Answer: 4 2/3
Step-by-step explanation:
14/3 is an improper fraction. Let's take the numerator and divide it by the denominator.
Divide 14 by 3. The quotient digit is 4.
Multiply the quotient digit 4 by the divisor 3.
Subtract 12 from 14.
The result of 14 divided by 3 is 4 with a remainder of 2.
Thus, 14/3 as a mixed number can be written as 4 2/3.
14/3 as it can't further cut out.
Because in a mixed number it is 4 2/3. This can be expressed as a fraction by multiplying the whole number (4) by the denominator (3) and adding it to the numerator (2), giving a fraction of 14/3.
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Determine the exact surface area of the cylinder in terms of π.
The exact surface area of the cylinder in terms of π is = 10 π
What is the answer for surface area?
As a refresher, the surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions. It is calculated in square units.
Where can I find the surface area?
A three-dimensional shape's surface area is the total area on its surface. Add the areas of each of the six rectangular sides of a cuboid to determine its surface area. The cuboid's length, width, and height can also be labeled, and the surface area (SA) can be calculated using the formula SA=2lw+2lh+2hw.
Given that :
Radius = 1 1/4 cm
Height = 2 3/4 cm
Surface area is 2π r h + 2π r² = 2π ( 1 1/4 cm*2 3/4 cm) + 2π (1 1/4)²
= 2π (55/16) + 2π (25/16)
= 160/16 π
= 10 π
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A company that makes chow mix and use 138 lb of peanuts for every 2/3 lb of reasons they make 245 lb of trail mix using only peanuts and raisins. How many pounds of peanuts do they use?
The number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.
To solve this problem, you can set up a system of equations to represent the given information. The first equation represents the fact that the company uses 138 pounds of peanuts for every 2/3 pound of raisins:
138 pounds peanuts / 2/3 pound raisins = x pounds peanuts
The second equation represents the fact that the company makes 245 pounds of trail mix using only peanuts and raisins:
x pounds peanuts + y pounds raisins = 245 pounds trail mix
To solve for the number of pounds of peanuts used, you can substitute the first equation into the second equation:
(138 pounds peanuts / 2/3 pound raisins) + y pounds raisins = 245 pounds trail mix
Multiplying both sides of the equation by 2/3 to eliminate the fraction, we get:
138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds trail mix)
Combining like terms, we get:
138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds)
Simplifying the right side of the equation, we get:
138 pounds peanuts + (2/3)y pounds raisins = 160 pounds
Subtracting 138 pounds from both sides of the equation, we get:
(2/3)y pounds raisins = 160 pounds - 138 pounds
Simplifying the right side of the equation, we get:
(2/3)y pounds raisins = 22 pounds
Dividing both sides of the equation by 2/3, we get:
y pounds raisins = (3/2)(22 pounds)
Simplifying the right side of the equation, we get:
y pounds raisins = 33 pounds
Substituting this value into the first equation, we get:
138 pounds peanuts / 2/3 pound raisins = 33 pounds raisins
Multiplying both sides of the equation by 2/3, we get:
138 pounds peanuts / (2/3)(33 pounds raisins) = 33 pounds raisins
Simplifying the right side of the equation, we get:
138 pounds peanuts / 22 pounds raisins = 33 pounds raisins
Dividing both sides of the equation by 22 pounds raisins, we get:
138 pounds peanuts / 22 pounds raisins / 33 pounds raisins = 33 pounds raisins / 22 pounds raisins
Simplifying the equation, we get:
6 pounds peanuts / 1 pound raisins = 33 pounds raisins / 22 pounds raisins
This equation shows that for every 1 pound of raisins the company uses, they use 6 pounds of peanuts.
Therefore, the number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.
