The table represents a linear function because the rate of change is constant or all the points lie on a straight line.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables
From the given table it is noticed that the line passes through points (-1, -2), (0, 0), (1. 2), and (2, 4).
The slope of the line is
Slope = (2- 0)/1-0)
The slope of the line is. It means the value of y increased by 5 if the value of x increased by 2.
From the given points we can notice that the value of y increased by 5 if the value of x increased by 2. So, the function has the same slope for any two points.
Since the rate of change (slope) is the same for all points, therefore the table represents a linear function.
Therefore, If we plot these points on a coordinate plane and connect then we get a straight line. I mean it is a linear function.
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Assume the following
actual machine hours during the period of 54000 hours
estimates machine hours to be worked during the coming period of 55000 hours manufacturing overhead applied to production during the period of 432000 estimated variable manufacturing overhead per machine hour of 2.7
which is the fixed MOH cost
Based on the manufacturing overhead applied to production during the period of $432,000, the fixed manufacturing overhead cost is $286,200.
What is the manufacturing overhead applied?The manufacturing overhead applied is determined as the product of the predetermined overhead rate and the actual machine hours consumed during the period.
Estimated machine hours to be worked = 55,000 hours
Actual machine hours during the period = 54,000 hours
Total manufacturing overhead applied to production = $432,000
Estimated variable manufacturing overhead per machine hour = $2.70
Total variable manufacturing overhead = $145,800 ($2.70 x 54,000)
Fixed manufacturing overhead (MOH) cost = $286,200 ($432,000 - $145,800)
Thus, the fixed manufacturing overhead cost is the difference ($286,200) between the total overhead cost applied and the variable manufacturing overhead cost.
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Describe how the graph of the function is a transformation of the original function f.
y=f(x+16)
The graph of the function y = f(x + 16) is a transformation of the original function f. This transformation has shifted the graph of f to the right by 16 units on the x-axis. This means that the value of x in the original function has been increased by 16, which has an effect on the corresponding value of y in the transformed function.
For example, if the point (a, b) is on the graph of f, then the point (a + 16, b) will be on the graph of y = f(x + 16). The x-coordinate of the point has been increased by 16, and since the transformation is a horizontal shift, the y-coordinate remains unchanged.
In summary, the graph of y = f(x + 16) is a reflection of the graph of f about the vertical axis. The transformation has the effect of shifting the graph to the right, but preserving the shape and overall form of the original function.
A solution contains furosemide (frusemide) 10 mg/mL. How many milligrams of frusemide are in 3 mL of solution?
Answer:
30mg
Step-by-step explanation:
10 mg/mL x 3 mL
evaluate without a calculator: sec 30°
Answer:
sec 30° = 1/cos 30° = 2.
Step-by-step explanation:
The secant function (sec) is the reciprocal of the cosine function. So, sec(x) = 1/cos(x). The value of cosine at 30 degrees is sqrt(3)/2, and its reciprocal is 2/sqrt(3), which can be simplified to 2. Hence, sec(30°) = 2.
URGENT!!!
Sharon invested $5,000 in a bond for 2 years. The total interest earned on the investment was $600. What was the interest rate on the investment?
The interest rate required to pay a simple interest of $600 from an investment of $5000 in 2 years is 6%.
What is the interest rate on the investment?Simple interest is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $5,000Interest I = $600Elapsed time t = 2 yearsInterest rate r = ?Plug the given values into the above formula and solve for r.
I = P × r × t
r = I / Pt
r = 600 / ( 5,000 × 2 )
r = 600 / ( 10,000 )
r = 0.06
Interest rate = r × 100%
Interest rate = 0.06 × 100%
Interest rate = 6%
Therefore, the interest rate is 6%.
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What is the sum of the measures of the exterior angles of the polygon shown below? If necessary, round to the nearest tenth.
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The sum of the measures of the exterior angles of the polygon is, 360°
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
Given that,
A polygon,
Having 9 equal sides,
The sum of the measures of the exterior angles of the polygon = ?
