The sum of 7/3 and four times a number is equal to 2/3 subtracted from five times the number?
Answer:
-3
Step-by-step explanation:
625^1+1 *125^-1-1 *25^-1+2
Answer:
626.968
Step-by-step explanation:
EMDAS rule
if y = k where k is a constant and y =24 when x =6 what is the value of y when x= 5
Answer:
20
Step-by-step explanation:
y=kx
24=6k
k=4
y=4*5=20
Help asap please!!..
Answer:
9x² - 4/3x + ¼
Step-by-step explanation:
(3x - ½)²
(3x - ½)(3x -½)
9x² - ⅔x - ⅔x + ¼
9x² - 4/3x + ¼
simplify 6 x + 3y /3
Answer:
6x + y
Step-by-step explanation:
6x + 3y/3
6x + y
Answer:
6x + y
Step-by-step explanation:
6x + 3y / 3
cancel 3y by 3
6x + y
Instructions: Solve the following linear
equation
4(n + 5) – 2(5 + 7n) = -70
n =
Answer:
Step-by-step explanation:
4*(n +5) - 2*(5 + 7n) = -70
4*n + 4*5 + 5*(-2) + 7n*(-2) = -70
4n + 20 - 10 - 14n = -70
4n - 14n + 20 - 10 = -70
- 10n + 10 = -70
Subtract 10 from both sides
-10n = -70 - 10
-10n = -80
Divide both sides by (-10)
n = -80/-10
n = 8
Step-by-step explanation:
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What is the length of my
?
M
3x
X + 8
7639
630
N
¿
O
A. 8
B. 4
C. 16
a
D. 12
Answer:
The length of MN is 4
Choose B
Please ignore the writing in blue as I tried to work it out but couldn’t
Answer:
[tex]k=35[/tex]°
Step-by-step explanation:
The degree measure of a straight line is (180) degrees. Therefore, when a line intersects another line, the sum of angle measures on any one side of the line is (180). One can apply this here to find the supplement (the angle on the same side of the line) of the angle with a measure of (130) degrees, and (85) degrees.
[tex]130 + (unknown_1)=180\\unknown_1=50\\\\85+(unknown_2)=180\\unknown_2=95[/tex]
The sum of angle measures in a triangle is (180) degrees, one can apply this here by stating the following;
[tex](unknown_1)+(unknown_2)+(k)=180[/tex]
Substitute,
[tex]50+95+k=180[/tex]
Simplify,
[tex]50+95+k=180\\\\145+k=180\\\\k=35[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND :}}}[/tex]
The measure of angle [tex]k[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {k\:=\:35°}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
➪ [tex]x[/tex] + 85° = 180°
➪ [tex]x[/tex] = 180° - 85°
➪ [tex]x[/tex] = 95°
Also,
Exterior angle of a triangle is equal to sum of two opposite interior angles.
And so we have,
➪ 130° = [tex]k[/tex] + [tex]x[/tex]
➪ [tex]k[/tex] + 95° = 130°
➪ [tex]k[/tex] = 130°- 95°
➪ [tex]k[/tex] = 35°
Therefore, the value of [tex]k[/tex] is 35°.
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex]\sf\blue{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ 50° + 35° + 95° = 180°
( where 50° = 180° - 130°)
➪ 180° = 180°
➪ L. H. S. = R. H. S.
Hence verified.
(Note: Kindly refer to the attached file.)
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
PLEASE I NEED HELP!!!!!
Find the volume of this sphere.
Use 3 for TT.
L-r=3ft
V [?]ft3
V = Tr3
Answer:
113.1 =VOLUME , 4/3 X 3.14 (3) ^3 = 113.1
what was the original price of the car? MUST SHOW ALL STEPS OF THE PROCESS.
Answer:
19219.48
Step-by-step explanation:
16540x0.162+16540
The original price would be 100%
It was marked down 16.2%
100 % - 16.2% = 83.8%
The price you paid was 83.8% of the original price.
To find the original price divide the amount you paid by the percentage of the original price:
16,540 / 0.838 = 19.737.47
Original price: $19,737.47
Restaurants sales totaled $38,676 for the week your customer count was $7,325 what did the average customer spend for the week
Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store's leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 10% higher than the market price the distributor pays for the beans. The current market price is $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild. The compositions of each coffee blend are as follows: Blend
Bean Regular DeCaf
Brazilian Natural 75% 40%
Columbian Mild 25% 60%
Romans sells the regular blend for $3.60 per pound and the Decaf blend for $4.40 per pound. Romans would like to place an order for the Brazilian and Columbian coffee beans that will enable the production of 1000 pounds of Romans Regular coffee and 500 pound of Romans DeCaf coffee. The production cost is $0.80 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.05 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Columbian Mild that will maximize the total contribution to profit. What is the optimal solution and what is the contribution profit?
