Yes, the line shown on the scatter plot is a good line of fit because the line follows the pattern.
What is a line of best fit?
The straight line that best depicts the overall picture of what the collected data is showing is known as the line of best fit, also known as a trendline or a linear regression. It aids in determining whether the two things under study are related or have a correlation. This trendline aids in our ability to forecast upcoming developments involving the data under study.
The line models a positive association is incorrect, because the plot has a negative slope which means that it has a negative association.
The data does not have a linear association is wrong because it can seen that the plot does show that most of the points are clustered around a path that would be a line through the points.
It is not necessary for a line of best fit to go through any of the original points so line does not pass through any of the data points is also incorrect.
Therefore, the line is a good fit as it follows the pattern.
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Answer:
Hope this help :)
Step-by-step explanation:
which of the following are not polynomials
The options A, B, C and E are the correct answers and the expressions in those options are not polynomial.
What is the polynomial?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
A) [tex]x^{\frac{2}{3}}+\sqrt{3}x+1[/tex]
Here, the exponent of variable is 2/3
So, the expression is not polynomial.
B) [tex]\frac{2}{3}x^{-2}+x+1[/tex]
Here, the exponent of variable is -2
So, the expression is not polynomial.
C) [tex]x^{-2}+x+1[/tex]
Here, the exponent of variable is -2
So, the expression is not polynomial.
D) x³+0x²+2x+√2
Here, the exponent of variables is 3, 2 and 1.
So, the expression is polynomial.
E) [tex]\frac{2}{x^3} +x+\frac{1}{2}=2x^{-3}+x+\frac{1}{2}[/tex]
Here, the exponent of variable is -3
So, the expression is not polynomial.
Therefore, the options A, B, C and E are the correct answers.
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From past experience, a restaurant owner has determined that 35% of those who visit his restaurant will spend at least $150. If 6 people will visit his restaurant tomorrow, find the probability that:
There is 0 probability that (a) 3 people will spend at least $150.
What do we mean by probability?The probability is simply the likelihood that something will happen. When we don't know how something will turn out, we might talk about the likelihood or probability of certain outcomes.
Analysis of events that fit a probability distribution is known as biostatistics.
So, we know that:
35% of those who visit his restaurant will spend at least $150.
People visit: 6
The probability that 3 will spend at least $150:
6/100 * 35
2.1
Rounding off: 2 people are 35% of 6 people
Since 35% is only 2 people. Then it is not possible that 3 people will spend at least $150.
Then, P(E) = 0.
Therefore, there is 0 probability that 3 people will spend at least $150.
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Complete Question is -
8) From past experience, a restaurant owner has determined that 35% of those who visit his restaurant will spend at least $150. If 6 people will visit his restaurant tomorrow, find the probability that:
a) 3 will spend more than $150.
b) at least 5 will spend more than $150.
C) 4 will spend more than $100
D) at least 3 will spend more than $250.
a) The probability that 3 out of 6 people will spend more than $150 is 21%.
b) The probability that at least 5 out of 6 people will spend more than $150 is 36%.
c) The probability that 4 out of 6 people will spend more than $100 is 24%.
d) The probability that at least 3 out of 6 people will spend more than $250 is 0
What do we mean by probability?The probability is simply the likelihood that something will happen. When we don't know how something will turn out, we might talk about the likelihood or probability of certain outcomes.
a) The probability that 3 out of 6 people will spend more than $150 is (6 choose 3)[tex]* (0.35)^3 * (0.65)^3 = 0.2096[/tex] or about 21%.
b) The probability that at least 5 out of 6 people will spend more than $150 is (6 choose 5)[tex]* (0.35)^5 * (0.65)^1 +[/tex] (6 choose 6) [tex]* (0.35)^6[/tex] = 0.3588 or about 36%.
c) The probability that 4 out of 6 people will spend more than $100 is (6 choose 4) [tex]* (0.65)^4 * (0.35)^2[/tex] = 0.2415 or about 24%.
d) The probability that at least 3 out of 6 people will spend more than $250 is 0, Because the chance of spending more than $250 is low, and this probability is not possible as per the given percentage.