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138 pounds peanuts / 2/3 pound raisins = x pounds peanuts
The second equation represents the fact that the company makes 245 pounds of trail mix using only peanuts and raisins:
x pounds peanuts + y pounds raisins = 245 pounds trail mix
(138 pounds peanuts / 2/3 pound raisins) + y pounds raisins = 245 pounds trail mix
138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds trail mix)
138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds)
138 pounds peanuts + (2/3)y pounds raisins = 160 pounds
(2/3)y pounds raisins = 160 pounds - 138 pounds
(2/3)y pounds raisins = 22 pounds
y pounds raisins = (3/2)(22 pounds)
y pounds raisins = 33 pounds
138 pounds peanuts / 2/3 pound raisins = 33 pounds raisins
138 pounds peanuts / (2/3)(33 pounds raisins) = 33 pounds raisins
138 pounds peanuts / 22 pounds raisins = 33 pounds raisins
138 pounds peanuts / 22 pounds raisins / 33 pounds raisins = 33 pounds raisins / 22 pounds raisins
6 pounds peanuts / 1 pound raisins = 33 pounds raisins / 22 pounds raisins
This equation shows that for every 1 pound of raisins the company uses, they use 6 pounds of peanuts.
Therefore, the number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.
find an equation of the tangent line to the curve at the given point. y = 3ex cos(x), (0, 3)
A equation of the tangent line to the curve is y = 3x + 3
The term tangent line in math is calculated as an equation of the tangent line we have to find the derivative of the function and its value at the given point.
And then we have to the function given is a product of an exponential and cosine function. We will have to use product rule.
Finally, we have to write the equation of tangent line by point slope form.
Here we have the curve equation as,
=> y = 3eˣcos(x)
Now, we have to calculate the derivative y' from the given equation, then we get,
=> y' = = 3(eˣ (−sin x) + (cos x) eˣ)
Now, it can be simplified as,
=>y' = 3eˣ(cos x − sin x)
Here we have given that the the slope of the tangent line at (0, 3), then the value of
=> 3e⁰(cos0−sin0) = 3(1−0) = 3
Then the equation is written as
=> y − 3 = 3(x − 0)
=> y = 3x + 3
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Can two triangles like SSS?
The two triangles are similar under SSS conditions if all three sides of one triangle are in proportion to the three sides of another triangle.
What is the SSS condition?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.
Slide, twist, flip, and turn these triangles to create an identical appearance.
They are in alignment with one another when moved.
According to the SSS test for triangle similarity, two triangles are considered similar if their third sides are proportionate to one another.
Therefore, the two triangles are similar under SSS conditions if all three sides of one triangle are in proportion to the three sides of another triangle.
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What is the formula for the complex?
An equation of the form z= a+ib, where a and b are real numbers, is defined to be a complex number. The real part is denoted by Re z = a and the imaginary part is denoted by Im z = ib.
Now, According to the question:
Let's know:
What are Complex Numbers?
A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z). Also, ib is called an imaginary number.
Representation of the Complex Numbers:
z = a + ib
'a' represent the Real part
'ib' represent imaginary number and imaginary part.
Some of the examples of complex numbers are :
2 + 3i , -3 - 4i , 1/2 + 1/3i etc.
Power of i
The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers. We have the value of [tex]i^2[/tex] = -1, and this is used to find the value of √-4 = √[tex]i^2[/tex]4 = ±2i The value of [tex]i^2[/tex] = -1 is the fundamental aspect of a complex number. Let us try and understand more about the increasing powers of i.
i = √-1[tex]i^2[/tex] = -1[tex]i^3[/tex] = i.[tex]i^2[/tex] = i(-1) = -i[tex]i^4[/tex] = [tex](i^2)^2[/tex] = [tex](-1)^2[/tex] = 1[tex]i^4^n[/tex] = 1[tex]i^4^n^+^1[/tex] = i[tex]i^4^n^+^2[/tex] = -1[tex]i^4^n^+^3[/tex] = -iLearn more about Complex numbers at:
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What does translation of a triangle mean?
A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation.
A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation. We can draw the translation in the coordinate plane if we know which way and how far to move the figure.
The triangle can be translated in the following ways:
Step 1: In the first step, determine the coordinates of each vertex of the triangle.
Step 2: To translate each point, add the horizontal translation value to the x-coordinate of each vertex and the vertical translation value to the y-coordinate of each point. Add a negative number if either the vertical or horizontal translation for these translations is downhill or to the left.
Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.
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A study indicated that residents of Hillsdale wasted 8,127 gallons of water this year. That is 10% less than they wasted last year. How many gallons of water did the city's residents waste last year?
