The unit of measurement used to describe how far a set of values are from the mean is the standard deviation. Therefore, the correct answer is (b) standard deviation.
The variance is another measure of spread, but it is not in the form of the original units of measurement. The median is a measure of central tendency and not a measure of spread. The mode is the most frequently occurring value in a set and is also not a measure of spread.
The unit of measurement used to describe how far a set of values are from the mean is the Standard Deviation (b). It is calculated by taking the square root of the variance and provides a measure of the average distance between each value in the set and the mean. The Median (c), on the other hand, is the middle value in a set when the values are arranged in numerical order.
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22. Look at the given triangles.
4x + 2
7x+7
C.
x+3
2x-5
X+7
5x-4
a Write an expression in simplest form for the perimeter of each triangle.
b. Write another expression in simplest form that shows the difference between the perimeter
of the larger triangle and the perimeter of the smaller triangle.
Find the perimeter for each triangle when x = 3
U
a. The perimeter of the first triangle is and the perimeter of the second triangle is
b. The difference between the perimeters is
c The perimeter of the triangles when x is 3 are
What is perimeter of triangle?Perimeter is a math concept that measures the total length around the outside of a shape.
The perimeter of a triangle = a+b+c
1. 4x+2 + 7x+7 + x+3
= 4x+7x+ x +2+7+3
= 12x +12
Perimeter of the second triangle
= 2x-5+x+7+5x-4
= 2x+5x+x-5+7-4
= 8x-2
2. The difference of the perimeters
= 12x+12 -( 8x-2)
= 12x-8x +12+2
= 4x +14
3. when x is 3
The perimeter of the first triangle
= 12(3) +12
= 36+12
= 48 units
The perimeter of the second triangle
= 8(3)- 2
= 22 units
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P,M and S are points on circle, centre O
The side PQ of triangle ΔPQS is a tangent of the circle C₂, given that
point Q is on the surface of circle C₂.
Correct response:
QS is not perpendicular to tangent PQ, therefore, QS is not a diameter of circle C₂
Here, we have,
Methods used to prove the property of QS
The given parameters are;
Points on the circle are; Q, P, and S
Tangent to circle, C₁ = RST
Point through which circle C₂ passes = Center O
Required:
To prove that SQ is not a diameter of circle C₂
Solution:
Given that RST is a tangent, we have;
OS is perpendicular to RST by definition of a tangent to a circle
Therefore;
90° = ∠OSQ + ∠QST
Which gives;
∠OSQ = 90° - 46° = 44°
ΔQOS is an isosceles triangle, by definition of isosceles triangles
Therefore;
∠QOS = 180° - 2 × 44° = 92°
∠QPS = 0.5 × 92° = 46° Angle at center is twice angle at the circumference
∠SOP = × ∠SQP
Let x represent the base angles of ΔSOP, we have;
∠SOP = 180° - 2·x
Therefore;
∠SQP = 90° - x
Which gives;
∠SQP = 90° - x < 90°
PQ is a tangent to circle, C₂, by definition of a tangent (number of points circle C₂ intersect PQ is one)
PQ is not perpendicular to QS, which gives;
QS is not made up of two radii, and therefore, QS is not a tangent of circle, C₂
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A student organization holds meetings every week, with one chosen leader and two assistants to run the meeting efficiently. If there are 14 weeks in a semester, how many students must be in the organization to guarantee that they can have a different set of leaders/assistants at every meeting?
To guarantee a different set of leaders/assistants at every meeting, the organization would need at least 45 students.
To see why, consider the first meeting. There are three students chosen to lead/assist, leaving (total number of students - 3) students who did not lead/assist.
For the second meeting, we need to choose three different students from the remaining pool of (total number of students - 3) students. This can be done in (total number of students - 3) choose 3 ways, which is equal to:
(total number of students - 3)! / [3!(total number of students - 6)!]