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Complete Question is - From past experience, a restaurant owner has determined that 35% of those who visit his restaurant will spend at least $150. If 6 people will visit his restaurant tomorrow, find the probability that:
a) 3 will spend more than $150.
b) at least 5 will spend more than $150.
c) 4 will spend more than $100
d) at least 3 will spend more than $250.
Consider the symmetry of the "no" symbol. what kind of reflectional symmetry does the symbol have? 1-fold 2-fold 3-fold 4-fold
Answer: 2-fold
The symbol has reflectional symmetry about the line containing the slash, and about the perpendicular bisector of the slash. There are two (2) axes of reflectional symmetry.
Step-by-step explanation:
Forces of 16 pounds and 20 pounds act on each other with an angle of 49°. Find the Magnitude of the resultant force, and the angle of the resultant force with the 16 and 20 pound force. Round all answers to 2 decimal places.
The resultant force is 15.4 pounds while the angle is 51.3°.
What is the resultant force?We knw that the resultant force has to do with the force that would have the same effect in magnitude and direction as two or more forces that are acting together.
Using the parallelogram law of vectors;
R^2 = a^2 + b^2 - 2ab Cosθ
a = 16 pounds
b = 20 pounds
θ = 49°
R= √(16)^2 + (20)^2 - 2(16 * 20) cos 49
R = √256 + 400 - 640cos 49
R = 15.4 pounds
The angle of the resultant is;
Tan-1(20/16) = 51.3°
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On a baseball diamond, the distance from first base to third base is approximately 127 feet. How many inches is the distance from first base to third base
From first to third base, it is 3 3/8 inches in length. 3 3/8 inches, or 127 feet, separate first base from third base.
First- and third-base lines' intersection is the starting point for all measurements taken from home base. An real square with 90-foot sides is what a baseball "diamond" looks like.
How far must the catcher throw from home plate if a runner attempts to steal second base in order to declare the runner "out"? Explain why more runners attempt to steal second base than third base given this information. but 127 feet to second and third base is established. 3 3/8 inches, or 127 feet, separate first base from third base.
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Find the slope of each line defined below and compare their values.
The slope of line A is:
The slope of line B:
And is the slope of line A greater or less?
Answer:
The slope of Line A: 3
The slope of line B: -1
The slop of Line A is greater that the slop of line B
Step-by-step explanation:
Connor had $42.50 in his wallet He
spent $9.36 at the bookstore and
$18.25 at a deli, Choose the best
estimate and the exact amount he
has left.
Answer:14.89
Step-by-step explanation:
Once you subtract everything from the original balance that is the balance left.
Answer:
Exact Amount Connor has left: $14.89
Step-by-step explanation:
I just took away the amounts he spent from the amount he had in his wallet. I'm not sure about the estimate. There wasn't anything to choose from.
Find the missing values in the ratio table. Then write the equivalent ratios in the order they appear in the table.
Calories 20, , 10,90
Miles 1/6, 2/3, , ,
Answer:
80 = 2/3
10 = 1/12
90 = 9/12 or 3/4
DO THE MATH: Jackie has a credit card charging 23% interest per month. If Jackie
charges $50 in January and makes no payments on the balance each month, how
much does Jackie owe at the end of the year?
The amount that Jackie owes at the end of the year is given as follows:
y = $599.55.
How to obtain the amount owed?As the amount increases by a fixed percentage each month, an exponential function is used to model the amount owed, as follows:
y = a(1 + r)^x.
For which the parameters are given as follows:
a is the initial amount owed.r is the growth rate of the amount owed, as a decimal.The parameter values for this problem are given as follows:
a = 50, r = 0.23.
