Answer:
The volume of each cylinder is given by the formula: V = πr^2h, where r is the base radius and h is the height of the cylinder.
When 25 cylinders are put into the half-filled container, the water level rises to the top of the container, which means that the total volume of the 25 cylinders is equal to the volume of the container. Let's assume the volume of the container is V_container.
So, 25 * πr^2 * h = V_container
Dividing both sides by 25πh gives: r^2 = V_container / (25πh)
Taking the square root of both sides gives: r = √(V_container / (25πh))
Since h = 10 cm, we can substitute this value in the formula above: r = √(V_container / (25π * 10))
Since r is the base radius of the cylinder, it must be positive. So, the final equation becomes:
r = √(V_container / (25π * 10)) cm = 5√(5/π) cm. shown
By using 3.14 for the value of π, we can calculate the value of r:
r = 5√(5/π) = 5√(5/3.14) = 5 * √(5/3.14)
= 5 * √(1.5873) = 5 * 1.259 = 6.295 cm (rounded to the first decimal place)
So, the base radius of the cylinder is approximately 6.3 cm.
How many solutions to the equation 5x=x+3
The equation 5x = x + 3 has 1 solution.
The solution to the equation 5x = x + 3 is x = 3.
in a continuous probability distribution, the random variable: group of answer choices can take on an infinite number of values. may have a probability greater than 1.00. has a limited number of values. is discrete.
The correct answer is option 1. In a continuous probability distribution, the random variable can take on an infinite number of values within a given range.
This range is typically represented by the interval between two points on the number line, such as 0 and 100. The probability of a particular value occurring is defined as the area under the curve of the probability density function for that distribution, rather than a single value.
Option 2, "may have a probability greater than 1.00" is incorrect as probabilities are always between 0 and 1, inclusive.
Option 3, "has a limited number of values" is incorrect as, by definition, continuous random variables can take on an infinite number of values.
Option 4, "is discrete" is incorrect as a continuous random variable is not limited to a finite or countable number of values.
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A pet store had 4 cats to feed.If they only had one-ninth of a bag of cat food and each cat got the same amount,what fraction of the bag would each cat get in all.
Answer:
0.02777777778 or 1/36
Step-by-step explanation:
1/9 divided by 4 = 0.02777777778 or 1/36
What is the y-intercept of the line?
Interpret the y-intercept in the context of the problem.
The point on a line where it crosses the y-axis is known as the y-intercept. To put it another way, it is the value of y when x is equal to 0. This can sometimes have real significance for the model that the line offers, but it can also have no significance. In this section, we will see examples of both categories.
How should the line's y-intercept be interpreted?The y-intercept can frequently be used as a beginning point when the line in question represents a group of data or observations.
How can the slope of a least squares regression line be recognised and interpreted?The formula m = r(SDy/SDx) can be used to get the slope of a least squares regression.
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Here we work in the system of integer polynomials. Those are polynomials of the Form f(x)=rnxn+···+r1x+r0 where every coefficient is an integer. General question: When does some combination of the polynomials ax + b and cx + d equal 1 ? That is, when do there exist integer polynomials P(x) and Q(x) with P(x)·(ax + b) + Q(x)·(cx + d) = 1 ? We concentrate here on cases when c = 0. (a) Prove: No combination of 2x + 5 and 3 can equal 1. That is, no integer polynomials P (x), Q(x) can satisfy: P (x)·2x + 5 + Q(x)·3 = 1. (b) Find a combination of 2x + 5 and 4 that equals 1. (c) Does some combination of 15x+9 and 25 equal 1? How about 15x+9 and 20? Explain your reasoning. (d) Investigate further examples of ax + b and d, deciding in each case whether 1 is a combination. What patterns do you detect? Can you prove that some of your observed patterns always hold true?
It appears that for any ax + b, a combination of ax + b and 2a+d equals 1. This can be proven by setting P(x) = -ax - b and Q(x) = 2a+d.
(a) No combination of 2x + 5 and 3 can equal 1.
