Answer:
a) The rotational speed of the clay: 3.45 rad/s.
b) The value of A in the equation of motion: 0.15 m.
c) The value of ϕi: 90° or π/2 rad.
Given that;
Revolution per minute( rpm) is = 33( 1/3) = 100/3
The frequency ( f) is= 100 / 3(60) = 0.55 Hz
a) Rotational speed W = 2πf
we substitute
W = 2π × 0.55
W = 3.45 rad/s
So, the rotational speed of the clay is 3.45 rad/s.
b) given equation; y(t)=Asin(ωt+ϕi)
given that radius = 0.15 m
y(t)=(0.2)sin(ωt+ϕi)
So, the value of A in the equation of motion is 0.15 m.
c) since y(t) has the maximum value at t =0
so at t=0
y(0) = (0.15)sin(ω(0)+ϕi)
= 0.15sin(ϕi)
this gives maximum value when ϕi = 90°
so,
y(0) = (0.15)sin(ω(0)+ϕi)
= 0.15sin(90°)
= 0.15
So, the value of ϕi is 90° or π/2 rad.
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The complete question is:
You are standing next to a table and looking down at a record player sitting on the table. Take the spindle (axis of rotation) to be the center of your coordinate system and the y-axis to be perpendicular to the side of the player you are standing next to. Long-playing records revolve 33(1/3) times per minute. You put a small blob of clay at the edge of a record that has a radius of 0.15 m, positioning the clay such that it is at its greatest value of y at t = 0.
Equation of motion for the y component of the clay's position: y(t)=Asin(ωt+ϕi)
Required:
a. What is the rotational speed of the clay?
b. Determine the value of A in the equation of motion.
c. Determine the value of ϕi in the equation of motion. Suppose that −π<ϕi≤π
Add or subtract the fractions, please It's like three am I need this
The addition and subtraction of the fractions gives 9/(x+3)²(x-3)²
What is a fraction?A fraction can be described as one part of a whole number, element or variable.
In mathematics, there are different types of fractions which includes;
Complex fractionsSimple fractionsImproper fractionsProper fractionsMixed fractionsFrom the information given, we have the fractions;
1/(x -3)² - 2/x² - 9 + 1/(x+3)²
Note that with the knowledge of difference of two squares;
x² - 9 is equivalent to (x+3)(x-3) = (x-3)²
Now, let's take the lowest common multiple
(x+3)² -2(x+3)(x-3) +(x-3)²/ (x+3)²(x-3)²
expand the bracket
x²+3x+3x+9 -2x² -6x +6x +9 + x² -3x -3x - 9/ (x+3)²(x-3)²
Add like terms
9/(x+3)²(x-3)²
Hence, the value is 9/(x+3)²(x-3)²
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Simplify the following expressions by combining like terms subtract (6x + 2) - (9x + 3)
Answer:-3x-1
Step-by-step explanation:
First we remove the parentheses and we will get 6x+2-9x-3
second, we combined like term 6x and -9x can combine and 2 and -3 can combine we will get 6x-9x and -1
third, we mix it together and can get -3x-1
The function F gives the number of copies a book has sold W weeks after that it was published the equation FW equals 500×2 to the W power defines this function 
Select all domains for which the average rate of change could be a good measure for the number of books sold
Good models are expected to reflect the number of books sold between zero and w numbers of weeks where w is defined.
What is a domain?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Here, we have
Given: The function f gives the number of copies a book has sold w weeks after it was published. The equation f(w) = 500 * 2^w defines this function.
The following are all domains for which the average rate of change could be a good measure of the number of books sold:
0 ≤ w ≤ 2
0 ≤ w ≤ 7
0 ≤ w ≤ 10
Hence, good models are expected to reflect the number of books sold between zero and w numbers of weeks where w is defined.
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Help due today help help
Interior angles on the same side The same-side interior angles are additional if a transversal connects two parallel lines.
what is triangle ?A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.
given
The Isosceles Triangle Theorem's opposite is also accurate.
