The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model. The silver model requires 1 minute in a grinder and 3 minutes in a bonder. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder. Because of maintenance procedures, the grinder can be operated no more than 30 hours per week and the bonder no more than 50 hours per week. The company makes $5 on each silver pen and $7 on each gold pen. How many of each type of pen should be produced and sold each week to maximize profits?
Answers
Answer:
Optimal production = 600 gold pens
Revenue = 600*7 = $4200 gold pens
Step-by-step explanation:
The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.
A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.
B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.
Because of maintenance procedures,
C. the grinder can be operated no more than 30 hours per week and
D. the bonder no more than 50 hours per week.
The company makes
E. $5 on each silver pen and
F. $7 on each gold pen.
How many of each type of pen should be produced and sold each week to maximize profits?
Solution:
We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.
1. From A and C, the maximum number of silver pens
x <= 30*60 / 1 = 1800 and
x <= 50*60 /3 = 1000 ....................(1) bonder governs
2. from A & D, the maximum number of gold pens
y <= 30*60 / 3 = 600 .....................(2) grinder governs
y <= 50*60 / 4 = 750
3. From D,
x + 3y <= 30*60 = 1800 ...................(limit of grinder) ..... (3)
3x + 4y <= 50*60 = 3000 .................(limit of bonder) .......(4)
Need to maximize profit,
Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.
The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4). Using slope intercept form,
(y-480) = -(5/7)(x-360)
or y=-(5/7)x + (737+1/7) [the purple line] which violates the red line, so not a solution.
Next try the point (0,600)
(y-600) = -(5/7)(x-0), or
y = 600 - (5/7)x [the black line]
As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of
Revenue = 600*7 = 4200 gold pens
Related Questions
The test statistic of zequalsnegative 3.43 is obtained when testing the claim that pless than0.39. a. Using a significance level of alphaequals0.05, find the critical value(s). b. Should we reject Upper H 0 or should we fail to reject Upper H 0?
Answers
Answer:
a
[tex]z_t = -1.645[/tex]
b
We should reject the Upper [tex]H_o[/tex]
Step-by-step explanation:
From the question we are told that
The test statistics is [tex]t_s = -3.43[/tex]
The probability is [tex]p < 0.39[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Now looking at the probability we can deduce that this is a left tailed test
The second step to take is to obtain the critical value of [tex]\alpha[/tex] from the critical value table
The value is
[tex]t_ {\alpha } = 1.645[/tex]
Now since this test is a left tailed test the critical value will be
[tex]z_t = -1.645[/tex]
This because we are considering the left tail of the normal distribution curve
Now since the test statistics falls within the critical values the Null hypothesis is been rejected
For each of the following determine a unit rate using the information given. Show the division that leads to your answer. Use appropriate units. All rates will be whole numbers. At a theatre, Mia paid $35 for five tickets
Answers
Answer:
Step-by-step explanation:
cool
Suppose we want to test the claim that the majority of adults are in favor of raising the vote age to 21. Is the hypothesis test left tailed, right tailed or two tailed
Answers
Answer:
The hypothesis test is right-tailed.
Step-by-step explanation:
We are given that we want to test the claim that the majority of adults are in favor of raising the voting age to 21.
Let p = proportion of adults who are in favor of raising the voting age to 21
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%
Alternate Hypothesis, [tex]H_A[/tex] : p > 50%
As we know that the majority is there when we have more 50% chance of happening of that event.
Here, the null hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is less or equal to 50%.
On the other hand, the alternate hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is more than 50%.
This shows that our hypothesis test is right-tailed because in the alternate hypothesis, the greater than sign is included.
The prices for a loaf of bread and a gallon of milk for two supermarkets are shown below. Sue needs to buy bread and milk for her church picnic. At Supermarket A, she would pay $137.24. At Supermarket B, she would pay $140.04. Which of the following system of equations represents this situation?