Let P(x) and Q(x) be two integer polynomials such that P(x)·(2x + 5) + Q(x)·3 = 1.
This can be written as P(x)·2x + P(x)·5 + Q(x)·3 = 1.
Rearranging, we get P(x)·2x + (P(x)·5 + Q(x)·3) = 0
This implies that P(x)·2x = -(P(x)·5 + Q(x)·3).
Since both P(x) and Q(x) are integer polynomials, it follows that P(x)·2x and (P(x)·5 + Q(x)·3) are both integers.
However, this is impossible since the left hand side is an even integer, while the right hand side is an odd integer.
Therefore, no combination of 2x + 5 and 3 can equal 1.
(b) A combination of 2x + 5 and 4 that equals 1 is P(x) = -2x - 5 and Q(x) = 4.
(c) No combination of 15x+9 and 25 equals 1. However, a combination of 15x+9 and 20 equals 1. This can be seen by setting P(x) = -15x - 9 and Q(x) = 20.
(d) Some examples of ax + b and d combinations that equal 1 are:
2x + 5 and 4
3x + 4 and 7
4x + 3 and 9
5x + 2 and 11
It appears that for any ax + b, a combination of ax + b and 2a+d equals 1. This can be proven by setting P(x) = -ax - b and Q(x) = 2a+d.
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if tyler paid 16 dollars per 4 tickets hw much would 1000 tickets cos 250 or 4000 dollars im cunfused
Answer:
16 per 4 tickets so that 4 a ticket so multiply 4 bye 1000 to get 4000
Step-by-step explanation:
Answer:
$4000 because the amount it costs is larger than the quantity, so the price will be more.
Step-by-step explanation:
Hope it helps! =D
PLS ASWNSER NO MATTER WHAT AWNSER CORRECTLY THIS IS A REVIEW AND IS GRADED OUT OF 100% I need 80% to get an A- PLS HELP
The scale factor of the dilation is given by the equation s = 2.5
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be represented as RST
Let the dilated triangle be represented as R'S'T'
Now , the coordinates of ΔRST is
The coordinate of R = R ( 0 , 4 )
The coordinate of S = S ( 2 , 4 )
The coordinate of T = T ( 2 , 2 )
And , the coordinates of ΔR'S'T' is
The coordinate of R' = R' ( 0 , 10 )
The coordinate of S = S ( 5 , 10 )
The coordinate of T = T ( 5 , 5 )
So , the dilation scale factor is given by coordinate of R' / coordinate of R
Substituting the values in the equation , we get
Scale factor s = 10/4
Scale factor s = 5/2
Scale factor s = 2.5
Hence , the dilation scale factor is 2.5
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A real estate agent has 17 properties that she shows. She feels that there is a 40% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling no more than 3 properties in one week
A real estate agent has 17 properties that she shows, the probability of selling no more than 3 properties in one week is 0.0464 or 4.64%.
There are only two possible outcomes for each attribute. Selling one home does not affect the likelihood of selling another. Therefore, to answer this query, we employ the binomial probability distribution.
Binomial probability distribution
The probability of precisely x successes on n repeated trials is known as a binomial probability, and X can only have two possible outcomes.
[tex]P(X=x) = C_{n} , x.P^x.(1-P)^{n-x}[/tex]
Given by the following formula.
[tex]C_{n} , x = \frac{n!}{x! (n-x)!}[/tex]
And p is the probability of X happening.
n = 17
P = 0.4
P(X≤3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
In which,
[tex]P(X=x) = C_{n} , x.P^x.(1-P)^{n-x}[/tex]
[tex]P(X=x) = C_{n} , x.P^x.(1-P)^{n-x}\\P(X=0) = C_{17} ,0.(0.4)^0.(0.6)^{17} = 0.0002\\P(X=1) = C_{17} ,1.(0.4)^1.(0.6)^{16}=0.0019\\P(X=2) = C_{17} ,2.(0.4)^2.(0.6)^{15}=0.0102\\P(X=3) = C_{17} ,3.(0.4)^3.(0.6)^{14}=0.0341[/tex]
P(X≤3) = P(X=0) + P(X=1) + P(X=2) + P(X=3) = 0.0002 + 0.0019 + 0.0102 + 0.0341 = 0.0464
Therefore probability of selling no more than 3 properties in one week is 0.0464 or 4.64%.