A triangle's opposite sides are congruent if two of the triangle's angles are.
Each right angle exists when two angles are complementary and congruent. Interior angles on the same side The same-side interior angles are additional if a transversal connects two parallel lines.
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Angles EBI and BCJ are corresponding angles. Use a transformation that takes angle EBI to angle BCJ to prove that corresponding angles are congruent
The angles EBI and BCJ are complementary. Show that the corresponding angles are congruent by transforming angle EB1 to angle BCJ. Orient point C at angle BCJ by 180 degrees. reflecting from line BCJ over angle BC Angle BCJ is translated by the directed line segment from C to B.
If the transversal intersects two parallel lines, the corresponding angle postulate states that the corresponding angles are congruent. In other words, the angles formed when a transversal crosses two parallel lines will always be equal.By transversal and parallel lines, corresponding angles are formed that are congruent. Corresponding angles created by transversal non-parallel lines are not equal.To know more about congruent angles here
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Melissa wants to check the accuracy of the finance charge on her promissory note. She has a $6,000, four-year loan at an APR of 3.11%. Round to the nearest cent.
a. What is her monthly payment?
b. What is the total of all her monthly
payments?
c. What is the total finance charge?
Solve using SOLVE format. Show your work
a) Melissa's monthly payment for the promissory note is $133.10.
b) The total monthly payment amounts to $6,388.80.
c) The total finance charge is $388.80, which is the difference between the total payment and the promissory note amount.
How is the monthly payment computed?The monthly payment represents the equal periodic payment made to settle the loan and the finance charge.
Using an online finance calculator, we can compute the monthly payment, total payments, and finance charges.
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 3.11%
PV (Present Value) = $6,000
FV (Future Value) = $0
Results:
PMT (Monthly Payment) = $133.10
Sum of all periodic payments (Total Payments) = $6,388.80
Total Interest (Finance Charge) = $388.80
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the diameter of the circle is 5.35, what is the area?
The area of the circle, considering it's diameter of 5.35, is given as follows:
22.48 units squared.
What is the area of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr²
The diameter for the circle in this problem is given as follows:
5.35.
The radius is half the diameter, hence it's length is given as follows:
r = 0.5 x 5.35
r = 2.675.
Hence the area of the circle is given as follows:
A = π x (2.675)²
A = 22.48 units squared.
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53, evaluate the definite integral
Please please help meeeee
We get the Polynomials quotient and remainder as 2x+7 and 5 respectively.
What are Polynomials ?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.
Polynomial long division is an extended variant of the well-known mathematical operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree. Due to the fact that it breaks down a more difficult division issue into simpler ones, it may be completed quickly by hand.
The polynomials are
2X^2 - X +16
and
x - 3
Dividing by 2X^2 - X +16 BY x-3 = 2x + 7
We get the quotiant and remainder as 2x+7 and 5 respectively.
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6/7 divided by 2/9 i dnt knowwwww
Answer: 6/7 / 2/9 = 3/1 or 3 ✅
PLEASEEEE GIVE BRANLIEST
Step-by-step explanation:
To divide two fractions, you can invert the second one (the one being divided by) and then multiply the two fractions.
So:
(6/7) / (2/9) = (6/7) * (9/2)
To multiply the fractions, you just multiply the numerators together and multiply the denominators together.
(6/7) * (9/2) = (69)/(72)
= 54/14
So the final answer is 54/14.
You can also simplify the fraction by dividing the numerator and denominator by their greatest common factor.
54/14 = 3/1
So the final answer is 3/1 which is 3.
Name an angle bisector
Down Below
Step-by-step explanation:Angle bisector
An angle bisector is a line segment, ray, or line that divides an angle into two congruent adjacent angles.
Line segment OC bisects angle AOB above. So, ∠AOC = ∠BOC which means ∠AOC and ∠BOC are congruent angles.