The sum of each interior & exterior angles are 180°
Suppose, interior angles are respectively
a, b, c, d, e, f, g, h, i,
Now, exterior angles are respectively
180°-a, 180°-b, 180°-c, 180°-d, 180°-e, 180°-f, 180°-g, 180°-h, 180°-i,
The sum of the measures of the exterior angles of the polygon =
180°-a + 180°-b +180°-c +180°-d + 180°-e + 180°-f + 180°-g +180°-h + 180°-i,
1620 - (a + b + c + d + e + f + g + h + i)
Sum of all the interior angles = (9-2)x180°
= 1260°
The sum of the exterior angles of the polygon = 1620 - 1260°
= 360°
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The probability that a passenger is chosen for customs inspection is 10 %. Emma and Michael go through customs. What is the probability that neither of them is chosen for inspection? The probability of one passenger being chosen is independent of that of other passengers.
a) 81 %
b) 90 %
c) 99 %
d) other
The probability that neither of them is chosen for inspection is given as follows:
a) 81 %
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 2, p = 0.1.
The probability of neither is P(X = 0), hence:
P(X = 0) = (1 - 0.1)² = 0.81.
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HELP
_______________
The correct statements regarding the translation from function f(x) to function g(x) are given as follows:
Function f is translated down 2 units.Function f is translated to left 3 units.What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The translations for this problem are defined as follows:
x - 2 to x + 1 -> x = x + 3 -> translated left 3 units.y -> y - 2 -> translation down 2 units.More can be learned about translations at brainly.com/question/28174785
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.42 is 1 tenth of what number
Answer: 4.2
Multiply both sides by 10
0.42 (10) = 0.1 (10)
4.2 = 1
Answer:
4.2
Step-by-step explanation:
A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people. Write a function relating the number of people, n, to the cost, C.
The value of function relating the number of people, n, to the cost, C is,
⇒ C (n) = 7n ; if 0 < n < 15
= 105n ; if n ≥ 15
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people.
Hence, he value of function relating the number of people, n, to the cost, C is,
⇒ C (n) = 7n ; if 0 < n < 15
= 105n ; if n ≥ 15
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Write an expression to represent:
3
33 minus the product of
2
22 and
�
xx.
The expression to represent the given statement is:33 - (2 * 22 * ½x)
The expression "33 - (2 * 22 * ½x)" represents a mathematical calculation. Breaking it down, we start with the product of 2 multiplied by 22, which equals 44. Then, we multiply the result by ½x, where ½ represents one-half and x is a variable. This gives us the term 44 * ½x. Finally, we subtract this term from 33. In simpler terms, we have 33 minus half of 44 times x. The expression allows us to compute the value of the expression based on the input for the variable x, providing a way to evaluate the equation numerically.Let's dive deeper into the explanation.
The given expression is "33 - (2 * 22 * ½x)".
To simplify it, let's break it down step by step:
The term "2 * 22" is a multiplication operation that calculates the product of 2 and 22, resulting in 44.
Next, we have "½x". Here, ½ represents one-half, or 0.5. Multiplying 0.5 by x gives us 0.5x.
Putting it together, we have the term "44 * ½x". This means multiplying 44 by 0.5x, resulting in 22x.
Finally, we subtract the term "22x" from 33, giving us the expression "33 - 22x".
In summary, the expression represents the number 33 minus the product of 22 and the value of x, denoted as 22x. This expression allows us to calculate the result by substituting a specific value for x. It provides a way to compute the numerical outcome based on the given mathematical relationship.
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What is the area of the parallelogram
Answer:
40 units^2
Step-by-step explanation:
The parallelogram shown is basically made of two triangles divided by the x-axis. The bases go from 3 to 13 on the axis, so they have a length of 10. The height of one triangle is from a 0 to 4, which is a height of 4.