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x is taken away by 1/6, then taken away by 1/13 and left with 1,000.
what is x?
So the initial value of x was 11142.86 when divided by 1/6, then divided by 1/13, and finally divided by 1,000.
What is equation?An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
Here,
Let's call the original value of x as X. Then, we can write the following equation:
X - X/6 - X/13 = 1000
Expanding the first two terms on the left-hand side:
X - X/6 - X/13 = 1000
7X/78 = 1000
X = 78 * 1000 / 7
X = 11142.85714
So, the original value of x was 11142.86 when x is taken away by 1/6, then taken away by 1/13 and left with 1,000.
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if the system has a radius of 40 cm, what is the tangential acceleration (in m/s2) of a point on its outermost edge at t = 0.5 s?
The angular acceleration of the system times the system's radius, which is 40 cm, or 0.4 m, gives rise to the tangential acceleration at the system's farthest edge at time t = 0.5 s. Thus, 0.4 m/s2 is the tangential acceleration.
The radius of the system multiplied by the system's angular acceleration gives the tangential acceleration of a point at its furthest edge. The system's radius in this instance is 40 cm, or 0.4 metres, and the time is 0.5 seconds. As a result, the tangential acceleration at time t = 0.5 s is equal to the system's angular acceleration times its radius, which is 0.4 m. We multiply the angular acceleration by the system's radius, which is 0.4 m, to determine the tangential acceleration. Thus, 0.4 m/s2 is the tangential acceleration at time t = 0.5 s. This indicates that a point on the system's outermost edge accelerates by 0.4.
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Use the image below to determine what relation ship exists between AGB and BGD
A: adjacent angles that form AGC
B: vertical angles
C: complementary angles
D: supplementary angles
Let f be the continuous function defined on (−1,8) whose graph, consisting of two line segments. Let g and h be the function defined by g(x)=√x^2−x−3 and h(x)=5e^x−9sinx. The function is defined by m(x)=f(x)/2g(x). Find m′(5).
The function is defined by m(x)=f(x)/2g(x) is m′(5))=[tex]\sqrt[3]{3/2}[/tex] on graph.
How to defined the function?A function is a relation that is "well-behaved," by which we mean that, given a starting point, we know the exact one ending spot to go to; given an x-value, we get only and precisely one corresponding y-value. As a result, even though all functions are relations [since they pair information], not all relations are functions. Family members who behave well are a subset of all your relations, just as well-behaved functions are a subset of all mathematical relations.)
f(x)=2x+3,XE[-1,2]
-2/3x+25/3, XE[2,8]
g(x)=√x^2−x+3 XE
m′(5))=[tex]\sqrt[3]{3/2}[/tex]
The thing to notice here is that f(x) is expressed differentially in different domain.
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Find an equation of the tangent plane to the given surface at the specified point.
z =( ex − y 5), (3, 3, 6)
Please explain steps
This is an equation is e⁻¹³⁸ˣ - 5e⁻¹³⁹ × 81y + z = 6
What do you mean by tangent?In mathematics, a tangent is a line that touches a curve at a single point and has the same slope as the curve at that point. The tangent can be thought of as an approximation of the curve at the point where it touches it.
The concept of the tangent is used in calculus and other branches of mathematics to study the properties of curves and to analyze their behavior. The derivative of a function at a point is defined as the slope of the tangent to the curve of the function at that point. The derivative is a fundamental concept in calculus and is used to study the rate of change of a function, the optimization of functions, and to solve problems in many different fields.
To find the equation of the tangent plane to the surface z = e^(x - y^5) at the point (3, 3, 6), we need to find the normal vector of the surface at that point, and use that to find the equation of the plane.