Answer:
z(max) = 2996.13 $
x₁ = 968 x₂ = 430 ( quantities of regular and Decaf coffee respectevely)
Total quantity of BN = 898 pounds
Total quantity of CM = 500 pounds
Step-by-step explanation:
Cost of the beans
Brazilian natural = Price market + 10 % = 0.47 + 0.047
BN Cost = 0.517 $/lb
Clombian Mild = Price market + 10 % = 0.62 + 0.062
CM Cost = 0.682 $/lb
Composition of the coffee blend
Regular coffee 0.75 BN + 0.25 CM
De Caf coffee 0.40 BN + 0.60 CM
PRICES
Regular Roman = 3.60 $
Decaf = 4.40 $
Production costs:
Regular Roman = 0.80 $/lb
Decaf = 1.05 $/lb
Packaging costs: 0.25 $/Lb both
Profit = Price - cost
Profit of regular coffee = 3.60 - 0.80 - 0.25 -Cost of bean
for regular coffee cost of BN + CM
BN is : 0.75*BN cost = 0.75*0.517 = 0.38775 and
CM is : 0.25*0.682 = 0.1705
Profit of regular coffee = 1.99175 $
Profit for Decaf coffee = 4.4 - 1.05 - 0.25 - ( 0.517*0.4 + 0.6*0.682)
Profit for Decaf coffee = 4.4 - 1.30 - 0.616
Profit for Decaf coffee = 2.484 $
Let´s call x₁ pounds of regular coffee and x₂ pounds of Decaf coffee then:
Objective Function is:
z = 1.99175*x₁ + 2.484*x₂ to maximize
Subject to:
Availability of beans for 1000 pounds of Regular coffee means:
750 pounds of BN + 250 pounds of CM
Availability of beans for 500 pounds of Decaf coffee means
200 pounds of BN + 300 pounds of CM
Then 750 + 200 = 900 pounds of BN
And 250 + 300 = 550 pounds of CM
Availability of beans for 1000 pounds of Decaf coffee correspond to
0.75 *x₁ + 0.40*x₂ ≤ 900
Availability of beans for 500 pounds of Regular coffee correspond to
0.25*x₁ + 0.60*x₂ ≤ 500
Then the model is:
z = 1.99175*x₁ + 2.484*x₂ to maximize
Subject to:
0.75 *x₁ + 0.40*x₂ ≤ 900
0.25*x₁ + 0.60*x₂ ≤ 500
General constraints x₁ ≥ 0 x₂ ≥ 0 both integers
After 6 iterations optimal solution ( maximum z) is
z(max) = 2996.13 $
x₁ = 968 x₂ = 430
x₁ and x₂ are quantities of Regular and Decaf coffee respectively, to find out quantities of Brazilian Natural and Colombian Mild
we proceed as follows
Regular coffee is : 0.75*968 = 726 pounds of BN
Decaf coffee is : 0.40*430 = 172 pounds of BN
Total quantity of BN = 898 pounds
Regular coffee is : 0.25*968 = 242 pounds of CM
Decaf coffee is : 0.6*430 = 258 pounds of CM
Total quantity of CM = 500 pounds
A town has a current population of 4,000. The population increased 4 percent per year for the past four years, Emergency response professionals
make up 3 percent of the town's population.
Part A
Write a function that represents the population (p) of the town in terms of the number of years (1) for the last four years.
Answer:
p=c(1+r)^t so the population will be 4679.43424 or rounded to 4679
Step-by-step explanation:
p=c(1+r)^t
p=4,000(1+.04)^t
p=4,000(1.04)^t
p=4,000(1.04)^4
p=4679.43424
p= the population you are solving for
c= the initial amount of the population
(1+r)= the rate of change
t= the period of time
The exponential equation that represents the population of the town in terms of the number of years : [tex]p=4000 (1+0.4)^{t}[/tex]
What is an exponential equation?An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.
It is similar to the amount received after investing a certain amount compounded annually.
Given,
Initial population = 4000
Rate of increase = 4%
Let current population be p.
Let number of years passed be t.
