The cost of the materials for the cheapest container is when width = 1.5 m
Given data ,
Let's use "w" metres to represent the rectangular storage container's width. The length would be "2w" metres since the base's length is twice as long as its width.
The container's height is indicated by the letter "h" metres.
Volume is determined by the following formula:
20 = (2w)(w)(h) 20 = 2w²h
The equation may be rearranged to represent "h" in terms of "w":
h = 20 / (2w²)
The container's "w" and "h" surface area is the next item to discuss. The surface area would be made up of the base and the four sides as the container has an open top.
We are given that the cost of material for the base is $20 per square meter and the cost of material for the sides is $3 per square meter
Cost of base material = 20 x 2w² = 40w² dollars
Cost of side material = 3 x 4wh = 12wh dollars
Total cost of material = Cost of base material + Cost of side material = 40w² + 12wh dollars
Now we can substitute the expression for "h" that we derived earlier:
Total cost of material = 40w^2 + 12w(20 / (2w²)) = 40w² + 120 / w
To find the value of "w" that minimizes the cost of material, we can take the derivative of the total cost of material with respect to "w" and set it equal to zero, then solve for "w":
d/dw (40w² + 120 / w) = 0
80w - 120 / w² = 0
On multiplying by w² on both sides , we get
80w = 120
Divide by 80 on both sides , we get
w = 3/4 m
Hence , the width of the rectangular box is w = 1.5 meter
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You work independently as a copier salesperson. Last month, you sold 26 printers at a cost of $1,750 each. The cost of goods sold for each printer is $975. Additional operating expenses include your salary ($3,000/month), advertising ($50/month), and office lease ($550/month). Use this information to calculate (a) your gross profit and (b) your net income.
(A) The gross profit is $20,150.
(B) The net income is $16,550
To solve this problem(A) To calculate the gross profit, we need to subtract the cost of goods sold from the total revenue generated by selling the printers.
Total revenue = 26 x $1,750 = $45,500
Cost of goods sold = 26 x $975 = $25,350
Gross profit = Total revenue - Cost of goods sold
Gross profit = $45,500 - $25,350
Gross profit = $20,150
Therefore, the gross profit is $20,150.
(B) To calculate the net income, we need to subtract all the operating expenses from the gross profit.
Gross profit = $20,150
Salary = $3,000
Advertising = $50
Office lease = $550
Total operating expenses = $3,600
Net income = Gross profit - Total operating expenses
Net income = $20,150 - $3,600
Net income = $16,550
Therefore, the net income is $16,550.
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Find the critical value zc necessary to form a confidence interval at the level of confidence shown below.
c =0.81
Hence, the critical value for the 81% confidence interval is 1.311 occurs while comparing equations (1) and (2).
Explain about the Critical Values:The cut-off scores used during confidence intervals, hypothesis testing, and other statistical techniques are known as the crucial values. They are used to establish the boundaries of confidence intervals in the case of confidence intervals.
Level of confidence c = 0.81
The degree of assurance c = 81%.
Now, the overall confidence level is shown as (1−α) , where α is the significance level.
= 1.0 - 0.81
= 0.19
Thus, the 81% confidence level suggests a significance level of 0.19.
Critical value Z(α/2) is:
P(Z > Z(α/2)) = (α/2)
= 0.19/2
P(Z > Z(α/2)) = 0.095 ...eq 1
Using the z-table online, check the p-value for the z 0.095.
P(Z > 1.311) = 0.095 ...eq 2
Hence, the critical value for the 81% confidence interval is 1.311 occurs while comparing equations (1) and (2).
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Ms. Rosen sells computers. Last month she sold 72 computers, and her
goal is to sell 12% more computers this month than she sold last month.
How many computers does she need to sell to reach her goal?
81
72 + (12% of 72) = 80.64 and since you can't sell .64 computers, she needs to sell 81.
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #2
Answer:
Whenever the base of an exponential function is less than 1 (5/7 < 1), the graph exhibits exponential decay and when the base is greater than 1, the graph exhibits exponential decay (7 > 1).
Final answer: a base of 7 will cause the graph to increase as you go from left to right in both the x coordinates and the y coordinates.