The area of a triangle is [tex]\frac{bh}{2}[/tex], so plugging those numbers in gets:
[tex]\frac{4*10}{2}[/tex] = 20
Since there are two triangles it would be double the area: 40 units^2
in 2010 an earthquake below the ocean floor initiated a devastating tsunami in Samatra. scientists can approximate the velocity V in feet per second of a tsunami in water of depth d feet with the formula [tex]\sqrt{16} \\[/tex] [tex]\sqrt{d}[/tex]. Determine the velocity of a tsunami in 300 feet of water. Write your answer in simplified radical form.
Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
here, we have,
Since the depth of the water 'd' (in feet) and the velocity of the wave 'v' (in feet per second) are related by the equation
v = √(16d)
a wave forms in water with a depth of 300 feet,
therefore d = 300 ft
so, we get,
velocity = √(16*300)
= 4√300
=4*17.32
=69.28
Hence, Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.
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Hey guys please help me with my quiz its about finding the values of letters in angles!!
The value of x is given as follows:
x = 24.
The measure of angle DFE is given as follows:
<DFE = 62º.
How to obtain the measures?To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.
The internal angle measures for this problem are given as follows:
180 - (5x - 14) -> each angle is supplementary with it's external.44º.3x - 10.Hence the value of x is obtained as follows:
180 - 5x + 14 + 44 + 3x - 10 = 180
228 - 2x = 180
2x = 48
x = 24.
The measure of angle DFE is obtained as follows:
<DFE = 3(24) - 10
<DFE = 72 - 10
<DFE = 62º.
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Which inequality does the graph represent? The graph with X-coordinate marks -2, 0, and 2; Y-coordinate marks -2, 0, and 2. There is a line which passes through the points (3, 3), and (2, 3.5). There is shaded region which is above the line. A. y > (–13 )x + 4 B. y ≥ (–13 )x + 4 C. y < (–13 )x + 4 D. y ≤ (–13 )x + 4
The values of {x} are given above upto 2³.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the graph with x - coordinate marks (-2, 0, and 2) and y -coordinate marks (-2, 0, and 2). There is a line which passes through the points (3, 3) and (2, 3.5).
The inequality line representing the shaded region as -
y ≥ - 13x + 4
Therefore, the inequality line representing the shaded region is y ≥ - 13x + 4.
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Which equation represents the graph? a graph of a line that passes through the points 0 comma negative 3 and 4 comma negative 1 y equals negative one half times x plus 6 y equals one half times x minus 3 y = 2x − 3 y = −2x + 6
the equation of line passes through points (0, -3) and (4, -1) is 4y = 3x -12.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, an equation of a line in the graph.
Since the graph shows that the line passes through points (0, -3) and (4, -1).
The slope-intercept form of the equation of a line
y=mx+b,
where m is the slope
b is the y-intercept (value of y at x =0)
since
slope = (y - y')/(x -x')
In our case,
slope (m) = (-1 - (-3))/(4 -0)
m = 3/4
b = -3
Thus, the equation of the line:
y = 3/4x - 3
or, 4y = 3x -12
therefore, the equation of the line will be 4y = 3x -12.
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Write the phrase as an expression. a number x divided by 2
Answer: x/2
Step-by-step explanation: Good morning. I am not sure what you mean by "A number x", so I suppose that is a typo.
Answer: x/2 IS CORRECT
Step-by-step explanation:
I TRIED IT :)
A cylinder has a volume of 243 pi
and a diameter of 18. What is its height?
Answer:
0.955
Step-by-step explanation:
Height= volume x pi x radius squared (h = V x pi x r^2)
Volume (V) = 243
Height (h) = ?
Pi = 3.14
Radius (r) = 9
Diameter to radius = 18/2 = 9
h = 243 x 3.14 x 9^2
=0.955
What is the surface area of the polyhedron
Answer: equal to the sum of the area of all of its faces
Step-by-step explanation:
if u help me for this its basically free brainliest
The required 3/4 is 11/3 and 26/3 times in fractions 11/4 and 6 1/2 respectively.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Given ration 3/4
(1)
Fraction 3/4 in 11/4
= 11/4 / 3/4
= 11/3
Although, 3/4 is 11/3 times in the value 11/4
Similarly
(2)
Fraction 3/4 in 6 1/2
= 13 / 2 / [3/4]
= 26/3
Although, 3/4 is 26/3 times the value of 6 1/2.