The exponential equation will be: [tex]p=4000 (1+0.4)^{t}[/tex]
(The population of the town has grown exponentially. This means that:
Initial population = 4000
Population in year I = 4000 + 4% of 4000 = 4000(1 + 0.4)
Population in year II = 4000 + 4% of 4000(1 + 0.4) = 4000(1 + 0.4)(1+0.4)
and this goes on.)
Learn more about exponential equation here
https://brainly.com/question/23729449
#SPJ2
hello can anyone help with this?
Answer:
<2 and <13 are alternate exterior angles.
In simple form, alternate exterior angles are the opposite angle on the opposing parallel line. So, to make you understand better, <4 and <15 are alternate exterior angles.
Hope this helps :D
angle P and angle Q are complementary. The measure of angle Q is 33.5°. What is the measure of angle P?
Answer:
56.5 degrees
Step-by-step explanation:
Because complementary angles are when their sum is 90, you get the equation:
P + Q = 90
Since Q is 33.5,
P + 33.5 = 90
Subtracting 33.5 from both sides,
P = 56.5
Marla scored 70% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the 70th percentile in mathematics. Explain the difference in these two scores.
Answer:
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
Step-by-step explanation:
Marla scored 70% on her last unit exam in her statistics class.
This means that in her statistics class, Marla got 70% of her test correct.
When Marla took the SAT exam, she scored at the 70th percentile in mathematics.
This means that on the SAT exam, graded on a curve, Marla scored better than 70% of the students.
Explain the difference in these two scores.
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
number of bald eagles in a country a discrete random variable, a continuous random variable, or not a random variable?
Answer:
Discrete random variable.
Step-by-step explanation:
Discrete variable:
Countable numbers(0,1,2,3,...)
Continuous variable:
Can assume decimal values, such as 0.5, 2.5,...
Number of bald eagles:
Number of bald eagles is a countable value, either there a 0, 100, 1000,... so it is a discrete random variable.
Answer:
Discrete random variable.
Step-by-step explanation:
Express the following composite numbers as products of prime factors 64
Answer:
64 is a composite number, and it is 8 squared. 64 = 1 x 64, 2 x 32, 4 x 16, or 8 x 8. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Prime factorization: 64 = 2 x 2 x 2 x 2 x 2 x 2, which can also be written 64 = 2⁶.
Geometry Oddsseseyware
2 triangles are shown. The first triangle has side lengths 35, 20, and 20. The second triangle has side lengths x, 44, 44.
What value of x will make the triangles similar by the SSS similarity theorem?
15.9
59
77
96.8
Answer:
[tex]x = 77[/tex]
Step-by-step explanation:
Given
[tex]First \to Second[/tex]
[tex]35 \to x[/tex]
[tex]20 \to 44[/tex]
[tex]20 \to 44[/tex]
Required
Find x by SSS
Represent the triangle sides as a ratio
[tex]35 : x = 20 : 44[/tex]
Express as fraction
[tex]\frac{x}{35} = \frac{44}{20}[/tex]
Multiply by 35
[tex]x = \frac{44}{20} * 35[/tex]
[tex]x = \frac{44 * 35}{20}[/tex]
[tex]x = \frac{1540}{20}[/tex]
[tex]x = 77[/tex]
Answer:
ccccccccccccccccccccccccccc
Step-by-step explanation:
The sum of two six-digit numbers is a seven-digit number
Answer
500,000 + 500,000 = 1,000,000
Step-by-step explanation:
Help me plz I can’t figure it out
Answer:
m = 60
Step-by-step explanation:
The context is very important, the 'm' represents the minutes late the parents are and from this we can eliminate some options :
- The last one because then a parent would drop their child off earlier
- The first one and the third one because it is too long
A circle has a circumference of 2cm. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determinec
The numerical values of the circumference and area of the circle are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
ОО
Answer:
The numerical values of the circumference and area of the circle are equal.
An item is regularly priced at $84. Ashley bought it on sale for 70% off the regular price.
Use the ALEKS calculator to find how much Ashley paid
Answer:
58.80
Step-by-step explanation:
84 x .7(70%) =58.80
Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches greater than the box he originally planned to build?
Answer:
The new volume is 3n^2+2n inches greater.
Step-by-step explanation:
Volume of a cube = s^3 where s is side of cube
Original volume = n^3
Volume of a Rectangular Prism = LBH
New Volume = (n+1)(n+2)(n)= n^3+3n^2+2n
DIfference = New- original = 3n^2+2n