The normal vector can be found using the gradient of the surface, which is given by the partial derivatives of the function:
∇f = ∇(e^(x - y^5)) = (e^(x - y^5), -5e^(x - y^5)y^4, 1)
Evaluating this at the point (3, 3, 6), we get:
∇f(3, 3, 6) = (e^(3 - 3^5), -5e^(3 - 3^5)3^4, 1) = (e^-138, -5e^-138 * 81, 1)
So the normal vector of the surface at the point (3, 3, 6) is (e^-138, -5e^-138 * 81, 1).
To find the equation of the tangent plane, we need to find a point on the plane, and use that along with the normal vector. We already know that the point (3, 3, 6) is on the surface, so we can use that as a point on the plane.
Using the point-normal form of a plane, the equation of the tangent plane is given by:
ax + by + cz = d
Where (a, b, c) is the normal vector and (x⁰, y⁰, z⁰) is a point on the plane.
Substituting the values, we get:
e⁻¹³⁸ˣ - 5e⁻¹³⁹ × 81y + z = 6
This is the equation of the tangent plane to the surface z = e^(x - y^5) at the point (3, 3, 6).
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how do the values of the 4s in 64.723 and 9.048 compare? the value of the 4 in 64.723 is times the value of the 4 in 9.048
The 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.
The values of the 4 in 64.723 and 9.048 are not directly comparable because they represent different places in the number and have different values as a result.
In 64.723, the 4 is the hundredths place, which means it represents 0.04. In this case, the value of the 4 is 0.04.
In 9.048, the 4 is the thousandths place, which means it represents 0.004. In this case, the value of the 4 is 0.004.
To compare the two values of 4, we can divide the value in 64.723 by the value in 9.048:
0.04 / 0.004 = 10
So the value of the 4 in 64.723 is 10 times the value of the 4 in 9.048. This means that the 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.
Therefore, the 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.
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The 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.
The values of the 4 in 64.723 and 9.048 are not directly comparable because they represent different places in the number and have different values as a result.
In 64.723, the 4 is the hundredth place, which means it represents 0.04. In this case, the value of the 4 is 0.04.
In 9.048, the 4 is the thousandths place, which means it represents 0.004. In this case, the value of the 4 is 0.004.
To compare the two values of 4, we can divide the value in 64.723 by the value in 9.048:
0.04 / 0.004 = 10
So the value of the 4 in 64.723 is 10 times the value of the 4 in 9.048. This means that the 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.
Therefore, the 4 in 64.723 has a value that is 10 times greater than the value of the 4 in 9.048.
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What is moment of inertia and how to calculate It for a rod?
I = (1/12) ML² is a common way to write the moment of inertia of a rod whose axis passes through its center and has mass (M) and length (L).
What is moment of inertia?A body's moment of inertia, which is determined by multiplying each particle's mass by the square of its distance from the rotational axis, is what causes it to resist angular acceleration.A measurement of an object's resistance to changes in its rotating motion is the moment of inertia. A body's resistance to variations in rotation is measured by its cross-moment section's of inertia. Depending on how far away from the center of the body each component is. The moment of inertia is calculated as the sum of the mass of the section and the square of the distance from the centroid of the section to the reference axis.Therefore,
When the rod's axis passes through the end of the rod, the moment of inertia can also be stated using a different formula. In this instance, we apply I = 13 ML².
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What percentage commission does a salesperson make if they earn $151.34 from selling $658 worth of goods?
Answer:
23%
Step-by-step explanation:
Which of the following gives the correct range for the graph?
−4 ≤ x ≤ 2
−3 ≤ x ≤ 5
−4 ≤ y ≤ 2
−3 ≤ y ≤ 5
The correct option regarding the range of the function graphed in this problem is given as follows:
−4 ≤ y ≤ 2.
How to obtain the range of a function?The range of a function is the set that contains all the output values that can be assumed by the function.
Hence, on the graph, the range of the function is given by the values of y assumed by the graph of the function.
