Equations:
8c + 4t = 45
3c + 2t = 20
Modify for elimination: ( multiply 2nd eq by -2)
8c + 4t = 45
-6c + -4t = -40
Subtract and solve for "c":
2c = 5
c = $2.50 (cost of one chair)
Solve for "t":
3c + 2t = 20
3(2.50) + 2t = 20
7.50 + 2t =20
2t=12.50
T= 12.50/2 =6.25
t = $ 6.25 (cost of one table)
Table = 6.25 each
Chair = 2.50 each
Check:
3(2.50) + 2(6.25) =
7.50 +12.50 = 20
8(2.50) + 4(6.25) =
20.00 + 25.00 = 45.00
What is 8q+3(10q^2+2)+8
A line passes through (−2, 5) and has slope 13 . What is an equation of the line in point-slope form
87 less than the quotient of an unknown number and 43 is -75.
What is the value of the unknown number?
twice a number added to 4 is 28
Sat scores are distributed with a mean of 1,500 and a standard deviation of 300. you are interested in estimating the average sat score of first year students at your college. if you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample?
To estimate the average SAT score of first-year students at a college with a 95% confidence interval and a margin of error of 25 points, you would need to sample approximately 554 students.
Explanation:This question involves using the concepts of mean, standard deviation, margin of error, and confidence intervals from probability and statistics. To determine the sample size needed to estimate the average SAT score with a certain margin of error, we'll use the formula for the sample size required for estimating a population mean in statistics:
n = (Z*σ/E)^2
Where:
n is the sample size Z is the Z-score (for a 95% confidence interval, Z is 1.96) σ is the standard deviation (300 in this case) E is the margin of error (25 in this case)
Plugging the values into the formula, we get:
n = (1.96*300/25)^2 ≈ 553.47
As we cannot have a fraction of a student, we always round up to ensure our margin of error requirement is met. Therefore, you would need to sample approximately 554 students.
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To limit the margin of error of your 95% confidence interval to 25 points, given the standard deviation is 300, use the formula for the margin of error for a confidence interval and solve for the sample size 'n'. Approximately 553 students should be sampled.
Explanation:For this question, we can use the formula for the margin of error for a confidence interval which is calculated as: Margin of Error = z * (σ/√n). Here, 'z' represents the z-score, 'σ' is the standard deviation, and 'n' is the sample size.
In this case, we wish to have a 95% confidence level. From z-tables, we know that the z-value for a 95% confidence level is approximately 1.96. We want a margin of error of 25 points. The standard deviation (σ) for the dataset is said to be 300.
So, we can rearrange our formula to solve for 'n', giving us: n = (z * σ / Margin of Error)². Substituting in our numbers, we get n = (1.96 * 300 / 25)². So, to limit the margin of error on your 95% confidence interval to 25 points, you will need to sample approximately 553 students.
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What is the length of LINE AC?
A. 128
B. 136
C. 144
D. 108
The area of a rectangular lot that is 50 feet wide by 100 feet deep is:
The area of a rectangle can be directly calculated using the formula:
A = l * w
Where l is the length or the depth while w is the width
Therefore,
A = 50 feet * 100 feet
A = 5000 square feet
You invest $3,756.00 and buy 100 shares of a company's stock. Their value increases by 12%. How much is each share worth?
Answer:
Each share worth is $42.0672 .
Step-by-step explanation:
As given
You invest $3,756.00 and buy 100 shares of a company's stock.
Their value increases by 12%.
12% is written in the decimal form
[tex]= \frac{12}{100}[/tex]
= 0.12
Share value increase = 0.12 × Investment cost
= 0.12 × 3756
= $450.72
Total value of shares becomes after increases of 12% = Share value increase + Investment cost .
Total value of shares becomes after increases of 12% = $3756+ $450.72
= $4206.72
[tex]Each\ shares\ worth = \frac{Total\ value\ of\ shares\ after\ increase\ of\ 12\%}{Number\ of\ shares}[/tex]
[tex]Each\ shares\ worth = \frac{4206.72}{100}[/tex]
Each shares worth = $42.0672
Therefore the each share worth is $42.0672 .
A shipping company offers various sized shipping boxes to its customers. Some of these boxes are cube-shaped, with equal height, width, and depth. As part of an upcoming sales promotion, the company will offer two cube-shaped boxes for the price of one.
a. Write an expression to represent the total volume of two different sized boxes as a sum of cubes if one of the boxes has sides with a length of 1 foot and the other has sides with a length of x feet.
b. Factor the sum of cubes.
c. Calculate the total volume of the two boxes if x = 3 feet.
The diameter of a large lawn ornament in the shape of a sphere is 16 inches. What is the approximate volume of the ornament? Use 3.14 for (PIE SYMBOLE) Round to the nearest tenth of a cubic inch.