Answers
Answer:
B. 3.19b + 4.59m = 137.24
3.49b + 4.39m = $140.04
Step-by-step explanation:
A B
Bread $3.19 $3.49
Milk $4.59 $4.39
Sue paid $137.24 in supermarket A
Sue paid $140.04 in supermarket B
Let
Price of bread A=$3.19
Price of bread B=$3.49
Price of milk A=$4.59
Price of milk B=$4.39
Quantity of Bread=b
Quantity of Milk=m
Pb=price of bread
Pm=price of milk
Qb=Quantity of bread
Qm=Quantity of milk
For each supermarket
Supermarket A Equation
PbQb + PmQm =$137.24
3.19b+ 4.59m = 137.24
Supermarket B Equation
PbQb + PmQm=$140.04
3.49b + 4.39m = $140.04
Combining both equations
3.19b + 4.59m = 137.24
3.49b + 4.39m = $140.04
A person standing close to the edge on top of a 96-foot building throws a ball vertically upward. The quadratic function (t) - - 161+ 804 + 96 models the ball's height about the ground, A(t), in feet, e
seconds after it was thrown.
a) What is the maximum height of the ball?
Preview
feet
b) How many seconds does it take until the ball hits the ground?
Preview
seconds
Answers
Answer:
196 ft
6 seconds
Step-by-step explanation:
Solution:-
We have a quadratic time dependent model of the ball trajectory which is thrown from the top of a 96-foot building as follows:
[tex]y(t) = -16t^2 + 80t + 96[/tex]
The height of the ball is modeled by the distance y ( t ) which changes with time ( t ) following a parabolic trajectory. To determine the maximum height of the ball we will utilize the concepts from " parabolas ".
The vertex of a parabola of the form ( given below ) is defined as:
[tex]f ( t ) = at^2 + bt + c[/tex]
Vertex: [tex]t = \frac{-b}{2a}[/tex]
- The modelling constants are: a = -16 , b = 80.
[tex]t = \frac{-80}{-32} = 2.5 s[/tex]
- Now evaluate the given function " y ( t ) " for the vertex coordinate t = 2.5 s. As follows:
[tex]y ( 2.5 ) = -16 ( 2.5 )^2 + 80*(2.5) + 96\\\\y ( 2.5 ) = 196 ft\\[/tex]
Answer: The maximum height of the ball is 196 ft at t = 2.5 seconds.
- The amount of time taken by the ball to hit the ground can be determined by solving the given quadratic function of ball's height ( y ( t ) ) for the reference ground value "0". We can express the quadratic equation as follows:
[tex]y ( t ) = -16t^2 + 80t + 96 = 0\\\\-16t^2 + 80t + 96 = 0[/tex]
Use the quadratic formula and solve for time ( t ) as follows:
[tex]t = \frac{-b +/- \sqrt{b^2 - 4 ac} }{2a} \\\\t = \frac{-80 +/- \sqrt{80^2 - 4 (-16)(96)} }{-32} \\\\t = \frac{-80 +/- 112 }{-32} = 2.5 +/- (-3.5 )\\\\t = -1, 6[/tex]
Answer: The value of t = -1 is ignored because it lies outside the domain. The ball hits the ground at time t = 6 seconds.
This afternoon, Vivek noticed that the temperature was above zero when the temperature was 17 5/8 degrees. Its evening now, and the temperature is -8 1/2 degrees. What does this mean?
Answers
Answer:
The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.
Step-by-step explanation:
Convert to a mixed number:
209/8
Divide 209 by 8:
8 | 2 | 0 | 9
8 goes into 20 at most 2 times:
| | 2 | |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
8 goes into 49 at most 6 times:
| | 2 | 6 |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 |
Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:
| | 2 | 6 | (quotient)
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 | (remainder)
The quotient of 209/8 is 26 with remainder 1, so:
Answer: 26 1/8° C
A person stands 15 ft from an elephant. Determine how tall the elephant is in feet, the given diagram.
Answers
Answer:
The height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].
Step-by-step explanation:
It is given that,
Distance between a person and an elephant is 15 ft
The angle of elevation of the elephant is 30 degrees.
We need to find the height of the elephant. For this let us consider that height is h. So,
[tex]\tan\theta=\dfrac{P}{B}\\\\\tan(30)=\dfrac{h}{15}\\\\h=15\times \tan(30)\\\\h=\dfrac{15}{\sqrt3}\ ft[/tex]
So, the height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].