The minimum and maximum values of y are given as follows:
Minimum of y = -4.Maximum of y = 2.As the function is continuous, the range is given as follows:
−4 ≤ y ≤ 2.
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Find the marginal probability mass function pX(x). Round the answers to two decimal places1) Px(0)
2) Px(1)
3) Px(2)
Answer Px1 and px2 is the same
Step-by-step explanation:
Without calculation, find one eigenvalue and two linearly independent eigenvectors of A ={2 2 2 }
one eigenvalue and two linearly independent eigenvectors of A ={2 2 2 } are [ 1, 2 ]
1st step:
Lambda I
here I is identity matrix.
As our matrix is 2X2 , so we will take I= [ 1 0, 0 1]
consider lambda is represented as $
so $I matrix will be [$ 0, 0 $]
2nd Step:
A - Lambda I
i.e .[2 2, 2] - [0, 0 $]
=> [2-$ 2, 2$]
3rd Step:
Det [A-$I]
i.e. [(2-$)(4-$) - (-2)(-4)] = 0
=>8-2$-4$+$²-8
=>$²-6$
4th Step:
Det [A-$I]=0
i.e. $²-6$ =0
$($-6)=0
i.e. $ =0, & $ =6 (eigen values)
5th Step
put these eigen values in [A-$I] matrix
i.e if we put $ =0
we get [2 -2, -4 4]
consider this matrix as B
then
B X⁻= 0⁻ (⁻ is a bar sign notation)
[2 -2, -4 4] [x₁ x₂] =[0 0]
by row reduction
-2R₁+ R₂ -> R₂
so
2X₁-2X₂=0
X₁=X₂
ie eigen vector will be [0 0]
now consider
i.e if we put $ =6
we get [-4 -2, -4 -2]
consider this matrix as B
then
B X⁻= 0⁻ (⁻ is a bar sign notation)
[-4 -2, -4 -2] [x₁ x₂] =[0 0]
by row reduction
R₁- R₂ -> R₂
so
-4X₁-2X₂=0
2X₁=X₂
if we put X₁=1
x₂=2
So eigen vector will be
[1 2]
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if f(3) = 15, f ' is continuous, and 7 f '(x) dx 3 = 16, what is the value of f(7)? f(7) =
The value of f(7) is 31
Now, According to the question:
First fundamental theorem of integral calculus states that “Let f be a continuous function on the closed interval [a, b] and let A (x) be the area function. Then A′(x) = f (x), for all x ∈ [a, b]”.
"Information available from the question"
If f(3) = 15, f ' is continuous, and 7 f '(x) dx 3 = 16,
Since ∀x, f'(x) = f(x) , f is a primitive function of f'.
Therefore,
[tex]=\int\limits^7_3f' {x} \, dx = f(x)|^7_3[/tex]
= f(7) - f(3)
= f(7) - 15 = 16
by the fundamental theorem of calculus (part 2) (because f' is continuous and thus integrable).
= f(7) = 16 + 15
=> f(7) = 31
Hence, The value of f(7) is 31
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Find the unit vectors that are parallel to the tangent line to the parabola y = x2 at the point (6, 36).
The tangent line to the parabola y = x² at the point (6, 36) is (0.141, 1.68)
How to find the unit vector parallel to the tangent lineThe equation of the tangent line at the point (6, 36) can be found using the derivative of the function and the point-slope form of a line:
f(x) = x²
f'(x) = 2x
y = f'(x) * (x - 6) + 36
Substituting f'(x) = 2x,
y = 2x * (x - 6) + 36
Now, we can find a unit vector that is parallel to this line by finding a non-zero multiple of the direction vector of the line, which is (1, 2x), and normalizing it.
To normalize, we divide by the magnitude, which is sqrt(1^2 + (2x)^2) = sqrt(1 + 4x^2).
Let's use x = 6:
y = 2 * 6 * (x - 6) + 36
y = 72
So, the direction vector is (1, 12) and its magnitude is sqrt(1 + 144) = sqrt(145) = 7.07.