Bisecting an angle with compass and ruler
In geometry, it is possible to bisect an angle using only a compass and ruler. To do so, use the following steps:
Place the point of the compass on vertex, O, and draw an arc of a circle such that the arc intersects both sides of the angle at points D and E, as shown in the above figure.Draw two separate arcs of equal radius using both points D and E as centers. Make sure the radius is long enough so the arcs of the two circles can intersect at point F.Use a ruler to draw a straight ray from O to F. OF bisects the angle AOB.Things to know about an angle bisector
If a point lies anywhere on an angle bisector, it is equidistant from the 2 sides of the bisected angle; this will be referred to as the equidistance theorem of angle bisectors, or equidistance theorem, for short.
In the figure above, point D lies on bisector BD of angle ABC. The distance from point D to the 2 sides forming angle ABC are equal. So, DC and DA have equal measures.
Conversely, if a point on a line or ray that divides an angle is equidistant from the sides of the angle, the line or ray must be an angle bisector for the angle.
Based on the equidistance theorem, it can be seen that when the two sides that make up an angle are tangent to a circle, the line segment or ray formed by the angle's vertex and the circle's center is the angle's bisector.
In the diagram above, the two sides of the angle are tangent to the circle and, DC and DA are the distances from the center of the circle to the sides. DC and DA are also the radii of the circle. Since all radii of a circle have equal measure, line BD bisects the angle.
Angle bisector theorem
For a triangle, like the one in the diagram below, if the bisector of angle A intersects side BC at point D, the ratio of the lengths of AB to AC equals the ratio of the length BD to DC. This can be written as: [tex]\frac{AB}{AC}=\frac{BD}{DC}[/tex]
The point at which the three interior angle bisectors intersect is known as the incenter of the triangle. Referencing the diagram below, the three bisecting rays intersect at point D. Point D is the incenter of the triangle and is a point that is equidistant from the three sides of the triangle.
Extra:
I hope this helped at all.
The rectangular prism below is labeled with its measured dimensions. Taking measurement
error into account, what are the minimum and maximum possible volumes?
12 in
13 in
9 in
Minimum possible volume =
Maximum possible volume =
in 3
in 3
The minimum and maximum possible volume for a rectangular right prism are 1221.875 and 1603.125 cubic inches.
What are the minimum and maximum possible volume of a rectangular prism?
In this problem we must determine the minimum possible and maximum possible volumes for a rectangular right prism, whose volume formula including length uncertainties is shown below:
V = (w ± Δw) · (l ± Δl) · (h ± Δh)
Where:
w - Width, in inches.l - Length, in inches.h - Height, in inches. Δw - Width uncertainty, in inches.Δl - Length uncertainty, in inches.Δh - Height uncertainty, in inches.Please notice that minimum possible volume is found when all "±" operators are replaced by "-" operators and that maximum possible volume is found when all "±" are replace by "+" operators. Given that statement does not mention the value of every length uncertainty, we assume that Δw = Δl = Δh = 0.5 in.
If we know that w = 12 in, l = 13 in, h = 9 in and Δw = Δl = Δh = 0.5 in, then the minimum and maximum possible volumes are:
Minimum possible volume
V = (12 in - 0.5 in) · (13 in - 0.5 in) · (9 in - 0.5 in)
V = (11.5 in) · (12.5 in) · (8.5 in)
V = 1221.875 in³
Maximum possible volume
V = (12 in + 0.5 in) · (13 in + 0.5 in) · (9 in + 0.5 in)
V = (12.5 in) · (13.5 in) · (9.5 in)
V = 1603.125 in³
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Question content area top
Part 1
Find the approximate side length of a square game board with an area of 151 in2.
The length of the side of the given square is 12.3 inches approx.
What is a square?Due to the fact that this particular group of numbers makes up a square, they are known as square numbers (or squared numbers).
Finding the area of a square is easy because they all have equal sides. Just "square" (multiply by itself) one of their sides!