For there to be a different set of leaders/assistants at every meeting, we need this number to be greater than or equal to 14 (the number of meetings in a semester). So we have:
(total number of students - 3)! / [3!(total number of students - 6)!] >= 14
Simplifying this inequality and solving for total number of students, we get:
(total number of students) * (total number of students - 1) * (total number of students - 2) >= 126
Since we want the smallest possible value for total number of students, we can start by guessing that it is around 10. If we plug in total number of students = 10, we get:
10 * 9 * 8 = 720
This is greater than 126, so we know that the organization needs at least 10 students. Trying total number of students = 11 gives:
11 * 10 * 9 = 990
This is also greater than 126, so we know that the organization needs at least 11 students. Continuing this way, we find that the smallest integer value of total number of students that satisfies the inequality is 45.
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Can anyone help me with this question please
Answer: The angle AOT is 66°. And the angle ACB is 90°.
Step-by-step explanation:
Given that A, B, and C are points on a circle, center O.
TA is a Tangent to the circle at A and OBT is a straight line.
AC is a diameter and angle OTA = 24°.
We know that a Tangent falls perpendicular to the point of contact on the circle:
Therefore, ∠OAT = 90°.
We also know that sum of all the angles of a triangle is 180°.
Therefore, ∠AOT +∠OAT +∠OTA = 180°.............(i)
Given, ∠OTA = 24°
∠OAT = 90°
Substituting both the values in equation (i).
∠AOT +∠OAT +∠OTA = 180°
∠AOT + 90° + 24° = 180°
∠AOT = 180° - 114°
∠AOT = 66°
For ∠ACB,
We know sum of angles on a straight line is 180°.
Therefore, ∠OAT + ∠COB =180°
∠COB= 180° - 66°
∠COB = 114°.
We know a line from the centre of a circle to its surface is known as radius of the circle. Therefore, OC and OB are radii of the circles.
We also know that angles opposite to the equal sides of a triangle are also equal. Therefore, ∠OCB =∠OBC...........(ii)
Since, we know that sum of all the angles of a triangle is 180°.
Therefore, ∠COB+∠OCB+∠OBC = 180°
From equation (ii), we get
∠COB + ∠OCB + ∠OCB = 180°
114° + 2*∠OCB = 180°
2*∠OCB = 180°-114°
2*∠OCB=66°
∠OCB=66°/2
∠OCB = 33°
Therefore, ∠AOT is 66° and ∠ACB is 33°.
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What is the surface area of this complex shape?
408 ft
458 ft
545 ft
720 ft
680 ft
1000 ft
GIVING BRAINLIEST TO WHO ANSWERS IT CORRECTLY
The surface area of the figure will be 458 square feet. Then the correct option is B.
What is the area?The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
The surface area of the figure is given as,
[tex]\sf SA = 2 [(12 \times 5) + (12 \times 5) + (7 \times 7) + (5 \times 12)][/tex]
[tex]\sf SA = 2 (60 + 60 + 49 + 60)[/tex]
[tex]\sf SA = 2 (229)[/tex]
[tex]\sf SA = 458 \ square \ feet[/tex]
The surface area of the figure will be 458 square feet. Then the correct option is B.
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if x initially contains the value 3, which of the following sets x to 7?
To set x to 7 when it initially contains the value 3, you would need to add 4 to x. Therefore, the option that would set x to 7 is x = x + 4.
This statement adds 4 to the current value of x (which is 3), resulting in x being equal to 7. It is important to note that there may be other ways to set x to 7 depending on the specific context and code. However, in the absence of further information, adding 4 to x is the most direct and simple solution.
Let's consider that x initially contains the value 3. We want to find an operation that sets x to 7. Since we're looking for a change of +4 (7 - 3), we can perform the following operation: x = x + 4. By adding 4 to the initial value of x, we get x = 3 + 4, which results in x = 7. Thus, the operation that sets x to 7 when it initially contains the value 3 is x = x + 4.