The unit vector that is parallel to the tangent line is (1/7.07, 12/7.07) = (0.141, 1.68).
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Use the Rational Root Theorem to determine all POSSIBLE rational zeros. f(x)=2x^3-6x^2+9x-27
Answer:
[tex]\displaystyle{\text{possible rational roots} = \pm 1, \pm \dfrac{1}{2}, \pm 3, \pm \dfrac{3}{2}, \pm 9, \pm \dfrac{9}{2}, \pm 27, \pm \dfrac{27}{2}}[/tex]
Step-by-step explanation:
Rational Root theorem is when we divide the factors of last term by the factors of first term:
[tex]\displaystyle{\text{possible rational roots} = \dfrac{\text{factors of the coefficient of last term (constant)}}{\text{factors of lead coefficient (coefficient of first term)}}}[/tex]
Our constant (last term) is -27. The factors of -27 can be ±1, ±3, ±9, ±27
Our lead coefficient is 2. The factors of 2 can be ±1 and ±2.
Hence:
[tex]\displaystyle{\text{possible rational roots} = \dfrac{\pm 1, \pm 3, \pm 9, \pm 27}{\pm 1, \pm 2}}\\\\\displaystyle{\text{possible rational roots} = \pm 1, \pm \dfrac{1}{2}, \pm 3, \pm \dfrac{3}{2}, \pm 9, \pm \dfrac{9}{2}, \pm 27, \pm \dfrac{27}{2}}[/tex]
All of these are possible roots, meaning that not all of them are real roots of the equation, just a possibility.
Factor out the greatet common factor. If the greatet common factor i 1, jut retype the polynomial. 30b^96b^818b^7–6
The 5x factored out will be 5x(4x+3)
What is the Greatest Common Factor?
The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's factors have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF)
The factors of 20x2 (all the values that will divide into 20x2:
1, 2, 4, 5, 10, 20, x, 2x, 4x, 5x, 10x, 20x, x2, 2x2, 4x2, 10x2, 20x2
The factors of 15x:
1, 3, 5, 15, x, 3x, 5x, 15x
The greatest ("largest") one that is common ("in both lists"):
5x
So, with the 5x factored out: 5x(4x+3)
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The full question
Factor out the greatest common factor.
20x2 + 15x
suppose that you pull out a toy at random, and you observe only the color, noting that it is red. conditional on just this information, what is the probability that the toy is not cool?
Without additional information, it is impossible to determine the probability that the toy is not cool.
Without additional information, it is impossible to determine the probability that the toy is not cool. This is because the color of the toy does not provide any information about its coolness. For example, a red toy could be a cool action figure or a boring stuffed animal. Therefore, the color of the toy does not provide any insight into its coolness, and thus any probability assigned to the toy being not cool would be purely speculative and not based on any information. In order to determine the probability that the toy is not cool, we would need additional information, such as what the toy is, what its features are, or who makes it.
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Penny's parents have agreed to loan her $4500 to pay her tuition. They are charging her an interest rate of
3% per annum, compounded monthly. Penny has arranged to pay them $160 per month to pay off the loan.
a) how long it takes Penny to pay off the loan b) the amount of her final payment
Answer:
$157.92.
Step-by-step explanation:
a) To calculate how long it takes Penny to pay off the loan, we can use the formula:
n = log(P/A) / log(1 + r/12),
where n is the number of months, P is the initial loan amount ($4500), A is the monthly payment ($160), and r is the annual interest rate (3%).
n = log(4500/160) / log(1 + 0.03/12)
n = log(28.125) / log(1.0025)
n = 3.7062
Rounding up, it takes Penny 4 months to pay off the loan.
b) To calculate the amount of Penny's final payment, we can use the formula:
P = A * (1 - (1 + r/12)^-n),
where P is the remaining balance, A is the monthly payment ($160), n is the number of months (4), and r is the annual interest rate (3%).