I provided a picture of a graph that shows both bases just in case you want to alter my answer slightly, but aren't sure how the graph would look
18. Un comerciante vende una vaca por S/700.
Si le había costados S/500, ¿qué parte
representa la ganancia sobre el costo?
a) 2/5
b) 3/5
c) 4/5
d) 1/5 e) 6/5
Super Markets Incorporated, is considering expanding into the Scottsdale, Arizona, area. You, as director of planning, must present an analysis of the proposed expansion to the operating committee of the board of directors. As a part of your proposal, you need to include information on the amount people in the region spend per month for grocery items. You would also like to include information on the relationship between the amount spent for grocery items and income. Your assistant gathered the following sample information.
Household Amount Spent Monthly Income
1 $ 555 $ 4,340
2 489 4,510
. . .
. . .
. . .
39 1,206 9,814
40 1,145 9,835
picture Click here for the Excel Data File
a-1. Draw a scatter diagram.
1. On the graph below, use the point tool to plot the point corresponding to the Monthly Income and the Amount Spent (Amount 1).
2. Repeat the process for the remainder of the sample (Amount 2, Amount 3, … ).
3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.
a-2. Based on these data, does it appear that there is a relationship between monthly income and amount spent?
b-1. Determine the correlation coefficient. (Round your answer to 4 decimal places.)
b-2. Can we conclude that there is a positive correlation between monthly income and amount spent? Use the 0.05 significance level.
c. Determine the coefficient of determination. (Round your answer to 4 decimal places.)
d. Determine the standard error of estimate. (Round your answer to 4 decimal places.)
e. Would you recommend using the regression equation to predict amount spent with monthly income?
multiple choice
Yes
No
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The above is an analysis of data related to income and expenditure. See the working below as well as the attached information.
What is the analysis of the given data?R Calculation
Note that:
X: X Values
Y: Y Values
Mx: Mean of X Values
My: Mean of Y Values
X - Mx & Y - My: Deviation scores
(X - Mx)2 & (Y - My)2: Deviation Squared
(X - Mx)(Y - My): Product of Deviation Scores
X Values
∑ = 273195
Mean = 6829.875
∑(X - Mx)2 = SSx = 119242794.375
Y Values
∑ = 33625
Mean = 840.625
∑(Y - My)2 = SSy = 2396869.375
X and Y Combined
N = 40
∑(X - Mx)(Y - My) = 15978328.125
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 15978328.125 / √((119242794.375)(2396869.375)) = 0.9451
Thus, the value of R is 0.9451.
4. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).
5) The value of R², the coefficient of determination, is 0.8932.
To drive this, just square the coefficient of determination. That is
R² = 0.9451² = 0.8932
5. To compute the standard errors of the estimate:
SE = √(SSE / (n-2))
where SSE is the sum of squared errors and n is the sample size.
From the regression output, we have SSE = 0.9326 and n = 40.
SE = √ (0.9326 / (40-2)) = 0.1570
Therefore, the standard error of estimate is 0.1570.
6) Yes, because the coefficient of determination is high (0.8932), indicating that 89.32 % of the variability i n the amount spent can be explained by the linear relationship with monthly income.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached.
figure B is a scaled copy of Figure A. What is the skill factor from Figure A to Figure B?
Answer:
1/4 = 0.25
Step-by-step explanation:
Scale Factor from Figure A to Figure B = Figure B dimensions ÷ Figure A dimensions
Take any one side of Figure B and compare it with the corresponding side of Figure A and the ratio will give the scale factor. Since the figures are similar, the ratios of the other corresponding sides will be the same
Take horizontal top side of A which has a length of 4
The corresponding side of B has a length of 1
Therefore scale factor = 1/4 = 0.25
The other ratios are the same:
1.1/4.4 = 1.5/6 = 1/4 = 0.25
Question 5
Which of the following functions best describes this graph?
4
Ay=x²-2x+4
OB. y +9x+18
OC. ys (x+5)(x-4)
Answer:
D. y = (x - 3)(x - 6)
Step-by-step explanation:
The graph shows a parabola and the parabola intersects the x-axis at (-6, 0) and at (-3, 0). When a function intersects the x-axis, the y value must automatically equal 0, since there is only horizontal movement on the x-axis.
(x-3)(x-6) is a binomial expression that will make a quadratic equation when expanded. We refer to the coordinate where a parabola intersects the x-axis as roots, which are numbers that make the quadratic equation equal 0.