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A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 4 hours. The company has only 800 work hours to use in manufacturing each day, and the packaging department can package only 300 trimmers per day. If the company sells the cord-type model for $22. 50 and the cordless model for $45. 00, how many of each type should it produce per day to maximize its sales?
The company should produce 200 cord-type trimmers and 100 cordless trimmers per day to maximize its sales. The total sales will be $10,500.
To maximize the sales, the company needs to determine how many units of each type of electric hedge trimmers it should produce, subject to the constraints of manufacturing time and packaging capacity. Let x be the number of cord-type trimmers and y be the number of cordless trimmers that the company produces per day.
Since the cord-type trimmer requires 2 hours to make and the cordless model requires 4 hours, the total manufacturing time can be expressed as:
2x + 4y ≤ 800
Similarly, the packaging department can package only 300 trimmers per day, which means:
x + y ≤ 300
We also know that the company sells the cord-type model for $22.50 and the cordless model for $45.00, so the total sales can be expressed as:
total sales = 22.50x + 45.00y
To maximize the total sales subject to the above constraints, we can use linear programming. Solving the above equations using the graphical method, we get the feasible region bounded by the lines 2x + 4y = 800 and x + y = 300. The corners of this feasible region are (0, 300), (200, 100), and (400, 0).
Now, we need to determine the values of x and y that maximize the total sales. We can evaluate the total sales at each of the corners of the feasible region and choose the corner that gives the maximum total sales.
At (0, 300), the total sales = 22.50x + 45.00y = 45.00 * 300 = $13,500.
At (200, 100), the total sales = 22.50x + 45.00y = 22.50 * 200 + 45.00 * 100 = $10,500.
At (400, 0), the total sales = 22.50x + 45.00y = 22.50 * 400 = $9,000.
Therefore, the company should produce 200 cord-type trimmers and 100 cordless trimmers per day to maximize its sales. The total sales will be $10,500.
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Use implicit differentiation to find ∂z/∂x and ∂z/∂y.x2 + 8y2 + 9z2 = 4
By using implicit differentiation ∂z/∂x= -2x/18z = -x/9z and ∂z/∂y = -8y/18z = -4y/9z.
To find ∂z/∂x and ∂z/∂y for the equation x^2 + 8y^2 + 9z^2 = 4 using implicit differentiation, we start by taking the partial derivative of both sides of the equation with respect to x, then with respect to y, and solve for ∂z/∂x and ∂z/∂y.
Taking the partial derivative of both sides of the equation with respect to x, we get:
2x + 0 + 18z(∂z/∂x) = 0
Solving for ∂z/∂x, we get:
∂z/∂x = -2x/18z = -x/9z
Taking the partial derivative of both sides of the equation with respect to y, we get:
0 + 16y + 18z(∂z/∂y) = 0
Solving for ∂z/∂y, we get:
∂z/∂y = -8y/18z = -4y/9z
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the vector equation ,0
Hello! It seems like your question might be incomplete or missing some details. However, I'll provide you with a brief explanation of a vector equation, and if you need more help, please provide additional information.
A vector equation is an expression that describes a vector in terms of its components, magnitude, and/or direction. It is often used to represent , such as displacement, velocity, and force, which have both magnitude and direction. In general, a vector equation can be written as:
Vector V = ai + bj + ck
Here, V is the vector, and a, b, and c are its components along the x, y, and z axes, respectively. i, j, and k are the unit vectors along the x, y, and z axes.
If you need help with a specific vector equation or problem, please provide more details, and I'll be happy to assist you.
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1.7. Use the rule n+1 ×2 to write the number of tiles if the figure number is n and (n-1).
Answer:
Step-by-step explanation:
Based on the calculations, the sequence defined by the given function are 0.75, 1.1, 1.45, 1.80 and 2.15.
How to create the terms of the sequence?
In this exercise, you're required to create the first five (5) terms of the sequence defined by the given function as follows:
For the first term, we have:
f(1) = 0.75
For the second term, we have:
f(2) = f(2-1) + 0.35
f(2) = 0.75 + 0.35
f(2) = 1.1.