Hence the function for the amount owed after x months is given as follows:
y = 50(1.23)^x.
December is 12 months after January, hence the amount owed is obtained as follows:
y = 50(1.23)^12
y = $599.55.
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Find the area of the shape. either enter an exact answer in terms of pi or use 3.14 and enter your answer as a decimal.
The area of the given shape is 84.78 square units.
What is an area?The space occupied by the object in a two-dimensional plane is called an area. The area of the circle is the space occupied by the circle in a two-dimensional plane is called the area of the circle.
Given that the shape is having a radius of 6 cm. The area of the given shape will be calculated by the formula as below,
Area = ( θ / 360 ) x πr²
Area = ( 270 / 360 ) x π x ( 6 )²
Area = 0.75 x 3.14 x 36
Area = 84.78 square cm
The missing image is attached with the answer below.
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What is the area of the following circle?
Either enter an exact answer in terms of \piπpi or use 3. 143. 143, point, 14 for \piπpi and enter your answer as a decimal.
As a result, when the circle's radius is specified as 7 units, its area is 49 units, or 153.86 units2.
what is circle ?A circle is formed when every point in the plane that is a specific distance apart from another point does so (center). Thus, it is a curve made up of points that are separated from one another by a set distance while moving in the plane. It is also rotationally symmetric about the center at all angles. A circle is a closed, two-dimensional object where each pair of points in the plane is equally separated from the "center." A specular symmetry line is made by drawing a line through the circle. It is also rotationally symmetric about the center at all angles.
given
Radius of the circle
Radius, = d / 2 = 7
Area of the circle = pi * r * r = pi *49 = 49pi
Substituting the value of π = 3.14,
Area of the circle = 49 * 3.14 = 153.86 unit²
As a result, when the circle's radius is specified as 7 units, its area is 49 units, or 153.86 units2.
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hi i will give you a crown and a heart if you can answer PLEASE
Answer:
A: 2 X 3/4= 1.5
B: 3 X 2/4= 1.5
C: 4 X 1/3= 4.3 (recurring)
D: 4 X 2/3= 2.66666667
5) (exact number) 2011.68
don't understand what number six is asking :/
Can someone help out with this question fast!?!?!
The solution to the inequality is as follows:
x > 1200 and x < 1600; Patrice needs to consume greater than 1200 calories but less than 1600 calories.
How to solve inequality?Patrice is trying a low calorie diet. She will like keep her calories consumed between the level shown in the following compound inequality:
2450 < 2x + 50 and 2x + 50 < 3250
Let's solve for x in the inequality.
2450 < 2x + 50'
subtract 50 from both sides of the inequality
2450 - 50 < 2x + 50 - 50
2400 < 2x
divide both side by 2
2400 / 2 < x
1200 < x
2x + 50 < 3250
subtract 50 from both sides of the inequality
2x + 50 - 50 < 3250 - 50
2x < 3200
divide both sides by 2
x < 3200 / 2
x < 1600
Therefore, x > 1200 and x < 1600, Patrice needs to consume greater than 1200 calories but less than 1600 calories.
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9. Here is a graph of the equation 2x - 3y = 15.
Please help I’m so confused
Answer:
2x+3y=15 =15÷3=52+3=5=5-5=0
Slope of x-2y=-1/2
Slope of -4x-8y=2
The slope of the of the equation of lines x - 2y = -1/2 and -4x - 8y = 2 are 1/2 and -1/2 respectively.
What are the slope of the given equations?The slope intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equations in the equation;
x - 2y = -1/2Slope = ?-4x - 8y = 2Slope = ?Find the slope of the first equation.
x - 2y = -1/2
To find the slope of the line represented by the equation x - 2y = -1/2, we rewrite the equation in slope-intercept form.
x - 2y = -1/2
Multiply each term by -1
-x + 2y = 1/2
Make 2y the subject of formula
2y = x + 1/2
Divide each term by 2
y = (1/2)x + 1/4
Hence, in this form, the slope m is 1/2.