If y ∝ 1∕x and y = –2 when x = 14, find the equation that connects x and y.
Question 11 options:
A)
y = –28x
B)
y = –7∕x
C)
y = –28∕x
D)
y = –7x
Answers
C. y= -28/x
y=k/x
cross multiply
k= y×x
k = -2×14
k = -28
y = -28/x [ equation connecting x and y]
The equation that connects x and y si y = –28∕x.
The correct option is (C)
What is proportionality constant?The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant. The proportionality constant's value is determined by the proportion between the two specified quantities.
For example, The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.
We have given that
y ∝ 1∕x
To remove proportional sign we use proportionality constant
y=k/x
Now, cross multiply
k= y×x
k = -2×14
k = -28
y = -28/x
Hence, the equation is y = -28/x .
Learn more about proportionality here:
https://brainly.com/question/8598338
#SPJ2
Match the following guess solutions yp for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below.
A. yp(x)=Ax2+Bx+C,
B. yp(x)=Ae2x,
C.yp(x)=Acos2x+Bsin2x,
D. yp(x)=(Ax+B)cos2x+(Cx+D)sin2x
E. yp(x)=Axe2x,
F.yp(x)=e3x(Acos2x+Bsin2x)
1. d2ydx2+4y=x−x220
2. d2ydx2+6dydx+8y=e2x
3. y′′+4y′+20y=−3sin2x
4. y′′−2y′−15y=3xcos2x
Answers
Answer and Step-by-step explanation:
1. Data provided
[tex]\frac{d^2y}{dx^2} + 4y = x - x^2 + 20\\\\ \frac{d^2y}{dx^2} + 4y = - x^2 + x + 20[/tex]
Now as a non homogeneous part which is
[tex]- x^2 + x + 20[/tex] let us assume the computation is
[tex]y_p(x) = Ax^2 + Bx + C[/tex]
2. Data provided
[tex]\frac{ d^2y}{dx^2} + \frac{6dy}{dx} + 8y = e^{2x}[/tex]
As a non homogeneous part is [tex]e^2x[/tex] , let us assume the computation is
[tex]y_p(x) = Ae^{2x}[/tex]
3. Data provided
[tex]y'' + 4y' + 20y = -3sin2x[/tex]
As a non homogeneous part −3sin(2x), let us assume the computation is
[tex]y_p(x) = Acos(2x) + Bsin(2x)[/tex]
4. Data provided
[tex]y'' - 2y' - 15y = 3xcos(2x)[/tex]
As a non homogeneous part 3xcos(2x), let us assume the computation is
[tex]y_p(x) = (Ax+B)cos2x+(Cx+D)sin2x[/tex]
If the sampled population is finite and at least _____ times larger than the sample size, we treat the population as infinite.
Answers
Answer:
The answer is "20".
Step-by-step explanation:
It is also known as the group of the study, that targets the population, which helps to find the survey, which is the sampled population. It is measured by an ideal world, which will be the same, and they're always unique.
Its sampling distribution of the "x bar" should also be naturally independent of the random sample, that is usually distributed. We consider the population as endless if the sampling size is at least 20 times greater than the sample size.An aquarium is to be built to hold 60 m3of volume. The base is to be made of slate and the sides aremade of glass, and it has no top. If stone costs $120/m2and glass costs $30/m2, find the dimensions which willminimize the cost of building the aquarium, and find the minimum cost.
Answers
Answer:
Aquarium dimensions:
x = 3,106 m
h = 6,22 m
C(min) = 1277,62 $
Step-by-step explanation: (INCOMPLETE QUESTION)
We have to assume:
The shape of the aquarium (square base)
Let´s call "x" the side of the base, then h ( the heigh)
V(a) = x²*h h = V(a)/x²
Cost of Aquarium C(a) = cost of the base (in stones) + 4* cost of one side (in glass)
C(a) = Area of the base *120 + 4*Area of one side*30
Area of the base is x²
Area of one side is x*h or x*V(a)/x²
Area of one side is V(a)/x
C(x) = 120*x² + 4*30*60/x
C(x) = 120*x² + 7200/x
Taking derivatives on both sides of the equation we get
C´(x) = 2*120*x - 7200/x²
C´(x) = 0 means 240 *x - 7200/x² = 0
240*x³ - 7200 = 0
x³ = 7200/240
x = 3,106 m and h = 60 /x² h = 6,22 m
and C (min) = 120*(3,106)³ - 7200 / 3,106
C(min) = 3595,72 - 2318,1
C(min) = 1277,62
The sum of three consecutive natural numbers is 555, find the numbers.