The number of gallons of water the city's residents waste last year are 7388.181 by percentage concept.
What is meant by percentage?A quantity or ratio that is expressed as a fraction of 100 is known as a "a%" in mathematics (from the Latin per centum, "by a hundred"). A% is a dimensionless (pure) number without any measuring units. The Latin word "percentum," which means "hundred" or "by the hundred," is the source of the English term "percent." Over time, the Italian term per cento, which originally meant "for a hundred," shrank to become the symbol for "percent." Per was frequently abbreviated to "p" and finally disappeared altogether.
No. of gallons of water wasted by Hillsdale are 8127 gallons.
110% -----> 8127
100% ----->?
x=(100×8127)/110
x= 7388.181
Therefore, the number of gallons of water the city's residents waste last year are 7388.181.
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What is the value of a Y in (( 13 20 )- A * 13 y ))= 168 * 13 22?
Given that value of y exceeds a, then value of a must be smaller than -8.2.
Define the term BODMAS?Children can use the acronym BODMAS to help them remember the right order to carry out mathematical operations while solving problems.We must utilize BODMAS since it has several assumptions in a single equation.Bracket Of Division, Multiplication, Addition, and Subtraction is abbreviated as BODMAS.It makes sense to proceed from division through subtraction as that is how each operation must be performed in an equation.The provided equation is-
(13-20- A* 13y)= 168* 13-22
We get,
By 260, divide both sides.
Y has a value of -8.265.
Thus, provided that y exceeds a, then value of a must be smaller than -8.2
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The correct question is-
What is the value of (a,y) in (13-20- A* 13y)= 168* 13-22?
The point A(7, 1) is reflected over the point (4, 0) and its image is point B. What are the coordinates of point B?
The coordinates of point B is (1, -1)
Define Reflection on a Point
A reflection point occurs when a figure is constructed around a single point known as the point of reflection or centre of the figure. For every point in the figure, another point is found directly opposite to it on the other side.
Given,
Point A (7, 1) is reflected over the point (4, 0)
We know that,
The reflected point will be equidistant from the point over which it is reflected as the original point and in the same line as the original point and the reflected point.
Find the difference between the x and y values of the given points
For x value = 4 - 7 = -3
For y value = 0 - 1 = -1
Now, add the value to the reflection point.
x - axis : 4 +(-3) = 1
y - axis : 0 + (-1) = -1
Hence, the coordinates of point B is (1, -1)
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What sides of a square are congruent?
Answer:
Square! #N#The sides and angles of a square: The sides of a square are all congruent (the same length.) The angles of a square are all congruent (the same size and measure.) Remember that a 90 degree angle is called a "right angle.". So, a square has four right angles. Opposite angles of a square are congruent.
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Step-by-step explanation:
A 900 car parking lot is divided into 3 sections. There are 330 spots in Section 1. Section 2 holds 160 more than the amount of cars in Section 3. How many spots does Section 3 have?
Section 3 have 205 spots, according to the given question.
What do you mean by section?
A section is a part or component that, when combined with the other components, forms the total. like the rhythm section of the band that is reviewed in the arts section of a newspaper.
According to the given question,
We have the given information:
A 900 car parking lot is divided into 3 sections. There are 330 spots in Section 1. Section 2 holds 160 more than the amount of cars in Section 3.
Firstly,
900 - 330 = 570 (spots in section 2 and 3)
Secondly,
There are x spots in section 3 and (x + 160) spots in section 2.
So we have :
x + x + 160 = 570
2x = 410
x = 205
Therefore, the section 3 have 205 spots.
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What is the discriminant of 3x² 2x 1 0?
Equation 3x2 + 2x + 1 = 0's discriminant is -8.
D = b2 - 4ac is the quadratic equation's discriminant.
where a, b, and c are the coefficients of the equation in the form ax² + bx + c = 0.
Therefore,
D = b² - 4ac
= 2² - 4(3)(1)
= -8
The discriminant of a quadratic equation is found by using the formula D = b² - 4ac, where a, b, and c are the coefficients of the equation in the form ax² + bx + c = 0. In this case, a = 3, b = 2, and c = 1, so the discriminant would be D = b² - 4ac = 2² - 4(3)(1) = -8.