For the third term, we have:
f(3) = f(3-1) + 0.35
f(3) = 1.1 + 0.35
f(3) = 1.45.
For the fourth term, we have:
f(4) = f(3-1) + 0.35
f(4) = 1.45 + 0.35
f(4) = 1.80.
For the fifth term, we have:
f(5) = f(3-1) + 0.35
f(5) = 1.80 + 0.35
f(5) = 2.15.
Therefore, the sequence defined by the given function are 0.75, 1.1, 1.45, 1.80 and 2.15.
determine the critical load of a round wooden dowel that is 0.75 m long. use e = 12 gpa. the diameter of the round wooden dowel is 10 mm. the critical load is n.
the critical load of the round wooden dowel is determined by using the Euler buckling formula, which is given by:
P_cr = (π^2 * E * I) / L^2
Where P_cr is the critical load, E is the modulus of elasticity (given as 12 GPa), I is the area moment of inertia (for a round wooden dowel it is π*d^4/64), and L is the length of the dowel (given as 0.75 m). Substituting these values, we get:
P_cr = (π^2 * 12e9 * π*(10/1000)^4/64) / (0.75^2)
P_cr = 91.34 N
Therefore, the critical load of the round wooden dowel is 91.34 N.
In explanation, the Euler buckling formula is used to determine the critical load of slender columns or rods that are subjected to compressive forces. The formula takes into account the modulus of elasticity of the material, the length of the column, and the area moment of inertia of the cross-section. The critical load is the maximum load that the column can withstand without buckling or collapsing under compressive forces.
the critical load of the round wooden dowel with a diameter of 10 mm and a length of 0.75 m is 91.34 N, which is the maximum load that the dowel can withstand without buckling or collapsing under compressive forces.
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5,322,093.05 in words
Answer:
five million three hundred twenty-two thousand ninety-three and five hundredths
Step-by-step explanation:
have a great day and thx for your inquiry :)
Answer:
five million, three hundred and twenty two thousand and ninety three point zero five
A distribution in which all the values have the same frequency is called a(n) ______ distributiorectangularbimodalstandard.
A distribution in which all the values have the same frequency is called a rectangular distribution. This type of distribution is also known as a uniform distribution ,
because the probability of any given value occurring is equal to every other value in the distribution. Rectangular distributions can be represented graphically by a flat, straight line that runs across the entire range of values, indicating that each value has an equal chance of occurring.
This type of distribution is commonly used in probability and statistics, as well as in financial analysis and risk management. While rectangular distributions are relatively simple and easy to understand, they may not always accurately reflect the true nature of a dataset, particularly if there is a significant amount of variation or outliers.
It is important to note that bimodal and standard distributions have different properties and are not the correct terms for this scenario. Bimodal refers to a distribution with two distinct peaks, while standard distribution typically refers to a normal distribution with a mean of 0 and a standard deviation of 1.
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Please try this ! Ill mark u as brainliest is do!!!
Answer: (50, 40)
Step-by-step explanation:
I am not a 100% sure if it is 40, but try that. if c is an equal distance to both a and b and the total distance between a and be is 40 (because 100-60 is 40), the middle of that would be 20. given that, 60 from the y axis minus 20 is 40.
* so try (50,40)
the region r in the first quadrant is enclosed by the lines x=0 and y=5 and the graph of y=x^2+1
Therefore, the area of the region r is 8 square units.
To start, let's graph the two lines and the equation y=x^2+1 in the first quadrant:
As we can see from the graph, the region r is a triangle with a curved bottom. To find the area of this region, we can use integration.