So, we have:
The area of the square is 151 in².
Area formula: s²
Now, calculate the length of the side as follows:
A = s²
151 = s²
s = √151
s = 12.3 approx
Therefore, the length of the side of the given square is 12.3 inches approx.
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477➗9 using distributive property
Answer:
53
Step-by-step explanation:
[tex]\frac{477}{9}[/tex]
53
9[477]
-45
27
-27
0
How does the rational root theorem and factor theorem helps you in solving polynomial equation?
The rational root theorem and factor theorem helps you in solving polynomial equation as they help in solving the question and finding the roots of it.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
here,
The rational root theorem and factor theorem helps you in solving polynomial equation as they help in solving the question and finding the roots of it.
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Sam is proving the product property of logarithms. Step justification given substitution which expression and justification completes the third step of her proof? ; power rule of exponents subtraction property of exponents multiplication rule of exponents division property of exponents.
Sam's rationale for the third step based on logarithm properties would be logb(b^x+y), power rule of exponents. Thus, the correct answer is C.
The first step of Sam's proof is to show that logb(MN) is equal to logb(b^x.b^y), which is a substitution of MN for b^x.b^y. This is based on the product property of logarithms, which states that logb(MN) = logb(M) + logb(N) for any positive numbers M and N and any base b, as long as b doesn't equal 1.
The third step of her proof is to simplify logb(b^x.b^y) further by applying the power rule of exponents, which states that:
b^(x+y) = b^x.b^ySo, by substituting b^(x+y) for b^x.b^y, we get:
logb(b^(x+y)) = logb(b^x+y)So, in short, the justification of the third step is based on the power rule of exponents, and it shows that logb(b^x.b^y) can be simplified further to logb(b^x+y).
The answer choice A, logb(b^xy), power rule of exponents, is incorrect because it implies that the third step is to multiply x and y instead of adding them.
This question should be provided with answer choices, which are:
A. logb(b^xy), power rule of exponents.B. logb(b^x-y), subtraction property of exponents.C. logb(b^x+y), power rule of exponents.D. logb(b^x/y), division property of exponents.The correct answer is C.
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Answer: its c
Step-by-step explanation:
cop a hoodie at moneymotivated.us thanks
What is 32.8 divided 5.
Answer:
Step-by-step explanation:
6.56
600=5+60 what was the annual interrest rate
On solving the provided question, annual rate is 2% while doing calculations through simple interest.
What is simple interest?Borrowers must pay simple interest to lenders as a fee for a loan. Compound interest is not taken into account while calculating it; just the principal is used. Simple interest is applicable to all loans. It is also the form of interest that banks give their customers on their savings accounts. Simple interest can be calculated using a simple formula. Simply multiply the loan's principal by the interest rate and the period to get the total. Although some mortgages employ this calculation approach, this type of interest typically relates to auto loans or short-term loans.
Let the annual rate be x%
Principal Amount (p)= $600
Annual Rate (r) = x % (Assumed)
Time (t) = 5 years
Simple Interest (I) = $60
Use the simple interest formula given below:
SI = p×r×t/100
r = 60 ×100/600× 5
r = 2%
Thus, the annual rate of interest is 2 %.
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Question:
April took out a $600 loan from the bank. At the end of 5 years, she pays back the principal, plus $60 simple interest. What was the interest rate? Enter your answer in the box.
The Hawaiian resort has large palm trees. In a photo the tree measures 6 inches tall. The scale is 1.5 inches = 2.5 feet. How tall is the actual palm tree?
(Please i need help )
By the way I'm not in high school I don't know why it says that.
Answer:
10 ft
Step-by-step explanation:
You have a photo of a palm tree in which the tree is 6 inches tall. The scale of the photo is 1.5 in : 2.5 ft, and you want the know the height of the actual tree.