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How do you find the number of special integers in an array?
Find the total digits' factorial. Add the factorial together and save it as a variable (s). Compare the total to the specified number (N). The number (N) is a special number if the total equals the number, else it is not.
An element that can be represented by the sum of two numbers, one of which is the opposite of the other, is referred to as a peculiar element. similar to Array is 22 and 121. In this case, 22 = 11 + 11, and 121 = 92 + 29. Consequently, both elements are unique. The PHP count() or sizeof() functions can be used to determine the number of values or elements in an array.
When a variable is initialized with an empty array, the count() and sizeof() functions return 0, but they may also return 0 when a variable is not set.
How many special integers are there in an array:
function findMagicNumber(arr[0...n])
spell n:= NaN
Then magic n:=arr[0] if n = 1
If n is more than 1,
then quicksort(arr) old n:= arr[0]
for i:= 1 to n cur n:= arr[i] repeat:= 0
repeat:=repeat plus one
If repeat is 1,
then magic n:=old n, old n:=cur n, and magic n:=repeat:=0
return magic n.
If cur n old n,
then repeat is 1,
then if repeat = 1
then magic n:=old n, cur_;
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The length of a rectangle is five times its width. If the perimeter is at most 96 centimeters, what is the greatest possible value for the width?
Question 4 options:
2w + 2 • (5w) ≤ 96
2w + 2 • (5w) ≥ 96
2w + 2 • (5w) < 96
2w + 2 • (5w) > 96
Answer:
A) 2w + 2 • (5w) ≤ 96----------------------------------
Given:
Width is w,Length is l = 5w.Perimeter is:
P = 2(l + w)or
2w + 2(5w)The perimeter is at most 96 cm (not greater than):
2w + 2(5w) ≤ 96The matching choice is A.
Find the unit rates for each size. Then
order the sizes from the least to
greatest unit rates.
A unit rate is a rate with a denominator of one.
What is unit rate?A unit rate is a rate where the bottom number is 1 (also called a single-unit rate). We can turn any rate into a unit rate.We want to know the price per apple unit so we set up a ratio with the number of apples in the denominator. The total price goes in the numerator. So the fraction is 1.80/3.Complete the division: 1.80 ÷ 3 = .60. You can conclude that the per apple price unit rate is $0.60/1. Ryan paid a unit price of $0.60 per apple (60 cents per 1 apple = .60/1).The unit rate compares a certain number of units of one quantity to units of another quantity. In other words, the second quantity in the comparison is always 1.To learn more about unit rate refer to:
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What is the result when you divide 3 4 by 2/3 *?
9/8 is the result when we divide 3/4 by 2/3
Method of Division of fraction:Step 1. Take reciprocal of the second fraction (the one you want to divide by)
Step 2. Multiply the first fraction by the second faction's reciprocal.
Step 3. Convert the result in the lowest form.
What is lowest form of fraction?When the numerator and the denominator of the fraction do not have any common factors, the fraction is said to be in its simplest form. For instance, 12 is the most basic version of 6/12.
so the result = (3/4) / (2/3)
=> (3/4) * (3/2)
=> (3*3)/(4*2)
=>9/8
so the result obtanied after the above division is 9/8.
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Binita is going to buy 450 envelopes.
Here is some information of the cos of the envelopes in two shops
LETTER2GO: pack of 25 envelopes cost £3.29
VALUEWORLD :packs of 10 envelopes cost £1.95 buy 2 packs and get one free
how much less in pounds will it cost banita to buy the envelopes from VALUEWORLD
It would cost 0.72 pounds to buy the envelopes from VALUEWORLD
How to solve for cost of envelopefirst of all, we would have to calculate what the cost would be for LETTER 2GO
This is 450 / 25 x 3.29
= 59.22 dollars
The next option would be for us to solve for the cost for Value 2 world.
This is given as 450 / 30 * 1.95*2
= 58.50 dollars
The cost of getting the envelope from value world would be given as 59.22 - 58.50
= 0.72 pounds
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4. Which graph best represents the equation that has the roots x
Answer:
B
Step-by-step explanation:
this just means that the graph has to have x-intercepts (y = 0) at these x-values.
so, which graph intersects the x-axis at x = -7/3 and x = 1/2 ?
only B does that.
the others have other x-intercept points.