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Find p and q , if X1 = 17, n1 = 25, X2 = 28, and n2 = 80
The solutions are given below:-
Part (a),
X₁ + X₂ have distribution Bi(n₁+n₂, p)
Part (b),
P(X ₁+ X₂ = 1 | X₂ = 0) = np(1-p)ⁿ¹⁻¹
P(X₁+X₂ = 1| X₂ = 1) = (1-p)ⁿ¹
P(X₁ + X₂ = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
What is binomial distribution?Since both variables are independent but they have the same probability parameter, you can interpret that as if the experiment that models each try in both variables is the same.
When you sum both random variables together, what you obtain as a result is the total amount of success in n₁+n₂ tries of the same experiment, thus X₁+X₂have distribution Bi(n₁ + n₂, p).
b)
Note that, if X₂ = k, then X₁ +X₂ = 1 is equivalent to X₁ = 1-k. Since X1 and X₂ are independent, then P(X₁ +X₂ = 1| X₂ = K) = P(X1=1-k|X₂=k) = P(X₁ = 1-k).
If k = 0, then this probability is equal to P(X₁ = 1) = np(1-p)ⁿ¹⁻¹
If k = 1, then it is equal to P(X₁ = 0) = (1-p)ⁿ¹
Thus,
P(X₁+X₂ = 1) = P(X₁+X₂ = 1| X₂ = 1) * P(X₂=1) + P(X₁+X₂ = 1| X₂ = 0) * P(X₂ = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹.
The complete question is given below.
Let X1 and X2 be two random variables following Binomial distribution Bin(n1,p) and Bin(n2,p), respectively. Assume that X1 and X2 are independent.
(a) The mgf of binomial distribution Bin(n, p) is (1 − p + pet)n. Use this fact to obtain the distribution of X1 + X2.
(b) Find the probability P(X1 + X2 = 1|X2 = k) for k = 0 and 1. Then use the law of total probability to find P (X1 + X2 = 1)
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What is the sum of 3 of the interior angles of a regular pentagon?
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Answer: 540°.
Step-by-step explanation:
by
Express it in mathematical phrases:
The quotient of a number by eight
The mathematical expression, for the given phrase is n / 8
What is an expression?A mathematical statement, containing variables and numbers related by a mathematical operator, is called an expression.
Given that, a mathematical phrase: The quotient of a number by eight, we are asked to convert it into a mathematical expression,
Let n be the unknown number,
The quotient shows a result of division of two numbers,
Therefore,
The quotient of a number, n by eight, can be written as,
n / 8
Hence, the mathematical expression, for the given phrase is n / 8
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ria is buying plates and cubs for a party. she wants the same numbers of each.Plates are sold in packs of 8. cups are sold in packs of 12. what is the least number of plates and cups that ria can buy
The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, ria is buying plates and cubs for a party. she wants the same numbers of each. Plates are sold in packs of 8. cups are sold in packs of 12.
Plates = 8 per pack
Cups = 12 per pack
the Lowest common multiple of 8 and 12
8 = 16, 24, 32, 40, 48, 56, 64, 72, 80
12 = 24, 36, 48, 60, 72
The Lowest common multiple of 8 and 12 is 24
The least number of plates and cups she can buy is 24
Packs of plates = 24 plates / 8 per pack
= 3 packs
She will buy 3 packs of plates
Packs of cups = 24 / 12 per pack
= 2 packs
She will buy 2 packs of cup
Therefore, The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup
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(x+2)^2=4(x+5)+y standard form
The standard form of the equation (x + 2)² = 4 (x + 5) + y is:
x² + y - 16 = 0
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The standard form of an equation is Ax + By = c.