Find the slope of the second equation.
-4x - 8y = 2
Multiply each term by -1
4x + 8y = -2
Make 8y the subject of formula
8y = -4x - 2
Divide each term by 8
y = (-1/2)x - 1/4
Hence, in this form, the slope m is -1/2.
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QUESTION 7 Ifz is a standard normal variable, find the probability: The probability that z is less than 1.13 0.8708 0.8907 0.8485 0.1292
The probability that z is less than 1.13 is 0.8708.
The z score represents a value on the standard normal distribution. To find the probability of being greater or less than a certain value, we consult a z-chart or use a calculator to find the area under the probability distribution curve to the right or left of the value given.
The standard normal distribution, also known as the normal distribution or the Gaussian distribution, is a probability distribution characterized by a bell-shaped curve. It is defined by its mean (μ) being 0 and its standard deviation (σ) being 1. The probability density function (PDF) for the standard normal distribution is given by:
f(x) = (1/sqrt(2π)) * e^(-(x^2)/2)
This distribution is used in many areas of statistics and data analysis, and it is a common way to model random variables that have a large number of possible values.
The chart I have specifies values of the area to the left of the z-score that I look up. For a z-score of 1.13, my chart tells me the area to the left of (which is the probability that a value is less than) 1.13 is 0.8708.
Therefore, The probability that z is less than 1.13.
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list the angles of MNO in order from smallest to largest if MN=9 NO=7.5 and OM=12
f N O M
g O M N
h O N M
j M O N
The list of angles M, N and O as required to be ordered from smallest to largest in the task content is; O < M < N.
What is the order of the angles M, N and O from smallest to largest?As evident in the task content;
MN = 9 NO = 7.5 and OM = 12
By simply creating a triangle and labelling the triangle according to the dimensions above; it follows that;
angle O is opposite side MN;
angle M is opposite side NO;
angle N is opposite side OM;
Also, recalling that the smaller an angle measure, the smaller is the side length opposite the angle. This is evident in the ratio as portrayed in the sine rule of triangles.
Therefore, the correct order of the angles from smallest to largest is; O < M < N.
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steve has 1 4/5 cups of flour. tyler has 1 2/3 cups of flour. do they have enough flour to bake a cake that needs 3 cups of flour. its fractions btw please help me its one of the last questions i asked about the other one as well so if you can please answer that it would be amazing
Answer:
Yes, they have enough flour to bake a cake that needs 3 cups of flour.
Step-by-step explanation:
1 4/5 = 9/5
1 2/3 = 7/3
We add both numbers
9/5 + 7/3 = 27/15 + 35/15 = 62/15 = 4.1 cup of floor
4.1 > 3
So,they have enough flour to bake a cake that needs 3 cups of flour,
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
In the triangle angle 5+ angle 6 = 180, angle 2+ angle 3 = angle 4, angle 2 + angle 5 = angle 6
What is exterior law of triangle?The exterior law of traingle states that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
The exterior angles in the triangle are angle 1 , 4 and 6.
the opposite angle to 4 is angle 2 and 5, therefore angle 2+ angle 5 = angle 4
the opposite angle to angle 6 is angle 2 and 3
therefore angle 2 + angle 3 = angle 6.
The opposite angle to angle 1 is 3 and 5
therefore angle 3+5 = angle 1.
Also angles on a straight line is 180°
angle 5+ angle 6 = 180°
angle 3+ angle 4 = 180°
angle 1+ angle 2 = 180°.
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Aidan collects leaves for an art project.
He picks leaves from 8 different trees.
He picks 12 leaves from each tree.
He loses 7 leaves on his way home.
The number of leaves left based on the information will be 89 leaves.
How to calculate the value?In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
In this situation, Aidan collects leaves for an art project. He picks leaves from 8 different trees. He picks 12 leaves from each tree. He loses 7 leaves on his way home.
