Answer:
[tex]x=12.07[/tex]
Step-by-step explanation:
From the question we are told that:
Mean [tex]\=x =12cm[/tex]
Standard deviation [tex]\sigma=0.04[/tex]
Significance level [tex]\alpha=5\%=0.05[/tex]
Therefore
Confidence level [tex]95\%=0.95[/tex]
From table [tex]P(z<1.645)=0.95[/tex]
Generally the equation for Z-score is mathematically given by
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]x=z\sigma+\mu[/tex]
[tex]x=1.645*0.04+12[/tex]
[tex]x=12.07[/tex]
The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 25. What is the probability we could select a sample of 80 adults and find the mean of this sample is between 95 and 105
Answer:
The probability is 0.6796
Step-by-step explanation:
Given
Population Mean - 100
Population Standard Deviation - 25
As we know
z = x-μ/σ, where:
z is the standard score
x is the raw score
μ is the population mean
σ is the population standard deviation
Z value for mean of sample = 95
z1 = -100+95/25 = -5/25 = -0.2
P value for Z = -0.2 is 0.2912
Z2 = 100-105/25 = 0.2
P(z > 0.2 = 1 - P(z ≤ 0.2) = 1 - 0.0294 = 0.9706
P(-0.2 < z < 0.2) = 0.9706 - 0.2912= 0.6796
The probability is 0.6796
Kilgore's Deli is a small delicatessen located near a major university. Kilgore does a large walk-in carry-out lunch business. The deli offers three luncheon chili specials, Wimpy, Dial 911, Fire Bowl. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes).
The profit on one serving of Wimpy is $0.6, on one serving of Dial 911 is $0.55, and on one serving of Fire Bowl is $0.65.
The following table shows the required ingredients to make one serving of each chili special, and the available amount of each ingredient for today :
Ingredient Required ingredient for each serving of Wimpy Required ingredient for each serving of Dial 911 Required ingredient for each serving of Fire Bowl Available Amount
Beef (lbs) 1 1 1.5 15
Onions (cup) 2 2 2 20
Special Sauce (oz) 5 2 3 90
Hot Sauce (oz) 0 5 6 60
Based on the historical sales data, Kilgore's Deli has the following considerations:
the number of servings for Fire Bowl must be at least 10% of the total number of servings for all three luncheon chili specials.
the number of servings for Fire Bowl, however, cannot exceed the number of Dial 911 by more than 3.
the available number of servings for Dial 911 must be at least 2.
(1.1) Develop the linear programming model to help determine the number of servings of Wimpy, Dial 911, and Fire Bowl to make in order to maximize his profit today. Type your algebraic formulation in the specified area in Q1 tab of the Excel template. Note you will not get full credits without including the algebraic formulation.
(1.2) Solve your LP model in Excel and fill in the following blanks (show your work in Q1 tab):
The optimal number of servings of Wimpy is
The optimal number of servings of Dial 911 is
The optimal number of servings of Fire Bowl is
The maximum possible profit is
Is there any leftover of ingredients as a result of this optimal solution? if yes, enter the amount. Otherwise, just type 0.
Amount of beef leftover
Amount of onion leftover
Amount of special sauce leftover
Amount of hot sauce leftover
Answer:
z (max) = 6.15
x₁ = 1 x₂ = 3 x₃ = 6
Amount of beef leftover 2 lb
Amount of onions leftover 0
Amount of Special Sauce leftover 61
Amount of Hot Sauce leftover 9
Step-by-step explanation:
Ingredients Beef Onions Special S Hot S Profit
Wimpy (x₁) 1 2 5 0 0.6
Dial 911 (x₂) 1 2 2 5 0.55
Fire Bowl (x₃) 1.5 2 3 6 0.65
Available 15 20 90 60
Objective Function z:
z = 0.6*x₁ + 0.55*x₂ + 0.65*x₃ to maximize
Subject to:
1) Quantity of beef : 15
x₁ + x₂ + 1.5*x₃ ≤ 15
2) Quantity of onions: 20
2*x₁ + 2*x₂ + 2*x₃ ≤ 20
3) Quantity of Special sauce: 90
5*x₁ + 2*x₂ + 3*x₃ ≤ 90
4) Quantity of hot sauce: 60
0*x₁ + 5*x₂ + 6*x₃ ≤ 60
5) Condition: The number of servings for Fire Bowl must be at least 10% of the total number of servings for all three luncheon chili specials.
x₃ ≥ 0.1 ( x₁ + x₂ + x₃ ) or x₃ ≥ 0.1*x₁ + 0.1 *x₂ + 0.1*x₃
x₃ - 0.1*x₁ - 0.1 *x₂ - 0.1*x₃ ≥ 0
- 0.1*x₁ - 0.1 *x₂ + 0.9 *x₃ ≥ 0
6)Condition: The number of servings for Fire Bowl, however, cannot exceed the number of Dial 911 by more than 3.