Answers
Answer:
184, 185, 186
Step-by-step explanation:
If the first number is x, the other numbers are x + 1 and x + 2, therefore we can write:
x + x + 1 + x + 2 = 555
3x + 3 = 555
3x = 552
x = 184 so the other numbers are 185 and 186.
Savita was given a set of 250 cherries and Gail was given a set
of 350 cherries. Both were also given a set of small plastic bags.
Savita had to pack 8 cherries in a bag and Gail had to pack 12
cherries in a bag. Explain how you know who will have more
bags of cherries at the end.
Answers
Answer:
Savita will have more bags
Step-by-step explanation:
Savita: 250 cherries, 8 cherries per bag
Gail: 350 cherries, 12 cherries per bag
Savita: 250/8 = 31.25 bags
Gail: 350/12 = 29.17 bags
Savita will have more bags since 31.25 > 29.17
Answer:
Savita will have more bags
Step-by-step explanation:
Savita has 250 cherries and 8 cherries per bag
Gail has 350 cherries and 12 cherries per bag
Savita
=250/8 = 31.25 bags
Gail
=350/12 = 29.17 bags
therefore Savita will have more bags since 31.25 is more than Gail with 29.17 bags
What is the value of x?
Answers
Answer:
13=x
Step-by-step explanation:
Since BE is a bisector
ABE = EBC
2x+20 = 4x-6
Subtract 2x from each side
2x+20-2x =4x-6-2x
20 = 2x-6
Add 6 from each side
20+6 = 2x-6+6
26 = 2x
Divide each side by 2
26/2 = 2x/2
13=x
Answer:
x = 13
Step-by-step explanation:
The angle bisector theorem means that m<ABE = m<EBC. Now that we know they are equal, we can set the equations to each other and solve for x.
2x + 20 = 4x - 6
26 = 2x
13 = x
So the value of x is 13.
Cheers.
Find the equation of a line parallel to −x+5y=1 that contains the point (−1,2)
Answers
Answer:
y=1/5x+11/5
Step-by-step explanation:
Find the slope of the original line and use the point-slope formula y-y^1=m(x-x^1) to find line parallel to -x+5y=1
Hope this helps
Answer: y = 1/5x+ 2.2
Step-by-step explanation:
First, change the expression into y-intercept form
-x+5y=1
5y=x+1
y=1/5x+1/5
For a line to be parallel to another line, it must have the same slope. Thus, the slope must be 1/5x. Then, to find the y-intercept simply do:
y = 1/5x+b, where x = -1 and y = 2
2=1/5(-1)+b
2 = -1/5+b
b = 2 1/5.
Thus, the equation y = 1/5x+ 2.2
Hope it helps <3
F(n)=6.5n+4.5 find the 5th term of the sequence defined by the given rule
Answers
Answer:
37
Step-by-step explanation:
To find the fifth term , we have to take the value of n as 5
So, F(5)= 6.5 (5) +4.5
= 32.5 + 4.5
= 37
A pyramid shaped building is 311 feet tall and has a square base with sides of 619 ft. The sides of the building are made from reflective glass. what is the surface area of the reflective glass
Answers
Answer:
Surface area of the reflective glass is 543234.4 square feet.
Step-by-step explanation:
Given that: height = 311 feet, sides of square base = 619 feet.
To determine the slant height, we have;
[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]
= 96721 + 95790.25
= 192511.25
⇒ l = [tex]\sqrt{192511.25}[/tex]
= 438.761
The slant height, l is 438.8 feet.
Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height
area = [tex]\frac{1}{2}[/tex] × 619 × 438.8
= 135808.6
= 135808.6 square feet
Since the pyramid has four reflective surfaces,
surface area of the reflective glass = 4 × 135808.6
= 543234.4 square feet
The population of a city can be modeled with a linear equation Y equals -80 X +3450 where X is the number of years after 2000 and why is the cities population by the description of the cities population based on equation
Answers
Answer:
retype that im not understanding .