First, we need to find the x-coordinates of the points where the line y=5 intersects with the curve y=x^2+1. To do this, we set the two equations equal to each other:
5 = x^2 + 1
Subtracting 1 from both sides gives us:
4 = x^2
Taking the square root of both sides, we get:
x = ±2
Since we are only interested in the positive x-value (since we are in the first quadrant), we have:
x = 2
Next, we need to set up our integral to find the area of the region r. Since the region is bounded by the lines x=0 and y=5, and the curve y = x^2+1, we can integrate with respect to y, using the limits of integration y=1 and y=5 (since the curve starts at y=1 when x=0).
The area of the region r can be found using the following integral:
A = ∫[1,5] [√y - 1] dy
Integrating, we get:
A = [2/3 y^(3/2) - y] [1,5]
A = [2/3 (5)^(3/2) - 5] - [2/3 (1)^(3/2) - 1]
A = 25/3 - 1/3
A = 8
Therefore, the area of the region r is 8 square units.
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the model of a river is constructed to a scale of 1/60. if the water in the river is flowing at 38 ft/s, how fast must the water flow in the model?
The water in the given model must flow at a constant speed of 2,280 ft/s to represent the actual water flow of 38 ft/s.
The speed of water flow in the model can be calculated as follows:
Model speed = Actual speed / Scale factor
Since the scale factor is 1/60, the model speed will be:
Model speed = 38 ft/s / (1/60) = 2,280 ft/s
Therefore, the water in the given model must flow at a constant speed of 2,280 ft/s to accurately and precisely represent the actual water flow of 38 ft/s.
Note: The calculated model speed seems unreasonably high, and it is likely that there is an error in the given values or in the calculation.
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The original price of a television was £300.
The price was reduced by 10% in a sale.
a) Work out 10% of the original price of the television.
b) Work out the sale price of the television.
Answer:
a) To work out 10% of the original price of the television, we can multiply the original price by 0.1:
10% of £300 = 0.1 × £300 = £30
Therefore, 10% of the original price of the television is £30.
b) To work out the sale price of the television, we can subtract 10% of the original price from the original price:
Sale price = Original price - 10% of original price
Sale price = £300 - £30
Sale price = £270
Therefore, the sale price of the television is £270.
HELP ASAP !!!!
The coordinates of a triangle are described by a matrix, where the rows represent each point, A, B, and C, from top row to bottom row, and column 1 represents the x coordinates and column 2 represents the y coordinates. What transformation does the following matrix represent when added to the first matrix?
A. A rotation about the origin clockwise by 90°
B. A flip over the y-axis
C. A translation to the left by 20 units and down by 20 units
D. A translation to the right by 20 units and down by 20 units
Answer:
D. A translation to the right by 20 units and down by 20 units
Step-by-step explanation:
You want to know the effect of adding (20, -20) to the (x, y) coordinates of the vertices of a triangle.
TransformationThe x-coordinate of a point tells you its position to the right of the y-axis. Adding 20 to the x-coordinate moves its position 20 units farther to the right.
The y-coordinate of a point tells you its position above the x-axis. Subtracting 20 from the y-coordinate moves its position down 20 units.
The matrix represents the transformation ...
A translation to the right by 20 units and down by 20 units, choice D.
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please help me with these asap, i will mark brilientest
The value of b is 50 in
What are similar shapes?Similar shapes are two figures having the same shape. For two shapes to be similar, the corresponding angles must be congruent.
The corresponding angles are
angle Y = angle D
angle X = angle A
angle Z = angle C
angle W = angle B
Also, the ratio of the corresponding sides of Similar shape are equal.
40/8 = b/10
400 = 8b
8b = 400
divide both sides 8
b = 400/8
b = 50 in
therefore the value of b is 50 in
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PLEASE HELP!! LIMITED TIME WILL GIVE BRAINLIEST/POINTS!
The number of cars waiting at a bank for 60 minutes is as follows.
Find the probability of 3 cars waiting in line.
P( 3 ) = [?]