x₃ - x₂ ≤ 3
7)the available number of servings for Dial 911 must be at least 2.
x₂ ≥ 2
General constraints:
x₁ ≥ 0 x₃ ≥ 0 all integers
With on-line solver solution is:
z (max) = 6.15
x₁ = 1 x₂ = 3 x₃ = 6
By sbstitution on the constraints
1) x₁ + x₂ + 1.5*x₃ ≤ 15 1 + 3 + 9 = 13
Amount of beef leftover 2 lb
2) 2*x₁ + 2*x₂ + 2*x₃ ≤ 20 2 + 6 + 12 = 20
Amount of onions leftover 0
3) 5*x₁ + 2*x₂ + 3*x₃ ≤ 90 5 + 6 + 18 = 29
Amount of Special Sauce leftover 61
4)0*x₁ + 5*x₂ + 6*x₃ ≤ 60 15 + 36 = 51
Amount of Hot Sauce leftover 9
The sum of two numbers is 27. The larger of the two numbers is 7 less than triple the smaller number. Indicate the two numbers below.
Answer: 69
Step-by-step explanation: EZ
Find the area of the shape below
No links, docs, files, drives etc
I will mark the correct answer brainlyest
You earn many points
Answer: 2200
Step-by-step explanation:
First we will find the area of the triangle, the formula for that is bh/2
(base multiplied by height divided by 2) then we input the numbers into our formula, 30 is the height of the triangle and 40 is the length of the base. So we have to solve 40*30/2 which is 600, then we solve for the square on the bottom which is b*h ( base multiplied by height) so it is 40*40, so we would get 1600, then we add 600 and 1600 together and get 2200.
Will you need to show that all of the parts of one triangle are congruent to all of the parts of the other triangle to prove they are congruent? Explain.
Answer:
will be sufficient to prove triangles congruent. If three sides of a triangle are congruent to three sides of another triangle, the triangles are congruent. If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Which of the following ratios is not 2:5
A. 40:100
B. 10:20
C. 16:40
D. 6:15
Answer:
Step-by-step explanation:
Option B is the correct answer
10 : 20
In its simplest form
1 : 2
What is the distance between points (8,11) and (8,−2) on a coordinate plane?
Enter your answer in the box.
units.
Last year the depth of the river was 4.2 feet deep.
This year it dropped 5%.
Find the depth of the river this year to cross it.
Answer:
3.15 ツ
Step-by-step explanation:
Describe how to graph the solution of y ≤ −x2 + 2x.
Answer:
See graph and explanation
Step-by-step explanation:
Assuming you mean y ≤ −x² + 2x, you graph y = −x² + 2x and then fill in the area beneath the curve of the parabola to represent the included values. See the graph for a visual.
2.) Combine like terms and simplify the expression: 2x +
5y+ 7x
Your answer
Answer:
9x + 5y
Step-by-step explanation:
Here, in 2x + 5y+ 7x, the 'like terms' are 2x and 7x, and the sum of these terms is 9x. Thus, 2x + 5y+ 7x becomes 9x + 5y.
Given the definitions of f (x) and g(x) below, find the value of f(g(-6)).
f(x) = x² – 2x +9
g(x) = -3x – 14
Answer:
17
Step-by-step explanation:
Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight-year life. What would be the present value of this loan if it carried a 10 percent interest rate?
Answer:
$919.98
Step-by-step explanation:
To solve using a financial calculator do
N=8
I/Y=10
PMT=85
FV=1000
CMPT PV get 919.98
To do by hand find the present value of the interst payments
85*(1-(1/1.1)^8)
which is 453.4687
Find the present value of the final ballon payment
1000*(1/1.1)^8
which is 466.507
take the sum
466.507+453.4678= 919.98
The sides of a square are all increased by 2 inches. The area of the NEW square is 49
inches squared. What is the length of a side of the original square?
A: 4.5 inches
B: 9 inches
C: 5 inches
D: 2 inches
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Answer:
C: 5 inches
Step-by-step explanation:
The length of the sides of the new square is the square root of the area:
s = √A = √49 = 7
The original square had sides 2 inches shorter, so they were ...
7 in -2 in = 5 in . . . . side length of original square
In XYZ the measure of Z=90 ZY=7, XZ=24 and YX=25 what ratio represents the cosine of X?
Answer:
24/25
Step-by-step explanation:
on delta math
The ratio of cosine of angle X is 24/25.
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.
Given a right triangle, XYZ with angle Y equals 90° and ZY=7, XZ=24 and YX=25
The ratio of the cosine of an angle is the ratio of the base to the hypotenuse of the right triangle,
Here, Cosine of angle X = XZ/YX
cosX = 24/25
Hence, The ratio of cosine of angle X is 24/25.
For more references on trigonometric ratios, click;
https://brainly.com/question/25122825
#SPJ2
please help, will award brainliest
Answer:
First one
Step-by-step explanation:
hello if anyone would pls help
Answer:
x = 12
Step-by-step explanation:
It is a 90° angle which means that both of the angles need to add up to 90. 90-20 =70. 6×12 = 72.