Step-by-step explanation:
what's the solution for 9ײ/81×⁵
Answers
Answer:
answer 1 /9x^3
Step-by-step explanation:
9ײ/81×⁵
change the expression to indices form
3^2 x^2 /3^4 x^5
1 /3^2 x^3
1 /9x^3
A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or an 8? Round to nearest thousandth
Answers
Answer: 0.476
Step-by-step explanation:
Let A = Event of choosing an even number ball.
B = Event of choosing an 8 .
Given, A lottery game has balls numbered 1 through 21.
Sample space: S= {1,2,3,4,5,6,7,8,...., 21}
n(S) = 21
Then, A= {2,4,6,8, 10,...(20)}
i.e. n(A)= 10
B= {8}
n(B) = 1
A∪B = {2,4,6,8, 10,...(20)} = A
n(A∪B)=10
Now, the probability of selecting an even numbered ball or an 8 is
[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]
[tex]=\dfrac{10}{21}\approx0.476[/tex]
Hence, the required probability =0.476
Which of the following situations may be modeled by the equation y = 2x +20
A. Carlos has written 18 pages of his article. He plans to write an
additional 2 pages per day.
B. Don has already sold 22 vehicles. He plans to sell 2 vehicles per
week.
C. Martin has saved $2. He plans to save $20 per month.
D. Eleanor has collected 20 action figures. She plans to collect 2
additional figures per month
Answers
Answer:
D.
m = 2 = figures/month
b = 20 = # of action figures
The function A(b) relates the area of a trapezoid with a given height of 10 and
one base length of 7 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
A(b) = 10.57?
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
O A. B(a) = -7
B. B(a) = 9, -5
Answers
Answer:
[tex]B(a)=\frac{a}{5} -7[/tex]
Step-by-step explanation:
The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.
y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),
y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )
Now switch the positions of y and b -
b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,
[tex]y+7=\frac{a}{5}[/tex],
[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]
Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7
WILL MAKE BRAINLIST. - - - If a golden rectangle has a width of 9 cm, what is its length?
Answers
Step-by-step explanation:
a = 14.56231 cm
b(width) = 9 cm
a+b = 23.56231 cm
A(area) = 343.1215 cm
Sorry if this doesnt help
Answer:
length = [9/2 + (9/2)sqrt(5)] cm
length = 14.56 cm
Step-by-step explanation:
In a golden rectangle, the width is a and the length is a + b.
The proportion of the lengths of the sides is:
(a + b)/a = a/b
Here, the width is 9 cm, so we have a = 9 cm.
(9 + b)/9 = 9/b
(9 + b)b = 81
b^2 + 9b - 81 = 0
b = (-9 +/- sqrt(9^2 - 4(1)(-81))/(2*1)
b = (-9 +/- sqrt(81 + 324)/2
b = (-9 +/- sqrt(405)/2
b = -9/2 +/- 9sqrt(5)/2
Length = a + b = 9 - 9/2 +/- 9sqrt(5)/2
Length = a + b = 9/2 +/- 9sqrt(5)/2
Since the length of a side of a rectangle cannot be negative, we discard the negative answer.
length = [9/2 + (9/2)sqrt(5)] cm
length = 14.56 cm
N
5. Use AABC to find the value of sin B.
A 7
B
25
B 24
C
24
А
C7
25
D 24
Answers
*see the attachment below for the missing figure
Answer:
[tex] sin B = \frac{24}{25} [/tex]
Step-by-step explanation:
Given a right angled triangle, ∆ABC
AB = 25
BC = 7
AC = 24
<ACB = 90°
Required:
Value of Sin B
Solution:
Using trigonometric ratio formula,
[tex] sin B = \frac{opposite}{hypotenuse} [/tex]
Opposite = AC = 24 (the side opposite to <B)
Hypotenuse = AB = 25 (the longest side facing the right angle)
[tex] sin B = \frac{24}{25} [/tex]
Shawn has 25 coins, all nickels and dimes. The total value is $2.00. How many of each coin does he have ?