ProportionThe heights of things in the photo are presumed to be related to their actual height by the given scale factor.
actual height / photo height = 2.5 ft / (1.5 in)
actual height / 6 in = (2.5 ft)/(1.5 in)
Multiplying by 6 in gives ...
actual height = (2.5 ft)(6/1.5) = 10 ft
The actual palm tree is 10 feet tall.
__
Additional comment
It says "high school" because that is the level you have on your Brainly profile. You can change this under Edit Profile > Preferences.
a polynomial function has zeros at "-4(multiplicity" 3), "-1(multiplicity" 1). which graph could represent this function?
Therefore the solution to the given question is option d)128.78 for this particular equation.
What is Equation?Many different definitions exist for a mathematical equation. In algebra, a statement that mathematically establishes the equality of two mathematical expressions is known as an equation.. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." Mathematical variables are used in even the most fundamental and straightforward algebraic equations.
Here,
=> v/9.4 = 13.7
Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal." Even the simplest and most easy algebraic equations need mathematical variables.
=> v = 13.7*9.4
=> v= 128.78
Therefore the solution to the given question is option d)128.78 for this particular equation
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What is the rule of substitution?
In this rule, we have to find the value of any of the variables either first or second and substitute its value in the other equation.
It is best to use the substitution method when equations are either given in form or can be gain into the form of x = ay + b and y = mx + n.
A procedure to answer a system of linear equations in more than two variables algebraically is the substitution method. In this process, we find the value of any one of the variables by alienating it on one side and taking every other term on the other side of the equation.
Then we substitute that first value in the second equation.
The substitution method is one of the algebraic processes to answer simultaneous linear equations. It implies substituting the value of any one of the variables from one equation into the other equation.
And at last, we can put the value of y in any of the given equations to find x.
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solve for x (x-1)(x-12)=0
Answer:
x = 1, 12
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{(x-1)(x-12)=0}[/tex]
This can be set as:
[tex]\displaystyle{x-1 = 0 \ \, \text{or} \ \, x - 12 = 0}[/tex]
Solve equations like linear, add both sides by 1 for x - 1 and add both sides by 12 for x - 12:
[tex]\displaystyle{x-1 +1= 0+1\ \, \text{or} \ \, x - 12+12 = 0+12}\\\\\displaystyle{x= 1\ \, \text{or} \ \, x = 12}[/tex]
Instead of using "or" for conjunction, we can simply write the solution as x = 1, 12 (or you can also write x = 12, 1)
Additional Info
If you see the equation in form of [tex]\displaystyle{(ax+b)(cx+d)=0}[/tex] then you can just simply solve like linear separately and combine solutions together as one.
The average of 5 numbers is 11. Which of the following must be true?
O The range of the 5 numbers is 55.
O The sum of the 5 numbers is 55.
O The median of 5 numbers is 11.
O The mode of 5 numbers is 11.
What is the formula of quadratic method?
We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. The formula is then updated with these coefficients:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We observed that many real-world scenarios can be represented by quadratic equations. Let's study about the many ways to solve quadratic equations now that we are familiar with what they are.
Three basic approaches can be used to resolve quadratic equations:
(1) The use of factors
(2) Using the square approach to finish
(3) Formula for a Quadratic Equation
The two approaches mentioned above are ineffective for some equations. Such equations call for a more robust approach. A technique that is applicable to all quadratic equations.
This is the formula for a quadratic equation in general. It is described as follows: The value of x is determined by the following equation if the quadratic equation ax2 + bx + c = 0 is true:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
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Which statements is/are TRUE in a 45° - 45° - 90° triangle?|. The legs are congruentII. The length of the hypotenuse is twice the length of the shorter legIII. The length of the longer leg is V3 times the length of the shorter legIV. The length of the hypotenuse is v2 times the length of a legA. I onlyB. I and IIC. II and IIID. I and IV
i and iv are correct in a 45° - 45° - 90° triangle?|. The legs are congruentII. The length of the hypotenuse is twice the length of the shorter leg.