P = 160 * (1 - (1 + 0.03/12)^-4)
P = 160 * (1 - (1.0025)^-4)
P = $157.92
Therefore, it takes Penny 4 months to pay off the loan and her final payment is $157.92.
A commission is a percentage of a sale. People who conduct sales earn a portion of their income based on how much they sell. Zachary earned 31% commission on a sale of $635. What is the amount of the commission?
The amount of the commission earned by Zachary on the $635 sale is $196.85.
What is the amount of the commission earned by Zachary?A commission is a percentage of a sale earned by a sales person.
Given that;
Commission = 31%Sale price = $635Commission amount = ?Since commission is a percentage of a sale earned
Commission amount = sale price × commission
Plug in the given values and simplify
Commission amount = $635 × 31%
Note that; 31% is the same as 31/100
Commission amount = $635 × 31/100
Commission amount = $635 × 0.31
Multiply $635 and 0.31
Commission amount = $196.85
Therefore, the amount of commission is $196.85.
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Picaro’s Packaging Plant wishes to design boxes with a volume of not more than 100 . Squares are to be cut from the corners of a 12-in. by 15-in. piece of cardboard (see figure), with the flaps folded up to make an open box. What size squares should be cut from the cardboard?
The size squares that should be cut from the cardboard is 0.692 inch
What size squares should be cut from the cardboard?Represent the cut-out with x
So, we have the following volume equation:
V(x) = (12 - 2x)(15 - 2x)x
The volume is 100
So, we have
(12 - 2x)(15 - 2x)x = 100
Using a graphing calculator, we have
x = 0.692
Hence, the solution is 0.692
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the number of visitors that the website receives on a given day d the list of visitor counts for the 42 days that were tracked b the average number of visitors per day for the 42 days that the administrator tracked f the average number of visitors per day that have come to the website since it was created a all the days that the website has been in existence c the 42 randomly selected days that the administrator tracked
Population, Statistic, sample, Variable, data, parameter are the correct matching vocabulary words.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The correct matching of the vocabulary words and the examples given of the web administrator's process are:
Population - All the days that the website has been in existence.
Statistic - The average number of visitors per day for the 42 days that the administrator tracked.
Sample - The 42 randomly selected days that the administrator tracked.
Variable - The number of visitors that the website receives on a given day.
Data - The list of visitor counts for the 42 days that were tracked.
Parameter - The average number of visitors per day that have come to the website since it was created.
Hence, Population, Statistic, sample, Variable, data, parameter are the correct matching vocabulary words.
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draw the graph of y=2x-3 for value of x from -1 to +3 use a scale of 2cm to the unit on both axis
The standard equation of a line is expressed as y = mx + b
How to graph the equation?m is the slope
b is the y-intercept
Given the equation y = 2x - 2
If x = -2
y = 2(-2) - 2
y = -4-2
y = -6
If x = 4
y = 2(4) - 2
y = 8-2
y = 6
This shows that the point (-2, -6) and (4, 6 )must be on the line graph. FInd the graph attached below.
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Use the graph of the function to determine the indicated limit, if it exists. lim f(x) Select the correct choice below and fill in any answer boxes in your choice. A. lim f(x) = B. The limit does not exist and is neither conor -
lim (x → a) f(x) = ∞ , The limit does not exist and is neither ∞ nor - ∞
What is function?The vertical line test is used to verify function. That is, a graph must have a unique y value for it to be referred to as a function for a certain (unique) value of x. If for a particular x, and y values are coming it means it is not a function. If it crosses y-axis twice it means for a particular x value , two different value of y will exist. And that is not possible for a function
From the graph, we know that limit at point a is:
lim (x→a) f(x) exists if and only if
lim (x →a⁺) f(x) = lim (x→a⁻) f(x) and ≠ ∞
∴ right hand side limit = left hand side limit
lim (x →a⁺) f(x) = - ∞
lim (x →a⁻) f(x) = - ∞
∴ lim (x → a) f(x) = ∞
thus, option B is the correct answer.
The limit does not exist and is neither ∞ nor - ∞
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