Answer:
2143.6 in
Step-by-step explanation:
SOMEONE PLEASE HELP!!!!
Which area formula or formulas show(s) a joint variation?
I A=s^2
II A=pir^2
III A=l*w
Select one:
a. III only
b. II and III
c. II only
d. I, II, and III
Answer:
Step-by-step explanation:
help factoring trinomial
need 2 numbers when added = 5 and when multiplied = -24
answer is D
-3+8 = 5
-3*8 = -24
you have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account and saves $19 per week. How many weeks will it take for you and your friends to have the same balance?
What is the solution set of the following equation? -5x + x + 9 = -4x + 12
The main cables of a suspension bridge are ideally parabolic. the cables over a bridge that is 400 feet logn are attached to towers that 100 feet tall. the lower point of the cable is 40 feet abouve the bdrige. find the equation that can be used to model the cables.
The equation to model the suspension cables of a bridge, where the lowest point of the cable is 40 feet above the bridge, and the towers are 100 feet tall and 200 feet from the center, is y = -0.0015x^2 + 60.
Explanation:To find the equation that models the suspension cable of a bridge, we use the properties of a parabolic shape. Since the cable is attached to towers that are 100 feet tall and the lowest point of the cable is 40 feet above the bridge, we know the vertex of the parabola is 60 feet (100 - 40) below the top of the towers.
Let's define the coordinate system with the origin at the lowest point of the cable. Then the towers are at (-200, 60) and (200, 60) because the bridge is 400 feet long, so each tower is 200 feet horizontally from the center. The parabolic equation takes the general form y = ax^2 + bx + c. Because the vertex is at (0, 60), c = 60.
Using the points (-200, 60), we can substitute into the parabolic equation and write a system to solve for a and b. Since the parabola is symmetric, b = 0. The system becomes 60 = a(-200)^2 + 60, which simplifies to a = -60/40000.
Thus, the equation to model the cables is y = -60/40000x^2 + 60, or simplified, y = -0.0015x^2 + 60.
What is the average rate of change from x = 2 to x = 3?
2
3
0
5
Answer:
The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.
Step-by-step explanation:
The average rate of a function f(x) on the interval [a,b] is defined as
[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]
The average rate of change from x = 2 to x = 3 is
[tex]m=\frac{f(3)-f(2)}{3-2}[/tex] .... (1)
From the given graph it is clear that the value of the function is -3 at x=2 and -1 at x=3. It means f(2)=-3 and f(3)=-1.
Put f(2)=-3 and f(3)=-1 in equation (1).
[tex]m=\frac{-1-(-3)}{3-2}[/tex]
[tex]m=\frac{-1+3}{1}[/tex]
[tex]m=\frac{2}{1}[/tex]
[tex]m=2[/tex]
The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.
Explain why two similar right triangles will have the same cosine ratios.
The data set shows the ages of the members of a book club. What is the shape of the distribution of this data set?
19, 21, 18, 19, 16, 21, 20, 17, 16, 17, 20, 18.
Answers: symmetrical, uniform, skewed to the left, skewed to the right.
If the length of a rectangle parking lot is 10 meters less than twice it's width, and the perimeter is 400 meters, find the length of the parking lot
The length of the rectangular parking lot is 130 meters.
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
Given, The length of a rectangular parking lot is 10 meters less than twice it's width.
Assuming the width of the rectangle is x meters, therefore length would be
(2x - 10) meters and the perimeter is 400 meters.
We know the perimeter of a rectangle is 2(length + width).
∴ 2( x + 2x - 10) = 400.
2(3x - 10) = 400.
6x - 20 = 400.
6x = 420.
x = 70 meters and length is (2.70 - 10) = 130 meters.
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The quotient of a number and 9. Algebraic expression.
The demand function for an auto parts manufacturing company is given by f(x) = 100000 - 2500x , where x represents price and f(x) represents quantity. f^-1 (x) = _______. In the inverse function, the variable X represents _____
Answer:
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
The variable X represents the quantity.
Step-by-step explanation:
We are given that
The demand function for an auto parts manufacturing company is fiven by
f(x)=100000-25 x
Where x=Represents price
f(x)= Represents quantity
We have to find inverse function [tex]f^{-1}(X)[/tex]
Let f(x)=X
[tex]X=100000-2500 x[/tex]
[tex]2500x=100000-X[/tex]
[tex]x=\frac{100000-X}{2500}[/tex]
Substituting the value of x then we get
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
Therefore, the inverse function
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
Where X= Represents the quantity
[tex]f^{-1}(X)[/tex]=Represents price
The diagram below shows equilateral triangle ABC sharing a side with square ACDE. The square has side lengths of 4. What is BE? Justify your answer.
BE is [tex]7.73[/tex]
What is Square?
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
What is equilateral triangle?