We know from the zero-product property, that when the product of two numbers is 0, at least on the numbers must be 0 (e.g., 4 * 0 = 0 or even 0 * 0 = 0). Thus, we can solve any quadratic equation in the the x-intercept form (i.e., the form tha (x-3)(x-6) is currently in) by setting both expressions equal to 0 and solving for x. This wil give an x-coordinate both times, but since you set the equations equal to 0, you know that your y-coordinate each time is 0:
Solution for x - 3 = 0:
x - 3 = 0
x = 3
Solving for x - 6 = 0
x - 6 = 0
x = 6
You can check by plugging in 3 for x and 6 for x and see if you get 0:
3 for x:
(3 - 3)(3 - 6) = 0
0 * -3 = 0
0 = 0
6 for x:
(6 - 3)(6 - 6) = 0
3 * 0 = 0
0 = 0
An integer A written in an n-based number system is 647, while written in an (n+2)-based number system is 513. Write the number A in the 10 number system! (n is of course a positive integer)
Answer:
79
Step-by-step explanation:
Let's start by writing out what we know:
A = 647 in base-n
A = 513 in base-(n+2)
To find A in base-10, we need to use the place value system and the definition of each base. Let's first convert A to base-10 using the given information.
In base-n, A is equal to:
A = 6n^2 + 4n + 7
In base-(n+2), A is equal to:
A = 5(n+2)^2 + 1(n+2) + 3
A = 5(n^2 + 4n + 4) + (n + 2) + 3
A = 5n^2 + 21n + 20
Now we have two expressions for A, so we can set them equal to each other and solve for n:
6n^2 + 4n + 7 = 5n^2 + 21n + 20
Simplifying and rearranging, we get:
n^2 + 8n + 13 = 0
Using the quadratic formula, we can solve for n:
n = (-8 ± sqrt(8^2 - 4(1)(13))) / (2(1))
n = (-8 ± 2) / 2
n = -3 or n = -5
Since n is a positive integer, we can disregard the negative solution and conclude that n = 3.
Now that we know n, we can substitute it back into the expression for A in base-n and solve for A in base-10:
A = 6n^2 + 4n + 7
A = 6(3^2) + 4(3) + 7
A = 79
Therefore, the number A written in base-10 is 79.
Hope this helps!
Find the square
(8m + 7)^2
Answer:
(8m + 7)^2 = 64m^2 + 112m + 49
(8m)^2 = 64m^2
2(8m)(7) = 112m
7^2 = 49
Professional Golfers’ Earnings Two random samples of earnings of professional golfers were selected. One sample was taken from the Professional Golfers Association, and the other was taken from the Ladies Professional Golfers Association. At , is there a difference in the means? The data are in thousands of dollars. Use the critical value method with tables.
PGA:
446, 1147, 9188, 5687, 4910
8553, 7573, 375
LPGA
76, 122, 466, 863, 100
1876, 2029, 4364, 2921
use u1 for the mean earnings of pga golfers. assume the variables are normally distributed and the variances are unequal
h0:
h1:
this hypothesis test is (one tailed or two tailed)
critical value(s)
t=
reject or do not reject the null hypothesis
is there enough evidence to support the claim
As per the hypothesis, t (1.7518) is less than the critical value (1.7823), we fail to reject the null hypothesis.
For this scenario, our null and alternative hypotheses can be stated as follows:
H0: u₁ - u₂ = 0 (There is no significant difference between the mean earnings of PGA and LPGA golfers)
H1: u₁ - u₂ > 0 (There is a significant difference between the mean earnings of PGA and LPGA golfers)
Assuming a level of significance (alpha) of 0.05, the degrees of freedom can be calculated as follows:
df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]
where s₁ and s₂ are the sample standard deviations, n₁ and n₂ are the sample sizes.
For the PGA sample, we have n₁ = 8, s₁ = 3139.71
For the LPGA sample, we have n₂ = 8, s₂ = 1232.59
Using the above formula, we get df = 12.61
Using a t-distribution table with 12 degrees of freedom and a one-tailed test, we find the critical value to be 1.7823.
Next, we need to calculate the test statistic t, which can be calculated as follows:
t = (x₁ - x₂) / √[s₁²/n₁ + s₂²/n₂]
where x₁ and x₂ are the sample means.
For the PGA sample, we have x₁ = 4358.22
For the LPGA sample, we have x₂ = 1128.50
Using the above formula, we get t = 1.7518.
Now, we can compare the test statistic t to the critical value 1.7823. Since In other words, we do not have enough evidence to support the claim that there is a significant difference between the mean earnings of PGA and LPGA golfers.