What is the median of the following number 10 6 4 4 6 4 1?
Answer: 4
Step-by-step explanation: 10, 6, 4, 4, 6, 4, 1.
In total, there are seven numbers.
The fourth number, number four (4), is the middle because it's in the middle.
Construct The Cumulative Frequency Distribution For The Given Data. Construct The Cumulative Frequency Distribution.
The cumulative frequency distribution is a type of statistical representation that shows the total number of data points in a sample that are less than or equal to a given value. It is often used to understand the distribution of data within a sample and to identify patterns or trends.
To construct a cumulative frequency distribution for given data, follow these steps:
Sort the data in numerical order from lowest to highest.Determine the number of data points in the sample. This is the total frequency for the distribution.Calculate the cumulative frequency for each data point by adding the frequency of that point to the cumulative frequencies of all previous points.Create a table or graph with the data points as the x-axis and the cumulative frequencies as the y-axis.For example, given the following data:
[tex]10, 15, 20, 25, 30, 35, 40, 45[/tex]The cumulative frequency distribution would be:
Data Point | Frequency | Cumulative Frequency
10 | 1 | 1
15 | 1 | 2
20 | 1 | 3
25 | 1 | 4
30 | 1 | 5
35 | 1 | 6
40 | 1 | 7
45 | 1 | 8
This distribution could be represented in a graph by plotting the data points on the x-axis and the cumulative frequencies on the y-axis and connecting the points with a line.
The answer is general since the data is not provided.
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What is the coefficient of x in the expression 5x³ 7x²?
The coefficient of x in the expression 5x³ 7x² is 5. This means that for every x in the expression, 5 will be multiplied by it. This means that in the expression 5x³ 7x², 5 will be multiplied by x three times and seven will be multiplied by x twice.
The coefficient of x in the expression 5x³ 7x² is 5. This means that for every x in the expression, 5 will be multiplied by it. To calculate the coefficient of x, we need to first expand the expression. The expanded form of the expression 5x³ 7x² is 5x³ + 7x². Here, we can see that 5 is multiplied by x three times and seven is multiplied by x twice. This indicates that the coefficient of x is 5. This can be understood by considering the following example:
Let's say we have the expression 5x³ 7x² = 5x³ + 7x².
Here, 5 is multiplied by x three times and seven is multiplied by x twice. This means that the coefficient of x is 5. This can be written as 5x³ + 7x² = 5x³ + 7x x 1 = 5x(x² + x). Hence, the coefficient of x in the expression 5x³ 7x² is 5.The coefficient of x in the expression 5x³ 7x² can be calculated using the following steps:
Expand the expression 5x³ 7x².
The expanded form of the expression is 5x³ + 7x².
Here, we can see that 5 is multiplied by x three times and seven is multiplied by x twice. This indicates that the coefficient of x is 5.
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What are some examples of short-term financial goals?
The activities you desire to do with your money during the next several months or years are considered short-term financial objectives.
What is compound interest?
When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. The interest you get is referred to as compound interest. Using simple math, you can see how this works: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 at the conclusion of the second year.
The activities you desire to do with your money during the next several months or years are considered short-term financial objectives as compound interest. Setting a budget, creating an emergency fund, and paying off debt are some important short-term objectives.
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A triangle has sides with lengths of 65 kilometers, 72 kilometers, and 97 kilometers. Is it a
right triangle?
Answer:
no
Step-by-step explanation:
Find The Area Of The Shaded Region. R^ 2 = Sin (2 Theta).
The area enclosed in the figure of the graph of r² = sin(2θ) is
1 square units.
What is polar equation?A polar equation of a curve is usually expressed in polar coordinates and written with {r} as a function of {θ}.
Given is a polar equation as follows -
r² = sin(2θ)
Area enclosed in the figure is equivalent to -
{A} = 2{∫1/2r²dθ}
{A} = ∫r²dθ
{A} = ∫sin(2θ) dθ
{A} = {- cos(2θ)/2} (integral limit -> 0 to π/2)
{A} = {- cos(π)/2 + cos(0)/2}
{A} = 1/2 + 1/2
{A} = 1
Therefore, the area enclosed in the figure of the graph of r² = sin(2θ) is
1 square units.