Now,
(x + 2)² = 4 (x + 5) + y
x² + 4x + 4 = 4x + 20 + y
x² + 4 = 20 + y
x² + y = 20 - 4
x² + y = 16
x² + y - 16 = 0
Thus,
x² + y - 16 = 0 is the standard form of an equation.
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13, 11, 9, 7 In the number pattern above, each term is 2 less than the previous term. Which of the following is also true about the pattern?
A. All the numbers are multiples of 3.
B. All the numbers are even.
C. All of the numbers are prime.
D. All the numbers are odd.
HURRY ITS DUE TODAY
The truth about the pattern that we have here is that all of the numbers are: odd.
What are odd numbers?In the number pattern given, each term is 2 less than the previous term. Starting from 13, we have 11 (13 - 2), 9 (11 - 2), and 7 (9 - 2). All of these numbers are odd, making answer D the correct choice.
A. All the numbers are multiples of 3: This is not true, as 9 is the only number that is a multiple of 3.
B. All the numbers are even: This is not true, as all of the numbers are odd.
C. All of the numbers are prime: This is not true, as 9 is not a prime number.
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solve the given initial-value problem. Dy dx + y = f(x), y(0) = 1, where f(x) = 1, 0 ≤ x ≤ 1; -1 , x ≥ 1
The general solution of the ODE is:
y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1
y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1
How did we get the values?This is a first-order linear ordinary differential equation (ODE) with constant coefficients. It can be solved using the method of integrating factors.
Let's multiply both sides by the integrating factor e^(∫p(x)dx), where p(x) = 1.
e^(∫p(x)dx) * Dy/dx + e^(∫p(x)dx) * y = e^(∫p(x)dx) * f(x)
D/dx (e^(∫p(x)dx) * y) = e^(∫p(x)dx) * f(x)
Integrating both sides, we get:
e^(∫p(x)dx) * y = ∫ e^(∫p(x)dx) * f(x) dx + C
where C is an arbitrary constant of integration.
Using the initial condition y(0) = 1, we can find the value of the constant C.
y(0) = 1 = e^(∫p(x)dx) * y(0) = e^(∫p(x)dx) * 1 = ∫ e^(∫p(x)dx) * f(x) dx + C
So, C = 1 - ∫ e^(∫p(x)dx) * f(x) dx
For 0 ≤ x ≤ 1, we have f(x) = 1 and:
∫ e^(∫p(x)dx) * f(x) dx = ∫ e^x dx = (e^x - 1) / 1
For x ≥ 1, we have f(x) = -1 and:
∫ e^(∫p(x)dx) * f(x) dx = ∫ -e^x dx = -(e^x - 1) / 1
Therefore, the general solution of the ODE is:
y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1
y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1
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Mr.Ramirez 24 cookies. 3 fourths were oatmeal. How many oatmeal cookies did Mr.Ramirez bake
The amount of oatmeal cookies with Mr. Ramirez is 18
How to find the amount to oatmeal cookiesThe problem is dealing with multiplication of fractions
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split.
In the problem saying that 3 fourths were oatmeal means that 3/4 of the cookies where oatmeal hence
number of cookies = 3/4 * 24
number of cookies = 18
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number 5 only please help
The series 1/2 + 1/5 + 1/10 + 1/17 + 1/26 + ... converges
How to determine the test of convergenceFrom the question, we have the following parameters that can be used in our computation:
1/2 + 1/5 + 1/10 + 1/17 + 1/26.....
To apply the Integral test to given series, we can compare it to the area under the function 1/x.
As a general rule, the function 1/x is a decreasing function on the interval (1, ∞),
This means that the series converges.
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Celine purchased a ball of red yarn costing $2.33. She gave the cashier $7.19. How much change did the cashier give back to Celine?
Answer:
$ 4.86
Step-by-step explanation:
Subtract 7.19 and 2.33
7.19-2.33=4.86