Answers
Answer:
[tex]\boxed{15 \ dime \ and \ 10 \ nickel \ coins}[/tex]
Step-by-step explanation:
1 dime = 10 cents
1 nickel = 5 cents
So,
If there are 15 dimes
=> 15 dimes = 15*10 cents
=> 15 dimes = 150 cents
=> 15 dimes = $1.5
Rest is $0.5
So, for $0.5 we have 10 nickels coins
=> 10 nickels = 10*5
=> 10 nickels = 50 cents
=> 10 nickel coins = $0.5
Together it makes $2.00
The sum of a number and 9 is subtracted from 60. The result is 10. Find the number.
Answers
Answer:
Number : 41
Step-by-step explanation:
Say that this number is x. The sum of this number ( x ) and 9 subtracted from 60 will be 10. Therefore we can create the following equation to solve for x,
60 - (x + 9) = 10,
60 - x - 9 = 10,
51 - x = 10,
- x = 10 - 51 = - 41,
x = 41
This number will be 41
The mean rate for cable with Internet from a sample of households was $106.50 per month with a standard deviation of $3.85 per month. Assuming the data set has a normal distribution, estimate the percent of households with rates from $100 to $115.
Answers
Answer:
The percent of households with rates from $100 to $115. is [tex]P(100 < x < 115) =[/tex]94.1%
Step-by-step explanation:
From the question we are told that
The mean rate is [tex]\mu =[/tex]$ 106.50 per month
The standard deviation is [tex]\sigma =[/tex]$3.85
Let the lower rate be [tex]a =[/tex]$100
Let the higher rate be [tex]b =[/tex]$ 115
Assumed from the question that the data set is normally
The estimate of the percent of households with rates from $100 to $115. is mathematically represented as
[tex]P(a < x < b) = P[ \frac{a -\mu}{\sigma } } < \frac{x- \mu}{\sigma} < \frac{b - \mu }{\sigma } ][/tex]
here x is a random value rate which lies between the higher rate and the lower rate so
[tex]P(100 < x < 115) = P[ \frac{100 -106.50}{3.85} } < \frac{x- \mu}{\sigma} < \frac{115 - 106.50 }{3.85 } ][/tex]
[tex]P(100 < x < 115) = P[ -1.688< \frac{x- \mu}{\sigma} < 2.208 ][/tex]
Where
[tex]z = \frac{x- \mu}{\sigma}[/tex]
Where z is the standardized value of x
So
[tex]P(100 < x < 115) = P[ -1.688< z < 2.208 ][/tex]
[tex]P(100 < x < 115) = P(z< 2.208 ) - P(z< -1.69 )[/tex]
Now from the z table we obtain that
[tex]P(100 < x < 115) = 0.9864 - 0.0455[/tex]
[tex]P(100 < x < 115) = 0.941[/tex]
[tex]P(100 < x < 115) =[/tex]94.1%
Daniels freezer is set to 0degrees Fahrenheit he places a load of bread that was at a temperature of 78 degrees Fahrenheit in the freezer the bread cooled at a rate of 11 degrees Fahrenheit per hour write and graph an equation that models the temperature t of the bread
Answers
Answer:
it took 7 hours for the bread to drop at a constent rate
Step-by-step explanation:
20 points! Brainliest will be given!
Answers
Answer:
I always factor out the -1 so my leading coefficient is 1
Step-by-step explanation:
-x^2 + 10x -24
I always factor out the -1 so my leading coefficient is 1
-1 ( x^2 -10x +24)
Then what 2 terms multiply to 24 and add to -10
-6*-4 = 24
-6+-4 = -10
-1( x-6)(x-4)
Out of 600 people sampled, 66 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A.
Required:
Use a 90% confidence level, and give your answers as decimals, to three places.
Answers
Answer:
11% of the Total the entire voting population
Step-by-step explanation:
Let's bear in mind that the total number of sample candidates is equal to 600.
But out of 600 only 66 preffered candidate A.
The proportion of sampled people to that prefer candidate A to the total number of people is 66/600
= 11/100
In percentage
=11/100 *100/1 =1100/100
=11% of the entire voting population