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
According to question, The diagram below shows equilateral triangle ABC sharing a side with square ACDE.
We have to find BE.
Now, AB [tex]= 4[/tex] and AE [tex]= 4.[/tex]
The angle EAB is [tex]90+60 = 150[/tex]°
Using the law of the cosines, we get
[tex]BE^2 = AE^2 + AB^2 - 2(AB)(AE)cos(150)[/tex]
[tex]=4^2 + 4^2 -[/tex][tex]2(4)(4)[/tex]×[tex]\frac{\sqrt{3} }{2}[/tex]
⇒[tex]BE=7.73[/tex]
Hence, we can conclude that BE is [tex]7.73[/tex]
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What is the area of a regular hexagon with a side of 5 and an apothem of 4.33
What is the solution to the following system?
3x+2y+z=20
x-4y-z=-10
2x+y+2z=15
A. (2, 3, 4)
B. (4, 3, –2)
C. (4, 3, 2)
D. (6, 7, –2)
Answer:
C. (4, 3, 2)
Step-by-step explanation:
Given : [tex]3x+2y+z=20[/tex]
[tex]x-4y-z=-10[/tex]
[tex]2x+y+2z=15[/tex]
To Find: Solution:
[tex]3x+2y+z=20[/tex] -1
[tex]x-4y-z=-10[/tex] --2
[tex]2x+y+2z=15[/tex] --3
Substitute the value of z from 1 in 2 and 3
So in 2 , [tex]x-4y-(20-3x-2y)=-10[/tex]
[tex]x-4y-20+3x+2y=-10[/tex]
[tex]4x-2y=-10+20[/tex]
[tex]4x-2y=10[/tex] ---4
So, in 3 , [tex]2x+y+2(20-3x-2y)=15[/tex]
[tex]2x+y+40-6x-4y=15[/tex]
[tex]-4x-3y=15-40[/tex]
[tex]-4x-3y=-25[/tex] -5
Now solve 4 and 5
Substitute the value of x from 4 in 5
[tex]-4(\frac{10+2y}{4})-3y=-25[/tex]
[tex]-1(10+2y)-3y=-25[/tex]
[tex]-10-2y-3y=-25[/tex]
[tex]-10-5y=-25[/tex]
[tex]-5y=-15[/tex]
[tex]y=3[/tex]
Now substitute the value of y in 4
[tex]4x-2(3)=10[/tex]
[tex]4x-6=10[/tex]
[tex]4x=10+6[/tex]
[tex]4x=16[/tex]
[tex]x=4[/tex]
Now substitute the value of x and y in 1 to get value of z
[tex]3(4)+2(3)+z=20[/tex]
[tex]12+6+z=20[/tex]
[tex]18+z=20[/tex]
[tex]z=20-18[/tex]
[tex]z=2[/tex]
Thus The solution is (4,3,2)
Hence Option c is correct.
I REALLY NEED HELP ON THESE QUESTIONS!!!! IM SOOO STUCK!!!!
A store is selling two mixtures of coffee beans in one-pound bags. The first mixture has 12 ounces of Sumatra combined with 4 ounces of Celebes Kalossi, and costs $15. The second mixture has 4 ounces of Sumatra and 12 ounces of Celebes Kalossi, and costs $21. How much does one ounce of Sumatra and one ounce of Celebes Kalossi cost?
How old is molly if she was 52 years old when she was fourteen years ago?
John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use?
A +B = 181
A=181-B
4.70A+5.90B= 967.10
4.70(181-B) +5.90B =967.10
850.70-4.70B+5.90B=967.10
850.70+1.2B =967.10
1.2B=116.40
B =116.40/1.2 = 97
A=181-97 = 84 pounds of type A coffee
Evaluate p(7,5) can someone help
Find the area of a regular hexagon with a 48-inch perimeter.
48√3 in2
96√3 in2
192√3 in2
in2 means inches squared
In the case of a triangle with angle measures of 30°, 60°, and 90° and a hypotenuse length equal to x, what is the perimeter of the triangle in terms of x?
For a 30-60-90 triangle with a hypotenuse of length x, the perimeter would be defined by the formula x(3 + √3)/2.
Explanation:In terms of mathematics, the question discusses a right triangle, specifically a 30-60-90 triangle. When it comes to a 30-60-90 triangle, certain ratios of sides exist. In this triangle, the ratio of the lengths of the sides opposite the 30°, 60° and 90° angles are 1:√3:2. Given that the length of the hypotenuse is x, the sides opposite the 30° and 60° angles would be x/2 and x√3/2, respectively. So, the perimeter of the triangle could be determined by adding up the lengths of all three sides i.e., x + x/2 + x√3/2. The simplified form of this equation indicates that the
perimeter
of the triangle = x(1 + 1/2 + √3/2), which can also be written as x(3 + √3)/2.
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