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How do you find the potential roots of a function?
We apply the rational root theorem to identify potential rational roots.
Given,
How do you identify a possible logical root?
We can utilize the following parameters in our calculation based on the question:
We have to calculate the potential rational root of a function;
Here,
The following procedures are used to apply the rational root theorem to the possible rational root.
Learn the constant term's components (p)Discover the factors that make up the leading coefficient (q)Discover each potential p/q value.Subtract duplicates from the aforementioned list of rational zeros.Learn more about potential roots here;
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You pull sideways on a 50 kg crate with a force of 450 n. There is also a 250 n frictional force on the box. What is the acceleration of the box?.
The acceleration of the box is 4m/s².
Acceleration is a vector quantity as it has both magnitude and direction. It is also the second derivative of position with respect to time or it is the first derivative of velocity with respect to time. The change in the velocity of an object could be an increase or decrease in speed or a change in the direction of motion.
We know the frictional force f=μN where N=normal force = mg
Given that,
Frictional force μ = 250N
Hence F(net)= F(app)- f = 450 - 250 = 200 N
We know Force(F)=ma
a=200/50 = 4m/s²
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We know the frictional force f=μN where N=normal force = mg
Given that,
Frictional force μ = 250N
Hence F(net)= F(app)- f = 450 - 250 = 200 N
We know Force(F)=ma
a=200/50 = 4m/s²
Leah buys 32 strips of ribbon. Each strip is 11.2 inches. Estimate the total length of ribbon that Leah buys.
The total length of ribbon that Leah bought is equal to 358.4 inches.
What is measurement?In Mathematics, measurement can be defined as an act or process through which the size, weight, magnitude, quantity, volume (capacity), dimensions (length and width), or distance traveled by a physical object or body is taken, especially for the purpose of an experiment.
In order to determine the total length of ribbon that was purchased by Leah, we would have to multiply the length of the strips of ribbon by the length of each of the strips as follows;
Total length of ribbon = Length of the strips of ribbon × Length of each of the strips
Substituting the given parameters into the formula, we have;
Total length of ribbon = 32 × 11.2 inches
Total length of ribbon = 358.4 inches.
In this context, we can reasonably infer and logically deduce that total length of ribbon that was purchased by Leah is equal to 358.4 inches.
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if keene company issues 9,000 shares of $5 par value common stock for $160,000, the account
Answer: $115,000
Step-by-step explanation:
The common stock is 9000 times 5 = $45000
To Paid-in Capital in Excess of Par = 160,000 - 45,000 = $115,000
How will you describe the graph of polynomial function if the degree is odd number and the leading coefficient is positive?
We say cubic polynomial if the degree of polynomial is odd number, and the graph is said cubic polynomial graph.
What is the degree of polynomial function?The equation which has only positive integer exponent are called polynomial function. Such as 6x³+4x²+2x+1=0 where the power 3,2, 1 are the degree of polynomial.
What is cubic polynomial?The polynomial function whose first degree is odd number is called cubic polynomial.
hence, the graph is cubic polynomial.
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How do you graph a function with two X variables?
To graph a function with two variables, you need to plot the points that satisfy the function in a coordinate system.
For example, suppose you have a function f(x,y) = x^2 + y^2. To graph this function, you can choose a set of values for x and y that satisfy the function, and plot these points in the coordinate system.
For example, if you choose x = 1 and y = 2, then the point (1,2) satisfies the function because f(1,2) = 1^2 + 2^2 = 1 + 4 = 5. Similarly, if you choose x = -2 and y = 3, then the point (-2,3) satisfies the function because f(-2,3) = (-2)^2 + 3^2 = 4 + 9 = 13.
You can repeat this process for a range of values for x and y to plot more points in the coordinate system. As you plot more points, you will start to see a pattern emerge, which is the graph of the function.
Note that the graph of a function with two independent variables will be a surface in three-dimensional space, rather than a curve in two-dimensional space like the graph of a function with only one variable.
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"How do you graph a function with two variables?"
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