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ASAP Dr. Rollins is both an anthropologist and archeologist. While excavating some ruins in South America, he discovered a scale drawing of a replica of a Mayan pyramid.
-The scale for the drawing to the replica was 1 inch : 2 feet.
- The scale for the replica to the actual pyramid was 1 foot : 14 feet.
If the height of the pyramid on the drawing was 3 1/2 inches, what was the height of the actual pyramid?
A. 98 feet
B. 49 feet
C. 91 feet
D. 196 feet
The height of the actual pyramid is 98 feet.
How to determine the height of the actual pyramid?
To determine the height of the actual pyramid, we need to use both scales and convert the measurements.
First, let's convert the height of the drawing to the height of the replica,
1 inch : 2 feet (scale for drawing to replica)
[tex]3 \frac{1}{2} \: inches[/tex] = 7 feet (height of the replica)
Next, let's convert the height of the replica to the height of the actual pyramid:
1 foot : 14 feet (scale for replica to actual)
7 feet = 7 x 14 = 98 feet (height of the actual pyramid)
Therefore, the height of the actual pyramid is 98 feet, so the answer is A) 98 feet.
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4) Construct the truth tables for the following
(a) pV r
The truth tables for the logic expression is
p q p v q
F F F
F T T
T F T
T T T
Constructing the truth tables for the logic expressionFrom the question, we have the following parameters that can be used in our computation:
p v r
The expression is pronounced p or r
The rule of the truth table is
The expression is true if any of p or q is trueThe expression is false if both p and q are falseUsing the above as a guide, we have the following truth tables
p q p v q
F F F
F T T
T F T
T T T
The above represents the truth tables for the logic expression
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Identify the domain and range of the function. y=√x−4
A. Domain: x≥−4, Range: y≥0
B. Domain: x≥4, Range: y≥0
C. Domain: x≤4, Range: y≤0
D. Domain: x≥0, Range: y≥4
Using the function y = √ (x-4) has the following:
Domain: x≥−4, Range: y≥0.
Correct answer is A.
Define a function?A function is a relationship between each element of a non-empty set A and at least one element of another non-empty set B. A relation f between a set A (the function's domain) and a set B is how a function is defined in mathematics (its co-domain). Anytime an A and b B exist, f = (a,b)|
The domain of the function y=√ (x-4) is restricted by the square root of a non-negative number, which means that x-4 must be greater than or equal to zero. Thus, we have:
x-4 ≥ 0
x ≥ 4
Therefore, the domain of the function is x≥4.
The range of the function is determined by the output values of the function. Since the square root of any non-negative number is always non-negative, the output values of the function y=√x-4 will always be non-negative. Thus, the range of the function is y≥0.
Therefore, the correct answer is A. Domain: x≥−4, Range: y≥0.
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Adjacent angles. View the photo ccd
Answer: ∠DEA
Step-by-step explanation:
Starting Angle: ∠FBG
Adjacent (SAME) Angle: ∠DEA
Which graph shows the image of ABC after a rotation about the origin
Answer:
I would say C. Because it shows ABC, and all the others are either upside down or lopsided. I hope it was correct for you
The ordered pairs represent an absolute value function (f): (-3,9) (-1,1) (2,5)
Describe the relationship between that function and g(x)=4|x+5|-3.
The graph of f is translated ___ units up and ___ units to the left from the graph of g.
The relationship between the functions f(x) and g(x) is not by translation
Describing the relationship between the functionsFrom the question, we have the following parameters that can be used in our computation:
Function f(x) = (-3, 9), (-1, 1) and (2, 5)Function g(x) = 4|x + 5| - 3When the ordered pairs and the graph g(x) are plotted on a graph, we can see that the function f(x) is not and cannot be translated in any way to get the function g(x)
This means that the relationship between the functions is not by translation
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A wildlife group is trying to determine how many wild hogs are in a certain area. They trapped, tagged, and released 20 wild hogs. Later, they counted 8 wild hogs out of the 40 they saw.