Answer:
The probability is 1/5 or 0.2
Step-by-step explanation:
Probability of 3 cars waiting in the line= the number of 3 cars waiting in the line/Total number of cars
T(c)=2+9+16+12+8+6+4+2+1=60
P=12/60
P=1/5 or 0.2
liam is buying tickets for a group of families going to an amusement park. he wants to have at least 20 tickets. each adult ticket costs $15.75 and each child ticket costs $13. liam wants to spend no more than $250. which system of inequalities can liam use to find the number of tickets he can buy?
Inequalities ensure that Liam buys enough tickets (at least 20), and also that he stays within his budget (spends no more than $250).
Let's use the variables "a" and "c" to represent the number of adult and child tickets Liam buys, respectively. Then the total number of tickets he buys is a + c, and the total cost of the tickets is 15.75a + 13c.
To find the system of inequalities, we need to use the given information:
Liam wants to have at least 20 tickets: a + c ≥ 20
Each adult ticket costs $15.75 and each child ticket costs [tex]$13: 15.75a[/tex] + 13c ≤ 250 (since Liam wants to spend no more than [tex]$250)[/tex]
So the system of inequalities is:
a + c ≥ 20
15.75a + 13c ≤ 250
These inequalities ensure that Liam buys enough tickets (at least 20), and also that he stays within his budget (spends no more than [tex]$250).[/tex]
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I need help pls quick
Answer:
14
Step-by-step explanation:
I think what you're asking is how many study Spanish. In the diagram, the spot for Spanish has the number 14.
consider the following function. f(x) = x1/7, a = 1, n = 3, 0.9 ≤ x ≤ 1.1
An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
The given function is f(x) = x1/7, where a = 1 and n = 3. The interval of interest is 0.9 ≤ x ≤ 1.1.
To evaluate the function, we substitute the value of x in the given equation:
f(0.9) = 0.9^(1/7) ≈ 0.956
f(1) = 1^(1/7) = 1
f(1.1) = 1.1^(1/7) ≈ 1.044
Therefore, for the given function and interval, the values of f(x) are approximately 0.956, 1, and 1.044 for x = 0.9, 1, and 1.1 respectively.
Hi! I'd be happy to help you with your question. Given the function f(x) = x^(1/7), a = 1, n = 3, and the interval 0.9 ≤ x ≤ 1.1, you may be looking for the value of the function within that specific range.
Within the interval 0.9 ≤ x ≤ 1.1, the function f(x) = x^(1/7) will output values according to the exponent. When x is closer to 0.9, the output will be lower, while when x is closer to 1.1, the output will be higher. For example, f(0.9) = 0.9^(1/7) ≈ 0.977 and f(1.1) = 1.1^(1/7) ≈ 1.014.
Please let me know if you need further clarification or if you have any other questions.
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▸
The functions f(x)=x²-1 and g(x)=x+4 are shown on the graph
f(x)=x²-1
3
6 7
g(x)=-2² +4
8 9
Explain how to modity the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
The solution to the given graph is (-√5/2, √5/2)
we have that Quadratic graph:
Given the following quadratic graph f(x)=x²-1 and g(x) = -x² + 4
The solution will be the point of intersection of the two curves.
Equate the functions
x²-1 = -x² + 4
Equate to zero
x²+x² - 1- 4 = 0
2x² -5 = 0
2x² = 5
x² = 5/2
x = ±√5/2
Hence the solution to the given graph is (-√5/2, √5/2)
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there are two samples, a and b, ere tested by rockwell hardness test. sample a is tested in b scale, shows hardness value 59 hrb. sample b is tested in f scale, shows hardness value 90.5 hrf. which sample is harder? (use your conversion chart if it is necessary)
sample B is harder than sample A.To compare the hardness values of samples A and B, we need to convert them to the same scale.
Rockwell hardness scales are designated by a letter, such as B or F, and each scale has a different range and units of measurement.