The number of leaves left will:
= (12 × 8) - 7
= 96 - 7
= 89 leaves
There'll be 89 leaves left.
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Aidan collects leaves for an art project.
He picks leaves from 8 different trees.
He picks 12 leaves from each tree.
He loses 7 leaves on his way home.
How many leaves does he have left?
In the diagram below of triangle FGHFGH, II is the midpoint of \overline{FH} FH and JJ is the midpoint of \overline{GH} GH . If m\angle HGF=67-8x∠HGF=67−8x, and m\angle HJI=2x+47∠HJI=2x+47, what is the measure of \angle HJI∠HJI?
The angle measure m∠HJI = 51°
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting
at a common vertex.
Given:
In the diagram below of triangle FGH,
I is the midpoint of HF,
and J is the midpoint of HG.
That means, JI is parallel to GF
And the angle measure:
m∠HGF = 67−8x
m∠HJI = 2x+47
So,
m∠HGF = m∠HJI
67−8x = 2x+47
8x + 2x = 67 - 47
10x = 20
x = 2
So, m∠HJI = 2(2)+ 47
= 51°
Therefore, m∠HJI = 51°
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When the scale factor is less than 1 The new image is?
The new image would be smaller in sample size than the original image.
For example, if the scale factor is 0.5, the new image will be half the size of the original image. To determine the exact size of the new image, the scale factor is multiplied with the width and height of the original image. For example, if the original image is 200 x 100 pixels, and the scale factor is 0.5, the new image will be
(200 x 0.5) = 100 x (100 x 0.5)
= 50 pixels.
The same concept applies when the scale factor is a decimal. For example, if the scale factor is 0.75, the new image will be three-quarters the size of the original image. In this case, the new image would be
(200 x 0.75) = 150 x (100 x 0.75)
= 75 pixels.
In summary, when the scale factor is less than 1, the new image will always be smaller than the original image, depending on the scale factor. The exact size of the new image can be determined by multiplying the width and height of the original image with the scale factor.
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A baker used 2 cups of flour to make 3 batches of brownies. He used ____ of a cup of flour to make 1 batch of brownies.
Answer: the Baker used 2/3 cups of flour for one batch.
Step-by-step explanation:
Cady found that she uses of a roll of paper towels each week. How many rolls of paper towels will she use in 8 weeks?
Answer:
8 rolls of towels
Step-by-step explanation:
First set up the equation:
Cady uses a roll of paper towels per week
Instead of writing out how many she will end up using week by week, simply multiply 1*8 (because 1 roll per week and we are asked how many in 8 weeks).
The stem-and-leaf plot shows house sale prices over the last week in Tacoma. The stem is in hundreds of thousands of dollars the leaf is in tens of thousands of dollars. What is the price of the most expensive house sold
Most expensive house sold in Tacoma over the previous week went at the price of $370,000.
How does a stem and leaf plot work?A stem and leaf plot is similar to a bar graph. The name comes from the fact that each number in the data is divided into a stem and a leaf. All but the last digit are included in the number's stem. The number's leaf will always be a single digit.
Determine the data's smallest and largest numbers to determine the stems. To identify the most expensive house sold in Tacoma, using the table, 3 is the highest number in hundred thousand on the stem column and on the row of 300,000, the highest number in the leaf column is 7 which is 70,000. Therefore the highest value is 3 and 7 = 37, i.e. $370,000.
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Identify the range of the function shown in the graph.
804
O A. y is all real numbers.
B. y<0
C. y 20
D. 0
10
8
6
INT
N
22
2449
8
8 10 1
Answer:
C. [tex]y \geq 0[/tex]
Step-by-step explanation:
The range is the set of [tex]y[/tex]-values.
what would these be on the graph
Answer:
Graph the points of those numbers.