What can the wildlife group estimate is the total population of wild hogs in that area
A. 80
B. 90
C. 100
D. 16
Answer:
The correct answer is 16
Step-by-step explanation:
Answer:
C. 100
Step-by-step explanation:
Assuming that the proportion of tagged hogs in the population is the same as the proportion of tagged hogs in the sample that was later observed, we can set up a proportion to estimate the total population of wild hogs:
tagged hogs in population / total population = tagged hogs in sample / size of sample
We know that 20 wild hogs were tagged and released, and that 8 out of 40 hogs observed were tagged. So we can plug these numbers into the proportion and solve for the total population:
20 / total population = 8 / 40
Simplifying this equation, we get:
total population = (20 * 40) / 8 = 100
Therefore, the wildlife group can estimate that the total population of wild hogs in the area is 100. Answer choice C is correct.
Hope this helps!
Al saves pennies he agreed to give 2/5 of his pennies to Bev if she would give 2/5 of what she got from Al to Carl and if Carl intern would give 2/5 of what he got from Bev to Danny Bev Carl and Danny agree and then he receives 48 pennies how many pennies did Al have initially
The requried, Al initially had 750 pennies.
Let's start by finding out how many pennies Bev got from Al. According to the problem, Al gave 2/5 of his pennies to Bev. So, if we let x be the number of pennies Al initially had, then Bev received 2/5 of x or (2/5)x pennies.
We know that Bev gave 2/5 of what she got from Al to Carl. So, Carl received 2/5 of (2/5)x or (4/25)x pennies.
Carl gave 2/5 of what he got from Bev to Danny. So, Danny received 2/5 of (4/25)x or (8/125)x pennies.
And we are told that Danny received 48 pennies. So, we can write:
(8/125)x = 48
Multiplying both sides by (125/8), we get:
x = 750
Therefore, Al initially had 750 pennies.
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6 The Montreal Biosphere is a geodesic dome that surrounds an environmental
museum in Montreal, Canada. The dome has a volume of 6,132,812.5 cubic feet.
The structure is 75% of a full sphere. What is the length of its diameter?
The geodesic dome has a diameter of 249.958 feet.
How to determine the diameter of the Montreal Biosphere
In this problem we must determine the diameter of a geodesic dome located in Montreal, Canada, (D), in feet. The volume of the geodesic dome (V), in cubic feet, is well described by this formula:
V = (3 / 4) · (π / 6) · D³
If we know that V = 6,132,812.5 ft³, then the diameter of the geodesic dome is:
6,132,812.5 = (3 / 4) · (π / 6) · D³
D³ = 15,617,078.79 ft³
D = 249.958 ft
The diameter of the geodesic dome is equal to 249.958 feet.
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CO (
Which of the following is the result of the operation below?
123 6
1.1
-2
0 2
1.
15
11
-R1+R2+R2
The result of the matrix operation is
1 2 3 6
0 -1 -2 -8
0 2 1 5
Identifying the result of the matrix operation?From the question, we have the following parameters that can be used in our computation:
Matrix A
Such that the matrix is
1 2 3 6
1 1 1 -2
0 2 1 5
The matrix operation is -R1 + R2 = R2
So, we have
1 2 3 6
0 -1 -2 -8
0 2 1 5
Hence, the result is the matrix above
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27. Find the value of x. Then tell whether the side lengths form a Pythagorean triple.
27.
X =
Triple?
Need 27
The square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given:
Let us consider one length i.e. 16 to be Perpendicular and other length i.e. 19 to be Width.
According to the Pythagoras theorem:
[tex]\text{Hypotenuse}^2=\text{Perpendicular}^2+\text{Base}^2[/tex]
Let us consider the value of Hypotenuse to be x.
[tex]x^2=19^2+16^2[/tex]
[tex]x^2=361+256[/tex]
[tex]x^2=617[/tex]
[tex]x=\sqrt{617}[/tex]
[tex]x=24.84[/tex]
Thus, from the value of x we can infer that the given lengths are not forming Pythagorean triple.
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Q2: The population of a herd of deer is represented by the function P(t) = 205(1.13)t where t is given in years. To the nearest whole number, what will the herd population be after 6 years?
Answer:
584
Step-by-step explanation:
To find the herd population after 6 years, we need to evaluate P(6) using the given function:
P(6) = 205(1.13)^6
Using a calculator, we get:
P(6) ≈ 584
Rounding this to the nearest whole number, we get:
The herd population after 6 years ≈ 584.
Need help answering all these questions
Vector operations are a powerful tool for solving mathematical and real-world problems that involve direction and magnitude.
What are the steps involved?Here are some general steps for using vector operations to solve problems:
Define the problem: Start by clearly defining the problem and the variables involved. Identify the quantities that need to be represented by vectors, such as position, velocity, force, or acceleration.