To convert sample A's hardness value from the B scale to the F scale, we can use the conversion chart. According to the chart, the conversion formula from B to F scale is HRF = (HRB x 1.000) + 18. Therefore, the converted hardness value for sample A is:
HRF = (59 x 1.000) + 18 = 77 HRF
Now we can compare the hardness values of both samples, and we see that sample B has a higher hardness value of 90.5 HRF, compared to sample A's value of 77 HRF. Therefore, we can conclude that sample B is harder than sample A.
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What is the answer I really need the answers
Answer:
the answer is 90°
Step-by-step explanation:
you can also do it the simple way
if you check Line EB clearly you will see that it is a straight line, and since angle DAB is 90° then angle DAE is also 90°
(7) Mary is 4 years older than Toni. Sam is twice as old
as Mary. The sum of their three ages is 8 times
Toni's age. How old are they?
Solving a system of equations we can see that:
Toni is 3 years old, Mary is 7 years old, and Sam is 14 years old.
How old are they?
First let's define the variables:
M = Mary's age.T = Toni's age.S = Sam's age.With the given information we can write 3 equations:
M = T + 4
S = 2*M
M + T + S = 8T
Now let's solve the system.
Replace thefirst equation into the second one to get:
S = 2*(T + 4)
Now we can replace the two equations in the last one to get:
T + 4 + T + 2*(T + 4) = 8*T
Now we can solve this for T.
4T + 12 = 8T
12 = 8T - 4T
12 = 4T
12/4 = T = 3
Now that we know that value, we can get the other two:
M = 4 + T = 4 + 3 = 7
S = 2*M = 2*7 = 14
These are the 3 ages.
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What is the best estimate for the volume of the pyramid
The best estimate for the volume of the pyramid is 1386.67 cubic units.
To calculate the volume of a pyramid, we use the formula V = (1/3) * B * h, where B is the area of the base and h is the height of the pyramid. In this case, we are given that the base of the pyramid is a rectangle with dimensions 15 units by 20 units, so the area of the base is B = 15 * 20 = 300 square units. We are also given that the height of the pyramid is 14 units. Therefore, the volume of the pyramid is V = (1/3) * 300 * 14 = 1400 cubic units. However, since this is an estimate, we should round our answer to a reasonable number of decimal places. In this case, we can round to two decimal places to get a final answer of 1386.67 cubic units. This estimate gives us a good approximation of the volume of the pyramid based on the information provided.
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For the given cost function C(x) = 1900 + 390x + 1.5x2 and the demand function p(x) = 1170 (i.e. the price p at the given volume of demand x). Find the production level that will maximaze the profit P(x)=r(x)-c(x), where r(x) is the revenue function.
The production level that will maximize the profit P(x)=r(x)-c(x) [where r(x) is the revenue function] is x = 260 units.
For the given cost function C(x) = 1900 + 390x + 1.5x^2 and the demand function p(x) = 1170, we will find the production level that will maximize the profit P(x) = r(x) - c(x), where r(x) is the revenue function.
Determine the revenue function r(x) by multiplying the demand function p(x) by x (i.e., the quantity sold):
r(x) = p(x) * x = 1170 * x
Calculate the profit function P(x) by subtracting the cost function C(x) from the revenue function r(x):
P(x) = r(x) - C(x) = 1170x - (1900 + 390x + 1.5x^2)
Simplify the profit function:
P(x) = 780x - 1900 - 1.5x^2
Step 4: To find the production level that maximizes the profit, we need to find the critical points of the profit function by taking its first derivative and setting it to zero:
P'(x) = d(P(x))/dx = 780 - 3x
Now set P'(x) to 0 and solve for x:
780 - 3x = 0
3x = 780
x = 260
The production level that will maximize the profit is x = 260 units.
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Which of the following properties prove that the triangles are congruent?
Answer: A) AAS Congruence Theorem
Step-by-step explanation:
If we look at what we are given, we see that we have two congruent angles and one congruent side. Next, we will look at the given congruence theorems. The one that lines up with our given measurements is option A, the AAS Congruence Theorem (which is the angle-angle-side theorem) since we have two angles in a row with a non-included side.