6×9= 72
72-2 = 70
It adds up.
Hope this helps.
Click on picture to see
Answer:
none of above
Step-by-step explanation:
Calculate (0.25) x (0.44). Show your work.
Answer:
0.11
Step-by-step explanation:
0.44/x=100/25
(0.44/x)*x=(100/25)*x
0.44=4*x
0.44/4=x
0.11=x
the cost of using broadband in a hotel is £30 per hour formula to work out this total this total cost is cost in pounds = 3× number of hours. Workout the total of using boardband for 2 hours and 5 hours
Answer:
10
Step-by-step explanation:
How much larger is the volume of a triangular prism when you double the height of the prism?
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Answer:
2 times
Step-by-step explanation:
Other things remaining the same, the volume of any prism is proportional to its height. If you double the height, it is like having two prisms of the same size. The volume doubles. The new volume is 2 times the original volume.
Degree and Radian Measures
What is the degree equivalent of π/4?
a. 180°
b. 90°
c. 120°
d. 45°
Please select the best answer from the choices provided
Answer:
D. 45°
Step-by-step explanation:
I calculated it logically
Find the slope of the line that passes through the points (-6,-2) and (-7,2)
Answer:
-4
Step-by-step explanation:
the steps are in the pic above
4a - 2b = 10
write down the value of 2b-4a
Answer:I think 11 will be the answer
-9x - 12 = -3
Step By Step Pls
Answer:
x = -1
Step-by-step explanation:
-3 +12 = 9
-9x = 9
-9(-1)=9
9 - 12 = -3
1) Simplify the product using the distributive property.
(x-2)(x+4)
Please help me answer this question
Launch Problem
a) There are two stores selling boxes of crackers. Based on the information below, which store should Sylvio
purchase the crackers from? Explain your answer.
Store 1
ion
Numbero Boed Cachers
3
5
6
00
9
B
12
2
bl...
Store 2:
C = 1.5b
c = cost and b = boxes of crackers
...
b) Sylvio also needs to purchase lemons. If Sylvio wants to buy 3 boxes of crackers and 6 lemons and he does
not want to go to both stores, which one should he shop at? Explain your answer.
Store 1:
Number of lemons
3
6
9
12
1
Cost (in dollars)
2
3
4
my best answer is B i hope this helps
Keisha had $54 when she went to a bookstore. She
had $12 left after buying some books. Which
equation can be used to find a, the amount Keisha
spent on books?
54 - a = 12
B
a - 54 = 12
a +54 = 12
12 + 54 = a
h(x) = x^2+ 2x- 6
what’s the answer
It equals this graph expression. it's a little cropped, but I'm Sure you know about the y & x axis.
In the coordinate plane, you are given JKL with J(2, 3), K(10,4), and L(6, 10). Using the distance formula, classify JKL
Answer:
Perimeter of JKL = 22.55 unit (Approx.)
Step-by-step explanation:
Given:
Coordinate of J = (2,3)
Coordinate of K = (10,4)
Coordinate of L = (6,10)
Find:
Perimeter of JKL
Computation:
Distance = √(x1 - x2)² + (y1 - y2)²
Distance between JK = √(2 - 10)² + (3 - 4)²
Distance between JK = √64 + 1
Distance between JK = √65
Distance between JK = 8.06 unit
Distance between KL = √(10 - 6)² + (4 - 10)²
Distance between KL = √16 + 36
Distance between KL = √52
Distance between KL = 7.21 unit
Distance between LJ = √(6 - 2)² + (10 - 3)²
Distance between LJ = √4 + 49
Distance between LJ = √53
Distance between LJ = 7.28 unit
Perimeter of JKL = Distance between JK + Distance between KL + Distance between LJ
Perimeter of JKL = 8.06 + 7.21 + 7.28
Perimeter of JKL = 22.55 unit (Approx.)
Item 1
Use the figure to find the measures of the numbered angles.
Parallel lines a and b are intersected by a transversal t. Angle 1 and angle 99 degrees are supplementary angles. Angle 1 and angle 3 are vertical angles. Angle 2 and angle 99 degrees are vertical angles. Angle 99 degrees and angle 4 degrees are corresponding angles on the same side of the transversal. Angle 1 and angle 5 are corresponding angles on the other side of the transversal. Angle 5 and angle 7 are vertical angles. Angle 6 and angle 4 are vertical angles.
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Answer:
∠1 = ∠3 = ∠5 = ∠7 = 81°
∠2 = ∠4 = ∠6 = 99°
Step-by-step explanation:
Vertical and corresponding angles are congruent. Angles 1 and 99° are supplementary, so ...
∠1 = 180° -99° = 81°
Then we have ...
∠1 = ∠3 = ∠5 = ∠7 = 81°
∠2 = ∠4 = ∠6 = 99°