The y axis is the vertical axis and x the x axis is the horizontal axis. Pretty much you take the number that is in the x column on the table and put it at the number of the value in the y column. For example in the second part of the table x is 6,000. And y is 4 so find 4 on the y axis and then go over till you reach 6,000 on the x axis and put a point.
Step-by-step explanation:
hope this helps
solve the initial-value problem. y″ + 4y′ + 6y = 0 , y(0) = 2 , y′(0) = 4
Solution of the initial-value problem. y″ + 4y′ + 6y = 0 , y(0) = 2 , y′(0) = 4 is
y(x) = 4√2e⁻²ˣsin(2x) + 2 e²ˣcos(2x)
The Initial Value Problem in Calculus: We have a second order differential equation with initial condition and we need to compute the general solution. If we are not able to make factor this quadratic equation, so we'll apply the quadratic formula. For an quadrtic equation
an² + bn+ c = 0 ----------(1)
the solution is n = (-b ±√b² - 4ac)/2a.
Now, the equation is y″+4y′+6y=0,
and y(0)= 2, y'(0) = 4
The auxiliary equation becomes,
n² + 4n+ 6 = 0,
As we see not possible to make factor in this quadratic equation, so we'll apply the quadratic formula, a = 1 , b = 4 , c = 6
=> n = ( - 4 ±√16 - 24 )/2
=> n =( - 4 ± √-8)/2
=> n = (-4 ± 2√2i )/2 = 2( - 2 ± √2i)/2
=> n = -2 ± √2
Hence the roots are n = -2 ± √2i
So, general solution will be written in the form:
y(x) = Ae⁻²ˣsin(√2x) + Be⁻²ˣ cos(√2x), where A, B are arbitrary constants. By initial conditions,
y(0)= , Ae⁻⁰sin(√2×0) + Be⁻⁰cos(√2× 0) = 2
=> B = 2 ----(*)
differentiating the general solution equation with respect to x, we get
y′(x) = −2A e⁻²ˣ sin(2x) + √2A e⁻²ˣ cos(2x) − 2Be⁻²ˣ cos(2x) − √2Be⁻²ˣ sin(−2x)
since, y'(0) = 4 , −2A e⁻⁰ sin(0) + √2A e⁻⁰ cos(0) − 2B e⁻⁰ cos(0) − √2B e⁻⁰ sin(0) =4
=> √2A + 2B = 4 and using (*),
A = 2- B = 4√2
So the general solution of the given initial value problem , y(x)=4√2e⁻²ˣsin(2x) + 2 e²ˣcos(2x).
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a) One number is five more than another number and the sum of the two numbers is 55, what are the numbers?
Answer:
25 and 30
Step-by-step explanation:
To solve this problem, we can do a system of equations. Let x and y be your unknown numbers;
[tex]x+5=y\\x+y=55[/tex]
We can substitute the first equation for y in the second equation.
[tex]x+(x+5)=55\\2x+5=55\\2x=50\\x=25[/tex]
Now that we know the value of x, we can plug x into the first equation to solve for y.
[tex]25+5=y\\y=30[/tex]
Thus, the two numbers are 25 and 30.
how many degrees does the minute hand of a clock turn in 45 minutes
The number of degrees which the minute hand of a clock turn in 45 minutes as required in the task content is; 270°.
What is the number of degrees which the minute hand turns in 45 minutes?As evident in the task content; it follows that the number of degrees which the minute hand of a clock turns over 45 minutes is to be determined.
Since there are 60 minutes in one complete revolution and;
Recall that the task sum of angles in a circle is 360°, it follows that the problem situation can be expressed as a proportion as follows;
45 / 60 = x° / 360°
where, x = the angle turned over 45 minutes.
Therefore, by cross-multiplication; we have;
60x = 45 × 360
x = ( 45 × 360 ) / 60
x = 45 × 6
x = 270°.
Ultimately, the number of degrees turned over 45 minutes is; 270°.
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