in 45 -45-90 triangle the legs are both 1 units in length and the hypotenuse is sqrt 2
sqrt2 ^2 = 1^2+1^2
this denotes our measurement is true
if the legs ofa right triangle are a and b and the hytponuse is c then
a²+b²=c²
lets say
a>b
so
longer leg is 4ft longer than shorter
a=4+b
hypotnuse is 8ft longer than shorter
c=8+b
teh equation in terms of b and solve
a²+b²=c²
subsitute
(b+4)²+b²=(b+8)²
b²+8b+16+b²=b²+16b+64
2b²+8b+16=b²+16b+64
minus (b²+16b+64) from both sides
b²-8b-48=0
what 2 numbers multiply to get -48 and add to get -8?
-12 and 4
(b-12)(b+4)=0
set equal to 0
b-12=0
b=12
b+4=0
b=-4
false, can't have negative length
b=12
so
a=4+b
a=4+12
a=16
c=8+b
c=8+12
c=2
shorter leg: 12ft
longer leg: 16ft
hypotonuse: 20ft
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Which of the following is an adjustment allowed by the IRS?A.) Dental ExpensesB.) Medical ExpensesC.) Work ExpensesD.) Moving Expenses
D) Moving Expenses is an adjustment allowed by the IRS.
The IRS allows certain deductions or adjustments to income for individuals who meet certain qualifications. Some examples of these deductions or adjustments include medical expenses, certain taxes, and certain work-related expenses.
Moving expenses are also an adjustment allowed by the IRS, if you move due to change in your job or business location, or because you start a new job or business. You can deduct certain expenses of moving to the area where you will be working, such as the cost of getting yourself and your household goods to your new home, and lodging during the move.
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Amount in Sales
(in dollars)
y
390
325
260
195
130
65
0
Daily Pizza Sales
●
10 20 30 40 50 60
Number of Pizzas Sold
C
Based on the line of best fit, how many pizzas were sold if $97.50 was earned in sales?
O A. 15
O B. 30
O C. 45
Therefore , the solution of bar graph is estimated number of the pizza sold on 30 days = 1200
What does a bar graph explain?A bar graph is a graphical depiction of information, amounts, or numbers using bars or strips. They are employed to contrast and compare various data types, frequencies, or other measurements of various categories of data.
Here,
Given : The data set from the bar chart is
20, 30, 40, 35, 25
Total number of pizza sold on a day = 20 + 30 + 40 + 35 + 25= 150
Number of pizza of type T3 sold on a day = 40
Estimated number of pizza sales (T3) on 30 days = 40
150×4500= 1200
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Here is another algebra math problem that I need help with, sorry I've been struggling in math. The math problem is in the picture below:
Answer: All Real Numbers Except "-8" (R - {-8})
Step-by-step explanation:
The domain of a function is all possible x values that the function can be defined with.
This means that if a value does not create any indeterminate situation, we can consider this value is in the domain of a function.
For this function, "-8" is not in the domain of the function because the denominator of a rational fraction cannot be zero in any case. This creates an indeterminate situation, therefore we do not consider "-8" in the domain of the function.
But for the other values, there is no problem since the denominator cannot be zero without x = -8.
In this figure, mCA=148∘, and mDB=42.
What is m∠CEA?
m∠CEA =
Answer:
∠ CEA = 95°
Step-by-step explanation:
the chord- chord angle CEA is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
∠ CEA = [tex]\frac{1}{2}[/tex] (CA + DB) = [tex]\frac{1}{2}[/tex] (148 + 42)° = [tex]\frac{1}{2}[/tex] × 190° = 95°
0.12 divided by 24.12
Answer:
0.00497512437
Step-by-step explanation:
calcuator
Answer: 0.00497512437
Step-by-step explanation:
To divide a decimal number by a whole number, long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend. If it does not divide evenly, add a 0 to the end of the dividend and continue dividing until there is no remainder.