Represent the vectors: Represent the vectors using appropriate notation. For example, a vector in two-dimensional space can be represented as (x, y), where x and y are its components along the x- and y-axes, respectively. A vector in three-dimensional space can be represented as (x, y, z).
Perform vector operations: Use vector operations such as addition, subtraction, scalar multiplication, dot product, cross product, and projection to manipulate the vectors and solve the problem. For example, to add two vectors, you simply add their components separately. To find the dot product of two vectors, you multiply their corresponding components and then add the products.
Interpret the results: Once you have obtained a solution, interpret the results in the context of the problem. Make sure your answer makes sense and is physically plausible.
Here are some examples of how vector operations can be used to solve real-world problems:
Finding the resultant force acting on an object: If multiple forces are acting on an object, you can use vector addition to find the resultant force, which is the net force that determines the object's motion. The direction and magnitude of the resultant force can be found using trigonometry.
Calculating the trajectory of a projectile: When a projectile is launched into the air, its motion can be described using vectors. By using the principles of projectile motion and vector operations, you can calculate the trajectory of the projectile, its maximum height, its range, and its time of flight.
Analyzing fluid flow: Fluid flow can be analyzed using vectors, particularly velocity vectors. By visualizing the flow using vector fields, you can determine the direction and magnitude of the flow at different points, and identify features such as vortices, eddies, and turbulence.
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Determine the length of a chord whose central angle is 80° in a circle with a radius of 4 centimeters. Question 9 options: 3.94 cm 2.57 cm 5.14 cm 7.88 cm
The length of the chord whose central angle is 80° in a circle with a radius of 4 centimeters is 5.14 cm using the law of cosines.
Given that,
Central angle of a chord = 80°
Radius of the circle = 4 centimeters
There will be a triangle formed by the chord and the two radius.
Let a be the length of the chord.
Using the law of cosines,
a² = 4² + 4² - (2 × 4 × 4) cos (80°)
a² = 16 + 16 - 32 cos (80°)
a² = 32 - 32 cos (80°)
a² = 26.4433
a = 5.14
Hence the length of the chord is 5.14 cm.
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The top and bottom margins of a poster are 6 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 380 square centimeters, find the dimensions of the poster with the smallest area.
Width =
Height =
Let's denote the width of the printed material on the poster as "x" cm and the height as "y" cm.
According to the given information, the top and bottom margins are each 6 cm, and the side margins are each 8 cm. This means that the actual width of the entire poster, including the margins, is "x + 2(8)" cm, and the actual height, including the margins, is "y + 2(6)" cm.
Given that the area of the printed material on the poster is fixed at 380 square centimeters, we can set up the following equation:
Actual Area of Poster = Area of Printed Material on Poster
(x + 2(8))(y + 2(6)) = 380
(x + 16)(y + 12) = 380
To find the dimensions of the poster with the smallest area, we need to minimize the product (x + 16)(y + 12).
Since the given area of the printed material on the poster is fixed at 380 square centimeters, the actual area of the entire poster, including the margins, will be minimized when (x + 16)(y + 12) is minimized.
To minimize the product (x + 16)(y + 12), we need to minimize both x + 16 and y + 12, as they are both positive quantities.
Since x and y represent the width and height of the printed material on the poster, respectively, the smallest possible values for x + 16 and y + 12 would be 0, which means x = -16 and y = -12. However, since width and height cannot be negative, we need to find the next best option.
The smallest possible values for x + 16 and y + 12 that are greater than or equal to 0 would be when x = 0 and y = 0. This means that the width of the printed material on the poster should be 0 cm and the height should be 0 cm, which would make the dimensions of the poster with the smallest area:
Width = 0 cm
Height = 0 cm
However, please note that this would mean there is no printed material on the poster, as the width and height are both 0. If you want to have a non-zero width and height for the printed material on the poster, you would need to adjust the given area of the printed material on the poster accordingly.
quadratic equations. A positive real number is 4 more than another. If the sum of the squares of the two numbers is 56, find the numbers.
Answer:
2√6 +2 and 2√6 -2
Step-by-step explanation:
You want two numbers such that one is 4 more than the other and the sum of their squares is 56.
SetupLet x represent the smaller number. The the sum of the squares of the two numbers is ...
x² +(x +4)² = 56
SolutionSimplifying the equation, we have ...
2x² +8x +16 = 56
x² +4x = 20 . . . . . . . . . subtract 16, divide by 2
x² +4x +4 = 24 . . . . . . add 4 to complete the square
(x +2)² = 2²·6 . . . . . . . write in terms of squares
x = 2√6 -2 . . . . . . . . positive square root, subtract 6
The two numbers are 2√6 -2 and 2√6 +2.
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Additional comment
Their approximate decimal values are 6.8990 and 2.8990. As you expect, the sum of the squares of the rounded values differs slightly from 56.
In In a study of the effects of college student employment on academic performance, two random samples (one from students who worked and the other from students who did not work) were selected from college students at a large university. The following summary statistics for GPA were reported. Employed students sample size 114
Mean GPA 3.15
Std deviation 0.485
Non-employed students
Sample size 114
Mean GPA 3.23
std deviation 0.524
Compute a 90% confidence interval for the mean GPAs of non-employed students. Assume that the normal condition is met.
a. Identify the variables needed to solve the problem.
b. Find the standard deviation.
c. Calculate the point estimate and margin of error.
d. Calculate the confidence interval
The standard deviation for non-employed students is given as 0.524,
the margin of error is 0.083 and the 90% confidence interval for the mean GPAs of non-employed students is (3.147, 3.313).
Variables needed to solve the problem Sample size (n)
Sample mean, Sample standard deviation (s), Confidence level (CL)
Margin of error (E)
b. The standard deviation for non-employed students is given as 0.524.
c. Point estimate:
The point estimate for the mean GPA of non-employed students is the sample mean, which is given as 3.23.
Margin of error:
We can use the formula for the margin of error:
E = z(s/√n)
For a 90% confidence level, the critical value is 1.645.
E = 1.645(0.524/√114) = 0.083
Therefore, the margin of error is approximately 0.083.
d. Confidence interval:
The confidence interval is given by the formula:
(3.23 - 0.083, 3.23 + 0.083)
= (3.147, 3.313)
Therefore, the 90% confidence interval for the mean GPAs of non-employed students is (3.147, 3.313).
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b) A rectangular table has length (3x+2) m and width 9m. If the area of the table is 153m square. Find the perimeter of the table
The perimeter of the rectangular table is 52m.
What are the rectangle's area and perimeter?
When calculating a rectangle's area, we multiply the length by the width of the rectangle. In essence, the area of a rectangle is equal to the sum of its length and breadth. The perimeter of a shape is the space surrounding it. Space inside a shape is measured by area.
Area of rectangular table = length * breadth
Here, length of the table = 3x+2
width of the table = 9
Area of rectangular table = 153m
(3x+2) * 9 = 153
3x + 2 = 153/9
3x = 17 -2
x = 15/3
x = 5
Now, the length of the table = 3x+2
= 3*5 + 2
= 15+2
= 17m
Perimeter of the rectangle = 2(length+width)
= 2(17+9)
= 2(26)
= 52m
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Make a rap about why a parallelogram is the best shape. Must be appropriate and at least a minute long. Giving brainless to whoever answers!!!
Ahem, here goes, my attempt at a minute-long rap in praise of the parallelogram:
Yo, listen up, the parallelogram is where it's at,
A shape so brilliant, the angles are sat.
Parallel sides that never converge,
Internal angles that never diverge.
Each side an equal length,
A geometry prodigy's dream length.
The diagonals intersect, another line through the middle they meet,
Creating symmetry so neat.
A rectangle it could be,
But it's oblong, not square, can't you see?
With depth and width in perfect balance we see,
A two-dimensional form of complexity.
While the square is simple, the parallelogram is hip,
A mathematical masterpiece, skip, skip, skip!
four right angles keep the shape so tight,
Parallel lines dominate left and right.
Rotated or reflected without a care,
Its structural integrity beyond compare.
triangles form at each corner you'll note,
Acute or obtuse, depends on the protractor's groove.
A versatile shape with reason and purpose galore,
The parallelogram, simply, carries the floor.
From geometry to art, its angles they intrigue,
As a basis for patterns, its potential we can truly plug.
A forgotten form that deserves more acclaim,
Put the parallelogram on geometry's game!
This shape so underrated, rarely appreciated it seems,
But with logic and virtue, strong foundations it gleams.
The parallelogram, the parallelogram, Hooray!
This is why the parallelogram is the best shape, I say!